Tie-line data for

Tie-line data for the system MEK-water-TCE percentages w/w, from Newman et al., Ind. Eng. Chem. 41, 2039 (1949). 

Table I. Solubility Curve and Tie-Line Data for the System Potassium Acetate—Water—Dioxane in Weight Percentage...

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.

Table 3.3 Mutual equilibrium (tie-line) data for furfural-ethylene glycof-water at 25°C, 101 kPa...

Table 13-Al. NRTL parameters and experimental tie line data for triethylamine (1), carbon tetrachloride (2), and acetic acid (3) at 293K and 1 atm (Sorensen and Arlt, 1980) alpha = 0.2, units... 

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. 

TABLE 15.1 Experimental tie line data for (water + 1-hexanol + TEA) at each temperature ... 

Table 20.4.12. Tie-line data for (a-tocopherol + olive oil + ethyl lactate) system at 298.2K and 288.2K (atmospheric pressure), w, mass fraction 1 a-tocopherol 2 olive oil 3 ethyl lactate. ...

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

Two further examples of type I ternary systems are shown in Figure 19 which presents calculated and observed selectivities. For successful extraction, selectivity is often a more important index than the distribution coefficient. Calculations are shown for the case where binary data alone are used and where binary data are used together with a single ternary tie line. It is evident that calculated selectivities are substantially improved by including limited ternary tie-line data in data reduction. 

Figure 4-19. Calculated selectivities in two ternary systems show large improvements when tie-line data are used to supplement binary VLB data for estimating binary parameters.

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

The optimum parameters for furfural-benzene are chosen in the region of the overlapping 39% confidence ellipses. The ternary tie-line data were then refit with the optimum furfural-benzene parameters final values of binary parameters were thus obtained for benzene-cyclohexane and for benzene-2,2,4-trimethyl-pentane. Table 4 gives all optimum binary parameters for this quarternary system. 

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 LLE for another ternary system, ethyl terf-butyl ether (ETBE) -t ethanol -l- [C4CiIm][TfO], at 298.15 K was studied by Arce et al. [35]. To determine the tie-line compositions, they used the NMR spectroscopy. The values of the solute distribution ratio fi = XEtoH V. EtoH / where II refers to an IL-rich phase) and selectivity (S = /SEtoH// EXBE) were calculated from tie-line data. In general, both the solute distribution ratio and the selectivity decreased as the molar fraction of efhanol in the organic-rich phase increased, the maximal values being ca. 3.5 and ca. 22, respectively. The ETBE + ethanol + IL system was compared to the ETBE + ethanol + water 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. 

Using the data from Table 7.1, generate a cubic spline interpolation formula for the saturated raffinate curve, one for the saturated extract curve, and one for the tie-line data (see the Mathcad program in Appendix G-l). Equations in the form... 

Problems 7.17 to 7.19 refer to the system cottonseed oil (A)-liquid propane (B)-oleic acid (C) at 372 K and 42.5 atm, Equilibrium tie-line data taken from Treybal (1980) in weight percent are given in Table 7.7. Oleic acid is a monounsaturated fatty acid found naturally in many plant sources and in animal products. It is an omega-nine fatty acid, and considered one of the healthier sources of fat in the diet. It s commonly used as a replacement for animal... 

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