Non-classical flow modeling of spontaneous imbibition in spatially heterogeneous reservoirs

In this study, imbibition process is investigated in heterogeneous hydrocarbon reservoir using the non-classical (effective viscous finger) model equations proposed by Luo et al. (SPE Res. Eval. Engineering, 20(4), 1-16 2017). Counter-current spontaneous imbibition is analyzed in different heterogeneous porous media. The heterogeneity is mainly due to the spatial variation of the porosity and absolute permeability. The proposed mathematical model is solved considering the Implicit Pressure Explicit Saturation Scheme (IMPES) via finite difference method (FDM). Effect of the viscosity ratio, growth rate exponent of the fingering function, and the maximum fingering cross section on the normalized water saturation are analyzed. The present model is verified in the limiting case of classical model equations in homogeneous medium. It is noted that rate and extent of the counter-current imbibition are significantly controlled by the distribution of heterogeneous parameters like porosity and absolute permeability of the reservoir.