In Figure 1, Aspen Plus applies the PC-SAFT EOS model to calculate both vapor-liquid and liquid-liquid equilibria for methanol-cyclohexane mixtures at
p = 1.013 bar. This mixture exhibits an azeotropic vapor-liquid equilibrium at
higher temperatures and shows a liquid-liquid equilibrium at lower
temperatures. Both pure and binary parameters used are taken directly from the paper by Gross and Sadowski (2002b). The results show that the PC-SAFT model with the association term included can correlate phase equilibrium data well for associating mixtures.
Figure 1. Isobaric vapor-liquid and liquid-liquid equilibria of methanol- cyclohexane at = 1.013 bar. Experimental data are taken from Jones and Amstell (1930) and Marinichev and Susarev (1965).
Figure 2 shows a model calculation for HDPE-Hexane mixtures. This system exhibits both lower critical solution temperature (LCST) and upper critical solution temperature (UCST) at p = 50 bar. The pure parameters are taken directly from papers Gross and Sadowski (2001; 2002a). The binary
parameter between hexane and ethylene segment is set to 0.012. The phase equilibrium calculations are carried by Flash3 block with Gibbs flash algorithm in Aspen Plus.
Figure 2. Liquid-liquid equilibria of HDPE-Hexane mixtures in a weight fraction-pressure plot by PC-SAFT EOS model. It shows both lower critical solution temperature (LCST) and upper critical solution temperature (UCST).
Figure 3 shows the vapor-liquid equilibrium of the mixture water-acetone at p = 1.703 bar. The dashed line represents PC-SAFT calculations where water is treated as an associating component and acetone as a polar component; the cross association in the mixture is not considered (
κ
ij = -0.15). The solid line represents PC-SAFT calculations where the cross association between water and acetone is accounted for (κ
ij = -0.055) using a simple approach by Sadowski & Chapman et al. (2006). In this approach, the association energy and effective volume parameters of the non-associating component (acetone) are set to zero and to the value of the associating component (water),respectively. Further, the polar component is represented by the three pure- component parameters without using the dipolar model.
Figure 3. Vapor-liquid equilibrium of the mixture water-acetone at p = 1.703 bar. Experimental data are taken from Othmer and Morley (1946).
Figure 4 shows the liquid-liquid equilibria of polypropylene (PP)-n-pentane at three temperatures in a pressure-weight fraction plot. The weight average molecular weight of PP is Mw = 50.4 kg/mol, Mw/Mn = 2.2. Both pure and binary parameters used are taken directly from the paper by Gross and Sadowski (2002a).
Figure 4. Liquid-liquid equilibria of PP-n-Pentane at three different
temperatures. Comparison of experimental cloud points (Martin et al., 1999) to PC-SAFT calculations (
κ
ij = 0.0137). The polymer was assumed to bemonodisperse at Mw = 50.4 kg/mol.
References
Gross, J., & Sadowski, G. (2001). Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res., 40, 1244-1260.
Gross, J., & Sadowski, G. (2002a). Modeling Polymer Systems Using the Perturbed-Chain Statistical Associating Fluid Theory Equation of State. Ind.
Eng. Chem. Res., 41, 1084-1093.
Gross, J., & Sadowski, G. (2002b). Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res., 41, 5510- 5515.
Kleiner, M., Tumakaka, F., Sadowski, G., Dominik, A., Jain, S., Bymaster, A., & Chapman, W. G. (2006). Thermodynamic Modeling of Complex Fluids using PC-SAFT. Final Report for Consortium of Complex Fluids. Universität
Martin, T. M., Lateef, A. A., & Roberts, C. B. (1999). Measurements and modeling of cloud point behavior for polypropylene/n-pentane and
polypropylene/n-pentane/carbon dioxide mixtures at high pressures. Fluid
Phase Equilibria, 154, 241.
Othmer, D. F., & Morley, F. R. (1946). Composition of Vapors from Boiling Binary Solutions – Apparatus for Determinations under Pressure. Ind. Eng.
Chem., 38, 751-757.
PRMHV2
The PRMHV2 property method is based on the Peng-Robinson-MHV2
equation-of-state model, which is an extension of the Peng-Robinson equation of state. The UNIFAC model is used by default to calculate excess Gibbs energy in the MHV2 mixing rules. Other modified UNIFAC models and activity coefficient models can be used for excess Gibbs energy.
Besides the acentric factor, up to three polar parameters can be used to fit more accurately the vapor pressure of polar compounds.
The MHV2 mixing rules predict the binary interactions at any pressure. Using the UNIFAC model the MHV2 mixing rules are predictive for any interaction that can be predicted by the UNIFAC model at low pressure.
The minimum parameter requirements of the PRMHV2 property method are given in the tables labeled Parameters Required for the PRMHV2 Property Method (below) and Parameters Required for Common Flexible and Predictive Models. For details about optional parameters, and calculation of pure
component and mixture properties, see Physical Property Models.
Mixture Types
You can use the PRMHV2 property method for mixtures of non-polar and polar compounds. For light gases UNIFAC does not provide any interaction.
Range
You can use the PRMHV2 property method up to high temperatures and pressures. You can expect accurate predictions (4% in pressure and 2% in mole fraction at given temperature) up to about 150 bar. You can expect reasonable results at any condition, provided the UNIFAC interaction
parameters are available. Results are least accurate close to the critical point.
Parameters Required for the PRMHV2 Property Method
Thermodynamic
Properties Models Parameter Requirements
Vapor and liquid mixture
Fugacity coefficient,