Computation of a Linear Flood by the Stabilized Zone Method

Introduction The purpose of this paper is to present the results obtained by solving thefractional flow and frontal advance equations to obtain oil recovery at waterbreakthrough as a function of the length of the system being flooded, thelinear velocity of injection and the displacing phase viscosity. The method ofsolution makes use of the stabilized zone concept first presented byTerwilliger, et al. when calculating saturation distributions in a gravitydrainage system. In order to check the calculated results, the equations andmethod of solution were applied to the system on which Rapoport and Leasreported experimental data. Method of Solution The solution of the fractional flow equation (Equation 1) and the frontal advance equation (Equation 2) is obtained by assuming that a water front forms to sweep the oil out ahead ofit. There is ample evidence that under the proper conditions a water front doesform. If this water front is not to dissipate, the water saturations whichcomprise it must have equal linear velocities. These water saturations are saidto comprise the stabilized zone. Equation (2) indicates that for all thesesaturations (Equation 3) and hence fw must plot as a straight line against saturation for those watersaturations comprising the stabilized zone. The water saturations lying between the highest in the stabilized zone andthe highest that can be achieved in the porous medium comprise the variablezone. T.N. 193