Abstract
This paper deals with approximate homotopy series solution of imbibition phenomenon occurring in multiphase flow during the secondary oil recovery process. In heterogeneous porous media, the geometry of pores is irregular while in homogeneous porous media, the geometry of pores is uniformly same. The comparative study of counter-current imbibition phenomenon in heterogeneous and homogeneous porous medium has been also discussed. The governing partial differential equation obtained by mathematical formation of imbibition phenomenon has been solved by the optimal homotopy analysis method. The numerical as well as graphical interpretation of the solution have been given.
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