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

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) 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 (I) calculating the pres-' sure 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 restrains 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 highspeed 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. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-