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.