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An existence result for a coupled system modeling a fully equivalent global pressure formulation for immiscible compressible two-phase flow in porous media. (English) Zbl 1271.76288

Summary: We consider a new model describing an immiscible, compressible two-phase flow, such as water-gas, through heterogeneous porous media. The main feature of this model is the introduction of a new global pressure and the full equivalence to the original equations. The resulting equations are written in a fractional formulation which leads to a coupled system of a nonlinear parabolic equation (the global pressure equation) and a nonlinear diffusion-convection one (the saturation equation). Under some realistic assumptions on the data, we show an existence result with the help of appropriate regularizations and a time discretization. We use suitable test functions to get a priori estimates. In order to pass to the limit in nonlinear terms, we also obtain compactness results which are nontrivial due to the degeneracy of the system.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76T10 Liquid-gas two-phase flows, bubbly flows
76S05 Flows in porous media; filtration; seepage
35Q35 PDEs in connection with fluid mechanics
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