Numerical Solution and Parameters Identification for the Integer-Fractal MIM Solute Transport Model

An integer-fractal mobile-immobile (MIM) model for reactive solute transport in a heterogeneous porous media is investigated, where the transport in the mobile zone is given by an advection-dispersion equation, and the diffusion in the immobile zone is described by a time fractional differential equation. A finite difference scheme is put forward to solve the MIM model, and convergence and stability of the scheme are proved based on the spectrum estimation of the coefficient matrix. An inverse problem of identifying the fractional order and the degradation coefficient is considered with the measured data in the mobile zone, and uniqueness of the inverse problem is proved by the method of Laplace transform. Numerical inversions with noisy data are presented to demonstrate a numerical stability of the inverse problem