mathematical modeling of counter-current spontaneous imbibition in a single block

We study counter-current imbibition, where a strongly wetting phase (water) displaces non-wetting phase spontaneously under the influence of capillary forces such that the non-wetting phase moves in the opposite direction to the water. in this study, we use the analytical solution of tavassoli et al for saturation profiles when the viscosity of the non-wetting phase is non-negligible. this makes the approach applicable to water flooding in hydrocarbon reservoirs, or the displacement of non-aqueous phase liquid by water. we find the recovery of non-wetting phase as a function of time for one-dimensional flow. we compare our predictions with experimental results in the literature. in this study, we used cylindrical and cubic cores whose laboratory data provided by standnes (2004) and simulated by kevin jørgensen and marco utsetø (2017) using eclipse100 software and compared them with the analytical model of tavassoli et al. tavassoli et al.'s analytical model consist of two parts: early time solution and late time solution, which were coded using the fortran programming language.