High-Pressure Adsorption Model for Middle-Deep and Deep Shale Gas
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摘要: 我国目前开发的中深层-深层页岩气藏储层压力高.低压下的吸附实验和理论难以满足勘探开发的需要.针对这一问题，对Uniform Langmuir模型进行了修正，发展了一个适用于中深层-深层页岩气的高压吸附模型，即修正的Uniform Langmuir（Unilan）模型.然后，利用文献发表的高压吸附实验数据对修正的Unilan模型进行了验证，并与其他高压吸附模型进行了对比，发现：相对于其他高压吸附模型，修正的Unilan模型具有拟合参数少和精度高的优点.最后，基于拟合得到的Unilan模型参数，结合页岩样品矿物组成，开展了模型参数分析，发现：有机质和黏土矿物对页岩气吸附均有贡献；吸附达到饱和时的吸附相体积大于微孔体积且小于总孔体积；吸附熵变主要与吸附态甲烷分子-页岩的相互作用强度有关.Abstract: The development depth is mostly greater than 2 000 m in major shale gas producing areas of China. As burial depth increases, reservoir pressure increases. The experimental and theoretical study of shale gas adsorption under low pressure is not suitable for the development of medium-deep and deep shale gas reservoirs. Thus, it modified the Uniform Langmuir model, and developed a high-pressure methane adsorption model, i.e., the modified Uniform Langmuir(Unilan)model. Then, we used the published experimental data under high pressure to validate the modified Unilan model. Moreover, we compared the modified Unilan model with other high-pressure adsorption models. It is found that the modified Unilan model with less fitting parameters is characterized by high precision, compared with other high pressure adsorption models. Finally, we investigated the fitted model parameters based on the mineral composition of the used shale samples. It is found that the adsorption capacity of shale is mainly controlled by organic matter and clay. Moreover, the volume of the adsorbed phase at maximum adsorption capacity is greater than micropore volume, but is less than total pore volume. Adsorption entropy change is mainly controlled by the interaction strength between adsorbed methane molecules and shale.
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图 1 高压吸附模型拟合结果
吸附实验数据来自Chen et al.（2019）. a. 修正的Unilan和DL模型；b. OK和SDA模型
Fig. 1. Model fitting results
图 3 Vmax、微孔体积和总孔体积三者的比较
微孔体积和总孔体积来自Li et al.（2017）
Fig. 3. Comparison between the micropore volumes and the maximum adsorbed volumes and total pore volumes of these samples
图 4 绝对吸附量预测结果
Fig. 4. Predicted absolute adsorption isotherms at different temperatures
表 1 模型验证所用的高压吸附实验数据
Table 1. High-pressure adsorption experimental data used for model validation
样品编号 实验温度范围（K） 实验压力范围（MPa） 样品产地 数据来源 X2 313.75~368.75 0.69~52.74 龙马溪组 Chen et al. (2019) FC-47 312.95~393.15 0.24~35.00 Lower Cambrian shale Li et al. (2017) FC-66 FC-72 X3 313.75~368.75 0.30~53.75 龙马溪组 Xiong et al. (2016) 1 348.75~368.75 0.50~52.20 龙马溪组 Zuo et al. (2020) 2 W1 313 0.50~51 龙马溪组 Shen et al. (2021) W2 W3 L1 L2 L3 
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表 2 修正的Unilan模型参数
Table 2. Fitted parameters of the modified Unilan model
样本 n0 (mol/kg) Vmax (cm3/g) Emax (kJ/mol) Emin (kJ/mol) -△S (J/mol/K) X2 0.35 0.013 26.41 9.84 100.13 FC-47 0.16 0.008 30.74 10.00 94.29 FC-66 0.28 0.012 32.30 11.95 101.40 FC-72 0.35 0.015 32.50 12.91 100.36 X3 0.18 0.008 28.39 7.98 98.49 1 0.18 0.007 21.51 12.73 92.40 2 0.31 0.010 35.02 11.14 114.76 W1 0.11 0.006 23.90 18.16 98.53 W2 0.20 0.009 25.84 17.61 98.15 W3 0.20 0.010 20.14 11.13 78.31 L1 0.20 0.009 28.32 20.00 105.32 L2 0.10 0.004 10.00 8.20 59.56 L3 0.15 0.006 10.57 3.08 49.00
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表 3 模型误差
Table 3. Relative error between model results and experimental data
样品 平均相对误差(%) 修正的Unilan OK DL SDA X2 4.24 10.31 2.79 8.00 FC-47 5.40 11.62 3.07 7.71 FC-66 3.90 10.38 2.44 7.40 FC-72 3.82 10.11 2.54 7.56 X3 7.84 10.59 3.93 5.84 1 3.16 4.72 3.34 4.71 2 3.54 8.59 2.29 3.68 W1 2.88 3.29 4.20 2.84 W2 2.10 3.00 1.85 1.74 W3 2.38 3.21 2.19 2.09 L1 2.29 3.07 1.84 1.70 L2 3.08 3.20 3.40 2.94 L3 2.17 2.91 2.02 1.91 平均值 3.60 6.54 2.76 4.47
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表 4 OK模型参数
Table 4. Fitted parameters of the OK model
样本 n0 (mol/kg) -εs/k (K) ρmax (mol/m3) X2 0.11 755.93 2.64×10-2 FC-47 0.05 1237.54 2.37×10-2 FC-66 0.09 1189.77 2.64×10-2 FC-72 0.12 1209.05 2.64×10-2 X3 0.05 900.09 2.30×10-2 1 0.07 679.87 2.64×10-2 2 0.10 774.66 2.64×10-2 W1 0.10 774.66 2.64×10-2 W2 0.09 957.96 2.23×10-2 W3 0.09 970.36 2.09×10-2 L1 0.09 972.37 2.17×10-2 L2 0.05 835.59 2.19×10-2 L3 0.07 999.20 2.29×10-2
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表 5 DL模型参数
Table 5. Fitted parameters of the DL model
样本 n0 (mol/kg) α’ A1 (MPa-1) E1 (kJ/mol) A2 (MPa-1) E2 (kJ/mol) Vmax (cm3/g) X2 0.32 0.26 2.55×10-5 19.74 1.63×10-3 15.98 0.013 FC-47 0.29 0.29 8.54×10-7 26.44 5.45×10-4 21.13 0.016 FC-66 0.30 0.39 7.01×10-6 23.64 8.38×10-4 20.14 0.014 FC-72 0.36 0.44 5.36×10-6 25.13 1.01×10-3 19.80 0.016 X3 0.15 0.12 1.64×10-4 17.03 5.54×10-1 7.43 0.007 1 0.19 0.23 1.05×10-4 16.68 2.83×10-3 12.47 0.008 2 0.20 0.09 9.99×10-5 20.02 2.02×10-4 30.06 0.007 W1 0.13 0.23 3.07×10-4 15.52 2.95×10-3 14.44 0.007 W2 0.21 0.06 3.99×10-4 16.92 12.95×10-3 25.21 0.010 W3 0.20 0.09 4.04×10-4 16.90 5.77×10-3 18.12 0.010 L1 0.20 0.09 4.00×10-4 16.90 5.86×10-3 18.20 0.010 L2 0.11 0.29 3.63×10-4 15.22 2.63×10-3 13.71 0.005 L3 0.15 0.12 3.96×10-4 16.88 4.69×10-3 17.05 0.007
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表 6 SDA模型参数
Table 6. Fitted parameters of the SDA model
样本 W0 (cm3/g) α (1/K) E (kJ/mol) t X2 0.012 5.47×10-4 5.73 1.00 FC-47 0.010 2.11×10-3 7.78 1.04 FC-66 0.016 1.78×10-3 7.11 1.00 FC-72 0.022 1.72×10-3 7.34 1.00 X3 0.007 1.38×10-3 6.33 1.00 1 0.005 2.42×10-4 6.94 1.46 2 0.009 1.49×10-4 7.16 1.18 W1 0.005 1.72×10-3 8.23 1.96 W2 0.009 9.63×10-4 9.41 1.99 W3 0.009 1.27×10-3 9.55 1.99 L1 0.009 1.09×10-3 9.54 1.99 L2 0.004 9.87×10-4 8.50 2.00 L3 0.006 8.59×10-4 9.70 1.99
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[1] Chen, G.H., Lu, S.F., Liu, K.Y., et al., 2020. Occurrence State and Micro Mechanisms of Shale Gas on Pore Walls. Earth Science, 45(5): 1782-1790 (in Chinese with English abstract). [2] Chen, L., Zuo, L., Jiang, Z. X., et al., 2019. Mechanisms of Shale Gas Adsorption: Evidence from Thermodynamics and Kinetics Study of Methane Adsorption on Shale. Chemical Engineering Journal, 361(C): 559-570. https://doi.org/10.1016/j.cej.2018.11.185 [3] Do, D., Do, H., 2003. Adsorption of Supercritical Fluids in Non-Porous and Porous Carbons: Analysis of Adsorbed Phase Volume and Density. Carbon, 41(9): 1777-1791. https://doi.org/10.1016/S0008-6223(03)00152-0 [4] Dubinin, M. M., Astakhov, V. A., 1971. Development of the Concepts of Volume Filling of Micropores in the Adsorption of Gases and Vapors by Microporous Adsorbents. Bulletin of the Academy of Sciences of the USSR, Division of Chemical Science, 20(1): 3-7. https://doi.org/10.1007/BF00849307 [5] Gao, Z. Y., Xiong, S. L., 2021. Methane Adsorption Capacity Reduction Process of Water-Bearing Shale Samples and Its Influencing Factors: One Example of Silurian Longmaxi Formation Shale from the Southern Sichuan Basin in China. Journal of Earth Science, 32(4): 946-959. https://doi.org/10.1007/s12583-020-1120-5 [6] Gasparik, M., Bertier, P., Gensterblum, Y., et al., 2014. Geological Controls on the Methane Storage Capacity in Organic-Rich Shales. International Journal of Coal Geology, 123: 34-51. https://doi.org/10.1016/j.coal.2013.06.010 [7] Guo, T.L., 2021. Progress and Research Direction of Deep Shale Gas Exploration and Development. Reservoir Evaluation and Development, 11(1): 1-6 (in Chinese with English abstract). [8] He, Z. L., Li, S. J., Nie, H. K., et al., 2018. The Shale Gas "Sweet Window": "The Cracked and Unbroken" State of Shale and Its Depth Range. Marine and Petroleum Geology, 101: 334-342. https://doi.org/10.1016/j.marpetgeo.2018.11.033 [9] Li, M., Zhou, L., Wu, Q., et al., 2002. Progress in Predicting the Equilibria of Multi-Component Gas/Solid Adsorption. Progress in Chemistry, 14(2): 93-97 (in Chinese with English abstract). [10] Li, T. F., Tian, H., Xiao, X. M., et al., 2017. Geochemical Characterization and Methane Adsorption Capacity of Overmature Organic-Rich Lower Cambrian Shales in Northeast Guizhou Region, Southwest China. Marine and Petroleum Geology, (86): 858-873. https://doi.org/10.1016/j.marpetgeo.2017.06.043 [11] Li, X.F., Pu, Y.C., Sun, C.Y., et al., 2014. Recognition of Absorption/Desorption Theory in Coalbed Methane Reservoir and Shale Gas Reservoir. Acta Petrolei Sinica, 35(6): 1113-1129 (in Chinese with English abstract). [12] Liu, Y., Guo, F. Y., Hu, J., et al., 2016. Entropy Prediction for H2 Adsorption in Metal-Organic Frameworks. Physical Chemistry Chemical Physics, 18(34): 23998-24005. https://doi.org/10.1039/c6cp04645b doi: 10.1039/C6CP04645B [13] Liu, Z.X., Feng, Z.C., 2012. Theoretical Study on Adsorption Heat of Methane in Coal. Journal of China Coal Society, 37(4): 647-653 (in Chinese with English abstract). [14] Ono, S., Kondo, S., 1960. Molecular Theory of Surface Tension in Liquids. Springer, Berlin, 134-280. [15] Polanyi, M., 1963. The Potential Theory of Adsorption. Science, 141(3585): 1010-1013. https://doi.org/10.1126/science.141.3585.1010 [16] Purewal, J., Liu, D. A., Sudik, A., et al., 2012. Improved Hydrogen Storage and Thermal Conductivity in High-Density MOF-5 Composites. The Journal of Physical Chemistry C, 116(38): 20199-20212. https://doi.org/10.1021/jp305524f [17] Ren, W. X., Guo, J. C., Zeng, F. H., et al., 2019. Modeling of High-Pressure Methane Adsorption on Wet Shales. Energy & Fuels, 33(8): 7043-7051. https://doi.org/10.1021/acs.energyfuels.9b01024 [18] Ren, W. X., Li, G. S., Tian, S. C., et al., 2017a. Adsorption and Surface Diffusion of Supercritical Methane in Shale. Industrial & Engineering Chemistry Research, 56(12): 3446-3455. https://doi.org/10.1021/acs.iecr.6b04432 [19] Ren, W. X., Tian, S. C., Li, G. S., et al., 2017b. Modeling of Mixed-Gas Adsorption on Shale Using HPC-SAFT-MPTA. Fuel, 210: 535-544. https://doi.org/10.1016/j.fuel.2017.09.012 [20] Rexer, T. F. T., Benham, M. J., Aplin, A. C., et al., 2013. Methane Adsorption on Shale under Simulated Geological Temperature and Pressure Conditions. Energy & Fuels, 27(6): 3099-3109. https://doi.org/10.1021/ef400381v [21] Sakurovs, R., Day, S., Weir, S., et al., 2007. Application of a Modified Dubinin-Radushkevich Equation to Adsorption of Gases by Coals under Supercritical Conditions. Energy & Fuels, 21(2): 992-997. https://doi.org/10.1021/ef0600614 [22] Shen, W. J., Li, X. Z., Ma, T. R., et al., 2021. High- Pressure Methane Adsorption Behavior on Deep Shales: Experiments and Modeling. Physics of Fluids, 33(6): 063103. https://doi.org/10.1063/5.0054486 [23] Shethna, H. K., Bhatia, S. K., 1994. Interpretation of Adsorption Isotherms at Above-Critical Temperatures Using a Modified Micropore Filling Model. Langmuir, 10(3): 870-876. https://doi.org/10.1021/la00015a043 [24] Soave, G. S., 1999. An Effective Modification of the Benedict-Webb-Rubin Equation of State. Fluid Phase Equilibria, 164(2): 157-172. https://doi.org/10.1016/S0378-3812(99)00252-6 [25] Stadie, N. P., Murialdo, M., Ahn, C. C., et al., 2013. Anomalous Isosteric Enthalpy of Adsorption of Methane on Zeolite-Templated Carbon. Journal of the American Chemical Society, 135(3): 990-993. https://doi.org/10.1021/ja311415m [26] Tang, X., Ripepi, N., Stadie, N. P., et al., 2016. A Dual-Site Langmuir Equation for Accurate Estimation of High Pressure Deep Shale Gas Resources. Fuel, 185: 10-17. https://doi.org/10.1016/j.fuel.2016.07.088 [27] Tian, S.C., Wang, T.Y., Li, G.S., et al., 2017. Molecular Simulation of Methane Adsorption Behavior in Different Shale Kerogen Types. Natural Gas Industry, 37(12): 18-25 (in Chinese with English abstract). [28] Wang, P.W., Chen, Z.H., Jin, Z.J., et al., 2019. Optimizing Parameter "Total Organic Carbon Content" for Shale Oil and Gas Resource Assessment: Taking West Canada Sedimentary Basin Devonian Duvernay Shale as an Example. Earth Science, 44(2): 504-512 (in Chinese with English abstract). [29] Xiong, W., Zuo, L., Luo, L. T., et al., 2016. Methane Adsorption on Shale under High Temperature and High Pressure of Reservoir Condition: Experiments and Supercritical Adsorption Modeling. Adsorption Science & Technology, 34(2/3): 193-211. https://doi.org/10.1177/0263617415623425 [30] Yang, F., Ning, Z. F., Zhang, R., et al., 2015. Investigations on the Methane Sorption Capacity of Marine Shales from Sichuan Basin, China. International Journal of Coal Geology, 146: 104-117. doi: 10.1016/j.coal.2015.05.009 [31] Yang, F., Xie, C. J., Xu, S., et al., 2017. Supercritical Methane Sorption on Organic-Rich Shales over a Wide Temperature Range. Energy & Fuels, 31(12): 13427-13438. https://doi.org/10.1021/acs.energyfuels.7b02628 [32] Ye, Z. H., Chen, D., Pan, Z. J., et al., 2016. An Improved Langmuir Model for Evaluating Methane Adsorption Capacity in Shale under Various Pressures and Temperatures. Journal of Natural Gas Science and Engineering, 31: 658-680. https://doi.org/10.1016/j.jngse.2016.03.070 [33] Yu, W., Sepehrnoori, K., Patzek, T. W., 2016. Modeling Gas Adsorption in Marcellus Shale with Langmuir and Bet Isotherms. SPE Journal, 21(2): 589-600. https://doi.org/10.2118/170801-PA [34] Zhou, S.W., Wang, H.Y., Xue, H.Q., et al., 2017. Discussion on the Supercritical Adsorption Mechanism of Shale Gas Based on Ono-Kondo Lattice Model. Earth Science, 42(8): 1421-1430 (in Chinese with English abstract). [35] Zhou, S. W., Xue, H. Q., Ning, Y., et al., 2018. Experimental Study of Supercritical Methane Adsorption in Longmaxi Shale: Insights into the Density of Adsorbed Methane. Fuel, 211: 140-148. https://doi.org/10.1016/j.fuel.2017.09.065 [36] Zhou, Z., Jiang, Z.X., Li, S.Z., et al., 2021. Biostratigraphic Characteristics of Black Graptolite Shale in Wufeng Formation and Longmaxi Formation in Jianshi Area of West Hubei. Earth Science, 46(2): 432-443 (in Chinese with English abstract). [37] Zhu, W. T., 2011. Basic Physical Chemistry. Tsinghua University Press, Beijing, 163 (in Chinese). [38] Zou, C. N., Dong, D. Z., Wang Y. M., et al., 2015. Shale Gas in China: Characteristics, Challenges and Prospects (I). Petroleum Exploration and Development, 42(6): 689-701 (in Chinese with English abstract). [39] Zou, C.N., Zhao, Q., Cong, L.Z., et al., 2021. Development Progress, Potential and Prospect of Shale Gas in China. Natural Gas Industry, 41(1): 1-14 (in Chinese with English abstract). [40] Zuo, L., Jiang, T. X., Wang, H. T., 2020. Calculating the Absolute Adsorption of High-Pressure Methane on Shale by a New Method. Adsorption Science & Technology, 38(1/2): 46-59. https://doi.org/10.1177/0263617420902658 [41] 陈国辉, 卢双舫, 刘可禹, 等, 2020. 页岩气在孔隙表面的赋存状态及其微观作用机理. 地球科学, 45(5): 1782-1790. doi: 10.3799/dqkx.2019.194 [42] 郭彤楼, 2021. 深层页岩气勘探开发进展与攻关方向. 油气藏评价与开发, 11(1): 1-6. https://www.cnki.com.cn/Article/CJFDTOTAL-KTDQ202101001.htm [43] 李明, 周理, 吴琴, 等, 2002. 多组分气体吸附平衡理论研究进展. 化学进展, 14(2): 93-97. https://www.cnki.com.cn/Article/CJFDTOTAL-HXJZ200202002.htm [44] 李相方, 蒲云超, 孙长宇, 等, 2014. 煤层气与页岩气吸附/解吸的理论再认识. 石油学报, 35(6): 1113-1129. doi: 10.3969/j.issn.1001-8719.2014.06.023 [45] 刘志祥, 冯增朝, 2012. 煤体对瓦斯吸附热的理论研究. 煤炭学报, 37(4): 647-653. https://www.cnki.com.cn/Article/CJFDTOTAL-MTXB201204023.htm [46] 田守嶒, 王天宇, 李根生, 等, 2017. 页岩不同类型干酪根内甲烷吸附行为的分子模拟. 天然气工业, 37(12): 18-25. https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG201712006.htm [47] 王鹏威, 谌卓恒, 金之钧, 等, 2019. 页岩油气资源评价参数之"总有机碳含量"的优选: 以西加盆地泥盆系Duvernay页岩为例. 地球科学, 44(2): 504-512. doi: 10.3799/dqkx.2018.191 [48] 周尚文, 王红岩, 薛华庆, 等, 2017. 基于Ono-Kondo格子模型的页岩气超临界吸附机理探讨. 地球科学, 42(8): 1421-1430. doi: 10.3799/dqkx.2017.543 [49] 周志, 姜振学, 李世臻, 等, 2021. 鄂西建始地区五峰-龙马溪组黑色页岩生物地层特征. 地球科学, 46(2): 432-443. doi: 10.3799/dqkx.2020.059 [50] 朱文涛, 2011. 基础物理化学. 北京: 清华大学出版社, 163. [51] 邹才能, 董大忠, 王玉满, 等, 2015. 中国页岩气特征、挑战及前景(一). 石油勘探与开发, 42(6): 689-701. https://www.cnki.com.cn/Article/CJFDTOTAL-SKYK201506002.htm [52] 邹才能, 赵群, 丛连铸, 等, 2021. 中国页岩气开发进展、潜力及前景. 天然气工业, 41(1): 1-14. https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202101002.htm -
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