Numerical Solution of the Buckley-Leverett Equations

摘要

A modified random choice method is described for solving simultaneously the Buckley-Leverett, incompressibility, and Darcy's Law equations for immiscible displacement in a porous medium. The main idea of the numerical method is to modify the one-dimensional Riemann solvers in the split random choice method so that the multidimensional flow is represented correctly. Other features include flux conserving differencing of pressure and velocity and an accurate description of sources and sinks. Numerical results for a two-dimensional five-spot waterflood indicate that the advancing front is kept sharp by the method, that the time of breakthrough is accurate, and that grid orientation effects are unimportant. 9 references, 10 figures. (ERA citation 09:000145)