Transient Pressure Distributions in Fluid Displacement Programs

Abstract

Abstract The use of a new laboratory model for studying transient fluid flow problems, is described. The theory of the model is based on the analogy between the equations which describe the flow of compressible fluids in porous media and the conduction of heat in solids. The "thermal model" is used to study the transient pressure distributions during fluid displacement in five standard well patterns. The studies indicate quantitatively how the pressures change with time at any point in the reservoir. It was found that, in general, the equipressure contours are more radial about the wells early in the program than after steady-state conditions are established. In addition two studies of fractured five-spot patterns are presented to illustrate the applicability of the model for a wide range of reservoir conditions. Introduction In reviewing the oil recovery techniques involving fluid displacement it was found that a very considerable quantity, if not all of the fluid within the pattern, may be displaced during a time-dependent or transient period rather than the usually applied steady-state conditions. Since the oil is displaced during a transient period, it was believed desirable to study the nature of the transients for several of the commonly used fluid displacement patterns. A literature review indicated fairly complete studies of the streamlines and isopotentials for steady-state, yet few data were available on the transient displacement process. Several simulated steady-state multiwell displacement programs were carefully mapped by Foster and Lodge on an electrical conducting sheet as early as 1875, but the more recent work of Muskat provides the best source for steady-state phenomena having direct petroleum production applications. In order to study the transient phenomena a new laboratory model was developed which is based on the similarity of the equations that describe the flow of fluids and the conduction of heat. The equations describing heat flow were developed early in the nineteenth century. Rigorous solutions for most transient problems are in general complex and usually limited to fairly restricted boundary conditions. The thermal model may be used to obtain approximate solutions for many transient problems without some of the restrictions required for analytical solution.