To predict the processes of «filtration-regeneration» of fast cone-shaped adsorption filters with piecewise homogeneous porous loads, mathematical models of their main technological modes are formed: filtration, backwashing, chemical regeneration and direct washing, taking into account the influence of temperature effects on the internal kinetics of mass transfer while maintaining constant speeds of the respective modes. Given that in the filtration mode the convective components of heat and mass transfer and physical and chemical adsorption prevail over the contribution of diffusion and physical desorption, in the chemical regeneration mode the convective components of heat and mass transfer and physical and chemical desorption prevail over the contribution of diffusion and physical adsorption. modes of reverse and direct washing convective components of heat and mass transfer and physical desorption and chemical adsorption prevail over the contribution of diffusion and physical adsorption, algorithms of numerical-asymptotic approximations of solutions of corresponding nonlinear singularly perturbed boundary value problems, bounded by given, smooth, orthogonal to each other along the edges, two equipotential surfaces and one flow surface and divided into several subregions by some given equipotential surfaces. The proposed models in the complex by taking into account the effect of changes in temperature and filtration flow rate along the filter height on the coefficients that characterize the mass transfer rates during physical and chemical adsorption and desorption, filtration coefficient, allow computer experiments to better investigate changes in impurity concentrations in filtration flow and on the surface of the loading adsorbent, retained by physical and chemical adsorption, filtration flow temperature, filtration coefficient and active porosity in each loading layer along the filter height and based on them predict more optimal use of adsorbents of each loading layer and time intervals of filters, respectively, in filtration, backwash, chemical regeneration and direct washing with constant speeds of the respective modes
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