VLE data

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-... 

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. 

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). 

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... 

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). 

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. 

Journals for the pubHcation of VLE data are available as is a comprehensive tabulation of a2eotropic data (28) if the composition and temperature of the a2eotrope are known (at a given pressure), then such information may be used to calculate activity coefficients. At the a2eotropic point, by definition, y. = xc, from equation 6,... 

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. 

Traditionally, the binary interaction parameters such as the ka, kb, k, ki in the Trebble-Bishnoi EoS have been estimated from the regression of binary vapor-liquid equilibrium (VLE) data. It is assumed that a set of N experiments have been performed and that at each of these experiments, four state variables were measured. These variables are the temperature (T), pressure (P), liquid (x) and vapor (y) phase mole fractions of one of the components. The measurements of these variables are related to the "true" but unknown values of the state variables by the equations given next... 

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... 

It is well known that cubic equations of state may predict erroneous binary vapor liquid equilibria when using interaction parameter estimates from an unconstrained regression of binary VLE data (Schwartzentruber et al.. 1987 Englezos et al. 1989). In other words, the liquid phase stability criterion is violated. Modell and Reid (1983) discuss extensively the phase stability criteria. A general method to alleviate the problem is to perform the least squares estimation subject to satisfying the liquid phase stability criterion. In other... 

Solution of the above constrained least squares problem requires the repeated computation of the equilibrium surface at each iteration of the parameter search. This can be avoided by using the equilibrium surface defined by the experimental VLE data points rather than the EoS computed ones in the calculation of the stability function. The above minimization problem can be further simplified by satisfying the constraint only at the given experimental data points (Englezos et al. 1989). In this case, the constraint (Equation 14.25) is replaced by... 

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