Optimal HAM Approach for Modeling Imbibition in Heterogeneous Porous Media

This paper investigates an approximate analytical solution of the imbibition phenomenon arising in multiphase flow during secondary oil recovery. Imbibition is a capillarity-driven displacement process in which a wetting phase penetrates a porous medium and displaces a non-wetting phase, significantly influencing recovery efficiency in fractured and water-wet reservoirs. The structural characteristics of the porous matrix play a decisive role in this mechanism. In heterogeneous porous media, pore geometry and permeability vary spatially, resulting in non-uniform flow behavior, whereas homogeneous media exhibit uniform pore distribution and consistent transport properties. A comparative analysis of counter-current imbibition in heterogeneous and homogeneous porous formations is presented to assess the influence of medium variability on saturation evolution and displacement dynamics. The governing nonlinear partial differential equation describing the imbibition process is formulated using fundamental principles of mass conservation and multiphase flow theory. Owing to the inherent nonlinearity of the model, obtaining closed-form exact solutions is generally intractable. To address this challenge, the Optimal Homotopy Analysis Method (OHAM) is employed to construct a convergent homotopy series solution. The method provides flexibility through an auxiliary convergence-control parameter, enabling improved accuracy and stability without requiring small perturbation parameters. The approximate analytical results are validated numerically, and graphical representations are presented to illustrate the effects of key physical parameters on fluid saturation profiles. The study demonstrates that OHAM serves as an efficient and reliable semi-analytical technique for modeling nonlinear imbibition processes and offers valuable insights into fluid transport behavior in complex porous systems relevant to enhanced oil recovery applications.