xb or yb benzene
FIG. 13-9 Isobaric vapor-liquid equilibrium data for benzene-toluence. (Brian, Staged Cascades in Chemical Processing, Prentice-Hall, Englewood Cliffs, NJ, 1972.)
phases become indistinguishable. The behavior of a complex mixture of hydrocarbons for a convergence pressure of 34.5 MPa (5000 psia) is illustrated in Fig. 13-15.
Two major graphical correlations based on convergence pressure as the third parameter (besides temperature and pressure) are the charts published by the Gas Processors Association (GPA, Engineering Data Book, 9th ed., Tulsa, 1981) and the charts of the American Petroleum Institute (API, Technical Data Book—Petroleum Refining, New York, 1966) based on the procedures from Hadden and Grayson [Hydrocarbon Process., Pet. Refiner, 40(9), 207 (1961)]. The former uses the method proposed by Hadden [Chem. Eng. Prog. Symp. Ser. 7, 49, 53 (1953)] for the prediction of convergence pressure as a function of composition. The basis for Hadden's method is illustrated in Fig. 13-16, where it is shown that the critical loci for various mixtures of methane-propane-pentane fall within the area circumscribed by the three binary loci. (This behavior is not always typical of more nonideal systems.) The critical loci for the ternary mixtures vary linearly, at constant temperature, with weight percent propane on a methane-free basis. The essential point is that critical loci for mixtures are independent of the concentration of the lightest component in a mixture. This permits representation of a multicomponent mixture as a pseudo binary. The light component in this pseudo binary is the lightest species present (to a reasonable extent) in the multicomponent mixture. The heavy component is a pseudo substance whose critical temperature is an average of all other components in the multicomponent
mixture. This pseudocritical point can then be located on a P-T diagram containing the critical points for all compounds covered by the charts, and a critical locus can be drawn for the pseudo binary by interpolation between various real binary curves. Convergence pressure for the mixture at the desired temperature is read from the assumed loci at the desired system temperature. This method is illustrated in the left half of Fig. 13-17 for the methane-propane-pentane ternary. Associated K values for pentane at 104°C (220°F) are shown to the right as a function of mixture composition (or convergence pressure).
The GPA convergence-pressure charts are primarily for alkane and alkene systems but do include charts for nitrogen, carbon dioxide, and hydrogen sulfide. The charts may not be valid when appreciable amounts of naphthenes or aromatics are present; the API charts use special procedures for such cases. Useful extensions of the convergence-pressure concept to more varied mixtures include the nomographs of Winn [Chem. Eng. Prog. Symp. Ser. 2, 48, 121 (1952)], Hadden and Grayson (op. cit.), and Cajander, Hipkin, and Lenoir [/. Chem. Eng. Data, 5, 251 (1960)].
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