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Perturbation theory for a displacement front passing discontinuities in capillary pressure and permeability in a porous medium
Author(s) -
Shaw D. C.,
Dawe R. A.
Publication year - 1985
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300010895
Subject(s) - classification of discontinuities , capillary action , porous medium , capillary pressure , mechanics , discontinuity (linguistics) , mathematics , displacement (psychology) , geometry , mathematical analysis , front (military) , computation , porosity , chemistry , physics , thermodynamics , psychology , organic chemistry , algorithm , meteorology , psychotherapist
Abstract When a displacement front meets a heterogeneity in a porous medium, its shape will be altered. The amount of distortion depends on the size and shape of the heterogeneity, the amount of variation of the heterogeneous properties, and the mobility ratio between the displaced and displacing fluids. The solution for a circular permeability discontinuity is known when the capillary pressure is uniform and the mobility ratio M is unity [4]. Here, we extend the theory to the case where there is a small change ε in capillary pressure as well as a nearly unit mobility ratio M = 1 + εγ. Corrections can then be found, in closed form, to first order in ε, to the shape of the front and the pressure field. Computations using these expressions are simpler than the full free‐boundary problem, and some analytical estimates are possible in further limits. Finally, the theory is extended to the case of a front passing a number of such heterogeneous patches which are widely spaced.