FRACTIONAL DIFFUSION MODEL FOR TRANSPORT THROUGH POROUS MEDIA

We model the transport of fluid through porous media in terms of fractional diffusion equation (FDE) for the pressure ( ,)p x t. Potential application could be to shale gas recovery in tight porous media. Specifically, we pose the time FDE in a finite domain of length L, 0 ( ,), 0, 0tD p Ap f x t x L t α = + ≤ ≤>, where A is a linear differential operator given by A a x x, where a κ µ = , κ is the permeability and µ is the viscosity, ( ,)f x t is a source term. 0 tD