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Evolution of Anisotropic Coal Permeability Under the Effect of Heterogeneous Deformation of Fractures

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Abstract

Permeability is one of the key parameters to better understand the processes of coalbed methane mining and carbon dioxide geological storage. As a unique porous medium, coal usually possesses distinct deformation characteristics. In this work, we used a cubic model to characterize the physical structure of coal. The fracture system in coal contained both soft and hard parts subject to the natural-strain-based Hooke law and engineering-strain-based Hooke law, respectively. By analyzing the changes in the soft and hard parts of fractures, we explored heterogeneous deformation in coal. However, coal usually exhibits strong anisotropy under reservoir conditions, and the permeability in each direction is different. First, based on the generalized Hooke law, we characterized fracture deformation in coal along all directions under stress. Moreover, based on the definition of the coal porosity, we proposed an anisotropic coal permeability model under heterogeneous fracture deformation, and the model was verified against experimental data reported in the literature. Second, based on our proposed model, we examined the influence of the soft/hard parts of fractures on permeability, and the contribution of gas adsorption to the coal permeability was also analyzed. When the confining pressure remained constant, a higher proportion of the soft parts of fractures corresponded to a larger permeability change, and a higher internal expansion factor corresponded to a lower permeability. In addition, we assessed the influence of slippage on the permeability in the effective stress change process and incorporated the slippage effect into the permeability model.

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References

  • An, H., Wei, X. R., Wang, G. X., Massarotto, P., Wang, F. Y., Rudolph, V., & Golding, S. D. (2015). Modeling anisotropic permeability of coal and its effects on CO2 sequestration and enhanced coalbed methane recovery. International Journal of Coal Geology, 152, 15–24.

    Article  Google Scholar 

  • Barton, N. R., Bandis, S. C., & Bakhtar, K. (1985). Strength, deformation, and conductivity coupling of rock joint deformation. International Journal of Rock Mechanics and Mining Sciences, 22, 121–140.

    Article  Google Scholar 

  • Chen, D., Pan, Z., Ye, Z., Hou, B., & Yuan, L. (2016). A unified permeability and effective stress relationship for porous and fractured reservoir rocks. Journal of Natural Gas Science and Engineering, 29, 401–412.

    Article  Google Scholar 

  • Chen, Z., Liu, J., Pan, Z., Connell, L. D., & Elsworth, D. (2012). Influence of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: Model development and analysis. International Journal of Greenhouse Gas Control, 8(5), 101–110.

    Article  Google Scholar 

  • Civan, F. (2010). Effective correlation of apparent gas permeability in tight porous media. Transport in Porous Media, 82(2), 375–384.

    Article  Google Scholar 

  • Fan, L., & Liu, S. (2018). Numerical prediction of in situ horizontal stress evolution in coalbed methane reservoirs by considering both poroelastic and sorption induced strain effects. International Journal of Rock Mechanics and Mining Sciences, 104, 156–164.

    Article  Google Scholar 

  • Fan, S., Zhang, D., Wen, H., Cheng, X., & Hu, B. (2020). Enhancing coalbed methane recovery with liquid CO2 fracturing in underground coal mine: From experiment to field application. Fuel. https://doi.org/10.1016/j.fuel.2020.119793

    Article  Google Scholar 

  • Gray, I. (1987). Reservoir engineering in coal seams. Part I. The physical process of gas storage and movement in coal seams. SPE Reservoir Evaluation Enging, 2, 28–34.

    Article  Google Scholar 

  • Gunter, W. D., Gentzis, T., Rottenfusser, B. A., & Richardson, R. J. H. (1997). Deep coalbed methane in Alberta, Canada: A fuel resource with the potential of zero greenhouse gas emissions. Energy Conversion and Management, 38, S217–S222.

    Article  Google Scholar 

  • Guo, P., Cheng, Y., Jin, K., Li, W., Tu, Q., & Liu, H. (2014). Impact of effective stress and matrix deformation on the coal fracture permeability. Transport in Porous Media, 103(1), 99–115.

    Article  Google Scholar 

  • Harpalani, S., & Schraufnagel, R. A. (1990). Shrinkage of coal matrix with release of gas and its impact on permeability of coal. Fuel, 69(5), 551–556.

    Article  Google Scholar 

  • Jiang, C., Zhao, Z., Zhang, X., Liu, J., & Cui, G. (2020). Controlling effects of differential swelling index on evolution of coal permeability. Journal of Rock Mechanics and Geotechnical Engineering, 12, 461–472.

    Article  Google Scholar 

  • Klinkenberg, L. J. (1941). The permeability of porous media to liquids and gases. In Drilling and production practice. American Petroleum Institute.

  • Laubach, S. E., Marrett, R. A., Olson, J. E., & Scott, A. R. (1998). Characteristics and origins of coal cleat: A review. International Journal of Coal Geology, 35(1–4), 175–207.

    Article  Google Scholar 

  • Li, B., Yang, K., Ren, C., Li, J., & Xu, J. (2019). An adsorption-permeability model of coal with slippage effect under stress and temperature coupling condition. Journal of Natural Gas Science and Engineering, 71, 102983–102983.

    Article  Google Scholar 

  • Li, J., Chen, Z., Wu, K., Li, R., & Li, X. (2018). Effect of water saturation on gas slippage in tight rocks. Fuel, 225, 519–532.

    Article  Google Scholar 

  • Li, T., Wu, C. F., & Liu, Q. (2015). Characteristics of coal fractures and the influence of coal facies on coalbed methane productivity in the South Yanchuan Block, China. Journal of Natural Gas Science and Engineering, 22, 625–632.

    Article  Google Scholar 

  • Li, Y., Dong, P., & Zhou, D. (2020). A dynamic apparent permeability model for shale microfractures: Coupling poromechanics, fluid dynamics, and sorption-induced strain. Journal of Natural Gas Science and Engineering, 74, 103104.

    Article  Google Scholar 

  • Liu, H. H., & Rutqvist, J. (2010). A new coal-permeability model: Internal swelling stress and fracture–matrix interaction. Transport in Porous Media, 82, 157–171.

    Article  Google Scholar 

  • Liu, H. H., Rutqvist, J., & Berryman, J. G. (2009). On the relationship between stress and elastic strain for porous and fractured rock. International Journal of Rock Mechanics and Mining Sciences, 46, 289–296.

    Article  Google Scholar 

  • Liu, J., Chen, Z., Elsworth, D., Qu, H., & Chen, D. (2011). Interactions of multiple processes during CBM extraction: A critical review. International Journal of Coal Geology, 87(3), 175–189.

    Article  Google Scholar 

  • Liu, Q. L., Li, Z. H., Wang, E. Y., Niu, Y., & Kong, X. G. (2020a). A dual-permeability model for coal under tri-axial boundary conditions. Journal of Natural Gas Science and Engineering, 82, 103524.

    Article  Google Scholar 

  • Liu, S., & Harpalani, S. (2013). A new theoretical approach to model sorption-induced coal shrinkage or swelling. AAPG Bulltin, 97(7), 1033–1049.

    Article  Google Scholar 

  • Liu, T., Lin, B., Fu, X., & Liu, S. (2020b). A new approach modeling permeability of mining-disturbed coal based on a conceptual model of equivalent fractured coal. Journal of Natural Gas Science and Engineering, 79, 103366.

    Article  Google Scholar 

  • Liu, T., Lin, B., & Yang, W. (2017). Impact of matrix–fracture interactions on coal permeability: Model development and analysis. Fuel, 207, 522–532.

    Article  Google Scholar 

  • Liu, Z., Liu, D., Cai, Y., & Pan, Z. (2020c). Experimental study of the effective stress coefficient for coal anisotropic permeability. Energy & Fuels. https://doi.org/10.1021/acs.energyfuels.0c00907

    Article  Google Scholar 

  • Lou, Z., Wang, K., Zang, J., Zhao, W., Qin, B., & Kan, T. (2020). Effects of permeability anisotropy on coal mine methane drainage performance. Journal of Natural Gas Science and Engineering, 86, 103733.

    Article  Google Scholar 

  • Lu, S. Q., Cheng, Y., & Li, W. (2016). Model development and analysis of the evolution of coal permeability under different boundary conditions. Journal of Natural Gas Science and Engineering, 31, 129–138.

    Article  Google Scholar 

  • Meng, Y., Li, Z., & Lai, F. (2021). Influence of effective stress on gas slippage effect of different rank coals. Fuel, 285, 119207.

    Article  Google Scholar 

  • Meng, Y., Wang, J. Y., Li, Z., & Zhang, J. (2017). An improved productivity model in coal reservoir and its application during coalbed methane production. Journal of Natural Gas Science and Engineering, 49, 342–351.

    Article  Google Scholar 

  • Mitra, A., Harpalani, S., & Liu, S. (2012). Laboratory measurement and modeling of coal permeability with continued methane production: Part I-laboratory results. Fuel, 94, 110–116.

    Article  Google Scholar 

  • Mukherjee, M., & Misra, S. (2018). A review of experimental research on enhanced coal bed methane (ECBM) recovery via CO2 sequestration. Earth-Science Reviews, 179, 392–410.

    Article  Google Scholar 

  • Niu, Q. (2019). Experimental study on the mechanical response mechanism and injectivity with supercritical CO2 injection in anthracite. China University of Mining and Technology (in Chinese).

  • Niu, Q., Cao, L., Sang, S., Wang, W., Zhou, X., Yuan, W., Ji, Z., Chang, J., & Li, M. (2021). Experimental study on the softening effect and mechanism of anthracite with CO2 injection. International Journal of Rock Mechanics and Mining Sciences, 138, 104614.

    Article  Google Scholar 

  • Niu, Q., Cao, L., Sang, S., Zhou, X., & Wang, Z. (2018). Anisotropic adsorption swelling and permeability characteristics with injecting CO2 in coal. Energy & Fuels, 32(2), 1979–1991.

    Article  Google Scholar 

  • Palmer, I., & Mansoori, J. (1996). How permeability depends on stress and pore pressure in coalbeds: A new model. In SPE annual technical conference and exhibition (pp. 557–564). SPE Reservoir Evaluation Engineering.

  • Pan, Z., & Connell, L. D. (2007). A theoretical model for gas adsorption induced coal swelling. International Journal of Coal Geology, 69(4), 243–252.

    Article  Google Scholar 

  • Pan, Z., & Connell, L. D. (2011). Modelling of anisotropic coal swelling and its impact on permeability behaviour for primary and enhanced coalbed methane recovery. International Journal of Coal Geology, 85(3–4), 257–267.

    Article  Google Scholar 

  • Pan, Z., & Wood, D. A. (2015). Coalbed methane (CBM) exploration, reservoir characterisation, production, and modelling: A collection of published research (2009–2015). Journal of Natural Gas Science and Engineering, 26, 1472–1484.

    Article  Google Scholar 

  • Pérez-López, R., Montes-Hernandez, G., Nieto, J. M., Renard, F., & Charlet, L. (2008). Carbonation of alkaline paper mill waste to reduce CO2 greenhouse gas emissions into the atmosphere. Applied Geochemistry, 23(8), 2292–2300.

    Article  Google Scholar 

  • Puri, R., & Yee, D. (1990). Enhanced coalbed methane recovery. In 65th annual technical conference and exhibition.

  • Robertson, E. P., & Christiansen, R. L. (2006). A permeability model for coal and other fractured, sorptive-elastic media. Society of Petroleum Engineers.

    Book  Google Scholar 

  • Seidle, J. R., & Huitt, L. G. (1995). Experimental measurement of coal matrix shrinkage due to gas desorption and implications for cleat permeability increases. Society of Petroleum Engineers Inc.

    Book  Google Scholar 

  • Shang, X., Wang, J., Zhizhen, J., Zhang, Z., & Gao, F. (2019). A three-parameter permeability model for the cracking process of fractured rocks under temperature change and external loading. International Journal of Rock Mechanics and Mining Sciences, 123, 104106–104106.

    Article  Google Scholar 

  • Shi, J. Q., & Durucan, S. (2004). Drawdown induced changes in permeability of coalbeds: A new interpretation of the reservoir response to primary recovery. Transport in Porous Media, 56, 1–16.

    Article  Google Scholar 

  • Si, L., Li, Z., & Yang, Y. (2018). Coal permeability evolution with the interaction between nanopore and fracture: Its application in coal mine gas drainage for Qingdong coal mine in Huaibei coalfield, china. Journal of Natural Gas Science and Engineering, 56, 523–535.

    Article  Google Scholar 

  • Si, L., Li, Z., & Yang, Y. (2019). Evolution characteristics of gas permeability under multiple factors. Transport in Porous Media, 127(2), 1–18.

    Article  Google Scholar 

  • Tan, Y., Pan, Z., Liu, J., Kang, J., Zhou, F., Connell, L. D., Zhou, F., Connell, L. D., & Yang, Y. (2018). Experimental study of impact of anisotropy and heterogeneity on gas flow in coal. Part I: Diffusion and adsorption. Fuel, 232, 444–453.

    Article  Google Scholar 

  • Tan, Y., Pan, Z., Liu, J., Wu, Y., & Connell, L. D. (2017). Experimental study of permeability and its anisotropy for shale fracture supported with proppant. Journal of Natural Gas Science and Engineering, 44, 250–264.

    Article  Google Scholar 

  • Teng, T., Wang, W., & Zhan, P. (2019). Evaluation criterion and index for the efficiency of thermal stimulation to dual coal permeability. Journal of Natural Gas Science and Engineering, 68, 102899.

    Article  Google Scholar 

  • Wang, C., Zhang, J., Chen, J., Zhong, R., & Chen, Z. (2021a). Understanding competing effect between sorption swelling and mechanical compression on coal matrix deformation and its permeability. International Journal of Rock Mechanics and Mining Sciences, 138(6), 104639.

    Article  Google Scholar 

  • Wang, C., Zhang, J., Chen, J., Zhong, R., Chen, Z., Cui, G., Jiang, Y., Liu, W., & Chen, Z. (2021b). Understanding competing effect between sorption swelling and mechanical compression on coal matrix deformation and its permeability. International Journal of Rock Mechanics and Mining Sciences, 138(6), 104639.

    Article  Google Scholar 

  • Wang, G., Ren, T., Wang, K., & Zhou, A. (2014a). Improved apparent permeability models of gas flow in coal with klinkenberg effect. Fuel, 128, 53–61.

    Article  Google Scholar 

  • Wang, H. C., Pan, J. N., Wang, S., & Zhu, H. T. (2015). Relationship between macro-fracture density, P-wave velocity, and permeability of coal. Journal of Applied Geophysics, 117, 111–117.

    Article  Google Scholar 

  • Wang, K., Zang, J., Wang, G., & Zhou, A. (2014b). Anisotropic permeability evolution of coal with effective stress variation and gas sorption: Model development and analysis. International Journal of Coal Geology, 130, 53–65.

    Article  Google Scholar 

  • Wang, Z., & Tang, X. (2018). New insights from supercritical methane adsorption in coal: Gas resource estimation, thermodynamics and engineering application. Energy & Fuels, 32(4), 5001–5009.

    Article  Google Scholar 

  • Wen, H., Wang, H., Fan, S., Li, Z., Chen, J., Cheng, X., Cheng, B., & Yu, Z. (2020). Improving coal seam permeability and displacing methane by injecting liquid CO2: An experimental study. Fuel, 281, 118747.

    Article  Google Scholar 

  • Wu, Y., Pan, Z., Zhang, D., Down, D. I., Lu, Z., & Connell, L. D. (2017). Experimental study of permeability behaviour for proppant supported coal fracture. Journal of Natural Gas Science and Engineering, 51, 18–26.

    Article  Google Scholar 

  • Zang, J., & Wang, K. (2017). Gas sorption-induced coal swelling kinetics and its effects on coal permeability evolution: Model development and analysis. Fuel, 189, 164–177.

    Article  Google Scholar 

  • Zeng, J., Liu, J., Li, W., Leong, Y. K., & Guo, J. (2020a). Evolution of shale permeability under the influence of gas diffusion from the fracture wall into the matrix. Energy & Fuels. https://doi.org/10.1021/acs.energyfuels.0c00219

    Article  Google Scholar 

  • Zeng, J., Liu, J., Li, W., Tian, J., & Guo, J. (2020b). Effects of heterogeneous local swelling and multiple pore types on coal and shale permeability evolution. In SPE Europec featured at 82nd EAGE conference and exhibition.

  • Zhang, Z., Zhang, R., Xie, H., & Gao, M. (2015). The relationships among stress, effective porosity and permeability of coal considering the distribution of natural fractures: Theoretical and experimental analyses. Environmental Earth Science, 73(10), 5997–6007.

    Article  Google Scholar 

  • Zhao, W., Wang, K., Liu, S., Ju, Y., Zhou, H. W., Fan, L., Yang, Y., Cheng, Y., & Zhang, X. (2020). Asynchronous difference in dynamic characteristics of adsorption swelling and mechanical compression of coal: Modeling and experiments. International Journal of Rock Mechanics and Mining Sciences, 135, 104498.

    Article  Google Scholar 

  • Zheng, J., Zheng, L., Liu, H. H., & Ju, Y. (2015). Relationships between permeability, porosity and effective stress for low-permeability sedimentary rock. International Journal of Rock Mechanics and Mining Sciences, 78, 304–318.

    Article  Google Scholar 

  • Zheng, Q., Yu, B., Duan, Y., & Fang, Q. (2013). A fractal model for gas slippage factor in porous media in the slip flow regime. Chemical Engineering Science, 87, 209–215.

    Article  Google Scholar 

  • Zhou, H. W., Rong, T. L., Wang, L. J., Mou, R. Y., & Ren, W. G. (2020a). A new anisotropic coal permeability model under the influence of stress, gas sorption and temperature: Development and verification. International Journal of Rock Mechanics and Mining Sciences, 132, 104407.

    Article  Google Scholar 

  • Zhou, H. W., Wang, L. J., Rong, T. L., Zhang, L., Ren, W. G., & Su, T. (2019a). Creep-based permeability evolution in deep coal under unloading confining pressure. Journal of Natural Gas Science and Engineering, 65, 185–196.

    Article  Google Scholar 

  • Zhou, H. W., Zhang, L., Wang, X. Y., Rong, T. L., & Wang, L. J. (2020b). Effects of matrix-fracture interaction and creep deformation on permeability evolution of deep coal. International Journal of Rock Mechanics and Mining Sciences, 127, 104236.

    Article  Google Scholar 

  • Zhou, J., Zhang, L., Li, X., & Pan, Z. (2019b). Experimental and modeling study of the stress-dependent permeability of a single fracture in shale under high effective stress. Fuel, 257, 116078.1-116078.12.

    Article  Google Scholar 

  • Zhou, Y., Li, Z., Yang, Y., Zhang, L., Qi, Q., Si, L., & Li, J. (2016a). Improved porosity and permeability models with coal matrix block deformation effect. Rock Mechanics Rock Engineering, 49, 3687–3697.

    Article  Google Scholar 

  • Zhou, Y., Li, Z., Yang, Y., Zhang, L., Si, L., Kong, B., & Li, J. (2016b). Evolution of coal permeability with cleat deformation and variable klinkenberg effect. Transport in Porous Media, 115(1), 153–167.

    Article  Google Scholar 

  • Zhu, C., Wan, J., Tokunaga, T. K., Liu, N., & Wu, H. (2019). Impact of CO2 injection on wettability of coal at elevated pressure and temperature. International Journal of Greenhouse Gas Control, 91, 102840.

    Article  Google Scholar 

  • Zou, J., Chen, W., Yang, D., Yu, H., & Yuan, J. (2016). The impact of effective stress and gas slippage on coal permeability under cyclic loading. Journal of Natural Gas Science and Engineering, 31, 236–248.

    Article  Google Scholar 

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Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (Grants Nos. 52064007, 51804085, and 51911530203) and Guizhou Provincial Science and Technology Foundation (Qianke Combination Foundation-ZK[2021]Key 052).

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Li, J., Li, B., Cheng, Q. et al. Evolution of Anisotropic Coal Permeability Under the Effect of Heterogeneous Deformation of Fractures. Nat Resour Res 30, 3623–3642 (2021). https://doi.org/10.1007/s11053-021-09889-3

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