Summary
The unsteady flow of a compressible liquid in a porous medium can be described in terms of a non-linear partial differential equation for the liquid pressure or a linear differential equation for the density if gravitational effects are negligible. In gravitational flow fields the formulation yields non-linear equations for both density and pressure. A transformation is given which shows that in the absence of gravitational effects, the solution of the non-linear boundary value problem in terms of the pressure involves no more labour than the solution of the linear problem in terms of the density, contrary to a misconception in the petroleum literature. Furthermore this transformation offers in addition the solution to a heretofore unsolved problem in gravity flow.
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References
Scheidegger, A. E., The Physics of Flow Through Porous Media, The MacMillan Company, New York, 1960.
Katz, D. L., et al, Handbook of Natural Gas Engineering, McGraw-Hill Book Company, New York, 1959.
Howard, D. S. and H. H. Rachford, Trans. AIME 207 (1956) 92.
Carslaw, H. S. and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, 1959.
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This research was supported in part by the Office of Naval Research under Contract Nonr-222(04).
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Selim, M.A., Chambré, P.L. On the unsteady flow of a compressible liquid through a porous medium. Appl. sci. Res. 10, 363 (1961). https://doi.org/10.1007/BF00411930
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DOI: https://doi.org/10.1007/BF00411930