Transient modeling of zinc extraction with D2EHPA in a Kühni column
Introduction
The modeling of liquid–liquid extraction (LLE) columns is a challenging field for engineers due to the simultaneous interactions between multiphase hydrodynamics and mass transfer during operation. Along the last decades different levels of modeling approaches were proposed to describe it (Zhang et al., 1985, Korschinsky and Bastani, 1993, Weinstein et al., 1997, Chouai et al., 2000, Attarakih et al., 2006, Morales et al., 2007, Gameiro et al., 2010, Ferreira et al., 2010, Safari et al., 2012). More recently, a given effort has been done on the use of population balance approaches (Bohro, 2002, Bart, 2005, Schmidt et al., 2006, Attarakih et al., 2006, Attarakih et al., 2009). It seems obvious that changes in the drop population characteristics along the column are crucial to better describe the behavior of columns, so population models is a promising tool. However the strong dependence on correlations having a number of fitting parameters to quantify rates of breakage and coalescence of drops is a hindering factor for their establishment as off-the-shelf approach. This endorses the opinion that a choice for a single approach, as a target for efforts on research, could in fact represent a technical fault, as long as the price for higher accuracy would be paid by the generation of unfriendly models sentenced to academic papers only (Grinbaum, 2006).
In this context, the present work aims to evaluate the applicability and performance of the following classical approaches on the description of LLE columns: the back-mixing and the forward-mixing models. The goals are: (i) to compare the predictive capacities of both approaches, and (ii) to check if their simplicity affects somehow their accuracy. For the fulfillment of these tasks, simulations were confronted with experimental data using the standard system of the European Federation of Chemical Engineering (Godfrey and Slater, 1994), i.e., the extraction of zinc sulfate with D2EHPA (di-2-ethylhexyl phosphoric acid), which were obtained by Mansur et al. (2003) in transient runs using a section of a Kühni column operated in closed-circuit.
Section snippets
Mathematical framework: back-mixing versus forward-mixing models
The plainest assumption to model a LLE column includes the existence of a plug flow regime for the disperse phase inside the equipment. This assumption harbors the ideas that all drops have equal size and velocity, or, in other words, that effects of breakage and coalescence of drops propagate rapid enough along the myriad of drops. This is however a very simple approach as the practice of LLE may exhibit an impressive divergence of such pattern. The main deviation of this approach is caused by
Modeling of zinc extraction with D2EHPA in a short Kühni column
Thermodynamics and kinetics aspects of zinc extraction with D2EHPA considered in the present study are given by Mansur et al., 2002a, Mansur et al., 2002b, respectively. The extraction process is described by means of an interfacial reaction between zinc and D2EHPA, resulting in the formation of a zinc complex species ZnR2RH in the organic phase (Eq. (4)), followed by the partial dissociation of this complex in the bulk of the organic phase forming ZnR2 and D2EHPA (Eq. (5)):
Results and discussion
Physical consistency of models was evaluated and it was verified that both models reproduced all typical transient concentration profiles at ends of column, thus corroborating experimental behavior obtained by Mansur et al. (2003). In the aqueous phase, zinc concentration diminished monotonically with time until reach equilibrium (the opposite was verified to proton concentration as expected), while in the organic phase a maximum point was observed in the zinc concentration profile curve with
Conclusions
In this work, the transient extraction of zinc with D2EHPA in a Kühni column section operated using a closed-circuit of aqueous and organic phases was modeled using classical back-mixing and forward-mixing approaches aiming to compare such simpler mathematical formulations in the description of complex operations. Simulations were confronted with experimental data and the following conclusions were drawn:
The transient behavior of zinc concentration in the aqueous and the organic streams leaving
Acknowledgments
Authors acknowledge Brazilian Governmental Agencies FAPEMIG (Edital 16/2010; Processo n°. TEC-APQ-04026-10) and CNPq (Edital 44/2010; Processo n°. 550243/2011-9) for funding the present research work.
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