A Non-Linear Model for Solute Transport, Accounting for Sub-diffusive Concentration Decline and Sorption Saturation

Abstract

Solute transport in porous media is very often complicated by solute immobilization on a solid matrix of porous media. Usually, immobilization is accounted by the mobile/immobile media approach (MIM). However, solute immobilization is very complicated phenomena with a variety of specific features. Therefore, in the literature there have been a lot of specific MIM-type models. Usually each model is constructed for to account one specific feature. Examples are the power decline of concentration in the large time limit at small concentration and the limitation of the immobilization process at high concentrations. Both effects have been evidenced by experiments. The present paper develops a hybrid nonlinear fractional MIM model potentially able to describe the above two features. A step-by-step process of constructing the nonlinear fractional MIM model is presented, and the main properties of the new model are discussed. Two limiting cases describe power law decline and sorption saturation have predicted by the new model equations. Numerical simulations illustrate limiting cases and the capabilities of new nonlinear fractional model.