Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

In the paper, a mathematical model for the filtration of two-component suspensions in a dual-zone porous medium is considered. The model consists of the mass balance equations, the kinetic equations for active and passive zones of porous medium for each component of the suspension and Darcy’s law. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of finite difference method. Based on numerical results, the main characteristics of suspension filtration in a porous medium are established. Influences of model parameters on transport and deposition of suspended particles of two-component suspension in porous media are analysed. It is shown that the polydispersity of suspension and multistage nature of the deposition kinetics can lead to various effects that are not characteristic for the transport of one-component suspensions with one-stage particle deposition kinetics. In particular, in distribution of the concentration of suspended particles in a moving fluid non-monotonic dynamics are obtained at individual points in the medium. It is shown that at the points of the medium near to the input section, the concentration of deposited particles can reach partial capacities in the passive zone.

The problem of suspension filtration in a porous medium consisting of active and passive zones is posed and numerically solved in the case of a multistage kinetics of particle deposition. Some mathematical model of the process is proposed that is based on the general conservation laws and additional phenomenological assumptions. The influence of the multistage kinetics of particle deposition on the filtration characteristics is considered. We establish that, as the parameter characterizing the duration of the stage of formation of the irreversible deposition increases, a region with complete saturation of the passive zone capacity appears near the filter inlet. No further increase of the deposition concentration in the passive zone is observed, while the process of particles movement in suspension and deposition of them in the active zone continues.

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.

BACKGROUND: The 3D printing is relevant as a manufacturing technology of functional models for forensic, pharmaceutical and bioanalytical applications such as drug delivery systems, sample preparation and point-of-care tests. OBJECTIVE: Melting behav

In this paper, the problem of solute transport in a fractured-porous medium taking into account the non-equilibrium adsorption kinetic is studied. The solute transport in fractured-porous medium consisting of two fractures and a porous block between them located in a symmetric form is considered. The problem is then solved numerically by using the finite difference method. Based on the numerical results, the solute concentration and adsorption fields in the fractures and porous blocks are shown in graphical form. The effect of adsorption on the solute transport in a fractured-porous medium is then analyzed. In the case of different parameters in two zones, asymmetric distribution of the solute concentration and adsorption is obtained. The nonlinear kinetics of adsorption leads to an increase in the adsorption effects, conversely slowing down the rate of the distribution of concentration of the solute in the fluid.