In order to understand the permeability evolution of coal under different temperature and pore pressure conditions, a series of experiments are carried out by simulating stress state and temperature conditions of coal in depth, meanwhile the permeability is obtained by calculation using fractional derivative calculation method. A damage-induced permeability model for the complete stress–strain process of deep coal considering temperature and pore pressure is proposed by introducing the non-uniform coefficient. The model is validated by experimental data from different perspectives. Results show that the initial permeability decreases with increasing temperature while it increases with pore pressure rising. Furthermore, the developed permeability model is proved to agree better with the experimental data of permeability evolution with pore pressure in comparison with the traditional models. The experimental results of permeability evolution caused by temperature and axial stress can be characterized by the proposed permeability model well. Finally, the model can accurately characterize the piecewise permeability evolution that it decreases in compaction stage and increases in dilation stage with axial strain. Discussions on the effects of non-uniform deformation coefficient and permeability-damage coefficient on the permeability model indicate that the increasing non-uniform deformation coefficient will accelerate permeability evolution. The permeability trend in the volumetric dilation stage is found to be more sensitive to the permeability-damage coefficient in comparison with the compaction stage.
AbstractSection Article highlights-
Considering temperature and pore pressure, a damage-based permeability model for the whole stress–strain process is established.
-
The experiments under different conditions are carried out to verify the permeability model.
-
The sensitivity of non-uniform deformation and the permeability-damage coefficient is analyzed.
References
An L, Zhou HW, Yang S, Sun XT, Wang L, Che J (2019) Fractional derivative permeability modeling approach to the influence of temperature on granite. Chin J Rock Mech Eng 10(S2):3672–3679 (in Chinese)
Chao JK, Yu MG, Chu TX, Han XF, Teng F, Li P (2019) Evolution of broken coal permeability under the condition of stress, temperature, moisture content, and pore pressure. Rock Mech Rock Eng 52:2803–2814. https://doi.org/10.1007/s00603-019-01873-x
Chen J, Hopmans JW, Grismer ME (1999) Parameter estimation of two-fluid capillary pressure-saturation and permeability functions. Adv Water Resour 22(5):479–493. https://doi.org/10.1016/S0309-1708(98)00025-6
Connell LD, Lu M, Pan Z (2010) An analytical coal permeability model for tri-axial strain and stress conditions. Int J Coal Geol 84(2):103–114. https://doi.org/10.1016/j.coal.2010.08.011
Cui XJ, Bustin RM (2005) Volumetric strain associated with methane desorption and its impact on coalbed gas production from deep coal seams. AAPG Bull 89(9):1181–1202. https://doi.org/10.1306/0511050
Gray I (1987) Reservoir engineering in coal seams: Part 1-The physical process of gas storage and movement in coal seams. SPE Reserv Eng 2:28–34. https://doi.org/10.2118/12514-PA
Guo PK, Cheng YP, Jin K, Li W, Tu QY, Liu HY (2014) Impact of effective stress and matrix deformation on the coal fracture permeability. Transp Porous Media 103(1):99–115. https://doi.org/10.1007/s11242-014-0289-4
Kovari K (1984) Suggested methods for determining the strength of rock materials in triaxial compression. Int J Rock Mech Min Sci Geomech Abstr 15:47–51. https://doi.org/10.1016/0148-9062(78)91677-7
Li BB, Gao Z, Yang K, Li JH, Ren CH, Xu J, Cao J (2020) Study on coal adsorption-permeability model under the coupling of temperature and pore pressure. Chin J Rock Mech Eng 39(4):668–681 (in Chinese)
Liu HH, Rutqvist J (2010) A new coal-permeability model: internal swelling stress and fracture-matrix interaction. Transp Porous Med 82:157–171. https://doi.org/10.1007/s11242-009-9442-x
Liu JS, Elsworth D (1999) Evaluation of pore water pressure fluctuation around an advancing longwall panel. Adv Water Resour 22(6):633–644. https://doi.org/10.1016/S0309-1708(98)00041-4
Liu QS, Xu XC (2000) Damage analysis of brittle rock at high temperature. Chin J Rock Mech Eng 19(4):408–411 (in Chinese)
Liu T, Lin BQ, Yang W (2017) Impact of matrix–fracture interactions on coal permeability: model development and analysis. Fuel 207:522–532. https://doi.org/10.1016/j.fuel.2017.06.125
Mainari F (2010) Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. Imperial College Press, London
Palmer I, Mansoori J (1996P) How permeability depends on stress and pore pressure in coalbeds: a new model. In: SPE Annual technical conference and exhibition. https://doi.org/10.2118/36737-MS
Perera MSA, Ranjith PG, Choi SK (2013) Coal cleat permeability for gas movement under triaxial, non-zero lateral strain condition: a theoretical and experimental study. Fuel 109:389–399. https://doi.org/10.1016/j.fuel.2013.02.066
Podlubny I (1999) Fractional differential equations. Academic Press, New York
Ren CH, Li BB, Xu J, Zhang Y, Li JH, Gao Z, Yu J (2020) A novel damage-based permeability model for coal in the compaction and fracturing process under different temperature conditions. Rock Mech Rock Eng 53:5697–5713. https://doi.org/10.1007/s00603-020-02236-7
Robertson EP, Christiansen RL (2008) A permeability model for coal and other fractured, sorptive-elastic media. SPE J 13:314–324. https://doi.org/10.2118/104380-MS
Shi JQ, Durucan S (2004) Drawdown induced changes in permeability of coalbeds: a new interpretation of the reservoir response to primary recovery. Transp Porous Med 56(1):1–16. https://doi.org/10.1023/B:TIPM.0000018398.19928.5a
Wang K, Du F, Wang GD (2017) Investigation of gas pressure and temperature effects on the permeability and steady-state time of Chinese anthracite coal: an experimental study. J Nat Gas Sci Eng 40:179–188. https://doi.org/10.1016/j.jngse.2017.02.014
Wu Y, Liu JS, Elsworth D, Siriwardane H, Miao XX (2011) Evolution of coal permeability: contribution of heterogeneous swelling processes. Int J Coal Geol 88:152–162. https://doi.org/10.1016/j.coal.2011.09.002
Xie HP, Xie J, Gao MZ, Zhang R, Zhou HW, Gao F, Zhang ZT (2015) Theoretical and experimental validation of mining enhanced permeability for simultaneous exploitation of coal and gas. Environ Earth Sci 73:5951–5962. https://doi.org/10.1007/s12665-015-4113-4
Xu J, Zhang DD, Peng SJ, Liu D, Wang L (2011) Experimental research on influence of temperature on mechanical properties of coal containing methane. Chin J Rock Mech Eng 30(S1):2730–2735 (in Chinese)
Xu XL, Karakus M (2018) A coupled thermo-mechanical damage model for granite. Int J Rock Mech Min Sci 103:195–204. https://doi.org/10.1016/j.ijrmms.2018.01.030
Xue Y, Gao F, Liu XG, Li J, Liang MY, Li XR (2016) Theoretical and numerical simulation of the mining-enhanced permeability model of damaged coal seam. Geotech Geol Eng 34:1425–1433. https://doi.org/10.1007/s10706-016-0052-4
Yang S, Zhou HW, Zhang SQ, Ren WG (2019) A fractional derivative perspective on transient pulse test for determining the permeability of rocks. Int J Rock Mech Min Sci 113:92–98. https://doi.org/10.1016/j.ijrmms.2018.11.013
Zhang LY, Mao XB, Li TZ (2010) Experimental research on thermal damage properties of marble at high temperature. J Min Safe Eng 27(04):505–511 (in Chinese)
Zhang M, Takahashi M, Morin R, Esaki T (2000) Evaluation and application of the transient-pulse technique for determining the hydraulic properties of low-permeability rocks—Part 2: experimental application. Geotech Test J 23(1):91–99. https://doi.org/10.1520/GTJ11127J
Zhou HW, Rong TL, Wang LJ, Mou RY, Ren WG (2020a) A new anisotropic coal permeability model under the influence of stress, gas sorption and temperature: development and verification. Int J Rock Mech Min Sci 132:104407. https://doi.org/10.1016/j.ijrmms.2020.104407
Zhou HW, Wang XY, Zhang L, Zhong JC, Wang ZH, Rong TL (2020b) Permeability evolution of deep coal samples subjected to energy-based damage variable. J Nat Gas Sci Eng 73:103070. https://doi.org/10.1016/j.jngse.2019.103070
Zhou HW, Zhang L, Wang XY, Rong TL, Wang LJ (2020c) Effects of matrix-fracture interaction and creep deformation on permeability evolution of deep coal. Int J Rock Mech Min Sci 127:104236. https://doi.org/10.1016/j.ijrmms.2020.104236
Zhu WC, Wei CH (2011) Numerical simulation on mining-induced water inrushes related to geologic structures using a damage-based hydromechanical model. Environ Earth Sci 62:43–54. https://doi.org/10.1007/s12665-010-0494-6
Acknowledgements
The present work is supported by the National Natural Science Foundation of China (51827901, 52121003), the 111 Project (B14006) and the Yueqi Outstanding Scholar Program of CUMTB (2017A03).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wang, X., Zhou, H., Zhang, L. et al. Research on damage-based coal permeability evolution for the whole stress–strain process considering temperature and pore pressure. Geomech. Geophys. Geo-energ. Geo-resour. 8, 149 (2022). https://doi.org/10.1007/s40948-022-00464-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40948-022-00464-5