Computational homogenization of fully coupled multiphase flow in deformable porous media

Abstract

In this paper, a computational modeling tool is developed for fully coupled multiphase flow in deformable heterogeneous porous medium that consists of complex and non-uniform micro-structures using the dual continuum scales based on the computational homogenization approach. The first-order homogenization technique is employed to perform the multi-scale analysis. The governing equations of two-phase flow of immiscible fluids, including an equilibrium equation and two mass continuity equations, are considered based on the appropriate main variables. According to the well-known Hill–Mandel principle of macro-homogeneity, the proper energy types are defined instead of conventional stress power for linking micro- and macro-scales, which plays a significant role in determination of consistent microscopic fields. The finite element squared strategy is utilized to resolve the two scales simultaneously. The periodic and linear boundary conditions are exploited in the micro-scale analysis, and the macroscopic quantities such as stress tensor, inertial force vector, flux vectors and fluid contents are determined from the boundary information of microscopic domain. Moreover, a general approach is defined depending on the type of boundary condition in which the macroscopic tangent operators can be extracted directly from the converged microscopic Jacobian matrix. Finally, in order to illustrate the efficiency and accuracy of the proposed computational algorithm, several numerical examples are solved, and the effects of various parameters, such as boundary conditions, RVE types, RVE length scale, and volume fraction of heterogeneities are investigated.