Approximate Analytical Study of Fingero-Imbibition phenomena of time-fractional type in double phase flow through porous media

Olaniyi Samuel Iyiola, Samson Babatunde Folarin

Abstract

We consider the nonlinear 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 [23] using Adomian Decomposition Method when $\alpha=1$ including numerical values.

Keywords

Fractional derivative; Fingero-imbibition; Double phase flow in porous media; Immiscible fluid; Homotopy Analysis Method

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