Simulação da operação de sedimentadores contínuos

Abstract

Settlers are equipments for solid-liquid separation that are very often used in chemical industries, wastewater treatment, and ore beneficiating industries to discarding or for the exploitation of powder solids. The more detailed study of phenomena involving solid-liquid separation is of fundamental importance in the design and evaluation of sediment and continuous filters. The processes of solid-liquid separation such as sedimentation of solid particles in aqueous media, can be modeled by the Mixture s Theory of Continuum Mechanics, using the continuity and momentum equations for the constituents of the mixture, and the incorporation of appropriate constitutive equations. Such constitutive equations for the pressure in solids and permeability of porous media must be obtained empirically and are essential in assessing the degree of freedom of the system so that the model can be resolved. In this work a mathematical model was developed for the phenomenon of continuous sedimentation, from the combination of the intrinsic principles to a phenomenological approach physically consistent, with mathematical concepts used to solve the problem of sedimentation, employing methods of numerical resolution which simplified considerably the complexity of the problem, eliminating the need of resolution by regions of mobile border and jump conditions. Numerical simulations for the continuous sedimentation are of great importance in the design of sediment, thus, have been realized simulation of the model proposed in this work and the simulation of a model presented in the literature. The methodology to the spatial discretization MUSCL of second-order was applied to partial differential equations an approach with the Method of Lines (MOL), determining a set of differential-algebraic equations. The resolution of the mathematical models of continuous sedimentation in transient regime was performed with the Software Scilab® by using the computational package DASSL. For the resolution of the models in the steady state the concentrations profiles concentration result in a solution of initial value problem, whose numerical resolution was performed with code LSODAR belonging the package ODEPACK, in a variant that finds the roots of a set of functions to the time integrating the system differential. The results of the numerical simulations showed that the mixed hyperbolicparabolic model presented describes qualitatively the physical phenomenon in all its domain, without the necessity of the use of jump conditions on the mobile borders.