On nonequilibrium models of spontaneous countercurrent imbibition

Abstract

Spontaneous displacement of the non-wetting phase by a wetting phase in a porous medium, known as spontaneous imbibition, is an important mechanism of oil recovery from fractured reservoirs. In this paper, we consider the nonequilibrium model, proposed by Aryana and Kovscek, where consitutive relationships for multiphase flow in porous media are functions of a locally moving time-average saturation, and allow relaxation time to be an explicit function of local saturation. We obtain asymptotic self-similar solutions for early and late times. At very early stages, the time-scale of the process characterizing the cumulative volume of displaced fluid is a power function with an exponent of $\frac {1}{2}+\frac {1}{2r+1}$ where r is the inverse of pore size distribution index of the medium in question. Additionally, the cumulative volume of displaced fluid at late times is independent of relaxation time, and this volume approaches the square root of time asymptotically. Finally, the late-time solution for recovery is compared with experimental observations.