Simultaneous Nonsteady Flow of Oil And Water Through Linear Porous Media

Abstract

Abstract This paper is concerned with the behaviour of a linear oil reservoir which is produced at constant terminal pressure and is fed b:r a finite aquifer with a sealed outer boundary. The study is confined to the case where the water saturation in the oil reservoir exceeds the so-called irreducible minimum. Specifically, this work presents a mathematical formulation of the system. The resulting partial differential equations express the pressure distribution in both zones, the wat.er saturation in the reservoir the oil and water flow rates, and the cumulative productions as functions of time. Although it appears that this set of equations can be solved only by numerical means, an approximate analytical solution, valid for large values of time is presented. Introduction SINCE AN OIL RESERVOIR call be exploited but once, and the possible exploitation schemes are many, it is necessary to predict the behaviour of the reservoir for each scheme, compare results and choose the scheme which is most suitable according to selected criteria. In order that this be done, mathematical formulation is required for each reservoir and scheme combination. The object of this study is to examine H linear oil reservoir which is fed by a finite aquifer with a sealed outer boundary. Given the situation in which the water saturation in the reservoir exceeds the critical and the reservoir is operated at some constant pressure at the producing face, the question is can the following be expressed as function of time?water saturation in the reservoirpressure distribution in the reservoirpressure distribution in the aquiferoil production ratewater prodLlction ratecumulative oil productioncumulative water production. If such functions can be formulated and the resulting equations solved, the information obtained may be used to predict the behaviour of such linear systems either in the field or laboratory. Problem Formulation If the cross-sectional area of the reservoir and aquifer are constant and equal, the system may he described pictorially by means of a plan view as shown in Figure 1, where zone I represents the reservoir, zone II represents the aquifer and I and L represent their respective lengths. For the case where the water saturation in the reservoir is greater than the critical, the pressure in both zones is initially equal and constant al some value, say p, and production is initiated and continued by dropping the pressure at the out flow face to some (Equation Available In Full Paper) fixed value, say p one may describe the situation mathematically by means of the following initial and boundary conditions. (Equation Available In Full Paper) In addition, zones I and II are coupled by virtue of the fact that the water flux must be continuous across the reservoir-aquifer boundary.