Method for equilibrium-stage calculations in liquid-liquid extraction. Application to countercurrent cascade design for a quaternary system

Abstract

An iteration-free method for equilibrium-stage calculations in multicomponent systems has been developed. The method is based on the interpolation method suggested in this paper which involves the fitting of the solubility surface of two polynomials (one for each phase) and their use together with the experimental tie-line data in order to calculate new equilibrium data. The method has been applied to a quaternary extraction example for the system water-acetone-acetic acid-chloroform at 25 OC. The suggested method has the advantages of any computer method as compared with the graphical methods. Compared to the other computer methods, it is much faster, since no iterations are needed to solve any equilibrium stage. The method is easily extended to higher order multicomponent systems.In recent years, the applications of multicomponent systems in liquid-liquid extraction processes have received increased interest in chemical technology. Stage calculations become complex when the feed is a mixture of three components or when a mixture of two solvents (either miscible (mixed solvent) or immiscible (double solvent) is used. In those cases, the corresponding quaternary liquid-liquid equilibria have to be considered.For isothermal conditions, it is possible to carry out the tie-line calculations by solving the material balances and equilibrium conditions simultaneously at each stage. Calculations can be done stage by stage by using equilibrium graphs. Thus, various graphical methods have ben proposed for quaternary systems, such as those described by Hunter (1942), Smith (1944, Cruickshank et al. (1950( ), Powers (1954, and Treybal(l963). However, these procedures all require extensive graphical construction and, in some cases, the use of a simplifying hypothesis to solve each stage and thus prove rather tedious in practice.Alternatively, calculations may be done by computer, provided that there is a suitable method for correlating the equilibria data. Hence, thermodynamic correlation methods such as the NRTL, Wilson, and UNIQUAC have proven to be useful. For example, Renon et al. (1971) reported a comprehensive computer calculation method for a staged extraction process using the NRTL model to correlate the equilibrium data, However, Sorensen et al. (1979) have concluded that such models, including NRTL and UNIQUAC, are not fully successful for liquid-liquid equilibria. For example, in the case of type I ternary systems, it is often not possible to represent both the binodal curve and the solute equilibrium ratios over the entire two-phase region with sufficient accuracy for extraction design purposes. When objective functions which emphasize the solute concentrations are used, the situation is somewhat improved. Obviously, this inaccuracy becomes more evident when multicomponent systems are involved. On the other hand, these methods require iterations at any equilibrium stage since they have to make equal the activity of both phases in equilibrium.Recently, Chimowitz et al. (1983) developed nonlinear local models ...

Study on Extraction Separation of Thioarsenite Acid in Alkaline Solution by CO32--Type Tri-n-Octylmethyl-Ammonium Chloride

“…However, it is obviously difficult to achieve this under laboratory conditions (Ma, 2009 ). Practical experience shows that in the cascade countercurrent extraction experiment, when the number of rows is ~3 N – 2 times of the number of stages, the extraction process will be close to equilibrium and reach a stable concentration value (Ruiz et al, 1986 ). Therefore, under the laboratory conditions, a total of 10 rows were carried out in the cascade extraction simulation experiment, and the raffinate of the 8, 9, and 10th rows was analyzed for As III content, with the results shown in Table 2 .…”

Visualization of High-Dimensional Liquid−Liquid Equilibrium Phase Diagrams

“…The procedure for parameter fitting and adjustment has been discussed elsewhere . As an alternative, the data can also be empirically correlated using a suitable model based on statistics . However, the range of available experimental data often limits the use of such methods for interpolation.…”

“…Cruickshank et al proposed a graphical projection method to represent a quaternary LLE phase diagram with one partially miscible pair. This projection has been used in the design of liquid−liquid extraction processes. , Frameworks for the representation of high-D SLE phase diagrams have been developed for nonreactive molecular systems, electrolyte mixtures, and systems involving polymorphs . In these frameworks, a sequence of cuts and projections of the high-D phase diagram is considered, to provide a mental picture of the system in its entirety.…”

New Method for Quaternary Systems Liquid−Liquid Extraction Tray to Tray Design

“…In a previous work (Ruiz et al 8 ) we suggested an interpolation method to run the equilibrium stage calculations for liquid-liquid extraction calculations for quaternary systems. The method was named as an iteration-free method and allowed the design of countercurrent cascades.…”