Abstract
This study presents the mathematical model of the counter-current imbibition phenomenon that occurs through inclined homogeneous and heterogeneous porous media. The effect of relative permeability, capillarity, and heterogeneity of porous materials such as glass beads, touchet silt loam, and fragmented mixture on the saturation rate of a reservoir is investigated and discussed. A variety of different types of sand have been considered for various lengths of time and distances in the current model in order to compare saturation levels between homogeneous and heterogeneous porous media. The reduced differential transform method (RDTM) is used to obtain an approximate analytical solution to the proposed model. The findings, illustrated both numerically and graphically, are presented for the distance and time variables.
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