Numerical simulation of two-phase fluid flow

Abstract

We simulate two-phase fluid flow using a stress–strain relation based on Biot’s theory of poroelasticity for partial saturation combined with the mass conservation equations. To uncouple flow and elastic strain, we use a correction to the stiffness of the medium under conditions of uniaxial strain. The pressure and saturation differential equations are then solved with an explicit time stepping scheme and the Fourier pseudospectral method to compute the spatial derivatives. We assume an initial pressure state and at each time step compute the wetting- and non wetting-fluid pressures at a given saturation. Then, we solve Richards’s equation for the non wetting-fluid saturation and proceed to the next time step with the updated saturations values. The pressure and saturation equations are first solved separately and the results compared to known analytical solutions showing the accuracy of the algorithm. Then, the coupled system is solved. In all the cases, the non-wetting fluid is injected at a given point in space as a boundary condition and capillarity effects are taken into account. The examples consider oil injection in a water-saturated porous medium.