The Use of High-Speed Computers for Predicting Flood-Out Patterns

Abstract

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 139–145. Abstract Two-dimensional analyses offer considerable promise in providing the basic information required to effect in ore precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-speed digital computer. The general approach is to (1) develop a representative numerical model of the reservoir and(2)employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially(1)calculating the pressure distribution in the reservoir and (2)tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restraints and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the high-speed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. Introduction One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs.