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E.A. Breitenbach

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Numerical Simulation Symposium, April 22–23, 1968

Paper Number: SPE-2019-MS

Abstract

Abstract This paper is on the MUFFS (internal program library name) computer program. It program library name) computer program. It also outlines potential applications in reservoir engineering. Actual uses range from small-scale studies of the basic fluid flow mechanics in particular circumstances to full-scale simulation particular circumstances to full-scale simulation of reservoir/aquifer systems. Potential applications in exploration, ground water, hydrology, and gas storage are also discussed. Emphasis is placed on the versatility of MUFFS in studying a wide range of problems involving immiscible flow of one, two, or three phases in one, two, or three dimensions. Gross phases in one, two, or three dimensions. Gross effects simulation of processes is also possible. The problem solution is conducted internally in terms of a system of finite difference equations based on fundamental fluid-flow concepts and on reservoir data and well data furnished by the user. However, mathematical solution results can be viewed in engineering-oriented formats in tables and figures. Some of the flexible input/output options of MUFFS are gained from auxiliary programs. Important among these is an economics program that may be used to analyze reservoir behavior predictions. The net result is an ability to make predictions. The net result is an ability to make combined engineering/economic forecasts of future reservoir performance. Introduction Petroleum reservoir engineering is a branch of applied science concerned with the quantity of fluid within rocks and the flow of such fluids through rocks. Reservoir engineering may be defined as the study of the microscopic and macroscopic behavior of multiphase fluid flow through porous systems (geometrically difficult to describe) and the application of the knowledge attained from such a study to the efficient operation of petroleum reservoirs. With modern developments in computing numerical analysis, the practical solution of a large class of multidimensional problems has been possible, and hence the introduction of the reservoir model, mathematical model, and the petroleum or natural gas reservoir simulator. petroleum or natural gas reservoir simulator. A simulation model may be either physical or mathematical, and may represent the behavior of laboratory experiments, individual wells, or complex reservoir-aquifer systems. The simulator enables the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. Historically, the prediction of the performance of a new reservoir was based on the performance of a new reservoir was based on the knowledge of the performance of a depleted or nearly depleted reservoir with similar properties.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Numerical Simulation Symposium, April 22–23, 1968

Paper Number: SPE-2020-MS

Abstract

American Institute of Mining, Metallurgical and Petroleum Engineers Inc. Abstract A fundamental flow equation can be derived for each of the oil, water, and gas phases by combining the law of conservation of mass, a law of force, and thermodynamic relationships that describe the pressure-volume-temperature behavior of the fluids. The law of conservation of mass states that the sum of mass flow into a cell equals the change of mass within a cell. The law of force describing flow through porousmedia is Darcy's law, which assumes that flow is within the laminar flow regime described by the law. The thermodynamic relationships used to describe the fluid behavior must (because of the lack of accurate analytical expressions) be those found experimentally in a "PVT" study. The first part of this report shows how these laws can be combined to give equations describing fluid flow through porous media. The next step in the development is the cabining of these equations with auxiliary equations so that the number of dependent variables is reduced. The result is an equation that can be assumed to be in terms of oil pressure only, so that it may be solved implicitly pressure only, so that it may be solved implicitly for pressures at the new time level. Separate from this pressure equation are the equations that are solved explicitly for saturations, using the newly computed pressures. Hence, there are three equations developed in final, finite difference form in this paper. 1) a pressure equation, 2) an oil saturation equation, pressure equation, 2) an oil saturation equation, and 3) a water saturation equation. The logic used in the computation of all pertinent terms is given in the final section pertinent terms is given in the final section of this report. Introduction The general aspects of numerical fluid flow simulation has been given elsewhere (1). The present paper gives the derivation of the fluid present paper gives the derivation of the fluid flow simulation equations. The numerical solution of these equations is given in (2). FUNDAMENTAL FLOW EQUATIONS Fig. 1 shows a differential element of porous media. Pounds of oil (w o) are flowing porous media. Pounds of oil (w o) are flowing into or out of two faces, with a well (w op)in the center of the elements. Weight rates of flow, rather than mass rates, are used here to simplify the final algebra; of course, this necessitates the assumption of constant acceleration of gravity. The rate of depletion (ROD) of oil from this element can then be defined as: ..........................................(1) where ROD is the rate of oil removal from the element in lb/day at reservoir conditions.