Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 81, Issue 3, Pages 1034-1051Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M1368513
Keywords
porous medium; permeability; multiple scales; effective material; conductivity; tortuosity
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This study homogenizes the problem of fluid flow through a periodic network of one-dimensional channels to Darcy flow using a discrete version of the method of multiple scales. The effective permeability in terms of channel conductances is obtained through a simple, low-dimensional linear algebra problem. The research investigates the statistical properties of effective permeability for various random networks and evaluates the correlation between permeability and network tortuosity.
Using a discrete version of the method of multiple scales, the problem of fluid flow through an arbitrary periodic network of one-dimensional channels is homogenized to give Darcy flow. A simple, low-dimensional, linear algebra problem gives the effective permeability in terms of the channel conductances. The results are illustrated with an investigation of the statistical properties of effective permeability for a variety of random networks, as well as an evaluation of the correlation between permeability and network tortuosity.
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