Research Article AGeneticAlgorithmBasedApproach toCoalescenceParametersEstimationin Liquid-LiquidExtractionColumns The population balance model is a useful tool for the design and prediction of a rangeofprocessesthatinvolvedispersedphasesandparticulates.Theinversepro- blem method for the droplet population balance model is applied to estimate coalescences parameters for two-phase liquid-liquid systems. This is undertaken for two systems, namely toluene/water and n-butyl acetate/water in a rotating disc contactor (RDC), using a droplet population balance model. In the litera- ture, the estimation procedure applied to this problem is often based on the de- terministic optimization approach. These methods generate instabilities near a lo- cal minimum, inevitably requiring information about the derivatives at each iteration. To overcome these limitations, a method providing an estimate for the coalescences parameters is proposed. It is based on a simple and adapted struc- ture of the genetic algorithm, for this particular problem. The agreement between the experimental observations and the simulations is encouraging and, in parti- cular, the models used have proven to be suitable for the prediction of hold-up and Sauter diameter profiles for these systems. Finally, these results demonstrate that the optimization procedure proposed is very convenient for estimating the coalescences parameters for extraction column systems. Keywords: Coalescences, Extraction, Modeling, Two-Phase systems Received: July 17, 2006; revised: August 17, 2006; accepted: September 23, 2006 DOI: 10.1002/ceat.200600218 1 Introduction The determination of the dispersed phase hold-up and the particle size distributions in two phase contactors is necessary for the computations involved in many chemical engineering processes, such as solvent extraction, absorption, reaction en- gineering, etc. The modeling of such systems mainly relies on the use of the population balance approach, which enables the description of the variations in size distribution of the dis- persed phase, by averaging functions relating to the behavior ofindividualparticlessuchasdropsorbubbles,aswellastheir interactions. The development of the corresponding models relies on a parameter fitting to match the experimental size distributions. This defines the so-called inverse problem, which is suitably considered when the mathematical solution to a population balance model is known, but phenomenologi- cal functions are not. Generally, a mathematical programming procedure has to beappliedtofindthebestfitoftheexperimentaldata.Theap- plication of an inverse problem leads to an explicit analytical or approximate solution, which is highly sensitive to errors in the experimental data [1]. The parameter-fitting problem is solved by a genetic algorithm (GA), where a finite volume and generalized fixed- pivot [2] techniques are used for solving the population balance problem and the calculation of the parametric deriva- tives of the solution. This approach is based on a global search method which has proven to be more robust than many traditional search techniques [3]. It possesses the following features: ± The GA makes no assumption about the function to be op- timized, and thus, it can also be used for nonconvex objec- tive functions; ± The GA makes a tradeoff between the exploration of new pointsinthesearchspaceandtheexploitationofthecurrent information; ± The GA is a randomized algorithm whose results are gov- erned by probabilistic transition rules rather than determi- nistic rules;  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com A.Hasseine 1 A.-H.Meniai 2 M.Korichi 3 M.BencheikhLehocine 2 H.-J.Bart 4 1 Dept. of Chemistry, University of Med Khider Biskra, Algeria. 2 Laboratoire de l'IngØnierie des ProcØdØs d'Environnement, University Mentouri Constantine, Algeria. 3 Dept. of Chemistry, University of Kasdi Merbeh, Ouargla, Algeria. 4 Dept. of Process Engineering, TU Kaiserslautern, Kaiserslautern, Germany. ± Correspondence: Prof. Dr. A.-H. Meniai (meniai@caramail.com), Laboratoire de l'IngØnierie des ProcØdØs d'Environnement, University Mentouri Constantine, Algeria. Chem. Eng. Technol. 2006, 29, No. 12, 1±9 1