Keywords: simulation of liquid-liquid systems, mixer-settler system.

The study of liquid-liquid extraction and mass transfer processes is of great importance in many industrial fields. The most used equipments are the extraction columns and mixer-settler batteries. Direct experimentation with such equipments is not feasible, due to their high complexity and cost. The possible alternative is computer simulation. Algorithms for fast and reliable simulation of single stirred vessels and extraction columns have already been published by some of the present authors, both for steady state and dynamic conditions [1,5,7]. Recent investigation of the present authors is concerned with the dynamic simulation of mixer-settlers in mass transfer conditions. Mixers can be simulated with homogeneous stirred vessels [7]. More complex equipments, such as extraction columns, may be simulated by combining those simpler structures [4]. In general, the knowledge about the settler behaviour is scarcer than the knowledge about the mixers and extraction columns, both in the steady state and in the transient state. Existing models for the settler apply to specific physical equipments of a laboratory scale [6,2]. More recently, an approach based on the population balance equation has been used [3,9]. In this paper we describe a direct numerical technique for the study of the wedge formed in a settler of an extraction system for the steady and transient states. The technique is an extension for the settler of the one used on the stirred vessel by Ribeiro [7]. In this study we used the mathematical model proposed by Ruiz for the steady state operation of a settler with a wedge-shaped dispersion band [8].

The aim of the method is to model the shape of the formed dispersion band: its length and thickness space. The main equation for the steady state model describes the balance of the number of drops in the system, as proposed by Ruiz [8]. In her original work, Ruiz employed the Gauss Legendre quadrature method for the numerical integration and the fourth-order Adams Moulton predictor corrector method for solving the differential equation. In our approach this equation has been solved numerically by time stepping with the Euler method. Much attention has been paid to the integration step. The results already obtained show that this computationally simpler approach works quite well, the algorithm's predictions being in agreement with the experimental results and those reported by Ruiz [8]. Some cinematic equations are being refined according to new laboratory results being produced in our chemical lab. Our algorithm for the transient state of the mixer-settler system uses iteratively the stationary state algorithm to integrate over the time variable. Starting from the stationary state we may change one of the parameters of the vessel (hold-up, flow rate or stirring speed) and simulate the changes on the dispersion band on the settler over time. As far as we know, no other study addresses the simulation of such a system in dynamic conditions.

The results obtained with the developed simulation model for the transient state of the mixer-settler were compared with the values of Ruiz [8]. The predicted values for the wedge of the dispersion band compared every 10 cm are in excellent agreement with those of Ruiz. The new numerical algorithm here presented has the advantage of adding little complexity for the calculations, being an iterative application of the steady state algorithm. It must be noticed that Ruiz's model was developed for a settler that is fed through a slot, the height of which defines the initial thickness of the dispersion band. Ruiz's calculation of an initial velocity depending on the initial thickness of the inlet slot of the settler of the dispersion band is also a limitation of her model. To overcome these problems, we are currently working on a new dynamic model using a kinetic formulation in which the movement of the dispersion is modelled as caused by gravity.

1

Gomes M.L.N., Comportamento Hidrodinâmico de Colunas Agitadas Líquido-Líquido, Ph.D. Thesis, Universidade do Minho, Portugal, 2000.

2

Hartland, S., Jeelani, S.A.K., Chapter in Gravity Settler in Liquid-Liquid Equipment edited by Godfrey, J.C. and Slatr, M.G. John Wiley & Sons Lda, London, 1994.

3

Padilla, Ruiz, Trujillo, Separation of liquid-liquid dispersions in a deep-layer gravity settler: Part I. Experimental study of the separation process. Hydrometallurgy, 42, 267-279, 1996. doi:10.1016/0304-386X(95)00095-X

4

Regueiras P.F.R., Gomes M.L., Ribeiro L.M., Guimarães M.M.L., Cruz-Pinto J.J.C., Efficient Computer Simulation of the Dynamics of an Agitated Liquid-Liquid Extraction Column, Proceedings of the 7th International Chemical Engineering Conference, Lisboa, Portugal, September, 1998.

5

Regueiras P.F.R., Ribeiro L.M., Guimarães M.M.L., Madureira C.M.N., Cruz-Pinto J.J.C., Precise and Fast Computer Simulations of the Dynamic Mass Transfer Behaviour of Liquid-Liquid Agitated Contactors, Value Adding Through Solvent Extraction, edited by D.C. Shallcross, R. Paimin, L.M. Prvcic, University of Melbourne, Vol. 1, Proceedings of ISEC'96, pp. 1031-1036, 1996.

6

Rommel, W., Meon, W., Blass, E., Hydrodynamic Modelling of Droplet Coalescence at Liquid-Liquid Interfaces, Separation Science and Technology, 27(2):129-159, 1992. doi:10.1080/01496399208018870

7

Ribeiro L.M., Simulação Dinâmica de Sistemas Líquido-Líquido. Um novo Algoritmo com Potencialidades de Aplicação em Controlo, Ph.D. Thesis, Universidade do Minho, Portugal, 1995.

8

Ruiz, M.C., Mathematical Modeling of a Gravity Settler, Ph.D. Th., Univ. of Utah, 1985.

9

Ruiz, Padilla, Separation of liquid-liquid dispersions in a deep-layer gravity settler: Part II. Mathematical modeling of the settler. Hydrometallurgy, 42, 281-291, 1996. doi:10.1016/0304-386X(95)00096-Y

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