Perturbed-chain Statistical Associating Fluid Theory Research Articles

Vapor−Liquid Equilibria of Acid Gas−Aqueous Ethanolamine Solutions Using the PC-SAFT Equation of State

Using the perturbed-chain statistical associating fluid theory (PC-SAFT), the vapor pressure, saturated liquid density, and heat of vaporization for monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA) were calculated. PC-SAFT accurately described the properties of the pure ethanolamines along the coexistence curve. Then, the vapor−liquid equilibria (VLE) of the aqueous ethanolamine solutions were calculated by temperature-independent binary interaction parameters. Using the binary interaction parameters for the systems DEA + water, DEA + methanol, and methanol + water, the VLE of the ternary system DEA + water + methanol was predicted. The results indicated that PC-SAFT successfully described the equilibrium properties of the aqueous ethanolamine solutions. Finally, the solubilities of carbon dioxide and hydrogen sulfide in the aqueous ethanolamine solutions were predicted and compared to the experimental data. While no adjustable parameters were used, PC-SAFT reasonably describe...

“Vapor–liquid” equilibrium measurements and modeling for the cyclohexane + cyclohexanol binary system

To simulate cyclohexane oxidation reactors using a dynamic model linking kinetics, thermodynamics and hydrodynamics, the acquisition and modeling of vapor–liquid equilibria of the key components, under the process conditions, are essential. In this work, the vapor–liquid equilibria of the cyclohexane + cyclohexanol system were determined at temperatures 424, 444, 464 and 484 K. The measurements were carried out using an apparatus based on the “static-analytic” method, with two ROLSI™ pneumatic capillary samplers. The generated data are successfully correlated using two equations of state, the Peng–Robinson (PR) and the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT). A comparison of model performances reveals the former being better in data representation, while the latter has a broader applicability over larger range of temperatures.

Study on the activity coefficients and solubilities of amino acids in aqueous solutions with perturbed-chain statistical associating fluid theory

Perturbed-chain statistical associating fluid theory (PC-SAFT) was applied for modeling the thermodynamic properties of aqueous amino acid solutions. To account for the association phenomena of amino acids occurring in the aqueous solution, the zwitterionic forms of amino acids are assumed to be associating species with proton donor and acceptor sites. Also, in order to reduce the number of adjustable parameters of PC-SAFT equation of state (EoS) for amino acids from five to three, it is assumed that segment numbers of amino acids are linearly related with the molecular weight of amino acids, and the association volume parameters of amino acids can be set to a fixed value. Thus, 3-parameters of PC-SAFT EoS for amino acids were estimated by simultaneously fitting the activity coefficients of amino acid and densities data in the aqueous amino acid solutions. The PC-SAFT EoS with estimated 3-parameters of amino acid is found to well describe activity coefficients of amino acid and densities of the aqueous amino acid solutions. Also, this equation was used for predicting solubilities of amino acids as well as the water activities and osmotic coefficients in the aqueous amino acid solutions. The predicted values of these properties are in good agreement with the experimental data.

Modeling of aqueous electrolyte solutions based on perturbed-chain statistical associating fluid theory incorporated with primitive mean spherical approximation

In this work an equation of state applicable to the system containing electrolytes has been developed by coupling the perturbed chain statistical associating fluid theory (PC-SAFT) with the primitive mean spherical approximation. The resulting electrolyte equation of state is characterized by 4 ion parameters for each of the cation and anion contained in aqueous solutions, and 4 ion specific parameters for each of six cations (Li+, Na+, K+, Rb+, Mg2+ and Ca2+) and six anions (Cl−, Br−, I−, HCO3−, NO3− and SO42−) were estimated, based upon the individual ion approach, from the fitting of experimental densities and mean ionic activity coefficients of 26 aqueous single-salt solutions at 298.15 K and 1 bar. The present equation of state with the estimated individual ion parameters has been found to satisfactorily describe not only the densities and mean ionic activity coefficients, but also osmotic coefficients and water activities of single-salt aqueous solutions. Furthermore, the present model was extended to two-salt aqueous solutions, and it has been found that thermodynamic properties such as mentioned above, of two-salt solutions, can be well predicted with the present model, without any additional adjustable parameters.

Modeling the Solubility of Pharmaceuticals in Pure Solvents and Solvent Mixtures for Drug Process Design

The knowledge of the solubility of pharmaceuticals in pure solvents and solvent mixtures is crucial for designing the crystallization process of drug substances. The first step in finding optimal crystallization conditions is usually a solvent screening. Since experiments are very time consuming, a model which allows for solubility predictions in pure solvents and solvent mixtures based only on a small amount of experimental data is required. In this work, we investigated the applicability of the thermodynamic model perturbed-chain statistical associating fluid theory (PC-SAFT) to correlate and to predict the solubility of exemplary five typical drug substances and intermediates (paracetamol, ibuprofen, sulfadiazine, p-hydroxyphenylacetic acid, and p-aminophenylacetic acid) in pure solvents and solvent mixtures. © 2009 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:4205–4215, 2009

Modeling the phase behavior in binary mixtures involving blowing agents and thermoplastic resins

AbstractThe thermophysical properties of mixtures of thermoplastic resins and blowing agents, together with the knowledge of the solubilities of these components, are the basis for the manufacturing of plastic foams. In this work, the solubilities of blowing agents trichlorofluoromethane, dichlorodifluoromethane, chlorodifluoromehane, and 1,2‐dichloro‐1,1,2,2‐tetrafluoroethane in thermoplastic resins poly(styrene), high density poly(ethylene), low density poly(ethylene), poly(propylene), poly(vinyl chloride), poly(carbonate) and poly(propylene oxide) were modeled by using the Perturbed Chain‐Statistical Associating Fluid Theory (PC‐SAFT) and the Sánchez‐Lacombe equations of state (EoS), fitting a single temperature‐dependent binary interaction parameter. PC‐SAFT is a theoretically based equation of state with three pure component parameters that describe efficiently the thermodynamics of complex systems. Earlier works with this EoS have already predicted the phase coexistence properties of various refrigerants and higher order alkane series compounds, along with their mixtures. The pure component parameters for the blowing agents were obtained by regression of vapor pressure and liquid density data, while the pure component parameters for the thermoplastic resins were obtained by regression of pure liquid PVT data. The parameter estimation was performed by using a modified maximum likelihood method. The solubility results obtained with both EoS have been compared; the results from PC‐SAFT showed a higher accuracy in terms of solubility pressure deviations. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Investigation of Bulk and Interfacial Properties for Nitrogen and Light Hydrocarbon Binary Mixtures by Perturbed-Chain Statistical Associating Fluid Theory Combined with Density-Gradient Theory

The perturbed-chain statistical associating fluid theory (PC-SAFT) and density-gradient theory (DGT) are used to construct an equation of state (EOS) for the phase behavior of the binary mixtures of nitrogen and light hydrocarbons. With the molecular parameters and influence parameters respectively regressed from bulk properties and surface tensions of pure fluids as input, both the bulk and the interfacial properties for binary mixtures are investigated. The calculated surface tensions of nitrogen−pentane, nitrogen−hexane, nitrogen−heptane, nitrogen−octane, nitrogen−decane, and nitrogen−toluene binary mixtures are satisfactory as compared to the experimental data. Our results show that PC-SAFT combined with DGT is able to describe the interfacial properties of the binary mixtures of nitrogen−light hydrocarbons in wide pressure range and illustrate the influences of temperature, pressure, and bulk properties on the interfacial properties.

Phase equilibria of carbon dioxide + poly ethylene glycol + water mixtures at high pressure: Measurements and modelling

Phase equilibria of carbon dioxide + poly ethylene glycol (PEG) of average mol weight 6000 g/mol + water mixtures has been measured by the static method at conditions of interest for the development of Particles from Gas Saturated Solutions (PGSS)-drying processes (pressure from 10 MPa to 30 MPa, temperature from 353 K to 393 K). A thermodynamic model based on the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state has been developed for correlating experimental data. The model is able to predict the composition of the liquid phase with an average deviation of 8.0%. However, the model does not calculate correctly the concentration of PEG in the gas phase. The model is also capable of predicting VLE data reported in the literature of PEG + CO 2 mixtures with PEGs of molecular weights ranging from 1500 g/mol to 18500 g/mol as well as solid–fluid equilibrium of carbon dioxide + PEG mixtures at pressures below 10 MPa.

Vapor–liquid equilibrium measurements and modeling of the n-butane + ethanol system from 323 to 423 K

Vapor–liquid equilibrium (VLE) data are presented for the n-butane + ethanol system in the temperature range from 323 to 423 K. Measurements were performed using a “static-analytic” apparatus, equipped with two electromagnetic ROLSI™ capillary samplers, and thermally regulated via an air bath. This work presents vapor compositions which have not been explicitly measured previously. The modeling of the data was performed using two models: the Peng–Robinson equation of state with the Wong and Sandler mixing rule and NRTL excess function (PR/WS/NRTL); and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. To assess the effect of dipole–dipole interactions present, a dipolar contribution developed by Jog and Chapman (1999) [20] was tested with the second model. Temperature dependent binary interaction parameters have been adjusted to the new data. The PR/WS/NRTL equation of state shows good correlation with the results, while the PC-SAFT is slightly less accurate.

Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO 2. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO 2) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter ( k ij ) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.

PC-SAFT Equation: A Predictive Tool to Determine Experimental Conditions for Polymer Blend Demixing

The perturbed-chain statistical associating fluid theory equation of state (PC-SAFT) was applied to predict the phase behavior of polymer solutions in order to determine the pressure – temperature region for the high molecular weight polymer blend separation by using n-alkanes at high pressure and high temperature. The polymer blends selected were physical blends of polyethylene (PE)/polystyrene (PS), and polypropylene (PP)/PS. The miscibility and immiscibility region of each polymer in different alkanes (n-pentane, n-hexane, and n-heptane) was studied and from this analysis, the experimental conditions of the polymer blend demixing were predetermined. The results obtained were validated with experimental data indicating that the PC-SAFT equation is a good tool to predict experimental conditions for the processing windows of polymer blend separation.

Mathematical modelling of the solubility of supercritical CO 2 in poly( l-lactide) and poly( d,l-lactide-co-glycolide)

Two mathematical models, Sanchez–Lacombe equation of state and the Perturbed-Chain Statistical Associating Fluid Theory were applied for modelling the phase equilibrium for the poly( l-lactide)–CO 2 and poly( d,l-lactide-co-glycolide)–CO 2 systems. Aspen Polymer Plus software was used. The results were compared with previously obtained experimental values for solubility. The solubility of scCO 2 in the two biodegradable polymers was calculated for three different temperatures (308, 313 and 323 K) in the pressure range (10–30 MPa). The characteristic parameters for the components and the binary interaction parameters for the models were optimized in order to obtain the best fit between the estimated and the experimental gas solubility data. The results suggest that both SL EOS and PC-SAFT are reliable models in describing the phase equilibrium of the PLLA–CO 2 and PLGA–CO 2 systems at the proposed working conditions.

Study of high-pressure adsorption from supercritical fluids by the potential theory

The multicomponent potential theory of adsorption (MPTA), which has been previously used to study low-pressure adsorption of subcritical fluids, is extended to adsorption equilibria from supercritical fluids up to high pressures. The MPTA describes an adsorbed phase as an inhomogeneous fluid with thermodynamic properties that depend on the distance from the solid surface (or position in the porous space). The description involves the two kinds of interactions present in the adsorbed fluid, i.e. the fluid–fluid and fluid–solid interactions, accounted for by means of an equation of state (EoS) and interaction potential functions, respectively. This makes it possible to generate the different MPTA models by combination of the relevant EoS/potentials. In the present work, the simplified perturbed-chain statistical associating fluid theory (sPC-SAFT) EoS is used for the thermodynamic description of both the adsorbed and the gas phases. We have also evaluated the performance of the classical Soave–Redlich–Kwong (SRK) EoS. The fluid–solid interactions are described by simple Dubinin–Radushkevich–Astakhov (DRA) potentials. In addition, we test the performance of the 10-4-3 Steele potential. It is shown that application of sPC-SAFT slightly improves the performance of the MPTA and that in spite of its simplicity, the DRA model can be considered as an accurate potential, especially, for mixture adsorption. We show that, for the sets of experimental data considered in this work, the MPTA is capable of predicting adsorption of pure components and binary mixtures in wide ranges of pressure and temperature. A good agreement with the theoretical predictions is achieved in most of the cases. The MPTA is capable to correctly describe complex physical behavior observed at supercritical/high-pressure conditions. Some limitations of the model are also discussed.

Modeling VLE of H2+ Hydrocarbon Mixtures Using a Group Contribution SAFT with akijCorrelation Method Based on London’s Theory

A group contribution perturbed-chain statistical associating fluid theory (GC-PC-SAFT) equation of state (Tamouza et al. Fluid Phase Equilib. 2004, 222−223, 67−76) combined with a recent method for correlating kij using only pure compound parameters (NguyenHuynh et al. Ind. Eng. Chem. Res., 2008. 47(22), 8847−8858) is extended here to model vapor−liquid phase equilibria of H2 + alkanes and H2 + aromatics mixtures. The correlation of kij is inspired by London’s theory of dispersive interactions, and uses “pseudo-ionization energies” Ji and Jj of compounds i and j as adjustable parameters. The GC-PC-SAFT parameters for alkanes and aromatics were reused from previous works when available. Otherwise, the missing parameters were estimated by regression of corresponding pure vapor−liquid equilibrium (VLE) data. Those of H2 were determined in this work by correlating some VLE data of H2 + n-alkane systems. Using the parameters thus obtained, the phase envelopes of other H2 + alkane and H2 + aromatic systems were fully predicted. The prediction tests were as comprehensive as possible. Correlations and predictions are qualitatively and quantitatively satisfactory. The deviations are within 5−6%, that is, comparable to those obtained on previously investigated systems. Mixtures containing H2 are modeled here with deviations that compare well with those of the Grayson−Streed model (Grayson, H.G.; Streed, C.W.; Proc., 6th World Pet. Congress, 1963, 169−181), which is often used by process engineers for hydrogen and hydrocarbon mixtures.

Application of the Simplified Perturbed-Chain SAFT to Hydrocarbon Systems with New Group-Contribution Parameters

A new group contribution (GC) method has been developed to estimate parameters of the simplified perturbed-chain statistical associating fluid theory (sPC-SAFT) for hydrocarbon. A key advantage of this method is that the binary interaction parameter between groups has been adopted in estimating the molecular parameter of pure component. Besides, parameters of all single groups are set to be the same for simplifying the model. Using genetic algorithm, twelve group interaction parameters are estimated on the basis of 71 sets of pure components of sPC-SAFT parameters. Tests and comparisons with other methods were performed in calculating the PVT and phase equilibrium data of heavy and branched hydrocarbon systems. The results show that the present GC method is better than the other predictive approaches in calculating parameters of sPC-SAFT.

Thermodynamic Modeling of Several Aqueous Alkanol Solutions Containing Amino Acids with the Perturbed-Chain Statistical Associated Fluid Theory Equation of State

The perturbed-chain statistical associated fluid theory EoS was applied to model the solubilities of glycine, dl-alanine, l-serine, l-threonine, and l-isoleucine in pure water, pure alcohols (ethan...

Analysis and applications of a group contribution sPC-SAFT equation of state

A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. In this paper, an investigation of the predictive capability of the GC sPC-SAFT EoS through comparison of the method’s predictions for compounds with high molecular weights and several selected binary mixtures of industrial significance with experimental data such as thiols, sulphides and polynuclear aromatics is presented. Additionally, predictions of activity coefficient at infinite dilution for athermal systems are compared with the results using existing activity coefficient models. The results show that calculated pure compound parameters using the proposed GC method allow satisfactory representation of experimental data of investigated systems with the sPC-SAFT EoS. Moreover, the variety of functional groups in the available GC scheme ensures broad applications of the GC sPC-SAFT EoS.

Application of sPC-SAFT and group contribution sPC-SAFT to polymer systems—Capabilities and limitations

A group contribution (GC) version of the simplified Perturbed-Chain Statistical Associating Fluid Theory (sPC-SAFT) Equation of State is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. The reported predictive capability of the model demonstrates satisfactory description of the fluid behaviour of several polymer systems, including both vapour–liquid equilibria and liquid–liquid equilibria. This work continues the systematic study on phase behaviour of polymer systems with the two versions of the sPC-SAFT model, with and without GC. The reported results contribute to a better understanding of the applicability of the sPC-SAFT model to binary polymer mixtures, and identify both models as good predictive tools for several industrial applications. Limitations are also identified and discussed.

Modeling the Phase Behavior of PEO−PPO−PEO Surfactants in Carbon Dioxide Using the PC-SAFT Equation of State: Application to Dry Decontamination of Solid Substrates

The phase behavior of several commercially available poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) block copolymers (PEO−PPO−PEO or Pluronics L) in compressed carbon dioxide has been investigated within the framework of dry nuclear decontamination. For this purpose, cloud points have been measured in the pressure and temperature range from P = (10 to 40) MPa and from T = (293 to 338) K, respectively. To find a reliable method for surfactant selection, the perturbed-chain statistical association fluid theory (PC-SAFT) equation of state (EoS) has been applied to model the experimental data. The pure-component and the respective homopolymer + CO2 binary interaction parameters have been fitted to liquid densities and to homopolymer + CO2 binary equilibrium data. The phase behavior of Pluronics L copolymers as a function of concentration, molar mass, and copolymer composition has been predicted very accurately using a constant PEO−PPO binary interaction parameter kPEO-PPO = 0.007. The PC-SAFT model was also successfully applied to Pluronics R copolymers (PPO—PEO—PPO), although a different kPEO-PPO = −0.018 was required to match the experimental data. The model predictions have shown that Pluronics L copolymers with molar mass M < 2750 g·mol−1 and a PEO mass fraction in the copolymer of less than 30 % have sufficiently low cloud-point pressures and are therefore the most suitable for the decontamination process.

Vapor−Liquid Equilibrium Data for the Nitrogen + n-Decane System from (344 to 563) K and at Pressures up to 50 MPa

A static-analytical apparatus with visual sapphire windows and pneumatic capillary samplers has been used to obtain new vapor−liquid equilibrium data for the N2 + C10H22 system over a wide temperature range from (344 to 563) K and at pressures up to 50 MPa. Equilibrium phase compositions and vapor−liquid equilibrium ratios are reported. The experimental data were modeled with the PR (Peng−Robinson) and PC-SAFT (perturbed-chain statistical association fluid theory) equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results from the modeling effort showed that the PC-SAFT equation was superior to the PR equation in correlating the experimental data of the N2 + C10H22 system over the whole temperature, pressure, and composition range studied.