PRSV equation

Table 3.1.1. Pure component parameters for PRSV equation of state...

PRSV equation for the substances considered here are given in Table 3.1.1 k of the PRSV equation is obtained by fitting pure component saturation pressure (P p) versus temperature data, A computer program to optimize k for a set of T versus / P data is provided on the diskette accompanying this monograph, and the program details are presented in Appendix D. The effect of this parameter on the accuracy of vapor pressure correlations for several fluids is shown in Figure 3.1.1. 

Figure 3J.1. Effect of the k] parameter on the pure component saturation pressure calculated with the PRSV equation of state. Points denote experimental saturation pressures of methanol (O) and butanol ( ) (Vargaftik 1975. Dashed lines represent results calculated with tfi =0, and solid lines are results calculated with /C values reported in Table 3.1.1.

Figure 3.1.2. The parameter a (see eqn. 3.1.3) as a function of reduced temperature (T/Tc). Points represent ff value.s required to reproduce experimentally reported compressibilities for various fluids, and lines signify calculated a values from the PRSV equation of state with different values of atj and acentric factor (w).

Figure 3.4.1. VLE correlation of the methane and n-pentane binary system at 310, 377, and 444 K with the IPVDW mixing rule and the PRSV equation of state. The lines represent VLE results calculated with the binary interaction parameter ki2 = 0.0215. (Data are from the DECHEMA Chemistry Series, Gmehling, and Onken 1977, Vol. 6, p. 445 data files for this system on the accompanying disk are C1C5310.DAT, C1C5377.DAT, and C1C5444.DAT.)...

Figure 3.5.1. VLE correlation of the n-pentane and ethanol binary system with the 2PVDW mixing rule and the PRSV equation of State. Solid lines are the results of correlation with k 2lk2i = 0.195/0,049 at 373 K, 0.2056/0.073 at 398 K, and 0.207/0.096 at 423 K, Short dashed lines are the results of VLE predictions widi k i/k2 = 0.200/0.073 at all temperatures, and the medium dashed lines are 1PVDW model cone-lations presented earlier in Figure 3,4,3. (Data are from Campbell et al., i 987 data files for this system on the accompanying disk are PE373.DAT, PE398.DAT and PE423.DAT.)...

Figure 3.5.3. VLB correlation of the 2-propanol and water binary system at 353 K with the 2PVDW mixing rule and the PRSV equation of state. Solid lines denote correlation results with 1 12/ 21 = 0.0953/0.0249. Dashed lines show IPVDW model correlations presented earlier in Figure 3.4.5. (Points are the data of Wu et ah, 1988 data file for this system on the accompanying disk is 2PW80.DAT.)...

Figure 3.5.5. VLB coiTelation of acetone and water binary system at 298 K with the 2PVDW mixing rule and the PRSV equation of state. Solid lines denote...

Figure 4.2.3. VLE correlation of the acetone and water binary system at 298 K with the Huron-Vidal original (HVO) mixing rule with the van Laar excess free-energy model and the PRSV equation of state. The dashed lines denote results calculated with van Laar model parameters = A12/A21 = 3.5121/2.2227 obtained from fitting the experimental data, and the solid lines represent the results obtained with model parameters I//0 = Aj2/A2] = 1.9399/1.8022 obtained at the same temperature from the DECHEMA Chemistry Series (Gmehling and Onken 1977, Vol. 1, Pt. l,p. 238).

Figure 4.3.1. The excess Gibbs and Helmholtz energies of mixing for the methanol and benzene binary system at 373 K calculated u ith the Wong-Sandler fWS) mixing rule and the PRSV equation of state at 1 and 1000 bar.

Figure 4.3.4. VLE correlation (solid lines) of the 2-propanol and water binary system at 353 K with the Wong-Sandler (WS) mixing rule combined with the NRTL excess free-energy model and the PRSV equation of state. The dashed lines are calculated with a = 0.2529, ri2/T2i =0,1562/2,7548, and with the Wong-Sandler mixing rule parameter k 2 = 0.2529 obtained by fitting the experimental data. The solid lines represents results calculated with a =0.2893 and T 2/t2i =0.1509/1.8051 obtained from the DECHEMA Chemistry Series at 303 K (Gmehling and Onken 1977, Vol.l, Pt. 1, p.

Figure 4.4.1. VLB correlations of the methane and n-pentane binary sy.stem with various approximate EOS-G models. Clockwise from top left HVOS, MHV2, MHV1, and LCVM mixing rules combined with the van Laar excess tree-energy model and the PRSV equation of state. Solid lin are model predictions. The points are measured VLE data at 444 K (A, A), 377 K ( , ) and 310 K ( , O) from the DECHEMA Chemistry Data Series (Gmehling and Onken 1977, Vol. 6, p. 445).

D.2. Program KOPT Evaluation of the (r ) Parameter for the PRSV Equation of State... 

The prograjTi KOPT is used for the evaluation of the k constant of pure fluids in the PRSV equation (see Section 3.1). The data required for this program are critical temperature (in Kelvin), critical pressure (in bar), and acentric factor of the fluid as well as data for the temperature (in Kelvin) versus vapor pressure (in any units). The program returns the Ki value, which minimizes the average difference between the estimated and experimental vapor pressures. A simplex optimization routine is used in the calculations. 

Example D.2.A Determination of Optimum k in the PRSV Equation of State with Existing Data... 

KOPT KAPPA-1 OPTIMIZATION FOR THE PRSV EQUATION temp.out... 

This example is presented to demonstrate a case for which no experimental VLE data are available, so that no data are entered to, or accessed from, the disk. The user should provide, following the commands that appear on the screen, T,., P,., the acentric factor and /C parameter of the PRSV equation of state for each compound in addition to a temperature, and the mixing rule parameter(s) kjj. The program returns isothermal x-y-P predictions at the temperature selected. 

If no experimental VI. R data are available, the program can be used for predictions using internally generated liquid mole fractions of species 1 in the range from 0 to 1 at intervals of 0.1. In this case the user must provide all model parameters and temperature in addition to pure component critical temperature and pressure, acentric factor, and the kti parameter of the PRSV equation of state for each compound. An example is given below (Example D.5.C) for this mode of operation of the program. 

In the first part of this example, we matched excess Gibbs energy from the PRSV equation of state with excess Gibbs energy from UNIFAC at 25°C and obtained... 

The program VDWMIX is used to calculate multicomponent VLE using the PRSV EOS and the van der Waals one-fluid mixing rules (either IPVDW or 2PVDW see Sections 3.3 to 3.5 and Appendix D.3). The program can be used to create a new input file for a multicomponent liquid mixture and then to calculate the isothermal bubble point pressure and the composition of the coexisting vapor phase for this mixture. In this mode the information needed is the number of components (up to a maximum of ten), the liquid mole fractions, the temperatures at which the calculations are to be done (for as many sets of calculations as the user wishes, up to a maximum of fifty), critical temperatures, pressures (bar), acentric factors, the /f constants of the PRSV equation for each compound in the mixture, and, if available, the experimental bubble point pressure and the vapor phase compositions (these last entries are optional and are used for a comparison between the experimental and calculated results). In addition, the user is requested to supply binary interaction parameteifs) for each pair of components in the multicomponent mixture. These interaction parameters can be... 

Sandoval, R., Wilseck-Vera, G., and Vera, J. H., 1989. Prediction of the ternary vapor-liquid equilibria with the PRSV equation of state. Fluid Phase Eq., 52 119-126. 

---