Equilibrium curves, extraction

For liquid/liquid extraction, data on mass transfer rate of the system at typical operating conditions are required. Also required are an applicable liquid/liquid equilibrium curve and data on chemical reactions occurring after mass transfer in the mixer. 

These are azeotropic points where the azeotropes occur. In other words, azeotropic systems give rise to VLE plots where the equilibrium curves crosses the diagonals. Both plots are however, obtained from homogenous azeotropic systems. An azeotrope that contains one liquid phase in contact with vapor is called a homogenous azeotrope. A homogenous azeotrope carmot be separated by conventional distillation. However, vacuum distillation may be used as the lower pressures can shift the azeotropic point. Alternatively, an additional substance may added to shift the azeotropic point to a more favorable position. When this additional component appears in appreciable amounts at the top of the column, the operation is referred to as an azeotropic distillation. When the additional component appears mostly at the bottom of the column, the operation is called extractive distillation. 

Fig. 119. Diagram of one- stage liquid-liquid extraction (1 - equilibrium curve, 2 - one-stage process)...

Counter-current extraction columns are used. Figure 7.12 shows the counter-current extraction column with a ternary diagram for material balance and equilibrium curve. 

For a linear equilibrium curve with constant film coefficients, Icl and Icq, the overall coefficient, Kl, will also be constant, but for the case of a non-linear equilibrium relationship, the value of m, which is the local slope of the equilibrium curve, will vary with solute concentration. The result is that the overall coefficient, Kl, will also vary with concentration, and therefore in modelling the case of a non-linear equilibrium extraction, further functional relationships relating the mass transfer coefficient to concentration will be required, such that... 

Mark required final raffinate composition, rm, on the equilibrium curve, at 10 per cent. Draw line from this point through point o to find final extract composition, e. ... 

The results of one such set of calculations are shown in Fig. 8.2. The more extractable species A competes strongly for the ligand, so that the equilibrium curve of A in the presence of B is depressed only slightly below that for the extraction of A on its own. In contrast, the equilibrium curve for the extraction of B in the presence of A is depressed markedly relative to the extraction of free B. The effect of this is to improve the product purity significantly over what would have been possible at low concentrations of the extracted species in the extract. Thus, at high concentrations, saturation effects can improve product purity to a far greater extent than the equilibrium isotherms of the individual species would indicate superficially. 

Figure 8.11 shows how the equilibrium curve shrinks in the presence of inefficiencies. In multicomponent systems where there is mutual interference in extraction by several components, the efficency shrinkage comes on top of the other reductions in the equilibrium curve, and for this reason there is stress in such systems on achieving high efficiency. 

Should the extraction be continued until substantial equilibrium between the phases occurs, then the material balance equation (7) shows that the concentrations in the liquids move along line AB extended until the equilibrium curve is reached at C, giving rise to the ultimate equilibrium concentrations xe and ye. A fractional stage efficiency E may then logically be defined (T3) as the ratio of the number of moles N of solute actually transferred in an extraction to Ne, the moles which would be transferred should equilibrium be reached ... 

Treybal, in his book Liquid Extraction [1], works equilibrium material balances with triangular coordinates. The most unique and simple way to show three-phase equilibrium is a triangular diagram (Fig. 7.1), which is used for extraction unit operation in cumene synthesis plants [2], In this process benzene liquid is used as the solvent to extract acetic acid (the solute) from the liquid water phase (the feed-raffinate). The curve D,S,P,F,M is the equilibrium curve. Note that every point inside the triangle has some amount of each of the three components. Points A,... 

The equilibrium diagram in Fig. 7.2 is considerably different from the triangular diagram in Fig. 7.1. It is the same extraction liquid-liquid equilibrium, with water the feed-raffinate, benzene the solvent-extract, and acetic acid the solute. The complete solution has been performed in Microsoft Excel, but other commercial software spreadsheets may also be used. Please notice first, as shown in the boxed area in columns A and B, that the equilibrium curve data have been entered. Next we will see how such a curve is made. 

We have looked at four KD equilibrium resources laboratory data, triangular equilibrium data from publications, Henry s law constants, and operating field data. All four are reliable data sources if applied with limitations as described. All can be applied to the rectangular equilibrium curve (the distribution coefficient equilibrium curve) as shown in Fig. 7.2, which includes a listing of laboratory data for the extraction process shown. Please notice the data table in the boxed area of columns... 

Figure 4. Equilibrium curve for the extraction of nitric acid using 2-ethyl-l-hexanol (2-EHOH) and 2-ethyl-l-hexanoic acid (2-EHA) T = 25°C.

In the case that carrier and solvent are immiscible, the concentration of solute in extract and raffinate can be graphically depicted with the equilibrium curve in the loading diagram. Together with the volumes of feed and solvent, the mass balance for the solute leads to the amount of solute that can be recovered. 

A reflux arrangement is now added at the lower end of the column. The extract is sent to a solvent removal unit, and the solvent-free extract is split into an extract product and an extract reflux which is sent back to the bottom of the column. Without the solvent, the extract reflux is now composed of the raffinate component and the solute (components R and E), so that this reflux is actually on the raffinate side of the equilibrium curve (Section 11.2 and Figure 11.2) flowing countercurrent to the extract phase. The extract phase is thus interacting with a raffinate phase which is richer in the solute than the feed. As a result, the extract enrichment with the solute is greater than it would be if the extract were interacting directly with the external feed in the absence of the extractor section below the feed. A higher-purity extract product can therefore be expected. 

Next, Qi, the raffinate product point is plotted on the raffinate equilibrium curve at Xq, = 0.12, as specified. The extract product point is located by joining Q, to M and extending the line to its intersection with the extract equilibrium curve at The product compositions are read from the diagram ... 

The extract composition on stage 2 L2) is found from the intersection of the operating line through (X j, X,J and (X q, X j,), and the extract equilibrium curve. 

The extract-side equilibrium curve is based on the follow ... 

The desired concentration of extract is set equal to, and the raffinate in equilibrium with the first stage, Xy, is determined from the equilibrium curve. With this value ofX, is calculated from the above operating equation then X2 is determined from the equilibrium line and the calculation procedure is continued until X X. ... 

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