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Analytical expressions for calculating vapor-liquid compositions, enthalpies, and entropies have been developed for hydrocarbon mixtures containing none or some of the nonhydrocarbon gases and evaluated against experimental measurements of vapor-liquid equilibria and enthalpies. The evaluation results show that the proposed equations can be applied over wide range of conditions with good accuracy. These equations are extensions and improvements of equations presented previously by Lee and Edmister (1971~) mainly for low temperature thermodynamic property calculations.

A new empirical equation has been developed for predicting the fugacity coefficients for pure hydrocarbons in the liquid phase. The parameters of this correlation are reduced pressure, reduced temperature, and acentric factor. There are 1 3 empirical constants and the equation is convenient for computer solution. Graphical comparisons show that this new equation agrees with values of f/P derived from P-V-T data. In addition to predicting reference state fugacities for activity coefficients, this equation can be used in the calculation of enthalpies of pure components at saturated liquid and compressed liquid states. Tabular comparisons show that the proposed new equation agrees with experimental values (H°-HL) and also values calculated from P-V-T data by others.

Vapor-liquid equilibrium distribution ratios for hydrocarbons can be computed by the new equations presented in this work with higher accuracy than i s possible by previous generalized methods. In this proposed new method, the three coefficients of the combination Yiyi/+i are newly developed and generalized functions.The vapor-phase fugacity coefficient @i was formulated via a new generalized equation of state, and the liquid-phase activity coefficient yi is predicted via a proposed new equation that contains three generalized binary interaction coefficients for each binary set in a mixture. These interaction coefficients were developed from experimental K value data. Two expressions are employed in predicting the liquid fugacity coefficient vi, one for the real liquid state and one for the hypothetical liquid state, the latter being developed empirically from experimental K value data also. These two vi equations are also generalized.This new K value prediction method gave an average absolute deviation of 5.25% on a total of 3,504 data points on 19 hydrocarbons in binary and ternary mixtures, these data points being selected so that they cover the range of pure component T r = 0.5 and up and pressures up to 0.9 of the true mixture critical pressure. inclusion of nonhydrocarbon-hydrocarbon systems in the evaluation gave an overall absolute deviation of 6.33% for 4,290 K value data points on 23 components.The phase distribution ratio, Ki = yi/xi, for the components of coexisting equilibrium vapor and liquid mixtures is a complex function of the conditions and compositions of the coexisting phases. Analytical prediction methods for the K value have been based on the equal-fugacity criterion of equilibria, that is, the fugacity of each component is the same in both vapor and liquid phases. Two approaches have been used in predicting equilibrium K values by this equal-fugacity criterion.In one approach, an equation of state, describing PVT behavior, is used to compute the fugacities for the components of both phases. In the other approach, liquidphase fugacities are found via an activity coefficient plus pure component reference state fugacity relationship and combined with equation of state vapor-phase fugacities to obtain the K values. MATHEMATICAL MODELIn terms of fugacity and activity coefficients, the equalfugacity criterion of equilibria may be written asThe left-hand side terms in Equation (1) ship for correlating and predicting K values of hydrocarbons. Chao and Seader ( 2 ) used Equation ( 2 ) as the basis for their generalized correlation. Equation ( 2 ) is the model for the present generalized K value prediction method.In the present work, as in the previous Chao-Seader ( 2 ) work, analytical expressions were derived for the three right-hand terms of Equation ( 2 ) . These semitheoretical expressions were based upon a vapor-phase equation of state and a large quantity of experimental vapor-liquid equilibria data, which were used to determine constants in the theoretical and empirical expressions derived ...

The possibility of calculating the isothermal enthalpy difference for a saturated liquid mixture by applying the isobaric Gibbs-Duhem equation is attractive, until one has tried it. After working with this calculation for some time, we have experienced some difficulties and write this paper to share our experience with others who might be intrigued, as we once were, with this enthalpy calculation method.Recent publications ( 5 , 6) have suggested the isobaric Gibbs-Duhem equation as a rigorous method for calculating the heats of vaporization of a mixture and then demonstrated the calculation via simplifying and nonrigorous assumptions, For engineering design applications, the chemical engineer needs an analytical, as well as rigorous, method for calculating the enthalpies of coexisting equilibrium vapor and liquid mixtures. In other words, graphical differentiations and simplifying assumptions are not acceptable. From this point of view we looked at this method. ISOBARIC GIBBS-DUHEM EQUATION BYUNG-IK LEE and WAYNE C. EDMISTEROklahoma Stote University, Stillwoter, Oklahomo research type of calculations, the graphical differentiation of computed lnfi values is an acceptable procedure. For repetitive applications, as in design work, analytical differentiation via a digital computer is the only acceptable technique and this is the method used in our work. DERIVATIVES OF FUGACITYThe temperature derivatives of In f i that appear in Equation (1) were evaluated by using an equation-of-state and temperature-composition data. An expression for (dlnfi/d'r)p will be derived from the definition of the fugacity coefficient, 4, that is f i = 4iPyi. Defining In& as a function of P, T and y leads to the following An exact and general form of the Gibbs-Duhem equaBy combining Equation (5)