Binary VLE data for

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. 

Broul et al. (13) and Hala (14) developed a correlation scheme for systems containing two solvents and one salt, which they applied to several salt concentrations, not just to the saturation level as in the studies mentioned above. They utilized the binary VLE data for the three binaries (solvent 1-salt solvent 2-salt and solvent 1-solvent 2) along with the ternary data to correlate successfully the ternary results. They employed the Margules equation (15) with the addition of a term to account for the coulombic interactions. 

The binary constants Ay and A are determined from binary VLE data. For a three-component system (Wohl, 1946), the liquid activity coefficients are calculated by Equation 1.35a ... 

Flgare 1.5-2 shows exparimental and correlated binary VLE data for three dioxane-n-alkane systems at 80°C.m The pressure levels are modest (0.2-1.4 amt) liquid-phase nonidealities are sufficiently large to promote a2eotropy in all threa cases. Equations (1.5-12)—(1.5-15) were used for the data reduction, with experimental values for the Pf1 and virial coefficients were estimated from the correlation of Tsono-poulos.7 Activity coefficients were assumed to be represented by the three-parameter Margules equation, aed (he products of the data rednction were seis of valnes for parameters Al2, Ait. and D in Eqs. (1.4-10) and (1.4-11). The parameters so determined produce the correlations of the data shown by the solid curves in Fig. 1.5-2. For all threa systems, the data are represented to within their exparimental uncertainty. 

Figure 16 shows observed and calculated VLE and LLE for the system benzene-water-ethanol. In this unusually fortunate case, predictions based on the binary data alone (dashed line) are in good agreement with the experimental ternary data. Several factors contribute to this good agreement VLE data for the mis-... 

A. The first four data cards contain control parameters which are read only once for a series of binary VLE data sets. 

The most recendy developed model is called UNIQUAC (21). Comparisons of measured VLE and predicted values from the Van Laar, Wilson, NRTL, and UNIQUAC models, as well as an older model, are available (3,22). Thousands of comparisons have been made, and Reference 3, which covers the Dortmund Data Base, available for purchase and use with standard computers, should be consulted by anyone considering the measurement or prediction of VLE. The predictive VLE models can be accommodated to multicomponent systems through the use of certain combining rules. These rules require the determination of parameters for all possible binary pairs in the multicomponent mixture. It is possible to use more than one model in determining binary pair data for a given mixture (23). 

Drawing pseudo-binaryjy—x phase diagrams for the mixture to be separated is the easiest way to identify the distillate product component. A pseudo-binary phase diagram is one in which the VLE data for the azeotropic constituents (components 1 and 2) are plotted on a solvent-free basis. When no solvent is present, the pseudo-binaryjy—x diagram is the tme binaryjy—x diagram (Eig. 8a). At the azeotrope, where the VLE curve crosses the 45° line,... 

Fig. 8. Pseudo-binary (solvent-free)jy-x phase diagrams for determining which component is to be the distillate where (—) is the 45° line, (a) No solvent (b) and (c) sufficient solvent to eliminate the pseudo-a2eotiope where the distillate is component 1 and component 2, respectively (51) and (d) experimental VLE data for cyclohexane—ben2ene where A, B, C, and D represent 0, 30, 50, and 90 mol % aniline, respectively (52).

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

It is well known that cubic equations of state have inherent limitations in describing accurately the fluid phase behavior. Thus our objective is often restricted to the determination of a set of interaction parameters that will yield an "acceptable fit" of the binary VLE data. The following implicit least squares objective function is suitable for this purpose... 

Constrained Gauss-Newton Method for Regression of Binary VLE Data... 

The implicit LS, ML and Constrained LS (CLS) estimation methods are now used to synthesize a systematic approach for the parameter estimation problem when no prior knowledge regarding the adequacy of the thermodynamic model is available. Given the availability of methods to estimate the interaction parameters in equations of state there is a need to follow a systematic and computationally efficient approach to deal with all possible cases that could be encountered during the regression of binary VLE data. The following step by step systematic approach is proposed (Englezos et al. 1993)... 

Englezos, P., N. Kalogerakis and P.R. Bishnoi, "A Systematic Approach for the Efficient Estimation of Interaction Parameters in Equations of State Using Binary VLE Data", Can. J. Chem. Eng., 71,322-326 (1993). 

Several authors have attempted to correlate the vapor-liquid equilibrium (VLE) data for binary systems in the presence of salts at various concentrations. Johnson and Furter (4) successfully correlated a large number of systems consisting of an alcohol, water, and a salt at saturation, by the following equation ... 

Figures 1-5 present plots of the average absolute error in y vs. a 2 for the five ternary systems considered in this study. For three of the four isobaric systems, two sources of VLE data for the MeOH-water binary have been used to demonstrate the impact on the correlation of the ternary data. While the difference is not drastic, the better data of Ramalho et al. (18) also provide better correlation, as evidenced by Figures 1-3. The ensuing discussion is based on the latter data. Table III presents the optimum a 2 in the positive and negative regions. Considering the diversity of the systems studied—e.g., three involved...

The lattice model thus provides the capability to obtain good, quantitative fits to experimental VLE data for binary mixtures of molecules below their critical point. Its value lies in the fact that it performs equally well regardless of the size difference between the component molecules. 

It is important to note, that the interaction parameters between the components (two per binary) were estimated solely from binary phase equilibrium data, including low-pressure VLE data for the binary acetone - water no ternary data were used in the fitting. The values of the interaction parameters obtained are shown in Table III. 

Values of parameters for the Margules, van Laar, Wilson, NRTL, and UNIQUAC equations are given for many binary pairs by Gmehling et al.t in a summary collection of the world s published VLE data for low to moderate pressures. These values are based on reduction of data through application of Eq. (11.74). On the other hand, data reduction for determination of parameters in the UNIFAC method (App. D) is carried out with Eq. (12.1). 

The binary mixture parameter has been fitted to VLE data for 29 systems its values are in Table 1. It should be noted that is independent of temperature and always very close to unity. The calculation of phase equilibria was performed by means of the algorithm of Deiters [8, 9], The reproduction of VLE data and the predictions of LLE data, of excess volumes, of virial coefficients are very good for all 29 binary mixtures investigated [3]. 

To test the NRTL equation for predicting VLE data for ternary mixtures, experimental data for the ternary mixtures and for the binary components of the mixtures are necessary. A literature survey showed that data were not readily available for any of the ternaries or for the two binaries ethanol-3-methyl-l-propanol and 3-methyl-l-butanol-water, and it was therefore necessary to obtain these data experimentally. 

The Redlich/Kister expansion, the Margules equations, and the van Laar equations are all special cases of a general treatment based on rational functions, i.e., on equations for G /x X2RT given by ratios of polynomials. They provide great flexibility in the fitting of VLE data for binary systems. However, they have scant theoretical foundation, and therefore fail to admit a rational basis for extension to multicomponent systems. Moreover, they do not incorporate an explicit temperature dependence for the parameters, though this can be supplied on an ad hoc basis. 

Again subscript i identifies species, and j and I are dummy indices. All summations are over all species, and Tjy = 1 fori = j. Values for tlie parameters ( ,7 —nyy) are found by regression of binary VLE data, and are given by Gmeliling et al. ... 

The results for the acetone and water system are similar. In Figure 3.5.5 we present the results of correlating VLE data for this binary mixture at 298 K. The use of the... 

Figure 5.1.4. VLE predictions for the acetone and water binary system at 298 K by various methods. Solid line with crosses represents the UNIFAC predictions, and the smooth solid line reflects the results of the WS model. The large, medium, and short dashed lines are from the HVOS, HVO, and MHVl models, respectively the dotted line is from the MHV2 model and the dot-dash line denotes the results of the LCVM model. (The points (O, ) are VLE data for this system at 298 K from Griswold and Wong 1952 the data file for this system on the accompanying disk is AW25.DAT.)...

We first investigated the behavior of mixtures of the normal paraffinic solvents pentane, heptane, and decane with gaseous methane. These mixtures consist of two main UNIFAC groups, methane and the main methyl group CH2 thus, there are only two binary interaction parameters to evaluate. We used the VLE data for the 377 K isotherm of the methane and n-heptane mixture to obtain these parameters for both the HVOS and LCVM models the parameter values are reported in Table 5.3.1. We then estimated the VLE at all other temperatures of the three mixtures. The results... 

The awlOO.dat file contains isothermal VLE data for the acetone-water binary system at 100" C.)... 

Before the activity coefficients are represented with an equation, it is important to check the VLE data for thermodynamic consistency against Equation 1.30. As concluded earlier, the error introduced by applying Equation 1.30 to binary isothermal data is usually negligible. The consistency check is described for this type of data, which is the most commonly used for equation development. Equation 1.30 is written for a binary as... 

---