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.

在本文中，基于计算均质化方法，使用双重连续标度，开发了一种用于在可变形非均质多孔介质中完全耦合的多相流的计算建模工具，该介质由复杂和不均匀的微结构组成。一阶均化技术用于执行多尺度分析。基于适当的主要变量，考虑了不混溶流体的两相流控制方程，包括一个平衡方程和两个质量连续性方程。根据众所周知的Hill-Mandel宏均匀性原理，定义了适当的能量类型，而不是用于连接微观和宏观尺度的常规应力功率，这在确定一致的微观场中起着重要作用。有限元平方策略被用来同时解析两个尺度。在微观分析中利用周期性和线性边界条件，并从微观域的边界信息中确定宏观量，例如应力张量，惯性力矢量，通量矢量和流体含量。此外，根据边界条件的类型定义了一种通用方法，在该方法中，可以直接从收敛的微观雅可比矩阵中提取宏观切线算子。最后，为了说明所提算法的有效性和准确性，对几个数值例子进行了求解，并研究了边界条件，RVE类型，RVE长度尺度和异质性体积分数等各种参数的影响。