Study on Permeability Anisotropy of Bedded Coal Under True Triaxial Stress and Its Application

  • Minke Duan
  • Changbao JiangEmail author
  • Quan Gan
  • Hongbao Zhao
  • Yang Yang
  • Zhengke Li


Anisotropy is a very typical observation in the intrinsic bedding structure of coal. To study the influence of anisotropy of coal structure and stress state on the evolution of permeability, a newly developed multifunctional true triaxial geophysical apparatus was used to carry out mechanical and seepage experiments on bedded coal. The permeability and deformation of three orthogonal directions in cubic coal samples were collected under true triaxial stress. It has detected the significant permeability anisotropy, and the anisotropy is firmly determined by the bedding direction and stress state of coal. Based on the true triaxial mechanical and seepage test results, the coal with bedding was simplified to be represented by a cubic model, and the dynamic anisotropic (D-A) permeability model was derived by considering the influence of bedding and stress state. The rationality of the permeability model was verified by the experimental data. Comparing the permeability model with Wang and Zang (W–Z) model, Cui and Bustin (C–B) model and Shi and Durucan (S–D) model, it is found that the theoretical calculated values of the D-A permeability model are in better agreement with the experimental measured values, reflecting the superiority of the D-A permeability model. Based on incorporating the model of D-A permeability under the concept of multiphysics field coupling, the numerical simulation experiments of coal seam gas extraction with different initial permeability anisotropic ratios were carried out by using COMSOL multiphysics simulator. The influence of initial permeability anisotropy ratio on gas pressure distribution in coal seam during gas extraction was explored, which provides theoretical guidance for the optimization of borehole layout for gas extraction in coal mine.


True triaxial stress Bedding Anisotropic permeability model Multiphysics field coupling 



This study was financially supported by the National Natural Science Foundation of China (51674048) and Fundamental and Advanced Research Projects of Chongqing (cstc2015jcyjA90009). The first author also acknowledges the financial support provided by the China Scholarship Council (CSC). We thank Bozhi Deng, Chao Liu, Zhenlong Song and Siyu Yin for their support of the experiment of our study. We are also grateful to Tang Yu and Cai Wei for their help of analyzing the data.


  1. An, H., Wei, X., Wang, G., Massarotto, P., Wang, F., Rudoph, V., Golding, S.D.: Modeling anisotropic permeability of coal and its effects on CO2 sequestration and enhanced coalbed methane recovery. Int. J. Coal Geol. 152, 15–24 (2015)CrossRefGoogle Scholar
  2. Cao, Y., Mitchell, G.D., Davis, A., Wang, D.: Deformation metamorphism of bituminous and anthracite coals from China. Int. J. Coal Geol. 43, 227–242 (2000)CrossRefGoogle Scholar
  3. Cui, X., Bustin, R.M.: Volumetric strain associated with methane desorption and its impact on coalbed gas production from deep coal seams. Am. Assoc. Pet. Geol. Bull. 89(9), 1181–1202 (2005)Google Scholar
  4. Cui, X., Bustin, R.M., Chikatamarla, L.: Adsorption-induced coal swelling and stress: implications for methane production and acid gas sequestration into coal seams. J. Geophys. Res. 112, B10202 (2007)CrossRefGoogle Scholar
  5. Chen, D., Pan, Z., Liu, J., Connell, L.D.: Characteristic of anisotropic coal permeability and its impact on optimal design of multi-lateral well for coalbed methane production. J. Petrol. Sci. Eng. 88–89, 13–28 (2012)CrossRefGoogle Scholar
  6. Duan, M., Jiang, C., Gan, Q., Li, M., Peng, K., Zhang, W.: Experimental investigation on the permeability, acoustic emission and energy dissipation of coal under tiered cyclic unloading. J. Nat. Gas Sci. Eng. (2019). CrossRefGoogle Scholar
  7. Faulkner, D.R., Mitchell, T.M., Healy, D., Heap, M.J.: Slip on ‘weak’ faults by the rotation of regional stress in the fracture damage zone. Nature 444(7121), 922 (2006)CrossRefGoogle Scholar
  8. Gan, Q., Elsworth, D.: Production optimization in fractured geothermal reservoirs by coupled discrete fracture network modeling. Geothermics 62, 131–142 (2016a)CrossRefGoogle Scholar
  9. Gan, Q., Elsworth, D.: A continuum model for coupled stress and fluid flow in discrete fracture networks. Geomech. Geophys. Geo-Energy Geo-Resour. 2(1), 43–61 (2016b)CrossRefGoogle Scholar
  10. Gu, F., Chalaturnyk, R.: Permeability and porosity models considering anisotropy and discontinuity of coalbeds and application in coupled simulation. J. Petrol. Sci. Eng. 74(3), 113–131 (2010)CrossRefGoogle Scholar
  11. Guo, P., Cheng, Y., Jin, K., Li, W., Tu, Q., Liu, H.: Impact of effective stress and matrix deformation on the coal fracture permeability. Transp. Porous Media 103(1), 99–115 (2014)CrossRefGoogle Scholar
  12. Harpalani, S., Schraufnagel, A.: Measurement of parameters impacting methane recovery from coal seams. Int. J. Min. Geol. Eng. 8, 369–384 (1990)CrossRefGoogle Scholar
  13. Jiang, C., Duan, M., Yin, G., Wang, J., Lu, T., Xu, J., Zhang, D., Huang, G.: Experimental study on seepage properties, AE characteristics and energy dissipation of coal under tiered cyclic loading. Eng. Geol. 221, 114–123 (2017)CrossRefGoogle Scholar
  14. Koenig, R.A., Stubbs, P.B.: Interference testing of a coalbed methane reservoir. In: SPE Unconventional Gas Technology Symposium (1986)Google Scholar
  15. Karacan, C.O., Ruiz, F.A., Cote, M., Phipps, S.: Coal mine methane: a review of capture and utilization practices with benefits to mining safety and to greenhouse gas reduction. Int. J. Coal Geol. 86, 121–156 (2011)CrossRefGoogle Scholar
  16. Li, M., Yin, G., Xu, J., Song, Z., Jiang, C.: A novel true triaxial apparatus to study the Geomechanical and fluid flow aspects of energy exploitations in geological formations. Rock Mech. Rock Eng. 49(12), 1–13 (2016a)Google Scholar
  17. Li, M., Yin, G., Xu, J., Cao, J., Song, Z.: Permeability evolution of shale under anisotropic true triaxial stress conditions. Int. J. Coal Geol. 165, 142–148 (2016b)CrossRefGoogle Scholar
  18. Li, Z., Liu, Y., Xu, Y.P., Song, D.: Gas diffusion mechanism in multi-scale pores of coal particles and new diffusion model of dynamic diffusion coefficient. J. China Coal Soc. 41, 633–643 (2016c). (in Chinere) Google Scholar
  19. Lin, B., Song, H., Zhao, Y., Liu, T., Kong, J., Huang, Z.: Significance of gas flow in anisotropic coal seams to underground gas drainage. J. Petrol. Sci. Eng. 180, 808–819 (2019)CrossRefGoogle Scholar
  20. Liu, J., Chen, Z., Elsworth, D., Miao, X., Mao, X.: Linking gas-sorption induced changes in coal permeability to directional strains through a modulus reduction ratio. Int. J. Coal Geol. 83(1), 21–30 (2010)CrossRefGoogle Scholar
  21. Liu, Q., Cheng, Y., Wang, H., Zhou, H., Wang, L., Li, W., Liu, H.: Numerical assessment of the effect of equilibration time on coal permeability evolution characteristics. Fuel 140, 81–89 (2015)CrossRefGoogle Scholar
  22. Liu, T., Lin, B., Yang, W.: Impact of matrix–fracture interactions on coal permeability: model development and analysis. Fuel 207, 522–532 (2017a)CrossRefGoogle Scholar
  23. Liu, T., Lin, B., Yang, W., Liu, T., Kong, J., Huang, Z., Wang, R., Zhao, Y.: Dynamic diffusion-based multifield coupling model for gas drainage. J. Nat. Gas Sci. Eng. 44, 233–249 (2017b)CrossRefGoogle Scholar
  24. Liu, T., Lin, B., Yang, W., Cheng, Z., Liu, D.: Coal permeability evolution and gas migration under non-equilibrium state. Transp. Porous Media 118(3), 393–416 (2017c)CrossRefGoogle Scholar
  25. Liu, Y., Li, M., Yin, G., Zhang, D., Deng, B.: Permeability evolution of anthracite coal considering true triaxial stress conditions and structural anisotropy. J. Nat. Gas Sci. Eng. 52, 492–506 (2018)CrossRefGoogle Scholar
  26. Liu, C., Yin, G., Li, M., Shang, D., Deng, B., Song, Z.: Deformation and permeability evolution of coals considering the effect of beddings. Int. J. Rock Mech. Min. Sci. 117, 49–62 (2019a)CrossRefGoogle Scholar
  27. Liu, Y., Yin, G., Li, M., Zhang, D., Deng, B., Liu, C., Lu, J.: Anisotropic mechanical properties and the permeability evolution of cubic coal under true triaxial stress paths. Rock Mech. Rock Eng. 52(8), 2505–2521 (2019b)CrossRefGoogle Scholar
  28. Massarotto, P., Rudolph, V., Golding, S.D., Iyer, R.: The effect of directional net stresses on the directional permeability of coal. In: International Coalbed Methane Symposium, Tuscaloosa, Alabama (2003)Google Scholar
  29. Massarotto, P.: 4-D Coal Permeability Under True Triaxial Stresses and Constant Volume Conditions. Division of Chemical Engineering, The University of Queensland, Brisbane (2002)Google Scholar
  30. Menezes, F.F.: Anisotropy of volume change and permeability evolution of hard sandstones under triaxial stress conditions. J. Petrol. Sci. Eng. 174, 921–939 (2019)CrossRefGoogle Scholar
  31. Ma, Y., Pan, Z., Zhong, N., Connell, L.D., Down, D.I., Lin, W., Zhang, Y.: Experimental study of anisotropic gas permeability and its relationship with fracture structure of Longmaxi Shales, Sichuan Basin, China. Fuel 180, 106–115 (2016)CrossRefGoogle Scholar
  32. Mckee, C.R., Bumb, A.C., Koenig, R.A.: Stress-dependent permeability and porosity of coal and other geologic formations. SPE Form. Eval. 3(1), 81–91 (1988)CrossRefGoogle Scholar
  33. Palmer, I., Mansoori, J.: How permeability depends on stress and pore pressure in coalbeds: a new model. SPE Reserv. Eval. Eng. 1, 539–544 (1998)CrossRefGoogle Scholar
  34. Pan, Z., Connell, L.D.: Modelling of anisotropic coal swelling and its impact on permeability behaviour for primary and enhanced coalbed methane recovery. Int. J. Coal Geol. 85, 257–267 (2011)CrossRefGoogle Scholar
  35. Pan, Z., Connell, L.D.: A theoretical model for gas adsorption-induced coal swelling. Int. J. Coal Geol. 69, 243–252 (2007)CrossRefGoogle Scholar
  36. Perera, M.S.A., Ranjith, P.G., Choi, S.K., Airey, D.: Investigation of temperature effect on permeability of naturally fractured black coal for carbon dioxide movement: an experimental and numerical study. Fuel 94, 596–605 (2012)CrossRefGoogle Scholar
  37. Reiss, L.H.: The reservoir engineering aspects of fractured formations. Editions Technip 27 Rue Ginoux 75737. Cedex, Paris, p. 15 (1980)Google Scholar
  38. Shi, J., Durucan, S.: Drawdown induced changes in permeability of coalbeds: a new interpretation of the reservoir response to primary recovery. Transp. Porous Media 56(1), 1–16 (2004)CrossRefGoogle Scholar
  39. Song, Z., Yin, G., Ranjith, P.G., Li, M., Huang, J., Liu, C.: Influence of the intermediate principal stress on sandstone failure. Rock Mech. Rock Eng. 52(9), 3033–3046 (2019)CrossRefGoogle Scholar
  40. Tan, Y., Pan, Z., Liu, J., Wu, Y., Haque, A., Connell, L.D.: Experimental study of permeability and its anisotropy for shale fracture supported with proppant. J. Nat. Gas Sci. Eng. 44, 250–264 (2017)CrossRefGoogle Scholar
  41. Tan, Y., Pan, Z., Liu, J., Zhou, F., Connell, L.D., Sun, W.: Experimental study of impact of anisotropy and heterogeneity on gas flow in coal. Part II: permeability. Fuel 230, 397–409 (2018)CrossRefGoogle Scholar
  42. Wang, G., Wei, X., Wang, K., Rudolph, V.: Sorption-induced swelling/shrinkage and permeability of coal under stressed adsorption/desorption conditions. Int. J. Coal Geol. 83, 46–54 (2010)CrossRefGoogle Scholar
  43. Wang, K., Zang, J., Wang, G., Zhou, A.: Anisotropic permeability evolution of coal with effective stress variation and gas sorption: model development and analysis. Int. J. Coal Geol. 130, 53–65 (2014)CrossRefGoogle Scholar
  44. Wang, D., Lv, R., Wei, J., Zhang, P., Yu, C., Yao, B.: An experimental study of the anisotropic permeability rule of coal containing gas. J. Nat. Gas Sci. Eng. 53, 67–73 (2018)CrossRefGoogle Scholar
  45. Wang, D., Lv, R., Wei, J., Yao, B.: An experimental study of seepage properties of gas-saturated coal under different loading conditions. Energy Sci. Eng. 7(3), 799–808 (2019a)CrossRefGoogle Scholar
  46. Wang, L., Chen, Z., Wang, C., Elsworth, D., Liu, W.: Reassessment of coal permeability evolution using steady-state flow methods: the role of flow regime transition. Int. J. Coal Geol. 211, 103–210 (2019b)Google Scholar
  47. Wang, S., Elsworth, D., Liu, J.: Permeability evolution in fractured coal: the roles of fracture geometry and water-content. Int. J. Coal Geol. 87, 13–25 (2011)CrossRefGoogle Scholar
  48. Wicks, D., Schwerer, F., Militzer, M., Zuber, M.: Effective production strategies for coalbed methane in the Warrior Basin. In: SPE Unconventional Gas Technology Symposium. Society of Petroleum Engineers (1986)Google Scholar
  49. Wu, Y., Liu, J., Chen, Z., Elsworth, D., Miao, X., Mao, X.: Development of anisotropic permeability during coalbed methane production. J. Nat. Gas Sci. Eng. 2(4), 197–210 (2010)CrossRefGoogle Scholar
  50. Wu, Y., Liu, J., Elsworth, D., Siriwardane, H., Miao, X.: Evolution of coal permeability: contribution of heterogeneous swelling processes. Int. J. Coal Geol. 88(2–3), 152–162 (2011)CrossRefGoogle Scholar
  51. Xu, K., Wang, B., Liu, Q.: Study on gas drainage radius and distance between boreholes based on dynamic fluid–solid coupling model. Coal Sci. Technol. 46(5), 102–108 (2018)Google Scholar
  52. Yan, F., Lin, B., Zhu, C., Shen, C., Zuo, Q., Guo, C., Liu, T.: A novel ECBM extraction technology based on the integration of hydraulic slotting and hydraulic fracturing. J. Nat. Gas Sci. Eng. 22, 571–579 (2015)CrossRefGoogle Scholar
  53. Yang, D., Qi, X., Chen, Z., Wang, S., Dai, F.: Numerical investigation on the coupled gas–solid behaviour of coal using an improved anisotropic permeability model. J. Nat. Gas Sci. Eng. 34, 226–235 (2016)CrossRefGoogle Scholar
  54. Yan, P., Liu, J., Wei, M.: Why coal permeability changes under free swellings: new insights. Int. J. Coal Geol. 133, 35–46 (2014)CrossRefGoogle Scholar
  55. Zang, J., Wang, K.: A numerical model for simulating single-phase gas flow in anisotropic coal. J. Nat. Gas Sci. Eng. 28, 153–172 (2016)CrossRefGoogle Scholar
  56. Zhao, Y., Lin, B., Liu, T., Li, Q., Kong, J.: Gas flow field evolution around hydraulic slotted borehole in anisotropic coal. J. Nat. Gas Sci. Eng. 58, 189–200 (2018)CrossRefGoogle Scholar
  57. Zhang, Z., Zhang, R., Xie, H., Gao, M., Xie, J.: Mining-induced coal permeability change under different mining layouts. Rock Mech. Rock Eng. 49(9), 3753–3768 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Minke Duan
    • 1
    • 2
  • Changbao Jiang
    • 1
    Email author
  • Quan Gan
    • 2
  • Hongbao Zhao
    • 3
  • Yang Yang
    • 1
  • Zhengke Li
    • 1
  1. 1.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingChina
  2. 2.Department of Geology and Petroleum Geology, School of GeosciencesUniversity of AberdeenAberdeenUK
  3. 3.School of Energy and Mining EngineeringChina University of Mining and Technology, BeijingBeijingChina

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