Numerical Analysis Saturation Profiles Compared with Analytical Solution of Buckley Leverett Equation

Abstract:

One of the simplest and most widely used methods of estimating the advance of a fluid displacement front in an immiscible displacement process is the Buckley-Leverett method. The Buckley-Leverett theory estimates the rate at which an injected water bank moves through a porous medium. The approach uses fractional flow theory and is based on the following assumptions and conditions: 1. D two-phase flow of incompressible fluids, e.g., Water displacing oil. 2. Oil and water are immiscible. 3. Homogeneous reservoir with constant properties. 4. Diffuse flow. 5. Gravity and capillary pressure effects are negligible. This method is well known; you almost always encounter this method when waterfloods are the topic of discussion. At many courses this method is taught as a general method for immiscible displacement, and then the interest normally stops. This study described a method for calculating saturation profiles when the effects of capillary pressure gradient and gravity are excluded. Based upon the solution of the basic partial differential equation, they found that, as time progresses, the saturation becomes a multiple-valued function of the distance coordinate X. Therefore, a numerical reservoir simulation model ECLIPSE® Simulation Software and analytical one has been developed for predicting the performance of two-phase fluid flow in a one-dimensional synthetic reservoir system. The validity of this synthetic reservoir model has been verified by comparing the solutions of numerical simulation with the analytical model from the Buckley-Leverett theory.