VTPR Parameters

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. 

For some important classes of compounds, methods have been developed to predict EOS parameters, including binary interaction parameters, from molecular structure. The PSRK method [44] has found significant use, and a promising new method is known as VTPR [45]. 

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

Figure 5.44 Experimental and correlated VLE, azeotropic, and data using the VTPR equation of state with g -mixing rules (UNIQUAC with temperature-dependent parameters) ...

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... 

Figure 5.108 Correlation results of the equation of state VTPR for the system acetone(l)-water(2) using temperature dependent UNIQUAC parameters au = 472.46 K, 021 = -585.54 K, bn = -0.40712, 2i = 2.5101.

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). 

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. 

Table K.2 Selected group interaction parameters for the VTPR GC-EOS [1]. 

To conclude, predictive cubic EoS (PPR78, PR2SRK, PSRK, VTPR, UMR-PR) make a perfect job to simulate the phase behaviour of crude oils, gas condensate and natural gases. For processes in which water and/or glycol are present (e.g. transportation processes), it is advised to use more complex EoS like the CPA (Cubic-Plus-Association) by (Derawi et al., 2003) or equation deriving from the SAFE (Statistical Associating Fluid Theory) which are however non predictive (many parameters have to be fitted on experimental data). 

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