We consider in this work, the extension to two-phase Darcy flows of the discontinuous pressure models in which the (d-1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix.The model accounts accurately for gravity effects inside the fractures, for discontinuous capillary pressure curves at the matrix fracture (mf) interfaces and for both drains and barriers. This can be achieved thanks to interfacial pressure and saturation unknowns accounting for the nonlinear two-phase Darcy flux conservation equations at mf interfaces. The first objective of this talk is to compare this model with more usual hybrid-dimensional approaches based on the elimination of the interfacial phase pressures using the linear single phase Darcy flux conservation equation at the mf interfaces for each phase or alternatively the pressure continuity assumption in the case of fractures acting as drains. Our second objective is to discuss discretization and solution strategies for this type of models.
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