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On the general equations for flow in porous media and their reduction to Darcy's Law
Author(s) -
Gray William G.,
O'Neill Kevin
Publication year - 1976
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr012i002p00148
Subject(s) - porous medium , darcy's law , mechanics , isotropy , flow (mathematics) , fluid dynamics , darcy number , newtonian fluid , classical mechanics , physics , mathematics , convection , geology , porosity , geotechnical engineering , natural convection , optics , rayleigh number
A technique of local averaging is applied to obtain general equations which describe mass and momentum transport in porous media. The averaging is performed without significantly idealizing either the porous medium or the pertinent fluid mechanical relations. The resulting general flow equation is simplified to treat flow of a Newtonian fluid in a slowly deforming solid matrix for two special cases. For flow in an isotropic medium where convective and inertial terms are important, an equation is developed which is dependent only on five medium parameters which could be evaluated by experiment. Flow in an anisotropic medium is also analyzed, and the general equation is reduced to Darcy's law when the convective and inertial terms are neglected.