Abstract—The paper considers the solute transport in a heterogeneous porous medium consisting of well-permeable and poorly permeable zones, taking into account nonequilibrium adsorption in the zones. In a well-permeable zone, there are two areas, in each of which there is an adsorption of a substance with reversible nonequilibrium kinetics. The exchange of solute with the second zone is modeled by the source term in the form of a fractional time derivative of the concentration of the substance in the first zone. The numerical implementation of the model is carried out and the effect of mass transfer to the second zone on the characteristics of the solute transport in the first zone is estimated. Nonlinear kinetics of particle deposition in both sections of the first zone is considered. It is shown that, within the framework of the assumptions made, the nonlinearity of the kinetics at unchanged values of the remaining parameters of the model leads to an intensification of particle deposition. As a consequence of this, the spread of solute in the mobile zone slows down.