Modeling non-Darcian flow and solute transport in porous media with the Caputo–Fabrizio derivative

Abstract

• Caputo–Fabrizio fractional derivative model for non-Darcian flow is established. • Caputo–Fabrizio fractional derivative model for diffusive transport is presented. • All proposed models are in good agreements with experimental results. In this study, the non-Darcian flow and solute transport in porous media are modeled with a revised Caputo derivative called the Caputo–Fabrizio fractional derivative. The fractional Swartzendruber model is proposed for the non-Darcian flow in porous media. Furthermore, the normal diffusion equation is converted into a fractional diffusion equation in order to describe the diffusive transport in porous media. The proposed Caputo–Fabrizio fractional derivative models are addressed analytically by applying the Laplace transform method . Sensitivity analyses were performed for the proposed models according to the fractional derivative order . The fractional Swartzendruber model was validated based on experimental data for water flows in soil–rock mixtures. In addition , the fractional diffusion model was illustrated by fitting experimental data obtained for fluid flows and chloride transport in porous media. Both of the proposed fractional derivative models were highly consistent with the experimental results.