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Zbl 0537.76062
Douglas, Jim jun.; Roberts, Jean E.
Numerical methods for a model for compressible miscible displacement in porous media. (English)
[J] Math. Comput. 41, 441-459 (1983). ISSN 0025-5718; ISSN 1088-6842/e

The authors derive a nonlinear parabolic system for single-phase, miscible displacement of one compressible fluid by another in a porous medium under the assumption that no volume change results from the mixing of the components and that a pressure-density relation exists for each component in a form that is independent of mixing implying that fluids are in the liquid state. They analyse two numerical schemes for approximating the solution of a two component system only for concentration of fluid and pressure using a parabolic Galerkin procedure for the concentration equation for both the schemes but a parabolic Galerkin procedure for the first scheme and a parabolic mixed finite element technique for the second numerical scheme for the pressure equation. \par It is claimed that the two procedures used for the two-component model can easily be generalized to treat an n-component model. The formulations and analysis are new and are of great interest to people working in 'numerical analysis' and 'petroleum engineering'. [This is an abridged version, the complete review is available on demand.]
[H.K.Verma]

MSC 2000:: *76S05 Flows in porous media
76T99 None of the above, but in this section
76M99 Basic methods in fluid mechanics
76N10 Compressible fluids, general

Keywords: mixing without volume change; nonlinear parabolic system; single-phase, miscible displacement; pressure-density relation; parabolic Galerkin procedure; concentration equation; parabolic mixed finite element technique; pressure equation; n-component model; petroleum engineering

Cited in: Zbl 0732.76081 Zbl 0661.76097

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