The Prediction of Oil Recovery by Gravity Drainage
Authors: Dykstra Herman 
Published: December 2007

An approximate theory of free-fall gravity-drainage recovery is expanded to account for residual oil saturation. The recovery equation is derived and seven comparisons are made of observed gravity-drainage recovery with calculated recovery. Examples show how the theory can be applied.

Introduction
The gravity-drainage mechanism is one of the most efficient ways of producing an oil field. Unfortunately, most oil fields cannot be produced economically under free-fall gravity alone because the effective oil permeability is too low, the oil viscosity is too high, or the dip of the formation is too small. Nevertheless, many reservoirs take advantage of the gravity component, especially under pressure maintenance in areas where gas is available, such as overseas, or where inert gas can be used. The most ideal system would be one where oil is produced only under free-fall gravity drainage, giving the highest possible recovery at the most efficient rate. However, because a producing mechanism must be justified economically as opposed to another producing mechanism must be justified economically as opposed to another producing mechanism, an engineer must calculate gravity-drainage recovery producing mechanism, an engineer must calculate gravity-drainage recovery as a function of time.An approximate theory of strict gravity drainage has been presented by Cardwell and Parsons. They ignored capillary pressure terms and show how gravity-drainage equations can be solved. They give only one comparison of recovery calculated from theory with recovery obtained experimentally from a draining column.In addition to that study, many other papers have been published describing how to calculate reservoir performance where gravity effects influence the production mechanism. An early investigation describing the potentially high recovery with gravity drainage is Katz's discussion of potentially high recovery with gravity drainage is Katz's discussion of Oklahoma City Wilcox sand. Katz also presented data on the low (6 to 8 percent) residual oil saturations that could be obtained from a completely percent) residual oil saturations that could be obtained from a completely drained portion of the Wilcox sand. Lewis enlarged upon the gravity- drainage mechanism for oil recovery and gave four examples of gravity- drainage fields. Beginning in 1949, more studies discussed methods of calculating the effect of gravity component on oil recovery during depletion or pressure maintenance, and case histories of fields where gravity was an important factor in production. All the papers describing a calculating procedure used the Buckley-Leverett method. These studies also used historical rates of production or a pre-selected rate of production to get the advance of gas-oil front and to calculate recovery. More recently, high-speed computers were used to solve mathematical equations of various reservoir simulators. These reservoir simulators still required that rates or drawdown be pre-selected as a boundary condition to the solutions of mathematical equations. Thus, these simulators could not be used to determine the free-fall, gravity-drainage rate of production.One study attempted to determine production rate based on the location of the gas-oil front below a stated level. Essley et al. determined an approximate producing rate by arbitrarily assuming a maximum capacity for each well remaining on production below a given subsea level and determining the total production rate from that. They did not state how the arbitrary assumption was made, nor how this rate was related to a true gravity-drainage rate.
JPT
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