Usmonali Saydullaev

A mathematical model of solute transport in porous media with two adsorption zones was developed, incorporating balance and kinetic equations, and initial and boundary conditions. The model was enhanced to account for multistage deposition kinetics in both adsorption zones, and numerical methods were employed to solve the problem. An algorithm using the finite difference method was presented as a solution. Computer experiments were conducted to ascertain the effect of different parameters of the model on solute transport, and the results of the study were analyzed. The primary focus of this study is to assess the impact of parameters within the kinetic equations on the transport process. These parameters are crucial in determining the intensity of adsorption during various stages of the process. The findings of this study demonstrate that multistage deposition kinetics significantly influences both the transport and adsorption processes. Furthermore, the presence of two distinct intensity areas in the concentration profile of the adsorbed substance is observed. This phenomenon is attributed to the effects of multistage kinetics.

In this paper, we consider a vertically positioned cylindrical filtering element. Filtering occurs in the radial direction, therefore, the direction of the velocities of the liquid and suspended particles coincide with this radial direction. The flow can be considered to be one-dimensional and radially axisymmetric. To describe such a filtering process, the axisymmetric Stefan problem will be formulated. The radial mass balance formalism and Darcy’s law are utilized to obtain a basic equation for cake filtration. The boundary condition at the moving surface is derived and the cake filtration is formulated in a Stefan problem. Equations are derived that describe the dynamics of cake growth in the cake filtration, and they are numerically solved. The influence of different model parameters on the compression and fluid pressure across the cake and the growth of its thickness are studied.

In this paper, filtration equations of suspensions through porous filters with forming a cake layer on the inlet surface of the medium, that can exhibit elastic-plastic properties, are derived. The filtration equations are numerically solved both at the loading and unloading regimes. Distributions of the cake concentration and its permeability are determined at pressure increasing and decreasing regimes that show their irreversible behaviour. According to irreversibility parameters residual effects can be different. At reloading of the system after some rest time the growth of the cake proceeds, but with another characteristics. The transit of filtration characteristics to former conditions, corresponding to the previous loading, occurs gradually, from point to point of the cake, but enough quickly. As a result, the elastic-plastic behaviour of the cake essentially changes both the growth dynamics and filtration characteristics.

The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake on the filter surface. It is supposed that the cake has elastic–plastic properties. Using the mass conservation equation and Darcy’s law, the suspension filtration equations at the elastic–plastic regime are derived, which characterize the partial irreversibility of the filtration characteristics when the system is unloaded after loading. An equation is also derived that describes the increase in the thickness of the cake. Problems of suspension filtering for the derived equations are posed and numerically solved. The role of partial irreversibility of deformation on the filtration characteristics is estimated. Distributions of compression pressure, the concentration of solid particles in the cake, relative permeability in the mode of primary and secondary loading of the system, as well as in the mode of unloading after the first loading are obtained. The growth dynamics of the cake thickness are also established. The parameters of plasticity in terms of particle concentration and permeability mainly affect the corresponding indicators, i.e., on the particle concentration distribution and on the relative permeability of the cake. It is shown, that depending on the change in the model parameters characterizing the elastic–plastic properties of the cake, the filtration characteristics change significantly. This indicates a significant effect of the elastic–plastic deformation of the cake on the suspension filtration characteristics.