A Computer Simulation Of Gravity Drainage In Oil Reservoirs

Abstract

Publication Rights Reserved This paper is to be presented at the 39th Annual Fall Meeting to be held in Houston, Tex., on Oct. 11–14, 1964, and is considered property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Engineers or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in JOURNAL OF PETROLEUM TECHNOLOGY or SOCIETY OF PETROLEUM ENGINEERS JOURNAL is granted on request, providing proper credit is given that publication and the original presentation of the paper. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper describes a comprehensive method for simulating on a computer the physical behavior of a gravity drainage reservoir during the production of oil and gas. A mathematical model of such an oil reservoir is constructed. It accounts for variations in sand thickness, well density, permeability, gas-cap size, production rate, fluid characteristics, dip angle and reservoir size and shape. Computation discloses pressure, production and fluid saturations as functions of time. Inherent in the model is the need for counterflow relative-permeability data. A laboratory investigation of this subject on equipment designed and built by the writer is underway at Stanford U. As several years will be required to collect needed data., the accepted practice of assuming relative permeabilities to be independent of the directions of flow of the coexisting fluids is adopted. The principal results from the model show in a quantitative manner how oil recovery increases with increasing dip angle, is comparatively insensitive to gas-cap size and how it decreases with increasing oil production rate. Introduction The main objective of this paper is to describe the development of a computer simulation model of a gravity drainage reservoir and to show typical examples of its application. Information generated with the model includes predictions of reservoir pressure distributions, fluid saturation distributions and oil production rates. This information could form the basis for economic studies in which gravity drainage performance could be compared to other methods of reservoir operation. A gravity drainage reservoir is defined in this paper as an inclined oil reservoir in-which the difference in density between the oil and gas phases creates a significant driving force. Under these conditions, the gaseous phase would tend to migrate upstructure and the oil phase downstructure. The resultant effect could be segregated counterflow of the two phases. It is the purpose of this model to predict the areas and subsequent volumes of counterflow and the effect it has on the performance of the reservoir under study. The fundamental equations governing the two-phase flow of oil and gas in reservoirs have been well established. However,, a numerical solution for a three-dimensional bounded region is not presently feasible because of the capacity limitations of even the largest electronic computers.