Simulacao dinamica de sistemas liquido-liquido Um novo algoritmo com potencialidades de aplicacao em controlo

Abstract

In this work we develop an entirely new and reliable algorithm for the simulation of the full trivariate (drop volume, solute concentration and age) unsteady-state behaviour of interacting liquid-liquid dispersions, in single continuous (or batch) stirred vessels. Both rigid and oscillating mass transfer models, as proposed by Cruz-Pinto (1979) and Cruz-Pinto et al. (1983), have been adopted and studied. Although we assume that drop interaction events are properly described by the Coutaloglou and Tavlarides (1977) interaction kernels, the algorithm, however, accepts virtually any alternative interaction models. Furthermore, the simulation approach followed here does not introduce any hypotheses, other than those of the underlying mathematical model; any level of statistical dependence of the drop properties that may develop is automatically and accurately taken into account. The numerical solution of the problem is carried out by an adequate space-time discretization of the integral-differential population balance equation and the coupled differential mass transfer equations, with the explicit calculation of time derivatives by means of a first-order backward finite-difference scheme. The procedure enables to simulate in detail all relevant aspects of the dynamics of interacting dispersions in mass transfer conditions, namely the gradual approaches to steady-state. Excellent agreement has been achieved between the predictions by this algorithm for the asymptotic steady state and those previously obtained, for the same conditions, by Guimaraes (1989)' Monte-Carlo technique - applicable only to steady-state conditions. The simulations by the present algorithm are significantly fast and require only modest computer resources - 2 minutes of CPU time on a DEC 3000 Model 500 AXP, for a full-featured simulation (individual drop volumes and solute concentrations) of the whole start-up period of the contactor. A streamlined version of the algorithm (applicable to oscillating drop behaviour) requires only 24 seconds on the same computer and 73 seconds on a 486-DX 66 MHz microcomputer..Available from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga