Reservoir Engineering - General - Three-Phase Reservoir Simulation

Mathematical simulation of reservoir behavior may be used to help understand reservoir processes and to predict reservoir behavior, thereby leading to the most economically desirable form of exploitation. In addition, simulation can be used as a tool for reservoir description to learn more about the physical nature of the reservoir and the mode of primary recovery. This use is essential in most reservoir studies and represents one of the more significant applications of simulation. Prediction of reservoir behavior provides information concerning displacement efficiency, optimum well locations, and the comparison of alternative producing processes. Since oil, water and gas all commonly occur in many reservoirs, a simulation that takes into account the simultaneous flow of three immiscible phases is a prerequisite for obtaining such information. Furthermore, a simulation that describes this flow in two dimensions provides the capability of evaluating combination gas- and water-drive reservoirs with either an areal or a cross-sectional description. Many reservoir problems require such a simulation. The objective of the research described here was to develop a mathematical model and associated computer program for accurate, efficient, and economical prediction of the reservoir flow of three phases in two-dimensional geometry. Several authors have discussed multidimensional reservoir simulation of two phases.l-3 Gottfried et al.' presented an analy- sis of three-phase simulation in one dimension. Fagin and Stewart" and Garrett6 have discussed the simulation of three-phase flow in two dimensions, but their solution techniques were different from the method discussed in this paper. In particular, previous models and computer programs have usually involved either fewer capabilities or inefficient and less rigorous descriptions resulting in limited applicability. In the following sections, we present a description of the model, an evaluation of the method, and the application to reservoir problems. Additional and supporting material is presented in the Appendix. The Three-Phase Model General Description The three-phase model consists of the mathematical description of the flow of oil, water and gas in a reservoir. Conceptually this description considers flow in all three space dimensions, but in the subject simulator it is assumed that no flow occurs in the third dimension. The model includes the effects on reservoir behavior of fluid and rock compressibility, viscosity, gravity, capillary pressure, relative permeability and gas solubility. Within the two-dimensional restriction, the reservoir considered may be completely heterogeneous and anisotropic. The differential equations governing multiphase, multidimensional flow in a reservoir are too complex to be solved analytically, so they are approximated by a system of finite difference equations and solved