Liquid–Liquid Equilibrium of Associating Fluid Mixtures Using Perturbed-Hard-Sphere-Chain Equation of State Combined with the Association Model

Abstract

Perturbed-hard-sphere-chain-association (PHSC-AS) equation of state, which is defined by incorporating the association term of the statistical associating fluid theory (SAFT) model into the PHSC equation of state with van der Waals-type dispersion term, is used to calculate the liquid−liquid equilibrium (LLE) for complex associating mixtures such as alcohol/alkane, water/alkane, acetic acid/alkane, alcohol/water, and carboxylic acid/water systems. In this work, the PHSC-AS models with two different chain terms have been investigated. One is the original model proposed by Song et al. [Macromolecules 1994, 27 (2), 441−448], and the other is the modified model whose chain term was replaced with that of the SAFT model. The calculated results of LLE for associating mixtures are compared with those by the purturbed-chain-SAFT (PC-SAFT) model as well. The results with PHSC-AS and PC-SAFT equation of state are in acceptable agreement with the experimental data. Despite the simple dispersion equation with van der Waals-type, PHSC-AS models show a reasonable calculation performance for LLE of associating fluid mixture. ■ INTRODUCTIONThe calculation of liquid−liquid equilibria (LLE) is of importance in the design and development of new separation processes, such as extraction and extractive distillation, and is also a challenge for nonideal mixtures with strong attractive interaction owing to hydrogen bonding. For accurate process modeling and design, the reliable model for associating fluids is essentially required and important.A great number of theoretical studies (i.e., excess Gibbs energy models, conductor-like screening model (COSMO)-based model, and equation of state (EOS)) have been mainly focused on theoretical models to account for the effects of solvation and association on the bulk properties and phase behaviors. Correlations of LLE has been done usually by using the excess Gibbs free energy (g E ) models, such as nonrandom two-liquid (NRTL), 1 universal quasichemical (UNIQUAC), 2 and UNIQUAC functional-group activity coefficients (UNI-FAC), 3 which have been successfully applied for the prediction and correlation of several liquid−liquid systems. The UNIFAC model is most extensively used as a predictive model because of the universal binary interaction parameters between each functional group. 4−6 More recently, COSMO-based models obtained from the results of quantum mechanical calculations, such as COSMO-RS (real solvents) 7,8 and COSMO-SAC (segment activity coefficient), 9,10 have been shown to provide reliable predictions for the various thermodynamic properties for many molecules. 11,12 Aside from excess Gibbs free energy models, the EOS provides a useful tool for describing phase equilibria of mixtures regardless of magnitude of pressure. The advance in statistical mechanics results in perturbation theories capable of accurately describing the thermodynamic properties for nonideal fluids. Wertheim 13,14 proposed the thermodynamic perturbation theory (TPT1) for hydrogen bonding fluids. The statistical-asso...

Correlation and prediction of liquid–liquid equilibria for alcohol/hydrocarbon mixtures using PC-SAFT equation of state at high pressure up to 150 MPa

“…3). For ethanol þ alkane mixtures, the new parameters obtained in this paper give good results in all cases, while the parameters of Gross and Sadowski [11] give poor ones in describing liquideliquid of ethanol þ alkane mixtures, that allow to conclude these new parameter sets were shown more superior than that determined by Gross and Sadowski [11] or Lee and Kim [1].…”

“…Prior to parameter estimation, an association scheme must be chosen, for methanol and ethanol, the 2B schemes was used, in agreement with previous investigations [5,7]. Throughout this manuscript the following notation will be used: À G&S: 2B parameters set taken from Gross and Sadowski [11] À L&K: 2B parameters set taken from Lee and Kim [1] À This work: new 2B parameters set obtained in this work …”

“…different sets of parameters may lead to nearly equivalent results in terms of deviations). In this context the parameter set giving the lowest deviation on pure VLE data may not be the most appropriate for calculating Table 3 Correlated (at 0.1 MPa) and predicted results of liquideliquid equilibria for binary systems at high pressure by PC-SAFT using different parameters set of methanol and ethanol: new parameters set proposed in this work, L&K [1] and G&S [11]. accurately the phase equilibria of mixtures [3,23].…”

“…molecules are formed by chains of freely jointed spherical segments, being expressed in terms of the reduced residual Helmholtz energy, which consists in of the following contributions: a res ¼ a hc þ a dis þ a asso (1) The first term, a hc is used to describe the formation of the chain. The second term, a disp , is called "dispersive" accounting for the London-type attractive interactions between segments.…”

“…The methanol and ethanol parameters set obtained from simultaneous fitting of vapor pressure and liquid density data results to the values of m ¼ 1.6 and ε AB ¼ 2750 K for methanol and m ¼ 3.1 and ε AB ¼ 2222 K for ethanol, which are in good agreement with the "expected" physically reasonable values of these parameters (Tables 1 and 2). For comparative purposes, graphical results with the 2B parameters set determined by Gross and Sadowski [11] and Lee and Kim [1] are included in this work.…”