Peng-Robinson EOS

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

The last term, the fluid s isothermal compressibility, can be reasonably predicted from a two-parameter, cubic equation of state (EOS) such as the Redlich-Kwong EOS or the Peng-Robinson EOS.(14,15) The fluid s isothermal compressibility was determined using the Redlich-Kwong EOS to evaluate the derivative ( Vmmob/3P) in eq. 12 due to the ease of finding an analytical solution,... 

Mixing rules used with the Peng-Robinson EOS ... 

Figure 2 Calibration curve of the humidity sensor at 32°C and 95 bar. The curve was calculated by the Peng-Robinson EOS.

Due to restriction for space the results on modeling the high-pressure phase behaviour of the system carbon dioxide-water-1 -propanol are presented only briefly. The model used in this work was the Peng-Robinson EOS [8] with an temperature dependent attractive term due to Melhelm et al. [9], Although several mixing rules have been tested, the discussion will be restricted to the two-parameter mixing rule of Panagiotopoulos and Reid [10],... 

Figure 4. Three-phase equilibrium LtL2V in the system carbon dioxide-water-1-propanol at 333 K and 13.1 MPa exp., this work — Calculated with Peng-Robinson EOS using Panagiotopoulos and Reid mixing rule, left side prediction from pure component and binary data alone, right side interaction parameters fitted to ternary three-phase equilibria at temperatures between 303 and 333 K...

Solubility of toluene in SC CO2 can be found in the literature [8]. In a previous study in our laboratory, the solubility of DCB in SC CO2 was measured by [9] and was thus available. Figure 1 gives the solubilities (mol fraction) of DCB in SC CO2 vs pressure calculated for 3 temperatures using the Peng-Robinson EOS with an interaction parameter ki2 = 0.1175... 

Calculations of the solubility with a modified Peng-Robinson-EOS lead to remarkably lower equilibrium pressures for the given temperature ranges. The reason for this effect is, that the calculations are done for two-component systems. The paraffin used for the measurements and the production of the workpieces, however, is a mixture of homologue n-alkanes, so the calculation should be done for a multicomponent system. Up to now it was not possible to find a set of thermodynamic data, which represent this n-alkane mixture and lead to two-component-calculation results according to the measurements. 

The predictive method suggested in this paper allows one to calculate the solubility of a solid in a binary mixture of SC fluids. The solubilities of three solids were predicted using only experimental data regarding the solubilities in the constituent binary mixtures (solid/SC fluid and solid/SC entrainer). Very good agreement was found between the experimental and predicted solubilities. For the solubilities of naphthalene and benzoic acid, the prediction of Eq. (42) provided even better agreement than the correlation [2] of experimental data based on the Peng-Robinson EOS with parameters determined from ternary data. 

For the prediction of the mixed-gas solubilities from the solubilities of the pure individual gases, the pressure dependence of the binary parameters ku is needed. The Peng—Robinson EOS was used to determine the binary parameters ku. The binary interaction parameter qi2 in the van der Waals mixing rule was taken from ref 28, where it was evaluated for the water-rich phases of water—hydrocarbon and water—carbon dioxide binary mixtures. The calculated binary parameters ku are listed in Table 1. One should note that, as expected for a liquid phase, the above parameters are almost independent of pressure, in contrast to their dependence on pressure in the gaseous phase near the critical point,... 

Example Estimate the molar density of liquid and vapor saturated ammonia at 353.15 K, using the Soave and Peng-Robinson EoS. 

The liquid density calculated from the Soave EoS is 24.2 percent below the DIPPR 801 recommended value of 29.69 kmol/m, while that calculated from the Peng-Robinson EoS is 13.9 percent below the recommended value. 

The experimentally determined S-L-V equilibrium data for salicylic acid (2-hydroxy-benzoic acid)-l-propanol-C02 were correlated by using the Stryjek-Vera modification of the Peng Robinson EOS in conjunction with Eq. (35) for the solid state fugacity of the solute (58,62), as described earlier. This procedure also yielded good agreement of the liquid phase compositions of salicylic acid in the temperature and pressure ranges of 273 to 367 K and 1.0 to 12.5 MPa. The P-Ttraces of S-L and L-V equilibria were calculated for a fixed solute concentration on C02-free basis, and subsequently the P-T trace for the S-L-V equilibrium was found from the point of intersection of these two lines. The liquid phase compositions of the solute as a function of pressure at a constant temperature at the condition of S-L-V equilibrium were calculated to assess the effect of pressure or addition of antisolvent on solute crystallization. It was reported that two isobaric points of the CO2 mole fraction could be observed on the curve of the S-L equilibrium temperature vs the CO2 mole fraction at constant temperature as it passes through a mini-... 

Find the Helmholtz Energy of Peng-Robinson eos Solution... 

Example 4.13 Internal Energy by Peng-Robinson eos The PR eos is differentiated to give... 

Using the Peng-Robinson eos, Equation (4.159), for illustration, we obtain from Exjuation (4.431) and Equation (4.432)... 

Using the Peng-Robinson eos for illustration, the excess Helmholtz energy is found by combining the Helmholtz energy given by Equation (4.280). Upon setting v = b in the excess function to attain infinite pressure. 

The Peng-Robinson eos has been presented as Equation (4.165). Using van der Waals mixing rules, the fugacity equation is obtained by substituting the eos in Equation (4.306), leading to the following ... 

Han et al. [10] made many comparisons of the Peng-Robinson eos K values ( )iL/( ),v calculated with experimental K values y/X . For the eos A"-value calculations, a cross-interaction coefficient k is determined for each binary system. For 20 symmetric binary systems for which the experimental temperature is below the critical of both components, the average absolute deviation (AAD) of the calculated from the experimental was found to be -2.5%. The AAD for the individual systems fall in the range from the smallest value of 1.0% for ethylene + propylene to the largest value of 4.3% for propylene + isobutene. 

Some success has, however, been obtained in predicting data involving solid phase, e.g., solubility of solid carbon dioxide in compressed air at 143°K (using a trancated second virial eos at pressures up to 40 atm). Good predictions were also realized for existence of solid carbon dioxide in liquid and gaseous mixtures of methane and carbon dioxide. The Peng-Robinson eos was used with success. 

Pressure-volume diagram for nitrogen Peng-Robinson eos. 

Lewis-Randall with corresponding states with Peng-Robinson eos Kay s Rule Prousnitz-Gunn Peng-Robinson e.o.s. directly (program PR 1)... 

To demonstrate the performance of the Peng-Robinson EOS with nonzero values of kjj and 17, we calculate the phase behavior for the isopropyl... 

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