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Une étude théorique sur la modélisation de G. Chavent des techniques d’exploitation secondaire des gisements pétrolifères. (French) Zbl 0545.76116

Summary: The aim of this paper is the theoretical study of water-oil displacements in a 2-D or 3-D porous field, with reference to G. Chavent’s modelization [e.g.: Lect. Notes Math. 503, 258-270 (1976; Zbl 0346.76071)]. This mathematical model, which takes into account the ”well- effect” on the outflow boundary, involves a degenerated nonlinear diffusion-convection equation. The degenerate case of immiscible displacements is approached through a non-degenerate problem for which the existence of a unique strong solution is proved. The study of the said problem is shown to prove the existence of a solution for the degenerated problem and some of its properties: decrease, asymptotic behaviour, dependence on the initial data, uniqueness in some particular cases.

MSC:

76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage

Citations:

Zbl 0346.76071
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