Some Model Studies Of Bottom Water Driven Reservoirs
Authors: Stephens A.C. , Moore T.F. , Caudle B.H. 
Published: December 2007

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This paper was presented at the University of Oklahoma-SPE Production Research Symposium in Norman, Okla., April 29–30, 1963, and is considered the property of the Society of Petroleum Engineers. Permission to published is hereby restricted to an abstract of not more than 300 words, with no Illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Technology or the Executive Secretary. Such abstract should contain conspicuous acknowledgement 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 providing proper credit is given that publication and the original presentation of the paper.
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Abstract
Previous theoretical and model studies of bottom water driven reservoirs have assumed that the isopotential surface was located at the initial water-oil contact. This paper describes model studies in which the isopotential surface is far removed [into the aquifer] from the initial water-oil contact. The studies indicate that the production performance is much poorer when the isopotential is at the initial water-oil contact than when it is far removed. We believe that most bottom water driven reservoirs are typified by the latter condition.

Introduction
The energy to produce oil from bottom water driven reservoirs is supplied by the upward movement of water from a thick, underlying aquifer. An early theoretical analysis of the performance of such reservoirs was reported by Muskat. For mathematical convenience he assumed that the fluid mobilities and densities in his system were equal and that an isopotential surface existed along the original water-oil contact throughout the producing life of the reservoir. This analysis was extended later by Hutchinson and Kemp to include the effects of gravitational forces and mobility ratios different from unity. Recently Henley, et al, presented results of model studies of bottom water driven reservoirs. As in the mathematical analyses, a constant pressure was maintained at the initial water-oil contact; and, as would be expected, their results agree with the Muskat and Hutchinson-Kemp data.
In a written discussion of Muskat's study, Lincoln Elkins pointed out that it would be more realistic to place the isopotential surface far below the original water-oil contact. Muskat estimated the effect and in his reply to Elkins stated that several times as much oil might be recovered before water breakthrough if the isopotential surface were indeed located far from the initial water-oil contact rather than at the water-oil contact.
The error caused by the assumption of an isopotential surface of the original water-oil contact becomes more evident as the penetration of the producing well increases. At 100 per cent well penetration the pressure gradients immediately beneath the well increase without limit. As a consequence of this "short circuit" the well produces essentially 100 per cent water from the start of production.