Perturbed-chain Statistical Associating Fluid Theory Research Articles

Vapor Liquid Equilibria of 1-Ethyl-3-methylimidazolium Triflate (C2mimTfO) and n-Alkyl Alcohol Mixtures.

The isobaric vapor liquid equilibria (VLE) of different binary mixtures of the ionic liquid (IL) 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (C2mimTfO) with the n-alkyl alcohols, methanol, ethanol, propan-1-ol, and butan-1-ol, are studied at the pressures of p = 500, 700, and 1000 mbar, covering a composition range 0.25-0.35 ≤ x(solvent) ≤ 1.0. Complementarily, the experimental results are compared with calculations by the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS). For deriving suitable PC-SAFT parameters, experimental liquid densities were determined for the neat IL C2mimTfO and its longer homologues, 1-butyl-3-methylimidazolium trifluoromethanesulfonate (C4mimTfO) and 1-hexyl-3-methylimidazolium trifluoromethanesulfonate (C6mimTfO), in a temperature range of 288.15 K ≤ T ≤ 363.15 K (C2mimTfO) and 293.15 K ≤ T ≤ 363.15 K (C4mimTfO and C6mimTfO), respectively. The PC-SAFT EoS is found to be suitable for describing the VLEs under study with good accuracy (AARDVLE ≤ 0.4%).

Experimental and Modeling of Densities and Viscosities of Binary Mixtures Containing MTBE/Alkan-2-ol

The density and viscosity of three binary mixtures composed of methyl tert-butyl ether (MTBE) with 2-propanol, 2-butanol, and 2-pentanol over the whole composition range at 293.15 to 323.15 K were measured. The excess molar volume and deviation in viscosity , were calculated and interpreted in terms of intermolecular interactions among the species in the mixtures. For all binary mixtures, negative values of and were fitted to the Redlich-Kister polynomial function. By increasing temperature, and were reduced and increased, respectively. The density of the binary systems was modeled in terms of the perturbed chain statistical associating fluid theory (PC-SAFT) and compared with the corresponding experimental data. Maximum of deviation between the experimental data and calculated values by this theory is 1.4% and belongs to the MTBE + 2-butanol system

Phase Behavior Modeling of Mixtures Containing N-, S-, and O-Heterocyclic Compounds Using PC-SAFT Equation of State

In this study, thermodynamic modeling of mixtures including heterocyclic compounds using the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is studied. The oxygen-, nitrogen-, or sulfur-containing heterocyclic molecules are modeled as nonassociating components. For some more aggregative associating compounds with −OH (furfuryl alcohol, tetrahydrofurfuryl alcohol, 2-thiophenemethanol, and 5-hydroxymethylfurfural) or −NH (azetidine, aziridine, pyrrole, pyrazole, pyrrolidine, pyrrolidone, piperidine, morpholine, imidazole, piperazine, and n-methylpiperazine) groups, two association sites are considered for each molecule. The pure component parameters of the PC-SAFT EoS are adjusted to vapor pressure and liquid density experimental data with average absolute relative deviation of 0.88 and 0.77%, respectively. Using the obtained parameters, the isobaric and isothermal phase behavior of binary systems is studied over a wide range of thermodynamic conditions. The average deviations between model calculations and experimental data for heterocycle + aromatics, heterocycle + cycloalkane, heterocycle + haloalkanes, heterocycle + alcohol, heterocycle + heterocycle, heterocycle + organic solvents, and heterocycle + hydrocarbon systems are about 1.79, 2.15, 1.03, 1.68, 2.81, 1.24, and 1.81% respectively. Furthermore, the solid–liquid equilibria of heterocycle mixtures have been predicted by estimation of melting and eutectic points over a wide range of compositions. The second-order-derivative thermodynamic properties of heterocyclic compounds including speed of sound (us) and heat capacity (Cp) have been also predicted. The obtained results are in good agreement with the experimental data.

Measurements and modeling of the density of rocket propellant RP-2 at temperatures to 573 K and pressures to 100 MPa

Liquid rocket propellants are subject to wide ranges of temperature and pressure when flowing through high performance liquid rocket engines. For example, as rocket propellant (RP) is used for regenerative cooling, near-wall fluid temperatures can exceed 700 K. The pressure can reach as high as 100 MPa when exiting the fuel pump. Therefore, accurate thermophysical property data, particularly density, are needed to accurately model the flow in rocket engines using computational fluid dynamics (CFD) and other engineering design tools. In this work, we report the density of two RP-2 samples at temperatures to 573 K and pressures to 100 MPa. A high-temperature, high-pressure (HTHP) variable-volume, windowed densimeter is used to determine the density. The experimental density data are satisfactorily correlated by the modified Tait equation that provides a means for interpolating the density within the experimental conditions investigated in this study. The HTHP perturbed-chain statistical associating fluid theory (PC-SAFT), Peng-Robinson (PR), and HTHP volume-translated PR equations of state are used to model RP-2 density over the entire temperature and pressure ranges.

New phase equilibrium data at ambient and high pressure for strongly asymmetric mixtures containing menthol

New data on phase equilibria in binary and ternary mixtures containing (−)-menthol, n-decane, 1-decanol and water are presented and discussed. In particular, experimental liquid-liquid equilibrium phase diagrams in ternary systems {(−)-menthol + (n-decane, or 1-decanol) + water} are reported along with the predictions by means of leading thermodynamic models, namely, perturbed-chain statistical associating fluid theory (PC-SAFT) and conductor-like screening model for real solvents (COSMO-RS). Freezing pressure data for binary systems {(−)-menthol + (n-decane, or 1-decanol)} are reported and the corresponding high-pressure solid-liquid equilibrium phase diagrams are discussed and analyzed by using the Yang equation. The measured data are referred to ambient-pressure phase diagrams published previously.

A comparative study of CPA and PC-SAFT equations of state to calculate the asphaltene onset pressure and phase envelope

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) and the Cubic-Plus-Association (CPA) EoS have been widely applied to describe the asphaltene precipitation onset in crude oils because the association term of these models can appropriately account for the polar-polar interactions between asphaltene and resin molecules. In this study we have compared the PC-SAFT and CPA EoS capabilities in the calculation of the Asphaltene Precipitation Envelope (APE) of eight oils from the literature and discuss the physical meaning of the cross-association energy parameter between asphaltene and resin. For all oils the PC-SAFT EoS predicts an increase in the stability of the oil at higher temperatures with the consequent closure of the APE while the CPA model predicts a decrease in the stability at higher temperatures. For both models the fitted values of the cross-association energy parameter between asphaltene and resin show a dependency on temperature, but for PC-SAFT model this parameter has a clearer physical meaning. Results indicate that the PC-SAFT EoS is more accurate for APE calculations outside the experimental temperature range.

Density and Volumetric Properties of Binary Mixtures of CO2 + Hexadecane from (303.2 to 473.2) K and Pressures up to 50.0 MPa

Densities of CO2 + hexadecane binary mixtures were measured by the capillary high-pressure optical cell method at temperatures from 303.2 to 473.2 K and pressures up to 50.0 MPa with CO2 molar fractions x1 = 0, 0.2555, 0.3703, 0.7348, and 0.8645. The density and excess molar volume of CO2 + hexadecane mixtures are the positive correlation function of pressure and the negative correlation function of temperature. The dissolution of CO2 increases the density of mixtures at low temperatures and decreases the density of mixtures at high temperatures. The crossover temperature increases with increasing pressure. The perturbed-chain statistical associating fluid theory (PC-SAFT) parameters of pure substances were fitted, and the densities of CO2 + hexadecane mixtures can be calculated accurately with the PC-SAFT model.

Application of the Perturbed-Chain SAFT to Phase Equilibria in the Fischer–Tropsch Synthesis

As an alternative route to produce liquid fuels, Fischer–Tropsch synthesis (FTS) has received considerable attention. Phase equilibria have been one of the key issues in the design and operation of not only an FTS reactor, but also relevant downstream processing, e.g., stepwise condensation of FTS products, wastewater treatment, and the recovery of α-olefins. These issues are extremely complex due to a wide spectrum of FTS products and the presence of noncondensable gas, nonpolar components, associating components, and highly polar components. To address these issues, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was evaluated using phase equilibrium data of binary and ternary mixtures containing water, alcohols, hydrocarbons, and noncondensable gases. The parameter values are available via a three-step parametrization strategy established in our previous work [Zheng et al. Ind. Eng. Chem. Res. 2018, 57, 3014]. A couple of popular benchmark models, namely the Soave–Redlich–Kwong (SRK) EoS with the modified Huron–Vidal second-order mixing rule (SRK/MHV2) and the predictive SRK (PSRK) EoS, were selected for comparison to put the performance of the PC-SAFT EoS into perspective. It was found that the PC-SAFT EoS gives reliable correlations/predictions in all the studied cases, whereas the other two models fail to do so. The three models were also employed to simulate hot and cold traps where the stepwise condensation of the reactor effluent occurs. It was found that all three models yield satisfactory results for the paraffin distribution of the liquid stream leaving the hot trap, while the SRK/MHV2 and PSRK models are less accurate for the olefin distribution, particularly at high temperature. It was also found that all three models are capable of predicting the composition of the two liquid streams (namely organic and aqueous) leaving the cold trap except that the SRK/MHV2 model fails to accurately reproduce the distribution of alcohols in the two liquid streams. This study advocates the practical use of the PC-SAFT EoS by its application to a complex, industrially important FTS process and a comprehensive evaluation, together with the two popular benchmark models.

Surrogate modeling of phase equilibrium calculations using adaptive sampling

Equation of state models as the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) model are accurate and reliable prediction models for phase equilibria. But due to their iterative nature, they are difficult to apply in chemical process optimization, because of long computation times. To overcome this issue, surrogate modeling – replacing a complex model by a black-box model – can be used. A novel surrogate modeling strategy for phase equilibria is presented, combining the training of a classifier model with regression models for the phase composition using a mixed adaptive sampling method. We discuss the selection of the parameters of the sampling algorithm and a suitable stop criterion for the example ternary liquid-liquid equilibrium system of n-decane, dimethylformamide and 1-dodecene in detail. The sequential mixed adaptive sampling method is compared to the one-shot Latin hypercube sampling design.

Simultaneous Prediction of Cosolvent Influence on Reaction Equilibrium and Michaelis Constants of Enzyme-Catalyzed Ketone Reductions.

Understanding and quantification of cosolvent influences on enzyme-catalyzed reactions are driven by a twofold interest. On the one hand, cosolvents can simulate the cellular environment for deeper understanding of in cellulo reaction conditions. On the other hand, cosolvents are applied in biotechnology to tune yield and kinetics of reactions. Further, cosolvents are even present inherently, for example, for reactions with cofactor regeneration or for enzymes that need cosolvents in a function of a stabilizer. As the experimental determination of yield and kinetics is costly and time consuming, this work aims at providing a thermodynamic predictive approach that might allow screening cosolvent influences on yield and Michaelis constants. Reactions investigated in this work are the reduction of butanone and 2-pentanone under the influence of 17 wt % of the cosolvent polyethylene glycol 6000, which is also often used as a crowder to simulate cellular environments. The considered reactions were catalyzed by a genetically modified alcohol dehydrogenase (ADH 270). Predictions of cosolvent influences are based on accounting for a cosolvent-induced change of molecular interactions among the reacting agents as well as between the reacting agents and the solvent. Such interactions were characterized by activity coefficients of the reacting agents that were predicted by means of electrolyte perturbed-chain statistical associating fluid theory. This allowed simultaneously predicting the cosolvent effects on yield and Michaelis constants for two-substrate reactions for the first time.

Thermodynamic Properties of Systems Comprising Esters: Experimental Data and Modeling with PC-SAFT and SAFT-γ Mie

In this work, new experimental vapor-pressure data of 14 esters were obtained using the transpiration method. Besides dimethyl fumarate, dimethyl maleate, diethyl maleate, benzyl ethanoate, benzyl propanoate, and benzyl butanoate, eight representatives of the homologous series of ethyl alkanoates were investigated. The pure-component vapor pressures and liquid densities were modeled by means of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) and SAFT-γ Mie. Satisfying modeling results could be achieved with both equations of state. Furthermore, the molar excess enthalpies of 12 binary mixtures benzyl ethanoate + n-alkane were modeled. Only one binary interaction parameter was fitted for PC-SAFT to quantitatively predict the molar excess enthalpies of all binary mixtures under study, while SAFT-γ Mie predicts these properties in qualitative agreement with the experimental data. Finally, the liquid–liquid equilibria of three binary mixtures ester (benzyl ethanoate, dimethyl maleate, and diethyl maleate) + water were investigated. These systems show a very low and almost temperature-independent solubility of the ester in the aqueous phase, whereas the moderate solubility of water in the organic phase is temperature-dependent. Promisingly, both PC-SAFT and SAFT-γ Mie predicted broad and unsymmetrical miscibility gaps for these mixtures, which is in qualitative agreement with the experimental data.

Modeling Thermodynamic Derivative Properties and Gas Solubility of Ionic Liquids with ePC-SAFT

In this work, the ion-specific electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) was extended to predict the second-order thermodynamic derivative properties and gas solub...

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Incorporating a concentration-dependent dielectric constant into ePC-SAFT. An application to binary mixtures containing ionic liquids

Primitive thermodynamic models for electrolyte solutions require the dielectric constant ε. This property strongly depends on the concentration of the electrolytes in the mixture. Neglecting this dependency might be reasonable for modeling solutions at low electrolyte concentrations. However, in solutions containing ionic liquids (ILs) and especially for the calculation of liquid-liquid equilibria (LLE) of systems with ILs, liquid phases often contain high IL concentrations. At such conditions, neglecting the influence of concentration on ε is an oversimplification. In this work, an approach to account for the concentration-dependent dielectric constant within the Debye-Hückel theory was implemented into electrolyte Perturbed-Chain Statistical Associating Fluid Theory (original ePC-SAFT). This new approach was then applied to model LLE of binary mixtures containing water and commonly used hydrophobic ILs. These common ILs are comprised of the IL-cations [Cnmim]+, [Cnpy]+, [Cnmpy]+, [Cnmpyr]+, [C4m4py]+ and the IL-anions [BF4]-, [NTf2]-, [PF6]-, [TFO]-. The LLE of binary mixtures water + IL were modeled at ambient pressure and different temperatures with the new ePC-SAFT and with the original ePC-SAFT [Ji et al. DOI: 10.1016/j.fluid.2012.05.029] without the concentration-dependent ε. Overall, the new approach within ePC-SAFT shows superior modeling as well as correlation capability compared to original ePC-SAFT, which was concluded by comparing both models with LLE data from literature.

Experimental Data and Thermodynamics Modeling (PC-SAFT EoS) of the {CO2 + Acetone + Pluronic F-127} System at High Pressures

In this study, we reported data of phase equilibria of the ternary {CO2 (1) + acetone (2) + pluronic F-127 (3)} system using the static synthetic method with a visual cell at temperatures ranging from 303 to 323 K, pressures near to 10 MPa, two concentrations of pluronic F-127 in acetone (0.01 g·cm–3 and 0.02 g·cm–3), and molar fractions varying between 0.3 to 0.9. The thermodynamic modeling using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EoS) was capable of describing the behavior of the experimental data (liquid–vapor transitions bubble points) satisfactorily.

Thermodynamic Modeling of Triglycerides using PC-SAFT

Vapor pressures for the saturated triglycerides (TGs) tricaprylin, tricaprin, and liquid densities of tricaprylin were experimentally determined. TG pure-component parameters for the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) were fitted to that data and validated with densities of the binary mixtures octanol/tricaprin and octanol/trilaurin at different temperatures and TG mass fractions. Furthermore, pure-component parameters of the unsaturated TGs triolein and trilinolein were estimated by a group-contribution method. Correctly predicted solid–liquid equilibria of mixtures containing the before-mentioned TGs revealed that intermolecular interactions among TGs are quantitatively described by PC-SAFT.

General method for prediction of thermal conductivity for well-characterized hydrocarbon mixtures and fuels up to extreme conditions using entropy scaling

A general and efficient technique is developed to predict the thermal conductivity of well-characterized hydrocarbon mixtures, rocket propellant (RP) fuels, and jet fuels up to high temperatures and high pressures (HTHP). The technique is based upon entropy scaling using the group contribution method coupled with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. The mixture number averaged molecular weight and hydrogen to carbon ratio are used to define a single pseudo-component to represent the compounds in a well-characterized hydrocarbon mixture or fuel. With these two input parameters, thermal conductivity predictions are less accurate when the mixture contains significant amounts of iso-alkanes, but the predictions improve when a single thermal conductivity data point at a reference condition is used to fit one model parameter. For eleven binary mixtures and three ternary mixtures at conditions from 288 to 360 K and up to 4,500 bar, thermal conductivities are predicted with mean absolute percent deviations (MAPDs) of 16.0 and 3.0% using the two-parameter and three-parameter models, respectively. Thermal conductivities are predicted for three RP fuels and three jet fuels at conditions from 293 to 598 K and up to 700 bar with MAPDs of 14.3 and 2.0% using the two-parameter and three-parameter models, respectively.

Prediction of the Water Activity in Multicomponent Solutions by a Simple and Accurate Equation and Derivation of Zdanovskii’s Rule

A simple equation is derived for the prediction of the water activity as a function of the molal concentrations of a multicomponent mixture, a1(m2, m3,…, mn+1). It consists basically of a series expansion whose coefficients are determined from the limiting behavior imposed by the thermodynamics of solutions. The validity of this equation was verified on 96 binary, ternary and quaternary systems involving electrolytic and molecular solutes as well as solutions containing both electrolytes and nonelectrolytes. The error was always lower than 1% for solutions with a1 ≥ 0.90. For electrolytic solutions its applicability range is moderately concentrated and dilute solutions (maximum molality mmax ≤ 1 mol·kg−1), while for the case of molecular solutes it extends to significantly more concentrated mixtures (3 ≤ mmax/mol·kg−1 ≤ 6). Moreover, it also allowed the derivation of a generalized form of Zdanovskii’s rule for multicomponent systems involving both electrolytic and molecular solutes as well as the verification of the Frolov–Rard hypothesis. Finally, the equation was used for the estimation of the vapor pressure of ternary solutions of non-volatile solutes, showing better descriptive capabilities than those calculated by the application of the perturbed-chain statistical associated fluid theory (PC-SAFT).

Thermodynamic properties of hydrophobic deep eutectic solvents and solubility of water and HMF in them: Measurements and PC-SAFT modeling

Recently, hydrophobic deep eutectic solvents (DESs) were proposed as interesting solvents for biorefinery processes, such as the production of 5-hydroxymethylfurfural (HMF) from glucose in an aqueous environment. Physicochemical property data of hydrophobic DES + water/HMF systems are of utmost importance for process design. In this work, density and vapor pressure of eight different hydrophobic DESs, as well as water solubility and HMF solubility in these DESs were experimentally determined. The solubility was modeled using the pseudo-pure component approach within the framework of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). New pure-component parameters for the eight hydrophobic DESs were obtained by fitting to measured density and vapor-pressure data, instead of to density data only. Based on these new pure-component parameters for the DESs, the solubilities of water and of HMF in the hydrophobic DESs were modeled in good agreement with the experimental data at 298 K and atmospheric pressure.