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This paper concerns the discretization of multiphase Darcy flows, in the case of
heterogeneous anisotropic porous media and general 3D meshes used in practice to represent
reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred
approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient
scheme (VAG), already introduced for single phase diffusive problems in [9], to multiphase
Darcy flows....
In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy’s law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....
In this paper, we consider a 2D mathematical modelling of the vertical
compaction effect in a water saturated sedimentary basin. This model is
described by the usual conservation laws, Darcy's law, the porosity as a
function of the vertical component of the effective stress and the
Kozeny-Carman tensor, taking into account fracturation effects. This model
leads to study the time discretization of a nonlinear system of
partial differential equations. The existence is obtained by a fixed-point
argument....
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