Tie Line Correlations

Tie Line Correlations Useful correlations of ternary data may be obtained by using the methods of Hand [/. Phys. Chem., 34(9), pp. 1961-2000 (1930)] and Othmer and Tobias [Ind. Eng. Chem., 34(6y pp. 693-696 (1942)]. Hand showed that plotting the equilibrium line in terms of mass ratio units on a log-log stiJe often gave a straight line. This relationship commonly is expressed as... 

Plot tie-line correlation curves according to Sherwood s method. 

Plot tie-line correlation curves of the Hand type. On the same set of coordinates, plot the binodal-solubility curves, as shown in Fig. 2.28. Determine the constants of Eq. (2.11). 

Devise a tie-line correlation curve for the rectangular coordinates of Problem 1 (5). 

The ternary diagrams shown in Figure 22 and the selectivi-ties and distribution coefficients shown in Figure 23 indicate very good correlation of the ternary data with the UNIQUAC equation. More important, however, Table 5 shows calculated and experimental quarternary tie-line compositions for five of Henty s twenty measurements. The root-mean-squared deviations for all twenty measurements show excellent agreement between calculated and predicted quarternary equilibria. 

The UNIQUAC model was successfully used to correlate the experimental liquid-liquid equilibria data. As it can be seen from figure 1, the predicted tie lines (dashed lines) are in good agreement with the experimental data (solid lines). In other words, the UNIQUAC equations adequately fit the experimental data for this multi-component system. 

Ail of the activity correlating equations contain empirical constants. The UNIQUAC equations have two constants for each pair of components in a multicomponent system. For liquid-liquid equilibrium purposes these constants can be determined fi om binary mutual solubihty and ternary tie line data. Anderson and Prausnitz (3) show that constants determined in this way can be used to predict approximately the LLE behavior of multicomponent systems. 

Figures 3.10c and 3.10d are representations of the same ternary system in terms of weight fraction and weight ratios of the solute. In Fig. 3.10d the ratio of coordinates for each point on the curve is a distribution coefficient K p.= YfiXf. If K p were a constant, independent of concentration, the curve would be a straight line. In addition to their other uses, x-y or X-Y curves can be used to obtain interpolate tie lines, since only a limited number of tie lines can be shown on triangular graphs. Because of this, x-y ot X-Y diagrams are often referred to as distribution diagrams. Numerous other methods for correlating tie-line data for interpolation and extrapolation purposes exist.

Distribution Curves. Many methods of plotting the concentrations of conjugate solutions, one against the other, have been devised for the purpose of correlating data and to facilitate interpolation and extrapolation. Preferably, such plots should be rectilinear for all systems, since then not only is extrapolation facilitated, but in addition two accurately determined tie lines can be used to predict the position of all other tie lines with considerable confidence. In order to describe these readily and to systematize them, the following notation will be used ... 

Locate point M. Xctt 0.126. Locate the tie line through M with the help of a tieline correlation curve and the available data, to give points E and R. From the graph,... 

FIGURE 14.7. Correlation diagram for the molecular orbital levels of an AH4 unit with the buneiftv (SF4.) geometry, with those of T- faaped AH3 and nonlinear AH2. As in earlier figures the effect of the extra orbitals is indicated by the use of dashed tie lines. 

The UNIQUAC model was successfully used to correlate the experimental LLE data. As it can be seen from Figure 4.1, the predicted tie lines (dashed lines) are in good agreement with the experimental data (solid lines). In other words, the UNIQUAC equations adequately fit the experimental data for this multi-component system. The optimum UNIQUAC interaction parameters uij between cyclohexane, methanoL and benzene were determined using the observed liquid-hquid data, where the interaction parameters describe the interaction energy between molecules i and j or between each pair of compounds. Table 4.4 show the calculated value of the UNIQUAC binary interaction parameters for the mixture methanol + benzene rrsing universal values for the UNIQUAC structural parameters. The equilibrium model was optimized rrsing an OF, which was developed by Sorensen (1980). 

The reliability of experimental measured tie-line data is determined by making an Othmer and Tobias correlation (Eq. 16) for the ternary system at each temperature. The linearity of the plots in Figure 11.7 indicates the degree of consistency of the related data (Othmer and Tobias, 1942). The Othmer and Tobias plots at different temperatures are shown in Figure 11.7 and the correlation parameters are given in Table 11.4. 

The consistency of ejqterimental tie-line data can bedetermined using the Othmer and Tobias correlation for the ternary system ... 

In this work, the LLE data for the ternary system of (water + 1-hexanol + TBA) at temperatures from (298.15 to 305.15 K) are presented. Here, TBA is used as a solvent in the separation of 1-hexanol from water. Complete phase diagrams are obtained by solubility and tie-line data simultaneously for each temperature. Selectivity values (S) are also determined from the tie-line data to establish the feasibility of the use of these liquid for the separation of (water + 1-hexanol) binary mixture. The experimental LLE data are correlated using the universal quasi-chemical (UNIQUAC). 

The LLE measurements for the ternary system were made at atmospheric pressure in the temperature range at (298.2, 303.2, and 305.2 2) K. The experimental and correlated LLE data of water, 1-hexanol and TEA at each temperature are obtained. Experimental tie line data for (water + 1-heaxol + TEA) at each temperature were reported in Table 15.1. 

The experimental and correlated tie lines for this system at 298.2 K were plotted in Figure 15.2. From the LLE phase diagram, (TEA + water) is the only pair that is partially miscible and two liquid pairs (water + 1-hexanol) and (1-hexanol + TEA) are completely nuscible. As it can be seen from Figure 15.2, the phase diagram shows plait point. At this point, only one liquid-phase exists and the compositions of the two phases are equal. 

X where n is the number of tie-lines, x and indicate the experimental and calculated mole fraction, respectively. The subscript i indexes components, j indexes phases and k = 1,2,..., n (tie-lines). The UNIQUAC model was used to correlate the experimental data at each temperature (298.15,303.15, and 305.15 K) with RMSD% values of 1.42, 1.97, and 1.33%, respectively. 

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