Uma contribuição ao estudo da sedimentação gravitacional em batelada

Abstract

Thickeners are equipments that uses the gravitational force as separating agent of suspended solid particle in liquid chains of industrial processes. The frequent use of the settlers in chemical industries is the reason of the interest on the development of studies on the subject. The batch sedimentation is the starting point for the project of continuous industrial units. The operation that consists on the separation of a solid-liquid suspension may have its phenomelogical representation through the introduction of the Mixtures Theory of Continuum Mechanics with the application of the continuity and movement equations for both the solid and liquid constituent and for the knowledge of constitutive equations to each system in particular. The knowledge of the particle concentration is of extreme importance for the description of the phenomenon. For diluted suspensions the solid concentration can be measured by sampling techniques, but the extension of such technique for more concentrated suspensions does not lead to the good results. In this work the batch sedimentation phenomena was studied in aqueous suspensions of different solid materials, using one not destructive technique based on the measure of gamma rays attenuation. Once the radiation beam crosses the environment as function of the local concentration for several vertical positions of the container, indirect measurements of the local concentration were done without the use of sampling for aliquot of the suspension. The batch sedimentation process presents as particular characteristic the formation of distinct regions, as the clean liquid, the free settling and the compacting region, each one separated for mobile borders that vary with the time and that increase the degree of complexity of the modelling of the phenomenon. For the description of the phenomenon it is necessary to determine the constituent equations for the pressure in solids and the permeability of the porous media, both as a function of the local solid concentration. So, a mathematical model for the unidimensional sedimentation was improved by the introduction of physical concepts of the model by d Ávila (1978) in the mathematical techniques introducted by Burger e Concha (1998). The differential-algebraic equations system was solved using the available computational package DASSL in the Scilab R , using the method of Finite Differences connected to the second order method MUSCL and the method of the lines (MOL). The Moving Mesh equations had been connected to the original system in order to increase the resolution of the problem for the estimate of the derivates of the function on each step of integration. It became possible the adaptative mesh at the regions next to the discontinuities of the phenomenon, characterizing the hy brid problem for fixed and adaptative meshes. Finally, experimental results of volumetric solid concentration as function of the position and the time of separation had been used for the validation of the model. The results of the numerical simulations had shown that the presented hyperbolic-parabolic mixed model adequately describes the physical phenomenon in all its domain without the necessity of the use of jump conditions on the mobile borders. Moreover, it was observed that quality of the solution is better for systems with low permeabilities and the quality of the simulations was restricted to the quality of the constituent equations for the solid material. Several results in static and dynamic analyses of the behavior of solid-liquids systems had become possible the physical description of the batch sedimentation based on the specific properties of the solid materials. A rigorous evaluation of the constituent equations pointed that the model of Tiller e Leu (1980) depends on the initial estimative of the adjusted parameters of the equation. According to analysis of the results it was possible to present a biparametric power model for the tension in solids. The use of good constitutive equations is the point of fundamental importance for the phenomenologial description of the batch sedimentation.