On the factors affecting the permeability of fractured porous media using finite element approach
Email:
banglh@utt.edu.vn
Keywords:
Coupling of Stokes-Darcy, fractured porous media, permeability, finite element method.
Abstract
In the field of civil engineering or geotechnical engineering, flow in fractured porous media has gained increasing attention from scientists. However, up to date, theoretical and practical basis on this problem still require detailed and in-depth knowledge. One of the approaches to deal with such a difficult problem lies in the coupling of Stokes-Darcy equations. In this study, an in-house Matlab numerical tool based on the finite element method was used to estimate the permeability of fractured porous media by solving the Stokes-Darcy coupling problem. The effective mechanical behavior of fractured porous media is often determined by many factors, namely the initial porosity, distribution and connectivity of the pore network, or the shape of fractures. The primary focus of this paper is on the factors affecting the flow characteristics in fractured porous media, such as the morphology of fractures and connectivity. The results showed that the above factors are crucial and have a significant effect on the macroscopic permeability of fractured porous media. For interconnected fractures network, the permeability was about 1000 times greater than that of the porous medium. Conversely, for isolated fractures, the macroscopic permeability depended on the shape of fractures, lower from 4 to 15 times the permeability of the medium surrounding the fracture.References
[1] D.T. Hai, Current status of existing railway bridges in Vietnam: An overview of steel deficiencies, Journal of Constructional Steel Research, 62 (2006) 987-994. https://doi.org/10.1016/j.jcsr.2006.01.009
[2] V. Zivica, A. Bajza, Acidic attack of cement-based materials—a review Part 2. Factors of rate of acidic attack and protective measures, Construction and Building Materials, 16 (2002) 215-222. https://doi.org/10.1016/S0950-0618(02)00011-9
[3] P. Dietrich, R. Helmig, M. Sauter, H. Hötzl, J. Köngeter, G. Teutsch, Flow and transport in fractured porous media, Springer Science & Business Media, 2005. https://doi.org/10.1007/b138453
[4] M. Sahimi, Flow and transport in porous media and fractured rock: from classical methods to modern approaches, John Wiley & Sons, 2011. https://doi.org/10.1002/9783527636693
[5] J.-L. Auriault, E. Sanchez-Palencia, Etude du comportement macroscopique d’un milieu poreux saturé déformable, Journal de Mécanique, 16 (1977) 575-603. https://www.researchgate.net/publication/279688679_A_Study_of_the_Macroscopic_Behavior_of_a_Deformable_Saturated_Porous_MediumETUDE_DU_COMPORTEMENT_MACROSCOPIQUE_D'UN_MILIEU_POREUX_SATURE_DEFORMABLE
[6] S. Whitaker, Diffusion and dispersion in porous media, AIChE Journal, 13 (1967) 420-427. https://doi.org/10.1002/aic.690130308
[7] C.Y. Wang, Stokes slip flow through square and triangular arrays of circular cylinders, Fluid Dynamics Research, 32 (2003) 233-246. https://doi.org/10.1016/S0169-5983(03)00049-2
[8] F.J. Alcocer, P. Singh, Permeability of periodic arrays of cylinders for viscoelastic flows, Physics of Fluids, 14 (2002) 2578. https://doi.org/10.1063/1.1483301
[9] M. Bai, D. Elsworth, J.-C. Roegiers, Modeling of naturally fractured reservoirs using deformation dependent flow mechanism, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30 (1993) 1185-1191. https://doi.org/10.1016/0148-9062(93)90092-R
[10] J.L. Auriault, C. Boutin, Deformable porous media with double porosity. Quasi-statics. I: Coupling effects, Transport in Porous Media, 7 (1992) 63-82. https://doi.org/10.1007/BF00617317
[11] J.L. Auriault, C. Boutin, Deformable porous media with double porosity. Quasi-statics. II: Memory effects, Transport in Porous Media, 10 (1993) 153-169. https://doi.org/10.1007/BF00617006
[12] J.L. Auriault, C. Boutin, Deformable porous media with double porosity III: Acoustics, Transport in Porous Media, 14 (1994) 143-162. https://doi.org/10.1007/BF00615198
[13] P. Royer, J.-L. Auriault, C. Boutin, Macroscopic modeling of double-porosity reservoirs, Journal of Petroleum Science and Engineering, 16 (1996) 187-202. https://doi.org/10.1016/S0920-4105(96)00040-X
[14] C. Boutin, P. Royer, J.-L. Auriault, Acoustic absorption of porous surfacing with dual porosity, International Journal of Solids and Structures, 35 (1998) 4709-4737. https://doi.org/10.1016/S0020-7683(98)00091-2
[15] X. Olny, C. Boutin, Acoustic wave propagation in double porosity media, The Journal of the Acoustical Society of America, 114 (2003) 73-89. https://doi.org/10.1121/1.1534607
[16] H.C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow, Turbulence and Combustion, 1 (1949) 27. https://doi.org/10.1007/BF02120313
[17] G.S. Beavers, D.D. Joseph, Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, 30 (1967) 197-207. https://doi.org/10.1017/S0022112067001375
[18] P.G. Saffman, On the boundary condition at the surface of a porous medium, Studies in Applied Mathematics, 50 (1971) 93-101. https://doi.org/10.1002/sapm197150293
[19] A. Mikelic, W. Jäger, On the interface boundary condition of Beavers, Joseph, and Saffman, SIAM Journal on Applied Mathematics, 60 (2000) 1111-1127. https://doi.org/10.1137/S003613999833678X
[20] M. Discacciati, A. Quarteroni, A. Valli, Robin–Robin domain decomposition methods for the Stokes–Darcy coupling, SIAM Journal on Numerical Analysis, 45 (2007) 1246-1268. https://doi.org/10.1137/06065091X
[21] W.J. Layton, F. Schieweck, I. Yotov, Coupling fluid flow with porous media flow, SIAM Journal on Numerical Analysis, 40 (2002) 2195-2218. https://doi.org/10.1137/S0036142901392766
[22] T. Arbogast, D.S. Brunson, A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium, Computational Geosciences, 11 (2007) 207-218. https://doi.org/10.1007/s10596-007-9043-0
[23] M. Fortin, Old and new finite elements for incompressible flows, International Journal for Numerical Methods in Fluids, 1 (1981) 347-364. https://doi.org/10.1002/fld.1650010406
[24] T. Arbogast, M.F. Wheeler, A family of rectangular mixed elements with a continuous flux for second order elliptic problems, SIAM Journal on Numerical Analysis, 42 (2005) 1914-1931. https://doi.org/10.1137/S0036142903435247
[25] K.A. Mardal, X.-C. Tai, R. Winther, A robust finite element method for Darcy–Stokes flow, SIAM Journal on Numerical Analysis, 40 (2002) 1605-1631. https://doi.org/10.1137/S0036142901383910
[26] H.-B. Ly, H.-L. Nguyen, M.-N. Do, Finite element modeling of fluid flow in fractured porous media using unified approach, Vietnam Journal of Earth Sciences, 43 (2020). https://doi.org/10.15625/0866-7187/15572
[2] V. Zivica, A. Bajza, Acidic attack of cement-based materials—a review Part 2. Factors of rate of acidic attack and protective measures, Construction and Building Materials, 16 (2002) 215-222. https://doi.org/10.1016/S0950-0618(02)00011-9
[3] P. Dietrich, R. Helmig, M. Sauter, H. Hötzl, J. Köngeter, G. Teutsch, Flow and transport in fractured porous media, Springer Science & Business Media, 2005. https://doi.org/10.1007/b138453
[4] M. Sahimi, Flow and transport in porous media and fractured rock: from classical methods to modern approaches, John Wiley & Sons, 2011. https://doi.org/10.1002/9783527636693
[5] J.-L. Auriault, E. Sanchez-Palencia, Etude du comportement macroscopique d’un milieu poreux saturé déformable, Journal de Mécanique, 16 (1977) 575-603. https://www.researchgate.net/publication/279688679_A_Study_of_the_Macroscopic_Behavior_of_a_Deformable_Saturated_Porous_MediumETUDE_DU_COMPORTEMENT_MACROSCOPIQUE_D'UN_MILIEU_POREUX_SATURE_DEFORMABLE
[6] S. Whitaker, Diffusion and dispersion in porous media, AIChE Journal, 13 (1967) 420-427. https://doi.org/10.1002/aic.690130308
[7] C.Y. Wang, Stokes slip flow through square and triangular arrays of circular cylinders, Fluid Dynamics Research, 32 (2003) 233-246. https://doi.org/10.1016/S0169-5983(03)00049-2
[8] F.J. Alcocer, P. Singh, Permeability of periodic arrays of cylinders for viscoelastic flows, Physics of Fluids, 14 (2002) 2578. https://doi.org/10.1063/1.1483301
[9] M. Bai, D. Elsworth, J.-C. Roegiers, Modeling of naturally fractured reservoirs using deformation dependent flow mechanism, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30 (1993) 1185-1191. https://doi.org/10.1016/0148-9062(93)90092-R
[10] J.L. Auriault, C. Boutin, Deformable porous media with double porosity. Quasi-statics. I: Coupling effects, Transport in Porous Media, 7 (1992) 63-82. https://doi.org/10.1007/BF00617317
[11] J.L. Auriault, C. Boutin, Deformable porous media with double porosity. Quasi-statics. II: Memory effects, Transport in Porous Media, 10 (1993) 153-169. https://doi.org/10.1007/BF00617006
[12] J.L. Auriault, C. Boutin, Deformable porous media with double porosity III: Acoustics, Transport in Porous Media, 14 (1994) 143-162. https://doi.org/10.1007/BF00615198
[13] P. Royer, J.-L. Auriault, C. Boutin, Macroscopic modeling of double-porosity reservoirs, Journal of Petroleum Science and Engineering, 16 (1996) 187-202. https://doi.org/10.1016/S0920-4105(96)00040-X
[14] C. Boutin, P. Royer, J.-L. Auriault, Acoustic absorption of porous surfacing with dual porosity, International Journal of Solids and Structures, 35 (1998) 4709-4737. https://doi.org/10.1016/S0020-7683(98)00091-2
[15] X. Olny, C. Boutin, Acoustic wave propagation in double porosity media, The Journal of the Acoustical Society of America, 114 (2003) 73-89. https://doi.org/10.1121/1.1534607
[16] H.C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow, Turbulence and Combustion, 1 (1949) 27. https://doi.org/10.1007/BF02120313
[17] G.S. Beavers, D.D. Joseph, Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, 30 (1967) 197-207. https://doi.org/10.1017/S0022112067001375
[18] P.G. Saffman, On the boundary condition at the surface of a porous medium, Studies in Applied Mathematics, 50 (1971) 93-101. https://doi.org/10.1002/sapm197150293
[19] A. Mikelic, W. Jäger, On the interface boundary condition of Beavers, Joseph, and Saffman, SIAM Journal on Applied Mathematics, 60 (2000) 1111-1127. https://doi.org/10.1137/S003613999833678X
[20] M. Discacciati, A. Quarteroni, A. Valli, Robin–Robin domain decomposition methods for the Stokes–Darcy coupling, SIAM Journal on Numerical Analysis, 45 (2007) 1246-1268. https://doi.org/10.1137/06065091X
[21] W.J. Layton, F. Schieweck, I. Yotov, Coupling fluid flow with porous media flow, SIAM Journal on Numerical Analysis, 40 (2002) 2195-2218. https://doi.org/10.1137/S0036142901392766
[22] T. Arbogast, D.S. Brunson, A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium, Computational Geosciences, 11 (2007) 207-218. https://doi.org/10.1007/s10596-007-9043-0
[23] M. Fortin, Old and new finite elements for incompressible flows, International Journal for Numerical Methods in Fluids, 1 (1981) 347-364. https://doi.org/10.1002/fld.1650010406
[24] T. Arbogast, M.F. Wheeler, A family of rectangular mixed elements with a continuous flux for second order elliptic problems, SIAM Journal on Numerical Analysis, 42 (2005) 1914-1931. https://doi.org/10.1137/S0036142903435247
[25] K.A. Mardal, X.-C. Tai, R. Winther, A robust finite element method for Darcy–Stokes flow, SIAM Journal on Numerical Analysis, 40 (2002) 1605-1631. https://doi.org/10.1137/S0036142901383910
[26] H.-B. Ly, H.-L. Nguyen, M.-N. Do, Finite element modeling of fluid flow in fractured porous media using unified approach, Vietnam Journal of Earth Sciences, 43 (2020). https://doi.org/10.15625/0866-7187/15572
Downloads
Download data is not yet available.
Received
25/11/2020
Revised
07/12/2020
Accepted
08/12/2020
Published
28/12/2020
Type
Research Article
How to Cite
Lý Hải, B., Phan Việt, H., & Nguyễn Ngọc, L. (1609088400). On the factors affecting the permeability of fractured porous media using finite element approach. Transport and Communications Science Journal, 71(9), 1082-1093. https://doi.org/10.47869/tcsj.71.9.7
Abstract Views
152
Total Galley Views
235
