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ADSORPTION MODELING OF COALBED GASES AND THE EFFECTS OF WATER ON THEIR ADSORPTION BEHAVIOR By SAYEED AHMED MOHAMMAD Bachelor of Science in Chemical Engineering Osmania University Hyderabad, India 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 2009 ii ADSORPTION MODELING OF COALBED GASES AND THE EFFECTS OF WATER ON THEIR ADSORPTION BEHAVIOR Dissertation Approved: Dr. Khaled A. M. Gasem Dissertation Adviser Dr. Robert L. Robinson, Jr. Dr. Jan Wagner Dr. William D. Warde Dr. A. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGMENTS I would like to express my gratitude to my adviser, Dr. Khaled Gasem, for giving me the opportunity to work with him on this project. I greatly appreciate his invaluable guidance, support and encouragement for conducting quality research, and for teaching me to be a "truth seeker" as a researcher. Through out my five years of work with him, I have learnt some great lessons in research and life. I would like to thank my coadviser, Dr. Robert Robinson, Jr., for his invaluable insight, supervision and thoughtful reviews of this work. I am also grateful to my advisory committee members, Dr. Jan Wagner and Dr. Bill Warde, for their valuable input and helpful suggestions. It has been a great honor for me to have worked with these distinguished members of the OSU Graduate Faculty. I also express my sincere appreciation and gratitude for my past colleagues in this project, Dr. James Fitzgerald and Ms. Jing Chen, for their support and help with this project. I also thank the many friends and acquaintances I made over the years, whose friendship I truly appreciate. I also acknowledge the support of the U.S. Department of Energy to our research group that made this project possible. I thank many of the friends at Stillwater Islamic Center for their good wishes. I would like to thank Dr. Saleh Ashaghathra, Dr. Ahmed Abo Basha, Dr. Mumtaz Hussain and Dr. Qamar Arsalan for their valuable friendship and encouragement. iv Finally, I am grateful to my parents, sister, brother and his family for their sacrifices, patience and prayers through out my graduate studies. Their support, understanding and encouragement were most crucial in my continued success away from home. Sayeed Mohammad May 8, 2009 v TABLE OF CONTENTS Chapter Page 1. INTRODUCTION .....................................................................................................1 1.1 Coalbed Methane and CO2 Sequestration ..........................................................1 1.2 Adsorption Models.............................................................................................2 1.3 Effect of Water on Coalbed Gas Adsorption Behavior .....................................3 1.4 Objectives ..........................................................................................................5 1.5 Organization .......................................................................................................8 2. EXPERIMENTAL METHODS, PROCEDURES AND RESULTS ......................10 2.1 Adsorption Isotherm Measurements ................................................................11 2.2 Gas Compressibility Factors ............................................................................14 2.3 Materials ..........................................................................................................14 2.4 Error Analysis ..................................................................................................16 2.5 Equilibrium Moisture of Coals and Activated Carbon ....................................16 2.6 Gas Solubility in Water ....................................................................................18 2.7 Adsorption Measurements on Wet Coals and Activated Carbon ....................20 2.8 Coal Swelling ...................................................................................................21 2.9 Gibbs and Absolute Adsorption .......................................................................23 2.10 Experimental Results .....................................................................................23 Adsorption of CO2 on Wet Argonne Coals................................................23 Adsorption of Methane, Nitrogen and CO2 on Dry and Wet Activated Carbon................................................................................32 2.11 OSU CBM Adsorption Database ...................................................................43 2.12 Monte Carlo Analysis of OSU Adsorption Error Analysis ...........................44 3. REVIEW OF ADSORPTION MODELS IN CBMRELATED WORK ................48 3.1 Adsorption Models in CBMRelated Work .....................................................48 3.2 TheoryBased Equilibrium Adsorption Models...............................................56 3.3 Example Studies of Adsorption Modeling .......................................................68 3.4 Limitations and Future Work ...........................................................................79 3.5 Conclusions ......................................................................................................80 vi Chapter Page 4. REVIEW OF PURE WATER ADSORPTION .......................................................82 4.1 Introduction ......................................................................................................82 4.2 Surface Characterization of Activated Carbons and Coals ..............................86 A Case Study of the SLDPR Model Applied to Pure Water Adsorption .......................................................................................94 4.3 The Physical State of Water Naturally Found on Coals ..................................99 4.4 Water Adsorption Models ..............................................................................111 4.5 Summary ........................................................................................................120 4.6 Modeling Approaches ....................................................................................121 4.7 Modifications to the SLDPR Model .............................................................123 5. SIMPLIFIED LOCALDENSITY/PENGROBINSON (SLDPR) ADSORPTION MODEL .....................................................................................124 5.1 Introduction ....................................................................................................124 5.2 SLDPR Adsorption Model ...........................................................................124 5.3 Modifications to SLDPR Model for Pure Water Adsorption Modeling ......131 5.4 Representation of Adsorbed Water Capacity with SLDPR Model ..............134 5.5 SLDPR Model for Mixed Gas Adsorption ...................................................136 5.6 SLDPR Modeling of CO2Water Mixture Adsorption on Wet Argonne Coals ........................................................................................141 5.7 Case Study Conclusions .................................................................................165 6. GENERALIZATION OF SLDPR MODEL.........................................................167 6.1 Generalization Approach ...............................................................................167 6.2 Database Employed in this Study ..................................................................168 6.3 SLDPR Model Representation of PureGas Adsorption Data......................172 6.4 Generalized Correlations ...............................................................................178 6.5 SLDPR Generalized Model for PureGas Adsorption on Coals ..................181 6.6 Previous Generalization Studies ...................................................................192 6.7 Sensitivity Analysis of SLDPR Model Generalization ................................196 6.8 SLDPR Generalized Model Predictions for MixedGas Adsorption ...........200 6.9 Validation of the SLDPR Generalized Model ..............................................213 6.10 Generalization Conclusions .........................................................................216 7. CONCLUSIONS AND RECOMMENDATIONS ................................................217 7.1 Conclusions ....................................................................................................217 7.2 Recommendations ..........................................................................................219 REFERENCES ......................................................................................................221 vii LIST OF TABLES Table Page 2.1 Compositional Analyses of Adsorbents Used in this Study ................................15 2.2 Parameters for Gas Solubility in Water at 318.2 K or 319.3 K ...........................19 2.3 Parameters for CO2 Solubility in Water at Multiple Temperatures .....................20 2.4 Gibbs Adsorption of Pure CO2 on Wet Beulah Zap Coal at 328.2 K ..................24 2.5 Gibbs Adsorption of Pure CO2 on Wet Illinois #6 Coal at 328.2 K ....................24 2.6 Gibbs Adsorption of Pure CO2 on Wet Pocahontas #3 Coal at 328.2 K .............25 2.7 Gibbs Adsorption of Pure CO2 on Wet Upper Freeport Coal at 328.2 K ............25 2.8 Gibbs Adsorption of Pure CO2 on Wet Wyodak Coal at 328.2 K .......................26 2.9 Gibbs Adsorption of Pure Nitrogen on Dry Activated Carbon at 328.2 K ...........................................................................................................33 2.10 Gibbs Adsorption of Pure Methane on Dry Activated Carbon at 328.2 K .........................................................................................................33 2.11 Gibbs Adsorption of Pure CO2 on Dry Activated Carbon at 328.2 K .........................................................................................................34 2.12 Gibbs Adsorption of Pure Nitrogen on Wet Activated Carbon at 328.2 K and 37% Moisture ...........................................................................34 2.13 Gibbs Adsorption of Pure Methane on Wet Activated Carbon at 328.2 K and 37% Moisture ...........................................................................34 2.14 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 27% Moisture ...........................................................................35 2.15 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 34% Moisture ...........................................................................35 viii Table Page 2.16 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 16% Moisture ..........................................................................36 2.17 Extended OSU Adsorption Database: New Systems in This Study .................44 3.1 Regressed Model Parameters for Representations of PureGas Adsorption on Dry and Wet Coals ......................................................................71 3.2 Sample Results for Model Representations of PureGas Adsorption on Dry and Wet Coals ......................................................................72 4.1 SLDPR Model Case Study for PureWater Adsorption on Activated Carbons from the Literature ...............................................................96 5.1 Physical Properties of Fluids Used in SLDPR Model .....................................128 5.2 A Case Study with the New Parameterization of SLDPR Model for Pure Water Adsorption on Activated Carbons..................................................137 5.3 A Case Study with the New Parameterization of SLDPR Model for Pure Water Adsorption on Coals ......................................................................137 5.4 SLDPR Model Representations of CO2Water Binary Mixture Adsorption on Wet Argonne Coals ..................................................................154 5.5 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Pocahontas Coal ...................................................................................161 5.6 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Upper Freeport Coal .............................................................................161 5.7 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Illinois #6 Coal .....................................................................................162 5.8 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Wyodak Coal ........................................................................................162 5.9 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Beulah Zap Coal ...................................................................................163 6.1 Adsorption Database Used For SLDPR Model Generalization ......................169 6.2 Compositional Analyses of OSU Coals Used in this Study .............................171 ix Table Page 6.3 Compositional Analyses of Argonne Premium Coals Used in this Study ........171 6.4 SLDPR Model Representations of PureGas Adsorption on Coals ................174 6.5 Correlation Matrix of SLDPR Model Regressed Parameters for Coals ..........177 6.6 Correlation Matrix of Coal Properties ..............................................................179 6.7 Summary Results of SLDPR PureGas Model Generalization for Coals .......183 6.8 Comparison of Generalized and Regressed Model Parameters ........................184 6.9 Sensitivity Analysis of SLDPR Model Parameters for PureGas Adsorption on Wet Fruitland Coal at 319.3 K ..................................................198 6.10 Summary Results of Generalized SLDPR Predictions for MixedGas Adsorption on Coals ..............................................................201 6.11 Validation Results for the Generalized SLDPR Model Predictions: CO2 Adsorption on 27 Coals Reported by Day et al. .....................................213 x LIST OF FIGURES Figure Page 2.1 Schematic Diagram of the Experimental Apparatus .........................................13 2.2 Comparison of CO2 Adsorption Data on Wet Beulah Zap Coal at 328.2 K: Effect of Gas Solubility in Water ...................................................28 2.3 CO2 Adsorption on Wet and Dry Beulah Zap Coal at 328.2 K ........................28 2.4 CO2 Adsorption on Wet and Dry Illinois #6 Coal at 328.2 K ..........................29 2.5 CO2 Adsorption on Wet and Dry Pocahontas Coal at 328.2 K ........................29 2.6 CO2 Adsorption on Wet and Dry Upper Freeport Coal at 328.2 K ..................30 2.7 CO2 Adsorption on Wet and Dry Wyodak Coal at 328.2 K .............................30 2.8 CO2 Adsorption on Wet Argonne Coals at 328.2 K .........................................32 2.9 Nitrogen Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture .............................................................................................38 2.10 Methane Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture .............................................................................................38 2.11 CO2 Adsorption on Wet Activated Carbon at 328.2 K at Different Moisture Contents ........................................................................40 2.12 Equilibration Times for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture ..........................................................................42 2.13 Pressure Drop Rate Data for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture: 4 and 12 MPa Pressure Steps..........................43 2.14 Comparison of Monte Carlo and Analytical Error Analyses for CO2 Adsorption on Dry Upper Freeport Coal .........................................................46 2.15 Histogram for the Distribution of Errors Evaluated from the Monte Carlo Error Analysis for CO2 Adsorption on Upper Freeport Coal ..........................47 xi Figure Page 3.1 OnoKondo Model for Monolayer Adsorption on Graphite Slit .......................63 3.2 Model Representations for the PureGas Adsorption on Dry Illinois6 Coal at 328 K ...............................................................................73 3.3 Model Representations for the PureGas Adsorption on Dry Beulah Zap Coal at 328 K ...........................................................................73 3.4 Model Representations for the PureGas Adsorption on Dry Wyodak Coal at 328 K ................................................................................74 3.5 Model Representations for the PureGas Adsorption on Dry Upper Freeport Coal at 328 K .....................................................................74 3.6 Model Representations for the PureGas Adsorption on Dry Pocahontas Coal at 328 K ............................................................................75 3.7 Model Representations for the CO2 Adsorption on Wet Illinois #6 Coal at 328 K .............................................................................76 3.8 Model Representations for the CO2 Adsorption on Wet Beulah Zap Coal at 328 K ...........................................................................76 3.9 Model Representations for the CO2 Adsorption on Wet Wyodak Coal at 328 K ................................................................................77 3.10 Model Representations for the CO2 Adsorption on Wet Upper Freeport Coal at 328 K ...................................................................77 3.11 Model Representations for the CO2 Adsorption on Wet Pocahontas Coal at 328 K .........................................................................78 4.1 Types of Physisorption Isotherms ....................................................................85 5.1 CO2 Adsorption on Wet Pocahontas Coal with 0.65% Moisture at 328.2 K: New Data Reduction Method .......................................................144 5.2 CO2 Adsorption on Wet Upper Freeport Coal with 1.10% Moisture at 328.2 K: New Data Reduction Method .......................................................145 5.3 CO2 Adsorption on Wet Illinois #6 Coal with 9.2% Moisture at 328.2 K: New Data Reduction Method .......................................................145 xii Figure Page 5.4 CO2 Adsorption on Wet Wyodak Coal with 28.0% Moisture at 328.2 K: New Data Reduction Method .......................................................146 5.5 CO2 Adsorption on Wet Beulah Zap Coal with 32.2% Moisture at 328.2 K: New Data Reduction Method .......................................................146 5.6 Idealized Depiction of Molecular Interactions of Water in the Slit ...............149 5.7 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Pocahontas Coal ................................................................................155 5.8 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Upper Freeport Coal ..........................................................................155 5.9 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Illinois #6 Coal ..................................................................................156 5.10 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Wyodak Coal .....................................................................................156 5.11 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Beulah Zap Coal ................................................................................157 5.12 Partial Fugacities of Water in Liquid and Gas Phases for CO2Water Mixture Adsorption on Wet Pocahontas Coal ................................................164 6.1 Deviation Plot of SLDPR Model Representations of PureGas Adsorption on Coals .......................................................................................176 6.2 Degree of Correlation between the Regressed Surface Areas for Methane, Nitrogen and CO2 on Coals.............................................................177 6.3 Comparison of Generalized and Regressed Model Parameters ......................185 6.4 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Fruitland Coal at 319.3 K ...................................................................186 6.5 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Illinois #6 Coal at 319.3 K .................................................................186 6.6 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Tiffany Coal at 327.6 K......................................................................188 xiii Figure Page 6.7 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Lower Basin Fruitland Coal at 319.3 K .............................................188 6.8 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Illinois #6 Coal at 328.2 K ..................................................................189 6.9 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Beulah Zap Coal at 328.2 K ...............................................................189 6.10 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Wyodak Coal at 328.2 K ...................................................................190 6.11 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Upper Freeport Coal at 328.2 K .........................................................190 6.12 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Pocahontas Coal at 328.2 K ................................................................191 6.13 Deviation Plot for the Generalized SLDPR Model Predictions for PureGas Adsorption on Coals........................................................................191 6.14 Sensitivity Analysis of SLDPR Generalized Model for Methane Adsorption on Wet Fruitland Coal at 319.3 K ................................................199 6.15 Sensitivity Analysis of SLDPR Generalized Model for Nitrogen Adsorption on Wet Fruitland Coal at 319.3 K ................................................199 6.16 Sensitivity Analysis of SLDPR Generalized Model for CO2 Adsorption on Wet Fruitland Coal at 319.3 K ................................................200 6.17 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/Nitrogen Mixtures on Wet Fruitland Coal at 319.3 K .......................................................................................................203 6.18 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Methane/Nitrogen Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................203 6.19 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................204 xiv Figure Page 6.20 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Methane/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................204 6.21 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................205 6.22 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................205 6.23 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/ Nitrogen Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................206 6.24 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Methane/ Nitrogen Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................207 6.25 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................207 6.26 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Methane/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................208 6.27 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................208 6.28 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................209 6.29 Generalized SLDPR Model Predictions for Methane/Nitrogen Mixture on Wet Tiffany Coal at 327.6 K ........................................................210 6.30 Generalized SLDPR Model Predictions for Methane/CO2 Mixture on Wet Tiffany Coal at 327.6 K ........................................................210 6.31 Generalized SLDPR Model Predictions for Nitrogen/CO2 Mixture on Wet Tiffany Coal at 327.6 K ........................................................211 xv Figure Page 6.32 Generalized SLDPR Model Predictions for Methane/Nitrogen/CO2 Ternary Mixture on Wet Tiffany Coal at 327.6 K ..........................................212 6.33 Deviation Plot for the Generalized SLDPR Model Predictions for MixedGas Adsorption on Coals ....................................................................212 6.34 Deviation Plot for the Generalized SLDPR Model Predictions for CO2 Adsorption on 27 Coals Reported by Day et al. ......................................214 6.35 %AAD Distribution of the Generalized SLDPR Model Predictions for CO2 Adsorption Data Reported by Day et al.. ................................................215 1 CHAPTER 1 INTRODUCTION 1.1 Coalbed Methane and CO2 Sequestration Fossil fuels have been the main resource for our increasing demand for energy. They have also been the source of the steady rise in the atmospheric concentration of CO2, which is hypothesized to be a significant contributor to global warming. Efforts to address climate change issues have culminated in the 1991 Kyoto Protocol, which mandates the signatory nations to reduce their carbon emissions and/or adopt environmentfriendly methods of energy usage by 2012. Several methods have been proposed to reduce carbon/CO2 emissions. These include “geological sequestration” of CO2, which involves capture and the subsequent storage of CO2 in saline aquifers, oil and gas shales, depleted oil reservoirs, or deep unmineable coalbeds. The latter is considered particularly attractive because of the potential for sequestering large amounts of CO2, with the important concomitant recovery of coalbed methane (CBM) gas. The recovery of coalbed methane is expected to (at least partially) offset the costs of CO2 sequestration and to provide an increased supply of our “cleanest” fossil fuel, natural gas. Further, the demand for natural gas is expected to rise steeply in the coming years. The Energy Information Administration (EIA) estimated that natural gas demand in the U.S. could be 24.4 trillion cubic feet by the year 2030.1 This accounts for an annual increase of 1.2% over the next twenty years. Coalbed methane has become 2 an important resource of natural gas since coalbeds contain an estimated 14% of U.S. natural gas reserves.2 The production of natural gas from coalbeds increased from 6% in 19973 to 10% in 2006.4 Therefore, this unconventional resource of natural gas has steadily gained in its economic importance. Moreover, the U.S. Department of Energy (DOE) has initiated research and development programs aimed at geologic CO2 sequestration.5 In pursuit of this goal, researchers at Oklahoma State University (OSU) have conducted adsorption measurements6, 7 and modeling studies.712 In coalbeds, natural gas (methane) resides within the microporous coal structure in an “adsorbed” state. In adsorption, the van der Waalstype gascoal interactions at the coalgas interface give rise to increased concentrations of the gas molecules near the coal surface, where the densities become comparable to those of liquids. Thus, coalbeds can actually hold more gas than a conventional gas reservoir of comparable volume. Since most of the coalbed gas is in the adsorbed state, simulations of coalbed methane (CBM) recovery and the design of optimal CO2 sequestration processes require a suitable model to describe the adsorption phenomena. Specifically, an adsorption model is needed to predict the gasinplace values as a function of coalbed reservoir temperature and pressure. 1.2 Adsorption Models As mentioned above, simulations of enhanced coalbed gas recovery require accurate adsorption models capable of a priori predictions of gas adsorption behavior in the presence of water. Some of the desired characteristics of a CBM adsorption model include: • Representing precisely highpressure puregas adsorption 3 • Facilitating generalized predictions of puregas adsorption based on accessible adsorbent and adsorbate properties • Predicting mixedgas adsorption based on puregas data • Accounting for the presence of moisture in the coal, since water is present in essentially all coalbeds Different models, ranging from very simple to complex, can be used to describe the adsorption behavior of CBM gases. These include the Langmuir model13, Brunauer EmmettTeller (BET) model14, Ideal Adsorbed Solution (IAS) theory15, twodimensional equations of state1618 (2D EOS), the OnoKondo lattice model1921 and the simplified localdensity model.2227 Although most of these models have good correlative capabilities for existing experimental data, only a few of them appear to be capable of accurate predictions of supercritical, highpressure adsorption systems encountered in CBMrelated work. Further, an adsorption model which can describe this effect at water levels that are below, at, and above the equilibrium moisture level will be crucial for reservoir modeling purposes. The CBM industry would benefit greatly from adsorption models which contain rigorous accounting for the effects of water on gas adsorption. Our analysis indicates that the simplified localdensity model is amenable to the modeling demands mentioned above. 1.3 Effect of Water on Coalbed Gas Adsorption Behavior Most coalbeds contain significant amounts of water. The presence of water in a gassolid adsorption system demands special attention, because water can significantly affect gas adsorption capacity by blocking the porous adsorbent structure and limiting the accessibility of an adsorbing gas like methane.28 Measurements of adsorption isotherms 4 on wet coals have also revealed marked effects of water on gas adsorption capacity. Joubert et al.29 reported adsorption data which showed that moisture can reduce methane adsorption by as much as 40% on Pittsburgh coal and 15% on Pocahontas coal. Clarkson and Bustin30 showed that 2% moisture can cause 20% reduction of both methane and CO2 adsorption capacity on a wet coal when compared to the adsorption on the dry coal. Similarly, Levy et al.31 observed that 4% moisture can reduce the methane adsorption by as much as 60% from that of the dry coal. Our own measurements on wet Illinois coal have shown that 9% moisture can cause 50% reduction of CO2 adsorption at 3 MPa.8 The above results demonstrate the significant effect of moisture on gas adsorption behavior. Thus, proper accounting for moisture effects is critical in experimental data reduction, interpretation and modeling. Current experimental data reduction techniques do not account for the presence and effect of moisture in all three equilibrium phases (gas, aqueous and adsorbed). This inadequacy in data reduction methods may result in significant errors in the estimated gas adsorption capacity, adsorbed phase density and (in gas mixtures) the partitioning of constituents among the equilibrium phases. The adsorption behavior of water is fundamentally different from other gases like methane.32 For water, the fluidfluid interactions are stronger than the fluidsolid interactions, and hydrogen bonding plays a significant role in water adsorption. Thus, the simultaneous, competitive adsorption of water and coalbed gases presents an equilibrium problem which requires accurate description of the different molecular interactions involved in the process. Accordingly, the present research places a particular emphasis on delineating the fluidfluid and fluidsolid molecular interactions of water, coalbed gases and 5 carbonaceous adsorbents, and proposing rigorous accounting procedures for the effects of moisture on the adsorption behavior of coalbed gases and their mixtures at typical reservoir temperatures and pressures. Further, the research included the development of a coalstructurebased generalized adsorption model for facilitating simulations of CBM recovery and CO2 sequestration. Therefore, the goal of this research addresses two important aspects of CBM adsorption research: A. Delineate the molecular interactions of adsorbed water with coals and other coalbed gases, and propose rigorous accounting procedures for the effects of water on gas adsorption behavior and B. Develop a coalstructurebased, predictive generalized adsorption model for CBM simulation purposes. As such, two tracks of CBM adsorption research were undertaken in parallel. The first addressed the need to incorporate more accurate physics in an adsorption model, whereas the second addressed the need to develop a generalized adsorption model that would be useful in coalbed reservoir simulations. Although the generalized model developed in this work (B) is based on the currently accepted, traditional modeling approach (where adsorbed water is treated as a "pacifier" of the matrix), the parallel development of a rigorous modeling approach for adsorbed water (A) has laid the foundation for further advancement of this method in future works on coalbed gas adsorption. 1.4 Objectives The basic premise of this research is that upon modification, the SLDPR model can describe accurately the equilibrium adsorption of water and coalbed gases on coals 6 and account for the effect of water on coalbed gas adsorption. As such, a major focus of this study was modifying the simplified localdensity/PengRobinson (SLDPR) model to meet the modeling demands of wet adsorbents. In particular, the SLDPR model was further developed to (a) include the polar interactions of water with the carbon surface, and (b) account more realistically for the effect of water adsorption by treating water as a separate adsorbed component in equilibrium with the bulk gas phase. Moreover, for engineering practice purposes, the SLDPR model was generalized (using the accepted, traditional modeling approach) to render the model suitable for use in simulations of coalbed methane recovery and CO2 sequestration. To accomplish the goal discussed above, the following objectives were undertaken: 1. Acquire accurate experimental data for adsorption of methane, carbon dioxide, and nitrogen on wet coals and on activated carbon at reservoir temperatures and pressures. 2. Review existing knowledge regarding pure water adsorption behavior on coals and activated carbons. 3. Use the SLDPR model to represent precisely the water adsorption capacity on activated carbons and coals. 4. Conduct a Gibbsenergy (or phasecheck) analysis for adsorption of CO2water mixtures on coals. 5. Generalize the SLDPR model by correlating the model parameters in terms of assessable coal properties. 7 In earlier studies6, 10, 33, the OSU Thermodynamics Group measured pure and mixedgas adsorption isotherms on wet coals. However, the moisture content of the coals in those measurements was well above the equilibrium moisture content (EMC) of the coals. At moisture contents above the EMC, the additional water does not significantly affect the gas adsorption capacity.29 Therefore, a need exists for measurements to elucidate the adsorption behavior of coalbed gases at different levels of moistureabove and below the EMC (Objective 1). Accounting properly for water adsorption behavior on activated carbons and coals and its modeling presents an interesting and challenging problem, due to the unique structure of the water molecule. The adsorption behavior of water on carbons is fundamentally different from that of simple, nonpolar fluids like nitrogen, methane and organic vapors. The difference arises mainly because the fluidfluid interactions for water are much more strongly attractive than the fluidsolid interactions, and because water forms hydrogen bonds with the oxygenated groups on the surface of the carbon matrix.32 This is in direct contrast to the adsorption behavior of nonpolar molecules. Therefore, a detailed review of water adsorption behavior on activated carbons and coals (Objective 2) was essential to an unambiguous understanding of pure water adsorption and, ultimately, of coalbed gas mixture adsorption in the presence of water. The prerequisite for the prediction of the watercoalbed gas mixture adsorption is the accurate modeling of the water adsorption capacity. The SLD model was modified to account for interactions of water with the coal surface; and the effect of this new parameterization of the SLD model was investigated by constructing different case studies (Objective 3). 8 The accurate modeling of watercoalbed gas mixture adsorption requires treating water as a separate adsorbed component. Water at reservoir temperatures is a subcritical component, while the coalbed gases are typically at supercritical conditions. The presence of the subcritical water may result in the formation of an additional (liquid) phase. The definitive method to determine the number of possible phases present at equilibrium is to conduct a Gibbs free energy or phasecheck analysis. Therefore, a phasecheck analysis was performed to investigate the phase behavior of this system (Objective 4). As mentioned in Section 1.2, simulations of coalbed methane recovery require an adsorption model to predict, a priori, the amounts adsorbed of coalbed gases. Frequently, this is necessary due to an absence of experimental data on the system of interest. Therefore, the SLDPR model was generalized in terms of coal characterization information (Objective 5). This facilitates a priori predictions of adsorbed amounts of gas and renders the model capable of use in simulations of coalbed methane recovery. Further, in developing the generalized model, the currently accepted approach for modeling wet adsorbents was adopted. The extension of the new modeling approach for wet adsorbents (developed in Objective 4) to the generalized model is not feasible at this stage for a variety of reasons, which include the unavailability of sufficient adsorption and vaporliquid equilibrium data for the systems of interest. 1.5 Organization This dissertation is organized as follows. Chapter 1 gives a brief introduction of coalbed methane and outlines the hypothesis of this research, the objectives undertaken and the ultimate goal of this study. Chapter 2 presents details of the experimental 9 methods and procedures used in this study and discusses the experimental data acquired in this project. Chapter 3 reviews a number of CBM adsorption models used in the literature and at OSU for modeling of CBM systems. Chapter 4 presents an interpretive review of pure water adsorption on activated carbons and coals. The SLD model for pureand mixedgas adsorption is discussed in Chapter 5. Also included in Chapter 5 are the SLD modeling results of CO2water mixture adsorption and the phasecheck analysis for these systems. A coalstructurebased generalized adsorption model is presented in Chapter 6. Finally, Chapter 7 contains the important conclusions and recommendations of this study. This study was part of a continuing research project dealing with highpressure gasadsorption modeling for CBM systems.8, 12 Therefore, the experimental data presented in Chapter 2 and discussion of the theoretical framework of SLDPR model presented in Chapter 5 represent a collective effort involving the author, Jing Chen27 and James Fitzgerald.25 Further, the OSU CBM adsorption database utilized for the generalized model development was gathered over a period of fifteen years by various authors.6, 8, 12 10 CHAPTER 2 EXPERIMENTAL METHODS, PROCEDURES AND RESULTS In this chapter, the experimental methods and procedures used to measure adsorption isotherms are discussed. Since this study is a continuation of previous works at OSU, some aspects of the following discussion of experimental methods are similar to previous descriptions.18, 20, 25, 34 Further, an outline of the various methods that can be used to measure gas adsorption equilibria are given elsewhere18 and, therefore, they are not discussed here. In particular, the chapter contains a discussion of the following aspects of this work: • Adsorption isotherms of pure CO2 on five wet Argonne coals measured at a temperature of 328.2 K and pressures to 13.8 MPa • Adsorption isotherms of pure methane, nitrogen and CO2 on wet and dry activated carbon measured at a temperature of 328.2 K and pressures to 13.8 MPa. In addition, the desorption measurements of CO2 on dry activated carbon are also discussed. • An introduction to the OSU adsorption database for coalbed methane gases.12 • A Monte Carlo analysis/confirmation of the analytical error analysis technique used to estimate the expected experimental uncertainties of the acquired data. 11 The following material in Sections 2.1 to 2.10 (Part A) has been reproduced with permission from [Mohammad, S. A.; Chen, J. S.; Fitzgerald, J. E.; Robinson, R. L., Jr.; Gasem, K. A. M., Adsorption of Pure Carbon Dioxide on Wet Argonne Coals at 328.2 K and Pressures up to 13.8 MPa. Energy & Fuels 2009, 23, (2), 11071117] Copyright [2008] American Chemical Society. 2.1 Adsorption Isotherm Measurements The experimental method used in the OSU adsorption laboratory is based on a mass balance principle, which employs precise measurements of pressure, volume and temperature. The experimental apparatus, shown schematically in Figure 2.1, has been used successfully in previous measurements.68 Brief descriptions of the experimental apparatus and procedures are provided below: The entire apparatus is maintained in a constant temperature air bath. The equilibrium cell (Figure 2.1) is filled with the adsorbent under study, and the cell is placed under vacuum prior to gas injection. The void (gas) volume, Vvoid, in the equilibrium cell is then determined by injecting a known quantity of helium from a calibrated injection pump (Ruska). Since the adsorption of helium is insignificant at the conditions of this study, the void volume can be determined easily from measured values of the temperature, pressure and amount of helium injected into the cell. The mass balance equation for the measurement of void volume is given as: pump void 2 1 2 1 cell P V ZT V P P Z T Z T = − (2.1) 12 where V is the volume of helium gas injected from the pump, Z is the compressibility factor of helium, T is the temperature, P is the pressure, subscripts “cell” and “pump” refer to conditions in the cell and pump sections of the apparatus, respectively, and “1” and “2” refer to conditions in the cell before and after an injection of gas from the pump, respectively. The helium void volume measurements were performed at the same temperature as the gas adsorption isotherms (328.2 K in this study) and over a range of pressures from atmospheric to about 13.8 MPa (2000 psia) in intervals of 1.4 MPa (200 psia). The several sequential injections of helium into the cell at different pressures showed consistency in the calculated void volume. Generally, the void volume calculated from sequential injections varied less than 0.3 cm3 from the average value of approximately 85 cm3. This helium void volume includes all the volume of the cell section exclusive of the adsorbent volume that is impenetrable to helium gas. The constancy of the calculated void volume from the incremental injections over a range of pressures confirmed the validity of our assumption that adsorption of helium is negligible at the conditions of the measurements and that the adsorbent volume impenetrable to helium remained constant. The Gibbs adsorption (also known as the excess adsorption) can be calculated directly from experimentally measured quantities. For puregas adsorption isotherm measurements, a known quantity, ninj, of gas (e.g., CO2) is injected from the pump section into the cell section. Some of the injected gas will be adsorbed, and the remainder, Gibbs unads n , will exist in the equilibrium bulk (gas) phase in the cell. 13 Vacuum Pump Pressure Temp. Heat Exchanger Ruska Pump Air Temperature Bath Vent Water Heater and Pump Pressure Equilibrium Cell Magnetic Pump Temp. Vent Air Temperature Bath Motor Sampling Valve He CH4 CO2 N2 C2 He Gas Chromotagraph Figure 2.1 Schematic Diagram of the Experimental Apparatus The mass balance used to calculate the Gibbsian amount adsorbed, Gibbs ads n , is Gibbs inj unads Gibbs ads n = n − n (2.2) where Gibbs unads n is the Gibbsian amount unadsorbed at given pressure and temperature. The amount injected can be determined from pressure, temperature and volume measurements of the pump section: inj pump P V n ZRT = (2.3) The amount of unadsorbed gas (Gibbsian amount unadsorbed) is calculated from conditions at equilibrium in the cell: Gibbs Void unads cell PV n ZRT = (2.4) where the pressure P is measured after equilibrium is reached in the cell (usually within 6 to 12 hours, depending on the adsorption capacity of the adsorbent), which occurs when 14 no further change in pressure is observed. In Equations (2.3) and (2.4), Z is the compressibility factor of the gas at the applicable conditions of temperature and pressure. The above steps are repeated at sequentially higher pressures to yield a complete adsorption isotherm. The amount adsorbed is usually reported as an intensive quantity (mmol adsorbed / g adsorbent, or mmol/g) by dividing Gibbs ads n by the mass of adsorbent in the cell. Equations (2.2)(2.4) reveal that the amount adsorbed can be calculated in a straightforward manner from the experimental measurements of pressures, temperatures and volumes, coupled with independent knowledge of the gas compressibility factors, Z, from an accurate equation of state. 2.2 Gas Compressibility Factors As evident from the above discussion, accurate compressibility factors are required for pure methane, nitrogen and CO2 for proper adsorption data analysis. These compressibility factors were calculated from highly accurate equations of state.3537 Further, for void volume determination, the helium compressibility factor was calculated with an expression based on experimental data from the National Bureau of Standards Technical Note 631 for helium.38 2.3 Materials The pure gases used in this work were obtained from AirgasPennsylvania with reported purities of about 99.99% and were used as received. The Argonne coal samples were obtained from the Argonne National Laboratory, Argonne, Illinois in ampoules containing 5 grams of 100mesh material of each coal. The compositional analyses of Argonne coals are presented in Table 2.1. The Illinois #6 coal is a highvolatile bituminous coal from the Illinois #6 or Herrin seam. The Wyodak coal is a sub 15 bituminous coal from the WyodakAnderson seam. The Upper Freeport coal is a mediumvolatile bituminous coal, Pocahontas coal is a lowvolatile bituminous coal and Beulah Zap coal is lignite.39 The activated carbon used was Filtrasorb 400, 12x40 mesh from Calgon Carbon Company. The compositional analyses of this activated carbon are also presented in Table 2.1. The composition of activated carbons is typically less complex than coals and provides a useful reference material prior to adsorption studies on coals. As evident from Table 2.1, the activated carbon has higher carbon content and significantly less volatile matter than mediumrank coals, which facilitates the modeling of the fluidsolid interactions in an adsorption process. The nitrogen BET surface area at 77 K of this carbon was reported to be 850 m2/g.40 Table 2.1 Compositional Analyses of Adsorbents Used in this Study Analysis* Beulah Zap Wyodak Illinois #6 Upper Freeport Pocahontas Activated Carbon Ultimate Carbon % 72.9 75.0 77.7 85.5 91.1 88.65 Hydrogen % 4.83 5.35 5.00 4.70 4.44 0.74 Oxygen % 20.3 18.0 13.5 7.5 2.5 3.01 Nitrogen 1.15 1.12 1.37 1.55 1.33 0.40 Sulfur % 0.70 0.47 2.38 0.74 0.50 0.73 Ash % 9.7 8.8 15.5 13.2 4.8 6.46 Proximate Moisture % 32.2 28.1 8.0 1.1 0.7  Vol. Matter % 30.5 32.2 36.9 27. 1 18.5 3.68 Fixed Carbon % 30.7 33.0 40.9 58.7 76.1 89.86 Ash % 6.6 6.3 14.3 13.0 4.7  *Analysis of coals provided by Argonne National Laboratory *Analysis of activated carbon provided by Huffman Laboratories, Inc., Golden, Colorado 16 2.4 Error Analysis Frequent instrument calibrations were performed during the course of the experiments. Usually, the calibrations were performed before the adsorption experiments on a new adsorbent sample. The thermocouples and resistance thermometers (RTDs) were calibrated against a Minco platinum reference RTD. Super TJE pressure transducers (range: 0 – 13.8 MPa) were calibrated using helium as the working fluid against a Ruska deadweight tester with a calibration traceable to the National Institute of Standards and Technology. Detailed information on calibration procedure is available elsewhere.34 The uncertainties in the experimentally measured quantities after calibrations were estimated as follows: temperature, 0.1 K; pressure, 6.9 kPa (1 psia); and injected gas volume, 0.02 cm3. A detailed error analysis was performed to estimate the uncertainty associated with each experimental data point by propagating the errors from the primary measurements of pressure, temperature and volume. The detailed error analysis expressions are given elsewhere.12, 20 2.5 Equilibrium Moisture of Coals and Activated Carbon Moisture equilibration of porous adsorbents such as coals is usually carried out using the standard ASTM D1412 method.41 This method consists of equilibrating the adsorbent samples at 30ºC (303.2 K) in a vacuum desiccator over a saturated solution of K2SO4 to maintain the relative humidity at 9697%. In the standard test method, the desiccator is used to equilibrate a previously "wetted" sample such that only the equilibrium moisture remains in the coal. However, the use of vacuum in a desiccator can often result in condensation problems when the pressure is restored, thus negating the 17 experiment.29, 42 Therefore, we used a modified method where the samples were equilibrated under an inert nitrogen atmosphere. The moisture content of the equilibrated sample was then determined by drying a part of the sample under vacuum at a temperature of about 313.2 K for 4872 hours. The weight of the sample was monitored, and the weight loss after 72 hours was taken as the moisture loss. The expected uncertainty in the measured moisture content is estimated to be about 0.1 wt. %. The Illinois #6 coal samples were equilibrated using the above method by placing them in a nitrogen atmosphere at 95100% relativity humidity in a Hotpack Model 434300 temperaturehumidity chamber. This resulted in a gain of only 1.2% moisture over the equilibrium value reported in the literature.39 Therefore, for the other four Argonne coals, namely, Beulah Zap, Pocahontas, Upper Freeport and Wyodak coals, the asreceived coal samples were placed directly in the equilibrium cell under inert atmosphere. This was done under the reasonable assumption that further moistening of the coal in the temperaturehumidity chamber would not greatly change the coal moisture content from its asreceived moisture. Moreover, the direct use of asreceived samples minimizes possible oxidation of the samples that can affect the integrity of the coal sample. Great care has been taken by the Argonne National laboratory to maintain the coal samples at their inseam conditions.39 Since the objective of our study was to simulate the conditions of a coalbed reservoir while measuring adsorption isotherms (in terms of pressure, temperature and moisture content), measuring the isotherms at their asreceived or inseam moisture values was considered greatly beneficial. These isotherms can be considered to be measured near or at the equilibrium moisture content of the coals. 18 In the present context, the term “wet” coal is used to signify saturation of coal with adsorbed moisture. For adsorption measurements on the dry Argonne coals, the coal samples were dried under vacuum in an equilibrium cell at 353 K for 36 hours following the National Energy Technology Laboratory (NETL) drying protocol before being used in the adsorption measurements. The adsorption data on dry coals were measured in an earlier work.21 The activated carbon was equilibrated as explained in the procedure above. Further, the raw activated carbon sample was first washed with deionized water to remove any impurities present in the carbon. This wetted sample was air dried for several days (to remove excess water) and then used for moisture equilibration as discussed above. For adsorption measurements on the dry activated carbon, drying of the sample was carried out under vacuum at about 313.2 K for 4872 hours. The lower drying temperature was used to avoid the loss of any volatile organics from the carbon surface and/or possible structural changes of the carbon sample. 2.6 Gas Solubility in Water In previous studies at OSU on wet adsorbents6, 8, we included a term in Equation (2.2) to account for the amount of gas, nsol, dissolved in the water. Gibbs Gibbs nads = ninj − nunads − nsol (2.5) To calculate the amount of gas soluble in water as a function of pressure, an empirical equation obtained from Amoco Corporation was used for temperatures at 318.2 K or 319.3 K. 19 gas 2 a bP cP x P + + = (2.6) Table 2.2 lists the parameter values for each gas. Since the solubilities of methane and nitrogen in water are small; the same equation and parameter values were used at other temperatures (e.g., 328.2 K in this study). Table 2.2 Parameters for Gas Solubility in Water at 318.2 K or 319.3 K Constant Units of Constant Methane Nitrogen CO2 a MPa 5302.07 10204.24 274.69 b  150.4 127.3 9.452 c 1/MPa 0.78 0.09 1.21 In comparison to nitrogen and methane, the solubility of CO2 is significant at temperatures near 318.2 K. To calculate the gas dissolved in water for use in Equation (2.5), literature data4345 were used to construct an empirical relationship for CO2water solubility at temperatures from 313.2 K to 348.2 K.8 In the 015 MPa range, the empirical function represents their data with an average absolute deviation of 1.5%. Thus, the mole fraction of CO2 present in water at temperature T (in K) and pressure P (in MPa) is given as: ( ) ( ) 2 1 0 1 0 CO2 a b b T P c c T P x P + + + + = (2.7) Table 2.3 lists the parameter values for this correlation. The amount of CO2 dissolved in water can be given as (1 x ) x n n 2 2 co co water sol − = (2.8) The denominator in Equation (2.8) is close to unity and therefore, the amount of gas dissolved in water was taken (approximately) as the product of mole fraction of CO2 and 20 the amount of water in moles in the system. Further, the amount of CO2 dissolved in water per unit mass of coal is expressed as: coal co water sol m x n n = 2 (2.9) where nwater is the amount of water in moles and coal m is the mass of coal in the system. The solubility of CO2 in water calculated with Equation (2.9) is a monotonic increasing function of pressure at a given temperature. Thus, the maximum solubility of CO2 in water was observed at 13.8 MPa and was about 2 mole percent. Table 2.3 Parameters for CO2 Solubility in Water at Multiple Temperatures Constant Value Units of Constant a 272.21 MPa b1 332.637  b0 1.06683 1/K c1 19.18 1/MPa c0 0.05609 1/(MPa K) As evident from the above discussion (Equation 2.5), accounting for the solubility of gas in waterrich adsorbed phase lowers the calculated Gibbs adsorption values. In the above discussion, we have assumed that all the water present in the system is adsorbed and, therefore, the amount of gas dissolved in water was estimated based on all the water present in the system. In addition, this means that we have assumed that the bulk gas phase was free from water (i.e., that yH2O = 0, where y is the gas phase mole fraction). 2.7 Adsorption Measurements on Wet Coals and Activated Carbon For the adsorption isotherm measurements on wet Argonne coals and wet activated carbon, care was taken to prevent moisture loss during the experiments. The coal samples were handled in a chamber filled with nitrogen. Since the evacuation step during the void volume measurement and at the beginning of the isotherm can result in 21 moisture loss, the system pressure was not reduced below 21 kPa at 328.2 K. This is slightly above the vapor pressure of water at this temperature, and this minimizes any potential water being removed from the coal or carbon surface. Further, before the start of the gas adsorption experiment, a small amount of the same adsorbing gas (methane, nitrogen or CO2) was injected into the cell until the pressure was 0.35 MPa to flush any remaining helium gas out. The adsorbing gas was then evacuated until the pressure was again about 21 kPa, and the flushing procedure was performed once more. To test for any moisture loss during the experiment on wet coals, two additional checks were performed. First, the equilibrium cell/coal sample was weighed before and after the adsorption isotherm. There was no significant mass loss observed from the equilibrium cell at the end of the isotherm. Second, the helium void volume was measured before and after the adsorption isotherm. The helium void volumes measured were within the experimental uncertainty of our void volume measurements (about 0.3%). The constancy in the calculated void volume further indicated that there was no significant moisture loss during the experiment. Given the size of our volumetric apparatus, any miniscule amount of water leaving the coal surface would introduce an uncertainty in the isotherm measurement, which is well within the reported experimental uncertainty of the isotherm as obtained by multivariate error propagation. These uncertainty estimates for each data point of each isotherm are included with Gibbs adsorption data. 2.8 Coal Swelling Another aspect of supercritical gas adsorption on coals that deserves consideration is the potential swelling of coal caused by adsorbates such as CO2. Some investigators 22 believe that adsorption of CO2 can significantly alter the porous coal structure and these changes, if left unaccounted for, can result in large errors in the modeling of supercritical CO2 adsorption on coals. In fact, several researchers have attempted to model the swelling of coal by incorporating volumetric corrections to the adsorption isotherm equations. Ozdemir et al.46 and Dutta et al.47 used different adsorption models to study the volumetric effects of CO2 adsorption on coals. Romanov et al.48 have also attempted to interpret the volumetric changes in coals under CO2 pressure. Pan and Connell49, balancing the change in surface energy due to adsorption to the change in elastic energy of the coal matrix, developed a theoretical model to describe adsorptioninduced coal swelling. Recently, Day et al.50 measured swelling on coals and corrected their adsorption measurements to account for volumetric changes to the sample. These corrections involved adjusting the void volume to account for an increased volume of coal sample. We have measured helium void volume before and after each adsorption isotherm experiment. The constancy of the calculated void volume within its experimental uncertainty of 0.3% indicated that there was no irreversible change to the volume of the sample. This result is also supported by the findings of Day et al.50, who found the coal swelling to be entirely reversible. Although they applied a correction to the isotherm, we have used a constant void volume in our data reduction procedures. Thus, the adsorption data reported in this study are under the assumption that there is no appreciable swelling of the coal. 23 2.9 Gibbs and Absolute Adsorption Adsorption data are typically reported either in terms of Gibbs or absolute adsorption. Gibbs adsorption is calculated directly from experimentallymeasured quantities and this accounts for the fact that there is additional material present near the adsorbent surface due to adsorption phenomenon. This additional material is in excess of that which would be present in the same (void) volume if there was no adsorption. This excess material is usually referred to as the Gibbs or excess adsorption. In contrast, the calculation of absolute adsorption requires a value for the adsorbed phase density, ρads, which is not readily accessible by experimental measurement. The exact mathematical expressions that highlight the physical interpretation of Gibbs adsorption and the approximate nature of calculated absolute adsorption have been presented elsewhere.7 The relationship between the two quantities is given as: − = ads gas Gibbs ads ads Abs ads ρ ρ ρ n n (2.10) where Abs ads n and Gibbs ads n are the absolute and Gibbs adsorption, respectively, and ρgas and ρads are the gas phase and the adsorbed phase densities, respectively. To calculate absolute adsorption from Equation (2.10), estimates of ρads are usually employed. Commonly used approximations are the liquid density at the normal boiling point, as was done by Arri and Yee51, or the reciprocal of the Van der Waals (VDW) covolume.8 2.10 Experimental Results A. Adsorption of CO2 on Wet Argonne Coals The experimental data from the present work for the CO2 adsorption on Beulah Zap, Illinois #6, Pocahontas #3, Upper Freeport and Wyodak coals are listed in Tables 24 2.42.8, respectively. All adsorption amounts are reported on a drymass basis. Tables 2.42.8 include the pressures (MPa), Gibbs adsorption (mmol/gm) and expected experimental uncertainties "σ" (mmol/gm) in the adsorption values for each datum. Table 2.4 Gibbs Adsorption of Pure CO2 on Wet Beulah Zap Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 1.02 0.135 0.053 1.50 0.179 0.053 2.82 0.262 0.052 4.22 0.324 0.052 5.91 0.372 0.051 7.15 0.369 0.051 8.35 0.357 0.053 9.71 0.327 0.068 11.05 0.312 0.094 12.04 0.248 0.107 13.57 0.089 0.120 Table 2.5 Gibbs Adsorption of Pure CO2 on Wet Illinois #6 Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.42 0.146 0.052 0.79 0.231 0.052 1.56 0.356 0.051 2.23 0.440 0.051 2.87 0.511 0.050 4.27 0.634 0.050 5.62 0.701 0.049 7.02 0.765 0.049 8.34 0.791 0.063 9.69 0.800 0.065 11.04 0.777 0.075 12.41 0.716 0.092 13.88 0.644 0.088 25 Table 2.6 Gibbs Adsorption of Pure CO2 on Wet Pocahontas #3 Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.40 0.281 0.040 .77 0.439 0.040 1.49 0.605 0.040 2.84 0.764 0.039 4.25 0.854 0.038 5.63 0.901 0.038 6.99 0.915 0.037 8.33 0.908 0.038 9.69 0.868 0.048 10.34 0.840 0.050 12.16 0.730 0.068 13.11 0.674 0.075 Table 2.7 Gibbs Adsorption of Pure CO2 on Wet Upper Freeport Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.40 0.239 0.043 0.81 0.363 0.043 1.47 0.482 0.042 2.86 0.624 0.042 4.24 0.698 0.041 5.64 0.739 0.041 7.00 0.756 0.040 8.35 0.758 0.041 9.67 0.742 0.052 10.75 0.737 0.056 12.31 0.667 0.073 13.86 0.593 0.082 26 Table 2.8 Gibbs Adsorption of Pure CO2 on Wet Wyodak Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.47 0.041 0.048 0.76 0.067 0.048 1.46 0.130 0.048 2.77 0.233 0.048 4.22 0.319 0.048 5.64 0.372 0.048 7.01 0.411 0.049 8.35 0.417 0.063 9.67 0.420 0.074 10.92 0.424 0.084 12.35 0.368 0.099 13.92 0.254 0.101 The decreasing order of Gibbs adsorption among the five coals is: wet Pocahontas, wet Illinois #6, wet Upper Freeport, wet Wyodak and wet Beulah Zap. In comparison, the decreasing order of the rank of these coals was: wet Pocahontas, wet Upper Freeport, wet Illinois #6, wet Wyodak and wet Beulah Zap. Thus, higher rank coals appear to have a larger capacity for CO2 adsorption; however, the coal moisture contents which vary significantly also play an important role in CO2 adsorption on these coals. The Gibbs adsorption data on three of the coals, namely, wet Beulah Zap, Illinois #6 and Pocahontas coals, have been published in an NETL interlaboratory study.52 The remaining two coals in this study (wet Pocahontas and upper Freeport coals) have not been published previously. The main objective of the NETL interlaboratory study52 was to investigate the reproducibility of CO2/coal adsorption isotherm measurements among various laboratories. In contrast, the objective of the present study is to investigate the 27 effect of water content of the coals on the experimental data, the data reduction, and the model analysis of these isotherms. The adsorption data published earlier52 did not include accounting for the solubility of CO2 in adsorbed water and, thus, differ from the results presented here. Neglecting the solubility in the earlier work was part of a specified data reduction procedure provided by NETL, designed to insure consistent data reductions among the participating laboratories in that study. Accounting for the dissolved CO2 in adsorbed water yields the actual amounts adsorbed on the wet coals, leading to lower values of the calculated Gibbs adsorption than previously published.52 For the higher moisture containing coals in this study, this correction is significant, and it also affects the subsequent model analysis of these isotherms. To highlight this difference, Figure 2.2 presents a comparison of CO2 adsorption data on wet Beulah Zap coal published in Goodman et al.52 and the data from this study. As evident from the figure, accounting for the gas solubility in adsorbed water can result in quite different calculated values of Gibbs adsorption. Figures 2.32.7 illustrate the Gibbs adsorption of CO2 on BeulahZap, Illinois #6, Pocahontas #3, Upper Freeport and Wyodak coals from this study, respectively. The CO2 adsorption on each of the dry coals is also illustrated for comparison. The adsorption data on dry coals were measured in an earlier study.21 For each coal, the CO2 adsorption on the wet coal was lower than that on the dry coal. Further, the reduction in the gas adsorbed from that on dry coals appears to be correlated positively with the moisture content of the coal. The Pocahontas, Upper Freeport, Illinois #6, Wyodak and Beulah Zap 28 0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Beulah Zap (With Solubility) Beulah Zap (Without Solubility) Figure 2.2 Comparison of CO2 Adsorption Data on Wet Beulah Zap Coal at 328.2 K: Effect of Gas Solubility in Water 0.20 0.20 0.60 1.00 1.40 1.80 2.20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Beulah Zap (32.2% Moisture) Beulah Zap (Dry) Figure 2.3 CO2 Adsorption on Wet and Dry Beulah Zap Coal at 328.2 K 29 0.00 0.40 0.80 1.20 1.60 2.00 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Illinois (9.2% Moisture) Illinois (Dry) Figure 2.4 CO2 Adsorption on Wet and Dry Illinois #6 Coal at 328.2 K 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Pochahontas (0.65% Moisture) Pochahontas (Dry) Figure 2.5 CO2 Adsorption on Wet and Dry Pocahontas Coal at 328.2 K 30 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) UFP (1.1% Moisture) UFP (Dry) Figure 2.6 CO2 Adsorption on Wet and Dry Upper Freeport Coal at 328.2 K 0.0 0.4 0.8 1.2 1.6 2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Wyodak (28.0% Moisture) Wyodak (Dry) Figure 2.7 CO2 Adsorption on Wet and Dry Wyodak Coal at 328.2 K 31 coals exhibited, respectively, about 19%, 17%, 48%, 76% and 79% reductions in the adsorption on the wet coals at 7 MPa when compared to the adsorption on the dry coals. Figure 2.8 compares the Gibbs adsorption of CO2 on all five wet coals. The adsorption isotherm for each of the wet coals exhibits a maximum between 812 MPa. For each case, the adsorption maximum on the wet coal occurs at a higher pressure than that for the dry coal. Note that some of the error bars have been omitted in Figure 2.8 for the sake of clarity. The error analysis indicates that the average uncertainties for the CO2 adsorption measurements are approximately 713% for Illinois #6, Upper Freeport, and Pocahontas coals. The higher percentage uncertainties are usually obtained at the higher pressures, due mainly to the lower value of the Gibbs adsorption for CO2 at the higher pressures and the higher uncertainties in the CO2 compressibility factors (due to its proximity to its critical point). The average uncertainties for Beulah Zap and Wyodak coals were around 34%. However, these higher percentage uncertainties are a result of lower adsorption amounts for these two wet coals and amounted to only about 0.06  0.07 mmol/gm, on average. In our data reduction technique, we accounted for the amount of gas dissolved in the waterrich adsorbed phase, which results in lower calculated adsorption amounts for higher moisture containing coals. The Beulah Zap and Wyodak coals contain 32.2% and 28% moisture, respectively. Chapter 5 presents an alternative approach wherein a different data reduction technique is used for estimating the amounts adsorbed. 32 0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Beulah Zap (32.2% Moisture) Wyodak (28% Moisture) Illinois#6 (9.2% Moisture) Upper Freeport (1.1% Moisture) Pocahontas (0.65% Moisture) Figure 2.8 CO2 Adsorption on Wet Argonne Coals at 328.2 K B. Adsorption of Methane, Nitrogen and CO2 on Dry and Wet Activated Carbon The experimental data for the adsorption of pure nitrogen, methane and CO2 on dry activated carbon are presented in Tables 2.92.11, respectively. These tables list the pressure (MPa), Gibbs adsorption (mmol/gm) and the expected experimental uncertainty "σ" (mmol/gm) for each datum. The adsorption data for these isotherms yielded expected uncertainties of 13%, on average. As expected, less gas adsorption is observed at 328.2 K than at 318.2 K (from our earlier experiments7); however, the new measurements agree with our previous data in regard to the relative amounts of nitrogen, methane and CO2 adsorbed. In both cases, an approximate ratio of 1:1.6:2.4 was obtained at 7 MPa. Further, the desorption of CO2 on dry activated carbon was also measured; and comparison of the adsorption and desorption isotherms indicated no hysteresis effect for this system. 33 The experimental data for the adsorption of pure nitrogen, methane and CO2 on the wet activated carbon are presented in Tables 2.122.16, respectively. Figures 2.92.11 illustrate the adsorption isotherms for pure nitrogen, methane and CO2 on wet activated carbon, respectively. The adsorption of these gases on dry activated carbon is also presented in these figures for comparison. Table 2.9 Gibbs Adsorption of Pure Nitrogen on Dry Activated Carbon at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.81 1.015 0.041 1.46 1.473 0.040 2.93 2.075 0.039 4.19 2.407 0.039 5.53 2.651 0.039 6.98 2.834 0.039 8.36 2.945 0.039 9.69 3.018 0.040 11.08 3.068 0.039 12.54 3.100 0.040 13.70 3.108 0.040 Table 2.10 Gibbs Adsorption of Pure Methane on Dry Activated Carbon at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 1.50 2.845 0.047 2.78 3.555 0.046 4.11 3.936 0.045 5.59 4.167 0.045 7.07 4.277 0.045 8.38 4.310 0.045 9.18 4.306 0.045 9.77 4.306 0.045 11.11 4.273 0.046 12.43 4.221 0.046 13.74 4.145 0.047 34 Table 2.11 Gibbs Adsorption of Pure CO2 on Dry Activated Carbon at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.33 2.432 0.117 0.74 3.684 0.115 1.49 4.887 0.113 2.85 5.885 0.110 4.22 6.321 0.108 5.62 6.462 0.107 7.07 6.396 0.106 8.31 6.134 0.105 9.62 5.616 0.106 11.11 4.524 0.132 12.49 3.522 0.137 Table 2.12 Gibbs Adsorption of Pure Nitrogen on Wet Activated Carbon at 328.2 K and 37% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 1.61 0.024 0.021 2.95 0.054 0.021 5.76 0.113 0.021 8.43 0.161 0.022 11.20 0.208 0.024 13.91 0.253 0.026 Table 2.13 Gibbs Adsorption of Pure Methane on Wet Activated Carbon at 328.2 K and 37% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.44 0.018 0.025 0.79 0.046 0.025 1.48 0.105 0.025 2.83 0.234 0.025 4.20 0.372 0.025 5.56 0.519 0.026 7.04 0.701 0.026 35 Table 2.14 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 27% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.50 0.489 0.048 0.85 0.753 0.047 1.44 1.138 0.047 2.74 1.976 0.050 4.03 3.244 0.057 5.41 4.561 0.049 6.90 5.340 0.049 8.41 5.414 0.056 9.79 5.048 0.076 11.02 4.417 0.092 12.40 3.681 0.105 13.74 3.057 0.105 Table 2.15 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 34% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.70 0.529 0.049 1.45 0.971 0.049 2.77 1.795 0.049 4.01 2.883 0.050 5.28 4.298 0.053 6.91 5.230 0.056 8.49 5.216 0.059 9.78 4.847 0.079 11.06 4.163 0.096 12.52 3.373 0.109 13.94 2.867 0.117 36 Table 2.16 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 16% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.39 0.690 0.037 0.74 1.018 0.037 1.43 1.444 0.036 2.74 2.114 0.044 4.00 3.347 0.056 5.31 4.823 0.079 6.99 5.473 0.144 8.50 5.448 0.113 11.11 4.405 0.082 13.09 3.456 0.137 Using modified ASTM procedures, we estimated the equilibrium moisture content of activated carbon to be 27%. To study the effect of moisture on adsorption capacity, we conducted isotherm measurements at moisture contents of 16%, 27%, 34% and 37%. The adsorption isotherm measurements for nitrogen were conducted at a moisture content of 37%, which is above the equilibrium moisture content of about 27%. The nitrogen adsorption isotherm for the wet activated carbon indicated significant reduction in adsorption capacity below 7 MPa when compared to the adsorption on the dry activated carbon. For example, at 5.5 MPa, the amount adsorbed on the wet activated carbon (37% moisture content) is only 4% of the amount adsorbed on dry activated carbon. Further, the nitrogen adsorption capacity on wet activated carbon (Figure 2.9) was less than 10% of the adsorption on the dry activated carbon, indicating the large effect of water on the carbon surface. The data for this isotherm yielded expected uncertainties of 30%, on average. However, higher percentage uncertainties are a result of the extremely low adsorption levels of this isotherm and translate to only about 0.022 mmol/gm of 37 adsorption, on average. As such, the experimental uncertainty in terms of actual adsorption amounts is small and such behavior is expected. The adsorption isotherm measurements for methane were also conducted at a moisture content of 37% and are shown in Figure 2.10. The data for this isotherm yielded expected experimental uncertainties of 28%, on average. As explained above, the large percentage uncertainties translate to small amounts of adsorption at these levels of moisture in the carbon. The amount of methane adsorbed on the wet activated carbon is significantly less than the amount adsorbed on dry activated carbon at comparable conditions (Figure 2.10). For example, at 2.8 MPa, the wet activated carbon (37% moisture content) adsorbed 93% less methane than the dry activated carbon. Similarly, at 7 MPa, the adsorption of methane on the wet carbon is 84% lower than the adsorption on dry activated carbon. Thus, even at higher pressures, the presence of water significantly lowers the methane adsorption. There is some confirmation in the literature of a significant reduction of methane adsorption on an activated carbon in the presence of moisture.53 Moreover, simulation results from the literature indicate that even small concentrations of water on the carbon surface can cause significant poreblocking, thus significantly reducing adsorption sites available to methane gas. In their simulation study on adsorption of watermethane mixtures on activated carbon, Muller et al.28 have shown that water can lead to 50% reduction in methane adsorption. Thus, the interconnectivity of water molecules across the pore entrances may further restrict methane adsorption on a wet carbon. 38 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/gm) N2Dry N237% Moisture Figure 2.9 Nitrogen Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture 0.0 1.0 2.0 3.0 4.0 5.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/gm) CH4Dry CH437% Moisture Figure 2.10 Methane Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture 39 The adsorption measurements for pure CO2 on wet activated carbon were conducted at three levels of moisture, as shown in Figure 2.11. The activated carbon has an equilibrium moisture content of 27%; thus, the three moisture contents were selected to represent supersaturated, saturated and undersaturated conditions of the wet activated carbon with respect to moisture. First, CO2 adsorption isotherm was measured at the equilibrium moisture content of 27%. Then, another isotherm was measured at moisture content of about 34%, which is 7% above the equilibrium moisture content. The third adsorption isotherm was measured at moisture content of about 16%, which is approximately onehalf the equilibrium moisture content. The adsorption data for each of these three isotherms yielded expected experimental uncertainties of 3%, on average. The adsorption of CO2 on wet activated carbon at 34% moisture content exhibited, on average, an 8% decrease in the amount of gas adsorbed when compared to the adsorption on wet activated carbon at its equilibrium moisture content. The adsorption of CO2 on wet activated carbon at 16% moisture content exhibited an increase of only 2% in the amount of gas adsorbed at 7 MPa when compared to the adsorption at a moisture content of 27%. For all three isotherms, the CO2 adsorption data displayed an unexpected change in concavity at moderate pressures between 3 and 6 MPa (Figure 2.11). In general, lower moisture content shifted this concavity change to lower pressures. Further, the wet activated carbon adsorption amount approaches that of the dry activated carbon at pressures above 8 MPa. This may be an artifact of our data reduction procedure, resulting from uncertainty in the gas density values we employed; this uncertainty could be caused by the presence of water vapor in the CO2 gas phase. Some experimental evidence suggests that the presence of small concentrations of water in the 40 gas phase can increase the CO2 gas density by as much as 10%.54 A correction of this magnitude can lead to the adsorption on the wet activated carbon becoming lower than the adsorption on the dry activated carbon at pressures higher than 8 MPa. Currently, we know of no equation of state capable of accurately calculating the densities of CO2–water mixtures at nearcritical conditions. Since the methane and nitrogen are well removed from their critical points, and water solubility in the gas phase is much lower than for CO2, the effect would be much smaller for the methane and nitrogen measurements. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/gm) CO2Dry CO2 34% Moisture CO2 27% Moisture CO2 16% Moisture Points that may not have reached equilibrium Figure 2.11 CO2 Adsorption on Wet Activated Carbon at 328.2 K at Different Moisture Contents As illustrated in Figure 2.11, our results indicate that even small amounts of moisture present in the adsorbent can lower significantly the gas adsorption, especially below 7 MPa, when compared with the adsorption on a completely dry adsorbent. 41 The kinetics of adsorption on wet activated carbon led to unusually long equilibration times (on the order of several days per datum) relative to our measurements on coals and on dry activated carbon, where the equilibration times are less than 24 hours. Lengthy equilibration time may be attributed to slow gas diffusion through the adsorbed water which covers some of the micropores of the carbon surface. Different mechanisms have been proposed for this adsorption behavior in the literature; however, most are centered on the fact that presence of moisture significantly blocks the pores of the carbon surface. The longest equilibration times occur between 3 and 7 MPa, which coincides with the region where the changes in concavity of the adsorption isotherm were observed. This may indicate that the stripping of adsorbed water, coupled with the slow dispersion of the adsorbing gas, is partly responsible for the long equilibration times. Figure 2.12 presents the equilibration times for CO2 adsorption isotherm on wet activated carbon at 34% moisture. The figure shows the total equilibration time for each data point of the isotherm. As evident from Figure 2.12, the equilibration times were much larger in the pressure range of 3 to 7 MPa. Figure 2.13 presents the pressure drop rate for data points at 4 and 12 MPa of the same isotherm studied in Figure 2.12. There appears to be a continued drop in pressure at 4 MPa even after 200 hours of equilibration time. In comparison, the drop in pressure at 12 MPa had essentially ceased after 48 hours, as evident from Figure 2.13. This contrasting behavior for moderate and high pressure data points of the same isotherm highlights the unexplained behavior observed in the 3 to 6 MPa region of this isotherm. 42 0 50 100 150 200 250 300 350 400 450 1 3 4 6 7 8 10 11 12 14 Pressure Step (MPa) Equlibration Time Allowed (Hours) 34% Moisture Figure 2.12 Equilibration Times for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture We also observed that the equilibration time allowed for the data point at 7 MPa appeared to be sufficient for stabilization of pressure. In contrast, the isotherm points between 3 and 6 MPa may have needed substantially longer equilibration times. Therefore, based on our experience in measuring adsorption isotherms, a decision was made to progress to the next higher pressure data point in the isotherm after the equilibration times shown in Figure 2.12 (in the 3 to 6 MPa region). This was necessitated by practical time constraints for these isotherms. As such, the isotherm data points between 3 and 6 MPa may not have reached their final equilibrium state. This region is also indicated by an “envelope” in Figure 2.11. 43 3.94 3.96 3.98 4.00 4.02 4.04 4.06 4.08 4.10 0 50 100 150 200 250 Equilibration Time(Hours) Pressure (MPa) 12.47 12.48 12.49 12.50 12.51 12.52 12.53 Pressure (MPa) CO2 34% Moisture (At 4 MPa) CO2 34% Moisture (At 12 MPa) Additional drop in pressure after 200 hrs. Figure 2.13 Pressure Drop Rate Data for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture: 4 and 12 MPa Pressure Steps To our knowledge, there are no literature data for the adsorption of CO2 under supercritical conditions on wet activated carbon at different levels of moisture. Since these appear to be the first measurements of their kind, additional work will be needed to delineate the cause of this unexpected behavior of CO2 isotherms on wet activated carbon. 2.11 OSU CBM Adsorption Database An adsorption database comprised of adsorption measurements for coalbed gases was assembled earlier.8 The database contains the pure, binary, and ternary mixture adsorption measurements conducted at OSU. There are 35 systems in that OSU adsorption database. As part of the current study, eleven new systems comprising thirteen independently measured isotherms have been added to the extended database. Thus, each 44 “system” consists of at least one gas isotherm on a specific adsorbent. Our newly acquired adsorption measurements are presented in Table 2.17, which includes the adsorbates, the adsorbent, number of points and the corresponding temperature and pressure ranges for each system. Table 2.17 Extended OSU Adsorption Database: New Systems in This Study Adsorbent Adsorbate Temp. (K) Pressure Range (MPa) NPTS Wet Illinois #6 Coal CO2 328 0.7 – 13.7 13 Wet Beulah Zap Coal CO2 328 0.7 – 13.7 11 Wet Wyodak Coal CO2 328 0.7 – 13.7 12 Wet Upper Freeport Coal CO2 328 0.7 – 13.7 12 Wet Pocahontas Coal CO2 328 0.7 – 13.7 12 Dry AC – F 400 N2 328 0.7 – 13.7 11 Dry AC – F 400 CH4 328 0.7 – 13.7 11 Dry AC – F 400 CO2 328 0.7 – 13.7 11 Wet ACF 400 CO2 328 0.7 – 13.7 33 Wet ACF 400 CH4 328 0.7 – 13.7 9 Wet ACF 400 N2 328 0.7 – 13.7 6 This extension of the database contains puregas adsorption measurements on six solid matrices: wet Illinois #6 coal, wet Beulah Zap coal, wet Wyodak coal, wet Upper Freeport coal, wet Pocahontas coal and wet/dry activated carbon. All isotherm measurements were conducted at 328.2 K and pressures to 13.8 MPa. Additional details of the OSU adsorption database can be found elsewhere.8 2.12 Monte Carlo Analysis of OSU Adsorption Error Analysis The following material in Section 2.12 has been reproduced with permission from [Mohammad, S. A.; Fitzgerald, J. E.; Robinson, R. L., Jr.; Gasem, K. A. M., Experimental Uncertainties in Volumetric Methods for Measuring Equilibrium Adsorption. Energy & Fuels 2009, DOI: 10.1021/ef8011257] Copyright [2009] American Chemical Society. 45 As mentioned above, a detailed error analysis was performed to estimate the uncertainty associated with each experimental datum by propagating the errors from the primary measurements of pressure, temperature and volume. The analytical error analysis was based on standard multivariate error propagation principles.55 The detailed derivation of the analytical error analysis has been summarized elsewhere.12, 20 In this study, a Monte Carlo analysis was conducted to confirm the validity of the analytical error analysis technique. In particular, a Monte Carlo analysis was performed for the CO2 adsorption on dry Upper Freeport coal, and the results were compared with the analytical error estimates. To conduct this analysis, all independent variables of the experiment were perturbed with a normallydistributed random error. The experimental estimates for the uncertainties in the primary measured quantities of pressure, volume and temperature were used as the random error of the corresponding perturbed variable in the Monte Carlo analysis. The Monte Carlo analysis was conducted for approximately 1000 sets of these perturbed variables. Thus, for each set of perturbed variables, an amount adsorbed was evaluated. The average of these runs at each pressure was taken as the amount adsorbed at that pressure for a given set of perturbed variables. Further, the standard deviation of the amount adsorbed evaluated from these 1000 sets was taken as an estimate of the uncertainty in the acquired data for comparison with the experimental error derived analytically. Figure 2.14 presents the comparison between analytical and Monte Carlo error estimates using the OSU adsorption apparatus for dry Upper Freeport coal. In this figure, sections marked as I, II and III represent three separate loadings of the pump that were required to complete the isotherm. The discontinuities at pressures around 10 and 12 MPa 46 are due to the reloading of pump, which was necessary for higher pressure injections. As evident from Figure 2.14, good agreement exists between the Monte Carlo and analytical error estimation methods. Thus, these results provide a reasonable confirmation of the analytical expressions that are used to estimate the uncertainties in the amount of gas adsorbed. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Error in Gibbs Adsorption (mmol/gm) Analytical Error Analysis Monte Carlo Error Analysis I II III Figure 2.14 Comparison of Monte Carlo and Analytical Error Analyses for CO2 Adsorption on Dry Upper Freeport Coal To test for the normality of the distribution of errors from the Monte Carlo analysis, the histogram and cumulative distribution of these errors are shown in Figure 2.15. In this figure, “X”, “Xbar” and “Sigma” represent the sample observation, mean and standard deviation of the distribution, respectively. As evident from the figure, the distribution displays essentially normal error distribution behavior. 47 0 20 40 60 80 100 120 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 (XXbar)/Sigma Frequency 0% 20% 40% 60% 80% 100% Cumulative Percentage Frequency Cumulative % 50.61% Figure 2.15 Histogram for the Distribution of Errors Evaluated from the Monte Carlo Error Analysis for CO2 Adsorption on Upper Freeport Coal 48 CHAPTER 3 REVIEW OF ADSORPTION MODELS IN CBMRELATED WORK The material in this chapter has been reproduced with permission from [Gasem, Khaled; Mohammad, Sayeed; Robinson, R. L., Jr.; Modeling Coalbed Methane Adsorption and CO2 Sequestration. Encyclopedia of Chemical Processing 2009, DOI: 10.1081/EECHP120043857] Copyright [2009] Taylor and Francis. In this chapter, a number of adsorption models that have been used for CBMrelated work are reviewed, and the potential weaknesses and strengths of some of these models are discussed. Among the adsorption models considered, this chapter concentrates on three theoreticallybased models that have been developed for use in CBM and CO2 sequestration modeling. The efficacy of these models in describing the adsorption behavior of coalbed gases is also discussed. Finally, the chapter outlines future work required to address some of the outstanding issues in adsorption modeling of CBM systems. The material presented herein is not intended to be allinclusive; rather, it is an overview of some of the pertinent efforts in equilibrium adsorption modeling of CBM systems. 3.1 Adsorption Models in CBMRelated Work Several frameworks can be used to describe the adsorption phenomenon and correlate pure and mixedgas adsorption isotherms in CBM systems. These include the Langmuir model13, extended Langmuir model56, the ideal adsorbed solution theory15, real adsorbed solution theory57, porefilling theory58 and its combination with the 49 vacancy solution model59, 60, twodimensional equationofstate (2D EOS) models16, 17, 18, the simplified localdensity (SLD) model25, the OnoKondo (OK) model20 and a variety of other models (see, e.g., Do61). These and some other models are briefly reviewed herein. Langmuir/Extended Langmuir Models The Langmuir model is the simplest adsorption model and is derived from kinetic considerations.13 The model assumes that: 1. The solid surface is composed of localized adsorption sites, and each site can hold only one adsorbate molecule 2. The adsorption sites are energetically equivalent 3. There are no adsorbateadsorbate interactions between neighboring adsorption sites 4. The molecules are adsorbed in a single layer only (monolayer coverage). In principle, the Langmuir model can describe only monolayer adsorption on an ideal surface. An ideal surface has periodic energy fluctuations which are equal in magnitude and this magnitude is larger than the thermal energy, KT. This trough of energy acts as an adsorption site. When a molecule hits a surface, it can either be reflected or adsorbed depending on whether the site is vacant or is already occupied by a molecule. The dynamic equilibrium is attained when the rate of adsorption is equal to the rate of desorption/evaporation. In terms of fractional loading, θ , the Langmuir model can be expressed as: 1 BP BP L ω θ + = = (3.1) 50 where θ and ω are the fractional loading and the amount adsorbed at pressure P, respectively, B is an affinity parameter with units of inverse pressure, and L is the theoretical maximum amount adsorbed at infinite pressure. The parameter B is a measure of the partitioning of the adsorbate molecules between the adsorbed and the gas phases. It also introduces implicitly the temperature dependence of the adsorption isotherms in the model (i.e., B is temperature dependent). The extended Langmuir model was first introduced by Markham and Benton56 to describe mixture adsorption. It can be represented as: +Σ ω = j j j i i i i 1 B Py L B Py j = 1, NC (3.2) where i L and i B are the temperaturedependent purecomponent Langmuir model parameters and i y is the gasphase mole fraction of the adsorbing specie “i”. The selectivity factor, α, can be expressed in terms of the extended Langmuir model parameters, as follows: j j i i j i ij L B L B y x y x α = = (3.3) where x and y are the adsorbed and gasphase mole fractions of the twocomponents, respectively, and L and B are the corresponding purecomponent model parameters. Equation (3.3) reveals that the extended Langmuir model predicts a constant (pressure and composition independent) value for α, since the right side of equation (3.3) depends only on purecomponent Langmuir model parameters. Thus, this model does not take into account mixedgas equilibria and system pressure to evaluate mixedgas 51 adsorption. As such, the extended Langmuir model is an entirely empirical model and is also thermodynamically inconsistent.51 Historically, the Langmuir and extended Langmuir models have been used extensively in the CBM field. Ease of application appears to be the main motivation for their use in CBM work. Arri and Yee51 used the Langmuir/extended Langmuir models in their compositional coalbed methane simulator. They observed that the extended Langmuir model underpredicted the adsorption in gas mixtures at higher pressures. Similarly, Chaback et al.62 applied the extended Langmuir model to model the adsorption/desorption of CO2, methane and nitrogen binary mixtures. Levy et al.31 correlated CO2 and nitrogen Langmuir model parameters with the corresponding values for methane for a set of Bowen Basin coals. They found a linear correlation between them and observed that the CO2 and nitrogen isotherms could be reliably predicted once the methane isotherm is known for such systems. However, this result is restricted to coals from a single basin. Ideal Adsorbed Solution (IAS) Theory Myers and Prausnitz15 introduced the ideal adsorbed solution (IAS) theory. This theory is an adsorption analog to Raoult’s law, which is used in vaporliquid equilibria. The IAS theory assumes that the gas and adsorbed phases form ideal solutions, i.e. all activity coefficients are unity. The equilibrium relation for the adsorbed and the gas phase in the IAS theory is given as: yiP = P0,i (π)x i (3.4) where 0 P is the equilibrium gas pressure corresponding to the temperature and spreading pressure, π, of the pure component, and xi and yi are the adsorbed and gasphase mole 52 fractions, respectively. The spreading pressure is defined as the difference in surface tension between a clean surface and a surface covered with an (monolayer) adsorbate.63 The IAS theory is used to extend a pureisotherm model to mixture adsorption. Any purecomponent isotherm model can be used with the IAS theory; several authors have used IAS theory to describe mixture adsorption. Valenzuela et al.64 used the Langmuir model with the IAS theory for different adsorption systems. Zhou et al.17 and Hall et al.6 utilized a 2D EOS with the IAS theory to model mixture adsorption. Similarly, Manik65 used the IAS theory with the Toth equation to model adsorption isotherms in their compositional coalbed methane simulator. Real Adsorbed Solution (RAS) Theory The real adsorbed solution theory takes into account the nonidealities in the adsorbed and the gas phases and, therefore, requires adsorbedphase activity coefficients. These activity coefficients are assumed to be unity in the IAS model. When the activity coefficients are considered, the real adsorbed solution (RAS) theory is obtained as follows57: 0 0 Pyiφi = Pi φi γixi (3.5) where 0 i φ is the gasphase fugacity coefficient of the pure component ‘i’ at its reference pressure 0 i P , i γ is the activity coefficient of the component ‘i’ in the adsorbed phase, and i y and i x are the mole fractions of the gas and adsorbed components, respectively. The adsorbedphase reference pressure is defined as the pressure exerted by the pure component adsorbate at the same spreading pressure and temperature as the mixture, 0 0 i i P = P (π,T) , where π is the spreading pressure derived from surface work. The 53 adsorbedphase activity coefficients are functions of temperature, pressure and composition. Since the spreading pressure is an intensive thermodynamic variable, the spreading pressure group,ψ, is defined as57: RT πA ψ = (3.6) where A is the surface area of the adsorbent. The spreading pressure of mixtures can be obtained from the Gibbs adsorption equation, which is related to the spreading pressure group as follows57: Σ= = − NC i 1 a T i i i dP ρ RT n dψ n dln(Py φ ) (3.7) where ρa is the molar density of the adsorbed phase, i n and T n are the amount adsorbed of component ‘i’ and the total adsorbed amount, respectively. Stevenson et al.57 applied the IAS and RAS theories to model mixture adsorption. Interestingly, they observed that the IAS theory was superior to the RAS theory, especially at the higher pressures where the activity coefficients are close to unity. This was attributed to errors in the adsorbedphase activity coefficients. In fact, no reported applications exist for estimating the adsorbedphase activity coefficients at higher pressures; therefore, use of the RAS theory has been very limited. Theory of Volume Filling of Micropores (TVFM) Dubinin66 extended Polanyi’s potential theory67 and developed the theory of volume filling of micropores (TVFM). This theory assumes that: 1. The adsorbate fills the adsorption surface through a porefilling mechanism 2. A discrete monolayer is never formed in the pores 54 Dubinin had hypothesized that the adsorption mechanism on microporous adsorbents would be better described by porefilling models (DubininPolanyi approach) than surface coverage models (Langmuir model, etc.). The two most common forms of the Dubinin’s porefilling models are the DubininRadushkevich (DR) and Dubinin Astakhov (DA) equations. The DubininAstakhov (DA) equation is given as68: = − n 0 0 0 P P ln βE RT V V exp (3.8) The DubininRadushkevich (DR) equation is obtained by setting n = 2 in Equation (3.8) above63: = − 2 0 0 0 P P ln βE RT V V exp (3.9) where V is the adsorbed volume, 0 V is the micropore saturation volume corresponding to the saturated pressure 0 P , n is a structuralheterogeneity parameter, β is an affinity coefficient and E0 is the characteristic heat of adsorption of the adsorbed molecule. A range of 14 has been reported for ‘n’60, and the values of β have also been compiled for a number of adsorbates.69 The Dubinin’s porefilling models are purecomponent isotherm models and, thus, require a mixture theory like the IAS theory to be extended to mixture adsorption. Several authors have used the porefilling models and found them to be superior to the Langmuir model. Clarkson and Bustin30 used the IAS theory and porefilling models and compared them with the extended Langmuir model. They found the IAS/DA model to perform better than the IAS/DR, IAS/Langmuir and extended Langmuir models. 55 However, they found that none of these models was able to describe accurately the selectivity of the adsorbates and yielded either a constant selectivity (extended Langmuir) or an increasing selectivity with increasing feed composition of the larger adsorbing gas (IAS/DR equation), both of which did not agree with their experimental data. Similarly, Harpalani et al.70 modeled data for adsorption isotherms with the Langmuir, DR and DA equations and found the DA equation to be superior to the other two models. An important aspect of the DA equation is the temperatureinvariance of the characteristic plots ( P P RT ln 0 vs. V). This feature can be used to predict adsorption at different temperatures based on data from a single isotherm. This capability notwithstanding, the porefilling models are, however, developed for subcritical adsorbates. Specifically, these models require the saturation pressure, P0, of the respective isotherms. As such, an empirical modification is introduced when using a porefilling model for CBM systems, which involve mostly nearcritical and supercritical adsorbates. Although, a variety of modifications have been proposed60, 71, there appears to be little theoretical justification behind them. Coal Swelling Another aspect of highpressure gas adsorption behavior in coalbeds is the potential swelling of coal caused by adsorbates such as CO2. Some investigators believe that adsorption of CO2 can significantly alter the porous coal structure and these changes, if left unaccounted for, can result in large errors in the modeling of supercritical CO2 adsorption on coals. In fact, several researchers have attempted to model the swelling of coal by incorporating volumetric corrections to the adsorption isotherm equations. Ozdemir et al.46 used a variety of adsorption models, including the DA model, to study 56 the volumetric effects of CO2 adsorption on coals. Similarly, Dutta et al.47 used the Langmuir and DA models to account for the swelling of coal and dissolution of CO2 in the coal matrix. Romanov et al.48 have also attempted to interpret the volumetric changes in coals under CO2 pressure. More recently, Pan and Connell49, balancing the change in surface energy due to adsorption to the change in elastic energy of the coal matrix, developed a theoretical model to describe adsorptioninduced coal swelling. 3.2 TheoryBased Equilibrium Adsorption Models Beyond sound theoretical framing of the adsorption model, several desired attributes are sought when modeling CBM systems, including the model’s ability to: 1. Correlate pure and mixedgas adsorption data within the experimental uncertainties at reservoir conditions 2. Facilitate generalized predictions of puregas isotherms based on accessible coal characterization and gas properties 3. Predict the individual component and the total adsorption of a multicomponent gas mixture based on puregas isotherms or purefluid model generalization 4. Account rigorously for the presence of moisture in the coal Although, the traditional adsorption models described above have been used in CBMrelated work, they lack some of these desired attributes. Moreover, they seem to lack the theoretical rigor of a multicomponent adsorption model that is needed in CBM work. In previous works at OSU8, 12, researchers have tested three theorybased adsorption models for their CBM adsorption modeling capabilities. Although based on very different theoretical basis, the twodimensional equationofstate, the OnoKondo, and the simplified localdensity models were found to be readily amenable to the modeling 57 demands of CBM systems.8, 12 Following is a brief description of these three models that have been found useful in CBMrelated work. TwoDimensional Equations of State The twodimensional (2D) equationsofstate (EOS) models are essentially analogs of the 3D EOS models used in vaporliquid equilibria calculations. One of the main incentives in developing the 2D EOS models is their potential for direct implementation in CBM simulations in a manner similar to 3D EOS models used in conventional oil and gas reservoir simulations. The 2D EOS models offer several advantages. Specifically, they17: 1. Permit simultaneous calculation of equilibrium adsorption and volumetric properties 2. Are particularly suitable for extending puregas adsorption isotherms to multicomponent mixture predictions, using appropriate mixing rules 3. Are amenable to modelparameter generalization 4. Utilize a proven, familiar model format for use in reservoir simulations. The assumptions used in developing the 2D EOS models include16: 1. The adsorbent surface can be treated as a twodimensional, imaginary mathematical surface; and this 2D phase possesses its own thermodynamic properties 2. The adsorbent is thermodynamically inert. 3. The adsorbent provides a temperatureinvariant surface area, which is accessible equally to all the adsorbate molecules. 58 4. The adsorbent surface is homotattic, i.e., it is made up of many homogeneous subregions. As mentioned earlier, the 2D EOS was developed by analogy to the 3D cubic EOS. A generalized form of the cubic 3D EOS used in vaporliquid equilibrium calculations can be written as: [1 b ] RT 1 Ub W(b ) a p 2 2 ρ = ρ − + ρ + ρ ρ + (3.10) where a and b are the EOS parameters and values of U and W are specified to give various forms of 3D EOS. The 2D EOS is obtained simply by replacing two terms in the 3D EOS  the bulk pressure, P, with the spreading pressure, π, and the bulk density, ρ, with the specific surface density, σ. The generalized 2D analog of the 3D EOS, then, is given as: [1 (b ) ] RT 1 Ub W(b ) a m 2 2 2 2 2 2 σ = σ − + σ + σ σ π + (3.11) or [1 ( ) ] RT 1 U W( ) A m 2 2 ω = βω − + βω+ βω αω π + (3.12) where A is the specific surface area of the adsorbent, π is the spreading pressure, σ is the surface density of the adsorbate, ω = σA is the specific amount adsorbed, a A 2 α = and b A 2 β = are the 2D EOS model parameters and m is an additional parameter used to provide more flexibility to the model.17 The model coefficients, U, W, and m are specified to obtain a particular form of the 2D EOS. For example, a 2D analog of the 3 D van der Waals (VDW) EOS is obtained by setting m = 1 and U = W = 0; similarly for the SoaveRedlichKwong (SRK) (m = U = 1 and W = 0); the PengRobinson (PR) (m = 59 1, U = 2, and W = 1); the Eyring (m = 1/2 and U = W = 0) EOS; and the ZhouGasem Robinson (ZGR) (m = 1/3 and U = W = 0) EOS.17 Equilibrium Relations for TwoDimensional EOS The governing equations for adsorption equilibrium are entirely independent of the equation of state used in the model. At equilibrium, the chemical potential of specie i in the gas phase is equal to that in the adsorbed phase (see, e.g., Zhou et al.17): g i a μi = μ and g i a i dμ = dμ (3.13) ∫ = ∫ P P g i π π a i * * dlnf dlnf ) ) (3.14) where μi is the component chemical potential, π* is the spreading pressure at the standard conditions, g i a i f and f ) ) are the component fugacities in the adsorbed phase and the gas phase, respectively. Integrating Equation (3.14): ( ) ( ) ( ) g ( * ) i g i a * i a i lnf π lnf π lnf P lnf P ) ) ) ) − = − (3.15) At very low pressure, * i P , ( ) * i a * fi π = π ) and ( ) * i g * i f P = P ) . Thus, P f (π) π f g (P) i * i a i * i ) ) = (3.16) At very low pressure, the 2D ideal gas law is obtained: π A ω RT * i * i = (3.17) where T is temperature, R is the universal gas constant, and * ωi is the amount adsorbed at low pressures. Further, the Henry’s constant i k can be defined as: * i * i i P ω k = (3.18) 60 Therefore, g i i a i i a i Af Ax πφ k RTf ) ) ) = = (3.19) For puregas adsorption, the equilibrium relation is given by: g i a a ωZ φ = k f (3.20) where ω is the amount adsorbed, a Z is the 2D compressibility factor, φa is the fugacity coefficient using the 2D EOS, f g is the fugacity for the gas phase. The fugacity for the 2D EOS is given by: ( ) a 0 i T,M ,n a i d ln Z A 1 RT ˆ 1 ln s j ω− ω − ∂ω ∂ π ω φ = ∫ ω (3.21) where A is the specific surface area and Ms is the mass of the adsorbent. As evident from the above relations, the 2D EOS enters the calculation through the fugacities and the 2D compressibility factor. To perform adsorption equilibrium calculations using Equation (3.20) requires the values of α, β, and k. They are determined normally by direct regression of adsorption isotherm data. As such, the 2D EOS is a threeparameter adsorption model. Several researchers have utilized the 2D EOS theory to model gas adsorption. Hill72 and de Boer73 used the van der Waals (VDW) EOS to correlate puregas adsorption. Hoory and Prausnitz74 extended the 2D VDW EOS to mixtures by introducing mixing rules. DeGance16 applied the 2D virial and Eyring EOS to correlate highpressure pure gas adsorption isotherms. Zhou et al.17 used the 2D EOS model to describe pure and mixedgas adsorption on different adsorbents. Pan18 introduced Gibbs Free energy mixing rules into the 2D EOS and developed temperature dependence relations for the 2D model parameters. 61 OnoKondo Lattice Model The OnoKondo (OK) adsorption model is based on lattice theory and was first proposed by Ono and Kondo.19 Since then, Aranovich and Donohue7577 have generalized the model expressions for application to the adsorption of solutes in liquid solutions. Sudibandriyo20 generalized the OK model parameters, extended the model to mixture adsorption of CBM systems and developed the temperature dependence relations for the model parameters. Key features of the OnoKondo model include its ability to: 1. Provide a layering analogue to adsorption 2. Generate independent estimates for the adsorbedphase densities 3. Incorporate accurate userprovided density estimates, which may reduce the correlative burden of the adsorption modeling. 4. Utilize the puregas adsorption isotherms to predict mixture adsorption without the use of binary interaction parameters The assumptions used in developing the lattice OnoKondo model are (see, e.g., Sudibandriyo20): 1. The fluid system is composed of one or more layers of lattice cells containing fluid molecules and vacancies. 2. Molecular interactions exist only between the nearest neighboring molecules, i.e. in the adjacent lattice cells. 3. Adsorption equilibrium between the adsorbed layers and the bulk lattice gas is given by the equality of the chemical potential in each layer and the bulk gas. 62 For an adsorptive system, more fluid molecules would reside in the cells of the adsorbedphase layers than in the cells of the bulkphase layers due to the molecular interactions with the adsorbent surface. The OK model expression for the thermodynamic equilibrium between the gasphase and a multilayer adsorbedphase is given as75: ln[x (1 x )/x (1 x )] z (x x )ε /kT (x 2x x )ε /kT 0 t b b t 0 t b ii t 1 t t 1 ii − − + − + − + = + − and t = 1, 2, 3… (3.22) where t represents the number of layers. For the first layer, ln[x (1 x )/x (1 x )] (z x x z x )ε /kT ε /kT 0 1 b b 1 1 1 2 0 b ii is − − + + − + = (3.23) where xt is the reduced density or fraction of sites occupied by adsorbed molecules in layer t, and xb is the fraction of sites occupied by fluid molecules in the bulk, z0 and z1 are the coordination numbers of the lattice cells, εii/kT is the fluidfluid interaction energy parameter, εis/kT is the fluidsolid interaction energy parameter, k is Boltzmann’s constant and T is the absolute temperature. For a hexagonal lattice, the coordination numbers z0 and z1 are 6 and 4, respectively. The Gibbs excess adsorption, Γ , in the OK model is given as: = Σ − m t t b Γ C (x x ) (3.24) where C is known as a "prefactor," which is related to the capacity of the adsorbent for a specific adsorbate. The index m is the number of layers for the adsorption isotherm and is typically determined from the best description of the adsorption data. The reduced densities xi and xb can be expressed as xi= ρi /ρmc and xb= ρb /ρmc, where ρi and ρb are the adsorbed and the bulk density of the adsorbate, respectively and ρmc is the maximum adsorbedphase density. The maximum adsorbedphase density, ρmc, can be estimated in 63 various ways. Two of the common ways of estimating the adsorbedphase density are to use the saturated liquid density at atmospheric pressure51 or the inverse of the VDW covolume.8 Further, Hocker and Donohue78 have used a theoretical value of the density of closepacked molecules. Although the OK model allows for the formation of multiple layers, a monolayer has been shown to provide a satisfactory description of the adsorption data.20 In the monolayer OK model, the adsorbed molecules are directly mapped onto parallel graphite planes, as shown in Figure 3.1. Further, when a 2Dhexagonal configuration is chosen, the thermodynamic equilibrium expression of Equation (3.22) simplifies as: ln[x (1 x )/x (1 x )] ((z 1)x z x )ε /kT ε /kT 0 ads b b ads 1 ads 0 b ii is − − + + − + = (3.25) Therefore, the Gibbs excess adsorption expression for the monolayer OK model becomes: = − = − mc b mc ads ads b ρ ρ ρ ρ Γ 2C (x x ) 2C (3.26) where ρads is the adsorbedphase density. GRAPHITE PLANE GRAPHITE PLANE Figure 3.1 OnoKondo Model for Monolayer Adsorption on Graphite Slit (Slit Depiction Adopted from Sudibandriyo20) The OK model thus has four parameters: ρmc, εii/k, εis/k and C. Two of these parameters can be estimated independently. Specifically, ρmc is estimated to be the inverse of the VDW covolume and εii/k can be evaluated as20: εii 0.432ε * = (3.27) 64 where ε * is the well depth of the 126 LennardJones potential. These assumptions yield the twoparameter (C and εis/k) OK model. Simplified LocalDensity/PengRobinson (SLDPR) Model The SLD model is a simplification of the more computationallyintensive localdensity theory. According to this theory, the density profile is obtained by minimizing the total energy function, which depends on all point densities and their spatial derivatives.79 The SLD model, thus, uses meanfield theory in calculating the chemical potential. In other words, the local fluctuations arising out of gradients in density are not considered in the micropores, where the majority of adsorption takes place. Further, the chemical potential of the fluid at each point is corrected for the proximity of the fluid molecule to the molecular wall of the adsorbent.25 The SLD model partitions the interactions of a gas molecule in the adsorbed phase into fluidsolid and fluidfluid interactions. The fluidsolid interactions are modeled through a potential function such as the 104 Lee's potential80 whereas the fluidfluid interactions are modeled through a modified 3D EOS.81 Specifically, the attractive parameter in the EOS is modified to account for the presence of the adsorbent wall. Several advantages distinguish the SLD framework. In particular, the model: 1. Provides a consistent framework that accounts for adsorbateadsorbate (fluidfluid) and adsorbateadsorbent (fluidsolid) molecular interactions 2. Delineates the adsorbent structural properties based on welldescribed physical geometries of the adsorbent and 3. Predicts the adsorbedphase density which facilitates prediction of absolute gas adsorption. 65 4. Offers the opportunity for model generalizations using molecular descriptors 5. Predicts the mixtureadsorption based solely on puregas isotherms or purefluid generalization A number of assumptions have been used in developing the SLD model22: 1. The chemical potential at any point near the adsorbent surface is equal to the bulk phase chemical potential. 2. The chemical potential at any point above the surface is the sum of the fluidfluid and fluidsolid interactions. 3. The attractive potential between fluid and solid at a point is independent of the number of molecules at and around that point. Different geometries such as rectangular slits8, 81, cylindrical pores82, flat surfaces8, etc. can be used to model the porous adsorbent structure. Using the slit geometry, the SLD model assumes the adsorbate molecules reside within a twosurface rectangularshaped slit. The distance between the slit surfaces is L and the position of a molecule within the slit is z. The position, z, is orthogonal to the solid surface formed by the carbon atoms on the slit wall. Therefore, the chemical potential of the fluid, μ, is expressed as the sum of the fluidfluid and fluidsolid potentials at a position, z. At equilibrium: μ(z) = μff (z) + μfs (z) = μbulk (3.28) where subscripts "bulk", "ff" and "fs" refer to bulk fluid, fluidfluid interactions, and fluidsolid interactions, respectively. The chemical potential of the bulk fluid is expressed in terms of fugacity as: = + 0 bulk bulk 0 f (T) RTln f μ μ (3.29) 66 where f is the fugacity, and μ0 is the chemical potential at the reference state. By analogy, the chemical potential from fluidfluid interactions is written as: = + 0 ff ff 0 f (T) RTln f (z) μ (z) μ (3.30) where fff (z) is the adsorbed fluid fugacity at a position z, and μ0 is the chemical potential at the same reference state as in Equation (3.29). As mentioned above, the fluidsolid interactions are accounted for through a fluidsolid potential function. As such, the fluidsolid chemical potential, μfs , is given as: μ (z) N [ (z) (L  z)] fs fs fs A = Ψ + Ψ (3.31) where Ψ(z) and Ψ(Lz) are the fluidsolid interactions from the two walls of a slit of length L, and NA is the Avogadro’s number. Substituting Equations (3.29), (3.30) and (3.31) into Equation (3.28) yields the SLD equilibrium relationship for modeling adsorption within the slit: + − = − kT Ψ (z) Ψ (L z) f (z) f exp fs fs ff bulk (3.32) where k is the Boltzmann’s constant. In Equation (3.32), Lee’s partiallyintegrated 104 potential80 is used to provide the fluidsolid interaction information, Ψfs(z)22, 81: ( ) + − ⋅ − = Σ= 4 i 1 4 ss 4 fs 10 10 2 fs atoms fs fs fs z' (i 1) σ σ 2 1 5(z') σ Ψ (z) 4πρ ε σ (3.33) εfs = εff × εss (3.34) where εfs is the fluidsolid interaction energy parameter, ρatoms = 0.382 atoms/Å2 and z' is the centercenter distance between fluid molecules and carbon atoms in the first plane. 67 The parameters σff and σss represent, respectively, the molecular diameter of the adsorbate and the carbon interplanar distances. The excess adsorption (nEx), when applying the SLD model, is given as: = ∫ ( ( )− ) Right Side of Slit Left Side of Slit bulk Ex ρ z ρ dz 2 A n (3.35) where nEx is the excess adsorption and A is the accessible surface area for the gas on a particular adsorbent. The left and right sides of the slit each comprise half of the total surface area, A/2. Thus, the excess adsorption can be calculated by numerical integration of Equation (3.35). Thus, the optimized parameters in the SLD model typically include the surface area A for each fluid, solidsolid interaction energy parameter εss/K and the slit length L.12 The SLD model was developed by Rangarajan et al.22 who used the van der Waals EOS to provide the fluidfluid interaction information. Any EOS with appropriate modifications can be used within the SLD framework. In fact, over the years, researchers have used different EOSs such as the PengRobinson, Bender and ElliotSureshDonohue (ESD) EOSs within the SLD framework to provide the fluidfluid interaction information.23, 24, 26, 81 Fitzgerald25 used the SLD model with a modified PengRobinson (PR) EOS83 to study the highpressure adsorption of coalbed gases and their mixtures on dry and wet coals and activated carbons. Further, the SLD model is capable of accounting for swelling of coal by varying the slit length with pressure. However, the modeling results obtained at OSU for highpressure adsorption systems without the use of coal swelling were found to be satisfactory; therefore, to date, the inclusion of this effect could not be justified. 68 Gibbs and Absolute Adsorption Adsorption data can be reported either in terms of Gibbs or absolute adsorption. Gibbs adsorption is calculated directly from experimentallymeasured quantities and this accounts for the fact that there is additional material present near the adsorbent surface due to adsorption phenomenon. This additional material is in excess of that which would be present in the same (void) volume if there was no adsorption. This excess material is usually referred to as the Gibbs or excess adsorption. In contrast, the calculation of absolute adsorption requires knowledge of the adsorbed phase density, ρads, which is not readily accessible by experimental measurement. The exact mathematical expressions that highlight the physical interpretation of Gibbs adsorption and the approximate nature of calculated absolute adsorption have been presented elsewhere.7 The relationship between the two quantities is given as − = ads gas Gibbs ads ads Abs ads ρ ρ ρ n n (3.39) where Abs ads n and Gibbs ads n are the absolute and Gibbs adsorption, respectively, and ρgas and ρads are the gas phase and the adsorbed phase densities, respectively. To calculate absolute adsorption from Equation (3.39), estimates of ρads must be employed. A commonly used approximation for ρads is the liquid density at the normal boiling point (as was done by Arri and Yee51) or the reciprocal of the VDW covolume.8 3.3 Example Studies of Adsorption Modeling In this section, the modeling capability of the 2D EOS, OK and SLDPR models as they apply to CBM systems is demonstrated. Specifically, the correlation capabilities of these models for puregas adsorption on dry and wet coals are illustrated. Several other 69 capabilities of these models that were demonstrated in earlier OSU studies have also been highlighted. Further, the generalization capabilities of these models are reviewed in Chapter 6. In particular, the coal structurebased generalization of SLD model is covered in Chapter 6, along with a review of other generalization efforts in the literature. Statistical Quantities Used In the results presented here, the sum of the squared weighted deviations, expressed in terms of the weighted root mean square, WRMS, was used for the objective function: NPTS σ n n WRMS 2 i NPTS i 1 exp calc exp Σ= − = (3.40) where NPTS is the number of data points, nexp is the experimental excess adsorption, ncalc is the calculated excess adsorption and σexp is the expected experimental uncertainty. In addition, the results were analyzed in terms of the average absolute percentage deviation (%AAD), the root mean square error (RMSE) and weighted average absolute deviation (WAAD): 100% NPTS n n n abs %AAD i NPTS i 1 exp calc exp × − = Σ= (3.41) ( ) NPTS n n RMSE 2 i NPTS i 1 calc exp Σ= − = (3.42) NPTS σ n n abs WAAD NPTS i 1 exp calc exp Σ= − = (3.43) 70 Modeling Discussion Correlation of PureGas Adsorption on Dry and Wet Coals The prediction of adsorption isotherms of pure methane, nitrogen and CO2 on five dry coals and the adsorption isotherms of pure CO2 on five wet coals are used to demonstrate the correlative abilities of the 2D EOS, OK and SLD models. Each of these three models was used to represent the adsorption data on these coals. Table 3.1 lists the regressed parameters for the 2D EOS, OK and SLDPR models for each coal. Three parameters (α, β, and k) were regressed for the 2D EOS model, two (εfs/k and C) for the OK model and three (surface area, εss/k and L) for the SLD model. Further, the SLD parameter “L” was fixed at 1.15 nm. for the modeling on wet coals since there were data for only one gas on the wet coals. Table 3.2 lists the summary statistics obtained for the three models on these coals. The overall WAAD for the five dry coals was 0.3, 0.4 and 0.5 for the 2D EOS, OK and SLD models, respectively. In comparison, the overall WAAD for the five wet coals was 0.5, 0.3 and 0.5 for the 2D EOS, OK and SLD models, respectively. Further, the overall %AAD for the five dry coals was 1.9%, 2.6% and 3.1% for the 2D EOS, OK and SLD models, respectively. The corresponding sta
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Title  Adsorption Modeling of Coalbed Gases and the Effects of Water on Their Adsorption Behavior 
Date  20090501 
Author  Mohammad, Sayeed Ahmed 
Keywords  Adsorption, CO2 Sequestration, Coalbed Methane, Coals, Moisture effect, Simplified local density model 
Department  Chemical Engineering 
Document Type  
Full Text Type  Open Access 
Abstract  The simplified localdensity/PengRobinson (SLDPR) adsorption model was utilized to investigate the adsorption behavior of coalbed gases on coals of varying rank. The model parameters were generalized in terms of readilyaccessible coal properties such as the ultimate and proximate analyses of the coals. Further, the effects of water present in coals on the gas adsorption behavior were studied. In particular, the SLDPR model was used to investigate this effect wherein water was treated as a separate adsorbed component in a binary mixture. To conduct this study, new highpressure gas adsorption measurements were acquired for CO2 on wet Argonne coals and for methane, nitrogen and CO2 on dry and wet activated carbon using a volumetric technique. The generalized SLDPR model was found to be capable of accurate predictions of the adsorption of coalbed gases and their mixtures on dry and wet coals. Specifically, the generalized model was capable of (a) predicting the puregas isotherms for methane, nitrogen and CO2 on coals within two times the expected experimental uncertainties and (b) predicting, a priori, the adsorption of mixtures formed by these gases within three times the expected experimental uncertainties, on average. The generalized model was validated with an external data set which comprised of CO2 adsorption isotherms on 27 diverse coals. CO2water binary mixed gas adsorption modeling results on wet coals indicated that the SLDPR model is capable of representing the adsorption of this highly asymmetric mixture within the experimental uncertainties, on average. The model parameterization used and the molecular interactions accounted for in describing water adsorption behavior on coals illustrated a viable method to obtain precise representations of this adsorbed mixture. The phasecheck analysis of the same mixture indicated that there is a potential for the formation of an aqueous phase in these systems for coals that contain large amounts of moisture, with the exception of Beulah Zap lignite coal. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  ADSORPTION MODELING OF COALBED GASES AND THE EFFECTS OF WATER ON THEIR ADSORPTION BEHAVIOR By SAYEED AHMED MOHAMMAD Bachelor of Science in Chemical Engineering Osmania University Hyderabad, India 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 2009 ii ADSORPTION MODELING OF COALBED GASES AND THE EFFECTS OF WATER ON THEIR ADSORPTION BEHAVIOR Dissertation Approved: Dr. Khaled A. M. Gasem Dissertation Adviser Dr. Robert L. Robinson, Jr. Dr. Jan Wagner Dr. William D. Warde Dr. A. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGMENTS I would like to express my gratitude to my adviser, Dr. Khaled Gasem, for giving me the opportunity to work with him on this project. I greatly appreciate his invaluable guidance, support and encouragement for conducting quality research, and for teaching me to be a "truth seeker" as a researcher. Through out my five years of work with him, I have learnt some great lessons in research and life. I would like to thank my coadviser, Dr. Robert Robinson, Jr., for his invaluable insight, supervision and thoughtful reviews of this work. I am also grateful to my advisory committee members, Dr. Jan Wagner and Dr. Bill Warde, for their valuable input and helpful suggestions. It has been a great honor for me to have worked with these distinguished members of the OSU Graduate Faculty. I also express my sincere appreciation and gratitude for my past colleagues in this project, Dr. James Fitzgerald and Ms. Jing Chen, for their support and help with this project. I also thank the many friends and acquaintances I made over the years, whose friendship I truly appreciate. I also acknowledge the support of the U.S. Department of Energy to our research group that made this project possible. I thank many of the friends at Stillwater Islamic Center for their good wishes. I would like to thank Dr. Saleh Ashaghathra, Dr. Ahmed Abo Basha, Dr. Mumtaz Hussain and Dr. Qamar Arsalan for their valuable friendship and encouragement. iv Finally, I am grateful to my parents, sister, brother and his family for their sacrifices, patience and prayers through out my graduate studies. Their support, understanding and encouragement were most crucial in my continued success away from home. Sayeed Mohammad May 8, 2009 v TABLE OF CONTENTS Chapter Page 1. INTRODUCTION .....................................................................................................1 1.1 Coalbed Methane and CO2 Sequestration ..........................................................1 1.2 Adsorption Models.............................................................................................2 1.3 Effect of Water on Coalbed Gas Adsorption Behavior .....................................3 1.4 Objectives ..........................................................................................................5 1.5 Organization .......................................................................................................8 2. EXPERIMENTAL METHODS, PROCEDURES AND RESULTS ......................10 2.1 Adsorption Isotherm Measurements ................................................................11 2.2 Gas Compressibility Factors ............................................................................14 2.3 Materials ..........................................................................................................14 2.4 Error Analysis ..................................................................................................16 2.5 Equilibrium Moisture of Coals and Activated Carbon ....................................16 2.6 Gas Solubility in Water ....................................................................................18 2.7 Adsorption Measurements on Wet Coals and Activated Carbon ....................20 2.8 Coal Swelling ...................................................................................................21 2.9 Gibbs and Absolute Adsorption .......................................................................23 2.10 Experimental Results .....................................................................................23 Adsorption of CO2 on Wet Argonne Coals................................................23 Adsorption of Methane, Nitrogen and CO2 on Dry and Wet Activated Carbon................................................................................32 2.11 OSU CBM Adsorption Database ...................................................................43 2.12 Monte Carlo Analysis of OSU Adsorption Error Analysis ...........................44 3. REVIEW OF ADSORPTION MODELS IN CBMRELATED WORK ................48 3.1 Adsorption Models in CBMRelated Work .....................................................48 3.2 TheoryBased Equilibrium Adsorption Models...............................................56 3.3 Example Studies of Adsorption Modeling .......................................................68 3.4 Limitations and Future Work ...........................................................................79 3.5 Conclusions ......................................................................................................80 vi Chapter Page 4. REVIEW OF PURE WATER ADSORPTION .......................................................82 4.1 Introduction ......................................................................................................82 4.2 Surface Characterization of Activated Carbons and Coals ..............................86 A Case Study of the SLDPR Model Applied to Pure Water Adsorption .......................................................................................94 4.3 The Physical State of Water Naturally Found on Coals ..................................99 4.4 Water Adsorption Models ..............................................................................111 4.5 Summary ........................................................................................................120 4.6 Modeling Approaches ....................................................................................121 4.7 Modifications to the SLDPR Model .............................................................123 5. SIMPLIFIED LOCALDENSITY/PENGROBINSON (SLDPR) ADSORPTION MODEL .....................................................................................124 5.1 Introduction ....................................................................................................124 5.2 SLDPR Adsorption Model ...........................................................................124 5.3 Modifications to SLDPR Model for Pure Water Adsorption Modeling ......131 5.4 Representation of Adsorbed Water Capacity with SLDPR Model ..............134 5.5 SLDPR Model for Mixed Gas Adsorption ...................................................136 5.6 SLDPR Modeling of CO2Water Mixture Adsorption on Wet Argonne Coals ........................................................................................141 5.7 Case Study Conclusions .................................................................................165 6. GENERALIZATION OF SLDPR MODEL.........................................................167 6.1 Generalization Approach ...............................................................................167 6.2 Database Employed in this Study ..................................................................168 6.3 SLDPR Model Representation of PureGas Adsorption Data......................172 6.4 Generalized Correlations ...............................................................................178 6.5 SLDPR Generalized Model for PureGas Adsorption on Coals ..................181 6.6 Previous Generalization Studies ...................................................................192 6.7 Sensitivity Analysis of SLDPR Model Generalization ................................196 6.8 SLDPR Generalized Model Predictions for MixedGas Adsorption ...........200 6.9 Validation of the SLDPR Generalized Model ..............................................213 6.10 Generalization Conclusions .........................................................................216 7. CONCLUSIONS AND RECOMMENDATIONS ................................................217 7.1 Conclusions ....................................................................................................217 7.2 Recommendations ..........................................................................................219 REFERENCES ......................................................................................................221 vii LIST OF TABLES Table Page 2.1 Compositional Analyses of Adsorbents Used in this Study ................................15 2.2 Parameters for Gas Solubility in Water at 318.2 K or 319.3 K ...........................19 2.3 Parameters for CO2 Solubility in Water at Multiple Temperatures .....................20 2.4 Gibbs Adsorption of Pure CO2 on Wet Beulah Zap Coal at 328.2 K ..................24 2.5 Gibbs Adsorption of Pure CO2 on Wet Illinois #6 Coal at 328.2 K ....................24 2.6 Gibbs Adsorption of Pure CO2 on Wet Pocahontas #3 Coal at 328.2 K .............25 2.7 Gibbs Adsorption of Pure CO2 on Wet Upper Freeport Coal at 328.2 K ............25 2.8 Gibbs Adsorption of Pure CO2 on Wet Wyodak Coal at 328.2 K .......................26 2.9 Gibbs Adsorption of Pure Nitrogen on Dry Activated Carbon at 328.2 K ...........................................................................................................33 2.10 Gibbs Adsorption of Pure Methane on Dry Activated Carbon at 328.2 K .........................................................................................................33 2.11 Gibbs Adsorption of Pure CO2 on Dry Activated Carbon at 328.2 K .........................................................................................................34 2.12 Gibbs Adsorption of Pure Nitrogen on Wet Activated Carbon at 328.2 K and 37% Moisture ...........................................................................34 2.13 Gibbs Adsorption of Pure Methane on Wet Activated Carbon at 328.2 K and 37% Moisture ...........................................................................34 2.14 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 27% Moisture ...........................................................................35 2.15 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 34% Moisture ...........................................................................35 viii Table Page 2.16 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 16% Moisture ..........................................................................36 2.17 Extended OSU Adsorption Database: New Systems in This Study .................44 3.1 Regressed Model Parameters for Representations of PureGas Adsorption on Dry and Wet Coals ......................................................................71 3.2 Sample Results for Model Representations of PureGas Adsorption on Dry and Wet Coals ......................................................................72 4.1 SLDPR Model Case Study for PureWater Adsorption on Activated Carbons from the Literature ...............................................................96 5.1 Physical Properties of Fluids Used in SLDPR Model .....................................128 5.2 A Case Study with the New Parameterization of SLDPR Model for Pure Water Adsorption on Activated Carbons..................................................137 5.3 A Case Study with the New Parameterization of SLDPR Model for Pure Water Adsorption on Coals ......................................................................137 5.4 SLDPR Model Representations of CO2Water Binary Mixture Adsorption on Wet Argonne Coals ..................................................................154 5.5 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Pocahontas Coal ...................................................................................161 5.6 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Upper Freeport Coal .............................................................................161 5.7 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Illinois #6 Coal .....................................................................................162 5.8 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Wyodak Coal ........................................................................................162 5.9 PhaseCheck Analysis for CO2water Mixture Adsorption on Wet Beulah Zap Coal ...................................................................................163 6.1 Adsorption Database Used For SLDPR Model Generalization ......................169 6.2 Compositional Analyses of OSU Coals Used in this Study .............................171 ix Table Page 6.3 Compositional Analyses of Argonne Premium Coals Used in this Study ........171 6.4 SLDPR Model Representations of PureGas Adsorption on Coals ................174 6.5 Correlation Matrix of SLDPR Model Regressed Parameters for Coals ..........177 6.6 Correlation Matrix of Coal Properties ..............................................................179 6.7 Summary Results of SLDPR PureGas Model Generalization for Coals .......183 6.8 Comparison of Generalized and Regressed Model Parameters ........................184 6.9 Sensitivity Analysis of SLDPR Model Parameters for PureGas Adsorption on Wet Fruitland Coal at 319.3 K ..................................................198 6.10 Summary Results of Generalized SLDPR Predictions for MixedGas Adsorption on Coals ..............................................................201 6.11 Validation Results for the Generalized SLDPR Model Predictions: CO2 Adsorption on 27 Coals Reported by Day et al. .....................................213 x LIST OF FIGURES Figure Page 2.1 Schematic Diagram of the Experimental Apparatus .........................................13 2.2 Comparison of CO2 Adsorption Data on Wet Beulah Zap Coal at 328.2 K: Effect of Gas Solubility in Water ...................................................28 2.3 CO2 Adsorption on Wet and Dry Beulah Zap Coal at 328.2 K ........................28 2.4 CO2 Adsorption on Wet and Dry Illinois #6 Coal at 328.2 K ..........................29 2.5 CO2 Adsorption on Wet and Dry Pocahontas Coal at 328.2 K ........................29 2.6 CO2 Adsorption on Wet and Dry Upper Freeport Coal at 328.2 K ..................30 2.7 CO2 Adsorption on Wet and Dry Wyodak Coal at 328.2 K .............................30 2.8 CO2 Adsorption on Wet Argonne Coals at 328.2 K .........................................32 2.9 Nitrogen Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture .............................................................................................38 2.10 Methane Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture .............................................................................................38 2.11 CO2 Adsorption on Wet Activated Carbon at 328.2 K at Different Moisture Contents ........................................................................40 2.12 Equilibration Times for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture ..........................................................................42 2.13 Pressure Drop Rate Data for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture: 4 and 12 MPa Pressure Steps..........................43 2.14 Comparison of Monte Carlo and Analytical Error Analyses for CO2 Adsorption on Dry Upper Freeport Coal .........................................................46 2.15 Histogram for the Distribution of Errors Evaluated from the Monte Carlo Error Analysis for CO2 Adsorption on Upper Freeport Coal ..........................47 xi Figure Page 3.1 OnoKondo Model for Monolayer Adsorption on Graphite Slit .......................63 3.2 Model Representations for the PureGas Adsorption on Dry Illinois6 Coal at 328 K ...............................................................................73 3.3 Model Representations for the PureGas Adsorption on Dry Beulah Zap Coal at 328 K ...........................................................................73 3.4 Model Representations for the PureGas Adsorption on Dry Wyodak Coal at 328 K ................................................................................74 3.5 Model Representations for the PureGas Adsorption on Dry Upper Freeport Coal at 328 K .....................................................................74 3.6 Model Representations for the PureGas Adsorption on Dry Pocahontas Coal at 328 K ............................................................................75 3.7 Model Representations for the CO2 Adsorption on Wet Illinois #6 Coal at 328 K .............................................................................76 3.8 Model Representations for the CO2 Adsorption on Wet Beulah Zap Coal at 328 K ...........................................................................76 3.9 Model Representations for the CO2 Adsorption on Wet Wyodak Coal at 328 K ................................................................................77 3.10 Model Representations for the CO2 Adsorption on Wet Upper Freeport Coal at 328 K ...................................................................77 3.11 Model Representations for the CO2 Adsorption on Wet Pocahontas Coal at 328 K .........................................................................78 4.1 Types of Physisorption Isotherms ....................................................................85 5.1 CO2 Adsorption on Wet Pocahontas Coal with 0.65% Moisture at 328.2 K: New Data Reduction Method .......................................................144 5.2 CO2 Adsorption on Wet Upper Freeport Coal with 1.10% Moisture at 328.2 K: New Data Reduction Method .......................................................145 5.3 CO2 Adsorption on Wet Illinois #6 Coal with 9.2% Moisture at 328.2 K: New Data Reduction Method .......................................................145 xii Figure Page 5.4 CO2 Adsorption on Wet Wyodak Coal with 28.0% Moisture at 328.2 K: New Data Reduction Method .......................................................146 5.5 CO2 Adsorption on Wet Beulah Zap Coal with 32.2% Moisture at 328.2 K: New Data Reduction Method .......................................................146 5.6 Idealized Depiction of Molecular Interactions of Water in the Slit ...............149 5.7 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Pocahontas Coal ................................................................................155 5.8 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Upper Freeport Coal ..........................................................................155 5.9 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Illinois #6 Coal ..................................................................................156 5.10 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Wyodak Coal .....................................................................................156 5.11 SLDPR Model Representations for CO2Water Mixture Adsorption on Wet Beulah Zap Coal ................................................................................157 5.12 Partial Fugacities of Water in Liquid and Gas Phases for CO2Water Mixture Adsorption on Wet Pocahontas Coal ................................................164 6.1 Deviation Plot of SLDPR Model Representations of PureGas Adsorption on Coals .......................................................................................176 6.2 Degree of Correlation between the Regressed Surface Areas for Methane, Nitrogen and CO2 on Coals.............................................................177 6.3 Comparison of Generalized and Regressed Model Parameters ......................185 6.4 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Fruitland Coal at 319.3 K ...................................................................186 6.5 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Illinois #6 Coal at 319.3 K .................................................................186 6.6 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Tiffany Coal at 327.6 K......................................................................188 xiii Figure Page 6.7 Generalized SLDPR Model Predictions for PureGas Adsorption on Wet Lower Basin Fruitland Coal at 319.3 K .............................................188 6.8 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Illinois #6 Coal at 328.2 K ..................................................................189 6.9 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Beulah Zap Coal at 328.2 K ...............................................................189 6.10 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Wyodak Coal at 328.2 K ...................................................................190 6.11 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Upper Freeport Coal at 328.2 K .........................................................190 6.12 Generalized SLDPR Model Predictions for PureGas Adsorption on Dry Pocahontas Coal at 328.2 K ................................................................191 6.13 Deviation Plot for the Generalized SLDPR Model Predictions for PureGas Adsorption on Coals........................................................................191 6.14 Sensitivity Analysis of SLDPR Generalized Model for Methane Adsorption on Wet Fruitland Coal at 319.3 K ................................................199 6.15 Sensitivity Analysis of SLDPR Generalized Model for Nitrogen Adsorption on Wet Fruitland Coal at 319.3 K ................................................199 6.16 Sensitivity Analysis of SLDPR Generalized Model for CO2 Adsorption on Wet Fruitland Coal at 319.3 K ................................................200 6.17 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/Nitrogen Mixtures on Wet Fruitland Coal at 319.3 K .......................................................................................................203 6.18 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Methane/Nitrogen Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................203 6.19 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................204 xiv Figure Page 6.20 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Methane/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................204 6.21 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................205 6.22 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland Coal at 319.3 K ........................................................................................................205 6.23 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/ Nitrogen Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................206 6.24 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Methane/ Nitrogen Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................207 6.25 Generalized SLDPR Model Predictions for Methane Component Adsorption in Methane/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................207 6.26 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Methane/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................208 6.27 Generalized SLDPR Model Predictions for Nitrogen Component Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................208 6.28 Generalized SLDPR Model Predictions for CO2 Component Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6 Coal at 319.3 K ........................................................................................................209 6.29 Generalized SLDPR Model Predictions for Methane/Nitrogen Mixture on Wet Tiffany Coal at 327.6 K ........................................................210 6.30 Generalized SLDPR Model Predictions for Methane/CO2 Mixture on Wet Tiffany Coal at 327.6 K ........................................................210 6.31 Generalized SLDPR Model Predictions for Nitrogen/CO2 Mixture on Wet Tiffany Coal at 327.6 K ........................................................211 xv Figure Page 6.32 Generalized SLDPR Model Predictions for Methane/Nitrogen/CO2 Ternary Mixture on Wet Tiffany Coal at 327.6 K ..........................................212 6.33 Deviation Plot for the Generalized SLDPR Model Predictions for MixedGas Adsorption on Coals ....................................................................212 6.34 Deviation Plot for the Generalized SLDPR Model Predictions for CO2 Adsorption on 27 Coals Reported by Day et al. ......................................214 6.35 %AAD Distribution of the Generalized SLDPR Model Predictions for CO2 Adsorption Data Reported by Day et al.. ................................................215 1 CHAPTER 1 INTRODUCTION 1.1 Coalbed Methane and CO2 Sequestration Fossil fuels have been the main resource for our increasing demand for energy. They have also been the source of the steady rise in the atmospheric concentration of CO2, which is hypothesized to be a significant contributor to global warming. Efforts to address climate change issues have culminated in the 1991 Kyoto Protocol, which mandates the signatory nations to reduce their carbon emissions and/or adopt environmentfriendly methods of energy usage by 2012. Several methods have been proposed to reduce carbon/CO2 emissions. These include “geological sequestration” of CO2, which involves capture and the subsequent storage of CO2 in saline aquifers, oil and gas shales, depleted oil reservoirs, or deep unmineable coalbeds. The latter is considered particularly attractive because of the potential for sequestering large amounts of CO2, with the important concomitant recovery of coalbed methane (CBM) gas. The recovery of coalbed methane is expected to (at least partially) offset the costs of CO2 sequestration and to provide an increased supply of our “cleanest” fossil fuel, natural gas. Further, the demand for natural gas is expected to rise steeply in the coming years. The Energy Information Administration (EIA) estimated that natural gas demand in the U.S. could be 24.4 trillion cubic feet by the year 2030.1 This accounts for an annual increase of 1.2% over the next twenty years. Coalbed methane has become 2 an important resource of natural gas since coalbeds contain an estimated 14% of U.S. natural gas reserves.2 The production of natural gas from coalbeds increased from 6% in 19973 to 10% in 2006.4 Therefore, this unconventional resource of natural gas has steadily gained in its economic importance. Moreover, the U.S. Department of Energy (DOE) has initiated research and development programs aimed at geologic CO2 sequestration.5 In pursuit of this goal, researchers at Oklahoma State University (OSU) have conducted adsorption measurements6, 7 and modeling studies.712 In coalbeds, natural gas (methane) resides within the microporous coal structure in an “adsorbed” state. In adsorption, the van der Waalstype gascoal interactions at the coalgas interface give rise to increased concentrations of the gas molecules near the coal surface, where the densities become comparable to those of liquids. Thus, coalbeds can actually hold more gas than a conventional gas reservoir of comparable volume. Since most of the coalbed gas is in the adsorbed state, simulations of coalbed methane (CBM) recovery and the design of optimal CO2 sequestration processes require a suitable model to describe the adsorption phenomena. Specifically, an adsorption model is needed to predict the gasinplace values as a function of coalbed reservoir temperature and pressure. 1.2 Adsorption Models As mentioned above, simulations of enhanced coalbed gas recovery require accurate adsorption models capable of a priori predictions of gas adsorption behavior in the presence of water. Some of the desired characteristics of a CBM adsorption model include: • Representing precisely highpressure puregas adsorption 3 • Facilitating generalized predictions of puregas adsorption based on accessible adsorbent and adsorbate properties • Predicting mixedgas adsorption based on puregas data • Accounting for the presence of moisture in the coal, since water is present in essentially all coalbeds Different models, ranging from very simple to complex, can be used to describe the adsorption behavior of CBM gases. These include the Langmuir model13, Brunauer EmmettTeller (BET) model14, Ideal Adsorbed Solution (IAS) theory15, twodimensional equations of state1618 (2D EOS), the OnoKondo lattice model1921 and the simplified localdensity model.2227 Although most of these models have good correlative capabilities for existing experimental data, only a few of them appear to be capable of accurate predictions of supercritical, highpressure adsorption systems encountered in CBMrelated work. Further, an adsorption model which can describe this effect at water levels that are below, at, and above the equilibrium moisture level will be crucial for reservoir modeling purposes. The CBM industry would benefit greatly from adsorption models which contain rigorous accounting for the effects of water on gas adsorption. Our analysis indicates that the simplified localdensity model is amenable to the modeling demands mentioned above. 1.3 Effect of Water on Coalbed Gas Adsorption Behavior Most coalbeds contain significant amounts of water. The presence of water in a gassolid adsorption system demands special attention, because water can significantly affect gas adsorption capacity by blocking the porous adsorbent structure and limiting the accessibility of an adsorbing gas like methane.28 Measurements of adsorption isotherms 4 on wet coals have also revealed marked effects of water on gas adsorption capacity. Joubert et al.29 reported adsorption data which showed that moisture can reduce methane adsorption by as much as 40% on Pittsburgh coal and 15% on Pocahontas coal. Clarkson and Bustin30 showed that 2% moisture can cause 20% reduction of both methane and CO2 adsorption capacity on a wet coal when compared to the adsorption on the dry coal. Similarly, Levy et al.31 observed that 4% moisture can reduce the methane adsorption by as much as 60% from that of the dry coal. Our own measurements on wet Illinois coal have shown that 9% moisture can cause 50% reduction of CO2 adsorption at 3 MPa.8 The above results demonstrate the significant effect of moisture on gas adsorption behavior. Thus, proper accounting for moisture effects is critical in experimental data reduction, interpretation and modeling. Current experimental data reduction techniques do not account for the presence and effect of moisture in all three equilibrium phases (gas, aqueous and adsorbed). This inadequacy in data reduction methods may result in significant errors in the estimated gas adsorption capacity, adsorbed phase density and (in gas mixtures) the partitioning of constituents among the equilibrium phases. The adsorption behavior of water is fundamentally different from other gases like methane.32 For water, the fluidfluid interactions are stronger than the fluidsolid interactions, and hydrogen bonding plays a significant role in water adsorption. Thus, the simultaneous, competitive adsorption of water and coalbed gases presents an equilibrium problem which requires accurate description of the different molecular interactions involved in the process. Accordingly, the present research places a particular emphasis on delineating the fluidfluid and fluidsolid molecular interactions of water, coalbed gases and 5 carbonaceous adsorbents, and proposing rigorous accounting procedures for the effects of moisture on the adsorption behavior of coalbed gases and their mixtures at typical reservoir temperatures and pressures. Further, the research included the development of a coalstructurebased generalized adsorption model for facilitating simulations of CBM recovery and CO2 sequestration. Therefore, the goal of this research addresses two important aspects of CBM adsorption research: A. Delineate the molecular interactions of adsorbed water with coals and other coalbed gases, and propose rigorous accounting procedures for the effects of water on gas adsorption behavior and B. Develop a coalstructurebased, predictive generalized adsorption model for CBM simulation purposes. As such, two tracks of CBM adsorption research were undertaken in parallel. The first addressed the need to incorporate more accurate physics in an adsorption model, whereas the second addressed the need to develop a generalized adsorption model that would be useful in coalbed reservoir simulations. Although the generalized model developed in this work (B) is based on the currently accepted, traditional modeling approach (where adsorbed water is treated as a "pacifier" of the matrix), the parallel development of a rigorous modeling approach for adsorbed water (A) has laid the foundation for further advancement of this method in future works on coalbed gas adsorption. 1.4 Objectives The basic premise of this research is that upon modification, the SLDPR model can describe accurately the equilibrium adsorption of water and coalbed gases on coals 6 and account for the effect of water on coalbed gas adsorption. As such, a major focus of this study was modifying the simplified localdensity/PengRobinson (SLDPR) model to meet the modeling demands of wet adsorbents. In particular, the SLDPR model was further developed to (a) include the polar interactions of water with the carbon surface, and (b) account more realistically for the effect of water adsorption by treating water as a separate adsorbed component in equilibrium with the bulk gas phase. Moreover, for engineering practice purposes, the SLDPR model was generalized (using the accepted, traditional modeling approach) to render the model suitable for use in simulations of coalbed methane recovery and CO2 sequestration. To accomplish the goal discussed above, the following objectives were undertaken: 1. Acquire accurate experimental data for adsorption of methane, carbon dioxide, and nitrogen on wet coals and on activated carbon at reservoir temperatures and pressures. 2. Review existing knowledge regarding pure water adsorption behavior on coals and activated carbons. 3. Use the SLDPR model to represent precisely the water adsorption capacity on activated carbons and coals. 4. Conduct a Gibbsenergy (or phasecheck) analysis for adsorption of CO2water mixtures on coals. 5. Generalize the SLDPR model by correlating the model parameters in terms of assessable coal properties. 7 In earlier studies6, 10, 33, the OSU Thermodynamics Group measured pure and mixedgas adsorption isotherms on wet coals. However, the moisture content of the coals in those measurements was well above the equilibrium moisture content (EMC) of the coals. At moisture contents above the EMC, the additional water does not significantly affect the gas adsorption capacity.29 Therefore, a need exists for measurements to elucidate the adsorption behavior of coalbed gases at different levels of moistureabove and below the EMC (Objective 1). Accounting properly for water adsorption behavior on activated carbons and coals and its modeling presents an interesting and challenging problem, due to the unique structure of the water molecule. The adsorption behavior of water on carbons is fundamentally different from that of simple, nonpolar fluids like nitrogen, methane and organic vapors. The difference arises mainly because the fluidfluid interactions for water are much more strongly attractive than the fluidsolid interactions, and because water forms hydrogen bonds with the oxygenated groups on the surface of the carbon matrix.32 This is in direct contrast to the adsorption behavior of nonpolar molecules. Therefore, a detailed review of water adsorption behavior on activated carbons and coals (Objective 2) was essential to an unambiguous understanding of pure water adsorption and, ultimately, of coalbed gas mixture adsorption in the presence of water. The prerequisite for the prediction of the watercoalbed gas mixture adsorption is the accurate modeling of the water adsorption capacity. The SLD model was modified to account for interactions of water with the coal surface; and the effect of this new parameterization of the SLD model was investigated by constructing different case studies (Objective 3). 8 The accurate modeling of watercoalbed gas mixture adsorption requires treating water as a separate adsorbed component. Water at reservoir temperatures is a subcritical component, while the coalbed gases are typically at supercritical conditions. The presence of the subcritical water may result in the formation of an additional (liquid) phase. The definitive method to determine the number of possible phases present at equilibrium is to conduct a Gibbs free energy or phasecheck analysis. Therefore, a phasecheck analysis was performed to investigate the phase behavior of this system (Objective 4). As mentioned in Section 1.2, simulations of coalbed methane recovery require an adsorption model to predict, a priori, the amounts adsorbed of coalbed gases. Frequently, this is necessary due to an absence of experimental data on the system of interest. Therefore, the SLDPR model was generalized in terms of coal characterization information (Objective 5). This facilitates a priori predictions of adsorbed amounts of gas and renders the model capable of use in simulations of coalbed methane recovery. Further, in developing the generalized model, the currently accepted approach for modeling wet adsorbents was adopted. The extension of the new modeling approach for wet adsorbents (developed in Objective 4) to the generalized model is not feasible at this stage for a variety of reasons, which include the unavailability of sufficient adsorption and vaporliquid equilibrium data for the systems of interest. 1.5 Organization This dissertation is organized as follows. Chapter 1 gives a brief introduction of coalbed methane and outlines the hypothesis of this research, the objectives undertaken and the ultimate goal of this study. Chapter 2 presents details of the experimental 9 methods and procedures used in this study and discusses the experimental data acquired in this project. Chapter 3 reviews a number of CBM adsorption models used in the literature and at OSU for modeling of CBM systems. Chapter 4 presents an interpretive review of pure water adsorption on activated carbons and coals. The SLD model for pureand mixedgas adsorption is discussed in Chapter 5. Also included in Chapter 5 are the SLD modeling results of CO2water mixture adsorption and the phasecheck analysis for these systems. A coalstructurebased generalized adsorption model is presented in Chapter 6. Finally, Chapter 7 contains the important conclusions and recommendations of this study. This study was part of a continuing research project dealing with highpressure gasadsorption modeling for CBM systems.8, 12 Therefore, the experimental data presented in Chapter 2 and discussion of the theoretical framework of SLDPR model presented in Chapter 5 represent a collective effort involving the author, Jing Chen27 and James Fitzgerald.25 Further, the OSU CBM adsorption database utilized for the generalized model development was gathered over a period of fifteen years by various authors.6, 8, 12 10 CHAPTER 2 EXPERIMENTAL METHODS, PROCEDURES AND RESULTS In this chapter, the experimental methods and procedures used to measure adsorption isotherms are discussed. Since this study is a continuation of previous works at OSU, some aspects of the following discussion of experimental methods are similar to previous descriptions.18, 20, 25, 34 Further, an outline of the various methods that can be used to measure gas adsorption equilibria are given elsewhere18 and, therefore, they are not discussed here. In particular, the chapter contains a discussion of the following aspects of this work: • Adsorption isotherms of pure CO2 on five wet Argonne coals measured at a temperature of 328.2 K and pressures to 13.8 MPa • Adsorption isotherms of pure methane, nitrogen and CO2 on wet and dry activated carbon measured at a temperature of 328.2 K and pressures to 13.8 MPa. In addition, the desorption measurements of CO2 on dry activated carbon are also discussed. • An introduction to the OSU adsorption database for coalbed methane gases.12 • A Monte Carlo analysis/confirmation of the analytical error analysis technique used to estimate the expected experimental uncertainties of the acquired data. 11 The following material in Sections 2.1 to 2.10 (Part A) has been reproduced with permission from [Mohammad, S. A.; Chen, J. S.; Fitzgerald, J. E.; Robinson, R. L., Jr.; Gasem, K. A. M., Adsorption of Pure Carbon Dioxide on Wet Argonne Coals at 328.2 K and Pressures up to 13.8 MPa. Energy & Fuels 2009, 23, (2), 11071117] Copyright [2008] American Chemical Society. 2.1 Adsorption Isotherm Measurements The experimental method used in the OSU adsorption laboratory is based on a mass balance principle, which employs precise measurements of pressure, volume and temperature. The experimental apparatus, shown schematically in Figure 2.1, has been used successfully in previous measurements.68 Brief descriptions of the experimental apparatus and procedures are provided below: The entire apparatus is maintained in a constant temperature air bath. The equilibrium cell (Figure 2.1) is filled with the adsorbent under study, and the cell is placed under vacuum prior to gas injection. The void (gas) volume, Vvoid, in the equilibrium cell is then determined by injecting a known quantity of helium from a calibrated injection pump (Ruska). Since the adsorption of helium is insignificant at the conditions of this study, the void volume can be determined easily from measured values of the temperature, pressure and amount of helium injected into the cell. The mass balance equation for the measurement of void volume is given as: pump void 2 1 2 1 cell P V ZT V P P Z T Z T = − (2.1) 12 where V is the volume of helium gas injected from the pump, Z is the compressibility factor of helium, T is the temperature, P is the pressure, subscripts “cell” and “pump” refer to conditions in the cell and pump sections of the apparatus, respectively, and “1” and “2” refer to conditions in the cell before and after an injection of gas from the pump, respectively. The helium void volume measurements were performed at the same temperature as the gas adsorption isotherms (328.2 K in this study) and over a range of pressures from atmospheric to about 13.8 MPa (2000 psia) in intervals of 1.4 MPa (200 psia). The several sequential injections of helium into the cell at different pressures showed consistency in the calculated void volume. Generally, the void volume calculated from sequential injections varied less than 0.3 cm3 from the average value of approximately 85 cm3. This helium void volume includes all the volume of the cell section exclusive of the adsorbent volume that is impenetrable to helium gas. The constancy of the calculated void volume from the incremental injections over a range of pressures confirmed the validity of our assumption that adsorption of helium is negligible at the conditions of the measurements and that the adsorbent volume impenetrable to helium remained constant. The Gibbs adsorption (also known as the excess adsorption) can be calculated directly from experimentally measured quantities. For puregas adsorption isotherm measurements, a known quantity, ninj, of gas (e.g., CO2) is injected from the pump section into the cell section. Some of the injected gas will be adsorbed, and the remainder, Gibbs unads n , will exist in the equilibrium bulk (gas) phase in the cell. 13 Vacuum Pump Pressure Temp. Heat Exchanger Ruska Pump Air Temperature Bath Vent Water Heater and Pump Pressure Equilibrium Cell Magnetic Pump Temp. Vent Air Temperature Bath Motor Sampling Valve He CH4 CO2 N2 C2 He Gas Chromotagraph Figure 2.1 Schematic Diagram of the Experimental Apparatus The mass balance used to calculate the Gibbsian amount adsorbed, Gibbs ads n , is Gibbs inj unads Gibbs ads n = n − n (2.2) where Gibbs unads n is the Gibbsian amount unadsorbed at given pressure and temperature. The amount injected can be determined from pressure, temperature and volume measurements of the pump section: inj pump P V n ZRT = (2.3) The amount of unadsorbed gas (Gibbsian amount unadsorbed) is calculated from conditions at equilibrium in the cell: Gibbs Void unads cell PV n ZRT = (2.4) where the pressure P is measured after equilibrium is reached in the cell (usually within 6 to 12 hours, depending on the adsorption capacity of the adsorbent), which occurs when 14 no further change in pressure is observed. In Equations (2.3) and (2.4), Z is the compressibility factor of the gas at the applicable conditions of temperature and pressure. The above steps are repeated at sequentially higher pressures to yield a complete adsorption isotherm. The amount adsorbed is usually reported as an intensive quantity (mmol adsorbed / g adsorbent, or mmol/g) by dividing Gibbs ads n by the mass of adsorbent in the cell. Equations (2.2)(2.4) reveal that the amount adsorbed can be calculated in a straightforward manner from the experimental measurements of pressures, temperatures and volumes, coupled with independent knowledge of the gas compressibility factors, Z, from an accurate equation of state. 2.2 Gas Compressibility Factors As evident from the above discussion, accurate compressibility factors are required for pure methane, nitrogen and CO2 for proper adsorption data analysis. These compressibility factors were calculated from highly accurate equations of state.3537 Further, for void volume determination, the helium compressibility factor was calculated with an expression based on experimental data from the National Bureau of Standards Technical Note 631 for helium.38 2.3 Materials The pure gases used in this work were obtained from AirgasPennsylvania with reported purities of about 99.99% and were used as received. The Argonne coal samples were obtained from the Argonne National Laboratory, Argonne, Illinois in ampoules containing 5 grams of 100mesh material of each coal. The compositional analyses of Argonne coals are presented in Table 2.1. The Illinois #6 coal is a highvolatile bituminous coal from the Illinois #6 or Herrin seam. The Wyodak coal is a sub 15 bituminous coal from the WyodakAnderson seam. The Upper Freeport coal is a mediumvolatile bituminous coal, Pocahontas coal is a lowvolatile bituminous coal and Beulah Zap coal is lignite.39 The activated carbon used was Filtrasorb 400, 12x40 mesh from Calgon Carbon Company. The compositional analyses of this activated carbon are also presented in Table 2.1. The composition of activated carbons is typically less complex than coals and provides a useful reference material prior to adsorption studies on coals. As evident from Table 2.1, the activated carbon has higher carbon content and significantly less volatile matter than mediumrank coals, which facilitates the modeling of the fluidsolid interactions in an adsorption process. The nitrogen BET surface area at 77 K of this carbon was reported to be 850 m2/g.40 Table 2.1 Compositional Analyses of Adsorbents Used in this Study Analysis* Beulah Zap Wyodak Illinois #6 Upper Freeport Pocahontas Activated Carbon Ultimate Carbon % 72.9 75.0 77.7 85.5 91.1 88.65 Hydrogen % 4.83 5.35 5.00 4.70 4.44 0.74 Oxygen % 20.3 18.0 13.5 7.5 2.5 3.01 Nitrogen 1.15 1.12 1.37 1.55 1.33 0.40 Sulfur % 0.70 0.47 2.38 0.74 0.50 0.73 Ash % 9.7 8.8 15.5 13.2 4.8 6.46 Proximate Moisture % 32.2 28.1 8.0 1.1 0.7  Vol. Matter % 30.5 32.2 36.9 27. 1 18.5 3.68 Fixed Carbon % 30.7 33.0 40.9 58.7 76.1 89.86 Ash % 6.6 6.3 14.3 13.0 4.7  *Analysis of coals provided by Argonne National Laboratory *Analysis of activated carbon provided by Huffman Laboratories, Inc., Golden, Colorado 16 2.4 Error Analysis Frequent instrument calibrations were performed during the course of the experiments. Usually, the calibrations were performed before the adsorption experiments on a new adsorbent sample. The thermocouples and resistance thermometers (RTDs) were calibrated against a Minco platinum reference RTD. Super TJE pressure transducers (range: 0 – 13.8 MPa) were calibrated using helium as the working fluid against a Ruska deadweight tester with a calibration traceable to the National Institute of Standards and Technology. Detailed information on calibration procedure is available elsewhere.34 The uncertainties in the experimentally measured quantities after calibrations were estimated as follows: temperature, 0.1 K; pressure, 6.9 kPa (1 psia); and injected gas volume, 0.02 cm3. A detailed error analysis was performed to estimate the uncertainty associated with each experimental data point by propagating the errors from the primary measurements of pressure, temperature and volume. The detailed error analysis expressions are given elsewhere.12, 20 2.5 Equilibrium Moisture of Coals and Activated Carbon Moisture equilibration of porous adsorbents such as coals is usually carried out using the standard ASTM D1412 method.41 This method consists of equilibrating the adsorbent samples at 30ºC (303.2 K) in a vacuum desiccator over a saturated solution of K2SO4 to maintain the relative humidity at 9697%. In the standard test method, the desiccator is used to equilibrate a previously "wetted" sample such that only the equilibrium moisture remains in the coal. However, the use of vacuum in a desiccator can often result in condensation problems when the pressure is restored, thus negating the 17 experiment.29, 42 Therefore, we used a modified method where the samples were equilibrated under an inert nitrogen atmosphere. The moisture content of the equilibrated sample was then determined by drying a part of the sample under vacuum at a temperature of about 313.2 K for 4872 hours. The weight of the sample was monitored, and the weight loss after 72 hours was taken as the moisture loss. The expected uncertainty in the measured moisture content is estimated to be about 0.1 wt. %. The Illinois #6 coal samples were equilibrated using the above method by placing them in a nitrogen atmosphere at 95100% relativity humidity in a Hotpack Model 434300 temperaturehumidity chamber. This resulted in a gain of only 1.2% moisture over the equilibrium value reported in the literature.39 Therefore, for the other four Argonne coals, namely, Beulah Zap, Pocahontas, Upper Freeport and Wyodak coals, the asreceived coal samples were placed directly in the equilibrium cell under inert atmosphere. This was done under the reasonable assumption that further moistening of the coal in the temperaturehumidity chamber would not greatly change the coal moisture content from its asreceived moisture. Moreover, the direct use of asreceived samples minimizes possible oxidation of the samples that can affect the integrity of the coal sample. Great care has been taken by the Argonne National laboratory to maintain the coal samples at their inseam conditions.39 Since the objective of our study was to simulate the conditions of a coalbed reservoir while measuring adsorption isotherms (in terms of pressure, temperature and moisture content), measuring the isotherms at their asreceived or inseam moisture values was considered greatly beneficial. These isotherms can be considered to be measured near or at the equilibrium moisture content of the coals. 18 In the present context, the term “wet” coal is used to signify saturation of coal with adsorbed moisture. For adsorption measurements on the dry Argonne coals, the coal samples were dried under vacuum in an equilibrium cell at 353 K for 36 hours following the National Energy Technology Laboratory (NETL) drying protocol before being used in the adsorption measurements. The adsorption data on dry coals were measured in an earlier work.21 The activated carbon was equilibrated as explained in the procedure above. Further, the raw activated carbon sample was first washed with deionized water to remove any impurities present in the carbon. This wetted sample was air dried for several days (to remove excess water) and then used for moisture equilibration as discussed above. For adsorption measurements on the dry activated carbon, drying of the sample was carried out under vacuum at about 313.2 K for 4872 hours. The lower drying temperature was used to avoid the loss of any volatile organics from the carbon surface and/or possible structural changes of the carbon sample. 2.6 Gas Solubility in Water In previous studies at OSU on wet adsorbents6, 8, we included a term in Equation (2.2) to account for the amount of gas, nsol, dissolved in the water. Gibbs Gibbs nads = ninj − nunads − nsol (2.5) To calculate the amount of gas soluble in water as a function of pressure, an empirical equation obtained from Amoco Corporation was used for temperatures at 318.2 K or 319.3 K. 19 gas 2 a bP cP x P + + = (2.6) Table 2.2 lists the parameter values for each gas. Since the solubilities of methane and nitrogen in water are small; the same equation and parameter values were used at other temperatures (e.g., 328.2 K in this study). Table 2.2 Parameters for Gas Solubility in Water at 318.2 K or 319.3 K Constant Units of Constant Methane Nitrogen CO2 a MPa 5302.07 10204.24 274.69 b  150.4 127.3 9.452 c 1/MPa 0.78 0.09 1.21 In comparison to nitrogen and methane, the solubility of CO2 is significant at temperatures near 318.2 K. To calculate the gas dissolved in water for use in Equation (2.5), literature data4345 were used to construct an empirical relationship for CO2water solubility at temperatures from 313.2 K to 348.2 K.8 In the 015 MPa range, the empirical function represents their data with an average absolute deviation of 1.5%. Thus, the mole fraction of CO2 present in water at temperature T (in K) and pressure P (in MPa) is given as: ( ) ( ) 2 1 0 1 0 CO2 a b b T P c c T P x P + + + + = (2.7) Table 2.3 lists the parameter values for this correlation. The amount of CO2 dissolved in water can be given as (1 x ) x n n 2 2 co co water sol − = (2.8) The denominator in Equation (2.8) is close to unity and therefore, the amount of gas dissolved in water was taken (approximately) as the product of mole fraction of CO2 and 20 the amount of water in moles in the system. Further, the amount of CO2 dissolved in water per unit mass of coal is expressed as: coal co water sol m x n n = 2 (2.9) where nwater is the amount of water in moles and coal m is the mass of coal in the system. The solubility of CO2 in water calculated with Equation (2.9) is a monotonic increasing function of pressure at a given temperature. Thus, the maximum solubility of CO2 in water was observed at 13.8 MPa and was about 2 mole percent. Table 2.3 Parameters for CO2 Solubility in Water at Multiple Temperatures Constant Value Units of Constant a 272.21 MPa b1 332.637  b0 1.06683 1/K c1 19.18 1/MPa c0 0.05609 1/(MPa K) As evident from the above discussion (Equation 2.5), accounting for the solubility of gas in waterrich adsorbed phase lowers the calculated Gibbs adsorption values. In the above discussion, we have assumed that all the water present in the system is adsorbed and, therefore, the amount of gas dissolved in water was estimated based on all the water present in the system. In addition, this means that we have assumed that the bulk gas phase was free from water (i.e., that yH2O = 0, where y is the gas phase mole fraction). 2.7 Adsorption Measurements on Wet Coals and Activated Carbon For the adsorption isotherm measurements on wet Argonne coals and wet activated carbon, care was taken to prevent moisture loss during the experiments. The coal samples were handled in a chamber filled with nitrogen. Since the evacuation step during the void volume measurement and at the beginning of the isotherm can result in 21 moisture loss, the system pressure was not reduced below 21 kPa at 328.2 K. This is slightly above the vapor pressure of water at this temperature, and this minimizes any potential water being removed from the coal or carbon surface. Further, before the start of the gas adsorption experiment, a small amount of the same adsorbing gas (methane, nitrogen or CO2) was injected into the cell until the pressure was 0.35 MPa to flush any remaining helium gas out. The adsorbing gas was then evacuated until the pressure was again about 21 kPa, and the flushing procedure was performed once more. To test for any moisture loss during the experiment on wet coals, two additional checks were performed. First, the equilibrium cell/coal sample was weighed before and after the adsorption isotherm. There was no significant mass loss observed from the equilibrium cell at the end of the isotherm. Second, the helium void volume was measured before and after the adsorption isotherm. The helium void volumes measured were within the experimental uncertainty of our void volume measurements (about 0.3%). The constancy in the calculated void volume further indicated that there was no significant moisture loss during the experiment. Given the size of our volumetric apparatus, any miniscule amount of water leaving the coal surface would introduce an uncertainty in the isotherm measurement, which is well within the reported experimental uncertainty of the isotherm as obtained by multivariate error propagation. These uncertainty estimates for each data point of each isotherm are included with Gibbs adsorption data. 2.8 Coal Swelling Another aspect of supercritical gas adsorption on coals that deserves consideration is the potential swelling of coal caused by adsorbates such as CO2. Some investigators 22 believe that adsorption of CO2 can significantly alter the porous coal structure and these changes, if left unaccounted for, can result in large errors in the modeling of supercritical CO2 adsorption on coals. In fact, several researchers have attempted to model the swelling of coal by incorporating volumetric corrections to the adsorption isotherm equations. Ozdemir et al.46 and Dutta et al.47 used different adsorption models to study the volumetric effects of CO2 adsorption on coals. Romanov et al.48 have also attempted to interpret the volumetric changes in coals under CO2 pressure. Pan and Connell49, balancing the change in surface energy due to adsorption to the change in elastic energy of the coal matrix, developed a theoretical model to describe adsorptioninduced coal swelling. Recently, Day et al.50 measured swelling on coals and corrected their adsorption measurements to account for volumetric changes to the sample. These corrections involved adjusting the void volume to account for an increased volume of coal sample. We have measured helium void volume before and after each adsorption isotherm experiment. The constancy of the calculated void volume within its experimental uncertainty of 0.3% indicated that there was no irreversible change to the volume of the sample. This result is also supported by the findings of Day et al.50, who found the coal swelling to be entirely reversible. Although they applied a correction to the isotherm, we have used a constant void volume in our data reduction procedures. Thus, the adsorption data reported in this study are under the assumption that there is no appreciable swelling of the coal. 23 2.9 Gibbs and Absolute Adsorption Adsorption data are typically reported either in terms of Gibbs or absolute adsorption. Gibbs adsorption is calculated directly from experimentallymeasured quantities and this accounts for the fact that there is additional material present near the adsorbent surface due to adsorption phenomenon. This additional material is in excess of that which would be present in the same (void) volume if there was no adsorption. This excess material is usually referred to as the Gibbs or excess adsorption. In contrast, the calculation of absolute adsorption requires a value for the adsorbed phase density, ρads, which is not readily accessible by experimental measurement. The exact mathematical expressions that highlight the physical interpretation of Gibbs adsorption and the approximate nature of calculated absolute adsorption have been presented elsewhere.7 The relationship between the two quantities is given as: − = ads gas Gibbs ads ads Abs ads ρ ρ ρ n n (2.10) where Abs ads n and Gibbs ads n are the absolute and Gibbs adsorption, respectively, and ρgas and ρads are the gas phase and the adsorbed phase densities, respectively. To calculate absolute adsorption from Equation (2.10), estimates of ρads are usually employed. Commonly used approximations are the liquid density at the normal boiling point, as was done by Arri and Yee51, or the reciprocal of the Van der Waals (VDW) covolume.8 2.10 Experimental Results A. Adsorption of CO2 on Wet Argonne Coals The experimental data from the present work for the CO2 adsorption on Beulah Zap, Illinois #6, Pocahontas #3, Upper Freeport and Wyodak coals are listed in Tables 24 2.42.8, respectively. All adsorption amounts are reported on a drymass basis. Tables 2.42.8 include the pressures (MPa), Gibbs adsorption (mmol/gm) and expected experimental uncertainties "σ" (mmol/gm) in the adsorption values for each datum. Table 2.4 Gibbs Adsorption of Pure CO2 on Wet Beulah Zap Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 1.02 0.135 0.053 1.50 0.179 0.053 2.82 0.262 0.052 4.22 0.324 0.052 5.91 0.372 0.051 7.15 0.369 0.051 8.35 0.357 0.053 9.71 0.327 0.068 11.05 0.312 0.094 12.04 0.248 0.107 13.57 0.089 0.120 Table 2.5 Gibbs Adsorption of Pure CO2 on Wet Illinois #6 Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.42 0.146 0.052 0.79 0.231 0.052 1.56 0.356 0.051 2.23 0.440 0.051 2.87 0.511 0.050 4.27 0.634 0.050 5.62 0.701 0.049 7.02 0.765 0.049 8.34 0.791 0.063 9.69 0.800 0.065 11.04 0.777 0.075 12.41 0.716 0.092 13.88 0.644 0.088 25 Table 2.6 Gibbs Adsorption of Pure CO2 on Wet Pocahontas #3 Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.40 0.281 0.040 .77 0.439 0.040 1.49 0.605 0.040 2.84 0.764 0.039 4.25 0.854 0.038 5.63 0.901 0.038 6.99 0.915 0.037 8.33 0.908 0.038 9.69 0.868 0.048 10.34 0.840 0.050 12.16 0.730 0.068 13.11 0.674 0.075 Table 2.7 Gibbs Adsorption of Pure CO2 on Wet Upper Freeport Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.40 0.239 0.043 0.81 0.363 0.043 1.47 0.482 0.042 2.86 0.624 0.042 4.24 0.698 0.041 5.64 0.739 0.041 7.00 0.756 0.040 8.35 0.758 0.041 9.67 0.742 0.052 10.75 0.737 0.056 12.31 0.667 0.073 13.86 0.593 0.082 26 Table 2.8 Gibbs Adsorption of Pure CO2 on Wet Wyodak Coal at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.47 0.041 0.048 0.76 0.067 0.048 1.46 0.130 0.048 2.77 0.233 0.048 4.22 0.319 0.048 5.64 0.372 0.048 7.01 0.411 0.049 8.35 0.417 0.063 9.67 0.420 0.074 10.92 0.424 0.084 12.35 0.368 0.099 13.92 0.254 0.101 The decreasing order of Gibbs adsorption among the five coals is: wet Pocahontas, wet Illinois #6, wet Upper Freeport, wet Wyodak and wet Beulah Zap. In comparison, the decreasing order of the rank of these coals was: wet Pocahontas, wet Upper Freeport, wet Illinois #6, wet Wyodak and wet Beulah Zap. Thus, higher rank coals appear to have a larger capacity for CO2 adsorption; however, the coal moisture contents which vary significantly also play an important role in CO2 adsorption on these coals. The Gibbs adsorption data on three of the coals, namely, wet Beulah Zap, Illinois #6 and Pocahontas coals, have been published in an NETL interlaboratory study.52 The remaining two coals in this study (wet Pocahontas and upper Freeport coals) have not been published previously. The main objective of the NETL interlaboratory study52 was to investigate the reproducibility of CO2/coal adsorption isotherm measurements among various laboratories. In contrast, the objective of the present study is to investigate the 27 effect of water content of the coals on the experimental data, the data reduction, and the model analysis of these isotherms. The adsorption data published earlier52 did not include accounting for the solubility of CO2 in adsorbed water and, thus, differ from the results presented here. Neglecting the solubility in the earlier work was part of a specified data reduction procedure provided by NETL, designed to insure consistent data reductions among the participating laboratories in that study. Accounting for the dissolved CO2 in adsorbed water yields the actual amounts adsorbed on the wet coals, leading to lower values of the calculated Gibbs adsorption than previously published.52 For the higher moisture containing coals in this study, this correction is significant, and it also affects the subsequent model analysis of these isotherms. To highlight this difference, Figure 2.2 presents a comparison of CO2 adsorption data on wet Beulah Zap coal published in Goodman et al.52 and the data from this study. As evident from the figure, accounting for the gas solubility in adsorbed water can result in quite different calculated values of Gibbs adsorption. Figures 2.32.7 illustrate the Gibbs adsorption of CO2 on BeulahZap, Illinois #6, Pocahontas #3, Upper Freeport and Wyodak coals from this study, respectively. The CO2 adsorption on each of the dry coals is also illustrated for comparison. The adsorption data on dry coals were measured in an earlier study.21 For each coal, the CO2 adsorption on the wet coal was lower than that on the dry coal. Further, the reduction in the gas adsorbed from that on dry coals appears to be correlated positively with the moisture content of the coal. The Pocahontas, Upper Freeport, Illinois #6, Wyodak and Beulah Zap 28 0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Beulah Zap (With Solubility) Beulah Zap (Without Solubility) Figure 2.2 Comparison of CO2 Adsorption Data on Wet Beulah Zap Coal at 328.2 K: Effect of Gas Solubility in Water 0.20 0.20 0.60 1.00 1.40 1.80 2.20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Beulah Zap (32.2% Moisture) Beulah Zap (Dry) Figure 2.3 CO2 Adsorption on Wet and Dry Beulah Zap Coal at 328.2 K 29 0.00 0.40 0.80 1.20 1.60 2.00 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Illinois (9.2% Moisture) Illinois (Dry) Figure 2.4 CO2 Adsorption on Wet and Dry Illinois #6 Coal at 328.2 K 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Pochahontas (0.65% Moisture) Pochahontas (Dry) Figure 2.5 CO2 Adsorption on Wet and Dry Pocahontas Coal at 328.2 K 30 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) UFP (1.1% Moisture) UFP (Dry) Figure 2.6 CO2 Adsorption on Wet and Dry Upper Freeport Coal at 328.2 K 0.0 0.4 0.8 1.2 1.6 2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Wyodak (28.0% Moisture) Wyodak (Dry) Figure 2.7 CO2 Adsorption on Wet and Dry Wyodak Coal at 328.2 K 31 coals exhibited, respectively, about 19%, 17%, 48%, 76% and 79% reductions in the adsorption on the wet coals at 7 MPa when compared to the adsorption on the dry coals. Figure 2.8 compares the Gibbs adsorption of CO2 on all five wet coals. The adsorption isotherm for each of the wet coals exhibits a maximum between 812 MPa. For each case, the adsorption maximum on the wet coal occurs at a higher pressure than that for the dry coal. Note that some of the error bars have been omitted in Figure 2.8 for the sake of clarity. The error analysis indicates that the average uncertainties for the CO2 adsorption measurements are approximately 713% for Illinois #6, Upper Freeport, and Pocahontas coals. The higher percentage uncertainties are usually obtained at the higher pressures, due mainly to the lower value of the Gibbs adsorption for CO2 at the higher pressures and the higher uncertainties in the CO2 compressibility factors (due to its proximity to its critical point). The average uncertainties for Beulah Zap and Wyodak coals were around 34%. However, these higher percentage uncertainties are a result of lower adsorption amounts for these two wet coals and amounted to only about 0.06  0.07 mmol/gm, on average. In our data reduction technique, we accounted for the amount of gas dissolved in the waterrich adsorbed phase, which results in lower calculated adsorption amounts for higher moisture containing coals. The Beulah Zap and Wyodak coals contain 32.2% and 28% moisture, respectively. Chapter 5 presents an alternative approach wherein a different data reduction technique is used for estimating the amounts adsorbed. 32 0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/g) Beulah Zap (32.2% Moisture) Wyodak (28% Moisture) Illinois#6 (9.2% Moisture) Upper Freeport (1.1% Moisture) Pocahontas (0.65% Moisture) Figure 2.8 CO2 Adsorption on Wet Argonne Coals at 328.2 K B. Adsorption of Methane, Nitrogen and CO2 on Dry and Wet Activated Carbon The experimental data for the adsorption of pure nitrogen, methane and CO2 on dry activated carbon are presented in Tables 2.92.11, respectively. These tables list the pressure (MPa), Gibbs adsorption (mmol/gm) and the expected experimental uncertainty "σ" (mmol/gm) for each datum. The adsorption data for these isotherms yielded expected uncertainties of 13%, on average. As expected, less gas adsorption is observed at 328.2 K than at 318.2 K (from our earlier experiments7); however, the new measurements agree with our previous data in regard to the relative amounts of nitrogen, methane and CO2 adsorbed. In both cases, an approximate ratio of 1:1.6:2.4 was obtained at 7 MPa. Further, the desorption of CO2 on dry activated carbon was also measured; and comparison of the adsorption and desorption isotherms indicated no hysteresis effect for this system. 33 The experimental data for the adsorption of pure nitrogen, methane and CO2 on the wet activated carbon are presented in Tables 2.122.16, respectively. Figures 2.92.11 illustrate the adsorption isotherms for pure nitrogen, methane and CO2 on wet activated carbon, respectively. The adsorption of these gases on dry activated carbon is also presented in these figures for comparison. Table 2.9 Gibbs Adsorption of Pure Nitrogen on Dry Activated Carbon at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.81 1.015 0.041 1.46 1.473 0.040 2.93 2.075 0.039 4.19 2.407 0.039 5.53 2.651 0.039 6.98 2.834 0.039 8.36 2.945 0.039 9.69 3.018 0.040 11.08 3.068 0.039 12.54 3.100 0.040 13.70 3.108 0.040 Table 2.10 Gibbs Adsorption of Pure Methane on Dry Activated Carbon at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 1.50 2.845 0.047 2.78 3.555 0.046 4.11 3.936 0.045 5.59 4.167 0.045 7.07 4.277 0.045 8.38 4.310 0.045 9.18 4.306 0.045 9.77 4.306 0.045 11.11 4.273 0.046 12.43 4.221 0.046 13.74 4.145 0.047 34 Table 2.11 Gibbs Adsorption of Pure CO2 on Dry Activated Carbon at 328.2 K Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.33 2.432 0.117 0.74 3.684 0.115 1.49 4.887 0.113 2.85 5.885 0.110 4.22 6.321 0.108 5.62 6.462 0.107 7.07 6.396 0.106 8.31 6.134 0.105 9.62 5.616 0.106 11.11 4.524 0.132 12.49 3.522 0.137 Table 2.12 Gibbs Adsorption of Pure Nitrogen on Wet Activated Carbon at 328.2 K and 37% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 1.61 0.024 0.021 2.95 0.054 0.021 5.76 0.113 0.021 8.43 0.161 0.022 11.20 0.208 0.024 13.91 0.253 0.026 Table 2.13 Gibbs Adsorption of Pure Methane on Wet Activated Carbon at 328.2 K and 37% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.44 0.018 0.025 0.79 0.046 0.025 1.48 0.105 0.025 2.83 0.234 0.025 4.20 0.372 0.025 5.56 0.519 0.026 7.04 0.701 0.026 35 Table 2.14 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 27% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.50 0.489 0.048 0.85 0.753 0.047 1.44 1.138 0.047 2.74 1.976 0.050 4.03 3.244 0.057 5.41 4.561 0.049 6.90 5.340 0.049 8.41 5.414 0.056 9.79 5.048 0.076 11.02 4.417 0.092 12.40 3.681 0.105 13.74 3.057 0.105 Table 2.15 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 34% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.70 0.529 0.049 1.45 0.971 0.049 2.77 1.795 0.049 4.01 2.883 0.050 5.28 4.298 0.053 6.91 5.230 0.056 8.49 5.216 0.059 9.78 4.847 0.079 11.06 4.163 0.096 12.52 3.373 0.109 13.94 2.867 0.117 36 Table 2.16 Gibbs Adsorption of Pure CO2 on Wet Activated Carbon at 328.2 K and 16% Moisture Pressure (MPa) Gibbs Adsorption (mmol/g) σ Gibbs (mmol/g) 0.39 0.690 0.037 0.74 1.018 0.037 1.43 1.444 0.036 2.74 2.114 0.044 4.00 3.347 0.056 5.31 4.823 0.079 6.99 5.473 0.144 8.50 5.448 0.113 11.11 4.405 0.082 13.09 3.456 0.137 Using modified ASTM procedures, we estimated the equilibrium moisture content of activated carbon to be 27%. To study the effect of moisture on adsorption capacity, we conducted isotherm measurements at moisture contents of 16%, 27%, 34% and 37%. The adsorption isotherm measurements for nitrogen were conducted at a moisture content of 37%, which is above the equilibrium moisture content of about 27%. The nitrogen adsorption isotherm for the wet activated carbon indicated significant reduction in adsorption capacity below 7 MPa when compared to the adsorption on the dry activated carbon. For example, at 5.5 MPa, the amount adsorbed on the wet activated carbon (37% moisture content) is only 4% of the amount adsorbed on dry activated carbon. Further, the nitrogen adsorption capacity on wet activated carbon (Figure 2.9) was less than 10% of the adsorption on the dry activated carbon, indicating the large effect of water on the carbon surface. The data for this isotherm yielded expected uncertainties of 30%, on average. However, higher percentage uncertainties are a result of the extremely low adsorption levels of this isotherm and translate to only about 0.022 mmol/gm of 37 adsorption, on average. As such, the experimental uncertainty in terms of actual adsorption amounts is small and such behavior is expected. The adsorption isotherm measurements for methane were also conducted at a moisture content of 37% and are shown in Figure 2.10. The data for this isotherm yielded expected experimental uncertainties of 28%, on average. As explained above, the large percentage uncertainties translate to small amounts of adsorption at these levels of moisture in the carbon. The amount of methane adsorbed on the wet activated carbon is significantly less than the amount adsorbed on dry activated carbon at comparable conditions (Figure 2.10). For example, at 2.8 MPa, the wet activated carbon (37% moisture content) adsorbed 93% less methane than the dry activated carbon. Similarly, at 7 MPa, the adsorption of methane on the wet carbon is 84% lower than the adsorption on dry activated carbon. Thus, even at higher pressures, the presence of water significantly lowers the methane adsorption. There is some confirmation in the literature of a significant reduction of methane adsorption on an activated carbon in the presence of moisture.53 Moreover, simulation results from the literature indicate that even small concentrations of water on the carbon surface can cause significant poreblocking, thus significantly reducing adsorption sites available to methane gas. In their simulation study on adsorption of watermethane mixtures on activated carbon, Muller et al.28 have shown that water can lead to 50% reduction in methane adsorption. Thus, the interconnectivity of water molecules across the pore entrances may further restrict methane adsorption on a wet carbon. 38 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/gm) N2Dry N237% Moisture Figure 2.9 Nitrogen Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture 0.0 1.0 2.0 3.0 4.0 5.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/gm) CH4Dry CH437% Moisture Figure 2.10 Methane Adsorption on Wet Activated Carbon at 328.2 K and 37% Moisture 39 The adsorption measurements for pure CO2 on wet activated carbon were conducted at three levels of moisture, as shown in Figure 2.11. The activated carbon has an equilibrium moisture content of 27%; thus, the three moisture contents were selected to represent supersaturated, saturated and undersaturated conditions of the wet activated carbon with respect to moisture. First, CO2 adsorption isotherm was measured at the equilibrium moisture content of 27%. Then, another isotherm was measured at moisture content of about 34%, which is 7% above the equilibrium moisture content. The third adsorption isotherm was measured at moisture content of about 16%, which is approximately onehalf the equilibrium moisture content. The adsorption data for each of these three isotherms yielded expected experimental uncertainties of 3%, on average. The adsorption of CO2 on wet activated carbon at 34% moisture content exhibited, on average, an 8% decrease in the amount of gas adsorbed when compared to the adsorption on wet activated carbon at its equilibrium moisture content. The adsorption of CO2 on wet activated carbon at 16% moisture content exhibited an increase of only 2% in the amount of gas adsorbed at 7 MPa when compared to the adsorption at a moisture content of 27%. For all three isotherms, the CO2 adsorption data displayed an unexpected change in concavity at moderate pressures between 3 and 6 MPa (Figure 2.11). In general, lower moisture content shifted this concavity change to lower pressures. Further, the wet activated carbon adsorption amount approaches that of the dry activated carbon at pressures above 8 MPa. This may be an artifact of our data reduction procedure, resulting from uncertainty in the gas density values we employed; this uncertainty could be caused by the presence of water vapor in the CO2 gas phase. Some experimental evidence suggests that the presence of small concentrations of water in the 40 gas phase can increase the CO2 gas density by as much as 10%.54 A correction of this magnitude can lead to the adsorption on the wet activated carbon becoming lower than the adsorption on the dry activated carbon at pressures higher than 8 MPa. Currently, we know of no equation of state capable of accurately calculating the densities of CO2–water mixtures at nearcritical conditions. Since the methane and nitrogen are well removed from their critical points, and water solubility in the gas phase is much lower than for CO2, the effect would be much smaller for the methane and nitrogen measurements. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Gibbs Adsorption (mmol/gm) CO2Dry CO2 34% Moisture CO2 27% Moisture CO2 16% Moisture Points that may not have reached equilibrium Figure 2.11 CO2 Adsorption on Wet Activated Carbon at 328.2 K at Different Moisture Contents As illustrated in Figure 2.11, our results indicate that even small amounts of moisture present in the adsorbent can lower significantly the gas adsorption, especially below 7 MPa, when compared with the adsorption on a completely dry adsorbent. 41 The kinetics of adsorption on wet activated carbon led to unusually long equilibration times (on the order of several days per datum) relative to our measurements on coals and on dry activated carbon, where the equilibration times are less than 24 hours. Lengthy equilibration time may be attributed to slow gas diffusion through the adsorbed water which covers some of the micropores of the carbon surface. Different mechanisms have been proposed for this adsorption behavior in the literature; however, most are centered on the fact that presence of moisture significantly blocks the pores of the carbon surface. The longest equilibration times occur between 3 and 7 MPa, which coincides with the region where the changes in concavity of the adsorption isotherm were observed. This may indicate that the stripping of adsorbed water, coupled with the slow dispersion of the adsorbing gas, is partly responsible for the long equilibration times. Figure 2.12 presents the equilibration times for CO2 adsorption isotherm on wet activated carbon at 34% moisture. The figure shows the total equilibration time for each data point of the isotherm. As evident from Figure 2.12, the equilibration times were much larger in the pressure range of 3 to 7 MPa. Figure 2.13 presents the pressure drop rate for data points at 4 and 12 MPa of the same isotherm studied in Figure 2.12. There appears to be a continued drop in pressure at 4 MPa even after 200 hours of equilibration time. In comparison, the drop in pressure at 12 MPa had essentially ceased after 48 hours, as evident from Figure 2.13. This contrasting behavior for moderate and high pressure data points of the same isotherm highlights the unexplained behavior observed in the 3 to 6 MPa region of this isotherm. 42 0 50 100 150 200 250 300 350 400 450 1 3 4 6 7 8 10 11 12 14 Pressure Step (MPa) Equlibration Time Allowed (Hours) 34% Moisture Figure 2.12 Equilibration Times for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture We also observed that the equilibration time allowed for the data point at 7 MPa appeared to be sufficient for stabilization of pressure. In contrast, the isotherm points between 3 and 6 MPa may have needed substantially longer equilibration times. Therefore, based on our experience in measuring adsorption isotherms, a decision was made to progress to the next higher pressure data point in the isotherm after the equilibration times shown in Figure 2.12 (in the 3 to 6 MPa region). This was necessitated by practical time constraints for these isotherms. As such, the isotherm data points between 3 and 6 MPa may not have reached their final equilibrium state. This region is also indicated by an “envelope” in Figure 2.11. 43 3.94 3.96 3.98 4.00 4.02 4.04 4.06 4.08 4.10 0 50 100 150 200 250 Equilibration Time(Hours) Pressure (MPa) 12.47 12.48 12.49 12.50 12.51 12.52 12.53 Pressure (MPa) CO2 34% Moisture (At 4 MPa) CO2 34% Moisture (At 12 MPa) Additional drop in pressure after 200 hrs. Figure 2.13 Pressure Drop Rate Data for CO2 Adsorption on Wet Activated Carbon at 328.2 K and 34% Moisture: 4 and 12 MPa Pressure Steps To our knowledge, there are no literature data for the adsorption of CO2 under supercritical conditions on wet activated carbon at different levels of moisture. Since these appear to be the first measurements of their kind, additional work will be needed to delineate the cause of this unexpected behavior of CO2 isotherms on wet activated carbon. 2.11 OSU CBM Adsorption Database An adsorption database comprised of adsorption measurements for coalbed gases was assembled earlier.8 The database contains the pure, binary, and ternary mixture adsorption measurements conducted at OSU. There are 35 systems in that OSU adsorption database. As part of the current study, eleven new systems comprising thirteen independently measured isotherms have been added to the extended database. Thus, each 44 “system” consists of at least one gas isotherm on a specific adsorbent. Our newly acquired adsorption measurements are presented in Table 2.17, which includes the adsorbates, the adsorbent, number of points and the corresponding temperature and pressure ranges for each system. Table 2.17 Extended OSU Adsorption Database: New Systems in This Study Adsorbent Adsorbate Temp. (K) Pressure Range (MPa) NPTS Wet Illinois #6 Coal CO2 328 0.7 – 13.7 13 Wet Beulah Zap Coal CO2 328 0.7 – 13.7 11 Wet Wyodak Coal CO2 328 0.7 – 13.7 12 Wet Upper Freeport Coal CO2 328 0.7 – 13.7 12 Wet Pocahontas Coal CO2 328 0.7 – 13.7 12 Dry AC – F 400 N2 328 0.7 – 13.7 11 Dry AC – F 400 CH4 328 0.7 – 13.7 11 Dry AC – F 400 CO2 328 0.7 – 13.7 11 Wet ACF 400 CO2 328 0.7 – 13.7 33 Wet ACF 400 CH4 328 0.7 – 13.7 9 Wet ACF 400 N2 328 0.7 – 13.7 6 This extension of the database contains puregas adsorption measurements on six solid matrices: wet Illinois #6 coal, wet Beulah Zap coal, wet Wyodak coal, wet Upper Freeport coal, wet Pocahontas coal and wet/dry activated carbon. All isotherm measurements were conducted at 328.2 K and pressures to 13.8 MPa. Additional details of the OSU adsorption database can be found elsewhere.8 2.12 Monte Carlo Analysis of OSU Adsorption Error Analysis The following material in Section 2.12 has been reproduced with permission from [Mohammad, S. A.; Fitzgerald, J. E.; Robinson, R. L., Jr.; Gasem, K. A. M., Experimental Uncertainties in Volumetric Methods for Measuring Equilibrium Adsorption. Energy & Fuels 2009, DOI: 10.1021/ef8011257] Copyright [2009] American Chemical Society. 45 As mentioned above, a detailed error analysis was performed to estimate the uncertainty associated with each experimental datum by propagating the errors from the primary measurements of pressure, temperature and volume. The analytical error analysis was based on standard multivariate error propagation principles.55 The detailed derivation of the analytical error analysis has been summarized elsewhere.12, 20 In this study, a Monte Carlo analysis was conducted to confirm the validity of the analytical error analysis technique. In particular, a Monte Carlo analysis was performed for the CO2 adsorption on dry Upper Freeport coal, and the results were compared with the analytical error estimates. To conduct this analysis, all independent variables of the experiment were perturbed with a normallydistributed random error. The experimental estimates for the uncertainties in the primary measured quantities of pressure, volume and temperature were used as the random error of the corresponding perturbed variable in the Monte Carlo analysis. The Monte Carlo analysis was conducted for approximately 1000 sets of these perturbed variables. Thus, for each set of perturbed variables, an amount adsorbed was evaluated. The average of these runs at each pressure was taken as the amount adsorbed at that pressure for a given set of perturbed variables. Further, the standard deviation of the amount adsorbed evaluated from these 1000 sets was taken as an estimate of the uncertainty in the acquired data for comparison with the experimental error derived analytically. Figure 2.14 presents the comparison between analytical and Monte Carlo error estimates using the OSU adsorption apparatus for dry Upper Freeport coal. In this figure, sections marked as I, II and III represent three separate loadings of the pump that were required to complete the isotherm. The discontinuities at pressures around 10 and 12 MPa 46 are due to the reloading of pump, which was necessary for higher pressure injections. As evident from Figure 2.14, good agreement exists between the Monte Carlo and analytical error estimation methods. Thus, these results provide a reasonable confirmation of the analytical expressions that are used to estimate the uncertainties in the amount of gas adsorbed. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Pressure (MPa) Error in Gibbs Adsorption (mmol/gm) Analytical Error Analysis Monte Carlo Error Analysis I II III Figure 2.14 Comparison of Monte Carlo and Analytical Error Analyses for CO2 Adsorption on Dry Upper Freeport Coal To test for the normality of the distribution of errors from the Monte Carlo analysis, the histogram and cumulative distribution of these errors are shown in Figure 2.15. In this figure, “X”, “Xbar” and “Sigma” represent the sample observation, mean and standard deviation of the distribution, respectively. As evident from the figure, the distribution displays essentially normal error distribution behavior. 47 0 20 40 60 80 100 120 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 (XXbar)/Sigma Frequency 0% 20% 40% 60% 80% 100% Cumulative Percentage Frequency Cumulative % 50.61% Figure 2.15 Histogram for the Distribution of Errors Evaluated from the Monte Carlo Error Analysis for CO2 Adsorption on Upper Freeport Coal 48 CHAPTER 3 REVIEW OF ADSORPTION MODELS IN CBMRELATED WORK The material in this chapter has been reproduced with permission from [Gasem, Khaled; Mohammad, Sayeed; Robinson, R. L., Jr.; Modeling Coalbed Methane Adsorption and CO2 Sequestration. Encyclopedia of Chemical Processing 2009, DOI: 10.1081/EECHP120043857] Copyright [2009] Taylor and Francis. In this chapter, a number of adsorption models that have been used for CBMrelated work are reviewed, and the potential weaknesses and strengths of some of these models are discussed. Among the adsorption models considered, this chapter concentrates on three theoreticallybased models that have been developed for use in CBM and CO2 sequestration modeling. The efficacy of these models in describing the adsorption behavior of coalbed gases is also discussed. Finally, the chapter outlines future work required to address some of the outstanding issues in adsorption modeling of CBM systems. The material presented herein is not intended to be allinclusive; rather, it is an overview of some of the pertinent efforts in equilibrium adsorption modeling of CBM systems. 3.1 Adsorption Models in CBMRelated Work Several frameworks can be used to describe the adsorption phenomenon and correlate pure and mixedgas adsorption isotherms in CBM systems. These include the Langmuir model13, extended Langmuir model56, the ideal adsorbed solution theory15, real adsorbed solution theory57, porefilling theory58 and its combination with the 49 vacancy solution model59, 60, twodimensional equationofstate (2D EOS) models16, 17, 18, the simplified localdensity (SLD) model25, the OnoKondo (OK) model20 and a variety of other models (see, e.g., Do61). These and some other models are briefly reviewed herein. Langmuir/Extended Langmuir Models The Langmuir model is the simplest adsorption model and is derived from kinetic considerations.13 The model assumes that: 1. The solid surface is composed of localized adsorption sites, and each site can hold only one adsorbate molecule 2. The adsorption sites are energetically equivalent 3. There are no adsorbateadsorbate interactions between neighboring adsorption sites 4. The molecules are adsorbed in a single layer only (monolayer coverage). In principle, the Langmuir model can describe only monolayer adsorption on an ideal surface. An ideal surface has periodic energy fluctuations which are equal in magnitude and this magnitude is larger than the thermal energy, KT. This trough of energy acts as an adsorption site. When a molecule hits a surface, it can either be reflected or adsorbed depending on whether the site is vacant or is already occupied by a molecule. The dynamic equilibrium is attained when the rate of adsorption is equal to the rate of desorption/evaporation. In terms of fractional loading, θ , the Langmuir model can be expressed as: 1 BP BP L ω θ + = = (3.1) 50 where θ and ω are the fractional loading and the amount adsorbed at pressure P, respectively, B is an affinity parameter with units of inverse pressure, and L is the theoretical maximum amount adsorbed at infinite pressure. The parameter B is a measure of the partitioning of the adsorbate molecules between the adsorbed and the gas phases. It also introduces implicitly the temperature dependence of the adsorption isotherms in the model (i.e., B is temperature dependent). The extended Langmuir model was first introduced by Markham and Benton56 to describe mixture adsorption. It can be represented as: +Σ ω = j j j i i i i 1 B Py L B Py j = 1, NC (3.2) where i L and i B are the temperaturedependent purecomponent Langmuir model parameters and i y is the gasphase mole fraction of the adsorbing specie “i”. The selectivity factor, α, can be expressed in terms of the extended Langmuir model parameters, as follows: j j i i j i ij L B L B y x y x α = = (3.3) where x and y are the adsorbed and gasphase mole fractions of the twocomponents, respectively, and L and B are the corresponding purecomponent model parameters. Equation (3.3) reveals that the extended Langmuir model predicts a constant (pressure and composition independent) value for α, since the right side of equation (3.3) depends only on purecomponent Langmuir model parameters. Thus, this model does not take into account mixedgas equilibria and system pressure to evaluate mixedgas 51 adsorption. As such, the extended Langmuir model is an entirely empirical model and is also thermodynamically inconsistent.51 Historically, the Langmuir and extended Langmuir models have been used extensively in the CBM field. Ease of application appears to be the main motivation for their use in CBM work. Arri and Yee51 used the Langmuir/extended Langmuir models in their compositional coalbed methane simulator. They observed that the extended Langmuir model underpredicted the adsorption in gas mixtures at higher pressures. Similarly, Chaback et al.62 applied the extended Langmuir model to model the adsorption/desorption of CO2, methane and nitrogen binary mixtures. Levy et al.31 correlated CO2 and nitrogen Langmuir model parameters with the corresponding values for methane for a set of Bowen Basin coals. They found a linear correlation between them and observed that the CO2 and nitrogen isotherms could be reliably predicted once the methane isotherm is known for such systems. However, this result is restricted to coals from a single basin. Ideal Adsorbed Solution (IAS) Theory Myers and Prausnitz15 introduced the ideal adsorbed solution (IAS) theory. This theory is an adsorption analog to Raoult’s law, which is used in vaporliquid equilibria. The IAS theory assumes that the gas and adsorbed phases form ideal solutions, i.e. all activity coefficients are unity. The equilibrium relation for the adsorbed and the gas phase in the IAS theory is given as: yiP = P0,i (π)x i (3.4) where 0 P is the equilibrium gas pressure corresponding to the temperature and spreading pressure, π, of the pure component, and xi and yi are the adsorbed and gasphase mole 52 fractions, respectively. The spreading pressure is defined as the difference in surface tension between a clean surface and a surface covered with an (monolayer) adsorbate.63 The IAS theory is used to extend a pureisotherm model to mixture adsorption. Any purecomponent isotherm model can be used with the IAS theory; several authors have used IAS theory to describe mixture adsorption. Valenzuela et al.64 used the Langmuir model with the IAS theory for different adsorption systems. Zhou et al.17 and Hall et al.6 utilized a 2D EOS with the IAS theory to model mixture adsorption. Similarly, Manik65 used the IAS theory with the Toth equation to model adsorption isotherms in their compositional coalbed methane simulator. Real Adsorbed Solution (RAS) Theory The real adsorbed solution theory takes into account the nonidealities in the adsorbed and the gas phases and, therefore, requires adsorbedphase activity coefficients. These activity coefficients are assumed to be unity in the IAS model. When the activity coefficients are considered, the real adsorbed solution (RAS) theory is obtained as follows57: 0 0 Pyiφi = Pi φi γixi (3.5) where 0 i φ is the gasphase fugacity coefficient of the pure component ‘i’ at its reference pressure 0 i P , i γ is the activity coefficient of the component ‘i’ in the adsorbed phase, and i y and i x are the mole fractions of the gas and adsorbed components, respectively. The adsorbedphase reference pressure is defined as the pressure exerted by the pure component adsorbate at the same spreading pressure and temperature as the mixture, 0 0 i i P = P (π,T) , where π is the spreading pressure derived from surface work. The 53 adsorbedphase activity coefficients are functions of temperature, pressure and composition. Since the spreading pressure is an intensive thermodynamic variable, the spreading pressure group,ψ, is defined as57: RT πA ψ = (3.6) where A is the surface area of the adsorbent. The spreading pressure of mixtures can be obtained from the Gibbs adsorption equation, which is related to the spreading pressure group as follows57: Σ= = − NC i 1 a T i i i dP ρ RT n dψ n dln(Py φ ) (3.7) where ρa is the molar density of the adsorbed phase, i n and T n are the amount adsorbed of component ‘i’ and the total adsorbed amount, respectively. Stevenson et al.57 applied the IAS and RAS theories to model mixture adsorption. Interestingly, they observed that the IAS theory was superior to the RAS theory, especially at the higher pressures where the activity coefficients are close to unity. This was attributed to errors in the adsorbedphase activity coefficients. In fact, no reported applications exist for estimating the adsorbedphase activity coefficients at higher pressures; therefore, use of the RAS theory has been very limited. Theory of Volume Filling of Micropores (TVFM) Dubinin66 extended Polanyi’s potential theory67 and developed the theory of volume filling of micropores (TVFM). This theory assumes that: 1. The adsorbate fills the adsorption surface through a porefilling mechanism 2. A discrete monolayer is never formed in the pores 54 Dubinin had hypothesized that the adsorption mechanism on microporous adsorbents would be better described by porefilling models (DubininPolanyi approach) than surface coverage models (Langmuir model, etc.). The two most common forms of the Dubinin’s porefilling models are the DubininRadushkevich (DR) and Dubinin Astakhov (DA) equations. The DubininAstakhov (DA) equation is given as68: = − n 0 0 0 P P ln βE RT V V exp (3.8) The DubininRadushkevich (DR) equation is obtained by setting n = 2 in Equation (3.8) above63: = − 2 0 0 0 P P ln βE RT V V exp (3.9) where V is the adsorbed volume, 0 V is the micropore saturation volume corresponding to the saturated pressure 0 P , n is a structuralheterogeneity parameter, β is an affinity coefficient and E0 is the characteristic heat of adsorption of the adsorbed molecule. A range of 14 has been reported for ‘n’60, and the values of β have also been compiled for a number of adsorbates.69 The Dubinin’s porefilling models are purecomponent isotherm models and, thus, require a mixture theory like the IAS theory to be extended to mixture adsorption. Several authors have used the porefilling models and found them to be superior to the Langmuir model. Clarkson and Bustin30 used the IAS theory and porefilling models and compared them with the extended Langmuir model. They found the IAS/DA model to perform better than the IAS/DR, IAS/Langmuir and extended Langmuir models. 55 However, they found that none of these models was able to describe accurately the selectivity of the adsorbates and yielded either a constant selectivity (extended Langmuir) or an increasing selectivity with increasing feed composition of the larger adsorbing gas (IAS/DR equation), both of which did not agree with their experimental data. Similarly, Harpalani et al.70 modeled data for adsorption isotherms with the Langmuir, DR and DA equations and found the DA equation to be superior to the other two models. An important aspect of the DA equation is the temperatureinvariance of the characteristic plots ( P P RT ln 0 vs. V). This feature can be used to predict adsorption at different temperatures based on data from a single isotherm. This capability notwithstanding, the porefilling models are, however, developed for subcritical adsorbates. Specifically, these models require the saturation pressure, P0, of the respective isotherms. As such, an empirical modification is introduced when using a porefilling model for CBM systems, which involve mostly nearcritical and supercritical adsorbates. Although, a variety of modifications have been proposed60, 71, there appears to be little theoretical justification behind them. Coal Swelling Another aspect of highpressure gas adsorption behavior in coalbeds is the potential swelling of coal caused by adsorbates such as CO2. Some investigators believe that adsorption of CO2 can significantly alter the porous coal structure and these changes, if left unaccounted for, can result in large errors in the modeling of supercritical CO2 adsorption on coals. In fact, several researchers have attempted to model the swelling of coal by incorporating volumetric corrections to the adsorption isotherm equations. Ozdemir et al.46 used a variety of adsorption models, including the DA model, to study 56 the volumetric effects of CO2 adsorption on coals. Similarly, Dutta et al.47 used the Langmuir and DA models to account for the swelling of coal and dissolution of CO2 in the coal matrix. Romanov et al.48 have also attempted to interpret the volumetric changes in coals under CO2 pressure. More recently, Pan and Connell49, balancing the change in surface energy due to adsorption to the change in elastic energy of the coal matrix, developed a theoretical model to describe adsorptioninduced coal swelling. 3.2 TheoryBased Equilibrium Adsorption Models Beyond sound theoretical framing of the adsorption model, several desired attributes are sought when modeling CBM systems, including the model’s ability to: 1. Correlate pure and mixedgas adsorption data within the experimental uncertainties at reservoir conditions 2. Facilitate generalized predictions of puregas isotherms based on accessible coal characterization and gas properties 3. Predict the individual component and the total adsorption of a multicomponent gas mixture based on puregas isotherms or purefluid model generalization 4. Account rigorously for the presence of moisture in the coal Although, the traditional adsorption models described above have been used in CBMrelated work, they lack some of these desired attributes. Moreover, they seem to lack the theoretical rigor of a multicomponent adsorption model that is needed in CBM work. In previous works at OSU8, 12, researchers have tested three theorybased adsorption models for their CBM adsorption modeling capabilities. Although based on very different theoretical basis, the twodimensional equationofstate, the OnoKondo, and the simplified localdensity models were found to be readily amenable to the modeling 57 demands of CBM systems.8, 12 Following is a brief description of these three models that have been found useful in CBMrelated work. TwoDimensional Equations of State The twodimensional (2D) equationsofstate (EOS) models are essentially analogs of the 3D EOS models used in vaporliquid equilibria calculations. One of the main incentives in developing the 2D EOS models is their potential for direct implementation in CBM simulations in a manner similar to 3D EOS models used in conventional oil and gas reservoir simulations. The 2D EOS models offer several advantages. Specifically, they17: 1. Permit simultaneous calculation of equilibrium adsorption and volumetric properties 2. Are particularly suitable for extending puregas adsorption isotherms to multicomponent mixture predictions, using appropriate mixing rules 3. Are amenable to modelparameter generalization 4. Utilize a proven, familiar model format for use in reservoir simulations. The assumptions used in developing the 2D EOS models include16: 1. The adsorbent surface can be treated as a twodimensional, imaginary mathematical surface; and this 2D phase possesses its own thermodynamic properties 2. The adsorbent is thermodynamically inert. 3. The adsorbent provides a temperatureinvariant surface area, which is accessible equally to all the adsorbate molecules. 58 4. The adsorbent surface is homotattic, i.e., it is made up of many homogeneous subregions. As mentioned earlier, the 2D EOS was developed by analogy to the 3D cubic EOS. A generalized form of the cubic 3D EOS used in vaporliquid equilibrium calculations can be written as: [1 b ] RT 1 Ub W(b ) a p 2 2 ρ = ρ − + ρ + ρ ρ + (3.10) where a and b are the EOS parameters and values of U and W are specified to give various forms of 3D EOS. The 2D EOS is obtained simply by replacing two terms in the 3D EOS  the bulk pressure, P, with the spreading pressure, π, and the bulk density, ρ, with the specific surface density, σ. The generalized 2D analog of the 3D EOS, then, is given as: [1 (b ) ] RT 1 Ub W(b ) a m 2 2 2 2 2 2 σ = σ − + σ + σ σ π + (3.11) or [1 ( ) ] RT 1 U W( ) A m 2 2 ω = βω − + βω+ βω αω π + (3.12) where A is the specific surface area of the adsorbent, π is the spreading pressure, σ is the surface density of the adsorbate, ω = σA is the specific amount adsorbed, a A 2 α = and b A 2 β = are the 2D EOS model parameters and m is an additional parameter used to provide more flexibility to the model.17 The model coefficients, U, W, and m are specified to obtain a particular form of the 2D EOS. For example, a 2D analog of the 3 D van der Waals (VDW) EOS is obtained by setting m = 1 and U = W = 0; similarly for the SoaveRedlichKwong (SRK) (m = U = 1 and W = 0); the PengRobinson (PR) (m = 59 1, U = 2, and W = 1); the Eyring (m = 1/2 and U = W = 0) EOS; and the ZhouGasem Robinson (ZGR) (m = 1/3 and U = W = 0) EOS.17 Equilibrium Relations for TwoDimensional EOS The governing equations for adsorption equilibrium are entirely independent of the equation of state used in the model. At equilibrium, the chemical potential of specie i in the gas phase is equal to that in the adsorbed phase (see, e.g., Zhou et al.17): g i a μi = μ and g i a i dμ = dμ (3.13) ∫ = ∫ P P g i π π a i * * dlnf dlnf ) ) (3.14) where μi is the component chemical potential, π* is the spreading pressure at the standard conditions, g i a i f and f ) ) are the component fugacities in the adsorbed phase and the gas phase, respectively. Integrating Equation (3.14): ( ) ( ) ( ) g ( * ) i g i a * i a i lnf π lnf π lnf P lnf P ) ) ) ) − = − (3.15) At very low pressure, * i P , ( ) * i a * fi π = π ) and ( ) * i g * i f P = P ) . Thus, P f (π) π f g (P) i * i a i * i ) ) = (3.16) At very low pressure, the 2D ideal gas law is obtained: π A ω RT * i * i = (3.17) where T is temperature, R is the universal gas constant, and * ωi is the amount adsorbed at low pressures. Further, the Henry’s constant i k can be defined as: * i * i i P ω k = (3.18) 60 Therefore, g i i a i i a i Af Ax πφ k RTf ) ) ) = = (3.19) For puregas adsorption, the equilibrium relation is given by: g i a a ωZ φ = k f (3.20) where ω is the amount adsorbed, a Z is the 2D compressibility factor, φa is the fugacity coefficient using the 2D EOS, f g is the fugacity for the gas phase. The fugacity for the 2D EOS is given by: ( ) a 0 i T,M ,n a i d ln Z A 1 RT ˆ 1 ln s j ω− ω − ∂ω ∂ π ω φ = ∫ ω (3.21) where A is the specific surface area and Ms is the mass of the adsorbent. As evident from the above relations, the 2D EOS enters the calculation through the fugacities and the 2D compressibility factor. To perform adsorption equilibrium calculations using Equation (3.20) requires the values of α, β, and k. They are determined normally by direct regression of adsorption isotherm data. As such, the 2D EOS is a threeparameter adsorption model. Several researchers have utilized the 2D EOS theory to model gas adsorption. Hill72 and de Boer73 used the van der Waals (VDW) EOS to correlate puregas adsorption. Hoory and Prausnitz74 extended the 2D VDW EOS to mixtures by introducing mixing rules. DeGance16 applied the 2D virial and Eyring EOS to correlate highpressure pure gas adsorption isotherms. Zhou et al.17 used the 2D EOS model to describe pure and mixedgas adsorption on different adsorbents. Pan18 introduced Gibbs Free energy mixing rules into the 2D EOS and developed temperature dependence relations for the 2D model parameters. 61 OnoKondo Lattice Model The OnoKondo (OK) adsorption model is based on lattice theory and was first proposed by Ono and Kondo.19 Since then, Aranovich and Donohue7577 have generalized the model expressions for application to the adsorption of solutes in liquid solutions. Sudibandriyo20 generalized the OK model parameters, extended the model to mixture adsorption of CBM systems and developed the temperature dependence relations for the model parameters. Key features of the OnoKondo model include its ability to: 1. Provide a layering analogue to adsorption 2. Generate independent estimates for the adsorbedphase densities 3. Incorporate accurate userprovided density estimates, which may reduce the correlative burden of the adsorption modeling. 4. Utilize the puregas adsorption isotherms to predict mixture adsorption without the use of binary interaction parameters The assumptions used in developing the lattice OnoKondo model are (see, e.g., Sudibandriyo20): 1. The fluid system is composed of one or more layers of lattice cells containing fluid molecules and vacancies. 2. Molecular interactions exist only between the nearest neighboring molecules, i.e. in the adjacent lattice cells. 3. Adsorption equilibrium between the adsorbed layers and the bulk lattice gas is given by the equality of the chemical potential in each layer and the bulk gas. 62 For an adsorptive system, more fluid molecules would reside in the cells of the adsorbedphase layers than in the cells of the bulkphase layers due to the molecular interactions with the adsorbent surface. The OK model expression for the thermodynamic equilibrium between the gasphase and a multilayer adsorbedphase is given as75: ln[x (1 x )/x (1 x )] z (x x )ε /kT (x 2x x )ε /kT 0 t b b t 0 t b ii t 1 t t 1 ii − − + − + − + = + − and t = 1, 2, 3… (3.22) where t represents the number of layers. For the first layer, ln[x (1 x )/x (1 x )] (z x x z x )ε /kT ε /kT 0 1 b b 1 1 1 2 0 b ii is − − + + − + = (3.23) where xt is the reduced density or fraction of sites occupied by adsorbed molecules in layer t, and xb is the fraction of sites occupied by fluid molecules in the bulk, z0 and z1 are the coordination numbers of the lattice cells, εii/kT is the fluidfluid interaction energy parameter, εis/kT is the fluidsolid interaction energy parameter, k is Boltzmann’s constant and T is the absolute temperature. For a hexagonal lattice, the coordination numbers z0 and z1 are 6 and 4, respectively. The Gibbs excess adsorption, Γ , in the OK model is given as: = Σ − m t t b Γ C (x x ) (3.24) where C is known as a "prefactor," which is related to the capacity of the adsorbent for a specific adsorbate. The index m is the number of layers for the adsorption isotherm and is typically determined from the best description of the adsorption data. The reduced densities xi and xb can be expressed as xi= ρi /ρmc and xb= ρb /ρmc, where ρi and ρb are the adsorbed and the bulk density of the adsorbate, respectively and ρmc is the maximum adsorbedphase density. The maximum adsorbedphase density, ρmc, can be estimated in 63 various ways. Two of the common ways of estimating the adsorbedphase density are to use the saturated liquid density at atmospheric pressure51 or the inverse of the VDW covolume.8 Further, Hocker and Donohue78 have used a theoretical value of the density of closepacked molecules. Although the OK model allows for the formation of multiple layers, a monolayer has been shown to provide a satisfactory description of the adsorption data.20 In the monolayer OK model, the adsorbed molecules are directly mapped onto parallel graphite planes, as shown in Figure 3.1. Further, when a 2Dhexagonal configuration is chosen, the thermodynamic equilibrium expression of Equation (3.22) simplifies as: ln[x (1 x )/x (1 x )] ((z 1)x z x )ε /kT ε /kT 0 ads b b ads 1 ads 0 b ii is − − + + − + = (3.25) Therefore, the Gibbs excess adsorption expression for the monolayer OK model becomes: = − = − mc b mc ads ads b ρ ρ ρ ρ Γ 2C (x x ) 2C (3.26) where ρads is the adsorbedphase density. GRAPHITE PLANE GRAPHITE PLANE Figure 3.1 OnoKondo Model for Monolayer Adsorption on Graphite Slit (Slit Depiction Adopted from Sudibandriyo20) The OK model thus has four parameters: ρmc, εii/k, εis/k and C. Two of these parameters can be estimated independently. Specifically, ρmc is estimated to be the inverse of the VDW covolume and εii/k can be evaluated as20: εii 0.432ε * = (3.27) 64 where ε * is the well depth of the 126 LennardJones potential. These assumptions yield the twoparameter (C and εis/k) OK model. Simplified LocalDensity/PengRobinson (SLDPR) Model The SLD model is a simplification of the more computationallyintensive localdensity theory. According to this theory, the density profile is obtained by minimizing the total energy function, which depends on all point densities and their spatial derivatives.79 The SLD model, thus, uses meanfield theory in calculating the chemical potential. In other words, the local fluctuations arising out of gradients in density are not considered in the micropores, where the majority of adsorption takes place. Further, the chemical potential of the fluid at each point is corrected for the proximity of the fluid molecule to the molecular wall of the adsorbent.25 The SLD model partitions the interactions of a gas molecule in the adsorbed phase into fluidsolid and fluidfluid interactions. The fluidsolid interactions are modeled through a potential function such as the 104 Lee's potential80 whereas the fluidfluid interactions are modeled through a modified 3D EOS.81 Specifically, the attractive parameter in the EOS is modified to account for the presence of the adsorbent wall. Several advantages distinguish the SLD framework. In particular, the model: 1. Provides a consistent framework that accounts for adsorbateadsorbate (fluidfluid) and adsorbateadsorbent (fluidsolid) molecular interactions 2. Delineates the adsorbent structural properties based on welldescribed physical geometries of the adsorbent and 3. Predicts the adsorbedphase density which facilitates prediction of absolute gas adsorption. 65 4. Offers the opportunity for model generalizations using molecular descriptors 5. Predicts the mixtureadsorption based solely on puregas isotherms or purefluid generalization A number of assumptions have been used in developing the SLD model22: 1. The chemical potential at any point near the adsorbent surface is equal to the bulk phase chemical potential. 2. The chemical potential at any point above the surface is the sum of the fluidfluid and fluidsolid interactions. 3. The attractive potential between fluid and solid at a point is independent of the number of molecules at and around that point. Different geometries such as rectangular slits8, 81, cylindrical pores82, flat surfaces8, etc. can be used to model the porous adsorbent structure. Using the slit geometry, the SLD model assumes the adsorbate molecules reside within a twosurface rectangularshaped slit. The distance between the slit surfaces is L and the position of a molecule within the slit is z. The position, z, is orthogonal to the solid surface formed by the carbon atoms on the slit wall. Therefore, the chemical potential of the fluid, μ, is expressed as the sum of the fluidfluid and fluidsolid potentials at a position, z. At equilibrium: μ(z) = μff (z) + μfs (z) = μbulk (3.28) where subscripts "bulk", "ff" and "fs" refer to bulk fluid, fluidfluid interactions, and fluidsolid interactions, respectively. The chemical potential of the bulk fluid is expressed in terms of fugacity as: = + 0 bulk bulk 0 f (T) RTln f μ μ (3.29) 66 where f is the fugacity, and μ0 is the chemical potential at the reference state. By analogy, the chemical potential from fluidfluid interactions is written as: = + 0 ff ff 0 f (T) RTln f (z) μ (z) μ (3.30) where fff (z) is the adsorbed fluid fugacity at a position z, and μ0 is the chemical potential at the same reference state as in Equation (3.29). As mentioned above, the fluidsolid interactions are accounted for through a fluidsolid potential function. As such, the fluidsolid chemical potential, μfs , is given as: μ (z) N [ (z) (L  z)] fs fs fs A = Ψ + Ψ (3.31) where Ψ(z) and Ψ(Lz) are the fluidsolid interactions from the two walls of a slit of length L, and NA is the Avogadro’s number. Substituting Equations (3.29), (3.30) and (3.31) into Equation (3.28) yields the SLD equilibrium relationship for modeling adsorption within the slit: + − = − kT Ψ (z) Ψ (L z) f (z) f exp fs fs ff bulk (3.32) where k is the Boltzmann’s constant. In Equation (3.32), Lee’s partiallyintegrated 104 potential80 is used to provide the fluidsolid interaction information, Ψfs(z)22, 81: ( ) + − ⋅ − = Σ= 4 i 1 4 ss 4 fs 10 10 2 fs atoms fs fs fs z' (i 1) σ σ 2 1 5(z') σ Ψ (z) 4πρ ε σ (3.33) εfs = εff × εss (3.34) where εfs is the fluidsolid interaction energy parameter, ρatoms = 0.382 atoms/Å2 and z' is the centercenter distance between fluid molecules and carbon atoms in the first plane. 67 The parameters σff and σss represent, respectively, the molecular diameter of the adsorbate and the carbon interplanar distances. The excess adsorption (nEx), when applying the SLD model, is given as: = ∫ ( ( )− ) Right Side of Slit Left Side of Slit bulk Ex ρ z ρ dz 2 A n (3.35) where nEx is the excess adsorption and A is the accessible surface area for the gas on a particular adsorbent. The left and right sides of the slit each comprise half of the total surface area, A/2. Thus, the excess adsorption can be calculated by numerical integration of Equation (3.35). Thus, the optimized parameters in the SLD model typically include the surface area A for each fluid, solidsolid interaction energy parameter εss/K and the slit length L.12 The SLD model was developed by Rangarajan et al.22 who used the van der Waals EOS to provide the fluidfluid interaction information. Any EOS with appropriate modifications can be used within the SLD framework. In fact, over the years, researchers have used different EOSs such as the PengRobinson, Bender and ElliotSureshDonohue (ESD) EOSs within the SLD framework to provide the fluidfluid interaction information.23, 24, 26, 81 Fitzgerald25 used the SLD model with a modified PengRobinson (PR) EOS83 to study the highpressure adsorption of coalbed gases and their mixtures on dry and wet coals and activated carbons. Further, the SLD model is capable of accounting for swelling of coal by varying the slit length with pressure. However, the modeling results obtained at OSU for highpressure adsorption systems without the use of coal swelling were found to be satisfactory; therefore, to date, the inclusion of this effect could not be justified. 68 Gibbs and Absolute Adsorption Adsorption data can be reported either in terms of Gibbs or absolute adsorption. Gibbs adsorption is calculated directly from experimentallymeasured quantities and this accounts for the fact that there is additional material present near the adsorbent surface due to adsorption phenomenon. This additional material is in excess of that which would be present in the same (void) volume if there was no adsorption. This excess material is usually referred to as the Gibbs or excess adsorption. In contrast, the calculation of absolute adsorption requires knowledge of the adsorbed phase density, ρads, which is not readily accessible by experimental measurement. The exact mathematical expressions that highlight the physical interpretation of Gibbs adsorption and the approximate nature of calculated absolute adsorption have been presented elsewhere.7 The relationship between the two quantities is given as − = ads gas Gibbs ads ads Abs ads ρ ρ ρ n n (3.39) where Abs ads n and Gibbs ads n are the absolute and Gibbs adsorption, respectively, and ρgas and ρads are the gas phase and the adsorbed phase densities, respectively. To calculate absolute adsorption from Equation (3.39), estimates of ρads must be employed. A commonly used approximation for ρads is the liquid density at the normal boiling point (as was done by Arri and Yee51) or the reciprocal of the VDW covolume.8 3.3 Example Studies of Adsorption Modeling In this section, the modeling capability of the 2D EOS, OK and SLDPR models as they apply to CBM systems is demonstrated. Specifically, the correlation capabilities of these models for puregas adsorption on dry and wet coals are illustrated. Several other 69 capabilities of these models that were demonstrated in earlier OSU studies have also been highlighted. Further, the generalization capabilities of these models are reviewed in Chapter 6. In particular, the coal structurebased generalization of SLD model is covered in Chapter 6, along with a review of other generalization efforts in the literature. Statistical Quantities Used In the results presented here, the sum of the squared weighted deviations, expressed in terms of the weighted root mean square, WRMS, was used for the objective function: NPTS σ n n WRMS 2 i NPTS i 1 exp calc exp Σ= − = (3.40) where NPTS is the number of data points, nexp is the experimental excess adsorption, ncalc is the calculated excess adsorption and σexp is the expected experimental uncertainty. In addition, the results were analyzed in terms of the average absolute percentage deviation (%AAD), the root mean square error (RMSE) and weighted average absolute deviation (WAAD): 100% NPTS n n n abs %AAD i NPTS i 1 exp calc exp × − = Σ= (3.41) ( ) NPTS n n RMSE 2 i NPTS i 1 calc exp Σ= − = (3.42) NPTS σ n n abs WAAD NPTS i 1 exp calc exp Σ= − = (3.43) 70 Modeling Discussion Correlation of PureGas Adsorption on Dry and Wet Coals The prediction of adsorption isotherms of pure methane, nitrogen and CO2 on five dry coals and the adsorption isotherms of pure CO2 on five wet coals are used to demonstrate the correlative abilities of the 2D EOS, OK and SLD models. Each of these three models was used to represent the adsorption data on these coals. Table 3.1 lists the regressed parameters for the 2D EOS, OK and SLDPR models for each coal. Three parameters (α, β, and k) were regressed for the 2D EOS model, two (εfs/k and C) for the OK model and three (surface area, εss/k and L) for the SLD model. Further, the SLD parameter “L” was fixed at 1.15 nm. for the modeling on wet coals since there were data for only one gas on the wet coals. Table 3.2 lists the summary statistics obtained for the three models on these coals. The overall WAAD for the five dry coals was 0.3, 0.4 and 0.5 for the 2D EOS, OK and SLD models, respectively. In comparison, the overall WAAD for the five wet coals was 0.5, 0.3 and 0.5 for the 2D EOS, OK and SLD models, respectively. Further, the overall %AAD for the five dry coals was 1.9%, 2.6% and 3.1% for the 2D EOS, OK and SLD models, respectively. The corresponding sta 



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