This paper describes an electrical model and its application to the analysis of four reservoirs in Saudi Arabia. The model has 2,501 mesh points and represents 35,000 sq miles of the Arab-D member. Details of modeling such as mesh size, control problems and standards of performance in matching reservoir history are discussed. The particular performance match achieved for the Arad-D member is presented. Details such as permeability barriers, aquifer depletion and interference between oil fields are given. The performance match realized in the Abqaiq pool is presented in detail. Introduction The resistor-capacitor network and associated control equipment described in this paper comprise an electrical analog of a reservoir system. Similar equipment has been used to study the transient response of reservoirs for many years. The unique feature of the model and application to be described is the extremely large size of the model and reservoir system, and the detail observed in simulating the reservoir with the model. The Arabian American Oil Co. first became interested in analog computers for simulation of oil reservoirs in 1949. Since that time, several models have been developed, each more elaborate and refined so that the reservoir system might be more closely simulated. The current model is the latest in a series designed, built and operated by the Field Research Laboratory of Socony Mobil Oil Co. in collaboration with Aramco. It has been and continues to be used to study the regional performance of the Arab-D member limestone reservoir. The Arab-D member is one of the Middle East's most prolific producing horizons. THE MODEL The theory of simulating a reservoir system with an electrical system has been presented in the literature. Therefore, this paper will not discuss the theoretical aspect of the problem except to point out the correspondence between the fluid system and electrical system, as shown in Table 1.In general, the complete model is made up of input devices, output devices, central control and a resistance- capacitance (RC) network. At times, the RC network alone is referred to as the "model". However, it should be evident from the text which meaning is attached to the word "model". A discussion of the equipment follows. THE RESISTANCE-CAPACITANCE NETWORK The RC network consists of 2,501 capacitance decades interconnected through 4,900 resistance decades. The components are arranged to form a rectangular network of 2,501 mesh points in a 41- X 61-mesh array. Imposing the mesh grid system on the continuous reservoir system divides the reservoir into discrete areal segments. These discrete segments may be of various sizes. More precisely, the mesh size need not be uniform throughout the model. The RC network is fabricated in two sections which are connected at the top, An inside view of the "tunnel" formed by the two sections is shown in Fig. 1. The height and width of the tunnel are shown in the figure. Numerals appear along the bottom and along the back opening of the tunnel. These numbers denote the x and y coordinate positions of mesh points. Fig. 2 presents a rear view of one-half the model. The length dimensions of the model, as well as a rear view of the capacitor decades, are shown in this figure. The control dials used in adjusting the resistance and capacitance values on the model can be seen in the enlarged portion of the model shown in Fig. 3.The electrical capacity at any mesh point can range from 0 to 1.0 microfarads set to the nearest tenth of a microfarad. The electric resistance connecting any two mesh points can range from 0 to 9,990,000 ohms set to the nearest 1,000 ohms. External capacitors may be added to any or all mesh points if the need arises. The values of electrical resistance and capacitance are adjusted manually by manipulating the two types of decade units. INPUT EQUIPMENT A considerable quantity of equipment is used to control the input to the RC network. TABLE 1 - CORRESPONDENCE BETWEEN FLUID AND ELECTRICAL SYSTEMS Fluid System Electrical System Item Units Item UnitsReservoir Pressure psi Voltage Volts Reservoir Production Reservoir B/D Current MicroamperesRate orInjectionRate Fluid Capacitance Reservoir bbl/psi Electrical MicrofaradsCapacitance Transmissibility, darcy-ft Electrical Mhos/cp Conductivity Real Time Months Model Time Seconds JPT P. 1275^
Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 132–138. Introduction In the past few years several articles and papers presenting results of solution gas-drive depletion calculations have appeared in the literature. Such calculations are of interest to the oil industry, for investment decisions must often be made before much is known about a reservoir. At other times, an estimate of the possible benefits to be realized from alternate production methods is desirable, and theoretical depletion calculations can serve as a floor or reference level from which to work. In any case, an estimate of ultimate oil recovery based upon engineering data is commonly required. An engineer confronted with the problem of obtaining, for a specific reservoir system, an estimate of ultimate oil recovery by solution gas-drive depletion usually will be forced to perform the calculations himself. This is despite the quantity of data in the literature. Rarely will either experience or the literature provide results from a reservoir system similar in all important respects to the one under consideration, and calculated results are not so plentiful that satisfactory interpolation procedures can be devised. Performing the calculations, however, is a tedious, time-consuming task unless an electronic computer is available, and, in practice, time and manpower are not always available for this purpose. A quick, simple, consistent method was needed for reducing the uncertainty in estimated oil recovery from solution gas-drive reservoirs when only minimum information about the reservoir system is available. Procedure Method of Calculation The usual requisite assumptions were made so that the material balance equation could be used to calculate data for the charts. The following assumptions were made:the reservoir is homogeneous and isotropic;oil recovery is due entirely to solution gas drive and neither a gas cap nor a water drive nor gravity drainage is present;the initial reservoir pressure is the bubble-point pressure of the reservoir fluid;initial total liquid saturation is 100 per cent of pore space;interstitial water saturation remains at the initial value as the reservoir pressure declines from the bubble-point pressure to atmospheric pressure;equilibrium gas saturation is 5 per cent of pore space; andoil and gas saturations are uniformly distributed throughout the reservoir at all times. There are no saturation gradients due to a wellbore, nor is the geometry of the reservoir system considered.
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