  Modeling of water and gas flow in low-permeability media is an important
topic for a number of engineering such as exploitation of tight gas and
disposal of high-level radioactive waste. It has been well documented in the
literature that Darcy's linear law of water flux and the hydraulic gradient is
not always adequate for low-permeability media. On the basis of the
Swartzendruber model, as a non-Darcian model of flow in low-permeability media,
a new nonlinear model of water flux and the hydraulic gradient is proposed
using fractional derivative. The analytic solution of fractional derivative
flow model is presented and all parameters of the fractional derivative flow
model are determined by the Levenberg-Marquardt method on the basis of the
experimental data of water flow in low-permeability media. It is indicated that
the results estimated by the fractional derivative flow model proposed in the
paper are in better agreement with the experimental data than the results
estimated by the Swartzendruber equation. In addition, a sensitivity study is
carried out, showing the effects of fractional derivative order and threshold
hydraulic gradient on water flux.
