Thermodynamic and Mass Transfer Modeling of Aqueous Hindered Amines for Carbon Dioxide Capture

Transcription

1 The Dissertation Committee for Brent Joseph Sherman certifies that this is the approved version of the following dissertation: Thermodynamic and Mass Transfer Modeling of Aqueous Hindered Amines for Carbon Dioxide Capture Committee: Gary T. Rochelle, Supervisor Michael Baldea Chau-Chyun Chen Eric Chen Gyeong Hwang

2 Thermodynamic and Mass Transfer Modeling of Aqueous Hindered Amines for Carbon Dioxide Capture by Brent Joseph Sherman, B.S.C.E. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN May 2016

3 To my parents, who sacrificed so much for the education of their children

4 Acknowledgments First and foremost, I would like to thank Dr. Rochelle. Whether in the lab, in front of the computer, in the caves of New Mexico, or in the tundra of Norway, he always led by example. I am indebted to his guidance and fortitude in the face of obstacles technical or otherwise. He has shifted the way I view the world, and I will carry this shift with me both at work and at home. I would like to thank my committee for volunteering their time and pointing me in the right direction. I would like to thank Dr. Eldridge for teaching and then allowing me to TA his separations course, Dr. Sepehrnoori for his numerical methods course, and Dr. Baldea for his mathematical modeling course. I want to thank Dr. Joel Kress for his support and sympathy in balancing the demands of CCSI and of the PhD. When I first started in the Rochelle group, I was fortunate enough to work with Dr. Han Li, whose work ethic and good demeanor positively influenced my lab work. Dr. Lynn Li helped us navigate the lab and track down the supplies and space we needed. I also want to thank Dr. Peter Frailie, Darshan Sachde, Steven Fulk, Matt Walters, and Yu-Jeng Lin for taking the time to listen and offer advice. I have had the pleasure of interacting with Tarun Madan, Kent Fischer, and Dr. Nathan Fine. Dr. Arlinda Ciftja has been a most gracious collaborator. I want to thank Dr. Fred Closmann for making the internship at Phillips 66 possible. It was a pleasure working with you and Dr. David van Wagener on the most challenging problem of my career. I enjoyed learning how to conduct research in an industrial environment and can only hope my future career is as fun. iv

5 I would also like to thank my family and friends for their support and company: my parents, my siblings, my Uncle Bob Sherman, who sparked my first interest in chemical engineering, Drs. Jie and Nathan Crook, Matthew Hausknecht, Dr. Man Liang, Dr. Zach Frye, Dr. Peach Kasemet, Dr. Erwan Chabert, Dr. Sunmi Lee, Dr. Bo Lu, Joseph Cheng, Stephen Blackwell, Jorge Vásquez, Dr. Beatrice Mabrey, Sarah and Noel Cody, Pat Carr, Wandalyn Savala, Kylia Miskell, and Brian Chen. I want to thank Coach John Myrick and the UT Climbing team for four great years of climbing. I want to thank Maeve Cooney who has carefully copy edited many a quarterly, booked itineraries, and given me New Yorker magazines that helped broaden my perspective. Thanks to Kate Baird for demystifying arcane policies, to Randy Rife for solving IT problems and for getting our group data backup system going, and to Steve Sorey for collecting the NMR spectra. This work would not have been possible without the financial support of the Luminant Carbon Management Program, the Texas Carbon Management Program, the Department of Energy through the Carbon Capture Simulation Initiative (373-DOE-FE UTEXAS), the Thrust Fellowship, and the Cockrell School of Engineering fellowship. I want to give a special thanks to Dr. Lynn Li. Her support throughout the Ph.D. process cannot be overstated. Her technical guidance was instrumental to its success, and she has put up with punctuating the distance apart with me writing when we are together. I look forward to building a life together. Many thanks are due to my parents. Their personal example of self-sacrifice for me and my siblings is inspiring. Their emphasis on excellence in education and willingness to sacrifice the finer things in life in favor of paying tuition set my feet on the path that has led to this day. v

6 Disclaimer Parts of this dissertation were prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of the author expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. vi

7 Thermodynamic and Mass Transfer Modeling of Aqueous Hindered Amines for Carbon Dioxide Capture Publication No. Brent Joseph Sherman, Ph.D. The University of Texas at Austin, 2016 Supervisor: Gary T. Rochelle With the detrimental effects of global climate change beginning to be felt, there is a growing consensus that something must be done. One part of the solution is carbon capture and storage using amine scrubbing to capture 90% of the CO 2 from power plants burning coal and natural gas. To actualize this solution, process models are necessary. A process model requires an accurate thermodynamic and mass transfer model with physically meaningful parameters. While hindered amines are commercially used, the reason for their mass transfer rates is still an open question. These two needs are addressed in this work. To improve thermodynamic modeling, the physical significance of the electrolyte non-random two-liquid (enrtl) regressed binary interaction parameters were examined. To improve mass transfer modeling, a response surface methodology (RSM) approach was used to give statistically significant regressed parameters. The mass transfer of two hindered amines, 2-amino-2-methyl-propan-1-ol (AMP) and 2-piperidineethanol (2PE) was studied to determine the role of carbamate. vii

8 The absolute difference in enrtl binary interaction parameters was found to moderately correlate with the pk a of the amine. An analogy method was developed to enable thermodynamic model creation for amines in the absence of some physical property data. The carbamate reaction plays a determining role in mass transfer of hindered amines. Based on Brønsted plots, 2PE appears to form carbamate using the same mechanism as unhindered, cyclic secondary amines, while AMP does not seem to use the same mechanism as unhindered, primary amines. The rate constant for bicarbonate formation for both amines is a factor of twelve faster than predicted from tertiary amine bicarbonate formation, indicating that neither seems to form bicarbonate using the tertiary amine mechanism. The six models constructed in this work enable process modeling and economic comparisons of solvents. Four binary interaction parameters were the most physically significant and should be regressed for future solvents. The high bicarbonate reaction rate of the hindered amines should be further investigated to determine if the mechanism is different or if this is model artifice, as either outcome will substantially improve mass transfer modeling for all amines. viii

9 Table of Contents Acknowledgments Abstract List of Tables List of Figures iv vii xvi xix Chapter 1. Introduction to Amine Scrubbing Motivation Process Description Context of This Work Research Objectives Chapter 2. Thermodynamic Modeling Methods Introduction Operating Conditions enrtl Framework Activity Coefficients Chemical and Vapor-Liquid Equilibrium Sequential Regression Single Amine Systems Pure Amine Regression Unloaded Regression Loaded Regression Blend Amine Systems Analogous Regression Regression Method Model Validation Conclusions ix

10 Chapter 3. Mass Transfer Modeling Methods Introduction Mass Transfer Framework Hydrodynamics Viscosity Density Diffusivity Kinetics Flowsheet Methods Manual Data Fit Response Surface Methodology Model Validation Conclusions Chapter 4. 2-Piperidineethanol (2PE) Introduction Methods Experimental Methods Sample preparation Thermodynamic Model Mass Transfer Model Hydraulics Diffusivity Flowsheet Reaction Set Brønsted Correlation Kinetic Parameter Regression Kinetic Analysis Results NMR Experimental Results x

11 4.3.2 Thermodynamic Results Mass Transfer Results Hydraulics Kinetic Parameter Regression Kinetic Analysis Conclusions Supporting Information Derivation of Equation (4.12) Chapter 5. 2-Amino-2-methylpropan-1-ol (AMP) Introduction Methods Thermodynamic Model Carbamate Sensitivity Mass Transfer Model Hydraulics Diffusivity Reaction Set Brønsted Correlations Flowsheet Kinetic Parameter Regression Kinetic Analysis Results Thermodynamic Model Carbamate Sensitivity Mass Transfer Model Hydraulics Mass Transfer Parameters Mass Transfer Analysis Conclusions Supporting Information xi

12 Chapter 6. 2-Methylpiperazine (2MPZ) Introduction Thermodynamic Methods Heat of Absorption Mass Transfer Methods Hydraulics Diffusivity Flowsheet Reaction Set Kinetic Parameter Regression Film Discretization Kinetic Analysis Thermodynamic Results and Discussion Heat of Absorption Mass Transfer Results and Discussion Hydraulics Mass Transfer Parameters Mass Transfer Analysis Conclusions Chapter 7. Piperazine Blends Introduction HMPD AMP MPZ Thermodynamic Methods PZ/HMPD PZ/AMP PZ/2MPZ Mass Transfer Methods PZ/HMPD Hydraulics xii

13 Diffusivity Reaction Set Kinetic Parameter Regression PZ/AMP Hydraulics Diffusivity Flowsheet Reaction Set Kinetic Parameter Regression PZ/2MPZ Hydraulics Diffusivity Flowsheet Reaction Set Kinetic Parameter Regression Thermodynamic Results and Discussion PZ/HMPD PZ/AMP PZ/2MPZ Mass Transfer Results and Discussion PZ/HMPD PZ/AMP PZ/2MPZ Conclusions Supporting Information Chapter 8. Thermodynamic Modeling Generalizations Introduction Methods Model Validation pk a Prediction τ i, j Physical Significance xiii

14 8.2.4 Comparison to Simplified Stoichiometric Model Results Model Validation pk a Prediction τ i, j Patterns Comparison to Simplified Stoichiometric Model Conclusions Chapter 9. Conclusions and Recommendations Summary Conclusions Thermodynamic Modeling Methods Mass Transfer Modeling Methods Piperidineethanol (2PE) Amino-2-methylpropan-1-ol (AMP) Methylpiperazine (2MPZ) Piperazine Blends Thermodynamic Modeling Generalizations Recommendations Thermodynamic Modeling Methods Mass Transfer Modeling Methods Piperidineethanol (2PE) Amino-2-methylpropan-1-ol (AMP) Methylpiperazine (2MPZ) Piperazine Blends Thermodynamic Modeling Generalizations Appendices 219 Appendix A. Nomenclature 220 xiv

15 Appendix B. Fortran Subroutines 223 B.1 vl2u2.f B.2 mul2u2.f B.3 masstransfer.f B.4 dl0.f B.5 area.f Appendix C. WWC Model Details 269 C.1 Transfers C.2 Design Specification C.3 Calculator Blocks C.3.1 C-FLUX C.3.2 C-KEQ C.3.3 C-LDGADJ C.3.4 C-SAT Appendix D. WWC VLE Data Quality 283 D.1 Operating Criteria D.2 Examples Appendix E. RSM MATLAB Code 288 Appendix F. 5 m 2MPZ Viscosity 291 Appendix G. HMPD pk a Data 293 Appendix H. 2 m PZ/3 m HMPD Reanalyzed Data 294 Appendix I. 2-Methylpiperazine Model Manual 296 Appendix J. Piperazine Blend Model Manuals 331 Appendix K. Plate and Frame Heat Exchanger Calculator 394 Works Cited 429 Vita 443 xv

16 List of Tables 2.1 Dielectric constant solvent parameters (CPDIEC) for Equation (2.2) Molecule and electrolyte components for enrtl τ i, j parameters Liquid film discretization Mass transfer coefficient driving force definitions for Equation (3.18) PE Thermodynamic data PE Thermodynamic data Predicted activity-based kinetic parameters (T ref = K) Mass transfer test matrix NMR speciation in mole fraction for 30 wt.% 2PE at 25 C m AMP thermodynamic data and fit m AMP interaction parameters PE (PZ) viscosity parameters for Equation (3.1) m 2PE density parameters of Equation (3.3) Loading adjustment for case 7 compared to data (Chen, 2011) m 2PE kinetic parameters Diffusion activation energy as calculated by Equation (4.18) Initial 2PE species definition Henry parameter values with PZ as analog (Frailie, 2014) wt.% 2PE NMR data Scalar pure component properties T-dependent parameters of 2PE as estimated by PCES NRTL parameters with MDEA as analog (Frailie, 2014) Viscosity fit of aqueous loaded and unloaded AMP Density fit of aqueous unloaded AMP AMP kinetic cases and fit xvi

17 5.4 VLE sensitivity to K c at 40 C AMP viscosity parameters of Equation (5.2) AMP density parameters of Equation (5.3) m AMP kinetic parameters and ARD Case 1 loading adjustment compared to data (Chen, 2011) Sensitivity to E A to k AMP bound k AMP AMP comparison to literature Diffusion activation energy correlated with viscosity at 60 C AMPCOO scalar pure component properties Pure component T-dependent parameters of AMPCOO Dielectric constant solvent parameters (CPDIEC) for Equation (5.25) Viscosity data for 2MPZ with ARD from model m 2MPZ viscosity parameters of Equation (3.1) Density Parameters of PZ/2MPZ m 2MPZ regressed kinetic parameters for Equation (3.14) m 2MPZ D Am parameters of Equation (3.7) m 2MPZ relative loading adjustment Available thermodynamic data for 2 m PZ/3 m HMPD MPZ/PZ thermodynamic data PZ/AMP hydraulic data PZ/2MPZ hydraulic data P HMP D parameters Regressed Parameters for PZ/HMPD VLE C ca, m parameters for 4 m PZ/4 m 2MPZ D ca, CO2 parameters for 4 m PZ/4 m 2MPZ Viscosity parameters of PZ/HMPD m PZ/3 m HMPD regressed kinetic parameters m PZ/4 m AMP viscosity parameters m PZ/4 m AMP density parameters m PZ/4 m AMP kinetic parameters m PZ/4 m AMP D Am parameters compared to others xvii

18 7.16 Loading adjustment for 2 m PZ/4 m AMP; data are Li et al. (2013a) m PZ/4 m 2MPZ viscosity parameters m PZ/4 m 2MPZ density parameters m PZ/4 m 2MPZ regressed kinetic parameters m PZ/4 m 2MPZ D Am parameters Loading adjustment for 4 m PZ/4 m 2MPZ HMPD and HMPDH component definition parameters Calculation of K i at P CO Pa and 40 C Calculated pk a at 25 C compared to experimental values τ i, j at K for m H 2 O τ m, ca τ ca, m at K for m H 2 O τ i, j at K for m Am τ m, ca τ ca, m at K for m Am τ i, j at K for m CO τ m, ca τ ca, m at K for m CO τ i, j at K for m HAmCOO τ m, ca τ ca, m at K for m HAmCOO Models made in this work; manuals available in the Appendices C.1 Design specification variable definitions C.2 C-FLUX variable definitions; I/O is input/output C.3 C-KEQ variable definitions; I/O is input/output C.4 C-KEQ variable definitions; I/O is input/output F.1 Detailed viscosity data for 8 m 2MPZ viscosity; % dev = std. dev {avg G.1 Dissociation constant, ln K a, of HMPD H.1 Reanalysis of 2 m PZ/3 m HMPD from raw data of Du (2016) xviii

19 List of Figures 1.1 Amine scrubbing PFD for capture from coal flue gas Sketch of operating conditions Sequential regression of a single amine system pk a regression schematic Sequential regression of a blend amine system D i at at 40 C D i at at 100 C WWC flowsheet RSM flow chart Speciation in loaded aqueous 2PE C NMR spectra for 30 wt.% 2PE VLE of 8 m 2PE m 2PE predicted H abs at 20 C increments using Equation (2.22) m 2PE speciation prediction at 40 C PE NMR comparison m 2PE activity coefficient prediction at 40 C Viscosity correlation of 8 m 2PE Density prediction of 8 m 2PE at 20 C intervals m 2PE flux ratio for case m 2PE flux ratio for case m 2PE flux ratio for case m 2PE flux ratio for case Sensitivity of kg 1 at 40 C Sensitivity of k 1 g at 100 C k 1 g asymptotes xix

20 4.17 Brønsted plot at 25 C for k 2P E 2P E Relative gas film resistance in 8 m 2PE k 1 g vs k 0 l in 8 m 2PE Molecular structure of AMPCOO m AMP VLE Speciation of 4.8 m AMP at 35 C Viscosity of 4.8 m AMP m AMP density prediction at 20 C intervals m AMP flux ratio m AMP predicted kg m AMP k 1 g asymptotes k AMP AMP Brønsted plot k AMP Brønsted plot Sensitivity of 4.8 m AMP kg 1 at 40 C Sensitivity of 4.8 m AMP k 1 g at 100 C m AMP boundary layer speciation Molecular structures of chiral 2MPZ Flowsheet for calculating H abs by calorimetry H abs predictions for 8 m 2MPZ Viscosity predictions for 8 m and 5 m 2MPZ Density predictions for 8 m 2MPZ m 2MPZ flux ratio vs loading m 2MPZ flux ratio vs T m 2MPZ VLE Viscosity correlation of 8 m 2MPZ ratioed to 8 m PZ Ratio of absorption ˆN CO2 for 8 m 2MPZ using µ 2MP Z and µ P Z Ratio of absorption ˆN CO2 for 8 m 2MPZ to 8 m PZ using µ P Z Molecular structure of HMPD HMPD pk a predictions compared to data (Appendix G) (Ciftja, 2016).151 xx

21 7.3 P Am for 2 m PZ/3 m HMPD VLE for 2 m PZ/3 m HMPD Differential H abs predictions for 2 m PZ/3 m HMPD Speciation predictions for 2 m PZ/3 m HMPD at 40 C γ i predictions for 2 m PZ/3 m HMPD at 40 C VLE for 2 m PZ/4 m AMP Differential H abs predictions for 2 m PZ/4 m AMP Speciation predictions for 2 m PZ/4 m AMP at 40 C γ i predictions for 2 m PZ/4 m AMP at 40 C γ CO2 predictions for 2 m PZ/4 m AMP at 20 C increments VLE for 4 m PZ/4 m 2MPZ Differential H abs predictions for 4 m PZ/4 m 2MPZ Speciation predictions for 4 m PZ/4 m 2MPZ at 40 C γ i predictions for 4 m PZ/4 m 2MPZ at 40 C γ CO2 predictions for 4 m PZ/4 m 2MPZ at 20 C intervals m PZ/3 m HMPD density predictions at 20 C intervals m PZ/3 m HMPD viscosity predictions m PZ/3 m HMPD flux ratioed to data (Du et al., 2016) m PZ/3 m HMPD predicted flux ratioed to data (Du et al., 2016) m PZ/3 m HMPD kg m PZ/4 m AMP viscosity predictions m PZ/4 m AMP density predictions at 20 C intervals m PZ/4 m AMP net forward rate at 40 C m PZ/4 m AMP flux ratio vs loading m PZ/4 m AMP flux ratio vs temperature m PZ/4 m 2MPZ viscosity predictions m PZ/4 m 2MPZ density predictions m PZ/4 m 2MPZ flux ratioed to data (Chen, 2011) m PZ/4 m 2MPZ flux ratioed to data (Chen, 2011) Analytical pk a calculation comparison Correlation for m H 2 O and ca AmH, HCO 3 with pk a xxi

22 8.3 Correlation for m H 2 O and ca AmH, HCO 3 with pk a Correlation for m H 2 O and ca AmH, HCO 3 with pk a Comparison of K eq from Aspen Plus to SSM D.1 WWC raw data example for 5 m PZ/2 m AEP D.2 Lower quality WWC data D.3 Poor WWC data xxii

23 Chapter 1 Introduction to Amine Scrubbing 1.1 Motivation The scientific consensus is clear that global climate change is not only happening and that humans are responsible for it, but that the negative impacts to ecology and human health are already being felt (IPCC, 2014). There is not only a practical need to mitigate climate change, there is also a moral imperative (Pope Francis, 2015). In addition to increased fuel and electricity efficiency, carbon capture and sequestration (CCS) is projected to account for 14% of the total emission reductions needed to meet keep the world below a 2 C global temperature increase (IEA, 2013). This work is on the capture portion of CCS. Coal-fired power plant flue gas is a concentrated point source of CO 2 that accounts for 28% of U.S. CO 2 emissions (EPA, 2016). There are a number of capture technologies being developed, but the closest to commercial is amine scrubbing (Rochelle, 2009). Amine scrubbing is absorption/stripping of CO 2 with fast chemical reaction. As amine scrubbing is a post-combustion technology, retrofit of existing coal power plants is possible. While no new coal power plants are under construction in the U.S., many existing plants will continue operating for decades. 1

24 P CO2 = 1.3 kpa P CO2 = 0.5 kpa CO 2 lean solvent CO 2 rich solvent CO 2 compression to 150 bar absorber CO 2 (g) 40 C 60 C 1 atm 90% removal reaction CO 2 (aq) stripper 100 C 150 C 2 10 bar CO 2 (aq) reverse reaction CO 2 (g) coal flue gas 12% CO 2 P CO2 = 12 kpa CO 2 rich solvent P CO2 = 5 kpa CO 2 lean solvent steam heater Figure 1.1: Amine scrubbing PFD for capture from coal flue gas 1.2 Process Description Since the 1930 s, amine scrubbing has been applied to acid gas sweetening to remove CO 2 and H 2 S from natural gas sources as well as synthesis gas in hydrogen and ammonia production. Experience in acid gas sweetening has been applied to carbon capture from flue gas, however the change in process conditions has created ample research questions. After conventional pollution control to remove NO x, SO x, and particulates, the flue gas goes through a direct contact cooler (DCC) to cool the gas to 40 C. Now the flue gas enters at the bottom-left of Figure 1.1 starts. The flue gas enters the bottom of the absorber where it counter-currently contacts amine solvent flowing down through structured packing. The CO 2 moves from the flue gas to the aqueous amine solvent through a fast, exothermic chemical reaction. 2

25 The solvent leaves the column with a rich CO 2 loading, then the solvent passes through a counter-current plate-and-frame heat exchanger. The solvent then enters the stripper, where it contacts hot steam that reverse the reaction. The CO 2 moves from the aqueous phase into the gas phase and out of the stripper to be compressed for sequestration. Meanwhile, the amine solvent has been stripped down to a lean loading of CO 2. The solvent goes back through the cross exchanger to the absorber to be circulated. The solvent is circulated at a rate to remove 90% of the CO 2 from the flue gas. The operating costs are tied to the thermodynamics while the capital costs are tied to mass transfer. The thermodynamics of the amine solvent dictate the CO 2 loading capacity of the solvent. Greater capacity means less solvent needs to be circulated, which means less solvent needs to be pumped, heated, and cooled. The mass transfer of the amine solvent dictates the area for CO 2 capture, which sets the size of the absorber and the amount of packing. 1.3 Context of This Work The thermodynamic models capable of representing electrolyte solutions fall into three categories. Empirical models, such as Kent-Eisenberg (Kent and Eisenberg, 1976), account for non-ideality through equilibrium constants. Equation of state model (Furst and Renon, 1993), usually reserved for the gas phase, are being developed for the liquid phase. Excess Gibbs energy models such as the electrolyte-nrtl (enrtl) model (Chen and Evans, 1986) and the euniquac model (Thomsen et al., 1996; Mehdizadeh et al., 2013) account for non-ideality through activity coefficients. The enrtl model has been used throughout this work. It is more physically representative than Kent-Eisenberg. This enhanced representation allows for interpolation, extrapolation, and sequential regression of single and blend amine systems. 3

26 euniquac is not available in Aspen Plus, and so it was not used. Aspen Plus is used for this work to enable process modeling. Many enrtl amine scrubbing models have been developed both commercially, such as the PZ/MDEA model of BASF, and in open literature, such as the work done by the Svendsen group (Pinto, 2014) and the example files of Aspen Plus. The commercial models are not usable for academic work due to their proprietary nature. The other models are undesirable due to apparent flaws, e.g. using the polynomial representation of K eq as done by Pinto (2014) and hidden flaws that are difficult to detect without making the model in house. For this reason, all models in this work have been developed in house. Within the Rochelle group, prior thermodynamic modeling work began with Austgen (1989) using the enrtl model to simulate the thermodynamics of monoethanolamine. Since then, there have been many students focused on thermodynamic modeling with the latest being Frailie (2014), who constructed a blend model of methyldiethanol amine and piperazine. Prior mass transfer modeling work in the Rochelle group began with Glasscock (1990), who used the enrtl model to develop a numerical model for mass transfer in single and blend amine solvents. Mass transfer modeling has continued to be refined with the last student being Frailie (2014). This work differs from the work of Frailie in that he focused solely on PZ/MDEA, while this work has developed a total of six single and blend amine models. Rather than use these models for process modeling as done by Madan (2013) and Frailie (2014) this work generalizes the model parameters. This work improves on prior thermodynamic and mass transfer modeling methods by moving from a model that just fits the data to a model that fits the data with statistically and physically significant parameters. 4

27 1.4 Research Objectives This work enhances modeling of amine scrubbing thermodynamics and mass transfer. The research objectives of this work can be categorized under modeling methods, model construction and analysis, and thermodynamic modeling generalizations. Modeling Methods ˆ ˆ Improve thermodynamic modeling methods to create a model when missing some thermophysical property data. Improve mass transfer modeling methods to give physically meaningful regressed parameters. Model Construction and Analysis ˆ ˆ Construct process models for industrially significant solvents, including 2-piperidineethanol, 2-amino-2-methylpropan-1-ol (AMP), 2-methylpiperazine (2MPZ) as well as blends of piperazine with one of the following: 4-hydroxy-1-methylpiperidine, 2MPZ, and AMP. Explain the mass transfer performance of hindered amines by analyzing the constructed models. Thermodynamic Modeling Generalizations ˆ Relate the regressed thermodynamic interaction parameters to physical properties of the solvent. 5

28 Chapter 2 Thermodynamic Modeling Methods 2.1 Introduction A thermodynamic model is the foundation of the mass transfer model. Together with a hydrodynamic model, these models comprise a process model. Aspen Plus is used for modeling due to its process modeling prowess. While the ultimate purpose of a thermodynamic model is for process modeling, capabilities of a thermodynamic model include: interpolating and extrapolating data, ensuring data consistency, and estimating one type of data from another. Using these capabilities, a small set of data can be used predict many properties, and, through this prediction, determine if additional data should be collected. Two different methods were used: sequential regression and analogous regression. Sequential regression is the traditional approach to making a thermodynamic model, wherein the pure amine is regressed first, followed by the aqueous amine, and lastly by the aqueous, loaded amine. It is discussed by Frailie (2014). Analogous regression is a novel approach, wherein a prior amine model is adapted to represent a different amine. No map is the territory, meaning that no matter how good a model is, it can only capture aspects of reality. Thus, before beginning the creation of any model its purpose must be well defined. The choice of which method to use depends on the amount of data available, the level of rigor required, and the time alloted. Sequential regression creates a robust model but requires a copious data from a variety of 6

29 sources. Analogous regression regresses a smaller set of data, relying on the analogous model to fill in the gaps. This results in a model that is less robust i.e., it cannot extrapolate Operating Conditions 150 T p Cq rams mol Am kg solvent α mol CO 2 mol alk Figure 2.1: Sketch of operating conditions. 1 Prior to regression, the purpose of the model was defined. This determined what range of data were collected and included, as a model can only be accurate over a limited domain. Figure 2.1 visualizes this domain. The widest operating conditions are T =r20, 150s C, α=r0.01, 0.7s mol CO 2, rams=r1, 55s wt.%. The minima for rams mol alk and α are in the water wash with the maximum α in the bottom of the absorber and the maximum rams in the thermal reclaimer. The maximum T occurs in the stripper bottom or thermal reclaimer, and the minimum T in the trim cooler and direct contact cooler (DCC). As amine concentration is the stiffest variable, defining the amine concentration is the most important. For blend systems, it is important to recall that enrtl in Aspen Plus is mole-fraction based. Thus, if a blend amine model is desired, single amine measurements should be done at the mole fraction of the blend. Once the 7

30 amine concentration is defined, the loading range needs to be defined. This depends on the capture source natural gas leads to leaner loading than coal and the process configuration overstripping or not. Lastly, temperature bounds are set based on thermal degradation enrtl Framework Activity Coefficients In this work the asymmetric enrtl model (in Aspen Plus ELECNRTL) is used to model the liquid phase (Chen and Song, 2004; Austgen, 1989). This model was chosen for continuity with prior models (Frailie, 2014; Plaza, 2011; Chen, 2011). enrtl is an activity-coefficient-based model. The excess Gibbs free energy G,ex is calculated by Equation (2.1), G,ex G,ex,lc G ex,p DH G Born (2.1) where G,ex,lc denotes local contributions, G ex,p DH the long range contributions (Pitzer-Debye-Hückel), G Born denotes the Born correction for changing from the long-range reference state of infinite dilution in mixed-solvent to the local reference state of infinite aqueous dilution, and denotes the asymmetric reference state. The dielectric constants necessary for the PDH term were left at the Aspen Plus databank value. The dielectric constant only applies to solvents, and all amines except AMP are treated as a Henry component thus, solutes in this work. The dielectric constants used are calculated by Equation (2.2), 1 ɛ A B T 1 C (2.2) 8

31 Table 2.1: Dielectric constant solvent parameters (CPDIEC) for Equation (2.2). Parameter H 2 O H 2 O AMP Source (Lide, 2004) ASPENPCD ELECPURE Element Element Element 3 (K) where A, B, and C are parameters and T is in Kelvin. The parameters used are listed in Table 2.1. The CRC value (Lide, 2004) was introduced by Hilliard (2008), and so all models constructed from his work use this value. These models include: MEA (Plaza, 2011), 2MPZ, PZ and PZ/MDEA (Frailie, 2014), PZ/HMPD, PZ/AMP, and PZ/2MPZ. The APSENPCD value is used by 2PE. The ionic radius necessary for the Born correction was left at the default of 3 Å. The use of an asymmetric reference state necessitates an aqueous system and the Born correction. The simpler symmetric model requires neither without compromising the thermodynamic model (Song and Chen, 2009). as derived from Equation (2.1) is shown in Equation (2.3), The activity coefficient γ i ln γ i 1 RT 1 RT BG,ex 1 BG,ex,lc Bn i T,P,n ji RT BG,ex,P DH 1 B G Born Bn i T,P,n ji RT Bn i T,P,n ji Bn i T,P,n ji (2.3) where i or j m, c, a, (molecule, cation, anion) and n I is the mole number of component I in the mixture. Equivalently, γ i can be written as in Equation (2.4). ln γ i ln γ,lc,p DH i ln γ i ln γ,born i (2.4) 9

32 The symmetric activity coefficient γ i can be calculated using Equations (2.3) and (2.4) mutatis mutandis. Ionic components have an asymmetric reference state of infinite dilution (γ i Ñ 1 as x i Ñ 0), while water and other solvents have a symmetric reference state of pure component (γ i Ñ 1 as x i Ñ 1). Henry components are solutes with an asymmetric reference state. In this work CO 2 and all amines except AMP were treated as Henry components. While all terms are used in the calculation, only parameters for the local contributions were regressed. (An explanation of the other terms is available (Chen and Song, 2004; Frailie, 2014).) At the local level, G,ex is computed by applying a mixing rule to Equation (2.5), G exp p ατq (2.5) where τ is the local binary interaction parameter, and α is the NRTL nonrandom factor. α defaults to 0.3 for molecule-molecule interactions (Renon and Prausnitz, 1968), 0.2 for electrolyte-electrolyte or molecule-electrolyte interactions where the molecule is water, and 0.1 where the molecule is solute. τ is defined by Equation (2.6) for molecule-molecule interactions, by Equation (2.7) for electrolyte-molecule interactions, and by Equation (2.8) for moleculeelectrolyte interactions. τ mm 1 A mm 1 B mm 1 T (2.6) τ ca,m C ca,m τ m,ca C m,ca D ca,m T D m,ca T (2.7) (2.8) 10

33 The default values for A, B, and D are zero, while for C ca,m and C m,ca are 2 and 10 when the molecule is solute, and 4 and 8 when the molecule is water. Older models used different defaults of 8 and Chemical and Vapor-Liquid Equilibrium One of the strengths of enrtl is the consistent handling of enthalpy, activity coefficients, and equilibrium through G,ex. Common practice (Pinto, 2014) is to create a model using a polynomial representation of the chemical equilibrium (Pinto, 2014), as shown in Equation (2.9), but this is a problematic approximation (Frailie, 2014) of Equation (2.10). ln K eq G m RT ln K eq A G f,m H f,m RT 0 B T H f,m RT C ln T DT (2.9) 1 T» T C p,m T 0 R dt» T C p,m T 0 R dt (2.10) Using Equation (2.9) introduces a thermodynamic inconsistency into the model. The speciation on the bottom absorber stage would be calculated using the K eq from the kinetics, i.e. Equation (2.10), while the composition of the stream leaving the bottom stage would be calculated by the thermodynamics, i.e. Equation (2.9). To be consistent, this work uses Equation (2.10), whose derivation is given by Hilliard (2008). The vapor phase is modeled by the Soave-Redlich-Kwong (SRK) equation of state. When the the liquid and vapor phases are in equilibirum, they have equal fugacity. Fugacity is calculated using Equation (2.11) for the symmetric reference state and using Equation (2.12) for the asymmetric reference state, y i φ i P x i γ i P 0 i (2.11) y i φ i P x i γ i H i H2 O (2.12) 11

34 where y i is the vapor phase mole fraction of component i, φ i is the fugacity coefficient of i, P is the total pressure of the vapor phase, P 0 i H i H2 O is the Henry s constant of i in water. is the vapor pressure of i, and The reference state for a Henry component is aqueous infinite dilution (asymmetric), and the temperature dependence of the Henry s constant is calculated from Equation (2.13), ln H i A i B i T C i ln T D i T E i T 2 (2.13) where A through E are adjustable parameters and T is the temperature in Kelvin. 2.2 Sequential Regression Single Amine Systems System Am A Am A+H 2 O Am A +H 2 O+CO 2 Data vapor pressure, heat capacity pk a, amine volatility, heat capacity VLE, amine volatility, heat capacity, heat of absorption, NMR Parameters Antoine, C p G 8,aq f,amh, H 8,aq f,amh, NRTL τ i,j, H Am, C p enrtl τ i,j, G 8,aq f Figure 2.2: Sequential regression of a single amine system, H 8,aq f Figure 2.2 gives an overview of the sequential regression process. The top row describes the apparent components, and the second row describes fitted data 12

35 corresponding to the regressed parameters of the bottom row. Sequential regression procedes from left to right. The parameters are specific to each column and are not regressed outside of that system. Sequential regression preserves the fit of each system allowing the model to reduce down consistently. If Am A parameters were changed to match Am A+H 2 O+CO 2 data, then when the system has little CO 2, such as in the water wash, model predictions would not be the same as the fit of Am A+H 2 O Pure Amine Regression This section details the first column of Figure 2.2. If the amine is not a databank component, then it must be defined. To do so, the component was added to the list of components. Then, the following parameters were defined: G f (DGFORM), H f (DHFORM), charge (CHARGE), and MW (MW). If data were lacking, they were estimated by drawing the molecular structure and using PCES (Property Component Estimation System). Amines were treated as a Henry component except for AMP. Defining a molecule as a Henry component changes it from a solvent to a solute, thus changing its reference state from symmetric to asymmetric. An additional option was used to set the reference state to infinite dilution in water rather than the default of dilution in mixed solvent. The choice of reference state affected the pk a calculation. With the amine component defined, pure component properties were regressed. For liquid amines, these were vapor pressure and heat capacity. The parameters were PLXANT and CPIG. PLXANT parameters govern the pure amine vapor pressure (e.g., the partial pressure of MEA over pure MEA liquid), while HENRY parameters govern the amine vapor pressure in the presence of a solute (e.g., the partial pressure of MEA over a mixture of MEA and water). 13

36 Unloaded Regression The middle column of Figure 2.2 describes a binary system. With more than one component, the system chemistry needed to be defined. Two separate reaction sets were used: one with protons and hydroxide ions and one without. Protons and hydroxide ions are in such low concentration that their inclusion is not warranted except for calculating pk a. The chemistry is shown in Equation (2.14) and Equation (2.15). AmH ô Am H (2.14) H 2 O ô H OH (2.15) The different data sets in order of importance are: pk a, amine volatility, and heat capacity. Matching the pk a is critical to matching the VLE and to matching speciation. Amine volatility is important for a process model, but this set of data was omitted for mass transfer models, e.g. 2-piperadineethanol (2PE). Lastly, heat capacity impacts the cross exchanger performance as well as the calorimetric heat of absorption. While unloaded heat capacity is helpful for dilute conditions, loaded heat capacity is far applicable. If the amine was defined as Henry component, then there were only two parameters for pk a regression. In this case, the DRS was not used to fit the data. However, if statistics, such as standard deviation and correlation, are desired, then DRS is justified. It is later shown that G 8,aq f, AmH can be calculated directly via Equation (8.16). As illustrated in Figure 2.3, changing Gf, AmH (DGAQFM) set the pk a at 25 8, aq C, and Hf, AmH (DHAQFM) set the slope. The pk a was calculated by Equation (2.16) using the predicted activities along with a conversion from molefraction basis to the experimental molality basis. Both used the asymmetric reference state. pk a log ¹ i a ν i i 1000 log MW H2 O 8, aq (2.16) 14

37 14 12 H 0 f, aq G 0 f, aq pk a 10 8 H 0 f, aq G 0 f, aq T p Cq Figure 2.3: pk a regression schematic For a Henry component, volatility was controlled by the parameters of Equation (2.13) (HENRY) and weakly affected by the NRTL interaction parameters for H 2 O/Am (NRTL). If the amine was not a Henry component, then the volatility was controlled by the NRTL parameters for H 2 O/Am. In either case, the DRS was used. α (NRTL/3) was usually left at the default value. For molecule-molecule interactions this is 0.3. For enrtl, α (GMENCE) for molecule-electrolyte or electrolyte-molecule interactions is 0.2 where the molecule is water and 0.1 where the molecule is solute. The ideal gas heat capacity CPIG of the amine was used to regress unloaded heat capacity. As these data span a much larger concentration range than necessary for the model, only relevant data were regressed. C p data were unavailable for all systems in this work Loaded Regression In the ultimate column of Figure 2.2, the system chemistry was fully defined. Unlike the penultimate column, chemistry without protons is used. This simplifies 15

38 the speciation and improves convergence by eliminating very low mole fraction values, which cause a badly scaled matrix. For tertiary amines, Equations (2.17) and (2.18) cover all possible chemistry. For amines with a single carbamate-forming nitrogen, Equations (2.17) to (2.19) apply. For amines with two carbamate-forming nitrogen groups, Equations (2.17) to (2.21) apply. True components are used rather than working with total amine, total water, and total CO 2, which are apparent components. Am CO 2 H 2 O ô HCO 3 AmH (2.17) Am HCO 3 ô CO2 3 AmH (2.18) 2 Am CO 2 ô AmCOO AmH (2.19) 2 AmCOO CO 2 ô Am COO 2 HAmCOO (2.20) Am AmCOO CO 2 ô Am COO 2 AmH (2.21) For systems where the zwitterion can form, a zwitterion was treated as a Henry component with a near zero Henry s constant. This is a workaround, as treating the zwitterion as an ion lead to charge imbalance errors (Frailie, 2014). Exploration of the new zwitterion option available in Aspen Plus may be more thermodynamically consistent. The two most important data sets are NMR and VLE. VLE is sufficient for non-hindered systems, as the speciation can be accurately predicted from the chemistry and VLE data (Li, 2015; Frailie, 2014; Plaza, 2011). However, for a hindered system, the system will tend to underpredict carbamate and overpredict total carbonate. NMR data can be regressed using the DRS system and a customized Fortran subroutine (Chen, 2011), but this was not necessary. In this work, G 8,aq f (DGAQFM) and H 8,aq f (DHAQFM) of the hindered amine carbamate were adjusted manually. This regression behaves analogously to the pk a regression of Figure 2.3. For other systems, NMR data were used only to check the regression. VLE a.k.a. CO 2 solubility data were fit with the enrtl binary interaction parameters τ i,j, viz. C (GMELCC) and D (GMELCD) of Equation (2.7) and Equation (2.8). 16

39 Table 2.2: Molecule and electrolyte components for enrtl τ i, j parameters Molecule Cation Anion Am AmH AmCOO HAmCOO Am COO 2 CO 2 HCO 3 H 2 O CO 2 3 (Appendix D provides a discussion of WWC VLE data quality.) Table 2.2 summarizes the species for τ i,j. Using this table, it is possible to write out all of the molecule-salt, salt-molecule, and molecule-molecule parameters. E.g. H 2 O{ AmH, AmCOO. Parameters involving CO 2 were not used for VLE regression but for fine-tuning γ CO 2 as discussed in 2.4. The defaults for parameters with water as the molecule are 8, 4 and for amine as the molecule 10, 2, and for CO 2 as the molecule 15, 8. For zwitterion as the molecule, either the water or molecule convention was followed. The default for GMELCD is 0, meaning the interaction parameters are not temperature-dependent. Through trial and error following rules of thumb, the interaction parameters to regress were chosen. The enrtl model is calculated using mole-fractions; therefore parameters associated with high concentration species have greater effect. Parameters involving water have the most effect at low loading, while those involving amine and zwitterion have more effect at high loading. The speciation was used to focus on the most concentrated species for the problematic loading range and temperature. GMELCC parameters were regressed first, with GMELCD parameters being regressed only if the fit was unsatisfactory. All models were more sensitive to C ca,m than C m,ca. In particularly difficult cases, regression of individual parameters to determine model sensitivity to that particular parameter proved insightful. Lastly, DRS depends heavily on the initialization of each parameter. All parameters were initialized at the default until a better fitting initialization was found. 17

40 2.2.2 Blend Amine Systems Regression of a blend amine system is more complex than a single amine system with two additional steps needed to join the single amine models into a cohesive blend amine model. The blend amine model is heavily dependent on the single amine models. The first column of Figure 2.4 shows the single amine model from the sequential regression method outlined in Figure 2.2. The last two columns are the combination of the two models. The penultimate column covers interactions of the two amines with water. The data included here are unloaded vapor pressure and heat capacity. This unloaded regression should be done together with the prior unloaded regressions of the individual amine systems. This is an exception to the sequential regression method, as previously regressed parameters are regressed again here. This means that the integrity of the two individual models needs to be checked again at this stage. This method was pioneered by Frailie (2014) for the creation of a PZ/MDEA model. The blend unloaded data are regressed with the NRTL interaction parameters for amine-amine interaction along with the individual amine parameters used for their respective unloaded regressions. Other properties are managed by a mixing rule and so depend on the single amine models. The ultimate column of Figure 2.4 covers the full blend amine system. The only remaining parameters were cross-term interaction parameters. A cross term is a term that involves both amines. Usually the cation and anion were from different amines. The guiding principles for the selection of the interaction parameters are the same as in with the added caveat that the dominant amine shifts through the loading region. E.g., in PZ/MDEA the lower loading is dominated by carbamate-forming PZ with the higher loading dominated by bicarbonate forming 18

41 System Data Parameters System Data Parameters Am A+H2O+CO2 Am A+Am B +H2O Am A+Am B +H2O+CO2 VLE, amine volatility, heat capacity, heat of absorption, NMR enrtl τi,j, G 8,aq f, H 8,aq f vapor pressure, heat capacity NRTL τi,j, HAm, Cp NMR, VLE, amine volatility, heat capacity, heat of absorption enrtl cross τi,j Am B+H2O+CO2 VLE, amine volatility, heat capacity, heat of absorption, NMR enrtl τi,j, G 8,aq f, H 8,aq f Figure 2.4: Sequential regression of a blend amine system 19

42 MDEA. Where this shift occurs depends on the ratio of the concentration of the two amines. 20

43 2.3 Analogous Regression Analogous regression is the creation of a model starting from another model. The resulting model is a palimpsest with parts of the model matching the data, while other parts match the analog. The resulting model is accurate only over the range of data regressed. Analogous regression is used when data and time are limited. Sequential regression always gives a superior model Regression Method Analogous regression followed the same principles as sequential regression, as discussed in 2.2. Prior to regression, an analog was selected. The choice of an analog was limited by model availablity. Beyond being the same class of amine, molecular weight and pk a were considered. The two models also needed to share a range of operation, especially amine concentration. Once the analog was selected, the analogous components were redefined. They were renamed and their structure, molecular weight, and other pure component properties were set. Then, pk a data were regressed as in Lastly, the available loaded data were regressed. These data were usually cursory CO 2 solubility data from screening. As in sequential regression, only the interaction parameters were regressed. This process was done for the single amine model for the blending with the PZ model. 2.4 Model Validation The thermodynamic model must be validated. All applicable properties from the following list were checked by plotting: for pure amine: C p, Am and P Am ; for aque- 21

44 ous amine: C p, Am H2 O, H mix, pk a, and H Am ; for loaded amine: C p, Am H2 O CO 2, CO 2 solubility, H abs, speciation, γ i, γ CO 2, and solid solubility. For all parameters regressed with the DRS, the standard deviation of the parameter should be less than the value of the parameter. If not, the use of parameter may still be justified to achieve a tight fit, but there is an increased risk of overfitting and degrading the physical significance of other regressed parameters. One way to validate a model is to predict the differential heat of absorption p H abs q. Li et al. (2014) carefully show the origin of Equation (2.22) as starting from the Gibbs-Helmholtz equation described in Lewis and Randall (1923). Additional discussion is given by Mathias and O Connell (2012). H abs RT 2 B ln fco2 BT P,x (2.22) Each isotherm should be smooth and start with the highest H abs at the lowest loading and decrease at higher loadings as the dominant reaction shifts from carbamate formation to bicarbonate formation to physical absorption. Blend amines should show an inflection where the dominant chemistry changes. In some cases, γ CO 2 was not increasing with loading and decreasing with temperature as expected. This was corrected by manually changing τ CO2, ca and τ ca, CO2. The VLE regression was repeated and these two steps iterated until satisfactory. 2.5 Conclusions The most important data sets to fit are pk a, followed by CO 2 solubility (VLE). The analogy method is effective at representing an amine with missing physical property data, where the properties of an analogous amine substitute for the missing data. The prediction of the heat of absorption by differentiating VLE serves as a test of model quality. 22

45 Finding a predictive means of choosing the binary interaction parameters for regression would accelerate regression and better avoid the pitfalls of over-fitting and distorted correlated parameters. Rigorous testing of the analogy method would determine the best criteria of an analog and determine if a there is an accuracy penalty or distortion in parameters for using analogous physical properties. The potential benefits of using the symmetric enrtl model(song and Chen, 2009) should be explored. As per the recommendation of the Aspen Plus manual, H 3 O + should be used instead of H for the pk a chemistry block. Exploration of the new zwitterion option is warranted. Other regression methods should be investigated, such as particle swarm optimization, which does not depend on initialization (Pinto, 2014). 23

46 Chapter 3 Mass Transfer Modeling Methods 3.1 Introduction A mass transfer model is necessary to model the absorber. The absorber is a major capital expense, and accurate simulation is key to sizing and costing it and associated equipment. Colloquially, this model is called a kinetic model (Frailie, 2014; Chen, 2011), but this term is inaccurate because a kinetic model does not necessarily include diffusion and hydrodynamics. Therefore, this work uses the term mass transfer model to describe a model comprised of kinetics, diffusion, and hydrodynamics. A mass transfer model is inherently more complex than a thermodynamic model as any errors in the thermodynamic model add to error in the mass transfer model. Additional complexity arises from the interconnection of Fortran subroutines, calculator blocks, design specifications, sensitivity case blocks, etc. The thermodynamic and mass transfer models are connected through the CO 2 vapor-liquid equilibrium (VLE), the equilibrium speciation, reaction equilibria, the activity coefficients, particularly that of CO 2. This connection is most important at the regressed mass transfer data conditions 20 C to 100 C and lean to rich loading and in the process model at absorber conditions 40 C to 60 C and lean to rich loading. 24

47 Throughout this work the mass transfer method has been continuously refined. Three different methods are discussed: manual regression ( 3.3.1), data fit ( 3.3.2), and response surface methodology (RSM) ( 3.3.3). All three share a common flowsheet and model framework that are discussed in 3.2. Validation of the model and limitations are covered in Mass Transfer Framework All models in this work share a common framework of hydrodynamics, diffusivity, kinetics, and the wetted-wall column (WWC) flowsheet in Aspen Plus. Two film theory is used Hydrodynamics Hydrodynamics encompasses the flow regime and the physical properties of the solvent, i.e. the hydraulics. The WWC is operated with laminar flow. The most important hydraulics are viscosity and density. Unfortunately, the majority of hydaulic data published is for unloaded systems. As these data are outside of the operating conditions, except for the water wash, they are only helpful to check the behavior at the boundaries. Regressions were done using either Solver in Excel or fitnlm in MATLAB. While the two methods yielded equivalent parameters, the latter method was preferred as it gave statistics Viscosity Viscosity has a major impact on mass transfer and process performance. Viscosity plays an important role in both the diffusivity of species as well as the liquid 25

48 film physical mass transfer coefficient kl 0, which is used to calculate the liquid film thickness. In the full scale process, high viscosity hinders heat transfer in the cross exchanger, contributing to capital expense (Lin et al., 2016). Viscosity was represented by a Fortran subroutine. The built in Aspen Plus routines are inadequate, failing to capture the increase in viscosity with loading (Aspen Technology, 2013d). Viscosity µ was calculated using Equation (3.1) for single amine solvents and Equation (3.2) for blend amine solvents, " µ exp rpaw Am bq T cw Am ds µ µ H2 O µ H2 O * rpew Am ft gq α 1s w (3.1) Am T 2 " exp rpaw Am 1 bw Am 2 cq T dw Am 1 ew Am 2 fs * rpgw Am 1 hw Am 2 it jq α 1s w (3.2) Am total T 2 where µ H2 O is the viscosity of water at T, a j are parameters, w i is mass fraction of i, T (K) is temperature, and α is loading p mol CO 2 {mol alkq. Equation (3.1) and Equation (3.2) use apparent speciation, making them partially independent of the true speciation, which prevents changes in speciation from affecting viscosity. These equations were developed by Frailie (2014) based off of the work of Weiland et al. (1998) Density Density plays less of a role in mass transfer than viscosity. Density is involved in converting mole-fraction based kinetic constants to concentration-based kinetic constants, converting the measured volumetric flow rate to a mass flow rate for simulation, and in calculating the thickness of the liquid film. 26

49 A Fortran subroutine was used to calculate density as the built in correlations were inadequate. The routine gives better performance with fewer parameters and is partially indpendent of the model true speciation. Density ρ was calculated by Equation (3.3) for single amine systems and by Equation (3.4) for blend amine systems, ρ x H2 Oρ H2 O x Am pat bq x CO2 pct dq (3.3) ρ x H2 Oρ H2 O x Am 1 pat bq x Am 2 pct dq (3.4) x CO2 rpet fq px Am 1 x Am 2 q pgt hqs where ρ H2 O is the density of pure water, a h are parameters, and x i is the mole fraction of i. The subroutine is actually a calculation of molar volume V m, so density is calculated by Equation (3.5), V m MW (3.5) ρ where MW is the molecular weight of the solvent. As MW comes from the true speciation, the density subroutine is still coupled to the thermodynamic model Diffusivity Two different effective diffusion coefficients were used in the aqueous phase: D CO2 for gaseous species, CO 2 and N 2, and D Am for all other species. D CO2 p m2 {secq is modeled by Equation (3.6) (Versteeg and Swaaij, 1988), and D Am by Equation (3.7), which generalizes the equation of Frailie (2014), 2119 D CO exp T µwater µ soln 0.8 (3.6) D Am D 0 T T ref α µ µ ref β (3.7) 27

50 where D 0 is a pre-factor, T ref is K, µ ref is the solvent viscosity at 40 C and midloading, and α and β are parameters. These references center the regression at absorber conditions. The form of Equation (3.7) is problematic as it leads to a counter-intuitive negative power on T due to the temperature-dependence of µ, cf. Table Physically, β should be a single value for all solvents. These problems led to overregression in the PZ/MDEA model Independence (Frailie, 2014), resulting in D Am D CO2. Therefore, all blend amine models with PZ suffer from D Am D CO2. This cannot be corrected without redoing the mass transfer regression of PZ. As the 2PE and AMP models were constructed after this problem was realized, in them D Am was set to half that of D CO2. This choice was based off of the fit of Chen (2013). All other models regressed the parameters of Equation (3.7). While there is a superfluity of measurements of diffusivity in unloaded solutions (Bougie and Iliuta, 2012), few measurements in loaded systems are reported (Dugas, 2009). Compounding the issue is that literature primarily studies either the diffusion of CO 2 (Hamborg et al., 2008) or the diffusion of amine (Snijder et al., 1993), making a direct comparison difficult. One study that looked at both found ammonia to diffuse at the same rate as CO 2 in aqueous solutions (Frank et al., 1996). However, extrapolating studies from an unloaded system with few components to a highly non-ideal, partially-ionic system with many components is speculation. This lack of data makes uncertainty quantification of D Am difficult. As the liquid film mass transfer coefficient is sensitive to D Am at the quarter power at 40 C, this is a problem. Intuitively, D Am D CO2 as the amine and products are larger than CO 2. Frailie (2014) and Dugas (2009) interpreted their work using Wilke-Chang theory, Wilke-Chang only applies to dilute solutions. Vignes theory or Caldwell and Babb s theory apply to concentrated systems and should be used instead. Aspen Plus uses 28

51 Nernst-Hartley for electrolytes and Wilke-Chang with Vignes correction for molecules in the ENRTL-RK models. 1E-9 D i m 2 sec 1E-10 1E-11 8 m 2PE 8 m 2MPZ 8 m 2MPZ (Chen) 4.8 m AMP 8 m PZ 7 m MDEA 7 m MEA loading (mol CO 2 /mol alk) Figure 3.1: D Am (solid) and D CO2 (dotted) at 40 C; PZ and MDEA (Frailie, 2014); MEA (Plaza, 2011); 2MPZ (Chen and Rochelle, 2013) Figure 3.1 and Figure 3.2 shows that the simple assumption that D Am is half that of D CO2 gives similar behavior to other correlations. D Am is greater than D CO2 for PZ and MDEA at all temperatures, and for MEA at T 80. C. The possibility of this artifact is avoided by not using Equation (3.7). If regression is warranted, the Arrhenius form of Equation (3.8) used by Chen and Rochelle (2013) is more physically consistent. D Am µ 0.72 T (3.8) The reference temperature should be changed to K. 29

52 1E-8 D i m 2 sec 1E-9 1E-10 1E-11 8 m 2PE 8 m 2MPZ 8 m 2MPZ (Chen) 4.8 m AMP 8 m PZ 7 m MDEA 7 m MEA loading (mol CO 2 /mol alk) Figure 3.2: D Am (solid) and D CO2 (dotted) at 100 C; PZ and MDEA (Frailie, 2014); MEA (Plaza, 2011); 2MPZ (Chen and Rochelle, 2013) Kinetics The kinetics were mole-fraction, activity-based (mole gamma) and represented by the termolecular mechanism. The kinetic reaction set was used in the absorber block, while the thermodynamic chemistry of without protons was used everywhere else in the model. Two example reactions are Equation (3.9) and Equation (3.10). k Am Am 2 Am CO 2 ÝÝÝÝÝá âýýýýý AmCOO AmH (3.9) k Am Am H 2 O CO 2 ÝÝá âýý HCO 3 AmH (3.10) In addition, the reaction set included proton exchange reactions that were at equilibrium. An example is Equation (3.11). Am HCO 3 ô AmH CO2 3 (3.11) 30

53 Most models have more reactions than Equations (3.9) (3.11). All models neglected the base-catalysis of water due to its low basic strength, and also the hydroxide ion was not modeled due to its low concentration. The reaction rate for Equation (3.9) was calculated by Equation (3.12) and that of Equation (3.10) by Equation (3.13), r CO2 k Am Am a CO2 a 2 Am (3.12) r CO2 k Am a CO2 a Am (3.13) where k i is the reaction rate constant p kmol {sec-m 3 q and a i is the activity of species i. The reaction rate constant k i was calculated using the Arrhenius relation of Equation (3.14), k i k 0 exp E A 1 R T 1 T ref (3.14) where k 0 is the reaction pre-exponential, E A is the activation energy, R is the universal gas constant, and T ref is the reference temperature of K. k 0 and E A are regressed parameters. Together with the D Am parameters, and the hydraulic parameters, these are all of the regressed parameters for a mass transfer model. The reaction equilibrium K eq was equated to the thermodynamic equilibrium by calculating the reverse reaction rate constant k r from the forward rate constant k f using Equation (3.15), where K eq is calculated from Equation (3.16), k r k f K eq (3.15) K eq ¹ i a ν i i (3.16) where ν i is the stoichiometric coefficient of i. Equation (3.16) is equivalent to Equation (2.10), which is the equilibrium constant calculated from Gibbs free energy. The forward and reverse reactions are modeled as separate reactions in Aspen Plus. 31

54 There is an inconsistency in this representation of kinetics that is problematic at temperatures far from T ref (Frailie, 2014). E A for the reverse reaction will not strictly satisfy Equation (3.15) as the temperature dependence of the activity coefficients is not encompassed by E A. This problem is avoided in the isothermal WWC simulation through a calculator block that recalculates the reverse reaction E A for each temperature. This solution is infeasible for a non-isothermal absorber. This can be done through a user Fortran subroutine reaction set as done by the MEA model of CCSI but as the inconsistency is not problematic within 20 C of T ref this was not done. Implementation of the subroutine would slow calculations and introduce another failure point for an accuracy improvement at an inapplicable temperature Flowsheet Figure 3.3 shows the Aspen Plus Ratesep model that replicates the WWC used to collect the mass transfer data (Chen and Rochelle, 2011). In lab, six flux points, three desorption and three absorption, are collected at each loading and temperature (Li, 2015). Figure 3.3 shows part of the flowsheet used to to simulate the fluxes. The greatest desorption and absorption fluxes were simulated as these points are furthest from equilibrium and thus have less experimental error. While the error has not been calculated, the WWC reproducibility was calculated as 8.5% for the liquid-side mass transfer coefficient, kg 1 for PZ (Li, 2015). This same value has been used for all amines in this study. The solvent was fed as separate streams to a mix block. Separate streams were used as pure component streams are more transparently manipulated than setting the flow rates of individual stream components. After the mix block a heater removed the heat of speciation and heat of mixing, as the flowsheet must mimic the isothermal experimental operation (Li, 2015). 32

55 lean lean flash Am 1 Am 2 H 2 O CO 2 lean gas out WWC gas in H 2 O saturator rich rich flash feed gas XS H 2 O Figure 3.3: Flowsheet of WWC model; second, identical WWC with different feed gas not shown Then, the lean solvent stream entered the WWC RadFrac block. This block used two custom Fortran subroutines: one for mass transfer ( B.3) and one for area ( B.5). The mass transfer subroutine implemented the same gas film resistance k g (Bishnoi and Rochelle, 2000) and the same physical liquid film resistance kl 0 (Pacheco, 1998) used to interpret the experimental data. The area subroutine set the area of the WWC to m2 {m 3. This number is the surface area of the WWC once the diameter has been scaled by 10. This scaling also appears in the mass transfer subroutine to convert the liquid flow rate into a velocity.this scaling prevented artificial wall effects. Due to this scaling, the flow rates of the inlet gas and liquid were scaled by 100 to maintain the same ratio of flow rate to cross-sectional area. 33

56 After the lean solvent passed through the RadFrac block, it exited as the rich stream and entered a flash block. This block was used to calculate P CO 2. The lean stream P CO 2 was calculated by transferring the whole stream to another stream to be flashed, shown in the inset of Figure 3.3. Both flashes were T-vapor-fraction flashes. The feed gas was a mix of CO 2 and N 2 that was fed along with water to a T-P flash block to saturate the gas stream. Excess water left the block to nowhere, while the saturated gas in stream is fed to the bottom of the WWC. The gas in stream exited the top as gas out. Not shown in Figure 3.3 is a second WWC RadFrac block that has a lean inlet stream identical to the lean stream, meaning the mixer and heater were omitted. The rest of the second WWC is identical to Figure 3.3. Running both the desorption and absorption cases simultaneously allows the use of a design specification to adjust the loading such that at zero driving force there is zero flux (Frailie, 2014). This adjustment corrected for both experimental error in loading and for model error in the VLE. Frailie (2014) limited the loading adjustment to 10% of the operational loading range. This limit was initially adopted in this work for 2MPZ but later relaxed. Ratesep uses film theory to describe the mass transfer, wherein the liquid close to the gas-liquid interface is divided into many discrete slices with heat and mass transfer calculations done in each slice. All models in this work used the discretization of Table 3.1, where δ is the dimensionless distance through the boundary layer. δ is zero at the gas-liquid interface and one at the bulk liquid. The flux ˆN CO2 was calculated by Equation (3.17), ˆN CO2 9n CO 2,in 9n CO2,out A (3.17) 34

57 Table 3.1: Liquid film discretization Point δ Point δ Point δ where 9n CO2,in p 9n CO2,outq is the molar flow rate of CO 2 in the inlet gas (outlet gas) and A is the interfacial area. The WWC mass transfer coefficients k i were calculated by Equation (3.18), k i ˆN CO2 P in P out log P in P out (3.18) where terms are defined in Table 3.2. in is the inlet gas, out is the outlet gas, int stands for the gas-liquid interface, top is the top stage of the WWC, and bot is the bottom stage of the WWC. Table 3.2: Mass transfer coefficient driving force definitions for Equation (3.18) Coeff. P in P out K g P CO2,in P CO 2,rich P CO2,out P CO 2,lean k g P CO2,out P CO 2,int,top P CO2,in P CO 2,lean kg 1 P CO2,int,top P CO 2,rich P CO2,int,bot P CO 2,lean 35

58 Four calculator blocks were used when running the flowsheet. The first calculated the flowrates of the solvent components Am, H 2 O, CO 2 from the solvent loading. This is for convenience. The second calculated the flux by Equation (3.17) and mass transfer coefficients by Equation (3.18). The third calculated k r at the system temperature by Equation (3.15), which ensures consistency between K eq of the kinetics and of the thermodynamics. The fourth adjusted the flowrate of water to the saturator block to avoid absorbing CO 2 from the gas stream. Feeding too much water to the saturator block could absorb some of the CO 2 and result in an artificially decreased driving force. The code for these calculator blocks is included in Appendix C. In short, one design specification and four calculator blocks are used with the WWC flowsheet. 3.3 Methods Low loading, low temperature data are most sensitive to the carbamate reaction rate, while high loading, high temperature data are more sensitive to the bicarbonate reaction rate. The high temperature data are also sensitive to D Am, and so D Am is used to fit 100 C data. Due to the implementation of diffusivities, the CO 2 flux has a 0.25 power dependence on D CO2, rather than 0.5, and a 0.25 power dependence on D Am rather than 0. This is described in detail by Sachde (Rochelle et al., 2015) Manual In this method, the parameters were manually changed to minimize the objective function, which was the absolute average relative deviation (ARD) (%) of the 36

59 flux as defined by Equation (3.19), ARD 100 n n ˆN i N i N i (3.19) where n is the number of data, N i is the experimental value, and ˆN i is the predicted value. A sensitivity block was used to run cases for each condition and the ARD computed. The parameters were changed by hand, and the sensitivity block was run again. This continued until the ARD could not be decreased any further. The benefits of this method were ease of use and transparency. By manually changing the parameters, it was straightfoward to understand their relationship to the predictions. There were many drawbacks. It was time consuming to regress the parameters, and the end results were parameter values without any statistics. This method was used for the following models: 2MPZ (discussed in Chapter 6), PZ/2MPZ, PZ/AMP, and PZ/HMPD (all three discussed in Chapter 7). This method grew out of the work of Dugas (2009) and Zhang et al. (2009) Data Fit The Aspen Plus Data Fit tool is designed to tune a model to plant data. Data fit can reconcile input variables and gives some statistics on regressed parameters. Data Fit was used to regress mass transfer parameters to fit the experimental data. Data Fit uses a maximum-likelihood method to minimize the objective function f 37

60 as defined by Equation (3.20a), f 1 2 RI RR N ri l1 N rr m1 N sets i1 tw i rri RRsu (3.20a) xri ˆx ri σ ri 2 (3.20b) xrr ˆx rr σ rr 2 (3.20c) where N sets is the number of data sets, W i is the weight of a data set, RI is reconciled variables, RR is results variables, and σ is the standard deviation. The regression was run by entering the data into a Data Fit Data Set. No inputs were reconciled, and the flux data were assigned a standard deviation of 1%. The flowsheet was initialized using measurements rather than a base case. Before running the regression, the manual method of was used to find a good initial guess and to set bounds on the parameters. The bounds for E A were 20 kj {mol to 90 kj {mol, while for k 0 they were one order of magnitude around the initial guess. Then, the regression was run. If a parameter reached itsbound, the bound would be changed so long as it was physically reasonable. Then, the regression would be rerun. The benefit of this method is that in addition to the point estimates of the manual method, this method gives statistics on the parameters, viz. the standard deviation, a 95% confidence interval, and a correlation matrix. The method suffers from a few drawbacks. In theory, Data Fit should lead to the optimal solution, but in practice manual regression always outperformed the Data Fit solution. Data Fit suffers from excessive run times of twenty minutes to two hours compared to the five minute or less run times for a manual regression. Lastly, it is not clear how Data Fit deals with convergence failure, which may account for the underperformance of the 38

61 regression. Convergence of the algorithm was a frequent hassle, as it rarely converged without either hitting a bound or stopping at a reported sub-optimal solution. In this work, Data Fit was used to regress the 2PE model (Chapter 4). This method was also used by Chen et al. (2013). However, Chen et al. (2013) chose to treat the loading as a reconciled input with a standard deviation of 5%. This approach was examined and found to result in even worse run times and to also adjust loading much more than 5% relative difference due to how the standard deviation is interpreted by Aspen Plus. For this reason, loading was adjusted as discussed previously in Response Surface Methodology To combine the speed of the manual method with the statistical rigor of the Data Fit method, response surface methodology (RSM) was used. This method is a refinement of the method used to create Independence (Frailie, 2014). RSM is a branch of statistical science that deals with relationships between many explanatory (independent) variables and one or more response (dependent) variables (Myers et al., 2016). The explanatory variables were the pressure, temperature, loading, kinetics, and D Am, while the response variable was the predicted flux. Figure 3.4 is a flow chart of the method. In the first row, the raw WWC data are processed in Excel to create the data set to be fit data. data includes the temperature, total pressure, experimental loading, flow rate of CO 2 and N 2 for the greatest desorption and absorption points, and the experimental flux of the greatest desorption and absorption points. data was entered into Aspen Plus as the cases of a sensitivity block where each case is the pair of desorption and absorption points at one temperature and pressure. 39

62 raw WWC data select data for sensitivity case k0,i basis, EA,i basis, data run basis case k0,i basis, EA,i basis, data ˆNCO 2 k0,i NCO 2 basis, basis, EA,i basis, data, α k 0,i j run k0,i i=i+1 i=n run non-linear fit algorithm k0,i reg, EA,i reg, data confirm fit no yes ˆNCO 2? NCO ˆNCO 2 2 NCO 2 reg Figure 3.4: RSM flow chart stop extrema conditions (data) ˆNCO 2 NCO 2 basis ˆNCO 2, α k 0,i NCO j 2 ˆNCO 2 NCO 2 reg, k0,i reg, EA,i reg ˆNCO 2 NCO 2 Aspen Plus MATLAB Excel input/output 40

63 In the next row, initial values of the reaction pre-exponential k 0,i basis and activation energy E A,i basis for each reaction i along with the data are used by Aspen Plus to run the WWC simulation. Dividing the predicted flux ˆN CO2 by the experimental flux N CO2 yields the basis flux ratio ˆN CO2 N CO2 basis. The next row develops the sensitivity of each data point to each k 0,i. This was done by individually increasing k 0 by 10% (i.e. 0.1) and running the data set. Then, the sensitivity α k 0,i j was calculated by Equation (3.21). α k 0,i j ln ˆN CO2 N CO2 basis ln k 0,i k 0,i basis 10% ln ˆN CO2 10% N CO2 basis ln 1.1 (3.21) Equation (3.21) gives identical results if the denominator is 1.1 instead of ln 1.1, but the natural log in the numerator is needed as the difference in predicted fluxes is very slight. (This could also be implemented in Aspen Plus Data Fit and may resolve the sub-optimal fit problem.) These sensitivities were used to construct the response surface of Equation (3.22). ˆN CO2 N CO2 ˆN CO2 N CO2 basis ¹ i k α 0,i k0,i j k 0,i basis (3.22) The output from this step produces the response surface, which serves as the model equation for the non-linear fitting algorithm of MATLAB. This response surface assumes the system is linear. As the system is non-linear, the basis must be close enough to the solution for local linearity to hold. To approach the solution, the manual method of was used. 41

64 In the next row, MATLAB uses the response surface to regress the kinetic parameters. nlinfit takes the response surface as the model and performs a weighted least squares regression of the kinetic parameters. Sample code is included in Appendix E. fitnlm is incapable of constrained regression. Therefore, if a parameter went beyond a bound, that parameter was fixed at the bound, and the regression repeated. This regression agrees with results from the Excel Solver add-in and has the added benefit of giving statistics, viz. confidence intervals, standard error, t-statistic, p-value, sum of squared errors, root mean squared error, and sum of squares regression, and correlation matrix. In the penultimate row, the regressed parameter values are checked by running the data set in Aspen Plus with the regressed values. If the predicted flux ratio from Aspen Plus agrees with that from MATLAB, then the regression is complete. If not, the basis values were selected too far from the regressed values, and the linearity assumption has been violated. In which case, a new basis is selected, and the whole process is repeated. This method combined the best of the manual and the Data Fit methods with minor drawbacks. The RSM method gave more statistics than Data Fit with less runtime. In addition, RSM was transparent in how convergence failures affect the regression. The drawback was the non-robust RS required using multiple bases when the final solution was far from the initial basis. This drawback could be overcome by improving on the form of the RS. This method was used to develop the AMP model Chapter 5. 42

65 3.4 Model Validation There is a misconception that a mass transfer model is a process model (Chen and Rochelle, 2013). As mass transfer in the WWC occurs under different conditions than a full-sized absorber, the model must be checked for behavior at scale. The major changes are in the mass transfer subroutine for the absorber model. The approximation of thermodynamic equilibrium through backcalculation by Equation (3.15) can be problematic. Without using a custom reaction set Fortran subroutine to maintain thermodynamic equilibrium in the kinetic reactions, the equilibrium only holds from 40 to 60 C (Frailie, 2014). To check if a mass transfer model can be a process model, the model was validated by running a simple absorber and simple stripper, as seen in the manuals included in the appendices. This is still a low level of validation, and pilot plant data reconciliation should be done to further validate the model. 3.5 Conclusions The response surface methodology (RSM) approach gives a more statistically and physically significant mass transfer model than manual regression or using Data Fit. The RSM approach developed sensitivities to the individual parameters using the full model in Aspen Plus, and then used these sensitivities to predict the model response. The parameters were then regressed using the predicted response. The model must be validated for process modeling, as the hydrodynamics and mass transfer correlations change from the wetted-wall column to the absorber. Additional experimental work measuring the diffusion of amine and products in loaded systems is of critical importance to validate the current assumption of half that of the diffusion of CO 2. Future modeling work should include refining 43

66 the response surface methodology approach to develop a more robust response surface capable of simulating a wider range of reaction rate constant values through a modern sampling method and a better formulated sensitivity calculation. This work should leverage the efforts of SolventFit by CCSI. More statistical rigor should be incorporated into regressions, particularly for blend amine systems, in order to understand the meaningful reactions and the role of ratioing reactions through Brønsted correlations. D Am should be corrected for PZ and PZ blend models, and different diffusivities should be used for different amines in a blend. 44

67 Chapter 4 2-Piperidineethanol (2PE) 4.1 Introduction 1 Amine scrubbing has been proposed as a way to dramatically reduce carbon dioxide emitted from fossil-fuel power plants (Rochelle, 2009). One of the most important choices in designing an amine scrubber is what solvent to use. Initial research in this field focused on amines used for natural gas sweetening: monoethanolamine and piperazine-promoted methyldiethanolamine. Sterically hindered amines have been proposed both on their own (Bougie and Iliuta, 2012; Endo et al., 2011; Sartori and Savage, 1983) or in a blend (Li et al., 2013b). Sterically hindered amines provide CO 2 capacity comparable to tertiary amines with kinetic rates a hundred times faster (Sartori and Savage, 1983). However, the reason for fast kinetics has not been fully explained. Sartori and Savage (1983) hypothesized that low carbamate stability leads to more free amine, but this does not explain the intrinsic rate of reaction. Bosch et al. (1990) created a numerical model to match 2-amino-2-methylpropanol (AMP) kinetic data at 25 C, and showed that the termolecular mechanism, AMP + H 2 O + CO 2 è AMPH + HCO 3, proposed by Chakraborty et al. (1986) is insufficient to explain the rates. 1 This chapter is based on a paper co-authored with Arlinda Ciftja and Gary Rochelle. Ciftja performed the experimental work and analysis and authored and Rochelle helped interpret results and direct the overall study. 45

68 However, Bosch et al. (1990) were unable to explain the reaction rate trend with pk a. This paper shows that the hindered amine 2-piperidinethanol (2PE) forms a carbamate and that this reaction explains the mass transfer performance. 2PE is a hindered, secondary amine that is more thermally and oxidatively stable than MEA (Freeman, 2011; Voice, 2013). Compared to AMP, 2PE shows similar capacity with 1.5 times faster mass transfer, despite its five times greater viscosity (Li, 2015). 2PE is less thermally stable but as oxidatively stable as AMP (Voice, 2013). Prior NMR studies reported no carbamate for 2PE (Fernandes et al., 2012; Paul et al., 2009), but in this work 2PE carbamate has been quantified using a technique that previously quantified carbamate formation in AMP (Ciftja et al., 2014). These speciation data were used to build a rigorous thermodynamic and mass transfer model of concentrated, aqueous 8 molal 2PE to test. A variety of regression cases and sensitivity studies tested the hypothesis and explain the contributions of kinetics and diffusivity to the observed mass transfer performance. A greater understanding of 2PE contributes to a broader understanding of sterically hindered amines. The importance of hindered amines is recognized in two patents covering 2PE (Sartori and Leder, 1978b; Sartori and Leder, 1978a), and furthermore, one commercial solvent, KS-1, is a hindered amine (Mimura et al., 1997). 4.2 Methods Experimental Methods Sample preparation Amine solutions were prepared from 2-piperidineethanol (with purity 96%) supplied by TCI Europe and were used as received without further purification. 46

69 Amine solutions were prepared with distilled water, and the resulting solution was 30 wt.% amine. The solutions were loaded with CO 2 (grade 5.0) supplied by AGA Gas (AGA Gas GmbH, Hamburg, Germany). The amine concentration was determined by acid-base titration with 0.1M H 2 SO 4 (Kim et al., 2008). Total CO 2 in the loaded samples was measured with BaCl 2 method (Ma mun et al., 2005). About 0.25 ml of loaded/unloaded solution was filled into 5 mm Wilmad 527-PP-7 NMR tubes and a Coaxial Insert WGS-5BL was inserted with known 1,4- dioxane and deuterium oxide (D 2 O). The tubes were weighed in a Mettler Toledo ME204 digital analytical balance with accuracy of g. About 10 mass % deuterium oxide (D 2 O) was added to provide a field-frequency lock and the chemical shifts were referenced to 1,4-dioxane. In order to identify the species formed in loaded and unloaded aqueous solutions, different techniques described by Ciftja et al. (2013) were used. First, qualitative analyses ( 1 H, 13 C, COSY, HSQC and HMBC) were carried out to identify the species, and then quantitative 13 C analyses were conducted to obtain the exact amount of each species formed in the systems. These experiments used special capillary tubes provided by Wilmad-Labglass for the mixture of 1,4 dioxane (99.9% purity) and deuterium oxide (99.8% purity) to avoid any dilution of the solvent. The NMR spectra were recorded on a Bruker Avance DPX 400 MHz NMR spectrometer operating at a frequency of MHz for 13 C and MHz for 1 H with a 5 mm DUAL 1 H/ 13 C probe head. Experimental details on quantitative 13 C NMR experiments and the estimated parameters are given by Ciftja et al. (2013). All the spectra were measured at 25 C with processing and integration done using MestReNova software V

70 The carbamate stability constant K c was reported on a non-activity, mole fraction basis using Equation (4.1) to allow for comparison to other work (Perinu et al., 2014). K c r2p ECOO s (4.1) r2p Es HCO 3 The reported value is the average of the lean and rich loading K c values at 25 C Thermodynamic Model The model was constructed in Aspen Plus V8.4 using the asymmetric electrolyte non-random two-liquid (enrtl) model for liquid phase and ESRK for vapor phase. The enrtl model is an activity coefficient excess Gibbs free energy model with demonstrated capability to model highly non-ideal aqueous amine systems (Zhang and Chen, 2011). The following APV84 databanks were used in this order: PCD, Aqueous, Solids, Inorganic, and Pure28. The 2PE components were defined using AMP analogs based on the model of Li et al. (2014). AMP was chosen as it has similar carbamate stability. The aqueous Gibbs free energy of formation G 8,aq f and the aqueous enthalpy of formation H 8,aq f for the ions, 2PECOO and 2PEH, and the Gibbs free energy of formation G f and the enthalpy of formation H f for the molecule 2PE were initialized at the values of AMPCOO, AMPH, and AMP as listed in Table PE was treated as a Henrys component with an ideal gas reference state. The reference state for water was pure (i.e., symmetric), while for the other species it was infinite dilution (i.e., asymmetric). The model chemistry is shown in Equations (4.2) through (4.7). Equations (4.2) through (4.4) were used throughout the model, except for the pk a regression. To regress pk a, Equations (4.5) through (4.7) were used. Proton and hydroxide ions were not used throughout the model as the magnitude of their mole fraction was less than Their inclusion would have hindered convergence by creating a poorly 48

71 scaled component matrix. 2 2PE CO 2 ô 2PECOO 2PEH (4.2) 2PE CO 2 H 2 O ô 2PEH HCO 3 (4.3) 2PE H 2 O ô 2PEH CO 2 3 (4.4) H 2 O ô H OH (4.5) HCO 3 ô CO2 3 H (4.6) 2PEH ô 2PE H (4.7) For each reaction, the mole-fraction, activity-coefficient-based equilibrium constant K eq was calculated using Equation (2.10). The available thermodynamic data are summarized in Table 4.1. The heat capacity data of Chiu et al. (2010) were not regressed as the measured 2PE concentration is significantly greater than 8 molal. Table 4.1: 2PE Thermodynamic data System Type data T Loading C Am Source pts. p Cq mol CO2 mol alk 2PE C p unloaded 100 wt.% (Chiu et al., 2010) 2PE C p unloaded x Am = (Chiu et al., 2010) 2PE+H 2 O pk a unloaded 0.1 M (Xu et al., 1992) 2PE+H 2 O+CO 2 NMR m this work 2PE+H 2 O+CO 2 VLE m (Chen, 2011) The G aq f and H aq f for 2PEH were manually adjusted to match the pk a data (Xu et al., 1992). G 8,aq f, 2P EH was set to match the pk a at 25 C, and H 8,aq f, 2P EH was set to match the change with temperature. 49

72 For the NMR data, G aq f and H aq f for 2PECOO were manually adjusted to minimize the absolute relative deviation (ARD) as defined by Equation (3.19). G aq f, 2P ECOO was set to match the measured concentration at 25 C. H aq f, 2P ECOO was adjusted until the amount of carbamate decreased with increasing temperature. This decrease was expected as carbamate formation is an exothermic reaction. Attempts to estimate a value of H aq f, 2P ECOO using AMP NMR data failed due to the narrow temperature range measured (Ciftja et al., 2014). The activity coefficients γ i of the species were correlated to fourteen VLE data (Chen, 2011) using the Aspen Plus Data Regression System (DRS). The enrtl model computes γ i from the excess Gibbs energy which is comprised of long-range and short-range interactions along with a Born correction for the infinite dilution reference state (Chen and Song, 2004). Only the short-range interactions of moleculesalt (m, ca) and saltmolecule (ca,m) were regressed. This was done with the binary interaction term τ i, j as defined by Equation (2.8) and Equation (2.7). Five parameters were used to fit the data: three C ca, m parameters (2PEH, CO 2 3 )/H 2 O, (2PEH, CO 2 3 )/2PE, (2PEH, HCO 3 )/2PE, and D H2 O{p2P EH, HCO 3 q and D p2p EH, HCO 3 q{h 2 O. The default for interactions for m H 2O is C pm, caq 10 and C pca, mq 2, while for m H 2 O it is C pm, caq 8 and C pca, mq 4. Regardless of the molecule D pm, caq D pca, mq 0. These defaults are set by Aspen Plus on the basis of the typical enrtl values (Zhang and Chen, 2011) Mass Transfer Model Hydraulics The available hydraulic data are summarized in Table 4.2. Most of the data are unloaded, which is not applicable to the loaded solvent used in CO 2 capture. For 50

73 Table 4.2: 2PE Thermodynamic data System Type data T Loading C Am Source pts. p Cq (wt %) 2PE+H 2 O mol CO 2 mol alk ρ unloaded 5 30 (Paul and Mandal, 2006) µ unloaded 5 30 ρ unloaded (Xu et al., µ unloaded 1992) 2PE+H 2 O+CO 2 µ (Chen, 2011) this reason, only the loaded viscosity µ data are regressed by fitting parameters a g of Equation (3.1). Fitting the change in viscosity with respect to loading is important for diffusion rates, which are most significant at high loading and high temperature. As the four data points are at constant temperature and amine concentration, the parameters most correlated to loading, e and g, were regressed in MATLAB using nlinfit. All other parameters were left at the values of piperazine (PZ) (Frailie, 2014). As no loaded density data are available for 2PE, PZ parameters were used for Equation (3.3) (Frailie, 2014). The use of PZ as a hydraulic basis is effective because of the wide range of data incorporated into the PZ correlations. Density is not a critical property for kinetic modeling or steady state operation, with its usage limited to the conversion of volumetric flow rates to mass flow rates. The impact on contact time in the WWC is negligible. For this reason, approximating the density of 2PE by that of PZ is expected to have a negligible impact on the results. 51

74 Diffusivity The diffusion of CO 2 in solvent is assumed to follow the correlation of Versteeg and van Swaaij (1988) given in Equation (3.6). In the absence of loaded diffusion data, D Am was estimated as one-half the value of D CO2. This simple expression gives very similar performance to the expression used by Chen and Rochelle (2013); a comparison to their expression for the fourteen different temperature and loading WWC conditions of 8 m 2PE regressed yielded ARD=4.9% Flowsheet The Aspen Plus Ratesep model shown in Figure 3.3 replicates the wettedwall column (WWC) used to collect the mass transfer data (Chen, 2011). The model flowsheet uses two absorber RADFRAC columns to simulate the greatest absorption and desorption fluxes of the six points. Experimental fluxes ranged from to mol {m 2 sec (Chen, 2011). The model flux is calculated by Equation (3.17). The reproducibility of the WWC is estimated as 8.5% for the liquid-side mass transfer coefficient, kg, 1 and this value is applied to the flux as an estimate of experimental error (Li, 2015) Reaction Set The reactions were modeled using activities a i and the termolecular mechanism (Crooks and Donnellan, 1989), as exemplified by Equation (4.8). r CO2 ka CO2 a Am a B (4.8) Only the most significant reactions were regressed; hence, H 2 O and OH were neglected as bases. At 50 wt.% 2PE, H 2 O was out competed by 2PE (Li, 2015), and the concentration of OH was negligibly small. The reaction set comprised two elementary kinetic reactions, Equation (4.9) and Equation (4.10), and one equilibrium 52

75 reaction, Equation (4.11). k 2P E 2P E 2 2PE CO 2 ÝÝÝÝÝÝá âýýýýýý 2PECOO 2PEH (4.9) 2PE CO 2 H 2 O k 2P E ÝÝÝá âýýý 2PEH HCO 3 (4.10) 2PE HCO 3 ô 2PEH CO 2 3 (4.11) The equilibrium reaction was an instantaneous proton exchange and therefore calculated by Equation (2.10). Aspen Plus calculated the mass transfer rates using Maxwell-Stefan equations (Krishna and Standart, 1976). The kinetic reactions were each modeled as a pair of forward and reverse reactions, with the reverse reaction calculated from Equation (5.9) through a Fortran calculator block. The rates were modeled by the Arrhenius power law of Equation (3.14) with T ref K Brønsted Correlation The rates of the kinetic reactions can be estimated using a Brønsted correlation (Versteeg and van Swaaij, 1988b), which correlates the kinetic constant with the pk a of the amine. k 0 of Equation (3.14) can be estimated by assuming that the bicarbonate-forming reaction for 2PE follows ln k 2 pk a rs m3 {mol-sec, which is the tertiary amine correlation by Versteeg and van Swaaij (1988a). First the concentration-based k 2 p m3 {mol-secq was found using the pk a at 20 C and then converted to an activity-basis at 40 C and a loading of mol CO 2 {mol alkusing Equation (4.12), k a k c ρ n γ n 1 2P E γ CO 2 (4.12) where k c pk a q is the concentration (activity)-based reaction rate constant, and n is the overall reaction order (here n=2). E A was assumed to be the same as that of MDEA as measured by Ko and Li (2000). 53

76 Following a similar procedure for the carbamate-forming reaction but using the termolecular (n=3) Brønsted correlation at 25 C log k 2 1.3pK a 7.83 rs m6 {kmol 2 -sec (Chen and Rochelle, 2013), the k 0 of Equation (3.14) was estimated. An alternate correlation was developed using the regressed value for the analogous carbamate reaction in the PZ model developed by Frailie (2014). The same slope of 1.3 was assumed and a new intercept was found using the activity-based k 0 at 40 C yielding log k 0 1.3pK a By using a 40 C value in a 25 C correlation, equivalent activation energies were assumed for each amine. For both cases, E A was set to 35 kj {mol based on literature (Bishnoi and Rochelle, 2000; Cullinane, 2005). The predicted values are summarized in Table 4.3. Table 4.3: Predicted activity-based kinetic parameters (T ref = K) Equation k 0 E A k 0 Basis 3 kmol kj sec-m mol (4.9) 10 Brønsted (Chen and Rochelle, 2013) PZ-Brønsted (Frailie, 2014) (4.10) Brønsted (Versteeg and van Swaaij, 1988a) Kinetic Parameter Regression In order to determine the effect of carbamate on mass transfer, nine different ways of fitting the data were explored as listed in Table 4.4, where k 2P E 2P E is the forward rate of Equation (4.9) and k 2P E is the forward rate of Equation (4.10), K c is the carbamate stability constant, Brønsted means the rate was set to the value predicted by the Brønsted correlation, and PZ-Brønsted means it was set to the value predicted from the Brønsted correlation with the intercept calculated from PZ. For cases where K c is set, it was set at the experimentally determined value as presented in the Thermodynamic Results section. For cases where K c was regressed, the amount 54

77 of carbamate was forced to decrease with increasing temperature at a similar rate as in cases where K c was not regressed. Table 4.4: Mass transfer test matrix Case K c k 2P E k 2P E 2P E % ARD 1 Brønsted PZ-Brønsted 24.1 regress Brønsted 3 regress instantaneous no 2PECOO regress no 2PECOO Brønsted regress regress 7.03 set 8 regress Brønsted PZ-Brønsted 18.2 For each case, the twenty-four strongest absorption and desorption fluxes spanning 40 C to 100 C and 0.20 mol CO 2 {mol alkto 0.70 mol CO 2 {mol alk were regressed (Chen, 2011). Ratesep uses film theory to describe the mass transfer, wherein the liquid close to the gas-liquid interface is divided into many discrete slices with heat and mass transfer calculations done in each slice. The thirty-two discretization points of Table 3.1 were used. For each loading and temperature, the loading was adjusted to ensure zero flux at zero driving force per Frailie (2014). This adjustment accounts for both experimental error as well as error in the thermodynamic model. This adjustment was run simultaneously with the kinetic parameter regression. 55

78 Kinetic Analysis To look at how the model performs under process-scale absorber conditions, the relative gas film resistance k g was calculated across loading and temperature along with calculating the effect of k 0 l on k 1 g at a fixed loading and at various temperatures. The overall gas-side mass transfer K g is represented by Equation (4.13), 1 K g 1 k g 1 k 1 g (4.13) where k g is the gas film mass transfer coefficient and k 1 g is the liquid film mass transfer coefficient. k 1 g Equation (4.14). Here H CO2 1 k 1 g comprises reaction and diffusion resistances as defined by H CO2 b D CO2 V m pk 2a 2 2P E k 1a 2P E a H2 Oq 1 k 0 l,prod is the Henry s constant of CO 2 in solution, k 0 l,prod BP CO2 B rco 2 s T (4.14) is the physical liquid film mass transfer coefficient for reaction products, and p BP CO 2 {B rco 2 s T q is the slope of the equilibrium curve. The reaction resistance is represented by the first term. This resistance dominates at low temperature and low loading, where the concentration of species in the liquid boundary layer is nearly equal to the concentration in the bulk liquid. Under these conditions, the system is in the pseudo first-order (PFO) regime. In the PFO regime, kg 1 is represented by Equation (4.15) (Chen and Rochelle, 2013). b kg,p 1 F O D CO2 k rams 2 γam 2? (4.15) γco2 H CO2, H 2 O Converting Equation (4.15) from a concentration basis to a mole-fraction basis yields Equation (4.16), k 1 g,p F O b DCO2 V m pk 2P E 2P E a 2 2P E k 2P Ea 2P E a H2 Oq? γco2 H CO2, H 2 O (4.16) 56

79 where D CO2 is the diffusion of CO 2 in solution. This expression was compared to the more rigorous expression of Equation (4.14) to determine whether or not the WWC operates in the PFO regime. The sensitivity of k 1 g to the reaction rate constants, D CO2, D Am, µ, and k l,0 was quantified by using a central difference to approximate the derivative. Each variable was changed 5% for each point. The rate constant of the carbamate reaction was compared to other cyclic secondary amines to determine if 2PE obeyed the Brønsted correlation. In order to do so, the rate constant was corrected using Equation (4.17) to account for an artificial dependence of k 1 g on the diffusion of the amine (Chen and Rochelle, 2013). k corr d D Am D CO2 k regressed (4.17) Here k corr is the corrected reaction rate constant, while k regressed is the regressed rate constant. D Am of 2PE was compared to other solvents to determine if the diffusivity is correlated with viscosity. To determine how strong a function of temperature diffusivity is, the diffusion activation energy E D of 2PE was calculated using an Arrhenius plot and Equation (4.18). E D R ln D Am 1 {T (4.18) 4.3 Results NMR Experimental Results The reaction between CO 2 and aqueous 2-piperidineethanol (2PE) at two different CO 2 loadings p mol CO 2 {mol alkq was studied at 25 C. The potential species formed in CO 2 loaded 2PE solution are 2PE, 2PEH, and 2PECOO. The molecular structure of the main species are shown in Figure 4.1. In addition, the following 57

80 Figure 4.1: Speciation in loaded aqueous 2PE species are present: H 2 O, H 3 O, OH, CO 2, HCO 3, and CO 2 3. Amine/protonated amine and bicarbonate/carbonate, both of which involve proton transfer have very rapid reaction rates with very small relaxation times. Therefore the 13 C NMR will average the peaks for these species (Ciftja et al., 2013). NMR spectra were acquired to identify any new species existing in the system. Figure 4.2 shows a quantitative 13 C NMR spectra for unloaded aqueous solution (red spectra) and CO 2 loaded aqueous solution of 2PE (blue and green spectra) at 25 C. The chemical shift for the system is in the range δ= ppm. Seven signals that belong to the 2PE/2PEH peaks are present in the unloaded solution shown in red. Table 4.5 gives the liquid phase speciation for aqueous 2PE calculated directly from the species concentrations obtained by NMR. The reaction products in the current system are predominately the bicarbonate species. Thus, the bicarbonate/carbonate levels increase with CO 2 loading, whereas the amine/protonated amine levels remain more or less constant. Table 4.5: NMR speciation in mole fraction for 30 wt.% 2PE at 25 C Loading x 2P E{2P EH x 2P ECOO x HCO 3 {CO

81 α= HCO 3- /CO 3 2- α= HCO 3- /CO α= Figure 4.2: Quantitative 13 C NMR spectra for 30 wt.% 2PE-CO 2 -H 2 O at 25 C Thermodynamic Results Table 4.6: 4.8 m AMP thermodynamic data and fit Data [2PE] T Loading Data ARD Source type ( C) p mol CO 2 {mol alkq points (%) pk a 0.1 M N/A (Xu et al., 1992) NMR 3.3 m this work VLE 8 m (Chen, 2011) The thermodynamic data incorporated is limited to pk a, NMR, and VLE as shown in Table 4.6. The average relative deviation (ARD) as defined by Equation (3.19) is used to quantify the goodness of fit. To fit the five pk a data points (Xu et al., 1992), the two parameters of 2PEH 8, aq were found to be: Gf J 8, aq {kmol and Hf J {kmol. 59

82 To fit the NMR data points, the two parameters of 2PECOO were found to be: 8, aq Gf J 8, aq {kmol and Hf J {kmol. The parameters of 2PE were left at the initial AMP-derived values of G f J {kmol and H f J {kmol. This fit resulted in a K c that changed from 0.90 at 40 C to 0.42 at 100 C. Examining other enrtl thermodynamic models at 20 C and 100 C showed a relative molality-based decrease in the maximum concentration of carbamate of 10% and 12% for models of MEA (Plaza, 2011) and 2MPZ. For AMP, this decrease is calculated as 39%. For 2PE, this decrease was 51%. 8, aq To check the model sensitivity to the chosen value of Hf, 2P ECOO, case 7 of Table 4.4 was repeated with the same relative decrease as AMP. The resulting reaction parameter values were within 2%, except for a 12% decrease in k 0 of k 2P E. Table 4.7: 4.8 m AMP interaction parameters Parameter Species Value σ C ca, m (2PEH, CO 2 3 )/H 2 O C ca, m (2PEH, CO 2 3 )/2PE C ca, m (2PEH, HCO 3 )/2PE D m, ca H 2 O/(2PEH, CO 2 3 ) D ca, m (2PEH, CO 2 3 )/H 2 O The VLE data were fit by the parameters shown in Table 4.7. Non-regressed binary interaction parameters were left at default or set to analogous values from the AMP model (Chapter 5). Figure 4.3 shows the thermodynamic model, the experimentally measured data, and the loading adjusted data. The loading range for coal conditions is approximately P CO 2 =0.5 5 kpa at 40 C, which is p mol CO 2 {mol alkq (Chen and 60

83 5E+3 5E+2 P CO2 (Pa) 5E+1 5E+0 5E-1 5E-2 WWC data prediction loading adjusted 5E loading (mol CO 2 /mol alk) Figure 4.3: 8 m 2PE VLE predictions at 20 C intervals with data from Chen (2011) Rochelle, 2011; Frailie, 2014). The VLE fit between these bounds is most important for predicting mass transfer performance. The differential heat of absorption is predicted from the VLE using the thermodynamic relationship of Equation (2.22). The predictions of Figure 4.4 are generated by applying Equation (2.22) to the VLE. As expected, no temperature inflection is observed, indicating the thermodynamic dominance of one reaction across the whole loading range. The good behavior of the predicted curves indicate that the model behavior in general is trustworthy. The rapid drop in H abs at 120 C is due to the high partial pressure of CO 2, resulting in the CO 2 being physically absorbed as free CO 2. Across typical absorber loading and temperature conditions, H abs of both AMP and 2PE show little loading dependence, while H abs of 2PE is 5 kj {mol (Li et al., 2014). The 61

84 C H abs kj mol C loading (mol CO 2 /mol alk) Figure 4.4: 8 m 2PE predicted H abs at 20 C increments using Equation (2.22) speciation predicted by the model at 40 C is shown in Figure 4.5 and compared to data in Figure 4.6. Using the model predictions for loadings corresponding to 0.5 and 5 kpa CO 2 at 25 C, the concentration-based mole fraction log K c is calculated from Equation (4.1). For 2PE, this is 1.08, which is greater than AMP, whose value is 0.56 (Ciftja et al., 2014). Thus, the carbamate of 2PE is more stable than that of AMP. This difference may be attributable to the higher pk a of 2PE than AMP (Li, 2015; McCann et al., 2011). The species activity coefficients are shown in Figure

85 8 6 m 4 2 2PECOO loading (mol CO 2 /mol alk) CO 3 2 Figure 4.5: 8 m 2PE speciation prediction at 40 C Table 4.8: 2PE (PZ) viscosity parameters for Equation (3.1) Parameter 2PE (PZ) 95% CI a 912 b 1890 c 968 d e 1.13 (9.46) [ 0.053, 2.20] f 5.40 g 2.81 ( 0.158) [2.31, 3.31] 63

86 1E+1 1E+0 1E-1 2PE/2PEH + HCO 3 /CO3 2 2PECOO 1E-2 m 1E-3 1E-4 CO 2 1E-5 1E-6 1E-7 1E loading (mol CO 2 /mol alk) Figure 4.6: Predictions (lines) at 30 wt.% 2PE and 25 C compared to data (points) Mass Transfer Results Hydraulics The viscosity correlation shown in Figure 4.8 shows a tight fit of the data (ARD=0.36%) and reasonable temperature behavior using the parameters of Table 4.8. The two regressed parameters are tightly correlated (ρ= 99.9), as expected. The unregressed parameters were fixed at the PZ value as this ensures a well behaved correlation due to the extensive data used to construct the PZ correlation (Frailie, 2014). The temperature dependence predicted for 2PE is similar to that observed in 40 wt.% MEA (Plaza, 2011) and 44 wt.% 2MPZ (Chen, 2011). As will be shown later, the mass transfer becomes more dependent on diffusion than reaction rate at higher temperatures and loadings, and as the liquid species diffusion depends on 64

87 2.00 CO 2 γ 1.00 CO 3 2 H 2 O loading (mol CO 2 /mol alk) Figure 4.7: 8 m 2PE activity coefficient prediction at 40 C viscosity to the 0.8 power, the temperature behavior of viscosity impacts the mass transfer regressions at these conditions. With no CO 2 loaded density data available for 2PE, the parameters were equated to those of PZ as listed in Table 4.9 (Frailie, 2014). This gives very similar performance to PZ. The density correlation is shown in Figure Kinetic Parameter Regression All cases of Table 4.4 were run until the best fit was achieved. These cases can be interpreted by considering the dominant characteristics at different loadings and temperatures. At low temperature with much carbamate present, the carbamate reaction is dominant. At higher temperature, there is little carbamate, and so the bicarbonate 65

88 1E+2 μ (cp) 1E+1 1E loading (mol CO 2 /mol alk) Figure 4.8: Viscosity correlation of 8 m 2PE; predictions are at 20 C intervals; points are data from Chen (2011). Table 4.9: 8 m 2PE density parameters of Equation (3.3) Parameter Value a b 1.99 c d 1.98 e f

89 1100 ρ kg m loading (mol CO 2 /mol alk) Figure 4.9: Density prediction of 8 m 2PE at 20 C intervals reaction becomes more important than the carbamate reaction. At high temperature, D Am P rod is the most important contribution to mass transfer, however as this property is fixed for all cases, the high temperature fit is controlled by the bicarbonate reaction. At low loading with plentiful free amine, the carbamate reaction is most important; whereas at high loading the free amine has been depleted, and the bicarbonate reaction becomes more important than the carbamate reaction. At high loading, there is little free amine, and so D Am P rod is the dominant mass transfer property. Again, as D Am P rod is the same for all cases, the high loading fit is controlled by the parameters of the bicarbonate reaction. Using these principles, the individual cases are interpreted. Cases 1 through 4 all suffer the problem of fitting only where carbamate is significant. The fit of case 67

90 1 is representative of these four cases, so it alone is shown infigure All of these cases underpredict N CO2 at high loading or high temperature, where carbamate is not significant. Case 4 shows the most pronounced bias due to the instantaneous rates leading to overprediction of N CO2 where the carbamate reaction is dominant and underprediction elsewhere. These first four cases demonstrate the sensitivity of the model to the equilibrium concentration of carbamate K c. By increasing the amount of carbamate at equilibrium, the flux is increased because more CO 2 can form carbamate before reaching equilibrium. As seen in Figure 4.12, case 5, which neglects carbamate entirely, underpredicts where carbamate would be important and overpredicts where bicarbonate is important. Cases 7 and 8 are able to match the data across the whole temperature and loading range as shown by Figure 4.10 and Figure That case 7 is a marginal improvement on case 8 shows that 2PE obeys the Brønsted prediction for the carbamate reaction. The E A of k 2P E 2P E was fixed as a simultaneous regression of all four parameters resulted in it not being regressed with statistical significance. Case 9 overpredicts where the carbamate reaction is significant, indicating that the carbamate rate is overpredicted by the PZ-Brønsted correlation. The adjusted loading for case 7 is shown in Table 4.10 and Figure 4.3, wherein the most significant adjustments occur at lean 40 C points. At lean loading, the necessary adjustment is due to the low CO 2 partial pressure, and for this reason the adjustment decreases with increasing temperature, which in turn increases the CO 2 partial pressure. The low loading, low temperature data have less flux, and so are more susceptible to experimental error. Additionally, error in loading will also have greater impact at low loading due to the greater slope of the equilibrium curve, as seen in Figure

91 Table 4.10: Loading adjustment for case 7 compared to data (Chen, 2011) T Loading Relative exp. adj. loading ( C) p mol CO 2 {mol alkq adj. (%) The estimated reaction rates and the results of the four best fitting cases from Table 4.4 are presented in detail in Table 4.11 and shown in Figures 4.10 to Comparing the regressed values to those predicted from Brønsted correlations shows that the bicarbonate reaction does not follow the correlation, whereas the carbamate reaction does. That the bicarbonate rate is so much faster than the correlation value is surprising, as it suggests that 2PE does not form bicarbonate using the same mechanism as a tertiary amine. This is unexpected. Figures 4.10 to 4.13 show no difference between the desorption and absorption points due to the loading adjustment. The predicted kg 1 for case 7 is shown in Figure Looking at the data this way shows that the second-highest loading 40 C point does not follow the trend of the other three 40 C points. Examining the flux values shows that the reported desorption flux for this point does not follow the expected order as it is greater than 69

92 Case k2p E 2P E k2p E ARD Brønsted PZ- Brønsted k0 EA k0 EA log Kc p kmol {sec-m 3 q p kj {mollq p kmol {sec-m 3 q p kj {molq Value σ Value σ Value σ Value σ (%) bound no 2PECOO Table 4.11: 8 m 2PE kinetic parameters; Kc is mole-fraction, concentration-based at 0.51 mol CO 2{mol alk and 40 C 70

93 C 60 C 80 C 100 C one line reproducibility bound 1.05 CO2 N CO loading (mol CO 2 /mol alk) Figure 4.10: 8 m 2PE flux ratioed to experimental flux (Chen, 2011) for case C 60 C 80 C 100 C one line reproducibility bound CO2 N CO loading (mol CO 2 /mol alk) Figure 4.11: 8 m 2PE flux ratioed to experimental flux (Chen, 2011) for case 8 71

94 C 60 C 80 C 100 C one line reproducibility bound 1.10 CO2 N CO loading (mol CO 2 /mol alk) Figure 4.12: 8 m 2PE flux ratioed to experimental flux (Chen, 2011) for case C 60 C 80 C 100 C one line reproducibility bound 1.10 CO2 N CO loading (mol CO 2 /mol alk) Figure 4.13: 8 m 2PE flux ratioed to experimental flux (Chen, 2011) for case 1 72

95 the highest loaded 40 C desorption flux (Chen, 2011). For this reason, the point was excluded from the regression. The highest loading 80 C point was excluded because the WWC was not operated in the absorption mode, making the loading adjustment calculation impossible. That this point is predicted by the model further validates the model. The reason that the 60 C curve lies above the 40 C curve is that at the reaction rate has increased from 40 C and diffusion is not yet limiting. At temperatures above 60 C, the reaction rate continues to increase, however now diffusion is controlling, so no additional mass transfer results from the higher reaction rate Kinetic Analysis Figure 4.14 and Figure 4.15 show the sensitivity of kg 1 for case 7 to the diffusion of CO 2 D CO2, to the diffusion of amine-products D Am, to the carbamate reaction k 2P E 2P E, to the bicarbonate reaction k 2P E, to the liquid film physical mass transfer coefficient kl 0, and to viscosity µ over a range of CO 2 partial pressure. These two figures allow for a comparison of the significant mass transfer variables at 40 C and 100 C. At 40 C the single most significant variable the carbamate reaction rate, indicating that kinetics are the most important mass transfer resistance (term one of Equation (4.14)). While at 100 C, the single most significant variable is kl 0, indicating that the diffusion resistance is most important (term two of Equation (4.14)). The high sensitivity to k 2P E 2P E at 40 C demonstrates the necessity of modeling the carbamate reaction and not just the bicarbonate reaction. In fact, a reasonable fit at 40 C could be obtained ignoring the bicarbonate reaction. The increasing sensitivity to kl 0 shows that the PFO assumption breaks down at high loadings, as is corroborated by Figure Another concordance between Figure 4.15 and Figure 4.16 is 73

96 seen in that there is still some dependence on k 2P E, and therefore the system is not instantaneous. The observed sensitivity to D Am at 40 C is not predicted by two-film theory. The equal dependence on D Am and D CO2 is a result of how Aspen Plus handles the forcing of the half-order dependence of kg 1 on D CO2 per penetration theory as shown in Equation (4.16) D Am +D CO2 k l, D Am k 2PE-2PE d ln k g d ln i 0.00 D CO2 k 2PE µ E+1 5E+2 5E+3 (Pa) P CO2 Figure 4.14: Sensitivity of k 1 g at 100 C for case 7 at P CO2 1.1P CO 2 Figure 4.16 expands on the PFO assumption of Equation (4.16) by showing how closely it matches the model predictions at 40 and 100 C. The mass transfer is not in the PFO regime at 100 C; at this temperature, diffusion cannot keep pace with the rate of reaction. At 40 C, kg 1 k1 g,p F O and at 100 C, the rate of reaction is nearly instantaneous. 74

97 0.75 k l,0 d ln k g d ln i D Am +D CO2 D Am k 2PE 0.00 k 2PE-2PE D CO E+1 (Pa) 5E+2 P CO2 µ Figure 4.15: Sensitivity of k 1 g at 100 C for case 7 at P CO2 0.5P CO 2 Figure 4.17 shows that the carbamate reaction rate for 2PE does obey the Brønsted correlation. The regressed rate was corrected using Equation (4.17). While Figure 4.17 shows that the reaction rate of 2PE is faster than PZ, the overall rate of mass transfer in 8 m PZ as measured using the same apparatus is faster by a factor of 2.5 at 40 C (Chen and Rochelle, 2011). Possibly this could be due to the accumulation of 2PE carbamate at the interface leading to a decrease in the net forward rate. This accumulation explains why the 40 C curve of Figure 4.16 is not completely in the PFO regime. Due to the low K c of 2PE compared to PZ, this accumulation of carbamate would be more problematic in 2PE than in PZ. Figure 4.17 compares the formation of the monocarbamate only, while PZ can also form a dicarbamate. A comparison of the rate of PZ dicarbamate formation and PZ 75

98 5.00E-06 k g mol sec Pa m E C 5.00E k g asp predicted k g,pfo 40 PFO 40 inst k g,instantaneous loading (mol CO 2 /mol alk) Figure 4.16: k 1 g asymptotes for case 7 at P CO2 1.1P CO 2 carbamate formation shows that the dicarbamate formation rate is less than 5% that of the carbamate formation rate (Frailie, 2014). The diffusion activation energy E D for various solvents at zero and rich loading are compared in Table There is a moderate linear correlation (R 2 =0.74) between activation energy and viscosity, E D 0.78µ 20, as suggested by Chen and Rochelle (2013). D Am is important for the rich loading conditions at low temperature and important for more and more loadings at higher and higher temperatures. For this reason, further research into loaded D Am is suggested. The contribution of gas film resistance in the WWC to the overall mass transfer in partial pressure units is shown in Figure As the temperature increases, the contribution of k g decreases, with the sharpest drop between 80 and 100 C. In the operational loading range of p mol CO 2 {mol alkq at process-scale absorber 76

99 6 2PE log k 2PE 2PE m 6 log kmol 2 sec 4 y = 1.30x R² = 1.00 PZ 2MPZ MOR MEA DEA y = 1.46x R² = DIPA pk a at 25 C Figure 4.17: Brønsted plot for the carbamate reaction (Chen and Rochelle, 2013) Table 4.12: Diffusion activation energy as calculated by Equation (4.18) Amine Molarity Loading µ at 60 C E D Source (M) (cp) 2PE 2MPZ MDEA PZ mol CO 2 mol alk kj mol this work (Chen and Rochelle, 2013) (Snijder et al., 1993) (Frailie, 2014) 77

100 conditions, the contribution of k g drops from 25% to 7%. At stripper conditions, k g does not contribute significantly. 40% 40 C K g k g 20% 100 C 0% loading (mol CO 2 /mol alk) Figure 4.18: 8 m 2PE gas film resistance at P CO2 1.1P CO 2 for case 7 By examining the variation of kg 1 with kl 0 plotted in Figure 4.19, the applicability of PFO is shown to shift to higher values of kl 0 as the temperature increases. Typical kl 0 values for 2PE in the WWC fall between and m {sec. Contactors can span a wide range of kl 0, with structured packing in a process-scale absorber having similar values to the WWC and laminar jet having much greater values. The significance of kl 0 increases at higher loadings and temperatures, as seen from Figure 4.14 and Figure

101 k g mol sec Pa m E C 100 C 1.00E-07 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 k 0 l m sec Figure 4.19: k 1 g vs k 0 l in 8 m 2PE at 0.53 mol CO 2 {mol alkand P CO2 1.1P CO 2 for case Conclusions Ciftja (Sherman et al., 2016) showed that 2PE forms a more stable carbamate (log K c =1.06) than AMP (log K c =0.70), as expected from the higher pk a of 2PE. At 40 C, kg 1 is most sensitive to the carbamate reaction rate and nearly insensitive to the bicarbonate reaction rate, proving the need to model the carbamate reaction for this sterically hindered amine. While the carbamate reaction rate follows the Brønsted correlation for three unhindered cyclic, secondary amines, suggesting a similar reaction mechanism, the bicarbonate reaction rate surprisingly is an order of magnitude faster than predicted by the Brønsted correlation for tertiary amines, suggesting a different reaction mechanism. As temperature increases, the pseudofirst order (PFO) assumption applies to the wetted-wall column data for increasingly 79

102 higher kl 0 and over a smaller loading range. The PFO assumption applies at 40 C up to a loading of 0.60 mol CO 2 {mol alk but not at greater temperature or loading. These results demonstrate the importance of accounting for the carbamate reaction in 2PE and more broadly for all hindered amines. Thus, for solvents blending a hindered amine with a rate promoter, modeling the hindered amine carbamate reaction is necessary to model the mass transfer performance. The model created by this work can be used for process modeling and design of a full-scale absorber and stripper. Fruitful research opportunities presented by this work include more loaded viscosity measurements as well as temperature-variable NMR measurements. The viscosity measurements would allow for more accurate diffusion coefficients, while the NMR measurements would validate the temperature dependence of K c Supporting Information Table 4.13: Initial 2PE species definition Species G f or G aq f H f or H aq f ( J {kmol 10 8 ) ( J {kmol 10 8 ) 2PE PECOO PEH Derivation of Equation (4.12) This equation converts from the concentration, ideal based k c to the molefraction, activity-coefficient based k a. It is derived by equating the two different bases and converting as demonstrated for the carbamate reaction. r CO2 k c rams 2 rco 2 s k a a 2 Ama CO2 80

103 k c rams 2 rco 2 s a 2 Am a k a CO 2 By definition, a i x i γ i. Substituting and canceling the concentration terms yields k c γ 2 Am γ CO 2 k a The conversion to an activity basis is complete, but unit analysis shows that an additional factor is needed for the concentration to mole-fraction conversion m 6 kmol 2 sec rs kmol m 3 sec This factor is the molar volume ρ 3. Repeating the unit analysis with this factor shows the units are now correct, and the conversion is complete. kmol 3 rs m 6 kmol 2 sec m 9 kmol m 3 sec Table 4.14: Henry parameter values with PZ as analog (Frailie, 2014) Component i 2PE Component j H 2 O Property units Pa Element Element Element 3 0 Element Element 5 0 Element 6 0 Element

104 Table 4.15: Chemical shift (δ) for loaded and unloaded 30 wt.% aqueous 2PE solution at 25 C with loading in mol CO 2 {mol alk Loading Peak δ in ppm HCO 3 /CO Table 4.16: Scalar pure component properties Units 2PE Source DGFORM J {kmol AMP (Li et al., 2014) DHFORM J {kmol AMP (Li et al., 2014) OMEGA J {kmol PZ (Frailie, 2014) PC N {m PCES RKTZRA =ZC TC K PCES m VC PCES kmol ZC PCES 82

105 Table 4.17: Pure component T-dependent parameters of 2PE as estimated by PCES CPIG PLXANT Temperature units K K Property units J {kmol-k Pa Element Element Element Element Element Element Element Element Element Element Element Table 4.18: NRTL parameters with MDEA as analog (Frailie, 2014) Component i H 2 O CO 2 Component j 2PE 2PE Temperature units K K Element Element Element Element Element Element Element Element Element Element Element Element

106 Chapter 5 2-Amino-2-methylpropan-1-ol (AMP) 5.1 Introduction While amine scrubbing has long been used to treat acid gas, amine scrubbing is now being used to treat flue gas from power plants. The largest operating process captures 90% of CO 2 from a 139 MW coal-fired unit (Stéphenne, 2014). Construction has begun for capture on a 240 MW coal-fired unit (Hirata et al., 2014). This unit will be using KS-1, a hindered amine solvent (Kadono et al., 2013; Hirata et al., 2014). Hindered amines have been extensively studied (Bougie and Iliuta, 2012). Sterically hindered amines offer high capacity with a 1:1 stoichiometry of amine:co 2, like tertiary amines. Unlike tertiary amines, the rates for sterically hindered amines are 100 times faster (Sartori and Savage, 1983). The exact reason for this stoichiometry and kinetic rate has not been satisfactorily explained. Prior work has proposed three different mechanisms to explain the high reaction rate and the principal reaction product being HCO 3. Chakraborty et al. (1986) proposed that 2-amino-2-methylpropan-1-ol (AMP) reacts like a tertiary amine, wherein AMP serves as a base to catalyze the reaction of water and CO 2 without any carbamate formation. Yih and Shen (1988) proposed the zwitterion mechanism to form bicarbonate, also without carbamate formation. Most researchers (Xu et al., 1996) interpret the reaction using the two-step zwitterion mechanism to form carbamate to explain the rates; then, to explain the stoichiometry, the carbamate 84

107 hydrolyzes to bicarbonate (Alper, 1990; Bosch et al., 1990; Saha et al., 1995; Xu et al., 1996; Ali, 2005). However, when explaining why AMP is much faster than a tertiary amine with the same pk a or slower than a corresponding primary amine, researchers hypothesize that carbamate forms an unstable intermediate that accelerates the absorption of CO 2 (Yih and Shen, 1988; Saha et al., 1995). This work proposes that the rates are explained by the formation of carbamate through a single, termolecular mechanism (Crooks and Donnellan, 1989) rather than the two-step zwitterion mechanism. The termolecular mechanism has been used to explain the mass transfer performance of many amine solvents (Chen, 2011; Li, 2015), and recent computational chemistry work shows that a trimolecular reaction is possible (Yamada et al., 2010; Ismael et al., 2009). This work shows that AMP does not seem to form carbamate using the same mechanism as an unhindered primary amine and that CO 2 is transported through the liquid film boundary layer in the form of carbamate, which subsequently reverts and forms bicarbonate as in the shuttle mechanism (Astarita et al., 1981). The stoichiometry is explained by reversion of the carbamate to free amine and CO 2 in parallel with base-catalyzed hydration of CO 2 as observed in tertiary amines. Recent computational chemistry work has suggested base-catalyzed hydration is more energetically favorable than hydrolysis (Yamada et al., 2010). 5.2 Methods Thermodynamic Model The model used is a derivative of the Aspen Plus model presented by Li et al. (2014), which used the asymmetric electrolyte non-random two-liquid (enrtl) activity-coefficient thermodynamic model for the liquid phase (ELECNRTL) and the Redlich-Kwong equation of state for the vapor phase (ESRK). The model of Li et al. 85

108 OH N C O O Figure 5.1: Molecular structure of AMPCOO (2014) was modified to include carbamate, whose molecular structure is shown in Figure 5.1. As the carbamate was not available in the Aspen Plus databank, the parameters needed to define it were set, such as charge and molecular weight. All parameters related to the carbamate were left at default with the exception of those listed in supplemental Tables 5.12 and Equation (5.1) was added to the model chemistry. 2 AMP CO 2 ô AMPCOO AMPH (5.1) With the carbamate component defined, the equilibrium of Equation (5.1) was adjusted to fit speciation data (Ciftja et al., 2014). The data from Ciftja et al. (2011) were excluded due to inconsistency with the fitted data and because the 2011 data were only at one temperature. The data set contained 183 data points at 25 C, 35 C, and 45 C (Ciftja et al., 2014). The goodness of fit metric used was the average 8, aq relative deviation (ARD) defined by Equation (3.19). Gf, AMP COO (DGAQFM) was regressed to fit the 25 8, aq C data, and Hf,AMP COO (DHAQFM) was regressed to fit the temperature dependence. The ARD was minimized in these regressions. 86

109 Carbamate Sensitivity To better understand the role of carbamate in CO 2 solubility, the VLE sensitivity to carbamate was quantified. The concentration of carbamate was varied by 8, aq varying Gf, AMP COO, and the effect on the VLE at 313 K was calculated relative to the basis thermodynamic model. This temperature was chosen as it is used to quantify the solvent capacity, set operating loading conditions, and characterize the mass transfer rate. Three different amines were studied: monoethanolamine (MEA) as represented by the Phoenix model (Plaza, 2011), 2-piperadineethanol (2PE) (Sherman et al., 2016), and AMP (this work). These amines illustrate the VLE sensitivity at the extremes of high and low carbamate stability Mass Transfer Model Hydraulics Table 5.1: Viscosity fit of aqueous loaded and unloaded AMP. ramps T Loading Data ARD Source m ( C) p mol CO 2 {mol alkq points % (Chen, 2011) (Bosch et al., 1990) 2.4, (Xu et al., 1991) The viscosity and density are necessary to model mass transfer. The viscosity plays an important role in both the diffusion rate of species as well as the liquid film physical mass transfer coefficient kl 0. As seen in Table 5.1, there was an abundance of unloaded data, which helped set the asymptotic behavior at zero loading. These data were fit along with the loaded data by regressing parameters a, b, and g of 87

110 Equation (5.2). " µ AMP exp rpaw AMP bq T cw AMP ds rpew AMP ft gq α 1s w AMP T 2 * (5.2) f was set to zero. The other parameters were left at values representative of methyldiethanolamine (MDEA) (Frailie, 2014), whose response to loading is similar to AMP. The regression was done using fitnlm in MATLAB. Table 5.2: Density fit of aqueous unloaded AMP. x AMP T Data ARD Source ( C) points (%) (Xu et al., 1991) (Chan et al., 2002) For density, no loaded data were available. a and b of Equation (5.3) were regressed with the unloaded data of Table 5.2 by minimizing the ARD. ρ AMP x H2 Oρ H2 O x AMP pat bq x CO2 pct dq (5.3) The behavior with loading was represented by using the same c and d values of MDEA (Frailie, 2014) Diffusivity There were two different effective liquid diffusion coefficients modeled: one for CO 2 and N 2, D CO2, and one for all other species, D Am. These are represented in the same manner as for 2PE (Chapter 4). 88

111 Reaction Set The kinetics were activity-based and utilize the termolecular mechanism. Two kinetic reactions are accounted for: the formation of carbamate, Equation (5.4), and the formation of bicarbonate, Equation (5.5). k AMP AMP 2 AMP CO 2 ÝÝÝÝÝÝÝá âýýýýýýý AMPCOO AMPH (5.4) k AMP AMP H 2 O CO 2 ÝÝÝá âýýý HCO 3 AMPH (5.5) The proton exchange reaction of Equation (5.6) was assumed to be at equilibrium. AMP HCO 3 ô AMPH CO2 3 (5.6) The base-catalysis of water was neglected because water is a much weaker base than AMP and because AMP was concentrated (30 wt.%). The hydroxide ion was not modeled due to its low concentration. The reaction rates were calculated by Equation (5.7) and Equation (5.8), r CO2 k AMP AMP a CO2 a 2 Am (5.7) r CO2 k AMP a CO2 a Am (5.8) where k AMP AMP is the rate constant of AMP catalyzed by AMP, k AMP is the rate constant of water catalyzed by AMP, and a i is the activity of species i. Both rate constants were calculated using the Arrhenius equation of Equation (3.14) with T ref = K. The kinetic reaction equilibrium K eq was calculated from the thermodynamic equilibrium by calculating the reverse reaction rate k r from the forward rate k f using Equation (5.9). k r k f K eq (5.9) 89

112 Brønsted Correlations As the reactions with CO 2 are base-catalyzed, they should obey Brønsted theory (Versteeg and van Swaaij, 1988a). A different Brønsted correlation was used for each reaction. For the bicarbonate reaction, it was assumed that the reaction mechanism is the same as that of tertiary amines. The tertiary amine correlation Equation (5.10) m was used to estimate k 3 AMP, c at 20 C (Versteeg and van Swaaij, 1988a). mol sec ln k AMP, c pk a (5.10) Equation (5.10) was developed from data using unloaded, dilute amine solutions (Versteeg and van Swaaij, 1988a). However, the order of the amine in Equation (5.5) was unaffected by amine concentration, therefore Equation (5.10) remained valid at the loaded, concentrated conditions of this work. As Equation (5.10) was developed using concentration-based, ideal kinetics, it was converted to a mole-fraction, activity basis using Equation (5.11), where γ AMP is the activity coefficient of AMP, γ CO 2 k AMP, a k AMP, c ρ 2 γ AMP γ CO 2 (5.11) is the asymmetric activity coefficient of CO 2, and ρ p kmol {m 3 q is the molar density. This conversion was done at mol CO 2{mol alk and 20 C, and then the rate was brought to the reference temperature using 44.9 kj {mol as E A (Ko and Li, 2000). For the carbamate reaction, there were multiple Brønsted correlations available in the literature (Chen and Rochelle, 2013; Li, 2015; Versteeg and van Swaaij, 1988b). The correlation by Versteeg and van Swaaij (1988b) was based on data using dilute, unloaded amine solvents collected using a variety of methods. These dilute 90

113 conditions make the formation of carbamate first order in amine as the contribution by other bases (e.g. H 2 O and OH ) was significant, while at concentrated conditions amine would have outcompeted the other bases. This correlation included both primary and secondary amines. Therefore, the Brønsted correlation of Versteeg and van Swaaij (1988b) was not appropriate for interpreting the kinetics of this work. The Brønsted correlation given in Chen and Rochelle (2013) reinterpreted the dilute, unloaded kinetic data using the termolecular mechanism. Their correlation separated amines based on cyclic or linear molecular structure, rather than distinguishing primary and secondary amines. For these reasons it was not used. The Brønsted correlation created by Li (2015) was based off of concentrated, loaded amines measured in a wetted-wall column (WWC) and interpreted using third order kinetics. Li (2015) found that primary and secondary amines had different correlations. Therefore, the primary amine correlation of Li (2015) was used in this work and is shown in Equation (5.12). log 10 k AMP AMP, c 0.706pK a (5.12) Equation (5.12) was developed at 40 C, so the corresponding pk a is used. k c, 3 is defined by Equation (5.13). k AMP AMP, c k AMP AMP, c γ CO 2 2 (5.13) Equation (5.13) was used to convert the result of Equation (5.12) to k MAP AMP,c prior to converting to a mole-fraction, activity basis with Equation (5.14). k AMP AMP, a k AMP AMP, c ρ 3 γ 2 AMP γ CO 2 (5.14) 91

114 Flowsheet The experimental WWC was simulated in Aspen Plus using a custom flowsheet, as described by Sherman et al. (2016). The physical liquid film resistance, gas film resistance, and boundary layer discretization are the same as Table Kinetic Parameter Regression The greatest desorption and absorption fluxes for each loading and temperature of the data (Chen, 2011) were fit. Fluxes ranged from to mol {sec-m 2, and the desorption and absorption fluxes for each condition were typically of similar magnitude. The loading for each point was adjusted to give zero flux at zero driving force as described in Sherman et al. (2016). This adjustment accounts for both experimental error and model fit error (i.e., error in the VLE). The regression was done using response surface methodology (RSM) developed from the work of Frailie (2014). First, the Aspen Plus model was run for all of the data points to establish a basis p basis q. Then, each parameter was individually increased by 10% and the data set reran 10%. The sensitivity αi to each parameter was calculated by Equation (3.21). As the response surface (RS) has a small region of validity, the basis was redone for each case of Table 5.3. The RS takes the form of Equation (3.22). A non-linear regression was done with the fitnlm command of MATLAB called with Equation (3.22) as the model equation. The adjustable parameters are k 0 and E A as defined by Equation (3.14). Once the parameters were regressed, the fit was checked with the Aspen Plus model. No major discrepancies between the RS and the Aspen Plus model were observed. As fitnlm does not allow for constraints, if a parameter went beyond a bound in 92

115 unconstrained regression, that parameter was fixed at the bound, and the regression rerun with the remaining parameters. The four cases listed in Table 5.3 were regressed. These different cases test the predictive capability of the Brønsted correlations and implicitly the reaction mechanisms. Table 5.3: 4.8 m AMP kinetic regression cases and resulting ARD as calculated by Equation (3.19) Case r HCO 3 r AMP COO ARD (%) Brønsted Brønsted Brønsted 25 1 regress regress Brønsted regress 15 3 regress Brønsted 17 4 regress none Kinetic Analysis As case 1 as was the best mass transfer fit, it was used to study mass transfer in AMP by examining the liquid film mass transfer coefficient kg 1 and diffusion effects. kg 1 is defined by Equation (5.15), k 1 g 1 1 K g 1 k g N CO2 P CO2,i P CO2,b LM (5.15) where K g is the overall gas-side mass transfer coefficient, k g is the gas film mass transfer coefficient, i denotes the interface, b denotes the bulk liquid, and LM is the log mean average. The sensitivity of kg 1 to individual variables was calculated using a 5% central difference to approximate the analytical derivative. 93

116 To determine how close the system approached the asymptotes of pseudo-first order (PFO), where kinetics controlled mass transfer and instantaneous reactions, where diffusion controlled mass transfer, both conditions were simulated. The instantaneous condition was simulated by changing the kinetic reactions, Equation (5.4) and Equation (5.5), to equilibrium. The PFO mass transfer coefficient kg,p 1 F O can be generally calculated by Equation (5.16) (Chen and Rochelle, 2013), k 1 g,p F O a DCO2 ka 2 Am? γco2 H CO2,H 2 O (5.16) where H CO2,H 2 O (Pa) is the Henry s constant of CO 2 in water (Carroll et al., 1991). Applying Equation (5.16) to AMP by accounting for the carbamate and bicarbonate reactions yields Equation (5.17), k 1 g,p F O b DCO2 V m pk AMP AMP a 2 AMP k AMP a AMP a H2 Oq? γco2 H CO2,H 2 O (5.17) where V m p m3 {molq is the molar volume. To correlate the viscosity and the temperature-dependence of the diffusion of amine and products D Am p m2 {secq, the diffusion activation energy E D was calculated by Equation (5.18). E D R ln D Am 1 {T (5.18) 5.3 Results Thermodynamic Model The addition of carbamate to the model of Li et al. (2014) did not appreciably change any aspect of the thermodynamic model beyond the speciation. Figure 5.2 shows that the VLE of the present model has no systematic bias. The speciation data were fit with two parameters: G aq,amp COO J {kmol and 94

117 1E+7 Chen, 2011 Li et al., 2014 Li and Chang, 1994 prediction loading adj. 160 C 1E+6 P CO2 (Pa) 1E+5 1E+4 1E+3 1E loading (mol CO 2 /mol alk) Figure 5.2: 4.8 m AMP VLE with loading adjusted data for case 1 H aq,amp COO J {kmol for an ARD of 12.9%. The fit of the 35 C data is shown in Figure 5.3. This fit is in line with prior work (Yoon and Lee, 2003; Chakraborty et al., 1986) and shows that Sartori et al. (1978c) over reported the amount of carbamate by a factor of five Carbamate Sensitivity To characterize the sensitivity of each solvent, the relative change in the VLE versus the change in K c as defined by Equation (5.19) was computed. K c ramcoo s (5.19) rams HCO 3 A concentration basis was used to allow for comparison to literature values. The VLE change was examined at 40 C by looking at the deviation from the original fit. A significant difference in VLE was defined as a 5% ARD. Table 5.4 shows the results. 95

118 AMP/AMPH + HCO 3 /CO E+00 m AMPCOO 1.E-01 1.E-02 prediction Ciftja et al., loading (mol CO 2 /mol alk) Figure 5.3: Speciation of 4.8 m AMP at 35 C Table 5.4: Necessary K c for a 5% ARD change in VLE System pk a log K c K c 7 m MEA m AMP m 2PE

119 The K c shown is the average of the rich and lean loadings, defined by P CO 2 5, 0.5 kpa, calculated at 40 C. These loadings are typical of capture from coal-fired power plant flue gas (Frailie, 2014). The pk a sources are Hamborg et al. (2009) for MEA, the fit of Sherman et al. (2016) for 2PE, and the fit of this work for AMP. The pk a is directly proportional trend to K c. This agrees with McCann et al. (2011) and Li (2015). They observed that greater steric hindrance reduces K c and that greater pk a correlated with greater K c. Table 5.4 shows that both effects must be considered as the two hindered amines obey the pk a effects, but both have a lower K c than MEA, which has a lower pk a. From Table 5.4, systems with less carbamate are more tolerant of changes in the carbamate concentration. To enable interpolation, a power function was fit to the data of Table 5.4. The amount of change in K c before significant change to VLE can be computed using Equation (5.20), p K c for 5% ARDq 10.3 log K 1.32 c (5.20) where K c is at 40 C. Equation (5.20) enables error quantification in the VLE from NMR error Mass Transfer Model Hydraulics The viscosity was predicted by the model using Equation (5.2) with the parameters of Table 5.5. Figure 5.4 shows the loaded viscosity predictions with the regressed data. The ARD for each data set is reported in Table 5.1 with the overall ARD being 5.2%. The correlation matrix shows that a and b are highly correlated (corr pb, aq 0.97) while g is moderately correlated (corr pg, aq 0.57; corr pg, bq 0.43). 97

120 5 µ (cp) prediction Chen, loading (mol CO 2 /mol alk) Figure 5.4: Viscosity of 4.8 m AMP Viscosity is used to calculate kl 0 and diffusion coefficients, both of which become more important at high loading and at high temperature. D i depends on µ to the 0.8 power, meaning that viscosity can have a significant impact on mass transfer performance. The predicted temperature dependence is approximated by that of MDEA (Frailie, 2014). This approximation does not impact the conclusions but could confound the predicted bicarbonate reaction rate. The density enters into mass transfer in a few ways. Firstly, in the calculation of the thickness of the liquid film at the one-sixth power, secondly in the conversion of the measured volumetric flow rate to a mass flow rate for simulation, and 98

121 Table 5.5: AMP viscosity parameters of Equation (5.2) Parameters Value SE Source a this work b this work c 1.34 (Frailie, 2014) d 3.69 (Frailie, 2014) e 2.22 (Frailie, 2014) f 0 fixed this work g this work Table 5.6: AMP density parameters of Equation (5.3) Parameters Value Source a 1.03 this work b 1240 this work c 3.82 (Frailie, 2014) d 12.1 (Frailie, 2014) in Equation (5.11) and Equation (5.14). The density predictions were made using Equation (5.3) with the parameters of Table 5.6 and yielded an overall ARD of 0.38% for the unloaded data (Chan et al., 2002; Xu et al., 1991). The fit for unloaded data ensures that ρ is well behaved at low loading, but the loaded predictions of Figure 5.5 are more important for loaded conditions, such as those of the mass transfer data and the CO 2 capture process. The estimation of ρ is not expected to have any impact on the conclusions. The largest effect would be in the conversion from literature concentration-based values to mole-fraction based values in Equation (5.11) and Equation (5.14). 99

122 C C ρ kg m C loading (mol CO 2 /mol alk) Figure 5.5: 4.8 m AMP density prediction at 20 C intervals Mass Transfer Parameters Table 5.7 reports the kinetic parameters for the four regression cases. For each regressed reaction, two parameters were regressed. In case 1, four parameters were regressed; while in the other three cases two parameters were regressed. An F -test comparing case 1 to the next best fit, case 4, was done at α 0.01, and the fit of case one is significantly better pf q. In all cases, k i and E A,i for a reaction are tightly correlated p 0.8 q, while between reactions the correlation is small p 0.04 q. The Brønsted case is not a regression, but illustrates the fit achieved using the Brønsted estimates. 100

123 Table 5.7: 4.8 m AMP kinetic parameters and ARD for the cases of Table 5.3 Case k AMP k AMP AMP ARD (%) k 0 p kmol {sec-m 3 q E A p kj {molq k 0 p kmol {sec-m 3 q E A p kj {molq value SE value SE value SE value SE Brønsted bound bound bound no carbamate in model 11.4 The standard error (SE) for the regressed parameter is equivalent to the standard deviation σ given by DRS. The two terms are used interchangeably when describing an estimator, i.e. a parameter (Navidi, 2008). However, there is a difference between the two terms when describing a population parameter, e.g. the mean. The difference is that the standard deviation quantifies the scatter in the population parameter θ while the standard error quantifies the scatter in the estimate of the population parameter based on the sample ˆθ pxq. The standard error is always less than the standard deviation and tends towards zero as the sample size n increases. For example, the standard error for the mean is σ {n. The standard error quantifies the uncertainty that ˆθ pxq is the same as θ. The loading adjustment for case 1 is shown in Figure 5.2 and listed in Table 5.8. The adjustment corrects for experimental error and model error. The adjustment is greatest for the two leanest loadings because these loadings fall outside or near the operational lean loading for which the thermodynamic model was developed (Li et al., 2014). As set by P CO and 5 kpa, the loading limits are 0.27 mol CO 2 {mol alk and 0.56 mol CO 2 {mol alk. Thus, the adjustment is mostly for model error. The mass transfer fit of case 1 is shown in Figure 5.6. The dashed lines represent the estimated 8.5% reproducibility of the experimental flux measurements (Li, 101

124 Table 5.8: Case 1 loading adjustment compared to data (Chen, 2011). T ( C) loading p mol CO 2 {mol alkq relative diff (%) exp adj ). The fit is tight and shows no significant biases with either loading or temperature. Table 5.9: Sensitivity to E A to k AMP bound k AMP k AMP AMP ARD k AMP 40 C k AMP 100 C k 0 E A k 0 E A kmol kj kmol kj sec-m mol sec-m mol (%) 3 kmol sec-m As the activation energy for the bicarbonate reaction is at the bound, the sensitivity of the fit to this bound was quantified by changing the bound by 10%. Table 5.9 shows that the kinetic parameters of k AMP AMP vary less than 1.8% while k 0,AMP varies by 13%. The relative difference in ARD is up to 3.3%, demonstrating 102

125 C 60 C 80 C 100 C reproducibility bound CO2 N CO loading (mol CO 2 /mol alk) Figure 5.6: 4.8 m AMP flux for case 1 ratioed to data of Chen (2011) that the model is sensitive to the bound selected. The rate of the bicarbonate reaction is unaffected at 100 C, but at 40 C it changes by 13%. Table 5.7 shows that the Brønsted estimate overpredicts by a factor of 12 for k AMP AMP, a and underpredicts by a factor of 18 for k AMP, a. Thence, the carbamate reaction does not follow the primary-amine mechanism, and the bicarbonate reaction does not follow the tertiary-amine mechanism. At 4.8 m AMP, the carbamate reaction, Equation (5.4), is best modeled as second order in amine. Table 5.10 lists prior measurements of the kinetics of AMP. Most prior work on AMP was done at dilute conditions and the kinetics were modeled 103

126 using the zwitterion mechanism that yielded a reaction that was first order in amine. It was not possible to reinterpret the higher concentration studies as third order due to a lack of raw data (Choi et al., 2007; Chakraborty et al., 1986). Table 5.10: Comparison of carbamate reaction second-order, ideal, concentrationbasis k 2 values at 40 C; ramp s avg is the average of the AMP concentration reported k AMP AMP Method ramp s avg Notes Source p m3 {kmol-secq (m) WS 2.16 (Seo and Hong, 2000) SF 0.17 (Ali, 2005) WWC 1.41 (Saha et al., 1995) WWC 1.29 (Yih and Shen, 1988) SC 1.69 (Xu et al., 1996) SF 0.50 (Alper, 1990) SC 1.38 (Messaoudi and Sada, 1996) SC 4.8 (Choi et al., 2007) SC 1.09 (Camacho et al., 2005) SC C (Chakraborty et al., 1986) Table 5.10 shows that the most common value of k 2 is 1,300 m3 {kmol-sec. The method used is designated as follows: SC=stirred-cell, SF=stopped-flow, WS=wettedsphere, WWC=wetted-wall column. The methods span a wide range of kl 0. A good discussion of the idiosyncrasies of these data is given by Saha et al. (1995) Mass Transfer Analysis The predicted k 1 g of Figure 5.7 shows good agreement with the data (Chen, 2011). The temperature dependence is the product of two factors that can be explained by examining the liquid film resistance represented by Equation (5.21), 1 k 1 g H CO2 b D CO2 V m pk AMP AMP a 2 AMP k AMP a AMP a H2 Oq 1 k 0 l,prod BP CO2 B rco 2 s T (5.21) 104

127 1E-6 60 C 80 C prediction Chen, C k g mol m 2 sec Pa 40 C 1E loading (mol CO 2 /mol alk) Figure 5.7: 4.8 m AMP k 1 g (lines) for case 1 with zero CO 2 in inlet gas where H CO2 is the Henry s constant of CO 2 in solution, kl,prod 0 is the physical liquid film mass transfer coefficient for reaction products, and p BP CO 2 {B rco 2 s T q is the slope of the VLE curve. The first term is the reaction resistance, and the second term is the diffusion resistance. As temperature increases, both the reaction rate and the slope of the equilibrium curve increase. As these increases are unequal, kg 1 initially increases going from 40 C to 60 C, due to the increasing reaction rate. Thereafter, the increasing equilibrium curve slope causes diffusion to dominate. The still increasing reaction rate becomes unimportant, and the net effect is kg 1 decreases above 60 C. 105

128 1E-4 1E-5 k g mol m 2 sec Pa 1E-6 1E-7 k g 100 C k g 40 C 1E loading (mol CO 2 /mol alk) Figure 5.8: 4.8 m AMP k 1 g prediction and asymptotes Figure 5.8 compares the predicted k 1 g to the k 1 g for instantaneous and PFO conditions as calculated by Equation (5.17). This shows that at 40 C, the system is in the PFO regime, and at 100 C, the system is neither PFO nor instantaneous. At 40 C, reaction resistance dominates k 1 g, while at 100 C the reaction resistance and diffusion resistance are both significant. The reaction resistance is due to slow bicarbonate reaction, as discussed later with Figure Prior to comparing the regressed reaction rate constants, a correction must be applied. Due to inconsistent implementation of film theory in Aspen Plus, there is an artificial 0.25 power dependence of k 1 g on D Am (Chen and Rochelle, 2013). The effect of this artifice on the reaction rate constants is corrected using Equation (5.22) (Chen and Rochelle, 2013). k corrected d D Am D CO2 k regressed (5.22) 106

129 k Am Am,3 m 6 kmol 2 sec 5E+4 AMP, predicted 5E+3 AMP, corrected 5E+2 AMP, lean Li, 2015 AMP, rich pk a at 40 C Figure 5.9: k AMP AMP compared to primary amines 1.E-01 AMP, corrected 2PE (Sherman et al., 2016) k Am,c m 3 mol sec 1.E-02 MDEA (Yu) TEA 2MPZ (Chen and Rochelle, 2013) MEA (Plaza, 2011) MDEA (Frailie, 2014) DMMEA MDEA MDEA (Ko and Li, 2000) TREA AMP, predicted 1.E pk a at 20 C Figure 5.10: k AMP compared to tertiary amines (Versteeg and van Swaaij, 1988a) 107

130 This correction is strictly valid only at PFO conditions and results in the corrected value being 71% of the regressed value. Figure 5.9 shows k Am Am,c after correction by Equation (5.22) compared to the primary amine Brønsted correlation of Li (2015) and to the rate constant extracted from kg 1 data at lean and rich loading also by Li (2015). As AMP lies so far from the curve, it appears that there is a different mechanism used by AMP to form carbamate than used by primary amines. As extracting the rate from kg 1 does not differentiate between the carbamate and bicarbonate, it is understandable that the corrected value of k AMP AMP is greater than that extracted by Li (2015). Figure 5.10 shows k Am,corrected on a concentration basis for comparison to experimental and regressed values. The regressed values were converted to a concentration basis using the same values of γ AMP, γ CO 2, and V m as for AMP. Again, these values were corrected with Equation (5.22). The three highest values shown are for hindered amines, while the other amines fall closer to the curve. For the hindered amines, the diffusion of carbamate may be underrepresented leading to inflation of the k Am values. Figure 5.11 plots the sensitivity of k 1 g at 40 C. k 1 g is sensitive to k AMP AMP at the 0.4 power. Above P CO kpa (0.50 mol CO 2 {mol alk), the importance of k AMP AMP decreases as k AMP increases. As Figure 5.12 shows at 100 C, kg 1 is least sensitive to k AMP AMP. kg 1 is most sensitive to the physical mass transfer coefficient k l,0 at 0.3, while k AMP a contributes at This contribution is why kg 1 is not instantaneous as was seen in Figure 5.8. The quarter power dependence on k AMP indicates the bicarbonate reaction is not instantaneous, while the near zero power dependence on k AMP AMP indicates that the carbamate reaction is instantaneous. 108

131 0.50 k AMP AMP 0.25 D CO2 d ln k g d ln i D AMPCOO k l, k AMP µ E+2 (Pa) 1E+3 P CO2 Figure 5.11: Sensitivity of k 1 g in 4.8 m AMP at 40 C, P CO2 1.1P CO k l,0 d ln k g d ln i 0.25 D AMPCOO k AMP-AMP k AMP 0.00 D CO µ E+2 (Pa) 1E+3 P CO2 Figure 5.12: Sensitivity of k 1 g in 4.8 m AMP at 100 C and P CO2 0.5P CO 2 109

132 1.002 x i x i,bulk H 2 O HCO AMPCOO CO 2 x i x i,bulk E-5 2E-1 4E-1 6E-1 8E-1 δ bulk liq. Figure 5.13: 4.8 m AMP boundary layer speciation at 40 C and 0.27 mol CO 2 {mol alk during desorption; inset table lists bulk liquid mole fraction. 110

133 Figure 5.13 shows the boundary layer concentration profile, wherein the carbamate is carrying most of the CO 2. This is the shuttle mechanism, previously observed for a blend of a fast, carbamate-forming amine with a slow, tertiary amine (Astarita et al., 1981). In the shuttle mechanism, the carbamate transports the CO 2 through the boundary layer, then, as the bulk liquid reaches equilibrium, the carbamate reverses to form bicarbonate with the tertiary amine. Here, the carbamate reverses to form bicarbonate with AMP. Table 5.11: Diffusion activation energy correlated with viscosity at 60 C. amine molarity loading viscosity E D Source (M) p mol CO 2 {mol alkq (mpa-sec) p kj {molq 2PE (Sherman et al., 2016) 2PE (Sherman et al., 2016) 2MPZ (Chen and Rochelle, 2013) 2MPZ (Chen and Rochelle, 2013) PZ (Frailie, 2014) PZ (Frailie, 2014) AMP this work AMP this work MDEA (Snijder et al., 1993) MDEA (Snijder et al., 1993) Table 5.11 shows that the activation energy of the diffusion coefficient E D is linearly proportional to viscosity. A linear fit of the data yields R and Equation (5.23), where µ is the viscosity (mpa-sec) at 60 C, and E D is in kj {mol. E D 0.81µ 20 (5.23) 111

134 Above 60 C, D Am is significant, and at 100 C it becomes dominant. Therefore, estimation of D Am is important for predicting mass transfer performance at elevated temperature. Using µ at 60 C and combining Equations (5.18) and (5.23), D Am can be estimated by Equation (5.24) µ D Am exp RT (5.24) 5.4 Conclusions The liquid film mass transfer coefficient kg 1 of 4.8 m AMP goes through a maximum at 60 C because the dominant liquid film resistance shifts from reaction rate resistance below 60 C to diffusion resistance above 60 C. kg 1 is most sensitive to the carbamate reaction rate at 40 C, while, at 100 C, it is most sensitive to k l,0. The regressed carbamate rate constant is a dozen times slower than that predicted for an unhindered primary amine of equal basicity, and the bicarbonate rate constant is eighteen times faster than that predicted for an equal basicity tertiary amine. Since the AMP values do not match either prediction, different reaction mechanisms are probably used. In the wetted-wall column, AMP reacts in the pseudo-first order regime at 40 C, and at 100 C, the system is not instantaneous due to the slow bicarbonate reaction. Most of the the CO 2 is transported through the boundary layer in the form of carbamate, followed by reversion of the carbamate, and subsequent formation of bicarbonate. This work provides insight into the mass transfer mechanism of hindered amines. A better understanding of CO 2 mass transfer in hindered amines requires more information on the diffusion of carbamate. This work suggests hindered amines 112

135 play a significant role in the kinetics of CO 2 absorption when blended with a fast primary or secondary amine. 5.5 Supporting Information Table 5.12: AMPCOO scalar pure component properties Parameter Units Value DGAQFM J {kmol DHAQFM J {kmol OMEGA J {kmol PC N {m RKTZRA 0.25 TC K VC m 3 {kmol ZC 0.26 The dielectric constant for a solvent was calculated by Equation (5.25), 1 ɛ A B T 1 (5.25) C where A, B, and C are parameters and T is in Kelvin. The parameters used are listed in Table

136 Table 5.13: Pure component T-dependent parameters of AMPCOO. Temperature units Property units PLXANT K N/SQM Element Element 2 0 Element 3 0 Element 4 0 Element 5 0 Element 6 0 Element 7 0 Element 8 0 Element 9 0 Element 10 0 Element Table 5.14: Dielectric constant solvent parameters (CPDIEC) for Equation (5.25). Parameter H 2 O AMP Source (Lide, 2004) ELECPURE Element Element Element 3 (K)

137 Chapter 6 2-Methylpiperazine (2MPZ) 6.1 Introduction While piperazine (PZ) is an excellent solvent (Rochelle et al., 2011), its limited solid solubility poses an operational hazard. As a derivative of PZ may offer similar beneficial properties without precipitation, Chen and Rochelle (2011) screened many derivatives and identified three competitive solvents: 2-methylpiperazine (2MPZ), 2- piperidineethanol (Chapter 4), and a blend of PZ/2MPZ (Chapter 7). In order to better understand these systems, a model was created for each one. N N N N (a) 2MPZ-(R) (b) 2MPZ-(L) Figure 6.1: Molecular structures of chiral 2MPZ The molecular structure of 2MPZ is shown in Figure m 2MPZ has a capacity of 0.93 mol CO 2 {kg solvent, a viscosity-normalized capacity of 0.89 mol CO 2 {kg solvent, H abs 72 kj {mol, and kg,avg mol {Pa-sec-m 2 (Li, 2015). Compared to 8 m PZ, these numbers represent an increase of 18%, 13%, 13%, and a reduction of 30%. While the rate of 2MPZ is less than that of PZ, this is offset by an increase in capacity even after accounting for viscosity. 2MPZ (T max 151 C) is less thermally 115

138 stable than PZ (T max 163 C) (Freeman, 2011). 2MPZ is slightly more volatile than PZ (Nguyen, 2013). 2MPZ does not precipiate, perhaps due to its chirality. Chen (2011) constructed a thermodynamic model of 2MPZ, and Chen and Rochelle constructed a mass transfer model (2013). Unfortunately, the model was not validated for process modeling. Attempts to use it for modeling a full scale process failed with the absorber desorbing or not converging as documented by Sherman (Rochelle et al., 2012a). While the cause of failure was never pinpointed, it likely resulted from the difference in mass transfer subroutines used by the wetted-wall column and the absorber as well as K eq inconsistencies in the excessive reaction set due to strong, non-monotonic with loading activity coefficients. In order to have a working process model, the 2MPZ model of Chen and Rochelle (2013) was redone. The thermodynamic model was lightly modified, and the mass transfer model was completely redone. After the overhaul, the model was validated with an absorber to ensure that it could indeed be used for process modeling, cf. Appendix I. In addition to creating a working process model, this allowed for the later creation of a blended PZ/2MPZ model (Chapter 7). 6.2 Thermodynamic Methods The thermodynamic model is a modification of the model of Chen (2011). The convergence was improved by eliminating proton and hydroxide ions from the chemistry, resulting in the chemistry of Equation (6.1) to Equation (6.5). 2 2MPZ CO 2 ô 2MPZCOO 2MPZH (6.1) 2 2MPZCOO CO 2 ô 2MPZ COO 2 H2MPZCOO (6.2) 2MPZCOO CO 2 H 2 O ô HCO 3 H2MPZCOO (6.3) 2MPZ H2MPZCOO ô 2MPZCOO 2MPZH (6.4) 2MPZCOO HCO 3 ô CO2 3 H2MPZCOO (6.5) All other parameter values are the same as reported by Chen (2011). 116

139 6.2.1 Heat of Absorption Figure 6.2: Flowsheet for calculating H abs by calorimetry The differential heat of absorption was computed two ways: from thermodynamics using Equation (2.22) and from calorimetry using Equation (6.6) (Frailie et al., 2011), H abs Q 9n CO2 (6.6) where Q is the net-duty of the flash block, and 9n CO2 is the molar flow rate of gaseous CO 2. The flowsheet of Figure 6.2 shows a T-vapor-fraction bubble-point flash. Loaded solvent LIQIN is fed in alongside a small amount of gaseous CO 2 GCO2. The whole system is operated in an isothermal, isobaric manner. A sensitivity block with cases was used to vary the loading and temperature. 6.3 Mass Transfer Methods The mass transfer model of Chen and Rochelle (2013) was completely replaced. This was done to create a working process model and to enable a PZ/2MPZ blend amine model by using correlations consistent with the Guy Fawkes model 117

140 of Frailie (2014). It is important to note that the conclusions drawn by Chen and Rochelle (2013) are still valid Hydraulics Table 6.1: Viscosity data for 2MPZ with ARD from model. Tabulated in Appendix Appendix F. Molality T loading N ARD Source (m) ( C) p mol CO 2 {mol alkq (%) (Chen, 2011) (Li, 2013) (Rochelle et al., 2013) Viscosity was represented by the same equations as the Fawkes model (Frailie, 2014) for consistency. To fit viscosity, the 72 data points listed in Table 6.1 were fit with the seven parameters of Equation (3.1). It is likely that the data reported by Chen (2011) were analyzed neither for total alkalinity (TA) nor for total inorganic carbon (TIC), and so have greater error than the data reported by Li (Rochelle et al., 2013) and in Appendix F. The regression was done by minimizing the sum of squared errors (SSE) using Solver in Excel. Six parameters of Equation (3.3) were used to fit 24 8 m 2MPZ density data points spanning 20 C to 60 C and 0.0 p mol CO 2 {mol alkq to 0.4p mol CO 2 {mol alkq (Chen, 2011). Again, the data were likely analyzed neither by TA nor by TIC. The regression was done in the same way as the viscosity regression Diffusivity No diffusivity of amine or products D Am data were available. The representation of D Am by Chen and Rochelle (2013) was changed to use the same correlation as 118

141 Guy Fawkes (Frailie, 2014), which is Equation (3.7). The three parameters of Equation (3.7) were regressed simultaneously with the kinetic parameters. This regression was done manually Flowsheet The flowsheet is similar to that of Frailie (2014), which used one WWC, rather than that of Chen and Rochelle (2013), which used six WWC s. The flow sheet is similar to the one described in 3.2.4, but with only one WWC and three fewer calculator blocks used: the calculator block adjusting the flowrate of water to the saturator, the calculator block recalculating k r, and the calculator block to calculate flowrates from loadings. This last calculation was done offline and entered manually. Without adjusting the water flow to the saturator, excess water could absorb CO 2 and artificially reduce the driving force for the absorption flux simulations. Not recalculating k r at each temperature introduces error in the fitting of the 80 C and 100 C data. These effects do not change the conclusions, but do affect the fit. The loading was adjusted as described in except that no design specification was used. Without modeling a second WWC, the design specification adjustment of loading is not possible. Therefore, the adjustment for each point was done manually by iterating on the following sequence: 1. Run desorption point and calculate flux ratio ˆN CO2 N CO2. 2. Run absorption point and calculate ˆN CO2 N CO2. 3. Compare ˆN CO2 N CO2 values. 4. If values were within 1% of each other or adjustment was greater than 10% of the operational loading range ( 0.01 mol CO 2 {mol alk), stop. Else, adjust loading and repeat from step

142 6.3.4 Reaction Set The kinetics were modeled as described in The reaction set of Chen and Rochelle (2013) included none kinetic reactions and five equilibrium reactions. That reaction set was reduced to Equation (6.7) to Equation (6.11), where Equation (6.7) to Equation (6.9) are kinetic reactions, and Equation (6.10) and Equation (6.11) are equilibrium reactions. k 2MP Z 2MP Z 2 2MPZ CO 2 ÝÝÝÝÝÝÝÝá âýýýýýýýý 2MPZCOO 2MPZH (6.7) k 2MP ZCOO 2 2MPZCOO CO 2 2MP ZCOO ÝÝÝÝÝÝÝÝÝÝá âýýýýýýýýýý 2MPZ COO 2 H2MPZCOO (6.8) 2MPZCOO CO 2 H 2 O k 2MP ZCCO âýýýýýýý ÝÝÝÝÝÝÝá HCO 3 H2MPZCOO (6.9) 2MPZ H2MPZCOO ô 2MPZCOO 2MPZH (6.10) 2MPZ HCO 3 ô 2MPZH CO 2 3 (6.11) This reduction was motivated by a couple of reasons. One, using fewer reactions reduces computation time while increasing numerical stability. Particularly beneficial is the elimination of protons and hydroxide ions as these cause a poorly scaled matrix. Two, this reduction reduces the chance of thermodynamic inconsitency. One possible reason that the model of Chen and Rochelle (2013) is incapable of converging at process modeling conditions is that the WWC regression utilized a calculator block to ensure that the E A for the forward and reverse reactions accorded with the K eq of the thermodynamic model. This calculator block is not possible to use when simulating a non-isothermal absorber. The E A used in the reaction set only ensures thermodynamic consistency for 20 C (Frailie, 2014) Kinetic Parameter Regression The manual method of was used to regress kinetic parameters. These were used to fit the data at low loading and low temperature, while the diffusion pa- 120

143 rameters were used to fit the data at high loading and high temperature. k 2MP Z 2MP Z and k 2MP Z were regressed. k 2MP ZCOO 2MP ZCOO was ratioed to k 2MP Z 2MP Z by using the Brønsted correlation of Chen and Rochelle (2013), yielding Equation (6.12). k 2MP ZCOO 2MP ZCOO 0.88k 2MP Z 2MP Z (6.12) In summary, three D Am parameters and four kinetic parameters were regressed for a total of seven parameters. Forty data points were fit. These points cover 40 C to 100 C, mol CO 2 {mol alk to mol CO 2 {mol alk, and CO 2 flux from mol {sec-m 2 to mol {sec-m Film Discretization The film discretization of Chen and Rochelle (2013) was reduced from 50 points to the 32 points listed in Table 3.1 to reduce computation time. Multiple flux calculations were run with both discretizations and found to give identical results. It is likely that far fewer points yet could have been used without compromising the accuracy (Zhang et al., 2009) Kinetic Analysis To understand how the viscosities of 8 m 2MPZ and 8 m PZ impact mass transfer, the two solvents were compared in two ways. One, 8 m 2MPZ was run using µ 2MP Z and µ P Z. This was done by replacing the Fortran subroutine for this work with that of PZ subroutine from Frailie (2014). Two, 8 m 2MPZ and 8 m PZ were both run with µ P Z. In short, the analysis looked at with different viscosities with the same kinetics, and different kinetics with the same viscosity. 121

144 6.4 Thermodynamic Results and Discussion Changing the model chemistry did not substantially change the thermodynamic fit of the model developed by Chen (2011), and so the reader is referred there for a discussion of pk a, P 2MP Z, VLE, speciation, and activity coefficients. The activity coefficients of the 2MPZ zwitterion and dicarbamate vary nonmonotonically over one or two orders of magnitude. This poor behavior distorts the kinetic rate constant parameters, degrading their physical significance, and precludes an accurate PZ/2MPZ model ( ). This is likely due to Chen (Chen, 2011) only regressing zwitterion interaction parameters, which forced the zwitterion to account for the non-ideality of the entire system Heat of Absorption C 75 H abs kj mol C 35 thermodynamic 25 C calorimetric loading (mol CO 2 /mol alk.) Figure 6.3: H abs predictions for 8 m 2MPZ at 20 C intervals except for 25 C 122

145 Figure 6.3 shows the differential heat of absorption H abs computed by both the thermodynamic relationship of Equation (2.22) and by calorimetry using Equation (6.6). There is less temperature dependence at loadings below 0.25 mol CO 2 {mol alk. H abs decreases with increasing loading due to a shift in the reaction stoichiometry from the formation of carbamate at low loading to the formation of bicarbonate at high loading. As the temperature increases, the isotherms show less loading dependence due to decreased formation of carbamate and dominance of the bicarbonate product. The two methods agree at loadings less than 0.25 mol CO 2 {mol alk. However, for loadings greater than 0.25 mol CO 2 {mol alk, the H abs by calorimetry is consistently greater than the H abs by thermodynamics. Frailie (Rochelle et al., 2011) ascribed a similar discrepancy for 8 m PZ to use of the polynomial form of K eq, Equation (2.9). However, use of the more rigorous K eq calculation, Equation (2.10) did not eliminate the discrepancy of either 8 m PZ, as discussed by Frailie (Rochelle et al., 2011), or 8 m 2MPZ. These two methods should agree for all conditions, and their disagreement may be due to the heat capacity of the solvent and in particular the handling of the partial heat capacity of CO 2. Aspen Plus calculates the heat capacity by a numerical derivative of the enthalpy near the system temperature. Aspen Technology (2016) recommends using the apparent approach to calculate the heat capacity for electrolyte systems as the heat of speciation is included in the heat capacity calculation. In the true approach, the heat capacity does not include the heat of speciation. However, this solution is impractical. 123

146 Table 6.2: 8 m 2MPZ viscosity parameters of Equation (3.1) Parameter Value Parameter Value a e 14.0 b f c 2.05 g 1.52 d E+1 50 C 8 m Chen 25 C 5 m Rochelle 40 C 8 m 5 m 8 m 40 C µ (cp) 5E+0 40 C 140 C 140 C 5E loading (mol CO 2 /mol alk) Figure 6.4: Viscosity predictions for 8 m and 5 m 2MPZ at 20 C intervals calculated by Equation (3.1) compared to data (Chen, 2011; Rochelle et al., 2013) and Appendix F. 124

147 6.5 Mass Transfer Results and Discussion Hydraulics For viscosity, the regressed parameters of Equation (3.1) are listed in Table 6.2. The overall ARD is 7.6% with the ARD for each individual data set given in Table 6.1. Figure 6.4 compares predicted viscosity for both 8 m and 5 m 2MPZ to data. The predictions increase with loading and decrease with temperature as expected. 8 m is more viscous than the corresponding 5 m isotherm, and the 5 m slope is less than that of 8 m. These observations indicate that the model behavior is appropriate. The 8 m 20 C data are poorly fit and have a very different slope than the other 8 m data. The 8 m 40 C data of Chen (2011) are consistently greater than the corresponding set reported by Li in (Rochelle et al., 2013), though the more variable 60 C data sets agree. Nevertheless, the fit is adequate for the WWC operating range of 40 C to 100 C and 0.27 mol CO 2 {mol alk to 0.37 mol CO 2 {mol alk. The 5 m data are uniformly overpredicted, though the slope is correct. This overprediction is due to more 8 m data than 5 m data. As all regressed mass transfer data are at 8 m, this overprediction does not impact mass transfer conclusions. Table 6.3: Density Parameters of Equation (3.3) where Am 1 2MPZ and Am 2 PZ Parameter Value Parameter Value a 3.66 f b g e h For density, the regressed parameters of Equation (3.4) are shown in Table 6.3. The ARD is 0.12%. Figure 6.5 shows the behavior is as expected: increasing with loading, decreasing with temperature. The temperature sensitivity increases with temperature, as seen by the spacing out of the isotherms. This effect may be due to 125

148 40 C ρ kg m C loading (mol CO 2 /mol alk) Figure 6.5: Density of 8 m 2MPZ at 20 C intervals; data (Chen, 2011) the change in equilibrium speciation, as the dicarbamate and carbonate are replaced by free CO 2 at high temperature (Chen, 2011). Regardless of the high temperature behavior, the fit is adequate for mass transfer modeling Mass Transfer Parameters Table 6.4: 8 m 2MPZ regressed kinetic parameters for Equation (3.14) Rate Constant Equation k 0 E A Source p kmol {sec m 3 q ( kj {molq k 2MP Z 2MP Z (6.7) ratioed k 2MP ZCOO 2MP ZCOO (6.8) ratioed k 2MP ZCOO (6.9) regressed 126

149 Table 6.5: 8 m 2MPZ D Am parameters of Equation (3.7) Parameter Value Units D m 2 {sec α 11.5 β 1.50 T ref K µ ref Pa-sec The regressed kinetic and D Am parameters are listed in Table 6.4 and Table 6.5. The equal E A for k 2MP Z 2MP Z and k 2MP ZCOO 2MP ZCOO are due to ratioing the two reactions. k 0 and E A of k 2MP ZCOO are both high compared to PZ systems, cf. Table This could be due to a difficulty in capturing the temperature behavior of the system. This difficulty is also evident in the exceptional temperature dependence of D Am. The value of α has no physical significance and is an artifact. Similar artifacts were produced in fitting the MEA model Phoenix (Plaza, 2011), wherein α was set to 22.6 for 7 m MEA and for 9 m MEA. Nevertheless, Phoenix was successfully used to reconcile pilot plant data (Plaza, 2011). The physical significance of the mass transfer parameters are degraded. Figure 6.6 and Figure 6.7 show the fit of the flux data. There is a difference between the absorption and desorption points due to limiting the loading adjustment. Figure 6.6 shows a parabolic trend that goes through a maximum at 0.16 mol CO 2 {mol alk. This indicates that the model has a systematic bias due to not representing the mass transfer phenomena. Figure 6.7 shows that the discrepancy between absorption and desorption grows with temperature. This increasing discrepancy is from model error in matching the VLE at the higher temperatures as seen in Figure 6.8. It may also be due to not maintaining precise thermodynamic consistency through the backcalculation of k r. 127

150 C 60 C 80 C 100 C CO2 N CO2 open points are desorption filled points are absorption dashed lines bound reproducability region loading (mol CO 2 /mol alk) Figure 6.6: 8 m 2MPZ flux ratioed to data (Chen, 2011) 1.75 open points are desorption filled points are absorption dashed lines bound reproducability region CO2 N CO T ( C) Figure 6.7: 8 m 2MPZ predicted flux ratioed to data (Chen, 2011) 128

151 1E C 1E+6 P CO2 (Pa) 1E+5 1E+4 1E+3 1E+2 1E+1 prediction WWC (Chen, 2011) adjusted loading total pressure (Xu and Rochelle, 2011) 1E loading (mol CO 2 /mol alk) Figure 6.8: 8 m 2MPZ predicted VLE (lines) at 20 C intervals The VLE fit shows that the model underpredicts most data for 60 C to 100 C. Table 6.6 shows that over half of the points have reached the loading adjustment bound of 0.1 mol CO 2 {mol alk. The largest loading adjustments occur for the 80 C and 100 C data, where the adjustment is for model error rather than experimental error Mass Transfer Analysis Figure 6.9 compares the viscosity of 8 m 2MPZ to that of 8 m PZ. At zero loading, µ 2MP Z 1.3µ P Z, as 2MPZ is inherently more viscous and is 5 wt.% more amine than 8 m PZ. As the loading increases, the ratio grows to 3.4 at 40 C and 2.5 at 100 C. The more rapid increase of 2MPZ may be due to solvation effects and 129

152 Table 6.6: 8 m 2MPZ relative loading adjustment T loading relative T loading relative exp adj difference exp adj difference ( C) p mol CO 2 {mol alkq (%) ( C) p mol CO 2 {mol alkq (%) C C 80 C μ 2MPZ μ PZ C loading (mol CO 2 /mol alk) Figure 6.9: Viscosity correlation of 8 m 2MPZ ratioed to 8 m PZ. 130

153 changes to the local electron environment at the hindered nitrogen atom. This could increase intermolecular hydrogen bonding leading to greater viscosity C 60 C 80 C 100 C N CO2 μ2mpz N CO2 μpz loading (mol CO 2 /mol alk) Figure 6.10: Ratio of absorption ˆN CO2 for 8 m 2MPZ using µ 2MP Z and µ P Z The effect of this viscosity ratio is seen in Figure 6.10, which shows the same flux points modeled using 8 m 2MPZ with the viscosity of 2MPZ and the viscosity of PZ. By only changing the solvent viscosity, the flux of CO 2 is reduced by up to 16%. Viscosity does not affect the kinetics, so the effect is least pronounced when the system is kinetically controlled. Viscosity does affect diffusivity. As the system is diffusion controlled at high loading, the increased viscosity has greater impact than 131

154 at low loading. The effect with temperature is less significant as the viscosity ratio is less and less steep as was shown in Figure 6.9. At a loading of 0.1 mol CO 2 {mol alk, the viscosity ratio is 1.5 and the reduced flux is 0.03, while at a loading of 0.35 mol CO 2 {mol alk, the viscosity ratio is 2.5 and the reduced flux is If the effect of viscosity were constant across this loading range, then the reduced flux should have only been If the viscosity of 2MPZ could be reduced to that of PZ, the mass transfer rates of 2MPZ would increase by up to 15% C 60 C 80 C 100 C 0.60 N CO2 2MPZ N CO2 PZ loading (mol CO 2 /mol alk) Figure 6.11: Ratio of absorption ˆN CO2 for 8 m 2MPZ to 8 m PZ using µ P Z 132

155 Figure 6.11 shows the effect of viscosity by showing the ratio of CO 2 flux for 8 m 2MPZ to that of 8 m PZ if both systems were to have the viscosity of PZ. While Figure 6.10 showed the effect of viscosity, Figure 6.11 shows the effect of kinetics and diffusivity in differentiating the two solvents. While reducing viscosity stood to increase the flux for 8 m 2MPZ by up to 15%, the kinetics and diffusivity account for up to 85% of the difference seen between the systems. Therefore, while viscosity may be the most important solvent property for heat exchanger performance, kinetics and diffusivity are far more important in absorber performance. 6.6 Conclusions The activity coefficients of the 2MPZ zwitterion and dicarbamate are strong, non-monotonic functions of loading, precluding an accurate PZ/2MPZ model. The decreased CO 2 flux of 8 m 2MPZ relative to 8 m PZ, is 15% due to viscosity with the remainder due to kinetics. A process model was developed and validated. A manual is included in Appendix I. When the model is converted from ELECNRTL to ENRTL-RK, the activity coefficient behavior should be corrected to enable blend modeling and improve the physical significance of the model parameters. After this upgrade, the differential heat of absorption by calorimetry and by differentiating the VLE should be repeated to help determine the source of the thermodynamic inconsistency. The viscosity correlation should be improved to better represent low temperature and low concentration data, as 4 m to 6 m 2MPZ is a better solvent than 8 m 2MPZ, as discussed by Yuan (Rochelle et al., 2015). The temperature dependence of D Am should be corrected, and the liquid film discretization could be further reduced. 133

156 Chapter 7 Piperazine Blends 7.1 Introduction Concentrated aqueous piperazine (PZ) outperforms monoethanolamine (MEA) in capacity, mass transfer, thermal and oxidative stability, and volatility (Li, 2015). While it suffers from a price that will remain double that of MEA, the main drawback of PZ is its limited solid solubility (Freeman, 2011). At concentrations 5 m, PZ is all liquid only within a range of loading. Outside of this loading range, PZ precipitates (Ma et al., 2012). While it is possible to operate within this loading window, pilot plant experience shows that precipitation occurs at some conditions, leading to plugging (Chen et al., 2013). For this reason, solvent screening efforts have focused on finding a suitable amine to blend with PZ. The desired outcome is a widening of the PZ solid solubility window while minimally compromising the benefits of PZ. This chapter describes three thermodynamic and mass transfer models of PZ blended with hindered and tertiary amines: 2-amino-2-methylpropan-1-ol (AMP), 4-hydroxy-1-methylpiperidine (HMPD), and 2-methylpiperazine (2MPZ). All three blends were identified as promising solvents (Li et al., 2014; Rochelle et al., 2015; Chen and Rochelle, 2011) HMPD 4-hydroxy-1-methylpiperidine (HMPD) is a cyclic, tertiary amine with the structure shown in Figure 7.1. HMPD is thermally and oxidatively stable, has low 134

157 OH N N Figure 7.1: Molecular structure of HMPD volatility, and has acceptable viscosity (Du et al., 2016). However, HMPD is very expensive at present ( 10 the price of PZ). This blend is designed for use at the higher CO 2 partial pressure in the combined membrane and amine scrubbing process proposed by Membrane Technology and Research, Inc. (Freeman et al., 2014). Higher partial pressure shifts the rich loading P CO 2 10 kpa, as discussed by Frailie (2014). This blend was developed to take advantage of the increased mass transfer in 5 m PZ due to lower viscosity (Li, 2015). Du et al. (2016) recommended 2 m PZ/3 m HMPD as the best blend AMP As discussed in Chapter 5, 2-amino-2-methylpropan-1-ol (AMP) is the most studied hindered amine solvent on its own. Naturally, this has lead to extensive work on AMP in solvent blends. Blending AMP with the following amines has been suggested as a viable solvent: MEA, DEA, and PZ (Bougie and Iliuta, 2012). These blends mostly focused on using the amine other than AMP as a promoter, ie adding the second amine in a small amount to increase the mass transfer performance of AMP. This work discusses AMP/PZ blend solvents that are rich in either AMP or PZ. There have been prior thermodynamic models of PZ/AMP constructed by Puxty and Roland (2011), Hartono et al. (2013), and Li et al. (2014). Puxty and Roland (2011) studied AMP-rich solvent, while Hartono et al. (2013) and Li et al. 135

158 studied (2014) solvents both rich and lean in AMP. This work extends the thermodynamic model of Li et al. (2014) by including AMP carbamate modeling mass transfer MPZ While Chapter 6 discussed 2-methylpiperazine (2MPZ) as a promising solvent on its own, blending 4 m 2MPZ with 4 m PZ results in greater mass transfer but less capacity relative to 8 m 2MPZ. The operating loading range lies between 8 m 2MPZ and 8 m PZ at 0.30 mol CO 2 {mol alk to 0.39 mol CO 2 {mol alk. 4 m PZ/4 m 2MPZ has equal capacity and viscosity-normalized capacity (Li et al., 2013b) of 0.88 mol CO 2 {kg solvent, kg, 1 avg mol {Pa-sec-m 2, and H abs 66 kj {mol (Li, 2015). This is an increase of 11%, a decrease of 16%, and negligible change respectively compared to 8 m PZ. The rich and lean solid solubility limits are expanded (Sherman et al., 2013). The stability of the blend is comparable to that of 8 m 2MPZ, which is less than 8 m PZ (Sherman et al., 2013). Sherman et al. (2013) offers a thorough summary of experimental work. 7.2 Thermodynamic Methods The thermodynamic framework discussed in was used. PZ was represented by the Independence (Frailie, 2014). All amines were represented as Henry s components PZ/HMPD In the absence of data for pure or aqueous HMPD, the sequential regression method ( 2.2.2) was unusable. The analogy method ( 2.3) was the only possibility. 136

159 The analogy method should follow the same steps as sequential regression, however the pure HMPD and aqueous HMPD were skipped due to a lack of data. The MDEA component of the Independence model was chosen as the analog for HMPD as both are tertiary amines. HMPD and HMPD were added to Independence. As HMPD is not a databank component, its parameters were equated to MDEA (Table 7.22) except for those regressed. Two different chemistries are used in the model, for reasons discussed in Equations (7.1) to (7.9) are only for the calculation of pk a. H 2 O ô OH H (7.1) CO 2 H 2 O ô HCO 3 H (7.2) HCO 3 ô CO2 3 H (7.3) HMPDH ô HMPD H (7.4) PZH ô PZ H (7.5) HPZCOO ô PZCOO H (7.6) PZ HCO 3 ô PZCOO H 2 O (7.7) PZCOO HCO 3 ô PZ COO 2 H 2 O (7.8) HMPD CO 2 H 2 O ô HCO 3 Equations (7.10) to (7.15) are used for all other simulation. HMPDH (7.9) 2 PZ CO 2 ô PZH PZCOO (7.10) 2 PZCOO CO 2 ô PZ COO 2 HPZCOO (7.11) PZCOO CO 2 H 2 O ô HCO 3 HPZCOO (7.12) PZ HPZCOO ô PZH PZCOO (7.13) HMPD CO 2 H 2 O ô HCO 3 HMPDH (7.14) HMPD HCO 3 ô CO2 3 HMPDH (7.15) The available thermodynamic data are listed in Table 7.1. The last column of Table 7.1 indicates whether the data set was regressed or not. At the time of regression, pk a data had not been collected. The pk a at 25 C was estimated using the 137

160 Table 7.1: Available thermodynamic data for 2 m PZ/3 m HMPD; all data except pk a from Du (2016); pk a is tabulated in Appendix G (Ciftja, 2016) System Type T Loading # of data Regressed? C p mol CO 2 {mol alkq VLE Y VLE Y 2 m PZ/3 m HMPD VLE Y P TOT N P Am unloaded 3 Y 0.3 m HMPD P Am unloaded 3 Y 0.1 M HMPD pk a unloaded 7 N updated PDS group-contribution method (Sumon et al., 2012). The pk a temperature dependence was estimated by adapting Equation (7.16) (Perrin et al., 1981), dpk a dt pk a 0.9 T a (7.16) where T is in units of K, and a is an adjustable parameter. a was regressed by fitting the pk a of MDEA (Oscarson et al., 1989; Kamps and Maurer, 1996; Kim et al., 2011; Littel et al., 1990; Schwabe et al., 1959). Then the pk a of HMPD was estimated via Equation (7.17), where β 25α pk a T 25 C and α pka T 25 C a. pk a β αt (7.17) However Equation (7.17) is not the correct integration of Equation (7.16); the proper integral is Equation (7.18), pk a 0.9 a 2 T C T (7.18) where C is an integration constant. The MDEA regression was repeated by minimizing the sum of squared relative errors to find a new a to check the estimate of pk a by Equation (7.17). 138

161 The pk a predicted by Equation (7.17) was reproduced in Aspen following the procedure of Following the sequential regression method for blend systems ( 2.2.2), the data sets of Table 7.1 were fit. P Am data sets were fit together by regressing the NRTL interaction parameters (same form as Equation (2.6)) along with the parameters for temperature dependence of Henry s law (Equation (2.13)), specifically, C HMP D, H2 O, A HMP D, H2 O, B HMP D, H2 O. Then, the VLE data of Table 7.1 were fit by regressing interaction parameters: C phmp DH, P ZCOO q{h 2 O, C phmp DH, P ZCOO q{p Z, and C phmp DH, HCO 3 q{hp ZCOO. Only interaction parameters with both PZ and HMPD were regressed to not disturb the aqueous PZ and aqueous HMPD models PZ/AMP The thermodynamic model used here is identical to the one used in Chapter 5. The methods are detailed in PZ/2MPZ The thermodynamic models of PZ (Frailie, 2014) and of 2MPZ (Chapter 6) were merged to form the basis of the PZ/2MPZ model. While Aspen Plus provides tools to clean parameters, these tools were more problematic to use than manually cleaning the parameters. Further complicating the merge is that the two models used different databases, with 2MPZ using ASPENPCD (Chen, 2011) and Independence using PURE25 (Frailie, 2014), leading to conflicting definitions for CO 2, HCO 3, CO 2 3, H, OH, H 2 O, and N 2. The definitions of Independence were adopted, which changed the thermody- 139

162 namics of the 2MPZ components slightly. The thermodynamics agree exactly with the base PZ model and are slightly different than the base 2MPZ model. Table 7.2: 2MPZ/PZ thermodynamic data Type N T Loading C Am Source ARD ( C) p mol CO 2 {mol alkq (m) (%) VLE WWC (Chen, 2011) 1.4 VLE T P , 7.86 (Xu, 2011) 1.9 P Am , (Nguyen, 2013) N/A Once the components were in the same model, the model chemistry was combined. For pk a calculations, Equations (7.19) to (7.29) were used. H 2 O ô OH H (7.19) CO 2 H 2 O ô HCO 3 H (7.20) HCO 3 ô CO2 3 H (7.21) 2MPZH ô 2MPZ H (7.22) PZH ô PZ H (7.23) H2MPZCOO ô 2MPZCOO H (7.24) HPZCOO ô PZCOO H (7.25) 2MPZ HCO 3 ô 2MPZCOO H 2 O (7.26) PZ HCO 3 ô PZCOO H 2 O (7.27) 2MPZCOO HCO 3 ô 2MPZ COO 2 H 2 O (7.28) PZCOO HCO 3 ô PZ COO 2 H 2 O (7.29) 140

163 For all other simulation, Equations (7.30) to (7.38) were used. 2 PZ CO 2 ô PZH PZCOO (7.30) 2 PZCOO CO 2 ô PZ COO 2 HPZCOO (7.31) PZCOO CO 2 H 2 O ô HCO 3 HPZCOO (7.32) PZ HPZCOO ô PZH PZCOO (7.33) 2 2MPZ CO 2 ô PZH PZCOO (7.34) 2 2MPZCOO CO 2 ô 2MPZ COO 2 H2MPZCOO (7.35) 2MPZCOO CO 2 H 2 O ô HCO 3 H2MPZCOO (7.36) 2MPZ H2MPZCOO ô 2MPZH 2MPZCOO (7.37) 2MPZCOO CO 2 HCO 3 ô CO2 3 H2MPZCOO (7.38) Once the blend model was created, the next sequential modeling steps of regressing blend unloaded data and blend loaded data, shown as the last two columns in Figure 2.4, were taken. The data available are listed in Table 7.2. The unloaded P Am data were first fit. The regression was flawed for two reasons. One, is that when the data were entered into DRS, the vapor phase mole fraction calculation included water without constraining the water component. Therefore, DRS was unable to fit the data. Even if this mistake had not been made, the fit would be sub-optimal as only the blend, unloaded data were fit. These data should have been fit together with the individual amine unloaded data, as described in At the time of regression, the sequential regression method was strictly followed, rather than simultaneously fitting unloaded blend and single amine data. Therefore, no parameters were regressed for this set of data, leaving the NRTL parameters to default. Moving on to the final step of fitting loaded data for the blend, it was attempted to fit the VLE data and loaded P Am data together. However, this was unsuccessful. Again, it is possible that this would have worked had the loaded P Am 141

164 data been treated differently. Nevertheless, only the VLE data were fit. To fit the VLE data, the 8 C ca,m parameters (defined by Equation (2.7)) listed in Table 7.7 were regressed. Only parameters involving both PZ and 2MPZ were regressed. These parameters were chosen by the method described in As no γ CO2 data were available for the loaded, blend solvent, the predicted trends with loading and temperature were checked for reasonable behavior. The D ca,m parameters for (2MPZH, PZ(COO ) 2 )/CO 2 and (PZH,2MPZCOO )/CO 2 of Equation (2.7) were adjusted to improve behavior as described in 2.4. In summary, 27 VLE data points were fit with 8 parameters, and an additional 2 parameters were adjusted for γ CO Mass Transfer Methods PZ/HMPD Hydraulics Prior to regressing mass transfer, the hydraulics were regressed. Lacking any loaded density data for HMPD or PZ/HMPD, the correlation for PZ/MDEA was used with HMPD substituted for MDEA (Frailie, 2014), which is of the same form as Equation (3.4). For viscosity, there were 37 data points available for various blends (5 m PZ/5 m HMPD, 5 m PZ/2 m HMPD, 4 m PZ/2 m HMPD, 2 m PZ/3 m HMPD) from 0 mol CO 2 {mol alk to 0.52 mol CO 2 {mol alk and for C. These were fit using parameters e, f, h, and j of Equation (3.2) where Am 1 HMP D and Am 2 P Z. These parameters were chosen for their lesser dependence on temperature than the other parameters. Of the 37 data points collected, the 7 points at 20 C with 2 m PZ/3 m HMPD data points were excluded due to a non-monotonic change with loading as were the three measurements at 0.26 mol CO 2 {mol alk, which were much greater than reasonable. This left 28 data points that were fit with four parameters using nlinfit 142

165 in MATLAB. The data show excessive scatter due to the lack of triplicates. The impact on accuracy of other changes to the experimental method of Freeman (2011) were not quantified by Du et al. (Du et al., 2016) Diffusivity The diffusion of CO 2 was modeled using Equation (3.6). Despite the erroneous result of D Am D CO2, the same diffusion of amine-products correlation as Independence was used to avoid altering the PZ kinetics (Frailie, 2014) Reaction Set The PZ/MDEA model (Frailie, 2014) reaction set was modified by replacing the MDEA component with HMPD to yield Equations (7.39) to (7.47), where Equations (7.39) to (7.44) are kinetic reactions and (7.45) to (7.47) are equilibrium reactions. HMPD CO 2 H 2 O k HMP D ÝÝÝÝá âýýýý HCO 3 HMPDH (7.39) HMPD PZCOO k P ZCOO HMP D CO 2 ÝÝÝÝÝÝÝÝÝÝÝá âýýýýýýýýýýý PZ COO 2 HMPDH (7.40) k P Z HMP D PZ HMPD CO 2 ÝÝÝÝÝÝÝá âýýýýýýý PZCOO HMPDH (7.41) k P Z P Z 2 PZ CO 2 ÝÝÝÝÝá âýýýýý PZCOO PZH (7.42) 2 PZCOO k P ZCOO P ZCOO CO 2 ÝÝÝÝÝÝÝÝÝÝÝÝá âýýýýýýýýýýýý PZ COO 2 HPZCOO (7.43) PZCOO CO 2 H 2 O k P ZCOO ÝÝÝÝÝÝá âýýýýýý HCO 3 HPZCOO (7.44) HMPD PZH ô HMPDH PZ (7.45) HMPD HCO 3 ô HMPDH CO 2 3 (7.46) PZCOO PZH ô HPZCOO PZ (7.47) 143

166 Kinetic Parameter Regression WWC mass transfer data for 2 m PZ/3 m HMPD from mol CO 2 {mol alk to mol CO 2 {mol alk and 20 C to 100 C were available (Du et al., 2016). Data at mol CO 2 {mol alk were excluded as they were gas-film controlled. Only the greatest desorption and absorption fluxes for each condition were fit for a total of forty data points. These data were collected with a method similar to Li (2015), however rather than always collecting six data points per condition, the number was reduced and varied. This inconsistency makes the error heteroskedastic and increases the probablity of erroneous data. The mass transfer regression was done using the framework described in 3.2 with the manual method described by The liquid film was discretized as in Table 3.1, where δ is the dimensionless distance from the gas-liquid interface (δ 0 at the interface and 1 at the bulk liquid). Using the tertiary amine Brønsted correlation from Versteeg and van Swaaij (1988), the bicarbonate reaction rate k HMP D was set. The activation energy E A for k HMP D was set at the measured value for MDEA (Ko and Li, 2000). Note that the estimated pk a used was 9.71, which is a half unit higher than the experimental value (Ciftja, 2016). Using this value would predict a k HMP D that is 64% greater than using true pk a value to predict the rate constant. k P ZCOO HMP D was estimated using a Brønsted correlation (Cullinane and Rochelle, 2006) with the same ratio used for MDEA catalyzing PZ (Frailie, 2014), i.e. k P ZCOO HMP D 1.36k P Z HMP D. In short, only two parameters were regressed: k 0 and E A of k P Z HMP D. 144

167 7.3.2 PZ/AMP Hydraulics Table 7.3: PZ/AMP hydraulic data Type N T Loading C AMP C PZ Source ARD ( C) p mol CO 2 {mol alkq m m % µ (Rochelle et al., 2012a) µ (Rochelle et al., 2012a) µ (Rochelle et al., 2012a) µ (Fu et al., 2014) ρ pure 0 (Xu et al., 1991) ρ pure 0 (Chan et al., 2002) N/A The base model by Li et al. (2014) used the default hydraulic correlations, which are the Jones-Dole correction to the Andrade liquid mixture viscosity correlation and the Clarke density correlation. For density, the default correlation increased with loading and decreased with temperature, but suffered from non-monotonic behavior, poor convergence, and crossing isotherms. For viscosity, the default correlation decreased with temperature and behaved erratically with loading (Rochelle et al., 2014). Therefore, these correlations were replaced with subroutines. The viscosity data listed in Table 7.3 were fit with Equation (3.2). The Fu et al. (2014) data were not published at the time of regression, and so were not 145

168 regressed. The three temperature points of 6.5 m PZ/3 m AMP at mol CO 2 {mol alk of Li (Rochelle et al., 2012a) were excluded as the reported viscosity did not follow the expected trend with loading. Seven parameters were regressed with thiry-two data points by minimizing the SSE with Solver. As there were no loaded PZ/AMP density data available, an attempt was made to use the PZ/MDEA density correlation of Independence (Frailie, 2014). However, this did not work. Therefore, the 140 data points of unloaded AMP in Table 7.3 were used to regressed parameters a and b of Equation (3.4). This regression was also done by minimizing the SSE with Solver. c was set to the value for PZ/MDEA (Frailie, 2014). The remaining five parameters were adjusted until the fit behaved reasonably Diffusivity D CO2 was modeled using Equation (3.6). D Am was regressed, which means that the PZ kinetics taken from Independence (Frailie, 2014) were affected. D Am was represented by Equation (3.7). As there is a lack of data to meaningfully regress all three parameters of Equation (3.7), D 0 and β were regressed. α was left at the value of PZ/MDEA (Frailie, 2014). The reference viscosity was changed to the 0.45 mol CO 2 {mol alk, 40 C viscosity of 2 m PZ/4 m AMP Flowsheet The mass transfer regression was done using the flowsheet described in 3.2.4, except no saturator calculator block was used Reaction Set The PZ/MDEA model (Frailie, 2014) reaction set was modified in two ways. One, the MDEA component was replaced with AMP. Two, the formation of AMP carbamate was added. The full reaction set is Equations (7.48) to (7.57), where 146

169 Equations (7.48) to (7.54) are kinetic reactions and (7.55) to (7.57) are equilibrium reactions. AMP CO 2 H 2 O é HCO 3 AMPH (7.48) AMP PZCOO CO 2 é PZ COO 2 AMPH (7.49) PZ AMP CO 2 é PZCOO AMPH (7.50) 2 PZ CO 2 é PZCOO PZH (7.51) 2 PZCOO CO 2 é PZ COO 2 HPZCOO (7.52) 2 AMP CO 2 é AMPCOO AMPH (7.53) PZCOO CO 2 H 2 O é HCO 3 HPZCOO (7.54) AMP PZH ô AMPH PZ (7.55) AMP HCO 3 ô AMPH CO2 3 (7.56) PZCOO PZH ô HPZCOO PZ (7.57) Kinetic Parameter Regression WWC mass transfer data for two different blends of PZ/AMP were available: 2 m PZ/4 m AMP and 5 m PZ/2.3 m AMP (Rochelle et al., 2012a). Only the first blend was regressed owing to time constraints. These data span loading mol CO 2{mol alk to mol CO 2 {mol alk, temperature from 20 C to 100 C, and flux from mol {sec-m 2 to mol {sec-m 2 (Rochelle et al., 2012a). Only the greatest desorption and absorption fluxes for each condition were fit for a total of thirty data points. For each pair of fluxes, the loading was adjusted per The loading was adjusted manually with the same criterion as the design specification described in For this system 10% of the operational loading range is 0.02 mol CO 2 {mol alk. The manual method of was used to regress two parameters of D Am and k parameters of Equation (3.14) for all reactions involving AMP for a total of ten parameters. 147

170 used. The same liquid film discretization, Table 3.1, as 2MPZ and PZ/HMPD was PZ/2MPZ Hydraulics Table 7.4: PZ/2MPZ hydraulic data Type N T Loading C Am Source ARD ( C) p mol CO 2 {mol alkq m % µ (Chen, 2011) N/A µ (Sherman et al., 2014) 6.3 µ , 5 (Rochelle et al., 2012b) 14 ρ (Freeman, 2011) 0.25 ρ (Freeman, 2011) 0.38 The available hydraulic data are listed in Table 7.4. The viscosity data of Chen (2011) were not fit as they were inconsistent with the data of Sherman et al. (2014). The data of Sherman et al. (2014) varied temperature, loading, and amine concentration, enabling the regression of all ten parameters of Equation (3.2). All density data of Freeman (2011) were fit using a modified form of Equation (3.4), wherein T was replaced throughout with ˆT T K. This centering at 40 C was affected to give the parameters more physical significance as a comparison of parameters for ρ or µ across models is currently not feasible. In short, 10 parameters were regressed with 48 data points for µ, while 8 were regressed with 42 data points for ρ. Both regressions were done by minimizing the sum of squared errors using the Solver tool in Excel. 148

171 Diffusivity The diffusion of CO 2 was modeled using Equation (3.6). While the same diffusion of amine-products correlation as Independence (Frailie, 2014) should have been used to avoid altering the PZ kinetics, the D Am parameters of Equation (3.7) were regressed Flowsheet The mass transfer regression was done using the flowsheet described in with the manual method described by The only difference being that no saturator calculator block was used. Using the data of Chen (2011), the greatest absorption and desorption fluxes for each loading and temperature were fit. This is a set of 32 points spanning 40 C to 100 C and mol CO 2 {mol alk to mol CO 2 {mol alk. The flux spanned mol {sec-m 2 to mol {sec-m 2 The loading was adjusted as described in Reaction Set Reactions were modeled as described in The reaction set is comprised of kinetic reactions, Equation (7.58) to Equation (7.67), and equilibrium reactions, 149

172 Equation (7.68) to Equation (7.71). 2 PZ CO 2 é PZCOO PZH (7.58) PZ 2MPZ CO 2 é PZCOO 2MPZH (7.59) 2 2MPZ CO 2 é 2MPZCOO 2MPZH (7.60) PZ 2MPZ CO 2 é 2MPZCOO PZH (7.61) 2 2MPZCOO CO 2 é 2MPZ COO 2 H2MPZCOO (7.62) 2 PZCOO CO 2 é PZ COO 2 HPZCOO (7.63) PZCOO 2MPZ CO 2 é PZ COO 2 2MPZH (7.64) PZCOO 2MPZCOO CO 2 é PZ COO 2 H2MPZCOO (7.65) 2MPZCOO CO 2 H 2 O é HCO 3 H2MPZCOO (7.66) PZCOO CO 2 H 2 O é HCO 3 HPZCOO (7.67) 2MPZCOO 2MPZH ô H2MPZCOO 2MPZ (7.68) 2MPZ HCO 3 ô 2MPZH CO2 3 (7.69) 2MPZ PZH ô 2MPZH PZ (7.70) PZCOO PZH ô HPZCOO PZ (7.71) Kinetic Parameter Regression All reactions without any 2MPZ species were left at the value of Independence (Frailie, 2014). Initially, all reactions without any PZ species were left at the regressed value of the 2MPZ model (Chapter 6); however, Equation (7.62) was later regressed. All reactions of PZ that were catalyzed by a PZ base and are now catalyzed by a 2MPZ base were left at the corresponding PZ value, viz. Equations (7.59), (7.62), and (7.65). E A of Equation (7.60) was assumed to be the same as Equation (7.58). After troubleshooting a process model absorber, two reactions were removed from the model in order to enable convergence. Equations (7.62) and (7.65) were removed due to the poor behavior of γ H2MP ZCOO. 150

173 For the 4 remaining kinetic reactions, k 0 and E A were regressed. In addition to these 8 parameters, the 3 parameters for D Am of Equation (3.7) were regressed for a total of 11 parameters. The liquid film discretization used was the same as that of 2MPZ, as shown in Table 3.1. This is different from the unreported discretization of PZ in Independence (Frailie, 2014), but this is expected to have no effect. 7.4 Thermodynamic Results and Discussion PZ/HMPD Eq. (7.17) model 9.50 Eq. (7.18) pk a T ( C) Figure 7.2: HMPD pk a predictions compared to data (Appendix G) (Ciftja, 2016). 151

174 The two pk a predictions, along with the model prediction are compared to experimental data in Figure 7.2. The model prediction was matched to the curve 8, aq labeled Equation (7.17) by setting the following parameters of HMPDH : Gf J 8, aq {kmol and Hf J {kmol. While the estimated and experimental slopes are similar, the estimated value is high by a half unit. This error is high for the method (Sumon et al., 2012), where the greatest error shown is for 1-methylpiperazine at 0.47 units. This error degrades the physical significance of the enrtl τ parameters, as they must correct for this incorrect equilibrium. However, this error does not preclude an acceptable thermodynamic (except for pk a ) and mass transfer model, as demonstrated by the Cinco de Mayo PZ model of Plaza (Plaza, 2011). The ARD is for the HMPD pk a is 3.4%. For the pk a temperature-dependence estimation, Perrin et al. recommended a P r 0.004, 0.004s (1981). For Equation (7.17), a with ARD=6.4% for MDEA. For Equation (7.18), a and C with ARD=0.65%. Nevertheless, the two predictions from Equation (7.17) and Equation (7.18) are within 2% of one another, as seen in Figure 7.2. Table 7.5: Regressed Parameters for P HMP D. A and B corresponed to H in Pa units. Parameter Value σ C HMP D, H2 O A HMP D, H2 O B HMP D, H2 O Figure 7.3 shows the amine volatility fit with the regressed parameters of Table 7.5. The ARD for the total pressure is 5.1%. There are a couple of systematic biases seen in Figure 7.3. At unloaded conditions, the amine partial pressure is overpredicted for all temperatures, and P HMP D is overpredicted at low loading and 152

175 1E+4 1E+3 P (Pa) 1E+2 1E+1 CO 2 HMPD PZ 1E+0 1E-1 60 C 50 C 40 C 1E loading (mol CO 2 /mol alk) Figure 7.3: P Am for 2 m PZ/3 m HMPD; lines are predictions; data (Du et al., 2016). underpredicted at high loading. The model systematically underpredicts the aqueous P HMP D data with an ARD of 45%. However, as P Am has no major impact on the process performance, these errors do not affect the model predictions except for amine loss. Figure 7.4 shows that the model is well behaved throughout the operational loading and temperature range. Due to more data at 40 C, the regression was naturally weighted towards that temperature. The regressed parameters are listed in Table 7.6. While the model represents the data well, the data are of lower quality than the rest of the data produced by the Rochelle group. The WWC was not operated according to Li (2015). The method used resulted in at least 1% greater error based on a reanalysis of 2PE data (Chen, 2011). In addition, the data analysis was flawed, leading to an additional 2% error, for a total of at least 3% additional error in P CO

176 5E C 5E+2 5E+1 40 C P CO2 (kpa) 5E+0 5E-1 5E-2 5E-3 loading adjusted loading adjusted WWC screening WWC FTIR prediction 5E loading (mol CO 2 /mol alk) Figure 7.4: VLE for 2 m PZ/3 m HMPD; predictions at 20 C intervals; data (Du et al., 2016); loading adjusted points of Table Table 7.6: Regressed Parameters for PZ/HMPD VLE Parameter Value σ C phmp DH, P ZCOO q{h 2 O C phmp DH, P ZCOO q{p Z C phmp DH, HCO 3 q{hp ZCOO

177 (The analysis by Du did not force the equilibrium partial pressure of CO 2 to go through the origin of the flux vs LMPD curve.) These errors were uncovered after the thermodynamic regression, so all regressions use the uncorrected values, which are presented in the figures. The corrected values were used in the mass transfer regression and are included in Appendix H. The high temperature total pressure data were collected without a functioning thermocouple, with temperature backcalculated from pressure, and with a potentially leaking apparatus. For this reason, they are excluded from the analysis. ΔH abs (kj/mol) C 40 C 60 C 80 C 100 C 120 C loading (mol CO 2 /mol alk) Figure 7.5: Differential H abs predictions for 2 m PZ/3 m HMPD at 20 C intervals as calculated by Equation (2.22) Predictions for H abs are shown in Figure 7.5. The behavior is reasonable. As expected, there are inflections at 0.30 mol CO 2 {mol alk where the dominant chemistry changes from PZ carbamate formation to bicarbonate and carbonate formation and 155

178 4.0 HCO HMPD HMPDH + m 2.0 PZ PZCOO HPZCOO 1.0 PZH + CO 3 2 CO loading (mol CO 2 /mol alk) Figure 7.6: Speciation predictions for 2 m PZ/3 m HMPD at 40 C at 0.68 mol CO 2 {mol alk where physical absorption of CO 2 occurs. The inflections correspond to the speciation shown in Figure 7.6. PZ (pk a 9.35 at 40 C (Hamborg and Versteeg, 2009)) is a stronger base than HMPD (pk a 8.85 at 40 C), however HMPD is preferentially used as a base as the formation of PZ carbamate is more stable. It is surprising that carbonate is formed rather than PZ dicarbamate. The lack of PZ dicarbamate can be explained from Figure 7.7. γ P ZpCOO q 2 is an order of magnitude greater than any other species. This is a modeling artifact, and so the lack of PZ dicarbamate in Figure 7.6 is also an artifact. The other activity coefficients look reasonable. An examination of γ CO2 shows that as temperature increases, γ CO2 decreases. and as loading increases, γ CO2 increases. The smooth behavior of γ CO2 as a function of loading is essential for reliable kinetic calculations. 156

179 PZCOO 2 1E+2 1E+1 PZ γ 1E+0 HPZCOO CO 2 HMPD PZCOO 1E-1 HCO 3 HMPDH + PZH + CO 3 2 1E loading (mol CO 2 /mol alk) Figure 7.7: γ i predictions for 2 m PZ/3 m HMPD at 40 C In addition to the data quality concerns, the mole fraction of total HMPD is greater than that of total PZ in 2 m PZ/3 m HMPD. Having PZ as the minor component means that the overall thermodynamic behavior is dictated by HMPD, and having skipped the regression of aqueous HMPD, model results should be viewed cautiously PZ/AMP The thermodynamic results for implementing AMP carbamate are discussed in Luckily, there is very little AMP carbamate, so aside from speciation all other thermodynamic properties are as reported by Li et al. (2014). The reader is referred there for the regressed parameters and select thermodynamic results. To supplement those results, additional results are presented here for VLE, differential 157

180 heat of absorption, speciation, and activity coefficients for 2 m PZ/4 m AMP. Only this concentration will be discussed as that is the concentration of mass transfer data fit. 1E+4 1E+3 P CO2 (kpa) 1E+2 1E+1 1E+0 1E-1 1E loading (mol CO 2 /mol alk) Figure 7.8: VLE for 2 m PZ/4 m AMP; lines are model predictions at 20 C intervals; are WWC data (Li et al., 2013a), are total pressure data (Rochelle et al., 2012a), and are loading adjusted points of Table Figure 7.8 compares the predicted VLE to data. The model is well behaved except for where the loading is greater than 0.65 mol CO 2 {mol alk and the temperature is between 20 C and 60 C. Here the isotherms nearly touch, indicating nearly zero heat of absorption. This looks to be a model artifact. The fit of the data shows no bias towards over- or under-prediction. 158

181 C 40 C 60 C 80 C 100 C 120 C H abs kj mol loading (mol CO 2 /mol alk) Figure 7.9: Differential H abs predictions for 2 m PZ/4 m AMP at 20 C intervals as calculated by Equation (2.22) The predicted differential heat of absorption is plotted in Figure 7.9. This plot seems to exhibit three surprising phenomena. First, the magnitude is very great at loading below 0.25 mol CO 2 {mol alk. For comparison, at 40 C and a loading of 0.05 mol CO 2 {mol alk, H abs is 82 kj {mol CO 2 for 2 m PZ/7 m MDEA (Frailie, 2014), while Figure 7.9 shows a value of 111 kj {mol CO 2. This is greater than the heat of absorption observed in MEA (Plaza, 2011), which is counter-intuitive. Second, there is no inflection when the dominant reaction changes at 0.40 mol CO 2 {mol alk. This inflection is seen with 5 m PZ/2.3 m AMP (Li et al., 2014) as well as 2 m PZ/7 m MDEA (Frailie, 2014). Third, the loading dependence seems extreme com- 159

182 pared to other blend solvents. However, across the operational loading range, the slopes for 2 m PZ/4 m AMP and 2 m PZ/7 m MDEA are nearly the same 114 kj-mol alk {mol-mol CO 2 and 113 kj-mol alk {mol-mol CO 2 (Frailie, 2014). Lastly, as expected, H abs drops to nearly zero for the 20 C isotherm at 0.66 mol CO 2 {mol alk. The maximum at 0.35 mol CO 2 {mol alk for 20 C is unexpected and does not make physical sense. This is an illustrative example of how H abs is a good diagnostic test of VLE predictions. 4.0 AMP AMP+ AMPCOO PZ(COO )₂ CO₂ HCO₃ PZ PZH+ PZCOO +HPZCOO CO₃ ² 3.0 m loading (mol CO 2 /mol alk) Figure 7.10: Speciation predictions for 2 m PZ/4 m AMP at 40 C The predicted solvent speciation is shown in Figure The model of Li et al. (Li et al., 2014) incorporated NMR data, however the AMP carbamate peak (δ 164 ppm for 13 C) was overlooked (Rochelle et al., 2012a). At 40 C, the pk a 160

183 of AMP is 9.26 (Kim et al., 2011), which is very close to that of PZ at 9.39 (Khalili et al., 2009). Therefore, while PZ is a better base, PZ is preferentially utilized as a means of forming carbamate due to its lack of hindrance. While it is impossible to distinguish in Figure 7.10, AMP does form carbamate on the order of 0.01 m in the blend. As was discussed when considering the heat of absorption, as the loading increases, the system chemistry shifts from a regime dominated by the formation of PZ carbamate to a regime dominated by the formation of bicarbonate and PZ dicarbamate. While it is possible that the heats of reaction are equal in these two regimes, it is highly unlikely. Therefore, it is strange that no inflection is seen in Figure 7.9. About 0.34 m of carbonate forms primarily at low loading, which is more than expected and more than 2 m PZ/7 m MDEA as well as at a lower loading. The activity coefficients span a large range as shown in Figure Most of the species behave non-monotonically. However, this behavior is less problematic than at first glance. For instance, γ P Z increases steeply after 0.50 mol CO 2 {mol alk, however at this point no free PZ is present in the solvent. Therefore, it has no effect. At 0.05 mol CO 2 {mol alk, multiple species exhibit a strange minimum. This has an imperceptible effect on the speciation at 40 C, but above 60 C it is noticeable in the speciation behavior of PZH. However, this low loading is outside of the operating range of the system, so again it is not problematic. As γ CO2 is especially important to the kinetics, it is examined across a range of temperatures in Figure The expected behavior is γ CO2 decreasing with temperature and increasing with loading. Here, the temperature and loading behavior is non-monotonic. WWC data spans 20 C to 100 C, so the two highest T isotherms can be ignored. Looking at the remaining curves, even though the behavior is not correct, γ CO2 falls in a tight range of values. Therefore, these ill behaviors can be overcome. The errors in γ CO2 are folded into the regressed mass transfer parame- 161

184 1.E+01 1.E+00 AMP AMP+ AMPCOO PZ(COO )₂ CO₂ HCO₃ PZ PZH+ PZCOO +HPZCOO CO₃ ² γ 1.E-01 1.E-02 1.E loading (mol CO 2 /mol alk) Figure 7.11: γ i predictions for 2 m PZ/4 m AMP at 40 C ters, and because the value range is tight, this should have a minimal effect on the parameter values PZ/2MPZ As the amine volatility data were not regressed, the NRTL parameters for PZ/2MPZ were all set to 0 except for α 0.3, meaning that the two molecules do not interact with each other. Parameters regressed to fit the VLE data of Table 7.2 are listed in Table 7.7. The parameters are all C ca, m of Equation (2.7), rather than any of the C m, ca terms of 162

185 C 40 C 60 C 80 C 100 C 120 C 140 C γ CO loading (mol CO 2 /mol alk) Figure 7.12: γ CO2 predictions for 2 m PZ/4 m AMP at 20 C increments Equation (2.8). The default for C ca,h2 O is 4, and two out of the three parameters are close to the default. C p2mp ZH, P ZpCOO q 2 q{h 2 O also has little statistical significance. However, efforts to eliminate this term degraded the fit. The default for C ca, HPZCOO is 4. Of the two parameters with HPZCOO, one is close to zero with a standard deviation larger than its value. Again, efforts to eliminate this term degraded the fit. Lastly, the default for the 2MPZ model of Chen (2011) followed the old Aspen Plus convention, wherein C ca, m 8 and C m, ca 15. The default for C ca, H2MPZCOO is 8, which is different from the analogous PZ species. 163

186 Table 7.7: C ca, m parameters for 4 m PZ/4 m 2MPZ Species Value σ (2MPZH, PZ COO 2)/ H2MPZCOO (2MPZH, PZCOO )/ H2MPZCOO (PZH, HCO 3 )/ H2MPZCOO (2MPZH, HCO 3 )/ HPZCOO (PZH, 2MPZCOO )/H 2 O (2MPZH, PZCOO )/H 2 O (2MPZH, PZ COO 2)/H 2O (2MPZH, PZCOO )/ HPZCOO The ARD for the individual VLE data sets is given in Table 7.2 while the overall ARD is 1.6%. While the data points are well matched, the model behavior is suboptimal as seen in Figure There should be no inflection point until the rich loading where the chemistry changes, however, there is an inflection at 0.26 mol CO 2 {mol alk. As H abs is proportional to the spacing between isotherms, when the 20 C and 40 C curves touch above 0.45 mol CO 2 {mol alk, this implies that H abs 0. Nevertheless, these errors do not invalidate using the model at operating conditions but make higher loading extrapolation suspect. While the inflection at 0.26 mol CO 2 {mol alk is difficult to spot in Figure 7.13, its effect is easy to see in Figure 7.14, where the 20 C and 40 C curves dip at the same loading. This illustrates the diagnostic utility of the H abs plot. In addition to the dip, the high loading behavior of H abs for the same two temperatures is likely an artifact. The behavior elsewhere is reasonable. The temperature dependence shows 10 kj {mol difference between 20 C and 140 C, which is similar to that of 8 m 2MPZ (Chen, 2011) and half that of 8 m PZ (Frailie, 2014). The inflection and decrease at 0.40 mol CO 2 {mol alk corresponds with the shift from carbamate-dominated chemistry to bicarbonate-dominated chemistry. 164

187 1.E+07 1.E+06 1.E C P CO2 (Pa) 1.E+04 1.E+03 1.E+02 1.E+01 WWC total pressure prediction adjusted loading 1.E loading (mol CO 2 /mol alk) Figure 7.13: VLE for 4 m PZ/4 m 2MPZ with model predictions at 20 C intervals; (Chen, 2011); (Xu, 2011) Figure 7.15 shows the chemistry shift comes at 0.40 mol CO 2 {mol alk as the free amine is depleted. While the system is equimolar, PZ is depleted more quickly than 2MPZ. This could be due to the greater basicity of PZ, as at 40 C the pk a of PZ is 0.23 greater than that of 2MPZ (Khalili et al., 2009). It could also be due to the greater carbamate stability of PZ. The greater carbamate stability explains the preference for PZ dicarbamate over 2MPZ dicarbamate. From 0.45 mol CO 2 {mol alk on the amount of protonated amine increases, which is not observed in either the PZ or 2MPZ systems (Frailie, 2014; Chen, 2011). For PZ, the total carbamate is being converted into bicarbonate, zwitterion, and protonated amine. Similarly, for 2MPZ 165

188 C 40 C 60 C 80 C 100 C 120 C 140 C ΔH abs (kj/mol) loading (mol CO 2 /mol alk) Figure 7.14: Differential H abs predictions for 4 m PZ/4 m 2MPZ at 20 C intervals as calculated by Equation (2.22) the total carbamate is converted to bicarbonate and protonated amine, while the zwitterion is converted back to protonated amine and bicarbonate as well as some free CO 2. While Figure 7.15 shows the molality of species at equilibrium, the kinetics depend on the activities of species. Figure 7.16 gives the other half of the story and helps to explain some of the phenomena observed in Figure Considering first the general trends, as loading increases the ionic strength of the solvent increases, salting in ions and salting out molecules. Thence, as loading increases γ decreases for ions but increases for molecules. While γ of the molecules is mono- 166

189 m 4 3 2MPZ 2MPZH+ 2MPZCOO 2MPZ(COO )₂ H2MPZCOO HCO₃ CO₂ PZ PZH+ PZCOO PZ(COO )₂ HPZCOO CO₃² loading (mol CO 2 /mol alk) Figure 7.15: Speciation predictions for 4 m PZ/4 m 2MPZ at 40 C tonic, γ of some of the ions is non-monotonic. Now considering the details, there is a marked difference between H2MPZCOO and HPZCOO. H2MPZCOO is much more non-ideal than HPZCOO. This difference seems larger than would be expected and precluded convergence of an absorber process model. For this reason, two reactions involving H2MPZCOO were excised as mentioned in That γ 2MPZpCOO q γ CO excised. is unexpected, and the only reaction involving it was also Table 7.8 shows the parameters set to produce the desired behavior of γ CO2 seen in Figure As expected, γ CO2 increases exponentially with loading and de- 167

190 1E+2 1E+1 2MPZ 2MPZH+ 2MPZCOO 2MPZ(COO )₂ H2MPZCOO HCO₃ CO₂ PZ PZH+ PZCOO PZ(COO )₂ HPZCOO CO₃² γ 1E+0 1E-1 1E-2 1E loading (mol CO 2 /mol alk) Figure 7.16: γ i predictions for 4 m PZ/4 m 2MPZ at 40 C crease with temperature. γ CO2 is used throughout the activity-based kinetics, and so its behavior plays a role in the physical significance of the mass transfer parameters. For this reason, the behavior at the WWC data conditions is most important, and while γ CO2 is non-monotonic, the overall trend is acceptable. 168

191 Table 7.8: D ca, CO2 parameters for 4 m PZ/4 m 2MPZ Species Value (2MPZH, PZ COO 2 )/CO (PZH, 2MPZCOO )/CO C 2.0 γ 140 C loading (mol CO 2 /mol alk) Figure 7.17: γ CO2 predictions for 4 m PZ/4 m 2MPZ at 20 C intervals 169

192 7.5 Mass Transfer Results and Discussion PZ/HMPD C ρ kg m C 140 C loading (mol CO 2 /mol alk) Figure 7.18: 2 m PZ/3 m HMPD density predictions at 20 C intervals Figure 7.18 and Figure 7.19 show the hydraulics are well behaved. The viscosity fit for blends of 5 m PZ/5 m HMPD, 5 m PZ/2 m HMPD, and 4 m PZ/2 m HMPD has an ARD of 6.3%, while the fit for 2 m PZ/3 m HMPD has an ARD of 9.7% for a combined ARD of 4.7%. Table 7.9 lists the regressed parameters. Figure 7.19 shows that predictions at certain loadings are unusually high, such as the highest loading point, while others are unusually low the two points at 0.43 mol CO 2 {mol alk and 0.47 mol CO 2{mol alk. This excessive variability is due to the lack of triplicates and changes 170

193 1E+1 40 C μ (cp) 1E C 100 C 1E loading (mol CO 2 /mol alk) Figure 7.19: 2 m PZ/3 m HMPD viscosity predictions at 20 C intervals; s were not fit; open and filled points indicate different runs by Du (2016). to the experimental method made despite the claim of Du et al. (Du et al., 2016) to have used the method of Freeman (2011). The regressed kinetic parameters are listed in Table k P Z HMP D and k P ZCOO HMP D have the same E A as their k 0 s were ratioed. No statistics are available as the manual method was used. The adjusted loading used in the regression is reported in Table The largest adjustments are the 100 C point and the leanest 20 C point. 171

194 C 40 C 60 C 80 C 100 C reproducibility bounds CO2 N CO loading (mol CO 2 /mol alk) Figure 7.20: 2 m PZ/3 m HMPD flux ratioed to data (Du et al., 2016) 1.25 reproducibility bound CO2 N CO reproducibility bound T ( C) Figure 7.21: 2 m PZ/3 m HMPD predicted flux ratioed to data (Du et al., 2016) 172

195 Table 7.9: Viscosity parameters of Equation (3.2) where Am 1 HMPD and Am 2 PZ Parameter Value SE Parameter Value SE a f b g c h d 0.00 i e j Table 7.10: 2 m PZ/3 m HMPD regressed kinetic parameters. k Equation k 0 kmol sec m 3 E A kj mol Method k HMP D (7.39) (Ko and Li, 2000) k P ZCOO HMP D (7.40) ratioed k P Z HMP D (7.41) regressed The fit of the flux data is plotted against loading in Figure 7.20 and against temperature in Figure The negative trend with increasing loading indicates that the carbamate reaction rate is overpredicted, while the bicarbonate reaction rate is underpredicted. The underprediction of flux at 60 C and 80 C indicates a systematic bias when diffusion becomes important. That the bicarbonate reaction rate is underpredicted is surprising, as the incorrect pk a used resulted in an estimated k 0 that is 64% greater than the correct pk a would yield. The predicted kg 1 is compared to data in Figure The general trend with T follows the experimental result. The 20 C and 40 C curves show a much stronger dependence at low P CO 2 than the other curves. kg 1 at these two temperatures is controlled by the reaction rate and at low P CO 2 the equilibrium concentrations of carbamate and bicarbonate have not yet peaked, so the total uptake of CO 2 is limited. 173

196 Table 7.11: Loading adjustment for 2 m PZ/3 m HMPD; data are Du et al. (2016) T loading relative T loading relative exp. adj. adj. exp. adj. adj. ( C) p mol CO 2 {mol alkq (%) ( C) p mol CO 2 {mol alkq (%) k g mol sec Pa m 2 1E-6 60 C 20 C points are reanalyzed data (Du et al., 2016) lines are predictions 40 C 20 C 40 C 60 C 80 C 100 C 100 C 80 C 1E-7 1E+2 1E+3 1E+4 P CO2 (Pa) Figure 7.22: 2 m PZ/3 m HMPD k 1 g compared to reanalyzed data (Du et al., 2016) 174

197 k 1 g would have been overpredicted at 80 C and 100 C due to the excessive D Am, but the low bicarbonate reaction rate causes the two errors to cancel out. Figure 7.22 plots the reanalyzed data of Du (2016). Du used the average of reported values for K g instead of the slope of the curve flux vs LMPD curve. Correcting this error and the incorrect P CO 2 resulted in differences up to 14% in the reported k 1 g values. (For other blends of PZ/HMPD the error is up to 49%.) The reanaylzed data are included in Appendix H PZ/AMP Table 7.12: 2 m PZ/4 m AMP viscosity parameters for Equation (3.2) where Am 1 AMP and Am 2 PZ Parameter Value Parameter Value a f 5.40 b g c h 1.74 d i e 1.20 j 3.71 Considering first the hydraulic fit, the viscosity correlation uses the ten parameters listed in Table The ARD for the individual regressed data sets is given in Table 7.3 with the overall ARD being 7.2%. The Fu et al. (2014) data were not published at the time of regression, but comparison to the regressed data indicates that the data are of sufficient quality for fitting. The fit for 2 m PZ/4 m AMP is shown in Figure Considering the data first, the high degree of scatter in the 80 C data is due to an inherent limitation of the experimental method. As the sample is neither sealed nor back-pressured, the CO 2 bubbles out of solution and shifts the loading during the course of the measurement. Now considering the fit, the data are underpredicted at 20 C and overpredicted at 40 C and 60 C. Fortunately, the bias 175

198 Li in (Rochelle et al., 2012a) prediction 5 µ (cp) loading (mol CO 2 /mol alk) Figure 7.23: 2 m PZ/4 m AMP viscosity at 20 C intervals is not great, but it is systematic and therefore affects the mass transfer regression results through D Am. Table 7.13: 2 m PZ/4 m AMP density parameters for the modified Equation (3.4) where Am 1 AMP and Am 2 PZ Parameter Value Parameter Value a 2.00 d b e 2.00 c f The density correlation uses the six parameters listed in Table The ARD for the individual data sets is given in Table 7.3 with the overall ARD being 0.38%. This goodness of fit is not meaningful as all the data fit were unloaded, rather the 176

199 1100 ρ kg m loading (mol CO 2 /mol alk) Figure 7.24: 2 m PZ/4 m AMP density predictions at 20 C intervals better test if the representation of density for 2 m PZ/4 m AMP shown in Figure The fit behaves as expected with mild wavering at temperatures 100 C. The rate constant values are listed in Table (Note there is an inconsistency in the k P ZCOO reactions as the forward reaction T ref is K, but the reverse is K.) Three k s have E A 10 kj {mol, which is surprisingly low. As this regression was done before the work on AMP in Chapter 5, the values for k AMP and k AMP AMP do not match the values used in the AMP model. k 0 of k AMP here is an order of magnitude greater and has an E A that is one fifth of the value for the AMP model. k 0 of k AMP AMP here is three orders of magnitude greater with roughly the same E A. k 0 of k AMP AMP and k P Z AMP are both unreasonably high. To show the relative contribution of each reaction, the net forward rate was computed using equilibrium activities. Figure 7.25 shows that CO 2 flux is due to 177

200 Table 7.14: 2 m PZ/4 m AMP kinetic parameters with T ref K;* denotes T ref K k Reaction k 0 E A Source p kmol {sec-m 3 q p kj {molq k P Z AMP (7.50) regressed k AMP AMP (7.53) regressed k P Z P Z (7.51) (Frailie, 2014) k P ZCOO P ZCOO (7.52) (Frailie, 2014) k P ZCOO AMP (7.49) regressed k AMP (7.48) regressed k P ZCOO (7.54) * 49.0 (Frailie, 2014) 1E+2 k AMP AMP 1E+1 k PZ AMP k PZCOO AMP r CO2 kmol sec m 3 1E+0 1E-1 k AMP 1E-2 k PZ PZ 1E loading (mol CO 2 /mol alk) Figure 7.25: 2 m PZ/4 m AMP net forward rate at 40 C 178

201 reactions involving AMP, in particular the formation of AMP carbamate catalyzed by AMP. Table 7.15: 2 m PZ/4 m AMP D Am parameters of Equation (3.7) alongside others Parameter 2 m PZ/ 4 m PZ/ PZ/ 8 m 2MPZ Units 4 m AMP 4 m 2MPZ MDEA Source this work this work (Frailie, 2014) Chapter 6 D m 2 {sec α β T ref K µ ref Pa-sec The diffusion parameters for this solvent are compared to other solvents in Table As the blend model parameters are neither the AMP model values nor the PZ model values, the blend model does not reduce down properly. This degrades the extrapolation capability of the model but does not invalidate conclusions drawn at the regressed conditions presented here. This also does not preclude using the model for process modeling. The loading adjustments are listed in Table 7.16 and shown in Figure 7.8. The model fit of the VLE is not exceptionally tight, and therefore model error is dominant in the 60 C data. The fit of the CO 2 flux data shown in Figure 7.26 is poor. There is a positive bias with increasing loading, and the errors are large. Examining the same data plotted against T in Figure 7.27 shows no systematic bias and elucidates that worst fit data are the 20 C data. 179

202 Table 7.16: Loading adjustment for 2 m PZ/4 m AMP; data are Li et al. (2013a). T loading relative T loading relative exp. adj. difference exp. adj. difference ( C) p mol CO 2 {mol alkq (%) ( C) p mol CO 2 {mol alkq (%) C 40 C 60 C 80 C 100 C solid is absorption open is desorption reproducibility bound CO2 N CO loading (mol CO 2 /mol alk) Figure 7.26: 2 m PZ/4 m AMP predicted flux ratioed to data (Rochelle et al., 2012a) 180

203 2.0 solid is absorption open is desorption 1.5 CO2 N CO T ( C) Figure 7.27: 2 m PZ/4 m AMP flux ratioed to data of Li (Rochelle et al., 2012a) PZ/2MPZ Table 7.17: 4 m PZ/4 m 2MPZ viscosity parameters for Equation (3.2) where Am 1 2MP Z and Am 2 P Z Parameter Value Parameter Value a 6.43 f b 5.43 g c 46.0 h 29.9 d 10.1 i e 340 j 2.72 The viscosity parameters for Equation (3.2) are listed in Table No statistics are available due to the use of Solver, nevertheless the significance of these parameters is of less interest than achieving a tight fit of the data. The ARD for the 181

204 C 50 C 40 C µ (cp) 60 C C loading (mol CO 2 /mol alk) Figure 7.28: 4 m PZ/4 m 2MPZ viscosity predictions at 20 C intervals; regressed (Sherman et al., 2014); not regressed with reported loading 2 (Chen, 2011) individual sets is listed in Table 7.4, and the overall ARD is 7.7%. The fit is well behaved and matches the data best at 40 C. The density parameters for Equation (3.4) are listed in Table Again, no statistics are available due to the use of Solver. The ARD for individual data sets is given in Table 7.4 with the overall ARD being 0.32%. The fit for 4 m PZ/4 m 2MPZ is shown in Figure The fit is well behaved, and shows that the second data point is biased high, indicating that the loading may be greater than that reported. 182

205 Table 7.18: 4 m PZ/4 m 2MPZ density parameters for the modified Equation (3.4) where Am 1 2MP Z and Am 2 P Z Parameter Value Parameter Value a 2.90 e 2.06 b f c 2.90 g 6.47 d h Table 7.19: 4 m PZ/4 m 2MPZ regressed kinetic parameters k Equation k 0 E A Source p kmol {sec-m 3 q p kj {molq k P Z P Z (7.58) (Frailie, 2014) k P Z 2MP Z (7.59) =Eq. (7.58) k 2MP Z 2MP Z (7.60) Chapter 6 k 2MP Z P Z (7.61) regressed k 2P ZCOO P ZCOO (7.63) (Frailie, 2014) k P ZCOO 2MP Z (7.64) regressed k 2MP ZCOO (7.66) Chapter 6 k P ZCOO (7.67) (Frailie, 2014) The regressed kinetic parameters are listed in Table As expected, the two bicarbonate reactions are the slowest. E A for Equation (7.66) is double that of the expected value. At the other extreme, Equation (7.61) is very low. The low E A coupled with the high k 0 suggests that these parameters were used to fit 40 C data, as it is unexpected that 2MPZ would form carbamate at 4 times the rate of the corresponding PZ reaction (Equation (7.58)). The diffusion parameters are compared to the single amine values in Table As the blend model parameters are neither the same as the 2MPZ model nor the PZ values, the model does not reduce down to either extreme. This degrades 183

206 C C ρ kg m loading (mol CO 2 /mol alk) Figure 7.29: 4 m PZ/4 m 2MPZ density predictions at 20 C intervals compared to data (Freeman, 2011). the extrapolation capability of the model but does not invalidate conclusions drawn at the regressed conditions presented here. The loading adjustments listed in Table 7.21 and shown in Figure 7.13 differentiate the sources of adjustment between model and experimental error. While the 60 C VLE is well matched by the model, meaning little model error, most of the loadings are adjusted down in response to experimental error. The mass transfer fit is shown in Figure 7.30 and Figure Looking first at the trend with loading in Figure 7.30, there is a clear bias towards underprediction 184

207 1.00 CO2 N CO open points are desorption filled points are absorption dashed lines bound reproducability region 40 C 60 C 80 C 100 C loading (mol CO 2 /mol alk) Figure 7.30: 4 m PZ/4 m 2MPZ flux ratioed to data (Chen, 2011) CO2 N CO open points are desorption filled points are absorption dashed lines bound reproducability region T ( C) Figure 7.31: 4 m PZ/4 m 2MPZ flux ratioed to data (Chen, 2011). 185

208 Table 7.20: 4 m PZ/4 m 2MPZ D Am parameters of Equation (3.7) compared to 2MPZ (Chapter 6) and PZ (Frailie, 2014). Parameter 4 m PZ/4 m 2MPZ PZ 2MPZ Units D m 2 {sec α β T ref K µ ref Pa-sec Table 7.21: Loading adjustment for 4 m PZ/4 m 2MPZ; data are Chen (2011) T loading relative T loading relative exp. adj. difference exp. adj. difference ( C) p mol CO 2 {mol alkq (%) ( C) p mol CO 2 {mol alkq (%) at increasing loading. This underprediction is due to the removal of (7.62) and Equation (7.65) after regression was complete. The fit before this removal is discussed by Sherman et al. (2014). Back to Figure 7.30, the desorption flux ratios tend to be greater than the absorption flux ratios. This could be an artifact of not using the saturator calculator block discussed in This saturator block was created to avoid CO 2 being absorbed by the water in the saturator, resulting in less CO 2 in the gas stream in the WWC. This would decrease the driving force for absorption, while increasing the driving force for desorption. However, this phenomena is muddled in the fit shown by Sherman et al. (2014). 186

209 Turning to the trend with temperature in Figure 7.31, there is a clear bias towards underprediction at low temperature. Again, this bias results from the removal of H2MPZCOO. These reactions had a strong effect at 40 C and a low E A, meaning they were much less significant at high temperature. The 4 m 2MPZ/4 m PZ model is not recommended for process modeling because of its poor mass transfer fit. 7.6 Conclusions While the detrimental effects of non-physically significant parameters are localized in a single amine model, when that model is incorporated into a blend amine model, these effects become systemic in both the thermodynamic and the mass transfer model. The interaction parameters compensate for thermodynamic misfitting, while the diffusion of amine D Am compensates for mass transfer misfitting. In a blend model, D Am is no longer able to compensate, and so the blend model kinetics are not well fit. For the 2MPZ/PZ model, the 2MPZ kinetic rate constants compensated for poorly behaved 2MPZ activity-coefficients, but this compensation did not work in a process absorber model for the blend. For PZ blended with HMPD, AMP, and 2MPZ, the regressed interaction parameters are primarily salt-molecule the temperature-independent term of τ ca, m with m=h 2 O or =zwitterion. Future work for these blends include the regression of a second set of wettedwall column mass transfer data for AMP/PZ, which would test the physical significance of the current mass transfer parameters. The diffusion subroutine should be modified in blend models to differentiate between the different amines and apply their respective diffusion coefficients, if data is sufficient to not assume that the amines diffuse at half the rate of CO 2. Amine concentration should be optimized by 187

210 calculating the viscosity-normalized capacity, k 1 g, and heat of absorption for each of the blends as was done by Frailie (Frailie, 2014). 7.7 Supporting Information Table 7.22: User defined HMPD and HMPDH scalar pure component properties where MDEA is from Frailie (2014) and PCES used the Benson method Parameter Units HMPD Source HMPDH Source DGFORM J {kmol PCES 0 default DHFORM J {kmol PCES 0 default DGAQFM J {kmol 0 default reg. DHAQFM J {kmol 0 default reg. OMEGA J {kmol MDEA default PC N {m MDEA default RKTZRA MDEA 0.25 default TC K 675 MDEA default VC m 3 {kmol MDEA default ZC MDEA 0.26 default 188

211 Chapter 8 Thermodynamic Modeling Generalizations 8.1 Introduction Over the years, the Rochelle group has authored many different thermodynamic models for amine scrubbing. Each model involved a significant investment of time and effort to fit the data. While the time and effort has been reduced by leveraging knowledge from prior models in the form of heuristics, a comprehensive study of extant models has never been done to enhance the physical understanding of the model parameters, especially the binary interaction parameters τ i, j. Prior work (Austgen et al., 1989; Bollas et al., 2008) has stated that these parameters are semi-empirical and have little physical significance for multicomponent systems. The original work (Chen, 1980; Chen et al., 1982) on enrtl development showed that there was some physical significance to the interaction parameters in binary systems. Therefore, there should be physical significance in the interaction parameters for a multicomponent system too. Currently, regression is done without understanding the physical significance through a process of heuristics and trial and error, as described in 2.2. As the regression process is not systematic, there have been problems with regressing too many parameters (overfitting) and using correlated parameters to compensate for a misregressed parameter (parameter compensation) as discussed in Chapter

212 By studying enrtl models of amine solvents, the physical understanding of the interaction parameters is enhanced. The available models are validated by checking the pk a at 25 C is against the experimental value. This property was chosen as the pk a is the single most important parameter shaping the VLE (Li, 2015), and the interaction parameters are used to fit the VLE. Thus, errors in fitting the pk a would be compensated by using the interaction parameters, which would degrade the physical significance of said parameters. This check expanded into developing a means to analytically fit the pk a at 25 C. The interaction parameters are used to determine which are the most significant, what are the best default values, and to search for a physical meaning. As an aside, the simplified stoichiometric model (SSM) of Li (Li, 2015) was compared to the models used in this work in order to validate the SSM. 8.2 Methods Model Validation To make this study tractable, the scope is restricted to thermodynamic models of single amine solvents, not blends. Based on the enrtl framework, thermodynamic models of blend amine solvents should follow the same rules observed here, although the treatment of the amines as Henry s components or not would have an impact due to the mixed-solvent reference state versus aqueous reference state. The models used in this study included those developed by the Rochelle group as well as the ELECNRTL and ENRTL-RK models (both V8.4) for acid gas treating developed by Aspen Technology. As the two sets of Aspen Tech. models have documentation sharing the same name and publication date, the bibliography differentiates them by appending ELECNRTL and ENRTL-RK to the entries. In later tables, * is used to denote the ENRTL-RK models. 190

213 Both the ELECNRTL and ENRTL-RK models use the enrtl thermodynamic framework. The chief difference is ENRTL-RK reduces to the NRTL formulation properly, while ELECNRTL does not (Aspen Technology, 2010). ELECNRTL has been maintained since V7.2 for compatibility purposes only. Additionally, ELECNRTL has separate routines to calculate the activity coefficient, the Gibbs free energy, and the enthalpy, whereas ENRTL-RK uses one routine for all three. As the binary interaction parameters τ i, j could be compensating for poor model parameters elsewhere, all models needed to be validated prior to study. The Rochelle group models have all received a high level of validation through at least process modeling and in many cases pilot plant data reconciliation (Zhang et al., 2009; Sachde et al., 2013). The level of validation for the Aspen Tech. models is unknown. While each Aspen Tech. model has an accompanying manual, the manuals fail to provide enough information to validate the model. As the pk a is the single most important parameter shaping the VLE (Li, 2015) and τ i, j is used to fit the VLE and has also been shown to correlate with pk a in binary component systems (Chen et al., 1982), checking the pk a is a quick way to test the quality of the thermodynamic model and avoid artificial influences on τ i, j. It is possible to have a thermodynamic model that fits all other properties except pk a and by extension ph, as the correlated τ i, j parameters can compensate for the misregressed parameters. The Cinco de Mayo model of Plaza (2011) exemplifies this. In this work, the pk a of HMPD (Chapter 7) is also offset and therefore its τ i, j parameters are expected to be compensating for the misfit. The pk a was computed by Equation (2.16) for cases where the amine is defined as a Henry s component. This makes the amine a solute with an asymmetric, ideal gas reference state. If the amine is not a Henry s component, then the amine is a solvent with an symmetric, aqueous reference state. Therefore, an additional correc- 191

214 tion is needed to compare to the experimental asymmetric, molality-based value. This difference in amine reference state does not impact the τ i, j values. Equation (8.1) was used for these cases, pk a log ¹ i a ν i i 1000 log MW H2 O 8, aq log γam (8.1) 8, aq where log γam is calculated from the NRTL binary interaction parameters by Equation (8.2) 8, aq log γam τ H 2 O Am τ Am H2 O exp ατ Am H2 O (8.2) pk a Prediction The pk a was derived from the equilibrium constant K a of either Equation (8.3) or Equation (8.4). AmH K a ðñ Am H (8.3) AmH H 2 O Ka ðñ Am H 3 O (8.4) K a like any other equilibrium constant is defined by Equation (8.5), ¹ K a a ν i Gr i exp RT i (8.5) where ν is the stoichiometric coefficient, i is a component, and G r is the change in Gibbs free energy of the reaction defined as G r ± i Gν i f, i. pk a Throughout this work and in all preceding models of the Rochelle group, the has been computed using ± i aν i i in , the pk a was fit by adjusting G f, AmH as shown in Equation (2.16). As described (DGAQFM) to match the 25 C point, and then the temperature dependence was matched by adjusting H f, AmH (DHAQFM). 192

215 G f, AmH However, no regression is necessary. Once G f, Am (DGFORM) is set, then (DGAQFM) can be set using Equation (8.5). As proof, this was done for many different models. To compute G r, all G f must be at the same condition of 8, aq infinite dilution in water; hence, Gf was computed. For an amine defined as a Henry s component, Aspen Plus uses Henry s law (HENRY) to convert from the ideal gas reference state to the aqueous infinite dilution 8, aq reference state. Hence, Gf, Am is defined for a Henry s component by Equation (8.6), G 8,aq f, Am Gig f, Am RT ln H Am, H 2 O P ref (8.6) where G ig f, Am is the Gibbs free energy of formation (DGFORM) for an ideal gas at 25 C and 1 atm, P ref is the reference pressure (also 1 atm), and H Am, H2 O is the Henry s constant for the amine in water. (Recall the Henry s constant reference state is infinite dilution in water, no mixed-solvent.) H Am, H2 O is calculated by Equation (8.7), H i, j a i, j b i, j T c i, j ln T d i, j T e i, j T 2 (8.7) where a e are parameters (HENRY), and T is in absolute units. 8, aq Gf for the ions needed no conversion as their reference state is infinite dilution in water in the asymmetric convention, therefore DGAQFM was used directly. Applying the definition of pk a as log K a to Equation (8.5), the pk a at 25 C was calculated by Equation (8.8), Gr pk a log RT 1000 log MW H2 O (8.8) where the second term is a correction from the Aspen Plus mole fraction basis to the experimental molality basis. As both the model and the experimental data are on an asymmetric basis, no other conversion is necessary. If the amine is not a Henry s component, an additional conversion is necessary (Equation (8.1)). 193

216 To check the validity of this approach, the pk a for various amines was computed using both the activities, as in Equation (2.16), and the Gibbs free energy, as in Equation (8.8). From each model, the following parameters were used: DGFORM of the amine, DGAQFM of the protonated amine and proton, and the five parameters for H Am, H2 O listed in Equation (8.7). The models used were: MEA (Plaza, 2011), PZ and MDEA (Frailie, 2014), AMP (Chapter 5), HMPD (Chapter 7), 2MPZ (Chapter 6), and 2PE (Chapter 4) τ i, j Physical Significance Most literature does not discuss the physical significance of τ i, j (Li et al., 2014; Frailie, 2014), and those that do suggest that the parameters are empirical with little physical significance (Austgen et al., 1989; Bollas et al., 2008). However, as Austgen et al. (1989) point out, the relative values of τ i, j are meaningful. As discussed by Chen (1980) and Chen et al. (1982) for the case of binary systems, there are systematic trends in τ i, j that can be attributed to the physical interaction between the components. Looking first at the individual parameter values, there is a trend. As demonstrated by Chen et al. (1982) and as seen in most of the Rochelle group models, τ m, ca is almost always positive and τ ca, m is almost always negative. The reason for this can be seen by looking at the definition of τ i, j in Equation (8.9), τ i, j g i, j g j, j RT (8.9) where g i, j and g i, i are energies of interaction between j-i and i-i species. They are symmetric, meaning g a, c g c, a where c represents a cation and a represents an anion. Applying Equation (8.9) to τ m, ca and to τ ca, m yields Equation (8.10) and 194

217 Equation (8.11), τ m, ca g m, i g c,a RT τ ca, m g i, m g mm RT (8.10) (8.11) where i is an ion. As the interaction energy follows the order of g c, a g i, m g m, m, τ m, ca is dominated by g c, a, and τ ca, m is dominated by g i, m. Since the energies of interaction are negative, τ m, ca should be positive, and τ ca, m should be negative. This shows there is some physical significance to the individual interaction parameters. There is also significance to the absolute difference between the interaction parameters. The greater the absolute difference between the binary parameters, the greater the interaction energy is between cation and anion (Chen et al., 1982). The stronger the interaction, the more likely the two ions are to associate with one another. This difference has been shown to correlate with pk a for strong acids (Chen et al., 1982). The absolute difference between binary interaction parameters was examined to determine if such a correlation held in the case of these multicomponent amine solvents. The binary interaction parameter values as well as the absolute difference were calculated at 25 C for four salts AmH, HCO 3, AmH, CO 2 3, AmH, AmCOO, and AmH, Am COO 2 and three molecules H 2O, Am, CO 2 as well as the zwitterion in the case of PZ and 2MPZ. The hydronium, proton, and hydroxide ions were ignored due to their low concentration in the system. All salt-salt interaction parameters were left at the default of zero in all models examined. The nonrandomness parameter α i, j was not examined. α i, j is involved in the calculation of the activity coefficients and is typically assigned a value of 0.1, 0.2, or 0.3 (Posey, 1996; Austgen et al., 1989). This assignment is based on the reciprocal 195

218 of the lattice coordination number as ionic salts have a typical coordination number of four to six. The models in this work used either 0.2 or Comparison to Simplified Stoichiometric Model A Kent-Eisenberg model was constructed by Li (2015) that correlated the VLE of a wide variety of amines and predicted the speciation. This model is called the simplified stoichiometric model (SSM). All of the system non-ideality was embedded in the equilibrium constants of two chemistry equations, Equation (8.12) and Equation (8.13). 2 Am CO 2 pgq K 1 ðñ AmH HAmCO 2 3 (8.12) AmCOO 2 H 2 O CO 2 pgq K 2 ðñ 2 HCO 3 AmH (8.13) As no activity coefficients are in the SSM, the equilibrium constants were calculated on a mole-fraction basis. K 1 and K 2 are the mole-fraction based equilibrium constant as defined by Equation (8.14) and Equation (8.15), which also show the relation to the true activity-based equilibrium constant. K 1 x AmCOO x AmH x 2 Am P CO 2 a AmCOO a AmH a 2 Am a CO 2 H CO2 H 2 O γ AmCOO γ AmH γ Am 2 (8.14) a 2 HCO 3 a AmH x AmH x 2 K 2 HCO 3 x AmCOO P CO2 a AmCOO a CO2 H CO2 H 2 O γ 2 HCO 3 γ AmH (8.15) γ AmCOO As a way of validating the SSM and its general conclusions, these equilibrium constants were computed using the corresponding enrtl models as listed in Table 8.1. The corresponding table in Li (2015) is Table

219 Table 8.1: Calculation of K i at P CO Pa and 40 C using the listed models along with the exp. pk a at 40 C. *ENRTL-RK; : interpolated Amine [Am] pk a ln pk 1 q ln pk 2 q enrtl Model (m) pk a Source 2PE : Chapter 4 (Xu et al., 1992) AMP (Aspen (Kim et al., Technology, 2013d) 2011) MEA (Aspen (Hamborg and Technology, Versteeg, 2009) 2013m)* MEA (Plaza, 2011) (Hamborg and DEA (Aspen Technology, 2013e)* DEA (Aspen Technology, 2013e)* DIPA (Aspen Technology, 2013i)* Versteeg, 2009) (Bower et al., 1961) (Bower et al., 1961) (Hamborg and Versteeg, 2009) 8.3 Results Model Validation The pk a at 25 C for every model used in this study is compared to the experimental value in Table 8.2. Generally speaking, the ELECNRTL Aspen Tech. models have a poor fit of the pk a. It is unclear how exactly a poor pk a fit impacts τ i, j. Therefore, the level of error tolerable is unknown. Fits with greater absolute error than 0.1 (corresponding to 25% relative error in K a ) were excluded from study. The high degree of error present demonstrates the importance of validating a model 197

220 Table 8.2: Calculated pk a at 25 C compared to experimental values. Amine pk a abs. exp. source pred. source exp. calc. error MDEA (Xu et al., 1992) (Aspen Technology, 2013k) NH (CRC Handbook) (Aspen Technology, 2013o) AMP (Kim et al., 2011) (Aspen Technology, 2013d) DEA (Xu et al., 1992) (Aspen Technology, 2013f) DGA (Khalili et al., 2009) (Aspen Technology, 2013g)* DGA (Khalili et al., 2009) (Aspen Technology, 2013h) HMPD (Ciftja, 2016) Chapter 7 DEA (Xu et al., 1992) (Aspen Technology, 2013e)* MEA (Hamborg and Versteeg, (Aspen Technology, 2013n) 2009) TEA (Khalili et al., 2009) (Aspen Technology, 2013q) DIPA (Hamborg and Versteeg, (Aspen Technology, 2013j) 2009) TEA (Khalili et al., 2009) (Aspen Technology, 2013c)* PZ (Khalili et al., 2009) (Aspen Technology, 2013b)* NH (CRC Handbook) (Aspen Technology, 2013a)* MDEA (Xu et al., 1992) (Frailie, 2014) AMP (Kim et al., 2011) Chapter 5 MEA (Hamborg and Versteeg, (Aspen Technology, 2013m)* 2009) PZ (Khalili et al., 2009) (Aspen Technology, 2013p) MEA (Khalili et al., 2009) (Plaza, 2011) DIPA (Hamborg and Versteeg, (Aspen Technology, 2013i)* 2009) 2PE (Xu et al., 1992) Chapter 4 MDEA (Xu et al., 1992) (Aspen Technology, 2013l) PZ (Khalili et al., 2009) (Frailie, 2014) 2MPZ (Khalili et al., 2009) Chapter 6 198

221 prior to use regardless of its origin. This also serves as a warning for work done with the default Aspen Plus models, particularly prior to the ENRTL-RK models. The cause for error was investigated. In the case of the DEA model, this error is due to failing to account for the impact of the NRTL parameters for Am/H 2 O on γ 8, aq Am. Zeroing out all NRTL interaction parameters for DEA/H 2O that is assuming the interaction is ideal results in a much better fit with an absolute pk a error of This was not the case for the AMP and DGA models. Other models were not investigated pk a Prediction PE pk a 9.5 PZ 2MPZ HMPD MEA 8.5 MDEA 5.50E E E E+07 ΔG rxn (J/kmol) Figure 8.1: pk a at 25 C by Equation (2.16) () compared to that computed by Equation (8.8) (line). 199

222 Figure 8.1 shows that as expected the pk a computed from Gibbs free energy matches that computed from activities. This means there is no longer a need to regress G f, AmH, but it instead can be set by Equation (8.16). 8, aq G f, AmH G 8, aq f, Am aq RT 10 pka T K G8, f, H 1000 MW H2 O (8.16) This reduces model error, accelerates thermodynamic model construction, and increases the physical significance of the interaction parameters by eliminating their compensation for pk a misfit τ i, j Patterns The binary interaction parameter values and the absolute difference between the parameters are presented for three different molecules and the zwitterion: water in Table 8.3 and Table 8.4, amine in Table 8.5 and Table 8.6, CO 2 in Table 8.7 and Table 8.8, and zwitterion in Table 8.9 and Table As expected, τ m, ca is almost always positive, and τ ca, m is almost always negative. Most parameters are at their default values, and most are not temperature dependent. As very little free CO 2 is present in the system, the interaction parameters for m CO 2 are mostly at default values. Similarly, as there is less free amine than water, most of those parameters are also at default. Before going forward, the default values need to be defined. The default values have changed over time with three different sets of defaults identified. All three conventions are still in use here and in the literature (Frailie, 2014; Li et al., 2014). The default molecule-molecule and salt-salt interactions are set to zero universally. Austgen et al. (1989) interpreted the work of Chen and Evans (1986) to set the default for all water-salt and salt-water interactions at 8.0 and 4.0 with α 0.2 and interpreted the work of Mock et al. (1986) to set the default for all amine-salt and 200

223 Table 8.3: τi, j at K for m H2O Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source τm, ca τca, m τm, ca τca, m τm, ca τca, m τm, ca τca, m PZ (Aspen Technology, 2013b)* PZ (Aspen Technology, 2013p) PZ (Frailie, 2014) MEA (Aspen Technology, 2013m)* MEA (Plaza, 2011) DIPA (Aspen Technology, 2013i)* NH (Aspen Technology, 2013a)* 2MPZ Chapter 6 2PE Chapter 4 AMP Chapter 5 MDEA (Frailie, 2014) MDEA (Aspen Technology, 2013l)* Table 8.4: τm, ca τca, m at K for m H2O Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source PZ (Aspen Technology, 2013b)* PZ (Aspen Technology, 2013p) PZ (Frailie, 2014) MEA (Aspen Technology, 2013m)* MEA (Plaza, 2011) DIPA (Aspen Technology, 2013i)* NH (Aspen Technology, 2013a)* 2MPZ Chapter 6 2PE Chapter 4 AMP Chapter 5 MDEA (Frailie, 2014) MDEA (Aspen Technology, 2013l)* 201

224 Table 8.5: τi, j at K for m Am Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source τm, ca τca, m τm, ca τca, m τm, ca τca, m τm, ca τca, m PZ (Aspen Technology, 2013b)* PZ (Aspen Technology, 2013p) PZ (Frailie, 2014) MEA (Aspen Technology, 2013m)* MEA (Plaza, 2011) DIPA (Aspen Technology, 2013i)* NH (Aspen Technology, 2013a)* 2MPZ Chapter 6 2PE Chapter 4 AMP Chapter 5 MDEA (Frailie, 2014) MDEA (Aspen Technology, 2013l)* Table 8.6: τm, ca τca, m at K for m Am Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source PZ (Aspen Technology, 2013b)* PZ (Aspen Technology, 2013p) PZ (Frailie, 2014) MEA (Aspen Technology, 2013m)* MEA (Plaza, 2011) DIPA (Aspen Technology, 2013i)* NH (Aspen Technology, 2013a)* 2MPZ Chapter 6 2PE Chapter 4 AMP Chapter 5 MDEA (Frailie, 2014) MDEA (Aspen Technology, 2013l)* 202

225 Table 8.7: τi, j at K for m CO2 Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source τm, ca τca, m τm, ca τca, m τm, ca τca, m τm, ca τca, m PZ (Aspen Technology, 2013b)* PZ (Aspen Technology, 2013p) PZ (Frailie, 2014) MEA (Aspen Technology, 2013m)* MEA (Plaza, 2011) DIPA (Aspen Technology, 2013i)* NH (Aspen Technology, 2013a)* 2MPZ Chapter 6 2PE Chapter 4 AMP Chapter 5 MDEA (Frailie, 2014) MDEA (Aspen Technology, 2013l)* Table 8.8: τm, ca τca, m at K for m CO2 Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source PZ (Aspen Technology, 2013b)* PZ (Aspen Technology, 2013p) PZ (Frailie, 2014) MEA (Aspen Technology, 2013m)* MEA (Plaza, 2011) DIPA (Aspen Technology, 2013i)* NH (Aspen Technology, 2013a)* 2MPZ Chapter 6 2PE Chapter 4 AMP Chapter 5 MDEA (Frailie, 2014) MDEA (Aspen Technology, 2013l)* 203

226 Table 8.9: τi, j at K for m HAmCOO Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source τm, ca τca, m τm, ca τca, m τm, ca τca, m τm, ca τca, m PZ (Aspen Technology, 2013b)* PZ (Frailie, 2014) 2MPZ Chapter 6 Table 8.10: τm, ca τca, m at K for m HAmCOO Amine AmH, HCO 3 AmH, CO 2 3 AmH, AmCOO AmH, Am COO 2 Source PZ (Aspen Technology, 2013b)* PZ (Frailie, 2014) 2MPZ Chapter 6 204

227 salt-amine as well as acid gas-salt and salt-acid gas to 15.0 and 8.0 with α 0.1. These were the defaults of Aspen 8.5, but by Aspen 9.2 the defaults had changed to 8 and 4 for water-salt and salt-water with α 0.2 and 10 and 2 for amine-salt and salt-amine with α 0.2 as well (Posey, 1996). These continue to be the defaults in V8.4 of Aspen Plus used in this work. The absolute difference in the defaults of 8 and 4 and 10 and 2 is twelve for both, suggesting the same interaction energy. As water is present in the solvents at the highest concentration, interactions with water should be the most important. Similarly, interactions with bicarbonate and carbamate should be important, though the most important one depends on the most abundant species as dictated by the system chemistry. For tertiary and hindered amines, the interaction with bicarbonate would be more important, while for unhindered primary and secondary amines carbamate would be more important. The importance of these parameters impacts the statistical significance of the regressed parameter. For all amines, bicarbonate, if not the most important CO 2 species, is a close second to carbamate. It is seen that the interaction between H 2 O/ AmH, HCO 3 is regressed for every system but 2MPZ and PZ. The pk a was correlated with τ H2 O{p AmH,HCO 3 q τ p AmH,HCO 3 q,h 2 O for the ENRTL-RK models, for the Rochelle group models, for the primarily bicarbonate forming amines, and for all models. The linear fits for the first three cases are shown in Figure 8.2, Figure 8.3, Figure 8.4. All cases have a negative slope, indicating that the strength of interaction decreases with increasing pk a. This observation is consistent with the observation made for strong acids binary systems (Chen et al., 1982). This is explained by the weaker acids disassociating less than the stronger acids. While the absolute difference in interaction energies has more physical significance than the individual parameters, regression of one or the other binary interaction parameters may be sufficient to model the system. Though the τ m, ca parameter should be 205

228 DIPA 14 MDEA y = x R² = NH MEA pk a PZ Figure 8.2: Correlation of absolute difference for m H 2 O and ca AmH, HCO 3 the predicted pk a at 25 C for ENRTL-RK models with the most important as it contains g ca, which is the strongest interaction, in practice τ ca, m is favored in both single and blend solvents. This is seen in 2PE (Chapter 4) and PZ/HMPD (Table 7.6), PZ/2MPZ (Table 7.7), and PZ/AMP (Li et al., 2014) where τ ca, m is used nearly exclusively. Other systems regressed both, eg MDEA, PZ, and PZ/MDEA (Frailie, 2014) and the Aspen Tech. ENRTL-RK models, or conversely favored τ m, ca, eg MEA (Plaza, 2011). Unfortunately, these correlations are not sufficiently robust to draw further conclusions. The combined fit of both the ENRTL-RK and Rochelle group models was particularly weak with a coefficient of determination of These weak correlations may be due to different model makers choosing to regress different τ i, j parameters. Therefore, though there seems to be physical significance in the absolute difference, the correlation of parameters is such that other correlated parameters can be ac- 206

229 14 12 MDEA MEA 2MPZ y = x R² = PZ AMP pk a 2PE Figure 8.3: Correlation of absolute difference for m H 2 O and ca AmH, HCO 3 the predicted pk a at 25 C for Rochelle group models with counting for the physical phenomena. In other words, if each model maker chose to regress the same parameters for each model, then this analysis would yield a definitive conclusion on the physical significance. As is, the result is inconclusive, but the consistent negative slope points towards some underlying physical significance. Interactions with the zwitterion for PZ and 2MPZ are given in Table 8.9 and Table The ELECNRTL PZ model (Aspen Technology, 2013p) treated the zwitterion as an ion with a very small charge and is not included. The Rochelle group models of 2MPZ (Chapter 6) and PZ (Frailie, 2014) treated the zwitterion as a Henry s component. The ENRTL-RK PZ model used a new feature that was not available for the other models to treat the zwitterion as a zwitterion. Looking at the absolute differences shows that if the binary interaction parameters were regressed, 207

230 16 DIPA MDEA MDEA y = x R² = AMP 10 8 NH pk a 2PE Figure 8.4: Correlation of absolute difference for m H 2 O and ca AmH, HCO 3 the predicted pk a at 25 C for primarily HCO 3 forming amines with the salt was AmH, HCO 3. This makes sense as the zwitterion concentration is high when the bicarbonate reaction is important Comparison to Simplified Stoichiometric Model Figure 8.5 shows that there is a very tight agreement between the Kent- Eisenberg calculated reaction equilibria and those calculated using the enrtl framework. The SSM model and the Aspen Technology models used different data sets with the SSM regressing all in house VLE data except for MEA (Li, 2015).This agreement not only bolsters the arguments laid out by Li (2015) but increases the confidence that the SSM model can be used for new amine solvents. 208

231 -5 y = x R² = K i (enrtl) -10 K 1 y = 1.067x R² = K K i (SSM) Figure 8.5: Comparison of K eq by Equations (8.14) and (8.15) 8.4 Conclusions Many Aspen Plus models have error in the pk a exceeding 0.1, particularly the older ELECNRTL models. An analytical method was developed to calculate the 8, aq Gf, AmH from the experimental pk a for amines treated as Henry s components. The consistent sign for the individual binary interaction parameters indicates physical significance. The absolute difference τ H2 O{p AmH,HCO 3 q τ p AmH,HCO 3 q{h 2 O moderately correlates with the pk a at 25 C. That this difference always decreases with increasing acidity demonstrates the connection of disassociation with the interaction energy embodied by the absolute difference. Most interaction parameters are not temperature dependent. Lastly, the simplified stoichiometric model was confirmed to accurately represent amine solvents, bolstering the claims of Li (2015). 209

232 Going forward, regressing parameters to fit the pk a is not advised. The method used here to calculated the Gibbs free energy of formation for the protonated amine should be extended to capture the observed temperature dependence of the pk a and calculate the enthalpy of formation for the protonated amine. Additionally, these two calculations should be done for whether or not the amine is treated as a Henry s component. In order to enhance the physical significance of the enrtl models, the regression of the binary interaction parameters should be systematized. This would allow for better generalization of the models. Regression of only one of the τ m, ca and τ ca, m parameters should be explored. Finally, it is recommended that current Aspen Plus models using ELECNRTL be converted to the ENRTL-RK formulation of enrtl in Aspen Plus as it is more thermodynamically consistent with NRTL (Aspen Technology, 2010), which has implications at water wash conditions. ENRTL-RK should be used for future models. If such a change is undertaken, examination of the symmetric enrtl model should also be investigated to avoid converting models twice. 210

233 Chapter 9 Conclusions and Recommendations 9.1 Summary This work developed regression methods to represent thermodynamic and mass transfer in amine solvents. The sequential regression method was modified to form the analogy method for thermodynamic modeling, where missing physical property data is equated to that of an analogous amine. A response surface method was developed for mass transfer modeling to enable regression with statistical measures such as confidence intervals and correlation of parameters while achieving an optimal fit. Models were developed for the three single, hindered: 2-piperidineethanol (2PE), 2-amino-1-methylpropan-1-ol (AMP), and 2-methylpiperazine (2MPZ). The bicarbonate rate constant for 2PE and AMP is an order of magnitude greater than expected tertiary amine of equal base strength. The carbamate rate constant of 2PE was similar to an unhindered, cyclic, secondary amine, while the carbamate rate constant of AMP was twelve times slower than expected for an unhindered primary amine of equal basicity. 2PE is carbamate more stable than AMP, which is expected from the greater pk a of 2PE. The greater viscosity of 8 m 2MPZ decreases the CO 2 flux by 15% compared to 8 m PZ. Models were constructed for PZ blended with HMPD, AMP, and 2MPZ. The binary interaction parameters for single amine solvent models have physical significance, with the absolute difference between corresponding 211

234 Table 9.1: Models made in this work; manuals available in the Appendices Amine Thermodynamic Basis Mass Transfer Basis Manual 2PE this work this work No AMP (Li et al., 2014) this work No 2MPZ (Chen, 2011) this work Yes PZ (Frailie, 2014) (Frailie, 2014) No PZ/HMPD this work this work Yes PZ/AMP (Li et al., 2014) this work No PZ/2MPZ this work this work Yes molecule-salt and salt-molecule parameters correlating with the acid disassociation constant. Table 9.1 lists the models used in this work. 9.2 Conclusions Thermodynamic Modeling Methods The most important data sets to fit are pk a, followed by CO 2 solubility (VLE). The analogy method is effective at representing an amine with missing physical property data, where the properties of an analogous amine substitute for the missing data. The prediction of the heat of absorption by differentiating VLE serves as a test of model quality Mass Transfer Modeling Methods The response surface methodology (RSM) approach gives a more statistically and physically significant mass transfer model than manual regression or using Data Fit. The RSM approach developed sensitivities to the individual parameters using the full model in Aspen Plus, and then used these sensitivities to predict the 212

235 model response. The parameters were then regressed using the predicted response. The model must be validated for process modeling, as the hydrodynamics and mass transfer correlations change from the wetted-wall column to the absorber Piperidineethanol (2PE) Ciftja (Sherman et al., 2016) showed that 2PE forms a more stable carbamate (log K c =1.06) than AMP (log K c =0.70), as expected from the higher pk a of 2PE. At 40 C, kg 1 is most sensitive to the carbamate reaction rate and nearly insensitive to the bicarbonate reaction rate, proving the need to model the carbamate reaction for this sterically hindered amine. While the carbamate reaction rate follows the Brønsted correlation for three unhindered cyclic, secondary amines, suggesting a similar reaction mechanism, the bicarbonate reaction rate surprisingly is an order of magnitude faster than predicted by the Brønsted correlation for tertiary amines, suggesting a different reaction mechanism. As temperature increases, the pseudofirst order (PFO) assumption applies to the wetted-wall column data for increasingly higher kl 0 and over a smaller loading range. The PFO assumption applies at 40 C up to a loading of 0.60 mol CO 2 {mol alk but not at greater temperature or loading Amino-2-methylpropan-1-ol (AMP) The liquid film mass transfer coefficient kg 1 of 4.8 m AMP goes through a maximum at 60 C because the dominant liquid film resistance shifts from reaction rate resistance below 60 C to diffusion resistance above 60 C. kg 1 is most sensitive to the carbamate reaction rate at 40 C, while, at 100 C, it is most sensitive to k l,0. The regressed carbamate rate constant is a dozen times slower than that predicted for an unhindered primary amine of equal basicity, and the bicarbonate rate constant is eighteen times faster than that predicted for an equal basicity tertiary amine. 213

236 Since the AMP values do not match either prediction, different reaction mechanisms are probably used. In the wetted-wall column, AMP reacts in the pseudo-first order regime at 40 C, and at 100 C, the system is not instantaneous due to the slow bicarbonate reaction. Most of the the CO 2 is transported through the boundary layer in the form of carbamate, followed by reversion of the carbamate, and subsequent formation of bicarbonate Methylpiperazine (2MPZ) The activity coefficients of the 2MPZ zwitterion and dicarbamate are strong, non-monotonic functions of loading, precluding an accurate PZ/2MPZ model. The decreased CO 2 flux of 8 m 2MPZ relative to 8 m PZ, is 15% due to viscosity with the remainder due to kinetics. A process model was developed and validated. A manual is included in Appendix I Piperazine Blends While the detrimental effects of non-physically significant parameters are localized in a single amine model, when that model is incorporated into a blend amine model, these effects become systemic in both the thermodynamic and the mass transfer model. The interaction parameters compensate for thermodynamic misfitting, while the diffusion of amine D Am compensates for mass transfer misfitting. In a blend model, D Am is no longer able to compensate, and so the blend model kinetics are not well fit. For the 2MPZ/PZ model, the 2MPZ kinetic rate constants compensated for poorly behaved 2MPZ activity-coefficients, but this compensation did not work in a process absorber model for the blend. For PZ blended with HMPD, AMP, and 2MPZ, the regressed interaction parameters are primarily salt-molecule the temperature-independent term of τ ca, m with m=h 2 O or =zwitterion. 214

237 9.2.7 Thermodynamic Modeling Generalizations Many Aspen Plus models have error in the pk a exceeding 0.1, particularly the older ELECNRTL models. An analytical method was developed to calculate the 8, aq Gf, AmH from the experimental pk a for amines treated as Henry s components. The consistent sign for the individual binary interaction parameters indicates physical significance. The absolute difference τ H2 O{p AmH,HCO 3 q τ p AmH,HCO 3 q{h 2 O moderately correlates with the pk a at 25 C. That this difference always decreases with increasing acidity demonstrates the connection of disassociation with the interaction energy embodied by the absolute difference. Most interaction parameters are not temperature dependent. Lastly, the simplified stoichiometric model was confirmed to accurately represent amine solvents, bolstering the claims of Li (2015). 9.3 Recommendations Thermodynamic Modeling Methods Finding a predictive means of choosing the binary interaction parameters for regression would accelerate regression and better avoid the pitfalls of over-fitting and distorted correlated parameters. Rigorous testing of the analogy method would determine the best criteria of an analog and determine if a there is an accuracy penalty or distortion in parameters for using analogous physical properties. The potential benefits of using the symmetric enrtl model(song and Chen, 2009) should be explored. As per the recommendation of the Aspen Plus manual, H 3 O + should be used instead of H for the pk a chemistry block. Exploration of the new zwitterion option is warranted. Other regression methods should be investigated, such as particle swarm optimization, which does not depend on initialization (Pinto, 2014). 215

238 9.3.2 Mass Transfer Modeling Methods Additional experimental work measuring the diffusion of amine and products in loaded systems is of critical importance to validate the current assumption of half that of the diffusion of CO 2. Future modeling work should include refining the response surface methodology approach to develop a more robust response surface capable of simulating a wider range of reaction rate constant values through a modern sampling method and a better formulated sensitivity calculation. This work should leverage the efforts of SolventFit by CCSI. More statistical rigor should be incorporated into regressions, particularly for blend amine systems, in order to understand the meaningful reactions and the role of ratioing reactions through Brønsted correlations. D Am should be corrected for PZ and PZ blend models, and different diffusivities should be used for different amines in a blend Piperidineethanol (2PE) These results demonstrate the importance of accounting for the carbamate reaction in 2PE and more broadly for all hindered amines. Thus, for solvents blending a hindered amine with a rate promoter, modeling the hindered amine carbamate reaction is necessary to model the mass transfer performance. The model created by this work can be used for process modeling and design of a full-scale absorber and stripper. Fruitful research opportunities presented by this work include more loaded viscosity measurements as well as temperature-variable NMR measurements. The viscosity measurements would allow for more accurate diffusion coefficients, while the NMR measurements would validate the temperature dependence of K c. 216

239 Amino-2-methylpropan-1-ol (AMP) This work provides insight into the mass transfer mechanism of hindered amines. A better understanding of CO 2 mass transfer in hindered amines requires more information on the diffusion of carbamate. This work suggests hindered amines play a significant role in the kinetics of CO 2 absorption when blended with a fast primary or secondary amine Methylpiperazine (2MPZ) When the model is converted from ELECNRTL to ENRTL-RK, the activity coefficient behavior should be corrected to enable blend modeling and improve the physical significance of the model parameters. After this upgrade, the differential heat of absorption by calorimetry and by differentiating the VLE should be repeated to help determine the source of the thermodynamic inconsistency. The viscosity correlation should be improved to better represent low temperature and low concentration data, as 4 m to 6 m 2MPZ is a better solvent than 8 m 2MPZ, as discussed by Yuan (Rochelle et al., 2015). The temperature dependence of D Am should be corrected, and the liquid film discretization could be further reduced Piperazine Blends Future work for these blends include the regression of a second set of wettedwall column mass transfer data for AMP/PZ, which would test the physical significance of the current mass transfer parameters. The diffusion subroutine should be modified in blend models to differentiate between the different amines and apply their respective diffusion coefficients, if data is sufficient to not assume that the amines diffuse at half the rate of CO 2. Amine concentration should be optimized by 217

240 calculating the viscosity-normalized capacity, k 1 g, and heat of absorption for each of the blends as was done by Frailie (Frailie, 2014) Thermodynamic Modeling Generalizations Going forward, regressing parameters to fit the pk a is not advised. The method used here to calculated the Gibbs free energy of formation for the protonated amine should be extended to capture the observed temperature dependence of the pk a and calculate the enthalpy of formation for the protonated amine. Additionally, these two calculations should be done for whether or not the amine is treated as a Henry s component. In order to enhance the physical significance of the enrtl models, the regression of the binary interaction parameters should be systematized. This would allow for better generalization of the models. Regression of only one of the τ m, ca and τ ca, m parameters should be explored. Finally, it is recommended that current Aspen Plus models using ELECNRTL be converted to the ENRTL-RK formulation of enrtl in Aspen Plus as it is more thermodynamically consistent with NRTL (Aspen Technology, 2010), which has implications at water wash conditions. ENRTL-RK should be used for future models. If such a change is undertaken, examination of the symmetric enrtl model should also be investigated to avoid converting models twice. 218

241 Appendices 219

242 Appendix A Nomenclature term definition units 2D NMR 2-dimensional NMR A wetted area m 2 C p heat capacity at constant pressure kj {kg-k COSY correlation spectroscopy DEA diethanolamine DIPA diisopropanolamine enrtl electrolyte non-random two liquid ESRK Redlich-Kwong equation of state f i fugacity HMBC heteronuclear multiple bond correlations HSQC hetero single quantum coherence kg, 1 P F O PFO liquid film mass transfer coefficient k B base-catalyzed hydration of CO 2 by base B k Am B base-catalyzed reaction of amine (Am) with CO 2 k c concentration-based reaction rate constant m 3 {kmol-sec k Am Am, 3 termolecular, concentration-based reaction rate constant divided by γco 2 2 K eq reaction equilibrium constant MOR morpholine PCES property constant estimation system PZ piperazine r CO2 rate of reaction of CO 2 SE standard error 2MPZ 2-methylpiperazine 2PE 2-piperadineethanol AMP 2-amino-2-methyl-1-propanol ARD average relative deviation 220

243 term definition units MDEA methyl diethanolamine PFO pseudo-first order RS response surface RSM response surface methodology VLE vapor-liquid equilibrium WWC wetted-wall column ˆ predicted value a i activity rco 2 s T total CO 2 concentration mol {m 3 D i diffusivity of i m 2 {sec D CO2 diffusivity of CO 2 and N 2 m 2 {sec D Am diffusivity of amine and products m 2 {sec E enhancement factor E A activation energy kj {mol E D diffusion activation energy J {mol 8, aq Gf, i aqueous Gibbs free energy of formation J {kmol 8, aq Hf, i aqueous enthalpy of formation J {kmol H CO2 Henry s constant of CO 2 in solution Pa H CO2,H 2 O Henry s constant of CO 2 in water Pa k i reaction rate constant kmol {sec-m 3 k 0 reaction rate constant pre-exponential kmol {sec-m 3 k a activity-based reaction rate constant kmol {sec-m 3 K c carbamate stability constant m 3 {mol kl 0 physical liquid mass transfer coefficient mol {sec-pa-m 2 K g overall gas side mass transfer coefficient mol {sec-pa-m 2 k g gas film mass transfer coefficient mol {sec-pa-m 2 k 1 g liquid film mass transfer coefficient in gas units mol {sec-pa-m 2 m molality mol solute {kg solvent n overall reaction order N i data point N CO2 experimental CO 2 flux mol {m 2 -sec P CO 2 equilibrium partial pressure of CO 2 Pa or kpa R universal gas constant J {mol-k T temperature K T p total pressure Pa or kpa 221

244 term definition units V m molar volume m 3 {mol w i mass fraction x i mole fraction β model parameters γ i activity coefficient γ i asymmetric activity coefficient µ viscosity mpa-sec ρ mass density kg {m 3 ρ molar density kmol {m 3 σ standard deviation enrtl binary interaction parameter τ i, j 222

245 Appendix B Fortran Subroutines The code included here comes from the AMP model of Chapter 5. In case of long lines, a line break is indicated by ãñ. B.1 vl2u2.f This subroutine calculates specific molar volume, which is then converted using the true component average molecular weight. It is called in the properties environment at Methods Selected Methods ELECNRTL on the tab Models. In the list, the relevant Property is VLMX, where the model name is set to VL2USR2 with data set as 1. On the tab Routes, the property VLMX is set to RHOLX1. C Log keyword added C C $ #1 BY: PING LI 14 - MAY USER ROUTINE FOR MIXTURE ãñ PROPERTIES USING C $ MIXING RULE C LAST MODIFIED : BY BRENT SHERMAN C modified to include AMP / PZ C BRENTJSHERMAN@GMAIL. COM C added in AMPCOO C updating component names C =================== cvs revision history =============== SUBROUTINE VL2U2 (T, P, X, N, IDX, XMW, SG, VLSTD, ãñ VL2U2A, * VI, DVI, DPVI, KSW, KOP, NDS, KDIAG, * VMX, DVMX, DPVMX, KER ) C ********************************************************** 223

246 C Template for VL2U2 routine for mixture liquid molar ãñ volume C and its temperature, pressure derivatives C C VMX is the calculated liquid mixture molar volume ( ãñ output ) C C DVMX is the temperature derivative of VMX ( output ) C C DPVMX is the pressure derivative of VMX ( output ) C C All input and output in this user routine are in SI ãñ Units C with Gas constant = C C ******************************************************** C ARGUMENT LIST VARIABLES : C C VARIABLE I/ O TYPE - SPEC DIMENSION DESCRIPTION AND ãñ RANGE C C T I REAL *8 OPERATING TEMPERATURE C P I REAL *8 OPERATING PRESSURE C Z I REAL *8 N COMPONENT MOLE ãñ FRACTION VECTOR C N I INTEGER NUMBER OF COMPONENTS ãñ IN MIXTURE C IDX I INTEGER N VECTOR OF COMPONENT ãñ POINTERS C XMW I REAL *8 NCC MOLECULAR WEIGHT FOR ãñ EACH COMPONENT C SG I REAL *8 NCC SPECIFIC GRAVITY FOR ãñ EACH COMPONENT C VLSTD I REAL *8 NCC STD. LIQUID VOLUME ãñ FOR EACH COMPONENT C VL2U2A I REAL *8 5, NCC USER DEFIND PARAMETER ãñ FOR THIS MODEL C VI I REAL *8 N PURE LIQUID MOLAR ãñ VOLUME 224

247 C DVI I REAL *8 N TEMPERATURE ãñ DERIVATIVE OF VI C DPVI I REAL *8 N PRESSURE DERIVATIVE ãñ OF VI C KSW I INTEGER 3 CALCULATION CODE C KSW (1) FOR PROPERTY C KSW (2) FOR TEMP. ãñ DERIVATIVE C KSW (3) FOR PRES. ãñ DERIVATIVE C VALUE = 1: CALCULATE C VALUE = 0: DO NOT ãñ CALCULATE C KOP I INTEGER 10 MODEL OPTION CODE C NDS I INTEGER DATA SET NUMBER C KDIAG I INTEGER MESSAGE PRINTING CODE C IF. GE. 2: PRINT ãñ ERROR MESSAGES C IF. GE. 3: PRINT ãñ WARNING MSGS. C VMX O REAL *8 LIQUID MOLAR VOLUME [ ãñ CUM / KGMOL ] C DVMX O REAL *8 TEMPERATURE ãñ DERIVATIVE OF VMX [ CUM / KGMOL -K] C DPVMX O REAL *8 PRESSURE DERIVATIVE ãñ OF VMX [ CUM / KGMOL -PA] C KER O INTEGER ERROR RETURN CODE C C ************************************************************ IMPLICIT NONE # include " dms_global. cmn " # include " dms_maxwrt. cmn "! for debugging C C DECLARE VARIABLES USED IN DIMENSIONING C INTEGER N C C DECLARE ARGUMENTS C 225

248 INTEGER IDX (N), KSW (3), KOP, NDS, KDIAG, KER INTEGER DMS_ KCCIDC, DMS_ KFORMC INTEGER IWATER, IPZCOO, ICO2, IPZCOO2, IHPZCOO, IHCO3 INTEGER IPZH, IPZ, ICO3, IMDEA, IMDEAH, IAMP, IAMPH, ãñ IAMPCOO REAL *8 X(N), T, P, XMW (N), SG (1), VLSTD (1), VL2U2A (5,1),. VI(N), DVI (N), DPVI (N), VMX, DVMX, DPVMX REAL *8 WATER, PZCOO, CO2, PZCOO2, HPZCOO, HCO3, PZH, PZ REAL *8 MDEA, MDEAH, CO3 REAL *8 A, B, C, D, E, F, MWT, VH2O, XCO2T, XPZCOO2, VPZ REAL *8 V2, G, H, XPZN, XH2ON, XMDEAN, XCO2N REAL *8 XPZT, AA, BB, ML, XH2O, LDG, RHOX REAL *8 PPUTL_ AVEMW, XMDEAT, XAMINE, RHOXMDEA, A3, B3, C3 REAL *8 A2, B2, C2, D2, E2, F2, D3 REAL *8 AA2, BB2, RHOXBLND, RHOXPZ REAL *8 MWPZ, MWPZCOO, MWPZH, MWHPZCOO, MWPZCOO2, MWHCO3 REAL *8 MWMDEA, MWMDEAH, MWH2O, MWCO2, MWCO3, MWAMP, ãñ MWAMPH,. MWAMPCOO REAL *8 MW1, MW2, MW3, AVGMW REAL *8 A4, B4, C4, D4, A5, B5, C5, D5, E5, F5, G5, H5, ãñ XAMPT,. RHOXAMP, XAMPN, RHOXH2O, RHOXAMPPZ C C DECLARE LOCAL VARIABLES C INTEGER IPROG (2) C C DATA STATEMENTS C DATA IPROG /4 HVL2U, 4 H2 / C C BEGIN EXECUTABLE CODE C VALUES OBTAINED FROM THE DENSITY REGRESSION C INTEGER I REAL *8 SUM, DSUM, DPSUM SUM = 0D0 DSUM = 0D0 226

249 DPSUM = 0D0 C MDEA +PZ coeffs. A = D0 B = D0 C = D0! PZ param D = D0! PZ param E = D0 F = D0 G = D0 H = D0 C PZ only coeffs. A2 = D0 B2 = D0 C2 = D0 D2 = D0 E2 = D0 F2 = D0 C MDEA only coeffs. A3 = D0 B3 = D0 C3 = D0 D3 = D0 C AMP only coeffs. A4 = D0 B4 = D0 C4 = D0 D4 = D0 C AMP /PZ coeffs. A5 = -2 D0 B5 = D0 C5 = D0 D5 = 1300 D0 E5 = 2D0 F5 = 1000 D0 C C CALCULATE AVERAGE MW MWT = PPUTL_ AVEMW ( N, IDX, X) 227

250 C Must use as Aspen inverts VMX using this. C INDEX VALUES FOR COMPONENTS IN SIMULATION C IWATER = DMS_KCCIDC ( H2O ) ICO2 = DMS_KCCIDC ( CO2 ) IHCO3 = DMS_KCCIDC ( HCO3 - ) ICO3 = DMS_KCCIDC ( CO3 -- ) IPZ = DMS_KCCIDC ( PZ ) IPZH = DMS_KCCIDC ( PZH + ) IPZCOO = DMS_KCCIDC ( PZCOO - ) IPZCOO2 = DMS_KCCIDC ( PZCOO -2 ) IHPZCOO = DMS_ KCCIDC ( HPZCOO ) IMDEA = DMS_KCCIDC ( C5H13-01 ) IMDEAH = DMS_KCCIDC ( C5H14-01 ) C IAMP = DMS_KCCIDC ( AMP ) IAMPH = DMS_KCCIDC ( AMP + ) IAMPCOO = DMS_ KCCIDC ( AMPCOO ) C Something is wrong with the indexing when pure systems are C encountered. C ASSIGNMENT OF INDEX NUMBERS FOR SPECIES PRESENT DO 50 I = 1, N IF ( IDX (I). EQ. IWATER ) IWATER = I IF ( IDX (I). EQ. ICO2 ) ICO2 = I IF ( IDX (I). EQ. IHCO3 ) IHCO3 = I IF ( IDX (I). EQ. ICO3 ) ICO3 = I IF ( IDX (I). EQ. IPZ ) IPZ = I IF ( IDX (I). EQ. IPZH ) IPZH = I IF ( IDX (I). EQ. IPZCOO ) IPZCOO = I IF ( IDX (I). EQ. IPZCOO2 ) IPZCOO2 = I IF ( IDX (I). EQ. IHPZCOO ) IHPZCOO = I 228

251 IF ( IDX (I). EQ. IMDEA ) IMDEA = I IF ( IDX (I). EQ. IMDEAH ) IMDEAH = I IF ( IDX (I). EQ. IAMP ) IAMP = I IF ( IDX (I). EQ. IAMPH ) IAMPH = I IF ( IDX (I).EQ. IAMPCOO ) IAMPCOO =I 50 CONTINUE C C MOLAR VOLUME OF WATER C VH2O = VI( IWATER ) MWH2O = XMW ( IWATER ) C C LOADING CALCULATIONS C XPZCOO2 = 2D0*X( IPZCOO2 ) C convert to apparent speciation XMDEAT = X( IMDEA )+X( IMDEAH ) XPZT = X( IPZCOO )+X( IPZCOO2 )+X( IHPZCOO )+X( IPZH )+X( IPZ ) XAMPT = X( IAMP )+X( IAMPH )+X( IAMPCOO ) XCO2T = X( ICO2 )+X( IHCO3 )+X( ICO3 ). +X( IPZCOO )+ XPZCOO2 +X( IHPZCOO ). +X( IAMPCOO ) XH2O = X( IWATER )+X( IHCO3 )+X( ICO3 ) C Correction for no loading glitch IF (X( ICO3 ).LT. 1D -15) THEN XCO2T = 0 END IF LDG = XCO2T /(2 D0* XPZT + XMDEAT + XAMPT ) XH2ON = XH2O /( XH2O + XCO2T + XPZT + XMDEAT + XAMPT ) XCO2N = XCO2T /( XH2O + XCO2T + XPZT + XMDEAT + XAMPT ) XMDEAN = XMDEAT /( XH2O + XCO2T + XPZT + XMDEAT + XAMPT ) XPZN = XPZT /( XH2O + XCO2T + XPZT + XMDEAT + XAMPT ) XAMPN = XAMPT /( XH2O + XCO2T + XPZT + XMDEAT + XAMPT ) C Kluge for pure AMP. IF ( XAMPT. EQ. 1) THEN 229

252 XH2ON = 0 END IF C C DENSITY CALCULATION C for PZ, MDEA, and PZ/ MDEA AA= XH2ON *( MWH2O /(1000* VH2O ))+ XMDEAN *(A*T+B)+ XPZN *(C*T+D) AA=AA+ XCO2N *(E*T+F)+ XCO2N *( XMDEAN + XPZN )*(G*T+H) RHOXBLND = AA RHOXPZ = XH2ON *( MWH2O /(1000* VH2O ))+ XPZN *( A2*T+B2). + XCO2N *( C2*T+D2)+ XCO2N * XPZN *( E2*T+F2) RHOXPZ = RHOXPZ *1000 RHOXMDEA = XH2ON *( MWH2O /(1000* VH2O ))+ XMDEAN *( A3*T+B3) RHOXMDEA = RHOXMDEA + XCO2N *C3+D3* XCO2N * XMDEAN C Calculate AMP density RHOXAMP = XH2ON *( MWH2O / VH2O )+ XAMPT *( A4*T+B4). + XCO2N *( C4*T+D4) C Calculate AMP / PZ density RHOXAMPPZ = XH2ON *( MWH2O / VH2O )+ XAMPT *( A5*T+B5)+ XPZN *( C5*T+ ãñ D5). + XCO2N *( E5*T+F5) C Calculate AMP / PZ density. C RHOAMPPZ = XH2ON *( MWH2O /(1000* VH2O ))+ XAMPN *( A5*T+B5)+ XPZN ãñ *( C5*T+D5) C RHOAMPPZ = RHOAMPPZ + XCO2N *( E5*T+F5)+ XCO2N *( XAMPN + XPZN )*( ãñ G5*T+H5) C C ASSIGNMENT OF DENSITY BASED ON SPECIES PRESENT C only works for AMP, PZ, and AMP / PZ C IF ( XAMPT.NE. 0. AND. XPZT.NE. 0) THEN C RHOX = RHOXAMPPZ C ELSE IF ( XPZT.NE. 0D0) THEN C RHOX = RHOXPZ C ELSE C RHOX = RHOXAMP C END IF RHOX = RHOXAMP 230

253 C write to the control panel for debugging C 1000 FORMAT ( XAMPN, D14.5, XCO2N, D14.5, XH2ON, D14 ãñ.5, C. TEMP, D14.5) C WRITE ( MAXWRT_ MAXBUF, 1000) XAMPN, XCO2N, XH2ON, T C CALL DMS_WRTTRM (1) C C C C VMX IF ( KSW (1).EQ. 1) VMX = MWT / RHOX dvmx /dt IF ( KSW (2). EQ. 1) DVMX = DPSUM dvmx /dp IF ( KSW (3). EQ. 1) DPVMX = DPSUM 200 CONTINUE RETURN END B.2 mul2u2.f This subroutine calculates viscosity. It is called in the properties environment at Methods Selected Methods ELECNRTL on the tab Models. In the list, the relevant Property is MULMX, where the model name is set to MUL2USR2 with data set as 1. On the tab Routes, the property MULMX is set to MUMLX-1. C Log keyword added C C $ #1 BY: PING LI 14 - MAY USER ROUTINE FOR MIXTURE ãñ PROPERTIES USING C $ MIXING RULE C LAST MODIFIED : BY BRENT SHERMAN C modified to include AMP / PZ C modified to include AMP C updated with MATLAB regressed values 231

254 C only good for AMP now ; stupid Aspen glitches with missing ãñ components C modified for sensitivity study C BRENTJSHERMAN@GMAIL. COM C ====== ====== ===== cvs revision history =============== SUBROUTINE MUL2U2 (T, P, X, N, IDX, XMW, SG, VLSTD, ãñ MULU2A, * MUI, DMUI, DPMUI, KSW, KOP, NDS, ãñ KDIAG, * MUMX, DMUMX, DPMUMX, KER ) C *********************************************************** C Template for MUL2U2 routine for mixture liquid viscosity C and its temperature, pressure derivatives C C MUMX is the calculated liquid mixture viscosity ( output ) C C DMUMX is the temperature derivative of MUMX ( output ) C C DPMUMX is the pressure derivative of MUMX ( output ) C C All input and output in this user routine are in SI ãñ Units C with Gas constant = C C *********************************************************** C ARGUMENT LIST VARIABLES : C C VARIABLE I/ O TYPE - SPEC DIMENSION DESCRIPTION AND ãñ RANGE C C T I REAL *8 OPERATING TEMPERATURE C P I REAL *8 OPERATING PRESSURE C Z I REAL *8 N COMPONENT MOLE ãñ FRACTION VECTOR C N I INTEGER NUMBER OF COMPONENTS ãñ IN MIXTURE C IDX I INTEGER N VECTOR OF COMPONENT ãñ POINTERS 232

255 C XMW I REAL *8 NCC MOLECULAR WEUGHT FOR ãñ EACH COMPONENT C SG I REAL *8 NCC SPECIFIC GRAVITY FOR ãñ EACH COMPONENT C VLSTD I REAL *8 NCC STD. LIQUID VOLUME ãñ FOR EACH COMPONENT C MULU2A I REAL *8 5, NCC USER DEFIND PARAMETER ãñ FOR THIS MODEL C MUI I REAL *8 N PURE LIQUID VISCOSITY C DMUI I REAL *8 N TEMPERATURE ãñ DERIVATIVE OF MUI C DPMUI I REAL *8 N PRESSURE DERIVATIVE ãñ OF MUI C KSW I INTEGER 3 CALCULATION CODE C KSW (1) FOR PROPERTY C KSW (2) FOR TEMP. ãñ DERIVATIVE C KSW (3) FOR PRES. ãñ DERIVATIVE C VALUE = 1: CALCULATE C VALUE = 0: NO ãñ CALCULATION C KOP I INTEGER OPTION CODE C NDS I INTEGER DATA SET NUMBER C KDIAG I INTEGER MESSAGE PRINTING CODE C IF. GE. 2: PRINT ãñ ERROR MESSAGES C IF. GE. 3: PRINT ãñ WARNING MSGS. C MUMX O REAL *8 LIQUID VISCOSITY C DMUMX O REAL *8 TEMPERATURE ãñ DERIVATIVE OF MUMX C DPMUMX O REAL *8 PRESSURE DERIVATIVE ãñ OF MUMX C KER O INTEGER ERROR RETURN CODE C C ********************************************************** IMPLICIT NONE # include " dms_global. cmn "! access to component indexing 233

256 # include " dms_maxwrt. cmn "! for debugging # include " dms_errout. cmn " # include " ppexec_user. cmn " # include " dms_plex. cmn "! needed for user parameters C C DECLARE VARIABLES USED IN DIMENSIONING C INTEGER N C C DECLARE ARGUMENTS C INTEGER IDX (N), KSW (3), KOP, NDS, KDIAG, KER INTEGER DMS_KCCIDC INTEGER IWATER, ICO2, ICO3, IHCO3,. IPZH, IPZ, IPZCOO, IPZCOO2, IHPZCOO,. IMDEA, IMDEAH, IAMP, IAMPH, IAMPCOO REAL *8 X(N), T, P, XMW (N), SG (1), VLSTD (1), MULU2A (5,1),. MUI (N), DMUI (N), DPMUI (N), MUMX, DMUMX, DPMUMX REAL *8 WATER, CO2, HCO3, CO3, MUW, XCO2T, XPZCOO2,. PZ, PZH, PZCOO, PZCOO2, HPZCOO,. LDG REAL *8 A1, B1, C1, D1, E1, F1, G1, H1, I1, J1,. A2, B2, C2, D2, E2, F2, G2,. A3, B3, C3, D3, E3, F3, G3,. A4, B4, C4, D4, E4, F4, G4, H4, I4, J4,. A5, B5, C5, D5, E5, F5, G5 REAL *8 XPZT, XMDEAT, XAMPT, XWPZ, MWPZ, MWH2O, MWCO2, ãñ MWT, XH2O REAL *8 MWMDEA, XWMDEA, XWAMINE, MUBLEND, MUPZ, MUAMP REAL *8 MUMDEA, XCO2T2, XAMP, XAMPH, AA, BB REAL *8 XWAMPPZ, MUAMPPZ, MWAMP, XWAMP, PPUTL_ AVEMW, FOO REAL *8 B (1) EQUIVALENCE (B (1), IB (1) ) INTEGER MUMOD, DMS_IFCMNC C C DECLARE LOCAL VARIABLES C INTEGER IPROG (2) 234

257 C C DATA STATEMENTS C DATA IPROG /4 HMUL2, 4 HU2 / C C BEGIN EXECUTABLE CODE C C Viscosity is calculated from the regressed data using ãñ Weiland et al FOR PZ C 5m, 7m, 9m. C JORGE M. PLAZA 05/04/09 C C VALUES OBTAINED FROM THE VISCOSITY REGRESSION INTEGER I REAL *8 SUM, DSUM, DPSUM SUM = 0D0 DSUM = 0D0 DPSUM = 0D0 C MDEA /PZ coeffs. A1 = D0 B1 = D0 C1 = D0 D1 = D0 E1 = D0 F1 = D0 G1 = D0 H1 = D0 I1 = D0 J1 = C PZ coeffs. A2 = D0 B2 = D0 C2 = D0 D2 = D0 E2 = D0 F2 = D0 G2 = D0 C MDEA coeffs. A3 = D0 235

258 B3 = D0 C3 = D0 D3 = D0 E3 = D0 F3 = D0 G3 = D0 C AMP coeffs. A5 = D0 B5 = D0 C5 = D0 D5 = D0 E5 = D0 F5 = 0D0 G5 = D0 C AMP /PZ coeffs. A4 = D0 B4 = D0 C4 = D0 D4 = D0 E4 = D0 F4 = D0 G4 = D0 H4 = D0 I4 = D0 J4 = D0 C INDEX VALUES FOR COMPONENTS IN SIMULATION IWATER = DMS_KCCIDC ( H2O ) ICO2 = DMS_KCCIDC ( CO2 ) IHCO3 = DMS_KCCIDC ( HCO3 - ) ICO3 = DMS_KCCIDC ( CO3 -- ) IPZ = DMS_KCCIDC ( PZ ) IPZH = DMS_KCCIDC ( PZH + ) IPZCOO = DMS_KCCIDC ( PZCOO - ) IPZCOO2 = DMS_KCCIDC ( PZCOO -2 ) IHPZCOO = DMS_ KCCIDC ( HPZCOO ) IMDEA = DMS_KCCIDC ( C5H13-01 ) 236

259 IMDEAH = DMS_KCCIDC ( C5H14-01 ) IAMP = DMS_KCCIDC ( AMP ) IAMPH = DMS_KCCIDC ( AMP + ) IAMPCOO = DMS_ KCCIDC ( AMPCOO ) C ASSIGNMENT OF INDEX NUMBERS FOR SPECIES PRESENT DO 50 I = 1, N IF ( IDX (I). EQ. IWATER ) IWATER = I IF ( IDX (I). EQ. ICO2 ) ICO2 = I IF ( IDX (I). EQ. IHCO3 ) IHCO3 = I IF ( IDX (I). EQ. ICO3 ) ICO3 = I IF ( IDX (I). EQ. IPZ ) IPZ = I IF ( IDX (I). EQ. IPZH ) IPZH = I IF ( IDX (I). EQ. IPZCOO ) IPZCOO = I IF ( IDX (I). EQ. IPZCOO2 ) IPZCOO2 = I IF ( IDX (I). EQ. IHPZCOO ) IHPZCOO = I IF ( IDX (I). EQ. IMDEA ) IMDEA = I IF ( IDX (I). EQ. IMDEAH ) IMDEAH = I IF ( IDX (I). EQ. IAMP ) IAMP = I IF ( IDX (I). EQ. IAMPH ) IAMPH = I IF ( IDX (I). EQ. IAMPCOO ) IAMPCOO = I 50 CONTINUE C VISCOSITY OF WATER C MUW = MUI ( IWATER )! varies with loading! C C LOADING CALCULATIONS C I think Peter was correcting the 0 loading glitch here. C I m going to remove the if switch and drop in my fix. C This would have to be verified prior to template modeling.. ãñ. 237

260 XPZCOO2 = X( IPZCOO2 )*2 D0 C XCO2T = X( IPZCOO )+X( IHPZCOO )+X( IHCO3 )+X( ICO3 ) C. + X( ICO2 )+ XPZCOO2 +X( IAMPCOO ) XCO2T = X( IHCO3 )+X( ICO3 )+X( ICO2 )+X( IAMPCOO ) XPZT = X( IPZCOO )+X( IPZCOO2 )+X( IHPZCOO )+X( IPZH )+X( IPZ ) XMDEAT = X( IMDEA ) + X( IMDEAH ) XAMPT = X( IAMP )+X( IAMPH )+X( IAMPCOO ) C takes care of the zero ldg glitch that is due to bad ãñ indexing IF (X( ICO3 ).EQ. 0) THEN XCO2T = 0 END IF C LDG = XCO2T /(2 D0* XPZT + XMDEAT + XAMPT ) LDG = XCO2T / XAMPT C C AMINE MASS FRACTION CALCULATION C C Something is wrong with the index values for the amines. C MWPZ = XMW ( IPZ )! gives 2 different wrong values... C MWAMP = XMW ( IAMP )! ibid. MWPZ = D0 MWAMP = D0 MWCO2 = XMW ( ICO2 ) MWH2O = XMW ( IWATER ) MWMDEA = XMW ( IMDEA ) C CALCULATE AVERAGE MW C XH2O = X( IWATER )+X( IHCO3 )+X( ICO3 ) C MWT = XCO2T * MWCO2 + XPZT * MWPZ + XH2O * MWH2O + XMDEAT * ãñ MWMDEA C. + XAMPT * MWAMP 238

261 MWT = XCO2T * MWCO2 + XH2O * MWH2O + XAMPT * MWAMP XWPZ = ( XPZT * MWPZ )/ MWT XWMDEA = ( XMDEAT * MWMDEA )/ MWT XWAMP = ( XAMPT * MWAMP )/ MWT XWAMINE = XWPZ + XWMDEA XWAMPPZ = XWPZ + XWAMP C C C VISCOSITY CALCULATION C MUBLEND =( A1* XWMDEA +B1* XWPZ +C1)*T+D1* XWMDEA +E1* XWPZ +F1 MUBLEND = MUBLEND *(( G1* XWMDEA +H1* XWPZ +I1*T+J1)* LDG +1 D0) MUBLEND = MUBLEND * XWAMINE /(T **2) MUBLEND = MUW * DEXP ( MUBLEND ) MUPZ =(( A2* XWPZ +B2)*T+( C2* XWPZ +D2))* XWPZ MUPZ = MUPZ *( LDG *( E2* XWPZ +F2*T+G2)+1) /(T **2) MUPZ = MUW * DEXP ( MUPZ ) MUMOD = DMS_IFCMNC ( MUMOD ) MUAMP =(( A5* XWAMP +B5)*T+( C5* XWAMP +D5))* XWAMP MUAMP = MUAMP *( LDG *( E5* XWAMP +F5*T+G5)+1) /(T **2) MUAMP = MUW * DEXP ( MUAMP )*B( MUMOD + IDX ( IAMP )) MUAMPPZ =( A4* XWAMP +B4* XWPZ +C4)*T+D4* XWAMP +E4* XWPZ +F4 MUAMPPZ = MUAMPPZ *(( G4* XWAMP +H4* XWPZ +I4*T+J4)* LDG +1 D0) MUAMPPZ = MUAMPPZ * XWAMPPZ /(T **2) MUAMPPZ = MUW * DEXP ( MUAMPPZ ) C If block needs to include AMP. C only works for PZ and AMP / PZ IF ( XAMPT.NE. 0. AND. XPZT.NE. 0) THEN MUMX = MUAMPPZ ELSE IF ( XAMPT. NE. 0) THEN MUMX = MUAMP ELSE MUMX = MUPZ 239

262 END IF C write to the control panel for debugging C 1000 FORMAT ( XPZT, D14.5, XCO2T, D14.5, IWATER, D14 ãñ.5, C. IAMPH, D14.5) C WRITE ( MAXWRT_ MAXBUF, 1000) XPZT, XCO2T, IWATER, X( ãñ IAMPH ) C CALL DMS_WRTTRM (1) C C C C MUMX IF ( KSW (1).EQ. 1) THEN MUMX = MUAMP END IF dmumx /dt IF ( KSW (2). EQ. 1) DMUMX = DSUM dmumx /dp IF ( KSW (3). EQ. 1) DPMUMX = DPSUM 200 CONTINUE RETURN END B.3 masstransfer.f This is the mass transfer subroutine for the WWC and calculates k g and k l,0. This subroutine is called in the simulation environment under Blocks WWC Packing Rating 1 Rate-based on the Correlations tab in the box labeled Mass transfer coefficient method. The correlation is set to User and the user number is set to 9.The relevant code is framed. The way this routine functions is by calculating everything in front of the diffusion coefficient (PREK) and assigning a power to the diffusion coefficient (EXPKD). C Brent Sherman C Modified for user parameters 240

263 SUBROUTINE USRMTRFC ( KSTG, NCOMPS, IDX, NBOPST, ãñ KPDIAG, 1 XCOMPB, FRATEL, YCOMPB, FRATEV, ãñ PRESS, 2 TLIQ, TVAP, AVMWLI, AVMWVA, ãñ VISCML, 3 DENMXL, SIGMAL, VISCMV, DENMXV, ãñ AREAIF, 4 PREK, EXPKD, COLTYP, USRCOR, ãñ TWRARA, 5 COLDIA, HTPACK, PACSIZ, SPAREA, ãñ CSIGMA, 6 PFACT, PKPRMS, VOIDFR, IPAKAR, ãñ IPTYPE, 7 IVENDR, IPMAT, IPSIZE, WEIRHT, ãñ DCAREA, 8 ARAACT, FLOPTH, NPASS, WEIRL, ãñ IFMETH, 9 SYSFAC, HOLEAR, ITTYPE, TRASPC, ãñ PITCH, A IPHASE, NINT, INT, NREAL, REAL ãñ ) IMPLICIT NONE INTEGER KSTG, NCOMPS, IDX ( NCOMPS ), NBOPST (6), KPDIAG, + COLTYP, USRCOR, IPAKAR, IPTYPE, IVENDR, IPMAT, ãñ IPSIZE, + NPASS, IFMETH, ITTYPE, NINT, INT ( NINT ), IPHASE, ãñ NREAL REAL *8 XCOMPB ( NCOMPS ), FRATEL, YCOMPB ( NCOMPS ), FRATEV, + PRESS, TLIQ, TVAP, AVMWLI, AVMWVA, VISCML, ãñ DENMXL, + SIGMAL, VISCMV, DENMXV, AREAIF, PREK, EXPKD, + TWRARA, COLDIA, HTPACK, PACSIZ, SPAREA, CSIGMA, + PFACT, PKPRMS ( 20), VOIDFR, WEIRHT, DCAREA, ãñ ARAACT, + FLOPTH, WEIRL, SYSFAC, HOLEAR, TRASPC, PITCH, + REAL ( NREAL ) C ***************************************************** 241

264 C LICENSED MATERIAL. PROPERTY OF ASPEN TECHNOLOGY, INC. TO ãñ BE C TREATED AS ASPEN TECH PROPRIETARY INFORMATION UNDER THE ãñ TERMS C OF THE ASPEN PLUS SUBSCRIPTION AGREEMENT. C ******************************************************* C C COPYRIGHT ( C) 2004 C ASPEN TECHNOLOGY, INC. C CAMBRIDGE, MA C C C DESCRIPTION : User provided RateSep routine to calculate ãñ the C liquid ( IPHASE =0) and vapor ( IPHASE =1) ãñ binary mass C transfer coefficient parameters ( PREK, ãñ EXPKD ). C C VARIABLES IN ARGUMENT LIST C C VARIABLE I/ O TYPE DIMENSION DESCRIPTION AND RANGE C ãñ C KSTG I I - SEGMENT NUMBER C NCOMPS I I - NUMBER OF COMPONENTS C IDX I I NCOMPS COMPONENT INDEX VECTOR C NBOPST I I 6 PHYSICAL PROPERTY ãñ OPTION C SET BEAD POINTER C KPDIAG I I - PHYSICAL PROPERTY C DIAGOSTIC CODE C XCOMPB I R NCOMPS BULK LIQUID MOLE ãñ FRACTION C FRATEL I R - FLOW OF LIQUID ( KMOL / ãñ SEC ) C YCOMPB I R NCOMPS BULK VAPOR MOLE ãñ FRACTION 242

265 C FRATEV I R - FLOW OF VAPOR ( KMOL / SEC ãñ ) C PRESS I R - PRESSURE (N/SQ.M) C TLIQ I R - LIQUID TEMPERATURE ( K) C TVAP I R - VAPOR TEMPERATURE ( K) C AVMWLI I R - AVERAGE MOLECULAR ãñ WEIGHT C OF LIQUID MIXTURE C (KG/ KMOL ) C AVMWVA I R - AVERAGE MOLECULAR ãñ WEIGHT C OF VAPOR MIXTURE ( KG/ ãñ KMOL ) C VISCML I R - VISCOSITY OF LIQUID C (N-SEC /SQ.M) C DENMXL I R - DENSITY OF LIQUID ãñ MIXTURE C ( KMOL /CU.M) C SIGMAL I R - SURFACE TENSION OF ãñ LIQUID C (N/M) C VISCMV I R - VISCOSITY OF VAPOR ãñ MIXTURE C (N-SEC /SQ.M) C DENMXV I R - DENSITY OF VAPOR ãñ MIXTURE C ( KMOL /CU.M) C AREAIF I R - INTERFACIAL AREA C ( SEE NOTE -1 BELOW ) C PREK O R - BINARY MASS TRANSFER = C EXPRKD O R - PREK * DIFFUSIVITY ** ãñ EXPKD C ( SEE NOTE -2 BELOW ) C COLTYP I I - TYPE OF COLUMN C 1 = PACKED C 2 = TRAY C USRCOR I I - CALCULATION METHOD ( I. E ãñ. 243

266 C CHOICE OF USER ãñ CORRELATION ) C 1 = USER1 C 2 = USER2 C 3 = USER3 C 4 = USER4 C TWRARA I R - CROSS - SECTIONAL AREA OF C TOWER (SQ.M) C COLDIA I R - COLUMN DIAMETER ( M) C HTPACK I R - HEIGHT OF PACKING IN ãñ THE C SEGMENT (M) C PACSIZ I R - SIZE OF PACKING ( M) C SPAREA I R - SPECIFIC SURFACE AREA ãñ OF C PACKING (SQ.M/CU.M) C CSIGMA I R - CRITICAL SURFACE ãñ TENSION C OF PACKING MATERIAL ( N/ ãñ M) C PFACT I R - PACKING FACTOR (1/ M) C PKPRMS I R 20 PACKING PARAMETERS C PKPRMS (1) = STICHLMAIR ãñ CONSTANT C1 C PKPRMS (2) = STICHLMAIR ãñ CONSTANT C2 C PKPRMS (3) = STICHLMAIR ãñ CONSTANT C3 C PKPRMS (4) = CL IN ãñ BILLET 93 C PKPRMS (5) = CV IN ãñ BILLET 93 C PKPRMS (6) = B IN BRF 85 C PKPRMS (7) = S IN BRF 85 C PKPRMS (8) = H IN BRF 85 C PKPRMS (9) = Fse IN BRF ãñ 92 C PKPRMS ( 10) = CE IN BRF ãñ

267 C PKPRMS ( 11) = THETA IN ãñ BRF 92 C VOIDFR I R - VOID FRACTION OF ãñ PACKING C IPAKAR I I - PACKING ARRANGEMENT C 1 = RANDOM C 2 = STRUCTURED C IPTYPE I I - PACKING TYPE C See IPTYPE in packsr. f C IVENDR I I - PACKING VENDOR CODE C IPMAT I I - PACKING MATERIAL CODE C IPSIZE I I - PACKING SIZE CODE C WEIRHT I R - AVERAGE WEIR HEIGHT ( M) C DCAREA I R - TOTAL AREA OF DOWNCOMER C ON TRAY (SQ.M) C ARAACT I R - TOTAL ACTIVE AREA ãñ AVAILABLE C ON TRAY (SQ.M) C FLOPTH I R - AVERAGE FLOWPATH LENGTH ãñ (M) C NPASS I I - NUMBER OF TRAY PASSES C WEIRL I R - AVERAGE WEIRH LENGTH ( M ãñ ) C IFMETH I I - FLOODING CALCULATION C METHOD ; REQUIRED FOR ãñ SIEVE C TRAY C SYSFAC I R - SYSTEM FACTOR ; REQUIRED ãñ FOR C SIEVE TRAY C HOLEAR I R - HOLE AREA / ACTIVE AREA ; ãñ REQUIRED C FOR SIEVE TRAY C ITTYPE I I - TRAY TYPE C 1 - BUBBLE CAPS C 2 - SIEVE C 3 - GLITSCH BALLAST C 4 - KOCH FLEXITRAY 245

268 C 5 - NUTTER FLOAT ãñ VALVE C TRASPC I R - TRAY SPACING ( M) C PITCH I R - SIEVE TRAY HOLE PITCH ( ãñ M) C IPHASE I I - PHASE QUALIFIER C 0 = LIQUID C 1 = VAPOR C NINT I I - Size of INT C INT I/ O I NINT User correlation INT ãñ array C NREAL I I - Size of REAL C REAL I/ O I NREAL User correlation REAL ãñ array C C NOTE -1: C SPECIFIC INTERFACIAL AREA " AREAIF " HAS THE FOLLOWING ãñ UNITS. C FOR PACKED COLUMNS, THE UNITS IS "SQ.M/CU.M OF ãñ PACKING " C FOR TRAY COLUMNS, THE UNITS IS " SQ. M/ SQ. M ACTIVE ãñ TRAY AREA " C C NOTE -2: C BINMTP = PREK * DIFFUSIVITY ** EXPKD C BINARY MASS TRANSFER COEFFCIENTS " BINMTP " HAVE UNITS ãñ ( KMOL / SEC ) C DIFFUSIVITY HAVE UNITS ( SQ. M/ SEC ) C BINMTP HAS MOLAR DENSITY AND INTERFACIAL AREA ãñ INCLUDED C C ************************************************* C Declare local variables used in the user correlations C # include " dms_global. cmn " # include " dms_errout. cmn " # include " ppexec_user. cmn " # include " dms_maxwrt. cmn " # include " dms_plex. cmn "! needed for user parameters 246

269 REAL *8 RS_BennettHL REAL *8 RS_BennettA REAL *8 RS_BennettC REAL *8 ScLB, ScVB, rholms, rhovms, ReLPrm, + dtemp, ul, uv, Fs, QL, + C, alphae, hl, ShLB, ReV, + vel, hydia, qsoln, w, dtempa REAL *8 B (1) EQUIVALENCE (B (1), IB (1) ) INTEGER KLMOD, IAMP, KLNOTI, KLNOTE INTEGER DMS_ KCCIDC, DMS_ IFCMNC KLMOD = DMS_IFCMNC ( KLMOD ) KLNOTI = DMS_ IFCMNC ( KLNOTI ) KLNOTE = DMS_ IFCMNC ( KLNOTE ) IAMP = DMS_KCCIDC ( AMP ) C C Instead of computing BINMTP from diffusivity as in ãñ RATEFRAC C compute PREK and EXPKD for RateSep C IF ( COLTYP. EQ. 1) THEN C C **** PACKED COLUMN c c This is the beginning of the Dugas Modification c IF ( USRCOR. EQ. 9) THEN C IF ( IPHASE.EQ.0) THEN C C Liquid phase C qsoln = FRATEL / DENMXL / 100 C The factor of 100 is needed since the simulation has 10 x ãñ diameter ( 100 x flow ). C w =

270 C w is the circumference of the column in meters. Diameter of ãñ WWC is m dtemp = 3** * 2** 0. 5 / ** 0. 5 dtemp = dtemp * qsoln **.3333*0.091**.5* w ãñ **.6667/ dtemp = dtemp * (9.81* DENMXL / VISCML * AVMWLI ) ãñ **.1667 C The proceeding equation is a simplification of the equations ãñ in C Cullinane s thesis, pages The simplification for ãñ theta is C used to allow the form Aspen requires. c The constants 0.091, , and refer to the height ãñ of the C WWC, the area of the WWC and acceleration due to gravity. C dtemp =B( KLNOTI + IAMP )! imports kl0 B( KLNOTE + IAMP )= dtemp! exports kl0 C CONVERT K FROM M/ S TO KMOL / S dtemp = dtemp * TWRARA * HTPACK * AREAIF * ãñ DENMXL C This is the conversion used in the Onda mass ãñ transfer routine PREK = dtemp * 1.0 *B( KLMOD + IAMP ) EXPKD = 0.5 D0 C ELSE C C Vapor phase C C From Pacheco s correlation : R*T*kg*d/ DCO2 =1.075( Re*Sc*d/h) ãñ ^0. 85 C Simplified, this gives RTkg =1.075* DCO2 ^.15* d ^.7*( v/h) ^.85 vel = FRATEV / TWRARA / DENMXV hydia = D0 248

271 C This corresponds to the estimated hydraulic diameter of the ãñ WWC, 0.44 cm. dtemp = D0 * hydia ** 0.7 D0 dtemp = dtemp *( vel / (0.091 D0)) ** 0.85 D0 C The constant, 0.091, corresponds to the height of the WWC. C Aspen has a argument for the height of a stage but nothing ãñ for the # C of stages. Therefore the total height was hardwired. dtemp = dtemp * DENMXV * AREAIF * TWRARA * ãñ HTPACK C This time the number of stages is not need b/ c this mass ãñ tranfer C coefficient is the moles reacted by stage C Note : this correlation results in a MT value ( in mol / s) 100 ãñ times C greater than the calculated excel value due to 10 x diameter. PREK = dtemp EXPKD = D0 END IF C END OF IF ( IPHASE ) END IF C END OF IF ( USRCOR ) c C This is the end of the Dugas Modification C IF ( USRCOR. EQ. 1) THEN C user subroutine example for packed column : Onda 68 C C Onda, K., Takeuchi, H. and Okumoto, Y., " Mass ãñ Transfer C Coefficients between Gas and Liquid Phases in ãñ Packed C Columns ", J. Chem. Eng. Jap., 1, (1968) P56 C 249

272 IF ( IPHASE.EQ.0) THEN C C Liquid phase C rholms = DENMXL * AVMWLI ul = FRATEL / TWRARA / DENMXL ReLPrm = rholms * ul / VISCML / AREAIF dtemp = ( rholms /9.81 D0/ VISCML ) **( D0) dtemp = D0 * ( ReLPrm **( D0)) + *(( SPAREA * PACSIZ ) **(0.4 D0)) / dtemp C C CONVERT K FROM M/ S TO KMOL / S dtemp = dtemp * TWRARA * HTPACK * AREAIF * ãñ DENMXL C C COMPOSITION INDEPENDENT PART OF SCHMIDT NUMBER ScLB = VISCML / rholms C PREK = dtemp / DSQRT ( ScLB ) EXPKD = 0.5 D0 C ELSE C C Vapor phase C rhovms = DENMXV * AVMWVA uv = FRATEV / TWRARA / DENMXV ReV = rhovms * uv / VISCMV / SPAREA dtemp = SPAREA * PACSIZ dtemp = dtemp * dtemp IF ( PACSIZ.GE D0) THEN dtemp = D0 / dtemp ELSE dtemp = 2.0 D0 / dtemp END IF dtemp = dtemp * ( ReV **(0.7 D0)) * SPAREA C C CONVERT K FROM M/ S TO KMOL / S 250

273 dtemp = dtemp * TWRARA * HTPACK * AREAIF * ãñ DENMXV C C COMPOSITION INDEPENDENT PART OF SCHMIDT NUMBER ScVB = VISCMV / rhovms C PREK = dtemp * ScVB ** D0 EXPKD = D0 END IF C END OF IF ( IPHASE ) C END IF C END OF IF ( USRCOR ) C ELSE IF ( COLTYP. EQ. 2) THEN C C **** TRAY COLUMN C IF ( USRCOR. EQ. 1) THEN C user subroutine example for tray column : AIChE 58 C C AIChE, Bubble Tray Design Manual : Prediction of ãñ Fractionation C Efficiency, New York, 1958 C C For bubble cap, valve, and sieve trays C IF ( IPHASE.EQ.0) THEN C C Liquid phase C rhovms = DENMXV * AVMWVA rholms = DENMXL * AVMWLI uv = FRATEV / DENMXV / ARAACT Fs = uv * DSQRT ( rhovms ) C = 0.5 D D0 * DEXP ( * WEIRHT ) QL = FRATEL / DENMXL ALPHAE = DEXP ( D0 *( uv* DSQRT ( RHOVMS / DABS ( ãñ RHOLMS - 251

274 1 RHOVMS ))) **0.91 D0) hl = ALPHAE *( WEIRHT + C*( QL/ WEIRL / ALPHAE ) **0.67 ãñ D0) dtemp = D0 *(0.4 D0*Fs D0) * hl + * ARAACT * DENMXL C PREK = dtemp EXPKD = 0.5 D0 C ELSE C C Vapor phase C rhovms = DENMXV * AVMWVA uv = FRATEV / DENMXV / ARAACT Fs = uv * DSQRT ( rhovms ) QL = FRATEL / DENMXL dtemp = * WEIRHT * Fs * QL/ WEIRL dtemp = dtemp * uv * ARAACT * DENMXV C C COMPOSITION INDEPENDENT PART OF SCHMIDT NUMBER ScVB = VISCMV / rhovms C PREK = dtemp / DSQRT ( ScVB ) EXPKD = 0.5 D0 END IF C END OF IF ( IPHASE ) C END IF C END OF IF ( USRCOR ) C END IF C END OF IF ( COLTYP ) C RETURN END 252

275 B.4 dl0.f This is the diffusion subroutine and calculates two diffusion coefficients. One for gaseous species, and one for all others. This code is called in the properties environment at Methods Selected Methods ELECNRTL on the tab Models. In the list, the relevant Property is DL, where the model name is set to DL0USR with data set as 1. C Log keyword added C C $ #1 BY: SUPHAT WATANASIRI 09 - SET USER ROUTINE FOR ãñ LIQUID BINARY C DIFFUSION COEFFICIENTS C LAST MODIFIED : BY BRENT SHERMAN C 12-08: Varying Dcarbamate C ===================== cvs revision history ================== SUBROUTINE DL0U ( T, P, X, N, IDX, IRW, IIW, KCALC, KOP, * NDS, KDIAG, QBIN, KER ) C ******************************************************** C Template for DL0U routine for binary liquid diffusion ãñ coefficients C STUB ROUTINE C C T = temperature C P = pressure ( system ) C X(N) = mole fraction C N = number of components present in X C IDX ( N) = index of component present C IRW = real work area index C IIW = integer work area index C KCALC = calculation code (0= do not calculate, 1 = ãñ calculate ) C KOP ( 10) = model option code C NDS = data set number C KDIAG = diagnostic message level C QBIN ( N, N) = results. Binary diffusion coeffcients. C QBIN ( i, j) is binary diffusion coefficient of component i ãñ in component j 253

276 C KER = error return code (0 = no error ) C All input and output in this user routine are in SI ãñ Units C with Gas constant = C ******************************************************* C IMPLICIT NONE C C DECLARE VARIABLES USED IN DIMENSIONING C INTEGER N # include " dms_global. cmn " # include " dms_errout. cmn " # include " ppexec_user. cmn " # include " dms_maxwrt. cmn " # include " dms_plex. cmn "! needed for user parameters C C DECLARE ARGUMENTS C INTEGER IDX (N), IRW, IIW, KCALC, KOP, NDS, KDIAG, KER INTEGER IWATER, IPZCOO, ICO2, IPZCOO2, IHPZCOO, IHCO3 INTEGER IPZH, IPZ, ICO3, IMDEA, IMDEAH, IN2, IO2,. IAMP, IAMPH, IAMPCOO INTEGER DMS_ KCCIDC, DMS_ IFCMNC REAL *8 X(N), QBIN (N,N), T, P REAL *8 WATER, PZCOO, CO2, PZCOO2, HPZCOO, HCO3, PZH, PZ,. CO3, MDEA, MDEAH,. XPZCOO2 REAL *8 IOND, CO2D, MDEAD, PZD, XMOLT, CO2DW REAL *8 MUMX REAL *8 A, E, BB, THET, C, MU0, MUW, R, HG REAL *8 VISC, LVISC, VM, D, B (1), DC C. ALPHA, BETA, TREF, MUREF, DNAUGHT EQUIVALENCE ( B (1), IB (1) )! needed for user params INTEGER ALPHA, BETA, TREF, MUREF, DNAUGHT, GAMMA, ZETA,. DAMMOD, DCO2MOD, DCO2NOT, DAMNOT integer nbopst (6), name (2) CHARACTER * 256 BUFFER (1) C 254

277 C DECLARE LOCAL VARIABLES C INTEGER IPROG (2), I, J, K C C DATA STATEMENTS C DATA IPROG /4 HDL0U, 4 H / C C BEGIN EXECUTABLE CODE C DIFFUSIVITIES CALCULATED BY (...) METHOD C VALUES OBTAINED FROM THE DIFFUSIVITY REGRESSION KER = 0 IF ( KCALC. EQ. 0) RETURN c C INDEX VALUES FOR COMPONENTS IN SIMULATION C IPZ = DMS_KCCIDC ( PZ ) IPZH = DMS_KCCIDC ( PZH + ) IPZCOO = DMS_KCCIDC ( PZCOO - ) IPZCOO2 = DMS_KCCIDC ( PZCOO -2 ) IHPZCOO = DMS_ KCCIDC ( HPZCOO ) IHCO3 = DMS_KCCIDC ( HCO3 - ) ICO3 = DMS_KCCIDC ( CO3 -- ) IAMP = DMS_KCCIDC ( AMP ) IAMPH = DMS_KCCIDC ( AMP + ) IAMPCOO = DMS_KCCIDC ( AMPCOO ) IMDEA = DMS_KCCIDC ( C5H13-01 ) IMDEAH = DMS_KCCIDC ( C5H14-01 ) IWATER = DMS_KCCIDC ( H2O ) IN2 = DMS_KCCIDC ( N2 ) IO2 = DMS_KCCIDC ( O2 ) ICO2 = DMS_KCCIDC ( CO2 ) C C C ASSIGNMENT OF INDEX NUMBERS FOR SPECIES PRESENT C 255

278 C DO 50 I = 1, N C IF ( IDX (I). EQ. IWATER ) IWATER = I C IF ( IDX (I). EQ. IPZCOO ) IPZCOO = I C IF ( IDX (I). EQ. ICO2 ) ICO2 = I C IF ( IDX (I). EQ. IPZCOO2 ) IPZCOO2 = I C IF ( IDX (I). EQ. IHPZCOO ) IHPZCOO = I C IF ( IDX (I). EQ. IHCO3 ) IHCO3 = I C IF ( IDX (I). EQ. IPZH ) IPZH = I C IF ( IDX (I). EQ. IPZ ) IPZ = I C IF ( IDX (I). EQ. ICO3 ) ICO3 = I C IF ( IDX (I). EQ. IMDEA ) IMDEA = I C IF ( IDX (I). EQ. IMDEAH ) IMDEAH = I C IF ( IDX (I). EQ. IN2 ) IN2 = I C IF ( IDX (I). EQ. IO2 ) IO2 = I C IF ( IDX (I). EQ. IAMPH ) IAMPH = I! ran C IF ( IDX (I). EQ. IAMPCOO ) IAMPCOO = I! ran C IF ( IDX ( I). EQ. IAMP ) IAMP = I! causes error C 50 CONTINUE C Viscosity of solution from Aspen in ( Pa - s) call PPUTL_GOPSET ( NBOPST, NAME ) CALL PPMON_ VISCL ( T, P, X, N, IDX, NBOPST, KDIAG, VISC, ãñ KER ) LVISC = VISC MUMX = LVISC C C Viscosity of water according to Likhachev E. R. Technical ãñ Physics, Vol. 48 N pp C Viscosity in Pa - s E = D0 MU0 = D0 THET = D0 A = D0 BB = D0! avoid name conflict with B (1) C = D0 R = D0 P = P / D0 HG = A * P +(( E - BB * P)/(R * (T - THET - C * P))) 256

279 MUW = MU0 * EXP (HG) C C ALPHA, BETA, GAMMA, and ZETA store the position of the ãñ parameters C They refer to the values set in Properties -- > Parameters -- > ãñ Pure Component -- > USRDEF ALPHA = DMS_IFCMNC ( ALPHA ) BETA = DMS_IFCMNC ( BETA ) GAMMA = DMS_IFCMNC ( GAMMA ) ZETA = DMS_IFCMNC ( ZETA ) DNAUGHT = DMS_ IFCMNC ( DNAUGHT ) TREF = DMS_IFCMNC ( TREF ) MUREF = DMS_IFCMNC ( MUREF ) DCO2MOD = DMS_ IFCMNC ( DCO2MOD ) DAMMOD = DMS_ IFCMNC ( DAMMOD ) DCO2NOT = DMS_ IFCMNC ( DCO2NOT ) DAMNOT = DMS_ IFCMNC ( DAMNOT ) C DIFFUSIVITY OF CO2 IN WATER C Versteeg 1988 Solubility and Diff. Acid Gases CO2DW = 2.35D -06 * EXP ( D0 / T) C C DIFFUSIVITY OF CO2 IN SOLUTION BASED ON VERSTEEG, 2003 CO2D = CO2DW * ( MUW / MUMX )**B( ZETA + IAMP ). *(( T/B( TREF + IAMP ))**B( GAMMA + IAMP )) CO2D =B( DCO2MOD + IAMP )* CO2D! sensitivity study B( DCO2NOT + IAMP )= CO2D C DIFFUSIVITY OF AMINE IN WATER VM = D0 C DNAUGHT = D -11 C ALPHA = D0 C BETA = D0 C TREF = D0 C MUREF = D0! Pa -s C D = DNAUGHT *(( T/ TREF )** ALPHA ) C D = D *(( MUMX / MUREF )** BETA ) 257

280 C B( ) is pointing to the parameter s # in the list of ãñ parameters. C D=B( DNAUGHT + IAMP ) *(( T/B( TREF + IAMP )) C. **B( ALPHA + IAMP )) C D = D *(( MUMX /B( MUREF + IAMP ))**B( BETA + IAMP )) C D=B( DAMMOD + IAMP )*D! sensitivity study C modification for DAm = DCO2 /2 D=B( DAMMOD + IAMP )*( CO2D /2) B( DAMNOT + IAMP )=DC C C C ASSIGNING VALUES IN THE DIFFUSIVITY MATRIX C C DO 200 I = 1, N DO 100 J = 1, N IF (I.EQ.J) THEN QBIN (I,J) = 0D0 ELSE QBIN (I,J) = D! =5.56D -10 for DCO2 sensitivity ãñ study IF (I.EQ. ICO2 ) QBIN (I,J) = CO2D IF (J.EQ. ICO2 ) QBIN (I,J) = CO2D IF (I.EQ.IN2 ) QBIN (I,J) = CO2D IF (J.EQ.IN2 ) QBIN (I,J) = CO2D IF (I.EQ.IO2 ) QBIN (I,J) = CO2D IF (J.EQ.IO2 ) QBIN (I,J) = CO2D END IF 100 CONTINUE 200 CONTINUE C write to the control panel for debugging C 1000 FORMAT ( I, D14.5, J, D14.5, N, D14.5, C. IAMPCOO, D14.5) C 1000 FORMAT ( IN2, I2, ICO2, I2, N, I2, C. IAMP, I2) 258

281 C WRITE ( MAXWRT_ MAXBUF, 1000) IN2, ICO2, N, IAMP C CALL DMS_WRTTRM (1) C WRITE VARIABLES TO HISTORY FILE C C THE WRITE TO UNIT USER_NHSTRY WRITES TO THE HISTORY ãñ FILE C WRITE ( BUFFER, *) Executed fortran subroutine C CALL DMS_ WRTALN ( USER_ NHSTRY, BUFFER (1) ) C WRITE ( BUFFER, *) Viscosity, MUMX C CALL DMS_ WRTALN ( USER_ NHSTRY, BUFFER (1) ) C WRITE ( BUFFER, *) Temperature, T C CALL DMS_ WRTALN ( USER_ NHSTRY, BUFFER (1) ) C WRITE ( BUFFER, *) LVISC, LVISC C CALL DMS_ WRTALN ( USER_ NHSTRY, BUFFER (1) ) C WRITE ( BUFFER, *) C CALL DMS_ WRTALN ( USER_ NHSTRY, BUFFER (1) ) C 999 RETURN END B.5 area.f area.f is called by the blocks WWC and WWC2. The call can be found in the simulation environment, under Blocks WWC Sizing and Rating Packing Rating 1 Rate-based, then on the Correlations tab under the box labeled Interfacial area method. Here Correlation is set to User and User number is set to 9. Most of this routine is not active, so only the relevant code is framed. The origin of the value of m2 {m 3 reproduce it failed. could not be found, and efforts to 259

282 SUBROUTINE AREA ( KSTG, NCOMPS, IDX, NBOPST, ãñ KPDIAG, 1 XCOMPB, FRATEL, YCOMPB, FRATEV, ãñ PRESS, 2 TLIQ, TVAP, AVMWLI, AVMWVA, ãñ VISCML, 3 DENMXL, SIGMAL, VISCMV, DENMXV, ãñ AREAIF, 4 COLTYP, USRCOR, TWRARA, COLDIA, ãñ HTPACK, 5 PACSIZ, SPAREA, CSIGMA, PFACT, ãñ PKPRMS, 6 VOIDFR, IPAKAR, IPTYPE, IVENDR, ãñ IPMAT, 7 IPSIZE, WEIRHT, DCAREA, ARAACT, ãñ FLOPTH, 8 NPASS, WEIRL, IFMETH, SYSFAC, ãñ HOLEAR, 9 ITTYPE, TRASPC, PITCH, NINT, INT, A NREAL, REAL ) IMPLICIT NONE INTEGER KSTG, NCOMPS, IDX ( NCOMPS ), NBOPST (6), KPDIAG, + COLTYP, USRCOR, IPAKAR, IPTYPE, IVENDR, IPMAT, ãñ IPSIZE, + NPASS, IFMETH, ITTYPE, NINT, INT ( NINT ), NREAL REAL *8 XCOMPB ( NCOMPS ), FRATEL, YCOMPB ( NCOMPS ), FRATEV, + PRESS, TLIQ, TVAP, AVMWLI, AVMWVA, VISCML, ãñ DENMXL, + SIGMAL, VISCMV, DENMXV, AREAIF, TWRARA, COLDIA, + HTPACK, PACSIZ, SPAREA, CSIGMA, PFACT, PKPRMS ãñ (20), + VOIDFR, WEIRHT, DCAREA, ARAACT, FLOPTH, WEIRL, + SYSFAC, HOLEAR, TRASPC, PITCH, REAL ( NREAL ) C ********************************************************** C LICENSED MATERIAL. PROPERTY OF ASPEN TECHNOLOGY, INC. TO ãñ BE C TREATED AS ASPEN TECH PROPRIETARY INFORMATION UNDER THE ãñ TERMS C OF THE ASPEN PLUS SUBSCRIPTION AGREEMENT. 260

283 C ********************************************************** C C COPYRIGHT ( C) 2004 C ASPEN TECHNOLOGY, INC. C CAMBRIDGE, MA C C C DESCRIPTION : User provided RateSep routine to calculate ãñ the C specific interface area AREAIF ( see NOTE -1) ãñ. C C VARIABLES IN ARGUMENT LIST C C VARIABLE I/ O TYPE DIMENSION DESCRIPTION AND RANGE C ãñ C KSTG I I - SEGMENT NUMBER C NCOMPS I I - NUMBER OF COMPONENTS C IDX I I NCOMPS COMPONENT INDEX VECTOR C NBOPST I I 6 PHYSICAL PROPERTY ãñ OPTION C SET BEAD POINTER C KPDIAG I I - PHYSICAL PROPERTY C DIAGOSTIC CODE C XCOMPB I R NCOMPS BULK LIQUID MOLE ãñ FRACTION C FRATEL I R - FLOW OF LIQUID ( KMOL / ãñ SEC ) C YCOMPB I R NCOMPS BULK VAPOR MOLE ãñ FRACTION C FRATEV I R - FLOW OF VAPOR ( KMOL / SEC ãñ ) C PRESS I R - PRESSURE (N/SQ.M) C TLIQ I R - LIQUID TEMPERATURE ( K) C TVAP I R - VAPOR TEMPERATURE ( K) C AVMWLI I R - AVERAGE MOLECULAR ãñ WEIGHT C OF LIQUID MIXTURE 261

284 C (KG/ KMOL ) C AVMWVA I R - AVERAGE MOLECULAR ãñ WEIGHT C OF VAPOR MIXTURE ( KG/ ãñ KMOL ) C VISCML I R - VISCOSITY OF LIQUID C (N-SEC /SQ.M) C DENMXL I R - DENSITY OF LIQUID ãñ MIXTURE C ( KMOL /CU.M) C SIGMAL I R - SURFACE TENSION OF ãñ LIQUID C (N/M) C VISCMV I R - VISCOSITY OF VAPOR ãñ MIXTURE C (N-SEC /SQ.M) C DENMXV I R - DENSITY OF VAPOR ãñ MIXTURE C ( KMOL /CU.M) C AREAIF O R - INTERFACIAL AREA C ( SEE NOTE -1 BELOW ) C COLTYP I I - TYPE OF COLUMN C 1 = PACKED C 2 = TRAY C USRCOR I I - CALCULATION METHOD ( I. E ãñ. C CHOICE OF USER ãñ CORRELATION ) C 1 = USER1 C 2 = USER2 C 3 = USER3 C 4 = USER4 C TWRARA I R - CROSS - SECTIONAL AREA OF C TOWER (SQ.M) C COLDIA I R - COLUMN DIAMETER ( M) C HTPACK I R - HEIGHT OF PACKING IN ãñ THE C SEGMENT (M) C PACSIZ I R - SIZE OF PACKING ( M) 262

285 C SPAREA I R - SPECIFIC SURFACE AREA ãñ OF C PACKING (SQ.M/CU.M) C CSIGMA I R - CRITICAL SURFACE ãñ TENSION C OF PACKING MATERIAL ( N/ ãñ M) C PFACT I R - PACKING FACTOR (1/ M) C PKPRMS I R 20 PACKING PARAMETERS C PKPRMS (1) = STICHLMAIR ãñ CONSTANT C1 C PKPRMS (2) = STICHLMAIR ãñ CONSTANT C2 C PKPRMS (3) = STICHLMAIR ãñ CONSTANT C3 C PKPRMS (4) = CL IN ãñ BILLET 93 C PKPRMS (5) = CV IN ãñ BILLET 93 C PKPRMS (6) = B IN BRF 85 C PKPRMS (7) = S IN BRF 85 C PKPRMS (8) = H IN BRF 85 C PKPRMS (9) = Fse IN BRF ãñ 92 C PKPRMS ( 10) = CE IN BRF ãñ 92 C PKPRMS ( 11) = THETA IN ãñ BRF 92 C VOIDFR I R - VOID FRACTION OF ãñ PACKING C IPAKAR I I - PACKING ARRANGEMENT C 1 = RANDOM C 2 = STRUCTURED C IPTYPE I I - PACKING TYPE C See IPTYPE in packsr. f C IVENDR I I - PACKING VENDOR CODE C IPMAT I I - PACKING MATERIAL CODE C IPSIZE I I - PACKING SIZE CODE C WEIRHT I R - AVERAGE WEIR HEIGHT ( M) 263

286 C DCAREA I R - TOTAL AREA OF DOWNCOMER C ON TRAY (SQ.M) C ARAACT I R - TOTAL ACTIVE AREA ãñ AVAILABLE C ON TRAY (SQ.M) C FLOPTH I R - AVERAGE FLOWPATH LENGTH ãñ (M) C NPASS I I - NUMBER OF TRAY PASSES C WEIRL I R - AVERAGE WEIRH LENGTH ( M ãñ ) C IFMETH I I - FLOODING CALCULATION C METHOD ; REQUIRED FOR ãñ SIEVE C TRAY C SYSFAC I R - SYSTEM FACTOR ; REQUIRED ãñ FOR C SIEVE TRAY C HOLEAR I R - HOLE AREA / ACTIVE AREA ; ãñ REQUIRED C FOR SIEVE TRAY C ITTYPE I I - TRAY TYPE C 1 - BUBBLE CAPS C 2 - SIEVE C 3 - GLITSCH BALLAST C 4 - KOCH FLEXITRAY C 5 - NUTTER FLOAT ãñ VALVE C TRASPC I R - TRAY SPACING ( M) C PITCH I R - SIEVE TRAY HOLE PITCH ( ãñ M) C NINT I I - Size of INT C INT I/ O I NINT User correlation INT ãñ array C NREAL I I - Size of REAL C REAL I/ O I NREAL User correlation REAL ãñ array C C NOTE -1: 264

287 C SPECIFIC INTERFACIAL AREA " AREAIF " HAS THE ãñ FOLLOWING UNITS. C FOR PACKED COLUMNS, THE UNITS IS "SQ.M/CU.M OF ãñ PACKING " C FOR TRAY COLUMNS, THE UNITS IS " SQ. M/ SQ. M ACTIVE ãñ TRAY AREA " C C ************************************************************* C Declare local variables used in the user correlations C REAL *8 WeL, dtemp, uv, rhovms, + ul, rholms, ReL, FrL, ul2, + ReV, d, Wprime, + AREAE, At, hp, Ft, Fse, ap, + S, cosg, pi, theta C C Compute specific interface area as described above C Check COLTYP / USRCOR if providing multiple area ãñ correlations C IF ( COLTYP. EQ. 1) THEN C C **** PACKED COLUMN C IF ( USRCOR. EQ. 1) THEN C user subroutine example for packed column : Onda 68 C C Onda, K., Takeuchi, H. and Okumoto, Y., " Mass ãñ Transfer C Coefficients between Gas and Liquid Phases in ãñ Packed C Columns ", J. Chem. Eng. Jap., 1, (1968) p. 56 C rholms = DENMXL * AVMWLI ul = FRATEL / TWRARA / DENMXL ul2 = ul * ul ReL = rholms * ul / VISCML / SPAREA FrL = SPAREA * ul2 / D0 265

288 C WHERE D0 IS GRAVITY CONSTANT IN M/ S **2 WeL = rholms * ul2 / SIGMAL / SPAREA dtemp = D0 *(( CSIGMA / SIGMAL ) **0.75 D0) + *( ReL **0.1 D0)*( FrL **( D0)) + *( WeL **0.2 D0) dtemp = 1. D0 - DEXP ( dtemp ) AREAIF = SPAREA * dtemp C Uses specific area of the packing for both random ãñ and structured ELSEIF ( USRCOR. EQ. 2) THEN AREAIF = SPAREA!(sq.m/cu.m) C Uses the Rocha - Bravo - Fair ( 1992) Model as defined ãñ in Aspen Plus ELSEIF ( USRCOR. EQ. 3) THEN IF ( SIGMAL. GE ) THEN cosg = 5.211*(10**( * SIGMAL )) ELSE cosg = 0.9 END IF pi = theta = PKPRMS (11) *pi /180 rholms = DENMXL * AVMWLI ul = FRATEL / TWRARA / DENMXL ul2 = ul * ul S = PKPRMS (7) WeL = ul2 * rholms * S / SIGMAL FrL = ul2 / (S * 9.81 D0) ReL = ul * S * rholms / VISCML 266

289 Ft = (29.12*(( WeL * FrL ) **0.15) *(S **0.359) )/( ãñ ReL **0.2) + /( VOIDFR **0.6) /( dsin ( theta ) ãñ **0.3) + /(1 -(0.93* cosg )) Fse = PKPRMS (9)! Surface enhancement factor ap = SPAREA! Specific area of packing C At = TWRARA ( cross sectional area of column ) C hp = HTPACK ( height of packing ) AREAIF = Ft*Fse *ap IF ( IPSIZE. eq AND. IPTYPE. eq. 701) THEN AREAIF = AREAIF * ELSE AREAIF = AREAIF END IF C AREAIF = dsin ( PKPRMS (11) *Pi) C WRITE (*,*) denmxl, avmwli, fratel, twrara, S Elseif ( USRCOR. EQ. 9) THEN AREAIF = D0 c Actual wetted area of the WWC is cm2. c Column diamter is listed as m ( a factor of 10 ãñ bigger than the area which matches gas flow area ) and ãñ height as 9.1 cm. c This gives a surface area of m2/ m3 for the ãñ Aspen Simulations. END IF C END OF IF ( USRCOR ) C ELSE IF ( COLTYP. EQ. 2) THEN C C **** TRAY COLUMN C 267

290 IF ( USRCOR. EQ. 1) THEN C user subroutine example for tray column : Scheffe - ãñ Weiland 87 C C Scheffe, R.D. and Weiland, R.H., " Mass Transfer C Characteristics of Valve Trays." Ind. Eng. Chem. ãñ Res. C 26, (1987) p. 228 C C The original paper only mentioned valve tray. C It is also used for bubble - cap tray and sieve tray ãñ. C C CHARACTERISTIC LENGTH IS ALWAYS 1 METER. d = 1.0 D0 rholms = DENMXL * AVMWLI rhovms = DENMXV * AVMWVA ul = FRATEL / TWRARA / DENMXL uv = FRATEV / TWRARA / DENMXV ReL = rholms * ul * d / VISCML ReV = rhovms * uv * d / VISCMV Wprime = WEIRHT / d AREAIF = D0 * ReV ** D0 * ReL ** D0 AREAIF = AREAIF * Wprime ** END IF C END OF IF ( USRCOR ) C END IF C END OF IF ( COLTYP ) C RETURN END 268

291 Appendix C WWC Model Details C.1 Transfers There are five transfer blocks. The ones with a 2 suffix are identical to the 1 version but for the second WWC (WWC2). ˆ T-LEAN transfers entire stream LEANIN to LEANFLSH ˆ T-P1 transfers the pressure of 2MPZ to 6 places * H2O stream * CO2 stream * FEEDGAS stream * GH2O stream * block WWC variable STAGE-PRES ID1: 1 * block SATURATE variable PRES ˆ ˆ T-P2 T-T1 transfers temperature of 2MPZ to 11 places * H2O stream * CO2 stream 269

292 * FEEDGAS stream * GH2O stream * block HTR variable TEMP * block SATURATE variable TEMP * block WWC variable TEMP-EST ID1: 1 * block WWC variable TEMP-EST ID1: 2 * block WWC variable TEMP-EST ID1: 3 * block LEANFLSH variable TEMP * block RICHFLSH variable TEMP ˆ T-T2 C.2 Design Specification There is one design specification DS-AUTOL, which adjusts the loading automatically. The variables are defined in Table C.1. The specification is DFLUX=0 with tolerance of The variable is the loading, Parameter 310, between 0.1 mol CO 2 {mol alk and 0.9 mol CO 2 {mol alk. Table C.1: Design specification variable definitions Variable DFLUX PFDES EFDES PFABS EFABS Definition Parameter Parameter no.=101 Parameter Parameter no.=21 Physical type=flux Parameter Parameter no.=102 Physical type=flux Parameter Parameter no.=22 Physical type=flux Parameter Parameter no.=103 Physical type=flux 270

293 C.3 Calculator Blocks There are four calculator blocks. The code included here comes from the PZ/HMPD mass transfer files. There are instances of hard coding that the user should be careful to overwrite. In case of long lines of code, a line break is indicated by ãñ. C.3.1 C-FLUX This block calculates the flux and mass transfer coefficients. Variable I/O Definition AINTF I Block-Var Block=WWC Variable=INTF-AREA Sentence=PROFRATE ID1=1 Units=sqm NCO2IN1 I Mole-Flow Stream=GASIN Substream=MIXED Component=CO2 Units=kmol/sec NCO2OU1 I Mole-Flow Stream=GASOUT Substream=MIXED Component=CO2 Units=kmol/sec NCO2IN2 I Mole-Flow Stream=GASIN2 Substream=MIXED Component=CO2 Units=kmol/sec NCO2OU2 I Mole-Flow Stream=GASOUT2 Substream=MIXED Component=CO2 Units=kmol/sec FLUX1 O Parameter Parameter no.=21 Initial value=0 FLUX2 O Parameter Parameter no.=22 Initial value=0 YCO2I1 I Block-Var Block=WWC Variable=YINTF Sentence=XY-RATE ID1=CO2 ID2=1 YCO2O1 I Block-Var Block=WWC Variable=YINTF Sentence=XY-RATE ID1=CO2 ID2=3 YCO2I2 I Block-Var Block=WWC2 Variable=YINTF Sentence=XY-RATE ID1=CO2 ID2=1 YCO2O2 I Block-Var Block=WWC2 Variable=YINTF Sentence=XY-RATE ID1=CO2 ID2=3 271

294 Variable I/O Definition LPVAP I Stream-Prop Stream=LOVHD Prop- Set=PPCO2PA Units=Pa RPVAP1 I Stream-Prop Stream=ROVHD Prop- Set=PPCO2PA Units=Pa RPVAP2 I Stream-Prop Stream=ROVHD2 Prop- Set=PPCO2PA Units=Pa KGP1 O Parameter Parameter no.=11 Initial value=0 KGP2 O Parameter Parameter no.=12 Initial value=0 BIGKG1 O Parameter Parameter no.=31 Initial value=0 BIGKG2 O Parameter Parameter no.=32 Initial value=0 DPIN O Parameter Parameter no.=14 Initial value=0 DPOUT O Parameter Parameter no.=15 Initial value=0 LMPD1 O Parameter Parameter no.=16 LMPD2 O Parameter Parameter no.=17 PCO2IN1 I Stream-Prop Stream=GASIN Prop- Set=PPCO2PA Units=Pa PCO2OU1 I Stream-Prop Stream=GASOUT Prop- Set=PPCO2PA Units=Pa PCO2IN2 I Stream-Prop Stream=GASIN2 Prop- Set=PPCO2PA Units=Pa PCO2OU2 I Stream-Prop Stream=GASOUT2 Prop- Set=PPCO2PA Units=Pa PSTAGE I Block-Var Block=WWC Variable=PRES Sentence=PROFILE ID1=1 Units=N/sqm DPINL O Parameter Parameter no.=18 DPOUTL O Parameter Parameter no.=19 DPING O Parameter Parameter no.=70 DPOUTG O Parameter Parameter no.=71 KGAS1 O Parameter Parameter no.=72 KGAS2 O Parameter Parameter no.=73 OUT1 O Parameter Parameter no.=74 OUT2 O Parameter Parameter no.=75 Table C.2: C-FLUX variable definitions; I/O is input/output. C Brent Sherman

295 C Updated on to clarify Kg and kg calcs. C Modified for 6 WWC C Modified for 2 PE only 1 WWC C Modified for 2 WWC C Added kg calculation. C Calculate the flux ( mol /m^2 - sec ). FLUX1 =(( NCO2IN1 - NCO2OU1 ) /(3* AINTF )) *1000 FLUX2 =(( NCO2IN2 - NCO2OU2 ) /(3* AINTF )) *1000 C Desorption mass transfer calculations. C Calculate overall gas mass tx. Kg IF ( NCO2IN1. NE. 0) THEN DPIN =( PCO2IN1 - RPVAP1 ) ELSE DPIN =(0 - RPVAP1 ) END IF DPOUT =( PCO2OU1 - LPVAP ) LMPD1 =( DPIN - DPOUT )/ DLOG (( DPIN )/( DPOUT )) BIGKG1 = FLUX1 / LMPD1 C Calculate kg prime. PCI = YCO2I1 * PSTAGE PCO = YCO2O1 * PSTAGE DPIN =( PCI - RPVAP1 ) DPOUT =( PCO - LPVAP ) LMPD1 =( DPIN - DPOUT )/ DLOG (( DPIN )/( DPOUT )) KGP1 = FLUX1 / LMPD1 C Calculate kg for gas side. IF ( NCO2IN1. NE. 0) THEN DPOUTG =( PCO2IN1 - PCO ) ELSE DPOUTG =(0 - PCO ) END IF DPING =( PCO2OU1 - PCI ) LMPD1 =( DPING - DPOUTG )/ DLOG (( DPING )/( DPOUTG )) KGAS1 = FLUX1 / LMPD1 OUT1 = PCO 273

296 OUT2 = DPOUTG C Absorption mass transfer calculations. C Calculate overall gas mass tx. Kg IF ( NCO2IN2. NE. 0) THEN DPIN =( PCO2IN2 - RPVAP2 ) ELSE DPIN =(0 - RPVAP2 ) END IF DPOUT =( PCO2OU2 - LPVAP ) LMPD2 =( DPIN - DPOUT )/ DLOG (( DPIN )/( DPOUT )) BIGKG2 = FLUX2 / LMPD2 C Calculate kg prime. PCI = YCO2I2 * PSTAGE PCO = YCO2O2 * PSTAGE DPINL =( PCI - RPVAP2 ) DPOUTL =( PCO - LPVAP ) LMPD2 =( DPINL - DPOUTL )/ DLOG (( DPINL )/( DPOUTL )) KGP2 = FLUX2 / LMPD2 C Calculate kg for gas side. IF ( NCO2IN2. NE. 0) THEN DPING =( PCO2OU2 - PCI ) ELSE DPING = PCO2OU2 END IF DPOUTG =( PCO2IN2 - PCO ) LMPD2 =( DPING - DPOUTG )/ DLOG (( DPING )/( DPOUTG )) KGAS2 = FLUX2 / LMPD2 C WRITE ( NTERM,*) FLUX C.3.2 C-KEQ This block calculates the reverse rates at the system temperature. The K eq at T ref is hard coded. 274

297 Variable I/O Definition K0F1 O React-Var Block=R-PZMP Variable=PRE-EXP Sentence=RATE-CON ID1=1 K0F4 O React-Var Block=R-PZMP Variable=PRE-EXP Sentence=RATE-CON ID1=4 K0F6 O React-Var Block=R-PZMP Variable=PRE-EXP Sentence=RATE-CON ID1=6 K0R1 O React-Var Block=R-PZMP Variable=PRE-EXP Sentence=RATE-CON ID1=11 K0R4 O React-Var Block=R-PZMP Variable=PRE-EXP Sentence=RATE-CON ID1=14 K0R6 O React-Var Block=R-PZMP Variable=PRE-EXP Sentence=RATE-CON ID1=16 EAR1 O React-Var Block=R-PZMP Variable=ACT- ENERGY Sentence=RATE-CON ID1=11 Units=kJ/kmol EAR4 O React-Var Block=R-PZMP Variable=ACT- ENERGY Sentence=RATE-CON ID1=14 Units=kJ/kmol EAR6 O React-Var Block=R-PZMP Variable=ACT- ENERGY Sentence=RATE-CON ID1=16 Units=kJ/kmol EAF1 O React-Var Block=R-PZMP Variable=ACT- ENERGY Sentence=RATE-CON ID1=1 Units=kJ/kmol EAF4 O React-Var Block=R-PZMP Variable=ACT- ENERGY Sentence=RATE-CON ID1=4 Units=kJ/kmol EAF6 O React-Var Block=R-PZMP Variable=ACT- ENERGY Sentence=RATE-CON ID1=6 Units=kJ/kmol OUT1 O Parameter Parameter no.=500 OUT2 O Parameter Parameter no.=501 OUT3 O Parameter Parameter no.=502 KF1 O Parameter Parameter no.=504 KF4 O Parameter Parameter no.=

298 Variable I/O Definition KF6 O Parameter Parameter no.=506 KR1 O Parameter Parameter no.=507 KR4 O Parameter Parameter no.=508 KR6 O Parameter Parameter no.=509 T I Stream-Var Stream=LEANIN Substream=MIXED Variable=TEMP Units=K XMP I Mole-Frac Stream=LEANIN Substream=MIXED Component=MP XMPH I Mole-Frac Stream=LEANIN Substream=MIXED Component=MPH+ XPZ I Mole-Frac Stream=LEANIN Substream=MIXED Component=PZ XPZH I Mole-Frac Stream=LEANIN Substream=MIXED Component=PZH+ XPZCOO I Mole-Frac Stream=LEANIN Substream=MIXED Component=PZCOO- XPZCOO2 I Mole-Frac Stream=LEANIN Substream=MIXED Component=PZCOO-2 XHPZCOO I Mole-Frac Stream=LEANIN Substream=MIXED Component=HPZCOO XHCO3 I Mole-Frac Stream=LEANIN Substream=MIXED Component=HCO3- XCO2 I Mole-Frac Stream=LEANIN Substream=MIXED Component=CO2 XH2O I Mole-Frac Stream=LEANIN Substream=MIXED Component=H2O GPZ I Stream-Prop Stream=LEANIN Prop-Set=GPZ GPZH I Stream-Prop Stream=LEANIN Prop-Set=GPZH GPZCOO I Stream-Prop Stream=LEANIN Prop- Set=GPZCOO GPZCOO2 I Stream-Prop Stream=LEANIN Prop- Set=GPZCOO2 GHPZCOO I Stream-Prop Stream=LEANIN Prop- Set=GHPZCOO GMP I Stream-Prop Stream=LEANIN Prop-Set=GMP 276

299 Variable I/O Definition GMPH I Stream-Prop Stream=LEANIN Prop-Set=GMPH GHCO3 I Stream-Prop Stream=LEANIN Prop- Set=GHCO3 GCO2 I Stream-Prop Stream=LEANIN Prop-Set=GCO2 GH2O I Stream-Prop Stream=LEANIN Prop-Set=GH2O AKEQ1 O Parameter Parameter no.=510 AKEQ4 O Parameter Parameter no.=511 AKEQ6 O Parameter Parameter no.=512 Table C.3: C-KEQ variable definitions; I/O is input/output. C Brent Sherman C C Modified for 2 PE. C If switch for T = TREF bug. C Modified for PZ/ MP C Calculates reverse reaction parameters using thermodynamic ãñ KEQ. C FYI This whole block could be a subroutine. C Outputs the reverse parameters and check. C Alternatively, I could use EA =0 and not hard code. C C This block solves for k0_ r. C These are the thermo eq. at 40 C specific to PZ/ MP. 40 KEQ1 = KEQ4 = KEQ6 = C C This saves me time to enter forward parameters. C Forward pre - exponentials. K0F1 = K0F4 = K0F6 = C Reverse pre - exponentials. K0R1 = K0F1 /40 KEQ1 K0R4 = K0F4 /40 KEQ4 277

300 K0R6 = K0F6 /40 KEQ6 C EA in J/ mol EAF1 =44900 EAF2 = EAF6 = C C This block solves for EA_ r. C Calculate kf at T. C R in J/mol -K; T in K R =8.314 TREF = KF1 = K0F1 * DEXP ( -( EAF1 /R) *((1/ T) -(1/ TREF ))) KF4 = K0F4 * DEXP ( -( EAF4 /R) *((1/ T) -(1/ TREF ))) KF6 = K0F6 * DEXP ( -( EAF6 /R) *((1/ T) -(1/ TREF ))) C Calculate species activities. AMP = GMP * XMP AMPH = GMPH * XMPH APZ = GPZ * XPZ APZH = GPZH * XPZH APZCOO = GPZCOO * XPZCOO APZCOO2 = GPZCOO2 * XPZCOO2 AHPZCOO = GHPZCOO * XHPZCOO AHCO3 = GHCO3 * XHCO3 ACO2 = GCO2 * XCO2 AH2O = GH2O * XH2O C Calculate reaction equilibria at T from activities. AKEQ1 =( AMPH * AHCO3 )/( AMP * AH2O * ACO2 ) AKEQ4 =( APZCOO * AMPH )/( APZ * AMP * ACO2 ) AKEQ6 =( APZCOO2 * AMPH )/( APZCOO * AMP * ACO2 ) C Calculate and export the EA_ r for the T. C This keeps the equilibrium at all T. KR1 = KF1 / AKEQ1 KR4 = KF4 / AKEQ4 KR6 = KF6 / AKEQ6 C Avoids errors at 40 C. IF (T.EQ. TREF ) THEN EAR1 =

301 EAR4 = EAR6 = ELSE EAR1 =- DLOG ( KR1 / K0R1 )*R /((1/ T) -(1/ TREF )) EAR4 =- DLOG ( KR4 / K0R4 )*R /((1/ T) -(1/ TREF )) EAR6 =- DLOG ( KR6 / K0R6 )*R /((1/ T) -(1/ TREF )) ENDIF C C This block checks the calculations. C Calculate reaction equilibria at T from k s. KR1K = K0R1 * DEXP ( -( EAR1 /R) *((1/ T) -(1/ TREF ))) KR4K = K0R4 * DEXP ( -( EAR4 /R) *((1/ T) -(1/ TREF ))) KR6K = K0R6 * DEXP ( -( EAR6 /R) *((1/ T) -(1/ TREF ))) KKEQ1 = KF1 / KR1K KKEQ4 = KF4 / KR4K KKEQ6 = KF6 / KR6K C Use a relative difference to check. RXN1 =( AKEQ1 - KKEQ1 )/ AKEQ1 RXN4 =( AKEQ4 - KKEQ4 )/ AKEQ4 RXN6 =( AKEQ6 - KKEQ6 )/ AKEQ6 C Debugging outputs. OUT1 = RXN1 OUT2 = RXN4 OUT3 = RXN6 C.3.3 C-LDGADJ This block calculates the stream flow rates given a loading. The amine molalities are hard coded. C Brent Sherman C C Updated for 2 PE only C Purpose : Use with sensitivity to run all cases. C Molalities. MMP =2 MPZ =4 279

302 Table C.4: C-KEQ variable definitions; I/O is input/output. Variable I/O Definition LDGADJ I Parameter Parameter no.=310 XMP O Parameter Parameter no.=302 XPZ O Parameter Parameter no.=322 XH2O O Parameter Parameter no.=303 XCO2 O Parameter Parameter no.=305 MWAVG O Parameter Parameter no.=300 MMP O Parameter Parameter no.=306 MPZ O Parameter Parameter no.=321 MCO2 O Parameter Parameter no.=311 Q O Parameter Parameter no.=301 QMP O Stream-Var Stream=MP Substream=MIXED Variable=MOLE-FLOW Units=kmol/sec QPZ O Stream-Var Stream=PZ Substream=MIXED Variable=MOLE-FLOW Units=kmol/sec QCO2 O Stream-Var Stream=CO2 Substream=MIXED Variable=MOLE-FLOW Units=kmol/sec QH2O O Stream-Var Stream=H2O Substream=MIXED Variable=MOLE-FLOW Units=kmol/sec MH2O O Parameter Parameter no.=315 T O Stream-Var Stream=MP Substream=MIXED Variable=TEMP Units=K P O Stream-Var Stream=MP Substream=MIXED Variable=PRES Units=N/sqm 280

303 MH2O = MCO2 = LDGADJ *(2* MPZ + MMP ) XMP = MMP /( MMPZ + MPZ + MCO2 + MH2O ) XPZ = MPZ /( MMPZ + MPZ + MCO2 + MH2O ) XCO2 = MCO2 /( MMPZ + MPZ + MCO2 + MH2O ) XH2O = MH2O /( MMPZ + MPZ + MCO2 + MH2O ) MWAVG = XMP * XPZ * XCO2 * XH2O *18.02 C Flow in kmol / sec C assumes Q is 4 ml/ s and rho is 1 g/ ml C applies 100 x scaling due to diameter 10 x scaling Q =0.4/ MWAVG C convert from mol / sec to kmol / sec QMP =Q* XMP QPZ =Q* XPZ QCO2 =Q* XCO2 QH2O =Q* XH2O C.3.4 C-SAT This block varies the amount of flow rate of water to the saturator block. Excessive water flow will remove CO 2 and result in an inaccurate driving force. C Brent Sherman C C Match the water flow to saturation. IF (T.EQ ) THEN GH2O =8D -6 ENDIF IF (T.EQ ) THEN GH2O =2D -5 ENDIF IF (T.EQ ) THEN GH2O =3D -5 ENDIF IF (T.EQ ) THEN GH2O =6D -5 ENDIF 281

304 GH2O2 = GH2O 282

305 Appendix D WWC VLE Data Quality D.1 Operating Criteria The criteria to consider when judging VLE data from a WWC column are: 1. absorption and desorption modes 2. number of points 3. spacing of points 4. driving force. Other major things to consider are how the loading and temperature are determined. The loading measurement is error prone and can have a profound impact on the data, as explained in of Li (2015). I m going to focus on the four criteria I ve laid out. I ll explain the rationale behind these criteria using Figure 1, which is high quality data. Taking the criteria in order, we see that we have run the column in both desorption and absorption mode. This means that when we determine the equilibrium point, we are interpolating rather than extrapolating. My feeling is that running in only absorption mode is still common practice, though any WWC should be able to run in both modes. 283

306 Figure D.1: Experimental CO 2 flux and partial pressure driving force measured for 5 m PZ/2 m AEP at 0.25 mol CO 2 {mol alk and 80 C. Reproduction of Figure 3.3 of Li (2015). Six points were collected: three desorption and three absorption. The number of points is the least settled of these criteria, and you ll frequently encounter data with fewer (or more rarely more) points. Six points is optimal in my opinion. More points yields diminishing returns, while fewer points is vulnerable to one data point ruining a set. You ve probably encounter data with only four points. The rationale is that cutting two points per set saves roughly twenty minutes. To me, this isn t worth the time savings as most of the time cost is spent getting the temperature stable. The points should be smoothly spaced. This allows for a high quality line to be drawn through them. Spacing the points poorly will weight the line artificially. This is why we want a symmetric distribution of points around the equilibrium, with 284

307 a balanced number of desorption points and absorption points. The standard spacing is to set the driving force, corresponding to the CO 2 partial pressure in the gas phase (P CO2 ) equal to 0, 0.3, 0.6, 1.4, 1.7, and 2 times the equilibrium CO 2 partial pressure of the solvent (P CO 2 ) (Chen and Rochelle, 2013). Lastly, let s consider the driving force. You ll notice that there are no points near the equilibrium. This is because the flux is calculated from the difference in two large numbers. Near the equilibrium that difference is small and can lead to bad errors. You ll also notice that the driving force of the strongest desorption and strongest absorption points is balanced. Again, this prevents skewing the data. In short, the best way to judge data is a plot like Figure D.1. Doing this allows you to immediately check all four criteria. Keep in mind that loading and temperature errors are not captured from this type of plot. D.2 Examples I ll show some lesser quality data and explain how I judged it as such. Figure D.2 shows data that passes the first two criteria and fails the last two. The WWC has been run in both desorption and absorption modes. Six points have been measured. However, the points are poorly spaced. The weakest two desorption points are too close. The driving force is also poor. The strongest absorption point has too high of a driving force, making the data set skew towards absorption. Also, the weakest desorption point is a bit close to equilibrium. However, these data are still good enough to use. Figure D.3 fails nearly all of the criteria. While the WWC was run in both modes, the number of points is too few and odd, the spacing is poor, and the driving forces are unbalanced. Additional points should be measured before using this data. 285

308 1.5E-8 flux (mol/sec-cm 3 ) 1.0E-8 5.0E-9 0.0E driving force (Pa) -5.0E-9-1.0E-8 Figure D.2: Lower quality data from 2 m PZ/3 m HMPD at 0.24 mol CO 2 {mol alk and 20 C (Du et al., 2016). 286

309 flux 1.5E-6 (mol/sec-cm 3 ) 1.0E-6 5.0E-7 0.0E+0-1.5E+4-1.0E+4-5.0E+3 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 driving force (Pa) -5.0E-7-1.0E-6 Figure D.3: Poor data from 2 m PZ/3 m HMPD at 0.24 mol CO 2 {mol alk and 80 C (Du et al., 2016). 287

310 Appendix E RSM MATLAB Code This is the code used to do the MATLAB step in the response surface methodology method flow chart of Figure 3.4 % Brent Sherman % % Mass Transfer RSM % Purpose : Regress kinetic constants and give statistics. % Version : V1 % Change log % V0: used xmincon ; abandoned due to problems of statistics % V1: uses fitnlm clc ; clear all ; close all %% Import data from XL sheetname = RSM.1.1 ; path =[ C:\ Users \ Brent \ Documents \ Research \... Aspen \ Spreadsheets \ AMP Mass Transfer V1. xlsx ]; % N. B. The XL file needs to be saved to update values. [T,loading, fd_basis, fa_basis, k1d_sens, k1a_sens, k9d_sens, ãñ k9a_sens ]=... AMP_RSM (path, sheetname,9,21) ; %% Import basis parameters x0 = AMP_import_basis ( path, sheetname,50,53) ; % X0 is [k0,1; EA,1; k0,9; EA,9] in kmol /sec -m3 and J/ mol %% Calculate basis rates ( kmol /sec -m3) R =8.314; %J/mol -K Tref =313.15; %K k k0*exp ( -( EA/R) *((1./ T) -(1/ Tref ))); 288

311 k1_basis =k(x0 (1),x0 (2),T); k9_basis =k(x0 (3),x0 (4),T); %% define function % using Peter Frailie s formulation for the response surface f_reg f_basis, k1_basis, k1_reg, k1_sens, k9_basis, k9_reg, ãñ k9_sens )... f_basis.*(( k1_reg./ k1_basis ).^ k1_sens ).*(( k9_reg./ k9_basis ãñ ).^ k9_sens ); %% try nonlinear fit function % stack desorption on top of absorption xdata =[[ T;T] [ fd_basis ; fa_basis ] [ k1_basis ; k1_basis ] [ k9_basis ãñ ; k9_basis ]... [ k1d_sens ; k1a_sens ] [ k9d_sens ; k9a_sens ]]; n= max ( size (T)) *2; % # of data pts (x2 accounts for des and abs ãñ ) fitted_data = table ( xdata (:,1),xdata (:,2),xdata (:,3),xdata (:,4), ãñ xdata (:,5),... xdata (:,6),ones (n,1), VariableNames,... { T, basis, k1_basis, k9_basis, k1_sens, k9_sens, ãñ target }); modelfun x (:,2).*( k(b (1),x0 (2),x (:,1) )./x(:,3) ).^x ãñ (:,5)....*( k(b (2),B (3),x (:,1) )./x(:,4) ).^x(:,6) ; x0fit =[ x0 (1) x0 (3) x0 (4) ] ; % initial guess % N. B. fitnlm cannot handle constrained parameters due to ãñ restrictions of % the algorithm. lsqcurvefit can handle constraints, but it ãñ does just as % little stats as xmincon. mdl = fitnlm ( fitted_data, modelfun, x0fit ); ci= coefci (mdl,0.05) ; D= sqrt ( eye ( size ( mdl. CoefficientCovariance,1) ).* mdl. ãñ CoefficientCovariance ); corr = tril ( inv (D)* mdl. CoefficientCovariance * inv (D)); 289

312 mdl. Coefficients mdl. SSE % table ( mdl. Coefficients, stdev_param, Rownames,{ k0,1 ; EA ãñ,1 ; k0,9 ; EA,9 }) 290

313 Appendix F 5 m 2MPZ Viscosity These data were collected by Nina Salta under the direction of Le Li using the method documented in the disseration of Li (2015). They were not reported, and so the data are tabulated here. 291

314 20 C 40 C 60 C Loading [2MPZ] % µ % µavg. % µ % dev µavg. % µ % µavg. % ldg mol alk/kg sol dev cp dev cp dev cp dev cp dev cp dev cp dev Table F.1: Detailed viscosity data for 8 m 2MPZ viscosity; % dev = std. dev {avg. 292

315 Appendix G HMPD pk a Data These data were collected by Arlinda Ciftja using the method described by Kim et al. (2011). The amine concentration was 0.01 mol {kg soln. The basis is asymmetric, molality. Two measurements were taken. Table G.1 reports the average along with the % deviation D calculated by Equation (G.1). %D σ2 px i q x avg 100 (G.1) Table G.1: Dissociation constant, ln K a, of HMPD T ln K a D C %

316 Appendix H 2 m PZ/3 m HMPD Reanalyzed Data These data were collected by Yang Du (2016) using less accurate method based off of Li (2015). The analysis by Du did not regress the equilibrium partial pressure of CO 2 to go through the origin of the flux vs LMPD curve. Therefore, the analysis was repeated and is presented here. For the WWC column for all blends of PZ/HMPD, Du used the average of reported values instead of the slope. This resulted in errors up to 49% in the reported kg 1 values. 294

317 Table H.1: Reanalysis of 2 m PZ/3 m HMPD from raw data of Du (2016) T loading P CO 2 k 1 g ( C) p mol CO 2 {mol alkq (Pa) p mol {sec-pa-m 2 q

318 Appendix I 2-Methylpiperazine Model Manual 296

319 CCSI Process Models User Manual Version November 15,

320 CCSI Process Models User Manual This material was produced under the DOE Carbon Capture Simulation Initiative (CCSI), and copyright is held by the software owners: ORISE, LANS, LLNS, LBL, PNNL, CMU, WVU, et al. The software owners and/or the U.S. Government retain ownership of all rights in the CCSI software and the copyright and patents subsisting therein. Any distribution or dissemination is governed under the terms and conditions of the CCSI Test and Evaluation License, CCSI Master Non-Disclosure Agreement, and the CCSI Intellectual Property Management Plan. No rights are granted except as expressly recited in one of the aforementioned agreements. Protected under CCSI MASTER NDA i 298

321 CCSI Process Models User Manual Table of Contents CCSI Process Models Abstract Reporting Issues Version Log MPZ CO 2 Capture Simulation Introduction Predicting CO 2 Solubility Features List Tutorial Absorber Simulation Stripper Simulation Usage Information Environment/Prerequisites Support Restrictions Next Steps Debugging How to Debug Known Issues Reporting Issues Model History Thermodynamic Model Kinetic Model References List of Figures Figure 1: CO 2 solubility in 8 m 2MPZ Figure 2: A simple absorber Figure 3: Excerpt of stream results Figure 4: Design specification REMOVAL results Figure 5: Packed column rating results Figure 6: Stripper simulation flowsheet Figure 7: Excerpt of stream results Figure 8: The design specification results Figure 9: Excerpt from packed column rating results Protected under CCSI MASTER NDA ii 299

322 CCSI Process Models User Manual Figure 10: Thermodynamic heat of absorption of 8 m 2MPZ calculated from Equation Figure 11: Calorimetric heat of absorption of 8 m 2MPZ calculated from Equation Figure 12: The absolute differences between the two heat of absorption calculations, which agree well until a loading of 0.25 mol CO 2 /mol alkalinity, where the zwitterion becomes significant Figure 13: WWC process flow diagram for Aspen Plus Figure 14: Boundary layer discretization. The x-axis is fraction through the boundary layer with the gas-liquid interface at left and the bulk liquid at right Figure 15: Brønsted plot showing the reaction rate constant (k Am-b ) versus the pka of a base for an amine catalyzed by a base, k Am-base Figure 16: 8 m 2MPZ kinetic fit. There is a linear bias with temperature. Filled points represent absorption, open points desorption. Dashed lines delineate the target range ±20% Figure 17: 8 m 2MPZ kinetic fit. Model flux ratioed to experimental flux shows no clear trend with loading. Filled points represent absorption, open points desorption. The dashed lines delineate the target range ±20% List of Tables Table 1: Excerpt of 2MPZ VLE Results... 4 Table 2: Boundary Layer Discretization... 9 Table 3: Variables for the LOADINGS Calculator Table 4: The Thunder Moon Chemistry Block Table 5: Reaction Set for 2MPZ with Forward Reactions above the Rule Table 6: Diffusivity Parameter Values To obtain support for the products within this package, please send an to ccsi-support@acceleratecarboncapture.org. Protected under CCSI MASTER NDA iii 300

323 CCSI Process Models User Manual CCSI Process Models 1.0 ABSTRACT 2MPZ Aspen Plus Process Model: This is an Aspen Plus absorption/stripping model for CO 2 capture from natural gas or coal-fired power plants using the solvent 8 molal 2-methylpiperazine (2MPZ). This model can be used for techno-economic assessments, pilot plant data reconciliation, and process design. The solvent has greater oxidative stability than MEA, is thermally stable up to 151 C, has a greater viscosity-normalized capacity (0.89 mol CO 2 /kg solvent vs 0.62 mol CO 2 /kg solvent), and has 37% faster mass transfer than 7 molal MEA. The solvent suffers from higher cost than MEA, five-times higher viscosity, and solid precipitation at very low CO 2 loading. The model was constructed using sequential regression of bench-scale experimental thermodynamic and mass transfer data. The thermodynamics are modeled using the asymmetric enrtl model to fit CO 2 solubility data. A custom flowsheet simulates the wetted-wall column used for mass-transfer data collection. The diffusion of amine and kinetic rate constants were regressed to match the experimental CO 2 flux data. Activity-based kinetics were used to account for the high non-ideality of the system. Protected under CCSI MASTER NDA

324 CCSI Process Models User Manual 2.0 REPORTING ISSUES To report an issue, please send an to 3.0 VERSION LOG Product Version Number Release Date Description CCSI Process Models /15/ November IAB Release 2MPZ CO 2 Capture Simulation /10/2013 Initial release. Protected under CCSI MASTER NDA

325 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 2MPZ CO 2 Capture Simulation 1.0 INTRODUCTION This document describes a 2-methylpiperazine (2MPZ) CO 2 capture system process simulation. The amine scrubbing system is divided into separate absorber and stripper simulations. The model consists of the ThunderMoon.bkp file with supporting subroutines full.dll and 2mpzloc.opt. This manual was written using Aspen Plus V Predicting CO 2 Solubility Knowing the solubility of CO 2 enables the user to select a loading range, as well as a stripper temperature and pressure. In this five minute example, a property analysis block is used to generate a series of isotherms for a fixed amine concentration and variable loading. 1. Open the ThunderMoon.bkp file, press F8 to open the Data Browser, and then under Setup change the Run type to Property Analysis. 2. In the left pane, navigate to Properties Analysis. Click New to create a new analysis block. Enter its ID as 82MPZVLE and then select the type as generic. Change the system basis to Mass and then set H2O to 1000 kg/sec. 3. On the Variable tab, change Temperature to Vapor Fraction and then set Vapor Fraction to 1e-05. Create three variables: (1) Temperature, (2) Mole Flow 2MPZ, and (3) Mole Flow CO2. Select these variables and then click Range/List at the bottom of the window to define them. a. Temperature is a list: , , , , b. Mole Flow 2MPZ is a list: 8 c. Mole Flow CO2 is a range: Lower=0, Upper=8, Points=20 4. On the Tabulate tab, select PPCO2-KP for the partial pressure of CO 2 in kilopascals. 5. Run the simulation. A pop-up window displays, Table generation completed with warnings. Results are present. Display Run-Status results form? Click Cancel. 6. To view the results, navigate to Properties Analysis 82MPZVLE Results. Some of the results are shown in Table 1. Using additional graphing software, the user can plot results as shown in Figure 1. Protected under CCSI MASTER NDA

326 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Table 1: Excerpt of 2MPZ VLE Results Temp K Mole Flow 2MPZ kmol/sec Mole Flow CO2 kmol/sec Vapor PPMX CO2 kpa Protected under CCSI MASTER NDA

327 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 1.00E E E+05 P*CO 2 (Pa) 1.00E E E E C 100 C 60 C 20 C 1.00E Figure 1: CO 2 solubility in 8 m 2MPZ. Using Property Analysis blocks, the user can explore many other properties of the solvent, such as vapor pressure or viscosity. 1.2 Features List Loading (mol CO 2 /mol alk.) This product is a thermodynamic and kinetic model of 2MPZ for amine scrubbing; therefore, it represents the CO 2 solubility, speciation, amine vapor pressure, heat capacity, pka, heat of absorption, density, and viscosity for 2MPZ. While the model can extrapolate over a range of amine concentration, loading, and temperature, it is based on data collected primarily at 8 m 2MPZ with loadings ranging from 0 to 0.4 mol CO 2 /mol alkalinity. Protected under CCSI MASTER NDA

328 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 2.0 TUTORIAL This tutorial assumes basic knowledge of Aspen Plus software. Consult the Aspen Plus documentation, Getting Started Building and Running a Process Model, for additional information. 2.1 Absorber Simulation Description This example describes how to simulate a rate-based absorber. It includes tips on converging simulations, using design specifications to meet process criteria, and determining the proper discretization to be used for rate-based calculations. Examples Setup 1. Build the flowsheet of Figure 2, using an ABSBR1 RadFrac column. In the Model Library pane at the bottom of the window, navigate to Columns RadFrac ABSBR1. (If the model library is not visible, press F10. ) Place the block on the flowsheet and name it ABSORBER. If a prompt to name the flowsheet does not display, right-click the block and then select Rename Block. Figure 2: A simple absorber. 2. Select Material STREAMS in the model library. Create GASIN by clicking the arrow on the left of the block (the feed) and then clicking elsewhere. Create RICH by clicking the arrow at the bottom (the bottoms). Create GASOUT by clicking the arrow at the top (the vapor distillate). Lastly, create LEAN by clicking the now blue arrow on the left (the feed). Protected under CCSI MASTER NDA

329 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 3. Double-click GASIN to configure it as follows: a. Temperature: 40 C b. Pressure: 1 atm c. Total flow: 5 kmol/sec d. Composition: Mole-Frac i. H2O: 7.3 ii. CO2: 12 iii. N2: 80.7 Note: Aspen normalizes the mole fractions to one. 4. Select LEAN from the left pane and configure it as follows: a. Temperature: 40 C b. Pressure: 1 atm c. Total flow: 20 kmol/sec d. Composition: Mole-Frac i. H2O: ii. CO2: 4.32 iii. 2MPZ: 8 5. In the left pane, navigate to Blocks ABSORBER and then configure its Setup as follows: a. On the Configuration tab: i. Calculation type: Rate-Based ii. Number of stages: 30 iii. Condenser: none iv. Reboiler: none b. On the Streams tab: i. GASIN On-Stage 30 ii. LEAN On-Stage 1 c. On the Pressure tab, set the Top stage pressure to 1 atm. 6. Configure the absorber Reactions with two sections: a. One starts on stage 1 and ends on stage 3 with Reaction ID ZERO. b. The other starts on stage 4 and ends on stage 30 with Reaction ID ZERO. Note: This reaction set is used to ease convergence of the simulation. It is the 2MPZ reaction set with all activation energies and reaction pre-exponentials set to 0. Protected under CCSI MASTER NDA

330 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 7. Create a new pack rating section 1. Configure its Specifications as follows: a. Starting stage: 1 b. Ending stage: 30 c. Type: MELLAPAK d. Vendor: SULZER e. Material: STANDARD f. Dimension: 250X g. Section diameter: 8 meter h. Section packed height: 15 meter Note: As the column is packed, the number of stages does not represent trays. It is purely a computational construct. The more stages, the more finely discretized the column. However, this results in more computation time. As a very rough approximation, one stage for every half meter of packing is recommended. Use more stages for greater temperature and mass transfer gradients. i. Navigate to Rate-based from the left pane ( Pack Rating 1 Rate-based ). Configure it as follows: i. Select the Rate-based calculations check box. ii. Flow model: Countercurrent iii. Film resistance: 1. Liquid phase: Discrxn 2. Vapor phase: Film j. On the Holdups tab, set the Holdup Method Correlation to Percent-Data and then set the Liquid Phase to Correlation with % of free volume set to 5. k. On the Design tab, select the Design mode check box to calculate column diameter with Base Stage as 30. Protected under CCSI MASTER NDA

331 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual l. On the Optional tab, set the Additional discretization points to the 32 shown in Table 2. Table 2: Boundary Layer Discretization Point Liquid Film Point Liquid Film E E Under Flowsheeting, navigate to Options Calculator and then create a new Calculator named C-RM. This block calculates the fraction of CO 2 captured. a. On the Define tab, create three variables: Variable Name Information Flow Definition REMOVE Export Parameter Parameter no. = 2 CO2IN CO2OUT Import Import Mole-Flow Stream = GASIN; Substream = MIXED; Component = CO2 Units=kmol/sec Mole-Flow Stream = GASOUT; Substream = MIXED; Component = CO2 Units=kmol/sec b. On the Calculate tab, type F REMOVE=(CO2IN-CO2OUT)/CO2IN. Note: Between F and REMOVE there are five spaces. Protected under CCSI MASTER NDA

332 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 9. Create a Design Spec named REMOVAL. Running the Simulation a. On the Define tab, create a variable REMOVE and assign it to parameter 2. b. On the Spec tab: i. Spec: REMOVE ii. Target: 0.90 iii. Tolerance: c. On the Vary tab: i. Type: Stream-Var ii. Stream: LEAN iii. Variable: MOLE-FLOW iv. Lower: 5 v. Upper: Deactivate the design spec by right-clicking on the design spec and then selecting Deactivate. 2. Run the simulation, which provides Aspen a good initial guess. 3. Change the absorber Reactions to R-1 from ZERO for stages one to three. Run the simulation. 4. Change the absorber Reactions to R-1 from ZERO for the remaining stages. Run the simulation. 5. Increase the section packed height under the pack rating to 12 m, and then run the simulation. 6. Review the C-RM calculator block results ( Flowsheeting Options Calculator C-RM Results on the Define Variable tab) to determine if the fractional CO 2 removal is approximately a. Increase the LEAN stream total flow in 10 kmol/sec increments until the percent removal is within 0.10 of Be sure to run the simulation after each increment. 7. Once approximately 90% removal has been achieved, activate the Design Spec REMOVAL by right-clicking on Design Spec Removal and then selecting Activate. Run the simulation. 8. The converged absorber should now be removing 90% of the incoming CO 2. Results should be similar to those shown in Figures 3 5 below. View the results by selecting Results Summary Streams, Flowsheeting Options Design Spec Removal Results, and Blocks ABSORBER Pack Rating 1 Results. Protected under CCSI MASTER NDA

333 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Figure 3: Excerpt of stream results. Protected under CCSI MASTER NDA

334 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Figure 4: Design specification REMOVAL results. Figure 5: Packed column rating results. Protected under CCSI MASTER NDA

335 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 2.2 Stripper Simulation Description This example is a guide to simulating a simple stripper and a heat exchanger. Examples Setup 1. Open the ThunderMoon.bkp file. 2. Construct the flowsheet shown in Figure 6. From Columns in the Model Library, select RadFrac STRIP1 for the stripper. From Heat Exchangers, select Heater for CX-COLD, CX-HOT, and HX-TRIM. From Pressure Changers, select pump for LEANPUMP. Create the streams using Material STREAMS. Figure 6: Stripper simulation flowsheet. Protected under CCSI MASTER NDA

336 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 3. Set HOTRICH to the values from the absorber example. a. Temperature: K b. Pressure: 11 bar c. Total flow: kmol/sec d. Composition: Mole-Frac i. H2O ii. CO iii. 2MPZ 8 Note: The pressure is set as if coming from a pump. This pump is neglected for simplicity. 4. Set CX-COLD : a. Pressure: 0 N/sqm b. Temperature: 85 C c. Valid phases: Liquid-Only Note: Pressure drop is neglected. 5. Configure the STRIPPER Setup as follows: a. On the Configuration tab: i. Calculation type: Rate-Based ii. Number of Sstages: 15 iii. Condenser: None iv. Reboiler: Kettle v. Reboiler duty: 225 MW b. On the Streams tab, set COLDRICH to stage 1 as liquid. c. On the Pressure tab, set the top stage pressure to 3 bar. 6. Set reactions in the stripper to stages 1 15 using Chemistry ID REDUCED. 7. Create a new Pack Rating for the stripper and configure it as follows: a. Under Setup, stages 1 14 use MELLAPAK, SULZER, STANDARD, 250X with a diameter of 5 m, and a section packed height of 2 m. b. Under Rate-Based, select the Rate-based calculations check box with Film Resistance set to Film for liquid and vapor phases. On the Design tab, select the Design mode check box to calculate column diameter and then set the base stage to Configure CX-HOT : a. Temperature: 50 C b. Pressure: 0 N/sqm 9. Configure LEANPUMP : a. Discharge pressure: 250 kpa Protected under CCSI MASTER NDA

337 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 10. Configure HX-TRIM : a. Temperature: 40 C b. Pressure: 0 N/sqm Note: This flowsheet takes the rich stream from the previous absorber tutorial, passes it through a cross-exchanger, and then to the stripper. CX-COLD and CX-HOT are used to simulate the cross exchanger. HX-TRIM is the trim cooler to lower the lean solvent down to 40 C prior to entering the absorber. 11. Create a LOADINGS calculator. a. Define the variables as shown in Table 3. b. The Fortran code is F F LLDG=(LCO2+LCO3+LHCO3+L2MPZCOO+2*L2MPZC2+LH2MPZC)/ (2*(L2MPZ+L2MPZH+L2MPZCOO+L2MPZC2+LH2MPZC)) F F RLDG=(RCO2+RCO3+RHCO3+R2MPZCOO+2*R2MPZC2+RH2MPZC)/ (2*(R2MPZ+R2MPZH+R2MPZCOO+R2MPZC2+RH2MPZC)) Table 3: Variables for the LOADINGS Calculator Variable Name Information Flow Definition RLDG Export Parameter Parameter no. = 3 LLDG Export Parameter Parameter no. = 4 LCO2 Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = CO2 L2MPZ Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = 2MPZ L2MPZH Import Mole-Frac Stream = STR-LEAN Substream = MIXED; Component = 2MPZH+ L2MPZCOO Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = 2MPZCOO L2MPZC2 Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = 2MPZCOO2 LH2MPZC Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = H2MPZCOO LHCO3 Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = HCO3- LCO3 Import Mole-Frac Stream = STR-LEAN; Substream = MIXED; Component = CO3-- R2MPZ Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = 2MPZ R2MPZH Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = 2MPZH+ R2MPZCOO Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = 2MPZCOO R2MPZC2 Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = 2MPZCOO2 RH2MPZC Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = H2MPZCOO RHCO3 Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = HCO3- RCO3 Import Mole-Frac Stream = HOTRICH; Substream = MIXED; Component = CO3-- Protected under CCSI MASTER NDA

338 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 12. Create a Design Spec named SETLEAN. a. Define LLDG as Parameter 4. b. Spec LLDG to 0.27 with a tolerance of c. On the Vary tab under Manipulated variable limits, Lower: 0 and Upper: 5.5E8 Watts. Under Manipulated variable set the following: i. Type: Block-Var ii. Block: STRIPPER iii. Variable: QN 13. Create a Design Spec named SETTEMP. Running the Simulation a. Define TEMP as Stream-Var Stream=STR-LEAN Substream=MIXED Variable=TEMP Units=K. b. Spec TEMP to K with a tolerance of c. On the Vary tab, set the manipulated variable limits to to N/sqm. Under Manipulated variable set the following: i. Type: Block-Var ii. Block: STRIPPER iii. Variable: STAGE-PRES iv. ID1: 1 1. Deactivate both design specs. 2. Run the simulation. 3. Review the lean loading (LLDG) in the LOADINGS calculator block by navigating to the Define Variable tab of Results. Decrease the stripper reboiler duty in 25 MW increments until the lean loading is close to the desired value of Run the simulation after each decrement. 4. Activate the SETLEAN design spec and then run the simulation. 5. Activate the SETTEMP design spec and then run the simulation. 6. Create a heat stream from CX-HOT to CX-COLD named Q-XC. To clear the temperature specification of CX-COLD, double-click the block, right-click temperature under flash specifications, and then select Clear. 7. Run the simulation. Results similar to those in Figures 8 9 should be displayed. To view these results, navigate to Results Summary Streams, Flowsheeting Options Design Spec SETLEAN Results, Flowsheeting Options Design Spec SETTEMP Results, and Blocks STRIPPER Pack Rating 1 Results. Protected under CCSI MASTER NDA

339 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Figure 7: Excerpt of stream results. Figure 8: The design specification results. Protected under CCSI MASTER NDA

340 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Figure 9: Excerpt from packed column rating results. Protected under CCSI MASTER NDA

341 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 3.0 USAGE INFORMATION 3.1 Environment/Prerequisites This product requires Aspen Plus V7.3 or newer with an Aspen Rate-Based Distillation license. As such, the supported environments are limited to: Windows XP SP3 Windows Vista Business SP2 Windows Vista Ultimate SP2 Windows 7 Ultimate (32- and 64-Bit) Windows 7 Professional (32- and 64-Bit) 3.2 Support Support can be obtained from ccsi-support@acceleratecarboncapture.org or by filling out the Submit Feedback/Request Support form available on the product distribution page. 3.3 Restrictions The model is centered at an amine concentration of 8 m. Extrapolating far from this concentration should be done with care. 3.4 Next Steps The next release will include a heat exchanger model that predicts area as a function of pressure drop and solvent viscosity and a model for k l a in the absorber and stripper as a function of viscosity. Protected under CCSI MASTER NDA

342 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 4.0 DEBUGGING The model is running correctly if it is converging for the above tutorials with similar results. If it is not, see the next section, How to Debug. 4.1 How to Debug Always run the simulation with the control panel visible. It is the only output available during computation, and it notifies the user whether or not the simulation will converge. This enables the user to avoid wasting time on fruitless computation. Furthermore, it alerts the user to any problems encountered during computation. Subroutine Errors If the following error message displays: *** SEVERE ERROR COULD NOT RESOLVE USER OR IN-LINE FORTRAN SUBROUTINE(S): the simulation will not run. The possible causes and solutions are: 1. The.bkp file and the.dll and.opt files are not located in the same directory. Move all the files into the same directory to resolve this. 2. The linker is not specified in the run settings. Set the linker to 2mpzloc.opt. Simulation Problems If warnings are displayed regarding unusual liquid molefrac profile or unusual component production profile, follow the suggested instructions in the error message. If a warning is displayed stating that the water liquid viscosity model MULH2O is violated due to the temperature being lower than the minimum temperature limit, something is not specified correctly. Review the inputs and re-run. Ignore flooding errors (TPSAR MESSAGE: XXX.XX% FLOOD IN COLUMN EXCEEDS 80%) unless it displays in the final step. Aiding Convergence Only reinitialize when absolutely necessary. Make small changes in a converged model. Converge an initial, simple case before enabling reactions and design specifications. It is recommended that only small changes are made; therefore, only turn on one of these at a time. Before enabling the design specification, the variable should be close to the desired value. Protected under CCSI MASTER NDA

343 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 4.2 Known Issues Flash errors can occur if the solvent goes above 0.5 mol CO 2 / mol alk. Multiple warnings display regarding property data while processing input specifications that follow this pattern, PARAMETER XXX DATA SET 1 FOR COMPONENT 2MPZ HAS BEEN ENTERED MORE THAN ONCE. THE LAST ENTRY WILL BE USED., where XXX is the parameter name. In running the tutorials, warnings display that the mole fractions are normalized to unity. Warnings display that IONRDL is missing for 2MPZCOO, 2MPZCOO2, and 2MPZH+. Using design mode to calculate column diameter for the absorber can lead to inconsistent results. With the absorber tutorial, the model may converge with a diameter of 4.58 m. 4.3 Reporting Issues To report an issue, please send an to ccsi-support@acceleratecarboncapture.org. Protected under CCSI MASTER NDA

344 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 5.0 MODEL HISTORY This section details the creation of Thunder Moon, including the data used in the regressions. 5.1 Thermodynamic Model Thunder Moon is based on previous work using the electrolyte NRTL model (Chen, 2011). The model is focused on the operating conditions for capture from a coal-fired power plant, meaning a loading range from 0.27 to 0.37 mol CO 2 /mol alkalinity. The thermodynamic framework was modified slightly in that the default chemistry used had proton and hydroxide ions removed to enhance convergence. The equilibrium chemistry is shown in Table 4. Table 4: The Thunder Moon Chemistry Block Model Chemistry 2 2MPZ + CO 2 2MPZCOO + 2MPZH + 2 2MPZCOO + CO 2 2MPZCOO2 + H2MPZCOO 2MPZCOO + CO 2 + H2O HCO 3 + H2MPZCOO 2MPZ + H2MPZCOO 2MPZH + + 2MPZCOO 2MPZCOO + HCO 3 CO 3 + H2MPZCOO Changing the chemistry reaction set did not significantly affect the thermodynamic model; therefore, all fits are the same as in (Chen, 2011). In the process of verifying all fits, a discrepancy between the calorimetric and thermodynamic methods for calculating heat of absorption was uncovered. (1) (2) where Q is the net-duty of the flash block, and n CO 2 is the molar flow rate of gaseous CO 2. The heat of absorption is calculated by sending a loaded solvent stream and a gaseous CO 2 stream to a flash block for a bubble point calculation. The latter method using Equation 1 is shown in Figure 10; while the former using Equation 2 is shown in Figure 11. (The process model uses the calorimetric heat of absorption.) The disagreement between the two methods occurs above a loading of 0.25, as shown in Figure 12. It is suspected that the deviation above a loading of 0.25 mol CO 2 /mol alkalinity is due to the zwitterion becoming a significant species. Protected under CCSI MASTER NDA

345 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual ΔH abs,thermo (kj/mol) C 40 C 60 C 80 C 100 C 120 C 140 C Loading (mol CO 2 /mol alk) Figure 10: Thermodynamic heat of absorption of 8 m 2MPZ calculated from Equation ΔH abs,cal (kj/mol) C 40 C 60 C 80 C 100 C 120 C 140 C Loading (mol CO 2 /mol alk) Figure 11: Calorimetric heat of absorption of 8 m 2MPZ calculated from Equation 2. Protected under CCSI MASTER NDA

346 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual ΔH abs,thermo ΔH abs,cal (kj/mol) C C C 40 C 60 C 80 C 140 C Loading (mol CO 2 /mol alk) Figure 12: The absolute differences between the two heat of absorption calculations, which agree well until a loading of 0.25 mol CO 2 /mol alkalinity, where the zwitterion becomes significant. In conclusion, the thermodynamic model represents amine volatility, CO 2 solubility, pk a, speciation, density, and viscosity data (Chen, 2011). Protected under CCSI MASTER NDA

347 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 5.2 Kinetic Model The kinetics were regressed using a wetted wall column (WWC) Aspen Plus simulation to adjust reaction rate constants, activation energies, and diffusion parameters to match experimental flux values within 20% (Plaza, 2011; Rochelle et al., 2012). Activity-based kinetics are used as in (Chen, 2011). The process flow diagram is shown in Figure 13. Figure 13: WWC process flow diagram for Aspen Plus. The solvent is fed as three separate streams of amine, water, and CO 2. When mixed, the solvent heats up due to heat of mixing and speciation; therefore, a heater is used to return it to the desired temperature for isothermal operation. The entire WWC is operated isothermally to mimic laboratory conditions. The gas is fed to a flash vessel, which saturates it with water. The gas and solvent are contacted in the WWC, which has the same height as the real life apparatus (9.1 cm) but a diameter that is 100x larger (0.44 cm x100). The rich and lean flash vessels flash the rich and lean amine streams after the heater to calculate the equilibrium partial pressure of CO 2. Aspen Plus discretizes the boundary layer to perform its mass transfer calculation for the reactions. The previous discretization used 50 the maximum number of points possible which means it requires the most computation time (Chen, 2011). Based on prior studies (Kucka et al., 2003) and looking at previous modeling work (Plaza, 2011), the number of discretization points was reduced without any loss of accuracy. The old and new discretizations are compared in Figure 14. Protected under CCSI MASTER NDA

348 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 2MPZ old 2MPZ new 1.00E E E E E E E+00 Figure 14: Boundary layer discretization. The x-axis is fraction through the boundary layer with the gas-liquid interface at left and the bulk liquid at right. The complete reaction set used is shown in Table 5. The forward and reverse kinetic reactions are represented separately in Aspen Plus using a powerlaw form shown in Equation 3. k k o δ/δ T E A 1 1 exp (3) R T To The forward reaction rates are calculated, and then the reverse rates are back-calculated using the reaction equilibrium constant. The bicarbonate-forming reaction was fixed using values from literature (Ko & Li, 2000), while the dicarbamate-forming reaction was ratioed to the carbamate-forming reaction by assuming the Brønsted plot of PZ holds (k carbamate = 0.88k dicarbamate ). This plot is shown in Figure 15. Thus, only the carbamate-forming reaction was regressed. Protected under CCSI MASTER NDA

349 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Figure 15: Brønsted plot showing the reaction rate constant (k Am-b ) versus the pka of a base for an amine catalyzed by a base, k Am-base. To calculate k o and E A, two points were chosen at different loadings: one where the bicarbonate reaction is insignificant and a second, higher one where the bicarbonate is significant. At each of these points, the 40 C and 60 C fluxes were examined. Using a fixed set of kinetic parameters, the loading was adjusted to ensure that at zero driving force there is zero flux. This adjustment was made until the ratio of predicted flux to actual flux for the absorption and desorption points were within 1% of each other, or until the loading had been adjusted up to 10% of the operational loading range. Therefore, the maximum loading adjustment was ±0.01 mol CO 2 /mol alk. Once this loading adjustment was completed, a design specification was used to match the flux exactly by varying the k o of one reaction. This is tested at two different temperatures to produce a coherent set of k o and E A for all reactions. The diffusivity parameters of Equation 4 were also adjusted. The diffusivity adjustments were made to fit the higher temperature data points primarily. T D D (4) o Tref With all parameters fixed, the WWC flux cases were all simulated. The power-law parameters, the loading, and the diffusivity parameters were adjusted. The flux cases were again simulated and this process was repeated until a satisfactory fit emerged. Using a very small reaction set, most of the data were matched within 20%. There were nine predicted fluxes not within 20% of the experimental fluxes. The kinetic fit is displayed in Figure 16 and Figure 17. As seen in Figure 16, the predictions worsen at higher temperatures as experimental error is expected to increase and as the mechanism shifts to diffusion-dominated. In addition to increasing scatter with increasing temperature, there is a linear systematic bias. Efforts to correct for this bias by changing the Protected under CCSI MASTER NDA

350 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual reference temperature for diffusivity were unsuccessful. Figure 17 shows no systematic trend with loading and the scatter with temperature remains approximately constant. Table 5 shows the power-law parameters, and Table 6 shows diffusivity parameters. While the dependence of diffusivity on viscosity is reasonable, its dependence on temperature is probably indicative not of a physical effect, but of the diffusivity being distorted to fit temperature dependence effects. Table 5: Reaction Set for 2MPZ with Forward Reactions above the Rule Reaction k o (kmol/s-m 3 ) E A (kj/mol) 2MPZCOO - + H 2O + CO 2 H2MPZCOO + HCO E MPZ + CO 2 2MPZH + + 2MPZCOO E MPZCOO - + CO 2 2MPZ(COO - ) 2 + H2MPZCOO 1.28E H2MPZCOO + HCO 3-2MPZCOO - + H 2O + CO E MPZH + + 2MPZCOO 2 2MPZ + CO E MPZ(COO - ) 2 + H2MPZCOO 2 2MPZCOO - + CO E8 129 Table 6: Diffusivity Parameter Values Diffusivity Parameter 8 m 2MPZ value D o 4.4E-11 m 2 /s α β T ref K Protected under CCSI MASTER NDA

351 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual Flux pred / Flux exp T ( C) Figure 16: 8 m 2MPZ kinetic fit. There is a linear bias with temperature. Filled points represent absorption, open points desorption. Dashed lines delineate the target range ±20% Flux pred / Flux exp 40 abs 40 des 60 des 60 abs 80 des 80 abs 100 des 100 abs Loading (mol/mol alk.) Figure 17: 8 m 2MPZ kinetic fit. Model flux ratioed to experimental flux shows no clear trend with loading. Filled points represent absorption, open points desorption. The dashed lines delineate the target range ±20%. Protected under CCSI MASTER NDA

352 CCSI Process Models Other Process Models CO 2 Compressor Simulation User Manual 6.0 REFERENCES Chen, X., Carbon Dioxide Thermodynamics, Kinetics, and Mass Transfer in Aqueous Piperazine Derivatives and Other Amines, The University of Texas at Austin, PhD Dissertation, Frailie, P., Plaza, J., Van Wagener, D., and Rochelle, G.T., Modeling Piperazine Thermodynamics, Energy Procedia, 4, 35 42, Freeman, S.A., Thermal Degradation and Oxidation of Aqueous Piperazine for Carbon Dioxide Capture, The University of Texas at Austin, PhD Dissertation, Hilliard, M.D., A Predictive Thermodynamic Model for an Aqueous Blend of Potassium Carbonate, Piperazine, and Monoethanolamine for Carbon Dioxide, The University of Texas at Austin, PhD Dissertation, Ko, J., and Li, M., Kinetics of Absorption of Carbon Dioxide into Solutions of N-Methyldiethanolamine + Water, Chem Eng Sci., 55: , Plaza, J.M., Modeling of Carbon Dioxide Absorption using Aqueous Monoethanolamine, Piperazine and Promoted Potassium Carbonate, The University of Texas at Austin, PhD Dissertation, Rochelle, G.T., Xi, C., Li, L., Namjoshi, O., Xu, Q., Nguyen, T., Frailie, P., Van Wagener, D., Plaza, J.M., Wang, C., Chen, E., Ziaii, S., Dunia, R., Cohen, S., Closmann, F., Freeman, S., Voice, A., Ashouripashaki, M., Fulk, S., and Rafique, H.A., CO 2 Capture by Aqueous Absorption, First Quarterly Progress Report Luminant Carbon Management Program, The University of Texas at Austin, Rochelle, G.T., Li, L., Nguyen, T., Li, H., Du, Y., Frailie, P., Chen, E., Sachde, D., Wang, C., Madan, T., Sherman, B., Walters, M., Ziaii, S., Cohen, S., Namjoshi, O., Voice, A., Fulk, S., Nielsen, P., Fine, N., and Ashouripashaki, M., CO 2 Capture by Aqueous Absorption, Second Quarterly Progress Report 2012, Luminant Carbon Management Program, The University of Texas at Austin, Rochelle, G.T., Li, L., Du, Y., Frailie, P., Chen, E., Sachde, D., Lin, Y., Wang, C., Madan, T., Sherman, B., Walters, M., Namjoshi, O., Voice, A., Fulk, S., Nielsen, P., and Fine, N., CO 2 Capture by Aqueous Absorption, Fourth Quarterly Progress Report 2012, Luminant Carbon Management Program, The University of Texas at Austin, Weiland, R.H., Dingman, J.C., Cronin, D.B., Browning, G.J., Density and Viscosity of Some Partially Carbonated Aqueous Alkanolamine Solutions and Their Blends, J. Chem. Eng. Data, 9568(1985), , Xu, Q., Thermodynamics of CO 2 Loaded Aqueous Amines, University of Texas at Austin, PhD Dissertation, Protected under CCSI MASTER NDA

353 Appendix J Piperazine Blend Model Manuals 331

354 CCSI Special Solvent Blend Model User Manual Version November

355 CCSI Special Solvent Blend Model User Manual This material was produced under the DOE Carbon Capture Simulation Initiative (CCSI), and copyright is held by the software owners: ORISE, LANS, LLNS, LBL, PNNL, CMU, WVU, et al. The software owners and/or the U.S. Government retain ownership of all rights in the CCSI software and the copyright and patents subsisting therein. Any distribution or dissemination is governed under the terms and conditions of the CCSI Test and Evaluation License, CCSI Master Non-Disclosure Agreement, and the CCSI Intellectual Property Management Plan. No rights are granted except as expressly recited in one of the aforementioned agreements. The University of Texas has prepared the PZ/2MPZ model in Aspen Plus with CCSI support. The starting point for this model is the Independence model for piperazine/mdea. If the PZ/2MPZ model is used with a specification of no 2MPZ, it is the Independence model for PZ. The Independence model is copyrighted by the University. CCSI has permission to include PZ/2MPZ model under the T&E, but any further commercial use will require a license from the University for Independence. The University of Texas has prepared the PZ/HMPD model in Aspen Plus with CCSI support. The starting point for this model is the Independence model for piperazine/mdea. If the PZ/HMPD model is used with a specification of no HMPD, it is the Independence model for PZ. The Independence model is copyrighted by the University of Texas. CCSI has permission to include PZ/HMPD model under the T&E, but any further commercial use will require a license from the University for Independence. Protected under CCSI MASTER NDA i 333

356 CCSI Special Solvent Blend Model User Manual Table of Contents CCSI Special Solvent Blend Model Abstract Reporting Issues Version Log MPZ/PZ CO 2 Capture Simulation Introduction Predicting CO 2 Solubility Features List Tutorial Absorber Simulation Stripper Simulation USAGE Information Environment/Prerequisites Support Restrictions Next Steps Debugging How to Debug Known Issues Reporting Issues Model History References Approximate HMPD/PZ CO 2 Capture Simulation Introduction Predicting CO 2 Solubility Features List Tutorial Absorber Simulation Stripper Simulation USAGE Information Environment/Prerequisites Support Restrictions Next Steps Debugging How to Debug Known Issues Reporting Issues Protected under CCSI MASTER NDA ii 334

357 CCSI Special Solvent Blend Model User Manual 5.0 Model History References List of Figures Figure 1: CO 2 solubility in 4 m 2MPZ/4 m PZ. Curves are spaced 20 C apart Figure 2: Simple absorber flowsheet Figure 3: Design spec results Figure 4: Column pack rating results Figure 5: Simple stripper flowsheet Figure 6: Activity coefficients at 40 C for species of reactions 2, 5, and Figure 7: 4 m 2MPZ/4 m PZ kinetic fit less reactions 5 and 10. Data are from Chen (2011) Figure 8: 4 m 2MPZ/4 m PZ kinetic fit less reactions 5 and 10. Data are from Chen (2011) Figure 9: CO 2 solubility in 2 m PZ/3 m HMPD Figure 10: Simple absorber flowsheet Figure 11: Simple stripper flowsheet Figure 12: Predicted pk a of HMPD (solid) compared to model fit (dashed) and experimental data (points) (Ciftja, 2015) Figure 13: Amine volatility comparison of 2 m PZ/3 m HMPD. Lines are correlations at 10 C intervals ( PZ, - - CO 2, HMPD) and points are data ( HMPD, CO 2, PZ) (Du, 2015) Figure 14: VLE comparison of 2 m PZ/3 m HMPD. Lines are the correlation in 20 C increments compared to data ( FTIR, WWC, WWC screening) Figure 15: Predicted heat of absorption of 2 m PZ/3 m HMPD by equation (5) at 20 C intervals Figure 16: Predicted activity coefficients of 2 m PZ/3 m HMPD at 40 C Figure 17: Predicted speciation of 2 m PZ/3 m HMPD at 40 C Figure 18: Predicted density of 2 m PZ/3 m HMPD using the same representation as Independence (Frailie, 2014) at 20 C intervals Figure 19: Viscosity correlation of 2 m PZ/3 m HMPD. Lines are correlation at 20 C intervals; points are data (Du, 2015) with different points indicating different runs Figure 20: Flux parity plot for 2 m PZ/3 m HMPD compared to data from Du (2015) Figure 21: Flux parity plot for 2 m PZ/3 m HMPD compared to data from Du (2015) Protected under CCSI MASTER NDA iii 335

358 CCSI Special Solvent Blend Model User Manual List of Tables Table 1: Excerpt of 2MPZ VLE Results... 3 Table 2: Boundary Layer Discretization... 8 Table 3: Stream Results Table 4: LOADINGS Variable Definitions Table 5: Stream Results Excerpt Table 6: D-LEAN Results Table 7: D-T Results Table 8: Pack Rating Results Table 9: Removed Reactions from 4 m 2MPZ/4 m PZ Kinetic Model Table 10: Excerpt of 2MPZ VLE Results Table 11: Boundary Layer Discretization Table 12: Stream Results Excerpt Table 13: DS-RM Results Table 14: Column Pack Rating Results Table 15: LOADINGS Variable Definitions Table 16: Stream Results Excerpt Table 17: DS-LEAN Results Table 18: DS-T Results Table 19: Pack Rating Results Table 20: PZ/HMPD Regressed Thermodynamic Data (Du, 2015) Table 21: Amine Volatility of 2 m PZ/3 m HMPD Regressed Parameters Table 22: VLE of 2 m PZ/3 m HMPD Regressed Parameters Table 23: Regressed Viscosity Data (Du, 2015) Table 24: Viscosity Parameters and Standard Deviations for PZ/HMPD of Equation (6) Table 25: Reaction Set for PZ/HMPD; Reactions below the Rule are in Equilibrium Table 26: PZ/HMPD Kinetic Parameters To obtain support for the products within this package, please send an to ccsi-support@acceleratecarboncapture.org. Protected under CCSI MASTER NDA iv 336

359 CCSI Special Solvent Blend Model User Manual CCSI Special Solvent Blend Model 1.0 ABSTRACT This is an Aspen Plus absorption/stripping model for CO 2 capture from natural gas or coal-fired power plants using the solvent 4 molal 2-methylpiperazine (2MPZ)/4 molal piperazine (PZ). This model can be used for techno-economic assessments, pilot plant data reconciliation, and process design. The solvent has greater oxidative stability than MEA, is thermally stable up to 155 C, has a greater viscosity-normalized capacity (0.88 mol CO 2 /kg solvent versus 0.62 mol CO 2 /kg solvent), and has 65% faster mass transfer than 7 molal MEA. The solvent suffers from higher cost than MEA, five-times higher viscosity, and solid precipitation at very low CO 2 loading. The model was constructed using sequential regression of bench-scale experimental thermodynamic and mass transfer data. The thermodynamics are modeled using the asymmetric enrtl model to fit CO 2 solubility data with an average relative deviation of 1.60%. A custom flowsheet simulates the wetted-wall column used for mass-transfer data collection. The diffusion of amine and kinetic rate constants were regressed to match the experimental CO 2 flux data with an average relative deviation of 4.80%. Activity-based kinetics were used to account for the high non-ideality of the system. 2.0 REPORTING ISSUES To report an issue, please send an to ccsi-support@acceleratecarboncapture.org. 3.0 VERSION LOG Product Version Number Release Date Description CCSI Special Solvent Blend Model /20/ November IAB Release Approximate HMPD/PZ CO 2 Capture Simulation /21/2015 Initial version. 2MPZ/PZ CO 2 Capture Simulation /31/2014 Initial version. Protected under CCSI MASTER NDA

360 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 2MPZ/PZ CO 2 Capture Simulation 1.0 INTRODUCTION This document describes a 2-methylpiperazine (2MPZ)/ piperazine (PZ) CO 2 capture system process simulation. The amine scrubbing system is divided into separate absorber and stripper simulations. The model consists of 2MPZ+PZ.bkp with supporting files 2mpzpz.dll and sub.opt. This manual was written using Aspen Plus V8.4 and is compatible with V8.4 and higher. The first example takes five minutes to complete, while the later two examples require 30 minutes each. 1.1 Predicting CO 2 Solubility The solubility of CO 2 dictates the operational loading range, as well as a stripper temperature and pressure. In this five minute example, a property analysis block is used to generate a series of isotherms for a fixed amine concentration and variable loading. 1. Open 2MPZ+PZ.bkp. When prompted to update databanks, decline. 2. In the Navigation Pane, select Properties and then navigate to Analysis. Click New to create a new analysis block. Enter its ID as VLE and select the type as generic. Change the system basis to Mass and then set H2O to 1000 kg/sec. 3. On the Variable tab, change Temperature to Vapor Fraction and then set it to 1e-05. Create four variables: (1) temperature, (2) mole flow 2MPZ, (3) mole flow PZ, and (4) mole flow CO2. Select each variable and define them by clicking the Range/List button. a. Temperature is a range: Lower=293.15, Upper=413.15, Increments=20 b. Mole flow 2MPZ is a list: 4 c. Mole flow PZ is a list: 4 d. Mole flow CO2 is a range: Lower=0.001, Upper=8, Points=20 4. On the Tabulate tab, select PPCO2-KP for the partial pressure of CO 2 in kilopascals. 5. To view the results, navigate to Properties Analysis VLE Results. Some of the results are shown in Table 1. Using additional graphing software, they are plotted in Figure 1. Protected under CCSI MASTER NDA

361 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual Table 1: Excerpt of 2MPZ VLE Results TEMP MOLEFLOW 2MPZ MOLEFLOW PZ MOLEFLOW CO2 VAPOR PPMX CO2 K kmol/sec kmol/sec kmol/sec kpa e Protected under CCSI MASTER NDA

362 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 1.E+07 1.E+06 1.E+05 P * CO2 (Pa) 1.E+04 1.E+03 1.E+02 1.E+01 1.E C 40 C Loading (mol CO 2 /mol alk) Figure 1: CO 2 solubility in 4 m 2MPZ/4 m PZ. Curves are spaced 20 C apart. Other property analysis blocks can be made to give properties such as speciation and volatility. 1.2 Features List This product is a thermodynamic and kinetic model of 4 m 2MPZ/4 m PZ for amine scrubbing process modeling. It is focused on capture from coal-fired power plant flue gas; therefore, it represents the CO 2 solubility, speciation, amine vapor pressure, heat capacity, pka, heat of absorption, density, and viscosity. While the model can extrapolate over a range of amine concentration, loading, and temperature, it is based on data collected primarily at 4 m 2MPZ/4 m PZ with loading from 0.15 to 0.4 mol CO 2 /mol alkalinity. Protected under CCSI MASTER NDA

363 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 2.0 TUTORIAL 2.1 Absorber Simulation Description This example describes how to simulate a rate-based absorber. It includes tips on: convergence, the use of design specifications to meet process criteria, and the proper boundary-layer discretization. Setup 1. Build the flowsheet of Figure 2 using an ABSBR1 RadFrac column. In the Model Palette at the bottom of the window, select Columns RadFrac ABSBR1. (If the user does not see the model library, press F10. If the user does not see the flowsheet, click the View tab of the ribbon and then under Show click Flowsheet.) Place the block on the flowsheet and name it ABSORBER. Figure 2: Simple absorber flowsheet. 2. Select Material at the left of the Model Palette. Create GASIN by clicking the red arrow on the left of the block (the feed) and then clicking elsewhere. Create RICH by clicking the red arrow at the bottom (the bottoms). Create GASOUT by clicking the red arrow at the top (the vapor distillate). Create LEAN by clicking the now blue arrow on the left (the feed). Protected under CCSI MASTER NDA

364 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 3. Double-click GASIN to configure it as follows: a. Temperature: 40 C b. Pressure: 1 atm c. Total flow: 5 kmol/sec d. Composition: Mole-Frac i. H2O: 7.3 ii. CO2: 12 iii. N2: 80.7 Note: Aspen will normalize the mole fractions to one. 4. Select LEAN from the Navigation Pane and configure it as follows: a. Temperature: 40 C b. Pressure: 1 atm c. Total flow: 20 kmol/sec d. Composition: Mole-Frac i. H2O: ii. CO2: 4.8 iii. 2MPZ: 4 iv. PZ: 4 5. Navigate to Blocks ABSORBER and configure its Setup as follows: a. On the Configuration tab i. Calculation type: Rate-Based ii. Number of stages: 50 iii. Condenser: none iv. Reboiler: none b. On the Streams tab i. GASIN On-Stage 50 ii. LEAN On-Stage 1 c. On the Pressure tab set the Top stage pressure to 1 atm. 6. Navigate to Specifications Reactions. Make two reaction blocks. a. Starting stage=1; ending stage=3; Reaction ID=Z-PZ2MPZ. b. Starting stage=4; ending stage=50; Reaction ID=Z-PZ2MPZ. Protected under CCSI MASTER NDA

365 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 7. Navigate to Sizing and Rating Packing Rating and then click New. Name the section 1, and then configure its Specifications as follows: a. Starting stage: 1 b. Ending stage: 50 c. Type: MELLAPAK d. Vendor: SULZER e. Material: STANDARD f. Dimension: 250X g. Section diameter: 8.5 meter h. Section packed height: 8 meter i. Be sure change the option from the default of Packed height per stage. Note: As the column is packed, the number of stages does not represent trays. As a very rough approximation, one stage for every half meter of packing is recommended. Use more stages for greater temperature and mass transfer gradients. i. Navigate to Packing Rating 1 Rate-based and then configure it as follows: i. Select the Rate-based calculations check box. ii. Flow model: Countercurrent iii. Film resistance 1. Liquid phase: Discrxn 2. Vapor phase: Film Protected under CCSI MASTER NDA

366 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual j. On the Optional tab, set the Additional discretization points to the 32 shown in Table 2. Table 2: Boundary Layer Discretization Point Liquid Film Point Liquid Film E E Navigate to Flowsheeting Options Calculator and then create a new Calculator named C-RM. This block will calculate the fraction of CO 2 captured. a. On the Define tab, create three variables: Variable Information Flow Definition REMOVE Export Parameter Parameter no.=2 CO2IN CO2OUT Import Import Mole-Flow Stream=GASIN Substream=MIXED Component=CO2 Units=kmol/sec Mole-flow Stream=GASOUT Substream=MIXED Component=CO2 Units=kmol/sec i. Type REMOVE in the first row under the Variable column. Select Export variable under the Information flow column. In the Reference box, set the Type to Parameter and the Parameter no. to 2. ii. Type CO2IN in a blank cell in the Variable column and select Import variable in the Information flow column. In the Reference box, set the Type to Mole-Flow, the Stream to GASIN, the Substream to MIXED, the Component to CO 2, and the Units to kmol/sec. Protected under CCSI MASTER NDA

367 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual iii. Type CO2OUT in a blank cell in the Variable column and select Import variable in the Information flow column. In the Reference box, set the Type to Mole-Flow, the Stream to GASOUT, the Substream to MIXED, the Component to CO 2, and the Units to kmol/sec. b. On the Calculate tab, be sure the Calculation method is set to Fortran. In the box under Enter executable Fortran statements, beginning on row 1 and in column 7 write REMOVE=(CO2IN-CO2OUT)/CO2IN. 9. Still under Flowsheeting options, navigate to Design Specs. Click New and then name it D-RM. a. On the Define tab, create a variable REMOVE and then under Reference set the Type to Parameter and the Parameter no. to 2. b. On the Spec tab i. Spec: REMOVE ii. Target: 0.90 iii. Tolerance: c. On the Vary tab Running the Simulation i. Type: Stream-Var ii. Stream: LEAN iii. Variable: MOLE-FLOW iv. Lower: 5 v. Upper: Deactivate the design spec by right-clicking it and then selecting Deactivate. 2. Run the simulation. This provides an initial guess. a. The user may see warnings about unusual liquid mole fraction and component production profiles. These can be ignored. b. Close the economic analysis if prompted. 3. Change the absorber Reactions for stages 1 to 3 to R-PZ2MPZ from Z-PZ2MPZ. Run the simulation. a. The user may see warnings about unusual liquid mole fraction and component production profiles. Again, these can be ignored. 4. Change the absorber Reactions for stages 4 to 50 to R-PZ2MPZ from Z-PZ2MPZ. Run the simulation. 5. Navigate to Flowsheeting Options Calculator C-RM Results and on the Define Variable tab, the fractional CO 2 removal is displayed. It should be ~57%. Protected under CCSI MASTER NDA

368 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 6. Increase the LEAN stream total flow in 5 kmol/sec increments until the percent removal is within 0.10 of Be sure to run the simulation after each increment. a. At 25 kmol/sec, removal is ~67%. b. At 30 kmol/sec, ~78%. c. At 35 kmol/sec, ~91%. 7. Activate the Design Spec D-RM by right-clicking it and then selecting Activate. Run the simulation. 8. The absorber is now removing 90% of the inlet CO 2. Results should be similar to those in Table 3 and Figures 3 and 4. View them by navigating to Results Summary Streams, Flowsheeting Options Design Spec D-RM Results, and Blocks ABSORBER Pack Rating 1 Results. Table 3: Stream Results GASIN GASOUT LEAN RICH Temperature K Pressure N/sqm Vapor Frac Solid Frac Mole Flow kmol/sec Mass Flow kg/sec Volume Flow cum/sec Enthalpy Gcal/hr Mole Flow kmol/sec H2O CO HCO CO H OH PZ PZCOO PZCOO PZH HPZCOO N O MPZ MPZCOO H2MPZCOO Protected under CCSI MASTER NDA

369 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual GASIN GASOUT LEAN RICH 2MPZCOO MPZH Figure 3: Design spec results. Figure 4: Column pack rating results. Protected under CCSI MASTER NDA

370 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 2.2 Stripper Simulation Description This example describes simulating a simple stripper and cross exchanger. It is recommended that the user model the absorber and stripper using separate files. Setup 1. Construct the flowsheet of Figure 5. From Columns in the Model Palette, select RadFrac STRIP1 for the stripper. From Exchangers, select Heater for CX-COLD, CX-HOT, and HX-TRIM. From Pressure Changers, select Pump for LEANPUMP. Create the streams using the Material button. Figure 5: Simple stripper flowsheet. Protected under CCSI MASTER NDA

371 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 2. Set HOTRICH to the values from the absorber example. a. Temperature: 325 K b. Pressure: 12 bar c. Total flow: kmol/sec d. Composition: Mole-Frac i. H2O ii. CO iii. 2MPZ 4 iv. PZ 4 Note: The pressure is set as if coming from a pump, which is omitted. 3. Set CX-COLD as follows: a. Pressure: 0 N/sqm b. Temperature: 85 C c. Valid phases: Liquid-Only Note: Pressure drop is neglected. 4. Configure STRIPPER Setup as follows: a. On the Configuration tab i. Calculation Type: Rate-Based ii. Number of Stages: 15 iii. Condenser: None iv. Reboiler: Kettle v. Reboiler Duty: 200 MW b. On the Streams tab, feed COLDRICH to stage 1 as liquid. c. On the Pressure tab, set the top stage pressure to 3 bar. 5. Navigate to Stripper Specifications Reactions, select starting stage as 1, ending stage as 15, and then Chemistry ID as REDUCED. 6. Navigate to Sizing and Rating Packing Rating and create a new Pack Rating for the stripper by clicking New. Let it be named 1, and configure it as follows: a. Under Setup, stages 1 14 use MELLAPAK, SULZER, STANDARD, 250X with a diameter of 4 m and a section packed height of 2 m. b. Under Rate-Based, check Rate-based calculations with Film Resistance set to Film for liquid and vapor phases. 7. Configure CX-HOT as follows: a. Temperature: 50 C b. Pressure: 0 N/sqm Protected under CCSI MASTER NDA

372 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 8. Configure LEANPUMP as follows: a. Discharge pressure: 250 kpa 9. Configure HX-TRIM as follows: a. Temperature: 40 C b. Pressure: 0 N/sqm Note: This flowsheet takes the rich stream from the previous absorber tutorial, passes it through a cross-exchanger, and then to the stripper. CX-COLD and CX-HOT will be used to simulate the cross exchanger. HX-TRIM is the trim cooler to lower the lean solvent down to 40 C prior to entering the absorber. 10. Create a LOADINGS calculator. a. Define the variables as shown in Table 4. b. Enter the Fortran code exactly as shown, with the periods in column six: LLDG=(LCO2+LHCO3+LCO3+L2MPZC+2*L2MPZC2+LH2MPZC. +LPZCOO+2*LPZCOO2+LHPZCOO) LLDG=LLDG/(2*(L2MPZ+LH2MPZ+L2MPZC+L2MPZC2+LH2MPZC. +LPZ+LHPZ+LPZCOO+LPZCOO2+LHPZCOO)) RLDG=(RCO2+RHCO3+RCO3+R2MPZC+2*R2MPZC2+RH2MPZC. +RPZCOO+2*RPZCOO2+RHPZCOO) RLDG=RLDG/(2*(R2MPZ+RH2MPZ+R2MPZC+R2MPZC2+RH2MPZC. +RPZ+RHPZ+RPZCOO+RPZCOO2+RHPZCOO)) Protected under CCSI MASTER NDA

373 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual Table 4: LOADINGS Variable Definitions Variable Name Information Flow Definition RLDG Export Parameter Parameter no.=3 LLDG Export Parameter Parameter no.=4 LCO2 Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=CO2 L2MPZ Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=2MPZ LH2MPZ Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=2MPZH+ L2MPZC Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=2MPZCOO L2MPZC2 Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=2MPZCOO2 LH2MPZC Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=H2MPZCOO LPZ Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZ LHPZ Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZH+ LPZCOO Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZCOO- LPZCOO2 Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZCOO-2 LHPZCOO Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=HPZCOO LHCO3 Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=HCO3- LCO3 Import Mole-Frac Stream=STR-LEAN Substream=MIXED Component=CO3-- R2MPZ Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=2MPZ R2MPZH Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=2MPZH+ R2MPZC Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=2MPZCOO R2MPZC2 Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=2MPZCOO2 RH2MPZC Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=H2MPZCOO RPZ Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZ RPZH Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZH+ RPZCOO Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZCOO- RPZCOO2 Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZCOO-2 RHPZCOO Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=HPZCOO RHCO3 Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=HCO3- RCO3 Import Mole-Frac Stream=HOTRICH Substream=MIXED Component=CO3-- Protected under CCSI MASTER NDA

374 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 11. Create a Design Spec named D-LEAN. a. Define LLDG as Parameter 4. b. Spec LLDG to 0.30 with a tolerance of c. On the Vary tab under Manipulated variable limits, Lower: 0 and Upper: 5.5E8 Watts. Under Manipulated variable set the following: i. Type: Block-Var ii. Block: STRIPPER iii. Variable: QN 12. Create a Design Spec named D-T. a. Define TEMP as Stream-Var Stream=STR-LEAN Substream=MIXED Variable=TEMP Units=K. b. Spec TEMP to K with a tolerance of c. On the Vary tab, set the manipulated variable limits to 900,000 to 1,800,000 N/sqm. Under Manipulated variable set the following: i. Type: Block-Var ii. Block: STRIPPER iii. Variable: STAGE-PRES iv. ID1: 1 Protected under CCSI MASTER NDA

375 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual Running the Simulation 1. Deactivate both design specs. 2. Run the simulation. a. Ignore warnings about excess flood. b. Close the economic analysis if prompted. 3. Review the lean loading (LLDG) in the LOADINGS calculator block by navigating to the Define Variable tab of Results. Decrease the stripper reboiler duty in 50 MW increments until the lean loading is close to the desired value of Run the simulation after each decrement. a. At 200 MW, lean loading is 0.24 mol CO 2 /mol alk. b. At 150 MW, 0.29 mol CO 2 /mol alk. 4. Activate the D-LEAN design spec and run the simulation. a. Converges to 141 Megawatts at a loading of 0.30 mol CO 2 /mol alk. b. Ignore flood warnings. 5. Activate the D-T design spec and run the simulation. 6. Create a heat stream from CX-HOT to CX-COLD by clicking the arrow next to Material in the Model Palette and clicking Heat from the drop-down menu. Name it Q-XC. To clear the temperature specification of CX-COLD, double-click the block, right-click temperature under flash specifications, and then select Clear. 7. Run the simulation. The results are similar to those of Tables 5 8. To view them, look at Results Summary Streams, Flowsheeting Options Design Spec D-LEAN Results, Flowsheeting Options Design Spec D-T Results, and Blocks STRIPPER Pack Rating 1 Results. Protected under CCSI MASTER NDA

376 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual Table 5: Stream Results Excerpt COLDLEAN COLDRICH HOTLEAN HOTRICH P-LEAN STR-LEAN VAPOR Temperature K Pressure N/sqm E E E E E+06 Vapor Frac Solid Frac Mole Flow kmol/sec Mass Flow kg/sec Volume Flow cum/sec Enthalpy Gcal/hr Mole Flow kmol/sec H2O CO HCO CO H OH PZ PZCOO PZCOO PZH HPZCOO N O MPZ MPZCOO H2MPZCOO MPZCOO MPZH Table 6: D-LEAN Results Variable Initial Value Final Value Units MANIPULATED WATT LLDG Protected under CCSI MASTER NDA

377 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual Table 7: D-T Results Variable Initial Value Final Value Units MANIPULATED N/SQM TEMP K Table 8: Pack Rating Results Variable Value Unit Section Starting Stage 1 Section Ending Stage 14 Column Diameter 4 meter Maximum Fractional Capacity Maximum Capacity Factor m/sec Section Pressure Drop N/sqm Average Pressure Drop/Height N/cum Maximum Stage Liquid Holdup cum Maximum Liquid Superficial Velocity m/sec Surface Area 256 sqm/cum Void Fraction st Stichlmair Constant 1 2nd Stichlmair Constant 1 3rd Stichlmair Constant 0.32 Protected under CCSI MASTER NDA

378 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 3.0 USAGE INFORMATION 3.1 Environment/Prerequisites This product requires Aspen Plus V8.4 or newer with an Aspen Rate-Based Distillation license. As such, the supported environments are limited to: Windows XP SP3 Windows Vista Business SP2 Windows Vista Ultimate SP2 Windows 7 Ultimate (32- and 64-Bit) Windows 7 Professional (32- and 64-Bit) 3.2 Support Support can be obtained from ccsi-support@acceleratecarboncapture.org or by filling out the Submit Feedback/Request Support form available on the product distribution page. 3.3 Restrictions The model is centered at an amine concentration of 4 m 2MPZ/4 m PZ. Extrapolating far from this concentration should be done with care. The model is best between 40 and 160 C and 0.15 and 0.4 mol CO 2 /mol alk. Kinetic modeling should be kept to C. 3.4 Next Steps Future releases will refine the kinetic fit. Protected under CCSI MASTER NDA

379 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 4.0 DEBUGGING The model is running correctly if it is converging for the above tutorials with similar results. If it is not, see the next section. 4.1 How to Debug Always run the simulation with the control panel visible. It is the only output available during computation, and it will tell the user whether or not the simulation will converge. This will allow the user to avoid wasting time on fruitless computation. Furthermore, it will alert the user to any problems encountered during computation. Additional debugging information is available in the history file, which can be viewed by selecting History from the ribbon in the Summary section of the Home tab. Subroutine Errors If the user sees, *** SEVERE ERROR COULD NOT RESOLVE USER OR IN-LINE FORTRAN SUBROUTINE(S): the simulation will not run. The possible causes and solutions are, 1. The.bkp file and the.dll and.opt files are not located in the same directory. Move them all into the same directory to resolve this. 2. The linker is not specified in the run settings. Press Ctrl+F7 and then under linker options type sub.opt. Simulation Problems If the user sees a warning stating that the water liquid viscosity model MULH2O is violated due to the temperature being lower than the minimum temperature limit, the simulation is trapped in a non-physical solution. Check the inputs and re-run. Ignore flooding errors (TPSAR MESSAGE: XXX.XX% FLOOD IN COLUMN EXCEEDS 80%) unless it is the final step, in which case adjust column diameter for desired flood. Aiding Convergence Only reinitialize when large changes have been made, such as adding or removing a flowsheet block. Make small changes in a converged model. Converge an initial, simple case before increasing complexity. Before enabling the design specification, the variable should be close to the desired value. Mass transfer models affect convergence and results substantially, so be sure to choose the appropriate model for the packing used. Protected under CCSI MASTER NDA

380 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 4.2 Known Issues The activity coefficient of H2MPZCOO is ill-behaved with loading and temperature. For this reason, two reactions involving it were removed to allow convergence of the absorber. This reduces the physical significance of this model. Flash errors can occur if the solvent goes above 0.5 mol CO 2 /mol alk, particularly at elevated temperatures. The user will see multiple warnings about property data while processing input specifications that follow this pattern, PARAMETER XXX DATA SET 1 FOR COMPONENT 2MPZ HAS BEEN ENTERED MORE THAN ONCE. THE LAST ENTRY WILL BE USED. where XXX is the parameter name. This is not a problem. In running the tutorials, the user will see warnings that the mole fractions are normalized to unity. The user will see warnings that IONRDL is missing for 2MPZCOO, 2MPZCOO2, and 2MPZH Reporting Issues To report an issue please send an to ccsi-support@acceleratecarboncapture.org. Protected under CCSI MASTER NDA

381 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual 5.0 MODEL HISTORY The model is detailed in: Sherman, B., Frailie, P. T., Le, L., Salta, N., & Rochelle, G. T. (2014). Thermodynamic and Kinetic Modeling of Piperazine/2-Methylpiperazine. Energy Procedia, 63: , doi: /j.egypro After publication, the model was modified to account for an unreasonable activity coefficient of the 2MPZ zwitterion. This was done by removing the two kinetic reactions of Table 9. Table 9: Removed Reactions from 4 m 2MPZ/4 m PZ Kinetic Model Stoichiometry Reaction PZCOO + 2MPZCOO + CO 2 PZ(COO ) 2 + H2MPZCOO 5 2 2MPZCOO + CO 2 2MPZ(COO ) 2 + H2MPZCOO 10 The reason this was necessary is due to the departure of the forward-reverse power-law reaction equilibria from the true thermodynamic reaction equilibria. Ideally, the following relationship holds true. K eq,j = G j 0 RT = k f k r (5) In practice, the second equality of Equation 5 only holds from 40 to 60 C. This is because k f k r does not account for the temperature dependence of the activity coefficients. Figure 6 shows the activity coefficients of the species involved in the 2MPZ zwitterion reactions at 40 C. γ H2MPZCOO is two orders of magnitude below the analogous PZ species. In addition, γ H2MPZCOO exhibits a minima and stronger loading dependence than γ HPZCOO. γ loading (mol CO 2 /mol alk) PZCOO PZCOO2 HPZCOO 2MPZCOO 2MPZCOO2 H2MPZCOO HCO3 CO2 H2O Figure 6: Activity coefficients at 40 C for species of reactions 2, 5, and 10. Protected under CCSI MASTER NDA

382 CCSI Special Solvent Blend Model 2MPZ/PZ CO 2 Capture Simulation User Manual Therefore, to converge the absorber process model reactions 5 and 10 were deleted. All kinetic and diffusivity parameters were left at the previous values, resulting in the kinetic fit of Figures 7 and N CO2 N CO T ( C) Figure 7: 4 m 2MPZ/4 m PZ kinetic fit less reactions 5 and 10. Data are from Chen (2011). Protected under CCSI MASTER NDA

383 CCSI Special Solvent Blend Model MPZ/PZ CO 2 Capture Simulation User Manual des 40 abs 40 des 60 abs 60 des 80 abs 80 des 100 abs 100 N CO2 N CO Figure 8: 4 m 2MPZ/4 m PZ kinetic fit less reactions 5 and 10. Data are from Chen (2011). As expected, the model now tends to under predict. There is a pronounced trend towards under prediction with increasing loading, and at 40 C the model always under predicts as compared with prior model results (Sherman, Frailie, Le, Salta, & Rochelle, 2014). 6.0 REFERENCES loading (mol CO 2 /mol alk) Chen, X. (2011). Carbon Dioxide Thermodynamics, Kinetics, and Mass Transfer in Aqueous Piperazine Derivatives and Other Amines. The University of Texas at Austin. Sherman, B., Frailie, P. T., Le, L., Salta, N., & Rochelle, G. T. (2014). Thermodynamic and Kinetic Modeling of Piperazine/2-Methylpiperazine. Energy Procedia, 63: , doi: /j.egypro Protected under CCSI MASTER NDA

384 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Approximate HMPD/PZ CO 2 Capture Simulation 1.0 INTRODUCTION This document describes an approximate piperazine (PZ)/4-hydroxy-N-methylpiperidine (HMPD) CO 2 capture system process simulation. Due to a lack of data, this model does not have the same level of rigor as other PZ blend Aspen Plus amine simulations. The amine scrubbing system is divided into separate absorber and stripper simulations. The model consists of HMPD+PZ.bkp with supporting files hmpdpz.dll and hmpdpzloc.opt. This manual was written using Aspen Plus V8.4 and is compatible with V8.4 and higher. The first example takes five minutes to complete, while the latter two examples require 30 minutes each. 1.1 Predicting CO 2 Solubility The solubility of CO 2 dictates the operational loading range, as well as a stripper temperature and pressure. In this five-minute example, a property analysis block is used to generate a series of isotherms for a fixed amine concentration and variable loading. 1. Open HMPD+PZ.bkp. If prompted to update databanks, decline. 2. In the Navigation Pane, select Properties and then navigate to Analysis. Click New to create a new analysis block. Enter its ID as VLE and select the type as generic. Change the system basis to Mass and then set H2O to 1000 kg/sec. 3. On the Variable tab, change Temperature to Vapor Fraction and then set it to 1e-05. Create four variables: (1) temperature, (2) mole flow MP, (3) mole flow PZ, and (4) mole flow CO2. Select each variable and define them by clicking the Range/List button. a. Temperature is a range: Lower=293.15, Upper=413.15, Increments=20 b. Mole flow MP is a list: 3 c. Mole flow PZ is a list: 2 d. Mole flow CO2 is a range: Lower=0.001, Upper=5.3, Number of intervals=20 4. On the Tabulate tab, select PPCO2KP for the partial pressure of CO 2 in kilopascals. 5. To view the results, navigate to Properties Analysis VLE Results. Some of the results are shown in Table 10. Using additional graphing software, they are plotted in Figure 9. Protected under CCSI MASTER NDA

385 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Table 10: Excerpt of 2MPZ VLE Results TEMP MOLEFLOW MP MOLEFLOW PZ MOLEFLOW CO2 VAPOR PPMX CO2 K kmol/sec kmol/sec kmol/sec kpa E E Protected under CCSI MASTER NDA

386 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual P * CO2 (kpa) 5.00E E E E E E E E C 140 C 5.00E loading (mol CO 2 /mol alk) 20 C 40 C 60 C 80 C 100 C Figure 9: CO 2 solubility in 2 m PZ/3 m HMPD. Other property analysis blocks can be made to give properties such as speciation and volatility. 1.2 Features List This product is a thermodynamic and mass transfer model of 2 m PZ/3 m HMPD for amine scrubbing process modeling. It is focused on capture from coal-fired power plant flue gas, so while the model can extrapolate over a range of amine concentration, loading, and temperature, it is based on data collected primarily at 2 m PZ/3 m HMPD with loading from 0.13 to 0.52 mol CO 2 /mol alkalinity. Protected under CCSI MASTER NDA

387 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 2.0 TUTORIAL 2.1 Absorber Simulation Description This example describes how to simulate a rate-based absorber. It includes tips on: convergence, the use of design specifications to meet process criteria, and the proper boundary-layer discretization. Setup 1. Build the flowsheet of Figure 10 using an ABSBR1 RadFrac column. In the Model Palette at the bottom of the window, select Columns RadFrac ABSBR1. (If the user does not see the model library, press F10. If the user does not see the flowsheet, click the View tab of the ribbon and then under Show click Flowsheet.) Place the block on the flowsheet and name it ABSORBER. Figure 10: Simple absorber flowsheet. 2. Select Material at the left of the Model Palette. Create GASIN by clicking the red arrow on the left of the block (the feed) and then clicking elsewhere. Create RICH by clicking the red arrow at the bottom (the bottoms). Create GASOUT by clicking the red arrow at the top (the vapor distillate). Create LEAN by clicking the now blue arrow on the left (the feed). Protected under CCSI MASTER NDA

388 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 3. Double-click GASIN to configure it as follows: a. Temperature: 40 C b. Pressure: 1 atm c. Total flow: 5 kmol/sec d. Composition: Mole-Frac i. H2O: 7.3 ii. CO2: 12 iii. N2: 80.7 Note: Aspen will normalize the mole fractions to one. 4. Select LEAN from the Navigation Pane and configure it as follows: a. Temperature: 40 C b. Pressure: 1 atm c. Total flow: 25 kmol/sec d. Composition: Mole-Frac i. H2O: 55.5 ii. CO2: 1.8 iii. PZ: 2 iv. MP: 3 5. Navigate to Blocks ABSORBER and configure its Setup as follows: a. On the Configuration tab i. Calculation type: Rate-Based ii. Number of stages: 50 iii. Condenser: none iv. Reboiler: none b. On the Streams tab i. GASIN On-Stage 50 ii. LEAN On-Stage 1 c. On the Pressure tab set the Top stage pressure to 1 atm. 6. Navigate to Specifications Reactions. Make two reaction blocks. a. Starting stage=1; ending stage=3; Reaction ID=Z-PZMP. b. Starting stage=4; ending stage=50; Reaction ID=Z-PZMP. Protected under CCSI MASTER NDA

389 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 7. Navigate to Sizing and Rating Packing Rating and then click New. Name the section 1, and configure its Specifications as follows: a. Starting stage: 1 b. Ending stage: 50 c. Type: MELLAPAK d. Vendor: SULZER e. Material: STANDARD f. Dimension: 250X g. Section diameter: 9 meter h. Section packed height: 8 meter i. Be sure change the option from the default of Packed height per stage. Note: As the column is packed, the number of stages does not represent trays. As a very rough approximation, one stage for every half meter of packing is recommended. Use more stages for greater temperature and mass transfer gradients. i. Navigate to Packing Rating 1 Rate-based and then configure it as follows: i. Select the Rate-based calculations check box. ii. Flow model: Countercurrent iii. Film resistance 1. Liquid phase: Discrxn 2. Vapor phase: Film j. On the Correlations tab, set the mass transfer coefficient method and the interfacial area method both to HanleyStruc (2010). k. On the Holdups tab, change the Holdup method to Percent-Data, and then set the % of free volume to 5. Protected under CCSI MASTER NDA

390 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual l. On the Optional tab, set the Additional discretization points to the 32 shown in Table 11. Table 11: Boundary Layer Discretization Point Liquid Film Point Liquid Film E E Navigate to Flowsheeting Options Calculator and then create a new Calculator named C-RM. This block will calculate the fraction of CO 2 captured. a. On the Define tab, create three variables: Variable Information Flow Definition REMOVE Export Parameter no.=1 CO2IN CO2OUT Import Import Mole-Flow Stream=GASIN Substream=MIXED Component=CO2 Units=kmol/sec Mole-flow Stream=GASOUT Substream=MIXED Component=CO2 Units=kmol/sec i. Type REMOVE in the first row under the Variable column. Select Export variable under the Information flow column. In the Reference box, set the Type to Parameter and the Parameter no. to 1. ii. Type CO2IN in a blank cell in the Variable column and select Import variable in the Information flow column. In the Reference box, set the Type to Mole-Flow, the Stream to GASIN, the Substream to MIXED, the Component to CO 2, and the Units to kmol/sec. Protected under CCSI MASTER NDA

391 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual iii. Type CO2OUT in a blank cell in the Variable column and select Import variable in the Information flow column. In the Reference box, set the Type to Mole-Flow, the Stream to GASOUT, the Substream to MIXED, the Component to CO 2, and the Units to kmol/sec. b. On the Calculate tab, be sure the Calculation method is set to Fortran. In the box under Enter executable Fortran statements, beginning on row 1 and in column 7 write REMOVE=(CO2IN-CO2OUT)/CO2IN. 9. Still under Flowsheeting options, navigate to Design Specs. Click New and then name it DS-RM. a. On the Define tab, create a variable REMOVE and then under Reference set the Type to Parameter and the Parameter no. to 1. b. On the Spec tab i. Spec: REMOVE ii. Target: 0.90 iii. Tolerance: c. On the Vary tab i. Type: Stream-Var ii. Stream: LEAN iii. Variable: MOLE-FLOW iv. Lower: 5 v. Upper: 300 Protected under CCSI MASTER NDA

392 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Running the Simulation 1. Deactivate the design spec by right-clicking it and then selecting Deactivate. 2. Run the simulation. This provides an initial guess. a. The user may see warnings about unusual liquid mole fraction and component production profiles. These can be ignored. b. Close the economic analysis if prompted. 3. Change the absorber Reactions for stages 1 to 3 to R-PZMP from Z-PZMP. Run the simulation. a. The user may see warnings about unusual liquid mole fraction and component production profiles. Again, these can be ignored. 4. Change the absorber Reactions for stages 4 to 50 to R-PZMP from Z-PZMP. Run the simulation. 5. Navigate to Flowsheeting Options Calculator C-RM Results and on the Define Variable tab, the fractional CO 2 removal is displayed. It should be ~62.5%. 6. Increase the LEAN stream total flow in 5 kmol/sec increments until the percent removal is within 0.10 of Be sure to run the simulation after each increment. a. At 30 kmol/sec, removal is ~74%. b. At 35 kmol/sec, ~83%. c. At 40 kmol/sec, ~88%. 7. Activate the Design Spec D-RM by right-clicking it and then selecting Activate. Run the simulation. 8. The absorber is now removing 90% of the inlet CO 2. Results should be similar to those in Tables View them by navigating to Results Summary Streams, Flowsheeting Options Design Spec DS-RM Results, and Blocks ABSORBER Pack Rating 1 Results. Protected under CCSI MASTER NDA

393 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Table 12: Stream Results Excerpt GASIN GASOUT LEAN RICH Temperature K Pressure N/sqm Vapor Frac Solid Frac Mole Flow kmol/sec Mass Flow kg/sec Volume Flow cum/sec Enthalpy Gcal/hr Mole Flow kmol/sec H2O CO < HCO CO H+ OH- PZ trace PZCOO PZCOO PZH PZH+2 HPZCOO trace C5H13-01 C5H14-01 N < O2 MP < MPH Table 13: DS-RM Results Variable Initial Value Final Value Units MANIPULATED KMOL/SEC REMOVE Protected under CCSI MASTER NDA

394 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Table 14: Column Pack Rating Results Variable Value Unit Section Starting Stage 1 Section Ending Stage 50 Column Diameter 9 meter Maximum Fractional Capacity Maximum Capacity Factor m/sec Section Pressure Drop N/sqm Average Pressure Drop/Height N/cum Maximum Stage Liquid Holdup cum Maximum Liquid Superficial Velocity m/sec Surface Area 256 sqm/cum Void Fraction st Stichlmair Constant 1 2nd Stichlmair Constant 1 3rd Stichlmair Constant 0.32 Protected under CCSI MASTER NDA

395 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 2.2 Stripper Simulation Description This example describes simulating a simple stripper and cross exchanger. It is recommended that the user model the absorber and stripper using separate files. Setup 1. Construct the flowsheet of Figure 11. From Columns in the Model Palette, select RadFrac STRIP1 for the stripper. From Exchangers, select Heater for CX-COLD, CX-HOT, and HX-TRIM. From Pressure Changers, select Pump for LEANPUMP. Create the streams using the Material button. Figure 11: Simple stripper flowsheet. 2. Set COLDRICH to the values from the absorber. a. Temperature: K b. Pressure: 12 bar c. Total flow: kmol/sec d. Composition: Mole-Frac i. H2O 55.5 ii. CO iii. PZ 2 iv. MP 3 Note: The pressure is set as if coming from a pump, which is omitted. Protected under CCSI MASTER NDA

396 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 3. Set CX-COLD as follows: a. Pressure: 0 N/sqm b. Temperature: 130 C c. Valid phases: Vapor-Liquid Note: Pressure drop is neglected. 4. Configure STRIPPER Setup as follows: a. On the Configuration tab i. Calculation Type: Rate-Based ii. Number of Stages: 15 iii. Condenser: None iv. Reboiler: Kettle v. Reboiler Duty: 200 MW b. On the Streams tab, feed COLDRICH to stage 1 as liquid. c. On the Pressure tab, set the top stage pressure to 3 bar. 5. Navigate to Stripper Specifications Reactions, select starting stage as 1, ending stage as 15, and then Chemistry ID as PZMP. 6. Navigate to Sizing and Rating Packing Rating and create a new Pack Rating for the stripper by clicking New. Let it be named 1, and configure it as follows: a. Under Setup, stages 1 14 use MELLAPAK, SULZER, STANDARD, 250X with a diameter of 5.1 m and a section packed height of 2 m. b. Under Rate-Based, check Rate-based calculations with Film Resistance set to Film for liquid and vapor phases. On the Correlations tab, change the mass transfer coefficient method and the interfacial area method to HanleyStruc (2010). 7. Configure CX-HOT a. Temperature: 70 C b. Pressure: 0 N/sqm 8. Configure LEANPUMP a. Discharge pressure: 250 kpa 9. Configure HX-TRIM a. Temperature: 40 C b. Pressure: 0 N/sqm Note: This flowsheet takes the rich stream from the previous absorber tutorial, passes it through a cross-exchanger, and then to the stripper. CX-COLD and CX-HOT will be used to simulate the cross exchanger. HX-TRIM is the trim cooler to lower the lean solvent down to 40 C prior to entering the absorber. Protected under CCSI MASTER NDA

397 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 10. Create a LOADINGS calculator by navigating to Flowsheeting Options Calculator and then clicking New. Name it LOADINGS. a. Define the variables as shown in Table 15. b. Enter the Fortran code as shown, with the periods in column six: LLDG=(LCO2+LHCO3+LCO3+LPZCOO+2*LPZCOO2+LHPZCOO). /(2*(LPZ+LPZH+LPZCOO+LPZCOO2+LHPZCOO)+LMP+LMPH) RLDG=(RCO2+RHCO3+RCO3+RPZCOO+2*RPZCOO2+RHPZCOO). /(2*(RPZ+RPZH+RPZCOO+RPZCOO2+RHPZCOO)+RMP+RMPH) Table 15: LOADINGS Variable Definitions Variable Name Information Flow Definition LLDG Export variable Parameter Parameter no.=2 RLDG Export variable Parameter Parameter no.=3 LPZ Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZ LPZH Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZH+ LPZCOO Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZCOO- LPZCOO2 Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=PZCOO-2 LHPZCOO Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=HPZCOO LHCO3 Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=HCO3- LCO3 Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=CO3-- LCO2 Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=CO2 LMP Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=MP LMPH Import variable Mole-Frac Stream=STR-LEAN Substream=MIXED Component=MPH+ RPZ Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZ RPZH Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZH+ RPZCOO Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZCOO- RPZCOO2 Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=PZCOO-2 RHPZCOO Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=HPZCOO RHCO3 Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=HCO3- RCO3 Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=CO3-- RCO2 Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=CO2 RMP Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=MP RMPH Import variable Mole-Frac Stream=HOTRICH Substream=MIXED Component=MPH+ Protected under CCSI MASTER NDA

398 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 11. Create a Design Spec named DS-LEAN. a. On the Define tab, define LLDG as Parameter 2. b. On the Spec tab, spec LLDG to target 0.26 with a tolerance of c. On the Vary tab under Manipulated variable limits, Lower: 100 and Upper: 500 Watts. Under Manipulated variable set the following: i. Type: Block-Var ii. Block: STRIPPER iii. Variable: QN iv. Units: MW 12. Create a Design Spec named DS-T. a. On the Define tab, define TEMP as Stream-Var Stream=STR-LEAN Substream=MIXED Variable=TEMP Units=K. b. On the Spec tab, spec TEMP to target K with a tolerance of c. On the Vary tab, set the manipulated variable limits to 1 to 10. Under Manipulated variable set the following: i. Type: Block-Var ii. Block: STRIPPER iii. Variable: STAGE-PRES iv. ID1: 1 v. Units: bar 13. To help converge these two design specs, navigate to Convergence Options Defaults and then on the Sequencing tab, change the Design spec nesting to Inside-Simultaneous. Protected under CCSI MASTER NDA

399 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Running the Simulation 1. Deactivate both design specs by right-clicking and then selecting Deactivate. 2. Run the simulation. a. Ignore the warning about excess flood. Ignore these throughout this tutorial. b. Close the economic analysis if prompted. 3. Create a heat stream from CX-HOT to CX-COLD by clicking the arrow next to Material in the Model Palette and then clicking Heat from the drop-down menu. Name it Q-XC. 4. Review the lean loading (LLDG) in the LOADINGS calculator block by navigating to the Define Variable tab of Results. It should be 0.17 mol CO 2 /mol alk. Before enabling the design spec, it should be closer to the target. 5. Reduce the stripper reboiler duty gradually in 25 MW increments, running after each change. a. 175 MW gives 0.19 mol CO 2 /mol alk. b. 150 MW gives 0.21 mol CO 2 /mol alk. c. 125 MW gives 0.25 mol CO 2 /mol alk. This is close enough to turn on the design spec. 6. Activate the DS-LEAN design spec and run the simulation. a. Converges to 121 MW at a loading of 0.26 mol CO 2 /mol alk. 7. Review the reboiler temperature by looking at Blocks STRIPPER Profiles and then look at the liquid temperature of stage 15. Right now it is 395 K. The target is 423 K, so again gradually adjust the variable before enabling the design spec. 8. Under Blocks STRIPPER Specification Pressure, increase the pressure in 1.5 bar increments, running after each change. a. 4.5 bar gives 406 K. b. 6 bar gives 414 K. c. 7.5 bar gives 421 K. This is close enough to turn on the design spec. 9. Activate the DS-T design spec and run the simulation. The results are similar to those of Tables To view them, look at Results Summary Streams, Flowsheeting Options Design Spec DS-LEAN Results, Flowsheeting Options Design Spec DS-T Results, and Blocks STRIPPER Pack Rating 1 Results. Protected under CCSI MASTER NDA

400 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Table 16: Stream Results Excerpt COLDLEAN COLDRICH HOTLEAN HOTRICH P-LEAN STR-LEAN VAPOR Temperature K Pressure N/sqm E E Vapor Frac Solid Frac Mole Flow kmol/sec Mass Flow kg/sec Volume Flown cum/sec Enthalpy Gcal/hr Mole Flow kmol/sec H2O E CO E HCO E CO E H E OH E PZ E PZCOO E PZCOO E PZH E PZH E HPZCOO E C5H E C5H E N E O E MP E MPH E Table 17: DS-LEAN Results Variable Initial Value Final Value Units MANIPULATED 1.21E E+08 WATT LLDG Protected under CCSI MASTER NDA

401 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Table 18: DS-T Results Variable Initial Value Final Value Units MANIPULATED N/SQM TEMP K Table 19: Pack Rating Results Variable Value Unit Section Starting Stage 1 Section Ending Stage 14 Column Diameter 5.1 meter Maximum Fractional Capacity Maximum Capacity Factor m/sec Section Pressure Drop N/sqm Average Pressure Drop/Height N/cum Maximum Stage Liquid Holdup cum Maximum Liquid Superficial Velocity m/sec Surface Area 256 sqm/cum Void Fraction st Stichlmair Constant 1 2nd Stichlmair Constant 1 3rd Stichlmair Constant 0.32 Protected under CCSI MASTER NDA

402 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 3.0 USAGE INFORMATION 3.1 Environment/Prerequisites This product requires Aspen Plus V8.4 or newer with an Aspen Rate-Based Distillation license. As such, the supported environments are limited to: Windows XP SP3 Windows Vista Business SP2 Windows Vista Ultimate SP2 Windows 7 Ultimate (32- and 64-Bit) Windows 7 Professional (32- and 64-Bit) Windows 8 (all versions) 3.2 Support Support can be obtained from ccsi-support@acceleratecarboncapture.org or by filling out the Submit Feedback/Request Support form available on the product distribution page. 3.3 Restrictions This model uses data that has a high degree of experimental error in addition to an incorrect pk a prediction. It should not be used for rigorous process design. The model is centered at an amine concentration of 2 m PZ/3 m HMPD. Extrapolating far from this concentration should be done with care. The model is best between 40 and 160 C and 0.13 and 0.52 mol CO 2 /mol alk. Kinetic modeling should be kept to C. 3.4 Next Steps No updates are planned. Protected under CCSI MASTER NDA

403 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 4.0 DEBUGGING The model is running correctly if it is converging for the above tutorials with similar results. If it is not, see the next section. 4.1 How to Debug Always run the simulation with the control panel visible. It is the only output available during computation, and it indicates whether or not the simulation will converge. Calculations can be stopped if the simulation begins to diverge. Any problems encountered during computation will be listed in the control panel. Additional debugging information is available in the history file, which can be viewed by selecting History from the ribbon in the Summary section of the Home tab. Subroutine Errors If the user sees, *** SEVERE ERROR COULD NOT RESOLVE USER OR IN-LINE FORTRAN SUBROUTINE(S): the simulation will not run. The possible causes and solutions are, 1. The.bkp file and the.dll and.opt files are not located in the same directory. Move them all into the same directory to resolve this. 2. The linker is not specified in the run settings. Press Ctrl+F7 and then under linker options type pzhmpdloc.opt. Simulation Problems If the user sees a warning stating that the water liquid viscosity model MULH2O is violated due to the temperature being lower than the minimum temperature limit, the simulation is trapped in a non-physical solution. Check the inputs and re-run. Ignore flooding errors (TPSAR MESSAGE: XXX.XX% FLOOD IN COLUMN EXCEEDS 80%) unless it is the final step, in which case adjust column diameter for desired flood. Aiding Convergence Only reinitialize when large changes have been made, such as adding or removing a flowsheet block. Make small changes in a converged model. Converge an initial, simple case before increasing complexity. Before enabling the design specification, the variable should be close to the desired value. Mass transfer models affect convergence and results substantially, so be sure to choose the appropriate model for the packing used. Protected under CCSI MASTER NDA

404 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 4.2 Known Issues The predicted pk a is ~0.5 log units high. Unusual liquid molefrac profile for PZCOO 2 and unusual component production profile for comp PZCOO 2 messages may appear. These are safe to ignore. Flash errors can occur if the solvent goes above 0.5 mol CO 2 /mol alk, particularly at elevated temperatures. In running the tutorials, the user will see warnings that the mole fractions are normalized to unity. There will be a warning about the vapor pressure for MP. Ignore it. There will be a warning about reaction 5 in the chemistry GLOBAL. Ignore it. There will be warnings that the structure of most of components is not defined. Ignore them. 4.3 Reporting Issues To report an issue please send an to ccsi-support@acceleratecarboncapture.org. Protected under CCSI MASTER NDA

405 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 5.0 MODEL HISTORY Thermodynamics The blend of 2 m PZ/3 m HMPD is 11.4 wt.% PZ, 22.8 wt.% HMPD, and 34.1 wt.% amine overall. As this model is designed for a higher concentration of inlet CO 2 than standard coal conditions, the rich loading is defined at 10 kpa with the lean loading at the usual 0.5 kpa, yielding a loading range of mol CO 2 /mol alk. The model was regressed using the analogy method with methyldiethanolamine (MDEA) serving as the analog for HMPD. The starting model was Independence, a PZ/MDEA model (Frailie, 2014). HMPD and HMPDH + components were added to the Independence model and the chemistry was modified to include: HMPD + CO 2 + H 2 O HMPDH + + HCO 3 (1) HMPD + HCO 3 HMPDH + + CO 3 2 (2) Then, parameters were set to MDEA and MDEAH + values until identical properties were observed for 5 m PZ with either 5 m MDEA or 5 m HMPD. All amines are treated as Henry s components. This was the model starting point. pk a is the first property to regress, however no pk a data were available. Therefore, the pka at 25 C was estimated using a group-contribution method (Sumon, Henni, & East, 2012). This gave a value of 9.60 at 25 C. Then, the derivative with respect to temperature was estimated using Equation (1). dpk a dt = (pk a 0.9) (1) T (K) This equation was developed from Equation (2) (Perrin, Dempsey, & Serjeant, 1981). dpk a dt = (pk a 0.9) ± (2) T (K) The adjustment factor was set to based off of fitting the known pk a of MDEA. This estimate was 0 0 fit by manually adjusting G aq,hmpdh + (DGAQFM) and H aq,hmpdh + (DHAQFM), giving 1.05E+08 J/kmol and 3.50E+08 J/kmol. Figure 12 compares the estimate to both the model fit and experimental data received after modeling (Ciftja, 2015). The model and prediction are greater than the data by 0.5. Protected under CCSI MASTER NDA

406 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 9.50 pk a T ( C) Figure 12: Predicted pk a of HMPD (solid) compared to model fit (dashed) and experimental data (points) (Ciftja, 2015). The thermodynamic data regressed are listed in Table 20. The wetted-wall column (WWC) method used lead to higher experimental error than the standard method (Chen, 2011), and, as discussed by Sherman, the data are expected to have at least 3% greater error (Rochelle et al., 2015). In addition, all WWC data were reanalyzed to give the best value of P * CO2, which is why they differ from the values reported by Du (Rochelle et al., 2015). Table 20: PZ/HMPD Regressed Thermodynamic Data (Du, 2015) Type System T Loading Method N C mol CO 2/mol alk VLE 2 m PZ/3 m HMPD WWC screening 5 VLE 2 m PZ/3 m HMPD WWC 20 VLE 2 m PZ/3 m HMPD FTIR 9 P Am 0.3 m HMPD unloaded FTIR 3 P Am 2 m PZ/3 m HMPD unloaded FTIR 3 The unloaded amine volatility data for HMPD and PZ/HMPD were regressed together using Aspen Plus DRS. The NRTL binary interaction parameters of the form shown in Equation (3) were regressed, τ i,j = C i,j + D i,j T + (3) along with the temperature dependence of Henry s law parameters shown in Equation (4). ln H i,a = a i,a + b i,a T + (4) Protected under CCSI MASTER NDA

407 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual The results are shown in Table 21 with the fit shown in Figure 13. Table 21: Amine Volatility of 2 m PZ/3 m HMPD Regressed Parameters Parameter Value (SI Units) Standard Deviation C HMPD,H2 O a HMPD,H2 O b HMPD,H2 O -8, E E C 50 C 40 C PP (Pa) 1.00E E E E E loading (mol CO 2 /mol alk) Figure 13: Amine volatility comparison of 2 m PZ/3 m HMPD. Lines are correlations at 10 C intervals ( PZ, - - CO 2, HMPD) and points are data ( HMPD, CO 2, PZ) (Du, 2015). Protected under CCSI MASTER NDA

408 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual After regressing volatility, all the CO 2 VLE data were regressed simultaneously using enrtl binary interaction parameters of the same form as Equation (3). The resulting parameters are listed in Table 22 with the fit shown in Figure 14. Table 22: VLE of 2 m PZ/3 m HMPD Regressed Parameters Parameter Value (SI Units) Standard Deviation C (HMPDH +,PZCOO ),H2 O C (HMPDH +,PZCOO ),PZ C (HMPDH +,HCO3 ),HPZCOO E E E C P * CO 2 (kpa) 5.00E E E E E loading (mol CO 2 /mol alk) Figure 14: VLE comparison of 2 m PZ/3 m HMPD. Lines are the correlation in 20 C increments compared to data ( FTIR, WWC, WWC screening). Protected under CCSI MASTER NDA

409 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual The predicted heat of absorption, calculated by Equation (5), is shown in Figure 15. H abs = R d(ln f CO 2 ) d( 1 T ) (5) C ΔH abs (kj/mol) loading (mol CO 2 /mol alk) Figure 15: Predicted heat of absorption of 2 m PZ/3 m HMPD by equation (5) at 20 C intervals. The predicted activity coefficients and speciation are given in Figures 16 and 17. The high γ PZ(COO )2 is unexpected and likely spurious. This leads to no PZ(COO ) 2 forming. Protected under CCSI MASTER NDA

410 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 1E+3 1E+2 1E+1 γ 1E+0 1E-1 1E loading (mol CO 2 /mol alk) PZ PZH+ PZCOO- PZCOO2 HPZCOO HMPD HMPDH+ HCO3- CO3-- CO2 Figure 16: Predicted activity coefficients of 2 m PZ/3 m HMPD at 40 C. 3.0 m loading (mol CO 2 /mol alk) PZ PZH+ PZCOO- PZCOO2 HPZCOO HMPD HMPDH+ HCO3- CO3-- CO2 Figure 17: Predicted speciation of 2 m PZ/3 m HMPD at 40 C. Protected under CCSI MASTER NDA

411 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Mass Transfer Hydraulics As no density data are available, the same correlation and parameters used in Independence (Frailie, 2014) were also used, resulting in the prediction of Figure C ρ (g/ml) loading (mol CO 2 /mol alk) Figure 18: Predicted density of 2 m PZ/3 m HMPD using the same representation as Independence (Frailie, 2014) at 20 C intervals. The regressed viscosity data are listed in Table 23. Table 23: Regressed Viscosity Data (Du, 2015) PZ (m) HMPD (m) T ( C) Loading (mol CO 2 /mol alk) N Protected under CCSI MASTER NDA

412 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual The method used is a modification of the method of Freeman (2011). The method did not use triplicates, changed the shear rate, run time, and sampling. This modified method gave erroneous and high error data that precluded regressing all terms of Equation (6), so only e, f, h, and j were regressed. [(ax HMPD + bx PZ + c)t + dx HMPD + ex PZ + f] = exp { μ H2O [(gx HMPD + hx PZ + it + j)α + 1] x HMPD+PZ} (6) T 2 μ HMPD+PZ The results are shown in Table 24. Table 24: Viscosity Parameters and Standard Deviations for PZ/HMPD of Equation (6) Parameter Value (σ 2 ) Parameter Value (σ 2 ) a 9.12E+02 f 3.28E+04 (4.60E+04) b 1.89E+03 g 7.42E-01 c 9.68E+02 h (2.99) d 0.00 i 7.81E-03 e 1.25E+05 (3.48E+05) j 3.41 (0.385) The high standard deviations indicate that the parameters have little physical significance, nevertheless the fit shown in Figure 19 is satisfactory. 2E+1 20 C μ 2E+0 (cp) 2E loading (mol CO 2 /mol alk) Figure 19: Viscosity correlation of 2 m PZ/3 m HMPD. Lines are correlation at 20 C intervals; points are data (Du, 2015) with different points indicating different runs. Protected under CCSI MASTER NDA

413 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Mass Transfer Framework The mass transfer framework used is similar to Independence (Frailie, 2014). MDEA was replaced with HMPD to form the reaction set shown in Table 25. Table 25: Reaction Set for PZ/HMPD; Reactions below the Rule are in Equilibrium HMPD + H 2 O + CO 2 HCO 3 + HMPDH + PZCOO + H 2 O + CO 2 HCO 3 + HPZCOO 2 PZ + CO 2 PZCOO + PZH + PZ + HMPD + CO 2 PZCOO + HMPDH + 2 PZCOO + CO 2 PZ(COO ) 2 + HPZCOO PZCOO + HMPD + CO 2 PZ(COO ) 2 + HMPDH + PZCOO + PZH + HMPD + PZH + HMPD + HCO 3 HPZCOO + PZ HMPDH + + PZ HMPDH + + CO 3 2 The diffusion of amine-products is the same as Independence, allowing the model to reduce to PZ when HMPD is removed. However, this leads predicting that the diffusion of amine-products is one order of magnitude greater than that of CO 2, which is physically counter-intuitive. The data were collected by Du (2015) on a WWC using a method similar to Chen (2011). The method was modified to reduce the number of points collected in most cases. It is not clear how much additional error this introduces. Forty (40) points ranging from mol CO 2 /mol alk and C were regressed manually using the method outlined by Sherman in (Rochelle et al., 2015) along with the relationships discussed by Frailie (2014). The rate of the formation of bicarbonate was set from the 3 Am Brønsted relationship (Versteeg & Swaaij, 1988). Protected under CCSI MASTER NDA

414 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual Results The fitted parameters are shown in Table 26 and the corresponding fits in Figures 20 and 21. Table 26: PZ/HMPD Kinetic Parameters Reaction Products k o kmol/sec m 3 E A kj/mol HCO 3 + HMPDH E PZCOO + HMPDH E PZ(COO) 2 + HMPDH E abs 40 abs 60 abs 80 abs 100 abs T ( C) Figure 20: Flux parity plot for 2 m PZ/3 m HMPD compared to data from Du (2015). Protected under CCSI MASTER NDA

415 CCSI Special Solvent Blend Model Approximate HMPD/PZ CO 2 Capture Simulation User Manual 20 abs 40 abs 60 abs 80 abs 100 abs 0.50 Figure 21: Flux parity plot for 2 m PZ/3 m HMPD compared to data from Du (2015). 6.0 REFERENCES loading (mol CO 2 /mol alk) Cifta, AF. Personal communication. July, Du, Y. Personal communication Chen X. Carbon Dioxide Thermodynamics, Kinetics, and Mass Transfer in Aqueous Piperazine Derivatives and Other Amines. The University of Texas at Austin. Ph.D. dissertation Frailie PT. Modeling of Carbon Dioxide Absorption / Stripping by Aqueous Methyldiethanolamine / Piperazine. The University of Texas at Austin. Ph.D. dissertation Freeman SA. Thermal Degradation and Oxidation of Aqueous Piperazine for Carbon Dioxide Capture. The University of Texas at Austin. Ph. D. dissertation Perrin DD, Dempsey B, Serjeant EP. pk a Prediction for Organic Acids and Bases. London, Chapman & Hall Rochelle GT et al. CO 2 Capture by Aqueous Absorption, Summary of First Quarterly Progress Reports Texas Carbon Management Program. The University of Texas at Austin Sumon K, Henni A, East A. Predicting pk a of Amines for CO 2 Capture: Computer versus Pencil-and-Paper. Ind Eng Chem Res. 2012;51: Versteeg GF, Swaaij WPM van. On the kinetics between CO 2 and alkanolamines both in aqueous and non-aqueous solutions II. Tertiary amines. Chem Eng Sci. 1988;43: Protected under CCSI MASTER NDA

416 Appendix K Plate and Frame Heat Exchanger Calculator 394

417 Heat Exchanger Model User Manual Version November 11,