PREDICTIVE MODELING OF METAL-CATALYZED POLYOLEFIN PROCESSES

Transcription

1 PREDICTIVE MODELING OF METAL-CATALYZED POLYOLEFIN PROCESSES Neeraj Prasad Khare Dssertaton submtted to the Faculty of the Vrgna Polytechnc Insttute and State Unversty n partal fulfllment of the requrements for the degree of DOCTOR OF PHILOSOPHY n Chemcal Engneerng 10:00 AM November 14, B Randolph Hall Blacksburg, VA Dr. Y. A. Lu, Charman (Chemcal Engneerng) Dr. Rchey M. Davs (Chemcal Engneerng) Dr. Donald G. Bard (Chemcal Engneerng) Dr. James E. McGrath (Chemstry) Dr. Slmane Adjerd (Mathematcs) Keywords: Zegler-Natta, metallocene, polymerzaton knetcs, model, smulaton, reactor, polyethylene, polypropylene, physcal propertes, phase equlbrum by Neeraj Prasad Khare All rghts reserved

2 Predctve Modelng of Metal-Catalyzed Polyolefn Processes Neeraj Prasad Khare Abstract Ths dssertaton descrbes the essental modelng components and technques for buldng comprehensve polymer process models for metal-catalyzed polyolefn processes. The sgnfcance of ths work s that t presents a comprehensve approach to polymer process modelng appled to large-scale commercal processes. Most researchers focus only on polymerzaton mechansms and reacton knetcs, and neglect physcal propertes and phase equlbrum. Both physcal propertes and phase equlbrum play key roles n the accuracy and robustness of a model. Ths work presents the fundamental prncples and practcal gudelnes used to develop and valdate both steady-state and dynamc smulaton models for two large-scale commercal processes nvolvng the Zegler-Natta polymerzaton to produce hghdensty polyethylene (HDPE) and polypropylene (PP). It also provdes a model for the soluton polymerzaton of ethylene usng a metallocene catalyst. Exstng modelng efforts do not nclude physcal propertes or phase equlbrum n ther calculatons. These omssons undermne the accuracy and predctve power of the models. The forward chapters of the dssertaton dscuss the fundamental concepts we consder n polymer process modelng. These nclude physcal and thermodynamc propertes, phase equlbrum, and polymerzaton knetcs. The later chapters provde the modelng applcatons descrbed above.

3 Table of Contents Chapter 1 Introducton Essental Components of a Polymer Process Model Flowchart for Developng a Polymer Process Model Organzaton of the Dssertaton... 6 Chapter 2 Physcal Propertes and Phase Equlbrum for Polymer Systems Introducton Physcal Propertes Introducton Speces vs. Segment-Based Accountng Pure-Component Propertes Mxture Propertes Phase Equlbrum Introducton VLE: The Ideal Case Equatons of State Consderng Sold Polymer n Phase Behavor Property Methods Appendces Resdual Thermodynamc Propertes from the Equaton-of-State Approach Model Constants for the PC-SAFT EOS Chapter 3 Polymerzaton Knetcs Introducton Notaton for Polymer Speces Mathematcal Treatment of Polymerzaton Knetcs Leadng Moments of the Molecular Weght Dstrbuton Polymer Propertes n Terms of Moment Expressons Zegler-Natta Polymerzaton Catalyst Chemstry Knetc Mechansm for Polymerzaton Development of Rate Expressons Metallocene Catalyzed Polymerzatons Catalyst Chemstry Knetc Mechansm for Polymerzaton Development of Rate Expressons Summary Chapter 4 Manuscrpt for the Slurry Polymerzaton of Hgh-Densty Polyethylene (HDPE) Usng a Zegler-Natta Catalyst Introducton Slurry HDPE Process Technology Modeled Processes Modelng Technology Physcal Propertes Introducton Sanchez-Lacombe Equaton of State for Polymer Systems... 83

4 4.2.3 Chao-Seader, Scatchard-Hldebrand, and Redlch-Kwong Models for Conventonal Speces Pure-Component Propertes Mxture Propertes Polymer Propertes Reactor Phase Equlbrum Polymerzaton Knetcs Introducton Homopolymerzaton Knetc Scheme Copolymerzaton Knetc Scheme Olgomer Producton Determnaton of Knetc Parameters Smulaton Results Steady- State Model Valdaton Dynamc Modelng Process Retroft Conclusons Chapter 5 Manuscrpt for the Gas-Phase Polymerzaton of Propylene Usng a Zegler- Natta Catalyst Introducton Gas-Phase Processes Usng Strred-Bed Reactors Modeled Process Modelng Technology Modelng Methodology Physcal Propertes and Thermodynamc Modelng Introducton PC-SAFT EOS Pure-Component Propertes Mxture Propertes Polymer Propertes Reactor Modelng Usng CSTRs n Seres Phase Equlbrum Polymerzaton Knetcs Introducton Homopolymerzaton Knetc Scheme Copolymerzaton Knetc Scheme Determnaton of Knetc Parameters Dynamc Modelng Introducton Control Scheme Smulaton Results Model Valdaton Model Applcaton Conclusons v

5 Chapter 6 Manuscrpt for the Soluton Polymerzaton of Ethylene Usng a Constraned- Geometry Catalyst Introducton Model Development Overvew Modeled Process Phase Equlbrum and Physcal and Thermodynamc Propertes Polymerzaton Knetcs Model Equatons Model Valdaton Case Study One Case Study Two Model Applcatons Varyng Feed Composton Varyng Reacton Knetcs The Impact of Physcal Propertes The Impact of Phase Equlbrum Energy-Balance Applcatons Conclusons Appendx Chapter 7 Conclusons and Future Work Acknowledgments Vta v

6 Lst of Fgures Fgure 1-1. The basc nputs and outputs of a polymer process model... 3 Fgure 1-2. Flowchart for developng and utlzng a polymer process model... 5 Fgure 2-1. Illustratng a segment-based consderaton of polymer chans n a mxture. Ths approach permts the consderaton of nteractons between each segment type and other speces Fgure 2-2. Pathway for computng the heat of polymerzaton for the EOS approach Fgure 2-3. Lattce consdered n the Sanchez-Lacombe equaton of state. Connected dots represent chemcal speces on a fxed-volume lattce Fgure 2-4. A physcal descrpton of the attractve and repulsve consderatons of the SAFT EOS Fgure 2-5. Comparng the ntermolecular (attractve) forces as modeled by the SAFT and PC-SAFT EOS Fgure 2-6. Comparng the actual stuaton n a slurry system wth a modelng assumpton where the polymer s dssolved n the lqud solvent Fgure 3-1. An example of a mechansm of catalyst actvaton by cocatalyst Fgure 3-2. Mechansm for ethylene addton to a growng chan for a Zegler-Natta catalyst, derved by Cossee. The ethylene double bond coordnates to the catalyst ste (M) and upon addton the empty ste mgrates back to ts orgnal poston. X represents the lgands of the transton metal, and s typcally Cl. R s ether the alkyl from the metal alkyl (e.g., Al(C 2 H 5 ) 3 ), or the growng polymer chan. Taken from Boor, p Fgure 3-3. The general structure for a metallocene catalyst Fgure 4-1. Flowchart of the slurry HDPE process Fgure 4-2. Process flow dagram for the parallel reactor confguraton Fgure 4-3. Process flow dagram for the seres reactor confguraton Fgure 4-4. Saturaton pressure of hexane Fgure 4-5. Saturated lqud densty of hexane Fgure 4-6. Densty of hydrogen vapor 11. The predctons of both property methods are almost dentcal Fgure 4-7. Densty of ethylene vapor Fgure 4-8. Heat of vaporzaton of hexane Fgure 4-9. Heat capacty of lqud and vapor hexane Fgure Heat capacty of HDPE Fgure Heat capacty of ethylene vapor Fgure Solublty of hydrogen n hexane Fgure Comparng the actual phase behavor n the reactor wth the modelng assumpton. The actual stuaton has vapor and lqud phases, wth sold polymer dspersed n the lqud phase. Our system consders the polymer as solublzed n the lqud phase Fgure Methodology for smultaneously determnng the knetc parameters for a sngle-ste catalyst to match plant data for multple HDPE grades Fgure GPC Deconvoluton results for a representatve HDPE sample from the parallel reactor confguraton. Fve catalyst ste types accurately descrbe the expermental molecular weght dstrbuton v

7 Fgure Methodology for smultaneously determnng the knetc parameters for a catalyst wth multple ste types to match plant data for several HDPE grades Fgure Comparng MWDs for two dfferent grades of HDPE. We hypothesze that the Zegler-Natta ste type producng hgh molecular weght polymer s nsenstve to hydrogen concentraton Fgure Comparng model predctons wth plant data for HDPE producton rate. 130 Fgure Comparng model predctons wth plant data for the number-average molecular weght of HDPE for each reactor Fgure Comparng model predctons wth plant data for HDPE polydspersty ndex Fgure Comparng model predctons wth plant data for the vapor flow rate n the reactor overhead Fgure Comparng model predctons wth plant data for reactor resdence tme. 134 Fgure Smplfed dagram of the control scheme for the parallel reactor confguraton Fgure Change n the H 2 /C 2 H 4 overhead rato durng the grade change n the parallel confguraton Fgure Effect of the grade change on the producton rate of HDPE n the parallel confguraton Fgure Effect of the grade change on the number-average molecular weght of HDPE Fgure Flowsheet for a process retroft appled to one reactor n the parallel confguraton. Increasng the producton rate ncreases the demands for heat removal, thereby necesstatng the addton of another pump and cooler to recycle lqud to the reactor Fgure 5-1. Smplfed flowchart for the gas-phase polypropylene process Fgure 5-2. An example of a gas-phase polypropylene process usng a strred-bed reactor Fgure 5-3. Procedure for developng the polypropylene process model Fgure 5-4. Comparng expermental data wth PC-SAFT predctons for heat capacty of superheated propylene and ethylene vapor. Data are from Beaton and Hewtt Fgure 5-5. Comparng expermental data wth PC-SAFT predctons for saturated lqud densty of propylene. Data are from Beaton and Hewtt Fgure 5-6. Comparng expermental data wth PC-SAFT predctons for superheated vapor densty of propylene and ethylene. The deal gas law s unable to descrbe the propylene densty at reactor condtons. Data are from Beaton and Hewtt Fgure 5-7. Comparng expermental data wth PC-SAFT predctons for polypropylene densty. Data are from Zoller Fgure 5-8. Comparng expermental data wth PC-SAFT predctons for propylene vapor pressure. Data are from Beaton and Hewtt Fgure 5-9. Comparng expermental data wth PC-SAFT predctons for the heat of vaporzaton for propylene and ethylene. Data are from Beaton and Hewtt Fgure Comparng expermental data wth PC-SAFT predctons for the solublty of ethylene n propylene. Data are from Ohgak et al Fgure Comparng expermental data wth PC-SAFT predctons for the solublty of hydrogen n propylene. Data are from Wllams and Katz v

8 Fgure Method for computng the heat of propylene polymerzaton for the equaton-of-state approach Fgure Comparng the actual reactor wth the modelng assumpton of four CSTRs n seres Fgure Iteratve methodology used to determne knetc parameters for the sngleste model Fgure Representatve MWD and deconvoluton results ndcatng that a four-ste knetc model s suffcent Fgure Iteratve methodology used to adjust the knetc parameters n the mult-ste model Fgure Comparson of model predctons wth plant data for polypropylene producton rate Fgure Comparson of model predctons wth plant data for polypropylene M n Fgure Illustratng model predctons for polypropylene polydspersty ndex Fgure Comparng model results wth plant data for polypropylene atactc fracton Fgure Illustratng model results for reactor mass holdup Fgure Change n the offgas H 2 /C 3 molar rato durng the grade change Fgure Effect of the grade change on the polypropylene producton rate Fgure Effect of the grade change on the polypropylene M n Fgure 6-1. Essental elements of a robust polymer process model Fgure 6-2. A schematc of the modeled process Fgure 6-3. Comparng expermental data wth PC-SAFT predctons for ethylene vapor molar volume. Data are from Beaton and Hewtt Fgure 6-4. Comparng expermental data wth PC-SAFT predctons for hydrogen vapor molar volume. Data are from Beaton and Hewtt Fgure 6-5. Comparng model predctons to expermental data for saturated lqud molar volume of toluene. Data are from Beaton and Hewtt Fgure 6-6. Comparng model predctons to expermental data for saturated vapor molar volume of toluene. Data are from Beaton and Hewtt Fgure 6-7. Comparng model predctons to expermental data for heat capacty of ethylene. Data are from Beaton and Hewtt Fgure 6-8. Comparng model predctons to expermental data for toluene heat capacty. Data are from Beaton and Hewtt Fgure 6-9. Comparng model predctons to expermental data for polyethylene heat capacty. Data are from Gaur and Wunderlch Fgure Comparng model predctons to expermental data for toluene vapor pressure. Data are from Beaton and Hewtt Fgure Comparng model predctons to expermental data for toluene heat of vaporzaton. Data are from Beaton and Hewtt Fgure Comparng model predctons to expermental data for ethylene solublty n toluene. Data are from Fallaha Fgure Comparng model predctons to expermental data for hydrogen solublty n toluene. Data are from Knapp et al Fgure The methodology used to adjust knetc parameters n case study one v

9 Fgure Comparng expermental data to model predctons for yeld n case study one. The average predcton error s 5.0% Fgure Comparng expermental data to model predctons for polymer M n n case study one Fgure Comparng expermental data to model predctons for number of long-chan branches per 1,000 carbon atoms n case study one Fgure Comparng expermental data wth model predctons for number of termnal double bonds per 1,000 carbon atoms n case study one Fgure The methodology used to adjust the knetc parameters n case study two Fgure Comparng expermental data to model predctons for yeld n case study two Fgure Comparng expermental data to model predctons for polymer molecular weght n case study two Fgure Comparng expermental data to model predctons for number of long-chan branches per 1,000 carbon atoms n case study two Fgure Comparng expermental data to model predctons for number of termnal double bonds per 1,000 carbon atoms n case study two Fgure The effect of changng the ethylene feed rate on polymer M n Fgure The effect of varyng the ethylene feed rate on ethylene converson Fgure The effect of varyng the catalyst feed rate on polymer M n Fgure The effect of varyng the catalyst feed rate on ethylene converson Fgure The effect of changng the solvent feed rate on the polymer M n Fgure The effect of varyng the solvent feed rate on ethylene converson Fgure The effect of changng the rate constant for chan propagaton on ethylene converson Fgure The effect of varyng the rate constant for chan transfer to hydrogen on the polymer M n Fgure The effect of changng the rate constant for β-hydrde elmnaton on the fracton of polymer chans contanng termnal double bonds (k β ) Fgure The effect of varyng the rate constant for ncorporaton of chans wth termnal double bonds on the number of long-chan branches (k tdb ) Fgure The volume dsplacement of 1,000 kg lqud toluene, as a functon of saturaton temperature Fgure The volumetrc flow rate of 50 kg/hr vapor toluene, as a functon of saturaton pressure Fgure Illustratng the effect of reactor temperature on equlbrum lqud holdup Fgure Showng the effect of temperature on resdence tme, correspondng to the results n Fgure Fgure The effect of changng the reactor resdence tme on ethylene converson Fgure Illustratng the effect of changng the reactor temperature on the lqud mole fracton of ethylene Fgure Illustratng the effect of reactor temperature on the reactor coolng duty Fgure The effect of solvent feed temperature on the reactor coolng duty x

10 Lst of Tables Table 2-1. Requred parameters for the deal-gas heat capacty model Table 2-2. Parameters used n the Sanchez-Lacombe equaton of state Table 2-3. Parameters for the PC-SAFT model Table 2-4. Propertes and model sources for the vapor phase n the equaton-of-state approach Table 2-5. Propertes and model sources for the lqud phase n the equaton-of-state approach Table 2-6. Model constants for eqs (43) and (44) n the PC-SAFT EOS Table 3-1. Polymer speces used n the development of polymerzaton knetcs Table 4-1. Unt operatons for whch we use the Sanchez-Lacombe and the Chao-Seader property methods Table 4-2. Components used n the slurry HDPE process model Table 4-3. Pure-component parameters for the Sanchez-Lacombe EOS. T *, P *, and ρ * are characterstc temperature, pressure, and densty, respectvely Table 4-4. Parameters for the deal-gas heat capacty (eq 4). Values were determned by regressng pure-component data. Unts for heat capacty are J/kmol-K Table 4-5. Values for bnary nteracton parameter η j for the Sanchez-Lacombe EOS.. 93 Table 4-6. Values for bnary nteracton parameter k j for the Sanchez-Lacombe EOS Table 4-7. Computng the heat of ethylene polymerzaton usng the Sanchez-Lacombe EOS. The results compare favorably wth the lterature value gven n eq Table 4-8. Representatve speces and mass fractons used for smulatng the phase separaton n a slurry HDPE reactor Table 4-9. Comparng the lqud compostons for cases where the HDPE has ts own lqud phase (VLLE) and when t s dssolved n the dluent (VLE) Table Comparng the vapor compostons for the VLE and VLLE cases Table Reacton subset used n the Zegler-Natta homopolymerzaton knetcs Table Smulaton targets for the models for catalysts wth sngle and multple ste types Table Base set of knetc parameters for the sngle-ste model. We do not consder temperature effects on the polymerzaton knetcs, and we therefore do not take actvaton energes nto account Table Deconvoluton results for a representatve sample of HDPE produced n the parallel process Table Smulaton targets for each polymer grade and the correspondng model parameters adjusted Table Comparng model predctons wth data for a parallel grade for Plant B Table Comparng model predctons wth data for a seres grade for Plant B Table Controlled and manpulated varables for the slurry HDPE process Table Specfcatons for the grade change n the parallel confguraton Table Comparson of HDPE flow rate and attrbutes for varyng ncreases n feed rates of raw materal for the process retroft Table 5-1. Components Used n the Model Table 5-2. Pure-component parameters for the PC-SAFT EOS Table 5-3. Parameters for the deal-gas heat-capacty model x

11 Table 5-4. Comparng PC-SAFT predctons for the heat of propylene polymerzaton wth an expermental value of kcal/mol at 25 C Table 5-5. Reacton subset used for the homopolymerzaton knetcs Table 5-6. Smulaton targets for models for catalysts wth sngle and multple ste types Table 5-7. Nomnal Set of Knetc Parameters for the Sngle-Ste Model Table 5-8. Deconvoluton results for a representatve polypropylene sample Table 5-9. Controlled and manpulated varables n the control scheme Table Specfcatons for the smulated grade change Table 6-1. Speces consdered n the model Table 6-2. Pure component parameters for the PC-SAFT EOS Table 6-3. Parameters for the deal-gas heat capacty model Table 6-4. Computng the heat of ethylene polymerzaton usng the PC-SAFT EOS. Results compare favorably wth the expermental value of kcal/mol Table 6-5. The reactons consdered n the knetc mechansm Table 6-6. Moment speces consdered n the model Table 6-7. Expermental data for case study one. Condtons for the CSTR reactor: T = 140 C,P = 34 bar Table 6-8. Polymer characterzaton results for case study one Table 6-9. Comparng model rate constants to expermentally estmated values. Model values are reasonably wthn the provded ranges Table Input data for case study two. Condtons for the CSTR reactor: T = 140 C, Table Polymer characterzaton results for case study two Table Rate constants used n case study two, compared to those used n case study one Table Stream flow rates and condtons for a smplfed polymerzaton scheme. We vary the product temperature, whch s equal to the reactor temperature Table Stream flow rates and condtons for a smplfed polymerzaton scheme. We vary the product temperature, whch s equal to the reactor temperature x

12 Chapter 1 Introducton The focus of ths work s the modelng of processes nvolvng the polymerzaton of olefns usng Zegler-Natta and metallocene catalysts. Modelng entals fundamental chemcal engneerng concepts, ncludng mass and energy balances, physcal propertes, thermodynamcs (phase equlbrum), and polymerzaton knetcs. Smulaton models play a key role n the development and operaton of polymerzaton processes. We can use a model to plan and optmze grade-change operatons, to debottleneck exstng processes, or to desgn new products. We can also use a model for scaleup calculatons, or for desgnng a process retroft. Companes can save manpower, raw materal, and energy resources by usng smulatons nstead of expermentng on a tral-and-error bass when tryng to tackle any one of these tasks. The sgnfcance of ths work s that t presents a comprehensve approach to polymer process modelng appled to large-scale commercal processes. Most researchers focus only on polymerzaton mechansms and reacton knetcs, and neglect physcal propertes and phase equlbrum. Both physcal propertes and phase equlbrum play key roles n the accuracy and robustness of a model. Ths work presents the fundamental prncples and practcal gudelnes used to develop and valdate both steady-state and dynamc smulaton models for two large-scale commercal processes nvolvng the Zegler-Natta polymerzaton to produce hgh-densty polyethylene (HDPE) and polypropylene (PP). It also provdes a model for the soluton polymerzaton of ethylene usng a metallocene catalyst. Exstng modelng efforts do not nclude physcal propertes or phase equlbrum n ther calculatons. These omssons undermne the accuracy and predctve power of the models. Secton 1.1 dscusses the essental components of a polymer process model. A robust model must consder physcal and thermodynamc propertes n addton to polymerzaton knetcs. Secton 1.2 gves a general flowchart for model development. 1

13 We use ths flowchart n each of our modelng applcatons. Secton 1.3 outlnes the remanng content of the dssertaton. 1.1 Essental Components of a Polymer Process Model Fgure 1-1 shows the basc nputs and outputs of a polymer process model. Each nput s essental to developng a comprehensve model for a polymerzaton process. We use fundamental mass and energy balances for each unt operaton n the model. These may nclude reactors, flash vessels, heat exchangers, compressors, and pumps. These balances are the most basc requrements of any process model. We must nclude physcal propertes, such as densty, to properly model vessel szng and volumetrc throughput. Densty also affects the reactor resdence tme, whch s an mportant varable that affects the polymerzaton phenomena. We also consder phase equlbrum for vessels contanng multple phases. Equlbrum calculatons are mportant to obtan correct phase compostons, whch affect the reacton knetcs. They are also mportant n downstream separaton unts, whch typcally recycle materal to the reactor. Fnally, we need polymerzaton knetcs to properly model the synthess of the polymer, and partcularly, the change n polymer propertes wth changes n reactor condtons. The polymerzaton knetcs represent the heart of a polymer process model. 2

14 physcal propertes phase equlbrum fundamental mass and energy balances polymerzaton knetcs POLYMER PROCESS MODEL polymer producton rate polymer molecular weght and ts dstrbuton polymer branchng content Fgure 1-1. The basc nputs and outputs of a polymer process model. 1.2 Flowchart for Developng a Polymer Process Model Fgure 1-2 shows the general flowchart that we use for developng and applyng a polymer process model. We begn by choosng approprate models for physcal propertes and phase equlbrum. We use heurstcs set forth by Boks et al. 1, for example, to choose approprate models. Next, we determne unary and bnary-nteracton parameters for the property models. We can use publshed values as long as they were determned under condtons that are close to those of the modeled process. Alternatvely, we can regress expermental data to determne the parameter values. Fnally, we valdate the predctons by comparng them to expermental data. Ths ensures that the model wll have accurate physcal-property and phase-equlbrum predctons. If necessary, we can use plant data to adjust the bnary-nteracton parameters to more closely match the phase-equlbrum behavor of the process. Note that we do not need a process model to complete the tasks up to ths pont. 1 Boks, C. P.; Orbey, H.; Chen, C.-C. Properly Model Polymer Processes. Chemcal Engneerng Progress 1999, 95, 39. 3

15 Next, we establsh a reacton mechansm that s approprate for the specfc polymerzaton. Once we have a set of elementary steps, we obtan nomnal knetc parameters from the open lterature. If possble, we nclude temperature dependence to the knetcs, snce most reacton rates change sgnfcantly wth small varatons n temperature. We buld a flowsheet model that contans the relevant unt operatons, usng fundamental mass and energy balances. In our applcatons, these can nclude reactors and subsequent separaton/recycle flash unts, heat exchangers, mxers, compressors, and pumps. We develop an teratve methodology for adjustng the knetc parameters to match the polymerzaton phenomena n the plant data. Ths s a key step because the reactons are usually hghly coupled, and changng the value of one parameter typcally affects several propertes smultaneously. As a result, t s very dffcult to establsh a set of knetc parameters that match plant data wthout usng a carefully developed methodology. If we are performng dynamc modelng, we ncorporate the control scheme. We also adjust the control parameters to match dynamc plant data, f avalable. Once we buld and valdate the process model, we can apply t to a varety of areas. We can debottleneck an exstng process, propose a process retroft, or desgn a new polymer grade. 4

16 STEP 1: Choose approprate models for physcal propertes and phase equlbrum. STEP 2: Regress pure-component and mxture data to determne unary and bnary-nteracton parameters for property models, or obtan establshed values from the open lterature. STEP 3: Valdate property predctons usng lterature or plant data. Use plant data to adjust bnary-nteracton parameters for phaseequlbru m modelng, f necessary. STEP 4: Choose approprate reacton mechansm wth nomnal knetc parameters from the open lterature. STEP 5: Buld flowsheet model usng fundamental prncples for unt operatons. STEP 6: Use teratve methodology to adjust knetc parameters to match plant data. STEP 7: Incorporate control scheme for dynamc modelng. STEP 8: Model applcaton. Fgure 1-2. Flowchart for developng and utlzng a polymer process model. 5

17 1.3 Organzaton of the Dssertaton The dssertaton contans two general parts. The forward chapters dscuss the fundamental concepts we consder n polymer process modelng. The later chapters provde the modelng applcatons. Chapter 2 deals wth physcal and thermodynamc propertes, and phase equlbrum. We dscuss the mportance of each property and ts role n model predctons. Chapter 3 covers polymerzaton knetcs. We focus on Zegler-Natta and metallocene mechansms ndvdually. We also descrbe the converson of the mechansms to algebrac rate expressons for use n a model. Chapter 4 descrbes the modelng of an ndustral slurry hgh-densty polyethylene (HDPE) process usng a Zegler-Natta catalyst. Chapter 5 dscusses our modelng of a gas-phase polypropylene process usng a Zegler-Natta catalyst. Chapter 6 detals a model for the soluton polymerzaton of ethylene usng a constraned-geometry catalyst. 6

18 Chapter 2 Physcal Propertes and Phase Equlbrum for Polymer Systems 2.1 Introducton In ths secton, we descrbe the varous physcal propertes that are necessary for comprehensve modelng of polymer synthess processes. We also present the thermodynamc models that we use n ths project work. Physcal-property modelng s essental to chemcal process smulaton, and cannot be gnored when performng desgn calculatons. The man physcal propertes we are concerned wth nclude densty, vapor pressure, heat capacty, enthalpy, heat of vaporzaton, and heat of polymerzaton. These propertes mpact phase equlbrum, equpment szng, and energy requrements, among other varables assocated wth process modelng and desgn. In polymerzaton engneerng, we are concerned wth mxtures of polymerc and nonpolymerc speces; these mxtures can exst n multple phases. There are several fundamental aspects of polymer systems that requre dfferent treatment than that for conventonal, low-molecular-weght systems. Frst, polymers are essentally nonvolatle. Also, unlke conventonal speces, polymers can experence change n molecular structure (chan length), and potentally ther composton 1. From a thermodynamc standpont, mxng hgh-molecular-weght polymers wth smaller speces nvolves an entropy of mxng, whch has a sgnfcant effect on phase behavor. Thermodynamc models must account for these dfferences n order to accurately descrbe the phase behavor and thermodynamc propertes of polymerc systems. In ths project work, we use equatons of state (EOS) for phase-equlbrum calculatons. Specfcally, we use the Sanchez-Lacombe (SL) and the perturbed-chan statstcal assocatng flud theory (PC-SAFT) EOS. 7

19 The prmary thermodynamc propertes we are concerned wth nclude enthalpy, entropy, Gbbs free energy, and fugacty. We must often consder these propertes when buldng a rgorous polymer process model. We use fugacty coeffcents to correct for deal phase-equlbrum behavor. We use enthalpy to perform energy balances. Entropy s useful for pump and turbne effcency calculatons. We usually obtan t from enthalpy and Gbbs energy. An accurate descrpton of phase behavor s crtcal to modelng polymer reactors and post-reactor devolatlzaton. Durng synthess, polymers can be n lqud or sold form. As a lqud, polymer can resde as dssolved n a solvent, creatng a sngle lqud phase, or reman as a separate lqud phase. In any of these cases, the reacton knetcs requre accurate concentraton predctons for the reactng phase. Many monomers resde n the vapor phase, and ther solublty n the reactng phase s mportant. Post-reactor devolatlzaton nvolves the removal of unreacted monomer, solvent, or other lght components from the polymer before downstream processng. Ths s the case whether the polymer s a lqud or sold. Rgorous consderatons requre energy balances for each unt operaton. Polymerzatons tend to be hghly exothermc, and accurate enthalpy predctons are essental for the desgn and optmzaton of polymer reactors. In some cases, nadequate coolng can lead to decomposton and reactor runaway. We can use thermodynamc models or emprcal correlatons to compute the enthalpes used n energy balances. The remander of ths chapter s organzed as follows. Secton 2.2 covers physcal propertes. Secton descrbes segment-based calculatons commonly used for polymerc systems. Secton dscusses pure-component propertes, and Secton deals wth mxture propertes. We cover phase equlbrum n Secton 2.3. Secton descrbes the relevant EOS mentoned earler. Secton descrbes the use of EOS property methods, whch combne varous physcal-property and thermodynamc models for comprehensve model predctons. We provde equatons and dervatons for thermodynamc propertes, as well as model constants, n Secton

20 2.2 Physcal Propertes Introducton Ths secton descrbes the varous physcal propertes requred for comprehensve modelng of polymer synthess processes. Accurate densty calculatons allow models to properly consder equpment szng and process throughput, as well as phase volumes and resdence tmes for reactors. Vapor pressure s mportant for phase-equlbrum calculatons. Heat of vaporzaton s mportant for proper heat-balance calculatons. Some reacton systems rely on the vaporzaton of a solvent to remove the heat of polymerzaton. Heat of polymerzaton and enthalpy are used n energy balances, whch are mportant for determnng requred heatng and coolng dutes Speces vs. Segment-Based Accountng There are two types of accountng systems commonly used for modelng physcal propertes and phase equlbrum for polymerc systems. Speces-based calculatons consder polymer chans as sngle molecules, and segment-based accountng treats every polymer repeat unt (segment) as an ndvdual molecule. The segment-based approach has the advantage of beng able to characterze polymer molecules by the chemcal propertes of the segments, or monomer unts, whch comprse them. Ths facltates the consderaton of the effect of segment composton on the thermodynamc propertes. Note that the use of the segment-based approach does not exclude the consderaton of chan length, whch s mportant for modelng many physcal propertes and phaseequlbrum behavor. Fgure 2-1 llustrates the segment-based approach for a polymer chan contanng dfferent segment types dssolved n a solvent medum. The nteractons between the varous segment types and the solvent molecules can be very dfferent, affectng the physcal propertes and phase behavor of such a system. 9

21 Polymer segment of type 1 Polymer segment of type 2 Solvent molecule Fgure 2-1. Illustratng a segment-based consderaton of polymer chans n a mxture. Ths approach permts the consderaton of nteractons between each segment type and other speces. The mole fracton of polymer chans s often not useful. Consder a mxture of 1 g polyethylene, of molecular weght 50,000, dssolved n 20 g n-hexane, of molecular weght 86. The mole fracton of polymer s 1 x = moles polymer 50,000 polymer 8.6E 5 moles solvent + moles polymer = = 86 50,000 (1) where x s the real mole fracton. Whle ths seems lke a vanshng amount of polymer, we now consder the mass fracton of polymer n the mxture: mass polymer 1 m polymer = = = (2) mass solvent + mass polymer where m s mass fracton. Although the mole fracton of polymer s tny, the polymer occupes about 5% of the mass of the mxture. In terms of physcal and thermodynamc propertes, t s more meanngful to consder mass fractons than mole fractons. Let us now consder the same mxture and apply the segment-based accountng. The ethylene segments have a molecular weght of 28, gvng the polymer a degree of 10

22 polymerzaton of 1,786 (= 50,000/28). We assume that each solvent molecule s a sngle segment. The mole fracton of polymer segments s then X polymer 1 moles polymer segments ,000 = = = 0.133(3) moles solvent + moles polymer segments ,000 where X s segment-based mole fracton. The segment mole fracton s more representatve of the amount of polymer n the system than s the mole fracton of whole polymer chans. Note that ths segment fracton would be equal to the total polymer mass fracton n the event that the segment molecular weght was the same as that for the solvent speces. The general expresson for convertng between real and segment-based mole fracton s X I xr, I = (4) I xr, I where subscrpt I refers to polymer segments, subscrpt refers to speces, and r,i s the number of segment type I n speces. The segment approach s useful for the consderaton of bnary nteractons between the dfferent types of segments n the polymer and the solvent speces. Ths accommodates EOS that utlze bnary nteracton parameters to correlate phase-equlbrum data. It also facltates modelng polymer propertes such as copolymer composton and sotactcty Pure-Component Propertes Introducton There are many physcal propertes that we must consder to properly model polymer processes. Pure-component propertes nclude densty, vapor pressure, enthalpy, heat of vaporzaton, heat capacty, and heat of polymerzaton. These propertes often form the bass for characterzng mxture propertes, e.g., computng a mxture property by usng a 11

23 mxng rule n conjuncton wth the pure-component propertes and mxture composton. In ths secton, we descrbe these propertes, ther modelng mportance, and relevant models Lqud Densty Snce many polymerzatons occur n the lqud phase, lqud densty s mportant for phase-volume and resdence-tme calculatons for reactors. It s also mportant for accurate phase concentratons, on whch the reacton knetcs rely. In process retroft and desgn, t s essental for modelng volumetrc throughput. Densty s also commonly used as a factor for qualty control for polymers. When usng an equaton of state for phase-equlbrum calculatons, we use the EOS to compute lqud densty Vapor Densty Vapor densty s mportant for equpment szng for reactor overhead unts and other operatons. We typcally use an equaton of state to compute the vapor-phase densty for both pure components and mxtures. Snce polymers are essentally nonvolatle, the vapor phase n any gven porton of a polymer process contans only conventonal speces. Ths allows more flexblty when choosng an EOS for vapor-phase calculatons. We descrbe the relevant equatons of state n Secton 2.3.3, and the EOS approach to property predcton n Secton Vapor-phase nondealty s typcally small compared to lqud non-dealty. However, the deal-gas law s only approprate for the few systems where pressure s close to atmospherc and the speces are non-assocatng Vapor Pressure An mportant pure-component property for modelng phase equlbrum s vapor pressure. When usng an equaton of state for phase-equlbrum calculatons, we can use t to compute the vapor pressure of each speces. 12

24 Ideal-Gas Enthalpy Enthalpy s used for computng energy balances for unt operatons. It s mportant for non-sothermal systems, where the energy balance determnes the system temperature. Enthalpy s partcularly essental n polymerzaton reactors, where a balance must often be struck between the exothermc heat of polymerzaton and the energy removed usng a heat jacket. Some reactors rely on the heat absorbed by vaporzaton of a solvent to remove some of the heat of polymerzaton. The deal gas s a hypothetcal state often used as a reference pont for calculatng thermodynamc propertes such as enthalpy. It represents the enthalpy of a pure speces at condtons of standard temperature and pressure (298 K and 1 atm, STP). We compute ts value usng T ( ) ref H = H T + C T (5) g ref g f, p, d T where H f, (T ref ) s the heat of formaton of speces at a reference temperature (usually 298 K), and C p, s the heat capacty for speces, as a functon of temperature. We can obtan expermental values for the heats of formaton from standard data references. Note that the deal-gas enthalpy s ndependent of pressure. Typcally, we use an emprcal expresson to represent the temperature dependence of the deal-gas heat capacty on temperature. A common form s the DIPPR model: 2 2 C T E T c = A + B + D g p, snh( C T) cosh( E T) (6) where A through E are adjustable parameters. Integratng eq (6) gves: T T g C E cp, dt = AT + B coth D tanh (7) T T 298K 298K Vapor Enthalpy 13

25 Snce polymer speces are nonvolatle, we only need to consder the vapor enthalpy for conventonal speces. We use equatons of state to compute vapor enthalpy. We represent the vapor enthalpy as a sum of deal-gas and resdual contrbutons V g res,v H = H + H (8) where H res,v s the resdual enthalpy for the vapor phase, computed usng the equaton of state. The deal-gas enthalpy for a mxture s the sum of the pure-component contrbutons, weghted by mole fracton n the vapor phase H g = yh (9) where H g s the deal-gas enthalpy for speces. We compute ts value as descrbed n the prevous secton. See Secton 2.4 for the expresson for the resdual contrbuton. g Lqud Enthalpy For an equaton of state, the computaton of lqud enthalpy s analogous to that for the vapor phase L g res,l H = H + H (10) where H res,l s the resdual enthalpy for the lqud phase, computed usng the equaton of state. The deal-gas enthalpy for a mxture s the sum of the pure-component contrbutons, weghted by mole fracton n the lqud phase g g H = xh (11) The expresson for the pure-component deal-gas enthalpy s gven n eq (5) Heat of Vaporzaton Accurate calculatons for the heat of vaporzaton are mportant for reactors, flash vessels, and other unt operatons that nvolve vapor and lqud n equlbrum. Heat of vaporzaton s partcularly mportant for non-sothermal modelng of reactors where vaporzaton of the solvent removes the heat of polymerzaton, such as n the slurry HDPE process. 14

26 When usng an equaton of state for phase-equlbrum calculatons, we do not need to compute the heat of vaporzaton drectly because the EOS computes the vapor and lqud enthalpes for each phase Heat Capacty Although heat capacty s not always used drectly n enthalpy calculatons, expermental data are usually n ths form. When usng an EOS for thermodynamc calculatons, we obtan the heat capacty by dfferentatng enthalpy wth respect to temperature: C p H = T Snce we compute enthalpy usng deal-gas and resdual contrbutons, we can break the rght-hand sde of eq (12) nto two parts: P (12) g res H H g p = + = p + p C C C T T P P (13) where C p s the constant pressure heat capacty, C g p s the deal-gas contrbuton and C p s the resdual contrbuton. Recall that the deal gas s a hypothetcal state at the system temperature and near zero pressure, and that a common modelng approach consders the deal gas as the reference state for each component. We can use a smple polynomal for the temperature dependence of the deal-gas heat capacty C = A + BT+ CT + DT (14) g 2 3 p, where A, B, C, and D are adjustable parameters correspondng to speces. Table 2-1 gves the requred parameters for the deal-gas heat capacty model. 15

27 Table 2-1. Requred parameters for the deal-gas heat capacty model. descrpton parameter unts parameter A J/mol-K parameter B J/mol-K 2 parameter C J/mol-K 3 parameter D J/mol-K 4 temperature T K We can use polynomals to model the heat capacty for polymer. For example, C A BT CT DT 2 3 p,l = (15) where A, B, C, and D are adjustable parameters determned usng expermental heatcapacty data Heat of Polymerzaton Many polymerzatons are hghly exothermc, and we must account for ths when computng reactor energy balances. These polymerzatons requre careful temperature control to avod thermal decomposton and reactor runaway. The rgorous method for computng the heat of polymerzaton s to take the dfference between the enthalpy, per segment, of polymer and the enthalpy of pure monomer at ther physcal states n the reactor 2. Fgure 2-2 llustrates ths computaton. We use an equaton of state to compute each transton along the path. 2 Leonard, J. Heats and Entropes of Polymerzaton, Celng Temperatures, Equlbrum Monomer Concentratons, and Polymerzablty of Heterocyclc Compounds. In Polymer Handbook; Brandrup, J., Immergut, E. H., Grulke, E. A., Eds.; Wley & Sons: New York, 1999; p II/

28 deal-gas monomer deal-gas polymer gas monomer sold polymer Fgure 2-2. Pathway for computng the heat of polymerzaton for the EOS approach 2. For ethylene, the reacton s 1 (16) n CH 2 4 CH 2 4 n ( g) ( ) ( s ) where n s the number of ethylene segments n the polymer Mxture Propertes Introducton In Secton 2.2.3, we provded the major pure-component propertes that we are concerned wth. In some cases, the effect of mxng s neglgble, and n others t s not. Here, we show how to compute physcal propertes of mxtures Mxture Densty (Molar Volume) We model the lqud mxture molar volume usng Amagat s law: L L v = xv (17) Ths assumes no excess volume of mxng. Ths s generally acceptable for the applcatons that requre an external correlaton for lqud densty. When usng an EOS for physcal-property and phase-equlbrum calculatons, we use the EOS to compute the mxture molar volume. 17

29 Mxture Enthalpy In the prevous sectons, we descrbe how to compute the pure-component enthalpes for vapor and lqud. Here, we explan how to compute enthalpy for a mxture, ether vapor or lqud Vapor Mxture Enthalpy Eq (18) gves the vapor mxture enthalpy: V v V g P V = + d T V v (18) h yh P T v where y s the vapor mole fracton of speces, h g s the deal-gas (pure-component) enthalpy, for speces, at the temperature of the system, and v V s the molar volume of the mxture, computed usng the EOS. We gnore the polymer contrbuton to the deal-gas enthalpy because the vapor-phase mole fracton for polymer s always nearly zero. As n the pure-component case, we compute the value of the ntegral n eq (18) by nsertng an expresson for pressure furnshed by a pressure-explct equaton of state Lqud Mxture Enthalpy The lqud calculaton s smlar to that for the vapor approach. The only dfference s that we use the lqud molar volume n place of the vapor molar volume: L v L g P L = + d T L v (19) h xh P T v where v L s the lqud molar volume of the mxture. 18

30 2.3 Phase Equlbrum Introducton The purpose of ths secton s to dscuss phase equlbrum for polymerc systems. We frst gve a bref overvew of the fundamentals of phase equlbrum. We then dscuss the EOS approach. We end the secton by descrbng treatment for sold polymer. The fundamental crteron for phase equlbrum s the sofugacty relaton for each speces n each phase. For a system where two phases are n equlbrum: f α = f (20) β where f α and f β are the fugactes for speces n phases α and β, respectvely. A key aspect of modelng phase equlbrum s the formulaton of fugacty expressons that accurately descrbe the behavor for each phase VLE: The Ideal Case The smplest relatonshp for VLE s Raoult s law: yp = xp (21) s where s P s the vapor pressure of speces. Ths relaton states that, n the absence of molecular nteractons, the partal pressure of a component n the vapor phase relates to the lqud mole fracton tmes the saturaton pressure of that component. In other words, the vapor partal pressure for a speces s drectly proportonal to ts lqud mole fracton, wth ts saturaton pressure as the constant. Ths relaton s somewhat accurate only for mxtures of non-assocatng speces at condtons close to STP Equatons of State Bass 19

31 EOS relate the molar volume of each speces to temperature and pressure. They are applcable to both vapor and lqud phases. They are applcable over wde ranges of temperature and pressure, are consstent n the crtcal regon, and provde unfed predcton of thermodynamc propertes. They do not generally perform well for hghly non-deal mxtures (polar and other assocatng systems). In the followng sectons, we gve detaled descrptons of the SL and PC-SAFT EOS. The smplest EOS s the deal-gas law: Pv= RT (22) where P s pressure, v s molar volume, R s the gas constant, and T s temperature. Ths EOS assumes no nteracton between molecules, and does not consder the fnte volume of the molecules. It s only useful for predctng vapor-phase molar volume as a functon of temperature and pressure for non-assocatng speces at condtons near STP. It does not apply to polymer speces. There exst more complex EOS models desgned specfcally for polymerc mxtures over wde ranges of temperature and pressure. These nclude the Sanchez-Lacombe 3 (SL) and the perturbed-chan statstcal assocatng flud theory 4 (PC-SAFT) EOS. We descrbe these models later n ths chapter. We can use an EOS to compute both the vapor and lqud propertes smultaneously. We defne the fugacty of each phase as follows: f = y Φ P f = xφ P (23) V V L L where y and x are the mole fractons of speces n the vapor and lqud phases, respectvely, and Φ V and Φ L are the fugacty coeffcents for speces n the vapor and lqud phases, respectvely. The fugacty coeffcents account for the nondealty of the phase behavor of mxtures. The resultng phase-equlbrum relaton for the EOS approach s 3 Sanchez, I. C.; Lacombe, R. H.; Statstcal Thermodynamcs of Polymer Solutons. Macromolecules 1978, 11, Gross, J.; Sadowsk, G.; Perturbed-Chan SAFT: An Equaton of State Based on a Perturbaton Theory for Chan Molecules. Industral and Engneerng Chemstry Research 2001, 40,