An Analytical Solution for Linear Waterflood Including the Effects of Capillary Pressure

Publisher Website
Google Scholar
Abstract
In this paper we develop exact solutions for a model linear [one-dimensional (1D)] waterflood that includes the effects of capillary pressure. We show that at constant injection rates an exact solution is possible for a water/oil displacement process, for which the mobility ratio has the functional form (1)kroμwkrwμo=F(S−Sor1−Swr−S), where S is the oil saturation and F is a parameter that can be taken as the water-to-oil viscosity ratio. Explicit analytical expressions for the oil saturation distribution as a function of position and time are derived that account for the effects of capillary pressure. The solution is expressed in terms of F and a dimensionless parameter, β2, that denotes the relative magnitude of viscous to capillary terms. At high injection rates (β→∞), the solution reduces to the familiar Buckley-Leverett expressions, including the shock front solution when F> 1. From the analytical results one can calculate the capillary effects on the performance of the model waterflood. This work, which for the first time presents an analytical solution for a linear waterflood that includes capillary effects, finds applications in two areas. First, it can be used to describe explicitly the performance of the model waterflood at low injection rates (small β), where the existing approximate solutions fail to account for the large capillary terms. Second, it can be used to check approximate analytical (such as the Buckley-Leverett), asymptotic, and numerical solutions.