TY - JOUR

T1 - Homogenization of two-phase flow in fractured media

AU - Yeh, Li-Ming

PY - 2006/10/1

Y1 - 2006/10/1

N2 - In a fractured medium, there is an interconnected system of fracture planes dividing the porous rock into a collection of matrix blocks. The fracture planes, while very thin, form paths of high permeability. Most of the fluids reside in matrix blocks, where they move very slow. Let ε denote the size ratio of the matrix blocks to the whole medium and let the width of the fracture planes and the porous block diameter be in the same order. If permeability ratio of matrix blocks to fracture planes is of order ε2, microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as ε goes to 0. If the ratio is smaller than order ε2, the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order ε2, then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.

AB - In a fractured medium, there is an interconnected system of fracture planes dividing the porous rock into a collection of matrix blocks. The fracture planes, while very thin, form paths of high permeability. Most of the fluids reside in matrix blocks, where they move very slow. Let ε denote the size ratio of the matrix blocks to the whole medium and let the width of the fracture planes and the porous block diameter be in the same order. If permeability ratio of matrix blocks to fracture planes is of order ε2, microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as ε goes to 0. If the ratio is smaller than order ε2, the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order ε2, then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.

KW - Dual-porosity model

KW - Fractured media

KW - Homogenization

KW - Two-scale convergence

UR - http://www.scopus.com/inward/record.url?scp=33749985055&partnerID=8YFLogxK

U2 - 10.1142/S0218202506001650

DO - 10.1142/S0218202506001650

M3 - Article

AN - SCOPUS:33749985055

VL - 16

SP - 1627

EP - 1651

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 10

ER -