Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

The flow of fluids in multi-phase porous media results due to many interesting natural phenomena. The counter-current water imbibition phenomena, that occur during oil extraction through a cylindrical well is an interesting problem in petroleum engineering. During the secondary oil recovery process, water is injected into a porous media having heterogenous and homogenous characteristics. Due to the difference in viscosities of fluids in oil wells, the counter-current imbibition phenomenon occurs. At that moment, the imbibition equation V
_i
=-V
_n
is satisfied by the viscosities of oil and water. In this article, we have analyzed the governing mathematical model of the imbibition phenomenon occurring during the secondary oil recovery process. A new soft computing algorithm is designed and adapted to analyze the mathematical model of dual-phase flow in detail. Weighted Legendre polynomials based artificial neural networks are hybridized with an efficient global optimizer the Whale Optimization Algorithm (WOA) and a local optimizer the Nelder-Mead algorithm. It is established, that our algorithm LeNN-WOA-NM is efficient and reliable in calculating high-quality solutions in less time. We have compared our experimental outcome with state-of-the-art results. The quality of our solutions is judged based on values of absolute errors, MAD, TIC, and ENSE. It is obvious that LeNN-WOA-NM algorithm can solve real application problems efficiently and accurately.