VLE

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

For all calculations reported here, binary parameters from VLE data were obtained using the principle of maximum likelihood as discussed in Chapter 6, Binary parameters for partially miscible pairs were obtained from mutual-solubility data alone. 

UNIQUAC equation with binary parameters estimated by supplementing binary VLE data with ternary tie-line data. 

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. 

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-... 

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems. 

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. 

For multicomponent VLE, the method used for obtaining binary parameters is of some, but not crucial, importance. Provided that the binary parameters give good representation of the binary data, good multicomponent results are usually obtained... 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

VLE data are correlated by any one of thirteen equations representing the excess Gibbs energy in the liquid phase. These equations contain from two to five adjustable binary parameters these are estimated by a nonlinear regression method based on the maximum-likelihood principle (Anderson et al., 1978). 

If only two parameters are fit, C must set to some arbitrary value, usually one, and only Pqj and P 2) estimated from the VLE... 

Three parameters are estimated from binary VLE data and correspond to ... 

The five binary parameters determined from VLE data are ... 

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

H. The next cards provide estimates of the standard deviations of the experimental data. At least one card is needed with non-zero values. Units are the same as those of the VLE data. FORMAT(4f10.2,I2). ... 

Multiple sets of binary VLE data may be correlated by continuing with another set of cards starting at part B. The last set of cards must be followed with a blank card to end the program. 

LOAD VLE DATA, ESTIMATED STANDARD DEVIATIONS, AND INITIAL PARAMETER EST IMATES... 

CHECK FOP MISMATCH BETWEEN URE COMPONENT DATA AND VLE DATA... 

READ STANDARD DEVIATIONS OF VLE MEASUREMENTS- ND IS THE NUMBER OF STANDARD DEVIATIONS WHICH ARE DUPLICATED (1.UE.NO.LE-NN). 

MAXIMUM LlKeLIHQOO ESTIMATION OF PARAMETERS FROM VLE OATA CONTROL PARAMETERS WERE SET AS FOLLOWS -... 

Selected physical properties of various methacrylate esters, amides, and derivatives are given in Tables 1—4. Tables 3 and 4 describe more commercially available methacrylic acid derivatives. A2eotrope data for MMA are shown in Table 5 (8). The solubiUty of MMA in water at 25°C is 1.5%. Water solubiUty of longer alkyl methacrylates ranges from slight to insoluble. Some functionalized esters such as 2-dimethylaniinoethyl methacrylate are miscible and/or hydrolyze. The solubiUty of 2-hydroxypropyl methacrylate in water at 25°C is 13%. Vapor—Hquid equiUbrium (VLE) data have been pubHshed on methanol, methyl methacrylate, and methacrylic acid pairs (9), as have solubiUty data for this ternary system (10). VLE data are also available for methyl methacrylate, methacrylic acid, methyl a-hydroxyisobutyrate, methanol, and water, which are the critical components obtained in the commercially important acetone cyanohydrin route to methyl methacrylate (11). 

T.eflux Tatio. Generally, the optimum reflux ratio is below 1.15 and often below 1.05 minimum. At this point, excess reflux is a minor contributor to column inefficiency. When designing for this tolerance, correct vapor—Hquid equiUbrium (VLE) and adequate controls are essential. 

Ideal gas properties and other useful thermal properties of propylene are reported iu Table 2. Experimental solubiUty data may be found iu References 18 and 19. Extensive data on propylene solubiUty iu water are available (20). Vapor—Hquid—equiUbrium (VLE) data for propylene are given iu References 21—35 and correlations of VLE data are discussed iu References 36—42. Henry s law constants are given iu References 43—46. Equations for the transport properties of propylene are given iu Table 3. 

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