Determination of representative area element size for 2D porous media with double porosity
Email:
tbthao.tran@utc.edu.vn
Keywords:
representative area element (RAE), effective permeability, double porosity, Monte-Carlo, boundary element method (BEM).
Abstract
A doubly porous medium can be considered and treated as a heterogeneous material consisting of a permeable matrix solid phase containing pores. Therein the numerical estimate of effective permeability from the constitutive law and the complexity of the microstructure is a fundamental and important subject in the context of double porous materials. In this work, the representative area element (RAE) is usually seen as an area containing doubly porous materials. It is sufficiently large to include many micro-pores, it must however remain small enough to be considered as an area element of continuum mechanics. The purpose of this work is therefore to numerically estimate/analyze the optimal size of the RAE of doubly porous material under consideration. To achieve this objective, the real microstructure is first idealized with a virtual microstructure. Here, the virtual microstructure of RAE is made of an isotropic permeable host matrix in which elliptical pores of arbitrary sizes are randomly distributed and oriented. Then, the well-known boundary element method (BEM) for the computation of the effective permeability of RAE has been used. The mean effective permeability of doubly porous material can be calculated by using the Monte-Carlo method. Finally, the quantitative estimation of the optimal size of the RAE will be discussed in detail.References
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[3] E. Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Physics, 127 (1981). https://doi.org/10.1007/3-540-10000-8
[4] S. Whittaker, Diffusion and dispersion in porous media, AlchE J., 13 (1967) 420-432. https://doi.org/10.1002/aic.690130308
[5] F. Alcocer, P. Singh, Permeability of periodic porous media, Phys. Rev. E, 59 (1999) 771. https://doi.org/10.1103/PhysRevE.59.711
[6] F. Alcocer, P. Singh, Permeability of periodic arrays of cylinders for viscoelastic flows, Phys. Fluids, 14 (2002) 2578-2581. https://doi.org/10.1063/1.1483301
[7] V. Monchiet, G. Bonnet, G. Lauriat, A fft-based method to compute the permeability induced by a stokes slip flow through a porous medium, C. R. Mécanique, 337 (2009) 192-197. https://doi.org/10.1016/j.crme.2009.04.003
[8]. A. T. Tran, H. Le Quang, Q. C. He, D. H. Nguyen, Determination of the effective permeability of doubly porous materials by a two‐scale homogenization approach, Transp. Porous Media, 145 (2022) 197–243. https://doi.org/10.1007/s11242-022-01846-9
[9]. A. T. Tran, H. Le Quang, Q. C. He, D. H. Nguyen, Micromechanical estimates for the effective permeability of 2D porous materials with arbitrarily shaped pores, J. Porous Media, 26 (2023) 57–77. 10.1615/JPorMedia.2022043450
[10]. A. T. Tran, H. Le Quang, D. H. Nguyen, V. H. Hoang, T. A. Do, Q. C. He, Combining the micromechanical approach and boundary element method for estimating the effective permeability of 2D porous materials with arbitrarily shaped pores, Comput. Mech., 75 (2025) 171–183. https://doi.org/10.1007/s00466-024-02498-w
[11]. A. A. Gusev, Representative volume element size for elastic composites: A numerical study, J. Mech. Phys. Solids, 45 (1997) 1449–1459. https://doi.org/10.1016/S0022-5096(97)00016-1
[12]. A. Lachihab, K. Sab, Does a representative volume element exist for fatigue life prediction? The case of aggregate composites, Int. J. Numer. Anal. Methods Geomech., 32 (2008) 1005–1021. https://doi.org/10.1002/nag.655
[13]. K. Terada, T. Ito, N. Kikuchi, Characterization of the mechanical behavior of solid-fluid mixture by the homogenization method, Comput. Methods Appl. Mech. Eng., 153 (1998) 223–257. 10.1016/S0045-7825(97)00071-6
[14]. M. Ostoja-Starzewski, Random field models of heterogeneous materials, Int. J. Solids Struct., 35 (1998) 2429–2455. https://doi.org/10.1016/S0020-7683(97)00144-3
[15]. T. Kanit, S. Forest, I. Galliet, V. Mounoury, D. Jeulin, Determination of the size of the reperentative volume element for random composites: statistical and numerical approach, Int. J. Solids Struct., 40 (2003) 3647–3679. https://doi.org/10.1016/S0020-7683(03)00143-4
[16]. A. T. Tran, H. Le Quang, Q. C. He, D. H. Nguyen, Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface, Appl. Math. Mech. -Engl. Ed., 42 (2021) 721–746. https://doi.org/10.1007/s10483-021-2733-9
[17]. C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, Cambridge, 1992.
[18]. C. A. Brebbia, J. Dominguez, Boundary elements An introductory course, WIT Press/Computational Mechanics Publications, Southamton, 1992.
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Received
19/02/2025
Revised
28/03/2025
Accepted
12/04/2025
Published
15/04/2025
Type
Research Article
How to Cite
Trần Thị Bích, T. (1744650000). Determination of representative area element size for 2D porous media with double porosity. Transport and Communications Science Journal, 76(3), 320-332. https://doi.org/10.47869/tcsj.76.3.10
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