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Exact solution for flow of slightly compressible fluids through multiple‐porosity, multiple‐permeability media
Author(s) -
Liu M.X.,
Chen Z.X.
Publication year - 1990
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/wr026i007p01393
Subject(s) - permeability (electromagnetism) , porous medium , porosity , compressibility , exact solutions in general relativity , mechanics , compressible flow , mathematics , flow (mathematics) , matrix (chemical analysis) , bounded function , materials science , mathematical analysis , geotechnical engineering , geology , physics , chemistry , composite material , membrane , biochemistry
This paper presents a model describing the flow of a slightly compressible fluid through a multiple‐porosity, multiple‐permeability medium. The model considers flow within each porous system and the cross flow between any two different porous systems using a matrix of cross‐flow coefficients. An exact solution for a bounded, closed cylindrical reservoir with a concentric well producing at a constant rate is obtained rigorously. Moreover, the solution is expressed in terms of Bessel functions, so there are no particular difficulties in computing the solution numerically. The key to the method of solution is an orthogonal matrix transformation that makes the n ‐coupled governing equations uncoupled.