(202f) Investigating the Ability of the RK-Aspen Equation of State to Correlate the High-Pressure Phase Behavior of Binary and Ternary CO2-Containing Systems

Supercritical CO₂ has long been investigated as a suitable mass separating agent to replace traditional organic solvents in systems where traditional separation techniques are infeasible, either due to crossover melting and boiling temperatures or complex phase behavior such as azeotropy. Due to the low operating temperatures (typically 310 to 360 K) CO₂ is also able to process thermally liable compounds. CO₂ is a popular alternative solvent as it is readily available, non-toxic and generally regarded as safe. It is thus suitable for application in the foodstuff, cosmetic and pharmaceutical industries where final product quality and allowable solvent residues are very stringently regulated. Studies have shown that CO₂ can be used to separate high molecular mass compounds of 1-alcohols and n-alkanes [1,2], as well as mixtures of methyl esters [3]. Although these pilot plant studies are useful to evaluate process feasibility, the experimentation is time-consuming, costly and the results are only applicable to the systems investigated. In order to evaluate the process feasibility of a variety of systems and conduct process optimisation and sensitivity analyses, it is desirable to rather identify suitable thermodynamic models to apply in commercial process simulators and simulate the proposed processes.

Many studies have looked at the phase behavior and thermodynamic modelling of CO₂-containing systems [4-15] and have shown that mixtures of CO₂ + 1-alcohols + n-alkanes [7-14], CO₂ + n-carboxylic acids + n-alkanes and CO₂ + methyl ester + n-alkanes [8,15] display complex phase behavior phenomenon such as co-solvency. This complicates the thermodynamic modelling of these systems.

Studies by Fourie [16], Ferreira [17] and Latsky [18] investigated the thermodynamic modelling of CO₂ + 1-alcohol + n­‑alkane systems. Fourie [16] and Ferreira [17] considered the ability of either Soave-Redlich Kwong (SRK) type cubic equations of state or the PC-SAFT [19,20] model to correlate the phase behavior and found that the cubic equations of state outperformed the PC-SAFT model. Ferreira [17] and Latsky [18] further considered the effect that the type of source data used to regress parameters have on model performance for the SRK type models. Ferreira [17] considered the effect of regressing solute + solute binary interaction parameters (BIPs) for the RK-Aspen [21], PSRK [22] and SR-Polar [21] models using low-pressure vapour liquid equilibrium (LPVLE), high-pressure bubble- and dew-point (HPBDP) and high-pressure vapor liquid equilibrium data (HPVLE) for the CO₂ + 1-decanol + n-tetradecane system. Latsky [18] further evaluated the effect of utilising HPBDP versus HPVLE data to regress parameters for the SRK [23], RK-Aspen, PSRK and CPA [24] models for the quarternary and comprising ternary systems of CO₂ + 1-decanol + n-dodecane + 3,7-dimethyl-1-octanol.

Ferreira [17] found that the RK-Aspen model including solute + solute BIPs that are regressed to HPBDP data outperforms regressions conducted using HPVLE or LPVLE data for each of the models considered, while the findings by Latsky [18] supported this finding when comparing the regressions obtained using HPBDP or HPVLE data. This was a desirable outcome, since HPBDP data are much easier, faster and cheaper to measure than HPVLE data. These conclusions are true for CO₂ + 1-alcohol + n-alkane systems, but evaluations for CO₂ systems with other solutes, such as n-carboxylic acids and methyl esters, have not been made. The aim of this work is therefore to evaluate the ability of the RK‑Aspen equation of state to model CO₂ + solute + solute systems, where the solutes are 1-alcohols, n‑­alkanes, n-carboxylic acids and methyl esters. This aim will be achieved by:

• Investigating the ability of the RK-ASPEN model to predict the ternary phase behavior by only incorporating solvent (CO₂) + solute BIPs regressed to binary data;
• Investigating the ability of the RK-ASPEN to correlate the ternary mixture data for several solute + solute combinations; and
• Investigating the effect of using either HPBDP or HPVLE data to regress the solute + solute BIPs on the model performance.

As the purpose of the study is to use the RK-Aspen model and to ultimately implement the model in a process simulator, Aspen Plus® V14 was used in combination with the Aspen Simulation Workbook (ASW) in MSExcel.

The RK-Aspen model is a modified version of the SRK equation of state where an additional pure component parameter, the polar parameter η, is introduced in the alpha function. The added parameter allows for improved correlation of the pure component phase behavior. The polar parameters were regressed against pure component vapor pressure data obtained from the NIST ThermoData Engine (TDE) available within Aspen Plus®, using the Aspen Plus® Data Regression System (DRS). The maximum likelihood objective function, minimising the pure component vapor pressure, was employed, with the Britt-Luecke minimisation algorithm.

The model is further extended to mixtures through incorporation of quadratic mixing rules and the inclusion of two BIPs. In this work the solvent + solute BIPs were regressed from previously measured binary solvent + solute phase behaviour data using the Aspen Plus® DRS through minimization of the maximum likelihood objective function together with the Britt-Luecke algorithm. For systems where only HPBDP data were available, the data were converted to HPVLE data by fitting pressure-composition curves through the HPBDP data and then calculating the compositions of the co-existing phases at 0.2 MPa intervals.

The method of correlation of the solute + solute BIPs depends on the type of source data used. For the LPVLE and HPVLE data, where the compositions of the co-existing phases are known, the same method as for the solvent + solute BIPs is used. For the HPBDP data an alternative method is required as the data are phase boundary data and therefore compositions of the co-existing phases are not known. Here the bubble or dew point is pressure predicted at a set temperature and composition using a flash drum in Aspen Plus® and the BIPs are systematically varied to minimize the error in the pressure prediction. The ASW in MSExcel was used to allow for a fine grid in the minimization procedure.

The results have shown where the inclusion of the solute + solute BIPs are required and in which types of systems HPVLE data are required for correlation of the solute + solute BIPs versus where only HPBDP data are needed. The study has also shown how the molecular interactions such as association and hydrogen bonding differs in different types of systems and how well the RK-Aspen model can predict or correlate the various interactions.

Although the RK-Aspen model has been shown to outperform other models such as CPA or PC-SAFT for CO₂ + 1-alcohol + n-alkane systems [16-18], it would be prudent to further investigate if these results can be generalised to systems containing other functional groups such as n-carboxylic acids and/or methyl esters.

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