Three-Phase Reservoir Simulation

Abstract

A mathematical model and associated computer program simulate three immiscible phases in two-dimensional geometry. The system, designed for heterogeneous reservoirs producing by any combination of gas and water drive, allows a comparison of alternative producing schemes. Introduction 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 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 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 phases in two-dimensional geometry. Several authors have discussed multidimensional reservoir simulation of two phases. Gottfried et al. presented an analysis of three-phase simulation in one dimension. Fagin and Stewart and Garrett 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 permeability and gas solubility. Within the two-dimensional restriction, the reservoir considered may be completely heterogeneous and anisotropic. JPT P. 211

Experimental validation of the theory of extending two‐phase saturation‐pressure relations to three‐fluid phase systems for monotonic drainage paths

“…Thus air-water capillary pressures are presumed to have no physical relevance as long as a discrete oil phase exists. Although (1} and (2) represent the most common method of depicting three-phase air-NAPL-water S-P relations [e.g., Sh•/.fietd, 1969; Kazemi et al, 1978;Coats, 1980;Aziz and Senari, 1979], other formulations have been suggested [e.g., Abriola, 1984;Peery and Herron, 1969;Shutlet, 1969]. Very little experimental research, however, has been conducted to directly test the assumptions implied by (1) and (2).…”

Numerical investigation of the problem of nonlinear three-phase filtration

“…And this, in turn, leads to the need to develop a numerical method for solving three-phase filtration problems described by a system of nonlinear partial differential equations. To study this process, numerical methods are mainly used [4,5].…”

“…In the works [6,7], the Buckley -Leverett model is used, and in [4] the effects of capillary forces are also calculated. And for the numerical solution of the problems obtained, the idea of the method is used [8].…”

“…And for the numerical solution of the problems obtained, the idea of the method is used [8]. However, this method does not take into account the characteristics of multiphase filtration, and in some cases gives qualitatively and quantitatively incorrect results [4].…”

“…Develop an algorithm for the difference-iterative method in moving grids. 4. On the basis of numerical experiments, discuss the issues of computational implementation of the proposed method and give practical recommendations for its application.…”