Statistical Associating Fluid Theory Research Articles

Evaluation of the perturbed hard-sphere-chain equation of state for calculations of methane hydrate formation condition in the presence of ionic liquids

This work aims to evaluate the performance of the Perturbed Hard-Sphere-Chain (PHSC) equation of state (EoS) for the calculation of methane hydrate formation in the presence of ionic liquids (ILs). The van der Waals and Platteeuw model is utilized to calculate the hydrate dissociation pressure. The performance of the PHSC model is compared to cubic EoSs and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) model. Two activity coefficient models are used to estimate the water activity in the presence of ILs. The results show that PHSC EoS with an activity coefficient model provides lower average error values (lower than 2%) and changing the activity coefficient models does not have a great effect on reducing the error. Also, the results of cubic-based EoSs are quite remarkable considering their simplicity. The PHSC model can be utilized as a robust and efficient thermodynamic model for hydrate dissociation pressure calculation in the presence of IL.

Modeling the solubility of oxaprozin and irbesartan in biorelevant complex solutions based on a combination of pH-dependent and micellar solubilization models

Biological solubility is one of the important basic parameters in the development process of poorly soluble drugs, but the current measurement methods are mainly based on a large number of experiments, which are time-consuming and cost-intensive. There is still a lack of effective theoretical models to accurately describe and predict the biological solubility of drugs to reduce costs. Therefore, in this study, osaprazole and irbesartan were selected as model drugs, and their solubility in solutions containing surfactants and biorelevant media was measured experimentally. By calculating the parameters of each component using the perturbed-chain statistical associating fluid theory (PC-SAFT) model, combined with pH-dependent and micellar solubilization models, the thermodynamic phase behavior of the two drugs was successfully modeled, and the predicted results were in good agreement with the experimental values. These results demonstrate that the model combination used provides important basic parameters and theoretical guidance for the development and screening of poorly soluble drugs and related formulations.

ML-SAFT: A machine learning framework for PCP-SAFT parameter prediction

The Perturbed Chain Polar Statistical Associating Fluid Theory (PCP-SAFT) equation of state (EoS) is widely used to predict fluid-phase thermodynamics, but parameterization of PCP-SAFT for individual molecules is often challenging. We propose a machine learning framework called ML-SAFT that can turn experimental data in predictive models of PCP-SAFT parameters. We demonstrate methods for automated large scale regression of PCP-SAFT parameters and thus create a large PCP-SAFT parameter dataset in the literature. We then evaluate several machine learning architectures for predicting PCP-SAFT parameters. We find that our best model provides accurate predictions for a wider range of molecules than existing predictive methods with 40 % average absolute deviation (% AAD) in vapor pressure predictions and 8 % AAD in density predictions.

Interactions at the interfaces of the H2-brine-cement systems at elevated pressures for H2 storage

There is a global demand on assessment of potential subsurface gas storage sites in view of safely injecting hydrogen or carbon dioxide. One relevant aspect that has already been subject to thorough investigation is the mutual interaction of all participating compounds in terms of the wetting behaviour that on its turn is directly related to the predominating capture mechanisms. Given the diversity of the geophysical and geochemical circumstances, transferability of results from work conducted on one geological site to another location is limited. For instance, there is a large number of publications on wettability of many different rock types in hydrogen atmosphere that are partly controversal and strictly applicable only to the respective reported system. Hence, there is a gap in finding general model approaches that serve for a holistic understanding of predominating mechanisms and building the fundamentals for predicting the behaviour of systems that have not been studied so far. The presented work addresses this gap by quantifying mutual interactions of the participating phases in a solid-liquid-gas systems and determining the respective interfacial tensions, γSV (solid-vapor), γLV, (liquid-vapor) and γSL (solid-liquid).Neumann and Good demonstrated how to determine the solid-fluid interfacial tension based on the contact angle and the liquid-gas interfacial tension by calculating a so-called molecular interaction parameter. Up to date, this method has been applied, among others, for systems containing CO2 and solids such a teflon, glass, and steel. The methodology could be confirmed by testing systems comprising steel - H2O - CH4 /H2 and comparing the results to the aforementioned literature data.As one of the critical parts in H2 underground storage, the completion system containing a common well cement, H2 and brine was subject to this work. The interfacial tension between H2 and brine as well as the contact angle between the fluid phases and the cement were investigated experimentally up to 20 MPa, temperatures from 313.15 to 353.15 K and NaCl – concentrations of up to 10% wt. As a theoretical approach, the interfacial tension of the system H2O+H2 was investigated using the density gradient theory (DGT) in combination with the perturbed chain statistical associating fluid theory equation of state (PC-SAFT). Finally, the H2-cement interfacial tension is determined through the calculation of a so-called molecular interaction parameter. The interfacial tension data of H2O+H2 experimentally and theoretically determined in this work agree among each other as well as with previous literature data. Likewise, agreement was found between the brine+H2 interfacial tension and previous studies. The contact angle appears to be influenced mostly by pressure, producing a less H2O/brine-wet system as pressure increases. The H2-cement interfacial tension decreases from approximately 150 mN/m down to 100 mN/m, as the pressure increases from 0.1 to 20 MPa. The presented data suggest H2 to be slightly adsorbed on the one hand but the capillary entry pressure to decrease on the other, causing concerns regarding the integrity of the completion system.

Theoretical and practical investigation of ion-ion association in electrolyte solutions.

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

Experimental measurement and modeling of the solubility of fluorinated compounds derived from dichlone in supercritical carbon dioxide

Dichlone, also known as 2,3-dichloronaphthalene-1,4-dione, is a solid organic substance employed in the field of agriculture for its fungicidal properties and as a retardant for vegetable decomposition. The bioactive properties of dichlone can be enhanced by modifying its structure, specifically through the synthesis of new derivatives achieved by replacing the functional groups within its molecular structure. Two new solid dichlone derivatives were synthesized in this work, namely 2-chloro-3-((4-fluorobenzyl)amino)naphthalene-1,4-dione (dCl-2B-F) and 2-chloro-3-((4-fluorophenethyl)amino)naphthalene-1,4-dione (dCl-3 P-F) and measured their solubility in supercritical carbon dioxide at (313, 323, and 333) K and pressures between (9. to 32) MPa. The results indicated that solubility ranged between 30.5 and 47.9 µmol of solute/mol of CO2 for dCl-2B-F, and from 2.2 to 243.5 µmol of solute/mol of CO2 for dCl-3 P-F. The solubility data of dichlone and its synthesized derivatives (dCl-2B-F, dCl-3 P-F, 2-chloro-3-((4-chlorobenzyl)amino)naphthalene-1,4-dione (dCl-2B-Cl), 2-chloro-3-((4-chlorophenethyl)amino)naphthalene-1,4-dione (dCl-3 P-Cl), 2-(benzylamino)-3-chloronaphthalene-1,4-dione (dCl-2B) and 2-chloro-3-(phenethylamino)naphthalene-1,4-dione (dCl-3 P)) was compared using the density-based correlation of Chrastil and the Statistical Associating Fluid Theory of Variable Range Mie-potential (SAFT-VR Mie) equation of state (EoS), to better comprehend the effects of the structural differences on the solubility. As a result, for the Chrastil model, a root mean square deviation (rmsd) of 3% was obtained for dCl-2B-F and 16% for dCl-3 P-F, whereas for the SAFT-VR Mie equation, it averaged 24% for dCl-2B-F and 28% for dCl-3 P-F. It was found that the solubility of the homologous compounds, differing only in one methylene group, increased with solute size (-2B derivatives were less soluble in CO2 than the −3 P ones), contrary to the expected trend, which could be attributed to the increased probability of ring-to-ring interactions as the chain length connecting the rings decreases. This demonstrates that geometric factors, along with the pressure and temperature, affect the behavior of the solubility and these should be accurately represented in the predictive models.

Hydrophobic interactions described using hetero-segmented PC-SAFT: 1. Alcohol/water mixtures

The hydrophobic effect plays a central role in aqueous systems containing molecules with hydrophobic moieties. Despite the relevance of this effect for chemical processes or pharmaceutical applications, modeling remains challenging even using molecular-based models such as different versions of the Statistical Associating Fluid Theory. This work shows the feasibility of hetero-segmented PC-SAFT for this purpose. This model was used as a group contribution method to build molecules from different functional groups, namely from CH2, CH3, and CH2OH groups. Saturated-liquid densities and vapor pressures of n-alkanes and n-alcohols as well as binary mixtures of these molecules were accurately described by this approach. The description of aqueous mixtures containing n-alkanes and n-alcohols was improved compared to state-of-the-art modeling by explicitly accounting for intermolecular interactions resulting in the hydrophobic effect. The so-obtained framework describes the two liquid−liquid equilibrium phases in mixtures of n-alkanes or n-alcohols with water equally well using a single set of transferable parameters. The model was also validated for vapor–liquid equilibria, solid–liquid equilibria, infinite-dilution properties, as well as octanol/water partition coefficients and showed quantitative agreement with experimental data.

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State.

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Density and viscosity measurement of R513A and a modified residual entropy scaling model for predicting the viscosity of HFC/HFO refrigerants

Liquid density and viscosity of alternative refrigerants R513A were measured with a vibrating-wire viscosimeter in the temperature of 253 K to 363 K when pressure changes from 1 MPa to 12 MPa. The combined expended uncertainties with a confidence level of 0.95 (k=2) of density and viscosity are 0.2% and 2%, respectively. In addition, a viscosity model of HFCs (fluorocarbons)/, HFOs (hydro-fluoroolefins) and their mixtures was provided by coupling the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state and a modified residual entropy scaling (RES) method. Obvious quasi-linear relation between the proposed entropy variable and the modified residual viscosity has been confirmed. The overall average absolute percentage deviations between the calculated results with the proposed RES model and the literature experimental data of pure and mixture refrigerants are 2.63% and 2.05, respectively.

Viscosities of inhomogeneous systems from generalized entropy scaling

This study extends entropy scaling to inhomogeneous fluids by using the classical density functional theory together with a new viscosity reference that takes into account the influence of solid–fluid interactions on the fluid viscosity. The density functional theory uses a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory; the local residual entropy per particle is determined from the temperature derivative of the Helmholtz energy functional in combination with an appropriate weighted density profile. The weighted density calculation requires a single transferable parameter, which is adjusted to a reference molecular dynamics simulation. In particular, local viscosity values for fluids under nanoconfinement near solid–fluid interfaces are predicted using the same entropy scaling parameters as for homogeneous fluids. We validate the model by comparing viscosity and velocity profiles with results from non-equilibrium molecular dynamics simulations of a Couette flow in a slit pore. Good agreement is found between the entropy scaling model and the non-equilibrium molecular dynamics results for both the viscosity and velocity profiles of the Lennard–Jones truncated and shifted fluid. The proposed model extrapolates well to systems with different temperatures, fluid densities, and shear forces as well as to systems with different wetting behaviors. These results demonstrate that entropy scaling can be generalized to inhomogeneous fluids using an appropriate combination of residual entropy profile and viscosity reference.

Predicting the density and viscosity of deep eutectic solvents at atmospheric and elevated pressures

Deep eutectic solvents (DESs) are promising and sustainable substitutes for organic solvents in various applications. The knowledge of their density and viscosity at different temperatures and pressures is crucial for the corresponding process design. However, most literature primarily focuses on predicting these properties at atmospheric pressure. In this study, we employed the perturbed chain polar statistical associating fluid theory (PCP-SAFT) model and entropy scaling method to predict DESs’ density and viscosity at atmospheric and elevated pressures. 2831 density data points of 38 DESs and 1018 viscosity data points of 31 DESs at different temperatures and pressures were used to evaluate the accuracy of the applied methods. The pure component PCP-SAFT parameters of choline chloride (ChCl) were regressed using density data of ChCl-based DES at various temperatures and pressures. It was found that the PCP-SAFT model can provide satisfactory density predictions for DESs at atmospheric pressure, even without using the system-specific binary interaction parameter (kij=0). However, accurate viscosity prediction at atmospheric pressure for DESs necessitated the inclusion of the binary interaction parameter (kij=aijT+bij) in the PCP-SAFT model. The system-specific coefficients aij andbij, derived from experimental data at atmospheric pressure, were used to predict the density or viscosity of DES at elevated pressures. Accurate predictions for density were observed across the entire pressure range, whereas effective viscosity predictions were confined to a specific pressure range.

Viscosity measurement and correlation for dense fluid mixture of carbon dioxide and ethanol at 313–343 K and 15–30 MPa

The viscosity ηm of dense fluid mixtures of carbon dioxide and ethanol was determined from the pressure drop between the inlet and outlet of a packed bed using the Ergun equation at temperatures from 313.2 K to 343.2 K and pressures from 15 MPa to 30 MPa over the entire range of ethanol composition. The ηm values for the fluid mixtures decreased with increasing temperature and increased with increasing pressure under isocratic conditions. In addition, the values measured ηm with Ergun eq. were correlated with the equation combining the Eyring theory and the perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) and with that based on the rough hard-sphere (RHS) model proposed by Dymond and Assael. The accuracies of the Eyring + PC-SAFT EoS and the RHS model were 8.7% and 12%, respectively, in terms of average relative deviation for 80 conditions over the entire range of ethanol composition.

Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior.

The use of amorphous solid dispersions (ASDs) in commercial drug products has increased in recent years due to the large number of poorly soluble drugs in the pharmaceutical pipeline. However, the release behavior of ASDs is complex and remains not well understood. Often, the drug release from ASDs is rapid and complete at lower drug loadings (DLs) but becomes slow and incomplete at higher DLs. The DL where release becomes hindered is termed the limit of congruency (LoC). Currently, there are no approaches to predict the LoC. However, recent findings show that one potential cause leading to the LoC is a change in phase morphology after water-induced phase separation at the ASD/solution interface. In this study, the phase behavior of ASDs in contact with aqueous solutions was described thermodynamically by constructing experimental and computational ternary phase diagrams, and these were used to predict morphology changes and ultimately the LoC. Experimental ternary phase diagrams were obtained by equilibrating ASD/water mixtures over time. Computational ternary phase diagrams were obtained by Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). The morphology of the hydrophobic phase was studied with fluorescence confocal microscopy. It was demonstrated that critical point (plait point) composition approximately corresponded to the ASD DL, where the hydrophobic phase, formed during phase separation, became interconnected and hindered ASD release. This work provides mechanistic insights into the ASD release behavior and highlights the potential of in silico ASD design using phase diagrams.

Thermodynamic analysis of a dual-pressure evaporation high-temperature heat pump with low GWP zeotropic mixtures for steam generation

High-temperature heat pumps (HTHPs) have gained attention due to their economic and environmental benefits in utilizing industrial waste heat for steam generation. This study focuses on improving the HTHPs’ performance by employing two-stage separation and dual-pressure evaporation technology in the auto-cascade heat pump cycle. Additionally, binary zeotropic refrigerant mixtures with low-GWP are selected using the polar perturbed-chain statistical associated fluid theory (PC-SAFT) equation of state. The findings indicate that the R1234ze(E)&R1233zd(E) refrigerant mixture outperforms other potential alternatives, exhibiting a thermodynamic effectiveness 0.85%–1.86% higher than the benchmark mixture, R134a&R245fa. The improved cycle demonstrates significant enhancements, achieving a 45.17% increase in heat source utilization efficiency and a 24.48% improvement in COP compared to the basic auto-cascade cycle. Effective temperature matching between refrigerant mixtures and heat sources/sinks is guaranteed in the improved cycle. Moreover, a parameter analysis reveals that increasing the subcooling degree of the cascaded heat exchanger and the separation dryness fraction at separator 2 enables improvements in both COP and heat source utilization efficiency. These findings provide valuable insights into the design of steam generation heat pumps and the selection of refrigerant mixtures.

Prediction of water anomalous properties by introducing the two-state theory in SAFT.

Water is one of the most abundant substances on earth, but it is still not entirely understood. It shows unusual behavior, and its properties present characteristic extrema unlike any other fluid. This unusual behavior has been linked to the two-state theory of water, which proposes that water forms different clusters, one with a high density and one with a low density, which may even form two distinct phases at low temperatures. Models incorporating the two-state theory manage to capture the unusual extrema of water, unlike traditional equations of state, which fail. In this work, we have derived the framework to incorporate the two-state theory of water into the Statistical-Associating-Fluid-Theory (SAFT). More specifically, we have assumed that water is an ideal solution of high density water molecules and low density water molecules that are in chemical equilibrium. Using this assumption, we have generalized the association term SAFT to allow for the simultaneous existence of the two water types, which have the same physical parameters but different association properties. We have incorporated the newly derived association term in the context of the Perturbed Chain-SAFT (PC-SAFT). The new model is referred to as PC-SAFT-Two-State (PC-SAFT-TS). Using PC-SAFT-TS, we have succeeded in predicting the characteristic extrema of water, such as its density and speed of sound maximum, etc., without loss of accuracy compared to the original PC-SAFT. This new framework is readily extended to mixtures, and PC-SAFT-TS manages to capture the solubility minimum of hydrocarbons in water in a straightforward manner.

Thermophysical properties of ethyl levulinate and n-alkanol systems

Some thermophysical properties such as densities, speeds of sound, refractive indices, and heat flows of the binary systems ethyl levulinate and n-alkanols (methanol, ethanol, 1-propanol, and 1-butanol) are reported in the temperature range T = (283.15–313.15) K and at p = 100 kPa. From these experimental data, the excess properties were calculated and correlated with the composition using a modified Redlich–Kister equation. The excess molar volumes were negative for short-chain alcohols and positive for 1-propanol and 1-butanol. The excess refractive indices exhibited the opposite behaviour. The excess isentropic compressibilities were negative and the excess molar enthalpies, were positive. The perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) was successfully applied to correlate the densities of the mixtures, and good qualitative results in the computation of the excess molar enthalpy were obtained. Furthermore, Schaaff’s collision factor theory (SCFT) and the Laplace mixing rule were coupled with PC-SAFT to predict the speed of sound and the refractive index, respectively.

Solubility of digitoxin in supercritical CO2: Experimental study and modeling

In this communication, the solubility of digitoxin drug in supercritical CO2 was studied at different operating conditions (311 < T (K) < 343, 120 < P (bar) < 300). The results revealed digitoxin drug solubility (in mole fraction) was between 0.095 × 10−5 to 1.12 × 10−5. In the case of thermodynamic solubility modeling, cubic and non-cubic equation of states i.e. SAFT (statistical associating fluid theory), SRK (Soave-Redlich-Kwong) and sPC-SAFT (simplified perturbed chain SAFT) EoSs and six density-based correlations (Chrastil, Kumar-Johnston (KJ), Mendez-Santiago-Teja (MST), Garlapati and Madras (GM), Bartle et al. and Sung-Shim models) were considered. All used equations indicated reasonable behavior with appropriate accuracy for the solubility of the digitoxin drug. Meanwhile, sPC-SAFT EoS and Kumar-Johnston correlation with AARD% set to 8.96 % and 6.25 %, respectively exhibited greater accuracy in fitting the solubility data. Moreover, total, solvation and vaporization enthalpies of the digitoxin/supercritical carbon dioxide binary mixture were calculated based on KJ, Chrastil and Bartle et al. models.

CO2 solubility and absorption rate analysis of a mixed poly(oxymethylene) dimethyl ethers (PODE3–5) solution

Efficient and economical carbon capture is critical to counteract the diverse problems of global warming. In this work, the solubility of carbon dioxide (CO2) in different poly(oxymethylene) dimethyl ethers (PODE) solutions was experimentally investigated at temperatures from 278.15 to 308.15 K and pressures up to 1.2 MPa. The Henry's law constants of CO2 in the PODE system were determined and compared with other types of physical absorbents, which revealed PODE3–5 has great CO2 absorption ability in terms of molar and mass fraction. Meanwhile, the initial absorption rate of the physical absorption process of PODE3–5 was calculated and compared with commercially available absorbents using a gas absorption rate relationship. It was shown that the absorption rate of PODE3–5 in the CO2 absorption process is faster than that of other commercial absorbents. The CO2 solubility data of PODE3–5 were also correlated using the Jou-Mather model and the perturbed-chain statistical association fluid theory (PC-SAFT) equation of state model, and the recycling performance of the PODE3–5 absorbent was tested.

Application of PC‐SAFT EoS and SCFT for the modeling of thermophysical properties comprising deep eutectic solvent and alcohols

AbstractZinc (II) chloride based deep eutectic solvent (DES) were formed by mixing zinc (II) chloride with phosphoric acid. Fourier‐transform infrared spectroscopy was used to identify any possible shifts when the two compounds were assorted, and differential scanning calorimetry (SDT Q600 V20.9 Build 2D) was utilized to evaluate the formation of deep eutectic solvent. Densities, , and speed of sound, u, of [ZnCl2][phosphoric acid] 1:2.5 with methanol, ethanol, or propanol have been measured at T = (293.15, 303.15, 308.15, and 313.15) K and at atmospheric pressure. Excess molar volumes (), isentropic compressibilities (), deviation in isentropic compressibility (), and intermolecular free length () were calculated from the densities, and speed of sound, respectively. To fit the excess molar volumes and deviation in isentropic compressibilities, the Redlich–Kister smoothing polynomial was used. Also, we have used perturbed chain statistical associating fluid theory equation of state (PC‐SAFT EoS) for modeling the densities of the binary mixtures, and Schaaff's collision factor theory (SCFT) and Nomoto's relation (NR) were used for modeling the speed of sounds for the binary mixtures.

Assessment and modeling of the isobaric vapor-liquid-liquid equilibrium for water + cyclopentyl methyl ether + alcohol (ethanol or propan-1-ol) ternary mixtures

The three-phase equilibria of water + cyclopentyl methyl ether (CPME) + ethanol or propan-1-ol ternary mixtures are explored from experimental determinations and theoretical modeling at a constant pressure (101.3 kPa), and over 350 K to 356 K. Experimental measurements are performed in a modified Guillespie phase equilibria dynamic cell, which includes an ultrasonic homogenizer. The reliability of the measured three-phase equilibria is validated by employing the Wisniak's L/W thermodynamic consistency test. The measured vapor-liquid-liquid equilibria (VLLE) data at 101.3 kPa are accurately predicted from the phase stability restriction coupled with the multiphase equilibrium criteria. The application of this combined approach is showcased as a thermodynamical tool to explore all possible phase equilibria regions (i.e., one-, two-, and three-phase), providing a robust representation of the multiphase equilibria. Both phase stability and the corresponding multiphase equilibria are calculated using the SAFT-VR-Mie EoS model (statistical associating fluid theory of variable range employing a Mie potential equation of state), where the association and polar nature of pure components and their binary interactions are explicitly considered.No ternary azeotropy is detected within the experimental range of stable VLLE for the water + CPME + ethanol ternary mixture, although the theoretical extrapolation of the experimental conditions using the SAFT-VR-Mie EoS suggests its existence. For the case of the water + CPME + propan-1-ol ternary mixtures, a stable VLLE with a heterogeneous ternary azeotrope is detected from the interpolation of the experimental determinations.The predicted heterogeneous ternary azeotrope supports use of the CPME as a potential entrainer candidate for dehydration of bio-alcohols (e.g., ethanol or propan-1-ol) as well as implying that the distillate products, bio-alcohols (ethanol or propan-1-ol) + CPME mixtures can be directly used as a renewable fuel without the need of additional separation stages.