SIMPLIFIED LOCAL-DENSITY MODELING OF PURE
AND MULTI-COMPONENT GAS ADSORPTION
ON DRY AND WET COALS
By
JING SHYAN CHEN
Bachelor of Science in Chemical Engineering
Oklahoma State University
Stillwater, Oklahoma
2005
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 2007
ii
SIMPLIFIED LOCAL-DENSITY MODELING OF PURE
AND MULTI-COMPONENT GAS ADSORPTION
ON DRY AND WET COALS
Dissertation Approved:
Dr. Khaled A.M. Gasem
Thesis Adviser
Dr. Robert L. Robinson, Jr.
Dr. Karen A. High
Dr. A. Gordon Emslie
Dean of the Graduate College
iii
PREFACE
Generalized correlations for the model parameters in the modified simplified
local-density/Peng-Robinson (SLD-PR) model were develop to provide reliable
predictions for the equilibrium adsorption of methane, nitrogen, CO2 and their mixtures
on dry and wet coals in the range of conditions encountered in coalbed methane (CBM)
production and CO2 sequestration. The adsorption of pure methane, nitrogen and CO2
and their mixtures on Argonne premium coals and OSU coals were considered in this
study. The coals used included five Argonne premium coals (Illinois #6, Beulah Zap,
Wyodak, Upper Freeport, Pocahontas coal) and five OSU coals (Illinois #6, Fruitland
OSU #1 and #2, Tiffany and Lower Basin Fruitland coal).
The SLD-PR model parameters (coal surface areas and solid-solid interaction
energy) were regressed to obtain precise representation of pure-gas adsorption on each
coal. The results obtained indicate that the SLD-PR model is able to represent the pure-gas
adsorption on these coals within expected experimental uncertainties.
The regressed model parameters were correlated (generalized) in terms of the
excess adsorption of adsorbates (methane or nitrogen or CO2) at 400 psia and the coal
characteristics, including the fixed carbon and the equilibrium moisture. The generalized
parameters facilitate the SLD-PR model prediction of the pure-gas adsorption on these
coals within twice the experimental uncertainties.
iv
The generalized model parameters from the pure-gas adsorption were used to
predict mixture adsorption of these gases on wet coals. Specifically, the mixed-gas
adsorption on wet Illinois #6, Fruitland OSU #1 and wet Tiffany coal were modeled.
With few exceptions, the model was able to predict the mixture adsorption within three
times the experimental uncertainties.
Furthermore, inclusion of binary interaction parameters (BIPs) in the SLD-PR
model improves the generalized prediction for mixture adsorption. Using generalized
model parameters from the pure gases, the BIPs were regressed to obtain a better
correlation for the mixture adsorption. When generalized in terms of coal
characterization or gas properties, the BIPs resulted in predictions of the mixed-gas
adsorption, on average, within twice of the experimental uncertainties.
v
ACKNOWLEDGMENTS
During the course of my graduate studies, there are many people for whom I
would like to show my appreciation. I would like to offer my sincere gratitude to my
advisor, Dr. Khaled A. M. Gasem, for giving me the opportunity to work on this project.
His enthusiasm for the research showed me the significance of the project, and made my
graduate studies very enlightening. Without his intelligence guidance, encouragement
and endless support, I could have not completed this work successfully.
I am also grateful to Dr. Robert L. Robinson, Jr. for his guidance, valuable advice
and encouragement during the course of my studies.
I would also like to thank my graduate advisory committee member, Dr. Karen
High, for her valuable input and suggestions.
I am thankful to my colleagues, Dr. James E. Fitzgerald and Sayeed Mohammad,
who have been great mentors to me. Their generous suggestions have helped me in
completing the study.
Most of all, I would like to thank my family for their patience, understanding, and
support during the course of my graduate program, especially my mother and father, Pek
Yong Lim and Ah Chong Chen. Also, I also appreciate the encouragement of my brother
(Foo Sen), sister-in-law (Miow Tieng) and sisters (Jing Voon and Jing Ting).
vi
TABLE OF CONTENTS
Chapter Page
1. INTRODUCTION .....................................................................................................1
Objectives ................................................................................................................6
Organization.............................................................................................................6
2. SIMPLIFIED LOCAL DENSITY MODEL..............................................................8
3. REPRESENTATION OF PURE-GAS ADSORPTION..........................................15
Model Development...............................................................................................16
Database Employed in this Study ..........................................................................18
Statistical Quantities Used in Data Reduction.......................................................23
Results and Discussions.........................................................................................24
Conclusions............................................................................................................41
4. GENERALIZED MODEL FOR PURE-GAS ADSORPTION...............................43
Generalized Correlations .......................................................................................44
Results and Discussions.........................................................................................47
Case 1: Methane-Based Generalizations .........................................................48
Case 2: Nitrogen-Based Generalizations .........................................................58
Case 3: CO2-Based Generalizations.................................................................68
Comparison of Generalized Predictions of Cases 1, 2 and 3...........................79
Conclusions............................................................................................................81
5. MULTI-COMPONENT GAS ADSORPTION MODELING.................................83
SLD-PR Model for Mixed-Gas Adsorption...........................................................83
Calculation Procedure............................................................................................86
Statistical Quantities Used in Data Reduction.......................................................88
Database Employed in this Study ..........................................................................88
The SLD-PR Generalized Model Parameters ........................................................89
Results and Discussions.........................................................................................91
vii
Chapter Page
Case 4: Mixture Adsorption Predictions Using Pure-Fluid Methane-Based
Generalized Parameters ...................................................................................92
Cases 5 and 6: Mixture Adsorption Predictions Using Pure-Fluid
Methane-Based Generalized Parameters and BIPs........................................104
Comparison of Generalized Predictions Using Methane, Nitrogen and CO2
Based Correlations .........................................................................................109
Conclusions..........................................................................................................112
6. CONCLUSIONS AND RECOMMENDANTIONS .............................................114
Conclusions..........................................................................................................114
Recommendations................................................................................................116
REFERENCES ..........................................................................................................117
APPENDICES ...........................................................................................................120
A. The Working Equations for the Simplified Local-Density / Peng-Robinson
EOS Model......................................................................................................120
B. Representation of Pure-Gas Adsorption..........................................................129
1. Representation of Modified SLD-PR Modeling on Dry Argonne
Premium Coals without Covolume Correction ( b = 0.0).........................129
2. Representation Results for Scenario 2 .......................................................131
C. Model Parameter Generalizations ...................................................................137
1. Generalization in the OSU FORTRAN Program.......................................137
2. Comparison of Generalized and Regressed Model Results.......................138
3. Generalization of Mixed-Gas Adsorption Using Nitrogen Excess
Adsorption..................................................................................................144
4. Generalization of Mixed-Gas Adsorption Using CO2 Excess
Adsorption..................................................................................................159
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LIST OF TABLES
Table Page
2.1 Fluid Physical Properties ..................................................................................12
3.1 Pure-Gas Adsorption Database Used in this Study: Argonne Premium
Coals .................................................................................................................19
3.2 Pure-Gas Adsorption Database Used in this Study: OSU Coals ......................20
3.3 Compositional Analysis of OSU Coals Used in this Study..............................21
3.4 Compositional Analysis of Argonne Premium Coals Used in this Study ........22
3.5 Scenario 1: Modified SLD-PR Model Representations of Pure-Gas
Adsorption on Dry and Wet Coals....................................................................25
3.6 Scenario 2: Modified SLD-PR Model Representations of Pure-Gas
Adsorption on Dry and Wet Coals....................................................................29
3.7 Scenario 3: Modified SLD-PR Model Representations of Pure-Gas
Adsorption on Dry and Wet Coals....................................................................32
4.1 Excess Adsorption of Adsorbates at 400 psia...................................................46
4.2 Combined Compositional Analysis of Lower Basin Fruitland and Tiffany
Coal Used in this Study.....................................................................................47
4.3 Case 1: Generalized Correlations of the Surface Areas and the Solid-Solid
Interaction Energy Parameter ...........................................................................48
4.4 Case 1: Generalized SLD-PR Model Parameters .............................................49
4.5 Case 1: Summary Results of the Generalized Parameters ................................49
4.6 Case 1: Summary Results for the Generalized SLD-PR Adsorption
Predictions.........................................................................................................52
ix
Table Page
4.7 Case 2: Generalized Correlations of the Surface Areas and the Solid-Solid
Interaction Energy Parameter ...........................................................................58
4.8 Case 2: Generalized SLD-PR Model Parameters .............................................59
4.9 Case 2: Summary Results of the Generalized Parameters ................................60
4.10 Case 2: Summary Results for the Generalized SLD-PR Adsorption
Predictions.........................................................................................................62
4.11 Case 3: Generalized Correlations of the Surface Areas and the Solid-Solid
Interaction Energy Parameter ...........................................................................69
4.12 Case 3: Generalized SLD-PR Model Parameters .............................................69
4.13 Case 3: Summary Results of the Generalized Parameters ................................70
4.14 Case 3: Summary Results for the Generalized SLD-PR Adsorption
Predictions.........................................................................................................72
5.1 Mixed-Gas Adsorption Database Used in this Study .......................................89
5.2 Case 1: Summary Results for SLD-PR Modeling of Pure and
Binary Mixture Adsorption on Wet Illinois #6 Coal at 115°F ........................93
5.3 Case 1: Summary Results for SLD-PR Modeling of Pure and
Binary Mixture Adsorption on Wet Fruitland OSU #1 Coal at 115°F ............94
5.4 Case 1: Summary Results for SLD-PR Modeling of Pure and
Mixture Adsorption on Wet Tiffany Coal at 130°F.......................................101
5.5 Generalized Correlations of the EOS BIPs Using Methane Excess
Adsorption at 400 psia (Case 1).....................................................................105
5.6 Case 1: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Illinois #6 Coal ...................................................................................105
5.7 Case 1: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Fruitland OSU #1 Coal.......................................................................106
5.8 Case 1: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Tiffany Coal .......................................................................................106
x
Table Page
5.9 Comparison for SLD-PR Modeling of Pure and Mixed-Gas
Adsorption on Wet Illinois #6 Coal at 115°F .................................................110
5.10 Comparison for SLD-PR Modeling of Pure and Mixed-Gas
Adsorption on Wet Fruitland OSU #1 Coal at 115°F.....................................110
5.11 Comparison for SLD-PR Modeling of Pure-Gas and Binary
Adsorption on Wet Tiffany Coal at 130°F......................................................111
5.12 Comparison for SLD-PR Modeling of Ternary Adsorption
on Wet Tiffany Coal at 130°F.........................................................................111
B.1 Modified SLD-PR Model Representations of Pure-Gas
Adsorption on Dry Argonne Premium Coals with Lb = 0.0 ..........................130
C.1 The Coal Numbers for the Argonne Premium and OSU coals in Model
Generalizations ..............................................................................................137
C.2 The System Numbers for the Argonne Premium and OSU coals in Model
Generalizations ..............................................................................................137
C.3 Case 1: Summary Results of the Generalized Parameters .............................138
C.4 Case 2: Summary Results of the Generalized Parameters .............................140
C.5 Case 3: Summary Results of the Generalized Parameters .............................142
C.6 Case 2: Summary Results for SLD-PR Modeling of Pure and
Binary Mixture Adsorption on Wet Illinois #6 Coal at 115°F ......................145
C.7 Case 2: Summary Results for SLD-PR Modeling of Pure and
Binary Mixture Adsorption on Wet Fruitland OSU #1 Coal at 115°F ..........146
C.8 Case 2: Summary Results for SLD-PR Modeling of Pure and
Mixture Adsorption on Wet Tiffany Coal at 130°F.......................................147
C.9 Generalized Correlations of the EOS BIPs Using Nitrogen Excess
Adsorption at 400 psia (Case 2).....................................................................148
C.10 Case 2: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Illinois #6 Coal ..................................................................................148
C.11 Case 2: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Fruitland OSU #1 Coal......................................................................149
xi
Table Page
C.12 Case 2: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Tiffany Coal ......................................................................................149
C.13 Case 3: Summary Results for SLD-PR Modeling of Pure and
Binary Mixture Adsorption on Wet Illinois #6 Coal at 115°F ......................160
C.14 Case 3: Summary Results for SLD-PR Modeling of Pure and
Binary Mixture Adsorption on Wet Fruitland OSU #1 Coal at 115°F ..........161
C.15 Case 3: Summary Results for SLD-PR Modeling of Pure and
Mixture Adsorption on Wet Tiffany Coal at 130°F.......................................162
C.16 Generalized Correlations of the EOS BIPs Using CO2 Excess Adsorption
at 400 psia (Case 3)........................................................................................163
C.17 Case 3: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Illinois #6 Coal ..................................................................................163
C.18 Case 3: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Fruitland OSU #1 Coal......................................................................164
C.19 Case 3: Regressed and Generalized EOS BIPs for CBM Gas Adsorption
on Wet Tiffany Coal ......................................................................................164
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LIST OF FIGURES
Figure Page
2.1 SLD Model Slit Geometry..................................................................................8
3.1 Representation of Pure-Gas Adsorption on Dry Illinois #6 Coal at 131°F ......35
3.2 Representation of Pure-Gas Adsorption on Dry Beulah Zap Coal at 131°F ....36
3.3 Representation of Pure-Gas Adsorption on Dry Wyodak Coal at 131°F .........36
3.4 Representation of Pure-Gas Adsorption on Dry Upper Freeport Coal
at 131°F ...........................................................................................................37
3.5 Representation of Pure-Gas Adsorption on Dry Pocahontas Coal at 131°F.....37
3.6 Representation of Pure-Gas Adsorption on Wet Illinois #6 Coal at 115°F ......38
3.7 Representation of Pure-Gas Adsorption on Wet Fruitland OSU #1 Coal
at 115°F.............................................................................................................38
3.8 Representation of Pure-Gas Adsorption on Wet Fruitland OSU #2 Coal
at 115°F.............................................................................................................39
3.9 Representation of Pure-Gas Adsorption on Wet Tiffany Coal at 130°F ..........39
3.10 Representation of Pure-Gas Adsorption on Wet Lower Basin Fruitland
Coal at 115°F ....................................................................................................40
3.11 Deviations Plot for SLD-PR Model Representation of Pure-Gas
Adsorption on Dry and Wet Coals....................................................................41
4.1 Case 1: Comparison of the Regressed and Generalized SLD-PR Model
Parameters.........................................................................................................50
4.2 Generalized Predictions of Pure-Gas Adsorption on Dry Illinois #6 Coal
at 131°F Using Methane Excess Adsorption at 400 psia..................................53
4.3 Generalized Predictions of Pure-Gas Adsorption on Dry Beulah Zap Coal
at 131°F Using Methane Excess Adsorption at 400 psia..................................53
xiii
Figure Page
4.4 Generalized Predictions of Pure-Gas Adsorption on Dry Wyodak Coal
at 131°F Using Methane Excess Adsorption at 400 psia..................................54
4.5 Generalized Predictions of Pure-Gas Adsorption on Dry Upper Freeport
Coal at 131°F Using Methane Excess Adsorption at 400 psia .........................54
4.6 Generalized Predictions of Pure-Gas Adsorption on Dry Pocahontas Coal
at 131°F Using Methane Excess Adsorption at 400 psia..................................55
4.7 Generalized Predictions of Pure-Gas Adsorption on Wet Illinois #6 Coal
at 115°F Using Methane Excess Adsorption at 400 psia..................................55
4.8 Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland OSU #1
Coal at 115°F Using Methane Excess Adsorption at 400 psia .........................56
4.9 Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland OSU #2
Coal at 115°F Using Methane Excess Adsorption at 400 psia .........................56
4.10 Generalized Predictions of Pure-Gas Adsorption on Wet Tiffany Coal
at 130°F Using Methane Excess Adsorption at 400 psia..................................57
4.11 Generalized Predictions of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F Using Methane Excess Adsorption at 400 psia..........57
4.12 Case 2: Comparison of the Regressed and Generalized SLD-PR Model
Parameters.........................................................................................................59
4.13 Generalized Predictions of Pure-Gas Adsorption on Dry Illinois #6 Coal
at 131°F Using Nitrogen Excess Adsorption at 400 psia..................................63
4.14 Generalized Predictions of Pure-Gas Adsorption on Dry Beulah Zap Coal
at 131°F Using Nitrogen Excess Adsorption at 400 psia..................................63
4.15 Generalized Predictions of Pure-Gas Adsorption on Dry Wyodak Coal
at 131°F Using Nitrogen Excess Adsorption at 400 psia..................................64
4.16 Generalized Predictions of Pure-Gas Adsorption on Dry Upper Freeport
Coal at 131°F Using Nitrogen Excess Adsorption at 400 psia .........................64
4.17 Generalized Predictions of Pure-Gas Adsorption on Dry Pocahontas Coal
at 131°F Using Nitrogen Excess Adsorption at 400 psia..................................65
4.18 Generalized Predictions of Pure-Gas Adsorption on Wet Illinois #6 Coal
at 115°F Using Nitrogen Excess Adsorption at 400 psia..................................65
xiv
Figure Page
4.19 Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland OSU #1
Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia .........................66
4.20 Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland OSU #2
Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia .........................66
4.21 Generalized Predictions of Pure-Gas Adsorption on Wet Tiffany Coal
at 130°F Using Nitrogen Excess Adsorption at 400 psia..................................67
4.22 Generalized Predictions of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia .........67
4.23 Case 3: Comparison of the Regressed and Generalized SLD-PR Model
Parameters.........................................................................................................70
4.24 Generalized Predictions of Pure-Gas Adsorption on Dry Illinois #6 Coal
at 131°F Using CO2 Excess Adsorption at 400 psia.........................................73
4.25 Generalized Predictions of Pure-Gas Adsorption on Dry Beulah Zap Coal
at 131°F Using CO2 Excess Adsorption at 400 psia.........................................73
4.26 Generalized Predictions of Pure-Gas Adsorption on Dry Wyodak Coal
at 131°F Using CO2 Excess Adsorption at 400 psia.........................................74
4.27 Generalized Predictions of Pure-Gas Adsorption on Dry Upper Freeport
Coal at 131°F Using CO2 Excess Adsorption at 400 psia ................................74
4.28 Generalized Predictions of Pure-Gas Adsorption on Dry Pocahontas Coal
at 131°F Using CO2 Excess Adsorption at 400 psia.........................................75
4.29 Generalized Predictions of Pure-Gas Adsorption on Wet Illinois #6 Coal
at 115°F Using CO2 Excess Adsorption at 400 psia.........................................75
4.30 Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland OSU #1
Coal at 115°F Using CO2 Excess Adsorption at 400 psia ................................76
4.31 Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland OSU #2
Coal at 115°F Using CO2 Excess Adsorption at 400 psia ................................76
4.32 Generalized Predictions of Pure-Gas Adsorption on Wet Tiffany Coal
at 130°F Using CO2 Excess Adsorption at 400 psia.........................................77
4.33 Generalized Predictions of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F Using CO2 Excess Adsorption at 400 psia.................77
xv
Figure Page
4.34 Comparison among the SLD-PR Model Parameter Generalizations as
Applied to Pure-Gas Adsorption on Dry Beulah Zap Coal at 131°F................80
4.35 Deviations Plot for SLD-PR Model Generalization of Pure-Gas
Adsorption on Dry and Wet Coals....................................................................81
5.1 Case 1: Methane Adsorption in Methane/Nitrogen Mixtures on Wet
Illinois #6 Coal at 115°F...................................................................................95
5.2 Case 1: Nitrogen Adsorption in Methane/Nitrogen Mixtures on Wet
Illinois #6 Coal at 115°F...................................................................................95
5.3 Case 1: Methane Adsorption in Methane/CO2 Mixtures on Wet Illinois #6
Coal at 115°F ....................................................................................................96
5.4 Case 1: CO2 Adsorption in Methane/CO2 Mixtures on Wet Illinois #6
Coal at 115°F ....................................................................................................96
5.5 Case 1: Nitrogen Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6
Coal at 115°F ....................................................................................................97
5.6 Case 1: CO2 Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6
Coal at 115°F ....................................................................................................97
5.7 Case 1: Methane Adsorption in Methane/Nitrogen Mixtures on Wet
Fruitland OSU #1 Coal at 115°F.......................................................................98
5.8 Case 1: Nitrogen Adsorption in Methane/Nitrogen Mixtures on Wet
Fruitland OSU #1 Coal at 115°F.......................................................................98
5.9 Case 1: Methane Adsorption in Methane/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ......................................................................................99
5.10 Case 1: CO2 Adsorption in Methane/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ......................................................................................99
5.11 Case 1: Nitrogen Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ....................................................................................100
5.12 Case 1: CO2 Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ....................................................................................100
5.13 Case 1: Methane/Nitrogen 50/50 Feed Gas Adsorption on Wet Tiffany
Coal at 130°F ..................................................................................................102
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Figure Page
5.14 Case 1: Methane/CO2 41/59 Feed Gas Adsorption on Wet Tiffany Coal
at 130°F...........................................................................................................103
5.15 Case 1: Nitrogen/CO2 20/80 Feed Gas Adsorption on Wet Tiffany Coal
at 130°F...........................................................................................................103
5.16 Case 1: Methane/Nitrogen/CO2 10/40/50 Feed Gas Adsorption on Wet
Tiffany Coal at 130°F .....................................................................................104
5.17 Case 1: Comparison of the Regressed and Generalized SLD-PR
Binary Interaction Parameters.........................................................................107
5.18 Deviations Plot for SLD-PR Model Generalization of Mixed-Gas
Adsorption on Wet OSU Coals.......................................................................112
A.1 Flowchart for the SLD-PR Model..................................................................127
A.2 Overview of the SLD-PR Model ...................................................................128
B.1 Scenario 2: Representation of Pure-Gas Adsorption on Dry Illinois #6
Coal at 131°F .................................................................................................132
B.2 Scenario 2: Representation of Pure-Gas Adsorption on Dry Beulah Zap
Coal at 131°F .................................................................................................132
B.3 Scenario 2: Representation of Pure-Gas Adsorption on Dry Wyodak
Coal at 131°F .................................................................................................133
B.4 Scenario 2: Representation of Pure-Gas Adsorption on Dry Upper
Freeport Coal at 131°F .................................................................................133
B.5 Scenario 2: Representation of Pure-Gas Adsorption on Dry Pocahontas
Coal at 131°F .................................................................................................134
B.6 Scenario 2: Representation of Pure-Gas Adsorption on Wet Illinois #6
Coal at 115°F .................................................................................................134
B.7 Scenario 2: Representation of Pure-Gas Adsorption on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................135
B.8 Scenario 2: Representation of Pure-Gas Adsorption on Wet Fruitland
OSU #2 Coal at 115°F ...................................................................................135
xvii
Figure Page
B.9 Scenario 2: Representation of Pure-Gas Adsorption on Wet Tiffany
Coal at 130°F .................................................................................................136
B.10 Scenario 2: Representation of Pure-Gas Adsorption on Wet Lower
Basin Fruitland Coal at 115°F .......................................................................136
C.1 Case 2: Methane Adsorption in Methane/Nitrogen Mixtures on Wet
Illinois #6 Coal at 115°F................................................................................150
C.2 Case 2: Nitrogen Adsorption in Methane/Nitrogen Mixtures on Wet
Illinois #6 Coal at 115°F................................................................................150
C.3 Case 2: Methane Adsorption in Methane/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................151
C.4 Case 2: CO2 Adsorption in Methane/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................151
C.5 Case 2: Nitrogen Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................152
C.6 Case 2: CO2 Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................152
C.7 Case 2: Methane Adsorption in Methane/Nitrogen Mixtures on Wet
Fruitland OSU #1 Coal at 115°F....................................................................153
C.8 Case 2: Nitrogen Adsorption in Methane/Nitrogen Mixtures on Wet
Fruitland OSU #1 Coal at 115°F....................................................................153
C.9 Case 2: Methane Adsorption in Methane/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................154
C.10 Case 2: CO2 Adsorption in Methane/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................154
C.11 Case 2: Nitrogen Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................155
C.12 Case 2: CO2 Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................155
C.13 Case 2: Methane/Nitrogen 50/50 Feed Gas Adsorption on Wet Tiffany
Coal at 130°F .................................................................................................156
xviii
Figure Page
C.14 Case 2: Methane/CO2 41/59 Feed Gas Adsorption on Wet Tiffany Coal
at 130°F..........................................................................................................156
C.15 Case 2: Nitrogen/CO2 20/80 Feed Gas Adsorption on Wet Tiffany Coal
at 130°F..........................................................................................................157
C.16 Case 2: Methane/Nitrogen/CO2 10/40/50 Feed Gas Adsorption on Wet
Tiffany Coal at 130°F .....................................................................................157
C.17 Case 2: Comparison of the Regressed and Generalized SLD-PR
Binary Interaction Parameters........................................................................158
C.18 Case 3: Methane Adsorption in Methane/Nitrogen Mixtures on Wet
Illinois #6 Coal at 115°F................................................................................165
C.19 Case 3: Nitrogen Adsorption in Methane/Nitrogen Mixtures on Wet
Illinois #6 Coal at 115°F................................................................................165
C.20 Case 3: Methane Adsorption in Methane/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................166
C.21 Case 3: CO2 Adsorption in Methane/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................166
C.22 Case 3: Nitrogen Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................167
C.23 Case 3: CO2 Adsorption in Nitrogen/CO2 Mixtures on Wet Illinois #6
Coal at 115°F .................................................................................................167
C.24 Case 3: Methane Adsorption in Methane/Nitrogen Mixtures on Wet
Fruitland OSU #1 Coal at 115°F....................................................................168
C.25 Case 3: Nitrogen Adsorption in Methane/Nitrogen Mixtures on Wet
Fruitland OSU #1 Coal at 115°F....................................................................168
C.26 Case 3: Methane Adsorption in Methane/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................169
C.27 Case 3: CO2 Adsorption in Methane/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................169
C.28 Case 3: Nitrogen Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................170
xix
Figure Page
C.29 Case 3: CO2 Adsorption in Nitrogen/CO2 Mixtures on Wet Fruitland
OSU #1 Coal at 115°F ...................................................................................170
C.30 Case 3: Methane/Nitrogen 50/50 Feed Gas Adsorption on Wet Tiffany
Coal at 130°F .................................................................................................171
C.31 Case 3: Methane/CO2 41/59 Feed Gas Adsorption on Wet Tiffany Coal
at 130°F..........................................................................................................171
C.32 Case 3: Nitrogen/CO2 20/80 Feed Gas Adsorption on Wet Tiffany Coal
at 130°F..........................................................................................................172
C.33 Case 3: Methane/Nitrogen/CO2 10/40/50 Feed Gas Adsorption on Wet
Tiffany Coal at 130°F ....................................................................................172
C.34 Case 3: Comparison of the Regressed and Generalized SLD-PR
Binary Interaction Parameters........................................................................173
xx
NOMENCLATURE
A surface area
a Peng-Robinson attractive parameter
aads local Peng-Robinson attractive parameter for adsorbed phase
%AAD average absolute deviation
b Peng-Robinson covolume
Car percentage carbon in basis of moisture and ash free
bads modified Peng-Robinson covolume for adsorbed phase
Cij binary interaction parameter for species i and j
C1-C3 Mathias Copeman Expression constants
f fugacity
F Fahrenheit
FC percentage fixed carbon
i dummy index
k Boltzmann constant
K Kelvin
L slit width; defined as the normal distance between the carbon planes
n amount of adsorption
xxi
NA Avogadro’s number
NC number of component
nEx amount of excess adsorption
NPTS number of data points
P pressure
psia pounds per square inch absolute
Q objective function for equilibrium criterion
R universal gas constant
RMSE root mean square error
T temperature
Vvoid void volume
W objective function for mass balance
WAAD weighted average absolute deviation
WRMS weighted root mean square
xi composition of species i in the adsorbed phase
Y coal or adsorbing fluid property
yi composition of species i in the bulk phase
Z compressibility factor
zi composition of species i in the feed gas
z normal position between carbon planes
z' dummy position variable: z' = z + 3sff/8
xxii
Subscripts and Superscripts
CH4@400 Methane at 400 psia
N2@400 Nitrogen at 400 psia
CO2@400 CO2 at 400 psia
ads adsorbed-phase property
bulk bulk phase
C critical condition
calc calculated
Ex excess
ff fluid-fluid interaction
fs fluid-solid interaction
gas gas phase
Gibbs Gibbsian adsorption quantity
He Helium
i component “i”
k Iteration number in Newton-Raphson method
LCL local
reg regressed
ss solid-solid interaction
tot total
0 reference state
xxiii
Greek
a(T) temperature dependent function for Peng-Robinson EOS
D difference
e interaction parameter
Lb Peng-Robinson EOS covolume “b” correction
μ chemical potential
r density
<r> average adsorbed-phase density
ratoms carbon density
s molecular diameter
sexp expected experimental uncertainty
number of regions divided in the slit interval
Y fluid-solid potential function
<xi> total adsorbed mole fraction of component “i”
C carbon weight fraction (%carbon / 100) in basis of moisture and ash free
M equilibrium moisture weight fraction
FC fixed carbon weight fraction
qVol volatile matter weight fraction
Abbreviation
FR Fruitland coal
LB FR Lower Basin Fruitland
1
CHAPTER 1
INTRODUCTION
A reliable energy supply is essential for our modern lifestyle. The current energy
supply relies to varying degrees on fossil fuels (oil, natural gas and coal), nuclear, bio-fuels,
hydropower, solar, and wind energy. Among these sources, the fossil fuels provide
more than 85% of all the energy consumed in the United States, including two-thirds of
the electricity and all of the transportation needs [1].
In the year 2000, natural gas provided 24% of the energy consumed in the United
States [2]. As such, it is a vital component of the Nation’s energy portfolio. Natural gas,
primarily composed of methane, is a cleaner fuel than coal and oil. Unlike coal and oil,
natural gas produces very small amounts of greenhouse gases (nitrogen oxides, sulfur
dioxide and others) during combustion. In contrast, the combustion products of coal and
oil consist of significant amounts of methane, nitrogen oxides and sulfur dioxide. These
are harmful products that are emitted into the atmosphere [3]. Hence, natural gas
represents a relatively clean supply of energy.
The current estimate of natural gas reserves in the United States is 1,279 Tcf
(trillion cubic feet) according to the Energy Information Administration (EIA), 1,451 Tcf
according to the National Petroleum Council (NPC) and 1,127 Tcf according to the
Potential Gas Committee (PGC). This estimated amount can last over 75 years based on
the current consumption rate [4].
2
Coalbed methane (CBM) is one of the unconventional forms of natural gas. It
represents a source for a large amount of methane that resides in coal seams as an
adsorbed gas on the surface of the coal. A good portion of this CBM gas can be
recovered and used for power generation and other applications. According to the United
States Geological Survey [5], the proven reserves of CBM are more than 700 Tcf, and
over 100 Tcf of this gas is economically recovered. This corresponds to 7.5% of the U.S.
natural gas production [5].
The primary approach to recover methane from coal seams is to depressurize the
coalbed by pumping the water out of the reservoirs. In the coalbed, methane resides on
the surface of the coal surrounded by water. Pumping water out of the reservoir
decreases the pressure within the coalbed; hence, methane is released from the coalbed
and is transported to processing facilities through pipelines. However, some solid
residues are also produced when water is pumped out of the coal; this raises
environmental issues concerning the disposal of water [5].
Further, to improve the recovery rates of this valuable resource, enhanced coalbed
methane (ECBM) recovery methods have been developed. These methods rely mainly
on nitrogen (N2), carbon dioxide (CO2) and/or their mixtures injected into coal seams.
Upon injection, the CO2 replaces the adsorbed methane on the coal matrix, and methane
is released. Two to three molecules of CO2 are adsorbed for each molecule of methane
released [6, 7].
Alternatively, methane can also be released by injecting the nitrogen into the coal.
Injected nitrogen is not highly adsorbed by the coal, which results in rapid breakthrough
3
of nitrogen in the recovered natural gas. This requires a separation process after recovery,
which increases the cost of production of coalbed methane [8].
Beyond the energy benefits derived from injecting CO2 in coals, such injections
may have a potential environmental benefit. CO2 is one the greenhouse gases that may
contribute to global warming. In 2005, the CO2 emissions in the United States were
6,008 million metric ton, which represents 84% of the total greenhouse gas emissions [9].
The Energy Information Administration reports that 98% of the CO2 emissions originated
from the combustion of fossil fuels [9]. Many researchers in the field have determined
that the presence of such a large quantity of CO2 in the atmosphere is a major contributor
to the rise of the global surface temperature. As such, sequestrating CO2 in coal seams
represents a promising strategy for reducing CO2 emissions, and thus, reducing its effect
on the climate.
To realize the full potential of CBM gas production and CO2 sequestration,
reliable equilibrium adsorption models are required to develop effective processes. Such
models should be capable of:
1. Representing precisely high-pressure pure-gas adsorption
2. Facilitating generalized predictions of pure-gas adsorption based on accessible
adsorbent and adsorbate characterization
3. Predicting mixed-gas adsorption based on pure-gas isotherms
4. Accounting for the presence of moisture in the coal, since the coalbed usually
contains water
Different models with various theoretical underpinnings have been applied to
describe the adsorption behaviors of CBM gases. These include the Langmuir equation
4
[10], Brunauer-Emmett-Teller (BET) model [11], Ideal Adsorbed Solution (IAS) theory
[12], Two-Dimensional equation of states (2-D EOS) [13, 14], the Ono-Kondo Lattice
model [15-17] and Simplified Local-Density model [18-22]. Most of these adsorption
models work well for low pressures systems; however, fewer are capable of describing
high-pressure adsorption adequately.
The Langmuir model was developed in 1918. This model describes the dynamic
equilibrium between the rates of adsorption and desorption of a gas on a solid adsorbent
[10]. Although this model is restricted to monolayer coverage, it is still applied widely
because of its simplicity and ability to represent low-pressure adsorption behavior. The
BET model, developed in 1938, is an extension of the Langmuir model which accounts
for multilayer adsorption [11]. The Ideal Adsorbed Solution (IAS) model is an
adsorption equilibrium analog to Raoult’s law, and it is applied to determine multi-component
adsorption equilibria based on pure-component adsorption data [12].
Recently at Oklahoma State University (OSU), the 2-D EOS, the Ono-Kondo
lattice and the simplified local-density models have been developed further to represent
and predict the adsorption of CBM gases. The 2-D EOS is an analog to 3-D EOS, which
has been implemented successfully for supercritical fluid adsorption on various matrices
[13]. More recently, Pan and coworkers [14] developed temperature relations for the 2-D
Peng-Robinson (PR) EOS to facilitate precise representation and predictions of high
pressure, supercritical pure-gas adsorption.
The Ono-Kondo lattice theory was developed in 1960 [15]. This model is based
on the lattice theory, which aims to describe the monolayer and multilayer adsorption.
Sudibandriyo [16] further developed the Ono-Kondo (OK) for high-pressure gas
5
adsorption and presented a strategy for generalizing the OK model parameters as they
apply to CBM systems. More recently, Arumugam [16, 17] implemented and further
refined these model generalizations for CBM gas adsorption on dry Argonne premium
coals.
The simplified local-density (SLD) model describes adsorption behavior using
fluid-fluid and fluid-solid interactions. The model delineates the adsorbent structural
properties with an assumed physical geometry of the adsorbent. It was first developed by
Rangarajan [18], who used the van der Waals EOS to provide the fluid-fluid interaction
information. Nevertheless, the SLD model can be applied with various EOSs capable of
describing the fluid-fluid interactions. Over the years, researchers have used different
equations, including the Peng-Robinson, Bender and Elliot-Suresh-Donohue EOSs to
provide fluid-fluid interaction information [19-22].
Recently, Fitzgerald [23] applied the SLD model with a modified PR EOS to
represent precisely the high-pressure adsorption of CO2, nitrogen, methane, and ethane
and their mixtures on dry and wet coals and activated carbons. Careful evaluations of the
model revealed several distinct advantages, including the ability to:
1. Correlate pure-gas adsorption on dry and wet coals within the expected
experimental uncertainties
2. Extend pure-gas adsorption to multi-component gas prediction using
appropriate mixing rules
3. Facilitate viable model parameter generalizations based on adsorbent
characteristics and gas properties
6
As such, the SLD-PR model provides a suitable framework for developing generalized
models for the prediction of CBM gas adsorption on wet coals.
Objectives
The purpose of this study is to develop the generalized correlations for the
modified SLD-PR model parameters. The goal is to render the SLD framework capable
of providing reliable predictions for the equilibrium adsorption of CO2, methane, nitrogen
and their mixtures on dry and wet coals in the range of conditions encountered in CBM
production and CO2 sequestration. The specific objectives of this study are to:
• Correlate precisely the CO2, methane and nitrogen adsorption on dry and wet
coals using the modified SLD-PR model
• Evaluate the quality of the representations of the modified SLD-PR model for
pure-gas adsorption
• Generalize the modified model parameters in terms of accessible coal
characterizations and fluid properties
• Extend the model generalization to binary and ternary gas adsorption on wet
coals based on pure-gas adsorption generalizations and, when needed,
generalized the binary interaction parameters
Organization
In this thesis, Chapter 2 provides an overview of the modified SLD-PR model. In
Chapter 3, the modified SLD-PR model representations of pure-gas adsorption are
evaluated. Chapter 4 presents the SLD-PR parameter generalization for pure-gas
7
adsorption and assesses the quality of pure-gas adsorption predictions. Chapter 5
describes methods used to extend the SLD-PR generalizations to mixed-gas adsorption
and examines the predictive capability of the generalized model for binary and ternary
mixtures. Chapter 6 presents the conclusions and recommendations of this study.
8
CHAPTER 2
SIMPLIFIED LOCAL-DENSITY MODEL
The Simplified local-density (SLD) model has been found capable of describing
the adsorption behavior of gases encountered in CBM production and CO2 sequestration.
This model superimposes the fluid-solid potential on a fluid equation of state to predict
the adsorption of supercritical fluids on a flat wall [18, 24].
For the slit geometry, the SLD model assumes the adsorbate molecules reside
between two-surface slit, as shown in Figure 2.1 [22]. The distance between surfaces is
L, and the position of a molecule within the slit is z. The position, z, is orthogonal to
surface of solid which is formed by carbon atoms. Within the slit, the adsorbate molecule
interacts with both the slit surfaces and the fluid molecules in the bulk gas.
Gas Solid Surface Molecule in Slit
z L - z
Figure 2.1 – SLD Model Slit Geometry
9
A number of assumptions have been made in developing the SLD model [18]:
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
fluid-fluid and fluid-solid interactions.
3. The attractive potential between fluid and solid is independent of the
number of molecules at and around the point.
Hence, at equilibrium, the chemical potential of the fluid, μ, is expressed as the sum of
the fluid-fluid and fluid-solid potentials as follows:
ff fs bulk μ(z) = μ (z) + μ (z) = μ (2-1)
where subscript “bulk” refers to bulk fluid, “ff” refers to fluid-fluid interactions, and “fs”
signify fluid-solid interaction.
The chemical potential of the bulk fluid is typically expressed in terms of fugacity
as:
= +
0
bulk
bulk 0 f
f
μ μ (T) RTln (2-2)
where subscript “0” designates the reference state and “f” refers to fugacity. Similarly,
the chemical potential from fluid-fluid interactions is:
= +
0
ff
ff 0 f
f (z)
μ (z) μ (T) RTln (2-3)
where “fff (z)” is fluid fugacity at a position z.
The fluid-solid interactions are accounted for through the potential energy
function. As such, the fluid-solid chemical potential is given as:
10
μ (z) N [ (z) (L - z)] fs fs
fs A = Y + Y (2-4)
where “NA” is Avogadro’s number, “ (z)” and “ (L-z)” are the fluid-solid interactions
for two-surface slits with the distance L.
Substituting Equations (2-2), (2-3) and (2-4) into Equation (2-1), one gets the
equilibrium relationship adsorption within the slit:
+ −
= −
kT
(z) (L z)
f (z) f exp
fs fs
ff bulk (2-5)
Typically, a van der Waals-type equation of state such as the Peng-Robinson [25]
equation and an integrated potential function (e.g., 10-4 Lennard-Jones model) are used
to determine the fluid-fluid and fluid-solid chemical contributions.
The SLD model is a simplification of local-density theory. According to this
theory, the density profile is obtained by minimizing the total energy functional, which
depends on all point densities and their spatial derivatives [26]. The term “local” refers
to the thermodynamics properties of a fluid at any local point z, where an average single
density value is calculated, r(z) [18]. In addition, the SLD model assumes a mean-field
theory in calculating the chemical potential. The mean-field theory replaces all
interactions with an effective or average interaction so that no fluctuations are considered
within the slit. Hence, the chemical potential of the fluid at each point is corrected for the
proximity of the fluid molecule to the molecular wall of the adsorbents [23].
Applying the SLD model, the excess adsorption (nEx) is given as:
= ( ( )− )
Right Side of Slit
Left Side of Slit
bulk
Ex z dz
2
A
n (2-6)
Here, nEx is the excess adsorption of adsorbate in number of moles per unit mass of
11
adsorbent, and “A” is the surface area of the adsorbate on particular solid. The lower
limit in Equation (2-6) is 3 ff/8, which is 3/8 of an adsorbed molecule touching the left
plane surface. The upper limit is L-3 ff/8, the location of an adsorbed molecule touching
right plane surface. The local density is assumed to be zero for the distance less than
3 ff/8 away from the wall. The value 3 ff/8 is chosen to account for most of the adsorbed
gas; details are given elsewhere by Fitzgerald [6]. The left and right sides of the slit each
comprise half of the total surface area, A/2.
Following previous studies at OSU [23], the Peng-Robinson equation of state (PR
EOS) is used to provide the bulk fluid fugacity and the fluid fugacity. The
compressibility factor, expressed in terms of density, is given as:
( ) RT [1 (1 2 ) b ][1 (1 2 ) b ]
a(T)
1 b
1
RT
P
+ − + +
−
−
= (2-7)
where
( )
( )
C
2
C
2
P
0.457535
T R T
a T = (2-8)
C
C
P
0.077796RT
b = (2-9)
The term,
(T) in Equation (2-8) is calculated using the Mathias-Copeman expression.
2
3
C
3
2
C
2
C
1 T
T
C 1
T
T
C 1
T
T
(T) 1 C 1
− +
− +
= + − (2-10)
12
The regressed coefficients, C1-C3 [27] along with the gas physical properties, are given in
the Table 2.1.
Table 2.1 – Fluid Physical Properties [27, 28]
Nitrogen Methane CO2
TC (K) 126.19 190.56 304.13
PC (MPa) 3.396 4.599 7.377
ff (nm) 0.3798 0.3758 0.3941
eff/k (K) 71.4 148.6 195.2
C1 0.43694 0.41108 0.71369
C2 -0.07912 -0.14020 -0.44764
C3 0.32185 0.27998 2.43752
The fugacity of a bulk fluid calculated using PR EOS, where:
( 2 2 )
bulk
RT 1 2b - b
a(T)
1 b
b
P
f
ln
+
−
−
=
+ − r
+ + r
−
−
r
−
1 (1 2) b
1 (1 2) b
ln
2 2bRT
a(T)
RT
Pb
RT
P
ln (2-11)
For adsorbing fluid, the fugacity for fluid-fluid interactions is as follows:
RT(1 2b (z) - b (z))
a (z) (z)
1 b (z)
b (z)
P
f (z)
ln 2 2
ff ads
+ r r
r
−
− r
r
=
+ − r
+ + r
−
−
r
−
1 (1 2) (z)b
1 (1 2) (z)b
ln
2 2bRT
a (z)
RT
Pb
RT (z)
P
ln ads (2-12)
The parameter “aads(z)” in Equation (2-12) varies with the position within the slit. Chen
et al. [22] provided the equations for “aads(z)” which depend on the ratio of slit width L to
the molecular diameter sff. Further details on these equations are given by Fitzgerald
[23].
13
Rearranging the equilibrium relationship given in Equation (2-6) yields the
working equation accounting for bulk, fluid-fluid and fluid-solid interactions:
Y + Y −
− =
kT
(z) (L z)
f
f [a (z), (z)]
ln
fs fs
bulk
ff ads (2-13)
In the previous studies [23, 29], Fitzgerald adjusted the covolume “b” in the PR
EOS to improve the predictive capability for adsorption of pure gases on activated carbon
and coals. The covolume has significant effect on the local density of the adsorbed fluid,
especially near the surface. In addition, the covolume is important in determining the
density profile at high pressures. Thus, a simple empirical correction was used to account
for the repulsive interactions of adsorbed fluid at high pressures. The covolume is
corrected by an adjustable parameter, Lb:
( ) ads b b = b 1+ (2-14)
Equation (2-12) then becomes:
[ 2 2 ]
ads ads
ads
ads
ff ads
RT 1 2b (z) b (z)
a (z) (z)
1 b (z)
b (z)
P
f (z)
ln
+ −
−
−
=
+ − r
+ + r
−
r
− r
−
ads
ads
ads
ads ads
1 (1 2) (z)b
1 (1 2) (z)b
ln
2 2b RT
a (z)
RT (z)
1 b (z)
ln (2-15)
The fluid-solid interaction, fs(z), is represented by Lee’s partially-integrated
Lennard-Jones 10-4 potential [30], the equation is shown below:
( )
+ − ×
= −
=
4
i 1
4
ss
4
fs
10
10
2 fs
atoms fs fs
fs
z' (i 1)
2
1
5(z')
(z) 4 (2-16)
fs ff ss = × (2-17)
where efs is the fluid-solid interaction energy parameter, and the ratoms = 0.382 atoms/Å2.
14
The parameters sff and sss signify, respectively, the molecular diameter of the adsorbate
and the carbon interplaner distances. The value of carbon interplaner is taken to be the
value of graphite, 0.335 nm [24], and values of sff and ff are taken from Reid [28]. The
fluid-solid molecular diameter, fs and dummy coordinate z’ are defined as:
2
ff ss
fs
+
= (2-18)
2
z' z ss = + (2-19)
In the bulk phase, the bulk fluid fugacity is calculated from the pressure and
temperature. For the adsorbed phase, the slit is divided into two halfs and each is
subdivided into 50 intervals. The local density is then calculated by solving the adsorbed
phase fugacity and equilibrium criterion (Equations (2-15) and (2-13), respectively)
simultaneously for each interval. Once the local density is determined across the slit, the
excess adsorption is calculated by integrating Equation (2-6) numerically using
Simpson’s Rule. The details of the calculation are discussed in Appendix A.
15
CHAPTER 3
REPRESENTATION OF PURE-GAS ADSORPTION
In previous studies at OSU, the Simplified Local-Density/Peng-Robinson (SLD-PR)
model with an adjusted PR covolume “b” was tested for its ability to correlate the
adsorption behavior on coals of interest. The model was found capable of correlating
adsorption data within the expected experimental uncertainties [23].
To correlate and predict the adsorption behavior on coals, the model requires
physical parameters which can characterize both the adsorbent and adsorbate. In the
modified SLD-PR model, all the adsorbates on a given adsorbent were analyzed
simultaneously; hence, a set of parameters for that adsorbent were regressed to correlate
to the respective adsorption data. These parameters are:
• A single value of surface area “A” for a given adsorbent applied to all
adsorbates
• A single value of slit length “L” for a given adsorbent to all adsorbates
• Fluid-solid interaction energy parameters “efs/k” for each adsorbate on a given
adsorbent
• Covolume correction “Lb” for each adsorbate
These parameters depend on either adsorbent or adsorbate; thus, attempts to generalize
the SLD-PR model parameters must account for adsorbent and adsorbate characteristics.
16
Model Development
The current study differs from the study described previously in that the surface
area and the fluid-solid interaction energy parameter are adjusted to obtain precise
representation of pure-gas adsorption. In the previous work, each adsorbent has a
specific value for the surface area (independent of the adsorbate) [23]. However, this
adsorbent-based surface area was not able to precisely quantify or differentiate the
amount of adsorption for each adsorbate. Therefore, in this study, each adsorbate is
allowed to have its own “accessible” surface area on a given adsorbent; thus, the
adsorption model is capable of providing a more precise correlation of the adsorption
data.
In addition, the solid-solid interaction energy parameter, ess/k, is regressed instead
of the fluid-solid interaction energy parameter, efs/k. The regressed fluid-solid interaction
energy for CO2 was found to be twice as large as those for methane and nitrogen [31, 32].
However, for some adsorbents used in this study, the regressed fluid-solid interaction
energy parameter for CO2 was more than three times larger than those for methane and
nitrogen and also greater than the value for CO2 on activated carbon. This discrepancy in
parameter values indicated that regressing directly the fluid-solid interaction energy
parameter is unreliable and a modification is required. In fact, beyond the empirical
evidence, separating the solid-solid and fluid-fluid interactions is advisable, since they
express two different types of interactions, of which the fluid-fluid interaction data are
available and the solid-solid interactions can be obtained by regression. The fluid-solid
interaction energy parameter is then described in the model as the geometric mean of the
17
fluid-fluid and solid-solid interaction energy parameter (eff/k and ess/k), as expressed in
Equation (2-17) [19, 32].
In this study, the fluid-fluid interaction parameter values are obtained from Reid
et al. [28], and the solid-solid interaction energy parameter is regressed from the
adsorption data to facilitate the development of generalized model(s) in terms of
adsorbent properties. As such, the solid-solid interaction energy parameter provides
specific information about the particular coal, independent of the type of adsorbate
involved.
For each adsorbent, the adsorption isotherms for different adsorbate gases are
correlated simultaneously to obtain single regressed values for the slit length and the
solid-solid interaction energy parameter. Therefore, the parameters regressed for each
adsorbent are:
• A separate surface area for each adsorbate
• Slit length
• Solid-solid interaction energy parameter “ess/k”
• A covolume correction “Lb” for each adsorbate
As such, for each adsorbent, there are a total of (2N +2) parameters, where N is the
number of adsorbates.
During the model parameter regressions, three different scenarios examining the
effect of the covolume correction and the slit length were investigated:
Scenario 1: All model parameters were regressed (2N + 2 parameters)
18
Scenario 2: Surface areas of all adsorbates, the solid-solid interaction energy
parameter and the slit length were regressed after fixing the
covolume correction “Lb” at a value of -0.20 (N + 3 parameters)
Scenario 3: In addition to Scenario 2, the slit length is fixed at 1.15 nm, and the
surface area for each adsorbate and the solid-solid interaction
energy parameters were regressed (N + 2 parameters)
The -0.20 value of the covolume correction used in Scenarios 2 and 3 was
established based on the results obtained in Scenario 1. This correction produced a
precise correlation for the experimental data considered. The slit length of 1.15 nm used
in Scenario 3 was the average value of the regressed slit lengths obtained in Scenario 2.
Database Employed in this Study
Experimental measurements were conducted at Oklahoma State University on ten
solid matrices, which include the following [17, 23]:
a) Pure methane, nitrogen and CO2 adsorption on dry Illinois #6, dry Beulah
Zap, dry Wyodak, dry Upper Freeport and dry Pocahontas coals
b) Pure methane, nitrogen and CO2 adsorption on the wet Illinois #6, wet
Fruitland OSU #1, wet Fruitland OSU #2, wet Lower Basin Fruitland, Wet
Tiffany coals
Coals listed in (a) were prepared by Argonne National Laboratory (Argonne
premium coals) and the respective isotherms were measured at 328.15K (131°F) and
pressures to 13.7 MPa (2000 psia). The measurements on the Fruitland OSU #1 and #2,
Lower Basin Fruitland and Ilinois #6 coals in category (b) were at 319.3K (115°F) and
19
pressures to 12.4 MPa (1800 psia) while the experiments on the Tiffany coal were
measured at 328.15K (131°F) and pressures to 12.4 MPa (2000 psia). These five coals
were classified as OSU coals to differentiate them from coals prepared by Argonne
National Laboratory.
The pure-gas adsorption database on dry Argonne premium coals and wet OSU
coals are presented in Tables 3.1 and 3.2, respectively. In the tables, the system number,
adsorbent, adsorbate, number of data points (NTPS), temperature and pressure ranges are
given.
Table 3.1 – Pure-Gas Adsorption Database Used in this Study:
Argonne Premium Coals
System
No.
Adsorbent Adsorbate NPTS
Temp
(K)
Pressure
Range
(MPa)
1 Dry Illinois #6 N2 16 328 0.7 – 13.7
2 Dry Illinois #6 CH4 15 328 0.7 – 13.7
3 Dry Illinois #6 CO2 22 328 0.7 – 13.7
4 Dry Beulah Zap N2 15 328 0.7 – 13.7
5 Dry Beulah Zap CH4 14 328 0.7 – 13.7
6 Dry Beulah Zap CO2 33 328 0.7 – 13.7
7 Dry Wyodak N2 14 328 0.7 – 13.7
8 Dry Wyodak CH4 14 328 0.7 – 13.7
9 Dry Wyodak CO2 22 328 0.7 – 13.7
10 Dry Upper Freeport N2 14 328 0.7 – 13.7
11 Dry Upper Freeport CH4 14 328 0.7 – 13.7
12 Dry Upper Freeport CO2 22 328 0.7 – 13.7
13 Dry Pocahontas N2 14 328 0.7 – 13.7
14 Dry Pocahontas CH4 14 328 0.7 – 13.7
15 Dry Pocahontas CO2 22 328 0.7 – 13.7
20
Table 3.2 – Pure-Gas Adsorption Database Used in this Study: OSU Coals
System
No.
Adsorbent Adsorbate NPTS
Temp
(K)
Pressure
Range
(MPa)
16 Wet Illinois #6 N2 20 319 0.7 – 12.4
17 Wet Illinois #6 CH4 20 319 0.7 – 12.4
18 Wet Illinois #6 CO2 30 319 0.7 – 12.4
19 Wet Fruitland OSU #1 N2 20 319 0.7 – 12.4
20 Wet Fruitland OSU #1 CH4 20 319 0.7 – 12.4
21 Wet Fruitland OSU #1 CO2 14 319 0.7 – 12.4
22 Wet Fruitland OSU #2 N2 37 319 0.7 – 12.4
23 Wet Fruitland OSU #2 CH4 20 319 0.7 – 12.4
24 Wet Fruitland OSU #2 CO2 38 319 0.7 – 12.4
25 Wet Tiffany N2 21 328 0.7 – 13.7
26 Wet Tiffany CH4 34 328 0.7 – 13.7
27 Wet Tiffany CO2 16 328 0.7 – 13.7
28 Wet LB Fruitland N2 17 319 0.7 – 12.4
29 Wet LB Fruitland CH4 16 319 0.7 – 12.4
30 Wet LB Fruitland CO2 48 319 0.7 – 12.4
Tables 3.3 and 3.4 give the compositional analyses of the OSU and Argonne
premium coals, respectively [23]. For the OSU coals, Illinois #6 is a highly volatile
bituminous coal. The Fruitland OSU #1 and #2 have different compositions; they are
both medium volatile bituminous coals from the San Juan Basin. The Lower Basin
Fruitland (#3a and #3b) is from the same coal seam as Fruitland OSU #1 and #2, but it
was taken from a different location. The Tiffany is the BP Amoco Tiffany Well #1 and
#10. These coals are moistened with water from 4 to 15% by weight, which is above the
equilibrium moisture content of all these coals [23]. From Table 3.3, the increasing order
in the percent carbon on a moisture and ash-free basis is as follows for these coals: Lower
Basin Fruitland, Tiffany, Fruitland OSU #2, Fruitland OSU #1, and Illinois #6. The
increasing order in percent fixed carbon for these coals is: Lower Basin Fruitland,
Tiffany, Illinois #6, Fruitland OSU #2 and Fruitland OSU #1.
21
Table 3.3 – Compositional Analysis of OSU Coals Used in this Study
Analysis*
Fruitland
OSU #1
Fruitland
OSU #2
Illinois #6
Lower Basin
Fruitland
OSU #3a
Lower Basin
Fruitland
OSU #3b
Tiffany
Well #1
Tiffany
Well #10
Ultimate
Carbon % 68.63 66.58 71.47 38.92 40.20 47.78 56.75
Hydrogen % 4.27 4.23 5.13 3.08 3.10 2.62 2.77
Oxygen % 0.89 5.08 9.85 3.75 2.87 6.19 5.16
Nitrogen % 1.57 1.47 1.46 0.87 0.89 0.92 1.02
Sulfur % 4.19 0.72 1.27 1.73 2.14 0.57 0.52
Ash % 20.45 21.92 10.81 51.66 50.81 49.71 47.74
Proximate
Vol. Matter % 20.20 20.33 30.61 20.01 14.00 15.48 15.35
Fixed Carbon % 59.35 57.75 55.90 28.33 35.19 34.82 36.91
Moisture % 2.20 2.20 3.90 4.00 4.00 3.80 3.70
* Huffman Laboratories, Inc., Golden, Colorado.
22
The percent carbon and percent fixed carbon of these coals range from 38.0 to
69.0% and 28.0 to 60.0%, respectively. The percentage volatile matter of these coals
ranges from 14.0 to 30.0%. The largest percent volatile matter is observed for the Illinois
#6 coal, followed by Fruitland OSU #2 and #1 coals. The Tiffany and Lower Basin
Fruitland coals have the smaller percentage of volatile matter. Regarding the equilibrium
moisture content, the Lower Basin Fruitland has the largest percentage of 4.0%, followed
by Illinois #6 and Tiffany coals, which have 3.9% and 3.75%, respectively. The
Fruitland OSU #1 and #2 coals have the lowest equilibrium moisture content of 2.2%.
Table 3.4 - Compositional Analysis of Argonne Premium Coals Used in this Study
Analysis* Beulah Zap Wyodak Illinois #6
Upper
Freeport
Pocahontas
Ultimate
Carbon % 72.9 75.00 77.70 85.50 91.10
Hydrogen % 4.83 5.35 5.00 4.70 4.44
Oxygen % 20.30 18.00 13.50 7.50 2.50
Sulfur % 0.80 0.63 4.83 2.32 0.66
Ash % 9.70 8.80 15.50 13.20 4.80
Proximate
Moisture % 32.20 28.10 8.00 1.10 0.70
Vol. Matter % 30.50 32.20 36.90 27.10 18.50
Fixed Carbon % 30.70 33.00 40.90 58.70 76.10
Ash % 6.60 6.30 14.30 13.00 4.70
* Argonne National Laboratory
Among the Argonne premium coals, Beulah Zap is a lignite coal while Wyodak is
a sub-bituminous coal. The Illinois #6, Upper Freeport and Pocahontas are high, medium
and low volatile bituminous coals, respectively. As mentioned previously, these coals are
prepared by Argonne National Laboratory, and the compositional ultimate and proximate
analyses are also provided from this laboratory. The increasing order of percent carbon
23
(moisture and ash free) and fixed carbon of the Argonne premium coals is: Beulah Zap,
Wyodak, Illinois #6, Upper Freeport and Pocahontas. The range of the percent carbon
and fixed carbon is from 72.9% to 91.1% and 30.7% to 76.1%. The increasing order of
equilibrium moisture content of these coals is opposite to the order of percent carbon and
fixed carbon. The percentage for equilibrium moisture ranged from 0.7% to 32.2%. The
largest percent volatile matter was 36.9% for Illinois #6, which was followed by Wyodak,
Beulah Zap, Upper Freeport and Pocahontas at 32.2, 30.5, 27.1 and 18.5% [17]. The dry
samples for pure-gas adsorption were dried under vacuum at 80°C for 80 hours. The wet
samples for pure CO2 adsorption are “as-received” coals; which means the moisture
content for adsorption is the equilibrium moisture content.
The adsorption isotherms of pure methane, nitrogen and CO2 on the dry Argonne
premium and the wet OSU coals were used to evaluate the correlative abilities of the
modified SLD-PR model, and the model parameters were then generalized in terms of
gas and adsorbent characteristics.
Statistical Quantities Used in Data Reduction
The objective function used in the parameter regressions was the sum of the
squared weighted deviation (or the weighted root mean square deviation, WRMS):
NPTS
n n
WRMS
2
i
NPTS
i 1 exp
calc exp
=
−
= (3-1)
Here, NPTS is the number of data points, nexp is the experimental excess adsorption, ncalc
is the calculated excess adsorption and sexp is the expected experimental uncertainty. In
addition, the weighted average absolute deviation (WAAD), the average absolute
24
percentage deviation (%AAD) and the root mean square error (RMSE) were calculated to
assess the quality of the representations of the adsorption model, and are expressed as:
NPTS
n n
abs
WAAD i
NPTS
i 1 exp
calc exp
=
−
= (3-2)
100%
NPTS
n
n n
abs
%AAD i
NPTS
i 1 exp
calc exp
×
−
=
=
(3-3)
( )
NPTS
n n
RMSE
2
i
NPTS
i 1
calc exp
=
−
= (3-4)
Results and Discussions
The regression results for Scenarios 1, 2 and 3 are presented in Tables 3.5 to 3.7,
respectively, for dry Argonne premium coals and wet OSU coals. The information given
in the tables include the adsorbent, the adsorbate and the regressed parameters (surface
area for each adsorbate, solid-solid interaction energy parameter, slit length and
covolume correction of each adsorbate). The statistics described in Equations (3-1)
through (3-4) are also provided.
As illustrated in Table 3.5, full regression of all the model parameters (Scenario
1) provides representation of the adsorption data within the expected experimental
uncertainties. The overall %AAD is 3.2%, which also corresponds to an overall WAAD
of 0.40, RMSE of 0.03 mmol/g, and WRMS of 0.55. The WRMS is less than the
experimental uncertainty because the experimental uncertainties were taken to be twice
the amount obtained from the raw data reduction procedure.
25
Table 3.5 – Scenario 1: Modified SLD-PR Model Representations of Pure-Gas Adsorption on Dry and Wet Coals
Parameters
Coal Adsorbate Area
(m2/g)
ess/k
(K)
L (nm) Lb
WAAD %AAD
RMSE
(mmol/g)
WRMS
CH4 74.8 0.00
Dry Illinois #6 N2 52.8 0.01
CO2 119.2
29.8 1.88
0.13
0.36 2.5 0.02 0.45
CH4 48.8 -0.11
Dry Beulah Zap N2 33.0 -0.09
CO2 113.8
52.2 1.62
0.06
0.43 2.9 0.04 0.54
CH4 50.2 -0.16
Dry Wyodak N2 32.2 -0.30
CO2 109.3
47.5 1.74
0.02
0.68 3.1 0.05 0.96
CH4 54.6 -0.07
N2 37.1 -0.15
Dry Upper
Freeport
CO2 66.5
38.2 1.29
-0.02
0.30 1.5 0.01 0.42
CH4 73.8 -0.07
Dry Pocahontas N2 51.6 -0.12
CO2 83.8
36.7 1.22
-0.05
0.40 1.8 0.02 0.59
Statistic for Dry Coals 0.43 2.4 0.03 0.59
26
Table 3.5 – Scenario 1: Modified SLD-PR Model Representations of Pure-Gas Adsorption on Dry and Wet Coals
(Continued)
Parameters
Coal Adsorbate Area
(m2/g)
ess/k
(K)
L (nm) Lb
WAAD %AAD
RMSE
(mmol/g)
WRMS
CH4 31.4 -0.23
Wet Illinois #6 N2 17.4 -0.34
CO2 52.0
20.9 1.36
-0.12
0.26 3.9 0.04 0.39
CH4 66.3 -0.16
N2 49.4 -0.21
Wet Fruitland
OSU #1
CO2 70.6
22.2 1.11
-0.22
0.28 1.9 0.03 0.41
CH4 68.7 -0.15
N2 43.1 -0.18
Wet Fruitland
OSU #2
CO2 66.1
20.8 1.11
-0.22
0.47 4.8 0.06 0.66
CH4 37.5 -0.12
Wet Tiffany N2 24.3 -0.10
CO2 55.7
19.6 1.11
0.01
0.51 5.0 0.02 0.44
CH4 15.0 -0.42
N2 10.0 -0.43
Wet Lower Basin
Fruitland
CO2 29.1
30.1 1.20
-0.13
0.34 4.7 0.02 0.66
Statistics for Wet Coals 0.37 4.1 0.03 0.51
Overall Statistics for Coals 0.40 3.2 0.03 0.55
27
The largest %AAD (5.0%) and largest RMSE (0.06 mmol/g) are observed for
pure-gas adsorption on wet Tiffany and wet Fruitland OSU #2, respectively. The largest
WAAD (0.68) and WRMS (0.96) are observed for the pure-gas adsorption on dry
Wyodak coal. The results indicate that regressing separate surface areas for each
adsorbate along with the solid-solid interaction energy parameter produces adsorption
data representations for both dry Argonne premium coals and wet OSU coals within the
expected experimental uncertainties.
As expected, the amount of CO2 adsorbed is higher than the amount of methane
and nitrogen adsorbed on all coals. Hence, the regressed surface area of CO2 is greater
than that of methane and that of nitrogen and the average surface area ratio of methane to
CO2 and nitrogen to CO2 is 0.66 and 0.47, respectively.
The average %AAD of the representations for wet OSU coals (4.1%) is larger
than that for dry Argonne coals (2.4%); however, larger experimental uncertainties are
estimated for the wet OSU coals than for the dry Argonne coals resulting in more precise
representation of pure-gas adsorption for the wet OSU coals compared to those for dry
Argonne coals. The respective WAAD is 0.37 and 0.41 for the OSU and Argonne coals,
respectively. The slit length of the dry Argonne coals is larger than that of the wet OSU
coals, and the new model parameter, ess/k, of the dry Argonne coals is larger than that of
wet OSU coals. The regressed covolume corrections for the dry Argonne coals are small
numbers that have a minor effect on the adsorbed-phase density.
Appendix B.1 presents the regression results for the SLD-PR model
representation when no covolume corrections are applied (Lb = 0) to the dry coals. In
comparison with the results given above that involved a covolume correction, a
28
significant difference in the results is not observed, which indicates that covolume
correction is not required for the dry Argonne coals. In contrast, the regressed covolume
corrections for the wet OSU coal are relatively large numbers, which have a significant
effect on the adsorbed-phase densities. Further, they affect the quality of the
representations. Therefore, the covolume corrections are required for modeling the
adsorption on wet OSU coals.
Table 3.6 documents the regression results for Scenario 2. The overall error for
the combined dry Argonne and wet OSU coals is 3.9 %AAD, with a WAAD of 0.50,
RMSE of 0.04 mmol/g and WRMS of 0.70. The largest average %AAD (5.6%) and
RMSE (0.06 mmol/g) are observed for the pure-gas adsorption on wet Lower Basin
Fruitland and wet Fruitland OSU #2 coals, respectively.
Pure-gas adsorption on the Wyodak coal has the largest WAAD and WRMS, 0.80
and 1.25, respectively. As shown in Table 3.6, the deviations for the dry coals have
increased significantly compared to that for Scenario 1. This is due to the value of -0.20
for the covolume corrections is too big for the dry coals (see individual Lb values in
Table 3.5). For wet coals, there is no significant increase in the deviations because the
correction value of -0.20, chosen based on the results of Scenario 1, is closer to the
average of the regressed values. Nevertheless, on average, the modified SLD-PR model
can represent the adsorption data within experimental uncertainties for the regression
including the fixed covolume correction of -0.20.
29
Table 3.6 – Scenario 2: Modified SLD-PR Model Representations of Pure-Gas Adsorption on Dry and Wet Coals
Parameters
Coal Adsorbate Area
(m2/g)
ess/k
(K)
L (nm)
Lb
(fixed)
WAAD %AAD
RMSE
(mmol/g)
WRMS
CH4 61.5
Dry Illinois #6 N2 45.5
CO2 77.5
30.4 1.34 -0.2 0.67 4.6 0.06 0.92
CH4 50.4
Dry Beulah Zap N2 35.7
CO2 92.8
37.7 1.30 -0.2 0.63 3.9 0.04 0.83
CH4 57.9
Dry Wyodak N2 45.2
CO2 96.4
31.6 1.32 -0.2 0.80 3.5 0.05 1.25
CH4 47.6
N2 36.0
Dry Upper
Freeport
CO2 54.1
37.5 1.18 -0.2 0.39 2.1 0.02 0.54
CH4 63.6
Dry Pocahontas N2 47.9
CO2 69.4
37.2 1.15 -0.2 0.46 2.2 0.03 0.68
Statistic for Dry Coals 0.59 3.3 0.04 0.84
30
Table 3.6 – Scenario 2: Modified SLD-PR Model Representations of Pure-Gas Adsorption on Dry and Wet Coals
(Continued)
Parameters
Coal Adsorbate Area
(m2/g)
ess/k
(K)
L (nm)
Lb
(fixed)
WAAD %AAD
RMSE
(mmol/g)
WRMS
CH4 34.2
Wet Illinois #6 N2 20.6
CO2 47.9
19.4 1.27 -0.2 0.28 4.4 0.04 0.41
CH4 62.5
N2 49.0
Wet Fruitland
OSU #1
CO2 72.0
22.9 1.11 -0.2 0.30 2.1 0.03 0.42
CH4 62.3
N2 40.7
Wet Fruitland
OSU #2
CO2 65.9
22.1 1.13 -0.2 0.48 4.9 0.06 0.66
CH4 39.5
Wet Tiffany N2 25.7
CO2 51.1
16.7 0.91 -0.2 0.57 5.4 0.02 0.74
CH4 26.9
N2 16.7
Wet Lower Basin
Fruitland
CO2 32.2
19.1 1.08 -0.2 0.45 5.6 0.02 0.55
Statistic for Wet Coals 0.42 4.5 0.03 0.56
Overall Statistics for Coals 0.50 3.9 0.04 0.70
31
For both the dry Argonne and the wet OSU coals, the regressed slit length is less
than 1.5 nm, and the solid-solid interaction energy parameter is less than 40K, which is
the reported value for activated carbon. Similar to Scenario 1, the %AAD of the
representation for the wet OSU coals (4.5%) is larger than that for the dry Argonne coals
(3.3%). However, the WAAD values are better for the wet OSU coals (0.42) than for the
dry Argonne coals (0.59).
Table 3.7 presents the regression results for Scenario 3. With fixed values for the
covolume correction (-0.20) and the slit length (1.15 nm), the overall statistics for the dry
and the wet coals is 4.5 %AAD, which corresponds to a WAAD of 0.57, RMSE of 0.04
mmol/g and WRMS of 0.75. Among all the coals, the largest %AAD of 6.4% is
observed for pure-gas adsorption on dry Illinois #6 coal, the largest RMSE of 0.06
mmol/g is observed for pure-gas adsorption on the wet Tiffany coal, and the largest
WAAD and WRMS, 1.04 and 1.39, respectively, are observed for the dry Wyodak coal.
For the dry coals, the regressed slit length of the dry Illinois #6, Beulah Zap and Wyodak
coals were greater than 1.30 nm; thus, the slit length of 1.15 nm did not provide a good fit
for the experimental data. Nevertheless, the deviations obtained were still within the
experimental uncertainties. For the wet coals, Fruitland OSU #1 and #2 and Lower Basin
have regressed slit lengths close to 1.15 nm, so results similar to those of Scenario 2 were
obtained. The regressed slit lengths for the wet Illinois #6 and Tiffany coals were 1.29
and 0.91 nm, respectively. The deviations have increased, but the representations are still
within the expected experimental uncertainties. Therefore, the modified SLD-PR with
constant values for covolume correction and slit length are capable for accurate
representation of the adsorption data.
32
Table 3.7 – Scenario 3: Modified SLD-PR Model Representations of Pure-Gas Adsorption on Dry and Wet Coals
Parameters
Coal Adsorbate Area
(m2/g)
ess/k
(K)
L (nm)
(fixed)
Lb
(fixed)
WAAD %AAD
RMSE
(mmol/g)
WRMS
CH4 71.1
Dry Illinois #6 N2 56.3
CO2 97.5
21.1 1.15 -0.2 0.84 6.4 0.05 1.08
CH4 58.9
Dry Beulah Zap N2 42.9
CO2 111.3
27.3 1.15 -0.2 0.72 5.3 0.05 0.91
CH4 68.8
Dry Wyodak N2 55.3
CO2 118.6
22.4 1.15 -0.2 1.04 5.6 0.06 1.39
CH4 48.9
N2 37.1
Dry Upper
Freeport
CO2 56.0
35.5 1.15 -0.2 0.39 2.2 0.02 0.55
CH4 63.4
Dry Pocahontas N2 47.7
CO2 69.0
37.5 1.15 -0.2 0.46 2.2 0.03 0.68
Statistic for Dry Coals 0.69 4.3 0.04 0.92
33
Table 3.7 – Scenario 3: Modified SLD-PR Model Representations of Pure-Gas Adsorption on Dry and Wet Coals
(Continued)
Parameters
Coal Adsorbate Area
(m2/g)
ess/k
(K)
L (nm)
(fixed)
Lb
(fixed)
WAAD %AAD
RMSE
(mmol/g)
WRMS
CH4 36.9
Wet Illinois #6 N2 22.2
CO2 54.0
17.4 1.15 -0.20 0.31 4.6 0.05 0.46
CH4 60.9
N2 47.8
Wet Fruitland
OSU #1
CO2 69.0
23.7 1.15 -0.20 0.35 2.2 0.03 0.45
CH4 61.3
N2 40.0
Wet Fruitland
OSU #2
CO2 64.4
22.7 1.15 -0.20 0.49 4.9 0.06 0.67
CH4 30.5
Wet Tiffany N2 19.6
CO2 36.6
24.4 1.15 -0.20 0.59 5.9 0.03 0.77
CH4 24.8
N2 15.3
Wet Lower Basin
Fruitland
CO2 29.0
22.0 1.15 -0.20 0.46 5.9 0.02 0.56
Statistics for Wet Coals 0.44 4.7 0.04 0.58
Overall Statistics for Coals 0.57 4.5 0.04 0.75
34
Similar to Scenario 1 and 2, the surface area of CO2 is greater than that of
methane and nitrogen. The average surface area ratio of methane to CO2 and nitrogen to
CO2 is 0.7 and 0.5, respectively. Comparing Scenario 2 and 3, coals with a regressed slit
length larger than 1.15 nm have larger surface areas but smaller solid-solid interaction
energy. The opposite result is observed for coals with regressed slit length less than 1.15
nm. When comparing the overall statistics of Scenario 3 to Scenario 2, the overall
%AAD for the representation of pure-gas adsorption on both dry and wet coals is
increased by 0.7 %AAD, which also corresponds to an increase in WAAD of 0.07,
WRMS of 0.05 and RMSE of 0.001 mmo/g. These small increases in deviation indicate
that the surface areas and solid-solid interaction energy can represent the pure-gas
adsorption on both dry and wet coals with fixed slit length.
These three scenarios demonstrate that the modified SLD-PR model capable of
correlating the adsorption data within the expected experimental uncertainties when using
constant values for the slit length and covolume correction.
Figures 3.1-3.10 present the adsorption representations of Scenarios 1 and 3. The
first five figures are for the dry Argonne coal, and the latter five figures are for the wet
OSU coals. The plots for Scenario 2 are given in Appendix B since Scenario 3 produces
representation results similar to Scenario 2.
As illustrated in Figures 3.1-3.10, Scenario 1 gives a better correlation of the
adsorption data on both the dry Argonne and the wet OSU coals. Scenario 3 provides a
less precise correlation of the adsorption behavior, especially for CO2 adsorption on dry
Illinois #6, dry Beulah Zap and dry Wyodak, as shown in Figures 3.1-3.3. Fixing the
values of the covolume correction and the slit length results in overestimation of the CO2
35
excess adsorption on these coals at low pressures (P < 1000 psia). On the other hand, for
the wet Illinois #6 and Fruitland OSU #2 coals, full regression of the parameters
underestimates the CO2 adsorption at pressures above 1200 psia, as shown for several
experimental runs in Figures 3.6 and 3.8, respectively. Figure 3.7 presents the adsorption
on the wet Fruitland OSU #1 coal. The CO2 excess adsorption at 1600 psia is considered
as an outlier and was excluded in all scenarios. Furthermore, no significant difference is
observed between Scenarios 1 and 3 for methane and nitrogen adsorption isotherms. This
demonstrates that the covolume correction and the slit length have only minor effects on
methane and nitrogen adsorption when other parameters are regressed.
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.1 – Representation of Pure-Gas Adsorption on Dry Illinois #6 Coal at
131°F
36
0.0
0.4
0.8
1.2
1.6
2.0
2.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.2 – Representation of Pure-Gas Adsorption on Dry Beulah Zap Coal at
131°F
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.3 – Representation of Pure-Gas Adsorption on Dry Wyodak Coal at 131°F
37
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.4 – Representation of Pure-Gas Adsorption on Dry Upper Freeport Coal at
131°F
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.5 – Representation of Pure-Gas Adsorption on Dry Pocahontas Coal at
131°F
38
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.6 – Representation of Pure-Gas Adsorption on Wet Illinois #6 Coal at
115°F
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.7 – Representation of Pure-Gas Adsorption on Wet Fruitland OSU #1 Coal
at 115°F
39
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.8 – Representation of Pure-Gas Adsorption on Wet Fruitland OSU #2 Coal
at 115°F
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.9 – Representation of Pure-Gas Adsorption on Wet Tiffany Coal at 130°F
40
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Scenario 1
Scenario 3
Figure 3.10 – Representation of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F
Figure 3.11 shows the deviation plot for the SLD-PR model representation of the
pure-gas adsorption on dry and wet coals. For all three scenarios, about 85% of the data
can be represented by the model within expected experimental data. As shown in the
figure, large deviation occurred mainly when the Gibbs excess adsorption values are
small at relatively low to medium pressures.
41
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
0 500 1000 1500 2000
Pressure, psia
Deviation, (ncalc-nexp )/s exp
Scenario 1
Scenario 2
Scenario 3
Figure 3.11 – Deviations Plot for SLD-PR Model Representation of Pure-Gas
Adsorption on Dry and Wet Coals
Conclusions
Using a separate surface area for each adsorbate and a common solid-solid
interaction energy parameter provides precise representations for the pure-gas adsorption
on both the dry and wet coals. With fixed values for the covolume correction and the slit
length, the SLD-PR model can represent the pure-gas adsorption on the coals considered
within the expected experimental uncertainties. The results of Scenarios 2 and 3 indicate
that the variation in the covolume and the slit length have no significant effect on the
methane or nitrogen adsorption but are more significant in representing or predicting the
CO2 adsorption.
Fixing the values of the covolume correction and the slit length proved beneficial
in reducing the number of regressed parameters in the SLD-PR model. Accordingly,
Scenario 3 was selected for model generalization because the respective overall %AAD is
42
comparable in value to that of Scenario 1; thus, only four parameters (surface areas for
methane, nitrogen and CO2; and the solid-solid interaction energy parameter) were
correlated in terms of coal or adsorbate properties.
43
CHAPTER 4
GENERALIZED MODEL FOR PURE-GAS ADSORPTION
To develop a generalized model for the prediction of pure-gas adsorption of
CBM-type systems, the regressed model parameters (Chapter 3) of the SLD-PR model
were correlated as mathematical relations in terms of accessible adsorbent or adsorbate
physical properties. As expected, these relations do not provide exact representations of
the model parameters; thus, the generalized predictions are less accurate than those made
directly from the regressed parameters. Nevertheless, useful predictions can be made for
cases where extensive data are not available.
To obtain the generalized model coefficients, the regressed parameters for each
coal were expressed in terms of the respective coal characteristics (such as carbon,
equilibrium moisture content), or adsorbate properties (such as fluid molecular diameter).
The pure methane, nitrogen and CO2 adsorption isotherms that were used for
evaluating the ability of the SLD-PR model to represent the data (Chapter 3) were used in
the model generalizations. The adsorption information and the analyses of these coals are
discussed in Chapter 2.
44
Generalized Correlations
Trends in the regressed SLD-PR model parameters were examined graphically.
The coal fixed carbon, the carbon weight fraction, and the equilibrium moisture content
showed reasonable correlation with the regressed parameters. In addition, as concluded
by Fitzgerald [33], the coal surface area could not be correlated adequately in terms of
coal physical properties. However, it was found to be proportional to methane excess
adsorption at 400 psia. The use of a single experimental data point is valuable in that it
can (at least partially) compensate for our lack of knowledge of the solid-gas interactions
in the model. It does, however, render the model a “calibrated, generalized” model rather
than a completely generalized one.
For this work, the regressed parameters (surface area for each adsorbate and the
solid-solid interaction energy parameter) of Scenario 3 used in the representation of pure-gas
adsorption (Chapter 3) were applied to develop the parameter generalizations as
follows:
1. A generalized correlation was obtained for the solid-solid interaction energy
parameter based on the observed graphical trends.
2. Using the solid-solid interaction energy parameters obtained from the above
correlation, the surface area for each adsorbed gas on each coal was re-regressed.
This was done to obtain the surface areas which can correlate
precisely the adsorption data using the predicted solid-solid interaction
energy.
45
3. A generalized correlation for each surface area (from 2, above) was developed
in terms of a single-point adsorbate excess adsorption, coal characteristics or
gas properties.
4. The generalized correlations for each model parameter were then incorporated
into the SLD-PR model, and the coefficients in the generalized correlations
were re-regressed simultaneously, using the entire data set. The objective
function (WRMS) expressed by Equation (3-1) was minimized. For details,
an outline for the generalization steps in the FORTRAN program is given in
Appendix C.1.
As stated earlier, the generalization results for the coals considered indicated that
surface areas were proportional to methane excess adsorption at 400 psia. As such, the
resultant generalization is restricted because it can be only applied when this information
on methane adsorption at 400 psia is available. Therefore, analogous correlations were
developed to predict the adsorbate surface areas in terms of the nitrogen and the CO2
excess adsorption at 400 psia. This means a set of generalized correlations can be applied
to perform adsorption predictions for the coal of interest based on the available
adsorption information at this pressure on any of the three gases.
To evaluate the efficacy of the proposed correlations, three case studies were
conducted addressing the surface area predictions:
Case 1 – The surface areas of methane, nitrogen and CO2 are correlated in terms
of methane excess adsorption at 400 psia.
Case 2 – The surface areas of methane, nitrogen and CO2 are correlated in terms
of nitrogen excess adsorption at 400 psia
46
Case 3 – The surface areas of methane, nitrogen and CO2 are correlated in terms
of CO2 excess adsorption at 400 psia
Values of the excess adsorption of these gases at 400 psia are listed in Table 4.1.
A generalized correlation for the solid-solid interaction energy parameter is
included in all the cases above; thus, a total of four correlations were developed for each
case.
Table 4.1 – Excess Adsorption of Adsorbates at 400 psia
Excess Adsorption at 400 psia,
Coal mmol/g dry coal
CH4 N2 CO2
Dry Illinois #6 0.51 0.22 1.11
Dry Beulah Zap 0.48 0.20 1.42
Dry Wyodak 0.49 0.22 1.40
Dry Upper Freeport 0.45 0.19 0.78
Dry Pocahontas 0.60 0.25 0.99
Wet Illinois #6 0.23 0.07 0.61
Wet Fruitland OSU#1 0.46 0.19 0.90
Wet Fruitland OSU#2 0.45 0.15 0.85
Wet Tiffany 0.22 0.07 0.47
Wet Lower Basin Fruitland 0.18 0.06 0.39
The adsorption on Tiffany coal samples from wells #1 and #10 are combined and
generalized as mixed Tiffany coal. Similarly, the adsorption on Lower Basin Fruitland
#3a and #3b coals are combined. For the mixed Tiffany and mixed Lower Basin
Fruitland coals, the characterization is the average value of the combined coals, e.g.,
FCmixed Tiffany = 0.5(FCTiffany well #1 + FCTiffany Well #10). The characterization for these two
coals is listed in Table 4.2.
47
Table 4.2 – Combined Compositional Analysis of Lower Basin Fruitland
and Tiffany Coal Used in This Study
Analysis*
Mixed Lower Basin
Fruitland
Mixed Tiffany
Ultimate
Carbon % 38.92 52.27
Hydrogen % 3.08 2.70
Oxygen % 3.75 5.68
Nitrogen % 0.87 0.97
Sulfur % 1.73 0.55
Ash % 51.66 48.73
Proximate
Vol. Matter % 20.01 15.42
Fixed Carbon % 28.33 25.87
Moisture % 4.00 3.80
For all the developed correlations, unless otherwise stated, the coal properties
applied are weight fractions. For example, fixed carbon refers to fixed carbon weight
fraction.
Results and Discussions
The summary results for the generalized predictions of pure-gas adsorption on all
coals are represented in Tables 4.3-4.14 and Figures 4.1-4.33. A total of ten figures are
shown for each case. The first five figures are for the pure-gas adsorption on dry coals,
while the latter five figures are for the pure-gas adsorption on wet coals. Following are
detailed discussions for each of the three cases considered.
48
Case 1: Methane-Based Generalizations
Table 4.3 presents the SLD-PR pure-fluid parameter generalizations of Case 1.
The table shows the generalized correlations for the surface areas and the solid-solid
interaction energy. In developing the methane-based generalization of this case, both the
surface areas of methane and nitrogen are expressed as a function of methane excess
adsorption at 400 psia only. However, the CO2 surface areas for the dry coals are not
correlated adequately by the methane calibration point. Hence, based on observed trends,
both the methane excess adsorption and the product of the equilibrium moisture and
carbon fraction are used.
Table 4.3 – Case 1: Generalized Correlations of the Surface Areas and
the Solid-Solid Interaction Energy Parameter
( )
( )
( ) ( )
= +
= + × −
= −
= +
FC
C
0.5
M
ss
M C
Ex
CO2 CH4@400
Ex
N2 CH4@400
Ex
CH4 CH4@400
12.16
1.505
k
A 117.82 n 125.69 6.76
A 91.42 n 1.20
A 110.66 n 5.40
j
Table 4.4 gives the model parameters generated from the generalized correlations
of Table 4.3. A comparison of the generalized and the regressed model parameters is
provided in Figure 4.1, and Table 4.5 documents the %AAD of generalized parameters
relative to the regressed model parameters. Additional details are given in Appendix C.2.
49
Table 4.4 – Case 1: Generalized SLD-PR Model Parameters
Surface Area (m2/g)
Coal
CH4 N2 CO2
Slit Length
(nm)
ess/k (K)
Dry Illinois #6 62.0 45.6 84.9 1.15 28.4
Dry Beulah Zap 58.5 42.7 110.7 1.15 31.5
Dry Wyodak 59.6 43.6 108.7 1.15 30.5
Dry Upper Freeport 55.1 39.9 58.4 1.15 32.1
Dry Pocahontas 71.5 53.4 73.6 1.15 32.6
Wet Illinois #6 30.3 19.3 40.7 1.15 23.2
Wet FR OSU #1 56.5 41.0 63.1 1.15 24.2
Wet FR OSU #2 55.4 40.1 61.7 1.15 24.2
Wet Tiffany 29.4 18.6 36.4 1.15 25.5
Wet LB FR 24.9 14.9 29.7 1.15 24.2
Table 4.5 – Case 1: Summary Results of the Generalized Parameters
%AAD
Coal
ACH4 AN2 ACO2 ess/k
Dry Illinois #6 16.3 19.1 12.9 9.0
Dry Beulah Zap 0.7 0.5 0.6 15.7
Dry Wyodak 13.4 21.2 8.4 0.0
Dry Upper Freeport 12.7 7.6 4.3 8.0
Dry Pocahontas 12.8 12.0 6.6 4.5
Wet Illinois #6 18.0 13.1 24.6 22.9
Wet FR OSU #1 7.3 14.2 8.5 1.7
Wet FR OSU #2 9.6 0.3 4.2 6.3
Wet Tiffany 3.8 5.2 0.7 5.5
Wet LB FR 0.5 2.3 2.5 0.0
Overall Total 9.5 9.5 7.3 7.4
As illustrated in Figure 4.1, the generalized surface areas of methane and nitrogen
approximate the regressed values well. As shown in Table 4.5, the overall %AAD
between generalized and regressed surface areas for these gases are both 9.5%. The
methane surface areas of the dry Illinois #6, Wyodak, Upper Freeport, Pocahontas and
wet Illinois #6 coals are different from the respective regressed values by at least 10%. It
is observed that the ascending order of the methane surface area for these coals is:
Pocahontas, Wyodak and Illinois, but the order of methane excess adsorption of these
50
coals is: Wyodak, Pocahontas and Illinois #6. Therefore, the methane surface areas are
not predicted accurately, which is similar to the surface area predictions of nitrogen for
dry Illinois #6, dry Wyodak and wet Fruitland OSU #1. This is because the regressed
surface areas of these coals are not proportional to the respective methane excess
adsorption.
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Regressed Model Parameters
Generalized Model Parameters
CH4
N2
CO2
ess/k
diagonal
Figure 4.1 – Case 1: Comparison of the Regressed and Generalized SLD-PR
Model Parameters
For CO2, the generalized surface areas of all coals except for dry and wet Illinois
#6 match the respective regressed values within 10%. The deviations for dry and wet
Illinois #6 are 12.9% and 24.6%, respectively. This discrepancy occurs because the
combination of the excess adsorption and the selected coal characteristic are not in order
with the regressed surface areas. For the solid-solid interaction energy parameters, most
51
of the generalized values differ from the regressed values, as shown in Figure 4.1. The
overall %AAD is 7.4% with the largest error contributions attributable to dry Beulah Zap
and wet Illinois #6. The corresponding solid-solid interaction energy parameters differ
by at least fifteen percent relative to the regressed parameters.
Summary results for the adsorption of all adsorbates on both dry and wet coals are
given in Table 4.6. The respective generalized predictions for the pure-gas adsorption on
these coals are given in Figures 4.2 through 4.11. As shown in Table 4.6, the overall
WAAD is 1.05, the %AAD is 7.1%, RMSE is 0.05 mmol/g and WRMS is 1.22. The
largest WAAD and WRMS, which are 2.30 and 2.67, respectively, are both observed for
the CO2 adsorption on dry Wyodak coal. Figure 4.4 indicates that the amount of CO2
adsorbed by this coal is under predicted at intermediate pressures. The largest %AAD of
20.4% is observed for the CO2 adsorption on wet Illinois #6 coal; however, the weighted
deviations are less than two because of relatively large experimental uncertainties.
The CO2 adsorption on dry Illinois #6 coal, as shown in Figure 4.2, is predicted
poorly due to the use of a smaller of surface area value with a larger solid-solid
interaction energy value. The statistics, WRMS, %AAD, RMSE and WAAD, for dry
Illinois #6 are 2.54, 7.2%, 0.11 mmol/g and 1.87, respectively. The methane adsorption
on the dry Upper Freeport and Pocahontas coals (Figures 4.5 and 4.6, respectively) are
predicted within three times the experimental uncertainties; however, the pure-gas
adsorption on the remaining coals is predicted within twice the experimental
uncertainties.
52
Table 4.6 – Case 1: Summary Results for the Generalized SLD-PR Adsorption Predictions
WAAD %AAD RMSE WRMS
Coal
CH4 N2 CO2 CH4 N2 CO2 CH4 N2 CO2 CH4 N2 CO2
Dry Illinois #6 1.30 0.72 1.87 6.5 8.0 7.2 0.05 0.02 0.11 1.48 0.75 2.54
Dry Beulah Zap 0.80 0.73 1.04 4.6 8.6 4.1 0.03 0.03 0.08 0.93 0.89 1.50
Dry Wyodak 0.39 0.95 2.30 2.0 8.8 7.8 0.02 0.02 0.13 0.55 0.97 2.67
Dry Upper Freeport 2.12 0.47 0.69 7.3 3.6 4.1 0.05 0.01 0.04 2.39 0.51 0.83
Dry Pocahontas 1.99 0.75 1.12 6.0 4.0 5.9 0.05 0.02 0.06 2.34 0.89 1.30
Wet Illinois #6 0.91 0.31 1.32 8.0 8.2 20.4 0.03 0.01 0.17 0.98 0.38 1.47
Wet FR OSU #1 1.74 1.74 1.25 6.0 13.2 9.7 0.03 0.04 0.10 1.91 1.78 1.35
Wet FR OSU #2 1.47 0.62 0.84 6.2 5.2 10.1 0.04 0.01 0.11 1.59 0.77 1.01
Wet Tiffany 0.72 0.66 0.60 4.5 7.1 8.2 0.01 0.01 0.05 0.87 0.82 0.79
Wet LB FR 1.07 0.42 0.52 5.4 4.8 8.4 0.01 0.01 0.03 1.22 0.56 0.63
Overall Statistics
for Coals
1.05 7.1 0.05 1.22
53
0.0
0.4
0.8
1.2
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.2 – Generalized Predictions of Pure-Gas Adsorption on Dry Illinois #6 Coal
at 131°F Using Methane Excess Adsorption at 400 psia
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Figure 4.3 – Generalized Predictions of Pure-Gas Adsorption on Dry Beulah Zap
Coal at 131°F Using Methane Excess Adsorption at 400 psia
54
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.4 – Generalized Predictions of Pure-Gas Adsorption on Dry Wyodak Coal
at 131°F Using Methane Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.5 – Generalized Predictions of Pure-Gas Adsorption on Dry Upper
Freeport Coal at 131°F Using Methane Excess Adsorption at 400 psia
55
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.6 – Generalized Predictions of Pure-Gas Adsorption on Dry Pocahontas
Coal at 131°F Using Methane Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.7 – Generalized Predictions of Pure-Gas Adsorption on Wet Illinois #6
Coal at 115°F Using Methane Excess Adsorption at 400 psia
56
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.8 – Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland
OSU #1 Coal at 115°F Using Methane Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Figure 4.9 – Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland
OSU #2 Coal at 115°F Using Methane Excess Adsorption at 400 psia
57
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.10 – Generalized Predictions of Pure-Gas Adsorption on Wet Tiffany Coal
at 130°F Using Methane Excess Adsorption at 400 psia
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.11 – Generalized Predictions of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F Using Methane Excess Adsorption at 400 psia
58
The model parameters are not correlated precisely with the coal properties for dry
and wet Illinois #6 and dry Wyodak, but for dry Beulah Zap, wet Fruitland OSU #2, wet
Tiffany and wet Lower Basin Fruitland, the model parameters are correlated closely with
coal properties. Nevertheless, the generalization using methane excess adsorption can
predict the pure-gas adsorption within three times the uncertainties.
Case 2: Nitrogen-Based Generalizations
The regressed surface areas for methane, nitrogen and CO2 are not correlated well
with the nitrogen excess adsorption at 400 psia; hence, coal properties such as fixed
carbon, volatile matter, and equilibrium moisture content are required to obtain improved
generalizations for the model parameters. Table 4.7 presents the generalized correlations
for both the surface areas using nitrogen excess adsorption at 400 psia and the solid-solid
interaction energy parameter. Table 4.8 provides the generalized model parameters from
these correlations.
Table 4.7 – Case 2: Generalized Correlations of the Surface Areas and
the Solid-Solid Interaction Energy Parameter
( )( )
( ) ( )
( ) ( ) ( )
= +
= + −
= + ×
= +
FC
C
0.5
M
ss
FC
0.5
M
Ex
CO2 N2@400
0.5
FC M
Ex
N2 N2@400
0.5
Vol
Ex
CH4 N2@400
8.14
2.831
k
A 195.84 n 503.23 13.16
A 173.61 n 51.04
A 407.81 n 16.04
j
j
j
59
Table 4.8 – Case 2: Generalized SLD-PR Model Parameters
Surface Area (m2/g)
Coal
CH4 N2 CO2
Slit Length
(nm)
ess/k (K)
Dry Illinois #6 69.2 46.5 87.1 1.15 25.5
Dry Beulah Zap 61.4 51.0 113.9 1.15 24.3
Dry Wyodak 67.3 54.0 118.3 1.15 23.8
Dry Upper Freeport 56.5 37.2 55.2 1.15 38.8
Dry Pocahontas 60.5 47.7 68.5 1.15 43.6
Wet Illinois #6 30.9 18.9 55.3 1.15 24.7
Wet FR OSU #1 50.1 38.1 67.5 1.15 28.5
Wet FR OSU #2 43.5 31.7 59.2 1.15 28.5
Wet Tiffany 27.8 18.7 36.4 1.15 26.4
Wet LB FR 26.5 15.4 26.6 1.15 25.3
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Regressed Model Parameters Generalized Model Parameters
CH4
N2
CO2
ess/k
diagonal
Figure 4.12 – Case 2: Comparison of the Regressed and Generalized
SLD-PR Model Parameters
60
Table 4.9 – Case 2: Summary Results of the Generalized Parameters
%AAD
Coal
ACH4 AN2 ACO2 ess/k
Dry Illinois #6 6.6 17.4 10.7 20.4
Dry Beulah Zap 4.2 18.9 2.4 10.8
Dry Wyodak 2.1 2.4 0.3 6.2
Dry Upper Freeport 15.5 0.4 1.4 9.4
Dry Pocahontas 4.6 0.0 0.8 16.1
Wet Illinois #6 16.3 14.8 2.3 42.1
Wet FR OSU #1 17.8 20.3 2.1 20.2
Wet FR OSU #2 29.0 20.8 8.1 25.6
Wet Tiffany 9.1 4.9 0.7 8.0
Wet LB FR 7.0 0.9 8.3 15.0
Overall Total 11.2 10.1 3.7 17.4
Figure 4.12 shows the comparison between the generalized and regressed model
parameters. Further, the quality of the parameter generalizations, as given by %AAD of
the generalized parameters relative to regressed parameters, is examined in Table 4.9
(Additional details on this comparison are given in Appendix C.2). Figure 4.12 shows
that the methane surface area is predicted less accurately than the nitrogen and CO2
surface areas.
As shown in Table 4.9, the %AAD for the generalized methane surface areas is
11.2%. The main contributions to the overall error are from the wet Fruitland OSU #2
and #1 (29.0% and 17.8%, respectively), wet Illinois #6 (16.3%) and dry Upper Freeport
(15.5%) coals. The methane surface areas for these coals are not predicted accurately.
Comparable results are observed for the generalized nitrogen surface areas, which yielded
%AAD of 10.1%. Among these coals, the generalized nitrogen surface areas of dry and
Illinois #6, dry Beulah Zap and wet Fruitland OSU #1 and #2 have %AAD of 17.4, 18.9,
19.5 and 17.5%, respectively. In contrast, the generalized CO2 surface areas are
61
comparable to the regressed values with a %AAD of 4.4%. The largest %AAD is
observed for dry Illinois #6 coal.
Figure 4.12 indicates that most of the solid-solid interaction energy parameters are
over predicted. As indicated in Table 4.9, only the solid-solid interaction energies of dry
Wyodak, Upper Freeport and wet Tiffany are comparable to calculated values; the others
have differences greater than 10%. These trends indicate that simultaneous regression of
the model parameters has resulted in some trade offs among the parameters estimates.
This is an expected outcome when the model parameters are not fully orthogonal.
Table 4.10 presents the summary results for the generalized SLD-PR model
predictions of pure-gas adsorption on both dry and wet coals. As documented, the overall
WAAD, %AAD, RMSE and WRMS are 1.05, 8.4%, 0.05 mmol/g and 1.47, respectively.
The quality of the corresponding generalized predictions is exhibited in Figures 4.13 to
4.22.
As discussed previously, the predicted methane surface areas for many coals
differ from the regressed values, and the solid-solid interaction energy parameters tend to
be over predicted. This results in large deviations for methane adsorption relative to the
expected experimental uncertainties. Specifically, the WRMS and WAAD of methane
adsorption on dry Upper Freeport and wet Fruitland OSU #2 are above 4.0. Methane
adsorption on dry Upper Freeport, shown in Figure 4.16, is more than five times the
experimental error due to the overestimation of the surface area from the parameter
generalization. The respective RMSE and %AAD are 0.10 mmol/g and 19.3%.
62
Table 4.10 – Case 2: Summary Results for the Generalized SLD-PR Adsorption Predictions
WAAD %AAD RMSE WRMS
Coal
CH4 N2 CO2 CH4 N2 CO2 CH4 N2 CO2 CH4 N2 CO2
Dry Illinois #6 0.60 1.17 1.61 3.8 12.6 6.0 0.02 0.03 0.11 0.74 1.20 2.33
Dry Beulah Zap 0.64 1.15 0.83 5.3 13.8 3.7 0.03 0.04 0.06 0.87 1.39 1.06
Dry Wyodak 0.52 0.54 1.66 3.4 6.4 5.4 0.02 0.01 0.09 0.64 0.62 2.06
Dry Upper Freeport 5.18 0.80 0.70 19.3 5.2 3.5 0.10 0.01 0.03 5.34 0.84 0.86
Dry Pocahontas 0.46 1.51 1.01 1.9 9.3 4.9 0.01 0.03 0.05 0.59 1.52 1.27
Wet Illinois #6 0.91 0.38 1.01 7.3 10.2 14.8 0.02 0.01 0.10 1.22 0.48 1.33
Wet FR OSU #1 2.63 1.38 0.79 9.9 10.3 5.5 0.07 0.04 0.07 2.85 1.51 0.94
Wet FR OSU #2 4.64 1.01 0.87 20.2 8.3 10.2 0.13 0.03 0.11 4.86 1.20 1.08
Wet Tiffany 1.16 0.60 0.66 6.6 6.7 8.6 0.02 0.01 0.05 1.35 0.76 0.83
Wet LB FR 2.44 0.79 0.53 12.2 9.2 8.0 0.03 0.01 0.03 2.76 0.95 0.63
Overall Statistics
for Coals
1.05 8.4 0.05 1.47
63
0.0
0.4
0.8
1.2
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.13 – Generalized Predictions of Pure-Gas Adsorption on Dry Illinois #6
Coal at 131°F Using Nitrogen Excess Adsorption at 400 psia
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Figure 4.14 – Generalized Predictions of Pure-Gas Adsorption on Dry Beulah Zap
Coal at 131°F Using Nitrogen Excess Adsorption at 400 psia
64
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.15 – Generalized Predictions of Pure-Gas Adsorption on Dry Wyodak Coal
at 131°F Using Nitrogen Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.16 – Generalized Predictions of Pure-Gas Adsorption on Dry Upper
Freeport Coal at 131°F Using Nitrogen Excess Adsorption at 400 psia
65
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.17 – Generalized Predictions of Pure-Gas Adsorption on Dry Pocahontas
Coal at 131°F Using Nitrogen Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.18 – Generalized Predictions of Pure-Gas Adsorption on Wet Illinois #6
Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia
66
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.19 – Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland
OSU #1 Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Figure 4.20 – Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland
OSU #2 Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia
67
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.21 – Generalized Predictions of Pure-Gas Adsorption on Wet Tiffany Coal
at 130°F Using Nitrogen Excess Adsorption at 400 psia
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.22 – Generalized Predictions of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F Using Nitrogen Excess Adsorption at 400 psia
68
The methane adsorption on wet Fruitland OSU #2 (Figure 4.20) is predicted
poorly because of surface area underestimation. The predicted adsorption is 20% lower
than the experimental data with a RMSE of 0.13 mmol/g. In comparison, methane
adsorption on wet Fruitland OSU #1 (Figure 4.19) and wet Lower Basin (Figure 4.22) are
predicted within three times the experimental uncertainties.
Compared to methane adsorption, both the nitrogen and CO2 adsorption are
predicted within twice the experimental uncertainty. For nitrogen adsorption, the largest
WAAD of 1.51 is observed for wet Fruitland OSU #1 and this value is followed by 1.39
for dry Beulah Zap. The %AAD values for these coals are 10.3% and 13.8% for the wet
Fruitland OSU #1 and dry Beulah Zap, respectively, and RMSE of 0.04 mmol/g for both
coals. For CO2 adsorption, both the dry Illinois #6 and dry Wyodak coals show relatively
larger WAAD values of 1.61 and 1.66, respectively.
Overall, the generalizations using nitrogen excess adsorption at 400 psia are able
to predict most of the pure-gas adsorption isotherms within two times the experimental
uncertainties, with the exception of the methane adsorption on the wet Fruitland OSU #2
and dry Upper Freeport coals.
Case 3: CO2-Based Generalizations
In this case, the surface areas of all coals are correlated as a function of the CO2
excess adsorption at 400 psia. Similar to Case 2, the methane, nitrogen and CO2 surface
areas of all coals are not correlated well with the CO2 excess adsorption. Thus, additional
coal properties are incorporated to achieve a better correlation with the surface area, as
shown in Table 4.11.
69
Table 4.11 presents the generalized correlations for the surface areas using CO2
excess adsorption at 400 psia and for the solid-solid interaction energy. The generalized
parameters are shown in Table 4.12, and the plots of comparison between generalized
parameters and regressed parameters are depicted in Figure 4.23. Also, an assessment of
the quality of the parameter generalization is provided in Table 4.13 in terms %AAD
values obtained for the predicted parameters relative to the regressed parameters. (The
details are in Appendix C.2).
Table 4.11 – Case 3: Generalized Correlations of the Surface Areas and
the Solid-Solid Interaction Energy Parameter
( )
( ) ( ) ( )
( ) ( )
= +
= − × −
= −
+
=
FC
C
0.5
M
ss
0.5
M C
Ex
CO2 CO2@400
FC
0.5
M
Ex
N2 CO2@400
0.5
C
Ex FC
CH4 CO2@400
7.80
2.143
k
A 72.82 n 43.95 3.52
A 61.019 n 149.57
1.46
A 72.482 n
j
j
j
Table 4.12 – Case 3: Generalized SLD-PR Model Parameters
Surface Area (m2/g)
Coal
CH4 N2 CO2
Slit Length
(nm)
ess/k (K)
Dry Illinois #6 60.0 50.7 88.5 1.15 22.7
Dry Beulah Zap 68.0 60.4 120.9 1.15 22.7
Dry Wyodak 68.6 59.2 118.3 1.15 22.1
Dry Upper Freeport 48.5 38.7 57.8 1.15 32.0
Dry Pocahontas 66.9 50.8 71.9 1.15 35.1
Wet Illinois #6 40.3 20.5 48.0 1.15 21.0
Wet FR OSU #1 62.3 42.0 67.6 1.15 23.7
Wet FR OSU #2 58.9 39.1 63.7 1.15 23.6
Wet Tiffany 29.8 18.5 37.0 1.15 22.7
Wet LB FR 25.3 15.1 30.1 1.15 21.7
70
Table 4.13 – Case 3: Summary Results of the Generalized Parameters
%AAD
Coal
ACH4 AN2 ACO2 ess/k
Dry Illinois #6 19.1 10.0 9.3 7.4
Dry Beulah Zap 15.6 41.0 8.6 16.8
Dry Wyodak 0.3 6.9 0.2 1.4
Dry Upper Freeport 0.8 4.4 3.3 9.8
Dry Pocahontas 5.6 6.6 4.2 6.4
Wet Illinois #6 9.3 7.6 11.2 20.8
Wet FR OSU #1 2.2 12.2 2.0 0.2
Wet FR OSU #2 3.9 2.1 1.1 4.3
Wet Tiffany 2.4 6.0 1.1 7.1
Wet LB FR 2.3 0.9 3.8 1.7
Overall Total 6.2 9.8 4.5 7.6
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Regressed Model Parameters
Generalized Model Parameters
CH4
N2
CO2
ess/k
diagonal
Figure 4.23 – Case 3: Comparison of the Regressed and Generalized
SLD-PR Model Parameters
71
As illustrated in Figure 4.23 and Table 4.13, the generalized methane surface
areas are comparable to the regressed values with an average difference of 6.2%;
however, large %AAD of 11.1 and 15.6% are observed for dry Illinois #6 and Beulah
Zap, respectively. The generalized methane surface area for the dry Illinois #6 is
overestimated while that for Beulah Zap is overestimated. However, the surface areas for
the remaining coals differ by less than 8.0% from the regressed surface areas.
The surface areas of nitrogen are also comparable to the regressed values. The
average difference is 9.8% with the largest %AAD (41.0%) observed for the dry Beulah
Zap coal. From Figure 4.23, this large error is due to an overestimation of the nitrogen
surface area due to a large CO2 excess adsorption.
Most of the generalized CO2 surface areas are predicted accurately compared to
the regressed values, as shown in Figure 4.23 and Table 4.13. The average %AAD is
4.5% with the largest difference of 11.2% observed for the wet Illinois #6 coal. As
shown in Figure 4.23, the generalized solid-solid interaction energy parameters compare
favorably with the regressed values; %AAD of less than 7.6% is reported in Table 4.13.
Table 4.14 presents the summary results of generalization using CO2 excess
adsorption at 400 psia. The generalized predictions for the adsorption are depicted in
Figures 4.24 through Figure 4.33. The overall WAAD, %AAD, RMSE and WRMS are
1.06, 7.70%, 0.04 mmol/g and 1.23, respectively. As mentioned previously, the methane
surface area of dry Illinois #6 and the nitrogen surface area of dry Beulah Zap and wet
Fruitland OSU #1 differ from the regressed values; thus, the respective adsorption are
predicted poorly.
72
Table 4.14 – Case 3: Summary Results for the Generalized SLD-PR Adsorption Predictions
WAAD %AAD RMSE WRMS
Coal
CH4 N2 CO2 CH4 N2 CO2 CH4 N2 CO2 CH4 N2 CO2
Dry Illinois #6 3.75 0.95 1.77 19.3 11.6 6.7 0.11 0.02 0.11 3.80 1.00 2.43
Dry Beulah Zap 1.46 2.20 1.16 9.2 22.3 5.3 0.05 0.08 0.08 1.59 2.70 1.43
Dry Wyodak 0.60 0.97 1.64 4.3 8.8 5.8 0.02 0.03 0.09 0.86 1.07 1.92
Dry Upper Freeport 1.40 0.31 0.66 5.8 3.2 3.9 0.03 0.01 0.03 1.47 0.40 0.74
Dry Pocahontas 0.93 0.54 0.97 2.8 2.8 5.1 0.03 0.01 0.06 1.13 0.64 1.15
Wet Illinois #6 2.74 0.26 0.62 20.2 6.7 10.6 0.06 0.01 0.10 3.08 0.32 0.76
Wet FR OSU #1 0.63 1.65 0.60 2.5 12.5 5.2 0.02 0.04 0.06 0.70 1.68 0.72
Wet FR OSU #2 0.42 0.38 0.76 1.7 3.1 8.9 0.01 0.01 0.09 0.53 0.46 0.95
Wet Tiffany 1.01 1.17 0.68 5.8 11.8 8.5 0.02 0.02 0.05 1.25 1.35 0.99
Wet LB FR 0.66 0.40 0.51 3.5 4.8 8.2 0.01 0.01 0.03 0.74 0.47 0.61
Overall Statistics
for Coals
1.06 7.7 0.04 1.23
73
0.0
0.4
0.8
1.2
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.24 – Generalized Predictions of Pure-Gas Adsorption on Dry Illinois #6
Coal at 131°F Using CO2 Excess Adsorption at 400 psia
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Figure 4.25 – Generalized Predictions of Pure-Gas Adsorption on Dry Beulah Zap
Coal at 131°F Using CO2 Excess Adsorption at 400 psia
74
0.0
0.4
0.8
1.2
1.6
2.0
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.26 – Generalized Predictions of Pure-Gas Adsorption on Dry Wyodak Coal
at 131°F Using CO2 Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.27 – Generalized Predictions of Pure-Gas Adsorption on Dry Upper
Freeport Coal at 131°F Using CO2 Excess Adsorption at 400 psia
75
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.28 – Generalized Predictions of Pure-Gas Adsorption on Dry Pocahontas
Coal at 131°F Using CO2 Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.29 – Generalized Predictions of Pure-Gas Adsorption on Wet Illinois #6
Coal at 115°F Using CO2 Excess Adsorption at 400 psia
76
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.30 – Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland
OSU #1 at 115°F Using CO2 Excess Adsorption at 400 psia
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Figure 4.31 – Generalized Predictions of Pure-Gas Adsorption on Wet Fruitland
OSU #2 Coal at 115°F Using CO2 Excess Adsorption at 400 psia
77
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.32 – Generalized Predictions of Pure-Gas Adsorption on Wet Tiffany Coal
at 130°F Using CO2 Excess Adsorption at 400 psia
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
N2
CO2
Figure 4.33 – Generalized Predictions of Pure-Gas Adsorption on Wet Lower Basin
Fruitland Coal at 115°F Using CO2 Excess Adsorption at 400 psia
78
The methane adsorption isotherm for dry Illinois #6, shown in Figure 4.24, is
predicted less accurately for all pressures. For this coal, the WRMS, RMSE, %AAD and
WAAD are 3.80, 0.11 mmol/g, 19.3% and 3.75, respectively. These deviations are large
because of the low values obtained for the generalized methane surface areas and the
relatively smaller experimental uncertainties. In comparison, the CO2 surface area is
slightly underestimated; nevertheless, the predictions produced relatively larger values
for the WRMS (2.43) and RMSE (0.11 mmol/g). Also, the methane adsorption for the
wet Illinois #6 coal is over predicted at lower pressures, as illustrated in Figure 4.29,
because the methane surface area is also overestimated. For this coal the WRMS, RMSE,
%AAD and WAAD are 3.08, 0.06 mmol/g, 20.2% and 2.74, respectively.
The nitrogen adsorption isotherm for dry Beulah Zap was not predicted
accurately, as listed in Table 4.14, the WRMS, RMSE, %AAD WAAD is 2.70, 0.08
mmol/g, 22.3% and 2.20, respectively. For wet Fruitland OSU #1, as shown in Figure
4.30, the nitrogen adsorption was under predicted because the surface area is
underestimated. For this coal the %AAD is 12.5% and RMSE is 0.04 mmol/g. In
comparison, the nitrogen adsorption isotherms were predicted generally within twice the
experimental uncertainties.
The results above for Case 3 indicate that the generalized parameters using CO2
excess adsorption are, on average, are capable of predicting the pure-fluid adsorption on
dry Wyodak, dry Upper Freeport, dry Pocahontas, wet Fruitland OSU #2, wet Tiffany
and wet Lower Basin Fruitland within twice the experimental uncertainties. More
importantly, the CO2-based generalized predictions provided sufficiently accurate results
for most CBM-type applications involving the coals considered.
79
Comparison of Generalized Predictions of Cases 1, 2 and 3
The results of the three cases demonstrate the generalized SLD-PR model is
capable of predicting the pure-gas adsorption on the considered dry and wet coals with an
overall WAAD of 1.10. This is comparable to the prediction results on activated carbon
and coals using generalized Ono-Kondo lattice model [16, 17] and 2-D EOS model [14,
34] (both within twice the experimental uncertainties).
Specifically, the SLD-PR generalization based on methane excess adsorption
predicts the pure-gas adsorption within three times the experimental uncertainties. In
comparison, generalization using CO2 excess adsorption provides pure-gas adsorption
predictions also within three times the experimental uncertainties with the exception of
the methane adsorption on dry Illinois #6 coal, which is predicted within four times the
experimental uncertainty.
Similar to the CO2 correlation, the generalization using nitrogen excess adsorption
is also able to provide predictions for most of the pure-gas adsorption within three times
the experimental uncertainties. However, the methane adsorption on dry Upper Freeport
and wet Fruitland OSU #2 yield deviations larger than four times the experimental
uncertainty. Figure 4.34 exemplifies the generalized predictions for pure-gas adsorption
on dry Beulah Zap coal for the three cases. The figure demonstrates a common
observation that the generalized SLD-PR model based on methane excess adsorption
gives more accurate predictions for the pure-gas adsorption on dry and wet coals.
Nonetheless, these generalizations (including nitrogen and CO2 excess
adsorption) account for the moisture effect on the adsorption based on one calibration
point (methane, nitrogen or CO2 excess adsorption at 400 psia). Moreover, in the current
80
data reduction procedure, a few assumptions are used for determining the measured
amount of gas adsorption on wet coals, which may affect the qualities of both the model
representation and generalization. These assumptions are: (1) the amount of gas
adsorbed is adjusted to account for the gas soluble in the adsorbed water, which is taken
to be the full amount of water injected; and (2) the bulk-phase densities are calculated
assuming the absence of water in that phase.
0.0
0.4
0.8
1.2
1.6
2.0
2.4
0 500 1000 1500 2000
Pressure, psia
Excess Adsorption, mmol/g
CH4
CO2
N2
Case 1
Case 2
Case 3
Figure 4.34 – Comparison among the SLD-PR Model Parameter Generalizations as
Applied to Pure-Gas Adsorption on Dry Beulah Zap Coal at 131°F
Figure 4.35 presents the deviation plot for the SLD-PR model generalization of
the pure-gas adsorption on dry and wet coals. The deviations of the model
representations produced by Scenario 3 are compared to those of the generalized model
predictions using methane excess adsorption (Case 1). From the figure, most of the data
81
are predicted by the methane-based generalization within three times the experimental
uncertainties.
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
0 500 1000 1500 2000
Pressure, psia
Deviation, (ncalc-nexp )/s exp
Scenario 3