Peng enthalpy

The methanol(l)/acetone(2) system serves as a specific example in conjunction with the Peng/Robinson equation of state. At a base temperature To of 323.15 K (50°C), both XT E data (Van Ness and Abbott, Jnt. DATA Ser, Ser A, Sel. Data Mixtures, 1978, p. 67 [1978]) and excess enthalpy data (Morris, et al., J. Chem. Eng. Data, 20, pp. 403-405 [1975]) are available. From the former. 

The value of (8Z/dT)P can be obtained from an equation of state, such as the Peng-Robinson equation of state, and the integral in Equation 4.78 evaluated3. The enthalpy departure for the Peng-Robinson equation of state is given by3 ... 

Now calculate the molar enthalpies of the vapor and liquid streams. Enthalpies were calculated here from ideal gas enthalpy data corrected using the Peng-Robinson Equation of State (see Chapter 4) ... 

Assume that reciprocating compressors are to be used. Enthalpies can be calculated from the Peng - Robinson Equation of State. 

Equation 9 was used to calculate H for steam + n-heptane as follows. The Peng-Robinson equation with parameters obtained from criticality conditions was used to calculate the residual enthalpy H of methyl fluoride. Peng-Robinson parameters for n-heptane were obtained by fitting to the residual enthalpy of the fluid at temperatures below the critical, and by using criticality conditions at higher temperatures. The mixing rules given in equation 4 with k.. = 1 were used to calculate H. As... 

The Peng-Robinson equation of state was used to estimate K values and enthalpy departures [as opposed to the De Priester charts used in Example 1 and by Seader (ibid.) who solved this problem by using the Thiele-Geddes (op. 

The graphs are based on the Peng-Robinson equation of state (1) as improved by Stryjek and Vera (2, 3). The equations for thermodynamic properties using the Peng-Robinson equation of state are given in the appendix for volume, compressibility factor, fugacity coefficient, residual enthalpy, and residual entropy. Critical constants and ideal gas heat capacities for use in the equations are from the data compilations of DIPPR (8) and Yaws (28, 29, 30). 

Peng-Robinson Cubic EOS Excess enthalpy from EOS... 

For computing the enthalpy departures of pure gases and gas mixtures, the equations of state of Sec. 14-2 may be used for both the vapor and liquid phases (1) modified versions of the BWR equation of state, such as the one proposed by Starling, (2) the Soave-Redlich-Kwong, and (3) the Peng-Robinson equation of state. Another method which has been tested extensively and found to give accurate results even for polar gas mixtures is the Yen-Alexander correlation.78... 

In particular, to obtain numerical values for the enthalpy or entropy departure for a fluid that obeys the Peng-Robinson equation of state, one uses the following procedure ... 

Using the Peng-Robinson equation-of-state programs or MATHCAD worksheets described in Appendix B, we obtain the results in Table 7.5-1. The vapor pressure as a function of temperature is plotted in Fig. 7.5-3. The specific volumes and molar enthalpies and entropies of the coexisting phases have been added as the two-phase envelopes in Figs. 6.4-3, 6.4-4, and 6.4-5.B... 

Peng and Robinson report the results of comparisons of their equation with Soaves. They find that the two equations give similar values for gas densities and gas-phase enthalpy deviations, but that the Peng-Robinson equation yields improved correlation of pure-component vapor pressures and better estimates of liquid densities. 

Therefore, the calculation of the fugacity coefficient by a cubic equation of state does not require much in terms of additional computations, since the required expressions for the residual enthalpy and entropy have been obtained already. In particular, the result for the Soave-Redlich-Kwong and the Peng-Robinson equation are... 

As with pure substances, the properties of mixtures can be tabulated for future reference. However, such tabulations quickly become impractical as the number of components increase. It is therefore of great practical value to be able to obtain the properties of mixture by calculation from an equation of state, as done for pure fluids. In general, equations of state developed for pure fluids maybe extended to mixtures provided that composition is properly accounted for. Cubic equations such as the Soave-Redlich-Kwong and the Peng-Robinson equation require two parameters, a and b (see Chapter 2). For mixtures, these parameters are typically calculated from the corresponding parameters of the individual components. In this approach, the effect of composition is reflected in the mixture parameters a and b. Once these parameters have been determined, the calculation is identical to that for pure components. This includes the calculation of the compressibility factor, molar volume, residual enthalpy, and residual entropy. 

E. Check. The results are checked throughout the trial-and-error procedure. Naturally, they depend upon the validity of data used for the enthalpies and Ks. At least the results appear to be self-consistent (that is, Z X = 1.0,1 y = 1.0) and are of the right order of magnitude. This problem was also solved using Aspen Plus with the Peng-Robinson equation for VLE (see Chapter 2 Appendix A). The results are x j = 0.0079, Xp = 0.5374, Xfj = 0.4547, L = 1107.8, and y j = 0.7424, yp = 0.2032, yjj = 0.0543, V = 392.2, and = 27.99°C. With the exception of the drum tenperature these results, which use different data, are close. 

This approximation is often useful for estimation enthalpies of vaporization in the vacuum region. For pressures greater than approx. 1 bar, a qualitatively wrong curvature is obtained thus, Eq. (3.65) cannot be recommended for general use. For v/, a cubic equation of state is more appropriate, for example, the Peng-Robinson equation of state, which is appropriate for the calculation of saturated vapor densities from the triple point to temperatures close to the critical point. 

The separation factors mainly depend on composition and temperature. The correct composition dependence is described with the help of activity coefficients. Following the Clausius-Clapeyron equation presented in Section 2.4.4 the temperature dependence is mainly influenced by the slope of the vapor pressure curves (enthalpy of vaporization) of the components involved. But also the activity coefficients are temperature-dependent following the Gibbs-Helmholtz equation (Eq. (5.26)). This means that besides a correct description of the composition dependence of the activity coefficients also an accurate description of their temperature dependence is required. For distillation processes at moderate pressures, the pressure effect on the activity coefficients (see Example 5.7) can be neglected. To take into account the real vapor phase behavior, equations of state, for example, the virial equation, cubic equations of state, such as the Redlich-Kwong, Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), the association model, and so on, can be applied. 

According to the Peng-Robinson equation of state, the specific enthalpy of the stream leaving the first block is determined to be hi = —163.3 kj/mol at Pi = 12.226bar. Using an activity coefficient model with an ideal gas phase, the coordinates for P2 = P] and I12 = refer to the liquid state at T2 = 430.% K. Using Cp - from Appendix A, the corresponding enthalpy difference... 

The residual part of the enthalpy of the saturated vapor can be determined with the Peng-Robinson equation of state using Eq. (6.53) ... 

The reason for the significant deviation of Option 3 is the poor representation of cp with Route A because of a limited quality of the Peng-Robinson equation in vapor enthalpy calculations and possibly a poor reproduction of the slope of the enthalpy of vaporization as a function of temperature. Over a limited temperature range, this can be corrected by an alternative adjustment of the coefficients in the correlation of the enthalpy of vaporization (Eq. (3.62)). With the new coefficients... 

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