Perturbed-chain Statistical Associating Fluid Theory Equation Research Articles

A Perturbed-Chain SAFT Equation of State Applied to Mixtures of Short- and Long-Chainn-Alkanes

A simplified hard-chain dimer theory is employed with perturbed-chain statistical associating fluid theory (PC-SAFT) in calculating the vapor pressures and saturated liquid volumes of pure n-alkanes from methane to n-eicosane. Compared to the original PC-SAFT, the developed model is in better agreement with the experimental vapor pressures and saturated liquid volumes of n-alkanes along the vapor–liquid coexistence curve and the critical properties from n-butane toward longer n-alkanes. Predicting the vapor–liquid equilibria (VLE) of binary mixtures containing methane and a long-chain n-alkane, the new model describes the mixtures more accurately than PC-SAFT. With no binary interaction parameter, the model adequately describes the experimental VLE data, in particular, near the critical points. In the prediction of the VLE of mixtures containing ethane, propane, n-hexane, and a long-chain n-alkane, the differences between the two models become less appreciable.

Evaluation of Cubic, SAFT, and PC-SAFT Equations of State for the Vapor–Liquid Equilibrium Modeling of CO2 Mixtures with Other Gases

Accurate thermodynamic models for phase equilibria calculations of carbon dioxide mixtures with other gases are of high importance for the safe and economic design of carbon capture and storage (CCS) technologies. In this work, we assess the capability of Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR) cubic equations of state (EoS), as well as Statistical Associating Fluid Theory (SAFT) and Perturbed-Chain SAFT (PC-SAFT) in modeling vapor–liquid equilibria for binary mixtures of CO2 with CH4, N2, O2, SO2, Ar, and H2S, and for the ternary mixture CO2–N2–O2. Liquid density calculations for some of these mixtures are also performed. Experimental data available are used to assess the accuracy of the models. Two different expressions are used for the calculation of parameter α in PR EoS. PC-SAFT is, on average, more accurate than cubic EoS and SAFT when no binary interaction parameter is used. However, when a binary interaction parameter fitted to the experimental data is used, model correla...

Modeling CO2 solubility in Aqueous Methyldiethanolamine Solutions by Perturbed Chain-SAFT Equation of State

CO2 capture by aqueous alkanolamines treating is one of the prevalent methods to reduce carbon dioxide emissions and to help environmental problems. For realizing more the thermodynamics of the CO2–MDEA–H2O, the PC-SAFT equation of state was used to simulate the absorption of carbon dioxide by MDEA (methyldiethanolamine). A correlation for temperature-dependent binary interaction parameter were calculated by excess enthalpy data for aqueous MDEA at low temperatures (lower than 350K), and then this binary interaction parameter used to predict phase equilibria of ternary aqueous mixtures of MDEA with carbon dioxide. Smith–Missen algorithm and PC-SAFT EOS have been used to determine concentration of species in chemical equilibrium and physical equilibrium, respectively. In addition, for determining parameter sets of MDEA, vapor pressure and saturated liquid density data were used and different and probable association schemes were considered in parameter estimations. Results show 4(2:2,0:0) association scheme for MDEA and 4(2:2) association scheme for water have better agreement with binary and ternary VLE experimental data.

Thermodynamic Modeling of Aqueous Ionic Liquid Solutions Using PC-SAFT Equation of State

In this work, an equation of state has been utilized for thermodynamic modeling of aqueous ionic liquid (IL) solutions. The proposed equation of state is a combination of perturbed chain statistical associating fluid theory (PC-SAFT) equation of state and mean spherical approximation (MSA) term. In this model, the ion-based approach has been used to adjust the model parameters. The ion parameters have been estimated through simultaneous fitting to experimental mean ionic activity coefficient and liquid density data of strong electrolytes. Using adjusted ion parameters, osmotic coefficients, mean ionic activity coefficients, liquid densities, apparent molar volume, and water activity of several ILs, assumed as chainlike electrolytes, have been calculated. Results show that PC-SAFT, in combination with the MSA term has acceptable accuracy for prediction of density, apparent molar volume, and activity coefficient of ILs. The average deviations of predicted mean ionic activity coefficients, liquid densities, water activity, and apparent molar volume are 6.43, 0.86, 0.033, and 8.20%, respectively.

Perturbed-Chain SAFT as a Versatile Tool for Thermodynamic Modeling of Binary Mixtures Containing Isoquinolinium Ionic Liquids

This contribution reports a recapitulation of our experimental and modeling study on thermodynamic behavior of binary systems containing N-alkylisoquinolinium ionic liquids (ILs) based on bis(trifluoromethylsulfonyl)imide anion, [CniQuin][NTf2] (n = 4,6,8). In particular, we report isothermal vapor-liquid equilibrium (VLE) phase diagrams and molar excess enthalpies of mixing (H(E)) for binary mixtures of [C8iQuin][NTf2] IL with various organic solutes including benzene, toluene, thiophene, pyridine, and butan-1-ol. The measured VLE data represented simple homozeotropic behavior with either negative or positive deviations from ideality, depending on polarity of the solute, temperature, and mole fraction of IL. In turn, the obtained data on H(E) were negative and positive for the mixtures containing aromatic hydrocarbons or thiophene and butan-1-ol, respectively, in the whole range of IL's concentration. All of the measured and some previously published data regarding phase behavior of [C8iQuin][NTf2] IL were analyzed and successfully described in terms of perturbed-chain statistical associating fluid theory (PC-SAFT). The methodology used in this work was described by us previously. In general, the proposed modeling results in VLE diagrams, which are in excellent agreement with experimental data. In the case of H(E), the results obtained are good as well but not so satisfactory such as those for VLE. Nevertheless, they seem to be very promising if one take into account the simplicity of the utilized molecular model against significant complexity of IL-based systems. Thus, we concluded that PC-SAFT equation of state can be viewed as a powerful and robust tool for modeling of systems involving ILs.

Thermodynamic Modeling of Ionic Liquid Systems: Development and Detailed Overview of Novel Methodology Based on the PC-SAFT

We present the results of an extensive study on a novel approach of modeling ionic liquids (ILs) and their mixtures with molecular compounds, incorporating perturbed-chain statistical associating fluid theory (PC-SAFT). PC-SAFT was used to calculate the thermodynamic properties of different homologous series of ILs based on the bis(trifluormethylsulfonyl)imide anion ([NTf2]). First, pure fluid parameters were obtained for each IL by means of fitting the model predictions to experimental liquid densities over a broad range of temperature and pressure. The reliability and physical significance of the parameters as well as the employed molecular scheme were tested by calculation of density, vapor pressure, and other properties of pure ILs (e.g., critical properties, normal boiling point). Additionally, the surface tension of pure ILs was calculated by coupling the PC-SAFT equation of state with density gradient theory (DGT). All correlated/predicted results were compared with literature experimental or simulation data. Afterward, we attempted to model various thermodynamic properties of some binary systems composed of IL and organic solvent or water. The properties under study were the binary vapor-liquid, liquid-liquid, and solid-liquid equilibria and the excess enthalpies of mixing. To calculate cross-interaction energies we used the standard combining rules of Lorentz-Berthelot, Kleiner-Sadowski, and Wolbach-Sandler. It was shown that incorporation of temperature-dependent binary corrections was required to obtain much more accurate results than in the case of conventional predictions. Binary corrections were adjusted to infinite dilution activity coefficients of a particular solute in a given IL determined experimentally or predicted by means of the modified UNIFAC (Dortmund) group contribution method. We concluded that the latter method allows accurate and reliable calculations of bulk-phase properties in a totally predictive manner.

Prediction of fluid density at extreme conditions using the perturbed-chain SAFT equation correlated to high temperature, high pressure density data

At pressures below ∼55MPa, the perturbed chain – statistically associated fluid theory (PC-SAFT) gives reliable density predictions within ±2% for n-alkanes and other hydrocarbons. However, PC-SAFT tends to over-predict density values by as much as 5% at higher pressures, particularly for normal and branched alkanes. For many compounds, literature values for the three pure-component PC-SAFT parameters m, σ, and ɛ/kB are typically obtained by fitting the equation to sub-critical PρT data or occasionally both sub-critical and supercritical density data. A new set of pure-component PC-SAFT parameters for density prediction at extreme conditions is reported here by fitting the PC-SAFT equation to single-component density data collected at temperatures from ambient to 533K and pressures from ∼6.9 to 276MPa, rather than sub-critical density data since these high temperature, high pressure (HTHP) conditions are similar to conditions typically associated with petroleum recovery from ultra-deep formations. Density predictions made using the new, HTHP PC-SAFT pure-component parameters at HTHP conditions are clearly superior to those obtained using the original PC-SAFT parameters. Although a correction term can be applied to the ɛ/kB parameter to make HTHP PC-SAFT pure-component density predictions at pressures below 6.9MPa only slightly inferior to predictions with the original PC-SAFT parameters, vapor–liquid equilibrium predictions with the original PC-SAFT parameters are clearly superior to predictions made with the HTHP parameters. Correlations are developed to accurately predict the HTHP PC-SAFT parameters for normal and branched alkanes for which there are either incomplete or nonexistent experimental density data sets.

Prediction of Phase Behavior for the System Methane-Carbon Dioxide- Hydrogen Sulfide-Water with the PR and PC-SAFT Equations of State

In this work, we present the predicted multiphase behavior (vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria) for a quaternary mixture containing methane, carbon dioxide, hydrogen sulfide, and water. The capabilities of the PR (Peng-Robinson) and PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equations of state (EoS) to predict the phase behavior exhibited by this mixture were compared and analyzed. The computer algorithm used for isothermal multiphase flash calculations is based on the minimization of the Gibbs energy along with stability analysis to find the most stable state of the system. The binary interaction parameters used with the PR EoS for modeling this system were taken from the literature whereas the interaction parameters for the PC-SAFT were obtained from the regression of binary vapor-liquid equilibrium data. The results obtained differ from each other and demonstrate different capabilities and accuracies of the present thermodynamic models in the predictions.

Experimental measurements and equation of state modeling of liquid densities for long-chain n-alkanes at pressures to 265 MPa and temperatures to 523 K

Experimental densities are reported for n-hexadecane, n-octadecane, and n-eicosane at pressures to ∼265 MPa and temperatures of 323.15, 423.15, and 523.15 K. The reported densities are in good agreement with the available literature data that cover limited pressure and temperature ranges. The Peng–Robinson equation of state (PR EOS), a new high-temperature high-pressure volume-translated Soave–Redlich–Kwong equation of state (HTHP-VT SRK EOS), and the perturbed-chain statistical associating fluid theory (PC-SAFT) are used to predict the reported densities. Both the HTHP-VT SRK and PC-SAFT equations exhibit mean absolute percent deviation (MAPD) values of 2.4–1.3% for the densities of all three hydrocarbons while the MAPD values for the PR EOS are all near 16%.

Thermodynamic modeling of hydrogen sulfide solubility in ionic liquids using modified SAFT-VR and PC-SAFT equations of state

Equations of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) and the perturbed chain statistical associating fluid theory (PC-SAFT) have been used to model the PVT behavior of ionic liquids and the solubility of H 2S in six imidazolium-based ionic liquids. The studied systems included [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], [bmim][NTF2] and [hmim][NTF2] at various temperatures and pressures. For pure components, parameters of the models have been obtained by fitting the models to experimental data on liquid densities; the average relative deviation between the calculated and experimental densities for ionic liquids is less than 2.42% in the PC-SAFT model and 5.44% in the SAFT-VR approach, the latter which incorporates the square-well potential for short-range interactions. In both models an additional term has been added to account for dipole–dipole interactions between solute molecules resulting from the permanent charges on the chain molecules of the solvents. The model parameters have also been correlated as functions of the molecular weight of the solvents. For binary mixtures of ionic liquids and H 2S, the association interactions between H 2S molecules and between the ionic liquids and H 2S molecules have also been taken into account in both approaches, using binary interaction coefficients. The results show an average deviation of less than 5% in the calculation of the mole fraction of H 2S in the ionic liquids. The effect of inclusion of the polar term has been studied for binary systems in both models.

Thermophysical behaviour of the mixture (±)-3,7-dimethyl-1,6-octadien-3-ol with ethanol

This paper reports the experimental values of density, speed of sound and refractive index of binary mixture of (±)-linalool + ethanol at four temperatures in the range of 283.15–328.15 K and 0.1 MPa. Excess molar volume, speed of sound deviation, refractive index deviation, molar refraction, molar refraction deviation and excess isentropic compressibility are also given at the same work conditions. Afterward, prediction of speed of sound and refractive index was carried out using several theoretical models or equations. The experimental density of the binary mixture was measured at high pressure between 20 and 40 MPa in the same range of temperature. Excess molar volume, isobaric thermal expansion, and isothermal compressibility were also calculated. Peng–Robinson (PR), Patel–Teja (PT), the Statistical Associating Fluid Theory (SAFT) and the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) were tested as predictive models of the PρT behaviour. The best predictions were obtained with the PC-SAFT equation of state (EOS).

Determining Force Field Parameters Using a Physically Based Equation of State

Force field parameters used in classical molecular simulations can be estimated from quantum mechanical calculations or spectroscopic measurements. This especially applies to bonded interactions such as bond-stretching, bond-bending, and torsional interactions. However, it is difficult and computational expensive to obtain accurate parameters describing the nonbonded van der Waals interactions from quantum mechanics. In many studies, these parameters are adjusted to reproduce experimental data, such as vapor-liquid equilibria (VLE) data. Adjusting these force field parameters to VLE data is currently a cumbersome and computationally expensive task. The reason is that the result of a calculation of the vapor-liquid equilibria depends on the van der Waals interactions of all atom types in the system, therefore requiring many time-consuming iterations. In this work, we use an analytical equation of state, the perturbed chain statistical associating fluid theory (PC-SAFT), to predict the results of molecular simulations for VLE. The analytical PC-SAFT equation of state is used to approximate the objective function f(p) as a function of the array of force field parameters p. The objective function is here for example defined as the deviations of vapor pressure, enthalpy of vaporization and liquid density data, with respect to experimental data. The parameters are optimized using the analytical PC-SAFT equation of state, which is orders of magnitude quicker to calculate than molecular simulation. The solution is an excellent approximation of the real objective function, so that the resulting method requires only very few molecular simulation runs to converge. The method is here illustrated by optimizing transferable Lennard-Jones parameters for the n-alkane series. Optimizing four force field parameters p = (ε(CH(2))(CH(2)), ε(CH(3))(CH(3)), σ(CH(2))(CH(2)), σ(CH(3))(CH(3))) we obtain excellent agreement of coexisting densities, vapor pressure and caloric properties within only 2 -3 molecular simulation runs.

Vapor−Liquid Equilibrium Data for the Nitrogen + Dodecane System at Temperatures from (344 to 593) K and at Pressures up to 60 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 + C12H26 system over the temperature range from (344 to 593) K and at pressures up to 60 MPa. Equilibrium phase compositions and vapor−liquid equilibrium ratios are reported. All of the measured vapor−liquid equilibrium data were subject to a thermodynamic consistency test of high-pressure vapor−liquid equilibrium data involving the calculation of the vapor-phase composition from the isothermal pressure liquid phase composition data. The consistency test showed that most of the data are thermodynamically consistent. The new results were compared with solubility data reported by other authors. The comparison showed that the vapor−liquid equilibrium data obtained in this study are in good agreement with those reported in the literature. The experimental data were modeled with the PR (Peng−Robinson) and PC-SAFT (perturbed-chain statistical associating fluid theory) equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results of the modeling indicated that the PC-SAFT equation of state represents better the measured data of the N2 + C12H26 system over the whole temperature, pressure, and composition range studied.

10.2478/s11814-009-0351-z

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.

Calculation of Pressure−Temperature Diagrams and Distance for Phase Transition in Polyethylene Solutions

Understanding the phase behavior of polymer solutions is of great theoretical and practical importance. Pressure versus temperature (P−T) isopleths allow one to determine the number of phases present at a given T, P, and overall mixture composition. In this work, the PC-SAFT (perturbed-chain statistical associating fluid theory) equation of state (EOS) was applied to simulate the curves that describe the boundaries between several distinct regions depicted in P−T isopleths. A new strategy was used, and the simulation results were found to show good agreement with experimental cloud-point isopleth data from the literature. In addition, a method was developed to calculate the distance between an operating point (pressure and temperature) and the corresponding point in the interface for fixed molecular weight and weight fraction of the polymer.

PρT Measurements of the (Ethanol + Linalool), (Propan-1-ol + Linalool), and (Propan-2-ol + Linalool) Mixtures: Cubic and Statistical Associating Fluid Theory-Based Equation of State Analyses

The density of the asymmetrical binary systems (ethanol + linalool), (propan-1-ol + linalool), and (propan-2-ol + linalool) has been measured (660 points) for nine different compositions including the pure compounds at four temperatures in the range (283.15 to 328.15) K and 5 isobars up to 20 MPa with a vibrating-tube densimeter. The experimental expanded uncertainty is estimated to be ± 0.5 kg·m−3. The isothermal compressibility, the isobaric thermal expansion, and the excess molar volume were derived from the experimental density data, revealing that a volume contraction occurs for these binary mixtures. Three different equations of state (EOS’s), Peng−Robinson (PR), statistical associating fluid theory (SAFT), and perturbed-chain statistical associating fluid theory (PC-SAFT), were applied to predict the volumetric behavior of the alkanolic mixtures. The best predictions were achieved with the PC-SAFT equation of state.

Renormalization-Group Corrections to the Perturbed-Chain Statistical Associating Fluid Theory for Binary Mixtures

Classical fluid theories do not describe the long-range fluctuations that occur in the vicinity of a pure component or mixture’s critical point. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is extended with a renormalization group theory for mixtures. The theory accounts for the long-range density fluctuations and the results reduce to the results of the classical PC-SAFT equation of state away from the critical point. Two approximation methods, the isomorphic approximation and phase-space cell approximation, are used for the renormalization group corrections of mixtures. The two variants are evaluated by comparison to experimental vapor−liquid data for systems of alkanes, carbon dioxide and hydrogen sulfide. Overall, the considered implementation of the phase-space cell approximation is slightly superior to the isomorphic approximation for the mixtures investigated here. The phase-space cell approximation tends to overestimate the renormalization corrections for so...

Vapor−Liquid Equilibrium Measurements and Modeling for Cyclohexane + Cyclohexanone

The characteristically low conversion in the oxidation of cyclohexane to form cyclohexanol and cyclohexanone requires significant recovery work via distillation. In this study, new isothermal vapor−liquid equilibria (VLE) are presented for the cyclohexane + cyclohexanone binary system. Measurements were performed at temperatures of (423, 444, 464, and 484) K, using an apparatus based on the “static−analytic” method, with two ROLSI pneumatic capillary samplers. The generated data are correlated using two equations of state, namely, the Peng−Robinson coupled with the Wong−Sandler mixing rules and the perturbed-chain statistical associating fluid theory (SAFT) with a dipolar contribution by Jog and Chapman. While both models perform reasonably well in describing the phase equilibria, the Peng−Robinson is slightly better than the perturbed-chain SAFT equation of state and tends to be more easily implemented in industrial process simulators.

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.

Compositional Polydispersity in Linear Low Density Polyethylene

A study of the effect of a short-chain branching distribution (SCBD) on the phase behavior of linear low density polyethylene (LLDPE) was conducted. The perturbed chain-SAFT equation of state was the underlying thermodynamic model chosen for the study; the branched polyolefins were described using a simple modeling concept previously proposed by Dominik and Chapman.(1) To isolate the effect of the SCBD on phase behavior, the copolymer systems were considered monodisperse in molecular weight. The study revealed that, in the case of low to moderate values of the polydispersity index of the SCBD, the compositional polydispersity affected the phase behavior at low polymer concentrations only. When the polydispersity index of the SCBD is high, or, in other words, when the difference in branch content between the components of the distribution is significant, additional phases appear. The formation of multiple phases results from the incompatibility of branched and linear polymers. Similar observations were made on the basis of experimental studies in the case of polymer blends. The SCBD of LLDPE was determined by the chemistry of the polymerization reaction. A broad SCBD was found to significantly affect the phase behavior of LLDPE solutions.