Fugacity coefficient calculated

The /<-values are calculated by Equation 1.25, with the vapor phase fugacity coefficients calculated from the equation of state and the liquid phase fugacity coefficients for an ideal solution calculated as... 

The fugacity in the gas phase can be obtained from the fugacity coefficient ( ), calculated with a suitable equation of state,... 

The fugacity coefficients calculated by this procedure are shown in Figure 7-4. 

With the critical data, acentric factors, and the binary parameters, the pure component and mixture parameters have to be calculated for a temperature of 723.15 K. As initial composition, the mole fractions determined assuming ideal gas behavior are used and the parameters required for the calculation of the fugacity coefficients calculated. 

SETNAK - CREATES THE PARAMETER ARRAYS FOR FUGACITY COEFFICIENT CALCULATIONS... 

With these expressions for the activity coefficients, the equilibrium constants and Henry s constant calculated with the fit equations (S.4) and (S.7)> and the fugacity coefficients calculated using Nakamura s method as outlined in Appendix 9.3, the nine unknown concentrations may be determined for set input amounts of HjO and SO2 with the Newton-Raphson method using equations (S.l). (S.2), (S.3), (S.5), (S.6), (S.8), (S.9), (S.IO) and (S.ll) as the system model. An example of such a calculation is shown in Figure 9.10. 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

Chapter 3 discusses calculation of fugacity coefficient < ). Chapter 4 discusses calculation of adjusted activity coefficient Y fugacity of the pure liquid f9 [Equation (24)], and Henry s constant H. 

The fugacity coefficient is a function of temperature, total pressure, and composition of the vapor phase it can be calculated from volumetric data for the vapor mixture. For a mixture containing m components, such data are often expressed in the form of an equation of state explicit in the pressure... 

It is important to be consistent in the use of fugacity coefficients. When reducing experimental data to obtain activity coefficients, a particular method for calculating fugacity coefficients must be adopted. That same method must be employed when activity-coefficient correlations are used to generate vapor-liquid equilibria. 

Figures 3 and 4 show fugacity coefficients for two binary systems calculated with Equation (10b). Although the pressure is not large, deviations from ideality and from the Lewis rule are not negligible.

To use Equation (13), it is first necessary to calculate the true fugacity coefficient (ft. This calculation is achieved by utilizing the Lewis fugacity rule... 

Figure 3-7. Fugacity coefficients for a saturated mixture of propionic acid (1) and raethylisobutylketone (2). Calculations based on chemical method show large variations from ideal behavior.

Details for calculating fugacity coefficients are given in Appendix A. 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Figure 13 presents results for a binary where one of the components is a supercritical, noncondensable component. Vapor-phase fugacity coefficients were calculated with the virial... 

As discussed in Chapter 3, the virial equation is suitable for describing vapor-phase nonidealities of nonassociating (or weakly associating) fluids at moderate densities. Equation (1) gives the second virial coefficient which is used directly in Equation (3-lOb) to calculate the fugacity coefficients. 

However, when carboxylic acids are present in a mixture, fugacity coefficients must be calculated using the chemical theory. Chemical theory leads to a fugacity coefficient dependent on true equilibrium concentrations, as shown by Equation (3-13). ... 

The Lewis fugacity rule is used for calculating the fugacity coefficients of the true species, and (2) the second virial co-... 

Subroutine MULLER. MULLER iteratively solves the equilibrium relations and computes the equilibrium vapor composition when organic acids are present. These compositions are used by subroutine PHIS2 to calculate fugacity coefficients by the chemical theory. 

IF BINARY SYSTEM CONTAINS NO ORGANIC ACIDS. THE SECOND VIRTAL coefficients ARE USED IN A VOLUME EXPLICIT EQUATION OF STATE TO CALCULATE THE FUGACITY COEFFICIENTS. FOR ORGANIC ACIDS FUGACITY COEFFICIENTS ARE PREDICTED FROM THE CHEMICAL THEORY FOR NQN-IOEALITY WITH EQUILIBRIUM CONSTANTS OBTAINED from METASTABLE. BOUND. ANO CHEMICAL CONTRIBUTIONS TO THE SECOND VIRIAL COEFFICIENTS. 

CALCULATE FUGACITY COEFFICIENTS FOR NQN-ASSOCI ATING COMPONENTS ... 

CALCULATE FUGACITY COEFFICIENTS FOR ASSOCIATING COMPONENTS WITH CHEMICAL THEORY. FIRST CALCULATE THE EOUILIBRIUM CONSTANTS. 

PHIS calculates vapor-phase fugacity coefficients, PHI, for each component in a mixture of N components (N 5. 20) at specified temperature, pressure, and vapor composition. 

PHIS CALCULATES VAPOR PHASE FUGACITY COEFFICIENTS PHI, FOR ALL N... 

CALCULATE VAPOR PHASE FUGACITY COEFFICIENTS FOR ACTUAL COMPOSITION OF... 

The fugacity coefficient of component i at saturation is obtained after the calculation of the vapor fugacity at saturation, by the relation ... 

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