Study of imbibition phenomenon in homogeneous porous medium model for oil recovery with temporal-fractional approach

In this article, the phenomenon of countercurrent imbibition in a specific displacement method occurs within a dipping homogeneous porous medium. This phenomenon plays a vital role in the process of oil recovery, which motivates our analysis. To overcome the difficulties associated with the nonlinear partial differential equation governing the countercurrent imbibition phenomenon, we have been using two distinct methods: the natural transform decomposition method and the variational iteration transform method with their convergence analysis for solutions. These techniques give different perspectives and enable us to obtain approximate solutions. Notably, both the proposed methods demonstrate the potential for substantial production of oil during the secondary oil recovery process in the petroleum industry. The obtained results by the proposed methods show the efficiency in optimizing the oil recovery rate.