The Effect of Differential Depletion on Recovery by Solution-Gas Drive
Authors: Thurber Stanley S. , Pirson Sylvain J. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
Differential depletion is the term applied to that phenomenon in solution-gas drive reservoirs in which large pressure and saturation gradients develop as a result of high production rates, high oil viscosities, or low formation permeabilities. This paper describes an investigation to ascertain the degree to which variations in the initial production rate and in reservoir fluid properties cause differential depletion to occur in a low permeability (10 md) reservoir, and the resultant effect on recovery at a reasonable economic abandonment rate.
The results of the rate-effect investigation indicate that for the type of reservoir modeled, i.e., thin, linear, horizontal, homogeneous and isotropic, the recovery at economic abandonment is almost completely independent of initial production rate. This fact is true even though the rates investigated varied three hundred fold and a large amount of differential depletion was induced at the higher rates. However, the producing gas/oil ratio behavior and time to abandonment are very definitely rate sensitive. From an economic rate of return standpoint, it appears that an operator can produce oil at a high rate, and thus achieve a greater present worth, while losing very little of the total recoverable oil.
The results of the variable fluid property investigation indicate that as the bubble point pressure and the solution-gas increase at constant API gravity, the amount of differential depletion decreases. This decrease is accompanied by an increase in the amount of total recoverable oil that had been recovered at economic abandonment. For the case of varying API gravity at constant bubble point solution-gas, the amount of differential depletion decreased slightly as the API gravity increased. This decrease in differential depletion was accompanied by the same trend as above.

Introduction
The mathematical prediction of solution-gas drive performance has been attempted for more than three decades. Muskat and Meres were some of the first to formulate the theory of two-phase fluid flow. Although their equations are referred to as exact, rather gross assumptions regarding such things as relative permeability and phase behavior are made.