Numerical Investigation of the Structure of Fracture Network Impact on the Fluid Flow through a Poroelastic Medium

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Abstract

Two-dimensional single-phase flow of a weakly compressible fluid through a deformable fractured-porous medium is considered. A poroelastic model is used for coupled simulation of the fluid flow and the related changes in the stress state of the medium. Fracture network is simulated using the discrete fracture model. The fractures in the region under consideration have random location and orientations, and the fracture length distribution follows a power law. The dependence of the hydraulic properties of fractured porous media on its stress-strain state and the structure of the fracture network is studied. Numerical study was performed for various realizations of fracture network obtained using multiple random generation. It is found that the permeability of the fractured porous medium is determined mainly by the structure of the fracture system characterized by the percolation parameter. According to the simulations results, hydraulic properties are significantly affected by the stress-strain state only for connected fracture systems. An approximation is proposed to define the dependence of the equivalent permeability of a fractured-porous medium on the following parameters: the connectivity of the fracture system, the stress-strain state of the medium, and fracture properties such as stiffness and aperture.

About the authors

D. Yu. Legostaev

Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences

Email: legostaevdy@yandex.ru
Tyumen, Russia

S. P. Rodionov

Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences

Author for correspondence.
Email: rodionovsp@bk.ru
Tyumen, Russia

References

  1. Smirnov N.N., Nikitin V.F., Kolenkina (Skryleva) E.I., Gazizova. D. R. Evolution of a phase interface in the displacement of viscous fluids from a porous medium // Fluid Dynamics. 2021. V. 56. № 1. P. 79–92. https://doi.org/10.1134/S0015462821010122
  2. Nikitin V.F., Skryleva E.I., Weisman Yu. G. Control of capillary driven fluid flows for safe operation of spacecraft fluid supply systems using artificial porous media // Acta Astronautica. 2022. V. 194. P. 544–548. https://doi.org/10.1016/j.actaastro.2021.12.009
  3. Dushin V.R., Smirnov N.N., Nikitin V.F., Skryleva E. I., Weisman Yu.G. Multiple capillary-driven imbibition of a porous medium under microgravity conditions: Experimental investigation and mathematical modeling // Acta Astronautica. 2022. V. 193. P. 572–578. https://doi.org/10.1016/j.actaastro.2021.06.054
  4. Kiselev A.B., Kay-Zhui L., Smirnov N.N., Pestov D.A. Simulation of Fluid Flow through a Hydraulic Fracture of a Heterogeneous Fracture-Tough Reservoir in the Planar 3D Formulation // Fluid Dynamics. 2021. V. 56. № 2. P. 164–177. https://doi.org/10.1134/S0015462821020051
  5. Smirnov N., Li K., Skryleva E., Pestov D., Shamina A., Qi C., Kiselev A. Mathematical Modeling of Hydraulic Fracture Formation and Cleaning Processes // Energies. 2022. V. 15. № 6. https://doi.org/10.3390/en15061967
  6. Голф-Рахт Т.Д. Основы нефтепромысловой геологии и разработки трещиноватых коллекторов. M.: Недра, 1986. 608 с.
  7. Nelson R.A. Geologic Analysis of Naturally Fractured Reservoirs. Gulf Professional Publishing, 2001. 352 p.
  8. Пичугин О.Н., Родионов С.П., Соляной П.Н., Гаврись А.С., Косяков В.П., Кошеверов Г.Г. Принципы оптимизации систем заводнения месторождений, осложненных малоамплитудными тектоническими нарушениями // Российская нефтегазовая техническая конференции SPE, Москва, Россия. 2015.
  9. Karimi-Fard M., Durlofsky L.J., Aziz K. An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators // SPE Journal. 2004. V. 9. № 2. P. 227–236. https://doi.org/10.2118/88812-PA
  10. Garipov T.T., Karimi-Fard M., Tchelepi H.A. Discrete fracture model for coupled flow and geomechanics // Computational Geosciences. 2016. V. 20. № 1. P. 149–160. https://doi.org/10.1007/s10596-015-9554-z
  11. Bai M. On equivalence of dual-porosity poroelastic parameters // Journal of Geophysical Research: Solid Earth. 1999. V. 104. № B5. P. 10461–10466. https://doi.org/10.1029/1999JB900072
  12. Chen H.-Y., Teufel L.W. Coupling Fluid-Flow and Geomechanics in Dual-Porosity Modeling of Naturally Fractured Reservoirs – Model Description and Comparison// SPE International Oil Conference and Exhibition in Mexico. 2000. https://doi.org/10.2118/59043-MS
  13. Rutqvist J., Stephansson O. The role of hydromechanical coupling in fractured rock engineering // Hydrogeology Journal. 2003. V. 11. № 1. P. 7–40. https://doi.org/10.1007/s10040-002-0241-5
  14. Biot M.A. General Theory of Three-Dimensional Consolidation // Journal of Applied Physics. 1941. V. 12. № 2. P. 155–164. https://doi.org/10.1063/1.1712886
  15. Coussy O. Poromechanics. John Wiley and Sons, Ltd, 2004. 315 p.
  16. Gutierrez M., Youn D.-J. Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses // Journal of Rock Mechanics and Geotechnical Engineering. 2015. V. 7. № 6. P. 626–637. https://doi.org/10.1016/j.jrmge.2015.07.006
  17. Liu R., Li B., Jiang Y., Huang N. Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks // Hydrogeology Journal. 2016. V. 24. № 7. P. 1623–1649. https://doi.org/10.1007/s10040-016-1441-8
  18. Bonnet E., Bour O., Odling N.E., Davy P., Main I., Cowie P., Berkowitz B. Scaling of fracture systems in geological media // Reviews of Geophysics. 2001. V. 39. № 3. P. 347–383. https://doi.org/10.1029/1999RG000074
  19. Bogdanov I.I., Mourzenko V.V., Thovert J.-F., Adler P.M. Effective permeability of fractured porous media in steady state flow // Water Resources Research. 2003. V. 39. № 1. https://doi.org/10.1029/2001WR000756
  20. Hyman J.D., Karra S., Carey J.W., Gable C.W., Viswanathan H., Rougier E., Lei Z. Discontinuities in effective permeability due to fracture percolation // Mechanics of Materials. 2018. V. 119. P. 25–33. https://doi.org/10.1016/j.mechmat.2018.01.005
  21. Jafari A., Babadagli T. A Sensitivity Analysis for Effective Parameters on 2D Fracture-Network Permeability // SPE Reservoir Evaluation & Engineering. 2009. V. 12. № 3. P. 455–469. https://doi.org/10.2118/113618-PA
  22. Bour O., Davy P. Connectivity of random fault networks following a power law fault length distribution // Water Resources Research. 1997. V. 33. № 7. P. 1567–1583. https://doi.org/10.1029/96WR00433
  23. de Dreuzy J.-R., Davy P., Bour O. Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1. Effective connectivity // Water Resources Research. 2001. V. 37. № 8. P. 2065–2078. https://doi.org/10.1029/2001WR900011
  24. de Dreuzy J.-R., Davy P., Bour O. Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on lognormal distribution of apertures // Water Resources Research. 2001. V. 37. № 8. P. 2079–2095. https://doi.org/10.1029/2001WR900010
  25. Masihi M., King P.R. Connectivity Prediction in Fractured Reservoirs With Variable Fracture Size: Analysis and Validation // SPE Journal. 2008. V. 13. № 1. P. 88–98. https://doi.org/10.2118/100229-PA
  26. Witherspoon P.A., Wang J.S.Y., Iwai K., Gale J.E. Validity of Cubic Law for fluid flow in a deformable rock fracture // Water Resources Research. 1980. V. 16. № 6. P. 1016–1024. https://doi.org/10.1029/WR016i006p01016
  27. Gao K., Lei Q. Influence of boundary constraints on stress heterogeneity modelling //Computers and Geotechnics. 2018. V. 99. P. 130–136. https://doi.org/10.1016/j.compgeo.2018.03.003
  28. Tang T., Hededal O., Cardiff P. On finite volume method implementation of poro-elasto-plasticity soil model // International Journal for Numerical and Analytical Methods in Geomechanics. 2015. V. 39. № 13. P. 1410–1430. https://doi.org/10.1002/nag.2361
  29. Kim J., Tchelepi H.A., Juanes R. Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits // Computer Methods in Applied Mechanics and Engineering. 2015. V. 200. № 13. P. 1591–1606. https://doi.org/10.1016/j.cma.2010.12.022
  30. Geuzaine C., Remacle J.-F. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities // International Journal for Numerical Methods in Engineering. 2009. V. 79. № 11. P. 1309–1331. https://doi.org/10.1002/nme.2579
  31. Легостаев Д.Ю., Родионов С.П. Численное исследование двухфазной фильтрации в трещиновато-пористой среде на основе моделей пороупругости и дискретных трещин // Прикладная механика и техническая физика. 2021. Т. 62. № 3. С. 126–136. https://doi.org/10.15372/PMTF20210312
  32. Berre I., Doster F., Keilegavlen E. Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches // Transport in Porous Media. 2019. V. 130. № 1. P. 215–236. https://doi.org/10.1007/s11242-018-1171-6
  33. Басниев К.С., Кочина И.Н., Максимов В.М. Подземная гидромеханика. М.: Недра, 1993. 416 p.
  34. Lei Q., Wang X., Min K.-B., Rutqvist J. Interactive roles of geometrical distribution and geomechanical deformation of fracture networks in fluid flow through fractured geological media // Journal of Rock Mechanics and Geotechnical Engineering. 2020. V. 12. № 4. P. 780–792. https://doi.org/10.1016/j.jrmge.2019.12.014
  35. Hestir K., Long J.C.S. Analytical expressions for the permeability of random two-dimensional Poisson fracture networks based on regular lattice percolation and equivalent media theories // Journal of Geophysical Research: Solid Earth. 1990. V. 95. № B13. P. 21565–21581. https://doi.org/10.1029/JB095iB13p21565
  36. Berkowitz B., Balberg I. Percolation theory and its application to groundwater hydrology // Water Resources Research. 1993. V. 29. № 4. P. 775–7941. https://doi.org/10.1029/92WR02707

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