The statistical characteristics of the displacement front in a randomly heterogeneous medium

The problem of the displacement of oil by water in a randomly hetrogeneous medium with specified statistical characteristics is considered. Using an improved perturbation theory within the framework of the Buckley – Leverret two-phase model, a statistical solution is constructed which enables the average shape of the displacement front to be obtained, and also the variance of the saturation and the longitudinal velocities on the displacement front, together with a variogram of the fluctuations of the front shape.