PSRK method

Fischer, K. Gmehling, J. Further development, status and results of the PSRK method for the prediction of vapor—liquid equilibria and gas solubilities. Eluid Phase Equilib. 1996, 121, 185-206. 

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]. 

In ASPEN PLUS, the RSTOIC subroutine is used with a feed stream containing I Ibmol/hr CO and 2 Ibmol/hr H2 and the PSRK method (Soave-Redlich-Kwong equation of state with Holderbaum-Gmehling mixing rules). To obtain the heat of reaction, the fractional conversion of CO is set at unity, with the product stream temperamre at 25°C and the vapor fraction at 1.0. The latter keeps the methanol product in the vapor phase at 2.44 psia, and hence both the reactants and product species are vapor. The heat duty computed by RSTOIC is —38,881 Btu/hr, and hence the heat of reaction is AH, = —38,881 Btu/lbmol CO. 

The PSRK model includes two molecular parameters, a volume parameter, r, and a surface area parameter, q. In this work, these molecular parameters are modified for ethanol, assuming them to be adjustable parameters. The VLE data for the binary systems acetic acid + ethanol, acetaldehyde + ethanol, fiirfiiral + ethanol, methanol + ethanol, and 1-pentanol + ethanol were used to obtain optimum values of r and q. This empirical approach tries to explain the modification of the molecular physical structure of ethanol mixed with some congener. An analogous empirical approach was applied for temperature-dependent variables in UNIFAC-Dortmund [16]. Then the method was validated with the binary system ethanol + water and three ternary systems, 1-pentanol + ethanol + water, 1-propanol + ethanol + water, and furfural + ethanol + water. 

Various thermodynamic methods based on -models (Wilson, NRTL, UNIQUAC) or group contribution methods (UNIFAC, modified UNIFAC, ASOG, PSRK) can be used for either calculating or predicting the required activity coefficients for the components under given conditions of temperature and composition (Reference 2). 

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.ll Predict the Henry constants of methane, carbon dioxide, and hydrogen sulfide in methanol in the temperature range —50 to 200 C with the help of the group contribution methods PSRK and VTPR. 

P8.12 In the free DDBSP Explorer Version, search for solid-liquid equilibrium data for the mixture 2-propanol-benzene. Regress the two datasets simultaneously using the Wilson. NRTL, and UNIQUAC model. Check the performance of the three models. Compare the data to the results of the predictive methods UNIFAC, modified UNIFAC. and PSRK. Examine the different graphical representations. 

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... 

For any of the methods to be useful requires values of T, pc and a> (see Chapter 3 and Section 5.3.2) to estimate a and b for the pure compounds. Values of T, Pc and co can be obtained from the American Institute of Chemical Engineers Design Institute for Physical Properties DIPPR ° or other handbooks or estimated from sources such as refs 108, 109 and 110. The temperature dependence of a is given by Mathias and Copeman for the PSRK, MHV2 and LCVM while for Wong-Sandler, the Stryjek and Vera method is used for the Peng-Robinson equation of state. Estimates of the vapour pressure can be obtained, for example, from ref 108, 110, 111 and 112. 

This method was first applied by Van Laar who provided an expression of the activity coefficients using the Van der Waals state equation. Unfortunately, the success of the Van Laar model was limited by the fact that the Van der Waals eqnation, which appUes to weakly imperfect gases, is veiy far from reahty when approaching the liquid phase and even more so for the latter. The method was subsequently used with greater success with more efficient state eqnations accompanied by sophisticated mixing laws. In particular, this is the case for the PSRK model which we will describe. 

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