SIMULATION OF MULTICOMPONENT POLLUTION FLUID FILTERING PROCESS USING N-LAYER FILTERS

. In this article we considered and resolved the issue of incorporation of feedback of the process (the concentration of contamination of fluid and sediment) on the medium characteristics (porosity coefficient, filtration, diffusion, mass transfer, etc.) It was made during the simulation of cleaning fluid from multi impurities in n-ply sorption filter. We had retrieved algorithm numerically-asymptotic approximation solution of the corresponding model problem which is described by a system of nonlinear singularly perturbed differential equations "convection-diffusion-mass transfer." On this basis, we made a corresponding computer experiment.


Introduction
Due to the imperfection of existing mathematical models of filtration processes (forecasting, management and operational control methods), many of the relevant characteristic parameters are ignored or set arbitrarily. In particular, in many cases, neglect diffusion coefficient (which is not always practical), and its "traditional" accounting often leads to significant and unnecessary computational costs. Also, to date, is not enough developed, haphazard or, generally missing nonlinear model mechanisms that take into account the feedback effects of various characteristics of the process (of pollution concentration of liquid and sludge) on environmental characteristics (porosity coefficient, filtering of diffusion mass transfer etc). Almost missing is the work aimed at the development of software for automated control system of the filtration processes. Important is also constructing new models of filtering processes, by perturbations of existing models describing processes, but do not take into account a number of important characteristics of the environment. Many of the filtration processes in general are described only on the basis of experimental data and are not based on mathematical apparatus. No less urgent is the problem of mathematical description analysis of experimental data and justification of adequacy of the constructed models.
These questions, in spite of large volumes of liquids, filters used in this filter materials, their relatively high cost, the size of material losses due to the insufficient treatment of process liquids in various industries and especially in the energy sector, the expansion of existing and potential environmental problems are urgent and important (as from a theoretical point of view, and for water management and other industries).

Statement of the problem and its relationship
to important scientific and practical tasks

Analysis of recent research and publications, which discuss current issues
Analysis of researched results [1][2][3][4][5][6][7][8][9][10][11]13] indicates that the complex structure of interdependencies of different factors that determine the processes of filtration and filtration through a porous medium, which are not considered in traditional (classical, phenomenological) models of such systems. Consideration of different offs and additional factors were included in the basic model for a deeper study of the process and leads to the necessity of building bulky and inefficient (for numerical implementation and practical use) mathematical models. However, in many cases of practical importance, in the study of such processes can be applied modeling of various disturbances known as (idealized, averaged, baseline) backgrounds. At the same time filtering helps to reduce the equivalent of diameter of the granules downloaded -one of the universally accepted methods of improving the efficiency of filters [1]. In complex technological conditions change, optimal grain size load should depend on time. However, due to the complexity of implementation and operation in practice, filtering is not widely known even filters out "continuously" uneven loading. For these same reasons, actually limited to various approximations of optimal grain size load equivalent, grain diameter is "continuously" reduces in the direction of filtering by a specific law for the use-layer filters. The precision of approximation results, obviously, are the highest and the greatest number of filter layers. According to complexity of operating-layers filters, in particular, due to complications regeneration boot with growth rising. Because of the uncertainty of maximum economic benefits that can be gained in the operation of filters with optimal granulometric composition is currently the contradiction between its approximation accuracy and complexity filter operation which is decided in favor of reducing the latter. In other words, the practice of filtering the most common two-and n-layer filters.

Highlight of the unsolved aspects of the problem
According to the above studies, the work shall be considered and resolved the issue of incorporation of feedback of the process (the concentration of contamination of fluid and sediment) on the medium characteristics (porosity coefficient, filtration, diffusion, mass transfer, etc.) during the simulation of cleaning fluid from multi impurities in n-layer sorption filter.

Formulation of the problem
In this article we considered and resolved the issue of incorporation of feedback of the process (the concentration of contamination of fluid and sediment) on the medium characteristics (porosity coefficient, filtration, diffusion, mass transfer, etc.).

. Statement of main research data with full justification of scientific results
We considered the one-dimensional spatial process of cleaning fluid filtration in n-ply filter layer thickness ( Fig. 1), which is identified with a segment of the axis. We assumed [1] that the particle pollution can go from one state to another (processes of capture, separation, adsorption, desorption), while the concentration of pollution affects the considered layer. im  ) in liquid filtering medium. The corresponding process of filtering with inverse of the process (the concentration of fluid contamination and sediment) on the medium characteristics (porosity coefficient, filtration, diffusion, mass transfer, and so on. [1,2]) can be expressed as the following model problem:

, , ,
, , , found in the form of asymptotic series [1,2]: The numerical calculations. For simplicity, we assumed that the concentration of pollution is a two-component, then the system (1) -(3) can be rewritten as: