This work is a continuation of Kou and Sun  where we present an efficient improvement on the IMplicit Pressure Explicit Saturation (IMPES) method for two-phase immiscible fluid flow in porous media with different capillarity pressures. In the previous work, we present an implicit treatment of capillary pressure appearing in the pressure equation. A linear approximation of capillary function is used to couple the implicit saturation equation into the pressure equation that is solved implicitly. In this paper, we present an iterative version of this method. It is well-known that the fully implicit scheme has unconditional stability. The new method can be used for solving the coupled system of nonlinear equations arisen after the fully implicit scheme. We follow the idea of the previous work, and use the linear approximation of capillary function at the current iteration. This is different from iterative IMPES that computes capillary pressure by the saturations at the previous iteration. From this approximation, we couple the saturation equation into the pressure equation, and establish the coupling relation between the pressure and saturation. We employ the relaxation technique to control the convergence of the new method, and we give a choice of relaxation factor. The convergence theorem of our method is established under the natural conditions. Numerical examples are provided to demonstrate the performance of our approach, and the results show that our method is efficient and stable.
The authors cheerfully appreciate the generous support of the university research fund to the Computational Transport Phenomena Laboratory at KAUST.