Multiphase flow in deforming porous media and finite element solutions

Abstract A numerical model to simulate the behaviour of porous media interacting with the flow of multiphase immiscible porous fluids is presented. The governing equations are derived in the light of the generalized Biot theory and a general formulation for effective stress is established. Two special cases are discussed in detail. The numerical modelling of porous media interacting with two immiscible porous fluids is discussed in more detail. The displacement of the solid, the pressure and saturation of the wetting fluid are taken as primary unknowns of the model. A generalized Galerkin procedure is devised to establish the coupled finite element equation set with u-p-S form. Unconditionally stable direct and staggered solution procedures are used for the time domain numerical solution. Examples are presented to illustrate the performance and capability of the approach.

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