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Experimental and Numerical Validation of an Effective Stress-Sensitive Permeability Model Under Hydromechanical Interactions

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Abstract

Water seepage in rocks, in geotechnical engineering such as the hydrofracturing of hard rocks, excavation of underground chambers, and prevention of mine water disasters, is a common problem. According to rock mechanics theory, the deformation and stress of rocks influence seepage behavior. In this study, a modified permeability model of argillaceous sandstone under coupled hydromechanical conditions was established to reveal the relationship between permeability and effective stress, including external stress and internal water pressure. The modeling results indicate a negative exponential relationship between the argillaceous sandstone permeability and the effective stress. The proposed effective stress-sensitive permeability model was validated by conducting two sets of seepage experiments based on controlling the water pressure and external stress, with the results obtained considered satisfactory. Based on the proposed permeability model, a fully coupled multifield model of the water seepage and rock deformation was developed. Fully coupled scenario-based numerical simulations were conducted in a finite element environment to investigate water seepage evolution and rock deformation. The experimental and numerical results show that the trends in the evolution of the entire compressive stress–strain and permeability curves are reversed, and the maximum value of the permeability was not consistent with the failure of argillaceous sandstone. This model and corresponding numerical simulations can provide insights for water seepage research and serve as a reliable theoretical basis for evaluating roof water injection and hydraulic fracturing in rock and mining engineering.

Article Highlights

  • Effective stress-sensitive permeability model was developed and validated experimentally

  • Established fully coupled model of water seepage and rock deformation

  • Numerical simulation revealed evolutions of the rock permeability and deformation

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References

  • Andreas, H., Espen, J., Jens, F., Paul, M., Anders, M.S.: A node-splitting discrete element model for fluid–structure interaction. Physica A 416, 61–79 (2014)

    Article  MathSciNet  Google Scholar 

  • Biot, M.A.: General theory of three dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941)

    Article  ADS  Google Scholar 

  • Biot, M.A., Willis, D.G.: The elastic coefficients of the theory of consolidation. ASME J. Appl. Mech. 24, 594–601 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  • Chen, L.W., Ou, Q.H., Peng, Z.H., Wang, Y.X., Chen, Y.F., Tian, Y.: Numerical simulation of abnormal roof water-inrush mechanism in mining under unconsolidated aquifer based on overburden dynamic damage. Eng. Fail. Anal. 133, 106005 (2022)

    Article  Google Scholar 

  • Cheng, C., Li, X., Li, S.D., Zheng, B.: Failure behavior of granite affected by confinement and water pressure and its influence on the seepage behavior by laboratory experiments. Materials 10, 798 (2017)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  • Chu, C.C.: Investigation on the responses of overburden stress and water pressure to mining under the reverse fault. Geofluids (2021). https://doi.org/10.1155/2021/5199755

    Article  Google Scholar 

  • Dalla, B.F., Picano, F.: A novel approach for direct numerical simulation of hydraulic fracture problems. Flow Turbul. Combust. 105, 335–357 (2020)

    Article  Google Scholar 

  • Du Xin, Lu.Z.W., Li, D.M., Xu, Y.D., Li, P.C., Lu, D.T.: A novel analytical well test model for fractured vuggy carbonate reservoirs considering the coupling between oil flow and wave propagation. J. Petrol. Sci. Eng. 173, 447–461 (2018)

    Article  Google Scholar 

  • Fan, J., Dou, L.M., He, H., Du, T.T., Zhang, S.B., Gui, B., Sun, X.L.: Directional hydraulic fracturing to control hard-roof rockburst in coal mines. Int. J. Min. Sci. Technol. 22(2), 177–181 (2012)

    Article  Google Scholar 

  • Golovin, S.V., Baykin, A.N.: Influence of pore pressure to the development of a hydraulic fracture in poroelastic medium. Int. J. Rock Mech. Min. 108, 198–208 (2018)

    Article  Google Scholar 

  • Guo, H.Y., He, M.C., Sun, C.H., Li, B., Zhang, F.: Hydrophilic and strength-softening characteristics of calcareous shale in deep mines. J. Rock Mech. Geotech. 4(4), 344–435 (2012)

    Article  Google Scholar 

  • Guo, T.K., Zhang, S.Z., Qu, Z.Q., Zhou, T., Xiao, Y.S., Gao, J.: Experimental study of hydraulic fracturing for shale by stimulated reservoir volume. Fuel 128, 373–380 (2014)

    Article  CAS  Google Scholar 

  • Guo, J.T., Teng, T., Zhu, X.Y., Wang, Y.M., Li, Z.L., Tan, Y.: Characterization and modeling study on softening and seepage behavior of weakly cemented sandy mudstone after water injection. Geofluids 2021, 7799041 (2021)

    Article  Google Scholar 

  • Hadi, F., Homayoon, K.: New empirical model to evaluate groundwater flow into circular tunnel using multiple regression analysis. Int. J. Min. Sci. Technol, 27, 415–421 (2017)

  • He, B., Zhuang, X.Y.: Modeling hydraulic cracks and inclusion interaction using XFEM. Undergr. Space 3, 218–228 (2018)

    Article  Google Scholar 

  • He, H., Dou, L.M., Fan, J., Xu, T.T., Sun, X.L.: Deep-hole directional fracturing of thick hard roof for rockburst prevention. Tunn. Undergr. Space Technol. 32, 34–43 (2012)

    Article  Google Scholar 

  • Jiang, H.P., Jiang, A.N., Zhang, F.R.: Experimental investigation on the evolution of damage and seepage characteristics for red sandstone under thermal–mechanical coupling conditions. Environ. Earth Sci. 80, 816 (2021)

    Article  ADS  Google Scholar 

  • Kacimov, A.R., Obnosov, Y.V., Šimůnek, J.: Seepage to staggered tunnels and subterranean cavities: analytical and HYDRUS modeling. Adv. Water Resour. 164, 104182 (2022)

    Article  Google Scholar 

  • Lei, Q.H., Latham, J.P., Tsang, C.F.: The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks. Comput. Geotech. 85, 151–176 (2017)

    Article  Google Scholar 

  • Lei, Q.H., Doonechaly, N.G., Tsang, C.F.: Modelling fluid injection-induced fracture activation, damage growth, seismicity occurrence and connectivity change in naturally fractured rocks. Int. J. Rock Mech. Min. 138, 104598 (2021)

    Article  Google Scholar 

  • Li, M., Liu, X.S.: Experimental and numerical investigation of the failure mechanism and permeability evolution of sandstone based on hydro-mechanical coupling. J. Nat. Gas Sci. Eng. 95, 104240 (2021)

    Article  Google Scholar 

  • Li, Q., Lian, J.J., Zhao, G.F.: A three-phase coupled numerical model for the hydraulic fracturing of rock. Int. J. Rock Mech. Min. 152, 105075 (2022)

    Article  Google Scholar 

  • Liu, A., Liu, S.M.: A fully-coupled water-vapor flow and rock deformation/damage model for shale and coal: its application for mine stability evaluation. Int. J. Rock Mech. Min. 146, 104880 (2021)

    Article  ADS  Google Scholar 

  • Lu, C.P., Dou, L.M., Zhang, N., Xue, J.H., Wang, X.N.: Microseismic frequency-spectrum evolutionary rule of rockburst triggered by roof fall. Int. J. Rock Mech. Min. 64, 6–16 (2013)

    Article  Google Scholar 

  • Obeysekara, A., Lei, Q., Salinas, P., Pavlidis, D., Xiang, J., Latham, J.P., Pain, C.C.: Modelling stress-dependent single and multi-phase flows in fractured porous media based on an immersed-body method with mesh adaptivity. Comput. Geotech. 103, 229–241 (2018)

    Article  Google Scholar 

  • Pan, C., Xia, B.W., Zuo, Y.J., Yu, B., Ou, C.N.: Mechanism and control technology of strong ground pressure behaviour induced by high-position hard roofs in extra-thick coal seam mining. Int. J. Min. Sci. Technol. 32, 499–511 (2022)

    Article  Google Scholar 

  • Shi, F., Wang, D.B., Chen, X.G.: A numerical study on the propagation mechanisms of hydraulic fractures in fracture-cavity carbonate reservoirs. CMES-Comper. Model Eng. 127, 2 (2021)

    Google Scholar 

  • Teng, T., Wang, W., Zhan, P.F.: Evaluation criterion and index for the efficiency of thermal stimulation to dual coal permeability. J. Nat. Gas Sci. Eng. 68, 102899 (2019)

    Article  CAS  Google Scholar 

  • Terzaghi, K.: Theorerical Soil Mechanics, pp. 4–10. Wiley, New York (1943)

    Book  Google Scholar 

  • Wen, G.J., Liu, H.J., Huang, H.B., Wang, Y.D., Shi, X.Y.: Meshless method simulation and experimental investigation of crack propagation of CBM hydraulic fracturing. Oil Gas Sci. Technol. 72, 73 (2018)

    Google Scholar 

  • Xiao, C.Y., Zhang, G.J., Yu, Y.D.: Numerical analysis of hydraulic fracturing processes for multi-layered fractured reservoirs. Energy Rep. 7, 467–471 (2021)

    Article  Google Scholar 

  • Yu, M.L., Zuo, J.P., Sun, Y.J., Mi, C.N., Li, Z.D.: Investigation on fracture models and ground pressure distribution of thick hard rock strata including weak interlayer. Int. J. Min. Sci. Technol. 32, 137–153 (2022a)

    Article  Google Scholar 

  • Yu, M.Y., Liu, B.G., Chu, Z.F., Sun, J.L., Deng, T.B., Qi, W.: Permeability, deformation characteristics, and damage constitutive model of shale under triaxial hydromechanical coupling. Bull. Eng. Geol. Environ. 81, 85 (2022b)

    Article  Google Scholar 

  • Zhang, Q.X., Hou, B., Lin, B.T., Liu, X., Gao, Y.F.: Integration of discrete fracture reconstruction and dual porosity/dual permeability models for gas production analysis in a deformable fractured shale reservoir. J. Nat. Gas Sci. Eng. 93, 104028 (2021)

    Article  Google Scholar 

  • Zhang, J., Gao, S., Xiong, W., Ye, L., Liu, H., Zhu, W., Sun, X., Li, X., Zhu, W.: An improved experimental procedure and mathematical model for determining gas-water relative permeability in tight sandstone gas reservoirs. Geoenergy Sci. Eng. 221, 211402 (2023)

    Article  Google Scholar 

  • Zhao, Y., Liu, Q., Zhang, C., Liao, J., Lin, H., Wang, Y.: Coupled seepage-damage effect in fractured rock masses: model development and a case study. Int. J. Rock Mech. Min. 144, 104822 (2021)

    Article  Google Scholar 

  • Zheng, J.T., Zheng, L.G., Liu, H.H., Ju, Y.: Relationships between permeability, porosity and effective stress for low-permeability sedimentary rock. Int. J. Rock Mech. Min. 78, 304–318 (2015)

    Article  Google Scholar 

  • Zhou, G., Wang, C.M., Liu, R.L., Li, S.L., Zhang, Q.T., Liu, Z., Yang, W.Y.: Variations in air humidity and the duration of roof exposure are known to significantly influence the stability of shale roof strata. Int. J. Rock Mech. Min. 150, 105024 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the National Natural Science Foundation (52004285), National Key R&D Program of China (2022YFC3004600), Fundamental Research Funds for the Central Universities from China University of Mining and Technology-Beijing (JCCXXNY06), Open Fund of State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University) (WS2021A03), and Open Fund of State Key Laboratory for Geomechanics and Deep Underground Engineering (SKLGDUEK2123).

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Authors and Affiliations

  1. State Key Laboratory for Geo-Mechanics and Deep Underground Engineering, China University of Mining and Technology-Beijing, Beijing, 100083, China

    Teng Teng

  2. School of Energy and Mining Engineering, China University of Mining and Technology-Beijing, Beijing, 100083, China

    Zhaolong Li, Yuming Wang, Kun Liu & Wenjian Jia

  3. State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University, Jiaozuo, 454003, China

    Teng Teng

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  1. Teng Teng
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  3. Yuming Wang
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  4. Kun Liu
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  5. Wenjian Jia
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by YW, ZL and KL. WJ is responsible for data visualization. The first draft of the manuscript was written by TT and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Teng Teng.

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Teng, T., Li, Z., Wang, Y. et al. Experimental and Numerical Validation of an Effective Stress-Sensitive Permeability Model Under Hydromechanical Interactions. Transp Porous Med 151, 449–467 (2024). https://doi.org/10.1007/s11242-023-02043-y

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  • DOI: https://doi.org/10.1007/s11242-023-02043-y

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