(88b) Estimation of the Density of CO2/Organic Solvent Systems with Peng-Robinson Equation of State

Supercritical fluids are the high density fluids in the state beyond the critical temperature and pressure. They have gas-like as well as liquid-like properties. In recent years, many attempts had been made to apply the supercritical fluids as alternative solvents and/or reactants. Among these fluids, supercritical water, carbon dioxide and alcohols (methanol and ethanol) have been attracting much attention from their environmentally benign, chemically stable natures. In particular, from its low critical conditions, non reactive and non-toxic natures, and the low price, supercritical carbon dioxide (scCO­₂) have been regarding as a promising solvent, and is expected to be applied to various industrial fields such as extraction, drying, polymer processing, and particle synthesis. To design these processes, physical properties of the solvents are the essential. A physical property measurement under high pressure requires specialized apparatus and takes up much time. Therefore, limited numbers of data were reported. Since many processes are mixture systems, the physical properties data of mixtures under high pressure are also required. However, from the stand points of cost as well as time, to measure all of the data is impossible. Thus, establishment of the estimation method with a high accuracy is inevitable.

With the use of the equation of state (EoS), it is possible to calculate not only the PVT relationship but also the thermodynamic quantities such as chemical potential, entropy, and isothermal compressibility. In fact, many kinds of the EoS are used in the various process simulators. One of the most important data referred in the simulators related to the EoS are the interaction parameters. They are that correct the differences between different molecules, and are determined from the physical property data of the mixtures. Among the physical properties of mixtures, density is particularly sensitive to the mixing. Thus, establishing the method that can be express the density well will result in to improve the estimation accuracy of the physic-chemical properties of the mixtures.

In this work, to investigate the effects of determination procedure of the interaction parameters on the density estimation, the densities of CO₂/ethylbenzene (C₂H₅C₆H₅) and CO₂/cyclohexane (C₆H₁₂) systems were measured as model systems, and widely used Peng-Robinson equation of state (PR EoS)¹⁾ was employed as the EoS. More specifically, the interaction parameters were determined from the vapor-liquid equilibrium (VLE) data, from the density, and from the excess molar volume, separately, and with thus determined interaction three sets of parameters, the densities of mixtures were prediction, and the accuracies were discussed.

In this study, the density of mixtures was measured with a high pressure vibration type density meter equipped with a circulation pump and a variable volume viewing cell. The calibration of the density meter was conducted with water and C₆H₁₂. The measurement was conducted at temperatures from 313.15 to 353.15 K and pressures up to 20 MPa. CO₂ compositions were changed from 0 (pure C₂H₅C₆H₅ or C₆H₁₂) to 80 mol%.

At low CO₂ compositions, the density of the CO₂/C₂H₅C₆H₅ system increased with increasing the CO₂ molar fraction. At high CO₂ compositions, it decreased and approached the density of CO₂. Similar tendency was observed for the CO₂/C₆H₁₂ system. These tendencies could be explained as follows: at low CO₂ compositions, penetration of the CO₂ into between organic molecules makes mixture dense. On the other hand, at high CO₂ compositions, organic molecules were surrounded by the CO₂, and the properties of the CO₂ became dominant. Three sets of interaction parameters were determined by correlating the VLE data in the literature²⁾³⁾, the experimentally obtained density, and the excess molar volume calculated from the experimentally obtained density and the pure component density, with the PR EoS minimizing Average Absolute Relative Deviation (AARD). In the calculation, the van der Waals one fluid model⁴⁾ was used for the mixing rule. In the mixing rule, there are two interaction parameters, k_ij and l_ij. The density was estimated from these three parameter sets, and the prediction accuracy was compared.

In the case of the correlation with the VLE data, the interaction parameters, k_ij, l_ij and the correlation error were 0.12, -0.13 and 0.57 %, respectively, for the CO₂/C₂H₅C₆H₅ system, and 0.16, -0.17 and 1.06 %, respectively, for the CO₂/C₆H₁₂ system. The prediction errors of the density with the obtained parameters were relatively large, 5.54 % and 6.84 % for (CO₂/C₂H₅C₆H₅ system) and (CO₂/C₆H₁₂ system), respectively. In addition, the estimated density behavior against CO₂ molar fraction was different from the experimental behavior, and monotonously decreased with the increase in the CO₂ composition.

In the case of the correlation with the density, k_ij, l_ij and the correlation error were 0.06, -0.02 and 0.60 %, respectively, for the CO₂/C₂H₅C₆H₅ system, and -0.16, -0.15 and 1.79 %, respectively, for the CO₂/C₆H₁₂ system. These results were a bit better from the results using the parameters determined from the VLE data. The density behavior against CO₂ molar fraction of the CO₂/C₂H₅C₆H₅ system could be expressed well though, that of CO₂/C₆H₁₂ system is still hard to be expressed. We speculate that these tendencies could be explained from the prediction accuracy of the density of the pure components, C₆H₁₂ and C₂H₅C₆H₅. The prediction accuracies of the pure C₂H₅C₆H₅ and C₆H₁₂ were 1.06 % (313.15 K, 1~20 MPa) and 5.48 % (313.15 K, 1~20 MPa), respectively. This was not a problem of the interaction parameters but a problem of the parameter representing pure substances (in the case of the PR EoS, they are the critical values and the acentric factor). With the parameters, the VLE was predicted. The prediction errors were 8.89 % and 281 % for CO₂/C₂H₅C₆H₅ system and CO₂/C₆H₁₂ system, respectively. It was not possible to estimate the VLE data for CO₂/C₆H₁₂ system.

In the case of the correlation with the excess molar volume, the interaction parameters, k_ij, l_ij and the correlation error were 0.11, -0.04 and 10.8 %, respectively for the CO₂/C₂H₅C₆H₅ system, and 0.13, -0.04 and 17.3 %, respectively for the CO₂/C₆H₁₂ system. The density prediction errors with these parameters were 5.54 % and 6.84 % for CO₂/C₂H₅C₆H₅ system and CO₂/C₆H₁₂ system, respectively. At the same time, with these parameters, the density behavior against CO₂ molar fraction of both systems could be well expressed (AARD was 2.88 % and 3.14% for CO₂/C₂H₅C₆H₅ and CO₂/C₆H₁₂ system, respectively). In addition, the VLE prediction error with these parameters were 8.73 % and 6.82 % for CO₂/C₂H₅C₆H₅ system and CO₂/C₆H₁₂ system, respectively. It was possible to estimate the VLE data for not only CO₂/C₂H₅C₆H₅ system but also CO₂/C₆H₁₂ system. Therefore, in the estimation of the VLE data, it was found that the density change behavior was important. These facts suggest that when estimate the physic-chemical properties, use of the fitting parameters determined on the same physical base (in this case, excess molar volume and density) is the important factor.

In conclusion, interaction parameters obtained by correlating the excess molar volume could be express not only the density, but also the VLE, and have the possibility to be applicable to calculate the other physical properties for mixtures.

References

1) Peng, D. Y., Robinson, D. B., Ind. Eng. Chem. Fundam, 15 (1976) 59-64

2) Andreas et al, Fluid Phase Equilibria, 97 (1994) 167-189

3) Taher et al. Fluid Phase Equilibria, 53 (1989) 31-37

4) M. L. Michelsen, H. Kistenmacher, Fluid Phase Equilibria, 58 (1990) 229-230