Numerical simulation of two-phase oil and water flow

methods. However, there exist numerous articles that attempt to develop and present analytical solutions in the literature for the two-phase flow of oil and water under some restricted assumptions (e.g., homogenous reservoir). Analytical solutions may be easy and fast to apply, but may not well represent the oil and water flow because of their restrictive assumptions. On the other hand, numerical methods are more appealing to solve the oil and water phase flow for more general cases. Due to its generality, in this study, we consider numerical based methods (i.e., finite difference methods) to solve the diffusivity equation for oil-water flow and investigate the pressure and water saturation behaviors of a vertical well and reservoir for the cases where analytical solutions are not available. A general discretized equationis derived for simulating two-phase water and oil flow in three-dimensional (3-D) r-θ-z cylindrical coordinate system using the finite difference method. Then, this general difference equation is solved by considering two different methods. The first method is based on a fully implicit solution of both pressure and saturation (FIMPS) using the Newton method, and the other method is based on a fully implicity solution of pressure and explicit solution of saturation, which is known as the IMPES method. Derivations for both methods are given in this study. The solutions generated from the simulators developed during the course of this work were compared and validated with the solutions generated from a commericial software CMG - IMEX.Moreover, we also validate the simulator for some benchamark cases taken from the papers presented in the literature. Finally, some well-test applications are run with the simulator and pressure differences and their derivatives (diagnostic plots) are analyzed. This process is achieved with the commercial well-test software ECRIN. Behaviour and effects of mechanical skin on diagnostic plots for injection and fall-off tests are discussed.