A convergence theorem for homogenization of two-phase miscible flow through fractured reservoirs with uniform fracture distributions

Abstract

The equations of fluid flow in naturally fractured porous media, with a given fracture distribution, can be modeled by using a method of homogenization. In contrast to the original flow equations, homogenized equations will have a new porosity, a new permeability, and a new matrix of dispersion. The purpose of this article is to give a mathematical proof of convergence for the homogenization of general two-phase miscible flow. A formal homogenization, with a convergence proof for some special cases, was given previously by Bourgeat^1-3

Keywords:

• Homogenization
• two-phase miscible flow
• fractured media

AMS(MOS):

• 76T05
• 35Q20
• 76S05