Numerical solutions of non-linear fractional transport models in unconventional hydrocarbon reservoirs using variational iteration method

Unconventional hydrocarbon reservoirs, such as, shale gas deposits, offer a new source of energy resources. These reservoirs consist of tight porous rocks which are characterized by nano-scale size porous networks with ultra-low permeability. The mathematical modeling of phenomena through such tight porous media provides its own challenges. In this study, we consider a relatively new approach by modeling the transport of gas by the time-fractional advection-diffusion equation