The Performance of Bottom Water-drive Reservoirs
Authors: Muskat Morris 
Published: June 2014

Abstract
A theory has been developed describing the behavior of wells and reservoirsproducing by the action of bottom Water drives. It is assumed that thepressures are maintained above the bubble point, and that the permeability toviscosity ratio of the water in the flooded zone is the same as for the oil inthe oil saturated pay. Accordingly, the treatment is based on the homogeneousfluid potential theory. The effect of the difference in density between the oiland water is neglected. After deriving the proper potential distributions, thenature of the rise of the water-oil interface below the producing wells iscalculated. The primary clean-oil-production phase is expressed in terms of thedisplacement efficiency, defined as the fraction of the pay flooded out by therising water table at the lime of first water entry. The variation of thisdisplacement efficiency is calculated as a function of the well spacing, paythickness, the ratio of the horizontal to vertical permeability, and the wellpenetration. The important parameter other than the well penetration is foundto be the ratio of the well separation to the thickness of the oil paymultiplied by th~ square root of the ratio of vertical to horizontalpermeability. It was found that the displacement efficiency continuallydecreases as this parameter increases. and' for values of the latter &gt; 3.5, the efficiency varies inversely as the square of the parameter. It alsoincreases with decreasing well penetration. Perhaps the most striking result ofthis phase of the analysis is the conclusion that in order to explain the delayin entry of water in wells producing by bottom water drives for periods longerthan a few days normal production, with drawdowns large compared with thedifferential density head between the oil and water, it is necessary to assumethat the vertical permeability is a very low fraction of the horizontalpermeability.
An analysis is also given of the production history after the water has brokenthrough, on the assumption that the production mechanism and details of theflow distribution continue to be the same as during the phase of clean-oilproduction. As is to be expected, it is found that the water cut will increaseat an accelerated rate as production proceeds. However, the initial differencesbetween systems of different well penetrations or well spacings with respect tothe total clean-oil production gradually decrease in terms of the variation ofthe water-oil ratio with cumulative production. In particular; by the time thewater-oil ratio has reached values of the order of 5 or greater the cumulativerecoveries will generally differ much less among various producing systems thantheir corresponding clean-oil recoveries.

Introduction
On the basis bf elementary geological principles one may classify effectivewater drive fields in two groups. In the first, the entry of water into theoil-producing formation may be characterized as an edge-water encroachment.This term is used to suggest that the motion of the water proceeds largely in adirection parallel to the planes of stratification. This type of waterintrusion occurs usually in thin producing zones and in strata lying alonestructural flanks of appreciable dip.
T.P. 2060