VTPR Group Contribution Equation of State

Equation of state Soave-Redlich-Kwong Volume-translated Peng-Robinson 

In the case of the group contribution equation of state VTPR, instead of temperature-independent group interaction parameters from original UNIFAC, temperature-dependent group interaction parameters as in modified UNIFAC are used. As for modified UNIFAC, the required temperature-dependent group interaction parameters of VTPR are fitted simultaneously to a comprehensive data base. Besides VLE data for systems with sub and supercritical compounds, gas 

Using the same group interaction parameters, other phase equilibria can be predicted as weU. The predicted SLE behavior of the binary system ethane-C02 

An overview about the development of group contribution methods and group contribution equations of state for the prediction of phase equilibria and other thermophysical properties can be found in [69]. 

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Schmid, B. and J. Gmehhng. 2012. Revised parameters and typical results of the VTPR group contribution equation of state. Fluid Phase Equilibria. 317, 110. 

Chapter 5 gives a comprehensive overview on the most important models and routes for phase equilibrium calculation, including sophisticated phenomena like the pressure dependence of liquid-liquid equilibria. The abilities and weaknesses of both models and equations of state are thoroughly discussed. A special focus is dedicated to the predictive methods for the calculation of phase equilibria, applying the UNIFAC group contribution method and its derivatives, that is, the Mod. UNIFAC method and the PSRK and VTPR group contribution equations of state. Furthermore, in Chapter 6 the calculation of caloric properties and the way they are treated in process simulation programs are explained. 

P5.12 Predict the solubility of methane, carbon dioxide, and hydrogen sulfide in methanol at a temperature of —30 °C for partial pressures of 5 bar, 10 bar, and 20 bar using the PSRK and VTPR group contribution equations of state. Compare the results with the solubilities obtained using Henry s law and the Henry constants predicted in problem PS.11. 

Instead of g -models also equations of state can be used for the determination of azeotropic behavior of binary or multicomponent systems. In Figure 5.54 the experimental and predicted azeotropic points using the group contribution equation of state VTPR (see Section 5.9.4) for the system ethane-C02 up to pressures of 80 bar are shown. 

If no experimental data are available gas solubilities can be predicted today with the help of group contribution equations of state, such as Predictive Soave-Redlich-Kwong (PSRK) [43] or VTPR [44]. These models are introduced in Sections 5.9.4 and 5.9.5. 

Table 5.20 Main differences between the new group contribution equation of state VTPR and the PSRK model.

Figure 5.102 Experimental and predicted SLE data for the system ethane (1)-C02 (2) experimental [3, 68] — group contribution equation of state VTPR.

Figure 5.103 Experimental and predicted phase equilibrium data and excess enthalpies for alkanes with ketones predicted using modified UNIFAC respectively the group contribution equation of state VTPR modified UNIFAC, — group contribution equation of state VTPR.

At the same time the group contribution equation of state VTPR in contrast to modified UN I FAC can be applied for the prediction of phase equilibria including compounds not covered by modified UNIFAC, for example, the various gases. The predicted LLE results for the ternary system nitrogen-C02-methane at 122 K and the binary system nitrogen-C02 as a function of temperature are shown in Figure 5.104 together with the experimental data. 

A group contribution equation of state shows in particular great advantages compared to the usual equation of state approach in the case of multicomponent mixtures, when the multicomponent mixture consists of gases and various alkanes, alcohols, alkenes, and so on. The reason is that the same parameters can be used for all alkanes, alcohols, alkenes, so that the size of the parameter matrix is small in comparison to tlie typical equation of state approach. The results of VTPR for a 12 component system consisting of nitrogen-methane-C02-alkanes are shown in Figure 5.105. As can be seen, excellent results are obtained with the six required parameters (66 binary parameters would be required for the classical equation of state approach). 

Compare the experimental data for the system ethanol-water measured at 70 ""C (see Figure 5.30 resp. Table 5.2) with the results of the group contribution method modified UNIFAC and the group contribution equation of state VTPR. 

Calculate the solubility of solid carbon dioxide in propane with the help of the group contribution equations of state PSRK and VTPR assuming simple eutectic behavior. Compare the results with the results assuming ideal behavior and the experimental data that can be downloaded from the textbook page on ivww.ddbst.com. All required parameters can be found in Appendix A. 

With the help of the group contribution equation of state VTPR, it should be checked whether the quaternary system carbon dioxide (1)-ethane (2)-hydrogen sulfide (3)-propane (4) shows binary, ternary, or quaternary azeotropes at 266.5 K. 

Stored in the DDB. For three binary systems, azeotropic behavior is calculated. No ternary or quaternary azeotropic point is found using the group contribution equation of state VTPR. A comparison with the experimental data stored in the DDB shows that this is in agreement with the experimental findings. 

The results of Examples 11.2 and 11.3 show that today even predictive models can be applied successfully to find the binary and higher azeotropes of a multicomponent system. With the development of the group contribution equations of state like PSRK and VTPR, the range of applicability was extended to compounds which are not covered by group contributions methods such as UNI FAC or modified UNIFAC... 

Instead of a -model or a group contribution method like modified UN I FAC also an equation of state or a group contribution equation of state can be used for the calculation of residue curves and distillation boundaries. In Figure 11.15, the results are shown for the ternary system carbon dioxide-hydrogen sulfide-ethane at 266.5 K using VTPR. As can be seen, two binary azeotropes and one distillation boundary is observed. 

Calculate the enthalpy of reaction for the ammonia synthesis at 450 C and a pressure of 600 atm using the value of the standard enthalpy of reaction at 450 °C in the ideal gas state calculated in Example 12.1. For the calculation of the residual enthalpies, the group contribution equation of state volume-translated Peng-Robinson (VTPR) should be applied. The required VTPR parameters are given in Appendix K. 

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