Derivation of the Double Porosity Model of Single Phase Flow via Homogenization Theory 论文

详细信息

发表期刊/会议

SIAM Journal on Mathematical Analysis

发表日期

1990-07-01

发表年份

1990

摘要

A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations describing Darcy flow in a reservoir, except that the porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter $\epsilon $ representing the size of the matrix blocks. This scaling preserves the physics of the flow in the matrix as $\epsilon $ tends to zero. An effective macroscopic limit model is obtained that includes the usual Darcy equations in the matrix blocks and a similar equation for the fracture system that contains a term representing a source of fluid from the matrix. The convergence is shown by extracting weak limits in appropriate Hilbert spaces. A dilation operator is utilized to see the otherwise vanishing physics in the matrix blocks as $\epsilon $ tends to zero.