A Mathematical Model of Thermal Oil Recovery in Linear Systems

Abstract

Gottfried, B.S., Junior Member AIME, Gulf Research and Development Co., Pittsburgh, Pa. Introduction Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are characterized by the simultaneous flow of two or three fluid phases in a variable-temperature field, accompanied by possible chemical reaction or phase-change effects. Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the Process, such as heat transfer, heat transfer with phase change, heat transfer with chemical reaction, or the hydrodynamics of three-phase flow. A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. SPEJ P. 196ˆ