Numerical treatment of temporal-fractional porous medium model occurring in fractured media

Abstract

This paper proposes a temporal-fractional porous medium model (T-FPMM) for describing the co-current and counter-current imbibition, which arises in a water-wet fractured porous media. The correlation between the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the reservoir. For different fractional orders in both porous matrix and fractured porous media, the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery rates. Finally, the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.