In this work, anomalous solute transport using adsorption effects and the decomposition of solute was studied. During the filtration of inhomogeneous liquids, a number of new phenomena arise, and this is very important for understanding the mechanisms of the filtration process. Recently, issues of mathematical modeling of substance transfer processes have been intensively discussed. Modeling approaches are based on the law of matter balance in a certain control volume using additional phenomenological relationships. The process of anomalous solute transport in a porous medium was modeled by differential equations with a fractional derivative. A new mobile—immobile model is proposed to describe anomalous solute transport with a scale-dependent dispersion in inhomogeneous porous media. The profiles of changes in the concentrations of suspended particles in the macropore and micropore were determined. The influence of the order of the derivative with respect to the coordinate and time, i.e., the fractal dimension of the medium, was estimated based on the characteristics of the solute transport in both zones. The hydrodynamic dispersion was set through various relations: constant, linear, and exponential. Based on the numerical results, the concentration fields were determined for different values of the initial data and different relations of hydrodynamic dispersion.

In this paper, a problem of anomalous solute transport in a coaxial cylindrical two-zone porous medium with fractal structure is posed and numerically solved. The porous medium is studied in the form of cylinder with two parts: macropore—with high permeability characteristics in the central part and micropore—with low permeability around it. Anomalous solute transport is modeled by differential equations with a fractional derivative. The solute concentration and pressure fields are determined. Based on numerical results, the influence of the fractional derivatives order on the solute transport process is analysed. It was shown that with a decrease in the order of the derivatives in the diffusion term of the transport equation in the macropore leads to a “fast diffusion” in both zones. Characteristics of the solute transport in both zones mainly depend on the concentration distribution and other hydrodynamic parameters in the macropore.

This study addresses a two-dimensional anomalous solute transport process within a two-zone fractal porous medium. A mathematical formulation is developed to characterise transport phenomena in a non-homogeneous porous domain. The medium consists of two interacting regions: one containing mobile fluid and the other containing immobile fluid, between which mass transfer occurs. In the mobile-fluid region, solute transport is governed by the convection–diffusion equation. In contrast, the immobile-fluid region is described using a first-order kinetic model. The problem of solute injection through a designated boundary point is formulated and numerically implemented. The effects of anomalous transport behaviour on solute migration and filtration characteristics are examined. The study further evaluates the pressure field, filtration velocity distribution, and solute concentration in both zones.

The manuscript considers the numerical solution of the multi-term time fractional diffusion equations in a finite region. We know that anomalous solute transpor The manuscript considers the numerical solution of the multi-term time fractional diffusion equations in a finite region. We know that anomalous solute transpor