Modeling of aqueous suspension fi ltration when combining downward and upward fl ows

Abstract

The physical domain is divided into two subareas of motion, and a nonlinear mathematical problem of water suspension filtration with linear kinetics of interphase detachment mass transfer is formulated with respect to each of them. The structure of gel-like deposit, the dependence of hydraulic conductivity on its concentration, and the relationship of mass transfer coefficients (attachment and detachment) with the filtration rate are taken into account. The corresponding mathematical models contain interconnected clarification and filtration fl ow compartments. After the introduction of dimensionless variables and parameters, as well as the application of the operational method, rigorous solutions of both problems are obtained. As a result, the most important dependencies and equations were derived for engineering calculations of key characteristics of filtration — concentration of dispersed impurity in filtrate and head losses in distinguished subareas and common in the whole operating layer. The mentioned formalisms were used to determine the main technological times, which limited the time of continuous filter operation due to excessive deterioration of the filtrate quality and mechanical energy consumption for filtration through the clogged medium. As a consequence, the permissible time of its continuous operation (filter run) based on the criteria of effective filtration was established. The similar technological approach to the estimation of the filter performance was applied in parallel to the high-rate filter at the traditional single-fl ow suspension feeding and the two-fl ow feeding investigated above. Comparative analysis was performed on test examples with typical initial data for practice of clarification of aqueous suspensions. As a result, it was obtained that the division of the initial fl ow of suspension into two components coming through the upper and lower bed surfaces can contribute to a significant intensification of the technological process. At the same time, it is realistic to increase the duration of filter runs by 50 % and more, which leads to a tangible decrease in the cost of filtrate. Thus, application of well sorbing filtering materials becomes justified.