Non-Darcy flow models in porous media via Atangana-Baleanu derivative

Abstract

Abstract Two fractional Swartzendruber models applying the Atangana-Baleanu (A-B) derivative are proposed to describe non-Darcy flow in porous media. The analytical solutions of models are obtained by using Laplace transform. Fitting curves with the experimental data display the proposed models are suitable to describe non-Darcy flow problems in low and high permeability media. In addition, sensitivity analysis is performed to clarify the influence of relevant parameters on the A-B Swartzendruber models. In the light of the two-scale thermodynamics, the physical explanations of A-B Swartzendruber model I and II are revealed. The proposed A-B Swartzendruber models connect fluid flow of different scales, and provide a unified description of non-Darcy flow in porous media with low and high permeability.