Abstract

This paper discusses a computational 3D dual porosity model of two-phase incompressible fluid filtration in a fractured-porous medium. The conservation laws are formulated in integral form, and for their spatial approximation a combination of a mixed finite element method to determine the total flow and pressure velocities and a finite volume method to determine the saturations in the porous blocks and in the fractures are used. The equations for saturations are approximated with an explicit upwind scheme to eliminate nonphysical oscillations. The model under consideration includes injection and production wells with given total flow rates. For the total velocities and pressures, a Neumann problem is formulated, for which a condition of unique solvability is used and a method for solving it without additional conditions is proposed. For the explicit upwind scheme used for solving the equations for saturations, a weak maximum principle is established, which is illustrated by computational experiments.

中文翻译：

---

破裂多孔介质中流体过滤的计算模型

摘要

本文讨论了裂缝-多孔介质中两相不可压缩流体过滤的计算 3D 双孔隙率模型。守恒定律以积分形式表达，并且为了它们的空间近似，使用混合有限元方法来确定总流动和压力速度以及使用有限体积方法来确定多孔块和裂缝中的饱和度。饱和方程近似于显式逆风方案以消除非物理振荡。所考虑的模型包括具有给定总流速的注入井和生产井。对于总速度和总压力，提出了一个诺依曼问题，对其使用了唯一可解性条件，并提出了一种无需附加条件的求解方法。