Fractional derivative approach to non-Darcian flow in porous media

Fractional Darcian model and fractional Swartzendruber model are proposed for non-Darcian flows with high and low velocity in the paper, respectively. The analytical solutions of the fractional derivative models are given and all parameters are determined based on test data. The dependence of fractional derivative models on parameters such as fractional derivative order and threshold hydraulic gradient are analyzed by sensitivity studies. The fractional derivative models provide better description of non-Darcian flow in porous media under the conditions of high and low velocity. Furthermore, the memory effectiveness of fractional calculus is discussed, showing that the fractional derivative order is an indicator of non-Darcian flow in porous media.