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

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 be-tween 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.(c) 2022 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

This paper proposes a temporal-fractional porous medium model for describing co-current and counter-current imbibition. The correlation between imbibition in fractures and porous matrix is examined to determine the saturation and recovery rate. The effects of different fractional orders, wettability, and inclination on saturation and recovery rate are also studied.