Depriester Charts
FIG. 1314 K values (K = y/x) in lighthydrocarbon systems. (a) Lowtemperature range. [DePriester, Chem. Eng. Prog. Symp. Sec. 7, 49,1 (1953).]
Preferred analytical correlations are less empirical in nature and most often are theoretically based on one of two exact thermodynamic formulations, as derived in Sec. 4. When a single pressurevolumetemperature (PVT) equation of state is applicable to both vapor and liquid phases, the formulation used is
where the mixture fugacity coefficients <t>L for the liquid and <t>,V for the vapor are derived by classical thermodynamics from the PVT expression. Consistent equations for enthalpy can similarly be derived.
Until recently, equations of state that have been successfully applied to Eq. (133) have been restricted to mixtures of nonpolar compounds, namely, hydrocarbons and light gases. These equations include those of Bene dictWebbRubin (BWR), Soave (SRK) [Chem. Eng. Sci., 27, 1197 (1972)], who extended the remarkable RedlichKwong equation, and PengRobinson (PR) [Ind. Eng. Chem. Fundam., 15,59 (1976)]. The SRK and PR equations belong to a family of socalled cubic equations of state. The Starling extension of the BWR equation (Fluid Thermodynamic Properties for Light Petroleum Systems, Gulf, Houston, 1973) predicts K values and enthalpies of the normal paraffins up through noctane, as well as isobutane, isopentane, ethylene, propylene, nitrogen, carbon dioxide, and hydrogen sul
fide, including the cryogenic region. Computer programs for K values derived from the SRK, PR and other equations of state are widely available in all computeraided process design and simulation programs. The ability of the SRK correlation to predict K values even when the pressure approaches the convergence pressure is shown for a multicomponent system in Fig. 1318. Similar results are achieved with the PR correlation. The WongSandler mixing rules for cubic equations of state now permit such equations to be extended to mixtures of organic chemicals, as shown in a reformulated version by Orbey and Sandler [AlChE J., 41, 683 (1995)].
An alternative Kvalue formulation that has received wide application to mixtures containing polar and/or nonpolar compounds is
where different equations of state may be used to predict the purecomponent liquid fugacity coefficient Of and the vapormixture fugacity coefficient, and any one of a number of mixture freeenergy models may be used to obtain the liquid activity coefficient y,L. At low to moderate pressures, accurate prediction of the latter is crucial to the application of Eq. (134).
When either Eq. (133) or Eq. (134) can be applied, the former is generally preferred because it involves only a single equation of state
applicable to both phases and thus would seem to offer greater consistency. In addition, the quantity OL in Eq. (134) is hypothetical for any components that are supercritical. In that case, a modification of Eq. (134) that uses Henry's law is sometimes applied.
For mixtures of hydrocarbons and light gases, Chao and Seader (CS) [AIChE, 7,598 (1961)] applied Eq. (134) by using an empirical expression for OL based on the generalized correspondingstates PVT correlation of Pitzer et al., the RedlichKwong equation of state for OV, and the regular solution theory of Scatchard and Hildebrand for The predictive ability of the lastnamed theory is exhibited in Fig. 1319 for the heptanetoluene system at 101.3 kPa (1 atm). Five purecomponent constants for each species (Tc, Pc, ffl, 8, and vL) are required to use the CS method, which when applied within the restrictions discussed by Lenoir and Koppany [Hydrocarbon Process., 46(11), 249 (1967)] gives good results. Revised coefficients of Grayson and Streed (Gs) (Pap. 20P07, Sixth World Pet. Conf., Frankfurt, June, 1963) for the OL expression permit application of the CS correlation to higher temperatures and pressures and give improved predictions for hydrogen. Jin, Greenkorn, and Chao [AlChE J, 41,1602 (1995)] present a revised correlation for the standardstate liquid fugacity of hydrogen, applicable from 200 to 730 K.
For mixtures containing polar substances, more complex predictive equations for ytL that involve binaryinteraction parameters for each pair of components in the mixture are required for use in Eq. (134), as discussed in Sec. 4. Six popular expressions are the Margules, van Laar, Wilson, NRTL, UNIFAC, and UNIQUAC equations. Extensive listings of binaryinteraction parameters for use in all but the UNIFAC equation are given by Gmehling and Onken (op. cit.). They obtained the parameters for binary systems at 101.3 kPa (1 atm) from best fits of the experimental Tyx equilibrium data by setting OV and OL to their idealgas, idealsolution limits of 1.0 and Psat/P respectively, with the vapor pressure Psat given by a threeconstant Antoine equation, whose values they tabulate. Table 132 lists their parameters for some of the binary systems included in
Table 131, based on the binarysystem activitycoefficientequation forms given in Table 133. Consistent Antoine vaporpressure constants and liquid molar volumes are listed in Table 134. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanolhexane system, whose activity coefficients are shown in Fig. 1320. For systems such as this, in which activity coefficients in dilute regions may
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