Binary data

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Predictions for the other isobaric systems (experimental data of Sinor, Steinhauser, and Nagata) show good agreement. Excellent agreement is obtained for the system carbon tetrachlor-ide-methanol-benzene, where the binary data are of superior quality. 

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... 

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone.

Unfortunately, good binary data are often not available, and no model, including the modified UNIQUAC equation, is entirely adequate. Therefore, we require a calculation method which allows utilization of some ternary data in the parameter estimation such that the ternary system is well represented. A method toward that end is described in the next section. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

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. 

Binary data only. ----- One tie-line plus binary data. 

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe. 

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. 

Guffey and Wehe (1972) used excess Gibbs energy equations proposed by Renon (1968a, 1968b) and Blac)c (1959) to calculate multicomponent LLE. They concluded that prediction of ternary data from binary data is not reliable, but that quarternary LLE can be predicted from accurate ternary representations. Here, we carry these results a step further we outline a systematic procedure for determining binary parameters which are suitable for multicomponent LLE. 

Type A. Component 1 is only partially miscible with components 2 through m, but components 2 through m are completely miscible with each other. Binary data only are required for this type of system ... 

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... 

Many well-known models can predict ternary LLE for type-II systems, using parameters estimated from binary data alone. Unfortunately, similar predictions for type-I LLE systems are not nearly as good. In most cases, representation of type-I systems requires that some ternary information be used in determining optimum binary parameter. 

Appendix C-7 gives interaction parameters for noncondensable components with condensable components. (These are also included in Appendix C-5). Binary data sources are given. 

LOADS ouPE COMPONENT AND BINARY DATA FOP USE IN THF VARIOUS CORRELATIONS FOR LIQUID AND VAPOP PHASE NONIDEALITIES, THEN DOCUMENTS THE INPUT DATA. 

VAPOR COMPOSITIONS Z. ENTH RETURNS ERE=0 UNLESS BINARY DATA ARE... 

Error flag, integer variable normally zero ERG = 1 indicates binary data are missing. 

RETURNS ERG=0 UNLESS BINARY DATA ARE MISSING FOR THE SYSTEM, IN WHICH... 

SET ERR RETURN FOR MISSING BINARY DATA 199 IFI IABS(ER).EQ.1 ) ERR=1 RETURN... 

Table 12.3 Formulae for various commonly used ways to compute the similarity or distance between molecules. For the binary data a is defined to be the number of bits on in molecule A, b is the number of bits on in molecule B and c is the number of bits that are on in both A and B. Table based on [Willett et al. 1998],...

A generalisation of the similarity formulae for binary data can be derived, based on the work of Tversky [Tversky 1977 Bradshaw 1997]. This takes the form ... 

Binary Data Source 1 Binary Triple 3 Binary Noisy Binary Data Channel Majority Decision on 3 Binary Digits Destination... 

B. Ternary Phase Diagram from Binary Data. 196... 

The equation of Krichevsky and Ilinskaya can readily be extended to high-pressure solutions of a gas in a mixed solvent, as shown by O Connell (01) and discussed briefly by Orentlicher (03). This extension makes it possible to predict the behavior of simple multicomponent systems using binary data only. 

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