Extensions of the Muskat Depletion Performance Equation

Abstract

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 285–291. Abstract Muskat's depletion performance equation is here derived considering the expansion behavior of the reservoir hydrocarbon system and a simple fractional-flow equation. This method of derivation leads logically to the two extensions that follow. The first of these is concerned with gravity segregation in a depletion-drive reservoir. The second is concerned with including an empirically determined term for water influx in the performance equation. The more general equation for gravity segregation when there is a primary gas cap and empirically-determined water influx is stated for completeness. These equations have been found useful in reservoir performance calculations in Eastern Venezuela. A discussion on the methods of solving these equations follows, and considers firstly the effect of taking finite intervals in the numerical integration, and secondly, methods of incorporating the time functions involved in segregation in with the expansion behavior. The paper concludes with a brief general discussion on further extensions to the depletion performance equation. Introduction The two fundamental sources of energy by which oil is produced from a reservoir result from pressure depletion inside the boundaries of the reservoir and fluid encroachment across the boundaries of the reservoir. The wells in either case form low pressure outlets through which oil and gas may be produced by the expansive force of the reservoir fluids and associated encroaching fluids. When the reservoir pressure is higher than the bubble-point pressure of the oil, so that there is no free gas in the reservoir, these expansive forces are the only ones available for the production of oil. However, when the reservoir pressure is less than the bubble-point pressure of the oil, free gas is vaporized as the pressure falls. With both oil and free-gas phases present, the additional forces of gravity and capillarity may operate on the gas-oil system, as they have previously operated on the oil-interstitial water system. Gravity tends to segregate the free gas from the oil due to their density difference. Capillarity opposes and eventually balances gravity as the more extreme free gas and oil saturations are reached, preventing the independent movement of free gas until it is above a certain saturation, and the independent movement of oil when it is below a certain saturation.