Extending the Application of Electric Analogy in Oil-reservoir Studies

Abstract

Abstract Solution by electric analogy of performance problems of reservoirs containingoil and gas has heretofore depended upon a process of successive approximationsbased on? material-balance calculations, because of variation in fluidcompressibility. By the addition or subtraction of electric condenser capacity, the analogy network can be adjusted automatically for changing compressibilitydue to evolution of gas in the reservoir. The addition of a condenser isaccomplished by an electronic circuit, which is described; subtracting acondenser is done by merely opening the electrical circuit by means of arelay. Introduction V. Paschkis and H. D. Baker first developed in this country a method ofapplying the analogy of flow of electric current in noninductive circuits tosolution of heat-flow problems and suggested its application for certain otherproblems, such as flow of fluids or mass transfer and chemical diffusion.Necessary details for applying the analogy to flow of fluids in porous mediawere developed by W. A. Bruce; he classified the types of analysis andpredictions that can be made by the analogy in class I, when the reservoircontains oil but no gas for the period under consideration; in Class 2, whenboth oil and gas exist in the free state in the reservoir sometime during theperiod under consideration.Duplication of bottom-hole pressure history andpredictions for class I reservoirs can be obtained directly by electricanalogy. Until now, the solution of problems pertaining to reservoirs in class2 was obtained by successive approximations along with material-balancecalculations. The object of this paper is to present a method for simplifyingthe application of electric analogy to class 2 reservoirs, resulting in asolution of these problems as direct as is possible for class I reservoirs.This is accomplished by an electronic control circuit, which adjusts theanalogy network for changing compressibilities of fluids contained in thereservoirs. Analogy Network In electrical phenomena the analogy to two-dimensional fluid flow in a porousmedia is that of current flow through an ideal conducting sheet. This sheet, perfectly insulated on both sides, has resistance and capacitance uniformlydistributed throughout its area but is of negligible inductance. The need forhaving the surface boundaries perfectly insulated is that good correspondencemay be had with a permeable fluid-conducting stratum bounded above and below byimpermeable media. In actual application the ideal conducting sheet, which hasdistributed parameters, is replaced by a network having lumped values ofresistance and capacitance--the resistances are series elements and thecapacitances are shunt elements. T.P. 2125