Some remarks on simplified double porosity model of immiscible incompressible two-phase flow

TL;DR

This paper introduces a new linearized imbibition equation for simplified double porosity models of immiscible two-phase flow in fractured media, improving approximation accuracy and eliminating complex cell problems.

Contribution

The authors propose a novel linear version of the imbibition equation that enhances the simplified dual porosity model for better accuracy and computational efficiency.

Findings

The new linearization yields a more accurate matrix-fracture exchange term.

Numerical results demonstrate improved approximation over previous models.

The approach simplifies the modeling process by removing the cell problem.

Abstract

The paper is devoted to the derivation, by linearization, of simplified (fully homogenized) homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified dual porosity model derived previously by the authors the matrix-fracture source term is approximated by a convolution type source term. This approach enables to exclude the cell problem, in form of the imbibition equation, from the global double porosity model. In this paper we propose a new linear version of the imbibition equation which leads to a new simplified dual porosity model. We also present numerical simulations which show that the matrix-fracture exchange term based on this new linearization procedure gives a better approximation of the exact one than the corresponding exchange term obtained earlier by the authors.