In this paper, we establish a homogenization result for a nonlinear degenerate system arising from two-phase flow through fractured porous media with periodic microstructure taking into account the temperature effects. The mathematical model is given by a coupled system of two-phase flow equations, and an energy balance equation. The microscopic model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy–Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation, i.e. the saturation of one phase, the pressure of the second phase and the temperature are primary unknowns. The fractured medium consists of periodically repeating homogeneous blocks and fractures, the permeability being rapidly oscillating discontinuous function. Over the matrix domain, the permeability is scaled by ${\epsilon }^2$, where $\epsilon$ is the size of a typical porous block. Furthermore, we will consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. The model involves highly oscillatory characteristics and internal nonlinear interface conditions accounting for discontinuous capillary pressures. We then show by a rigorous mathematical argument that the solution of this microscopic problem converges as $\epsilon$ tends to zero to the solution of a double-porosity model of the global macroscopic flow. Our techniques make use of the two-scale convergence method combined to extension and dilation operators in the homogenization context. The memory effects of usual double porosity media are reproduced by this model. We show how the effective coefficients of the porous medium are determined in a precise way by certain physical and geometric features of the microscopic fracture domain, the microscopic matrix blocks, and the interface between them.

在本文中，我们建立了一个非线性退化系统的均质化结果，该系统由两相流经具有周期性微观结构的裂隙多孔介质引起，并考虑了温度影响。数学模型由两相流方程和能量平衡方程的耦合系统给出。微观模型由从两种流体的质量守恒以及达西-穆斯卡特（Darcy-Muskat）和毛细压力定律得出的通常方程组成。问题是根据相的形式来写的，即一相的饱和度，第二相的压力和温度是主要未知数。压裂介质由周期性重复的均质块体和裂缝组成，渗透率迅速振荡不连续函数。在矩阵域上${\epsilon }^{\mathrm{2个}}$， 在哪里 $\epsilon$是典型的多孔块的大小。此外，我们将考虑由几个具有不同特征的区域组成的区域：孔隙度，绝对渗透率，相对渗透率和毛细管压力曲线。该模型涉及高度振荡特性和内部非线性界面条件，这些条件考虑了不连续的毛细管压力。然后，我们通过严格的数学论证表明，该微观问题的解收敛为$\epsilon$对全局宏观流的双孔隙率模型的解趋于零。我们的技术利用了在均质化上下文中结合扩展和扩张算子的两尺度收敛方法。该模型再现了通常的双重孔隙介质的记忆效应。我们展示了如何通过微观断裂区域，微观基质块以及它们之间的界面的某些物理和几何特征，以精确的方式确定多孔介质的有效系数。