EXPERIMENTAL AND THEORETICAL STUDIES ON THE HEAT TRANSFER ENHANCEMENT OF ADSORBENT COATED HEAT EXCHANGERS LI ANG NATIONAL UNIVERSITY OF SINGAPORE

Transcription

1 EXPERIMENTAL AND THEORETICAL STUDIES ON THE HEAT TRANSFER ENHANCEMENT OF ADSORBENT COATED HEAT EXCHANGERS LI ANG NATIONAL UNIVERSITY OF SINGAPORE 2014

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3 EXPERIMENTAL AND THEORETICAL STUDIES ON THE HEAT TRANSFER ENHANCEMENT OF ADSORBENT COATED HEAT EXCHANGERS LI ANG (B.Eng, National University of Singapore, Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014

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6 Acknowledgements ACKNOWLEDGEMENTS First and foremost, I would like to express my deepest sense of gratitude and indebtedness to my supervisor Professor Ng Kim Choon for your invaluable guidance and tireless support throughout my Ph.D candidature. I am truly thankful for your wisdom, passion, and insights in research that have inspired and motivated me all along. I wish to extend my sincere thanks to Professor Harry F. Ridgeway from AquaMem Scientific Consultants, Professor Bidyut Baran Saha of Kyushu University, Assoc.Professor Christopher Yap of National University of Singapore, and Dr. Yanagi Hideharu from Cyclect Singapore for your precious advice and help in my research projects. I am grateful for your patience and enthusiasm that have made the discussion fruitful and enjoyable. I am deeply indebted to Dr. Kyaw Thu, Dr. Loh Wai Soong, Dr. Jayaprakash Saththasivam, Dr. Kazi Afzalur Rahman, Dr. M Kumja, Dr. Filian Arbiyani and Dr. Aung Myat for their continuous efforts rendered in many aspects without which I could not be possible to complete this thesis. My special thanks also go to Mr. Sacadevan Raghavan and Mr. Tan Tiong Thiam for their skillful technical assistances. I am also greatly thankful to my closet lab pals, Dr. Muhammad Wakil Shahzad, Dr. Azhar Bin Ismail, Dr. Oh Seung Jin and Mr. Muhammad Burhan who accompanied and helped me throughout my Ph.D journey. Meanwhile, I would like to take this opportunity to express my appreciation to my friends, Mr. Wen Zhanhua, Dr. Shang Jiangwei, Mr. Zheng i

7 Acknowledgements Yongming, Mr. Zheng Lisheng, Mr. Li Jinxin, Mr. Fan Zhitao, Ms. Li Yuxi, Mr. Cheng Bin, Mr. Liu Nannan, Ms. Li Huimin, Dr. An Hui, Mr. Gao Zheng, and Mr. Liu Zhi. Thank you very much for so many memorable moments, cheering me up and de-stressing me always. Last but not least, I would like to record my heartfelt gratitude to my respected parents and beloved fiancée Wang Wenxia for your unconditional love, support and sacrifice, which are far more than words can describe. My every bit of happiness and achievement belong to you. You are forever my spiritual pillar and motivation. Li Ang 22 July 2014 ii

8 List of Publications LIST OF PUBLICATIONS Journal Publications 1. A. Li, A. B. Ismail, K. Thu, K. C. Ng, and W. S. Loh, "Performance evaluation of a zeolite water adsorption chiller with entropy analysis of thermodynamic insight," Applied Energy, vol. 130, pp , A. Li, W. S. Loh, and K. C. Ng, "Transient modeling of a lithium bromide water absorption chiller," Applied Mechanics and Materials, vol. 388, pp , A. B. Ismail, A. Li, K. Thu, K. C. Ng, and W. Chun, "On the thermodynamics of refrigerant + heterogeneous solid surfaces adsorption," Langmuir, vol. 29, pp , A. B. Ismail, A. Li, K. Thu, K. C. Ng, and W. Chun, "Pressurized adsorption cooling cycles driven by solar/waste heat," Applied Thermal Engineering, vol. 67, pp , A. Li, A. B. Ismail, K. Thu, K.C. Ng, and W. Chun, "Enhancement of heat and mass transfer of adsorbent embedded heat exchangers through bindercoating method," International Journal of Heat and Mass Transfer. (Under Review) iii

9 List of Publications 6. A. Li, A. B. Ismail, K. Thu, and K. C. Ng, "Advanced energy distribution function incorprating statistical rate theory for a universal adsorption isotherm model," Langmuir. (Under Review) 7. A. Li, A. B. Ismail, K. Thu, M. W. Shahzad, K. C. Ng, and B. B. Saha, "Formulation of water equilibrium uptakes on silica gel and ferroaluminophosphate zeolite for adsorption cooling and desalination applications," Evergreen, vol. 01, issue 02, pp , A. Li, K. Thu, and K.C. Ng, "Transient heat transfer correlation for bindercoated adsorbent-adsorbate heat exchanger," International Journal of Heat and Mass Transfer. (Under Review) 9. A. Li, K. Thu, and K. C. Ng, "Dynamic simulation and experimental validation on a low grade heat driven adsorption chiller with heat recovery scheme," Applied Thermal Engineering. (Under Review) 10. K. C. Ng, K. Thu, S. J. Oh, A. Li, M. W. Shahzad, A. B. Ismail, "Recent developments in thermally-driven seawater desalination: Energy efficiency improvement by hybridization of the MED and AD cycles, " Desalination, (In Press) iv

10 List of Publications Conference Publications 1. W. S. Loh, J. S. H. Ng, A. Li, and K. C. Ng, "Performance evaluation of enhanced two-phase vapor chamber heat sinks," in Proceedings of the third International Forum on Heat Transfer, Nagasaki, Japan, A. Li, W. S. Loh, and K. C. Ng, "Transient modeling of a lithium bromide water absorption chiller," presented at the 5th International Meeting on Advances in Thermofluids, Bintan, Indonesia, A. Li, K. Thu, W. S. Loh, A. B. Ismail, and K. C. Ng, "Performance evaluation of a zeolite - water adsoroption chiller with entropy analysis of thermodynamic insight," presented at the 6th International Conference on Applied Energy, Pretoria, South Africa, A. B. Ismail, A. Li, W. S. Loh, K. Thu, and K. C. Ng, "Dynamic behavior and performance evaluation of a two-bed activated carbon powder + propane adsorption prototype," presented at the 6th International Meeting on Advances in Thermofluids, Singapore, A. Li, A. B. Ismail, K. Thu, M. W. Shahzad, and K. C. Ng, "Dynamic modeling of a low grade heat driven zeolite water adsorption chiller," presented at the 6th International Meeting on Advances in Thermofluids, Singapore, v

11 List of Publications 6. A. Li, M. W. Shahzad, A. B. Ismail, and K. C. Ng, "Experimental investation of design parameters for a cogeneration system with a microturbine generator and an adsorption chiller," in The 3rd International Symposium on Innovative Materials for Processes in Energy Systems, Fukuoka, Japan, 2013, pp A. Li, A. B. Ismail, K. Thu, M. W. Shahzad, K. C. Ng, and W. Chun, "Improvement of adsorbent embedded heat transfer through introduction of binder," presented at the 7th Asian Conference on Refrigeration and Air Conditioning, Jeju, Korea, A. B. Ismail, A. Li, W. S. Loh, K. Thu, and K. C. Ng, "A modeling and experimental study of a low-temperature application miniature pressurized adsorption chiller (PAC)," presented at the 7th Asian Conference on Refrigeration and Air Conditioning, Jeju, Korea, A. Li, K. C. Ng, H. Ridgway, K. Thu, and M. W. Shahzad, "Molecular dynamic modeling on a novel zeolite," presented at the 6th International Symposium on Microchemistry and Microsystems Singapore, A. Li, A. B. Ismail, K. Thu, and K. C. Ng, "Binder influence on the water adsorption uptake of silica gels," presented at the 7th International Meeting on Advances in Thermofluids, Kuala Lumpur, Malaysia, vi

12 Table of Contents TABLE OF CONTENTS ACKNOWLEDGEMENTS... i LIST OF PUBLICATIONS... iii SUMMARY... xi LIST OF TABLES... xiii LIST OF FIGURES... xv NOMENCLATURE... xxiii CHAPTER 1 INTRODUCTION Background Adsorption Chillers at a Glance A Green Solution to Energy and Environmental Concerns Limitations of Adsorption Chillers Objectives and Scopes Thesis Organization... 9 CHAPTER 2 THEORIES OF PHYSICAL ADSORPTION Introduction Adsorption Isotherms Literature Survey on Adsorption Isotherms Homogeneous Surface Adsorption Heterogeneity Surface Adsorption Adsorption Kinetics Literature Survey on Adsorption Kinetics Kinetics Formulation Thermodynamic Properties of Adsorbed Phase Gibbs Free Energy of Adsorbed Phase Entropy of Adsorbed Phase Enthalpy of Adsorbed Phase Isosteric Heat of Adsorption vii

13 Table of Contents Specific Heat Capacity of Adsorbed Phase Specific Volume of Adsorbed Phase Summary CHAPTER 3 TRANSIENT ADSORPTION HEAT TRANSFER Introduction Binder Selection Materials BET Surface Area from Nitrogen Adsorption Binder Comparison Optimum Binder Ratio Experiment on Transient Adsorption Heat Transfer Experimental setup and procedures Results and Discussion Summary CHAPTER 4 ADSORPTION MASS TRANSPORT Introduction Experimental Setup and Procedures Governing Theories Data Reduction Isotherm Regression Results and Discussion Comparison with Literature Data Binder Effect on Silica Gel Type 3A Adsorption Binder Effect on Silica Gel Type RD Powder Adsorption Estimation of Uptake Reduction from Surface Coverage Net Binder Influence on the Adsorption Mass Transport A New Water Adsorbent Zeolite FAM Z Adsorbent Characteristics Water Adsorption Characteristics with and without Binder Molecular Dynamics Simulation on the Zeolite FAM Z01-Water Adsorption Modeling of Molecular Structure viii

14 Table of Contents Water Transport in the Zeolite FAM Z01 Framework Summary CHAPTER 5 LOCAL ADSORPTION HEAT TRANSFER COEFFICIENT Introduction Calculation of Local Adsorption Heat Transfer Coefficient Overall Thermal Resistance Convection near the Tube Inner Wall Conduction through the Tube Wall Conduction through the Fins Adsorbent-Adsorbate Interaction Thermal Layer Results and Analysis Prediction of Local Adsorption Heat Transfer Coefficient Derivation on the Coefficient Results and Discussion Summary CHAPTER 6 DYNAMIC BEHAVIOR OF AN ADSORPTION CHILLER Introduction System Description Adsorbent-Adsorbate Pair Operation Description of Adsorption Chiller Structural Innovation Mathematical Modeling of the Adsorption Chiller Driving Force of the Refrigerant Modeling of Adsorption / Desorption Period Modeling of Switching Period Computation of Efficiency Entropy Study of the Adsorption Chiller Adsorption / Desorption Period Switching Period Experimental Investigation of the Adsorption Chiller ix

15 Table of Contents Temperature and Pressure Profiles Influence of Heat Source Temperature Influence of Adsorption / Desorption Cycle Time Model Validation Results of Entropy Analysis Temporal Entropy Generation Entropy and Heat Source Temperature Entropy and Adsorption / Desorption Cycle Time Summary CHAPTER 7 CONCLUSION Major Findings of This Thesis Future Work Recommendations REFERENCES APPENDICES Appendix A: Adsorption Isotherm Data of Silica gel-water Pairs Appendix B: Adsorption Isotherm Data of Zeolite -Water Pairs Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller272 x

16 Summary SUMMARY The increasing demand on cooling and its environmental concerns have drawn much attention to the development of adsorption cooling cycles, a green technology that utilizes environmentally benign adsorbent-adsorbate pairs, and low-grade waste heat from industrial exhausts or renewable energies such as solar and geothermal. A conventional adsorption chiller has, hitherto, been handicapped by the low COPs and large plant footprint, caused mainly by the poor heat transfer phenomena of the granular-adsorbent packed heat exchangers. The motivation of present research is to improve the overall performance the exchangers by incorporating better heat and mass transfer of adsorbate uptake onto the adsorbent, using the powder adsorbent coated by binder on the fin surfaces of exchangers. This method of making the adsorbent-adsorbate heat exchangers significantly improves the heat transfer coefficients but most importantly reduces the capital cost of making such exchangers. The key step lies in the selection of a suitable binder. Experiments have determined that a hydroxyethyl cellulose (HEC) to adsorbent weight ratio of 3.3% yielded the best performance for adsorbents, such as silica gels or zeolite FAM Z01. At this optimum weight ratio, the reduction of surface pore area of adsorbent remains relatively low for water uptake. The HEC-coated powdered adsorbent heat exchangers give as much as three to four-fold increase in the heat transfer rates per unit mass of adsorbent basis when compared with the xi

17 Summary conventional granular-based heat exchangers. A detailed characterization on the heat transfer processes and the thermal resistances of the powder-coated heat exchangers is reported in the thesis. As there is a dearth of transient data for water uptake in such a unique exchanger configuration, a new correlation is proposed for the transient heat transfer coefficients. The data of water adsorption isotherms for the silica gel and zeolite FAM Z01 are presented in the thesis. They depict, respectively, Type I and Type V isotherm behavior. Using a unified thermodynamic framework, a single asymmetrical energy distribution function (EDF) is proposed in the thesis that relates the EDF directly to their isotherm types and the proposed EDF fits well with the statistical rate theory of adsorption. Experiments are conducted on a low-grade waste heat driven adsorption chiller constructed with zeolite FAM-Z01 coated heat exchangers for evaluating the chiller performance. A thermodynamic framework is developed to simulate the chiller operation involving the proposed correlations of heat transfer and adsorption characteristics, and validated by the experiments. Various internal irreversibilities of the chiller are studied using the entropy generation analysis. xii

18 List of Tables LIST OF TABLES Chapter 3 Table 3.1: Thermophysical properties of silica gel type 3A, type RD powder and granule Table 3.2: Slope and y-intersection values of multipoint BET plot for silica gel type 3A, RD powder and granules from nitrogen adsorption at 77.3 K Table 3.3: Comparison of various binders on the silica gel and metal fin binding. The mixing ratio of all binders is fixed at 10 wt% of adsorbent Table 3.4: Properties of hydroxyethyl cellulose (HEC) Table 3.5: Specifications of the two-pass copper plain fin-tube heat exchanger used in the adsorption heat transfer experiment Chapter 4 Table 4.1: Value of the regression parameters of Tóth, DA, and proposed isotherm models for silica gel type 3A, type RD powder with and without HEC addition Table 4.2: Summary of surface area and average uptake reduction on the silica gels as a result of 3.3 adsorbent wt% HEC Table 4.3: Adsorption kinetics equations for the computation of instantaneous and cumulative water uptake Table 4.4: Thermophysical properties of zeolite FAM Z Table 4.5: Value of the regression parameters of the proposed isotherm models for zeolite FAM Z01 with and without HEC addition Table 4.6: Weight and atomic ratio of each element in the zeolite FAM Z Table 4.7: Elemental composition used in the molecular modeling of zeolite FAM Z xiii

19 List of Tables Chapter 5 Table 5.1: Value of parameters for the calculation of local adsorption heat transfer coefficient Table 5.2: Summary on the equations of adsorption characteristic parameters Table 5.3: Properties of water and silica gel type RD powder with 3.3 adsorbent wt% HEC Chapter 6 Table 6.1: Correlations for the local heat transfer coefficient of the tube side and shell side heat exchanger Table 6.2: Operation conditions of zeolite water adsorption chiller Table 6.3: Values of parameters used in the adsorption chiller simulation xiv

20 List of Figures LIST OF FIGURES Chapter 1 Figure 1.1: Working principle of an adsorption chiller (ADS: adsorption process; DES: desorption process)... 2 Chapter 2 Figure 2.1: Graphical presentation of an adsorbent-adsorbate system Figure 2.2: IUPAC classification of adsorption isotherms Figure 2.3: Illustration of adsorption on homogeneous surface Figure 2.4: Illustration of a heterogeneous adsorbent surface with different energy distribution Figure 2.5: Step-like profile yielded from Equation 2.23 at temperatures 10 K, 300 K and 500 K Figure 2.6: Symmetrical Gaussian function to represent the adsorption site energy distribution for Langmuir-Freundlich isotherm model Figure 2.7: Asymmetrical Gaussian function to represent the adsorption site energy distribution for Dubinin-Astakhow isotherm model Figure 2.8: A proposed asymmetrical Gaussian function to represent the adsorption site energy distribution for Tóth isotherm model Chapter 3 Figure 3.1: A pictorial view of a typical adsorbent embedded heat exchanger using conventional wire mesh packing method Figure 3.2: Schematic representation of AUTOSORB-1 analyzer Figure 3.3: Pictorial view of the AUTOSORB-1 analyzer and its components xv

21 List of Figures Figure 3.4: Multipoint BET plot for silica gel of type 3A, RD powder and granules from nitrogen adsorption at 77.3 K Figure 3.5: BET surface area and total pore volume of the HEC adhered silica gel type 3A samples at assorted HEC weight percentage Figure 3.6: Dubinin Astakhov (DA) micropore size distribution of pure silica gel 3A, and HEC adhered silica gel type 3A samples with various HEC weight percentages Figure 3.7: Field emission scanning electron microscopic (FESEM) photos for (a) parent silica gel type 3A, (b) silica gel type 3A with 3.3 adsorbent wt% HEC, and (c) 3.3 adsorbent wt% corn flour Figure 3.8: Schematic representation of the adsorption heat transfer experimental apparatus Figure 3.9: Pictorial view of the adsorption heat transfer experimental apparatus Figure 3.10: Location of thermistor thermometers on and around the silica gel embedded heat exchanger in the adsorption chamber Figure 3.11: Pictorial views of the base case in which the heat exchanger is embedded with silica gel type RD granules by wire mesh. The pictures show (left) the exchanger in the loading process and (right) its final appearance Figure 3.12: Pictorial views of the silica gel type 3A case in which the heat exchanger is coated with the silica gel using 3.3 adsorbent wt% HEC. The pictures show (left) the exchanger in the coating process and (right) its final appearance Figure 3.13: Pictorial views of the silica gel type RD powder case in which improved coating method is applied for the heat exchanger using 3.3 adsorbent wt% HEC. The pictures show (left) the exchanger in the coating process and (right) its final appearance Figure 3.14: Temporal temperature difference between the inlet cooling water T i,cw and the silica gel average T ads at various cooling water temperatures for the silica gel type 3A coated heat exchanger and the base case Figure 3.15: Temporal temperature difference between the inlet cooling water T i,cw and the silica gel average T ads at various cooling water temperatures for the silica gel type RD powder coated heat exchanger and the base case xvi

22 List of Figures Figure 3.16: Temporal overall heat transfer coefficient of the 3A type silica gel coated heat exchanger and the base case at various cooling water temperatures Figure 3.17: Temporal overall heat transfer coefficient of the RD powder type silica gel coated heat exchanger and the base case at various cooling water temperatures Figure 3.18: Cyclical average of the transient overall heat transfer coefficient over 500 s adsorption cycle time for various cooling water inlet temperatures. The coefficient is normalized with unit mass of the adsorbent Figure 3.19: Heat leak of the adsorption heat transfer experiment for (a) silica gel type 3A coated, (b) silica gel type RD powder coated heat exchangers, and (c) the base case Chapter 4 Figure 4.1: Schematic representation of HYDROSORB analyzer Figure 4.2: Pictorial view of the HYDROSORB analyzer and its components Figure 4.3: Comparison of the adsorption isotherms of silica gel type 3A-water pair between the present experimental data and Tóth regression relation provided by Ng et al. [33]. The current data are displayed with 5% error bar Figure 4.4: Comparison of the adsorption isotherms of silica gel type RDwater pair between the present experimental data and Tóth regression relation provided by Ng et al. [33]. The current data are displayed with 5% error bar Figure 4.5: Experimental water adsorption equilibrium uptake on silica gel type 3A at temperatures from 25~45 o C. The data are regressed with (a) the Tóth and DA models, and (b) the proposed model of this work. The present data are displayed with 5% error bar Figure 4.6: Experimental water adsorption equilibrium uptake on silica gel type 3A against relative pressure at temperatures from 25~45 o C Figure 4.7: Experimental water adsorption equilibrium uptake on silica gel type 3A added with 3.3 adsorbent weight % HEC at temperatures from 25~45 o C. The data are regressed with (a) the Tóth model and DA model, and (b) the xvii

23 List of Figures proposed model of this work. The present data are displayed with 5% error bar Figure 4.8: Experimental water adsorption equilibrium uptake on silica gel type 3A added with 3.3 adsorbent weight % HEC against relative pressure at temperatures from 25~45 o C Figure 4.9: Comparison of experimental water adsorption uptake against relative pressure for a typical temperature 35 o C on pure silica gel type 3A and silica gel type 3A added with 3.3 adsorbent weight % HEC Figure 4.10: Distribution of water uptake reduction due to addition of HEC binder onto silica gel type 3A Figure 4.11: Adsorption site energy distribution of the proposed isotherm model for silica gel type 3A with and without 3.3 adsorbent weight % HEC addition at a typical temperature 35 o C Figure 4.12: Experimental water adsorption equilibrium uptake on silica gel type RD powder at temperatures from 25~45 o C. The data are regressed with (a) the Tóth and DA model, and (b) the proposed model of this work. The present data are displayed with 5% error bar Figure 4.13: Experimental water adsorption equilibrium uptake on silica gel type RD powder against relative pressure at temperatures from 25~45 o C Figure 4.14: Experimental water adsorption equilibrium uptake on silica gel type RD powder added with 3.3 adsorbent weight % HEC at temperatures from 25~45 o C. The data are regressed with (a) the Tóth and DA model, and (b) the proposed model of this work. The present data are displayed with 5% error bar Figure 4.15: Experimental water adsorption equilibrium uptake on silica gel type RD powder added with 3.3 adsorbent weight % HEC against relative pressure at temperatures from 25~45 o C Figure 4.16: Comparison of experimental water adsorption uptake against relative pressure for a typical temperature 35 o C on pure silica gel type RD powder and silica gel type RD powder added with 3.3 adsorbent weight % HEC Figure 4.17: Distribution of water uptake reduction due to addition of HEC binder into silica gel type RD powder xviii

24 List of Figures Figure 4.18: Adsorption site energy distribution of the proposed isotherm model for silica gel type RD powder with and without 3.3 adsorbent weight % HEC addition at a typical temperature 35 o C Figure 4.19: Instantaneous rate of water uptake on the (a) silica gel type 3A coated, (b) silica gel type RD powder coated heat exchanger, and (c) the base case during the adsorption heat transfer process at various cooling water temperatures Figure 4.20: Comparison of instantaneous rate of uptake at 35 o C cooling water for silica gel type 3A, RD powder coated heat exchanger and the base case Figure 4.21: Cumulative water uptake on the (a) silica gel type 3A coated, (b) silica gel type RD powder coated heat exchanger, and (c) the base case during the adsorption heat transfer process at various cooling water temperatures Figure 4.22: Comparison of cumulative water uptake at 35 o C cooling water for silica gel type 3A, RD powder coated heat exchanger and the base case 119 Figure 4.23: Field emission scanning electron microscopic (FESEM) photos of zeolite FAM Z Figure 4.24: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 at temperatures from 25~45 o C with regression by the proposed model of this work. The present data are displayed with 5% error bar Figure 4.25: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 against relative pressure at temperatures from 25~45 o C Figure 4.26: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 added with 3.3 adsorbent weight % HEC at temperatures from 25~45 o C with regression by the proposed model of this work. The present data are displayed with 5% error bar Figure 4.27: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 added with 3.3 adsorbent weight % HEC against relative pressure at temperatures from 25~45 o C Figure 4.28: Comparison of experimental water adsorption uptake against relative pressure for a typical temperature 35 o C on pure and 3.3 adsorbent weight % HEC added zeolite FAM Z Figure 4.29: Adsorption site energy distribution of the proposed isotherm model for zeolite FAM Z01 with and without 3.3 adsorbent weight % HEC addition at a typical temperature 35 o C xix

25 List of Figures Figure 4.30: Comparison of water uptake capacity against relative pressure for a typical adsorption temperature 35 o C on zeolite FAM Z01, silica gel type 3A and RD powder Figure 4.31: Elemental composition of zeolite FAM Z01 from Energydispersive X-ray (EDX) test on a 250 μm x 200 μm sample area Figure 4.32: AFI type molecular framework of zeolite FAM Z01. (Yellow: Al, purple: P, cyan balls: Fe, red: O, white: H) Figure 4.33: Illustration of the four types of molecular window in the framework of zeolite FAM Z01, namely, large channel, medium channel, small channel and inner pore Figure 4.34: The minimum PWM velocity, minimum temperature and potential energy barrier of each molecular window structure obtained from the MD simulation Chapter 5 Figure 5.1: Schematic representation of an adsorbent embedded heat exchanger section Figure 5.2: Thermal layers encountered in an adsorbent embedded heat exchanger during adsorption process Figure 5.3: Temporal variation of the surface efficiency of the silica gel type RD powder coated heat exchanger during adsorption processes at various cooling water temperatures Figure 5.4: Temporal local adsorption heat transfer coefficient of the silica gel type RD powder coated heat exchanger during adsorption processes at various cooling water temperatures Figure 5.5: Comparison of temporal overall and local adsorption heat transfer coefficient of the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature Figure 5.6: Temporal thermal resistance of various layers in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature Figure 5.7: Percentage contribution of each layer s thermal resistance in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature xx

26 List of Figures Figure 5.8: Percentage contribution of the adsorption layer from thermal mass effect in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature Figure 5.9: Percentage contribution of the fin from thermal mass effect in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature Figure 5.10: Illustration of the heat flux flow direction on the heat exchanger during a typical adsorption process Figure 5.11: Predicted results of Equation 5.39 on the local adsorption heat transfer coefficient of the silica gel type RD powder and 3.3 adsorbent wt% HEC coated heat exchanger during water adsorption processes at cooling water temperature (a) 25 o C, (b) 30 o C, (c) 35 o C, and (d) 40 o C. The experimental results are displayed in 10% error bars Figure 5.12: Comparison of cooling water heat removal rate obtained from experiment and predicted by the adsorption characteristic equations listed in Table 5.2. The temperature of the cooling water is 25 o C for both cases Chapter 6 Figure 6.1: Schematic presentation of the zeolite-water adsorption chiller in adsorption / desorption period (ADS: adsorption bed, DES: desorption bed) Figure 6.2: Schematic presentation of the zeolite-water adsorption chiller in (a) heat recovery interval and (b) hold interval of the switching period (ADS: adsorption bed, DES: desorption bed) Figure 6.3: Pictorial view of the zeolite-water adsorption chiller Figure 6.4: Temperature profile of the zeolite water adsorption chiller at hot water temperature of 65 o C and adsorption / desorption cycle time of 250 s 201 Figure 6.5: Pressure profile of the zeolite water adsorption chiller at hot water temperature of 65 o C and adsorption / desorption cycle time of 250 s 201 Figure 6.6: Influence of hot water inlet temperature to (a) total heat input, (b) cooling capacity, and (c) COP of the adsorption chiller at various adsorption / desorption cycle times xxi

27 List of Figures Figure 6.7: Influence of adsorption / desorption cycle time to (a) total heat input, (b) cooling capacity, and (c) COP of the adsorption chiller at various hot water inlet temperatures Figure 6.8: Computation flowchart on the simulation of the adsorption chiller Figure 6.9: Validation of numerical model with experimental data of the outlet thermal source temperature of respective chiller components Figure 6.10: Temporal entropy generation rate of chiller major components in a typical half operation cycle. The result is computed from the simulation in the conditions of hot water inlet temperature 65 o C and adsorption / desorption cycle time 200 s Figure 6.11: Cyclic average entropy generation rate of the chiller major components in a half operation cycle at 200 s adsorption / desorption cycle time and increasing temperature of inlet hot water Figure 6.12: Percentage of entropy generation of the chiller major components in a half operation cycle at 200 s adsorption / desorption cycle time and increasing temperature of inlet hot water Figure 6.13: Percentage of entropy generation of the adsorption / desorption period and switching period in a half operation cycle at 200 s adsorption / desorption cycle time and increasing temperature of inlet hot water Figure 6.14: Specific entropy generation, COP and Carnot COP of the adsorption chiller at 200 s adsorption / desorption cycle time and assorted temperature of inlet hot water Figure 6.15: Cyclical average entropy generation rate of the chiller major components in a half operation cycle at 65 o C inlet hot water and various adsorption / desorption cycle times Figure 6.16: Percentage of entropy generation of the chiller major components in a half operation cycle at 65 o C inlet hot water and various adsorption / desorption cycle times Figure 6.17: Percentage of entropy generation of the adsorption / desorption period and switching period in a half operation cycle at 65 o C inlet hot water and various adsorption / desorption cycle times Figure 6.18: Specific entropy generation, COP and Carnot COP of the adsorption chiller at 65 o C inlet hot water and assorted adsorption / desorption cycle times xxii

28 Nomenclature NOMENCLATURE Abbreviations ADS CA Cond COP CVVP DA DES Evap FAM Z01 FESEM HEC LDF LF NRMSE PWM PVA R 2 Tóth Adsorption bed Condensation approximation Condenser Coefficient of performance Constant volume variable pressure method Dubinin-Astakhow isotherm model Desorption bed Evaporator Functional adsorbent material zeolite Z01 Field emission scanning electron microscopy hydroxyethyl cellulose Linear driving force model Langmuir-Freundlich Normalized root mean square error to the mean experimental data Probe water molecule Polyvinyl alcohol Coefficient of determination Tóth isotherm model Symbols A Area, [m 2 ] Ad Adsorption number, [-] Bi Biot number, [-] b van der Waals volume, [m 3 /kg] C Regression constant in Equation 4.8, [-]; molecular velocity, [m/s] Cp Specific heat capacity, [kj/kg.k] d Diameter, [m] D so Pre-exponential factor for surface diffusion, [m 2 /s] E Energy, [kj/kg] E a Activation energy, [kj/kmol] E c Characteristic energy in DA and Equation 4.8, [kj/kg] Fo Fourier number, [-] G Gibbs free energy, [kj/kg] H Enthalpy, [kj] xxiii

29 Nomenclature h t Local heat transfer coefficient, [W/m 2.K] h Specific enthalpy, [kj/kg] K Pre-exponential constant of adsorption, [P -1 ] k Boltzmann constant, [J/K]; thermal conductivity, [W/m.K] M Mass, [kg] m Mass flow-rate, [kg/s] m* Mass of molecules, [kg/kmol] N Number of gaseous molecules adsorbed, [-] Nu Nusselt number, [-] n Number of locally adsorbed gaseous molecules, [-] P Pressure, [kpa] P 0 Saturation Pressure, [kpa] P l Longitudinal tube pitch, [m] Pr Prandtl number, [-] P t Transverse tube pitch, [m] Q E Cooling capacity, [kw] Q H Heat input, [kw] Q st Isosteric heat of adsorption, [kj/kg] q Adsorbate uptake, [kg/kg of adsorbent] q* Equilibrium adsorbate uptake, [kg/kg of adsorbent] R Universal gas constant, [kj/kmol.k] ; thermal resistance, [K/W] Re Reynolds number, [-] R eq Equivalent radius to circular fins, [m] R p Average radius of adsorbant particles, [m] r Radius, [m] S Number of adsorption sites, [-]; Entropy [kj/k] S gen Entropy generation, [kj/k] s Number of local adsorption sites, [-]; specific entropy, [kj/kg.k] T Temperature, [K] t Time, [s]; surface heterogeneity, [-] t cycle Cycle time, [s] U Overall heat transfer coefficient, [kw/m 2.K] v Specific volume, [m 3 /kg] W s Power input of spray pump, [kw] z Adsorbed phase molecular partition function, [-] z 0 Pre-exponential constant of molecular partition function, [-] Greek Symbols α Thermal expansion coefficient, [K -1 ]; non-ideality correction factor [torr -1 ] β Boltzmann factor, [mol/j], energy term in Equation 4.8, [-] xxiv

30 Nomenclature γ Dubinin-Astakhow power factor, [-] δ Operation indicator, [-]; thickness, [m] ε Adsorption site energy, [kj/kmol, or kj/kg] ε c Equilibrium adsorption site energy, [kj/kmol, or kj/kg] ε t Tóth reference energy, [kj/kmol] ε 0 Langmuir-Freundlich reference energy, [kj/kmol] ε 1 Dubinin-Astakhow reference energy, [kj/kmol] η fin efficiency, [-] θ Operation indicator, [-]; adsorption uptake, [kg/kg of adsorbent] Local adsorption uptake, [kg/kg of adsorbent] κ Diffusion constant in LDF model, [-] μ chemical potential, [kj/kmol] ρ Density, [kg/m 3 ] Pre-exponent constant in Equation 4.8, [-] χ(ε) Energy distribution function, [-] ψ Temperature dimensionles number, [-] Subscript α ads b c chi cw des e eff f fin g hw hx i ini o sg tw zl Adsorbed phase Adsorption bed; adsorbent-adsorbate interaction layer Boiling point Condenser Chilled water Cooling water Desorption bed Evaporator Net effect Liquid phase Heat exchanger fins Gaseous phase Hot water Heat exchanger Inlet; inner Initial state Outlet; outside Adsorbent or silica gel Tube wall Zeolite xxv

31 Chapter 1: Introduction CHAPTER 1 INTRODUCTION 1.1. Background Adsorption Chillers at a Glance Adsorption is an uptake of gaseous or liquid molecules onto the pore surfaces of a solid by van der Waals and electrostatic forces [1]. The equilibrium concentration of the adsorbed molecules is determined by temperature and pressure of adsorbent-adsorbate pair. When these conditions change, the concentration varies, leading to dis-equilibrium between the surface and the surrounding molecules. The non-equilibrium creates a driving force to either attract more fluid molecules to the surface, or release some adsorbed molecules to the surroundings. Utilizing this principle, adsorption cooling cycles are configured. The adsorption-desorption processes can replace the need of mechanical compressors as in the conventional vapor compression plants, in which working fluids are thermally-compressed through adsorption cycles. Figure 1.1 illustrates the working principle of an adsorption chiller. It operates among three thermal sources known as low, medium and high temperature reservoirs. The low temperature reservoir is an evaporator where cooling is produced. The high temperature reservoir supplies heat source to drive the thermal compression. Rejected heat goes to the medium temperature reservoir which is normally the ambient. One adsorption cycle discretely comprises an adsorption process (ADS) and a desorption process (DES). In the former, the working fluid draws out heat to evaporate in the evaporator, 1

32 Chapter 1: Introduction creating cooling effect Q L in the low temperature reservoir, and then undergoes adsorption in an adsorbent-packed bed, rejecting heat Q M1 to the medium temperature reservoir. In the other process, the bed receives heat Q H from the high temperature reservoir and releases the working fluid to a condenser where heat Q M2 is discarded again to the medium temperature reservoir. Due to the equilibrium concentration difference in the bed during the two processes, the working fluid is effectively migrated from the evaporator to the condenser, and meanwhile its temperature and pressure are boosted. One may use an imaginary work done W to analog the thermal compression with the mechanical compression. High Temperature Reservoir (Heat Source) Q H Adsorption Chiller DES Medium Temperature Reservoir (Ambient) Q M2 Q M1 ADS W Q L Low Temperature Reservoir (Cooling) Figure 1.1: Working principle of an adsorption chiller (ADS: adsorption process; DES: desorption process) 2

33 Chapter 1: Introduction A Green Solution to Energy and Environmental Concerns The economic growth of emerging third world countries has increased the energy demand of the world. In a recent forecast of Shell 1, the total world s primary energy demand will rise by 40 % to reach 700 exa-joules (10 18 joules) per year by 2030, among which the conventional fossil fuels will still dominant 60 % of the supply. With greater awareness in environment pollution such as carbon dioxide (CO 2 ) emission leading to global warming, the continued burning of fossil fuels is to be reduced for sustainability. Alternatively, the emergence of renewable energies, for instance, solar, wind, biomass and geothermal energy, etc., is able to tackle the energy and environmental issues; they are yet mass-producible due to high cost and region-dependency. The renewable energies are hardly dominant in the energy supply of the near future. A major field aggravates the increasing energy demand is cooling. Isaac and van Vuuren [2] from Netherlands Environmental Assessment Agency estimated that air conditioning demand from residential sectors will grow 40 folds this century without climate changing. Together with heating demand, the associated CO 2 emission will contribute to 12 % of the total emission from energy usage, leading to a corresponding deterioration of environment. If a warmer climate is assumed, another 72% more energy demand for cooling will be incurred. To meet such tremendous rise of cooling needs but in the meantime minimize the consequent energetic and environmental problems, green solutions need to be developed. Cooling by the conventional vapor 1 Source: Shell Energy Scenarios to 2050, Retrieved from 3

34 Chapter 1: Introduction compression chillers consumes much electricity at 0.8 to 1.2 kwh/rtons. However, improvements to energy efficiency of key chiller components have been reported to have reached their asymptotic peaks, and huge investment is needed for only marginal improvements. An alternative method to promote the energy efficiency is to focus on the development of thermally-driven cycles. Amongst these approaches, adsorption chiller has been mooted as one of the most attractive technologies [3, 4]. Being low-grade heat driven, maintenance free and environment benign are main advantages of the adsorption chillers [5]. The system operates normally at heat source temperature 55 o C to 85 o C. In the advanced development, a multi-stage adsorption chillers that was able to utilize as low as 40 o C heat sources has been reported by Saha et al. [6, 7]. Such low temperature allows the chiller to integrate with waste heat which is available in abundance from exhausts of industrial processes or renewable energy sources such as solar and geothermal heat [8]. No additional CO 2 is emitted alongside cooling production. Moreover, there are no major moving parts constructed in the adsorption chiller structure. It delivers quieter operation as opposed to mechanical chillers and requires only minimum maintenance. High durability of adsorbent materials adds as a plus for its long lasting performance. What is more, the green nature of the technology also comes from the utilization of natural refrigerants like water that are safe, non-ozonedepleting and environmental-friendly. On the other hand, absorption chiller (AB chiller) is another thermally-driven cooling technology existing in the market. However, it requires higher heat source temperature to operate. The lifetime of the AB chiller is also shorter than the adsorption systems because 4

35 Chapter 1: Introduction of the use of corrosive solvents. Replacement of the solvents every 4 to 5 years is necessary [9]. The benefits of the adsorption technology have sparked a wave in the global research and development activities. Several adsorption chiller prototypes have been successfully deployed in Europe and Japan [10]. Its application has also been extended to other fields such as desalination [11-14], dehumidification [15, 16] and gas storage [17-19] Limitations of Adsorption Chillers In the current stage, some limitations faced by adsorption chillers still restrict their wide deployment. Low efficiency, measured by the coefficient of performance (COP), is one. This is caused mainly by two aspects. Firstly, utilization of low grade waste heat inherently sets a rather low theoretical Carnot limit to the adsorption cooling cycle, which is far inferior to that of the conventional vapor compression chillers that are powered by high grade electrical energy. Enormous energy losses associated with the electricity generation and transmission are not counted in the calculation of the vapor compression chillers COP [20]. Secondly, the efficiency of the adsorption chiller is also bottlenecked by the irreversibilities encountered due to poor performance of adsorbent embedded heat exchangers and frequent switching between heating and cooling of adsorbent-adsorbate pair. Another major drawback of the adsorption chiller is its large footprint area. It is partially attributable to the low COP, while mostly constricted by the uptake capacity of the adsorbents. Both limitations demand further developments on the adsorption chiller technology. 5

36 Chapter 1: Introduction 1.2. Objectives and Scopes The motivation of the current work is to improve the performance of a core component of the adsorption chiller, that is, the adsorbent embedded heat exchanger by introducing binders. Experimental and theoretical studies will be conducted to understand overall heat and mass transfer effect of the binder with the following scopes: (1) To study the adsorption science and thermodynamic theories that establishes the theoretical framework of adsorption chillers. In the present work, the use of statistical rate theory to provide the theoretical basis on the classic semi-empirical adsorption isotherm models will be reviewed. These classic models include Langmuir, Langmuir-Freundlich, Dubinin-Astakhov, Dubinin-Radushkevitch and Tóth equations. Thermodynamic properties of adsorbed phase, containing enthalpy, entropy, specific heat capacity and isosteric heat of adsorption, will be derived from the statistical rate theory. These adsorption characteristic and thermodynamic theories provide necessary fundamentals to design and model an adsorption chiller. (2) To select a suitable binder for designated adsorbent-adsorbate pairs. It is aimed to select a suitable binder for the silica gel-water pair which is frequently used in adsorption chillers. Several binders will be tested among which the one produces the best binding results and possesses minimum impact on the adsorbent surface area will be used for further testing. 6

37 Chapter 1: Introduction Measurement will be conducted to identify the optimum binder weight percentage in mixing with the adsorbent. (3) To experimentally investigate the overall heat transfer improvement of an adsorbent embedded heat exchanger due to the binder addition Upon selection of binder and its optimum weight ratio, a heat exchanger prototype that applies the binder to adhere the silica gel onto the metal fins will be fabricated. A test rig will be constructed to investigate the overall heat transfer coefficient of the prototype. To identify the binder effect, the same heat exchanger that uses the conventional method to pack the silica gel will be also tested and compared. (4) To measure the influence of the binder on the mass transport of the adsorbate. The water equilibrium uptakes on the pure silica gel and silica gel-binder mixture will be measured to understand the reduction on the adsorption capacity of the adsorbent due to the binder. Suitable adsorption isotherm models will be used to regress the experimental results of corresponding adsorbent-adsorbate pairs.. (5) To conduct an analysis on the shell side local adsorption heat transfer phenomenon With adequate information on the overall heat and mass transfer of the adsorbent embedded heat exchanger, a further analysis will be conducted to examine the thermal resistance of every layer along the heat transfer path. The 7

38 Chapter 1: Introduction significance of the shell side local adsorption heat transfer phenomenon will be emphasized. (6) To study the adsorption characteristics of a newly developed adsorbent material and its feasibility for adsorption chiller applications A novel water adsorbent that was specially developed for adsorption chillers, namely zeolite FAM Z01 will be studied. The water adsorption uptake of the zeolite and its mixture with the binder will be experimentally measured and compared with the conventional water adsorbent, silica gel. (7) To experimentally investigate the performance of an adsorption chiller that incorporates with the novel zeolite-water pair and the heat exchangers coated with adsorbent using binder An adsorption chiller prototype utilizing the novel zeolite FAM Z01-water pair and adsorbent coated heat exchangers by using binder will be experimentally evaluated. The heat input, cooling capacity and COP of the chiller will be investigated at various heat source temperatures and half cycle times. The cyclical behavior of the chiller will be studied in detail. (8) To simulate the operation of the adsorption chiller cycle. A thermodynamic framework will be developed to simulate the operation of the zeolite-water adsorption chiller. A transient approach will be used to capture the variation of the conditions of the chiller components with respect to time. An entropy analysis will be conducted to identify the source of irreversibilities associated with the chiller which are responsible for the low efficiency of the system. 8

39 Chapter 1: Introduction 1.3. Thesis Organization This thesis comprises of seven chapters that describe the experiment, simulation and analysis conducted in the research work to accomplish the research objectives. The contents of each chapter are organized as follows. In this opening chapter, Chapter 1, the adsorption chiller technology is firstly overviewed. The objectives and scopes of this research work are set from the advantages and the limitations of such technology. The outline of the thesis is also presented in the chapter. In Chapter 2, a literature review is provided to establish a theoretical framework on the adsorption science and thermodynamics to serve as a theoretical foundation for the entire thesis work. The derivation from the statistical rate theory to the classic semi-empirical models, including Langmuir, Langmuir-Freundlich, Dubinin-Astakhov, Dubinin-Radushkevitch and Tóth adsorption isotherms are firstly shown. It is followed by the linear driving force model that formulates the kinetics of the adsorption process. The development of equations for the adsorbed phase thermodynamic properties from the statistical rate theory is presented lastly. Chapter 3 focuses on the overall heat transfer performance of an adsorbent embedded heat exchanger that utilizes the proposed binder method to coat the adsorbent as a thin layer onto the metal fins. The chapter first describes the selection process of an appropriate binder for such application. Several binders of various types are tested and compared on a commonly used adsorbent in adsorption chillers - silica gel, from which the most suitable binder is chosen. The BET surface area of the binder added silica gel samples exhibiting good 9

40 Chapter 1: Introduction adhesive results is measured by AUTOSORB-1 analyzer, which is also used to determine the optimum binder weight ratio. Next, the chapter presents the experimental setup and procedures to investigate the transient overall heat transfer coefficient of a silica gel coated heat exchanger using the selected binder with the optimum weight ratio. These experimental results are compared with that of the conventional method in which the silica gel is packed by wire mesh. Chapter 4 presents the water adsorption isotherms of the pure and corresponding binder added adsorbents, through which the binder influence on the adsorption capacity is identified. It is started with the measurement on silica gel type 3A and type RD powder samples. The results are regressed with a proposed isotherm model and compared with the classic Dubinin-Astakhov and Tóth models. Upon obtaining accurate isotherm data, the net effect of the binder on the mass transport during adsorption heat transfer processes is calculated. A second part of the chapter introduces a novel adsorbent zeolite. The water adsorption isotherms of the material with and without binder are measured and fitted by the proposed model. A molecular dynamic simulation is conducted to investigate the water adsorption mechanism of the zeolite from molecular scales. With adequate information on the transient overall heat transfer performance of the heat exchanger and the adsorption isotherms of the adsorbents obtained from previous chapters, the shell side transient local adsorption heat transfer coefficient is determined and presented in Chapter 5. Experimental values of the coefficient are computed by subtracting the thermal resistance of each layer along the heat transfer path from the overall 10

41 Chapter 1: Introduction thermal resistance. Meanwhile, the thermal mass effect on the adsorption heat transfer process is analyzed in detail. Furthermore, a new correlation is proposed to predict the local adsorption heat transfer coefficient utilizing the specifications of the heat exchanger and the adsorption characteristics of the adsorbent-adsorbate pair. The prediction results are validated by the experimental values. In Chapter 6, mathematical modeling and experimental investigation on the operation of a zeolite-water adsorption chiller are presented. A transient model is developed to simulate the dynamic behavior of the chiller that is reflected by the variation of temperatures of corresponding components. Experiment is conducted to investigate the influence of heat source temperatures and half cycle durations on the heat input, cooling capacity and COP of the chiller. The experimental data are also used to validate the simulation results. Last but not least, an entropy analysis is performed to understand the source of irreversibilities associated with the chiller which are responsible for the loss of efficacy of the system. The last chapter, Chapter 7, summarizes the major findings of this work and suggests future research activities. 11

42 Chapter 2: Theories of Physical Adsorption CHAPTER 2 THEORIES OF PHYSICAL ADSORPTION 2.1. Introduction Physical adsorption describes a phenomenon in which molecules in the fluid phase (liquid and gas) are attracted to and attached on a solid surface through van der Waals and electrostatic forces. The fluid adsorbed is referred as adsorbate and the solid is named as adsorbent [1]. Porous structures formed on the adsorbent surface provide a favorable energy state to accommodate the adsorbate molecules. By means of sizes, the porous structures are categorized as macropores with an average diameter greater than 50 nm, micropores that are smaller than 2 nm, and mesopores having the size in between [21], as illustrated in Figure 2.1. Physical adsorption differs with chemisorption in that it includes only intermolecular forces, and hence reversible by heating, pressurization and other means [22], whereas chemisorption essentially involves the formation of comparatively much stronger chemical bonds that requires even higher process energy and is normally irreversible [23, 24]. In the physical adsorption, the adsorbate molecules from fluid phase transit to an energetically lower adsorbed phase, which is therefore an exothermic process [25]. The reverse process is named as desorption, and is endothermic in nature. 12

43 Chapter 2: Theories of Physical Adsorption Micropore Pore size < 2nm Mesopore Pore size ~ 2-50nm Macropore Pore size > 50nm Fluid phase Adsorbed phase Adsorbate Adsorbent Figure 2.1: Graphical presentation of an adsorbent-adsorbate system The science of physical adsorption mainly includes quantitative interaction between adsorbent and adsorbate in equilibrium, namely isotherms, rate of adsorption prior reaching equilibrium, namely kinetics, and thermodynamic properties of the adsorbed phase. This chapter provides a review on the literature of the physical adsorption and establishes a theoretical framework that serves the entire thesis from which the results of the present work are derived, formulated and explicated. In addition, this work focuses on the adsorption phenomenon between gases and solids which is utilized in the most thermally driven adsorption systems. 13

44 Chapter 2: Theories of Physical Adsorption 2.2. Adsorption Isotherms When a surrounding adsorbate gas interacts with a porous adsorbent for a sufficiently long time, the amount of the adsorbate molecules adsorbed on the adsorbent surface approaches saturation. The amount of uptake for a particular adsorbent-adsorbate pair (q) is determined by temperature (T) and pressure (P) of the pair. [26]. In graphical presentations, the plots of q against P at constant temperatures are known as the adsorption isotherms. The adsorption isobars are named for the graphical plots of q against T at constant pressures. Furthermore, if the adsorbate uptake amount is fixed, the pressure variation with respect to temperatures is called the adsorption isosteres. The three terms are easily interchanged when one of the relations is known Literature Survey on Adsorption Isotherms In studies of adsorption equilibrium, the isotherm is more commonly used than the isobar and isostere. It is also a key parameter in designing adsorption related processes and machineries. For any adsorbent-adsorbate pair, the isotherms are usually measured by experiment which is based on volumetric, thermogravimetric or dynamic column breakthrough methods [27]. The results are then regressed in relation with the experimental conditions. In the literature, a variety of adsorption isotherms have been identified, which changes significantly for different adsorbent-adsorbate pairs. According to the shapes, IUPAC categorized the isotherms into six types, as illustrated in Figure 2.2. Type I to Type V was originally summarized by Brunauer et al. [28]. The last 14

45 Adsorbate Uptake, q Chapter 2: Theories of Physical Adsorption type was included by IUPAC [22, 26]. Classical theories to fit the isotherms include Langmuir [29], Langmuir-Freundlich (LF) [30], Tóth [31], Dubinin- Astakhov (DA) [32] models, and so on. To date, however, no theory can be generalized to predict the relation in detail for any adsorbent-adsorbate pairs from known parameters. I II III IV V VI Relative Pressure, P/P s Figure 2.2: IUPAC classification of adsorption isotherms Type I isotherms are frequently found in the silica gel-water, and activated carbon-refrigerant pairs. Ng et al. [33] and Chua et al. [34] adopted the constant volume variable pressure (CVVP) apparatus to measure the isotherms 15

46 Chapter 2: Theories of Physical Adsorption of Fuji Davison type A, 3A and RD silica gel with water in sub-atmospheric conditions. The results were fitted by Tóth isotherm model. Wang et al. [35] implemented the CVVP and thermogravimetric methods separately to investigate type A and RD silica gel and water vapor adsorption. Both methods yielded almost identical results. A similar comparison was conducted by Ismail et al. [36, 37] recently to study the adsorption equilibria of propane vapor on Maxsorb III activated carbon in high pressure conditions. The thermogravimetric measurement utilized a high-accuracy magnetic suspension balance supplied by Rubotherm. The authors found 6% deviation between the two methods. Activated charcoal-methanol, activated carbon fibre-ethanol uptake characteristics were explored by Exell [38], and Saha et al.[39]. Loh et al. [40] studied the adsorption isotherms of refrigerant R134a, R290, R410a, and R507a on Maxsorb III type and ACF-A20 type activated carbon using CVVP techniques. DA isotherm model was used to fit all the isotherm data within 5 % error range. The adsorption characteristics of activated carbon and other ASHRAE designated refrigerants were filed in the reference [41-51]. Besides type I, other types of adsorption isotherms were also studied. Maglara et al. [52] performed an experiment on various zeolite samples with nitrogen at 77K, as well as argon at 77 K and 87 K based on a modified volumetric technique. The isotherms exhibited type V feature. They could be further processed to compute the pure size distribution and BET surface area of the adsorbent samples. Another type V isotherm was contributed by Dreisbach et al. [18] who implemented a combined thermogravimetricvolumetric method to measure the adsorption on activated carbon with the mixture of water vapor and ethanol. Gruszkiewicz et al. [53] investigated the 16

47 Chapter 2: Theories of Physical Adsorption water adsorption capacity of various synthetic or natural porous adsorbent between 105 o C to 250 o C through a high-temperature gravimetric method. Activated carbon F with nitrogen and butane was tested by Weireld et al. [54] using Rubotherm magnetic suspension balance. The former adsorbentadsorbate pair presented type I curve, whereas the latter was found more suitable for type II isotherms. Since adsorption is taking place in the adsorbent surface, it is ideal to study the phenomenon by assuming a homogeneous surface, upon which more practical features are added in subsequently. This will be followed by the content below to provide understanding of the adsorption phenomenon from the statistical rate theory approach. It will demonstrate that by giving suitable surface features and Gaussian distribution function of adsorption sites, the classical isotherm theories can be successfully derived Homogeneous Surface Adsorption The simplest adsorption isotherm model, i.e. the Langmuir model [29], was introduced based on assumptions of homogeneous surface and monolayer adsorption. It was assumed that the adsorbent surface was uniform where energetically equivalent adsorption sites were equally distributed. Each site was filled by a single adsorbed molecule. A monolayer was formed on the surface without interaction among the adsorbed molecules. This primarily treated the adsorption process as single molecular events, as illustrated in Figure 2.3. Starting from this concept, the fraction of the adsorption sites filled 17

48 Chapter 2: Theories of Physical Adsorption by the gaseous molecules, which is equivalent to the amount of adsorption uptake, is defined as, N S (2.1) where N is the number of gaseous molecules adsorbed, and S denotes the total number of adsorption sites. Invoking the time-dependent Schrödinger equation with the first-order perturbation analysis, and substituting the Boltzmann definition of entropy, the rate of gas molecules filling the adsorption sites was given by Ward and co-workers as [55-58], d g g K e x p e x p d t R T R T (2.2) in which, K is regarded as the exchange rate of the adsorbate molecules between the gaseous and the adsorbed phase in equilibrium at temperature T, R is the universal gas constant, μ g and μ α represent chemical potential of gaseous and adsorbed phase, respectively. The equation originally assumes that the energy of an adsorbate molecule contains many quantum states. From an initial state, the molecule is free to move to any quantum states in adsorbed or desorbed configuration. This is correlated by the exponential terms in the equation in which the first exponential term describes the rate of the molecule transiting to the adsorbed configuration, and the second one denotes that to the desorbed configuration. Hence, the combination of the two terms presents the net rate of adsorption on the adsorbent surface. 18

49 Chapter 2: Theories of Physical Adsorption N Adsorbed molecules S Homogeneous adsorption sites Figure 2.3: Illustration of adsorption on homogeneous surface Assuming ideal behavior, the chemical potential of the gaseous phase adsorbate molecules is expressed as, 0 ln (2.3) R T P g g where, P is the bulk gaseous pressure and μ g 0 the chemical potential of a reference state. In correspondence with the assumptions of homogeneous adsorption sites, single-molecular site occupancy, and null interaction between the adsorbed molecules, the chemical potential of adsorbed phase is given as [59, 60], RT ln z 1 (2.4) where z is the adsorbed phase molecular partition function and defined by adsorption energy ε, Boltzmann factor β and a pre-exponential constant z 0 as, (2.5) z z e x p 0 and the Boltzmann factor is, 19

50 Chapter 2: Theories of Physical Adsorption 1 (2.6) RT Substitute Equation 2.3 and 2.4 to Equation 2.2, d g g K e x p e x p d t R T R T 0 R T ln P R T ln g z 1 e x p RT K 0 R T ln R T ln P g z 1 e x p RT (2.7) 0 g e x p ln P ln R T z 1 K 0 g e x p ln ln P z 1 R T 0 0 z 1 g 1 g K P e x p e x p R T z 1 P R T Rearrange the above equation, d 1 g K z e x p e x p P 0 d t R T R T K g 1 e x p e x p z R T R T P (2.8) To simplify the expression, define K A and K D to represent the two groups of constants as follows, K A e x p g K z 0 RT 0 (2.9) and, 20

51 Chapter 2: Theories of Physical Adsorption K D K e x p z 0 0 g R T (2.10) Hence, the equation on the rate of adsorption can be rewritten as, d 1 1 K e x p P K e x p A D d t R T R T P 1 (2.11) As the system approaches equilibrium, d dt reduces to zero, then, 1 1 K e x p P K e x p A D R T R T P 1 (2.12) Solve the equation with respect to the amount of adsorption uptake θ. Given that θ > 0, a positive solution is obtain as, K A K D e x p RT P K A 1 e x p P K D RT (2.13) To further simply the equation by defining a constant K, where, K K A e x p g z0 K R T D 0 (2.14) Rewrite Equation The expression of the Langmuir isotherm model is thus yielded. In this model, the energy term ε denotes the isosteric heat of adsorption. K e x p RT P 1 K e x p P RT (2.15) 21

52 Chapter 2: Theories of Physical Adsorption The expression suggests that at sufficiently large pressure, the adsorption sites on the adsorbent surface are fully occupied by the adsorbate molecules, that is, lim 1 (2.16) P When the pressure is small, the Langmuir isotherm model approaches to linear behavior at a constant temperature which is known as Henry s region [61]. lim P 0 K ex p P RT (2.17) Heterogeneity Surface Adsorption In the previous model, the adsorption sites are assumed to be energetically homogeneous. However, on a real solid surface where geometrical roughness is inevitably introduced during formation, the energetic heterogeneity cannot be ignored. The gas molecules experience different potential as adsorption sites of uneven energy are reached, as illustrated in Figure 2.4. ε 2 ε 3 ε 4 Adsorption Energy ε 1 ε 5. Figure 2.4: Illustration of a heterogeneous adsorbent surface with different energy distribution 22

53 Chapter 2: Theories of Physical Adsorption For the purpose of analysis, consider a heterogeneous surface that is consisted of a number of small local surfaces with varying site energy ε 1, ε 2, ε 3, respectively. Each local surface is treated as homogeneous. Denoting the j th local surface that possesses adsorption energy ε j is containing s j number of adsorption sites and n j number of adsorbed molecules, the surface coverage of the j th local surface is expressed as n j j (2.18) s j The total coverage on the general surface is the summation of all local surfaces, and given by, N S n n n... n S s n s n s n s n j j S s S s S s S s j j (2.19) s s s s j j S S S S It is noted that the term s j S is in fact the probability of distribution of local adsorption sites with energy ε j. One can define a continuous function to correspond to the probability, in which, s S j j j (2.20) and, 23

54 Chapter 2: Theories of Physical Adsorption 0 s j d 1 j S (2.21) j Rewrite Equation 2.19, i i d (2.22) i 0 The above equation implies that the surface coverage of the adsorbent by the adsorbate molecules can be conveniently represented if the solutions of and are known. For the local surface coverage function, the solution can be obtained from the Langmuir isotherm equation, since the local surface is regarded homogeneous in nature. Hence, rewrite Equation 2.15 in the following form, c e x p RT c 1 e x p RT (2.23) where, in the equilibrium conditions, let, KP e x p c RT (2.24) and thus, ln (2.25) c R T K P Figure 2.5 plots Vs at temperature 10 K, 300 K and 500 K. It is c noted that as T tends to zero, Equation 2.23 approaches to a step-like diracdelta function as shown in Equation 2.26 below. It indicates that adsorption 24

55 Chapter 2: Theories of Physical Adsorption and desorption could be separated by a clearly identified energy barrier at moderate temperatures, in which decreasing energy below ε c corresponds to adsorption, and vice versa for desorption. lim T 0 c 0 1 fo r fo r c c (2.26) Figure 2.5: Step-like profile yielded from Equation 2.23 at temperatures 10 K, 300 K and 500 K Applying condensation approximation (CA) [62, 63] at moderate temperatures, c, the total adsorbate surface coverage on a heterogeneous surface can be simplified to, 0 c 0 d d 0 1 d c (2.27) c d 25

56 Langmuir-Freundlich isotherm model Chapter 2: Theories of Physical Adsorption To obtain a solution of to represent the site energy allocation for a real adsorbent surface is difficult. However, it is possible to simplify the solution by approximating to a continuous probability distribution function. Assuming a symmetrical Gaussian distribution with the centre of peak 0 and standard deviation c is applied [61], 1 e x p 0 c c 1 e x p c 0 2 (2.28) Substitute the equation into Equation 2.27, c = c = 10 c = , [kj/mol] Figure 2.6: Symmetrical Gaussian function to represent the adsorption site energy distribution for Langmuir-Freundlich isotherm model 26

57 Chapter 2: Theories of Physical Adsorption e x p 1 e x p 1 e x p 1 e x p c c c c c c d d c c c (2.29) Invoking ln c R T K P of Equation 2.25, the Langmuir-Freundlich isotherm model can be derived K P e x p ln 1 e x p 1 K P e x p RT c RT c R T K P RT c RT (2.30) Dubinin-Astakhow isotherm model In an unbalanced case for the function, Rudzinski et al [59] suggested an asymmetrical Gaussian function as shown in Equation 2.31, from which Dubinin-Astakhow (DA) isotherm model can be reached ex p r r r r E E (2.31) Then, Equation 3.35 becomes

58 Chapter 2: Theories of Physical Adsorption r 1 r 1 1 d e x p d r c c E E c 1 e x p E r r (2.32) Again, substitute ln in Equation 2.36, c R T K P r c 1 RT 1 e x p e x p ln K ln P E E E r (2.33) 1 Let ln P ln K, the Dubinin-Astakhow isotherm equation is obtained. 0 RT R T R T P0 ex p ln P ln P 0 ex p ln E E P r r (2.34) in which if the quantity r is equal to 2, Equation 3.24 is known as the Dubinin- Radushkevich (DR) isotherm model r = r = r = , [kj/mol] Figure 2.7: Asymmetrical Gaussian function to represent the adsorption site energy distribution for Dubinin-Astakhow isotherm model 28

59 Chapter 2: Theories of Physical Adsorption Tóth isotherm model The Tóth isotherm model is a modification from the Langmuir equation by adding in a structural heterogeneity term, t. Jaroniec and Tóth [64] proposed an asymmetrical Gaussian function is proposed to represent the adsorption site energy distribution for Tóth isotherm model. The function, as expressed in Equation 2.35, yields the exact Tóth equation after integration. 1 t e x p R T R T t 1 t 1 e x p RT t t t (2.35) Figure 2.8 illustrates the energy distribution profile of the above equation. It is observed that at t equals to 1, the profile exhibits symmetrical Gaussian distribution which is the same as the Langmuir-Freundlich model. When the value of the heterogeneity t increases, the distribution becomes asymmetrical, more concentrated and shifting to the higher energy level. This indicates that for the Tóth isotherm in which t is normally greater than 1, most of adsorption sites have energy larger than the reference energy t. Substitute Equation 2.35 to Equation 2.27, and invoke ln, the Tóth isotherm equation can be obtained as, c R T K P 29

60 Chapter 2: Theories of Physical Adsorption d c c 1 R T t e x p R T t 1 e x p RT t t t 1 t d (2.36) t KP e x p RT t 1 KP e x p RT t 1 t where the energy term t is the isosteric heat of adsorption. It is noted that the temperature affects the energy distribution of the adsorption surface. The proposed distribution function owns neater and simpler form that founded in the literature [65] t = t = t = , [kj/mol] Figure 2.8: An asymmetrical Gaussian function to represent the adsorption site energy distribution for Tóth isotherm model 30

61 Chapter 2: Theories of Physical Adsorption 2.3. Adsorption Kinetics At a given temperature and pressure, the adsorption capacity of a particular adsorbent-adsorbate pair in equilibrium is well described by the isotherm data. However, in many practical applications, the adsorption processes are operated far before the equilibrium is reached. In order to design these adsorption systems adequately, it is essential to study the dynamic behavior of the adsorption uptake [66-69]. The adsorption kinetics theory describes the instantaneous mass transport rate of adsorbate onto an adsorbent when adsorption takes place towards equilibrium. This process is featured by the adsorbate molecules at bulk gaseous phase moving to the adsorbent surface through diffusion in the interlinked porous network of the adsorbent apparent volume [70]. It is influenced by the characteristics of the surface porous structure, the instantaneous concentration of the adsorbed phase, and thermodynamic conditions in which the adsorption is occurring [71] Literature Survey on Adsorption Kinetics In the effort to represent adsorption kinetics mathematically, the Linear Driving Force (LDF) model is the most widely used equation. It was first proposed by Glueckauf and Coates [72, 73] in The model describes that the rate of change of the adsorbate concentration on the adsorbent is proportional to the difference between its equilibrium and the instantaneous concentration. It has been successfully adopted to fit experiment data on the kinetics of a variety of adsorbent-adsorbate pairs. Malek and Farooq [74] 31

62 Chapter 2: Theories of Physical Adsorption experimentally studied the adsorption rate of methane, ethane and propane onto silica gel and active carbon, and approximated the results by the LDF model. Aristov and co-workers [75-78] measured the kinetics of water adsorption onto a family of material, namely selective water sorbents (SWS) that confined salts such as CaCl 2 and LiBr into silica gel or other porous host matrix. Li et al. [79] investigated the uptake rate of water vapor on three types of silica gel at 30 o C and varying relative humidity, and correlated the experimental data with the LDF equation. Reid et al. [80, 81] approximated the molecular sieves carbon (MSC) uptake kinetics with LDF equation for air seperation purposes. Similar mathematical representation was obtained from the adsorption of water vapor [82], n-octane, n-nonane [83], benzene, methanol [84] onto type BAX 950 activated carbon. In addition, the dynamic behavior of ethanol on a fibre type active carbon was investigated by El- Sharkawy et al. [68] and Saha et al. [85] using the linear driving force mechanism. Concurrently with successful regression on the experimental adsorption kinetics data, the LDF model is also enriched with meaningful explanation and improved accuracy. Li and Yang [86] suggested that a generalized 5 th -order binomial uptake profile resulted in LDF equation directly without yielding physically unrealistic results that would happen in parabolic profile [87, 88]. Sircar and Hufton [89] pointed out that despite the adsorption kinetics could be more accurately represented by Fickian Diffusion (FD) model, the LDF model with a lumped mass transport coefficient described well the mechanism of adsorption process at particle, colume and overall level in which FD model may be lost in the integration from the partical level adsorption. Besides, LDF 32

63 Chapter 2: Theories of Physical Adsorption model offers considerable benefits due to its simplisity and physical consistency. However, the imperfection of the linear driving force model cannot be ignored. Nakao and Suzuki [90] stated that the constant mass transport coefficient in the LDF equation is not desirable in transient processes. The authors proposed a dependency of the coefficient with half cycle time, yet the relation still faced difficulty in the startup and short cycle time processes. El- Sharkawy [69] also reported that the LDF equation showed a substantially underestimated uptake rate in the early adsorption / desorption process, and overestimated rate in the later process as compared to FD model. To tackle the problem, the author introduced dimensionless temperature dependent correlation factor and dimensionless time correction factor in the LDF equation. Moreover, the LDF model is based on an assumption that the adsorption process is conducted in isothermal conditions. However, this is only true when the cooling of the adsorbent is sufficient enough to remove the heat of adsorption released such that the temperature fluctuation during the process is neglected. One may well control the temperature by introducing differential changes in the adsorbate concentration in the measurement. Yet small temperature variation may still yield incorrect diffusivity value [91, 92]. Due to the significance of the temperature variation on the adsorption uptake, thermal effect is introduced in the kinetics theory. Ilavský et al. [93] reported that an over 20 o C temperature difference was observed between the center of a zeolite pellet and surrounding gas during adsorption. Voloshchuk and co-workers [94-97] also studied the non-isothermal phenomena on several types of zeolite adsorption. The temperature effect on the active carbon 33

64 Chapter 2: Theories of Physical Adsorption adsorption kinetics was investigated by Meunier et al. [98] Fiani et al. [99], and Loh et al. [100]. Several works formulated the thermal effect for the adsorbate diffusivity in the kinetic process using FD model, including Armstrong et al. [101, 102], Brunovská et al. [ ], Lee and Ruthven [ ], Particularly, Aristov et al. [109] studied the kinetics of type RD silica gel water pair by TG differential step method and identified the diffusivity values used in the Fickian diffusion model. On the other hand, He et al. [110] and El-Sharkawy et al. [111] investigated the pressure effect on the adsorption uptake rate. In addition, Ward et al. [55], Elliott et al. [56-58], Rudzinski et al. [59] adopted the statistical rate theory to explain the adsorption kinetics. Recently, Ismail et al. [112] measured the rate of uptake of propane on active carbon Maxsorb III using a magnetic suspension balance implementing thermal gravimetric approach. The authors regressed the experimental data with a kinetics model derived from the statistical rate theory, and determined the coefficient of particle phase transfer. It is noted that the weight of the adsorbent used in the experiment is corrected by eliminating the buoyancy effect of the surrounding bulk gas Kinetics Formulation In the mathematical formulation of the adsorption kinetics, the Linear Driving Force (LDF) model is expressed as d q ( t ) dt * q q t (2.37) 34

65 Chapter 2: Theories of Physical Adsorption where, q denotes instantaneous adsorbate uptake at time t; q* is the equilibrium uptake; and κ is the effective particle phase transfer coefficient. In an isothermal condition, the coefficient κ yields an constant value. If a nonisothermal situation is encountered, it is related to the surface diffusion coefficient D s, the average adsorbent particle radius R p and a constant F o, and expressed as, F D o s 2 (2.38) R p in which 15 is recommended to F o for spherical adsorbent particles [69], and, D s D so e x p E a RT (2.39) where, E a is the activation energy of the adsorbate, and D so is a preexponential constant. Hence, 15D R 2 p so ex p E a R T (2.40) Integrate Equation 2.37 and substitute condition, at t = 0, q t q in i One can obtain, the initial amount of adsorbate uptake on the adsorbent in i (2.41) * * q ( t ) q q q e x p t Substitute back to Equation 2.37, d q ( t ) dt * q q e x p in i t (2.42) 35

66 Chapter 2: Theories of Physical Adsorption 2.4. Thermodynamic Properties of Adsorbed Phase The adsorption isotherms identify the uptake capacity of an adsorbentadsorbate pair, while the kinetics reveal its dynamic interaction. However, in the practices such as designing adsorption chillers, not only these two terms, the energy flow involved in the adsorption processes must be considered. This requires precise definition of the thermodynamic properties of the adsorbentadsorbate system. During the adsorption process, heat is released as the adsorbate molecules sacrifice degree of freedoms when they are transferring from the gaseous phase to the energetically more stable adsorbed phase locating on the adsorbent surface [113]. From the thermodynamic point of view, this indicates that the adsorbed phase is also a distinguishable state. Hence, its thermodynamic properties including entropy, enthalpy, specific heat capacity, and heat of adsorption can be defined from the independent conditions like temperature, pressure and amount of uptake [114]. In the literature, early development on the adsorption thermodynamic framework was contributed by Everett [ ], Hill [119, 120], Young and Crowell [121]. Recently, Myers [122] developed formulation on the properties of the adsorbent-adsorbate system under the assumption of isothermal adsorption, and concluded that the heat capacity of the adsorbed phase is identical to the perfect gaseous phase. Chua et al. [123], however, pointed out that this conclusion differed significantly with many practical situations. The authors reformulated the equations based on the framework that was originally derived for the absorption (liquid-vapor) pairs. In a later development from Chakraborty et al. [124, 125], the adsorbed phase volume was assumed approximately equal to the gaseous phase. Rahman et al. [126] invoked the 36

67 Chapter 2: Theories of Physical Adsorption correction for the adsorbed phase specific volume and incorporated Dubinin- Astakhov micropore filling theory in the derivation. More recently, Ismail et al. [37] expanded the results of the statistical rate theory to re-establish the thermodynamic framework of adsorbent-adsorbate pairs. The heterogeneity of the adsorbent is well reflected by a constant K that corrosponds to the adsorbed phase molecular partition function. A more accurate correction of the adsorbed phase specific volume originally introduced by Srinivasan et al. [127] was incorporated in the development. After rigorous thermodynamic derivation, a much simpler and computation-friendly formulation is yielded Gibbs Free Energy of Adsorbed Phase The adsorption takes place spontaneously alongside releasing the isosteric heat, since the adsorbed phase is a lower and thermodynamically more stable energy state than the gaseous phase, [128, 129]. Due to the additional van der Waals and electrostatic forces of the adsorbent surface, the adsorbate molecules in the adsorbed phase possess one degree of translational freedom less than the gaseous which originally owns three [ ]. This is expressed by the Gibbs free energy at constant temperature and pressure as [133], G H T S a d s a d s a d s (2.43) where, ΔH ads is the isosteric heat of adsorption and also represented by Q st, It is defined as the enthalpy difference between the adsorbed (subscript α) and gaseous phase (subscript g). 37

68 Chapter 2: Theories of Physical Adsorption (2.44) H H H g From the Gibbs free energy, the chemical potential of the adsorbed and gaseous phases are defined as [134], G N T, P (2.45) g G N g g T, P (2.46) In the equilibrium between the adsorbed and gaseous phases, (2.47) g Entropy of Adsorbed Phase The chemical potential of the adsorbed phase is a function of temperature, pressure and adsorbate uptake. Its differential is expressed mathematically as, d d T d P d N T P N P, N T, N T, P (2.48) Invoke the Maxwell relations, S T N P, N T, P (2.49) V P N T, N T, P (2.50) 38

69 Equation 2.48 can be re-expressed as, Chapter 2: Theories of Physical Adsorption S V d d T d P d N N N N T, P T, P T, P (2.51) Similarly for the gaseous phase, S V g g g d d T d P d N g N N N g g g T, P T, P T, P g (2.52) In the phase transfer process of the adsorbate molecules, d N d N g (2.53) and define, S i N i T, P s i (2.54) V N T, P v i (2.55) Substitute Equation 2.51 to 2.55 back to Equation 2.47, one may reach the classical Clausius-Clapeyron equation [135], s d T v d P s d T v d P (2.56) g g dp s s g d T v v g (2.57) Rearrange the equation, the entropy of the adsorbed phase can be written as, dp s s v v dt g g a N (2.58) 39

70 Chapter 2: Theories of Physical Adsorption In the previous section, it has been demonstrated that at equilibrium, ln in Equation 2.25 [59], then, c R T K P P 1 c e x p K R T (2.59) Differentiate P with respect to T, one yield, P c e x p P c ln 2 T K R T R T T N KP (2.60) Therefore, the expression of the adsorbed phase entropy is obtained. s s P v v K P T ln g g a (2.61) Enthalpy of Adsorbed Phase In the previous work [124, 125], the formula to calculate the enthalpy of the adsorbed phase involved the latent heat term h fg while neither liquid phase or condensation is related to the adsorbed phase [136]. Moreover, the derivation is based on the assumption of ideal gas behavior. Ismail et al. [37] pointed out that the concept from the ideal gas law treated the adsorbate molecules as no interaction and occupying inherent volume, while this differed significantly from the practical applications, especially when high pressure and low temperature is encountered. Hence, without invoking the ideal gas equation, the correction for the specific volume of the adsorbed phase is utilized to capture the non-ideality of the substances. In the condition of constant 40

71 Chapter 2: Theories of Physical Adsorption temperature and pressure at equilibrium, one may obtain the enthalpy of adsorption from the Gibb s free energy equation as [137], H T S (2.62) a d s a d s h h T s s g g (2.63) Substitute Equation 2.61 to 2.63, ln h h P v v K P g g a (2.64) Isosteric Heat of Adsorption The isosteric heat of adsorption was defined by Do [138] as the differential change of adsorbate enthalpy per differential change in the amount of uptake. The concept of this quantity is analog to the latent heat of any substances. It explains the phase change phenomenon in the adsorption process when the adsorbate molecules move from a higher to a lower energy state [139]. However, comparing to the latent heat of vaporization, the isosteric heat of adsorption is 30% to 100% bigger [140]. Mathematically, it is expressed as, st g g a ln Q h h P v v K P (2.65) It is noted that the term ln(kp) is negative, which yields a positive value in the isosteric heat of adsorption that aligns with the exothermic nature of the adsorption process. 41

72 Specific Heat Capacity of Adsorbed Phase Chapter 2: Theories of Physical Adsorption Previously, the value assigned to the specific isobaric heat capacity of adsorbed phase from several models was equal to either that of the liquid phase, or gaseous phase of the adsorbate [141, 142]. However, with these models there were problems in thermodynamic consistency. Walton and Levan [143] pointed out the possibility of these values becoming negative at high uptake levels. From the enthalpy obtained in Equation 2.64, the specific isobaric heat capacity of the adsorbed phase along the isoteres is [144], Cp h h g Q st T T T N a N a N a (2.66) in which, at constant P, Q st P v v ln g K P T T N a P ln K P v g v T T N a N a (2.67) Since v v q, T relation [145], g g, one may write v v g g T T N a q. Invoking the cyclic v g T q T q v q v g g T 1 (2.68) v v g q g T T q q v g T (2.69) 42

73 Chapter 2: Theories of Physical Adsorption P P ln KP v T T g T q P v g T v g (2.70) The term v T N a is insignificant as compared to v g T N a. Hence, P P ln KP Q T T v st g P ln K P T N P a v g T 2 P ln K P v v g g P ln K P T P T T P (2.71) Similarly, h g q T T h q N g a T h g 1 (2.72) h h g g q T q T N a T h g (2.73) P P ln h g T T h T P q h P T KP Cpg P v P g P P T v T g T h h h T T T ln KP (2.74) v g C p P ln g K P T P v T g Hence, the specific isobaric heat capacity of the adsorbed phase can be derived. v ln g v P K P v g g C p C p P ln K P 2 g T T T P P 2 P (2.75) 43

74 Specific Volume of Adsorbed Phase Chapter 2: Theories of Physical Adsorption For more accurate computation of the adsorbed phase thermodynamic properties, it is indispensible to know the adsorbed phase specific volume. Dubinin proposed a correction to relate this quantity to the boiling phenomenon as follows [146], v v e x p T T b b (2.76) where, the subscript b represents normal boiling point; α α denotes the thermal expansion of the adsorbed phase and given by ln b v T cri b T b (2.77) And, b is the van der Waals volume as explained by Akkimaradi et al. [147] and Saha et al. [51] On the other hand, Srinivasan et al. [127] proposed a linear function of temperature to correlate the specific volume of the adsorbed and bulk gaseous phase and expressed in Equation The correlation is based on the assumption that the adsorbed phase is a condensed equilibrium phase analog to the liquid phase. 1 1 A B T (2.78) v v g where A and B are constants, rearrange, v A B T v 1 g 1 (2.79) from which the expansion of the adsorbed phase can be derived as, 44

75 Chapter 2: Theories of Physical Adsorption v g B v g (2.80) Ismail et al. [37] has shown that the specific volume of the adsorbed phase acquired from the experimental data exponentially increases with temperature, yet its gap with respect to the gaseous phase decreases. This phenomenon is naturally reflected by the adsorption process itself, whereas it is underestimated by the liquid phase assumption and not described by the gas phase postulation [148]. 45

76 Chapter 2: Theories of Physical Adsorption 2.5. Summary This chapter provides a comprehensive summary of the theories of the physical adsorption contributed from literature, mainly including the adsorption isotherms, kinetics and thermodynamic properties of the adsorbed phase. The objective of this chapter is to establish a theoretical framework for the derivation and analysis of the results of present thesis. The adsorption isotherms are studied based on the statistical rate approach, from which the classic isotherm theories, namely Langmuir, Langmuir- Freundlich, Dubinin-Astakhov, Dubinin-Raduskevich and Tóth are derived. The Langmuir isotherm is the simplest model by assuming energetically homogeneous adsorbent surface and monolayer adsorption. The rest consider the surface as inherently heterogeneous, and approximate the energy distribution of the adsorption sites with symmetrical or asymmetrical Gaussian functions. The Linear Driving Force model is used to formulate the adsorption kinetics. The thermal effect to the adsorption process is also involved such that the change of adsorbate uptake rate due to temperature variation is effectively captured. The kinetic coefficient appears in the LDF model will be especially utilized to define the mass transport influence on the adsorption heat transfer in Chapter 5. The results of the statistical rate theory are expanded to develop general expressions for the thermodynamic properties of the adsorbed phase for any adsorbent-adsorbate systems. They comprise entropy, enthalpy, specific isobaric heat capacity, and specific volume of the adsorbed phase, as well as 46

77 Chapter 2: Theories of Physical Adsorption the heat of adsorption. The properties, alongside the isotherm and kinetics theories, will be used to simulate the operation process of a typical adsorption chiller in Chapter 6. 47

78 Chapter 3: Transient Adsorption Heat Transfer CHAPTER 3 TRANSIENT ADSORPTION HEAT TRANSFER 3.1. Introduction In any adsorption chiller, one of the core components is the adsorption / desorption bed, also named as adsorber / desorber [6, 148]. It is a set of fintube heat exchangers embedded with adsorbent materials. In the adsorption processes, cooling source flows in the tube side of the heat exchanger to remove the heat of adsorption released from the adsorbent-adsorbate pair. In the desorption processes, the adsorbent is heated to discharge the adsorbate by supplying hot fluids into the tube side of the heat exchanger. Conventionally, the adsorbent solids are packed in between the heat exchanger fins and fixed in position by wire meshes. The major drawback of this method is the poor contact not only between adsorbent and metal fins, but also among adsorbent solids [149], inducing very low heat transfer efficiency. The same problem is faced by many thermally driven desiccant dehumidifiers. Figure 3.1 is a picture of a typical conventional wire mesh packed adsorbent embedded heat exchanger, which has a dimension of 200 mm x 150 mm x 24 mm, fin thickness 0.2 mm and spacing 3 mm, and 6 tube passes with tube diameter mm. 48

79 Chapter 3: Transient Adsorption Heat Transfer Heat Exchanger Wire Mesh Adsorbent (Silica Gel) Figure 3.1: A pictorial view of a typical adsorbent embedded heat exchanger using conventional wire mesh packing method Low heat transfer efficiency consequently leads to many problems in adsorption chillers. First of all, since the contact thermal resistance dominants the overall heat transfer resistance, the poor contact creates a steep temperature gradient from the metal fins to the adsorbent [150]. High entropy is generated during the operation processes that severely affect the coefficient of performance of the adsorption chillers. Moreover, due to the fact that the adsorption capacity of the adsorbent is inversely affected by the temperature, high temperature gradient leads to insufficiently cooled or heated adsorbent at adsorption or desorption processes respectively, and hence low mass transport capacity during both processes. Since mass transport capacity determines the cooling capacity of the chiller or the useful effect of any other adsorption based thermal-driven machines, one has to enlarge the machine scale to meet the required demand, or deliver only limited useful effect if space is a constraint. In addition, low heat transfer efficiency elongates the duration of the adsorbent approaching saturation. This unavoidably extends the redundant production period in which the mass transport is drastically diminished, 49

80 Chapter 3: Transient Adsorption Heat Transfer resulting in long cycle time and low average rate of cooling production. Large footprint and low COP are currently two major disadvantages of the adsorption chillers, which can be well debottlenecked by improving the heat transfer of the adsorbent embedded heat exchangers. In the effort to increase the heat transfer between the adsorbent and the heat exchanger fins as well as among adsorbent particles, methods from literature can be classified into two approaches. One was to mix the adsorbent with high thermal conductivity additives and apply compression to improve the physical contact among solid particles. Guilleminot et al. [151] consolidated zeolite into metallic foam by compression and sintering. The new material showed significant reduction on the conduction thermal resistance but increasing mass transfer resistance. A similar method was employed by Tatlıer and Erdem-Şenatalar [152, 153] to synthesize zeolite 4A with metal supports. The authors found that the method not only eliminated the limitations caused by inefficient heat transfer, but also provided means of loading more amount of adsorbent into the adsorber as compared to the conventional adsorption heat pumps. In addition, the optimum thickness of the zeolite 4A was dominantly determined by the mass diffusivity of the adsorbate in the adsorbent. Hu et al. [154] and Wang et al. [155] synthesized a high thermal conductivity polymer, polyaniline, together with zeolite to create high conductive matrix coating on the zeolite particles. The new product increased heat conductivity two to three folds than the original zeolite without influencing its adsorption capacity. Eun et al. [156] added natural expandable graphite powders into silica gel powders. The mixture was then consolidated to form a composite block via compression moulding. The block had significantly higher thermal conductivity of

81 Chapter 3: Transient Adsorption Heat Transfer W/m.K than the 0.17 W/m.K obtained from conventional silica gel. However, the water adsorption ability of the silica gel powders in the composite block was not affected. Jakubinek et al. [157] measured the thermal conductivity of powdered polycrystalline zeolite NaX experimentally, and concluded that such adsorbent had a glass-like thermal conductivity features. The other approach was to use binder to seal up the space that caused the poor contact and increase the overall thermal conduction. Yanagi and Ino [158] tested a consolidated silica gel adsorption heat exchanger in which the composite contains 4.3 wt% graphite, 86.4% silica gel and binders, and compared it with the conventional granular heat exchanger. The results showed that the consolidated exchanger improves the heat transfer efficiency by 38.8% over the conventional one in the beginning of desorption cycle and 1.37 times through the desorption process. Schnabel and Schmidt [159] coated aluminophosphate AlPO-18 nano- crystalline on to a metal layer with polyvinyl alcohol (PVA) as binder. The metal layer was made of aluminium and pre-etched in sodium hydroxide solution before coating. The authors measured the adsorption kinetics of the sample, and concluded that the thickness of the coating significantly affect the kinetics process and should be considered in the early design process of the adsorption based chillers and dehumidifiers. The same binder was used by Chang et al. [160] to paste silica gel onto stainless steel to study the influence of adsorbent layer thickness and particle size to the heat and mass transfer during adsorption. As expected, thinner layer owned smaller thermal and mass diffusion resistances. Larger particles generally adsorb faster, whereas have negligible effects on the heat transfer. Basile et al. [161] consolidated a composite using natural zeolite with 51

82 Chapter 3: Transient Adsorption Heat Transfer an organic binder, PTFE. From the thermal conductivity measurement, they concluded that the composite possessed low thermal resistance between the adsorbent and the heat exchanger due to smooth surface and well-suited contact. Besides, the composite was durable without mass loss after many adsorption / desorption cycles. Pino et al. [162] implemented both binders (PTFE and aluminum hydroxide) and additives (SiC, Si 3 N 4, and graphite) to zeolite 4A, and concluded that PTFE with additives did not help improve the overall heat transfer of the zeolite, whereas only Al(OH) 3 binder added sample showed significant increase in the thermal conductivity. Ouchi et al. [163] coated porous alumina thin film onto an aluminium plate and proved that such method improved the thermal conductivity as compared to the particle packed bed. In this chapter a method utilizing binder is proposed to increase the overall heat transfer efficiency of the adsorbent embedded heat exchanger. The adsorbent is coated as a thin layer onto the metal fins of the heat exchangers. Silica gel-water is the adsorbent-adsorbate pair focused in the following work. This will improve the design and performance of the existing silica gel-water adsorption chillers which are using the conventional method in which the silica gel is packed in between the heat exchanger fins by wire meshes. The proposed method can be generalized for other adsorbent-adsorbate pairs. In the below content, a selection procedure to find a suitable binder for such application is described in Section 3.2. Experiment is conducted to examine the effect of the binder on the transient overall heat transfer coefficient of the heat exchanger, and presented in Section 3.3. The results are compared with the conventional method. The last section summarizes the chapter. 52

83 Chapter 3: Transient Adsorption Heat Transfer 3.2. Binder Selection Materials As adsorption is a surface phenomenon taking place in the solid gas interface [1, ], the amount of the adsorbate being adsorbed is significantly influenced by the exposed surface area of the adsorbent [37]. Introduction of a binder to the interface may effectively improve the physical contact and reduce thermal resistance among adsorbent solids. However, it also covers the solid surface and may affect the adsorbate uptake quantity. Hence, a suitable binder must fulfil the following criteria to balance the gain in the thermal performance and interference on the adsorption mass transport. Possess good adhesive ability between the adsorbent and metal fins, as well as among the adsorbent solids. Lead to improved contact heat transfer between the adsorbent and metal fins, as well as among the adsorbent solids. Own insignificant impact on the amount of adsorbate uptake, i.e. the isotherm. Be chemically inert to the adsorbent and adsorbate. Be highly durable. In the present work, powdered silica gel type 3A and type RD are used as adsorbents in the binding and heat transfer test. The advantages of using the powdered adsorbents are that it is relatively easier to mix evenly with the binders, and coat a thin layer onto the metal fins. For comparison, the conventional mesh packing method utilizing granular silica gel type RD is also presented, and entitled as the base case. The thermophysical properties of the 53

84 Chapter 3: Transient Adsorption Heat Transfer three types of silica gel are listed in Table 3.1 [33], whose water adsorption isotherms will be presented in Chapter 4. Table 3.1: Thermophysical properties of silica gel type 3A, type RD powder and granule Properties Type 3A Type RD (Powder) Type RD (Granule) Average particle diameter [mm] BET surface area [m 2 /g] Porous volume [ml/g] Apparent density [kg/m 3 ] Thermal conductivity [W/m.K] Specific heat capacity [kj/kg.k] Mesh size > BET Surface Area from Nitrogen Adsorption The AUTOSORB-1 analyzer measures the amount of nitrogen adsorbed onto and desorbed from a porous solid at assorted equilibrium pressures in a constant temperature condition according to the constant volume variable pressure (CVVP) method [167]. It is manufactured by Quantachrome Instruments. The amount of the gas adsorbed or desorbed is equal to the difference between the quantity entering or leaving the sample cell and that needed to fill up the void space around the adsorbent in the cell when equilibrium is established. Data acquisition and reduction are conducted by Quantachrome AS1Win software based on selected adsorption models, from which the adsorption / desorption isotherm, BET surface area, pore size 54

85 Chapter 3: Transient Adsorption Heat Transfer distribution, etc, can be obtained. The schematic representation of the analyzer is shown in Figure 3.2. The pictorial view of the machine and its components are shown in Figure 3.3. Turbo Pump Diaphragm Pump Helium P T Fine Vacuum Coarse Vacuum Nitrogen Manifold P P T Liquid N 2 Cold Trap Liquid N 2 Dewar T Temperature Sensor P Pressure Transducer Heater Tape Sample Cell Reference Cell Out-gassing Station Figure 3.2: Schematic representation of AUTOSORB-1 analyzer Out-gassing Station Liquid N 2 Cold Trap N 2 Cylinder Sample Cell Data Acquisition / AS1Win software Reference Cell Liquid N 2 Dewar Out-gassing Heater Figure 3.3: Pictorial view of the AUTOSORB-1 analyzer and its components 55

86 Chapter 3: Transient Adsorption Heat Transfer Prior to the nitrogen adsorption analysis, mg the sample is loaded into the sample cell, and degassed in the out-gassing station at 120 o C and vacuum condition for 6 8 hours. The weight of the samples is measured by Ohaus E12140 mass balance with accuracy ±0.1 mg. During the analysis, nitrogen of purity 99.99% is used as the adsorbate gas. The adsorption / desorption process is conducted at temperature 77.3K which was maintained by submerging the sample cell into a liquid nitrogen dewar. 55 data points in the relative pressure range 1x10-5 to 1 for the adsorption process, and 20 data points in the relative pressure range 5x10-2 to 1 for the desorption process are obtained in a single isotherm curve. According to the multipoint Brunauer-Emmett-Teller (BET) method [163], the surface area of solid materials can be calculated from the following equation, 1 1 C 1 P P0 m C m C P m m 0 m 1 P (3.1) where m is the mass of adsorbate gas adsorbed by the solid materials at a relative pressure P P ; m 0 m denotes the mass of the adsorbate that forms a monolayer on the solid surface; and C is BET constant which is related to the energy of the monolayer adsorption. m m is proportional to the total surface area of the solid, and can be determined from of a linear plot 1 m P P 1 vs P P obtained from the experimental isotherm data, in which, the slope s 0 and y-axis intersection b are expressed as, 0 56

87 Chapter 3: Transient Adsorption Heat Transfer s C 1 (3.2) m m C b m 1 (3.3) m C For microporous solids that use N 2 as the adsorbate, the plot is usually restricted to a limited P P range of 0.05 to Eliminate the BET constant 0 C from the above two equations, m m 1 s b (3.4) The total surface area of the solids A t is then computed in terms of m m, Avogadro s number N A (6.023 x molecules/mol), the cross-sectional area A cs and the molecular weight M of the adsorbate. The value of A cs is 16.2 Å 2 for nitrogen molecules hexagonally close-packed monolayer at 77.3K. The molecular weight of N 2 is g/mol. A t m N A m A c s (3.5) M The BET surface area A s, or in other words the specific surface area per unit mass of the solid, is given by Equation 3.6 below. A s A t (3.6) m Figure 4.2 shows the plot 1 m P P 1 0 vs P P for Silica gel type 3A, 0 type RD powder and granules from nitrogen adsorption experimental data at 77.3 K. The slope and y-axis intersection values for each plot are tabulated in Table 3.2. Applying Equation 3.4 to 3.6, the multipoint BET surface area of 57

88 1/[m(P 0 /P - 1)] [g -1 ] Chapter 3: Transient Adsorption Heat Transfer the three types of silica gel listed in Table 3.1 is computed. The same method will be applied to calculate the BET surface of the samples with binders that exhibit good adhesive ability. 2 Silica Gel 3A Silica Gel RD Powder Silica Gel RD Granular Relative Pressure, P/P 0 [-] Figure 3.4: Multipoint BET plot for silica gel of type 3A, RD powder and granules from nitrogen adsorption at 77.3 K Table 3.2: Slope and y-intersection values of multipoint BET plot for silica gel type 3A, RD powder and granules from nitrogen adsorption at 77.3 K Material Slope (s) Y-intersection (b) Silica gel type 3A Silica gel type RD powder Silica gel type RD granules

89 Chapter 3: Transient Adsorption Heat Transfer Binder Comparison To select a suitable binder, seven types of binder are tested with silica gel type 3A, namely, epoxy, polyvinyl alcohol (PVA), corn flour, hydroxyethyl cellulose (HEC), gelatin, bentonite, and sepiolite. The first five types are organic in nature, whereas the last two are inorganic. For each binder, testing samples are made by mixing the binder with silica gel type 3A in the mass ratio of 1: 10. The mixture is dissolved by distilled water to form suspension solution. Stirring is applied to the solution until on clear boundary between solids and water is observed. The solution is then coated onto 20 x 20 x 0.4mm aluminium laminas. After coating, the samples are dried at the room temperature (25 o C to 28 o C) for 24 hours and cured in the oven under 120 o C for 12 hours. The first criterion implemented in the selection process is to investigate if the binder exhibits good adhesive ability between the silica gel and the metal fins as well as among the silica gel solids. For the binders that successfully achieve this criterion after curing, the samples are sent to test the BET surface area using the AUTOSORB-1 analyzer The performance of the seven binders is summarized in Table 3.3. It is shown that the inorganic binders, i.e. bentonite and sepiolite, exhibit poor adhesive ability, indicating that both types of binders are not suitable for this application. The organic binders, in contrast, are generally good in binding silica gel solids. However, the epoxy adhered samples show an extremely low BET surface area, implying that the porous surface of the silica gel is severely damaged. Moreover, the samples appear brown in colour after curing. The gelatin and PVA are not ideal for pasting the solids onto the metal fins as the 59

90 Chapter 3: Transient Adsorption Heat Transfer adsorbent has chances to peer off at the given binder weight percentage. The corn flour and HEC possess excellent binding quality between the adsorbent and aluminium fins, as well as among the silica gel solids. The two binder adhered samples also have higher surface area than other binders. However, degradation is observed with time for the corn flour adhered samples. This is not found for the HEC samples. Table 3.3: Comparison of various binders on the silica gel and metal fin binding. The mixing ratio of all binders is fixed at 10 wt% of adsorbent Binder name Type Adhesive ability BET surface area [m 2 ] Epoxy Polyvinyl alcohol (PVA) Corn flour Hydroxyethyl cellulose (HEC) Organic Organic Organic Organic Good between silica gel and fins, as well as on silica gel solids Appears brown colour after curing Good on silica gel solids; Fair between silica gel and fins, some samples peer off from fins Good between silica gel and fins, as well as on silica gel solids Binding degrades with time Good between silica gel and fins, as well as on silica gel solids Gelatin Organic Good on silica gel solids; Fair between silica gel and fins; some samples peer off from fins Bentonite Inorganic Poor between silica gel and fins, as well as among silica gel solids Sepiolite Inorganic Poor between silica gel and fins, as well as among silica gel solids

91 Chapter 3: Transient Adsorption Heat Transfer From the comparison, HEC has been found most suitable for the silica gel binding among the seven tested binders. The binder has a softening temperature greater than 140 o C that is well above the application temperature of a typical silica gel-water adsorption chiller (below 100 o C). Hence, HEC is selected for further testing. On the other hand, the nitrogen adsorption test at 77K using AUTOSORB-1 analyzer shows that HEC has rather low BET surface area and porous volume, and thus negligible contribution on the adsorption capacity. The properties of HEC are summarized in Table 3.4 [168]. Table 3.4: Properties of hydroxyethyl cellulose (HEC) Properties Value BET surface area [m 2 /g] Porous volume [ml/g] Apparent density [kg/m 3 ] 600 Specific heat capacity [kj/kg.k] ~3.851 Softening temperature [ o C] > 140 C Decomposition temperature [ o C] 205 C Optimum Binder Ratio Comparing Tables 3.1 and 3.3 from the previous sections, an observation is the introduction of binders reduces the surface area of the original adsorbent due to the binder coverage. In particular, HEC has shown extremely low surface area and porous volume in contrast with silica gel, indicating that the binder is not equipped with porous structures. When HEC is pasted, the 61

92 Chapter 3: Transient Adsorption Heat Transfer original microporous structures on the silica gel are blocked. This well explains the reduction of the surface area on the samples as a result of HEC binding. Moreover, for the silica gel-water adsorption, the hydrogen bonds exposed on the solid surface play an important role to attract water molecules. The reduction of exposed surface area eventually reduces the number of active hydrogen bonds and hence shrinks the adsorption capacity of the adsorbent. Thus one can use the BET surface area as an indicator for the binder influence on the adsorption uptake. The binder weight percentage to the adsorbent can be optimized by identifying the ratio with which the samples exhibit the maximum surface area and yet retain the adhesive performance. Silica gel type 3A samples with HEC of various weight percentages of adsorbent, i.e wt%, 3.33 wt%, 6.67 wt% and 10 wt%, are prepared and analyzed by the AUTOSORB-1 instrument. The binding performance is good for all the percentages. The results on the BET surface area and porous volume are plotted in Figure 3.5. As illustrated, both parameters are affected by the binder quantity. The peak of both curves are observed when HEC is 3.3 wt% of adsorbent, which has 507 m 2 /g of BET surface area and ml/g of pore volume. In other words, the porous surface is least influenced by this HEC weight percentage. It is evident from the micropore size distribution based on the Dubinin-Astakhov model shown in Figure 3.6. Though negligible influence is observed on the pore distribution pattern, the pore volume of the binder adhered samples is lower than that of pure silica gel type 3A at all micropore radii. The total porous volume of an adsorbent equals to the integration of the pore volume at all radii. For HEC of 3.3 wt% and greater, the pore volume at every radius reduces as more HEC is added, and so does 62

93 BET Surface Area [m 2 /g] Pore Volume [ml/g] Chapter 3: Transient Adsorption Heat Transfer the total pore volume, as shown in Figure 3.5. For the one with 1.67 wt%, despite the fact that its small radius pores are less affected as compared to the 3.3 wt%, the binder blocks more amount of bigger pores. This explains the drop of total surface area and the pore volume at the lower end of the binder quantity in the figure. 600 BET Surface Area Porous Volume Binder Weight Percentage of Adsorbent [%] Figure 3.5: BET surface area and total pore volume of the HEC adhered silica gel type 3A samples at assorted HEC weight percentage 63

94 Pore Volume, dq v /dr, [ml/g/å] Chapter 3: Transient Adsorption Heat Transfer HEC 0 wt% (Pure Silica Gel) HEC 1.67 wt% HEC 3.33 wt% HEC 6.67 wt% HEC 10 wt% Pore Radius [Å] Figure 3.6: Dubinin Astakhov (DA) micropore size distribution of pure silica gel 3A, and HEC adhered silica gel type 3A samples with various HEC weight percentages Figure 3.7 illustrates the microscopic photos of pure silica gel 3A, and its mixture with 3.3 adsorbent wt% HEC and corn flour for comparison, taken by Field Emission Scanning Electron Microscopy (FESEM) method. The spherical 3A solids are clearly visualized at 35 times magnification and above. At the magnification of 50,000 times and higher, the porous structure of the solid surface are captured. Comparing the pure silica gel (Figure 3.7a) with the HEC (Figure 3.7b) and corn flour (Figure 3.7c) adhered samples, a clear evidence is that the binders appear in void space among the adsorbent solids, and build links for conduction heat transfer among the solid materials. The binder adhered samples appear more consolidated than the pure silica gel, which helps to increase the packing density of the silica gel in the adsorbent embedded heat exchangers. On the other hand, the surface coverage by the binders is observed in the microscopic pictures, though the porous structures 64

95 Chapter 3: Transient Adsorption Heat Transfer still extensively exist shown at high magnification. This also provides the evidence on the explanation of surface area reduction on the binder adhered samples. However, there is a need to understand the precise impact of the binder on the adsorption capacity of the adsorbent through isotherm measurements, which will be discussed in detail in Chapter 4. (a) Parent silica gel 3A 65

96 Chapter 3: Transient Adsorption Heat Transfer (b) Silica gel type 3A with 3.3 wt% HEC (c) Silica gel type 3A with 3.3 wt% corn flour Figure 3.7: Field emission scanning electron microscopic (FESEM) photos for (a) parent silica gel type 3A, (b) silica gel type 3A with 3.3 adsorbent wt% HEC, and (c) 3.3 adsorbent wt% corn flour 66

97 Chapter 3: Transient Adsorption Heat Transfer 3.3. Experiment on Transient Adsorption Heat Transfer This section describes the experimental investigation on the influence of binder on the transient overall heat transfer coefficient of an adsorbent embedded heat exchanger. The motivations of measuring the transient overall heat transfer coefficient instead of the thermal conductivity studied in many literatures [ , 161] are as follows. Firstly, the adsorption heat transfer process is highly dynamic in which the amount of adsorbate uptake, heat flux and the temperature of the system, etc. vary with time, whereas the thermal conductivity measurement is normally conducted in steady state conditions. It is insufficient to quantify a transient process with steady state values. Secondly, the adsorption process involves several parallel phenomena, including heat generation from the phase change of the adsorbate molecules, conduction through the adsorbent material, and convective interaction with the surrounding gases. The thermal conductivity only plays part of role in the overall process. Last but not least, the measurement of the thermal conductivity cannot reveal the effect of the binder on the adsorbate mass transport, like uptake kinetics, diffusivity in the adsorbent, etc. which influences the heat transfer process. The transient overall heat transfer coefficient, however, is measured in the conditions close to the real world applications, and can effectively present the net effect of binder on the adsorption heat transfer process. 67

98 Experimental setup and procedures Chapter 3: Transient Adsorption Heat Transfer The testing facilities and experimental procedures to study the influence of the binder on the overall heat transfer performance of an adsorbent embedded heat exchanger are described below. A two-pass copper plain fin-tube heat exchanger is fabricated for the experiment. Its specifications are listed in Table 3.5. The proposed method to embed the adsorbent is to coat it as a thin layer onto the both sides of the heat exchanger fins by utilizing HEC of 3.3 adsorbent wt%. The rationale of choosing HEC and determining its quantity has been stated in the previous sections. In this method the fine powder-like adsorbents, silica gel type 3A and type RD powder are used. For the comparative study purpose, the conventional way of packing the granular silica gel type RD by wire mesh is also employed on the same heat exchanger, and entitled as the base case. Table 3.5: Specifications of the two-pass copper plain fin-tube heat exchanger used in the adsorption heat transfer experiment Properties Values Properties Values Tube material Copper Fin material Copper Surface finish Lead coating Fin thickness [mm] 0.25 Tube outer diameter [mm] Fin spacing [mm] 5 Total surface area [m 2 ] No. of fins 28 The experimental apparatus for the adsorption heat transfer test is schematically illustrated in Figure 3.8. A pictorial view of the setup is shown in Figure 3.9. The apparatus consists of mainly an adsorption chamber, an evaporator, two water circulators, a vacuum pump, and a data acquisition 68

99 Chapter 3: Transient Adsorption Heat Transfer system. The silica gel embedded heat exchanger is located in the adsorption chamber. To maintain the evaporation temperature during the experiment, the evaporator is submerged into a water pool whose the temperature is controlled by a chilled water circular. The temperature measurement is assisted by OMEGA themistors with accuracy ± 0.15 o C. The probe type thermistors are installed for the cooling water and the evaporator temperatures. The point type thermistors are embedded into the heat exchanger and silica gel. Figure 3.10 indicates the location of these thermistors. The pressure is gauged by GEMS pressure transducer with accuracy ± 0.25 kpa. The temperature and pressure sensors are connected to an Agilent 34970A data acquisition unit. The chamber, evaporator and respective accessories are vacuum-proof equipment. Heater tape is wrapped around the vapor pipe and adsorption chamber to prevent condensation. Insulation is applied at the required locations to minimize heat leak. F T T P T V1 F T P Flow-meter Temperature Sensor Pressure Transducer Heater Tape Data Acquisition System T P V4 V3 Evaporator V5 V6 V2 Water Circulator (Cooling Water) Adsorption Chamber (Inside: Silica Gel Embedded Heat Exchanger) Vacuum Pump Water Circulator (Evaporator) Figure 3.8: Schematic representation of the adsorption heat transfer experimental apparatus 69

100 Chapter 3: Transient Adsorption Heat Transfer Water Circulator (Evaporator) Evaporator Heater Tape Heater Tape Controller Water Circulator (Cooling Water) Data Acquisition System Vacuum Pump Flow-meter Adsorption Chamber Figure 3.9: Pictorial view of the adsorption heat transfer experimental apparatus T8 T5 T7 T12 T11 T10 T6 T9 T3 Fin Silica Gel T4 T1 T2 Figure 3.10: Location of thermistor thermometers on and around the silica gel embedded heat exchanger in the adsorption chamber 70

101 Chapter 3: Transient Adsorption Heat Transfer In the base case scenario, 98.9 g of granular silica gel type RD is loaded in between the heat exchanger fins. The wire mesh used is No. 300 type and has a weight of 6.1 g. Photos of the exchanger in the loading process and its final appearance are given in Figure For the proposed coating method, 65.6 g silica gel type 3A is coated onto both sides of copper fins with average coating thickness 1.3 mm. A pectoral view of the exchanger is shown in Figure In the silica gel type RD powder case, 37.4 g of the powder is used to form an average coating thickness 0.7 mm, as given in Figure In the both proposed cases the weight value excludes the weight of the HEC. Ohaus E12140 mass balance with accuracy ±0.1 mg is employed to obtain all mentioned weights. In the experiment preparation, distilled water is filled into the evaporator. It performs the role of the adsorbate and working fluid. The vacuum pump is used to pull out the air from the evaporator and adsorption chamber, such that a sub-atmospheric state is created. Four cooling water temperatures, viz., 25 o C, 30 o C 35 o C and 40 o C are tested to understand the overall heat transfer performance of the adsorption process in the three cases. During the experiment of each cooling water temperature, regeneration is first conducted for the silica gel in the following procedures. It is started by shutting the valve V1. 90 o C hot water is circulated into the heat exchanger tube to heat up the adsorbent. The vacuum pump takes away the moisture desorbed from the solids till the silica gel is sufficiently dry and vacuum is established in the adsorption chamber. After the regeneration, the cooling water is supplied to the exchanger. The evaporator water pool temperature is remained in 5 o C. Until the system reaches steady state, open the valve V1 to initiate the 71

102 Chapter 3: Transient Adsorption Heat Transfer adsorption process. The flow-rate of the cooling water is set at 1 LPM. The heater tape is maintained at 50 o C through the experimental process to prevent water vapor condensation onto the chamber inner wall. Figure 3.11: Pictorial views of the base case in which the heat exchanger is embedded with silica gel type RD granules by wire mesh. The pictures show (left) the exchanger in the loading process and (right) its final appearance 72

103 Chapter 3: Transient Adsorption Heat Transfer Figure 3.12: Pictorial views of the silica gel type 3A case in which the heat exchanger is coated with the silica gel using 3.3 adsorbent wt% HEC. The pictures show (left) the exchanger in the coating process and (right) its final appearance Figure 3.13: Pictorial views of the silica gel type RD powder case in which improved coating method is applied for the heat exchanger using 3.3 adsorbent wt% HEC. The pictures show (left) the exchanger in the coating process and (right) its final appearance 73

104 Results and Discussion Chapter 3: Transient Adsorption Heat Transfer Governing equations The transient overall heat transfer coefficient (U) of the adsorbent embedded heat exchanger during adsorption process is calculated as below, U m C p To Ti cw t (3.7) A T T a d s i, cw where T ads denotes an average instantaneous temperature of the adsorbent, the subscript cw represents cooling water; i and o mean inlet and outlet. A is the total surface area of fin-tube heat exchanger. The rest of the symbols have their usual means. It is noted that in the right hand side of the equation, the value of T ads and T o,cw are changing with respect to time Temperature difference between cooling source and adsorbent The experimental results of the heat transfer for the three cases during adsorption process are presented below. When the adsorption process starts, disequilibrium of vapour pressure between the adsorbent surface and the evaporator creates a strong driving force to migrate the water vapor. The vapor molecules turn their state from gaseous to adsorbed phase, and release a tremendous amount of heat, named as heat of adsorption that is usually bigger than the latent heat of the adsorbate [37]. As the process continues, the water uptake approaches saturation, alongside decaying rate of mass transport and the heat released. The heat of adsorption is rejected to the cooling water that circulates through the heat exchanger tubes. 74

105 Temperature Difference T ads - T i,cw [ o C] Chapter 3: Transient Adsorption Heat Transfer Figure 3.14 illustrates the temporal temperature difference between the silica gel average T ads and inlet cooling water T i,cw at various cooling water temperatures for the type 3A coated heat exchanger and the base case. The x- axis is time in logarithmic scale. A comparison between the two cases clearly shows that temperature raises more rapidly and a larger temperature difference takes place in the early process for the latter, implying a bigger amount of heat is cumulated in the mesh packed silica gel. The type 3A coated heat exchanger reaches a peak difference of 6.9 o C to 7.4 o C in the experimental range, while the base case doubles the gap. In addition, in the both cases temperature difference generally decreases with ascending cooling water temperature. Similar observations are found from the comparison between the silica gel type RD powder coated heat exchanger and the base case, as shown in Figure Base 25 C Base 30 C Base 35 C Base 40 C 25 C 30 C 35 C 40 C 15 Base case: Silica gel RD granular with mesh Silica Gel 3A with 3.3wt% HEC Time [s] Figure 3.14: Temporal temperature difference between the inlet cooling water T i,cw and the silica gel average T ads at various cooling water temperatures for the silica gel type 3A coated heat exchanger and the base case 75

106 Temperature Difference, T ads - T i,cw [ o C] Chapter 3: Transient Adsorption Heat Transfer 20 Base 25 C Base 30 C Base 35 C Base 40 C RD 25 C RD 30 C RD C RD 40 C 15 Base case: Silica gel RD granular with mesh Silica Gel RD Powder with 3.3wt% HEC Time [s] Figure 3.15: Temporal temperature difference between the inlet cooling water T i,cw and the silica gel average T ads at various cooling water temperatures for the silica gel type RD powder coated heat exchanger and the base case Transient overall heat transfer coefficient Figure 3.16 shows the instantaneous overall heat transfer coefficients of the base case and silica gel type 3A coated exchanger at various cooling water temperatures, calculated from Equation 3.7. Comparing the both cases, a significant improvement by the binder coating method can be observed, which can be stated from two aspects. First of all, the coefficient value of the type 3A coated exchanger is higher than that of the base case through all the adsorption processes. The maximum value experienced by former is more than 2.8 times of the latter. Regarding to the steady cooling in the later part of the processes, the former s average is 54.1 W/m 2.K, or 1.5 times higher than 35.8 W/m 2.K of the latter. Secondly, the improvement is achieved with respect to response time. The heat exchanger with binder reacts much faster to heat than the base 76

107 Overall Heat Transfer Coefficient, U [W/m 2.K] Chapter 3: Transient Adsorption Heat Transfer case. This is reflected by a rapid growth of its overall heat transfer coefficient in the beginning of the adsorption process. Moreover, higher U value for the coating method is possessed in the first 100 s in which the mass transport is most substantial. This effectively reduces the heat accumulation in the same time interval, and maintains a much lower adsorption temperature than the conventional mesh packing method. Figure 3.17 is the comparison of the transient overall heat transfer coefficient value between the silica gel type RD powder coated heat exchanger and the base case. The results again prove the benefits of the HEC binder on the adsorption heat transfer process. 140 Base 25 C Base 30 C Base 35 C Base 40 C 25 C 30 C 35 C 40 C Silica gel 3A with 3.3wt% HEC Base case: Silica gel RD granular with mesh Time [s] Figure 3.16: Temporal overall heat transfer coefficient of the 3A type silica gel coated heat exchanger and the base case at various cooling water temperatures 77

108 Overall Heat Transfer Coefficient, U [W/m 2.K] Chapter 3: Transient Adsorption Heat Transfer 120 Base 25 C Base 30 C Base 35 C Base 40 C RD 25 C RD 30 C RD 35 C RD 40 C Silica Gel RD Powder with 3.3wt% HEC Base case: Silica gel RD granular with mesh Time [s] Figure 3.17: Temporal overall heat transfer coefficient of the RD powder type silica gel coated heat exchanger and the base case at various cooling water temperatures A further investigation of the heat transfer performance with respect to cooling water temperature for the three cases is described in Figure It illustrates the cyclical average of the instantaneous overall heat transfer coefficient over 500 s adsorption cycle time which is typically used in the operation strategy of a silica gel-water adsorption chiller. The average coefficient value is normalized by the unit mass of the adsorbent utilized. This eliminates the influence of mass transport since the total heat of adsorption that determines the coefficient is proportional to the total amount of adsorbate uptake, while more adsorbent helps to increase the uptake amount. The results indicate that a sight appreciation of the coefficient magnitude is gained at increasing cooling water temperature in all cases. This may be subjected to that, on one hand, increasing temperature improves the cooling water Nusselt number and hence the tube side heat transfer. On the other hand, since the 78

109 Average Overall Heat Transfer Coefficient per Adsorbent Mass, [W/m 2.K/kg of adsorbent] Chapter 3: Transient Adsorption Heat Transfer shell side adsorption is strongly dominant the overall thermal resistance, the observation entails an increase of the heat transfer with respect to the ascending adsorption temperature. Furthermore, besides the improvement from the binder coating cases as compared to the base case, the heat transfer performance of the silica gel type RD powder coated heat exchanger outperforms the type 3A one 37.3 % on average with the same binder weight percentage. Due to the fact that both coating cases have similar specifications rather than the coating thickness, the results indicate the benefits of the thin coating layer. In general, the RD powder and the 3A cases improve the average overall heat transfer coefficient per unit mass of adsorbent by 4.6 and 3.4 folds of the base case RD Powder 3A Base Case Temperature of Cooling Water Inlet, T i,cw [ o C] Figure 3.18: Cyclical average of the transient overall heat transfer coefficient over 500 s adsorption cycle time for various cooling water inlet temperatures. The coefficient is normalized with unit mass of the adsorbent. 79

110 Heat Loss, Q loss [W] Chapter 3: Transient Adsorption Heat Transfer Heat leak test on the experimental setup For the experiment of each adsorption heat transfer case, the amount of heat leak of from the adsorption chamber is measured. It is conducted by allowing the chamber naturally to cool down, and logging the rate of decrease of the adsorbent average temperature, T ads. The heat leak, Q loss, is computed from the multiple of the thermal mass of the heat exchanger and the temperature decrease rate, and is plotted against the temperature difference, ΔT, between the T ads, and the chamber surrounding ambient, T sur. The relation is fitted by a third order polynomial for ease of computation. It will be used to compensate the heat flux during the adsorption processes for the further analysis in Chapter 5. Figure 3.19 shows the experimental heat leak plot for the three each adsorption heat transfer cases Q loss = E-06ΔT E-04ΔT E-03ΔT R² = Temperature Difference, ΔT [ o C] (a) Silica gel type 3A case 80

111 Heat Loss, Q loss [W] Heat Loss, Q loss [W] Chapter 3: Transient Adsorption Heat Transfer Q loss = E-05ΔT E-03ΔT E-02ΔT R² = Temperature Difference, ΔT [ o C] (b) Silica gel type RD powder case Q loss = 5.269E-06ΔT E-04ΔT E-02ΔT R² = Temperature Difference, ΔT [ o C] (c) Base case Figure 3.19: Heat leak of the adsorption heat transfer experiment for (a) silica gel type 3A coated, (b) silica gel type RD powder coated heat exchangers, and (c) the base case 81

112 Chapter 3: Transient Adsorption Heat Transfer 3.4. Summary In this chapter, a new method is proposed to improve the heat transfer efficiency of silica gel embedded heat exchangers. It is to coat the powder-like silica gel as a thin layer onto the heat exchanger fins through introduction of binder, instead of the conventional way in which granular silica gel is packed by wire mesh in between the fins. Seven types of binder are tested for such application. It is shown that among all the binders, Hydroxyethyl cellulose (HEC) appears best binding results between the silica gel and metal fins, as well as among the silica gel particles. Its adhered samples exhibit relatively low surface area reduction and no degradation with time. In addition, the optimum binder weight percentage for the HEC is 3.3 adsorbent wt% which gives maximum BET surface area among different silica gel and binder mixing ratios. Experiments are conducted to evaluate the binder effect on the overall heat transfer of the silica gel embedded heat exchanger during adsorption processes. The results show that the RD powder and 3A cases utilizing the proposed binder coating method improve significantly the heat transfer efficiency per unit mass of adsorbent used by 4.6 and 3.4 folds of the conventional wire mesh packing method. Moreover, the new method reacts much faster to the heat of adsorption. This will help increase the COP of the adsorption chillers and effectively reduce the plant footprint. 82

113 Chapter 4: Adsorption Mass Transport CHAPTER 4 ADSORPTION MASS TRANSPORT 4.1. Introduction In the previous chapter, the utilization of binder to coat adsorbent onto the heat exchanger fins has been proven to tremendously enhance the heat transfer efficiency of adsorbent embedded heat exchangers as compared to the conventional method using wire mesh. However, the adsorption heat transfer process is highly interlaced with the adsorbate mass transport. Both processes determine the overall performance of the heat exchanger in an adsorption chiller. Hence the influence of the binder on the adsorbate mass transport must be examined. If a severe suppression on the mass transport is observed as a result of the binder, the heat exchanger may eventually underperform. This chapter describes the experiment conducted to measure the influence of the binder HEC with 3.3 adsorbent wt% mixing ratio on the water adsorption capacity of silica gel type 3A and RD powder, aligning with the heat transfer experiment. The pure and corresponding binder added samples are tested. The obtained isotherm data are regressed by a newly proposed isotherm model. Its regression accuracy is evaluated by comparing with the classic Dubinin-Astakhov and Tóth models. With the accurate isotherm measurement and the results from heat transfer experiment, the net effect of the binder on the mass transport during adsorption process is then evaluated. 83

114 Chapter 4: Adsorption Mass Transport A second part of the present chapter introduces a novel water adsorbent zeolite FAM Z01 that is specifically designed for adsorption chillers and dehumidifiers. The material exhibits unique S-shape isotherms that belong to Type V category. Experiment is conducted to measure the water adsorption isotherms of the zeolite with and without binder at typical adsorption chiller operation temperatures. The proposed model is found able to accurately fit the isotherm data. Last but not least, the material s water adsorption mechanism is investigated from nano-scale by molecular dynamic simulation Experimental Setup and Procedures The adsorption isotherms of the pure and binder added adsorbent samples are measured using HYDROSORB analyzer manufactured by Quantachrome Instruments. The analyzer is specially designed to measure the water vapor adsorption / desorption capacity of any porous adsorbent and operated in the sub-atmospheric conditions. Its working principle is based on the constant volume variable pressure (CVVP) method. The water equilibrium uptake on the adsorbent during adsorption / desorption process is determined by calculating the amount of water vapor entering / leaving the sample cell and filling the void space around the adsorbent in the cell through pressure change. Only initial and equilibrium pressure readings are used in the calculation. Data acquisition and reduction are performed by Quantachrome HydroWin software. A schematic representation of the HYDROSORB analyzer is shown in Figure 4.1. The pictorial view of the analyzer and its accessories are shown in 84

115 Chapter 4: Adsorption Mass Transport Figure 4.2. In the analyzer, two major components, i.e. a water reservoir and a manifold, are located inside a heater oven that maintains internal temperature at 100 o C. In other words, the water vapor generated for the adsorption prior entering the sample cell is at the same temperature. Before any sample is tested, an empty sample cell to be utilized in the experiment is calibrated to determine the volume of the cell and the manifold at every experimental adsorption temperature. For a particular adsorbent sample, the experimental procedures of its water isotherm measurement are described as follows. First of all, the weight of the empty sample cell and the adsorbent sample are measured by Ohaus E12140 mass balance with accuracy ± 0.1 mg. Before an adsorption analysis, the sample cell is degassed by wrapping the degasser heater and vacuumed by the Edwards type 18 vacuum pump. The degassing is 6 8 hours at 120 o C. The dry weight of the sample is again measured after the degassing as the input data for calculation. During the adsorption analysis, the sample cell is partially immerged into a temperature dewar which sets the adsorption temperature and is maintained by Julabo F12 water circular with ± 0.1 o C temperature control accuracy. The sample cell is vacuumed again and then dosed by water vapor stored in the manifold till equilibrium is achieved between the adsorbent and water vapor at preset pressure range. The pressure of the manifold and the sample cell is measured by a 100 torr transducer with resolution 0.01% of the full scale. High purity nitrogen (99.99%) is used for backfill purpose during the measurement. 85

116 Chapter 4: Adsorption Mass Transport Nitrogen T Heater Oven Manifold Fine Vacuum Coarse Vacuum Vacuum Pump P Water Reservoir T T Temperature Sensor P Pressure Transducer Heater Oven Sample Cell Temperature Dewar Water Circulator Figure 4.1: Schematic representation of HYDROSORB analyzer Control & Data Acquisition N 2 Cylinder Heater Oven Water Reservoir Vacuum Pump Degasser Heater Temperature Sensor Sample Cell Temperature Dewar Water Circulator Figure 4.2: Pictorial view of the HYDROSORB analyzer and its components 86

117 Chapter 4: Adsorption Mass Transport 4.3. Governing Theories Data Reduction The data reduction in the HYDROSORB analyzer is as follows. Firstly, the mass of water vapor dosed from the manifold into the sample cell (denoted as m 1 ) is calculated. The cell is partially immerged into a temperature dewar, named as cold zone. The other heated part is named as warm zone. For the cell without loading any samples, when it achieves pressure equalization with the manifold, according to the mass conservation, m m m 1 H C (4.1) where m denotes the mass of water vapor; and the subscript H and C represent the warm and cold zones, respectively. Assuming both temperature zones are apportioned with no temperature gradient in between, invoking ideal behavior in the warm zone, and non-ideality correction for the cold zone, the above equation becomes, m 1 P V P V 1 P C H H C (4.2) R T R T H C in which, the Greek letter α is the non-ideality correction factor, and has a value 3 x 10-5 /torr for water vapor. Other alphabets have their usual means. Since the pressure in the sample is equal anywhere, that is, ΔP H = ΔP C = ΔP, rewrite Equation 4.2, m 1 P V V 1 P H C R T T H C (4.3) 87

118 Chapter 4: Adsorption Mass Transport When the adsorbent of mass M and true density ρ is present in the sample cell, the mass of water vapor leaving from the manifold to the sample cell after pressure equalization but before adsorption occurring is, m 1 V M 1 P C P V H R T T H C (4.4) At the moment adsorption starts to take place, the sample cell is isolated from the manifold. If equilibrium between the water vapor and adsorbent sample is not achieved within the preset pressure range, m 1 is recorded as the mass of water vapor adsorbed by the adsorbent for that particular dose action. If the equilibrium is established within the preset pressure range, Equation 4.4 can also be used to determine the mass of water vapor adsorbed, by replacing ΔP with the pressure difference between the start of adsorption and the end equilibrium, ΔP e, and also P with the final equilibrium pressure, P e. The final mass of water vapor adsorbed by an adsorbent at preset pressure after n time dose actions is given by, n 1 m m m i 1 i n V M 1 P R T T n 1 C i P V i H i 1 H C V M 1 P C e P V e H R T T H C (4.5) 88

119 Chapter 4: Adsorption Mass Transport Isotherm Regression The water adsorption isotherms of the adsorbent presented in this work are from two categories. The silica gel-water pairs belong to Type I category, and the zeolite FAM Z01-water is Type V. The Type I isotherms can be fitted by classical Dubinin-Astakhov (DA) and Tóth models as reviewed in Chapter 2. The equations of the two models are re-expressed below. DA model: * q R T P s e x p ln q E P 0 c (4.6) where, q* is the equilibrium adsorption uptake at temperature T and pressure P; q 0 denotes the limiting uptake of the adsorbate at the saturation pressure P s of the temperature T, R, E c and γ represent the universal gas constant, characteristic energy; and exponential constant, respectively. Tóth Model: q q * 0 K T Q st P e x p RT Q st 1 K P e x p T RT t 1 t (4.7) in which, Q st is the isosteric heat of adsorption; t is surface heterogeneity factor, and K T is the Tóth pre-exponential constant. However, both models are not suitable for the zeolite FAM Z01-water pair. The adsorption isotherms of the pair exhibits unique S-shape with respect to the relative pressure, defined as the ratio of the absolute pressure to the 89

120 Chapter 4: Adsorption Mass Transport saturation pressure of water at adsorption temperature. As shown below in Section 4.6, the water uptake increases linearly both when relative pressure is small (Henry s region) and approaching unity, and rises sharply in between the both linear regions. In the recent literature, attempts have been made to fit such isotherms. Sun and Chakraborty [169, 170] developed two new models to generate the S-shape with four, and three regression parameters, respectively. However, the two models yield null uptake in the Henry s region, and saturated uptake in the high relative pressure region. A hybrid Henry and Sips isotherm model developed by Kim et al [171], in contrast, well captures the trend in the lower end. Yet the formulation requires nine parameters to regress, which still does not effectively avoid the saturation problem at high relative pressure. In the present work, a novel model is proposed to fit the adsorption isotherms of the zeolite FAM Z01-water pair. As demonstrated below, the model fits accurately the three regions of the isotherms at all experimental conditions. Moreover, the model is not restricted to Type V isotherms. It is able to generate more precise data regression for Type I silica gel-water pairs than the classic DA and Tóth equations. Furthermore, only four parameters are needed to regress for the different types of isotherms. The mathematical form of the novel model is expressed below as, q P P P A e x p ( ) C P P P s s s t 1 e x p ( ) P P s s q 0 P P (4.8) and, 90

121 Chapter 4: Adsorption Mass Transport E c e x p RT (4.9) A 1 e x p ( ) e x p ( ) t C (4.10) where, the alphabet, C, are constants; t is surface heterogeneity factor and E c denotes the characteristic energy of the adsorbent-adsorbate pair. These four parameters are required to calculate in the regression process. The rest of the letters have their usual means. The equation satisfies the conditions of the adsorption thermodynamics as follows. 1) When pressure is far below saturation pressure, the equation reduces to Henry s linear relation, i.e., P at 1, then, e x p ( ) 1, and A C P s P P s q q P P 0 s 2) When pressure is approaching to zero, the adsorbent has null uptake, P at 0, then, P s lim q 0, q P / P s 0 0 3) When pressure is close to saturation, the adsorbate equilibrium uptake reaches its limiting amount at saturation conditions, P at 1, then, P s lim q 1 q P / P s

122 Chapter 4: Adsorption Mass Transport From the results of the statistical rate theory reviewed in Chapter 2 and applying the same technique to develop the classic LF, DA and Tóth equations, the proposed isotherm model in Equation 4.8 can be derived by using an asymmetrical adsorption site energy distribution function shown as: * * ( 1) C A e x p ( ) t 1 * * * * * e x p ( ) 1 1 e x p ( ) t 1 RT 2 * * Ct e x p ( ) (4.11) where the variable β* is a function of the adsorption site energy ε and expressed as, * 2 E c e x p RT (4.12) From Equation 2.27 in Chapter 2, the equilibrium adsorption uptake fraction θ equals to c d. Hence, integrate Equation 4.11, one can obtain, A e x p * d (4.13) t c 1 e x p * * C * * c Invoke ln R T K P, c when, the variable β* becomes, c * 2 E E E e x p c c e x p c K ex p c P R T R T R T (4.14) 92

123 Similar to Equation 2.34 in deriving DA equation, let, Chapter 4: Adsorption Mass Transport c ln (4.15) E R T K P s 1 P s E c K e x p R T (4.16) Thus, * e x p E P P c R T P P s s (4.17) when, the variable β* becomes, * 0 (4.18) Hence, substituting the two boundary conditions in to Equation 4.13, the exact form of Equation 4.8 is yielded. It is emphasized by Equation 4.13 that only the adsorption site energy ranged at (ε c, ) is concerned due to the condensation approximation. Therefore, a constraint imposed on the distribution function that is given in Equation 2.21 becomes, d 1 (4.19) c Since d, and 1 only at P P, one can obtain that particularly s c for the proposed isotherm model of the present work, (4.20) c E c 93

124 Chapter 4: Adsorption Mass Transport 4.4. Results and Discussion Comparison with Literature Data Experimental results of the silica gel-water isotherms from the Hydrosorb analyzer are benchmarked with the literature provided by Ng et al. [33]. Figure 4.3 illustrates the comparison of the current data with the Tóth regression relation given by the literature on silica gel type 3A-water pair. The present batch of type 3A has similar physical properties with the one tested by Ng and co-authors. A good agreement between the results is realized from the figure, with the coefficient of determination (R 2 ) and the normalized root mean square error to the mean experimental data (NRMSE) 4.11 % being observed. The silica gel type RD-water adsorption characteristics of the present work and the literature Tóth regression are shown in Figure 4.4. It is noted that the current type RD is in the powder form grinded originally from granules of the same type used in the literature. The surface feature and pore distribution of the powder may differ from the granular type, though adsorption mechanism remains unchanged. As expected, isotherms of the current type RD powder deviate slightly with the previous work. A reasonable R 2 value of 0.97 and NRMSE of % are noticed. 94

125 Adsorbate Uptake, q* [kg/kg of Adsorbent] Adsorbate Uptate, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C Present 35 C present 40 C Present 30 C Ng et al (2001) 35 C Ng et al (2001) 40 C Ng et al (2001) Pressure [kpa] Figure 4.3: Comparison of the adsorption isotherms of silica gel type 3Awater pair between the present experimental data and Tóth regression relation provided by Ng et al. [33]. The current data are displayed with 5% error bar C Present 35 C Present 40 C Present 30 C Ng et al (2001) 35 C Ng et al (2001) 40 C Ng et al (2001) Pressure [kpa] Figure 4.4: Comparison of the adsorption isotherms of silica gel type RDwater pair between the present experimental data and Tóth regression relation provided by Ng et al. [33]. The current data are displayed with 5% error bar. 95

126 Binder Effect on Silica Gel Type 3A Adsorption Chapter 4: Adsorption Mass Transport The influence on the silica gel type 3A-water adsorption due to the addition of 3.3 adsorbent wt% HEC is described in this section. Prior engaging the binder, the water uptake of the pure type 3A at various temperatures are first understood, and presented in Figure 4.5. The vertical axis represents mass of water vapor uptake per kg of silica gel, and the horizontal axis is absolute pressure. The data are presented in Appendix A. The isotherms typically exhibit Type I feature in the experimental conditions. Particularly in Figure 4.5(a), the data are fitted by the classic Tóth and DA isotherm models. It is found that Tóth is more suitable than DA, as the former yields R 2 value and NRMSE 2.63 % in contrast with the latter s and 5.27 % respectively. The DA equation incurs large deviation with the experimental values at low pressure Henry s region. Comparably, Figure 4.5(b) illustrates the data regression by the proposed model of Equation 4.8. The model very well captures the isotherm characteristics at full pressure range. Its R 2 and regression error are and 2.23 % correspondingly which improves the accuracy as compared to the Tóth model. Table 4.1 summarizes the regression parameters of the respective models. The water equilibrium uptake on the silica gel type 3A with respect to relative pressure and the regression by the proposed model are plotted in Figure 4.6. It is interesting to observe that the isotherms of various temperatures fall onto the same trend line, which implies that the isotherms out of the experimental temperature range can be interpolated or extrapolated from the trend line. This is especially useful in the design and performance 96

127 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport prediction of an adsorption based instrument when precise isotherm data are not available. On the other hand, the figure clearly indicates the Henry s region occurring at below relative pressure 0.7, in which the uptake is linearly proportional to the pressure due to monolayer adsorption. Moreover, the uptake at saturation vapor pressure, q 0, which are formulated in various isotherm models, can be determined from the graph. For the silica gel type 3A-water pair in the experimental conditions, q 0 equals to 0.43 kg/kg of adsorbent C 30 C 35 C 40 C 45 C Tóth DA Pressure [kpa] (a) Regression by DA and Tóth models 97

128 Adsorbate Uptake, q* [kg/kg of Adsorbent] Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Proposed model Pressure [kpa] (b) Regression by the proposed model Figure 4.5: Experimental water adsorption equilibrium uptake on silica gel type 3A at temperatures from 25~45 o C. The data are regressed with (a) the Tóth and DA models, and (b) the proposed model of this work. The present data are displayed with 5% error bar C 30 C 35 C 40 C 45 C Proposed model Relative Pressure, P/P s [-] Figure 4.6: Experimental water adsorption equilibrium uptake on silica gel type 3A against relative pressure at temperatures from 25~45 o C. 98

129 Chapter 4: Adsorption Mass Transport When binder is used to stick the silica gel solids together, it is inevitable that the binder blocks the porous structures on the silica gel surface. Since the adsorption is a surface phenomenon, the capacity of uptake may be altered consequently. This can be effectively reflected by the equilibrium uptake amount on the adsorption isotherms. Figure 4.7 plots the isotherms of water on silica gel type 3A with 3.3 adsorbent wt% of HEC at several temperatures. Comparing the data with the pure type 3A-water isotherms shown in Figure 4.5, one may easily conclude that profile of the isotherm is changed due to the presence of the HEC. The relation of the water uptake and pressure at middle pressure range is no longer linear, instead, a concave trend line is observed due to binder coverage on the pores of different sizes. Neither Tóth nor DA equation are able to capture the concave feature, as shown in Figure 4.7(a). As a result, both classical models yield relatively high error, with 9.84 % and 9.63 %, respectively. In contrast, the regression is significantly improved by the proposed model in Figure 4.7(b) which reduces the error to 4.39 %, and offers R 2 value The parameters of regression for the respective models are listed in Table 4.1. The data are shown in Appendix A. Another significant effect from the binder is that it considerably reduces the adsorption capacity of the adsorbent. As shown in Figure 4.8 which illustrates the water uptake respect to the relative pressure, the amount of equilibrium uptake at saturation vapor pressure decreases to kg/kg of adsorbent. On the other hand, similar to the pure silica gel type 3A, the water adsorption isotherms of the binder added type 3A at various temperatures against relative pressure also coincide to a single trend line. Owing to this feature, it is able to compare general aspects of the silica gel type 3A-water 99

130 Chapter 4: Adsorption Mass Transport isotherm with and without HEC binder at a typical temperature. Figure 4.9 plots the isotherms at 35 o C for both samples. It is observed that a significant reduction is shown on the water uptake capacity of HEC added silica gel as compared to the pure silica gel sample. The reduction distribution at increasing relative pressure is given in Figure The uptake reduction is highest up to 38% to 43 % at relative pressure 0.4, whereas lower at both ends. An average reduction of 27.3 % is noted though the experimental conditions. In the design of thermally driven adsorption chillers in which adsorbent is frequently swapped between adsorption and desorption, the uptake difference Δq*, rather than the absolute amount of uptake, is used to represent the adsorption capacity. This can be conveniently analyzed from the trend line in Figure 4.9. For instance, for a silica gel-water adsorption chiller that is operated in a typical condition of evaporator temperature 12 o C, and adsorption bed temperature 35 o C, the relative pressure of adsorption equals to the water saturation pressure at 12 o C divided by that at 35 o C, that is, Similarly, if the condenser and desorption bed temperature are 35 o C and 75 o C respectively, the relative pressure of desorption is As such, the HEC added silica gel type 3A only offers kg/kg of adsorbent uptake difference, which is half of the adsorption capacity of the normal type 3A, as indicated in Figure 4.9. This implies a decreased mass transport in the adsorption system. However, the mass transport in the adsorption system is not solely due to the isotherm data, but also influenced by the heat transfer and cycle time, etc. The net effect of the HEC binder on the silica gel is further discussed in Section 4.5 below. 100

131 Adsorbate Uptake, q* [kg / kg of Adsorbent] Adsorbate Uptake, q* [kg / kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Tóth DA Pressure [kpa] (a) Regression by DA and Tóth models C 30 C 35 C 40 C 45 C Proposed model Pressure [kpa] (b) Regression by the proposed model Figure 4.7: Experimental water adsorption equilibrium uptake on silica gel type 3A added with 3.3 adsorbent weight % HEC at temperatures from 25~45 o C. The data are regressed with (a) the Tóth model and DA model, and (b) the proposed model of this work. The present data are displayed with 5% error bar. 101

132 Adsorbate Uptake, q* [kg/kg of Adsorbent] Adsorbate Uptake, q* [kg / kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Proposed model Relative Pressure, P/P s [-] Figure 4.8: Experimental water adsorption equilibrium uptake on silica gel type 3A added with 3.3 adsorbent weight % HEC against relative pressure at temperatures from 25~45 o C Silica Gel 3A Silica Gel 3A with 3.3 wt% HEC Proposed model Δq* = 0.05 Δq* = Relative Pressure, P/P s [-] Figure 4.9: Comparison of experimental water adsorption uptake against relative pressure for a typical temperature 35 o C on pure silica gel type 3A and silica gel type 3A added with 3.3 adsorbent weight % HEC. 102

133 Adsorbate Uptake Reduction [-] Chapter 4: Adsorption Mass Transport 50% 25 C 30 C 35 C 40 C 45 C 45% 40% 35% 30% 25% Average Reduction = 27.3 % 20% 15% 10% 5% 0% Relative Pressure, P/P s [-] Figure 4.10: Distribution of water uptake reduction due to addition of HEC binder onto silica gel type 3A. According to Equation 4.11, the adsorption site energy distributions of silica gel type 3A with and without HEC are plotted in Figure In the figure the distribution at a typical temperature 35 o C is used for both samples. Because of the effect of the binder that alters the adsorbent microporous structure, the energy distribution is also changed with respect to the pure silica gel. It is also noted that when the site energy is approaching the equilibrium energy ε c, the probability of the site energy increase instead of continuing the decline to zero. This is a consequence of the condensation approximation as described in Figure 2.5 in Chapter 2. Due to the approximation, the uptake on the homogeneous pieces of the surface that have energy slightly above ε c is increased to unity. Subsequently, the probability of the site having the energy is also forced to rise to satisfy the condition stated in Equation

134 Chapter 4: Adsorption Mass Transport 0.06% Silica Gel 3A Silica Gel 3A with 3.3 wt% HEC 0.05% 0.04% 0.03% 0.02% 0.01% 0.00% , [kj/kg] Figure 4.11: Adsorption site energy distribution of the proposed isotherm model for silica gel type 3A with and without 3.3 adsorbent weight % HEC addition at a typical temperature 35 o C Binder Effect on Silica Gel Type RD Powder Adsorption In this section, the same analysis technique is utilized to investigate the binder effect on the silica gel type RD powder adsorption characteristics. Type RD offers comparable water adsorption isotherms as type 3A. Figure 4.12 indicates the type RD powder-water uptake data regressed by Tóth and DA equation in Figure 4.12(a), and the proposed model (Equation 4.8) in Figure 4.12(b). The data are tabulated in Appendix A. The parameters of regression are also listed in Table 4.1. Once again, the proposed isotherm equation is demonstrated more accurate for the isotherm regression. The isotherm data with respect to the relative pressure are plotted in Figure

135 Chapter 4: Adsorption Mass Transport Table 4.1: Value of the regression parameters of Tóth, DA, and proposed isotherm models for silica gel type 3A, type RD powder with and without HEC addition Adsorbent Tóth Model DA Model Proposed Model Silica gel type 3A Silica gel type 3A & 3.3 adsorbent wt% HEC Silica gel type RD powder Silica gel type RD powder & 3.3 adsorbent wt% HEC q 0 (kg/kg) 0.43 q 0 (kg/kg) 0.43 q 0 (kg/kg) 0.43 Q st (kj/kg) 2522 Ec (kj/kg) Ec (kj/kg) K T (kpa -1 ) 4.5x10-12 γ (-) (-) 2.64x10-6 t (-) C (-) 1.24 t (-) *R R R **Error 2.63% Error 5.27 % Error 2.23 % q 0 (kg/kg) q 0 (kg/kg) q 0 (kg/kg) Q st (kj/kg) Ec (kj/kg) Ec (kj/kg) K T (kpa -1 ) 2.5x10-12 γ (-) (-) 1.0x10-6 t (-) C (-) t (-) R R R Error 9.84 % Error 9.63 % Error 4.39 % q 0 (kg/kg) q 0 (kg/kg) q 0 (kg/kg) Q st (kj/kg) Ec (kj/kg) Ec (kj/kg) K T (kpa -1 ) 4.5x10-12 γ (-) (-) 2.54x10-4 t (-) 10.3 C (-) t (-) R R R Error 6.6 % Error 6.85 % Error 3.15 % q 0 (kg/kg) q 0 (kg/kg) q 0 (kg/kg) Q st (kj/kg) Ec (kj/kg) Ec (kj/kg) K T (kpa -1 ) 4.5x10-12 γ (-) 1.46 (-) 8.27x10-4 t (-) C (-) t (-) R R R Error 6.42 % Error 6.61 % Error 3.08 % *Coefficient of determination ** Normalized root mean square error to the mean experimental data 105

136 Adsorbate Uptake, q* [kg/kg of Adsorbent] Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Tóth DA Pressure [kpa] (a) Regression by DA and Tóth models C 30 C 35 C 40 C 45 C Proposed model Pressure [kpa] (b) Regression by the proposed model Figure 4.12: Experimental water adsorption equilibrium uptake on silica gel type RD powder at temperatures from 25~45 o C. The data are regressed with (a) the Tóth and DA model, and (b) the proposed model of this work. The present data are displayed with 5% error bar. 106

137 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Proposed model Relative Pressure, P/P s [-] Figure 4.13: Experimental water adsorption equilibrium uptake on silica gel type RD powder against relative pressure at temperatures from 25~45 o C. The water adsorption isotherms of silica gel type RD powder added with 3.3 adsorbent wt% HEC against absolute pressure and relative pressure are presented in Figure 4.14 and The former figure provides the Tóth, DA fitting, and more accurate regression with 3.08 % error from the proposed model. The detailed regression parameter is summarized in Table 4.1. The Data are tabulated in Appendix A. Comparing the water adsorption characteristics of pure silica gel type RD powder and that added with 3.3 adsorbent wt% HEC, negligible effect due to the binder addition is observed. This is clearer in Figure 4.16 for a typical isotherm at 35 o C for both samples. The binder added sample shows little adsorption reduction at all tested pressure range. Consequently, the binder added sample offers the same equilibrium uptake difference at typical adsorption chiller operation conditions. The water uptake reduction due to the binder coverage at various temperatures is shown in Figure The next figure (Figure 4.18) plots the adsorption site 107

138 Chapter 4: Adsorption Mass Transport energy distribution of the two samples at 35 o C. The two distribution curves are almost coincident to each other again because of the null effect of the binder on the adsorption isotherms. Moreover, the pattern of the distribution is close to that of silica gel type 3A, since both silica gels belong to the same substance. Since HEC has negligible water adsorption capacity, its binding effect inevitably covers the water affiliative surface structure, and reduces the adsorption capacity of the silica gel. Silica gel type 3A has much larger average particle diameter of 0.2 mm than the type RD powder s 0.07 mm, as explained in Section 2 of Chapter 3. In the case of silica gel type 3A, its surface area is largely due to the surface porous structures, rather than the area offered inherently by its particle size. On the contrary, the surface area due to inherent particle size plays a much bigger role in the silica gel type RD powder. Hence, when the same amount of the HEC binder is used, the surface area of type 3A granules is more severely reduced than the type RD powder. As a result, water adsorption capacity is proportionally reduced for the type 3A. In conclusion, the fine powder form silica gel type RD with 3.3 adsorbent wt% HEC is more suitable to retain the water adsorption capacity and yet serve the binding purpose. 108

139 Adsorbate Uptake, q* [kg/kg of Adsorbent] Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Tóth DA Pressure [kpa] (a) Regression by DA and Tóth models C 30 C 35 C 40 C 45 C Proposed model Pressure [kpa] (b) Regression by the proposed model Figure 4.14: Experimental water adsorption equilibrium uptake on silica gel type RD powder added with 3.3 adsorbent weight % HEC at temperatures from 25~45 o C. The data are regressed with (a) the Tóth and DA model, and (b) the proposed model of this work. The present data are displayed with 5% error bar. 109

140 Adsorbate Uptake, q* [kg/kg of Adsorbent] Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Proposed model Relative Pressure, P/P s [-] Figure 4.15: Experimental water adsorption equilibrium uptake on silica gel type RD powder added with 3.3 adsorbent weight % HEC against relative pressure at temperatures from 25~45 o C Silica Gel RD Powder Silica Gel RD Powder with 3.3 wt% HEC Proposed model Δq* = 0.05 Δq* = Relative Pressure, P/P s [-] Figure 4.16: Comparison of experimental water adsorption uptake against relative pressure for a typical temperature 35 o C on pure silica gel type RD powder and silica gel type RD powder added with 3.3 adsorbent weight % HEC. 110

141 Adsorbate Uptake Reduction [-] Chapter 4: Adsorption Mass Transport 25% 25 C 30 C 35 C 40 C 45 C 20% 15% 10% 5% 0% -5% -10% Average Reduction = 1.6 % -15% -20% -25% Relative Pressure, P/P s [kpa] Figure 4.17: Distribution of water uptake reduction due to addition of HEC binder into silica gel type RD powder. 0.05% 0.04% 0.04% 0.03% 0.03% 0.02% 0.02% 0.01% 0.01% 0.00% Silica Gel RD Powder Silica Gel RD Powder with 3.3 wt% HEC , [kj/kg] Figure 4.18: Adsorption site energy distribution of the proposed isotherm model for silica gel type RD powder with and without 3.3 adsorbent weight % HEC addition at a typical temperature 35 o C. 111

142 Chapter 4: Adsorption Mass Transport Estimation of Uptake Reduction from Surface Coverage From the BET surface area and isotherm measurements, it is found that the average reduction of the water equilibrium uptake on the silica gel due to binder can be estimated from the surface area reduction. As summarized in Table 4.2, HEC of 3.3 adsorbent wt% causes approximately the same reduction on the surface area and the adsorption capacity of the original silica gel type 3A and type RD powder. Since the microporous structures on the surface provide adsorption sites to accommodate the adsorbed water molecules, the water equilibrium uptake is proportional to the surface area of the silica gel at given temperature and pressure. This validates the selection method of optimum binder weight percentage through BET surface area test, as described in Section 3.2, Chapter 3. However, the reduction on the equilibrium uptake is not uniform for all pressures. It is recommended to conduct adsorption isotherm measurement for precise binder influence if desired. Table 4.2: Summary of surface area and average uptake reduction on the silica gels as a result of 3.3 adsorbent wt% HEC Adsorbent BET surface area [m 2 /g] without HEC with HEC Surface area reduction Average uptake reduction Type 3A % 27.3 % Type RD Powder % 1.6 % 112

143 Chapter 4: Adsorption Mass Transport 4.5. Net Binder Influence on the Adsorption Mass Transport In Chapter 3, the binder hydroxyethyl cellulose has been proven to significantly enhance the heat transfer rate of the adsorbent embedded heat exchanger. It consequently lowers the temperature of silica gel during the adsorption process. From the nature of the silica gel-water isotherm described in Section 4.4, low temperature is favourable to obtain more water uptake. As such, the enhancement of heat transfer indirectly promotes the water adsorption. The same benefits is also applied to the desorption process in which higher heat transfer rate increases the regeneration temperature, leading to more complete water removal. However, diminished the surface area and microporous volume of the adsorbents are observed due to the coverage of the binder on the silica gel surface. The amount of equilibrium water uptake is reduced accordingly. Hence, the net effect of binder on the adsorbate mass transport is determined by the competition of the two phenomena. Substitute the profiles of the silica gel average temperature of the three adsorption heat transfer cases described in Chapter 3 into the kinetics equations as summarized below in Table 4.3, the instantaneous rate and cumulative quantity of the water uptake during adsorption processes can be computed. Figure 4.19(a) illustrates the rate of uptake in the silica gel type 3A coated heat exchanger at different cooling water temperatures. The highest rate takes place in the beginning of the process due to the high affinity of silica gel surface to the water. The rate decreases as the water uptake approaches saturation. On the other hand, it is noticed that in the first 30 seconds, the rate is higher in the hotter cooling water cases. The trend is yet reversed in the later part of the processes. A similar phenomenon is observed in the silica gel type 113

144 Chapter 4: Adsorption Mass Transport RD powder coated heat exchanger as shown in Figure 4.19(b). However, this is not repeated in the base case in which the superior of the uptake rate in the low cooling water temperature is generally maintained through the processes (See Figure 4.19(c)). Table 4.3: Adsorption kinetics equations for the computation of instantaneous and cumulative water uptake * * q ( t ) q q q e x p t in i d q ( t ) dt 15D 2 R * q q e x p t in i p so E a ex p R T Equations where, D so = m 2 /s E a = kj/kmol R p = 0.2 mm for silica gel type 3A & RD powder = 0.25 mm for silica gel type RD granules References Equation 2.40, 2.41 & 2.42 in Chapter 2 By plotting the instantaneous rate of uptake of the three cases in the same figure, the net influence of the binder can be clearly recognized. This is presented in Figure 4.20 for typical scenario of 35 o C cooling water. Both binder applied cases exhibit significantly higher water uptake rate than the base case. This implies the dominance of temperature in the water adsorption. Low adsorption temperature benefitted from the binder promoted heat transfer simultaneously improves the mass transport. In addition, the type 3A coated heat exchanger has slower uptake rate than the type RD powder case, indicating the negative influence of the binder on the mass transport due to the surface coverage. 114

145 Rate of Uptake, dq/dt [g/kg of adsorbent/s] Rate of Uptake [g/kg of adsorbent/s] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C Time [s] (a) Silica gel type 3A coated heat exchanger by 3.3 adsorbent wt% HEC 0.6 RD 25 C RD 30 C RD 35 C RD 40 C Time [s] (b) Silica gel type RD powder coated heat exchanger by 3.3 adsorbent wt% HEC 115

146 Rate of Uptake [g/kg of adsorbent/s] Rate of Uptake, dq/dt [g/kg of adsorbent/s] Chapter 4: Adsorption Mass Transport Base 25 C Base 30 C Base 35 C Base 40 C Time [s] (c) Base case: silica gel type RD granule packed heat exchanger by wire mesh Figure 4.19: Instantaneous rate of water uptake on the (a) silica gel type 3A coated, (b) silica gel type RD powder coated heat exchanger, and (c) the base case during the adsorption heat transfer process at various cooling water temperatures 0.6 RD 35 C Base 35 C 35 C Time [s] Figure 4.20: Comparison of instantaneous rate of uptake at 35 o C cooling water for silica gel type 3A, RD powder coated heat exchanger and the base case 116

147 Chapter 4: Adsorption Mass Transport The cumulative water uptake on the adsorbents at various cooling water temperatures for the three adsorption heat transfer cases are shown below. Figure 4.21(a) represents the type 3A case. The results indicate that the silica gel at lower temperature is able to adsorb more water, yet takes longer time to reach equilibrium. The same pattern is repeated in Figure 4.21(b) for the type RD powder case and Figure 4.21(c) for the base case. A comparison of the cumulative water uptake among the three adsorption heat transfer cases at 35 o C cooling water is shown in Figure A faster accumulation of adsorbed water is realized in both binder added cases, attributing to the higher instantaneous rate of uptake than the base case. This will help tremendously increase the cooling capacity of a conventional adsorption chiller implementing the base case method by shorten the operation cycle time. For example, if the chiller is operated at a typical 400 s adsorption / desorption cycle time, the same amount of mass transport can be achieved in less than 200 s by using type RD powder coating method. In other words, the specific cooling capacity, defined as the cooling capacity per unit mass of adsorbent, will be doubled for the latter. Due to such benefit, the footprint of the adsorption chiller can be significantly reduced. In addition, even with reduced adsorption capacity by the binder, the silica gel type 3A case is still favourable than the conventional method for operation cycle time less than 650 s. 117

148 Adsorbate Uptake [kg / kg of adsorbent] Adsorbate Uptake [kg/kg of adsorbent] Chapter 4: Adsorption Mass Transport 25 C 30 C 35 C 40 C Time [s] (a) Silica gel type 3A coated heat exchanger by 3.3 adsorbent wt% HEC RD 25 C RD 30 C RD 35 C RD 40 C Time [s] (b) Silica gel type RD powder coated heat exchanger by 3.3 adsorbent wt% HEC 118

149 Adsorbate Uptake [kg/kg of adsorbent] Adsorbate Uptake [kg/kg of adsorbent] Chapter 4: Adsorption Mass Transport Base 25 C Base 30 C Base 35 C Base 40 C Time [s] (c) Base case: silica gel type RD granule packed heat exchanger by wire mesh Figure 4.21: Cumulative water uptake on the (a) silica gel type 3A coated, (b) silica gel type RD powder coated heat exchanger, and (c) the base case during the adsorption heat transfer process at various cooling water temperatures RD 35 C Base 35 C 35 C Shorter cycle time for the same amount of water uptake Time [s] Figure 4.22: Comparison of cumulative water uptake at 35 o C cooling water for silica gel type 3A, RD powder coated heat exchanger and the base case 119

150 4.6. A New Water Adsorbent Zeolite FAM Z01 Chapter 4: Adsorption Mass Transport Adsorbent Characteristics In this section, a novel water vapor adsorbent, namely Zeolite FAM Z01 (Composition: Fe x Al y P z O 2 nh 2 O, x = , y = , z = , n = 0 1), is introduced. It is an iron aluminophosphate based material that belongs to a family of water adsorption zeolite entitled as Functional Adsorbent Material (FAM) originally developed by Kakiuchi et al.[172]. The same family also includes silicoaluminophosphate based zeolite Z02 [173] and aluminophosphate based zeolite Z05 [174]. The zeolite FAM Z01 sample employed in the present work is supplied by Mitsubishi Plastics, Inc. under the brand name AQSOA. The material has a one-dimensional AFI type molecular sieve structure with a molecular window of diameter 0.73nm. Only molecules smaller than this dimension such as water molecules are permitted free migration though the window. FAM Z01 owns S-shape water vapor adsorption isotherms with excellent durability over 200,000 adsorption / desorption cycles and little hysteresis behavior. Adsorption takes place dramatically in a narrow range of relative pressure while out of which the amount of vapor uptake possesses little changes with respect to the relative pressure [175]. This is in contrast with the linear behavior observed for the silica gel-water adsorption. A field emission scanning electron microscopic (FESEM) photo of Z01 is shown in Figure The thermophysical properties of the zeolite are summarized in Table 4.4 [175]. 120

151 Chapter 4: Adsorption Mass Transport Figure 4.23: Field emission scanning electron microscopic (FESEM) photos of zeolite FAM Z01 Table 4.4: Thermophysical properties of zeolite FAM Z01 Properties Value BET surface area [m 2 /g] Average particle diameter [μm] 100 Porous volume [ml/g] Average pore diameter (Å) Apparent density [kg/m 3 ] Thermal conductivity [W/m.K] (30 o C) (70 o C) Heat of adsorption (H 2 O) [kj/kg of H 2 O] 3110 (25 o C) Specific heat capacity [kj/kg.k] (30 o C) (70 o C) 121

152 Chapter 4: Adsorption Mass Transport Water Adsorption Characteristics with and without Binder The water adsorption isotherms of zeolite FAM Z01 exhibit typically Type V isotherm characteristics. They are experimentally investigated in this section through the volumetric based Hydrosorb analyzer apparatus. The measurement covers the typical adsorption temperatures found in the adsorption chiller, i.e., 25 o C to 45 o C with a 5 o C increment in the range. The same test is repeated for the zeolite FAM Z01 added with 3.3 adsorbent wt% HEC. The uptake data of the both samples are fitted by the proposed model described in Equation 4.8. Figure 4.24 shows the zeolite FAM Z01-water adsorption isotherms with respect the absolute pressure at various temperatures. It is clearly observed that the water uptake increases sharply in a very narrow pressure range for all adsorption temperatures. Outside this pressure range, the uptake increments much less with respect to the elevating pressure. Moreover, the uptake increases linearly when the pressure is approaching the saturation pressure of the water. The water uptake data plotted against relative pressures are shown in Figure The figure shows that the kick-off pressure range at which the sharp uptake increase takes place shifts towards right hand side as the adsorption temperature rises. The range falls typically between the relative pressures 0.15 to This is especially beneficial to the adsorption machines which operate in the similar relative pressure range. The dramatic increase of the adsorbent uptake capacity permits large mass transport. From Figure 4.25, the limiting water uptake on the Z01 at the saturation pressure of respective adsorption temperatures is approximately kg/kg of adsorbent. Its S-shape Type V characteristics are accurately fitted by the 122

153 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport proposed model given in Equation 4.8. The model not only predicts well the kick-off pressure range, the upward trend of the isotherm at lower and higher end of the pressure is also well captured. Generally the model provides high regression accuracy with the coefficient of determination of 0.993, and normalized error of 6.05% at the experimental conditions. A summary of the regression parameters is provided in Table 4.5. The experimental data are tabulated in the Appendix B C 30 C 35 C 40 C 45 C Proposed model Pressure [kpa] Figure 4.24: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 at temperatures from 25~45 o C with regression by the proposed model of this work. The present data are displayed with 5% error bar. 123

154 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport 25 C 30 C 35 C 40 C 45 C Proposed model Relative Pressure, P/P s [-] Figure 4.25: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 against relative pressure at temperatures from 25~45 o C. Table 4.5: Value of the regression parameters of the proposed isotherm models for zeolite FAM Z01 with and without HEC addition Proposed Model Parameters Zeolite Z01 Zeolite Z01 & 3.3 adsorbent wt% HEC q 0 (kg/kg) Ec (kj/kg) (-) 6.59 x x 10-7 C (-) t (-) *R **Error 6.05 % 5.89 % *Coefficient of determination ** Normalized root mean square error to the mean experimental data The water adsorption isotherms of the zeolite FAM Z01 added with 3.3 adsorbent wt% HEC against absolute vapor pressure at various adsorption temperatures are displayed in Figure The same data plotted with respect to relative pressure is illustrated in Figure Both figures show similar 124

155 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport characteristics as the pure Z01-water isotherms. This indicates a null effect of the binder on the adsorption mechanism of the zeolite Z01. The proposed model is also able to accurately fit the isotherm data. As shown in Table 4.5, it yields R 2 value and NRMSE error 5.89% in the full relative pressure range of the experimental adsorption conditions. The regression parameters of the model are also listed in the same table. The data are given in Appendix B C 30 C 35 C 40 C 45 C Proposed model Pressure [kpa] Figure 4.26: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 added with 3.3 adsorbent weight % HEC at temperatures from 25~45 o C with regression by the proposed model of this work. The present data are displayed with 5% error bar. 125

156 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport C 30 C 35 C 40 C 45 C Proposed model Relative Pressure, P/P s [-] Figure 4.27: Experimental water adsorption equilibrium uptake on zeolite FAM Z01 added with 3.3 adsorbent weight % HEC against relative pressure at temperatures from 25~45 o C. Known that the water adsorption isotherms of the zeolite samples with respect to relative pressure for various temperatures coincide with each other with only small deviation at kick-off pressures, a typical temperature 35 o C is used to represent the adsorption capacity of the pure and binder added zeolite FAM Z01 samples and plotted in Figure Similar to the silica gel type RD powder case, as expected, the water uptake of the HEC added Z01 has little reduction in comparison with the pure Z01 due to its fine powdered form. Both samples deliver 0.17 kg/kg of adsorbent uptake difference in a typical adsorption chiller operation range of 0.15 to 0.25 relative pressures. Besides, the adsorption site energy distribution of the proposed isotherm model in Equation 4.11 for both zeolite samples is also almost the same, as shown in Figure They are however different from the silica gels due to the dissimilar element composition and adsorption mechanism. 126

157 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport Zeolite Z01 Zeolite Z01 with 3.3 wt% HEC Proposed model Δq* = Relative Pressure, P/Ps [-] Figure 4.28: Comparison of experimental water adsorption uptake against relative pressure for a typical temperature 35 o C on pure and 3.3 adsorbent weight % HEC added zeolite FAM Z % 0.14% 0.12% 0.10% 0.08% 0.06% 0.04% 0.02% Zeolite Z01 Zeolite Z01 with 3.3 wt% HEC 0.00% , [kj/kg] Figure 4.29: Adsorption site energy distribution of the proposed isotherm model for zeolite FAM Z01 with and without 3.3 adsorbent weight % HEC addition at a typical temperature 35 o C. 127

158 Chapter 4: Adsorption Mass Transport To understand which adsorbent is more suitable for the adsorption chiller, a comparison of the water adsorption capacity for the three types of adsorbent introduced in the present work, namely, zeolite FAM Z01, silica gel type 3A and type RD powder is provided in the Figure The isotherm each of the adsorbent at 35 o C is plotted. From the figure, one can observe firstly the difference between the Type I and Type V adsorption characteristics. As mentioned before, both types of silica gel belong to Type I group that is concave to the pressure axis, whereas the zeolite s Type V feature exhibit S- shape. Secondly, in terms of the water uptake, the two types of silica gel are comparable. Zeolite FAM Z01 has more water uptake over the silica gels only at relative pressure 0.2 to 0.35, out of which is far lower. For the limiting uptake when relative pressure equals to 1, the zeolite is half of the silica gels. However, the zeolite is more suitable than silica gel to cooperate with water as working pair for adsorption chiller. First of all, this is due to the fact that for the uptake difference at typical adsorption chiller operation range 0.15 to 0.25 relative pressures, the zeolite FAM Z01 is able to migrate amount of water 3.4 times that of the silica gels. This means for the same design capacity, the zeolite FAM Z01 equipped chiller has much smaller size than the conventional silica gel-water chiller. It also means for the same amount of the adsorbent, the zeolite FAM Z01 can produce much more cooling capacity. This advantage well addresses the drawback of large footprint area faced by the conventional silica gel-water adsorption chiller. Secondly, the cooling capacity produced by the zeolite FAM Z01 equipped chiller is approximately a constant in a typical operation range, given that the uptake difference experiences little changes when the relative pressures shift. This is an another 128

159 Adsorbate Uptake, q* [kg/kg of Adsorbent] Chapter 4: Adsorption Mass Transport advantage over the silica gel-water adsorption chiller whose cooling capacity deviates significantly at different operation conditions. As such, it is easier to design the accessories and conjugate cogeneration plants for the Z01 adsorption chiller Zeolite Z01 Silica Gel RD Powder Silica Gel 3A Proposed model Δq* = 0.05 Δq* = Relative Pressure, P/P s [-] Figure 4.30: Comparison of water uptake capacity against relative pressure for a typical adsorption temperature 35 o C on zeolite FAM Z01, silica gel type 3A and RD powder 129

160 Chapter 4: Adsorption Mass Transport 4.7. Molecular Dynamics Simulation on the Zeolite FAM Z01- Water Adsorption Modeling of Molecular Structure In the study of zeolite FAM Z01 and silica gels on the water adsorption, questions arose from the distinct behaviors of the two types of adsorbent. What could be the reason for the unique S-shape observed in the zeolite FAM Z01-water isotherms? Owning a much smaller BET surface area than the silica gel, the water uptake on the zeolite FAM Z01 at certain pressures is yet higher. All these phenomena imply a different adsorption mechanism for the novel zeolite as compared to the surface micropore filling on the conventional silica gel. This motivates a further investigation at molecular level to understand the interaction between the water molecules the zeolite structure. It is aimed to simulate the behavior of the water molecules on the novel zeolite structure through molecular dynamics (MD) simulation, and hence to predict the zeolite FAM Z01-water adsorption characteristics. This is an on-going work to establish the connections between the simulation at molecular level and experimental adsorbate uptake data obtained at macro scale, and provide fundamental explanation on the adsorption science. Molecular dynamics is a computational method that describes the timedependent and equilibrium interactions between the molecules. It computes the bonded and nonbonded forces and determines the positions and velocities of the molecules through Newton s equation of motion. The bonded forces include the bond stretch, bending and rotation. The nonbonded forces comprise of Van der Waals forces and electrostatic forces. Since the 130

161 Chapter 4: Adsorption Mass Transport adsorption process involves no chemical reaction between the substances, the MD simulation only utilizes only the nonbonded force field. Prior to simulation on the adsorption behavior, the virtual substance must be constructed. Hence it is necessary to understand the macular structure, the element type and ratio of the zeolite FAM Z01. The zeolite family has more 180 types of molecular structures with various pore topologies [176]. It is known that zeolite FAM Z01 has AFI structure type. Its elemental composition is obtained from Energy-dispersive X-ray (EDX) test. Figure 4.31 shows the EDX test result of the Z01 over a 250 μm x 200 μm sample area. It indicates the zeolite is mainly made of aluminium (Al), phosphorous (P), iron (Fe) and oxygen (O). The composition ratio of each element is listed in Table 4.6. Figure 4.31: Elemental composition of zeolite FAM Z01 from Energydispersive X-ray (EDX) test on a 250 μm x 200 μm sample area 131

162 Chapter 4: Adsorption Mass Transport Table 4.6: Weight and atomic ratio of each element in the zeolite FAM Z01 Element Weight % Atomic % O K Al K P K Fe K Total The virtual zeolite FAM Z01 model is constructed in HyperChem molecular modeling environment. The original AFI type zoelite structure is provided by the Database of Zeolite Structures in the International Zeolite Association (IZA-SC) Website 2. Figure 4.32 shows the molecular structure model of the zeolite FAM Z01 developed in the present work. In this model, the atomic ratio of Al and P is 1:1. Both atoms substitution follows the Lowenstein Rule, which states that only one tetrahedron center can be occupied by aluminium when two tetrahedra are joined by an oxygen bridge; the other center must be taken up by small ion of electrovalence 4 or more, for instance, silica and phosphorus, etc [177]. In other words, there is no Al-O-Al structure in the molecular framework. The maximum ratio of Al atom substitution is no more than 50 %. Moreover, there are 60 iron atom substitutions that carry +4 charges to neutralize the net charge of the Z01 framework. The surface of the framework is covered by hydroxide. The elemental composition used in the Z01 molecular modeling is summarized in Table 4.7. The composition is aligned with the EDX test results. 2 International Zeolite Association (IZA-SC) Website: 132

163 Chapter 4: Adsorption Mass Transport Figure 4.32: AFI type molecular framework of zeolite FAM Z01. (Yellow: Al, purple: P, cyan balls: Fe, red: O, white: H) Table 4.7: Elemental composition used in the molecular modeling of zeolite FAM Z01 Element type Atom number Atom charge Total charge Atom weight Total weight Atomic weight % Aluminium (Al) Phosphorous (P) Iron (Fe) Oxygen (O) Hydrogen (H) Net Charge: 0 Total Mass:

164 Chapter 4: Adsorption Mass Transport Water Transport in the Zeolite FAM Z01 Framework In the molecular structure of the zeolite FAM Z01, four types of molecular window has been identified, namely, the small, medium, large channel and inner pore, as shown in Figure The first three channels are named according to the size. The inner pore is located on the inner wall of the large channels. These molecular windows potentially permit the transport of water molecules. Since the water uptake on the Z01 increases dramatically at 0.15 to 0.25 relative pressure ranges, the molecular windows may be responsible for the accommodation of the large amount of the incoming water molecules. A molecular dynamics simulation is conducted to understand the role of the four types of the molecular window in the water adsorption. Inner Pore TIP3P Water Probe Molecule Small Channel Medium Channel Large Channel Figure 4.33: Illustration of the four types of molecular window in the framework of zeolite FAM Z01, namely, large channel, medium channel, small channel and inner pore 134

165 Chapter 4: Adsorption Mass Transport In the modeling approach, a single "probe water molecule" (PWM) is assigned a velocity vector towards the molecular window opening. The kinetic energy of the PWM is maintained at a constant. This essentially holds an isothermal condition for the system, which creates a similar thermal condition as the isotherm measurement. Such approach permits to calculate the minimum velocity, or kinetic energy required to allow the PWM to fully enter a particular molecular structure. The potential energy of the system is obtained by integration of force field along the PWM trajectory. The force field applied is Amber 94/99. Dielectric, electrostatic and VDW scale factors are 1.0, and 0.5, respectively. The TIP3P model is used for water molecule. In the simulation, the main framework atoms are frozen; only the OH groups at the surface are permitted mobility (Harry F. Ridgeway, personal communication). Figure 4.34 shows the minimum PWM velocity, the minimum temperature and the potential energy barrier of each molecular window structure obtained from the MD simulation. The minimum temperature is computed from the PWM velocity C, mass m*, and Boltzmann constant k as follows, T 2 m C 3k 2 * 2 (4.21) The result shows that the large channel has smallest potential energy barrier and requires smallest minimum PWM velocity and temperature to penetrate. The inner pore ranks the second smallest, while the small channel possesses largest energy level. The energy level of the molecular window is inverse proportional to the window size. Furthermore, from the aspect of the minimum temperature that is needed to penetrate a particular molecular 135

166 Minimum PWM Velocity [Å/ps] Minimum Temperature [K] Potential Energy Barrier [kj/kg] Chapter 4: Adsorption Mass Transport window, only the large channel and the inner pore have the value well below the adsorption isotherm measurement temperatures. Since the volume of the two molecular channels is much larger than the surface structures, the result indicates the possibility that the sharp increase of the water uptake on the Z01 is due to the accommodation provided by the large channel and the inner pore. Before the sharp increase, the surface porous structures dominate the water adsorption. As the pressure increase, the water molecules gain sufficient energy to enter the large channel, such that the zeolite is able to tremendously expand its accommodation volume by opening its interior. Known that the inner pore is located inside the large channel, a higher energy is needed to permit the entrance of the water molecules. On the other hand, due to steric hindrance and repulsive intermolecular force between the PWM and the Z01 atoms, water molecules are effectively excluded from entering the small and medium channels. Min. Velocity Min. Temperature Potential Energy Barrier kj/kg kj/kg kj/kg K kj/kg 1625 K K K 15 Å/ps 50 Å/ps 10 2 Å/ps 5 Å/ps 1 Large Channel Inner Pore Medium Channel Small Channel Figure 4.34: The minimum PWM velocity, minimum temperature and potential energy barrier of each molecular window structure obtained from the MD simulation 136

167 Chapter 4: Adsorption Mass Transport 4.8. Summary In this chapter, the influence of the HEC binder on the adsorption mass transport phenomenon is evaluated. The measurement of water uptake on the pure silica gel type 3A, type RD powder and the corresponding 3.3 adsorbent wt% HEC adhered samples at 25 o C to 45 o C adsorption temperatures is firstly described. The results suggest that an average reduction of 27.3 % on the water equilibrium uptake is observed on the type 3A due to the HEC addition, which is aligned with the surface area results. However, the binder has negligible effect on the silica gel type RD powder. A new isotherm model proposed in the present chapter is used to fit the equilibrium uptake data of all samples. The model can be derived from the results of the statistical rate theory using an asymmetrical adsorption site energy distribution function given in this work. It offers more precise regression than the classic D-A and Tóth equations. The error for the proposed model is only % compared to that for the classic medals of %, and %, respectively. From the accurate adsorption isotherm data, and the adsorbent temperature profile obtained from the heat transfer experiment as described in the previous chapter, the overall influence of the binder on the mass transport during adsorption heat transfer process is determined. The result shows the adsorbate uptake rate due to binder addition is two folds faster than the conventional method. The chapter also introduces a new water adsorbent zeolite, FAM Z01 that owns unique S-shape water adsorption isotherms. The results of isotherm 137

168 Chapter 4: Adsorption Mass Transport measurement indicate that the new adsorbent has 3.4 times higher water uptake capacity than the silica gel at typical adsorption chiller operation conditions. Insignificant reduction of the adsorption capacity is observed due to 3.3 adsorbent wt% HEC. Moreover, the isotherm data are also accurately regressed by the proposed model, with error of 6.05 % and 5.85 % respectively for the pure and binder added samples. Last but not least, a molecular dynamic simulation shows that besides the surface, two molecular windows (the large channel and the inner pore) provide significantly large volume to accommodate the adsorbed water molecules in the adsorbent interior at near room temperature conditions. 138

169 Chapter 5: Local Adsorption Heat Transfer Coefficient CHAPTER 5 LOCAL ADSORPTION HEAT TRANSFER COEFFICIENT 5.1. Introduction From the previous chapters, experiments have been conducted on the transient overall heat transfer coefficient of a silica gel coated heat exchanger, and the water adsorption isotherms of the silica gel at corresponding temperatures. With these careful measurements and the regression models, it is possible to investigate the heat transfer phenomenon from the metal fins to the adsorbent by eliminating the effect of other thermal layers, and develop accurate prediction equations for the coefficient of the local adsorption heat transfer. An accurate interpretation of the adsorption heat transfer will aid designers in optimizing the adsorption chillers and other thermally driven adsorption systems, and shortening design period. To the date, the design of adsorbent embedded heat exchangers relies on designers skilled art. Understanding and development of the adsorption heat transfer are rarely found in the literature. Many researchers simulate highly transient performance of adsorption beds by using a constant heat transfer coefficients [ ]. Mayer et al. [183] characterized the heat transfer in the reaction bed by a constant thermal conductivity. Bjurström et al. [184], Tsotsas and Martin [185], and Murashov and White [186] focused on the thermal conductivity measurement of the adsorbents. Freni et al. [187], however, pointed out that the thermal conductivities of the CaCl 2 /SiO 2 and 139

170 Chapter 5: Local Adsorption Heat Transfer Coefficient LiBr/SiO 2 composite sorbents was considerably affected by the amount water adsorbed. A constant conductivity value could yield error as big as 30% in the cooling powder calculation of the adsorption chillers. Kim et al. [188] used both transient one- and two-dimensional models to study the heat transfer effect to the temperature swing adsorption process. The temperature gradients in the axial and radial directions were simulated for an adsorption bed surrounded by adiabatic, near-adiabatic and non-adiabatic column walls. However, the authors failed to mention the values or the formulas of the heat transfer coefficient between the bed and the wall. In the context below, the local heat transfer between the heat exchanger metal fins and adsorbent-adsorbate interaction layer is investigated. The theories involved in the computation of the instantaneous local adsorption heat transfer coefficient from the transient overall heat transfer coefficient are described in Section 5.2. In Section 5.3, a new equation is proposed to predict the instantaneous local adsorption heat transfer coefficient through the properties of adsorbent and the specifications of heat exchanger. It is validated by the experimental data obtained from the adsorption heat transfer test of the silica gel RD powder coated heat exchanger described in Chapter 3. The last section summarizes the chapter. 140

171 Chapter 5: Local Adsorption Heat Transfer Coefficient 5.2. Calculation of Local Adsorption Heat Transfer Coefficient Overall Thermal Resistance For an adsorbent embedded heat exchanger, during adsorption process, the heat of adsorption released by the adsorbate molecules is eventually transferred from the adsorbent-adsorbate interface to the cooling water. A few thermal layers are passed through by the heat, they are, interaction of the adsorbent-adsorbate, conduction through the fin, the tube wall, and convection between the inner tube wall and cooling water bulk flow. As illustrated in Figure 5.1 and 5.2, each layer possesses not only thermal resistance. The thermal mass of each layer can neither be ignored due to dynamic heat and mass transfer nature of the adsorption process. Besides, the heat transfer in the adsorbent-adsorbate interaction layer cannot be categorized into a single phenomenon. It is in fact a net effect of several parallel events, including the phase change of the adsorbate that results in heat generation, the conduction through the adsorbent solids and vapor that fills up the void space, as well as the contact resistance in between the substances and metal fins. A separate analysis of each parallel phenomenon is rather complicated due to the interlacement among the phenomena and inhomogeneity at different locations. They are hence grouped together by a single term, named as local adsorption heat transfer coefficient that is defined as the amount of heat flux across the temperature difference between the fin surface and the average of the adsorbent-adsorbate interaction layer, to study their net influence. 141

172 Chapter 5: Local Adsorption Heat Transfer Coefficient Silica Gel T ads T i,tw T o,tw T fin Fin Cooling Water T i,cw Tube Wall Figure 5.1: Schematic representation of an adsorbent embedded heat exchanger section Q adsorption + Q superheating ( ) ht,ads A r o ln(r o /r i ) 1 h t,ads A η -1 k tw A o h t,i A i T ads T fin T o,tw T i,tw T i,cw Q loss M sg Cp ads M fincp fin M twcp tw Q cw Figure 5.2: Thermal layers encountered in an adsorbent embedded heat exchanger during adsorption process Concerning transient heat transfer in each thermal layer, the net amount of heat flux passes through the layer is equal to the total entering heat flux minus the heat reserved in the layer s thermal mass. The temperature difference between boundaries of the layer in the heat transfer direction is created as the net heat flow is resisted by the thermal resistance. Particularly to the adsorbent-adsorbate interaction layer, the temperature difference is calculated from the following equation: 142

173 Chapter 5: Local Adsorption Heat Transfer Coefficient T T R Q M C p a d s fin a d s eff sg a d s dt dt ads (5.1) where, the subscript ads means the adsorbent-adsorbate system, including adsorbent (subscript sg), adsorbed phase of the adsorbate (subscript α) and additives like binder (subscript b), etc.; the letter R denotes thermal resistance, and the rest of the symbols represent their usual means. The effective specific heat capacity of the adsorption system is computed as, C p C p q C p M C p M b a d s s g b (5.2) sg and, q is the instantaneous amount of adsorbed phase. The amount of net heat enters into the adsorbent-adsorbate system, Q eff, is the total effect of heat of adsorption, vapor superheating and heat loss to the surrounding, and expressed as, Q Q Q Q e ff a d so rp tio n su p e rh e a tin g lo ss d q d q M Q M h T h T P d t d t M a d s a d s, sg st, a d s sg g e g e sg dq dt ads Q lo ss (5.3) In this equation, Q st,ads is the heat of adsorption per unit mass of adsorbate conducting phase change and calculated from Equation 2.65 described in Chapter 2. The term dqads dt denotes the rate of adsorption and can be obtained from Equation 2.42 in Chapter 2. The superheating term, Q superheating, concerns the temperature raise of the vapor from the evaporator (represented by the subscript e) to the adsorption chamber. 143 Q lo ss is normalized heat loss per unit mass of phase changing adsorbate from the total heat loss, Q loss.

174 Chapter 5: Local Adsorption Heat Transfer Coefficient For the conduction layers in the fin and tube wall, as well as the convection layer in the cooling water, similar equations are applied for the boundary temperature difference. dt T T R Q M C p M C p d t ads fin o, tw fin e ff sg a d s fin fin dt d t fin (5.4) dtads Q M C p e ff sg a d s dt T T R o, tw i, tw tw dt fin M C p M C p d t fin fin tw tw dt d t tw (5.5) T T R Q (5.6) i, tw i,c w i c w Energy balance of the adsorption heat transfer process is written as, d T dt d T Q Q M C p M C p M C p d t d t d t a d s fin tw (5.7) cw eff sg a d s fin fin tw tw Add up Equation 5.1, 5.4 to 5.6, and divide Q cw on both sides of the equation, the overall transient thermal resistance can be obtained as below, 1 T T a d s i, c w R R i U t A Q R R fin ads cw tw dt Q M C p M C p d t Q ads e ff sg a d s fin fin Q M C p e ff sg a d s Q cw dt dt cw ads dt d t fin (5.8) Theories used to calculate the thermal resistance of convection near the tube inner wall R i, the conduction through the tube wall R tw, the fin R fin, and 144

175 Chapter 5: Local Adsorption Heat Transfer Coefficient derivation on the adsorbent-adsorbate interaction R ads are described in the following sections Convection near the Tube Inner Wall The convection thermal resistance between the cooling water bulk flow and the circular tube inner wall is given by, R i h 1 (5.9) t, i A i where h t,i denotes local convection heat transfer coefficient near the tube inner wall. A i is the inner surface area of the tube. For turbulent boundary layer formed near the tube inner wall at Reynolds number greater than 2300, Dittus-Boelter correlation can be applied to predict the value of h t,i [189]. h t, i N u k cw (5.10) d i The Nusselt number Nu is calculated from an empirical relation, 0.8 n (5.11) N u R e P r The exponent n equals to 0.4 for heating the water bulk flow and 0.33 for cooling conditions. 145

176 Chapter 5: Local Adsorption Heat Transfer Coefficient Conduction through the Tube Wall The conduction thermal resistance through the tube wall is a function of tube inner and outer radii r i and r o, material thermal conductivity k tw and the outer surface area of the tube A o, and given by, R tw r ln o r r o i (5.12) k tw A o Conduction through the Fins For the heat transfer in the fins, the thermal resistance is computed from the heat exchanger surface efficiency by the following equation, R fin h A t, a d s (5.13) where, η denotes the surface efficiency and is expressed in Equation 5.14; h t,ads represents the local adsorption heat transfer coefficient from the fin surface to the average of the adsorbent-adsorbate layer; and A is the total surface of the fin tube heat exchanger. For the plain fin-tube type heat exchanger, its heat transfer efficiency can be determined from Schmidt equations [159, 167, 190]. A fin 1 1 fin (5.14) A The fin efficiency η fin, defined as the proportion of the actual heat transfer rate to the ideal one obtained when the fin surface is at the base temperature, is given by, 146

177 Chapter 5: Local Adsorption Heat Transfer Coefficient fin tan h r o (5.15) r o where, r o is the outer radius of the tube, including the collar fin thickness, and, 2 h t, a d s (5.16) k fin fin Re q Re q ln r r o o (5.17) The symbol R eq denotes equivalent radius to circular fins, and is defined by the following equations for different tube layout. For the staggered tube layout, R eq X X M L r r X o o M 1 2 (5.18) In the case of inline tubes layout, or one-row coil, R eq X X M L r r X o o M 1 2 (5.19) The geometric parameters, X L and X M are defined as below. X L Pl 2 2 P 2 P t 2 l for staggered tubes for inline and one-row tubes (5.20) X M P 2 (5.21) t where, P l and P t are longitudinal and transverse tube pitch, respectively. Hong and Webb [191] suggested that the Schmidt equation will give more than 5% 147

178 Chapter 5: Local Adsorption Heat Transfer Coefficient error if 3 R r and R r 2 e q o however, are well within the limits.. Most of the practical applications, e q o Adsorbent-Adsorbate Interaction Thermal Layer The net heat transfer phenomenon through the adsorbent-adsorbate interaction layer during adsorption process is characterized by the local adsorption heat transfer coefficient, h t,ads, that addresses the temperature difference between the fin surface and the average of the adsorbent occupied volume. Its effective thermal resistance R ads can be expressed as, R ads h 1 (5.22) t, a d s A Substitute Equation 5.9, 5.12 and 5.13 into Equation 5.8 and invoke the energy balance of Equation 5.7, the effective thermal resistance of the adsorbentadsorbate interaction layer can also be obtained as, R ads 1 1 r ln r r o o i U A h A k A t, i i tw o dt fin 1 M C p Q M C p d t fin fin c w tw tw Q cw dt d t tw (5.23) Combine Equation 5.22 and 5.23 by eliminating R ads, h t,ads can be computed from the overall heat transfer coefficient, thermal masses and resistances of other thermal layers with established theories. 148

179 Chapter 5: Local Adsorption Heat Transfer Coefficient h t, a d s dt fin 1 M C p Q M C p d t fin fin c w tw tw 1 A A r ln r r o o i U h A k A t, i i tw o Q cw dt d t tw (5.24) and the transient overall heat transfer coefficient can be rwritten as: A A r ln r r o o i h A k A t, i i tw o U dt fin 1 dt M C p fin fin Q M C p c w tw tw d t d t Q h c w t, a d s tw 1 (5.25) Results and Analysis Experiment is conducted to measure the transient overall heat transfer coefficient of the adsorbent embedded heat exchangers and has been described in Chapter 3. The proposed binder method of coating silica gel powder as a thin layer onto the exchanger fins has been proven to tremendously promote both heat and mass transfer during the adsorption process as compared to the conventional mesh packing method (See Chapter 3 & 4). Among the three tested cases, silica gel type RD powder coated heat exchanger has highest overall heat transfer value per unit mass of the adsorbent. It is selected as a case study to further analyze the local adsorption heat transfer. The cooling water flowrate in the tube side of the heat exchanger is fixed at 1 LPM. Computation on the Reynolds number in the experimental conditions yields 3110 to 4200, indicating that turbulent boundary layer is formed near the tube inner wall. Water properties are obtained from 149

180 Chapter 5: Local Adsorption Heat Transfer Coefficient REFPROP software. To calculate the local adsorption heat transfer coefficient h t,ads, Equation 5.24 and the surface efficiency of the heat exchanger η are required to be solved simultaneously with iteration. Table 5.1 listed the specification of the heat exchanger needed in the calculation. The heat loss from the system has been quantified in Figure 3.19 (b) in Chapter 3. Table 5.1: Value of parameters for the calculation of local adsorption heat transfer coefficient Parameters Values Parameters Values Tube (copper) Inner diameter, d i [mm] Thermal conductivity, k tw [W/m.K] 385 Outer diameter, d o [mm] Thermal mass, M tw Cp tw [kj/k] Length, L tw [m] Total surface area, A [m 2 ] Fin (copper) Fin thickness, δ fin [mm] 0.25 Thermal conductivity, k fin [W/m.K] 385 Fin area, A fin [m 2 ] Thermal mass, M fin Cp fin [kj/k] 0.04 The results of temporal surface efficiency of the heat exchanger during adsorption processes are shown in Figure 5.3. The computation is provided for 25 o C, 30 o C, 35 o C and 40 o C cooling water temperatures. It is observed that the efficiency increases with time and stabilizes at around 96% after 150s for all the temperature cases. The deviation takes place in the early period of the adsorption processes in which a lower temperature delivers comparatively higher efficiency. 150

181 Heat Exchanger Surface Efficiency, η [-] Chapter 5: Local Adsorption Heat Transfer Coefficient Figure 5.4 shows the local adsorption heat transfer coefficient in the same conditions. It is expected that the coefficient generally increases positively with the cooling water temperature, which aligns with the overall heat transfer coefficient in Figure 3.17 in Chapter 3. However, an opposite trend with respect to temporal changes is evident between the local and overall values, as plotted in Figure 5.5 for a typical cooling water inlet temperature 30 o C. The local heat transfer rate is highest in the beginning of the process, whereas overall transfer rate is suppressed. This implies that inertia is encountered along the thermal path. To further investigate the deviation, it is necessary to understand the temporal thermal resistance of each layer. 100% 25 C 30 C 35 C 40 C 80% 60% 40% 20% 0% Time [s] Figure 5.3: Temporal variation of the surface efficiency of the silica gel type RD powder coated heat exchanger during adsorption processes at various cooling water temperatures 151

182 Heat Transfer Coefficient [W/m 2.K] Local Adsorption Heat Transfer Coefficient, h t,ads [W/m 2. K] Chapter 5: Local Adsorption Heat Transfer Coefficient C 30 C 35 C 40 C Time [s] Figure 5.4: Temporal local adsorption heat transfer coefficient of the silica gel type RD powder coated heat exchanger during adsorption processes at various cooling water temperatures Local Adsorption Heat Transfer Coefficient Overall Heat Transfer Coefficient Time [s] Figure 5.5: Comparison of temporal overall and local adsorption heat transfer coefficient of the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature 152

183 Chapter 5: Local Adsorption Heat Transfer Coefficient Figure 5.6 illustrates the thermal resistance of each layer along the adsorption heat transfer path, namely the adsorbent-adsorbate interaction layer, conduction layers in the fin and tube wall, as well as convection in the cooling water. The values for the fin and the adsorbent-adsorbate layer include the thermal mass factor formulated in Equation 5.8. The cumulative value is the overall thermal resistance. The figure clearly shows that the adsorbentadsorbate layer is dominant, followed by the convection layer in the cooling water, and the conduction in the fin. The resistance of the tube is negligible as compared to other layers. In the beginning of the adsorption process, the overall resistance is as high as 0.81 K/W. It gradually stabilizes at average of 0.29 K/W after 150 s. The adsorbent-adsorbate layer and the fin contribute and K/W in the beginning process. The stabilized value for the both layers after 150 s is K/W and K/W, respectively. The tube wall and the cooling water convection layer keep relatively constant values with K/W and K/W correspondingly throughout the process. The percentage contribution of each layer to the overall thermal resistance is plotted in Figure 5.7. The adsorption layer and fin count for 72% and 22.4% of the initial overall thermal resistance. At the same period, the contribution by the cooling water convection is as low as 5.5%. However, in the steady portion the resistance from the fin declines to 4.4%. The gap is filled by the cooling water convection layer which rises to average of 15.7% after 150 s. Another 79.8% is from the adsorption layer. Despite the dominance of the adsorbent-adsorbate interaction layer on the overall adsorption heat transfer path, its big variation of on the thermal resistance as well as that of the fin draws attention. This entails that inertia 153

184 Chapter 5: Local Adsorption Heat Transfer Coefficient is faced by both layers in the beginning of the adsorption process. It is known that the transient nature of the adsorption heat transfer adds thermal mass factors on both layers, the calculation on the degree of the thermal mass effect shows that it is responsible for the inertia. Figure 5.8 illustrates of the percentage contribution the thermal mass effect, the thermal resistance solely due to the heat transfer coefficient as described in Equation 5.22, and the net thermal resistance of the adsorption layer to the overall thermal resistance. The result shows a strong contribution from the thermal mass effect, especially in the beginning of the period, indicating that most of the heat released in this period is stored in the thermal mass instead of transferring to the cooling water. Out of the 72% of contribution by the adsorbent-adsorbate layer in the initial process, 70.8% is due to the thermal mass effect. This well explains the initial large deviation between the local adsorption heat transfer coefficient and the overall heat transfer coefficient, and also the sharp increase of the adsorbent temperature in the period. On the other hand, for the process after 60 s the thermal mass effect becomes negative. It compensates the heat transfer by reducing the net resistance of the adsorption layer. This is align with the temperature profile of the adsorbent (shown in Figure 3.15 in Chapter 3) that the adsorbent temperature reaches maximum at 60 s and starts to cool down afterwards. In addition, a similar phenomenon is experienced by the fin, and this is quantified in Figure

185 Percentage Contribution [-] Thermal Resistance, R [K/W] Chapter 5: Local Adsorption Heat Transfer Coefficient 0.9 Adsorption Layer Fin Tube Wall Cooling Water Convection Layer Time [s] Figure 5.6: Temporal thermal resistance of various layers in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature 100% Adsorption Layer Fin Tube Wall Cooling Water Convection Layer 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Time [s] Figure 5.7: Percentage contribution of each layer s thermal resistance in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature 155

186 Percentage Contribution [-] Percentage Contribution [-] Chapter 5: Local Adsorption Heat Transfer Coefficient 100% Thermal Resistance Thermal Mass Net Thermal Resistance 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Time [s] Figure 5.8: Percentage contribution of the adsorption layer from thermal mass effect in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature 25% Thermal Resistance Thermal Mass Net Thermal Resistance 20% 15% 10% 5% 0% Time [s] Figure 5.9: Percentage contribution of the fin from thermal mass effect in the silica gel type RD powder coated heat exchanger during adsorption process at 30 o C cooling water temperature 156

187 Chapter 5: Local Adsorption Heat Transfer Coefficient 5.3. Prediction of Local Adsorption Heat Transfer Coefficient Derivation on the Coefficient In the previous section, the temporal local adsorption heat transfer coefficient is calculated by eliminating the thermal resistance and thermal mass effect of other layers from the overall resistance. In the application, however, there is a need to predict the coefficient precisely such that desired performance is obtained in the design of adsorbent embedded heat exchangers. In the following content, effect is made to derive a transient correlation equation to perform the prediction from the heat exchanger geometry and adsorbentadsorbate pair properties. That a transient equation is favorable here instead of a steady state one is due to the dynamic nature of the adsorption process in which temporal variation on the adsorption rate of uptake causes instantaneous change on the thermal conditions. Water Gas Phase Q st T ads Q loss Water Adsorbed Phase Control Volume T fin Silica Gel Fin Cooling Water T i,cw Tube Wall Figure 5.10: Illustration of the heat flux flow direction on the heat exchanger during a typical adsorption process 157

188 Chapter 5: Local Adsorption Heat Transfer Coefficient Figure 5.10 illustrates the heat flux flow direction on the heat exchanger during adsorption processes. The control volume is defined as the enclosed space occupied by the adsorbent material and adsorbed phase of the adsorbate. The local adsorption heat transfer coefficient is concerning the rate of heat flux across the temperature difference between the control volume and the fin surface, and is based on the assumptions below. Adsorbent material is located evenly on the fins of the heat exchanger. Adsorption takes place uniformly in the control volume. Temperature variation in the control volume is negligible. Heat flux transferred due to the direct contact of the adsorbent and the tube wall is omitted. Fin is the sole heat transfer path. Heat loss to the surrounding is neglected. Concerning the energy balance on the control volume, the equation is, dt dq ads M C p M Q h A sg a d s sg st, a d s t, a d s T T t fin a d s d t d t (5.26) where the term on the left hand side of the equation denotes the rate of heat reserved in the control volume, and on the other side the terms mean the heat of adsorption added to the control volume, and the heat transferred into the fin, respectively. The mass of the adsorbent can be expressed as, M A (5.27) sg sg sg 158

189 Chapter 5: Local Adsorption Heat Transfer Coefficient Substitute Equation 5.27, and Equation 2.42 in Chapter 2 for the rate of uptake dq dt into Equation 5.26, the equation becomes, t d T ads * t A C p A q q e Q dt s g s g a d s s g s g in i s t, a d s t, a d s fin a d s h A T T t (5.28) Solve the adsorbent temperature T ads from the above equation with respect to time t. The rest of the parameters have negligible variance with time and treated as constant. An equation is obtained as follows. h A t, a d s T t T c e x p a d s fin 1 t A C p s g s g a d s A q q Q h A A C p * s g s g in i s t, a d s t, a d s s g s g a d s e x p t (5.29) Eliminate the area A, h t, a d s T t T c e x p a d s fin 1 t Cp s g s g a d s q q Q h C p * s g s g in i s t, a d s t, a d s s g s g a d s e x p t (5.30) Apply initial condition: t = 0, T ads (0) - T fin = T ini - T fin, where T ini is the initial temperature of the adsorbent upon the adsorption starts, c T T 1 in i fin q q Q * s g s g in i s t, a d s h C p t, a d s s g s g a d s (5.31) 159

190 Substitute c 1 into Equation 5.30, Chapter 5: Local Adsorption Heat Transfer Coefficient T a d s t T T T fin in i fin q q Q * s g s g in i s t, a d s h C p t, a d s s g s g a d s h t, a d s e x p t Cp s g s g a d s q q Q h C p * s g s g in i s t, a d s t, a d s s g s g a d s e x p t (5.32) Rearrange, h t, a d s T t T T T e x p t a d s fin in i fin Cp sg sg a d s q q Q h C p * sg sg in i st, a d s t, a d s sg sg a d s (5.33) h t, a d s e x p t e x p Cp sg sg a d s t Regroup the parameters by introducing dimensionless groups, and define Biot number: Bi h t, a d s sg (5.34) k sg Fourier number: F o k sg t 2 (5.35) Cp sg sg a d s Equation 4.32 can be simplified as: 160

191 Chapter 5: Local Adsorption Heat Transfer Coefficient e x p T t T T T B i F o a d s fin in i fin 1 B i F o 1 Cp * t q q Q in i s t, a d s t e x p B i F o e x p ads (5.36) Divide both sides of the equation by Tin i T, fin T t T a d s T T in i fin fin * e x p B i F o in i q q Q s t, a d s C p T T a d s in i fin e x p B i F o 1 t t e x p B i F o (5.37) To further simply the equation, two more dimensionless groups are defined, namely, temperature number and adsorption number. The temperature number is the ratio of instantaneous to the initial temperature difference at the moment adsorption starts between the adsorbent-adsorbate control volume and fin surface, and expressed as follows. a d s in i T t T T T fin fin (5.38) The adsorption number is a new dimensionless group introduced in the present work. It is defined as, Ad * in i q q Q C p T T st, a d s a d s in i fin (5.39) The numerator in this expression calculates the total heat of adsorption released from initiation of the adsorption till saturation. The denominator 161

192 Chapter 5: Local Adsorption Heat Transfer Coefficient describes the amount of heat reserved in the adsorbent-adsorbate system from initiation to reach fin surface temperature. The ratio of the two quantities reflects the magnitude of the heat of adsorption being accumulated inside the adsorbent-adsorbate interaction layer during adsorption processes. Large adsorption number implies fast heat transfer out of the system. Hence, the equation to predict the transient local adsorption heat transfer performance is written as, Ad e x p B i F o e x p t e x p B i F o B i F o 1 t (5.40) where, the transient local adsorption heat transfer coefficient h t,ads can be computed by solve the Biot number iteratively from the equation with the specification of the adsorbent coating and properties of the adsorbentadsorbate pair. The first term on the right hand side of the equation describes the rate of natural convection out of the control volume. The difference between this phenomenon and the heat generation rate inside the control volume is indicated in the other term. The heat generation is due to the mass transport in which the adsorbate experiences phase change from gaseous to the adsorbed phase. Clearly, the temperature of the adsorbent-adsorbate system is determined by the competition of mass transport and the convective heat transfer out of the system. In addition, equation 5.39 is qualified by the nature of the adsorption heat transfer process in which, at t = 0, L im t 0 1, or T ads = T ini, and, at t =, 0, or T ads = T fin L im t 162

193 Results and Discussion Chapter 5: Local Adsorption Heat Transfer Coefficient Equation 5.40 is implemented to predict the local adsorption heat transfer coefficient of the silica gel type RD powder coated heat exchanger with 3.3 adsorbent wt% HEC during adsorption at o C cooling water. The results are validated with the experimental data stated in Section 5.2. The adsorption characteristic parameters of the silica gel-water pairs are obtained from the classical and newly proposed theories from the present work and summarized in Table 5.2. The value of parameters for the equilibrium uptake of the pair has been given in Table 4.1 of Chapter 4. Fin surface temperature is obtained from the experimental data with Equation 5.4 to 5.7. The parameters substituted in the calculation are summarized in Table 5.3 [168]. Table 5.2: Summary on the equations of adsorption characteristic parameters Equations Coefficient of the adsorption kinetics (LDF model) 15D E so a e x p 2 R R T t p a d s Heat of adsorption Q P v v ln K P st, a d s g a Equilibrium uptake (Present work) q * P P P A e x p ( ) C P P P s s s t 1 e x p ( ) P P s s q 0 P P Specific heat of adsorbed phase where, A E c e x p R T ads t 1 e x p ( ) e x p ( ) 2 t C v ln g v P K P v g g C p C p P ln K P 2 g T T T P P P References Equation 2.40 in Chapter 2 Equation 2.65 in Chapter 2 Equation in Chapter 4 Equation 2.75 in Chapter 2 163

194 Chapter 5: Local Adsorption Heat Transfer Coefficient Table 5.3: Properties of water and silica gel type RD powder with 3.3 adsorbent wt% HEC Parameters Values Parameters Values Adsorbent (silica gel RD powder) M sg [g] Cp sg [kj/kg.k] ρ sg [kg/m 3 ] 800 k sg [W/m.K] δ sg [mm] Binder (HEC) M b [kg] Cp b [kj/kg.k] Kinetics constant (κ) & Heat of adsorption (Q st ) D so [m 2 /s] R p [mm] 0.2 E a [kj/kmol] K [kpa -1 ] The results of the prediction from Equation 5.40 are illustrated in Figure The predicted local adsorption heat transfer coefficient yields good estimation on the experimental data, with the coefficient of determination (R 2 ) of and normalized root mean square error to the mean experimental data (NRMSE) 13.8% achieved. A further investigation of the prediction errors shows that the sources are mainly from the determination of the characteristic parameters of adsorbent-adsorbate pairs. El-Sharkawy [69] pointed out that the LDF model considerably underestimate the rate of water uptake approximately kg/kg of silica gel in the early period of the adsorption process, whereas overestimate the rate around kg/kg of adsorbent in the later period. The inaccuracies of the heat of adsorption [145] and the adsorption isotherm equations also contribute to the error. The imprecision resulted from the calculation of the adsorption characteristic parameters in illustrated in Figure The figure compares the experimentally measured heat removal rate by the cooling water, and that calculated from these parameters through Equation 164

195 Local Adsorption Heat Transfer Coefficient, ht,ads [W/m 2.K] Local Adsorption Heat Transfer Coefficient, ht,ads [W/m 2.K] Chapter 5: Local Adsorption Heat Transfer Coefficient 5.3. The accuracy of the local adsorption heat transfer coefficient can be further improved if more precise adsorption characteristic equations are applied C Predicted Time [s] (a) 25 o C C Predicted Time [s] (b) 30 o C 165

196 Local Adsorption Heat Transfer Coefficient, ht,ads [W/m 2.K] Local Adsorption Heat Transfer Coefficient, ht,ads [W/m 2.K] Chapter 5: Local Adsorption Heat Transfer Coefficient C Predicted Time [s] (c) 35 o C C Predicted Time [s] (d) 40 o C Figure 5.11: Predicted results of Equation 5.39 on the local adsorption heat transfer coefficient of the silica gel type RD powder and 3.3 adsorbent wt% HEC coated heat exchanger during water adsorption processes at cooling water temperature (a) 25 o C, (b) 30 o C, (c) 35 o C, and (d) 40 o C. The experimental results are displayed in 10% error bars 166

197 Heat Rejection to Cooling Water, Q cw [kw/k] Chapter 5: Local Adsorption Heat Transfer Coefficient 40 Experiment Predicted Time [s] Figure 5.12: Comparison of cooling water heat removal rate obtained from experiment and predicted by the adsorption characteristic equations listed in Table 5.2. The temperature of the cooling water is 25 o C for both cases 167

198 Chapter 5: Local Adsorption Heat Transfer Coefficient 5.4. Summary In this chapter, the local adsorption heat transfer coefficient of an adsorbent embedded heat exchanger is investigated to understand the heat transfer phenomenon of adsorbent-adsorbate interaction layer during the adsorption process, and meanwhile fill this gap in the literature. It is defined as rate of heat flux transferred between the temperature difference of the fin surface and the average layer temperature. The experimental values of the local adsorption heat transfer coefficient at various cooling water conditions are calculated by eliminating the thermal resistance of other layers. The coefficient exhibits exponentially decaying trend with respect to time. An analysis on the contribution of the thermal resistance from each layer shows that the adsorbent-adsorbate interaction layer and the fin contributes to 72 % and 22.4 % of the overall thermal resistance in the initial adsorption process, out of which 70.8 % and 21.5 %, respectively, are due to the thermal mass effect. In the steady cooling of the later process, the percentage of the adsorption layer is average 79.8%, followed by the cooling water convection layer of average 15.7%. A new equation is proposed in this work to predict the local heat transfer coefficient with the adsorbent coating specifications and the properties of the adsorbent-adsorbate pair. The predicted results show good agreement with the experimental data, with the R 2 value and NRMSE error 13.8%. 168

199 Chapter 6: Dynamic Behavior of an Adsorption Chiller CHAPTER 6 DYNAMIC BEHAVIOR OF AN ADSORPTION CHILLER 6.1. Introduction This chapter focuses on mathematical modeling and experimental evaluation of a solar or low grade waste heat driven adsorption chiller. The chiller utilizes many findings and achievements of the present thesis described in the previous chapters. The adsorbent-adsorbate pair applied in the chiller is the novel zeolite FAM Z01 and water presented in Chapter 4. It has been demonstrated that Zeolite FAM Z01 owns water adsorption capacity 3.4 times higher than silica gel in typical chiller operation conditions. Moreover, the zeolite powder is coated onto heat exchanger fins using binder instead of the conventional packing method by wire mesh. As described in Chapter 3 and 4, the coating method significantly improves the heat and mass transfer 3 to 4 folds in the adsorption beds. In addition, the thermodynamic properties of the adsorbed phase derived from statistical rate theory in Chapter 2, and the proposed local adsorption heat transfer coefficient correlation in Chapter 5 are invoked to model the dynamic behavior of the adsorption chiller. Extensive work has been performed in the literature to study the feasibility of various adsorbent-adsorbate pairs to perform adsorption cooling cycle. Silica gel-water is one of the most common pairs that have received considerable attention. Adsorption chillers using this pair was investigated in 169

200 Chapter 6: Dynamic Behavior of an Adsorption Chiller the earlier years by Sakoda and Suzuki [192], Boelman et al.[193, 194], Chua et al. [34, 178, 195], Wang X. et al. [196], Tahat [197], Wang D. et al. [198, 199], Liu et al. [200]. Recently, 25% improvement on the COP of the chiller was achieved by Daou et al. [201] and Saha et al. [202] to impregnate CaCl 2 into silica gel. Similar developments by adding other inorganic salts were studied by Aristov and co-workers [75, 203]. Silica gel-water adsorption chillers usually operate at heat source temperature 55 o C 90 o C with the COP ranged from 0.2 to Another frequently used adsorbent is zeolite. Due to the variety of molecular structures, many synthetic types were developed, such as zeolite 4A, 5A,10X and 13X, etc. [204]. The zeolite water [ ] chillers require higher heat source temperatures than the silica gel-water type. In addition to water as adsorbate, silica gel, zeolite and active carbon with methanol [ ], as well as active carbon with ethanol [39] pairs were also tested for the adsorption cooling cycles. Due to the thermodynamic properties of the adsorbate, adsorption chillers applying the above mentioned adsorbent-adsorbate pairs operate in subatmospheric conditions. Some natural and AC-HFC refrigerants, on the other hand, perform at the pressures above the ambient [212, 213]. Such adsorption chillers demand different engineering skills and art from the vacuum types. Lambert [214] designed an adsorpotion heat pump utilizing carbon-ammonia pair for residential cooling or heating. The system was desired to work between 2 to 30 bars pressure and 170 o C heat source. An improved heat exchanger design is constructed in the adsorption beds in which coarse metal wool is introduced among the fins to enhance contact with the adsorbent. The author conservatively esitmated the COP of 1.5 could be achieved for the 170

201 Chapter 6: Dynamic Behavior of an Adsorption Chiller cooling cycle. Azhar et al. [215] evaluated and compared active carbonpropone, R134a, R570 and R32 pairs for adsorption cooling and refrigerantion cycles. A concept implemented in the work to select suitable adsorbentadsorbate pair for desired operation pressure, heat source and cooling production temperatures provides a useful means in the practical applications. Adsorption chiller is normally operated in batch-mode in which the beds periodically swap the rules to perform adsorption and desorption. In order to provide continuous cooling, the simplest configuration is single stage with two beds. Further development on top of this configuration has been demonstrated significant improvement on the performance of the chillers. A multistage design from Saha and co-workers [7, 216, 217] effectively brought down the minimum heat source temperature to near ambient for a silica gel-water adsorption chiller. The authors experimentally tested a three stage and later a two stage chiller, and achieved heat source temperature as low as 50 o C from the former and 55 o C from the latter with 30 o C cooling water in both situations. Saha et al. [6], Wang et al. [196], Alam et al. [218], and Ng et al. [179] investigated operational strategies of multi-bed adsorption systems. Comparing to the two-bed configuration, the multi-bed (more than two) gained more specific cooling capacity, and produced smoother chilled water temperature profile. Gordon et al. [219], Ng et al. [220, 221], and Saha et al. [222] successfully integrated thermoelectric and silica gel-water adsorption cycle into an electro-adsorption chiller (EAC) to cool electronics. Chen et al. [223] tested an adsorption chiller that eliminates the vacuum valves in the structure. Ng and his research group [224, 225] innovatively utilize adsorption cooling cycles for desalination. Recent achievement from the group is a 171

202 Chapter 6: Dynamic Behavior of an Adsorption Chiller creative hybridization of adsorption and multi-effect desalination (MED), which breaks through lower temperature limit of the conventional MED to below ambient condition [226, 227]. Given the research activities conducted in the adsorption cooling field, Choudhury et al [228] comprehensively summarized the development of this technology from three aspects, i.e., thermal energy harvesting, heat and mass transfer enhancement, and lastly advanced cycles and stages. Numerical studies establish theoretical framework on the adsorption cooling systems. They are frequently used to design and optimize the systems, and explore the behavior of the system in extreme conditions. A lumped modeling method was used by Cho and Kim [229], Saha et al. [230], Chua et al. [231], Schicktanz and Núñez [181], Rezk and Al-Dadah [232], etc. to model adsorption chiller operation. The major components of the chiller were assumed to have uniform properties. They are modeled through mass balance and energy conservation. Miyazaki et al. [233] simulated an adsorption chiller with a new cycle time allocation strategy in which one bed is conducting preheating, desorption and pre-cooling, while in the same period the other bed only perform adsorption. The new strategy reduced output fluctuation and increased the cooling capacity by 6%. Zhao et al. [234] included adsorbate diffusion model to simulate adsorbate mass transport in adsorption bed. Zhang and Wang [235] performed a three-dimensional modeling on the heat transfer paths of the adsorption heat exchangers. While research and development on adsorption chillers has made enormous progress, the vast application of this green technology is stilled bottlenecked by low COP and relatively larger foot-print. The existing 172

203 Chapter 6: Dynamic Behavior of an Adsorption Chiller adsorption chillers operate well below the theoretical Carnot limit. Meunier et al [236] explained the reason through thermodynamic second law analysis. Meunier and co-authors suggested that in the conditions of isothermal heat reservoirs and ideal transfer, a temperature gap existed between the bed sorption cycles and heat reservoirs, which were responsible for the thermal irreversibilities. Even infinite cascades of sorption reactors yield no more than 68 % of the ideal efficiency [237]. Chua et al. [238] pointed out that the largest portion of entropy was generated by sorption heat transfer. Ng [239] suggested that the COP of such thermally driven adsorption systems was normally lower than 1. On the other hand, the size of the chiller is bounded by the characteristics of the adsorbent-adsorbate pair. In order to achieve desired cooling capacity, the amount of evaporated refrigerant must be adsorbed simultaneously by the solids. This requires large amount of adsorbent and sufficient void space to be introduced into adsorption beds. In the following content, a detailed description of the zeolite FAM Z01- water adsorption chiller is firstly presented in Section 6.2. The next section describes a transient mathematical model developed to simulate the operational behavior of the zeolite-water adsorption chiller, followed by an entropy study stated in Section 6.4. Experiment is conducted in Section 6.5 to evaluate the chiller s performance with respect to key parameters, which are heat source temperatures and adsorption / desorption cycle times. The results of the entropy analysis for various operation conditions are expressed lastly to identify the source of irreversibilities incurred in the chiller interior. 173

204 6.2. System Description Chapter 6: Dynamic Behavior of an Adsorption Chiller Adsorbent-Adsorbate Pair The zeolite FAM Z01 used in the chiller is one of the novel water adsorbents from a family of specially designed zeolite materials for adsorption cooling and dehumidification. As studied in Chapter 4, FAM Z01 has an AFI type molecular sieve structure. Two kinds of molecular window on this structure, namely large channel and inner pore, are able to provide significant accommodation volume for the adsorbed water molecules. Due to this feature, FAM Z01 exhibits unique S-shape water adsorption isotherms and offers 3.4 times higher on water uptake difference than the conventional silica gel in typical operation conditions of an adsorption chiller. This eventually translates to a much larger cooling capacity over conventional silica gel-water adsorption chillers, and further results in a compact chiller design. In addition, the adsorbent has excellent durability over 200,000 adsorption - desorption cycles and little hysteresis behavior [175]. For the adsorbate, on the other hand, owning big latent heat, being absolutely environmental friendly and inexpensive, water has its intrinsic advantages to be a refrigerant Operation Description of Adsorption Chiller In the adsorption / desorption beds, the adsorbent material is constructed stationary on heat exchanger fins. To achieve continuous cooling, the adsorption cooling cycle is divided into two major periods, namely adsorption / desorption and switching, in order for the two beds to alternate their roles to 174

205 Chapter 6: Dynamic Behavior of an Adsorption Chiller perform adsorption (ADS) and desorption (DES). In the adsorption / desorption period, as illustrated in Figure 6.1, ADS bed interacts only with evaporator. Mass transport spontaneously takes place when zeolite attracts water vapor onto its solid surface. As water undergoes a state change from gaseous to a lower energy and more thermodynamically stable adsorbed phase, heat of adsorption is released [129, 240]. To sustain this process, the temperature of the zeolite must remain low. This is achieved by pumping cooling water into the adsorption bed heat exchanger to remove the heat generated in this process. In the evaporator, as a result of vapor transport, pressure is evacuated and triggers refrigerant boiling, though which chilling effect is obtained. Simultaneously, DES bed that has saturated with adsorbed phase water is linked to a condenser. Thermal energy supplied by hot water desorbs refrigerant water molecules from the zeolite surface. The refrigerant water vapor rejects heat at the condenser and the condensate flows back to the evaporator via a U-tube. During the switching period, the two beds swap their roles. In other words, cooling water is applied to the DES bed to prepare it for adsorption in the coming adsorption / desorption period, while at the same time the ADS bed is preheated. Both beds are isolated from the evaporator or condenser, and no mass transport occurs. Particularly to the adsorption chiller introduced in the present work, a heat recovery mechanism is designed such that a part of the thermal energy in DES bed can be utilized to preheat the ADS bed. This further divides the switching period into two time intervals, they are, heat recovery interval and hold interval. Figure 6.2 shows the flow pattern of thermal sources for the respective intervals. In the former, residual heat of 175

206 Chapter 6: Dynamic Behavior of an Adsorption Chiller desorption bed is transferred to the adsorption bed via cooling water which no longer enters the condenser. The condenser is activated again in the hold interval in which the ADS bed remains preheated condition by shut off its heat exchanger. After sufficient pre-heating or pre-cooling in the switching period, the beds are then ready for the next sorption process. A detailed operation strategy of the zeolite-water adsorption is given in Appendix C. Figure 6.1: Schematic presentation of the zeolite-water adsorption chiller in adsorption / desorption period (ADS: adsorption bed, DES: desorption bed) 176

207 Chapter 6: Dynamic Behavior of an Adsorption Chiller (a) Heat recovery interval (b) Hold interval Figure 6.2: Schematic presentation of the zeolite-water adsorption chiller in (a) heat recovery interval and (b) hold interval of the switching period (ADS: adsorption bed, DES: desorption bed) 177

208 Structural Innovation Chapter 6: Dynamic Behavior of an Adsorption Chiller There are two innovative features in the design of the current beds. First of all, the zeolite is coated onto fins of the heat exchangers by using an organic binder instead of the conventional method in which the adsorbent is packed among the fins by wire meshes. Poor contact among fin surfaces and adsorbent solids exposed in the conventional method causes very big thermal resistance along the adsorption heat transfer paths, resulting in a large swing of the chiller performance due to adsorbent packing density [158]. By introducing binder, the new method well addresses this bottleneck. Results from Chapter 3 and 4 of the present thesis shows that the binder coating method significantly increases the overall heat transfer by 2.8 times in the beginning period and 1.5 times at the steady cooling process. Negligible impact on the zeolite adsorption capacity is observed as a result of binder addition. Moreover, as the improved heat transfer effectively brings down the adsorbent temperature, the mass transport is boosted two times faster during adsorption process. Due to the enhancement on both heat and mass transfer, the performance of the chiller can be considerably improved. Secondly, valves between the beds and evaporator or condenser are utilizing a valve-less mechanism instead of butterfly valves used in typical adsorption chillers. This mechanism is basically a counter-weight lever whose opening and closing are triggered by pressure difference of adjacent chambers. For instance, in the beginning of the adsorption period, the pressure in the adsorption bed is lower than the evaporator. The pressure difference creates lifting force that effectively pushes the lever up and starts the mass transport. 178

209 Chapter 6: Dynamic Behavior of an Adsorption Chiller In the case of saturation or swapping to desorption by flushing in the hot water, the pressure of the bed will increase and shut the connection to the evaporator. The same principle is implemented between the DES bed and the condenser. Because of low density of the refrigerant vapor, the jointed components require large cross-section pipes to reduce pressure drop. The valve less design saves the space taken up by conventional pipes and valves, and further eliminates the valve control panel and accessories. Hence the structure of the adsorption chiller system is greatly simplified. 179

210 Chapter 6: Dynamic Behavior of an Adsorption Chiller 6.3. Mathematical Modeling of the Adsorption Chiller A thermodynamic frame work to simulate the operation of the zeolite-water adsorption chiller is developed in this section. The chiller s major components are modeled through energy and mass conservation. The driving force of the refrigerant circulation is determined by adsorption isotherm and kinetics theories. As the chiller is operated in batch-mode in which a regular interchange of roles between both beds takes place, a transient model is applied to simulate the time evolution of the chiller s conditions. To simplify the mathematic model, the following assumptions are made: Adsorbent is distributed evenly on the heat exchanger fins of the adsorption / desorption beds Adsorbed phase water molecules are uniformly attached on the adsorbent during adsorption / desorption processes. Temperature is uniform in the control volume. Heat exchanger material is having the same temperature evolution gradient with the adsorbent. The properties (specific heat capacity, thermal conductivity and density) of the heat exchanger material and adsorbent are assumed to be constant over the operation temperature and pressure range. Heat loss to the surrounding is omitted since the major components are well insulated. Meanwhile the hot components are wrapped by heater tapes to compensate heat dissipation. 180

211 Driving Force of the Refrigerant Chapter 6: Dynamic Behavior of an Adsorption Chiller The refrigerant circulation is driven by the disequilibrium of the adsorbate uptake on the adsorbent surface that creates attraction or repulsion forces to transport adsorbate molecules. The rate of the transport is predicted by the Linear Driving Force (LDF) model described in Section 2.3 of Chapter 2. It expresses that the rate of adsorbate uptake is proportional to the difference between the equilibrium uptake q*, and instantaneous uptake q. Effect of temperature to the magnitude of proportion has been taken into this model. The equation is written below as, E a RT q q ( t ) dq ( t ) 15 D exp * dt so (6.1) 2 R p where D so is a pre-exponential factor for surface diffusion, E a denotes the activation energy of adsorption system, and R p is the average radius of adsorbent particles. The equilibrium uptake q* is obtained from the adsorption isotherms of the zeolite FAM Z01-water pair given in Section 4.6 of Chapter 4. The unique S- shape isotherms of the pair have been accurately regressed by a newly proposed equation as given below, q * P P P A e x p ( ) C P P P s s s t 1 e x p ( ) P P s s q 0 P P where, (6.2) 181

212 Chapter 6: Dynamic Behavior of an Adsorption Chiller E c e x p RT and, (6.3) A 1 e x p ( ) e x p ( ) t C (6.4) where, q 0 is the limiting uptake at the saturation pressure P s ; E c denotes the characteristic energy;, C, and t are constants. The heat of adsorption, denoted as Q st, is the total thermal energy released or required during phase change of a unit mass of adsorbate between gaseous and adsorbed phase at given temperature and pressure during adsorption / desorption processes. It can be analog to the latent heat of a pure substance. The expression of the quantity is derived from the statistical rate theories as shown in Section 2.4 of Chapter 2, and given as below,,, ln Q h T P h T P P v v K P st g g a (6.5) in which, the subscription g and α denote the gaseous and adsorbed phase, respectivey; K is the statistical rate constant. From the same theories, the specific heat capacity of the adsorbed phase adsorbate is derived and computed by, v ln g v P K P v g g C p C p P ln K P 2 g T T T P P 2 P (6.6) 182

213 Chapter 6: Dynamic Behavior of an Adsorption Chiller Modeling of Adsorption / Desorption Period During the adsorption / desorption period, the adsorption bed is coupled with the evaporator, and the desorption bed interacts with the condenser by opening valves installed in between the respective components. The interaction equalizes the pressure of the linked chambers, resulting in disequilibrium of adsorbed phase on the adsorbent surface and its surrounded pressure, which drives the refrigerant flow. Meanwhile, heat transfer takes place across the heat exchanger of each major component between the refrigerant and respective thermal sources Adsorption bed To model the operation of the adsorption bed, it is defined that the control volume is the inner wall of the bed chamber. Energy balance of the adsorption bed in the adsorption / desorption period can be expressed as, M C p M C p M q C p h x, b e d z l z l a d s dqads M h T h T P z l dt dqads M Q, T, P z l s t a d s a d s dt m C p T o T i, g e g a d s e c w, a d s e dt dt ads (6.7) Where, the Greek alphabet δ is an operation indicator that depends on the process of the beds. In the beginning of each adsorption / desorption period, a backward flow of refrigerant vapor may take place from the adsorption bed to the evaporator because of pressure swing desorption, which, however, has 183

214 Chapter 6: Dynamic Behavior of an Adsorption Chiller negligible influence on chiller operation [241]. The introduction of the operation indicator helps to tackle the phenomenon. δ equals to 1 for normal adsorption and 0 to filter out the backward desorption. The subscript hx, bed, zl, and e represent heat exchanger, bed, adsorbent zeolite, and evaporator, respectively. The adsorption bed control volume is expressed specifically by the subscript ads. Cooling water is denotes as cw, while its inlet and outlet is described by the subscript i and o. The rest of alphabets have their usual means. The terms on the left hand side of the equation represent the sensible heat of the content in the adsorption bed control volume, including heat exchanger, adsorbent zeolite as well as the adsorbed phase water. The first term on the right hand side of the equation implies super heating of the water vapor due to temperature difference between the bed and evaporator. The second term calculates the total heat of adsorption released during phase change of the adsorbate. Finally, the last term gives the heat removed by cooling water Desorption bed Similar to ADS bed, in the desorption process, energy balance of the desorption bed interacted the condenser is written as below. 184

215 Chapter 6: Dynamic Behavior of an Adsorption Chiller M C p M C p M q C p h x, b e d z l z l d e s dq z l dt d e s 1 M h T h T, P dqdes M Q, T, P z l s t d e s d e s dt m C p T i T o hw g c g d e s e c dt dt d e s (6.8) Where, the Greek alphabet θ is another operation indicator which is defined as 1 for normal desorption and 0 for backward adsorption. The subscript des, c, and hw correspond to the desorption bed control volume, the condenser and hot water, respectively. The terms in the equation have similar means as the adsorption bed Condenser In the condenser, the structure is designed such that it retains a fixed amount of liquid in the chamber. Its energy conservation is regarded as below: M C p M C p h x, c f, c dt dt dq m C p T T M h T dt d e s i o zl f c c w, c, 1 h T P h T M g d e s c g c c zl dq dt d e s (6.9) In the equation, the left hand side represents the sensible heat of material in the condenser, containing heat exchanger fins and tubes, and liquid. The first term on the right hand side counts for heat removal by cooling water. Mass transport out and into the condenser is expressed by the last two segments. 185

216 Chapter 6: Dynamic Behavior of an Adsorption Chiller Evaporator Similar to the condenser, the equation of energy conservation for the evaporator is constructed as following, in which the subscript e implies the evaporator. M C p M C p h x, e f, e dt dt dq m C p T T M h T dt d e s i o z l f c c h i 1, ads h P T h T M g e a d s g e z l e dq dt (6.10) Mass conservation of refrigerant across the evaporator is, dm d q d q M M zl zl d t d t d t f, e d es a d s (6.11) External thermal sources The outlet temperatures of each external thermal source, including hot water, cooling water and chilled water are determined from the log mean temperature difference (LMTD) method. They are solved jointly with the energy and mass conservation of respective components. T T o, h w / c w / c h i i, h w / c w / c h i T T d e s/, /, / / 1 e x p a d s c e i h w c w c h i UA m C p d e s/ a d s, c / e h w / c w / c h i (6.12) Where, U is overall heat transfer coefficient which is calculated from Equation 6.13 below, and A denotes total area of the heat exchanger. Due to the fact that 186

217 Chapter 6: Dynamic Behavior of an Adsorption Chiller the cooling water in sequence flows through the ADS bed and the condenser, T i,cw,c = T o,cw,ads. A A r ln r r o o i h A k A t, i i tw o U dt fin 1 dt M C p Q M C p fin fin tw tw d t d t Qht,o tw 1 (6.13) In the above equation, A i and A o denote the inner and outer area of the plain tubes; Q is the total heat transferred to the thermal source; h t,i and h t,o are the local heat transfer coefficient of the tube side and shell side, and determined by corresponding correlations summarized in Table 6.1. The subscripts fin and tw represent heat exchanger fins and the plain tube outer wall. 187

218 Chapter 6: Dynamic Behavior of an Adsorption Chiller Table 6.1: Correlations for the local heat transfer coefficient of the tube side and shell side heat exchanger Shell side Tube side Adsorption / Desorption Bed: Present work (Chapter 5) Ad e x p e x p e x p B i F o 1 t where, h t,o B i F o t B i F o Bi k a d s zl in i z l T t T T T fin fin F o Ad k 2 zl Cp zl zl a d s * q q Q in i C p T T t st, a d s a d s in i fin Condenser: Nusselt falling film condensation correlation for horizontal tube bundles 1/ 4 3 N u d h g / n k v T o fg f g f f where, h t,o N u k d o f T T T sa t tw n = number of tubes Evaporator: Shahzad Bubble-Assisted Film Evaporation Correlation for pure water (salinity = 0) [189] h t, o / f T v sa t Q g R e P r g k T A T v f f ref ref where, 4 Re o, c h i T T T f v ref = m 3 /kg at 295K sa t = mass flowrate / tube length T ref = 322K Adsorption / Desorption Bed / Condenser / Evaporator: Dittus-Boelter correlation where, 0.8 N u R e P r h t, i N u k d i n cw n = 0.4 for heating the bulk flow n = 0.33 for cooling the bulk flow 188

219 Modeling of Switching Period Chapter 6: Dynamic Behavior of an Adsorption Chiller In the switching period, pre-heating or pre-cooling is introduced to the cool or hot beds of the past sorption stage. To the bed that transform from desorption to adsorption (DE-AD), a sudden drop of the thermal source temperature rapidly reduces its pressure till below the condenser level, and triggers the lever valve to shut. A similar mechanism is applied to the earlier adsorption bed and the valve linking to the evaporator. Refrigerant therefore becomes stagnant due to the closure of the vapor pathways. On the other hand, alternative cooling and heating of the beds in adsorption cooling cycles implies a possibility of saving input thermal energy by reusing the residual heat of one bed to warm up the other. This is realized in the first time interval of the switching period. In the content below, separate mathematical model of the major components is derived for both time intervals contained in the switching period. The equations are to be solved together with the external thermal sources that are provided in Equation 6.12 above Heat recovery time interval During the first interval, the cooling water in turn flows through the prior desorption bed and adsorption bed. Two merits are appreciated from the flow configuration. Firstly, the DE-AD bed is pre-cooled, and secondly, residual heat of the same bed is harvested to pre-heat the other bed which changes from adsorption to desorption (AD-DE). Here, the residual heat comes from two sources, i.e. the hot water of previous cycle that is retained in the heat 189

220 Chapter 6: Dynamic Behavior of an Adsorption Chiller exchanger tubes and sensible heat of the adsorbent. In this interval, the behavior of the two beds is modeled as below. M C p M C p M q C p h x, b e d z l z l a d s m C p T T i o c w, d e a d dt d e a d dt (6.14) M C p M C p M q C p h x, b e d z l z l d e s m C p T T i o h w, a d d e dt a d d e dt (6.15) Both beds share the same thermal source stream and thus, T i,hw,ad-de = T o,cw,de-ad The condenser is temporarily suppressed in which no heat transfer and mass transport is occurring. Ignoring its heat leak to the surroundings, the state of the chamber is remained, and expressed as: dt c dt 0 (6.16) In contrast, the evaporator content is still exchanging heat with the chilled water in the switching period. Its behavior is described as follows. dte M C p M C p m C p T T dt h x, e f, e i o c h i (6.17) Hold time interval In the Hold interval of the switching process, conditions are remained for the DE-AD bed and the evaporator. However, the AD-DE bed maintains the temperature from heat recovery by terminating communication with the cooling water. Instead, the condenser is activated by the cooling water again 190

221 Chapter 6: Dynamic Behavior of an Adsorption Chiller flushes into its heat exchanger. The behavior of the latter two components is presented below. dt a d d e dt 0 (6.18) dtc M C p M C p m C p T T dt h x, c f, c o i c w, c (6.19) Computation of Efficiency The cyclical average cooling capacity Q E and heat input Q H of the zeolitewater adsorption chiller is expressed in terms of the chilled and hot water conditions, respectively as follows: m Cp Q T T t ch i cycle E i o t 0 cycle dt ch i (6.20) m Cp Q T T t hw cycle H i o t 0 cycle dt hw (6.21) where t cycle denotes cycle time, i.e. period of a complete adsorption cycle, which is a sum of two adsorption / desorption and two switching periods. Coefficient of performance of the adsorption chiller, defined as the ratio of useful effect and total energy input, is C O P Q H Q E W S (6.22) where W S is the work done of a spray pump located in the evaporator. The theoretical coefficient of performance of the presented single-effect adsorption chiller, COP thoery, is defined from the latent heat of the adsorbate at 191

222 Chapter 6: Dynamic Behavior of an Adsorption Chiller the evaporator condition and the isosteric heat of adsorption at desorption temperature and pressure, and given as, C O P th eo ry h T fg e (6.23) Q st, d es T P d es, c The equation implies that for a given adsorbent- adsorbate pair, the efficacy of the adsorption chiller is bounded by the relative magnitude between the latent heat and heat of adsorption. However, the latter is bigger than the former, entailing that such machine can hardly have COP greater than 1 for single effect configuration [239]. On the other hand, the efficiency of the chiller can also be improved by utilizing adsorbent-adsorbate pair that possesses closer energy level between adsorption and vaporization. The Carnot COP of the adsorption chiller is regarded with the temperature of thermal reservoirs where the chiller operates. It has set a theoretical limit on the performance of such heat driven machine, and given by, 1 T T T i, cw o, ch i i, h w C O P T T T ca rn o t o, ch i i, h w i, cw (6.24) 192

223 Chapter 6: Dynamic Behavior of an Adsorption Chiller 6.4. Entropy Study of the Adsorption Chiller The irreversibilities associated with the operation encumber the adsorption chiller efficiency well below the Carnot limit. Internal dissipation of the chiller contributes to the largest portion of the total irreversibilities, such as finite rate mass and heat transfer, fluid friction, etc. that are involved in the phase change of refrigerant, its interaction with the solid adsorbent as well as exterior cooling and heating sources. The following section focuses on the chiller s internal inefficiency by analyzing the entropy generation of the major components throughout a complete operation cycle. Entropy generation is calculated through the conditions of inlet and outlet streams, and the initial and final states of the content of the component control volume. It is noted that the same control volume for each component defined in the modeling process is used in the entropy analysis. Moreover, due to the feature of batch-wise operation, entropy variation of the adsorbent and the heat exchanger materials is taken into account as a significant amount of heat is reserved or emitted from the solid, especially in the beginning of the adsorption / desorption period. In addition, the dissipation due to pressure drop of the thermal sources in the heat exchanger is unknown unless the exact design of the exchanger is provided, which is, however, insignificant on the properties of the fluids as compared to the heat transfer [242], and thus omitted from the entropy calculation. 193

224 Adsorption / Desorption Period Chapter 6: Dynamic Behavior of an Adsorption Chiller In the bed that is undergoing adsorption process, the instantaneous rate of entropy generation is expressed as: ads ds M C p M C p M q C p g e n h x, a d s z l z l a d s dt d t T d t, dq Q T, P ads s t, a d s a d s e M m s s d t T ads dq M s T P s T dt ads z l g a d s e g e z l o i ads ads c w, a d s (6.25) In the right hand side of Equation 6.25, the first term represents cooling of control volume content; the second term denotes superheating of water vapor due to temperature difference between the ADS bed and evaporator; the next term is the entropy change of refrigerant vapor as a result of phase change from gaseous to adsorbed phase; and the final term counts for the cooling water flashing through the ADS heat exchanger. The rate of entropy generation possessed by the adsorption bed is calculated by the sum of the above terms, and is given on the other side of the equation. Comparably, the rate of entropy generation associated with the desorption bed is described below, with the terms owning similar representation as Equation d e s ds M C p M C p M q C p g e n h x, d e s z l z l d e s dt d t T d t d e s 1 M s T, P s T dq Q T, P d e s s t, d e s d e s c M m s s d t T d e s dq dt z l g d e s c g c z l i o d e s hw d e s (6.26) 194

225 Chapter 6: Dynamic Behavior of an Adsorption Chiller For the condenser, a similar technique is applied to compute entropy generation, and expressed as below. c ds M C p ( M C p ) g e n h x, c f, c dt d t T d t c c dq m s s M s T dt d e s o i z l f c c w, c, 1 dq d e s s T P s T M g d e s c g c z l dt (6.27) where, the terms on the right hand side in sequence denotes entropy variation of internal substance, heat rejection to the cooling water, refrigerant water transporting into and out of the condenser. The entropy generated in the evaporator in the adsorption / desorption period is calculated in Equation e ds M C p ( M C p ) g e n h x, e f, e dt d t T d t e e dq m s s M s T dt d e s i o z l f c c h i 1, dq ads s P T s T M g e a d s g e z l dt (6.28) The total rate of internal dissipation of the adsorption chiller during adsorption / desorption period is captured by the sum of entropy generation of all major components, and expressed as a d s d e s c e d S d S d S d S d S g e n g e n g e n g e n g e n (6.29) d t d t d t d t d t 195

226 Switching Period Chapter 6: Dynamic Behavior of an Adsorption Chiller During the switching period, the beds act as closed containers where the energy exchange is solely heat transfer from or to the external heating or cooling water sources. This process inevitably introduces entropy to the system. In the Heat Recovery time interval, for the beds that are performing DE-AD and AD-DE, the thermodynamic second law analysis is conducted respectively as below, ds M C p M C p M q C p d t T d t d e a d, sw g e n h x, b e d zl zl a d s a b e dtdead m s s o i c w, d e a d ads (6.30) ds M C p M C p M q C p d t T d t a d d e, sw g e n h x, b e d zl zl d e s a b e dtad d e m s s i o h w, a d d e d e s (6.31) The corresponding equations for the condenser and evaporator during the same time interval of the switching period are, c, sw ds g e n dt 0 (6.32) e, sw ds M C p ( M C p ) g en h x, e f, e dte m s s i d t T d t e o ch i (6.33) As mentioned that the AD-DE bed and the condenser behaves distinctly as a consequence of route change of the cooling water, the rate of entropy generation of the two said components in the Hold time interval is described below. 196

227 Chapter 6: Dynamic Behavior of an Adsorption Chiller a d d e, sw ds g e n dt 0 (6.34) c, sw ds M C p ( M C p ) g en h x, c f, c dtc m s s o d t T d t c i cw, c (6.35) The total rate of entropy generation for Heat Recovery and Hold time intervals respectively is expressed as: sw d e a d, sw a d d e, sw c, sw e, sw d S d S d S d S d S d t d t d t d t d t g en g en g en g en g en (6.36) 197

228 Chapter 6: Dynamic Behavior of an Adsorption Chiller 6.5. Experimental Investigation of the Adsorption Chiller An experimental study of the zeolite-water adsorption chiller is carried out to investigate its dynamic behavior and the influence of key parameters to its performance. A pictorial view of the chiller is displayed in Figure 6.3. The behavior is reflected by the outlet temperature of the thermal source of the respective components and the pressure inside the chambers. Inlet temperature of hot water is one variable changing from 55 o C to 95 o C. The chilled water outlet temperature is maintained at 12 o C ± 2 o C except that in the 55 o C heat source condition 18 o C ± 1 o C is observed due to the chiller limitation. The other key parameter to be studied is the adsorption / desorption cycle time. A range between 100 s to 400 s is tested. Other operation parameters are listed in Table 6.2. Control panel Condenser Vacuum Pump Adsorption / Desorption Beds Spray Pump Evaporator Figure 6.3: Pictorial view of the zeolite-water adsorption chiller 198

229 Chapter 6: Dynamic Behavior of an Adsorption Chiller Table 6.2: Operation conditions of zeolite water adsorption chiller Parameter Inlet temperature of hot water Inlet temperature of cooling water Outlet temperature of chilled water Flow-rate of hot water Flow-rate of cooling water Flow-rate of chilled water Adsorption / desorption period Switching, heat recovery interval Switching, hold interval Value 55 o C 95 o C 27 o C ± 1 o C 12 o C ± 2 o C 3.8m 3 /hr 8.2m 3 /hr 2.3m 3 /hr 100s 400s 16s 6s Temperature and Pressure Profiles The cyclical manner of the temperature and pressure profiles is a consequent result from batch-wise operation of the chiller. Figure 6.4 displays the beds temperature history during a typical cycle at the hot water inlet temperature of 65 o C and the adsorption / desorption cycle time of 250 s. The reflected parameters are the outlet temperature of the thermal source at the relevant components. One can observe, in an adsorption / desorption period, a rapid change of the values is taking place in the beginning, whereas the profile tends to be steady afterwards. As illustrated in the first adsorption / desorption cycle time, for example, bed 1 starts desorption at an intermediate temperature. This is due to the fact that at the end of switching from cooling to heating source, the bed still remains at a relatively cool state. The large temperature difference between the bed and the heat source drives a faster heat transfer than any other part of the period. The adsorption for bed 2 can be explained in a similar way. In contrast, mass transport plays a major role in the variation of chilled water 199

230 Chapter 6: Dynamic Behavior of an Adsorption Chiller and cooling water outlet temperature. The initiated adsorption and desorption triggers massive molecular transfer from the evaporator and to the condenser, leading to an accelerated cooling production and heat rejection at the early stage of adsorption / desorption period. With the ongoing sorption process in the later stage, both beds are moving towards saturation, flattening the respective temperature profiles. In addition, the temperature profiles in the switching period are determined by the flow pattern of thermal sources. The temporal pressure profiles of the four chambers at the same period as above are shown in Figure 6.5. They reflect clearly the interactions of the components. During the adsorption / desorption period, the pressure of the adsorption (or desorption) bed is equalized with the evaporator (or condenser) after the valve in between is open. However, at the start of the switching period, a sudden change in the heat source also alters the pressure of the beds, causing their pressure departs from the condenser or evaporator. As a result, lever valves are shut and stop mass transport in this period. Besides, preheating the ADS bed increases its pressure, and vice versa for DES bed. This also indicates that the valve-less valves have fulfilled the functions of traditional electrical or pneumatic activated butterfly valves. 200

231 Pressure [Torr] Temperature [ o C] Chapter 6: Dynamic Behavior of an Adsorption Chiller Bed 1 Outlet Bed 2 Outlet Chilled Water Outlet Cooling Water Outlet Adsorption / Desorption Period A Complete Cooling Cycle Switching Period Desorption (DES) 40 Adsorption (ADS) Time [s] Figure 6.4: Temperature profile of the zeolite water adsorption chiller at hot water temperature of 65 o C and adsorption / desorption cycle time of 250 s Bed 1 Bed 2 Evaporator Condenser 50 Adsorption / Desorption Period A Complete Cooling Cycle Switching Period Desorption (DES) Adsorption (ADS) Time [s] Figure 6.5: Pressure profile of the zeolite water adsorption chiller at hot water temperature of 65 o C and adsorption / desorption cycle time of 250 s 201

232 Chapter 6: Dynamic Behavior of an Adsorption Chiller Influence of Heat Source Temperature This subsection describes the effect of the hot water inlet temperature to the performance of the adsorption chiller. Evaluation parameters are presented in terms of total heat input, cooling capacity as well as the COP in various adsorption / desorption cycle times. In Figure 6.6(a), the demand to the total heat input increases with assorted hot water temperature. The trend tends to be smaller at higher end, which is more clear when the adsorption / desorption cycle time is long. Moreover, the input at 95 o C is approximately double of that at lower end. On the contrary, cooling capacity is not following the trend. As shown in Figure 6.6(b), the cooling production experiences a peak as the hot water temperature increases. At the adsorption / desorption cycle time of 100 s to 200 s, the maximum is obtained at around 85 o C with the highest recored production of kw at the latter. In the rest of the adsorption / desorption cycle times, the cooling effect is caped at 65 o C to 75 o C. It is observed that peak cooling capacity shifts towards to the left as the adsorption / desorption cycle time lasts longer. In addition, a significant reduction is realized at 55 o C. It shows that regeneration of the bed is not sufficiently conducted at this temperature level. Furthermore, a spray pump located in the evaporator has a constant power consumption of 0.6 kw. With the presence of the pump power, heat input and cooling capacity, the chiller s COP can be computed. The experiment indicates that the maximum COP is observed at hot water inlet temperature of around 65 o C for all adsorption / desorption cycle times, as illustrated in 202

233 Heat Input, Q H [kw] Chapter 6: Dynamic Behavior of an Adsorption Chiller Figure 6.6(c). The highest COP value is 0.44 when the adsorption / desorption cycle time is set to 400 s. The hot water temperature determines the desorption process and hence the cooling production of the chiller. In a given adsorption / desorption cycle time, the quality of bed regeneration has a direct relation with the bed thermal status. The isotherm theory of adsorption indicates that the amount of equilibrium uptake of vapor reduces when the temperature raises, meaning that a higher heat source temperature gives a better regeneration condition [40]. However, hotter heat source leads to higher desorption and condensation temperature, and hence the pressure. As the equilibrium uptake tends to increase with the pressure, the regeneration of the DES bed is inversely affected. This competing effect may explain the variation of the cooling capacity at different hot water temperatures. 100 s 150 s 200 s 250 s 300 s 350 s 400 s Temperature of Inlet Hot Water, T i,hw [ o C] (a) Total heat input 203

234 Coefficien of Performance [-] Cooling Capacity, Q E [kw] Chapter 6: Dynamic Behavior of an Adsorption Chiller s 150 s 200 s 250 s 300 s 350 s 400 s Temperature of Inlet Hot Water, T i,hw [ o C] (b) Cooling capacity s 150 s 200 s 250 s 300 s 350 s 400 s Temperature of Inlet Hot Water, T i,hw [ o C] (c) Coefficient of Performance (COP) Figure 6.6: Influence of hot water inlet temperature to (a) total heat input, (b) cooling capacity, and (c) COP of the adsorption chiller at various adsorption / desorption cycle times 204

235 Chapter 6: Dynamic Behavior of an Adsorption Chiller Influence of Adsorption / Desorption Cycle Time A further investation of the role of adsorption / desorption cycle time is provided in this subsection. Figure 6.7(a) shows its influence on the total heat input. Generally, increasing adsorption / desorption cycle time helps to ease the demand of thermal energy. The influence is stronger on the shorter periods and high hot water temperature since trend lines are steeper. A major cause to this phenomenon is due to the water mixing. At the moment the beds swaps the function, an amount of cooling water is mixed into the hot water stream. Part of the heat input is inevitably lost because of the invasion of the low temperature source. If shorter adsorption / desorption cycle time is used, more frequent switching takes place, which may translate to increasing heat loss during the role swapping period and hence growing energy consumption. Compared to the heat input, the cooling capacity in Figure 6.7(b) at elongated adsorption / desorption cycle time is not monotonic. It increases till 200 s and then starts droping, while after 300 s becomes stable. At 55 o C hot water temperature the cooling production at all adsorption / desorption cycle time is exceptionally lower than other temperature, indicating that the chiller has reached its lower limit. In general, however, the influence of adsorption / desorption cycle time to the cooling production is insignificant as compared to the heat input. As expected, the dominance of the heat input leads to an increase of the COP with respect to the duration of the adsorption / desorption period (See Figure 6.7(c)). The adsorption / desorption cycle time affects both beds. For desorption, a more thorough regeneration can be achieved when the sorption duration is 205

236 Heat Input, Q H [kw] Chapter 6: Dynamic Behavior of an Adsorption Chiller longer. This is beneficial to the next cycle s cooling production as a better regeneration condition is able to provide greater adsorption driving force to the evaporated refrigerant molecules, especially in the beginning period of the process. However, adsorption rate reduces extensively when the adsorbate uptake is approaching to saturation. Long exposure to the evaporator eventually leads to diminishing cooling rate, especially at the end of the adsorption / desorption period. This may explain the relative insensitivity of the cooling capacity to the various adsorption / desorption cycle time. 55 C 65 C 75 C 85 C 95 C Adsorption / Desorption Cycle Time [s] (a) Total heat input 206

237 Coefficient of Performance [-] Cooling Capacity, Q E [kw] Chapter 6: Dynamic Behavior of an Adsorption Chiller C 65 C 75 C 85 C 95 C Adsorption / Desorption Cycle Time [s] (b) Cooling capacity C 65 C 75 C 85 C 95 C Adsorption / Desorption Cycle Time [s] (c) Coefficient of Performance (COP) Figure 6.7: Influence of adsorption / desorption cycle time to (a) total heat input, (b) cooling capacity, and (c) COP of the adsorption chiller at various hot water inlet temperatures 207

238 6.6. Model Validation Chapter 6: Dynamic Behavior of an Adsorption Chiller The adsorption characteristic equations, energy and mass conservation equations of the major adsorption chiller components that are described in Section 6.3 are solved numerically in FORTRAN 90 Developer Studio software. FORTRAN is a general-purpose programming language supported by various mathematical libraries. It is frequently used by researchers and engineers to perform numerical and scientific computation. The modeling equations in each operation period are a set of coupled ordinary differential equations with given initial conditions which are required to be solved simultaneously. The calculation is achieved with an initial problem solver developed under the DIVPAG double precision subroutine of the IMSL library of FORTRAN. It is highlighted that the equations are computed in an iterative basis, employing Gear s Backward Differentiation Formulas (BDF) method. The computation algorithm of the modeling equations entails interaction between main program and initial problem solver (or, DIVPAG subroutine), as shown in Figure 6.8. The program is started by specifying the chiller s starting temperature and pressure of major components, and operation conditions such as inlet temperature of hot water, cooling water and chilled water, as well as duration of each operation period, etc. Solutions of each period are then obtained from the initial problem solver in temporal manner. In the solver, computation is commenced with initialization of variables by starting conditions for the first adsorption / desorption period, or results of the ending point of previous period for the subsequent periods. The program stops when the chiller reaches cyclical steady state, i.e. the results of variables in the adjacent same period converge in the tolerance range. 208

239 Solve the next half cycle Chapter 6: Dynamic Behavior of an Adsorption Chiller Initial Problem Solver START Initialization Components initialized from starting conditions or conditions of the ending point of previous period (time, t = 0) Time increment (t++) t Given period? Call DIVPAG from IMSL To solve energy, mass conservation and entropy equations OUTPUT Temperature, pressure, entropy, COP etc STOP Y N Half Cycle START INPUT Thermal source conditions, sorption & switching periods, components starting state SOLVE (Initial problem solver) Adsorption / Desorption Period SOLVE (Initial problem solver) Switching, Heat Recovery Interval SOLVE (Initial problem solver) Switching, Hold Interval If X j -X j END Y N Figure 6.8: Computation flowchart on the simulation of the adsorption chiller The simulation model is validated with the experimental data obtained in a typical operation conditions of hot water inlet temperature 65.0 o C, cooling water inlet temperature 26.9 o C, chilled water inlet temperature 16.1 o C, and adsorption / desorption cycle time 300 s. Value of constants used in the simulation program is listed in Table 6.3. Water properties are calculated from functions provided by Wagner et al [ ]. Figure 6.9 illustrates the respective simulated and experimentally tested outlet temperature of the thermal sources of the beds, the evaporator and the condenser. The numerical solution shows in general good agreement with the experimental data. The simulated chilled water outlet temperature is slightly lower than the measured value due to the ignorance of heat loss to the evaporator surroundings. There is 209

240 Temperature [ o C] Chapter 6: Dynamic Behavior of an Adsorption Chiller a minor mismatch encountered for the switching period. It is subjected to the limitations of the modeling in which the complicated valve control strategy of the prototype chiller is simplified, and the associated time delay and thermal source mixing are underestimated. Table 6.3: Values of parameters used in the adsorption chiller simulation Parameter Symbol Value Operation conditions Flow-rate of hot water, 3.8 m 3 /hr Flow-rate of cooling water, 8.2 m 3 /hr Flow-rate of chilled water, 2.3 m 3 /hr Heat recovery interval t sw,hr 16 s Hold interval t sw,ho 6 s Adsorption isotherm and kinetics Surface diffusion factor, D so 2.54 x 10-4 m 2 /s Activation energy, E a 4.55 x 10 4 kj/kmol Average radius of zeolite particles, R p 1.0 x 10-4 m Statistical rate constant for Q st K 2.71 x kpa -1 Mass of the FAM Z01 zeolite, M zl 12 kg 70 Bed 1 Outlet (Exp.) Chilled Water Outlet (Exp.) Simulation Bed 2 Outlet (Exp.) Cooling Water Outlet (Exp.) Time [s] Figure 6.9: Validation of numerical model with experimental data of the outlet thermal source temperature of respective chiller components 210

241 6.7. Results of Entropy Analysis Chapter 6: Dynamic Behavior of an Adsorption Chiller Temporal Entropy Generation A computational result of the entropy generation on the cyclical steady operation period for the zeolite water adsorption chiller is presented below. The computation is performed based on the simulation results at various inlet hot water temperatures and the adsorption / desorption cycle times. The irreversibilities of the chiller major components are analyzed with respect to the two aspects. A term named as specific entropy generation, which is defined as the cyclical average entropy generation per unit power of cooling capacity, is used to reveal the behavior of the chiller. Figure 6.10 displays the temporal entropy generation rate of each major component and the total value in a half operation cycle (an adsorption / desorption period and a subsquent switching period) in the conditions of the hot water inlet temperature 65 o C and adsorption / desorption cycle time 200 s. The cooling water inlet and chilled water outlet are 26.5 o C and 11 o C, respectively. In the early stage of adsorption / desorption period and the switching period, as illustrated, a significant amount of entropy is produced by both beds. The degree of magnitude is two orders greater than that of the evaporator and condenser. It is observed that in these periods a large temperature difference exists between the beds and the respective thermal sources, the significant entropy production is expected. In the same duration, negligible irreversibility is generated in the condenser. This is due to the null mass transport before the lever valves open and small temperature difference across the shell and tube side of the condenser heat exchanger. In the later 211

242 Entropy Generation Rate, ds gen /dt [W/K] (Evap & Cond) Entropy Generation Rate, dsgen/dt [W/K] (ADS, DES, and Total) Chapter 6: Dynamic Behavior of an Adsorption Chiller stage of the adsorption / desorption period, however, the entropy generation of both beds decreases rapidly as time proceeds. As the beds approach the thermal source temperature and adsorbed phase saturation, irreversibility is also diminished. Comparatively, entropy production of the evaporator is more consistent throughout the cycle. In the overall process, the cyclic average of total entropy production is 5.09 W/K, in which the DES bed encounters the most irreversibility, followed by the ADS bed. The smallest entropy generation is observed in the condenser. 5 4 Evap Cond ADS DES Total Adsorption / Desorption Period Switching Period Time [s] 0.01 Figure 6.10: Temporal entropy generation rate of chiller major components in a typical half operation cycle. The result is computed from the simulation in the conditions of hot water inlet temperature 65 o C and adsorption / desorption cycle time 200 s 212

243 Chapter 6: Dynamic Behavior of an Adsorption Chiller Entropy and Heat Source Temperature Cyclical average entropy generation rate of every component in the half operation cycle with respect to the temperature of inlet hot water is illustrated in Figure The adsorption / desorption cycle time is fixed at 200 s. It is shown that production of entropy escalates to the heat source temperature for all components among which the desorption bed is influenced most severely as a result of lowest heat transfer efficiency. Furthermore, increasing hot water temperature enlarges the temperature disparity between adsorption and desorption state, leading to a growing temperature gap between the DES bed contents and the heat source in the initial stage of the adsorption / desorption period and the switching period. Since the two durations are responsible for provoking tremendous amount of dissipation, the cyclical average of the entropy generation in the DES bed is more profoundly influenced. On the other hand, with the help of more effective heat transfer, the ADS bed acts more resistively to the irreversibility as the hot water temperature increases. The evaporator and condenser are impacted through indirect ways by mass transport. A further investigation of contribution of each component to the total entropy generation at 200 s adsorption / desorption cycle time and various heat source temperatures is represented in Figure Clearly, the DES bed is responsible for the biggest portion of dissipation, approximately % of the total, among four components. Both beds account 80 % in average of entropy generation, implying the importance of addressing high irreversibilities of the beds. It validates the effort of the work from previous chapters to promote the adsorption heat and mass transfer by introducing 213

244 Chapter 6: Dynamic Behavior of an Adsorption Chiller binder. Figure 6.13 shows the percentage contribution of the adsorption / desorption period and switching period to the total entropy generation of a half operation cycle. Despite of much shorter duration of the latter, it produces as much irreversibilities as, or even higher the former. It is known that the cooling production is suppressed in the switching period. The switching mechanism is another major dissipation that caused the low COP of the adsorption chillers. Entropy generation is a direct measurement of inefficiency of a system. It reveals how far away the system is to the thermodynamic limit, or the Carnot COP. Figure 10 illustrates specific entropy generation, COP and Carnot COP of the adsorption chiller at the tested hot water temperature range. Although increasing heat source temperature brings up the theoretical Carnot limit, the chiller s real COP is following an opposite trend after 65 o C. This is, however, not unpredictable as specific entropy generation rate rises exponentially after this temperature. More irreversibilities are generated to produce per unit power of useful effect, leading to the growing gap between the chiller s efficiency to the Carnot limit. 214

245 Percentage Contribution Entropy Generation Rate, ds gen /dt [W/K] Chapter 6: Dynamic Behavior of an Adsorption Chiller 14 ADS DES Evap Cond Total Temperature of Inlet Hot Water, T i,hw [ o C] Figure 6.11: Cyclic average entropy generation rate of the chiller major components in a half operation cycle at 200 s adsorption / desorption cycle time and increasing temperature of inlet hot water 100% 80% 4% 5% ADS DES Evap Cond 10% 12% 13% 9% 8% 18% 19% 14% 60% 58% 40% 53% 51% 56% 69% 20% 0% 33% 19% 18% 16% 14% Temperature of Inlet Hot Water, T i,hw [ o C] Figure 6.12: Percentage of entropy generation of the chiller major components in a half operation cycle at 200 s adsorption / desorption cycle time and increasing temperature of inlet hot water 215

246 Specific Entropy Generation [W/K-kW] & Coefficien of Performance [-] Coefficient of Performance, Carnot [-] Percentage Contribution Chapter 6: Dynamic Behavior of an Adsorption Chiller 100% Adsorption/desorption period Switching period 80% 44% 45% 47% 49% 60% 73% 40% 20% 27% 56% 55% 53% 51% 0% Temperature of Inlet Hot Water, T i,hw [ o C] Figure 6.13: Percentage of entropy generation of the adsorption / desorption period and switching period in a half operation cycle at 200 s adsorption / desorption cycle time and increasing temperature of inlet hot water Specific Entropy Generation COP COP Carnot Temperature of Inlet Hot Water, T i,hw [ o C] Figure 6.14: Specific entropy generation, COP and Carnot COP of the adsorption chiller at 200 s adsorption / desorption cycle time and assorted temperature of inlet hot water 216

247 Chapter 6: Dynamic Behavior of an Adsorption Chiller Entropy and Adsorption / Desorption Cycle Time Figures 6.15 to 6.18 display the entropy generation analysis of the chiller components with respect to the duration of adsorption / desorption period. The inlet hot water temprature is fixed at 65 o C. It has indicated the most of entropy is produced in the beginning of the adsorption / desorption period and the switching period. However, increasing adsorption / desorption duration mainly affects the later part of the adsorption / desorption period in which the dissipation is insigificant. As a result, the average generation rate of both beds in a half operation cycle decreases in Figure On the contrary, the evaporator behaves in an oppsite manner. Due to the dominance of the beds in terms of percentage contribution (See Figure 6.16), the total average entropy production is thus decreased. However, the percentage contribution of entropy generation of the beds are shrinking at elongating adsorption / desorption duration. As shown in Figure 6.17, on the other hand, the influence of the adsorpton / desorption period is growing as its duration increases. This is mostly attribute to its ascending dominance on the time scale as compared to the switching period. Last but not least, in Figure 6.18, the Carnot COP of the chiller is fairly a constant regardless of adsorption / desorption cycle time because of a maintained thermal reservior temperatures. It is clearly indicated that at the same thermal reservior temperature, minimum specific entropy generation leads to the maximum COP of the adsorption chiller. 217

248 Percentage Contribution Entropy Generation Rate, ds gen /dt [W/K] Chapter 6: Dynamic Behavior of an Adsorption Chiller 7 ADS DES Evap Cond Total Adsorption / Desorption Cycle Time [s] Figure 6.15: Cyclical average entropy generation rate of the chiller major components in a half operation cycle at 65 o C inlet hot water and various adsorption / desorption cycle times 100% 80% ADS DES Evap Cond 5% 8% 10% 11% 12% 6% 12% 13% 14% 18% 22% 24% 25% 25% 60% 40% 66% 57% 53% 48% 45% 44% 43% 20% 23% 21% 19% 19% 19% 18% 19% 0% Adsorption / Desorption Cycle Time [s] Figure 6.16: Percentage of entropy generation of the chiller major components in a half operation cycle at 65 o C inlet hot water and various adsorption / desorption cycle times 218

249 Specific Entropy Generation [W/K-kW] & Coefficien of Performance [-] Coefficient of Performance, Carnot [-] Percentage Contribution Chapter 6: Dynamic Behavior of an Adsorption Chiller 100% Adsorption/desorption period Switching period 80% 58% 49% 44% 39% 36% 35% 35% 60% 40% 20% 42% 51% 56% 61% 64% 65% 65% 0% Adsorption / Desorption Cycle Time [s] Figure 6.17: Percentage of entropy generation of the adsorption / desorption period and switching period in a half operation cycle at 65 o C inlet hot water and various adsorption / desorption cycle times 1.2 Specific Entropy Generation COP COP Carnot Adsorption / Desorption Cycle Time [s] Figure 6.18: Specific entropy generation, COP and Carnot COP of the adsorption chiller at 65 o C inlet hot water and assorted adsorption / desorption cycle times 219

250 Chapter 6: Dynamic Behavior of an Adsorption Chiller 6.8. Summary In this chapter, mathematical modeling, experimental investigation and entropy analysis are conducted for a low grade waste heat driven adsorption chiller utilizing zeolite FAM Z01-water pair. Several findings from the previous chapters are applied to study the chiller, including coating of adsorbent onto the bed heat exchanger by binder to promote heat and mass transfer, local adsorption heat transfer correlation, and thermodynamic formulation on the adsorbent-adsorbate pair, etc. A transient mathematical model is developed to simulate the chiller performance and dynamic behavior of its major components. The simulation results show good agreement with the experimental data. Experimental evaluation indicates that the cooling capacity increases with heat input over the supplied hot water temperatures. The peak of cooling capacity occurs at 65 o C to 85 o C for a wide range of cycle time. Optimum hot water temperature for most efficient operation is 65 o C. However, the cooling capacity reduces at longer sorption duration due to diminishing uptake potential of adsorbent. The experiments indicated an optimum adsorption / desorption cycle time for the present zeolite-water adsorption chiller is between 200 s to 300 s. Entropy generation of the adsorption chiller is presented for (i) the adsorption / desorption cycle time, (ii) the hot water inlet temperature. The results suggest that the cyclical average entropy generation rate rises with increasing hot water temperature and reduces with decreasing cycle time. It is found that, amongst all components in the system, the desorption bed 220

251 Chapter 6: Dynamic Behavior of an Adsorption Chiller contributes to the biggest portion of irreversibilities. This is followed by the adsorption bed, evaporator and condenser unit. Furthermore, the contribution from the switching period is as significant as the adsorption / desorption period. As the entropy generation is dominated by the heat and mass transfer in the chiller components, the analysis indicates the importance to promote the efficiency of heat exchangers, especially for the adsorption beds. This validates the effort of the previous chapters to promote heat and mass transfer of adsorbent embedded heat exchangers using binder. On a specific entropy generation basis, defined as entropy generation per unit mass of useful effect, it demonstrates the optimized efficiency of the adsorption chiller, i.e., the highest COP occurs when the specific entropy generation is smallest. 221

252 Chapter 7: Conclusion CHAPTER 7 CONCLUSION 7.1. Major Findings of This Thesis In this work, the performance of the adsorbent embedded heat exchanger is improved by introducing binders and coating the adsorbent as a thin layer onto the metal fins. The binder influence on the heat and mass transfer of the heat exchanger is studied from both experimental and theoretical perspectives. This proposed method will help significantly increase the COP and reduce the plant size, and hence the material and engineering cost of the conventional adsorption chillers. The major findings of the present thesis are as follows: 1. Several types of binder, namely epoxy, polyvinyl alcohol (PVA), corn flour, hydroxyethyl cellulose (HEC), gelatin, bentonite, and sepiolite are tested amongst which the HEC appears best binding ability between metal fins and silica gel as well as among silica gel particles, relatively low surface area reduction on the original adsorbent and long lasting. The HEC of 3.3 adsorbent weight percentages give maximum BET surface area among various silica gel and HEC mixing ratios. The same binder is also found suitable for zeolite FAM Z01-water pair. 2. A new method is proposed to embed silica gel onto a heat exchanger. It is to coat a thin layer of the powdered silica gels (type 3A and type RD powder) directly onto the exchanger fins by applying 3.3 adsorbent wt% HEC, instead of using the conventional mesh packing method. Experiment is conducted to evaluate the new method on the overall heat transfer 222

253 Chapter 7: Conclusion performance of the heat exchanger during adsorption processes and show that it improves significantly the cyclical average heat transfer coefficient per unit mass of adsorbent by 4.6 and 3.4 folds, respectively in the two application cases over the conventional method. The proposed method also reacts more actively to the heat flux. 3. The influence of the HEC binder on the adsorption capacity is investigated by measuring the water uptake of the pure silica gel type 3A, RD powder and the corresponding 3.3 adsorbent wt% HEC adhered samples at 25 o C to 45 o C. It is shown that the binder reduces an average 27.3 % of water equilibrium uptake on the type 3A but possesses negligible effect on the type RD powder. A new isotherm model that can fit both Type I and Type V isotherm categories is proposed, which can be derived from the results of the statistical rate theory of adsorption using an asymmetrical energy distribution function given in this work. For the four tested silica gel-water pairs that belong to Type I, the proposed model significantly reduces the regression error of the classic DA and Tóth model of % and % respectively to as small as %. 4. The net influence of HEC on the mass transfer during adsorption process is determined from the experimental data of the heat transfer and adsorption isotherms, since the rate of uptake is a function of both adsorbent temperature and adsorption capacity. The results show that the water uptake rate on the silica gel due to HEC coating method is two folds faster than the conventional technique. 223

254 Chapter 7: Conclusion 5. A new water adsorbent, zeolite FAM Z01 is studied in this thesis. An experiment is conducted to measure the water adsorption isotherms of the zeolite with and without 3.3 adsorbent wt% HEC and shows that 1) the isotherms belong to Type V category; 2) HEC has negligible influence; and 3) the zeolite possesses 3.4 times higher water uptake capacity than silica gel at typical adsorption chiller operation conditions. The data are regressed accurately by the proposed isotherm model, with error of 5.85 % to 6.05 %. Last but not least, a molecular dynamic simulation is conducted to investigate the water adsorption mechanism of zeolite FAM Z01 from nano-scale, and indicates that two window structures on the zeolite molecular frame, namely large channel and inner pore, are responsible for providing significantly large volume in the adsorbent interior to accommodate the adsorbed water molecules at near room temperature conditions. It explains the sharp increase of water uptake on the zeolite FAM Z01 in a narrow pressure range, and the higher water adsorption capacity than silica gel at typical adsorption chiller operation conditions. 6. The transient local adsorption heat transfer phenomenon between the heat exchanger fins and the adsorbent-adsorbate interaction layer is studied in detail to fill this gap in the literature. The experimental value of the coefficient that quantifies this phenomenon is calculated by eliminating the thermal resistance of other layers along the heat transfer paths. A further analysis on the contribution of thermal resistance from each layer illustrated that the adsorbent-adsorbate interaction layer and fin are attributable to 72 % and 22.4 % of the overall thermal resistance accordingly in the early adsorption process, out of which 70.8 % and 224

255 Chapter 7: Conclusion 21.5 %, respectively, are due to thermal mass effect. In the later stage of the process where steady cooling takes place, the average contribution of the adsorbent-adsorbate interaction layer is 79.8 %, followed by 15.7 % from tube side cooling water convection. 7. In this thesis, a novel correlation is proposed to predict the adsorption local heat transfer coefficient. It utilizes the specifications of heat exchangers and the thermodynamic properties of an adsorbent-adsorbate pair. A new dimensionless group is defined in the correlation, named as adsorption number which describes the magnitude of heat of adsorption being accumulated inside the adsorbent-adsorbate interaction layer during an adsorption process. The accuracy of the correlation is validated by experimental data, with R and error 13.8% being achieved. 8. Several previous findings are applied to study a low grade waste heat driven adsorption chiller. The chiller utilizes zeolite FAM Z01-water as adsorbent-adsorbate pair. The adsorbent is coated a thin layer onto the heat exchanger fins to promote heat and mass transfer. A transient mathematical model, incorporating with the local adsorption heat transfer correlation and thermodynamic formulation on the adsorbent-adsorbate pair, is developed to simulate the dynamic behavior of chiller. It is validated by the experimental temperature profile of the chiller major components. An experiment is conducted to evaluate the performance of the chiller. The results show that the maximum cooling capacity is produced at heat source temperature 65 o C to 85 o C depending on the cycle time. Generally maximum COP of the chiller occurs at 65 o C heat source. The experiment also suggests the optimum adsorption / desorption cycle 225

256 Chapter 7: Conclusion time for the present zeolite-water adsorption chiller is between 200 s to 300 s. 9. The irreversibilities encountered by the zeolite FAM Z01-water adsorption chiller are analyzed through entropy generation. It is shown that amongst all the components of the chiller, desorption bed induces largest portion of entropy generation, followed by adsorption bed, evaporator and condenser. Moreover, the switching period contributes to the dissipation as significantly as the adsorption / desorption period. Known that irreversibilities are dominantly incurred from heat and mass transfer, it is crucial to improve the performance of the heat exchangers of respective components, by which the efficiency of the transfer phenomena can be promoted. This is especially important for the adsorption / desorption beds. The entropy analysis validates the effort of this work to increase the heat and mass transport of the adsorbent embedded heat exchangers by utilizing binder, so as to increase the efficiency, reduce the plant footprint as well as the engineering cost of the conventional adsorption chillers. 226

257 Chapter 7: Conclusion 7.2. Future Work Recommendations Based on the present thesis, the following are recommended for future work. 1. Through the study of energy distribution invoked in the statistical rate theory, a universal isotherm model is possibly derived for the various types of isotherm. A further analysis on the isotherm models for different isotherm categories is needed. The adsorption kinetics can also be investigated using the theory. 2. Binder selection for other adsorbent-adsorbate pairs, such as active carbonmethane, propane, etc, can be conducted to improve the efficiency of the adsorption gas storage and refrigeration systems. 3. Further molecular dynamic simulation can be performed to understand the adsorption associated molecule behavior, energy exchange, etc from nanoscale. A theoretical link between the macro-scale adsorption phenomena and the molecular level will be established, in order that characteristics of any adsorbent-adsorbate pairs can be predicted. 4. A study may be undertaken on the integration of the low grade waste heat driven adsorption chiller with cogeneration plants to provide district cooling. A temperature cascaded configuration can be applied to increase the energy utilization efficiency of the system. Experiments are required to evaluate the performance of the overall system. 227

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294 Appendix A: Adsorption Isotherm Data of Silica gel-water Pairs APPENDICES Appendix A: Adsorption Isotherm Data of Silica gel-water Pairs Table A1: Adsorption isotherm data of silica gel type 3A-water pair T P q* T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

295 Appendix A: Adsorption Isotherm Data of Silica gel-water Pairs Table A2: Adsorption isotherm data of 3.3 adsorbent wt% HEC added silica gel type 3A-water pair T P q* T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

296 Appendix A: Adsorption Isotherm Data of Silica gel-water Pairs Table A3: Adsorption isotherm data of silica gel type RD powder-water pair T P q* T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

297 Appendix A: Adsorption Isotherm Data of Silica gel-water Pairs Table A4: Adsorption isotherm data of 3.3 adsorbent wt% HEC added silica gel type RD powder-water pair T P q* T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

298 Appendix B: Adsorption Isotherm Data of Zeolite-Water Pairs Appendix B: Adsorption Isotherm Data of Zeolite -Water Pairs Table B1: Adsorption isotherm data of zeolite FAM Z01-water pair at 25 o C, 30 o C and 35 o C T P q* T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

299 Appendix B: Adsorption Isotherm Data of Zeolite-Water Pairs Table B2: Adsorption isotherm data of zeolite FAM Z01-water pair at 40 o C and 45 o C T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

300 Appendix B: Adsorption Isotherm Data of Zeolite-Water Pairs Table B3: Adsorption isotherm data of 3.3 adsorbent wt% HEC added zeolite FAM Z01-water pair at 25 o C, 30 o C and 35 o C T P q* T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

301 Appendix B: Adsorption Isotherm Data of Zeolite-Water Pairs Table B4: Adsorption isotherm data of 3.3 adsorbent wt% HEC added zeolite FAM Z01-water pair at 40 o C and 45 o C T P q* T P q* [ o C] [kpa] [kg/kg] [ o C] [kpa] [kg/kg]

302 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller The operation strategy of the zeolite-water adsorption chiller is performed by controlling the flow patterns of the hot, cooling and chilled water in the following sequence through operation of valves: Z A-1 A B A+1 B+1 A+2 B+2 HR-A HR-B HoA HoB Figure C1: Flow pattern sequence of the zeolite-water adsorption chiller 272

303 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller (a) Flow Pattern Z (b) Flow Pattern A-1 273

304 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller (c) Flow Pattern A (d) Flow Pattern A+1 274

305 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller (e) Flow Pattern A+2 (f) Flow Pattern HR-A 275

306 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller (g) Flow Pattern HoA (h) Flow Pattern B 276

307 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller (i) Flow Pattern B+1 (j) Flow Pattern B+2 277

308 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller (k) Flow Pattern HR-B (l) Flow Pattern HoB Figure C2: Flow patterns of the zeolite-water adsorption chiller 278

309 Appendix C: Operation Strategy of the Zeolite-Water Adsorption Chiller Table C1: Valve sequence of the zeolite-water adsorption chiller 279