Approximate Analytical Study of Fingero-Imbibition Phenomena of Time-Fractional Type in Double Phase Flow through Porous Media

We consider the non-linear partial differential equation of time-fractional type describing the spontaneous imbibition of water by an oil-saturated rock (double phase flow through porous media). The fact that oil and water form two immiscible liquid phases and water represents preferentially wetting phase are the basic assumption of this work. The Homotopy Analysis Method is used to obtain the saturation of injected water. We obtain the graphical representation of solution using MATLAB R2007b and Microsoft Excel 2010 with different fractional order (alpha > 0) and the comparison is made with the solution obtained in [19] using Adomian Decomposition Method when alpha = 1 including numerical values.