Generalized correlations fugacity coefficient

According to equation 184, all fluids having the same value of CO have identical values of Z when compared at the same T and P. This principle of corresponding states is presumed vaHd for all T and P and therefore provides generalized correlations for properties derived from Z, ie, for residual properties and fugacity coefficients, which depend on T and P through Z and its derivatives. 

One of the most versatile and accurate generalized correlations for the prediction of the fugacity coefficient (3) involves a three-parameter generalized correlation which takes advantage of the acentric factor. The correlation breaks the fugacity coefficient into two parts (j) and ( ). ... 

The fugacity coefficients in Equation (7.29) can be calculated from pressure-volume-temperature data for the mixture or from generalized correlations. It is frequently possible to assume ideal gas behavior so that 4>A = 1 for each component. Then Equation (7.29) becomes... 

This is the choice made here, and Figs. 11.2 through 11.5 provide a three-parameter generalized correlation for the fugacity coefficient. Figures 11.2 and 11.4 for d>° can be used alone as a two-parameter correlation which does not incorporate the refinement introduced by the acentric factor. 

The appropriate expression for the equilibrium equation is Eq. (15.23). equation requires evaluation of the fugacity coefficients of the species prese equilibrium. Although the generalized correlation of Sec. 11.4 is applicable calculations involve iteration, because the fugacity coefficients are functions of sition. For purposes of illustration, we carry out only the first iteration, based assumption that the reaction mixture is an ideal solution. In this case Eq. (1 reduces to Eq. (15.24), which requires fugacity coefficients of the pure reacting at the equilibrium T and P. Since v = = -1, this equation becomes... 

Although we have omitted an identifying subscript in the preceding equations, their application so far has been to the development of generated correlations for pure gases only. In the remainder of this section we show how the virial equation may be generalized to allow calculation of fugacity coefficients < , of species in gas mixtures. 

Fugacity coefficient (d>) The Lee-Kesler generalized correlation for fugacity coefficient is... 

The fugacity coefficient 0 is generally calculated from an equation of state. However, many equations of state require a knowledge of the critical parameters of the solute, which may not always be available. Nevertheless, solubilities can be correlated, and sometimes extrapolated, using this approach. The addition of more solutes poses few problems from a thermodynamic viewpoint, as long as the appropriate solid-state fugacity is used in the calculations. This type of approach may also be used to study... 

The description of vapour-liquid equilibrium behaviour can be obtained from analytical equations and generalized correlations. The generalized conelations are generally for the equilibrium ratio, K, and the fugacity coefficients. 

This equation, used in conjunction with Eqs. (4-77) and (4-78), provides a useful generalized correlation for the fugacity coefficients of pure species. 

The liquid-phase fugacity coefficient = /f/P may be calculated from a generalized correlation in terms of reduced temperature and pressure such as those of Lydersen et al.42 and Curl and Pitzer.15 Chao and Seader used a modified form of the Curl and Pitzer correlation. The correlation was modified by use of experimental data such that appropriate values of could be computed for the case where a component does not exist as a liquid and for the case of low temperatures. The following expression was proposed for the calculation of the fugacity coefficient for any component / in the liquid phase... 

The approximation to ideality is not very satisfactory for equilibrium reactions which occur at high pressure, such as the synthesis of ammonia. It is however generally assumed in chemical kinetics. To check the validity of this approximation, the Redlich and Kwong state equation (cf Chap. Ill) will be used. These authors have also suggested correlations which permit the fugacity coefficients to be estimated. ... 

Using the generalized correlations for gases, estimate the compressibility factor, fugacity coefficient, and residual enthalpy for hydrogen at 350 K and 100 atm. 

The separation of the vapor and liquid fugacities and the activity coefficients in the fundamental equilibrium relationship allow great flexibility, and a multitude of choices, in the selection of the thermodynamic relationships or empirical equations for estimation of each of these quantities. For the vapor fugacity coefficient any of the equations of state mentioned earlier or some other, such as the virial equation, may be used. In the latter case, the virial coefficients may be determined experimentally or estimated using three- or four-parameter generalized correlations. 

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