Application of Finite Difference Methods to Analogue Computational Techniques

Abstract

Joint Rocky Mountain Meeting of the Society of Petroleum Engineers of AIME, 23–24 May, Billings, Montana Abstract The intent of this paper is two-fold - [1] to clarify the interpretation of analogue studies and [2] to stimulate interest in the use of finite difference approximations. Analogue methods, as applied to date to the problems of reservoir engineering, are reviewed briefly. Methods of interpreting results from detailed, two-dimensional analogue studies in light of finite difference methods are also discussed. While the treatment in the paper is confined largely to undersaturated reservoir systems, the concepts of finite difference approximations apply equally well to the complex problems of gas evolution and relative permeability. In fact, the finite difference methods are among the very few capable of resolving the complex non-linear differential equations of interest to the reservoir engineer. Introduction Subsequent to Bruce's introduction of the electric analyzer many and varied application have been made of electric analogue methods practical reservoir behavior analyses. These analogue methods were designed primarily for gross reservoir behavior analyses, and for this purpose, the so called "single condenser", "multiple condenser" and "pool unit" studies have a great deal of merit. The author has been concerned with problems associated with detailed [" Detailed" is used here and throughout the presentation to designate a minute representation of the reservoir and its behavior, and implies an abundance of detail rather than exhaustiveness in detail.] analyses of pressure distribution and fluid movements in under-saturated reservoir systems. Such problems have stimulated considerable interest in detailed analogue studies and the application of finite difference methods to them. This paper presents a method of extending the usefulness of analogue methods and introduces the concepts of finite difference approximations. However, the methods and concepts presented herein are, for the most part, extensions of previously published methods.