Coupled model of fluid-saturated porous materials based on a combination of discrete and continuum approaches

Abstract


The numerical model of fluid-saturated porous brittle materials is proposed. The model is based on a hybrid approach combining the particle-based numerical method with finite difference method. In the framework of the model an enclosing porous solid is described with the discrete element method. An ensemble of discrete elements is used to model the processes of deformation of a porous solid and filtration of single-phase fluid in interconnected network of “micropores” (which are the pores, channels and other discontinuities enclosed in the volume of discrete elements). Relations between stress and strain of a discrete element, the change in volume of its pore space and fluid pore pressure in the “micropores” are proposed. Fluid mass transfer between the “micropores” and “macropores” (which are considered as the areas between spatially separated and non-interacting discrete elements) is calculated on the finer grid freezed in the laboratory system of coordinates. The developed coupled model was applied to study the mechanical response of samples of elastic-brittle material with water-saturated pore space under uniaxial compression. It is shown that the strength of fluid-saturated samples is determined by not only the strength properties of “dry” (unfilled) material and the fluid pore pressure, but largely by sample aspect ratio, rate of deformation and the characteristics of porosity of the material. Analysis of simulation results allowed authors to suggest a generalizing dependence of the uniaxial compressive strength of water-saturated permeable brittle material on the reduced diameter of filtration channels, which is the ratio of the characteristic diameter of the filtration channels to the square root of the sample strain rate. Presented results demonstrate the ability of the developed model to study nonstationary processes of deformation and fracture of fluid-saturated materials under dynamic loading.

About the authors

A V Dimaki

Institute of Strength Physics and Materials Science SB RAS

Email: dav@ispms.tsc.ru

E V Shilko

Institute of Strength Physics and Materials Science SB RAS

Email: shilko@ispms.tsc.ru

S V Astafurov

Institute of Strength Physics and Materials Science SB RAS

Email: svastafurov@gmail.com

S Yu Korostelev

Institute of Strength Physics and Materials Science SB RAS

Email: sergeyk@ispms.tsc.ru

S G Psakhie

Institute of Strength Physics and Materials Science SB RAS

Email: sp@ispms.tsc.ru

References

  1. Zhejun P., Connell L.D. A theoretical model for gas adsorption-induced coal swelling // Int. J. of Coal Geol. - 2007. - Vol. 69. - No. 4. - Р. 243-252.
  2. Taylor D. Fracture and repair of bone: a multiscale problem // J. Mater. Sci. - 2007. - Vol. 42. - Р. 8911-8918.
  3. Jing L., Stephansson O. Fundamentals of discrete element method for rock engineering: theory and applications. - London: Elsevier, 2007. - 562 p.
  4. Biot M.A. General theory of three-dimensional consolidation // J. of Appl. Phys. - 1941. - Vol. 12. - Р. 155-164.
  5. Biot M.A. The elastic coefficients of the theory of consolidation // J. appl. Mech. - 1957. - Vol. 24. - Р. 594-601.
  6. Detournay E., Cheng A.H.-D. Fundamentals of poroelasticity. Chapter 5 in Comprehensive Rock Engineering: Principles, Practice and Projects. Vol. II. Analysis and Design Method / ed. C. Fairhurst. - Pergamon Press, 1993. - Р. 113-171.
  7. Hamiel Y., Lyakhovsky V., Agnon A. Coupled evolution of damage and porosity in poroelastic media: theory and applications to deformation of porous rocks // Geophys. J. Int. - 2004. - Vol. 156. - Р. 701-713.
  8. Lyakhovsky V., Hamiel Y. Damage Evolution and Fluid Flow in Poroelastic Rock // Izvestiya, Physics of the Solid Earth. - 2007. - Vol. 43. - No. 1. - Р. 13-23.
  9. Мейрманов А.М. Метод двухмасштабной сходимости Нгуетсенга в задачах фильтрации и сейсмоакустики в упругих пористых средах // Сибирский математический журнал. - 2007. - Т. 48, № 3. - С. 645-667.
  10. Бочаров О.Б., Рудяк В.Я., Серяков А.В. Простейшие модели деформирования пороупругой среды, насыщенной флюидами // Физико-технические проблемы разработки полезных ископаемых. - 2014. - № 2. - С. 54-68.
  11. Coupled fluid flow and geomechanical deformation modeling / S.E. Minkoff, C.M. Stone, S. Bryant, M. Peszynska, M.F. Wheeler // J. of Petroleum Sci. and Eng. - 2003. - Vol. 38. - Р. 37-56.
  12. Micromechanically Based Poroelastic Modeling of Fluid Flow in Haversian Bone / C.C. Swan, R.S. Lakes, R.A. Brand, K.J. Stewart // J. of Biomech. Eng. - 2003. - Vol. 125. - Р. 25-37.
  13. Silbernagel M.M. Modeling Coupled Fluid Flow and Geomechanical and Geophysical Phenomena Within a Finite Element Framework. - Golden, CO: Colorado School of Mines, 2007. - 218 р.
  14. White J.A., Borja R.I. Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients // Comput. Methods Appl. Mech. Eng. - 2008. - Vol. 197. - Р. 4353-4366.
  15. Jha B., Juanes R. Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering // Water Resour. Res. - 2014. - Vol. 50. - Iss. 5. - Р. 3776-3808.
  16. Turner D.Z., Nakshatrala K.B., Martinez M.J. Framework for Coupling Flow and Deformation of a Porous Solid // Int. J. Geomech. - 2014. - Р. 04014076. (in press).
  17. Masson Y.J., Pride Y.J., Nihei K.T. Finite difference modeling of Biot’s poroelastic equations at seismic frequencies // J. Geophys. Res. - 2006. - Vol. 111. - B10305.
  18. Finite element modelling of the effective elastic properties of partially saturated rocks / D. Makarynska, B. Gurevich, R. Ciz, C.H. Arns, M.A. Knackstedt // Computers & Geosciences. - 2008 - Vol. 34. - Р. 647-657.
  19. Наседкина А.А., Наседкин А.В., Иоване Ж. Моделирование нестационарного воздействия на многослойный пороупругий пласт с нелинейными геомеханическими свойствами // Физико-технические проблемы разработки полезных ископаемых. - 2009. - № 4. - С. 23-32.
  20. Наседкина А.А. Моделирование нестационарных процессов фильтрации в пороупругих средах с физическими нелинейностями // Вестник Нижегород. ун-та им. Н.И. Лобачевского. - 2011. - № 4-3. - С. 1006-1008.
  21. Доброскок А.А., Линьков А.М. Моделирование течения, напряженного состояния и сейсмических событий в породах при сбросе давления в трещине гидроразрыва // Физико-технические проблемы разработки полезных ископаемых. - 2011. - № 1. - С. 12-22.
  22. Численное моделирование динамики составного пороупругого тела / Л.А.Игумнов, С.Ю. Литвинчук, Д.В. Тарлаковский, Н.А. Локтева // Проблемы прочности и пластичности. - 2013. - № 75, Т. 2. - С. 130-136.
  23. Rieth M. Nano-engineering in science and technology: An Introduction to the World of Nano-Design. - Singapore: World Scientific, 2003. - 164 p.
  24. Cundall P.A., Strack O.D.L. A discrete numerical model for granular assemblies // Geotechnique. - 1979. - Vol. 29. - Р. 47-65.
  25. Mustoe G.G.W. A generalized formulation of the discrete element method // Eng. Comp. - 1992. - Vol. 9. - Р. 181-190.
  26. Shi G.H. Discontinuous deformation analysis - a new numerical model for statics and dynamics of block systems // Eng. Comp. - 1992. - Vol. 9. - Iss. 2. - Р. 157-168.
  27. Munjiza A.A., Knight E.E., Rougier E. Computational mechanics of discontinua. - Chichester: Wiley, 2012. - 276 p.
  28. Lisjak A., Grasseli G. A review of discrete modeling techniques for fracturing processes in discontinuous rock masses // Int. J. Rock. Mech. Min. Sci. - 2014 - Vol. 6. - Р. 301-314.
  29. Munjiza A. The combined finite-discrete element method. - Chichester: Wiley, 2004. - 352 p.
  30. Bićanić N. Discrete element methods // Encyclopedia of computational mechanics / eds. Stein E., Borst R., Hughes T.J.R. Vol. 1: Fundamentals. - Chichester: Wiley, 2004. - P. 311-371.
  31. Jing L., Stephansson O. Fundamentals of discrete element method for rock engineering: theory and applications. - Elsevier, 2007. - 562 p.
  32. Williams J.R., Hocking G., Mustoe G.G.W. The Theoretical basis of the discrete element method // Numerical methods of engineering, theory and applications / ed. A.A. Balkema. - Rotterdam: NUMETA, 1985.
  33. Potyondy D.O., Cundall P.A. A bonded-particle model for rock // Int. J. Rock. Mech. Min. Sci. - 2004. - Vol. 41. - P. 1329-1364.
  34. Хан Г.Н. О несимметричном режиме разрушения массива горных пород в окрестности полости // Физ. мезомех. - 2008. - Т. 11, № 1. - С. 109-114.
  35. Zhao G.F., Khalili N. A Lattice Spring Model for Coupled Fluid Flow and Deformation Problems in Geomechanics // Rock Mech. and Rock Eng. - 2012. - Vol. 45. - P. 781-799.
  36. Cook B.K., Noble D.R. A direct simulation method for particle-fluid systems // Eng. Comp. - 2011. - Vol. 21. - No. 2/3/4. - P. 151-168.
  37. Sakaguchi H., Muhlhaus H.-B. Hybrid Modelling of Coupled Pore Fluid-solid Deformation Problems // Pure appl. geophys. - 2000. - Vol. 157. - P. 1889-1904.
  38. Han Y., Cundall P.A. Lattice Boltzmann modeling of pore-scale fluid flow through idealized porous media // Int. J. Numer. Meth. Fluids. - 2011. - Vol. 67. - P. 1720-1734.
  39. Han Y., Cundall P.A. LBM-DEM modeling of fluid-solid interaction in porous media // Int. J. Numer. Analyth. Meth. Geomech. - 2013. - Vol. 37. - Iss. 10. - P. 1391-1407.
  40. Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials / S. Psakhie, E. Shilko, A. Smolin [et al.] // Fracture and Structural Integrity. - 2013. - Vol. 24. - P. 59-91.
  41. A mathematical model of particle-particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic-plastic materials / S.G. Psakhie, E.V. Shilko, A.S. Grigoriev, S.V. Astafurov, A.V. Dimaki, A.Yu. Smolin // Engineering Fracture Mechanics, 2014 (in press).
  42. Hybrid Cellular Automata Metod. Application to Research on Mechanical Response of Contrast Media / S. Zavsek, A.V. Dimaki, A.I. Dmitriev, E.V. Shilko, J. Pezdic, S.G. Psakhie // Phys. Mesomech. - 2013. - Vol. 1. - P. 42-51.
  43. Approach to simulation of deformation and fracture of hierarchically organized heterogeneous media, including contrast media / S.G. Psakhie, E.V. Shilko, A.Yu. Smolin [et. al.] // Phys. Mesomech. - 2011. - Vol. 14. - No. 5-6. - P. 224-248.
  44. Развитие формализма метода частиц для моделирования отклика флюидонасыщенных пористых геологических материалов / А.В. Димаки, Е.В. Шилько, С.В. Астафуров, С.Г. Псахье // Известия ТПУ. - 2014. - Т. 324, № 1. - С. 102-111.
  45. Cundall P.A. Formulation of a three-dimensional distinct element model - Part I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks // Int. J. Rock Mech, Min. Sci. Geomech. Abstr. - 1988. - Vol. 25. - Iss. 3. - P. 107-116.
  46. Hwang J.-Y., Ohnishi Y., Wu J. Numerical analysis of discontinuous rock masses using three-dimensional discontinuous deformation analysis (3D DDA) // Geotech. Eng. - 2004. - Vol. 8. - Iss. 5. - P. 491-496.
  47. Hahn M., Wallmersperger T., Kroplin B.-H. Discrete element representation of discontinua: proof of concept and determination of material parameters // Comp. Mat. Sci. - 2010. - Vol. 50. - P. 391-402.
  48. Garagash I.A., Nikolaevskiy V.N. Non-associated laws of plastic flow and localization of deformation // Adv. Mech. - 1989. - Vol. 12. - Iss. 1. - P. 131-183.
  49. Stefanov Yu.P. Deformation localization and fracture in geomaterials. Numerical simulation // Phys. Mesomech. - 2002. - Vol. 5-6. - P. 67-77.
  50. Wilkins M.L. Computer simulation of dynamic phenomena. - Heidelberg: Springer-Verlag, 1999. - 246 p.
  51. Kushch V.I., Shmegera S.V., Sevostianov I. SIF statistics in micro cracked solid: effect of crack density, orientation and clustering // Int. J. Eng. Sci. - 2009. - Vol. 47. - P. 192-208.
  52. Permeability of Wilcox shale and its effective pressure law / O. Kwon, A.K. Kronenberg, A.F. Gangi, B. Johnson // J. Geophys. Res. - 2001. - Vol. 106. - No. b9. - P. 19339-19353.
  53. Paterson M.S., Wong T.F. Experimental Rock Deformation. The Brittle Field. - Berlin-Heidelberg: Springer-Verlag, 2005. - 347 p.
  54. Yamaji A. An Introduction to Tectonophysics: Theoretical Aspects of Structural Geology. - Tokyo: TERRAPUB, 2007. - 378 p.
  55. Experimental Deformation of Sedimentary Rocks Under Confining Pressure: Pore Pressure Tests / J. Hangin, R.V.Hager, M. Friedman, J.N. Feather // AAPG Bulletin. - 1963. - Vol. 47. - Iss. 5. - P. 717-755.
  56. Ставрогин А.Н., Тарасов Б.Г. Экспериментальная физика и механика горных пород. - СПб.: Наука, 2001. - 343 с.
  57. Robin P.-Y.F. Note on Effective Pressure // J. Geophys. Res. - 1973. - Vol. 78. - No. 14. - P. 2434-2437.
  58. Gangi A.F., Carlson R.L. An asperity-deformation model for effective pressure // Tectonophysics. - 1996. - Vol. 256. - P. 241-251.
  59. Boitnott G.N., Scholz C.H. Direct Measurement of the Effective Pressure Law: Deformation of Joints Subject to Pore and Confining Pressure // J. Geophys. Res. - 1990. - Vol. 95. - No. B12. - P. 19279-I9298.
  60. Хавкин А.Я. Наноявления и нанотехнологии в добыче нефти и газа. - М.; Ижевск: Регулярная и хаотическая динамика, 2010. - 692 с.
  61. Басниев К.С., Кочина И.Н., Максимов В.М. Подземная гидромеханика. - М.: Недра, 1993. - 416 с.
  62. Лейбензон Л.С. Движение природных жидкостей и газов в пористой среде. - М.; Л.: Гос. изд-во технико-теорет. лит., 1947. - 244 с.

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Copyright (c) 2014 Dimaki A.V., Shilko E.V., Astafurov S.V., Korostelev S.Y., Psakhie S.G.

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