SAFT Equation Research Articles

Prediction of Solubility of Cholesterol in Supercritical Solvents

In this study the solubility of cholesterol was calculated in two supercritical pure solvents (carbon dioxide and ethane) as binary systems, and four supercritical solvent/co-solvent systems as ternary systems (cholesterol/carbon dioxide/methanol, cholesterol/ethane/acetone, cholesterol/ethane/hexane, cholesterol/ethane/propane) in various temperatures by SRK, PR, and SAFT equations of state. Pure molecular parameters of SAFT equation of state were obtained by fitting vapor pressure and liquid density data. Also the molecular parameters of cholesterol were obtained by fitting the solubility data of binary systems in one temperature, then they were used for the same system in other temperatures and for ternary systems with the same solvent. Results show that the SAFT equation of state can predict the trend and amount solubility of cholesterol in supercritical solvents much better than the other equations of state.

Application of Restrictive Primitive SAFT Coupled with Different Hard-Sphere Equations to Model Mean Ionic Activity Coefficients of Electrolyte Solutions

In this work, the primitive SAFT equation of state along with three different hard-sphere equations was used to correlate and predict mean ionic activity coefficients of aqueous electrolyte solutions. The mean ionic activity coefficient of aqueous electrolyte solutions was considered as the contribution of hard-sphere and dispersion effects. The Mansoori (M), Wang-Khoshkbarchi-Vera (WKV) and Ghotbi-Vera (GV) hard-sphere equations were applied in correlating the mean ionic activity coefficient of electrolyte solutions. The comparison among above indicated equations was shown. First, vapor pressure and densities of water in the temperature range of 373.15 to 423.15 K was regressed by SAFT equation of state. In the restrictive primitive mean spherical model, ions were hard spheres without any chain structure. Neither association effects were considered in this study. Clearly, in common used five SAFT parameters were decreased to three, which were calculated by using the experimental mean ionic activity coefficients of electrolyte solutions. The comparison among three hard-sphere equations of state approved that Ghotbi-Vera hard-sphere model (GV) correlated the experimental data accurately than the others; two hard-sphere models. The mean ionic activity coefficients of some electrolyte solutions were being predicted by taking the advantage of the regressed values surely, in a wide range of molality.

Capturing the Solubility Minima ofn-Alkanes in Water by Soft-SAFT

The purpose of this work is twofold: (1) to provide an accurate molecular model for water within the soft-SAFT equation of state [Blas, F.J.; Vega, L.F. Mol. Phys. 1997, 92, 135; Llovell, F., et al. J. Chem. Phys. 2004, 121, 10715] and (2) to check the capability of this molecular-based equation of state for capturing the solubility minima of n-alkanes in water experimentally found at room temperature for these mixtures. Water was modeled as a Lennard-Jones sphere with four associating sites, with parameters obtained by fitting to experimental vapor-liquid equilibrium data. Special care was taken to the value of these parameters depending on the range of applicability of the equation, which turned out to be essential for accurate predictions for mixtures. A correlation available in the literature was used for the molecular parameters of the n-alkane series. The crossover soft-SAFT equation was able to accurately describe the phase behavior of water near to and far from the critical point, up to 350 K. If instead of obtaining an overall good agreement one is interested in a more precise description of the near-ambient conditions, a more refined fitting of the parameters is needed. The model was used to describe the water+methane up to water+n-decane binary mixtures. The equation was able to predict the mutual solubilities in almost quantitative agreement with experimental data, including the presence of the solubility minima at ambient temperature, with a single transferable energy binary parameter, independent of temperature and chain length. Predictions obtained from the soft-SAFT approach are clearly superior than those obtained from the Huang and Radosz version of the SAFT equation [Economou, I. G.; Tsonopoulos, C. Chem. Eng. Sci. 1997, 52, 511], due to the more refined reference term and the more accurate radial distribution function used in the chain and association terms. This is the first time a SAFT approach is able to describe this minima.

Phase Behavior of Hyperbranched Polymer Systems: Experiments and Application of the Perturbed-Chain Polar SAFT Equation of State

Vapor-liquid equilibrium data for systems of hyperbranched polymer (HBP) and carbon dioxide are reported for temperatures of 285-455 K and pressures up to 13 MPa. The bubble-point pressures of (CO2 + hyperbranched polyester) and of (CO2 + hyperbranched polyglycerol + CH3OH) samples with fixed compositions were measured using a Cailletet apparatus. The system (CO2 + polyglycerol + CH3OH) also exhibits a liquid-liquid phase split characterized by lower critical solution temperatures. For this system cloud point curves and vapor-liquid-liquid bubble-point curves were also measured. Moreover, a thermodynamic model has been developed for HBP mixtures in the framework of the perturbed-chain polar statistical association fluid theory (PCP-SAFT) equation of state accounting for branching effects. There is no additional binary interaction parameter introduced along with the branching contributions to the model. Although the miscibility gap in the system (CO2 + polyglycerol + CH3OH) is not predicted by the model, PCP-SAFT including branching effects gives a good representation of the bubble-point curves of this system at temperatures lower than the lower solution temperature (LST).

A new algorithm for estimating association parameters in molecular-based equations of state by quantum chemistry

This note presents a new algorithm for estimating association parameters within molecular-based equations of state that allows the user to incorporate results from quantum chemistry. Using the simplified SAFT equation as an example, we show that the traditional parameter estimation approach (i.e., fitting parameters to vapor pressure and liquid density data) provides results that run counter to quantum chemistry findings on association strengths. Numerical results show that the parameter estimation approach proposed in this work provides a much more appropriate match to quantum chemistry results and gives markedly different amounts of site–site bonding.

Predictions of the Joule-Thomson Inversion Curve for Water and Methanol from the LJ-SAFT EOS

In this work, we have calculated the Joule-Thomson inversion curve of two important associating fluids, namely water and methanol, from the SAFT equation of state. Comparisons with the available experimental data, for water and methanol indicate that this molecular based equation of state gives good prediction of the low temperature branch; but, unfortunately, due to lack of isenthalpic data for high-pressure-high- temperature gas condensate for water and methanol, the reliability of model predictions could not be completely verified. We have also reported the influence of the molecular dipole moment and the segment number on the Joule-Thomson inversion curve.

Predicting VLE of heavy esters and their mixtures using GC-SAFT

A group contribution method combined with a SAFT equation of state (GC-SAFT from Tamouza et al. [S. Tamouza, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Fluid Phase Equilibria 222/223 (2004) 67–76; S. Tamouza, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Fluid Phase Equilibria 228/229 (2005) 409–419], previously extended to polar molecular fluids NguyenHuynh et al. [D. NguyenHuynh, J.-P. Passarello, P. Tobaly and J.-C. de Hemptinne, Fluid Phase Equilibria 264 (2008) 62–75], is here applied to model vapor–liquid phase equilibria of various ester containing binary mixtures such as: ester + ester, ester + alkane, ester + cyclohexane, ester + alkyl-benzene, ester + xylene and ester + alcohols. These systems are modeled using three different versions of SAFT-EOS (original, VR-SAFT and PC-SAFT) in a purely predictive manner: binary interaction parameters k ij and l ij are all set to zero. In the case of ester + alcohol systems, a cross-association interaction between ester and alcohol molecules is shown to improve significantly the predictivity of the method for VLE calculations. The corresponding parameters are estimated by simple hypotheses, using auto-association parameters of pure 1-alkanols. The above cited systems have been treated in a comprehensive manner. The general agreement between GC-SAFT and experimental data is good (within 4–5% deviation on pressure), similar to the one obtained on previously investigated systems.

Modeling of solid–liquid equilibria for systems with solid-complex phase formation

The Perturbed-Chain SAFT (PC-SAFT) equation of state (EOS) is applied to model the solid–liquid equilibria (SLE) of binary and ternary systems showing a solid-complex phase formation. Modeling results for mixtures composed of associating components, e.g. water, alcohols, phenol, bisphenol A (BPA), as well as acetamide are presented. The solid-complex phase formation is modeled as a chemical reaction between species in liquid phase and governed by an equilibrium constant. To calculate the crystallization line of the solid-complex, the stoichiometric composition of the solid-complex and the enthalpy of melting at a reference temperature are required. The phase diagrams for the systems under consideration with various types of SLE are successfully described using only one binary interaction parameter k ij for the PC-SAFT EOS. This approach even allows the simultaneous description of vapor–liquid, liquid–liquid as well as solid–liquid equilibria as shown for the phenol–water mixture. Moreover, it was successfully extended to describe the ternary BPA–phenol–water system.

Critical points of hydrocarbon mixtures with the Peng–Robinson, SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.

Phase equilibria in water containing binary systems from molecular based equations of state

This paper presents a study of phase equilibria for water + carbon dioxide, water + nitrogen and water + n-alkane binary mixtures using the CPA, SAFT and PC-SAFT molecular-based equations of state together with a simple monoparametric mixing rule. These systems have Type III phase behaviour according to the Van Konynenburg classification, with the critical line having a temperature minimum and extending to temperatures above the water critical temperature, with gas–gas immiscibility of the second kind at high pressures. We consider different association models for water and their influence upon phase equilibria correlations. These models predict the general shape of the global phase diagrams of these mixtures qualitatively using a single binary interaction parameter for the whole temperature range. However, the simultaneous prediction in a quantitative way of critical loci, three-phase equilibria and equilibrium compositions is only possible with the PC-SAFT model. We consider transferable binary interaction parameters for n-alkane containing series.

Application of GC-SAFT EOS to polycyclic aromatic hydrocarbons

The group contribution method for pure compound parameters proposed by Tamouza et al. [Tamouza, et al., Fluid Phase Equilibr., 222/223 (2004) 67–76] is extended for the calculation of vapor pressures and saturated liquid volumes of polyaromatic hydrocarbons (PAHs). It has been tested successfully using three versions of SAFT equation of state (EOS): PC-SAFT, VR-SAFT and the original SAFT-EOS slightly modified. An additional quadrupolar contribution to the EOS is found necessary here. The method is used for prediction of equilibrium properties of PAHs, including branched compounds and mixtures containing such components. In all three cases, similar and encouraging results are obtained. Reasonable computations are obtained on pure alkyl PAHs and on some mixtures that were not included in the regression database.

Modeling Phase Equilibrium of H2 + n-Alkane and CO2 + n-Alkane Binary Mixtures Using a Group Contribution Statistical Association Fluid Theory Equation of State (GC−SAFT−EOS) with a kij Group Contribution Method

A group contribution (GC) method combined with a SAFT equation of state (EOS) [Tamouza et al., Fluid Phase Equilib. 2004, 222−223, 67 and 2005, 228−229, 409] is extended here to model vapor−liquid phase equilibria of binary mixtures of H2 + n-alkanes and CO2 + n-alkanes. Modeling these systems requires binary interaction parameters kij that are estimated here in the same spirit as pure compound GC−SAFT parameters, i.e., through a specific group contribution method. Molecule−group interaction parameters (kH2,CH2, kH2,CH3, kCO2,CH2, and kCO2,CH3) are used rather than molecule−molecule interaction parameters. Two versions of SAFT are tested here: the Perturbed-Chain SAFT (PC−SAFT) [Gross and Sadowski, Ind. Eng. Chem. Res. 2000, 40, 1244] and Variable-Range SAFT (VR−SAFT) [Gil-Villegas et al., J. Chem. Phys. 1997, 106, 4168]. The results are very encouraging, particularly for predicting binary mixtures of CO2 and heavy n-alkanes. Mixtures that contain H2 are modeled here with deviations that compare well with those of the classically used Grayson−Streed model.

Phase behavior of olive and soybean oils in compressed propane and n-butane

The aim of this work is to report the experimental data and thermodynamic modeling of phase equilibrium of binary systems containing soybean and olive oils with propane and n-butane. Phase equilibrium experiments were carried out using the static synthetic method in a high-pressure variable-volume view cell in the temperature range from 30 to 70ºC and varying the solvent overall composition from 5 to 98 wt%. Vapor-liquid, liquid-liquid and vapor-liquid-liquid phase transitions were observed at relatively low pressures. The Peng-Robinson and the SAFT equations of state without any binary interaction parameters were employed in an attempt at representing the phase behavior of the systems. Results show the satisfactory performance of SAFT-EoS in predicting qualitatively all phase transitions reported in this work.

Bulk and Interfacial Properties of Polymers from Interfacial SAFT Density Functional Theory

Bulk and interfacial properties of n-alkanes and polymers are modeled in the framework of the interfacial statistical associating fluid theory (iSAFT) density functional theory (DFT). The theory reduces to an equivalent of the SAFT equation of state in the bulk, thus making possible the modeling of both bulk and interfacial properties with a single set of parameters. The performance of iSAFT is illustrated through comparisons of the theory predictions with molecular simulation as well as experimental data for vapor−liquid surface tension. The formulation of iSAFT DFT preserves the computational efficiency of an atomic DFT, thus enabling the theory to deal with molecules comprising hundreds or even thousands of segments, such as the polystyrene and polyethylene included in the present work.

Solubility of Amino Acids: Influence of the pH value and the Addition of Alcoholic Cosolvents on Aqueous Solubility

The solubility of dl-methionine in pure water has been measured in a temperature range of 293.15−353.15 K by means of on-line attenuated total reflection−Fourier transform infrared (ATR−FTIR) spectroscopy. These experimental data, as well as literature data for the solubility of glycine and dl-alanine in aqueous and alcohol solutions, were modeled using the PC−SAFT equation of state. Pure-component parameters for glycine, dl-alanine, and dl-methionine were fitted to the vapor pressures and to the densities of their aqueous solutions. Only one temperature-independent binary parameter is required for each system. The solubility of amino acids in water−alcohol mixtures (ternary systems) was then predicted without fitting any additional parameters. The results of the prediction correspond well to literature data. To retrieve the pH dependency, the solubility of dl-methionine in different HCl and NaOH solutions in the pH range of 1.5−9.5 was determined via gravimetric measurements. Using the knowledge of the a...

Efficient Solution of the Association Term Equations in the Statistical Associating Fluid Theory Equation of State

This paper proposes a hybrid successive substitution/modified Newton method for the solution of the nonlinear equations describing association effects in the SAFT equation of state. Extensive computational experiments are reported to show that the proposed method performs efficiently and reliably over wide ranges of conditions for multicomponent systems involving up to 57 distinct types of association sites.

Phase Equilibria Calculations of Polyethylene Solutions from SAFT-Type Equations of State

We present here phase equilibria calculations of polyethylene solutions in different solvents as obtained with two versions of the SAFT equation of state, soft-SAFT and PC-SAFT. The objective of this work is twofold: to check the accuracy of the soft-SAFT equation in providing reliable polymer solutions behavior and to propose a methodology from which systematic studies on polymer solutions can be made by the use of transferable molecular parameters. Some issues regarding the fitting of molecular parameters from polymer data as well as the numerical problems associated with polymer phase equilibria calculations are also mentioned. The methodology is applied to model the phase equilibria of polyethylene solutions with several solvents, differing in size and polarity, including n-pentane, n-hexane, butyl acetate, and pentanol, and results are compared to available experimental data. The phase behavior explored in this work is wide, from vapor−liquid equilibria to liquid−liquid equilibria, displaying upper critical solution temperatures and lower critical solution temperatures. We have also calculated the solubility of ethylene in polyethylene with the same models. Results obtained from the soft-SAFT equation are slightly more accurate in some of the cases than the PC-SAFT equation. Both equations, soft-SAFT and PC-SAFT, follow most of the experimental trends, providing accurate predictions from pure component parameters in some of the cases, while a binary interaction parameter was needed for the butyl acetate, 1-pentanol, and ethylene binary mixtures.

An equation of state contribution for polar components: Polarizable dipoles

AbstractThe renormalized perturbation theory for polarizable polar fluids of Wertheim is applied in combination with a dipole contribution for non‐spherical molecules to account for the non‐additive induction interactions due to the polarization of molecules. A comparison to simulation data of pure polarizable dipolar fluids and mixtures reveals a good to excellent agreement between the renormalized perturbation theory and the simulations. The model framework is applied with the Perturbed‐Chain SAFT equation of state to model phase equilibria of mixtures containing strongly polar components. The considered values of dipole moments and of average molecular polarizabilities stem from independent sources, and there is thus no additional adjustable parameter introduced along with the polar contributions to the equation of state. It is confirmed that accounting for dipolar interactions not only reduces the value of the binary interaction parameter, but in many cases significantly improves the description of pure‐component and mixture phase equilibria. Accounting for molecular polarizability and the dipole induction effects only leads to slightly improved results compared to the case where a permanent dipole moment is considered in the calculations. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Application of group contribution SAFT equation of state (GC-SAFT) to model phase behaviour of light and heavy esters

The group contribution SAFT approach developed for pure compounds in an earlier work [S. Tamouza, J.-P. Passarello, J.-C. de Hemptinne, P. Tobaly, Fluid Phase Eq. 222–223 (2004) 67] is here extended for the treatment of ester series. Parameters for groups CH 2 and CH 3 previously determined were reused for the alkyl chains while new parameters were determined for COO and HCOO groups. The polarity of these molecules was taken into account by the addition to the equation of state (EOS) of a dipole–dipole interaction term due to Gubbins and Twu [K.E. Gubbins, C.H. Twu, Chem. Eng. Sci. 33 (1978) 863]. This term requires an additional parameter, the dipole moment which was correlated to the COO chemical group position in the ester chain. Three different versions of SAFT were used here to test the validity of the method: the original SAFT [W.G. Chapman, G. Jackson, K.E. Gubbins, M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 1709], VR-SAFT [A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, A.N. Burgess, J. Chem. Phys. 106 (1997) 4168] and PC-SAFT [J. Gross, G. Sadowski, Fluid Phase Eq. 168 (2000) 183; J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244]. In all three cases, similar and encouraging results are obtained. Reasonable predictions are found on heavy esters that were not included in the regression database.

Modeling of Polar Systems with the Perturbed-Chain SAFT Equation of State. Investigation of the Performance of Two Polar Terms

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to model phase equilibria and the thermodynamic properties of ethers and esters. A systematic study of these two homologous series is conducted, and the performance of two different approaches for including the dipolar interactions in the equation of state is evaluated. Although both Polar PC−SAFT [dipolar contribution due to Jog and Chapman, Mol. Phys. 1999, 97, 307−319] and PC−SAFT + Fischer [dipolar contribution by Saager and Fischer, Mol. Simul. 1991, 6, 27−49] yield similar results for the considered systems, the parameters of Polar PC−SAFT are more physically meaningful than those of PC−SAFT + Fischer. Consequently, Polar PC−SAFT is considered to be more suitable for extrapolations, and for application to components that have multiple polar groups in the chain.