PR EOS

The compressibility Z can be calculated using Equation 1.145b. Equation 1.145b can have three routes the largest value is applicable for the vapor phase and the smallest one is applicable for the liquid phase. Knowing the value of compressibility. Equation 1.148 can be used to calculate fugacity for both liquid and vapor phases. 

For a particular pressure, the fugacity coefficient for both liquid and vapor phases will be the same. This pressure is the vapor pressure of the component at that temperature. The pressure is established using a trial-and-error method. 

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Figure 2.1 Hexane and C02 at 25 °C as predicted by the PR-EOS (a) volumeexpansionofthe liquid phase with pressurization of C02 and (b) solvent mixture density and molar volume with pressurization of C02.

As it was pointed out by Chen et al. [22] the calculation of solubility data requires a proper estimation of sublimation pressures. The data were correlated using the PR EOS with classical mixing rules and the UNIFAC model with previously determined anu, parameters. 

The importance of a suitable G.C. method for evaluating the pure solid properties was evidenced. The limitations of the different G.C. methods are due to the limited experimental data available in the literature for heavy multifunctional compounds. The PR EOS with classical mixing rules gives the same results than the most complex UNIFAC approach. The importance of the sublimation pressure for correlating solubility data was underlined. 

Again for consistency, the critical density will be estimated using the PR EoS and not the more accurate value from tabulated data. For COz the critical density used for this purpose is 419.2 kg/m3. 

Further, the fugacity coefficient was calculated as a function of X2, and the value of K2 was obtained from the slope of the curve In 02 against X2 (for additional details see Appendix 2). The calculated values of K2 for the CO2 + naphthalene and CO2 + pyrene systems are plotted in Figure 1. Similar calculations were carried out using the Peng—Robinson (PR) EOS. Good agreement was found between the values of K2 obtained from the two equations of state. 

For the calculations presented in this paper, we first elected to use three simple cubic equations of state PR-EOS SRK-EOS and RK-EOS. For the pure components, critical properties (Pq, Tq) and Pitzer s acentric factor (ci>) are needed to obtain a and b . Critical properties have been measured for most of the low molecular weight components and are reported by Reid et al. 

The optimum binary interaction parameters are shown in Table 111. An example of the results is shown in Figure 1 for the PR-EOS applied to carbon dioxide/methyl oleate at 70 C. Comparing the results of those three simple equations of state, the Redlich-Kwong equation of state gave the poorest prediction. 

The fugacity coefficient of species i in a one-phase mixture is obtained from the PR-EOS using IPVDW as follows ... 

Note that with this modification to the van der Waals one-fluid model, the fugac-ity coefficient expression for species i given in eqn. (3.3.9) will change because an additional compositional dependence has been introduced to the a term of the EOS. For the PR EOS, with the van der Waals one-fluid model, a more general form of the fugacity coefficient expression of species i in a mixture is... 

The first logarithmic term in eqn. (C.l) is zero in the limit of infinite pressure because for the PR EOS... 

Because the excess Helmholtz free energy is closely related to this departure term (see Wong and Sandler 1992 for details) the same C term appears in the excess Helmholtz free-energy term obtained from the PR EOS. 

Figure 8 Effect of density on solid ((i-carotene) solubility in SCCO2 experimental data at 40°C ( ), 50°C (A), 60°C ( ) calculated values (solid curves) by the PR EOS (65).

The PR eos has been extended by Stryjek and Vera [10] to polar substances by introducing a substance-specific parameter. The modification also gives improved fitting of the vapor pressure of normal fluids. The function of the PRSV equation is given by... 

Substituting Equation (4.278) into Equation (4.275) and then integrating gives the residual Hehnholtz energy by the PR eos,... 

The integral in Equation (4.282) for the PR eos will be taken from Equation (4.279). The pv term in Equation (4.282) will be formed by using the PR eos presented in Equation (4.278). It follows that... 

Example 4.13 Internal Energy by Peng-Robinson eos The PR eos is differentiated to give... 

Substituting p of Equation (4.159) and its derivative Equation (4.292) into Equation (4.291) and integrating, we obtain internal energy by PR eos. 

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