1 Desorption and Adsorption of Subsurface Shale Gas

Desorption and Adsorption of Subsurface Shale Gas

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

in the Graduate School of The Ohio State University

Fengyang Xiong, M.S.

Graduate Program in School of Earth Sciences

The Ohio State University

2020

Dissertation Committee:

Joachim Moortgat, Advisor

David Cole

Tom Darrah

Derek Sawyer

Copyrighted by

Fengyang Xiong

2020

Abstract

Storage of subsurface shale gas is challenging to characterize because nanoporous shales consist of almost all commonly observed minerals and develop a wide pore size distribution of 0.4 nm to 1 ��. Petroleum geoscientists classify the subsurface shale gas into three components: free gas in the pore space, adsorbed gas on mineral surfaces, and dissolved gas in formation fluids and organic matter. Based on investigations of shale gas plays in the United States, the adsorbed gas can contribute up to 85% of the total shale gas- in-place (GIP). And the storage of adsorbed shale gas, which mainly consists of methane, is determined by multiple geological properties, e.g., pore structure, mineral composition, temperature, pressure, and water saturation. These complex multivariate relationships complicate the assessment of subsurface adsorbed gas, which is still challenging for exploration geoscientists to quantitatively characterize.

In this dissertation, we investigate the pore structure of shales, including the roles of organic matter, mainly insoluble kerogen, and inorganic minerals in pore development using Soxhlet extraction and low-pressure nitrogen and carbon dioxide adsorption isotherms. We then study the relationship between in-situ desorbed gas and mineralogy on large core samples. Most importantly, we propose an experimental procedure to estimate the pressure-dependent density of adsorption, which will significantly improve future estimates of adsorbed gas in shale GIP assessment. Finally, we modify and compare a ii number of currently widely used supercritical adsorption models to obtain critical thermodynamic parameters that are significant in the shale GIP evaluation and exploitational design.

iii

Dedication

Dedicated to my advisors, committee members, and friends for your patient help; my family for unconditional encouragement and accompany.

Acknowledgments

As the one whom I learned from and admire most, Dr. Joachim Moortgat deserves all the honor that I received through the past four post-graduate years, for revision of all my submitted journal manuscripts, proposals of my research and travel grants, scholarship application, and writing all the letters of reference. Thanks for every group meeting, house cooking, and big event gathering at Ethyl & Tank. Beyond supervising, he is more like a good friend to me, shaping my professional attitude and value to his best.

I am also deeply grateful to my committee members, Dr. Derek Sawyer, Dr. Tom

Darrah, and Dr. David Cole for their time, advice, and strong support for my research and dissertation writing. Especially, specific thanks to Dr. Derek Sawyer for his guidance for the AAPG/SEG student chapter and training of seismology interpretation; Dr. Tom

Darrah for providing shale samples for my research and sharing the room with me at GSA

2017 Annual Meeting; Dr. David Cole for communicating with ORNL, providing samples and facilities for my research, and SEED and CERTAIN grants for my research and student chapter outreach, respectively.

Additionally, I would like to truly thank Dr. Amin Amooie and Dr. Reza

Soltanian, who have left OSU and are currently pursuing a higher level of academic development. Their friendly advice, encouragement, and mentoring help me live through the beginning of my PhD life. Specific thanks to Dr. Amin Amooie for helping me settle v down at Columbus; Dr. Reza Soltanian for helping my search for postdoc positions. And

I am grateful to my other group fellows, Dr. Di Zhu, Dr. Mengnan Li, Billy Eymold, and

Derrick James, for their advice and encouragement.

Also, I am thankful to my collaborators, Dr. David Tomasko, Dr. Gernot Rother,

Julie Sheet, Susan Welch, Alex Swift, Bohyun Hwang, and Yiwen Gong. Big thanks for their time and help with my training and experiments at OSU and ORNL.

I also acknowledge Theresa Mooney, Angie Rogers, Steven Lower, and

Matthew Saltzman for their help with my travels and purchase orders, academic affairs, teaching associate, and scholarship application.

Lastly, I want to thank my younger and older sister for taking care of my mother during my PhD study, which helps me comfort and focus on my study and life in the United

States. And thanks to all my brothers, sisters, uncles and aunts for your love, support, and encouragement.

Vita

2009-2013 China University of Petroleum, Beijing (B.Sc. of geological engineering)

2013-2016 China University of Petroleum, Beijing (Master of petroleum geology)

2016-2020 The Ohio State University (PhD program in Earth Sciences/Geology)

2019 Summer Oak Ridge National Lab (visiting student)

Publications

[18] Xiong, F., Rother, G., Tomasko, D., Pang, W., Moortgat, J. On the pressure and

temperature dependence of adsorption density and other thermodynamic properties

in gas shales. Chemical Engineering Journal 2020, 395, 124989.

[17] Xiong, F., Jiang, Z., Huang, H., Wen, M., Moortgat, J. Mineralogy and gas content

of Upper Paleozoic Shanxi and Benxi Shale Formations in the Ordos Basin, Energy

& Fuels 2019, 33, 1061–1068.

[16] Xiong, F.Y., Jiang, Z.X., Li, P., Wang, X.Z., Bi, H., Li, Y.R., Wang, Z.Y., Amooie,

M.A., Soltanian, M.R., Moortgat, J. Pore structure of transitional shales in the Ordos

Basin, NW China: effects of composition on gas storage capacity. Fuel 2017, 206,

504–515.

[15] Xiong, F.Y., Jiang, Z.X., Chen, J.F., Wang, X.Z., Huang, Z.L., Liu, G.H., Chen, F.R.,

Li, Y.R., Chen, L., Zhang, L.X. The role of the residual bitumen in the gas storage

vii

capacity of mature lacustrine shale: A case study of the Triassic Yanchang shale,

Ordos Basin, China. Marine and Petroleum Geology 2016, 69, 205-215.

[14] Xiong, F.Y., Jiang, Z.X., Tang, X.L., Li, Z., Bi, H., Li, W.B., Yang, P.P.

Characteristics and origin of the heterogeneity of the Lower Silurian Longmaxi

marine shale in southeastern Chongqing, SW China. Journal of Natural Gas and

Engineering 2015, 27, 1389-1399.

[13] Huang, H., Li, R., Xiong, F., Huang, S., Sun, W., Jiang, Z., Chen, L., Wu, L., 2020.

A method to probe the pore-throat structure of tight reservoirs based on low-field

NMR: Insights from a cylindrical pore model, Marine and Petroleum Geology 2020,

104344.

[12] Gong, Y., Mehana, M., El-Monier, I., Xu, F., Xiong, F., Machine learning for

estimating rock mechanical properties beyond traditional considerations,

Unconventional Resources Technology Conference, Denver, Colorado 2019, 466-

480.

[11] Huang, H., Sun,W., Xiong, F., Chen, L., Li, X., Gao, T., Jiang, Z., Ji,W., Wu, Y., Han,

J. A novel method to estimate subsurface shale gas capacities, Fuel 2018,232, 341–

350.

[10] Gao, F., Song, Y., Li, Z., Xiong, F., Chen, L., Zhang, Y., Liang, Z., Zhang, X., Chen,

Z., Moortgat, J. Lithofacies and reservoir characteristics of the Lower Cretaceous

continental Shahezi Shale in the Changling Fault Depression of Songliao Basin, NE

China, Marine and Petroleum Geology 2018, 98, 401-421.

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[9] Gao, F., Song, Y., Li, Z., Xiong, F.Y., Moortgat, J., Chen, L., Zhang, X., Chen, Z.

Quantitative characterization of pore connectivity using NMR and MIP: A case

study of the Wangyinpu and Guanyintang Shales in the Xiuwu Basin, Southern

China, International Journal of Coal Geology 2018, 197, 53-65.

[8] Wang, Z., Liu, L., Pan, M., Shi, Y., Xiong, F., High-Frequency Sequence

Stratigraphy and Fine-Scale Reservoir Characterization of the Devonian Sandstone,

Donghe Formation, North Uplift of the Tarim Basin, Acta Geologica Sinica-English

Edition 2018, 92(5), 1917-1933.

[7] Wang, Z., Pan, M., Shi, Y., Liu, L., Xiong, F., Qin, Z., Fractal analysis of

Donghetang sandstones using NMR measurements, Energy & Fuel 2018, 32, 2973-

2982.

[6] Huang, H., Chen, L., Sun, W., Xiong, F., Ji, W., Jia, J., Tang, X., Zhang, S., Gao, J.,

Luo, B., Investigation of Pore Structure and Fractal Characteristics in the Shihezi

Formation Tight Gas Sandstone from the Ordos Basin, China, Fractals 2018, 26,

1840005,1-22.

[5] Bi, H., Jiang, Z.X., Li, J.Z., Xiong, F.Y., Li, P. Ono-Kondo model for supercritical

shale gas storage: A case study of Silurian Longmaxi shale in southeastern

Chongqing, SW China, Energy & Fuels 2017, 31(3), 2755-2764.

[4] Amooie, M.A., Soltanian, M.R., Xiong, F., Dai, Z., Moortgat, J., Mixing and

spreading of multiphase fluids in heterogeneous bimodal porous media,

Geomechanics and Geophysics for Geo-Energy and Geo-Resources 2017, 3, 1-20.

[3] Soltanian, M.R., Amooie, M.A., Gershenzon, N., Dai, Z., Ritzi, R., Xiong, F., Cole,

D.R., Moortgat, J., Dissolution trapping of carbon dioxide in heterogeneous aquifers.

Environmental Sciences & Technology 2017, 51(13), 7732-7741.

[2] Li, P., Jiang, Z.X., Zheng, M., Bi, H., Yuan, Y., Xiong, F.Y. Prediction model for gas

adsorption capacity of the Lower Ganchaigou Formation in the Qaidam Basin,

China. Journal of Natural Gas and Engineering 2016, 31, 493-502.

[1] Tang, X.L., Jiang, Z.X., Huang, H.X., Jiang, S., Yang, L., Xiong, F.Y., Chen, L., Feng,

J. Lithofacies characteristics and its effect on gas storage of the Silurian Longmaxi

marine shale in the southeast Sichuan Basin, China. Journal of Natural Gas and

Engineering 2016, 28, 338-346.

Fields of Study

Major Field: Earth Sciences/Geology

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vii

List of Tables ...... xvi

List of Figures ...... xix

Chapter 1. Introduction ...... 1

References ...... 3

Chapter 2. Geological Background ...... 5

References ...... 13

Chapter 3. Pore Structure of Transitional Shales in the Ordos Basin, NW China: Effects of Composition on Gas Storage Capacity ...... 18

3.1. Introduction ...... 19

3.2. Samples and Experiments ...... 22

3.2.1. Geological Setting and Samples ...... 22

3.2.2. Experiments ...... 23 xi

3.3. Results and Discussion ...... 24

3.3.1 Geochemical Characteristics and Mineral Compositions ...... 24

3.3.2 Petrological Characteristics ...... 30

3.3.3 Effects of Composition (Organic and Inorganic) in the Pore Structure of

Transitional Shales ...... 30

3.4. Conclusions ...... 43

Acknowledgements ...... 45

References ...... 45

Chapter 4. Mineralogy and Gas Content of Upper Paleozoic Shanxi and Benxi Shale

Formations in the Ordos Basin ...... 55

4.1. Introduction ...... 56

4.2. Samples and Methods ...... 58

4.2.1 Canister Desorption Test...... 60

4.2.2 Geochemical Analysis ...... 62

4.2.3 Mineralogy ...... 63

4.3. Results ...... 63

4.3.1 CDT Gas Emission from Transitional Shale Samples ...... 63

4.3.2 Relationships between Composition and Depositional Environments ...... 66

4.4. Discussion ...... 70

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4.5. Conclusions ...... 74

Associated Content ...... 76

Acknowledgement ...... 77

References ...... 77

Chapter 5. On the Pressure and Temperature Dependence of Adsorption Densities and

Other Thermodynamic Properties in Gas Shales ...... 82

5.1 Introduction ...... 83

5.2 Theoretical Framework ...... 87

5.2.1 Langmuir Model ...... 91

5.2.2 OK Gas Lattice Theory ...... 92

5.2.3 Theoretical Constraints on Densities ...... 94

5.3 Experiments and Results ...... 96

5.3.1 Basic Geological Properties ...... 96

5.3.2 Low-pressure Nitrogen Isotherms to Determine SSA ...... 97

5.3.3 Low-pressure Carbon Dioxide Isotherms to Determine SSA ...... 97

5.3.4 High-pressure Methane Excess Adsorption Isotherms ...... 98

5.4 Interpretation and Discussion of Adsorption Data ...... 100

5.4.1 Langmuir and Ono-Kondo Fitting of Excess Adsorption Data ...... 100

5.4.2 Pressure Dependence of Adsorption Layer Densities ...... 105

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5.4.3 Temperature Dependence of Adsorption Behavior ...... 106

5.4.4 Analyses of Independent Data Sets ...... 108

5.4.5 Volume of Adsorption Layer ...... 111

5.5 Conclusions ...... 113

Acknowledgements ...... 116

References ...... 117

Chapter 6. Insights into Supercritical Gas Adsorption Theories in Nano-porous Shales under Geological Conditions ...... 125

6.1 Introduction ...... 126

6.2. Materials and Methods ...... 129

6.2.1 Experimental Data ...... 129

6.2.2 Adsorption Theories and Models ...... 130

6.3. Results and Discussions ...... 144

6.3.1 Comparison of Fitting Performance ...... 144

6.3.2 Estimation of Accessible SSA for Methane and According Density of

Adsorption Phase ...... 148

6.3.3 Calculation of Isosteric Enthalpy of Adsorption ...... 150

6.4. Conclusions ...... 156

Acknowledgements ...... 157

xiv

References ...... 158

Chapter 7. Conclusions and Future Work ...... 161

Bibliography ...... 164

Appendix A. Supporting Information for Mineralogy and Gas Content of Upper

Paleozoic Shanxi and Benxi Shale Formations in the Ordos Basin ...... 191

Appendix B. Raw Data and Fitting Parameters of the Langmuir and Ono-Kondo Models

...... 199

Appendix C. Langmuir and OK Fitting of Literature Data ...... 202

Appendix D. Fitting of other Literature and Previous Work Data ...... 207

Appendix E. An Independent Case in the Literature for Verification of Conclusions on

Fitting ...... 209

List of Tables

Table 3. 1 Statistics of TOCs of transitional Shanxi and Benxi shales from the Q14 and

Q25 wells, Yanchang area, Ordos basin...... 25

Table 3. 2 Organic matter macerals of Shanxi and Benxi shales, Yanchang area, Ordos basin...... 28

Table 3. 3 Statistics of clay minerals of Shanxi and Benxi shales, Yanchang area, Ordos basin...... 30

Table 3. 4 Pore structure parameters of transitional shale samples, Yanchang area, Ordos basin...... 33

Table 3. 5 Pore volume parameters of H13 shale sample and H13 isolated OM, Yanchang area, Ordos Basin...... 36

Table 3. 6 Pore structure parameters of transitional shale samples, Yanchang area, Ordos

Basin...... 40

Table 3. 7 Pore specific surface areas (SSA) of H13 shale samples and H13 isolated OM,

Yanchang area, Ordos Basin...... 41

Table 5. 1 Summary of basic geological properties (Q-F is quartz + feldspar; data for the

Posidonia shale sample from Gasparik et al. [63]...... 97

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2 3 Table 5. 2 SSA from CO2-DR and N2-BET (m /g). Adsorption layer density (kg/m ) at

15 MPa and each measurement temperature computed from measured � using Eq. (5.3) with SSABET, assuming a monolayer with a width of H = 0.38 nm...... 100

Table 6. 1 Summary of the fitted thermodynamic parameters by the eight supercritical adsorption models. Note that the interaction energy between the adsorbed gas molecules is

0 for the OK1 and OK3 models, and -0.001 for the OK3s model; the A is 0 for the SDR+ and SDR models...... 147

Table A. 1 CDT data for Sample 1-1, well Q14, Yanchang Oil field, Ordos basin...... 191

Table A. 2 CDT data for Sample 4-1, well Q14, Yanchang oil field, Ordos basin...... 192

Table A. 3 Data of canister desorption tests and mineral composition. Sample ID, TOC, and the final cumulative gas volumes at the reservoir temperature (Vres) and at 95 ℃ (V95).

...... 194

Table A. 4 Results of multi-linear regression fitting the emitted gas volumes at reservoir temperature to TOC and mineral compositions (significance level= 0.05)...... 196

Table A. 5 Results of multi-linear regression fitting the emitted gas volumes at 95 ℃ to

TOC and mineral compositions (significance level= 0.05)...... 197

Table B. 1 High-pressure methane isotherms for Shanxi 2-3, Shanxi 3-3, and Posidonia

...... 199

Table B. 2 Fitting parameters of Langmuir (L) and Ono-Kondo (OK) models...... 200

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Table B. 3 Linear fitting of Langmuir (L) and Ono-Kondo (OK) models as a function of temperature...... 200

Table B. 4 Linear fitting of Langmuir (L) and Ono-Kondo (OK) models as a function of temperature...... 201

Table C. 1 Linear fitting of Langmuir (L) and Ono-Kondo (OK) models as a function of temperature...... 202

xviii

List of Figures

Figure 2. 1 Structural map of Ordos Basin, NW China...... 6

Figure 2. 2 Map showing the relationship of blocks around the North China Block, where the Odors Basin is located. Modified from [10]...... 9

Figure 2. 3 Stratigraphy of the Upper Paleozoic, Ordos Basin. Modified from [26]...... 10

Figure 2. 4 Paleo sedimentary facies of Benxi (a) and Shanxi (b) periods. Modified from

[10]...... 12

Figure 3. 1 TOC distribution and trend lines (in blue) of Shanxi (a) and Benxi (b) shales, and histogram of TOC of Shanxi (c) and Benxi (d) shales from the Q14 and Q25 wells,

Yanchang area, Ordos Basin. Samples from well Q25 and Q14 are shown with red and black color, respectively...... 26

Figure 3. 2 Vitrinite reflectance distribution of Shanxi (a) and Benxi (b) shales. Samples from well Q25 and Q14 are shown with red and black color, respectively...... 27

Figure 3. 3 Triangle of composition of Shanxi and Benxi shales. Ellipse I: Benxi shale samples from Q14; Ellipse II: Shanxi shale samples from Q14; Ellipse III: Benxi shale samples from Q25; Ellipse IV: Shanxi shale samples from Q25...... 29

xix

Figure 3. 4 The PSDs of pore volume of shale samples from the N2 adsorption isotherms by the BJH method. V: Volume; D: Diameter; STP: Standard Temperature and Pressure.

...... 32

Figure 3. 5 (a) The PSDs of pore volume of H13 shale samples and H13 isolated OM from the N2 adsorption isotherms by the BJH method. (b) Absolute pore volume of 1 g shale sample and 0.0382 g (1 g × TOC) OM. V: Volume; D: Diameter; STP: Standard

Temperature and Pressure...... 34

Figure 3. 6 (a) The PSDs of pore volume of H13 shale samples and H13 isolated OM from the CO2 adsorption isotherms by the DFT method. (b) Absolute pore volume of 1 g shale sample and 0.0382 g (1 g × TOC) OM. V: Volume; D: Diameter; STP: Standard

Temperature and Pressure...... 35

Figure 3. 7 The PSDs of pore SSA of shale samples from the N2 adsorption isotherms by the BJH method. S: Pore Surface; D: Diameter; STP: Standard Temperature and Pressure.

...... 39

Figure 3. 8 (a) Comparison of PSD of pore specific surface area (dS/dD) of H13 shale samples and H13 isolated organic matter (OM) from the N2 adsorption isotherms by the

BET method. (b) Absolute pore specific surface area (SSA) of 1 g shale sample and 0.0382 g (1 g × TOC) OM. S: Pore Surface; D: Diameter; STP: Standard Temperature and Pressure.

...... 39

Figure 3. 9 (a) Comparison of PSD of pore specific surface area of H13 shale samples and

H13 isolated organic matter (OM) from the CO2 adsorption isotherms by the DFT method.

(b) Absolute pore specific surface area (SSA) of 1 g shale sample and 0.0382 g (1 g × TOC)

OM. S: Pore Surface; D: Diameter; STP: Standard Temperature and Pressure...... 40

Figure 3. 10 Classification of nitrogen adsorption/desorption hysteresis loops and reflected pore types. Modified from IUPAC [112, 113]...... 42

Figure 3. 11 N2 adsorption/desorption isotherms of transitional shale samples H18, H34,

H13 and isolated transitional shale OM sample H13, Yanchang area, Ordos Basin...... 43

Figure 4. 1 Geological map of Ordos Basin in NW China showing the location of sample wells. The grey area in the bottom represents the targeted Upper Paleozoic shale formation.

Modified from Xiong et al. (2017) [59]...... 59

Figure 4. 2 Schematic of canister desorption test. An over-saturated NaCl-water brine is used in the desorption canister and inverted graduated cylinder...... 62

Figure 4. 3 (a) Cumulative volume of gas released at atmospheric pressure from sample 4-

1, Benxi shale of well Q14. (b) Volumetric rate of gas release. The tup indicates the time when the temperature of the desorption canister was raised to 95 ℃ (from the reservoir temperature of 80 ℃). Segments I, II, and III indicate three stages of desorption...... 64

Figure 4. 4 Correlation between gas emission at 95 ℃ and the reservoir temperature (Tres) for the Lower Paleozoic (a), which includes two subformations: the Lower Permian Shanxi shales from deltas (b) and the Upper Carboniferous Benxi shales from lagoons (c)...... 65

xxi

(c). The Longmaxi shale was deposited in a deep shelf. The Eagle Ford shale was deposited in a platform and trough between reefs [127]. The Barnett shale was deposited in a deeper water foreland basin with euxinic bottom water [67]. The Lower Permian Shanxi shale was deposited in a delta, and the Upper Carboniferous Benxi shale was deposited in a lagoon, which tends to comprise of more clay minerals due to its nature of low water energy and reducing settings...... 67

Figure 4. 6 Correlation between clay and TOC (a) and quartz and clay (b) in shale cores from the Lower Paleozoic, Ordos Basin (depth >3,000 m). Samples are over-mature and in the gas window. Blue circle points represent Shanxi shale, red square points for Benxi shale.

...... 69

Figure 4. 7 Correlation between emitted gas and TOC at the Shanxi shale (a), and at the

Benxi shale (b). The gas volumes have been corrected to STP for comparison. The circles represent emission at the reservoir temperature, with triangles for emission at 95 ℃. .... 73

Figure 5. 1 Schematic illustration of surface absolute and excess adsorption by the layer model (a and c) and the Gibbs representation (b and d) (modified from Lowell et al. [141]).

The green circles in (c) and (d) are the molecules of adsorptive. c or ρ represents the local concentration or mass density of adsorptive; � or � represents the concentration or mass density of bulk gas phase; z is the distance from the surface; GDS is Gibbs dividing surface; nabsolute is the amount adsorbed in the layer model; nbulk in (a and c) is the amount remaining in the bulk gas phase; nexcess describes the surface excess amount in the Gibbs representation; nbulk in (b and d) is the amount counted in the bulk gas phase. The adsorbing

xxii space is the volume of adsorption in this context. Only the amount of gas molecules in the red dashed outline is counted as nexcess...... 88

Figure 5. 2 Procedure of the proposed experimental method of estimating the density of adsorption phase at different pressures for each high-pressure methane excess adsorption isotherm...... 91

Figure 5. 3 Low-pressure nitrogen isotherms at -196 ℃ on (a) Shanxi 2-3, (b) Shanxi 3-3, and (c) Posidonia shale samples. P0 is the saturation vapor pressure of nitrogen...... 98

Figure 5. 4 Measured excess adsorption isotherms at 65, 75, and 95 ℃ for Shanxi 2-3,

Shanxi 3-3, and Posidonia shale samples. Fitted excess and absolute adsorption isotherms from the Langmuir and multilayer OK models are extended to pressures up to 100 MPa.

...... 103

Figure 5. 5 Adsorption layer densities derived from the Langmuir and OK model fitting in

Fig. 5.4. Also shown are the bulk density and �⁄� ratios...... 104

Figure 5. 6 Scaling of maximum adsorption layer density � and adsorbent-adsorbate energy �⁄� with temperature...... 107

Figure 6. 1 Schematic of the Langmuir theory. The green circles denote the gas molecules.

GDS represents the Gibbs dividing surface. All the gas molecules in the volume of the adsorption phase are regarded as the absolute adsorbed gas. Only the gas molecules in a red outline are what we directly measure as excess adsorbed gas...... 130

Figure 6. 2 Schematic of bilayer adsorption at the atomic scale...... 133

Figure 6. 3 Schematic of Ono-Kondo gas lattice model at equilibrium...... 138

xxiii

Figure 6. 4 Excess and absolute adsorption isotherms fitted to experimental data for

Sample 4 and 5 [158] via eight different supercritical adsorption models (18 more isotherms are fitted in Fig. D.1)...... 145

Figure 6. 5 Underestimation of the nitrogen BET SSA for the total accessible SSA for methane. Isotherms 1-9 denote Shanxi 2-3 at 65, 75, and 95 °C, Shanxi 3-3 at 65, 75, and

95 °C, and Posidonia at 65, 75, and 95 °C, respectively...... 150

Figure 6. 6 Comparison between the estimated isosteric heat of adsorption by the commonly used (a) Xia’s equations and (b) Van’t Hoff equation...... 151

Figure 6. 7 Estimation of isosteric heat of adsorption using the Van’t Hoff equation at different absolute adsorption for (a) sample 4 and (b) sample 5...... 152

Figure 6. 8 The increase of isosteric heat of adsorption shows both a linear (sample 5 and

6) and a nonlinear (sample 4) relationship with absolute adsorption. Sample 6 (YC4-61) is added for comparison [158]...... 153

Figure A. 1 Canister desorption tests. The final volumes at the reservoir and elevated temperatures (indicated by solid dots) were used in the analyses of the emitted gas volumes as a function of TOC and mineral compositions...... 193

Figure C. 1 Measured excess adsorption isotherms at 35, 50, and 65 °C for Samples 3-6, corresponding to YC4-33, YC4-47, YC4-54, and YC4-61 in Tian et al. [158]. Fitted excess and absolute adsorption isotherms with either pressure-independent (with fitting parameters from Tian et al. [158], denoted as LT in the legend) or pressure-dependent �.

xxiv

The latter is modeled with both Langmuir (L, solid) and Ono-Kondo (OK, dotted) models.

...... 203

Figure C. 2 Adsorption layer densities derived from the Langmuir model fitting in Fig.

C.1. Also shown are the bulk density and �⁄� ratios. Finally, we include adsorption layer densities computed from GCMC simulations in 5 nm carbon-slit pores at 60 °C in the

65 °C panels [130,183]...... 204

Figure C. 3 SSA estimates from 4 different approaches: (� − �)⁄� with pressure- dependent �(�) (denoted as p-fit in the legend), (� − �)⁄� with pressure-

independent � , and − !" # derivatives directly from the measured data and evaluated from a Langmuir model fit...... 205

Figure C. 4 Langmuir and OK fitting of excess and absolute adsorption amounts as well as adsorption layer densities from [130]. Excess adsorption measurements and GCMC simulated densities are shown in circles. The data are fitted with twice the SSA measured

2 with low pressure nitrogen isotherms (2 × 5.6 m /g) to agree with GCMC estimates of �.

...... 206

Figure D. 1 Fitting of other six shale samples in Tian et al. (2016) using all eight supercritical adsorption models [158]...... 207

Figure D. 2 Fitting of three shale samples in Xiong et al. (2020) with estimated SSAs [193].

...... 208

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Figure E. 1 Fitting of four Posidonia shale samples in Rexer et al. (2014) with estimated

SSAs [69]. For the shale sample with a SSA higher than 10 m2/g, the fitting often ends up with the same estimated SSA as the measured one...... 209

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Chapter 1. Introduction

Shale is an important component of the fined-grained sedimentary rock group, which contributes about two thirds of all sedimentary deposits [1]. Shale is a type of clastic sedimentary rock that contains organic matter and over 50% particles (component grain, crystal, or biochemical product) smaller than 62.5 µm by volume or weight and which develops fissility [2]. However, there is still no clear consensus across disciplines in how to classify shales given the incredibly small size of the particles and the high compositional variation [1]. High-resolution imaging techniques suggest that highly heterogeneous minerals can be observed including all common grain types from sandstones, limestones, and pelagic sediments to inorganic and biogenic products after sedimentation [1,3-5].

Discrimination of particles can be theoretically achieved by the improvement of high- resolution imaging methods because the current resolution limit is likely below the lower limit of constituent particles [6,7]. Considering the tripartite compositional classification,

Milliken (2014) tried to classify fine-grained sedimentary rocks (e.g., shale, mudstone, and claystone) based on extrabasinal and intrabasinal components [1]. Tang et al. (2016) proposed another compositional classification exclusively for shales within the scope of clastic sedimentary rock to differentiate from carbonate rocks, which possess a well- established classification modified from Dunham (1962) and Folk (1980) [2,8,9].

Unfortunately, a universally accepted classification has not been established to date. 1

Besides classification, several critical questions remain regarding even the gas storage capacities of subsurface shales, which is significant for geologists and engineers to plan exploration and exploitation. The research in this thesis aims to address, among others, the following questions:

• How do organic and inorganic minerals contribute to the development of shale pore

systems that fundamentally determine the storage capacity?

• How is the amount of shale gas related to mineralogy?

• How can we estimate the amounts of adsorbed gas on the pore surfaces?

• How can we accurately estimate the total amount of shale gas including free gas,

adsorbed gas, and dissolved gas?

These are critical questions to design optimal production strategies of shale gas.

The United States initiated the shale gas revolution. More recently and continuing into the future, Canada, China, and European countries have followed, but compared to the well-studied Barnett, Bakken, and Marcellus shales in the US, the properties of shale formations in the rest of the world are still poorly documented.

In this work, we study shale samples from the Ordos basin, NW China and

Posidonia shale in Germany. Chapter 2 introduces the basic geological background of the

Ordos Basin and the study area; the subsequent four chapters address the aforementioned questions. Specifically, in Chapter 3, the roles of organic and inorganic minerals in pore development are investigated. We used Soxhlet extraction and low-pressure gas adsorption isotherms to investigate the contribution of organic and inorganic minerals to the total pore

2 structure, which helped us better understand the relationship between the mineralogy and pore structure; in Chapter 4, we apply multilinear regressions to investigate the relationships between stored gas and mineralogy measured by canister desorption testing; in Chapter 5, to better understand subsurface supercritical adsorption, we propose an experimental procedure to obtain the pressure-dependent density of adsorption layers at different temperatures and discuss the temperature and pressure dependence of important thermodynamic parameters in the assessment of subsurface adsorbed gas; in Chapter 6, we modify and compare various commonly used adsorption models under supercritical conditions (e.g., Langmuir, Brunauer-Emmett-Teller, supercritical Dubinin-Radushkevich, and Ono-Kondo models) in terms of assumption, fitting performance, advantages, and limitations.

References

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migrating floccule ripples. Science 2007, 318, 1760–1763.

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Chapter 2. Geological Background

The Ordos basin is located in the western North China block (also called Sino-

Korean platform) and with a surface area of 320,000 km2 (i.e., 124,000 mi2) it is the second largest sedimentary basin in China [10,11]. Six 2nd order structural units make up this craton basin: Jinxi folding belt, Yimeng uplift, Yishan slope, Tianhuan depression, Western edge thrust belt, and Weibei uplift (Fig. 2.1). The Ordos basin is bounded by the Yin,

Luliang, Qinling, Liupan, and Helan Mountains on the north, east, south, southwest, and northwest, respectively (Fig. 2.1) and provides the largest intraplate basin of the Yellow

River drainage area [11]. Petroleum discoveries in the Ordos basin initiated in 1907 and began to attract intensive attention of exploration geologists by the 1930s to 1940s due to significant hydrocarbon discoveries [10].

The tectonic evolution of the Ordos basin has almost reached a universal agreement in which its development can be divided into three or four major stages. The basement of the Ordos basin is pre-Sinian metamorphic rock [11], e.g., Archean granulites and lower

Proterozoic greenschists [10]. The work by Sun et al. (1989), who divided the evolution of the Ordos basin into three major stages, became an important reference for later research in the Ordos basin [10,12]. Sun et al. (1989) proposed an early Paleozoic marine carbonate platform stage, a late Paleozoic-early Mesozoic intermediate stage of alternation from marine to inland basinal facies, and a final Mesozoic-Cenozoic polycyclic inland basin 5 stage [10,12]. Yang et al. (2005) later suggested that the tectonic evolution of the Ordos basin in the Paleozoic-Mesozoic can be further divided into three major stages: the

Cambrian-Early Ordovician cratonic basin with divergent margins, the Middle Ordovician-

Middle Triassic cratonic basin with convergent margins, and the Late Triassic-Early

Cretaceous intraplate remnant cratonic basin [10]. Xiao et al. (2005) divided the tectonic evolution into four major evolutionary stages, i.e., the early Paleozoic marine platform stage, the late Paleozoic marine and terrestrial alteration stage, the Mesozoic foreland basin stage, and the Cenozoic basin margin faulting and subsidence stage [13-15].

Figure 2. 1 Structural map of Ordos Basin, NW China.

Specifically, as a sub-tectonic unit to the North China Plate, the Ordos Basin experienced tectonic events together with the North China Plate in the period of Late

Paleozoic (Fig. 2.2). During the Cambrian to the Early Ordovician (Caledonian Movement), divergent continental margins of the paleo-Asian sea and the Paleo Qinling sea developed at the north and south of the Ordos Bains, respectively (Fig. 2.2) [10, 11]. Due to the subduction of the Qaidam block to the south and the Paleo Asian ocean plate to the north of the Ordos area during the Middle Ordovician-Silurian (Fig. 2.2), no sedimentation was recorded within the Middle Ordovician to the Mississippian, resulting in a regional unconformity [10,16]. From the Pennsylvanian to the Early Permian (Variscan Orogeny), due to the collision between the Tarim – North China block and Siberia microcontinent –

Mongolian arcs, north-south folding of Helan-Liupan mountains developed on the west, while the Yin mountains were gradually uplifted on the north and became the main sediment input for the Ordos Basin (Fig. 2.2) [10,11]. The initial framework of the Ordos basin formed. Almost at the same time, the South China block began to subduct beneath the North China block from the east and migrated west beneath the Qiangtang block during the Late Permian-Middle Triassic (Fig. 2.2) [10,16,17]. The Ordos basin has been described as a stable slowly subsiding landmass during the Variscan Orogeny [11]. Also due to the subduction of the South China block beneath the Qiangtang block, a remnant ocean basin developed in the Songpan-Ganzi area during the Late Permian-Middle Triassic

(Fig. 2.2) [10,16]. The Permian sea retreated from the southern and southwestern Ordos

7 area and an emergent landmass developed [11]. From the latest Early Triassic to the beginning of the Early Jurassic (Indosian Orogeny), due to collisions between the North and South China blocks, and the Qiangtang block and Eurasian plate (Fig. 2.2), three phases of tectonic movements reactivated the folding of the Qingling geosyncline to the south [11], allowed the thrust of Liupan Mountains on the southwest (Fig. 2.1) [10,18], and resulted in a closed basin in the Late Triassic. Although the Ordos basin was a low landmass, it still experienced intensive denudation during this time, which caused a regional unconformity between the Triassic and Jurassic formations [10,11,19]. During the late Early Jurassic-early Late Cretaceous (Yanshanian Orogeny), due to the subduction of the Kula-Pacific plate underneath the Eurasian plate and the collision between the Lhasa block and the Eurasian plate, the Luliang Mountains (Fig. 2.2) [10,12,20] and the Helan fold-thrust belt [10,18] formed, respectively. At the end of the Late Jurassic-beginning of the Early Cretaceous, the Ordos basin was tilted westerly and the sedimentary formations were folded into a north-northeasterly trending synclinorium with scattered faults [10,21].

At the end of the Early Cretaceous, the Ordos basin with surrounding Pacific areas in

Eastern China was uplifted, leading to the cessation of deposition [10,22]. During the

Tertiary Himalayan Orogeny, active tectonic events resulted in a distinct graben fault in the southern area, reactivation of the overthrusts along the western border, and basaltic eruption to the northeast [11].

Figure 2. 2 Map showing the relationship of blocks around the North China Block, where the Odors Basin is located. Modified from [10].

The sedimentation of the Ordos basin mainly includes the Paleozoic and Mesozoic formations [10,11]. In the period of Cambrian-Early Ordovician, shallow marine and tidal flat deposition of open platform limestone and platform evaporates extensively occurred in the main Ordos area, due to a large-scale marine transgression followed by marine regression [10,11]. Subsequently, during the gap of the Middle Ordovician-Mississippian, the Cambrian and the Early-Middle Ordovician strata were intruded by igneous rocks

[11,23] and the deposited Ordovician dolomites experienced karstification [10]. During the

Pennsylvanian-Permian, the Ordos area accumulated the richest coal seams in North China

(Fig. 2.3) [10,11,23]. In the Pennsylvanian, the Ordos Basin experienced a regional marine

9 transgression again, depositing the Benxi Formation that includes extensive sediments of a tidal flat in the central-eastern, basal bauxitic mudstones, and combination of shales and thin limestones (Fig. 2.3) [10,24]. Afterward, the Pennsylvanian Taiyuan Formation consists of extensive shallow marine and tidal flats, and minor delta facies on the northern side, including shales, sandstones, carbonates, and coals. In the Lower Permian, the Shanxi

Formation developed in the central and southern Ordos basin consisting of extensive delta and shallow lacustrine mudstones and shales interbedded with coal and minor marine carbonates (Fig. 2.3) [10,25,26].

In this work, we target the shales in the Benxi and Shanxi Formations.

Figure 2. 3 Stratigraphy of the Upper Paleozoic, Ordos Basin. Modified from [26].

Regarding the depositional setting and deposition of the Upper Pennsylvanian (or

Carboniferous) Benxi formation, there is some disagreement in the literature. Fu et al.

(2003) and Yang et al. (2005) suggest that the Benxi formation consists of bauxitic mudstones and shales interbedded with limestones, which deposited in an extensive tidal- flat or restricted platform in the central and eastern Ordos basin (Fig. 2.4a) [10,24]. Xiao et al., (2005) describe the depositional settings of Benxi and Shanxi as a marine shore plain and swamp [13]. Liu et al. (2009) summarize that the depositional environment of the

Benxi formation consists of clays, sandstones, and coal and was deposited in a delta and lagoon environment [27]. Wang et al. (2015) and Sun et al. (2017) agree with Yang et al.

(2005) that the Benxi formation deposited in a tidal flat or restricted platform [10,28,29].

Li et al. (2019) describe the Benxi formation as a clastic coast sedimentary system affected by seawater transgression with coal in shallow lagoons and peat swamps behind a barrier island [30,31]. With respect to the Shanxi formation of thin fine sandstone, gray mudstone, thick shale, and coal, almost all the literature suggests that its deposition occurred in fluvial, delta, shallow lacustrine, and swamp environments (Fig. 2.4b) [10,25,27,29,31-33].

Figure 2. 4 Paleo sedimentary facies of Benxi (a) and Shanxi (b) periods. Modified from [10].

Our study area is part of the Yanchang Oilfield on the southern Yishan slope (Fig.

2.4). Based on the paleo-geographical maps in the Pennsylvanian and Early Permian, the targeted Benxi shale was considered as deposition in tidal flats and lagoons, while the

Shanxi shales deposited as sediments in deltas and shallow lakes (Fig. 2.4) [10,11]. Lee

(1986) reported that the kerogen type of the Benxi and Shanxi formations is a humic type

12 with low ratios between the hydrocarbon and organic carbon [11,34]. Xiao et al. (2005) analyzed the macerals of the coal seams and associated mudstone and suggested that the same maceral contained a vitrinite and inertinite content of >85%, indicating a type III kerogen [13]. Subsequent works in the literature followed the same categorization of type

III kerogen [35-37]. Sun et al. (2017) tested the organic carbon isotopic composition

(� �) of 17 Shanxi core samples, ranging from -24.8 to -23.6 ‰, concluding that the kerogen type was type III based on an evaluation standard in the literature [29,38]. Li et al. (2019) analyzed 6 Shanxi and 3 Benxi mudstone/shale samples and observed 65%-

85% vitrinite and 11%-35% inertinite with negligible liptinite and no sapropelite, also suggesting that the kerogen in the Benxi and Shanxi formations is type III [31].

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controls in the western Ordos basin, China: Basin Research 2000, 12, 1–18.

[19] Liu, S. The coupling mechanism of basin and orogen in the western Ordos basin and

adjacent regions of China. Journal of Asian Earth Sciences 1998, 16, 369–383.

[20] Klimetz, M.P. Speculations on the Mesozoic plate-tectonic evolution of eastern China.

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depositional system distribution of late Paleozoic era in Ordos basin (in Chinese).

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an integrated stratigraphic forward and petroleum system modeling. Marine and

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Chinese with English abstract).

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Chapter 3. Pore Structure of Transitional Shales in the Ordos Basin, NW China:

Effects of Composition on Gas Storage Capacity

[Published in: Fuel, 206 (2017), 504-515]

The recoverable resource of shale gas is 25 trillion cubic meter, 33% of which is stored in transitional shales in China. This work investigates the effects of organic and inorganic compositions on the development of Upper Paleozoic transitional shale pore structures through a combination of petrophysical and geochemical measurements. 42 shale samples were collected from marsh-lagoon and coastal delta settings in the Ordos Basin,

NW China. The samples include the Upper Permian Shanxi shale (average total organic carbon (TOC) of 1.58 wt.%, Type III kerogen, average vitrinite reflectance (Ro) 2.6%), and the Upper Carboniferous Benxi shale (average TOC of 1.91 wt.%, Type III kerogen, average Ro 2.74%) at the over-mature stage or dry gas window. An important characteristic of these shales is the large proportion of clay minerals (~69% in Benxi shale and 54% in Shanxi shale). The quartz content is ~17% and 40% for Benxi and Shanxi shales, respectively. The pore structure of three samples and one isolated kerogen sample is analyzed via both low- pressure nitrogen and carbon dioxide adsorption methods. Low pressure nitrogen adsorption experiments show that Benxi and Shanxi shales characterized by ultra-low porosity and permeability develop mainly silt-shaped pores and potentially ink-bottle-shaped pores. We find

18 that increasing fractions of organic matter (OM) result in a decrease in both total pore volume and specific surface area (SSA). Low pressure carbon dioxide adsorption experiments show that micropore volumes nonlinearly increase with increasing OM, although the contribution of organic micropore volume is limited. The mesopore and macropore volumes of inorganic compositions contribute mostly to the total pore volume.

The OM in transitional shales in Yanchang mainly develop mesopores (with <5 nm diameters), which significantly contribute to the SSA, while micropores are the main contributor to SSA in the inorganic matter. For thermally over-mature transitional shales, clay minerals contribute the most to SSA and pore volume as well as the storage capacity of absorbed and free gas.

3.1. Introduction

During the past two decades, the shale gas revolution has dramatically changed the natural gas market structure in the US and China. This is related to the success of emerging technologies in horizontal drilling and hydraulic fracturing [39-46]. Approximately one third of the US energy consumption is from natural gas compared to other fossil fuels and renewable energies [47]. Shale gas is recognized as the cleanest fossil fuel [48]. In 2015, it produced ~47% of US natural gas, up from 34% of the total U.S. dry natural gas production in 2011 [47].

Increasing commercial importance has drawn more attention to shale and shale gas

[49-56]. Understanding the pore structure of shales is critical in the evaluation, exploration and exploitation of shale gas. The pore systems of gas shales are commonly characterized by, micropores (pore diameter < 2 nm), mesopores (2-50 nm) and macropores (>50 nm) 19

[55]. Shale gas has been recognized to exist in three phases: 1) compressed free gas in the shale pore space, 2) adsorbed gas on the surface of organic pores and clay minerals and 3) dissolved gas in the fluid and organic matter within shales [56]. Free gas is frequently calculated by the reservoir pore volume and gas equation-of-state, which is a function of pressure, temperature, and gas compressibility factor. The amount of free gas is thought to correlate well to the volume of meso- and macropores, which account for most of the absolute pore volume. Adsorbed gas has a much higher (heterogeneous) density than free gas at the same temperature and pressure and accounts for most of the gas in micro- and mesopores. Adsorption may account for 20%-85% of total shale gas-in-place (GIP) [56,

57]. Its contribution is commonly estimated by high pressure methane adsorption isotherms.

Recent studies show that dissolved gas could also be significant in oil-window mature shales. The fraction of dissolved gas correlates with organic pores, fluid and reservoir pressure, and temperature [58, 59].

Unlike conventional resources, shale has long been thought of as a source rock, characterized by ultra-low porosity and permeability matrix and extreme heterogeneity.

Loucks et al. [60] suggested that organic matter (OM) within shales controls the development of abundant nanopores and plays a significant role in shale gas storage [58-

67].

OM in marine and continental gas shales has been shown to principally contribute to the development of micropores and mesopores as well as clay minerals. These are the main contributors to adsorbed gas. Inorganic particles mainly develop macropores that provide the free gas storage [58,60,63-69]. The development of organic pores is

20 complicated by the content, type, and maturity of OM [50,66,70-72]. Kerogen is often classified into three types: I, II, and III. Higher kerogen types (e.g., III) typically have larger fractions of micropores, gas-wet aromatics, and polar function groups [60, 66], which together provide a higher adsorption capacity.

The total organic carbon (TOC) content is positively correlated with shale gas adsorption capacity and content of shale gas [60,66,73-76]. However, exceptions do exist because the contribution of clay minerals can complicate shale gas adsorption capacity and content. It has recently been suggested that OM can develop nanopores in pyrobitumen and kerogen and that organic porosity generally increases with increasing maturity [77-83].

However, many researches have mainly focused on marine and terrestrial shales and less attention has been given to transitional shales [42,59,79-81, 84-89]. Transitional shale refers to the shale deposited between terrestrial and marine settings, e.g., lagoon, delta, beach and tidal flat. In addition, the role of OM in transitional shales remains poorly understood. Low pressure carbon dioxide and nitrogen isotherms are universally used to characterize pore size distribution of micropores and mesopores, respectively [58,61,69].

Previous studies mainly focused on the relationship between TOC and shale gas adsorption capacity and content [62,66,69,90]. However, few studies were conducted on the pore structure of isolated kerogen.

The Late Paleozoic transitional shales in Ordos Basin distribute widely and develop dark organic rich shales. It is regarded as one of the most important transitional shale gas targets in China [91]. The goal of this paper is to investigate the pore structure of transitional shales in Ordos Basin. We focus on the effect of shale composition on the

21 formation of pore size distribution. We present geochemical and petrological characteristics of transitional shales in Section 3.3.1 and 3.3.2. The roles of OM in transitional shale pore system as well as shale gas storage are considered in Section 3.3.3.

3.2. Samples and Experiments

3.2.1. Geological Setting and Samples

The Ordos Basin is the second largest sedimentary basin in China. It is a craton basin located on the central North China Plate that consists of six 2nd order structural units.

Our study area is part of the Yanchang Oilfield on the southern Yishan slope (Fig. 2.1).

The transitional shale samples are from recently drilled wells (Q14 and Q25) that target the Upper Carboniferous Benxi and the Lower Permian Shanxi (Fig. 2.4) with an average thickness of 30 and 95 m in the study area, respectively. These shales were regarded as deposition in marsh-lagoon and coastal delta environments, and developed sandstone, coal, and dark shale/mudstone that widely distributed in the tectonically stable

Ordos Basin. During the past few years, Yanchang Oilfield Company has targeted the

Upper Triassic mature lacustrine Chang 7 and 9 shales as potential terrestrial shales for shale gas and oil with vitrinite reflectance of 0.83%-1.10%. Recently, Benxi and Shanxi shales, which are buried by over 3000 meters, were targeted to investigate the shale gas capacity of transitional shales due to the kerogen of type III and higher thermal maturity than Triassic lacustrine shales [10]. There were 42 core samples collected from Q14 and

Q25 wells to carry out geochemical experiments. 38 of the 42 samples were further used for petrological measurements. Three of the 38 samples with different TOCs were further

22 chosen to characterize the pore structure of the Late Paleozoic transitional shales and the effects of shale composition on pore size distribution of transitional shales.

3.2.2. Experiments

3.2.2.1 Organic Geochemistry

The organic geochemistry experiments were conducted at State Key Laboratory of

Petroleum Resource and Prospecting in China University of Petroleum, Beijing. The collected 42 shale samples were powdered and less than 200 mesh particles were used to conduct the TOC analysis. Rock-Eval analysis was performed using Leco CS-230 carbon analyzer and OGE-II rock pyrolyzer. Before carrying out TOC and Rock-Eval analysis, about 100 mg sample powder was placed in a crucible with 5% HCl at 80℃ to remove the inorganic carbon within carbonate.

The macerals and maturity of organic matter were determined using MPV-SP microscope, photometer and 308-PV microscope photometer. The results of Rock-Eval analysis, the maximum volatilization temperature of hydrocarbons (Tmax) were also used to determine the maturity data. Two sets of maturity data were compared to obtain the maturity of the targeted transitional shales.

Isolated kerogen was prepared according to the standard procedure: the shale sample was treated with hydrofluoric and hydrochloric acid to remove the inorganic composition of shales except OM [92]. Pore size distribution measurements were performed on the isolated kerogen powder.

3.2.2.2 Mineralogy

X-ray diffraction (XRD) analysis was carried out on shale powder less than 200 mesh (i.e. <75 μm) using a Bruker D8 DISCOER diffractometer (Co Kα-radiation, 45 kv,

35 mA) following the two independent processes of the CPSC procedure. A scintillation was used to measure the diffracted beam with 0.02°2θ step size and 20s step time.

Diffractograms were derived from 2° to 76°2θ.

3.2.2.3 Porosity, PSD, and SSA

Porosities of all three collected shale core samples were determined using Helium porosimeter. Low-pressure N2 and CO2 isotherms were measured using Autosorb iQ

Station 1 (77 K) and 2 (273 K) of Quantachrome® ASiQwin™ v4.0. The specific surface area (SSA) was determined by the Brunauer-Emmett-Teller (BET) model [93] and the pore size distribution (PSD) by the Barret-Joyner-Halenda (BJH) theory [94].

The shale samples were subsequently manually ground and sieved into grains of

80-120 mesh size (i.e. 0.12-0.18 mm), dried and degassed in a vacuum oven at 200℃ for

24 h to remove adsorbed gas, moisture and volatile matter before low-pressure N2 and CO2 isotherms measurements.

3.3. Results and Discussion

3.3.1 Geochemical Characteristics and Mineral Compositions

3.3.1.1 Organic Matter Richness

TOC measurements for the 42 fresh drilling cores show that both the transitional

Shanxi and Benxi shales are organic-rich in the Q14 well and organic-moderate in the Q25

24 well (Table 3.1). The distribution of sampling and TOCs is present in Fig. 3.1a, b. The

TOC of Shanxi ranges 0.01-13.68 wt.%, averaging 1.91wt.% (Fig. 3.1c), and Benxi ranging 0.07-9.92 wt.% with an average of 1.58 wt.% (Fig. 3.1d). Fig. 3.1c, d shows that transitional shales in the Q25 well have higher heterogeneity than those in the Q14 well.

The most promising shale intervals may locate at the bottom of the transitional pyrite- bearing shales that probably deposited at deeper water depths.

Table 3. 1 Statistics of TOCs of transitional Shanxi and Benxi shales from the Q14 and Q25 wells, Yanchang area, Ordos basin.

Strata Shanxi TOC (wt.%) Benxi TOC (wt.%) Statistic Min Max Mean Min Max Mean Q14 1.09 13.68 3.40 0.19 9.92 3.33 Q25 0.01 4.31 1.38 0.07 2.70 0.70 Total 0.01 13.68 1.91 0.07 9.92 1.58

Figure 3. 1 TOC distribution and trend lines (in blue) of Shanxi (a) and Benxi (b) shales, and histogram of TOC of Shanxi (c) and Benxi (d) shales from the Q14 and Q25 wells, Yanchang area, Ordos Basin. Samples from well Q25 and Q14 are shown with red and black color, respectively.

3.3.1.2 Maturity and Macerals of Organic Matter

The maturity was derived from vitrinite reflectance (Ro) measurements (Fig. 3.2).

The Tmax of Rock-Eval results were also used to compare to the vitrinite reflectance data.

The Tmax of the samples ranges from 541 to 584 °C. The results show that the average maturity of Shanxi shales is 2.6% and that of Benxi shales is 2.74%, indicating that the

Carboniferous-Permian transitional shales are at over mature stage at present, i.e. dry gas window.

Figure 3. 2 Vitrinite reflectance distribution of Shanxi (a) and Benxi (b) shales. Samples from well Q25 and Q14 are shown with red and black color, respectively.

The macerals of organic matter of core samples are presented in Table 3.2. The transitional shale samples were mainly regarded to consist of type III organic matter [26，

95,96]. And Shanxi and Benxi shales show an average 76.4% and 61.7% of vitrinite, respectively. The higher vitrinite in the Shanxi shales is likely because it was deposited in shallower water depth with a higher input of high-level plants.

Table 3. 2 Organic matter macerals of Shanxi and Benxi shales, Yanchang area, Ordos basin.

Vitrinite + Inertinite (%) Vitrinite Ratio of unstructured Va (%) Min Max Mean Mean (%) Q25 90 100 98.2 74.0 / Q14 97.3 100 99.6 76.4 / Shanxi 90 100 98.6 74.6 72.72 Q25 88.9 100 96.4 61.0 / Q14 93.1 100 97.5 62.2 / Benxi 88.9 100 97.0 61.7 67.91 a unstructured V.: unstructured vitrinite.

3.3.1.3 Mineral Composition

Shanxi and Benxi shale samples both contain rich clay minerals with average compositions of 54.6% and 68.9%, respectively (Fig. 3.3). The second highest composition is quartz (averaging 39.7%) in Shanxi shales and pyrite (averaging 23%) in Benxi shales.

Clay minerals and quartz account for 94.3% of Shanxi shales and 85.6% of Benxi shales.

This is dramatically different than marine and terrestrial shales [59]. Generally, the Benxi shales have higher clay minerals (14.3% higher than Shanxi shales), as shown in Fig. 3.3. 28

The clay minerals are dominated by illite/smectite mixed layers (averaging 25.1% of shales, 46.2% of total clay minerals) and illite (averaging 12.6% of shales, 23.2% of total clay minerals) in Shanxi shales, and kaolinite (averaging 50.3% of shales, 72.7% of total clay minerals) and chlorite (averaging 17.7% of shales, 12.1% of total clay minerals)

(Table 3.3).

Table 3. 3 Statistics of clay minerals of Shanxi and Benxi shales, Yanchang area, Ordos basin.

I-S (%) Illite (%) Kaolinite (%) Chlorite (%) Clay (%) Rel.a Abs.b Rel. a Abs. b Rel. a Abs. b Rel. a Abs. b Q25 54.6 45.3 24.9 23.2 12.7 18.4 9.9 13.1 7.1 Q14 54.6 48.9 25.6 23.1 12.3 18.9 11.5 9.1 5.2 Shanxi 54.6 46.2 25.1 23.2 12.6 18.5 10.3 12.1 6.6 Q25 63.2 5.3 3.2 2.0 1.2 71.3 45.3 21.5 13.5 Q14 73.5 7.8 5.5 3.8 2.7 73.8 54.3 14.6 11.0 Benxi 68.9 6.7 4.5 3.0 2.0 72.7 50.3 17.7 12.1 # All values are mean values. a Rel.: Relative content. b Abs.: Absolute content.

3.3.2 Petrological Characteristics

The primary features of transitional Shanxi and Benxi shales are low porosity and permeability. Fu et al. [97] reported that the porosity of Shanxi shales is 0.92%-12.36%, with an average of 6%, and permeability of 10-8 - 10-5 μm2. Benxi shales have porosities of

4.3%-12.2% (an average of 9%) and permeability less than 10-8 - 10-5 μm2. Other studies found the porosity of Shanxi and Benxi shales at about 4% [98,99].

3.3.3 Effects of Composition (Organic and Inorganic) in the Pore Structure of

Transitional Shales

3.3.3.1 Pore Size Distribution

To investigate the role of organic matter on the pore structure of transitional shales, we select three samples with different amounts of TOC. The PSDs of mesopores were

30 determined from nitrogen adsorption isotherms by the Barrett-Joyner-Halenda (BJH) method (Fig. 3.4) [94]. The micropore volume was obtained from carbon dioxide adsorption isotherms using the Dubinin-Radushkevich (DR) method (Table 3.4) [100].

Surprisingly, as shown in Fig. 3.4 (and Table 3.4), in our samples the total pore volume decreases with increasing TOC. This could be due to pore space collapse as the organic matter and associated compressibility increase. This distinguishes our findings at over 3000 m depths from earlier research at shallower depths, where pore space was observed to increase with TOC [80]. Further research is needed to discover how the correlation between total pore volume and TOC evolves, e.g., in different depositional environments and burial depths (and maturity).

The relative volumes of micro-, meso- and macro-pores are summarized in Table

3.4. The micropore volume increases non-linearly with increasing TOC. This suggests that the development of micropores is related to the amount of organic matter, especially because the clay content is decreasing with increasing TOC in our samples (Table 3.4).

This is in line with earlier studies [50,80].

The volume proportion of mesopores is seen to decrease with increasing TOC. The development of mesopore volume has been thought to correlate with both inorganic matter and organic matter. Our experiments suggest that increasing organic matter will increase the compressibility of shale and result in more compaction. Another reason may be that mesopores are formed first in inorganic particles but are later filled with OM as the TOC increases. This would result in a decrease in mesopores and an increase in micropore volume.

Macropores are thought to mainly relate to inorganic components. According to our results from N2 adsorption isotherms, the percentage of macropore volume decreases dramatically with increasing TOC, or perhaps more importantly, with decreasing clay content (Table 3.4). This decrease in porosity is likely caused by compressibility and diagenetic compaction. However, we note that the N2 adsorption method only measures

50-300 nm of macropores.

Figure 3. 4 The PSDs of pore volume of shale samples from the N2 adsorption isotherms by the BJH method. V: Volume; D: Diameter; STP: Standard Temperature and Pressure.

Table 3. 4 Pore structure parameters of transitional shale samples, Yanchang area, Ordos basin.

Pore Volume (cc/g) Average TOC Clays Quartz pore Sample Micropores Mesopores Macropores (wt.%) (%) (%) diameter Total (nm) a PV Pct Pct Pct PV PV PV (%) (%) (%) H18 1.31 58.4 37.1 3.414 0.073 0.002 2.74 0.028 38.38 0.040 58.90 H34 2.70 55.8 22.7 3.425 0.063 0.007 11.10 0.018 29.19 0.040 59.70 H13 3.82 40.7 54.5 6.558 0.020 0.009 45.00 0.006 31.20 0.010 23.80 a PV: Pore volume. Pct: Percentage.

To investigate the role of organic matter on the PSD of shales, we isolated the organic matter in the H13 sample to measure N2 and CO2 adsorption isotherms repeatedly.

The PSDs of the H13 organic matter and of the full H13 shale sample are presented in Fig.

3.5a, 3.6a, respectively. The results show that the PSD of organic matter has a bimodal distribution, while the PSD of the full shale sample has a unimodal distribution. The OM has developed more abundant micropore and mesopore volume per gram than the full shale samples (Fig. 3.5a), indicating that OM could also potentially provide abundant pore volume for free gas storage.

To clearly illustrate the relationship between the pore structure of OM and of the full shale sample, we calculate and compare the absolute pore volume of 1 g H13 shale sample (TOC 3.82 wt.%) and 0.0382 g organic matter (Fig. 3.5b, 3.6b). We find that the pore volume of organic matter contributes much less to the total pore volume of shale sample and that inorganic pore volume primarily comprises the total pore volume of our

33 shale samples (Fig. 3.5b, 3.6b). However, we should note that accumulated OM is a rich subsurface. A large fraction of OM within shale formations would still be important for the shale gas reserve.

Figure 3. 6 (a) The PSDs of pore volume of H13 shale samples and H13 isolated OM from the CO2 adsorption isotherms by the DFT method. (b) Absolute pore volume of 1g shale sample and 0.0382 g (1 g × TOC) OM. V: Volume; D: Diameter; STP: Standard Temperature and Pressure.

The relative volume of micro-, meso-, and macropores of measured H13 shale samples of 4.619 g and according organic matter of 0.1764 g (4.619 g × TOC) are present in Table 3.5 respectively.

Table 3. 5 Pore volume parameters of H13 shale sample and H13 isolated OM, Yanchang area, Ordos Basin.

Pore Volume (cc/g) Average Mass pore Micropores Mesopores Macropores Sample (g) diameter a Total PV Pct Pct Pct (nm) PV PV PV (%) (%) (%) H13 Shale 4.619 6.558 0.0924 0.0416 45.00 0.0288 31.20 0.0220 23.80 core H13 OM 0.1764 3.409 0.00405 0.0005 13.09 0.0019 46.67 0.0016 40.49 a PV: Pore volume. Pct: Percentage.

Fig. 3.5b suggests that the OM mainly contributes to the organic mesopore volume of less than 5 nm and larger than 20 nm diameter, and inorganic particles (mainly clay minerals in this sample) contributes mostly to the mesopore and macropore volume within shales, which may to some degree explain the differences between the extracted shale samples by two kinds of organic solvents and original shale samples from Triassic Chang

7 and 9 shales, Yanchang area by Xiong et al. [59]. However, in previous research by Xiong et al. [59], only the N2 adsorption method was used. In our work, the contribution of OM to micro- and mesopores were investigated by both N2 and CO2 adsorption methods. The data of Fig. 3.6 show that the OM contributes less to the micropore volume of the H13 shale core sample, indicating that inorganic composition sometimes could also develop micropores in organic-moderate-to-rich shale samples. In this case, the maturity and maceral of OM may complicate the results, which may require further research.

For over-mature transitional shales, the average pore diameter of OM is approximately half that of the full shale sample (Table 3.5). OM accounts for 9.74% of the 36 total pore volume and 1.20% of micropores, 6.60% of mesopores and 7.27% of macropores.

This implies that clay minerals could also dramatically impact the development of micropores and mesopores and OM may not closely correlate with the micropore volume.

3.3.3.2 Specific Surface Area

The Brunauer-Emmett-Teller (BET) method was used to calculate the Specific surface area (SSA) of the shale samples [63]. The PSDs of pore surface area are derived from N2 and CO2 adsorption isotherms (Fig. 3.7-3.9) [94]. The SSAs of three collected shale samples are presented in Table 3.6, and measured H13 shale core sample of 4.619 g and for the isolated OM of 0.1764 g (4.619 g × TOC) is presented in Table 3.7.

Fig. 3.7 shows that with increasing TOC, the pore SSA of shales decreases, showing a similar trend as the pore volume of shales. This might support the explanation above that the organic-rich transitional shales were subject to intense compaction, which could reduce both the pore volume and SSA. Organic mesopores, especially less than 10 nm, play a significant role in the total SSA of shales (Fig. 3.7, 3.8): per gram the SSA of

OM mesopores is up to ~7 times higher than for the full sample, which results in OM contributing up to ~30% of SSA despite a TOC of only 3.82%.

On the other hand, we observe that OM does not contribute much SSA of micropores less than 1.5 nm (Fig. 3.9). For transitional clay-rich shales at over-mature stage both OM and clay minerals generally develop micro-, meso- and macro-pores.

However, clay minerals develop abundant micropores and mesopores (mainly larger than

10 nm diameter). Considering the low percentage of OM compared to inorganic components, the SSA of OM contributes less than the total SSA of transitional clay-rich

37 shales. It is important to note that in the over-mature stage, the shales have extremely low water saturation because of the expulsion of shale oil and gas [101,102]. In shales at mature or low-mature stages, adsorption will be more affected by the occupation of adsorption sites by abundant water molecular.

Based on the relative volumes of micro-, meso-, and macropores of our shale samples (Table 3.6), we find that as TOC increases and clay content decreases, the SSA of micropores also dramatically increases while the SSA of mesopores decreases. This indicates the significance of OM. However, based on the relative volumes of micro-, meso-, and macropores of the full H13 core versus the H13 isolated OM samples (Table 3.7), the

SSA from OM only accounts for 1.94% of the total SSA. This suggests that inorganic SSA dominates the total SSA of shales and OM may be significant for the relationship of co- occurrence with clay minerals. For OM itself, SSA of micropores accounts for 72.37% of total organic SSA, and 25.79% for mesopores, 1.84% for macropores. In terms of contribution to total SSA of shales, SSA of OM accounts less to total SSA than inorganic particles. Considering the proportion of OM within shales, OM does do a significant contribution to SSA of shales (Fig. 3.8a), which in turn affects the shale gas capacity of shales. However, clay minerals in the over-mature clay-rich transitional shales, could be the dominant controlling factor of shale gas capacity.

Figure 3. 7 The PSDs of pore SSA of shale samples from the N2 adsorption isotherms by the BJH method. S: Pore Surface; D: Diameter; STP: Standard Temperature and Pressure.

Figure 3. 8 (a) Comparison of PSD of pore specific surface area (dS/dD) of H13 shale samples and H13 isolated organic matter (OM) from the N2 adsorption isotherms by the BET method. (b) Absolute pore specific surface area (SSA) of 1 g shale sample and 0.0382 g (1 g × TOC) OM. S: Pore Surface; D: Diameter; STP: Standard Temperature and Pressure. 39

Figure 3. 9 (a) Comparison of PSD of pore specific surface area of H13 shale samples and H13 isolated organic matter (OM) from the CO2 adsorption isotherms by the DFT method. (b) Absolute pore specific surface area (SSA) of 1 g shale sample and 0.0382 g (1 g × TOC) OM. S: Pore Surface; D: Diameter; STP: Standard Temperature and Pressure.

Table 3. 6 Pore structure parameters of transitional shale samples, Yanchang area, Ordos Basin.

Pore Specific Surface Area (m2/g)

Sample Total Micropores Mesopores Macropores PSSAa 2 (m /g) PSSA Pct (%) PSSA Pct (%) PSSA Pct (%) H18 15.820 8.024 50.70 6.588 42.00 1.208 7.64 H34 25.154 19.544 77.70 4.634 18.00 0.976 3.88 H13 26.818 25.295 94.30 1.384 5.20 0.139 0.52 a PSSA: Pore specific surface area. Pct: Percentage.

Table 3. 7 Pore specific surface areas (SSA) of H13 shale samples and H13 isolated OM, Yanchang area, Ordos Basin.

Pore Specific Surface Area (m2/g) Average Micropores Mesopores Macropores Mass pore Sample Total (g) diameter a Pct Pct Pct PSSA PSSA PSSA PSSA (nm) (%) (%) (%)

H13 Shale 4.619 6.558 123.872 116.838 94.32 6.393 5.16 0.642 0.52 core H13 OM 0.1764 3.409 2.402 1.738 72.37 0.620 25.79 0.044 1.84 a PSSA: Pore specific surface area. Pct: Percentage.

3.3.3.3 Pore Type

The hysteresis loop formed by N2 adsorption/desorption isotherms is measured to investigate the shale pore shapes [103,104]. The four-type classification of hysteresis loops

IUPAC suggested based on De Boer’s categories was used in this research (Fig. 3.10).

Figure 3. 10 Classification of nitrogen adsorption/desorption hysteresis loops and reflected pore types. Modified from IUPAC [102,103].

The S-like shapes of hysteresis loops reflect that generally, the transitional shale samples develop slit-shaped pores due to the presence of abundant plate-like clay minerals in the collected shale samples (Fig. 3.11). Shale sample H13 contains a higher percentage of quartz than shale sample H18 and H34, and the shape of the hysteresis loop of H13 indicates a combination of slit-shaped pores and ink-bottle-shaped pores.

Comparing the full sample to the isolated OM, the pore type of the OM seems to contain narrow slit-like pores, besides the slit-shaped pores and ink-bottle-shaped pores that the full shale sample H13 develops. This is attributed to the development of microstructures within the OM in shale.

Figure 3. 11 N2 adsorption/desorption isotherms of transitional shale samples H18, H34, H13 and isolated transitional shale OM sample H13, Yanchang area, Ordos Basin.

3.4. Conclusions

A series of geochemical and petrological measurements were carried out to investigate the effects of composition (organic and inorganic) on the development of pore structure in transitional shales as well as its effects on the shale gas storage capacity. Both low pressure N2 and CO2 adsorption techniques were used to characterize the pores of transitional shales from the Upper Paleozoic Ordos Basin, China. Below is a summary of our main conclusions: 43

(1) The organic moderate-to-rich Upper Paleozoic transitional shales at over- mature

stage (average over 2.6%) mainly comprise of vitrinite (average over 60%), with

additional contributions from inertinite, some exinite but no sapropelinite. The

dominant minerals are clay minerals (average over 54.6%) and quartz (average

28.2%).

(2) For thermally over-mature transitional shales, clay minerals are the dominant

controlling factor of total specific surface area as well as absorbed gas.

(3) Micropore volume increases with increasing TOC and decreasing clay content.

However, mesopore and macropore volumes of inorganic particles mainly contribute

to the total pore volume of transitional shales. Micropores account for most of the

total specific surface area of transitional shales.

(4) Despite low TOC values of less than 4%, OM contributes significantly (up to ~30%)

to the specific surface area of mesopores in transitional shales in the study area,

especially for those with less than 10 nm diameter. Clay minerals are another

important factor for the development of micropores at over-mature stage and

potentially provide abundant absorption sites for absorbed gas and pore space for

free gas. If, however, the water content under reservoir conditions is not negligible,

the importance of clay relative to OM may be reduced.

Acknowledgements

The author would like to acknowledge the financial support of National Natural

Science Foundation of China (Grant No. 41472112), National Science and Technology

Major Project (Grant No. 2011ZX05018-02), and China Geological Survey project (Grant

No. 12120114046701). This work was supported in part by The Ohio State University

Office of Energy and Environment. Special acknowledge are given to the Shaanxi

Yanchang Petroleum (Group) Co., Ltd. for providing drilling cores used in this research.

M.R. Soltanian was supported by the U. S. Department of Energy’s (DOE) Office of Fossil

Energy funding to Oak Ridge National Laboratory (ORNL) under project FEAA-045.

ORNL is managed by UT-Battelle for the U.S. DOE under Contract DE-AC05-

00OR22725.

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Chapter 4. Mineralogy and Gas Content of Upper Paleozoic Shanxi and Benxi Shale

Formations in the Ordos Basin

[Published in: Energy & Fuel, 33 (2019), 1061-1068]

To directly measure the gas content in the Benxi and Shanxi sub-formations of the

Ordos Basin in NW China, a series of canister desorption tests (CDT) were carried out on

33 over-mature Lower Permian to Upper Carboniferous fresh shale cores (>3,000 m) at both the reservoir temperature (75 to 80 °C) and an elevated temperature of 95 °C. Organic chemistry and X-ray diffraction (XRD) analyses of 33 replicate samples were used to establish relationships between the gas content and rock composition.

Geochemical measurements show that the total organic carbon (TOC) contents range from 0.49 wt.% to 13.7 wt.%. The organic matter is mainly Type III arising from lagoon and delta depositional settings. The dominant minerals are clay (25-97 wt.%, average 59 wt.%) and quartz (1-62 wt.%, average 33 wt.%). A new ternary diagram is proposed based on the origin and brittleness of the minerals.

Multiple linear regressions of emitted gas volumes with respect to the full mineralogy and TOC show a strong positive correlation with TOC and a weak one with clay composition. This is consistent with independent high-pressure methane adsorption experiments in the literature. 55

Elevating the temperature resulted in an incremental gas production of 12% for the

Lower Permian Shanxi facies versus 62% from the Upper Carboniferous Benxi shale (with a weighted average of 43%). This may be indicative of more significant gas adsorption

(related to the pore size distribution and specific surface areas) in the Benxi lagoon environment, which has more functional components (TOC and clay) and micropore volume than the Shanxi delta deposits, which are more quartz-rich.

4.1. Introduction

Increased carbon dioxide (CO2) concentrations in the atmosphere have resulted in a strong interest in low CO2-emission energy resources [105]. The development of shale gas as an unconventional resource alternative to oil and coal has led to an energy revolution in the United States [58, 90, 106-111]. According to EIA (2017), shale gas, together with gas in tight oil plays, will contribute approximately two-thirds of the total energy production in the United States by 2040 [112]. An accurate assessment of shale gas capacity is therefore necessary prior to exploration and exploitation and plays a crucial role in the shale gas production process [88, 113-114].

Researchers currently determine the gas content in place based on indirect and direct methods [115,116]. In the indirect method, the total gas in place is obtained from the sum of free gas, adsorbed gas, and dissolved gas as classified by Curtis et al. (2002) [56].

Free gas is calculated from an equation of state when porosity, reservoir temperature, and pressure are known. Adsorbed gas is measured by high-pressure methane (and other hydrocarbons) isotherms under reservoir conditions. Under reservoir conditions, a certain

56 amount of gas may also have dissolved in water, oil, and the organic matter (OM), such as kerogen and pyrobitumen.

In direct approaches, shale cores are retrieved from the reservoir and then sealed in an airtight container. A certain amount of gas is already emitted during this recovery progress (i.e., from the uplift to the time before sealing), which is referred to as ‘lost gas’.

After sealing, desorption and diffusion will continue inside the container. The measured gas at this stage of a ‘canister desorption test’ (CDT) is often referred to as ‘desorbed’ gas

[85,116]. However, the gas volume from CDT consists of desorbed gas, free gas, and potentially dissolved gas [85, 117]. In the following, we therefore use ‘emitted gas’ instead of ‘desorbed gas’ to refer to any of those components. When no more gas is emitted from the cores, ‘residual gas’ is measured in the lab by crushing the cores. Lost gas is estimated by backwards extrapolation of the early emitted gas evolution over time. Summing lost gas, emitted gas, and residual gas renders the total gas content in place. In the industry, this direct approach is commonly used owing to its simplicity and low cost.

In these direct methods, the relationship between the measured desorbed gas content and (early) time is critical to estimate the lost gas. This approach, referred to as the

United States Bureau of Mines (USBM) method, was first widely used in 1973 to measure gas contents in coal bed methane (CBM) at shallow depth, based on the idea that the desorbed gas volume is linearly correlated with the square of lost time (the time from drilling the cores to the first desorption measurements) [118,119]. However, this method was proven problematic when applied to shale gas because the composition, structure, and depth of shales are remarkably different from those of coal beds [120]. Several methods,

57 such as modified USBM in 1991 and curve fitting methods in 1993, have been proposed to better estimate shale gas in place [121,122]. However, all such empirical methods either overestimate or underestimate lost gas, which indicates that the relationship between lost gas and petrological characteristics remains poorly constrained as well as the relationship between the measured emitted gas and emission time [123]. Investigating the relationship between emitted gas and properties of shales will lay a foundation for the development of better lost gas estimates, as part of shale gas resource evaluation.

One of the objectives of this study is to document emission behavior, using CDT, of transitional shales, which refer to shales deposited in deltas, beaches, lagoons, and tidal flats. Note that even though TOC has been proven important in the high-pressure methane adsorption isotherms, the relationship between TOC and emission in CDT experiments has never been well documented. This is the first investigation of the relationship between emitted gas and properties of shales (geochemical and petrological), attempting to shed light on the impact of composition on emission behavior with the additional goal of improving lost gas estimates in the future.

4.2. Samples and Methods

Thirty-three deep (>3000 m) over-mature shale cores were collected with similar spacings from Upper Paleozoic shale formations to conduct the CDTs. All the core samples come from the Q14 and Q25 wells that are located in the Yanchang Oil field in the Ordos

Basin, NW China (Fig. 4.1).

Figure 4. 1 Geological map of Ordos Basin in NW China showing the location of sample wells. The grey area in the bottom represents the targeted Upper Paleozoic shale formation. Modified from Xiong et al. (2017) [59].

The Ordos basin is the second largest sedimentary basin in China, located in the western North China Craton. The basin experienced a multi-cycle structural evolution and deposited sediments from marine to continental environments without strong tectonic deformations. The targeted Upper Paleozoic transitional shales are in one of the three 59 hydrocarbon-bearing sequences and were deposited on a gently west-dipping slope. More detailed information on the geology and stratigraphy can be found in Xiong et al. (2017) and Yang et al. (2017a) [59,124].

4.2.1 Canister Desorption Test.

The CDT equipment used in this work was manufactured by China Kedi Co. (Fig.

4.2). The procedure of CDT is summarized below.

(1) Clean and seal: The desorption canister was filled with an over-saturated NaCl solution to measure free (rather than dissolved) gas and heated to the reservoir temperature.

Fresh cores were uplifted from the borehole to the surface in-situ and quickly sealed in the airtight canister to conduct CDTs after removing the drilling mud. The times of uplift onset, uplifting to the ground surface, and sealing into the canister were recorded.

(2) Sampling: For each core sample used in CDT, a replicate sample was collected from the same location to conduct geochemical and petrologic measurements because long- term soaking (~16 h) in the high temperature water in the canister may alter the pore structure (e.g., smectite swelling) and geochemical properties. The thickness of the collected shale cores was less than 3 cm (with a diameter of ~9.3 cm) to facilitate the completion of each CDT before the arrival of the next set of drilling cores. In general, formation water can affect adsorption, but in this study all the samples are of comparable depth (~3000 m) and a high maturity of ~2.6 (vitrinite reflectance), with a negligible water content [102].

(3) Desorption measurements: Before recording the desorption data, the tubes connecting the canisters and the measuring cylinders were filled up with over-saturated 60

NaCl solution to prevent atmospheric gas from entering the equipment, and to guarantee that the emitted gas is directly measured by the graduated cylinder. The measuring cylinder was kept in a vertical position and the initial water levels in the canisters and measuring cylinders were kept at the same elevation to eliminate head effects. The ambient temperature and pressure (of the graduated cylinder) were measured to allow conversion of volumes to standard conditions. Gas emission follows a diffusion-type curve, with high rates at early times and an asymptotically decreasing rate at later times (see the Appendix

A. Supporting Information S1). For this reason, gas volumes were measured at short

(from 2 min) to longer (up to 1 h) time intervals, as provided in the Appendix A.

Supporting Information S2. Once the released gas volumes plateaued to less than 1 ml/h, the temperature was increased to 95°C to desorb the remaining gas.

(4) Post-measurement: After CDT, the samples were dried with a towel and weighed. The cores were kept in marked sample bags for later measurements of residual gas in the lab.

Note that the emitted gas was released at the reservoir temperature and elevated temperature of 95 °C but measured in the cylinder (Figure 2) at ambient temperature and pressure. The van der Waals equation of state was used to convert all measured volumes to standard conditions in subsequent analyses.

Figure 4. 2 Schematic of canister desorption test. An over-saturated NaCl-water brine is used in the desorption canister and inverted graduated cylinder.

4.2.2 Geochemical Analysis

All geochemical and petrologic measurements were carried out using the undesorbed replicate core samples at the State Key Laboratory of Petroleum Resource and

Prospecting in China University of Petroleum, Beijing. Core samples were ground into powder sizes of less than 200 mesh (i.e., 74 ��). Approximately 100 mg of powdered sample was pretreated with 5% HCl at 80 ℃ to remove the inorganic carbon within carbonate, followed by drying at 60 ℃ overnight, to measure TOC. TOC analysis was performed with a Leco CS-230 carbon analyzer. About 100 mg of powder was also dried at 60 ℃ overnight for Rock Eval Pyrolysis with an OGE-II rock pyrolyzer.

The macerals and vitrinite reflectance of organic matter were measured with a

MPV-SP and 308-PV microscope photometer, respectively. The maturity of shale samples

62 was determined by both vitrinite reflectance and the maximum volatilization temperature of hydrocarbons (Tmax) from the Rock-Eval analysis [109].

4.2.3 Mineralogy

Shale powder (particle size less than 200 mesh, i.e., 74 ��) was used to perform

X-ray diffraction (XRD) with a Bruker D8 DISCOER diffractometer (Co Ka-radiation, 45 kv, 35 mA) following the two independent processes of the Continuous Position Sensitive

Proportional Counter (CPSC) procedure. To measure the diffracted beam, scintillation was used with 0.02°2� step-size and 20 s step-time at a temperature of 25 ℃. Diffractograms were derived from 2° to 76°2 �.

4.3. Results

4.3.1 CDT Gas Emission from Transitional Shale Samples

Canister desorption tests were performed on all 33 samples immediately upon reaching the surface. The full time-series data are provided for one representative core

(Sample 4-1 from well Q14) in the Appendix A. Supporting Information S2 and Fig.

4.3. Similar emission curves are given for all 33 samples in the Appendix A. Supporting

Information S1, with all final volumes at the reservoir temperature (Vres) and at the elevated temperature (V95) tabulated in the Appendix A. Supporting Information S1.

Note that the reservoir temperature is 75 ℃ in Shanxi and 80 ℃ in the deeper Benxi.

Figure 4. 3 (a) Cumulative volume of gas released at atmospheric pressure from sample 4- 1, Benxi shale of well Q14. (b) Volumetric rate of gas release. The tup indicates the time when the temperature of the desorption canister was raised to 95 ℃ (from the reservoir temperature of 80 ℃). Segments I, II, and III indicate three stages of desorption.

The cumulative amount of emitted gas first increases steeply and then slowly flattens off to the maximum amount of emitted gas at the reservoir temperature (Fig. 4.3).

After elevating the sample to a higher temperature of 95 ℃, the trend of emission is similar to that that observed at the reservoir temperature (Fig. 4.3). Segments I and III (Fig. 4.3, inset) indicate that at a given temperature, the rate of emission first declines steeply and then asymptotically vanishes. Segment II is the segment during which the core was heated, which increases the rate of emission. The steep increase during Segment II and the

64 difference between the emitted gas under reservoir temperature and 95 ℃ reflects the impact of temperature on gas emissions (e.g., due to desorption).

As mentioned above, the volumes of emitted gas for all 33 core samples were converted from the site’s temperature (20 ℃) and pressure (1.01 × 10 Pa) to standard temperature and pressure (STP, i.e., 0 ℃ and 1.01 × 10 Pa). The cumulative gas volumes released at 95 ℃ are tightly (linearly) correlated to those at the reservoir temperature (Fig.

4.4). In other words, for all 33 samples, 43% more gas was released at 95 ℃ than at the reservoir temperature (R2 = 0.93). More interestingly, Fig. 4.4b and 4.4c show the correlation within each sub-formation (the Lower Permian Shanxi shales and the Upper

Carboniferous Benxi shales, respectively), which formed in different depositional environments: delta and lagoon, respectively.

The incremental gas release for Shanxi shale is only 12% (R2 = 0.91) when the temperature is raised, while Benxi shale shows a considerably higher increment of 62%

(R2 = 0.97). The Benxi shales were deposited in a lagoon with low water energy and reducing conditions and the formation has a higher content of ‘functional components,’ such as clay minerals and OM, including pyrobitumen and kerogen, than the Shanxi shales that deposited in a deltaic environment. Clays and OM are both known to provide adsorption sites and pore volumes, which helps explain the higher gas content of the Benxi samples. These implications are discussed further in Section 4.3.2.

4.3.2 Relationships between Composition and Depositional Environments

Transitional shales (i.e., shales that deposited in settings such as tidal flats, beaches, deltas, and lagoons) have a different mineral composition compared to continental and marine shales (Fig. 4.5). We measured the mineral composition of 33 transitional shale cores, and compared them with other transitional, continental and marine shales in the literature

[50,67,125,126].

We adopt the conventional abbreviations of K, Q, and C to represent the carbonate, quartz, and clay compositions, respectively. K [%] includes all carbonate minerals, which are of similar origin and brittleness, such as calcite, dolomite, pyrite, and siderite. Q [%] consists of quartz, feldspar, and plagioclase. While all of these minerals could be mainly of continental origin, quartz can sometimes be related to biosiliceous organisms of a marine origin [50,125]. Finally, C [%] comprises of ductile clay minerals and mica. This type of ternary diagram can clearly distribute sample points based on origin and brittleness, which is practical in industry and engineering. 66

Figure 4. 5 Mineral compositions of continental, marine, and transitional shales for the samples in this work, as well as literature data [50,67,125,126]. Ternary diagram of mineral compositions for different subfacies of transitional (a), marine (b), and continental shales (c). The Longmaxi shale was deposited in a deep shelf. The Eagle Ford shale was deposited in a platform and trough between reefs [127]. The Barnett shale was deposited in a deeper water foreland basin with euxinic bottom water [67]. The Lower Permian Shanxi shale was deposited in a delta, and the Upper Carboniferous Benxi shale was deposited in a lagoon, which tends to comprise of more clay minerals due to its nature of low water energy and reducing settings.

Even within the categorization of marine or transitional shale, the mineral compositions vary significantly in terms of depositional settings or subfacies (Fig. 4.5a), consistent with our previous work [8,40]. Marine shale tends to be either siliceous (as in the case of Barnett, associated with biosiliceous silica) or carbonate-rich (as in the case of

Eagle Ford, closely associated with fossiliferous carbonate) (Fig. 4.5b). Transitional shale is clay-rich based on our measurements. Further, the subfacies of low water energy and commonly observed reducing conditions, such as those found in a lagoon, contain a higher content of clay minerals (Fig. 4.5a). As for continental shales (Fig. 4.5c), the accessible shale core samples were mostly from lacustrine settings. We also expect that mineral compositions of continental shales that are deposited in rivers and lakes would be different, and even more so for shallow, semi-deep, and deep lakes. However, this requires further sampling and analyses.

We do not observe a clear correlation between TOC and clay minerals within the

Lower Paleozoic transitional shale in the Yanchang oil field (Fig. 4.6a). This contrasts with studies for other formations, which have suggested that clay minerals will absorb OM during deposition and preservation, resulting in a positive correlation between TOC and clay minerals [128,129]. However, these two observations are not necessarily in conflict since it is possible that a correlation between the original organic carbon and the clay minerals initially existed but due to subsequent diagenetic processes and the generation and expulsion of hydrocarbons, the TOC (residue of organic carbon) may have changed non-trivially. At the same time, different depositional environments in lagoons versus

68 deltas may have played a role as well, with a subset of samples (circled) showing a stronger correlation between TOC and clays than the rest (Fig. 4.6a).

In our samples, clay minerals show a negative correlation with quartz (Fig. 4.6b).

This mostly reflects that clay and quartz make up the bulk of the compositions while the four outliers have a more significant fraction of pyrite or siderite (see the Appendix A.

Supporting Information S1). The quartz is thought to have a continental origin, which is different from the Barnett [40]. The relationship between clays and quartz in a delta is also distinct from that in a lagoon. Generally speaking, in a delta, deposition is mainly controlled by water energy. The higher the water energy, the higher the amount of quartz, 69 and the lower the content of clays. However, in a lagoon, the water energy is low, and the deposition of clays is mainly determined by the input of sediments.

4.4. Discussion

The mineral composition of shale is strongly dependent on depositional settings and, along with diagenesis, will determine its permeability and pore structure. The effective permeability involves both the exceedingly tight shale matrix as well as small fractures in brittle minerals. Unlike in conventional reservoirs, gas contents cannot be determined by total pore volume (porosity) alone, but also depend strongly on pore size distributions (PSD) and specific surface areas (SSA), such as those provided by OM (kerogen and pyrobitumen) and clay minerals, because a large fraction of gas can be adsorbed onto those surfaces [130].

Pore connectivity plays another important role in these low porosity materials.

The gas content consists of 1) free or bulk gas with properties similar to conventional reservoirs settings, 2) molecules adsorbed in single or multiple layers onto the pore walls, which can have up to ~20 times higher densities than the free gas, e.g., for methane in nano-pores [131] and 3) dissolved gas inside the solid OM [132].

The transport mechanisms and their associated driving forces (e.g., gradients in pressure, composition, or chemical potentials) have still not been rigorously established in these unique materials [132] with nanometer-size pores and extremely low permeabilities

(though various models are being used in the literature [133] such as Klinkenberger slip,

Knudsen diffusion, Hagen-Poiseuille [134], and dusty gas models). However, the temperature dependence of some effective diffusion coefficient is unlikely to explain up to

62% incremental gas recovery by a temperature increase of 15 ℃. 70

The above complexities of shale formations preclude comprehensive modeling of

CDT experiments. However, we can attempt to infer semi-quantitative information from this rich dataset. We make the (approximate) assumptions that 1) free gas will emit most readily, e.g., at the initial reservoir temperature, 2) the incremental gas release from the

15℃ - 20 ℃ temperature increase is mostly gas that was initially adsorbed, and 3) methane dissolved in OM is released most slowly and makes up a large fraction of the (22% on average, the ratio of residual gas to sum of residual and desorbed gas) residual gas that is measured in the lab after crushing the samples.

If we only consider the first two components in the CDT data, we can write b for the fraction of the pore volume associated with adsorbed gas (with 1-b the fraction of free gas) and use a to denote the fraction of adsorbed gas released at the reservoir temperature

(and 1-a at 95 ℃). We can then use the ratios of emitted volumes ( $% is 1.121 for Shanxi, &!' and 1.621 for Benxi) in Fig. 4.4 as

$%&!' $% 0.11 for Shanxi, = 1 − = (1 − �)� = (4.1) $% &!' 0.38 for Benxi.

In the limit � = 0, meaning that only free gas was emitted at the reservoir pressure, this would suggest that 11% of the gas in the Shanxi samples was initially adsorbed on the pore surfaces (�), whereas Benxi has 3.5 times more adsorbed gas (38%). This is a conservative estimate: the above relation allows for an upper limit of � = 100% adsorbed gas with 89% versus 62% of that gas emitted at the reservoir temperature (�). For reasons discussed next, the former estimates are more reasonable.

We performed extensive multiple linear regressions to relate the emitted gas volumes at both temperatures to 1) the full sample compositions (TOC, clay, quartz, feldspar, plagioclase, calcite, dolomite, siderite, and pyrite), 2) TOC and the lumped C, Q,

K compositions in the ternary diagram (Fig. 4.5), 3) only TOC and clay or pyrite, and 4) only TOC. Because the gas emissions in Shanxi and Benxi exhibit profoundly different behavior, we analyze each separately. Regression statistics are provided in the Appendix

A. Supporting Information S2.

In both subformations, the emitted gas volumes show by far the strongest correlation to TOC, as shown in Fig. 4.7, with R2 values of 80%-90% for Benxi and a lower

~70% for Shanxi. Including more independent variables (mineral compositions) generally improves multilinear fits, but the contributions of most individual minerals are not significant. The clay contents do not seem to affect gas volumes in Shanxi but show a borderline significant correlation for Benxi. Denoting the gas volumes emitted at the reservoir temperature and at 95 ℃ as Vres and V95, respectively, we find for Benxi:

� = 0.088 × TOC + 0.007 × clay − 0.421 (� = 0.88), (4.2)

� = 0.15 × TOC + 0.010 × clay − 0.595 (� = 0.93). (4.3)

Figure 4. 7 Correlation between emitted gas and TOC at the Shanxi shale (a), and at the Benxi shale (b). The gas volumes have been corrected to STP for comparison. The circles represent emission at the reservoir temperature, with triangles for emission at 95 ℃.

Note that these correlations are close to those for TOC alone in Fig. 4.7b. Both OM and clay are known to develop porosity as well as adsorption sites for methane and other hydrocarbons, but these analyses suggest a stronger dependence on TOC.

Benxi shows a stronger correlation with TOC, higher emission volumes at both temperatures, and a larger incremental gas release from raising the temperature (note that the reservoir temperature in Benxi is 80 ℃ versus 75 ℃ in Shanxi, so the larger gas volumes at 95 ℃ are despite a smaller temperature increase). This suggests that Benxi has both a higher effective total porosity, and most likely a pore-size distribution that contains more micro- and meso-pores that offer relatively high specific surface areas for adsorption.

Further implications are summarized in the Conclusions below.

We acknowledge that one source of uncertainty can be attributed to the experimental procedure in which TOC and mineral compositions are measured on replicate samples that are closely spaced but not identical to the samples used in the CDT experiments and shales are known to be heterogeneous [67]. Another source of uncertainty in CDT is the amount of gas that was already released during the drilling and uplifting of the samples, which is not necessarily the same for, e.g., Shanxi and Benxi samples with different mineral compositions and fractions of adsorbed gas. Still, the strong correlations of gas volumes with TOC and moderate relation to clays for our transitional shale samples for the Ordos Basin are consistent with findings for marine and terrestrial shales elsewhere.

4.5. Conclusions

Canister desorption tests, organic geochemistry, and XRD analyses were conducted on 33 transitional shale cores from the Lower Paleozoic formation in the Ordos Basin in

NW China to investigate the geological controls of TOC and mineral compositions on the emission behavior of shale gas.

From the measured ratios of gas volumes emitted at 95 ℃ versus the reservoir temperature (Fig. 4.7) and the correlations of gas release with respect to TOC (Fig. 4.4), we can draw the following conclusions.

1. The average gas volumes released from the Benxi samples are 24% and 37%

higher than the Shanxi samples at the reservoir and final temperatures,

respectively. If we exclude the single Shanxi sample with an unusually high

TOC of 14%, these numbers are 38% and 50%, respectively. The latter is

consistent with porosity measurements of 6% in Shanxi and 9% in Benxi [95]. 74

2. Of the total gas in place, a larger fraction appears to be adsorbed gas in Benxi

in order to explain the 62% (versus 12%) incremental gas recovery from raising

the temperature. We derived lower-bound estimates of the fraction of adsorbed

gas of 11% for Shanxi and 38% for Benxi. i.e. different by a factor ~3.5.

3. The correlations of emitted volumes with respect to TOC (and to a lesser extent

clay) in Fig. 4.7 are expected to originate from two factors: 1) higher total

porosities developing in more OM-rich shales, and 2) TOC offering more

specific surface area and adsorption sites (and high-density adsorption layers).

Fig. 4.7 suggest that these processes are more pronounced (i.e. at a given TOC)

in Benxi than Shanxi, presumably due to its greater depth and maturity. The

slope of � versus TOC is approximately 3 times higher for Benxi than Shanxi,

consistent with the previous conclusion. Interestingly, the dimensionless

incremental gas recovery (1 − �/�) does not correlate with TOC (not

shown, but clear from the linear scaling of � and � with TOC), which

would suggest that the fraction of adsorbed gas (e.g., �) is similar for all TOC.

This work illustrates the importance of subfacies and depositional settings on gas resource availability. Specifically, we considered transitional shales which have been studied in less detail than marine and terrestrial shales. We find that the Upper

Carboniferous Benxi shales that developed in lagoon environments hold a greater promise than the Lower Permian Shanxi shales with a deltaic origin. The former tends to have a higher content of functional minerals, as illustrated in the new ternary diagram in Fig. 4.5,

75 which helps to develop porosity and retain natural gas, e.g., through adsorption on the specific surface area provided by OM and clay.

The findings in this work are consistent with more common lab experiments such as high-pressure adsorption and desorption isotherm measurements. While these canister desorption tests are less controlled, they are faster and cheaper and allow for the analyses of many (33 in this work) large and heterogeneous samples under real reservoir conditions in terms of fluids in place. As such, they offer an important complementary technique to assess the gas-in-place resources in current and future shale gas developments.

Associated Content

Appendix A. Supporting Information

S1-Experimental record

1). Record form of two representative samples

2). CDT records of all 33 Shanxi and Benxi shale cores

3). Geochemical and petrological characteristics of all 33 Shanxi and Benxi shale cores

S2-Results of modeling

1). Results of multiple linear regression of all 33 samples at reservoir temperature

2). Results of multiple linear regression of all 33 samples at 95 ℃

Acknowledgement

We acknowledge the financial support of AAPG Grant-in-Aid, Alumni Grants for

Graduate Research and Scholarship at The Ohio State University, National Natural Science

Foundation of China (Grant No.41472112), National Science and Technology Major

Project (Grant No. 2011ZX05018-02), and China Geological Survey project (Grant No.

12120114046701). This work was supported in part by The Ohio State University Office of Energy and Environment and the donors of the American Chemical Society Petroleum

Research Fund. Special thanks are given to the Shaanxi Yanchang Petroleum (Group) Co.,

Ltd. for providing drilling cores used in this research.

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Chapter 5. On the Pressure and Temperature Dependence of Adsorption Densities

and Other Thermodynamic Properties in Gas Shales

[Published in: Chemical Engineering Journal, 395 (2020), 124989]

Black shale source rocks have become a key natural gas resource in the US and

China. Unlike in conventional hydrocarbon reservoirs, a significant fraction of the gas in shales is adsorbed onto the inordinate specific surface areas (SSA) of micropores inside organic matter with densities exceeding those of bulk gas by an order of magnitude. Yet, the distribution of adsorbed versus bulk gas remains poorly understood. Experiments measure excess adsorption isotherms, which are corrected to absolute adsorption amounts by a factor that involves the density, �, of the adsorption layer(s). Constant values of

� are widely used in the literature but, we argue, are inconsistent with the pressure- and temperature-dependence of adsorption behavior. In this work, we propose a more reliable approach that assumes a constant volume of each adsorption layer that can be determined from the SSA of the substrate.

We measure nine high-pressure methane excess adsorption isotherms up to 15 MPa for three shale samples from China and Germany at temperatures of 65, 75, and 95 ℃, and low-pressure carbon dioxide and nitrogen isotherms to estimate the SSA. We also investigate another 24 isotherms at 35, 50, and 65 ℃ for 8 Chinese shale samples and 3 82 isotherms at 60, 90, and 120 ℃ for an Argentinian shale sample from the literature. A new variation of the multi-layer Ono-Kondo lattice model is introduced to derive the temperature and pressure dependent adsorption layer densities, which are subsequently used to obtain the absolute adsorption isotherms of interest. This practical methodology has the potential to significantly improve our estimates of shale gas-in-place resources, and adsorption modeling more broadly.

5.1 Introduction

To satisfy increasing global energy demands over the next decades, natural gas is a critical component that already accounts for a third of energy consumption in the United

States [135,136]. Shale gas, one of the largest natural gas resources, is mainly comprised of methane and ethane (typically over 75% CH4), whose products are only water and carbon dioxide, without the sulfur and nitric oxide associated with crude oil and coal [137].

Because of the concerns of carbon emissions on air quality and global climate change, shale gas that can be commercially exploited via hydraulic fracturing and horizontal drilling recently attracts sufficient investigators’ attention worldwide, and is thought to bridge between conventional fossil fuels (e.g., crude oil and coal) and renewable clean energy resources (e.g., solar, wind, wave, and geothermal) [136].

Organic-rich black shale is a heterogeneous geomaterial comprised of a wide range of minerals, such as organic matter (OM), clay minerals, quartz, calcite, dolomite, feldspar, plagioclase, siderite, and pyrite [58,63,138]. Due to its nature of nano-scale pore size, i.e., extremely high potential of adsorption, it exhibits a wide pore-size-distributions (PSD) with much of the gas residing in nano-meter to micro-meter sized pores that, however, have 83 extraordinarily large SSA [60,56,58,109]. Also, other application arises in CO2 sequestration and control of environmental radionuclides due to a greater affinity for CO2 than CH4 and composite adsorbents that developed an extremely high SSA, methylene blue capacity, and functional groups (e.g., carboxylic, lactone, and hydroxyl) on mineral surfaces [139,140]. These formations have attracted significant interest in the past decades as part of the shale gas revolution [58,90,110,138,141-143]. Compared to conventional oil and gas in siliciclastic and carbonate reservoirs, shales consist of insoluble kerogen, pyrobitumen, and various clay minerals, which are favorable for adsorption that enriches and complicates estimation of shale gas-in-place (GIP) [137]. Also, due to a low cost and a high gas reserve, black shales have become a critical energy resource in their own right

[50,57,144,145].

In conventional reservoirs, initial GIP can be estimated directly from the porosity, because gas can be considered to be primarily in a free, or bulk, phase. In shales, on the other hand, there are three significant components: 1) bulk gas in the pore space, 2) dissolved gas in OM and formation fluids, and 3) adsorbed gas on the pore surfaces [56].

Due to cracking of kerogen and pyrobitumen and the pressure shadow of rigid grains within gas shale matrices, numerous nano-to-micro pores develop and preserve inside OM and flexible clay minerals. This results in considerable SSA on which up to 85% of the total gas content is adsorbed [50,56,59,78,109,144].

Adsorption has long been investigated in geological, chemical and environmental engineering but has recently received increasing attention due to its importance in estimating GIP in shales through the application of high- pressure gas adsorption isotherms

[67,108,146-153]. Adsorption includes physisorption (van der Waals force between the adsorbent and adsorbate molecules) and chemisorption (chemical bonds between the surface and adsorbate molecules) [141,142]. Research on the heat of adsorption and standard entropy suggests that physisorption is dominant on the surface of kerogen and clay minerals [66,154]. To obtain the amount of adsorbed gas and GIP, several models, such as Langmuir [146], Brunauer- Emmett-Teller (BET) [93], Supercritical Dubinin-

Radushkevich (SDR) [155], and Ono-Kondo (OK) [108,156] were developed to acquire critical thermodynamic parameters such as the capacity of monolayer adsorption and the density of the adsorption phase.

Measurements of adsorption amounts compare the volume or weight of adsorptive gas uptake (such as methane) over increasing pressures to that of a non-adsorbing gas like helium. These measurements, referred to as excess adsorption amounts ( � ), underestimate the true, or absolute, amount of adsorption (�) by an amount of ��, with

� the bulk density of adsorptive and � the volume of adsorption. Alternatively, from the average density in the adsorption layer(s) � = �/�, one can relate the excess and absolute adsorption amounts as � = �(1 − �/�) [141,142,157].

It has been recognized that this correction can be significant at formation pressures, which are considerably higher than experimental conditions, and is thus critical in obtaining accurate estimates of adsorbed gas amounts. Surprisingly, though, a pressure- independent value for � is typically used in the correction, either as a fitting parameter

[63,69,108,155,158-161] or using values of 424 kg/m3 (liquid methane at the boiling

85 temperature for 0.1 MPa) or 373 kg/m3 (saturated methane calculated by the van der Waals equation under critical conditions) [162-166].

These assumptions are problematic for a number of reasons. Fitted (constant) � values often exceed even the density of closest packing adsorbate molecules

[69,74,155,158,167], and there is no physical justification of why the density of adsorbed methane would be 373 kg/m3 or 424 kg/m3 from the lowest (< 1 MPa) experimental pressures all the way to formation pressures (dozens of MPa). Moreover, a constant adsorption layer density implies an adsorption volume that increases with the same pressure dependence as the absolute adsorption amount. Instead, Grand Canonical Monte

Carlo (GCMC) and density functional theory simulations have demonstrated that the adsorption volume (�) is constant because molecules adsorb within approximately one

(or multiple, for multilayer adsorption) molecular diameter from adsorbent surfaces

[130,143,151,168-170]. A robust model for adsorption therefore requires the adsorption densities to be pressure dependent, which has important implications in deriving total adsorption amounts and GIP from excess adsorption measurements.

This work presents a thorough framework of how to apply these theoretical concepts to true heterogeneous shale samples from a number of different formations. We measure excess adsorption isotherms at 65, 75, and 95 ℃ for pressures up to 15 MPa for two samples from the Ordos Basin in NW China and one from SW Germany. The latter serves as a ‘benchmark’ that was part of a multi-laboratory comparison study [63]. We further consider literature data for an additional 8 samples from the Sichuan Basin in SW

China at 35, 50, and 65 ℃ [158] and an Argentinian sample at 60, 90, and 120 ℃ [130] for

86 which excess adsorption isotherms were presented. Both Langmuir and multilayer Ono-

Kondo models are explored to analyze the adsorption behavior and to determine whether adsorption is in fact mono- or multi-layer.

For all 12 samples (from China, Germany, and Argentina), the adsorption volumes were estimated based on SSA measured by low pressure nitrogen adsorption-desorption isotherms. However, due to different gas behavior, molecular sizes, and experimental conditions, debate continues in the literature on how to most reliably determine the true

SSA accessible to adsorptive molecules [171,172]. Low-pressure CO2 isotherms can be used to determine the SSA of the smallest (≤ 2 nm) pores that are inaccessible to N2 but can contribute significant SSA [171]. We measure such CO2 isotherms for our own 3 samples, but often only N2 BET values of SSA are provided in the literature. To partially alleviate these concerns, we propose novel lower and upper bounds on the SSA that can be derived directly from the excess adsorption measurements.

The proposed methodology is a considerable improvement over current practices and can improve our understanding of supercritical adsorption and future assessments of critical shale gas resources as well as recovery processes.

5.2 Theoretical Framework

The measured the amount of (specific) excess adsorbed gas, � [kg/g], per gram of sample with specific surface area SSA [m2/g] (Fig. 5.1).

Figure 5. 1 Schematic illustration of surface absolute and excess adsorption by the layer model (a and c) and the Gibbs representation (b and d) (modified from Lowell et al. [141]). The green circles in (c) and (d) are the molecules of adsorptive. c or ρ represents the local concentration or mass density of adsorptive; � or � represents the concentration or mass density of bulk gas phase; z is the distance from the surface; GDS is Gibbs dividing surface; � is the amount adsorbed in the layer model; � in (a and c) is the amount remaining in the bulk gas phase; � describes the surface excess amount in the Gibbs representation; � in (b and d) is the amount counted in the bulk gas phase. The adsorbing space is the volume of adsorption in this context. Only the amount of gas molecules in the red dashed outline is counted as �.

H nex = SSA (r(z) - rb ) dz º (SSA´ H) rex , (5.1) ò0

is related to the actual, or absolute, amount of adsorbed gas ( nabs [kg/g]) by

H nabs = SSA r(z) dz º (SSA´ H) rabs , (5.2) ò0

such that, in terms of a constant volume of adsorption layer(s), Vs = SSA´ H ,

nabs nex = rabs = rex + rb = + rb , (5.3) Vs Vs

æ r ö ç b ÷ nex = nabs ç1- ÷ (5.4) è rabs ø

3 3 with rb [kg/m ] the bulk gas density, r [kg/m ] the (heterogeneous) density profile inside one or more adsorption layers with a total effective thickness of H [m] , and

3 3 rex [kg/m ] and rabs [kg/m ] defined as the averaged effective excess and absolute densities within the adsorption layer(s) volume. Note that, in heterogeneous shale samples, estimated adsorbed densities and volumes are effective values averaged over all accessible mineral surfaces and pore sizes. Eq. (5.4) translates between measured excess adsorption values and absolute amounts that are ultimately the quantity of interest.

The approach that is most commonly used to interpret measured nex is to adopt a

model for nabs ( p) as a function of pressure, p , (such as Langmuir, SDR, OK, discussed

in the next Section) and then fit nex ( p) from Eq. (5.4) for the unknown fitting parameters of mentioned models [146,155,156]. In doing so, typically a constant value of the unknown

3 rabs in the ‘correction term’ is used. For methane, values of 424 and 373 kg/m have been

widely used for CH4. Alternatively, if rabs were known, nabs can be obtained directly without fitting, which has been done under the same assumption of constant values, as well as with improved estimates of pressure-dependent densities obtained from GCMC simulations [130].

The constant-density approaches, we argue, are inconsistent. For any definition of the adsorption volume, Eqs. (5.3)-(5.4) clearly show that

æ r ( p)V ö ç b s ÷ nex ( p) = nabs ( p)ç1- ÷ = nabs ( p) - rb ( p)Vs . (5.5) è nabs ( p) ø

Fitting nabs ( p) = rabs ( p)Vs with any choice of pressure-dependent model, while

assuming a pressure-independent (constant) value of rabs in the term in parentheses in Eq.

(5.4) cannot be justified and can also lead to negative absolute adsorption predictions, even at moderate pressures £15 MPa [130].

We therefore propose to directly use Eq. (5.5), as we will do in this study. Unlike

Wu et al. [130], who assumed known pressure-dependent adsorption layer densities obtained from GCMC simulations in carbon-slit pores, we attempt to obtain both adsorption layer densities and total absolute adsorption amounts simultaneously from the excess adsorption data (Fig. 5.2).

Figure 5. 2 Procedure of the proposed experimental method of estimating the density of adsorption phase at different pressures from high-pressure methane excess adsorption isotherms.

5.2.1 Langmuir Model

The simplest and widely used model to fit nabs ( p) are the Langmuir isotherms

[146], assuming a single adsorption layer (referred to as monolayer):

nmax p rmax p nabs ( p) = or rabs ( p) = (5.6) p + pL p + pL

in which the two fitting parameters are the maximum (specific) capacity of adsorbed gas,

nmax [kg/g] and the Langmuir pressure, pL [MPa], at which nabs = nmax/2 (with nmax and

pL both depending on temperature, T , and sample properties, such as mineralogy, TOC,

pore structure, etc.). For measured or known bulk gas densities rb ( p) , e.g., from an

91 equation-of-state or the National Institute of Standards and Technology (NIST) Chemistry

Webbook, [172] and a given adsorption volume Vs (discussed further below), the excess adsorption measurements are fitted by

n p æ r p ö max ç max ÷ nex ( p) = - rb ( p)Vs = ç - rb ( p)÷Vs . (5.7) p + pL è p + pL ø

in terms of pL and either nmax, or rmax .

5.2.2 OK Gas Lattice Theory

The OK multilayer adsorption model [156,169] assumes a three-dimensional lattice of adsorbate molecules (methane in our case) in contact with a planar adsorbent surface ~ and allows for adsorbate-adsorbent interactions with energy e s as well as adsorbate- adsorbate interactions with energy e~ . For notational convenience, we introduce the ~ ~ normalized energies e s = e s /kBT and e = e/kBT with kB Boltzmann’s constant. Together

with maximum density, rmax , in each layer, these are the three fitting parameters of the

OK model.

Consider n adsorption layers, labeled by i = 1,!,n with densities rabs,i and occupation fractions

rabs,i rb xi = and xb = . (5.8) rmax rmax

In terms of these parameters, the excess adsorption is expressed directly as

n (5.9) nex = rmaxVs å(xi - xb ), i=1

92 which is equivalent to Eq. (5.3):

æ 1 n ö rex = ç årabs,i ÷ - rb. (5.10) è n i=1 ø

After fitting Eq. (5.9), the absolute adsorption for the multilayer OK model simply follows from:

n (5.11) nex = rmaxVs åxi . i=1

In the mean-field approximation and requiring thermodynamic equilibrium, the occupation fractions are given by

é x1(1- xb )ù lnê ú + (z1x2 + z2 x1 - z0 xb )e +e s = 0, i =1, (5.12) ë xb (1- x1)û

é xi (1- xb )ù lnê ú + (z1xi+1 + z2 xi + z1xi-1 - z0 xb )e = 0, i >1, (5.13) ë xb (1- xi )û

with the volume coordination number z0 = 6, the monolayer coordination number z2 = 4,

and z1 = (z0 - z2 )/2 =1 for a simple cubic packing (SCP), while a tighter hexagonal closest

packing (HCP) has z0 =12 , z2 = 6, and z1 = 3.

Most commonly, methane adsorption in shales is assumed to remain within a monolayer (e.g., in the Langmuir model), but GCMC simulations under various conditions suggest that weaker adsorption in a second, and still weaker adsorption in a third, layer may be appreciable in small pores (e.g., £ 4 nm) [143,169].

In this work we allow for up to three adsorption layers, such that xi+1 = x4 = xb in

Eq. (5.13) (similarly, a monolayer model is obtained by only considering Eq. (5.12) with

93 x2 = xb ). A Sequential Quadratic Programming algorithm is used to solve the non-linear

Eqs. (5.12)-(5.13) for x1 , x2 and x3 for a given set of fitting parameters rmax , e , and e s .

Note that if adsorption indeed occurs only within a single monolayer, the three- layer model automatically reduces to the monolayer expression and a best fit of excess

adsorption data will result in x2 = x3 = xb .

5.2.3 Theoretical Constraints on Densities

All commonly used adsorption models assume that the absolute adsorption

isotherms plateau to some maximum specific amount nmax, which may depend on PSD and

SSA in addition to other parameters (temperature, mineralogy). Eqs. (5.7) and (5.9)

illustrate that when Vs is known, we can instead consider the adsorption layer densities and

their plateau at rmax as a more universally applicable parameter. Moreover, while nmax is

hard to constrain from first principles, rmax has clear theoretical upper limits ( rmax,th ).

Specifically, treating methane molecules as spherical particles with a kinetic diameter of H = 0.38 nm, one can easily calculate the closest possible (number or molecules) packing per surface area, in one or more layers. Division by Avogadro’s constant gives the associated molar density, and through the molecular weight of methane

3 ( 16 g/mol) we find the mass densities, which are rSCP = 485 kg/m for a SCP and

3 rHCP = 560 kg/m for a HCP in a single layer. For comparison, the ‘maximum’ densities of bulk supercritical methane at exceedingly high pressures (1000 MPa) are 558, 556, and

551 kg/m3 at 65, 75, and 95 ℃. For multiple HCP layers (mHCP) that are off-set parallel

94 to the surface by H/2 and slightly embedded in each other, one could theoretically have an

3 even higher density of rmHCP = 663 kg/m for a HCP bilayer. In summary, regardless of temperature and sample properties the density cannot exceed these theoretical maxima. For

example, for monolayer adsorption of methane: rmax = nmax/(SSA´ H) < rHCP .

When rabs is assumed to be known, whether as constant or pressure-dependent values from, e.g., GCMC simulations [130], the absolute adsorption amounts can be determined without fitting from Eq. (5.4). This is desirable, but the down side is that for a

given choice of rabs there is no guarantee that nabs will show the expected behavior of

plateauing to a constant nmax at high pressures [130]. Conversely, by using Langmuir, OK,

or other fitting models, nabs and rabs will plateau to constant nmax and rmax by

construction, but we have to evaluate whether the resulting rabs ( p) are reasonable. For

example, one could argue that the effective rabs for real heterogeneous shale samples should perhaps not exceed those predicted from GCMC simulations for small (~2–10 nm) idealized carbon-slit pores [130,169].

In the next section, we discuss the experimental results for low-pressure nitrogen

and high-pressure methane isotherm to measure the SSA and nex for three samples from

Germany and China.

5.3 Experiments and Results

All experiments were performed on two shale core samples from the Lower

Permian Shanxi Formation (Ordos Basin, NW China) and a Lower Jurassic sample from the Posidonia Shale (SW Germany) [63].

5.3.1 Basic Geological Properties

The basic organic geochemistry and mineralogy of the Chinese shale samples was analyzed in the Key State Laboratory of Petroleum Resources and Prospecting in China

University of Petroleum (Beijing), including the total organic carbon (TOC) content, vitrinite reflectance (Ro, maturity of OM), macerals (type of OM), and X-ray Diffraction

(XRD) mineralogy [59,109,138].

The burial depth of the two Shanxi shale samples is over 3000 m, where the maturity of the gas shale reaches the stage of over-mature. TOC contents are > 2 wt.%.

Maceral is dominated by vitrinite and inertinite ( > 95 wt.%) as well as a small amount of exinite. Clay minerals make up the largest fraction, followed by quartz. Small amounts of plagioclase and siderite are observed as well. The Posidonia shale sample is of lower maturity, 0.5%, but a higher TOC, 13.7%. The mineralogy is mainly comprised of carbonate, followed by clay minerals and quartz. This information is summarized in Table

5.1.

Table 5. 1 Summary of basic geological properties (Q-F is quartz + feldspar; data for the Posidonia shale sample from Gasparik et al. [63]. Sample ID Depth Ro TOC Clay Q-F Plagioclase Carbonate Siderite (m) (%) (wt %) (%) (%) (%) (%) (%) Shanxi 2-3 3136 2.41 2.01 59.8 36.7 1.3 0.0 2.2 Shanxi 3-3 3142 2.47 3.82 40.7 54.5 4.8 0.0 0.0 Posidonia - 0.50 13.70 20.3 10.6 0.0 64.6 0.0

5.3.2 Low-pressure Nitrogen Isotherms to Determine SSA

The same samples were used for all high-pressure methane, low-pressure carbon dioxide, and low-pressure nitrogen adsorption isotherms to minimize the impact of heterogeneity between different measurements. The samples were pretreated by in-situ drying with vacuum at 110 ℃ overnight. The SSA was measured by low-pressure N2 adsorption isotherms at Oak Ridge National Laboratory (ORNL) using a Belsorp analyzer with the BET method. The isotherms are shown in Fig. 5.3 and the derived SSA summarized in Table 5.2. Although the Posidonia shale sample has a higher TOC than the

Shanxi samples, it has a lower maturity (0.5%) which may explain the lower BET SSA.

5.3.3 Low-pressure Carbon Dioxide Isotherms to Determine SSA

The samples were pretreated by in situ drying with vacuum at 110 °C for 3 h. The carbon dioxide adsorption isotherms at 273 K was measured at ORNL using a Belsorp analyzer as well. The adsorption data was analyzed with the Dubinin-Radushkevich (DR) method to obtain the micropore SSA for pores of 0.4–1 nm [141,157] given in Table 5.2.

Figure 5. 3 Low-pressure nitrogen isotherms at -196 ℃ on (a) Shanxi 2-3, (b) Shanxi 3-3, and (c) Posidonia shale samples. P0 is the saturation vapor pressure of nitrogen.

5.3.4 High-pressure Methane Excess Adsorption Isotherms

High pressure methane excess adsorption isotherms were measured using a gravimetric high-resolution (±10 µg) magnetic suspension balance (MSB) Rubotherm instrument at ORNL. To consider the temperature dependence of adsorption behavior, the experiments were repeated for 65, 75, and 95 ℃ for each sample, and for pressures up to

15 MPa. A Julabo circulating oil bath was used to keep temperature fluctuations within ±

0.1 ℃.

The MSB procedure is as follows.

Pretreatment. The core sample was manually ground into powder and particles less than 200 mesh (i.e., 74 µm) were sieved. To remove residual gas and moisture, ∼1 g of the

98 powder sample was pretreated at 110 ℃ with a high-quality vacuum (down to 0.1 mbar) until the mass remained constant.

Buoyancy measurement. Helium was used to successively measure three positions: the Zero Point (ZP, weighing tare alone), Measure Point 1 (MP1, weighing tare + sample), and Measure Point 2 (MP2, weighing tare + sample + sinker) at several pressures to obtain the mass and volume of the powder sample after the buoyancy analysis of the empty sample cell.

Methane excess adsorption isotherm. After removing the helium by vacuum, methane of a research standard with a purity of 99.995% was used to successively measure

ZP, MP1, and MP2 at equilibrium at the same set of pressures as the buoyancy measurements. The difference of weight measured in methane and helium at the same pressures is the amount of excess adsorbed methane in units of mg/g, STP (standard T and p, i.e., 0 ℃ and 0.101 MPa).

All experimental data are provided in Table B.1. Model interpretation is discussed in the next section (and Fig. 5.4). To test the repeatability and error of the experiments, excess adsorption measurements for the Shanxi 3-3 sample at 75, and 95 ℃ were repeated twice showing an average relative error of 3% (Fig. B.1).

To further explore the validity and range of applicability of our new approach, we also investigate independent data from the literature that include SSA measurements and high-pressure methane excess adsorption isotherms for 8 Chinese shale samples at temperatures of 35, 50, and 65 ℃ [158] and an Argentinian sample at 60, 90, and 120 ℃

[130].

5.4 Interpretation and Discussion of Adsorption Data

5.4.1 Langmuir and Ono-Kondo Fitting of Excess Adsorption Data

Before we consider any model fitting of excess adsorption data, we make an important observation. If we simply take the highest measured excess adsorption amount at 15 MPa (for each temperature), divide by the monolayer adsorption volume associated with the BET SSA for each sample, and add the known bulk density, we should find the absolute densities of the adsorption layer at 15 MPa (Eq. (5.5)). However, all but two of the values summarized in Table 5.2 exceed the theoretical maximum of a HCP monolayer, even though 15 MPa is a relatively low pressure (the same is true for the data in Wu et al.

[130]).

2 3 Table 5. 2 SSA from CO2-DR and N2-BET (m /g). Adsorption layer density (kg/m ) at 15 MPa and each measurement temperature computed from measured � using Eq. (5.3) with SSABET, assuming a monolayer with a width of H = 0.38 nm.

Sample ID SSA SSA DR BET �max (65ºC) �max (75ºC) �max (95ºC) Shanxi 2-3 5.78 7.07 621 552 508 Shanxi 3-3 8.16 5.64 859 812 708 Posidonia 7.34 5.52 830 718 605

There are only three ways to explain this discrepancy:

1. Are the measured excess adsorption amounts too high? While we verified that

our measurements are repeatable with an accuracy of ±5% within the same

100

ORNL lab, a large international inter-laboratory comparison study found that

the reproducibility across different facilities showed much large variation [63].

For the same Posidonia sample at 65 ℃, ten isotherms measured by different

labs ranged between 1.1 and 2.4 mg/g at 15 MPa. Our measurement of 1.5 mg/g

seems reasonable and falls on the lower end of that range. A value of � (15

3 MPa) = 1.0 mg/g would be required to satisfy � (15 MPa) = 560 kg/m for a

SSA of 5.52 m2/g, which falls outside the range of all the isotherms in the

aforementioned study.

2. Are we seeing multilayer adsorption? Multilayer adsorption results in a higher

amount of adsorption while the density in each layer may remain below a given

� (see Eq. (5.9)). This is a tempting explanation but 1) the excess amounts

already exceed the maximum monolayer densities at relatively low pressures

of 6–12 MPa and 2) as demonstrated below, all 9 isotherms are fitted best by a

monolayer model, either Langmuir or OK. Fitting with a 3-layer OK model

self-consistently finds that the densities in the second and third layer are the

bulk density.

3. Are the SSA underestimated? The low-pressure nitrogen isotherm

measurements and BET analyses are also repeatable with high accuracy (±2%).

However, while debate remains in the literature [173], it has been argued that

due to experimental conditions (e.g., temperature) different probe gases are

more suitable for different ranges of pore sizes [174-176]. Commonly, CO2 is

used to probe 0.33–2 nm pores and N2 for the 2–100 nm range [177,178]. The

101

0.33–2 nm pores can contain a substantial fraction of total SSA (PSD is shown

for Posidonia shale in Gasparik et al. [63]). A recent detailed study by Psarras

et al. [171] found that for two samples, 50% and 70% of SSA was missed by

N2 isotherms. Our own measurements of CO2 and N2 SSA in Table 5.2 show

that SSADR (micropores) as a fraction of SSABET+SSADR cannot be simply

added to obtain the true total SSA accessible to CH4 adsorption, but these ratios

are remarkably consistent with those in Psarras et al. [171].

While uncertainties in Vs negatively affect our proposed approach, this in itself provides a useful independent lower limit on the (accessible) SSA of a sample, even when no measurements of SSA are performed. Specifically:

æ n ( p) ö ç ex ÷ Vs > maxç ÷. (5.14) è rHCP - rb ( p) ø

To find a tighter lower limit, one can fit nex for Vs with rmax = rHCP fixed.

Because SSADR (from CO2) data are far less common in industry and the literature than SSABET (from N2), including literature data analyzed below, we continue our analyses with a simple conservative estimate that 60% of SSA is underestimated by N2 BET.

With this assumption, we fit the excess adsorption data both with the Langmuir

isotherm (Eq. (5.7) with two fitting parameters rmax and pL ) and a 3-layer OK model

(Eq. (5.9), (5.12)-(5.13) with three fitting parameters rmax , e , and e s ). In addition, we compute and plot the absolute adsorption isotherms (Eqs. (5.6) and (5.11) for Langmuir and OK, respectively), and we extend the fitted excess and absolute isotherms up to a

102 pressure of 100 MPa to include all relevant reservoir pressures and more clearly see the trends in adsorption behavior.

The measured data and all fitting results are shown in Fig. 5.4 for all samples and temperatures. The derived absolute adsorption layer densities, bulk methane densities, and ratios between the two are given in Fig. 5.5.

Shanxi 2-3, 65 °C Shanxi 2-3, 75 °C Shanxi 2-3, 95 °C 3.5 3.5 3.5 3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 Sorption amount (mg/g) Sorption amount (mg/g) Sorption amount (mg/g) 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa) Shanxi 3-3, 65 °C Shanxi 3-3, 75 °C Shanxi 3-3, 95 °C 3.5 3.5 3.5 3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 Sorption amount (mg/g) Sorption amount (mg/g) Sorption amount (mg/g) 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa) Posidonia, 65 °C Posidonia, 75 °C Posidonia, 95 °C 3.5 3.5 3.5 Data Excess L Absolute L 3 3 3 Excess OK Absolute OK 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 Sorption amount (mg/g) Sorption amount (mg/g) Sorption amount (mg/g) 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa)

Figure 5. 4 Measured excess adsorption isotherms at 65, 75, and 95 ℃ for Shanxi 2-3, Shanxi 3-3, and Posidonia shale samples. Fitted excess and absolute adsorption isotherms from the Langmuir and multilayer OK models are extended to pressures up to 100 MPa.

103

Shanxi 2-3, 65 °C Shanxi 2-3, 75 °C Shanxi 2-3, 95 °C 600 600 600 14 14 14 ) ) )

3 500 3 500 3 500 12 12 12 400 10 400 10 400 10 (kg/m (kg/m (kg/m g 300 8 g 300 8 g 300 8 6 6 6

and 200 and 200 and 200 Density ratio Density ratio Density ratio

abs 4 abs 4 abs 4 100 100 100 2 2 2 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa)

Shanxi 3-3, 65 °C Shanxi 3-3, 75 °C Shanxi 3-3, 95 °C 600 600 600 14 14 14 ) ) )

3 500 3 500 3 500 12 12 12 400 10 400 10 400 10 (kg/m (kg/m (kg/m g 300 8 g 300 8 g 300 8

200 6 200 6 200 6 and and and Density ratio Density ratio Density ratio

abs 4 abs 4 abs 4 100 100 100 2 2 2 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa)

Posidonia, 65 °C Posidonia, 75 °C Posidonia, 95 °C 600 600 600 14 14 Absolute L Absolute OK Bulk 14 ) ) )

3 500 3 500 3 500 Ratio L Ratio OK 12 12 12 400 10 400 10 400 10 (kg/m (kg/m (kg/m g 300 8 g 300 8 g 300 8

200 6 200 6 200 6 and and and Density ratio Density ratio Density ratio

abs 4 abs 4 abs 4 100 100 100 2 2 2 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa)

Figure 5. 5 Adsorption layer densities derived from the Langmuir and OK model fitting in

Fig. 5.4. Also shown are the bulk density and rabs /rb ratios.

The fitting parameters are summarized in Table B.2. Note that e = 0 in all the OK best fits, indicating that adsorbate-adsorbent are much stronger than adsorbate-adsorbate interactions. This is a common assumption [156], which we did not enforce a priori in the

fitting. Note that with e = 0 , the set of rmax , e s , and Vs (or SSA) constitutes another alternative set of 3 fitting parameters (with the caveats discussed above).

Interestingly, while we allow for up to 3 adsorption layers, the best fitting model for all samples at all temperatures is monolayer adsorption (the fitted densities in the second and third layers exactly equal bulk density and are therefore not shown in Fig. 5.5).

104

For the same reason, Langmuir and OK can fit the data with similar accuracy.

However, the two models diverge at higher pressures. The Langmuir isotherms (and rabs )

have still not plateaued at 100 MPa and the rmax , which are constrained to be £ rHCP , are significantly higher than those from OK. The OK model has a stronger physical underpinning, fewer limiting assumptions, and more reasonable behavior in the high pressure regime.

The fitted rmax in Table 5.4 also provide some a posteriori justification of our assumption of a 60% underestimate of SSA across all 3 samples (despite different maturity

and compositions). The Langmuir-fitted rmax at 65 ℃ are all within 2% from the

theoretical maximum rmax,th = rHCP , which would not allow an underestimate of SSA less than 59%. The OK densities are lower, fall within 15% from each other, with the Shanxi

2-3 sample requiring only a 47% underestimate in SSA before exceeding rmax,th = rHCP at

65 ℃. Given that rmax will be higher at lower temperatures, an underestimate in SSA of the order of 60% is still consistent with these findings.

5.4.2 Pressure Dependence of Adsorption Layer Densities

The behavior of the (absolute) density of the adsorption layer is of key interest in

this work. This density approaches and plateaus at its maximum density rmax at pressures in the 20–40 MPa range (i.e., for typical formation pressures), while the bulk methane density is still increasing at 100 MPa. As a result, the ratio of adsorbate-to-bulk densities approaches unity at high pressures for both Langmuir and OK models. At the low-pressure

105 end, the Langmuir and OK models agree best and both predict similar adsorbate-to-bulk

density ratios of 10–15. The pressure dependence of rabs is investigated in further detail below for a number of independent data-sets.

5.4.3 Temperature Dependence of Adsorption Behavior

The temperature dependence of the Langmuir and OK fitting parameters are shown in Fig. 5.6 and Tables 5.5 and 5.6. The R2 values are high and similar for Langmuir and

OK, but the latter predicts lower rmax at all temperatures by on average 17%. This obviously has important implications at typical reservoir pressures that are much higher ~ than the experimental conditions. The OK adsorbent-adsorbate energy e s = e s /kBT is

~ consistent with being constant, such that e s is linear in temperature.

106

Figure 5. 6 Scaling of maximum adsorption layer density rmax and adsorbent-adsorbate energy e s /kB with temperature.

Over the considered range, the temperature dependence of all fitting parameters is weak. Nearly identical R2 values are obtained by fitting with other temperature

dependencies proposed in the literature, e.g., rmax µ T versus 1/rmax µ T , or pL µT

versus ln pL µ1/T [154,158,179-182].

107

5.4.4 Analyses of Independent Data Sets

To further demonstrate the importance of considering the pressure (and temperature) dependence of adsorption layer densities in interpreting excess adsorption data, we consider other extensive data sets (27 isotherms) from the literature [130,158].

First, Tian et al. [158] provide SSA (from low pressure nitrogen adsorption isotherms) and excess adsorption data for 8 Chinese shale samples over a similar range of pressures (up to

14.2 MPa) and at 3 temperatures. The data appear of high quality and, unlike ours, show a maximum in excess adsorption at relatively low pressures ( < 10 MPa).

However, in interpreting the excess adsorption data by fitting with Langmuir and supercritical Dubinin-Radushkevich (SDR) [155] models, the authors assume a constant

value of rabs in Eq. (5.4) together with Eq. (5.7), which we argue is inconsistent. Moreover,

for some samples nmax µ rmax is found to be temperature independent, whereas temperature dependent values are found for others. In addition, about half the fitted

(pressure independent) rabs values from the Langmuir model exceed the theoretical

maximum of rHCP .

To allow a direct comparison between the common approach of using a pressure-

independent rabs versus our improved method of using self-consistent pressure-dependent

rabs in Eq. (5.7), we focus on the Langmuir model (but also provide the fitting parameters and isotherms for OK). We use the fitting parameters in Table 3 of Tian et al. [158] for the former (converted from volume to mass based) and summarize our fitting parameters in

Table 5.7 for all 8 samples and all 3 temperatures (using the BET SSA values from Table 108

1 in Tian et al. [158] without modification).

Table C.1 shows that all maximum adsorption layer densities fall well below the

2 limit of rHCP and both 1/rmax and pL show tight ( 0.92 < R < 1.0) linear increases with temperature for all samples (figures and tables of these temperature correlations are omitted

for brevity but can be readily derived from the data in Table C.1). As before, the rmax from the OK model are lower than those from Langmuir.

To investigate the importance of considering the pressure dependence of rabs in more detail, we show the derived fits for excess and absolute adsorption isotherms from both Langmuir approaches (and OK) in Fig. C.1 for 4 of the samples, which all have

rabs > rHCP when fitted with a constant rabs at some or all temperatures. Even though both approaches have comparable fitting errors within the range of experimental pressures, they diverge widely at more typical higher (formation) pressures. The Langmuir and OK fits

with pressure-dependent rabs ( p) are comparable for these samples. As before, three adsorption layers were modeled but only the first layer density exceeds that of the bulk, indicating that a monolayer model best fits the data.

The associated pressure-dependent rabs from our Langmuir and OK approaches

are given in Fig. C.2 and show that rabs increases and then plateaus to rmax while the bulk

density is still increasing. At the highest pressures, the bulk density rb also approaches

rmax , such that 1- r g /rabs ® 0 and the excess adsorption amount approaches zero in

Figure 9. This phenomenon is obviously not observed when rabs is kept constant well 109

3 above rHCP , such as the values up to 1027 kg/m (sample 5 at 35 ℃) in Tian et al. [158] and similar elsewhere in the literature.

As a final interesting observation, the rabs derived from our approach are remarkably similar to those derived from GCMC simulations [130,183] for all 8 samples.

The GCMC results were computed at 60 ℃ and are compared to our fitted results at the closest temperature of 65 ℃ (Fig. C.1). The GCMC densities [130] can be fitted well by a

3 Langmuir curve with a rmax = 378.6 kg/m and all fitted rmax in Table 5.7 are within 0.2

– 11.7% from that value. This consistency in adsorption density predictions across 8 samples and from independent theoretical approaches is encouraging, given the differences in mineralogy, TOC, PSD, maturity, etc. across samples. Zhao et al. [183] and others already argue from simulations that the average adsorption layer densities may be insensitive to pore sizes.

Further research is required to prove the range of applicability of these densities,

which would allow the direct use of known rabs (and rb ) in correcting excess to absolute adsorption amounts by Eq. (5.4) [130].

In this context, we also re-investigate the modeling of excess adsorption data in Wu et al. [130] with our proposed approach in Figure 11 for a shale sample from the Vaca

Muerta formation, Neuquén Basin, in Argentina. Similar to the interpretation of our own excess adsorption data (Fig. 5.4), fitting with the reported nitrogen BET SSA measurements implies (monolayer) adsorption layer densities in excess of the theoretical

maximum density of rmax,th = rHCP . Twice the SSA is required for the fitted rabs (and

110 associated nabs ) to agree with GCMC simulations. Swelling of the substrate and small differences in pore volumes accessible to helium versus methane (and even larger hydrocarbons) may pose additional complexities [130].

5.4.5 Volume of Adsorption Layer

In this final section, we explore a number of different ways to estimate the volume of the adsorption layer(s). By definition, and regardless of any fitting model,

Vs = (nabs - nex )/rb from Eq. (5.5).

In our approach, Vs is assumed to be constant and given by Vs = SSA´ H , where

H is the kinetic diameter of a methane molecule for a monolayer or a multiple of that for multiplayer (or slightly less for nested HCP). Figure C.3 shows that indeed (by construction) this is the case for fitted excess and absolute adsorption isotherms, and as a

result, rabs has to be pressure-dependent.

Conversely, in the common approach of assuming a constant rabs in Eq. (5.4) to

correct excess to absolute isotherms, Vs becomes pressure dependent itself (Fig. C.3). The

fitted (nabs - nex )/rb for the approach in Tian et al. [158] result in different Vs at each temperature and pressure, ranging between 28% and 79% of SSA ´ H at the maximum pressure of 100 MPa with no clear trend (e.g., no monotonic dependence on temperature).

Careful analyses of Eqs. (5.5) and (5.7), together with basic physics arguments,

suggest several more useful estimates. Eq. (5.14) provides a lower limit on Vs based on the

requirement that rabs cannot exceed the density of a closest HCP packing of molecules.

111

Can we also determine an upper limit on Vs ? Indeed, we argue that the maximum

adsorption density rmax should not be less than rb over a certain range of pressures

(excess adsorption would become negative): r g £ rabs £ rmax £ rHCP . If we require this not

to happen for pressures up to, say, 100 MPa with an associated bulk density of rb,max = rb

(100 MPa), that provides an upper limit on Vs . This limit is hard to evaluate directly from the excess adsorption data, but can be checked a posteriori from the fitted absolute adsorption isotherms. Interestingly, the Langmuir isotherms for all 8 samples (and

temperatures) imply rmax that are only a few percentage points below rb,max . A few of the

OK results (8 out of 24) have rmax that are down to 4% below rb,max , which means that the (accessible) SSA should be reduced by that much to satisfy this upper limit.

There is another lower limit on Vs (in addition to Eq. (5.14)) that can be derived

directly from the measured nex . At any pressure, we have

dn dn dr ex = abs -V g . (5.15) dp dp s dp

Regardless of specific models, it is widely acknowledged that nabs approaches a

dn constant maximum value at high pressures. In that limit, abs ® 0 and dp

-1 æ dr ö dn dn ç g ÷ ex ex (5.16) -ç ÷ = - £Vs . è dp ø dp drg

This means that even without detailed fitting of the functional dependence of

nabs ( p) (other than plateauing at high pressures), the slope of the measured excess

112 adsorption data provides a lower limit on Vs . For excess adsorption isotherms that show a

significant decreasing trend towards zero, Eq. (5.16) can be used directly to estimate Vs .

For methane, this requires higher pressures than are generally achievable experimentally,

but for other gases such as ethane and CO 2 , this may be feasible [130].

Fig. C.3 shows such estimates directly from the slope of the measured nex as well

as from the Langmuir fitted nex over the extrapolated pressure regime. Note that the

maximum Vs derived from the Tian et al. [158] fitted data are below this lower limit for several of the samples and temperatures.

The fitted Eq. (5.16) shows at what pressures Eq. (5.16) becomes a good estimate

of Vs (or SSA in the figure). For example, considering all 24 isotherms, Eq. (5.16) evaluated at a maximum experimental pressure of 15 MPa would estimate between 42% and 65% of the ‘true’ adsorption volume (or SSA). In other words, if no (reliable) measurements of SSA are available, one could use twice the value from Eq. (5.16) at the highest measurement pressures as an estimate, and then use that value to obtain the absolute adsorption isotherm.

In our case, the slope of the measured excess adsorption data is consistent with the

SSA obtained through low pressure nitrogen isotherms, which provides confidence in our proposed derivation of absolute adsorption isotherms.

5.5 Conclusions

In this work, we used a total of 36 high-pressure methane excess adsorption isotherms for pressures up to 15 MPa and temperatures of 35, 50, 60, 65, 75, 90, 95, and 113

120 ℃ to thoroughly analyze adsorption behavior in 10 gas shale samples from China,

Germany, and Argentina.

From our analyses we draw the following conclusions and recommendations:

1. Absolute adsorption amounts are directly proportional to the density in

adsorption layer(s) ( nabs = rabsVs , with Vs the volume of the adsorption layer) and thus exhibit the same pressure dependence. To obtain the absolute adsorption density or amount

therefore requires Vs to be known (or estimated).

2. For monolayer adsorption, we assume that Vs = SSA´ H with H the kinetic diameter of the adsorbate molecules. The specific surface area, SSA, can be obtained from, e.g., low-pressure nitrogen, CO2 and/or argon isotherms, but challenges remain in identifying the true pore size distribution and SSA accessible to adsorbate molecules. The impact of mineralogy and moisture poses additional complexities. To constrain these uncertainties, we propose several novel lower and upper limits on the SSA that are based on the realizations that 1) the adsorption layer density cannot exceed that of hexagonal-

3 close-packing molecules (560 kg/m ), 2) rabs should exceed the density of the bulk phase, and 3) the absolute adsorption density (and amount) likely plateau to a constant maximum value at high pressures.

3. The aforementioned bounds can be estimated from raw excess adsorption

data, i.e. without any model assumptions, and further refined by fitting the data with common models (e.g., Langmuir, Ono-Kondo, SDR, BET). When SSA has been measured, these limits can verify whether those SSA values truly represent the surface area available

114 to adsorption, and when no SSA data are available they provide reasonable estimates that can be used to obtain absolute adsorption amounts.

4. Modeling with a three-layer Ono-Kondo model indicates that all 36 isotherms considered are best fitted with monolayer adsorption.

5. Langmuir and monolayer OK models can fit excess adsorption data with similar accuracy, but diverge at pressures beyond the experimental conditions (including typical formation pressures), with the OK adsorption layer densities lower by up to:17% than those obtained by Langmuir fitting for the samples and temperatures considered.

6. As for the temperature dependence of adsorption behavior:

- We observe monotonic trends of all Langmuir and OK fitting parameters with temperature but the dependence is weak and we are hesitant to make strong claims regarding its functional dependence.

- All Langmuir pressures are well below typical reservoir pressures at which

the adsorption layer densities are close to rmax . As a practical consequence, this means that at reservoir pressures the adsorption layer densities can be reasonably estimated from

rmax values obtained at moderately close temperatures.

- With the experimental fitting method using the Ono-Kondo model, we find that the equivalent adsorbate-adsorbate interaction energy is negligible as compared to the equivalent adsorbate-adsorbent (i.e., fluid-surface) energy, and that the dimensionless ~ equivalent adsorbate-adsorbent energy e/(kBT) appears to be constant. The former means that OK effectively reduces to a 2-parameter model, just like the Langmuir approximation.

115

Further research is clearly needed ina this area, but the recommendations proposed in this work are able to improve the interpretation of excess adsorption measurements in the scientific and industry communities.

Acknowledgements

We acknowledge the financial support of Center for Energy Research, Training, and Innovation (CERTAIN Seed Grant), Friends of Orton Hall (FOH) Grants, AAPG

Grant-in-Aid, Ohio Department of Natural Resources, Division of Geological Survey

Grant (ONDR Rock Grant), Alumni Grants for Graduate Research and Scholarship at The

Ohio State University, American Chemical Society Petroleum Research Funding, National

Natural Science Foundation of China (Grant No.41472112), National Science and

Technology Major Project (Grant No. 2011ZX05018-02), and China Geological Survey project (Grant No. 12120114046701). This work was supported in part by The Ohio State

University Office of Energy and Environment. Special thanks are given to the Shaanxi

Yanchang Petroleum (Group) Co., Ltd. for providing drilling cores used in this research.

Contributions to measurements of experimental data and manuscript preparation by G.R. were supported by the U.S. Department of Energy, Office of Science, Office of Basic

Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division.

116

Appendix B. Raw Data and Fitting Parameters of the Langmuir and Ono-Kondo

Models

Table B.1 provides the measurement data for high-pressure methane adsorption isotherms for Shanxi 2-3, Shanxi 3-3, and Posidonia shale samples at three temperatures.

Table B.2 provides the fitting parameters of those data by the Languir, Eq. (5.7), and Ono-

Kondo, Eqs. (5.9) – (5.13), models.

Tables B.3 and B.4 summarize the parameters of the associated fitting with respect to temperature.

Fig. B.1 shows the relative erros between the two repeated measurements of high-pressure methane excess adsorption isotherms for sample Shanxi 3-3.

Appendix C. Langmuir and OK Fitting of Literature Data

Table C.1 presents Langmuir fitting of 8 samples at 3 temperatures of excess adsorption data reported in Tian et al. [129].

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124

Chapter 6. Insights into Supercritical Gas Adsorption Theories in Nano-porous

Shales under Geological Conditions

[In preparation, will submit to: Chemical Engineering Journal]

Adsorption is one of the most important phenomena in surface chemistry, especially for a nano-porous geomaterial (e.g., shales). In the shale gas-in-place, adsorbed gas could contribute up to 85%. However, adsorption is hard to quantitatively characterize due to different adsorption mechanisms (e.g., physisorption and chemisorption), patterns

(e.g., monolayer and multilayer adsorption), surfaces (e.g., organic matter and clay minerals), and pore sizes (e.g., micropore, mesopore, and macropore). Moreover, key thermodynamic parameters, such as the enthalpy of adsorption, are challenging to determine due to uncertainties in adsorbed gas densities used in constructing absolute isotherms. In this paper, we extend the Brunauer, Emmett, and Teller (BET) and Ono-

Kondo (OK) models for subsurface shales, and compare the performance of commonly used mono- and multilayer adsorption models (e.g., Langmuir, supercritical Dubinin-

Radushkevich (SDR), supercritical BET (SBET), and simplified OK (OKS) models) to develop a practical and reliable methodology that can be used in the supercritical state, typical for subsurface black shale conditions.

125

Three independent data sets were used for nitrogen and methane adsorption isotherms at diverse temperatures. We demonstrate that adsorption by the SDR model is comparable or lower than predicted by the SBET model, but higher than the Langmuir and

OK models. The nitrogen BET method tends to underestimate the accessible SSA for methane. Measurement of isosteric heat of adsorption is suggested instead of the experimental fitting method, due to the significant difference between the results by two commonly used methods. Experimental fitting and simulation methods are also compared to guide future research on shale gas adsorption.

6.1 Introduction

During the past half century, a rapid growth in population and a sharp modernization with intensive industrial activities have resulted in the deterioration of ecosystems including the water and atmosphere, especially in developing countries [184].

With the continuously increasing release of greenhouse gases into our environment, carbon dioxide (CO2) storage in the subsurface is recognized as a potential technology to decrease the level of carbon in the atmosphere [185], and an exampe in which adsorption of supercritical gas (CO2) plays an important role. Adsorption is also a critical mechanism in wastewater treatment to remove contaminants in industrial waste streams using membranes, filtration, biological function, adsorption and so on [186-190]. In this work, however, we focus on the role of supercritical adsorption in the assessment of shale gas resources or gas- in-place (GIP).

Black shale is a prominent geomaterial in the domain of energy and environment due to the shale gas revolution and the development of carbon dioxide sequestration 126

[135,152,185]. Gas-bearing shale is a nanoscale structurally porous media, which consists of an extremely heterogeneous packing of organic matter (OM) (e.g., kerogen and pyrobitumen) and various inorganic minerals (e.g., quartz, clay minerals, feldspar, calcite, dolomite, siderite, pyrite, etc.) [57-59,67,80,106,109,138]. Among the minerals, OM and clays have been recognized as the critical components, which are largely responsible for the development of micropores, mesopores and specific surface area (SSA) within shale matrices [58,66,79,80,109,110,191]. The degree of adsorption is dramatically impacted by temperature, pressure, water saturation, those functional minerals, and the associated pore structures (e.g., OM and clay minerals) [58,63,66,90,154,191]. Yet, the precise mechanism of adsorption of supercritical gas on shale substrates remains poorly understood.

Theories of monolayer and multilayer adsorption have been studied for over 100 years [93,141,142,146,147,149,155,156]. Since Freundlich first reported an empirical relationship between the amount of adsorption and pressure in 1907, Langmuir proposed the well-known Langmuir model to characterize single layer (‘monolayer’) physisorption isotherms in 1917 based on his pioneering work of adsorption in bulbs [142,146]. However, on the surface of many engineered materials, adsorption was observed to occur in multiple playes (‘multilayers’) instead of a monolayer, especially in the subcritical state, for example, nitrogen adsorption on microporous carbon cloths at low temperatures [141,142].

Subsequently, a multilayer adsorption model was developed based on the basic Langmuir equilibrium equation of condensation and evaporation by Brunauer, Emmett, and Teller, known as the BET model at subcritical states [93]. Although the Langmuir and BET models do not explicitly consider the interaction between adsorbate molecules, nor between the

127 adsorbate molecules and the adsorbent molecules, the two models are commonly used due to their simplicity, while the more complicated models initially received less attention

[141,142]. Dubinin and Radushkevich (1947) extended the Polanyi theory [141,142] and developed a model of adsorption (known as the DR model) for microporous media, which was also utilized by some investigators to study the behavior of gas adsorption in shales

[158,169,170,192]. The characteristic curves based on the Polanyi theory were also applied to calculate the shale gas capacity [151]. Next, Ono and Kondo proposed a lattice model based on the second law of thermodynamics to describe multilayer adsorption isotherms in surface chemistry in 1960 [108]. This model was first introduced to estimate the shale gas capacity in geosciences by Bi et al. (2017), and recently compared to Grand Canonical

Monte Carlo (GCMC) simulations [108,169]. However, compared to such computationally expensive simulations, no reliable practical supercritical adsorption model has been widely accepted to characterize shale gas adsorption and to derive the critical thermodynamic parameters of interest such as the adsorption capacity and adsorbate-adsorbent interaction variables (e.g., enthalpy and entropy).

In this work, we review and compare four commonly used multilayer physisorption models (Langmuir, BET, DR, and OK), as well as four new modified alternative models, to shed light on their applicability in the supercritical state. This study builds on our previous work on the temperature-pressure-dependent densities of the adsorption phase

[193]. First, we explore monolayer (e.g., Langmuir) and three supercritical multilayer adsorption models (e.g., SDR, SBET, and OKs). Then, we compare the models to the full

OK model that agrees best with molecular simulation in terms of fitting performance and

128 the ability to provide the properties of the adsorption phase. We discuss the factors that influence key thermodynamic parameters and illustrate the advantages and disadvantages of all 8 models.

6.2. Materials and Methods

6.2.1 Experimental Data

A total of 15 core samples and 45 high-pressure methane adsorption isotherms used in this study were compiled from our previous work and the literature to cover a wide range of experimental temperatures of high-pressure adsorption isotherms ranging 35.4 to 95 °C

[69,158,193]. The detailed locations of the gas wells, information on the shale cores, and experimental conditions are discussed in prior works [69,138,158,193]. All TOC-rich marine gas shale samples from Tian et al. (2016) are overmature from the Upper

Ordovician Wufeng and the Lower Silurian Loangmaxi formations in Sichuan basin [158].

The high-pressure methane adsorption isotherms are at 35.4, 50.4, and 65.4 °C. We focus on two representative examples from that dataset: sample 4 or YC4-47 (3.34 wt.%) and sample 5 or YC4-54 (4.52 wt.%), which contain type I-II kerogen and originate from the

Lower Silurian Longmaxi shale formation with a vitrinite reflectance of 2.64%-3.55%

(maturity of OM) [158]. High-pressure methane adsorption isotherms of two over-mature transitional Chinese and one immature marine German shale samples were measured in our previous work at 65, 75, and 95 °C [193]. Another independent series of high-pressure methane adsorption isotherms of four (maturities of two immature and two gas-window)

129 organic-rich marine Posidonia shale samples (WIC7145, WIC7155, HAD7090, and

HAD7119) from Rexer et al. (2014) were conducted at 45, 65, and 85 °C [69].

6.2.2 Adsorption Theories and Models

6.2.2.1 Langmuir Theory

The Langmuir model is based on a kinetic balance between adsorption and desorption rates to describe Type I vapor chemisorption as classified by the International

Union of Pure and Applied Chemistry (IUPAC) (Fig. 6.1), which is commonly used to characterize absolute adsorption isotherms in mesopores [104,141].

Adsorptive

Condensation Evaporation

Adsorbate Volume of adsorption GDS Adsorbent

!! !"

Figure 6. 1 Schematic of the Langmuir theory. The green circles denote the gas molecules. GDS represents the Gibbs dividing surface. All the gas molecules in the volume of the adsorption phase are regarded as the absolute adsorbed gas. Only the gas molecules in a red outline are what we directly measure as excess adsorbed gas.

At equilibrium, for the gas molecules in the volume of the adsorption phase, the rate of condensation should equal to that of evaporation [141,146]:

130

+,* (××)×* = � × � × � × � -. (6.1), √

-1 in which � is Avogadro’s number, [mol ]; �, [Pa], is the experimental pressure; � and

�, [ ], are the fractions of the surface unoccupied and occupied by the adsorbate in a monolayer, respectively; �, [ ], denotes the condensation coefficient/constant, i.e., the probability of being adsorbed when contacting the surface; �, [kg mol-1], is the adsorbate molecular weight; �, [kg m2 s-2 K-1 mol-1], is the gas constant; �, [K], is the absolute

-2 temperature; �, [m ] is the number of adsorbate molecules in a unit area of an entirely

-1 covered monolayer; �, [s ], is the vibrational frequency of the adsorbed gas normal to the

2 -2 -1 surface; �, [kg m s mol ], is the molar energy of adsorption between the adsorbent and other gas molecules.

In terms of energy, at equilibrium, the work of adhering to the surface of the adsorbent that an adsorptive should overcome should be equal to that of escaping from the surface that an adsorbate molecule should overcome. In other words, the chemical potential of the gas molecule should be the same in the bulk gas and adsorption phase at equilibrium

[142]. Note that the sum of � and � is unity (Fig. 6.1), thus, we have:

/#' × � = = (6.2), 0/" ×

(×* � = +,* (6.3), 0×*× -. ×√ or

= + (6.4), /#' ×0/" 0/"

-1 where �, [mg g ], is the absolute amount of adsorbed gas at each equilibrium pressure;

-1 �, [mg g ], is the maximum or capacity of adsorbed gas for one layer, i.e., the amount 131 of adsorbed gas at complete coverage of monolayer; K, [s2 m kg-1 or Pa-1], is the Langmuir coefficient/constant or the adsorption coefficient, which is associated with a positive value of the energy of adsorption.

To obtain the thermodynamic parameters (e.g., nmax and K or PL ) by fitting measured excess adsorption data by the Langmuir model, a correction factor, 1 − # , is /#' necessary , which relates excess to absolute adsorption:

0/"× # � = × 1 − (6.5), 1 /#'

-3 where PL =1/K , [Pa], is the Langmuir pressure; rb , [kg m ], is the bulk density of

-3 methane [172] and �, [kg m ], is the density of the adsorption layer at each pressure.

The densities of adsorption at different pressures can be calculated from molecular simulations or a constant adsorption volume (CAV) approach [193].

In the work, Eq. (6.5) is denoted as the L model.

6.2.2.2 SBET Theory

After the Langmuir monolayer chemisorption model was originally proposed in

1917, multilayer physisorption, i.e. bound by van der Waals forces, attracted the attention of material scientists and surface chemists in the 1930s [146]. Based on the same idea of kinetic equilibrium between the condensation and evaporation of the adsorbate molecules in the adsorption phase, Brunauer, Emmett, and Teller extended the Langmuir equation to multilayer adsorption beyond the first layer in 1938 (Fig. 6.2) [93].

132

Figure 6. 2 Schematic of bilayer adsorption at the atomic scale.

The binding force of the second layer is from the product of all the potentials from the polarization of the first adsorbate molecules and the interaction of other adsorptive molecules [93]. In other words, the effective adsorption in the second layer only occurs on the basis of the first adsorbate. Due to the input of the second layer, the first and second adsorption layer reach a new equilibrium. Thus, for the second and higher adsorption layers under subcritical conditions (i.e., allowing for liquefaction below critical temperature), we have

+,2 (××*×2 = � × � × � × � -. (6.6), √

+,3 (××3+*×3 = � × � × � × � -. (6.7), √

� + � +∙∙∙ +� +∙∙∙≅ 1 (6.8),

133

th in which, � and � are the fraction of the surface covered by the second and i layer adsorbate, respectively; � denote the adsorption and desorption coefficients in the second layer; � is the vibrational frequency of the adsorbed gas normal to the surface of the first layer; � is the molar energy of adsorption between the first layer of adsorbate and other adsorptive gas molecules, or the work of escaping from the adsorption phase that an adsorbate gas molecule should overcome. Note that for multiple layers of adsorption, � is referred to as the fraction that is covered by � layers of adsorbate molecules (Fig. 6.2), �

th and � denote the adsorption and desorption coefficients in the � layer, respectively. � is the molar energy of adsorption between the (� − 1)th layer of adsorbate and other adsorptive gas molecules.

Then, by assuming the same value of energy of adsorption as the liquefaction

energy, EL , and the same thermodynamic properties for the second and higher layers

[141,142], we have

� = � = ∙∙∙= � =∙∙∙= � (6.9),

(×* = �, (×2 =∙∙∙= (×3 =∙∙∙= � (6.10), 0×*×√ 0×2×√ 0×3×√

� + � +∙∙∙ +� +∙∙∙≅ 1 (6.11),

,* � = � ∙ �, � = � ∙ �-. ∙ � (6.12),

, 1 � = � ∙ � = � ∙ � ∙ �, � = � ∙ �-. ∙ � (6.13), where, g , [s2 m kg-1], h , [s2 m kg-1], g , [ ], and w , [ ], are coefficients.

By assuming a constant, �, [ ], Eq. (6.13) can be transformed into (i >1)

134

,*+,1 � = � ∙ � ∙ � , � = = ∙ � -. (6.14),

Then, under supercritical conditions (i.e., no liquefaction but densification beyond the critical temperature), for a finite number of adsorption layers, n, we have [93]:

n n i i nabs = nmax åiq = nmaxCq0 åiw , (6.15), i=1 i=1

� + � +∙∙∙ +� ≅ 1 (6.16),

4 45* # 0/"∙∙ ()∙ ∙ # � = � ∙ 1 − = ∙ 45* ∙ 1 − (6.17). /#' ()∙∙ /#'

Also, for supercritical adsorption, we have

,*+,2 ,*+,2 *×2 � = × � -. ≈ � -. (6.18), *×2

,2 (×2 � = × �-. × � = � ∙ � (6.19), 0×2×√ where C is associated with the net molar energy of adsorption for a specific adsorbent- adsorbate system [142]; w is a variable associated with the required energy of compressing the gas molecules from the bulk gas phase to the adsorption phase. We define an ‘affinity

-1 coefficient’, X F , [Pa ], to characterize the ease of higher-layer adsorption on a specific

adsorbate-adsorbent system. Theoretically, X F is determined by the adsorbate-adsorbent

system and temperature. In the case of gas shales, X F is associated with the mineralogy,

pore structure, and temperature. In Eqs. (6.17) and (6.19), X F , C, and nmax are the three parameters we need to obtain by fitting the excess adsorption data.

For infinite adsorption layers, i.e., subcritical conditions (n → +∞), Eq. (6.17) can be simplified to [93]

135

# 0/"∙∙ # � = � ∙ 1 − = ∙ 1 − (6.20), /#' ()∙(∙) /#'

where w is often replaced by P/Po for subcritical condensation/adsorption [141,142] and

Po , [Pa], is the saturation vapor pressure of the adsorptive.

Eqs. (6.18) and (6.19) can be rewritten in a more convenient form as:

ln(�) = �� *×2 + *1 (6.21), *×2

ln(�) = �� (×2 + 1 (6.22), 0×2×√

which can be used to estimate the temperature dependence of C and X F for supercritical adsorption.

We also compare to a variation of the BET model [161] in which � = �⁄� and

rabs = radc (in Eq. (6.17)) with radc assumed a constant density of adsorption. This model will be referred to as BETC.

6.2.2.3 SDR Theory

The classic DR model was proposed by Dubinin and Radushkevich in 1947 and follows the idea of characteristic curves in the early potential theory of Polanyi [142]. It was originally applied to micropores and subcritical gas (below the critical point), in which the adsorbed molecules fill up the micropore volume rather than covering the surface due to an overlapping adsorption potential of the pore walls. The empirical relationship between the fractional micropore filling and the micropore volume with a Gaussian micropore size distribution can be expressed in the form [141,142]:

2 = �∙8 (6.23), 036&7

136

3 -1 in which V, [cm g ], is the specific volume occupied by the adsorbate molecules; �,

[cm3 g-1], denotes the total specific micropore volume; k, [s4 mol2 kg-2 m-4], is a

-1 characteristic dimensionless coefficient; Ed , [J mol ], is a difference in chemical

potentials given by RT ln(Po/P) .

For the Gibbs excess adsorption, the classic DR model can be written as:

2 ∙[ (9/)] # � = � ∙ � ∙ 1 − (6.24), /#' where D = k(RT )2 , [ ], is a coefficient that describes the affinity between the adsorbent and adsorbate for a specific adsorbate-adsorbent system.

In 2007, Sakurovs et al. modified the classic DR equation to be used in the supercritical state as [155]:

2 ∙[ (/#'/#)] # � = � ∙ � + � ∙ � ∙ 1 − (6.25), /#' where the first and second terms in Eq. (6.25) characterize the adsorbed and absorbed gas, respectively, and A, [m 3 kg -1 ], is a coefficient for a specific system of adsorbent and adsorbate. The second term in Eq. (6.25) considers the effects of swelling due to sorption

(adsorption and absorption) of gas. We will refer to Eq. (6.24) and Eq. (6.25) as the SDR and SDR+ models, respectively.

6.2.2.4 Ono-Kondo Theory

In 1960, Ono and Kondo proposed a lattice gas model to describe the Gibbs excess adsorption based on the study of surface tension in liquids [156]. Aranovich and Donohue developed the Ono-Kondo (OK) model in the late 1990s for multilayer adsorption of supercritical fluids in surface chemistry [156]. Bi et al. (2017) first used this model to 137 estimate shale gas capacity [108]. Pang et al. (2019b) compared the OK model and dynamic molecular simulations in estimating the absolute adsorption isotherms [169]. The OK model takes into account both the interactions between adsorbate-adsorbate molecules as well as adsorbate-adsorbent molecules.

The OK theory is based on the second law of thermodynamics, which is expressed at equilibrium [156] as:

∆� − � ∙ ∆� = 0 (6.26), where ∆�, [J]. and ∆�, [J K-1], are the change of enthalpy and entropy, respectively, and � is the absolute temperature.

At equilibrium, the change of Gibbs free energy is zero between State A (the adsorption site i that is occupied by a adsorbate molecule and an infinitely distant site that is occupied by a vacancy) and State B (the adsorption site i is occupied by a vacancy and the infinitely distant site is occupied by a adsorbate molecule) (Fig. 6.3).

Figure 6. 3 Schematic of Ono-Kondo gas lattice model at equilibrium.

138

The change of enthalpy is expressed as (� ≥ 2):

∆� = −�(�� + �� + �� − ��) (6.27), where � (<0), [J], is the molecule-molecule interaction energy; �, [ ], is the probability of the molecule on the site in the ith layer (i = 0 represents the sorbent wall surface), equaling

th the ratio of absolute density of the i adsorption layer, �_, to the maximum of monolayer adsorption, �, i.e., �_⁄�, � is the probability at infinite distance, i.e., the bulk gas density � = � = �⁄�; �, is the coordination number in the bulk or volume coordination number, �, the coordination number within a monolayer, and �, equaling

(� − �)/2.

The change of entropy can be written as (� ≥ 2):

3(#) ∆� = �� (6.28), #(3)

-1 where �, [J K ], is the Boltzmann constant.

From Eqs. (6.26)-(6.28), we have (� ≥ 2):

�� 3(#) + (*35*23*3+*)#) = 0 (6.29), #(3) : with a boundary condition of i = 1, for an energetic homogeneous surface, the relationship is [156]:

�� *(#) + (*22*)#) + ' = 0 (6.30), #(*) : : in which � (<0), [J], is the interaction energy between the adsorbate and adsorbent surface.

139

In the following, we will derive a simplified (linearized) form of the OK model.

For the layers � ≥ 2, we can linearize the first term in Eq. (6.29) with respect to a small

e (xi - xb ) dimensionless variable, s i = ® 0 to obtain: kBT

(6.31)

Combining Eqs. (6.29) and (6.31), we have

� − � ∙ � + � = 0 (6.32), where,

� = − : − 2 (6.33). *#(#) *

The general solution of Eq. (6.32) can be obtained in the form:

� = �� + �� (6.34), in which, � and �, [ ], are coefficients; � and �, [ ], are the roots of the characteristic equation,

� − � ∙ � + 1 = 0 (6.35).

Based on Eq. (6.35), we have

b b 2 b b 2 f = - -1,f = + -1. (6.36). 1 2 4 2 2 4

For supercritical fluids, the experimental temperature, T , is higher than the critical

temperature, Tc , [156]:

140

) � > � = (6.37), :

which together with Eqs. (33) and (36) and xb =1- xb , (i.e., xb =1/2) implies

� = − : − 2 ≥ − : − 2 > ∙) − 2 = 2 (6.38) *#(#) * * * ∙* * thus, we find

0 < � < 1, �� = 1 (6.39).

For finite n layers adsorption, assume � ≫ � ≈ �, � = � , based on Eqs.

(6.34) and (6.39), we then have

(;5*#) � = = �� + �� = 0 (6.40), :

� = −�� (6.41).

From the boundary condition, i.e., Eq. (6.30), assume |�| ≫ |�|, and � is also applicable for the 1st layer due to a small �, we can also write

# � = <' (6.42), = . #(#) :

(*#) = �� + �� (6.43), :

# � = <' − � 2;5* (6.44). = . (** ): #(#) :

To calculate the occupation of any adsorption layer, �, we start with

(3#) = �� + �� (6.45), : combine Eqs. (6.39), (6.41), and (6.44), to find the explicit expression

3 2;52+3 � = � + * * * * : (6.46).

Now we can compute the Gibbs excess adsorption from: 141

n nex = nmax å(xi - xb ). (6.47) i=1

Substituting Eq. (6.46) into Eq. (6.47), for a specific number of adsorption layers, n, in the porous media, the excess adsorption can also be written as

n C1kBT i 2n+2-i nex = nmax å(f1 -f1 ). (6.48) e i=1

Combing Eqs. (6.44) and (6.48), we have

;5* # * � = � <' − � ; (6.49). = . (*)(* ) #(#) :

For infinite adsorption layers under subcritical conditions, i.e., n → +∞, it can be simplified to:

# � = � <' − � (6.50), = . * #(#) :

In this work, we allow up to three adsorption layers. Thus, from Eq. (6.49) with n=3 we have

2 # (*)* � = � <' − � > (6.51). = . * #(#) :

For a simple cubic packing (SCP), �=6, �=4, and �=1; for a hexagonal closest packing (HCP), �=12, �=6, and �=3. Combining Eqs. (6.33), (6.36), and (6.49), the key thermodynamic parameters, �, can be estimated.

In the work, Eq. (6.30) is referred to as OK1 (i.e., OK model within monolayer) model, Eqs. (6.30) and (6.29) with i = 1, 2, 3 as OK3 (i.e., three-layer OK model), and Eqs.

(6.33), (6.36), and (6.49) as OK3s (i.e., our simplified three-layer OK model) model.

142

6.2.2.5 Data Fitting and Error Monitoring

A Sequential Quadratic Programming algorithm is utilized in the fitting of excess adsorption data with all the adsorption models [143,193]. A least-squares method is used to quantify the error, ∆�:

N 1 2 measured fitted (6.52) Dn = å[nex (i) - nex (i)] , N i=1

where, � (�) and � (�) are the measured and fitted excess adsorption amount at the ith set of temperature and pressure. N is the number of measured points.

The correlation coefficient, R2 , is also calculated for each fitting.

6.2.2.6 Isosteric Enthalpy of Adsorption

The isosteric enthalpy of adsorption is the heat that is released or absorbed during the process of adsorption, which is the negative of the heat of adsorption. The isosteric enthalpy of adsorption can be either negative (exothermal) or positive (endothermal).

Standard enthalpy of adsorption, ∆�, [J mol-1], is expressed by the Van’t Hoff equation

[69]:

∆) = − 2 (6.53), where s is the absolute amount of adsorbed gas at constant surface coverage.

We will use the integrated form of Eq. (6.53):

) �� = ∆ + � (6.54), where B , [ln(Pa)], is the intercept of the linear fitting of the isosteres in a plot of ln P versus 1/(RT ) and the slope provides the enthalpy of adsorption.

143

Another way to calculate the isosteric enthalpy of adsorption and even entropy of adsorption is applied in the literature [66, 154,158,180,181]:

) ) �� = − ∆ + ∆ + �� (6.55)

0 -1 -1 6 where DS is standard entropy of adsorption in J mol K ; � is a pressure of 0.1×10 Pa, at the perfect-gas reference state [154,158].

6.3. Results and Discussions

6.3.1 Comparison of Fitting Performance

Over the range of experimental pressures (< 20 MPa), all 8 models can fit the experimental excess adsorption data well (Figs. 4 and D.1) with correlation coefficients

R2 > 0.98. However, at higher pressures, including more realistic formation pressures and up to 100 MPa, the trends of the eight models vary significantly, resulting in vastly different absolute adsorption isotherms and sets of fitted thermodynamic parameters (Table 6.1).

144

Sample-4 35.4 °C Sample-4 50.4 °C Sample-4 65.4 °C 5 5 5 Data n OK1 ex n OK1 4 4 4 abs n OK3 ex n OK3 3 3 3 abs n OK3s ex n OK3s abs n L 2 2 2 ex n L abs n SBET 1 1 1 ex Adsorption (mg/g), STP Adsorption (mg/g), STP Adsorption (mg/g), STP n SBET abs n BETC ex 0 0 0 n BETC 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 abs n SDR+ Pressure (MPa) Pressure (MPa) Pressure (MPa) ex n SDR+ abs n SDR ex Sample-5 35.4 °C Sample-5 50.4 °C Sample-5 65.4 °C n SDR 5 5 5 abs

4 4 4

3 3 3

2 2 2

1 1 1 Adsorption (mg/g), STP Adsorption (mg/g), STP Adsorption (mg/g), STP

0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Pressure (MPa) Pressure (MPa) Pressure (MPa)

Figure 6. 4 Excess and absolute adsorption isotherms fitted to experimental data for Sample 4 and 5 [158] via eight different supercritical adsorption models (18 more isotherms are fitted in Fig. D.1).

All three OK models (OK1, OK3, and OK3s) fit the data equally well and provide nearly identical thermodynamic parameters, justifying the simplifying assumptions in the

OK3s model. The SDR+ and SDR models also lead to the same fitting (i.e., the fitted

A = 0 in the SDR+ model), which may indicate that the effect of swelling due to adsorption is negligible, at least when averaged over a full heterogeneous sample.

For all eight supercritical adsorption models, the fitted monolayer adsorption

3 densities, rmax , are well below the theoretical upper limit or 560 kg/m , the maximum density of a completely covered monolayer [193]. The SDR+ and SDR models suggest the

145 highest monolayer adsorption capacity, followed by the L, SBET, OK1, OK3, OK3s, and

BETC models.

Considering the correction from excess isotherms to absolute isotherms, the SBET and BETC absolute adsorption isotherms have not reached a plateau even at 100 MPa and the BETC predictions are significantly higher than the others, likely overestimating the amount of adsorbed gas-in-place. The BETC model tends to extrapolate to negative excess adsorption, which is physically unreasonable. In our previous work, we demonstrated that a constant density of adsorption for all pressures is not physically reasonable [193], which also leads to the inconsistency between the constant density values [161] and fitted

monolayer capacity, rmax in Table 6.1. A constant density of adsorption may also result in negative excess adsorption at relatively low pressures and a corresponding underestimate of the absolute amount of adsorption. This is in addition to other reasons that have been proposed to explain measurements of negative excess adsorption, such as the swelling of kerogen and differences in pore accessibility between helium and methane [130].

146

Table 6. 1 Summary of the fitted thermodynamic parameters by the eight supercritical adsorption models. Note that the interaction energy between the adsorbed gas molecules is 0 for the OK1 and OK3 models, and -0.001 for the OK3s model; A = 0 for the SDR+ and SDR models.

Sample Sample 4 Sample 5 Temperature (°C) 35.4 50.4 65.4 35.4 50.4 65.4 Model OK1, OK3, and OK3s ∆� 0.0123 0.0097 0.0073 0.0156 0.0124 0.0108 R2 0.9814 0.9870 0.9917 0.9794 0.9866 0.9892

3 �!"# (kg/m ) 351 326 309 355 340 330 � $ -3.1005 -2.9766 -2.9022 -3.3574 -3.2066 -3.0219 �%�

Model L ∆� 0.0120 0.0094 0.0071 0.0154 0.0122 0.0106 R2 0.9824 0.9877 0.9922 0.9798 0.9871 0.9896

3 �!"# (kg/m ) 378 352 334 377 363 355 K 0.3721 0.3366 0.3143 0.4802 0.4092 0.3319

Model SBET ∆� 0.0115 0.0091 0.0087 0.0152 0.0117 0.0102 R2 0.9836 0.9886 0.9883 0.9803 0.9880 0.9904

3 �!"# (kg/m ) 370 345 340 377 356 348 C 381 343 289 469 396 320

XF 0.0010 0.0010 0.0010 0.0010 0.0011 0.0011

Model BETC ∆� 0.0066 0.0055 0.0042 0.0081 0.0065 0.0054 R2 0.9946 0.9959 0.9973 0.9945 0.9963 0.9973

3 �!"# (kg/m ) 259 239 227 269 255 244 C 29 24 21 50 45 37

3 �"&'* (kg/m ) 275 248 227 367 369 372

Model SDR+ and SDR ∆� 0.0094 0.0094 0.0097 0.0091 0.0097 0.0081 R2 0.9891 0.9879 0.9854 0.9930 0.9917 0.9939

3 �!"# (kg/m ) 394 366 350 417 404 402 D 0.1392 0.1548 0.1680 0.1211 0.1388 0.1674

* a constant density of adsorption, �?@A, for all the experimental pressures in Zhou et al., (2019) [161]. 147

To compare to the OK models, we used the three-layer SBET and BETC models to fit the data and recommend the number of fitted parameters to be no more than than 3. The best fitted OK1 and OK3 are the same, indicating monolayer adsorption (equivalently, the best fitted density in the second and third adsorption layers in OK3 equal the bulk density).

When the number of adsorption layer is set to 1, the SBET model will give the same results as the L model. Without considering the interaction between the adsorbent and the adsorbate atoms or molecules, the L model slightly overestimates the absolute amount of adsorbed gas as well as the SDR model, which cannot provide the information of adsorption layers either.

We acknowledge that the ‘apparent’ monolayer adsorption is likely an effective average or superposition of multilayer adsorption on kerogen and clay mineral surfaces in a certain pore-size-distribution, with weaker monolayer adsorption on other inorganic surfaces and in larger pores.

6.3.2 Estimation of Accessible SSA for Methane and According Density of Adsorption

Phase

The measured SSA by low-pressure nitrogen isotherms likely underestimates the

SSA that methane molecules can access, partially due to 1) the difference of kinetic diameter (N2, 0.36 nm; CH4, 0.38 nm); 2) the challenging measurements of slow diffusion of nitrogen into the smallest micropores at an exceedingly low relative pressure range

-7 ( �⁄� , ~10 ) and experimental temperature (77K or -196.15 ℃ ); and 3) specific

148 interaction between nitrogen molecules and various exposed ions or surface functional groups on the mineral surfaces [157].

To the best of our knowledge, the exact threshold of accessible pores size for methane molecules is now well known. Fitting excess adsorption data may provide a complimentary approach to put constraints on accessible SSA for methane. For the SBET and BETC models, 5 fitting parameters are needed if we also attempt to fit the number of adsorption layer and the SSA. Hence, fitting for accessible SSA is carried out by the other models, i.e., the OK, Langmuir, and SDR models. We consider high-pressure methane adsorption isotherm data from our previous work and the literature for this discussion

[158,193]. For three shale samples (Shanxi 2-3, Shanxi 3-3, and Posidonia), we observe that the accessible SSA should be at least 1.5 (up to 3.4) times the nitrogen BET SSA so that the monolayer adsorption density will not exceed the theoretical maximum of monolayer absolute adsorption density, i.e., 560 kg/m3 (Figs. 6.5 and D.2) [193]. And generally, the estimated accessible SSA for methane by the SDR model is higher than that by the Langmuir and OK models (Fig. 6.5). Conversely, Tian et al. (2016) report particularly high values of nitrogen BET SSA [158], and as a result, the fitted adsorption densities do not exceed the upper limit for a monolayer. Given the importance of SSA in estimating the amount of adsorbed methane and thus the total GIP in a formation, there is a need for more sophisticated measurements such as additional gas adsorption isotherms

(using CO2, argon, etc.), Nuclear Magnetic Resonance (NMR), nano Computed

Topography (CT), or neutron scattering.

149

4 3.5

2.5 2

1.5 OK 1 Langmuir 0.5 SDR 0 Ratio of total SSA to measured SSA Ratio of total SSA 0 5 10 Isotherm #

Figure 6. 5 Underestimation of the nitrogen BET SSA for the total accessible SSA for methane. Isotherms 1-9 denote Shanxi 2-3 at 65, 75, and 95 °C, Shanxi 3-3 at 65, 75, and 95 °C, and Posidonia at 65, 75, and 95 °C, respectively.

6.3.3 Calculation of Isosteric Enthalpy of Adsorption

The isosteric enthalpy of adsorption is generally estimated in one of two ways in the literature: the Van’t Hoff equation (Eq. (6.53)) [69,158] and an equation derived from the Langmuir model (Eq. (55)) by Xia et al. (2006) and Xia and Tang (2012)

[66,154,158,180,181]. We calculate the isosteric enthalpy of adsorption by both methods, using pressure dependent adsorption densities, and show the fitted results in Fig. 6.6.

150

Figure 6. 6 Comparison between the estimated isosteric heat of adsorption by the commonly used (a) Xia’s equations and (b) Van’t Hoff equation.

Using the Van’t Hoff equation, for Sample 4 and 5, the estimated isosteric heats of adsorption are 9.2 and 12.7 kJ/mol, respectively, which are higher than the 4.9 and 10.7 kJ/mol by the Xia’s equation with a relative difference of 47% and 16%, respectively. We used the absolute adsorption data at 0.4 mg/g (i.e., 0.025 mmol/g or 0.56 cm 3 /g) to calculate the isosteric heat of adsorption using the Langmuir model. Our results suggest that a higher absolute adsorption will result in a higher isosteric heat of adsorption (Fig.

6.7), unlike prior estimates based on a constant density of adsorption [158]. Moreover, our results show that using a constant density of adsorption will increasingly underestimate the absolute adsorption at higher temperatures if the pressure-dependent densities are lower than the assumed constant density of adsorption (e.g., 424 or 373 kg/m 3 ), based on Eq.

(6.56):

151

n n = ex . (6.56) abs r 1- b rabs

9 9 (a) Sample 4 0.2 mg/g 0.4 mg/g 0.6 mg/g 0.2 mg/g 0.4 mg/g 0.6 mg/g 8.5 8.5 (b) Sample 5 0.8 mg/g 1.0 mg/g 1.2 mg/g 0.8 mg/g 1.0 mg/g 1.2 mg/g

8 y = -1421x + 12.314 8 R² = 0.9963 7.5 y = -1309.6x + 11.642 7.5 y = -1643.9x + 12.618 R² = 0.9959 R² = 0.9973 y = -1603.9x + 12.194 7 y = -1224.6x + 11.029 7 R² = 0.9969 R² = 0.9955 y = -1157.6x + 10.422 y = -1571.9x + 11.766 6.5 R² = 0.9952 6.5 R² = 0.9964 ln(P) (ln(kPa)) ln(P) ln(P) (ln(kPa)) ln(P) y = -1545.6x + 11.302 6 y = -1103.4x + 9.7477 6 R² = 0.996 R² = 0.995 y = -1523.7x + 10.742 5.5 5.5 R² = 0.9957 y = -1058.6x + 8.8245 y = -1505.2x + 9.9111 R² = 0.9948 5 5 R² = 0.9954 0.0029 0.003 0.0031 0.0032 0.0033 0.0029 0.003 0.0031 0.0032 0.0033 -1 -1 1/T (K ) 1/T (K )

Figure 6. 7 Estimation of isosteric heat of adsorption using the Van’t Hoff equation at different absolute adsorption for (a) sample 4 and (b) sample 5.

However, the increase gives out a complicated relationship (Fig. 6.8 and Table 6.2).

The relative differences of calculated isosteric heat of adsorption between the lowest and highest absolute adsorption, 0.2 and 1.2 mg/g, are 25.42%, 8.76%, and 15.89%. As a high uncertainty of estimation of the isosteric heat of adsorption by the experimental process exists, this method can be only used for a rough estimation and a more accurate way is to measure the isosteric heat of adsorption by a calorimeter [141,142].

152

15.0 Sample 4 Sample 5 Sample 6 14.0 13.0 12.0 11.0 10.0 9.0 8.0

Isosteric heat of adsorption (kJ/mol) of adsorption heat Isosteric 0.0 0.5 1.0 1.5 Absolute adsorption (mg/g)

Figure 6. 8 The increase of isosteric heat of adsorption shows both a linear (sample 5 and 6) and a nonlinear (sample 4) relationship with absolute adsorption. Sample 6 (YC4-61) is added for comparison [158].

Table 6. 2 Estimation of isosteric heat of adsorption at different absolute adsorption.

Enthalpy of adsorption (kJ/mol) Absolute adsorption (mg/g) sample 4 sample 5 sample 6

0.2 8.8 12.5 9.0 0.4 9.2 12.7 9.2 0.6 9.6 12.9 9.5 0.8 10.2 13.1 9.8 1.0 10.9 13.3 10.2 1.2 11.8 13.7 10.7

153

6.3.4 Comparison between molecular simulation and experimental fitting methods

During the past decade, significant advances have been made in molecular simulations (e.g., using Grand Canonical Monte Carlo (GCMC), Density Functional

Theory (DFT), and other methods) to investigate the excess and absolute adsorption of light hydrocarbons (e.g., methane, ethane, and propane) on pure kerogen (e.g., type II) and clay structural models (e.g., montmorillonite, illite, and kaolinite). At the same time, improvements have been made in directly fitting experimental data for larger scale heterogeneous shale samples.

GCMC has been used to simulate the interaction between adsorbate molecules and pore walls at the molecular scale, based on well-established potential field theories. This method can shed light on the microscopic mechanism of adsorption between two individual media, for example, methane molecules and pore surface within a specific pore diameter

(or pore width in the commonly simulated silt-like pores). Three-component (pore wall and a mixture of methane and carbon dioxide) and four-component (pore surface with pre- adsorbed water molecules and a mixture of methane and carbon dioxide) systems have been investigated as well and show, for instance, the competitive adsorption between

methane and water or CO 2 [194]. Pang et al. (2019) incorporated pore size distributions into their modeling of adsorption of methane on kerogen surfaces to better represent adsorption on macroscopic shale samples [170]. The effects of different accessibility between helium and methane molecules, as well as kerogen swelling, were also studied through molecular simulations [130,195].

154

At the same time, molecular dynamics simulations do not yet capture the full complexity and physical scale of a macroscopic shale sample, let alone the formation scale.

These complexities include the full composition of a shale rock (kerogen and inorganic minerals such as clays, feldspar, calcite, siderite, etc.), various pore shapes, pore size distributions from 0.4 nm to 1 µm, pore throats, wettability, various surface functional groups, and surface roughness.

For this reason, we seek a complementary approach of an empirical model that can be applied directly to experimental adsorption measurements on heterogeneous samples yet yield meaningful predictions of adsorption behavior at reservoir conditions, such as the total amount of gas in place.

From our analyses, as well as prior works [170], it appears that the Langmuir, BET, and SDR models are too simplistic to yield such predictions. The OK model is built on a more solid theoretical framework and allows for multiple layers, and both adsorbate/adsorbate and adsorbate/adsorbent interaction. A number of recent papers

[108,169,170,193] have compared the OK model to GCMC simulations and found surprisingly good agreement, especially when pore size distributions (PSD) were included in the GCMC simulations. Such simulations also demonstrate directly that the density in each adsorption layer depends on temperature and pressure (and can certainly not be assumed to be constant). In fact, pressure-dependent adsorption density profiles from

GCMC simulation have been applied directly to obtain absolute adsorption isotherms from excess adsorption measurements [130,183]. Note, however, that the GCMC adsorption densities are upper limits of the actual methane density in an adsorption layer with more

155 complicated surface mineralogies, roughness, pore-shapes, competitive adsorption (e.g., water and/or CO2 molecules). In other words, adsorption layer densities that are derived from excess adsorption measurements in macroscopic and heterogeneous shale samples are average or effective equivalent densities that will be lower than those predicted by

GCMC, e.g., on pure kerogen and/or clays.

6.4. Conclusions

In this work, we compared 4 widely used empirical adsorption models, and 4 modified versions of those models for supercritical methane adsorption in nanoporous shales. The objective is to extrapolate laboratory excess adsorption experiments, which are typically performed for pressures up to no more than 20 Mpa, to reservoir conditions in order to estimate shale gas capacities and thermodynamic parameters of interest. We also discussed the complementary relationship between these empirical models and more detailed, but also more idealized, simulations at the molecular scale. In comparing the full range of empirical models, we draw the following conclusions:

(1) Fitting excess adsorption data with multilayer adsorption models suggest that

the densities in all but the first layer are equal to the bulk density. This implies

that adsorption in a macroscopic shale sample can be described as an (effective)

monolayer. Conditions apply where a simplified OK model can fit the data just

as well as more non-linear monolayer and multilayer OK models, and obtain

the same thermodynamic parameters. The OK model also agrees best with

GCMC simulations. Comparing with the other models, the absolute adsorption

by the OK, Langmuir, and SDR models all plateau at high pressures, but the 156

maximum adsorption capacity by the SDR model is higher than that of the

Langmuir and OK models. The absolute adsorption from the SBET model is

comparable or lower than that by the SDR model, but higher than that by the

Langmuir and OK models. The BETC with a constant adsorption density

estimates the highest absolute adsorption and is more likely to extrapolate to

negative excess adsorption at high pressures;

(2) The nitrogen BET method likely underestimates the accessible SSA for

methane. Assuming an upper limit of 560 kg/m3 on the density inside any

adsorption layer implies ratios of total accessible SSA for methane to measured

nitrogen BET SSA ranging from 1.5 to 3.4 depending on what model is used;

(3) The isosteric heats of adsorption by two commonly used methods are

significantly different. A calorimeter is suggested for the measurement of

isosteric heat of adsorption instead of either experimental fitting method;

(4) Empirical models can be helpful in obtaining important thermodynamic

parameters for a whole shale core sample, while GCMC simulation are

necessary to discover the fundamental mechanisms at the atomic scale.

Acknowledgements

We acknowledge the financial support of Center for Energy Research, Training, and Innovation (CERTAIN Seed Grant), Friends of Orton Hall (FOH) Grants, AAPG

Grant-in-Aid, Ohio Department of Natural Resources, Division of Geological Survey 157

Grant (ONDR Rock Grant), Alumni Grants for Graduate Research and Scholarship at The

Ohio State University, American Chemical Society Petroleum Research Funding. This work was supported in part by The Ohio State University Office of Energy and

Environment. Special thanks are given to the Shaanxi Yanchang Petroleum (Group) Co.,

Ltd. for providing drilling cores used in our previous work. Contributions to previous measurements of experimental data and manuscript preparation by G.R. were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences,

Chemical Sciences, Geosciences and Biosciences Division.

Appendix D. Fitting of other Literature and Previous Work Data

Figs. D.1 and D.2 provides the fitting of other excess data in the literature and previous project.

Appendix E. Fitting of other Literature and Previous Work Data

Figs. E.1 shows that all the fitting of excess data using the supercritical adsorption models with three unknown parameters, indicating the importance of measured SSAs.

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Radushkevich model for the accurate estimation of high-pressure methane

adsorption on shales. International Journal of Coal Geology 2018,193, 1–15.

159

[193] Xiong, F., Rother, G., Tomasko, D., Pang, W., Moortgat, J. On the pressure and

temperature dependence of adsorption density and other thermodynamic properties

in gas shales. Chemical Engineering Journal 2020, in revision.

[194] Huang, L., Ning, Z., Wang, Q., Qi, R., Zeng, Y., Qin, H., Ye, H., Zhang, W.

Molecular simulation of adsorption behaviors of methane, carbon dioxide and their

mixtures on kerogen: Effect of kerogen maturity and moisture content. Fuel 2018,

211, 159–172.

[195] Li, J., Wu, K., Chen, Z., Wang, K., Luo, J., Xu, J., Li, R., Yu, R., Li, X. On the

negative excess isotherms for methane adsorption at high pressure: Modeling and

experiment. SPE Journal 2019,24, 2504–2525.

160

Chapter 7. Conclusions and Future Work

In this dissertation, we addressed some of the critical challenges in estimating gas- in-place (GIP) in shale formations, related to pore structures, mineralogy, and our understanding of subsurface supercritical desorption and (especially) adsorption and its geological controls.

In Chapter 2, we summarized the unique geology and tectonic evolution of the

Ordos basin and our study area in NW China, as well as sedimentary stratigraphy and depositional settings.

In Chapter 3, we studied the pore structures of shales and the effects of mineralogy on the development of pore systems. Our findings showed that clay minerals play an important role in adsorption for over-mature shales. Both clays and kerogen developed micropores, mesopores, and macropores. Micropores contribute most to the specific surface area, which fundamentally determines the amount of the adsorption. However, the effect of moisture not considered, which requires future research. Additionally, in micropores, the storage mechanism is pore filling, which is different from the layer adsorption in the mesopores and macropores. Combining multilayer adsorption with pore- filling models for non-trivial pore-size-distributions also requires further research.

Chapter 4 presented measurements of in-situ desorbed or emitted gas, including dynamic desorption curves and the total amounts of the desorbed gas through canister 161 desorption tests. The relationships between the amount of desorbed gas and minerals were discussed.

In Chapter 5, we proposed an experimental procedure to obtain the pressure- dependent density of adsorption under dry conditions. This method helps better estimate the actual adsorbed gas by replacing a widely yet physically unreasonable constant density of adsorption phase with a new series of pressure-dependent adsorption densities. Also, the temperature and pressure dependence of other key thermodynamic parameters were studied as well as the lower and upper limits of the parameters. The following remaining questions could guide future work in this area:

• How to estimate the accessible SSA for methane molecules? Both our own research

and numerous works in the literature prove that the widely used nitrogen BET

measurements underestimate the SSA. Low-pressure CO2 isotherms help but the

combination of N2 and CO2 isotherms still has limitations.

• How to verify the estimated density of adsorption? The calculation of the pressure-

dependent densities of adsorption is based on the measured excess adsorption

isotherms and the demonstration of monolayer via an experimental fitting method.

Whether experimental fitting methods lead to the physical meanings of the fitted

thermodynamic parameters remain further verification as well as the conclusion of

the equivalent monolayer by neutron scattering techniques.

In Chapter 6, we obtained 8 modified models used for supercritical adsorption. All the models may be used in the estimation of subsurface adsorbed gas under certain

162 reservoir pressures; however, one should realize that the variation between the models beyond the common reservoir pressure range vastly increases as well as the estimated thermodynamic parameters. Future work could include:

• comparison between the estimated and measured densities of adsorption by the

models and neutron scattering methods, respectively;

• investigation of the physical meanings of the fitted thermodynamic parameters

when the number of variables exceeds 4, 5 or a higher value;

• evaluation of assumptions of models and their impacts on the estimated

thermodynamic parameters.

163

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