A MATHEMATICAL MODEL OF IMBIBITION PHENOMENON IN HOMOGENEOUS POROUS MEDIA

摘要

In this article, the phenomenon of counter-current imbibition in a particular displacement method concerning two immiscible fluids through a dipping homogeneous porous medium has been discussed under certain conditions. This phenomenon plays a very essential role in the oil recovery process. A nonlinear partial differential equation was given out as the governing equation of this phenomenon, whose exact analytical solution is almost impossible to find.Here we have solved it by two different methods: homotopy perturbation sumudu transform method and successive linearization method (a newly developed method). By comparison of solution using these two methods, it has been concluded that by the successive linearization method, a good amount of oil can be produced during a secondary oil recovery process in the petroleum technology. Also, the fraction of oil recovered to dimensionless time is studied, which is the main goal of any oil recovery process and the proposed method can be used to optimize the oil recovery rate.