Quick Determination of Pressures in Well-Spacing Patterns

Abstract

American Institute of Mining, Metallurgical and Petroleum Engineers Inc. Abstract A quick method to determine the pressure distribution between wells for various well patterns is presented. In the determinations, patterns is presented. In the determinations, the effect of well diameter may be included. Comparison of the results with potentiometric models presented in the literature showed excellent agreement. By the method presented, it would be easy to obtain quickly the pressure distribution in an entire reservoir. The computer program uses the flowing well pressures at bottom of wells to calculate the pressures at bottom of wells to calculate the pressure distribution throughout the entire pressure distribution throughout the entire reservoir. The program is relatively short and uses the grid method for solution. It uses the point successive over relaxation technique point successive over relaxation technique [Liebmann accelerator] and has an open subroutine to increase the size of the accelerator if the progress of the computation so requires. Use of the program saves construction of a potentiometric model. The printed pressure potentiometric model. The printed pressure distribution can be obtained quickly. Another advantage is that the effect of any change in the location of wells or pressures about the wells can be ascertained quickly—average computer time was less than 2 minutes. Introduction The literature mentions that a series of steady-state flow equations may be used to mathematically represent unsteady-state flow after the initial withdraw of a small quantity of fluid. As a result, pattern efficiency in reservoirs can be investigated reasonably accurately by assuming steady-state flow during the period of interest. The advantage of steady-state flow is the reduction in time needed to obtain a solution. The results presented in this report are steady-state presented in this report are steady-state solutions except in one instance where an unsteady-state calculation for a slightly compressible liquid was used to obtain well pressures for subsequent steady-state solution of the pressure distribution throughout the reservoir. pressure distribution throughout the reservoir. Streamlines may be drawn on plots of the pressure distributions obtained using this pressure distributions obtained using this method. The shape factors and areas of the cells formed by the resulting flow nets may be calculated and the resulting data used in the prediction of fluid injection performance. However, obtaining the streamlines performance. However, obtaining the streamlines and shape factors are not included in this paper. paper. THEORY The solution by finite differences [numerical methods] of the Laplace equation to determine the potential distribution in two dimensions has been reported in the literature.