PC-SAFT Equation Research Articles

Measuring and modeling the solubility of sulfasalazine in supercritical carbon dioxide to select methods for producing nanoparticles

In the present study, the solubility of sulfasalazine in carbon dioxide was investigated at temperatures ranging from 313 K to 343 K and pressures ranging from 12 to 30 MPa. The experimentally determined molar solubilities of sulfasalazine in ScCO2 were found to be in the range of 4.08 × 10− 5 to 8.61 × 10− 5 at 313 K, 3.54 × 10− 5 to 11.41 × 10− 5 at 323 K, 3.04 × 10− 5 to 13.64 × 10− 5 at 333 K, and 2.66 × 10− 5 to 16.35 × 10− 5 at 343 K. The solubility values were correlated via a number of different types of equations, such as semi-empirical correlations, the Peng-Robinson, the PC-SAFT equation, and the regular solution. Furthermore, the findings demonstrate that semi-empirical, equation of state models, and the regular solution model possess the capability of precisely determining the solubility. Moreover, the solubility magnitude suggests that the gas anti-solvent method may be a viable approach for nanoparticle production.

Modeling the Vapor–Liquid Equilibria of Sustainable Aviation Fuel Components with Nitrogen Using the PC-SAFT Equation of State

Modeling the Vapor–Liquid Equilibria of Sustainable Aviation Fuel Components with Nitrogen Using the PC-SAFT Equation of State

Development of a new parameterization strategy and GC parameters of halogenated hydrocarbons for PC-SAFT equation of state

Statistical Associating Fluid Theory (SAFT) equations of state (EoSs) have been extensively used in the prediction of fluid phase equilibria and thermodynamic properties. For each fluid, determining the component-dependent parameters typically involves fitting experimental data with a local optimization algorithm. SAFT-type EoSs are highly nonlinear due to the high-order functions used to describe different contribution terms. This nonlinearity leads to the presence of multiple local optima, making parameter optimization very sensitive to initial values. Hence, it is crucial to determine the starting point for the optimization process, yet little attention has been paid to how initial parameter sets are selected. In this paper, a method based on group contributions to establish an appropriate initial value for the optimization process is proposed and applied to Perturbed-Chain SAFT (PC-SAFT). The optimized PC-SAFT parameters for a total of 74 substances from 11 different chemical families have been evaluated. The fitting results for saturated pressure, liquid density, and vapor density showed overall average absolute relative deviations (AARD) of 0.050 %, 0.042 %, and 0.151 %, respectively. This paper also provided group contribution parameters for halogenated hydrocarbons to estimate PC-SAFT parameters. Additionally, an assessment of global and local optimization algorithms was conducted. The results demonstrate that the global algorithm not only requires longer computation time but also exhibits significantly lower accuracy compared to the local algorithm. The overall AARD for the global algorithm is 9.493 %, whereas for the local algorithm, it stands at 0.068 %.

Analysis of Thermodynamic Models for Liquid-Vapor Equilibrium: Evaluating Accuracy and Applicability

This article investigates the liquid-vapor equilibrium of four binary refrigerant systems: R134a + R290, R152a + R1234ze, R152a + R1243zf, and R1243zf + R134a. The study employs three thermodynamic models for accurate predictions: the Peng-Robinson equation with the classical mixture rule of van der Waals (vdW) and the Wilson model, the PC-SAFT equation, and the PR-MC-WS-NRTL model. Activity coefficients are determined using the Peng-Robinson equation with vdW and the Wilson model. The PC-SAFT equation and the PR-MC-WS-NRTL model are also applied to model the data. The calculated results show good agreement with reference data. Favorable agreements exist between the calculated results and the reference data, with relative errors remaining below (0.15 and 0.42) % for the molar fraction and the pressure, respectively. This research provides valuable insights into the accuracy and applicability of different thermodynamic models in predicting liquid-vapor equilibrium within refrigerant systems.

Geraniol and hydrophobic geraniol:thymol eutectic mixtures: Structure and thermophysical characterization

The properties of essential oils as food preservatives are well-established. These components have also been used as neoteric solvents to prepare eutectic mixtures. Their high capacity to dissolve poorly water-soluble substances makes them particularly interesting in the biotechnology industry. To implement them, it is essential to determine the structural and chemical-physical properties, as well as develop models to predict the behaviour under any operational condition. Herein, pure geraniol and geraniol/thymol mixtures are studied. Nuclear magnetic resonance experiments and molecular dynamics are used to evaluate the fluid structure. In addition, seven thermophysical properties are measured and correlated. The experimental densities, surface tensions, and viscosities were lower than 952 kg m–3, 33 mN m–1, and 36 mPa s, respectively. These values were adequate for the industrial application of these mixtures. PC-SAFT equation of state well predicted the density with an average deviation of 0.13 %, and the isobaric molar heat capacity with a deviation of 6.9 %. Greater compaction was observed at higher thymol molar ratios and dispersive interactions were predominant. Depending on the composition, geraniol was both an acceptor and donor of hydrogen bonds; conversely, thymol acted as a donor. The article provides the necessary knowledge to be able to use these mixtures and design new ones, as ecological solvents in different applications including those in the agri-food sector.

Unveiling the high-pressure behavior of thymol+carvone NADES: A combined experimental-computational approach

this study considers the high-pressure behavior of thymol + carvone Natural Deep Eutectic Solvent using a combined experimental and computational approach. Experimentally, PVT (pressure – volume/density - temperature) measurements were conducted to characterize the fluid volumetric behavior as well as compressibility and internal pressure, which are directly related with hydrogen bonding and nanoscopic structuring. Likewise, these measurements provide crucial insights into the thermodynamic properties of the considered fluid under high pressure, which is pivotal for scaling up and process design for high pressure operations. Computationally, the PC-SAFT equation of state was employed to predict phase equilibria and PVT behavior, Machine Learning for density predictions, while Density Functional Theory and Classical Molecular Dynamics simulations were considered for the structural and dynamic characterization. These simulations provides insights into the electronic structure, intermolecular interactions (hydrogen bonding), liquid structuring and they unveil the pressure's impact on microscopic interactions, structural organization, and transport properties. This comprehensive investigation aims to shed light on the behavior under high pressure, facilitating their optimization for applications in chemical processing, energy storage, and materials science.

Kinetic modeling of palmitic acid hydrodeoxygenation incorporating phase-equilibria predictions from the GC-PC-SAFT equation of state

In this work, we investigated the phase equilibria and the kinetics of palmitic acid hydrodeoxygenation over Pt/C to produce liquid hydrocarbons as drop-in biofuels. To describe the reaction mixture in detail, the binary interaction parameters of water/hydrogen, water/palmitic acid, water/n-hexadecane, and water/hexadecan-1-ol were estimated for a group contribution model based on the PC-SAFT equation of state using experimental solubility data taken from literature. Kinetic modeling using a power law model based on concentrations, a power law model based on fugacities, and a coupled VLE/power-law model were conducted to evaluate the effects of considering the non-ideality and the phase equilibria of the system. Under the operational conditions studied, the power law model based on concentrations was deemed more suitable to describe the process since it provided a faster implementation and similar outcomes compared to the fugacity-based and the VLE coupled models.

Liquid-liquid equilibrium of binary ethanol–polyisobutene and ternary ethanol–water–polyisobutene systems under low- and high-pressure conditions: An assessment using the PC-SAFT equation of state

Sugarcane bioethanol in either anhydrous or hydrous forms stands out as an economically viable bioproduct that can be used as a fuel or feedstock in various innovative applications, reducing human-generated greenhouse gas emissions. Low-molar-mass polyisobutene (PiB) is used as a lubricant in sugarcane-processing plants and is a possible contaminant of sugarcane bioethanol. Understanding the liquid–liquid equilibrium (LLE) of ethanol–PiB binary systems and ethanol–water–PiB ternary systems is essential to avoid undesired phase separation at high-pressure engine conditions and other potential innovative applications. However, the experimental investigation of these systems is significantly hampered by very low polymer solubilities in aqueous ethanol. The LLE of ethanol-PiB and ethanol–water–PiB mixtures was qualitatively investigated using the PC-SAFT equation of state through the development and implementation of extrapolation strategies allowing to estimate ethanol–PiB and water–PiB binary parameters using experimental data obtained for other systems containing lighter alkanes. Phase diagrams were calculated considering temperatures ranging from 298.15 K to 350 K and pressures ranging from 1 bar to 200 bar. It was shown that lower pressures, higher temperatures, lower PiB molar masses, and lower water contents increase the polymer solubility in the solvents. Thus, the risk of liquid–liquid separation can be mitigated by correctly managing such operational parameters. The obtained phase diagrams may present significant quantitative deviations from reality because of the model’s sensitivity to the estimated binary parameters. Thus, they should be interpreted as general qualitative guidelines to avoid and manage undesired phase separation in industrial processes and engines rather than phase equilibrium predictions.

Experimental investigation and thermodynamic modeling for isobaric heat capacity of ethanol at elevated temperatures and pressures

Ethanol is a promising sustainable fuel for its environmental friendliness and renewability. Due to the association effect in ethanol molecules, the particular behavior in isobaric heat capacity was explored by combining experimental and theoretical methods. Experimental isobaric heat capacity measurements of ethanol were performed over the temperature range from (298.15 to 573.15) K and at pressures up to 15 MPa in both liquid and vapor phases by a flow calorimeter. Different association schemes were combined respectively with PC-SAFT equation of state and SAFT-VR Mie equation of state to compare their accuracy in isobaric heat capacity prediction, and it could be concluded that two-site (2B) model was better than three-site (3B) model. It was also found that PC-SAFT equation of state was able to yield good results in predicting the isobaric heat capacity far from the saturated state and critical region, however, SAFT-VR Mie equation of state showed better prediction performance near the saturated state and critical region.

Deep eutectic solvents and traditional refrigerants in absorption refrigeration cycles using molecular approaches

Absorption Refrigeration Cycles (ARC) represent a sustainable technology capable of effectively producing cold with modest energy consumption from waste heat or renewable sources. However, the right choice of working fluid pair absorbent–refrigerant is essential for the system to work properly. This contribution is devoted to analysing the performance of an ARC using a wide variety of refrigerants in combination with selected deep eutectic solvents (DES) as absorbents. Three choline chloride-based and one ionic liquid (IL)-based DESs as absorbers are combined with sixteen refrigerants. The PC-SAFT equation of state is employed to assess the thermophysical properties. Accurate modelling of the absorption cycle has revealed that the phase behaviour of the working mixture significantly constrains the temperature and pressure range within which the cycle can operate. Idealised ARCs are insufficient for accurately representing the capabilities and limitations of these systems. Of the sixty-four working pair mixtures, only eighteen are suitable for ARCs based on technical and thermodynamics criteria. The Coefficient of Performance (COP) has been updated with additional key performance indicators that consider environmental and safety factors. The maximum values of the COP for this mixture are around 0.92, while many options lie in ranges around 0.60. This comprehensive analysis helps establish a ranking of the best options. The results have shown that the IL-based DES using R227ea or R236ea is the most efficient system among all the systems studied, with performances of 0.92 and 0.74.

Thermodynamic modeling of anticancer drugs solubilities in supercritical CO2 using the PC-SAFT equation of state

In this research, the solubility of anticancer drugs in the supercritical CO2 is modeled using the PC-SAFT equation of state (EoS). Ten anticancer drugs containing Empagliflozin, Sorafenib tosylate, Verapamil, Sodium valproate, Aprepitant, Sunitinib malate, Tamsulosin, Imatinib mesylate, Capecitabine, and Docetaxel are studied to evaluate the model performance. For each component, three temperature-independent model parameters are optimized by the experimental solubility data. The CO2 is modeled as associative molecules with four associating sites and four association sites are considered on anticancer molecules. Therefore, the cross-association between anticancer and CO2 molecules is considered. The average ARD, RMSE, and AAD values of the PC-SAFT EoS for the aforementioned anticancer drugs are obtained 11.45 %, 0.067, and 0.00026 %, respectively. The PC-SAFT EoS results are compared to various types of cubic EoSs and semi-empirical models. The results show that the PC-SAFT EoS with three model parameters can be used as a robust and efficient thermodynamic model to calculate the solubility of complex molecules in supercritical CO2 up to high pressures and temperatures.

CO2 sorption of elastomer poly(ionic liquid)s with imidazolium cations having different alkyl chains: Structure-morphology-property relationships and thermodynamic modelling by the PC-SAFT equation of state

In this work related to Carbon Capture and Storage (CCS), the CO2 sorption capacities of a new family of elastomer poly(ionic liquid)s (PILs) with imidazolium cations having different alkyl chains were studied. These PILs were synthesized by chemical modification of polyepichlorohydrin (polyECH) obtained by living anionic polymerization. PolyECH was quaternized with different 1-alkylimidazoles (alkyl = methyl, n-butyl, and n-hexyl) and followed by anion exchange to obtain three PILs: PIL-Me, PIL-nBu, and PIL-nHex. They were analyzed by NMR (1H, 13C, 2D 1H/13C HSQC, APT 13C) and characterized by SEC, DSC, calorimetry, rheology, and XRD SAXS/WAXS. The influence of the alkyl chain on the PIL CO2 sorption was studied with a magnetic suspension balance (MSB) at 35 °C and CO2 pressures varying from 1 to 10 bar. The best results were obtained with PIL having methyl chains (9.60 mg CO2/g PIL at 1.1 bar and 159.28 mg CO2/g PIL at 10.0 bar at 35 °C). Finally, the CO2 sorption properties of these PILs were modeled with the PC-SAFT equation of state (EoS). The pure-component parameters were obtained from model regression of the PILs densities calculated by the Bondi's and Van Krevelen's methods. The binary interaction parameters of the systems CO2/PIL were optimized with average absolute deviations (AAD) lower than 6.3 % for the three PILs. The PC-SAFT modelling of their sorption properties opens interesting prospects for modelling the CO2 sorption process for CCS facilities.

Data-efficient surrogate modeling of thermodynamic equilibria using Sobolev training, data augmentation and adaptive sampling

Modern thermodynamic models, such as the PC-SAFT equation of state, are very accurate but also computationally intensive, which limits their applicability to process design optimization, for example. Surrogate models, which can be evaluated quickly, can be used to approximate the thermodynamic equilibria. However, this requires many data points from the flash calculation routine. In this paper, we investigate three approaches to reduce the number of samples and thus the effort needed to train the surrogate models. First, Sobolev training is used, where the surrogate model is trained not only on the output values, but also on derivative information. Second, data augmentation along the tie lines in LLE systems is proposed to generate samples without additional flash calculations. Third, adaptive sampling is revisited with a novel quality criterion. It is shown that the combination of these techniques can be used to significantly reduce the number of samples required.

Classical density functional theory in three dimensions with GPU-accelerated automatic differentiation: Computational performance analysis using the example of adsorption in covalent-organic frameworks

We show how classical density functional theory can greatly benefit from algorithmic advances in machine learning, especially neural networks. By exploiting GPU-accelerated backward automatic differentiation, we overcome the often cumbersome and error-prone implementation of functional derivatives for classical density functional theory computations. This provides an efficient and straightforward solution for computing functional derivatives, opening up a wide range of applications. We show the gain in computational performance by using backward automatic differentiation to compute the functional derivatives on GPUs, and exemplify the use of this easy-to-implement and highly extensible classical density functional theory framework to predict the adsorption isotherms of a methane/ethane mixture described by a Helmholtz energy functional based on the PC-SAFT equation of state in the covalent-organic framework 2,3-DhaTph. Together with this manuscript, we provide the full classical density functional theory code as supplementary material.

PρT measurements of 3-aminopropan-1-ol and N-(2-hydroxyethyl)morpholine from (293.15 to 473.15) K and up to 40 MPa and modeling with modified Tait and PC-SAFT equations

New density data has been reported for 3-aminopropan-1-ol (AP) and N-(2-hydroxyethyl)morpholine (NHEM) at temperatures ranging from (293.15–473.15) K at 19 pressures ranging from (0.1–40) MPa. The experimental measurements were carried out using an Anton Paar high-pressure vibrating tube densimeter with a combined expanded uncertainty of 1 kg m−3 at a 95 % confidence level. Contributions considered in the uncertainty analysis included the impurities in the materials used and apparatus specification. In addition, the density and speed of sound at ambient pressure (81.5 kPa) and temperatures (293.15–343.15) K were measured. The experimental density data were correlated with the modified Tait equation. Values of thermal expansion coefficient (αP ) and isothermal compressibility (κT) were calculated. The work is completed with the modeling of the experimental data using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The parameters of the PC-SAFT equation of state, for the pure compounds, were determined by fitting the equation to the liquid PρT experimental data. Thermodynamic properties such as thermal expansion coefficient (αP), isothermal compressibility (κT), isobaric heat capacity (CP), and speed of sound (u) were calculated with the obtain parameters. Good agreement between experimental data and derived properties represented the modeling accuracy with the obtained parameters.

Phase behavior of supercritical CO2 + nonionic ethoxylated surfactants + methanol: Experimental data and modeling with PC-SAFT equation of state

The use of surfactants for oil and gas purposes has been explored and extensively applied. However, such systems' thermodynamic and predictability behavior still needs further investigation. This work aims to describe the phase behavior of the systems composed of nonionic ethoxylated surfactants (nonylphenyl ethoxylated surfactants—IGEPAL CO-630 and CO-720) + carbon dioxide (CO2) with additional methanol in wide ranges of temperature (T = 313 to 413 K), pressure (P = 0.8 to 54.8 MPa), and CO2 molar compositions (up to 90.0 %). It was observed for all systems studied that CO2 solubility was inversely proportional to temperature and the number of ethoxylated units for pure surfactants. The addition of methanol greatly increases the overall CO2 solubility. The thermodynamic modeling through the PC-SAFT equation of state was also evaluated. Bubble pressure deviations of 13.63 % and 13.49 % were obtained for pure IGEPAL CO-630 and IGEPAL CO-720 + CO2, respectively, and 12.63 % for the ternary system (IGEPAL CO-720 + methanol + CO2). A new set of binary interaction parameters was also provided for IGEPAL CO-630 and IGEPAL CO-720 + CO2.

Solubility of o-toluidine in supercritical carbon dioxide at high-temperatures and high-pressures

In many technological applications the solubility (VLE data) of materials (solid or liquids) in SC CO2 is required. It is essential to understand the solubility and other properties of o-toluidine in the SC CO2 due to their technological importance. This paper presents a new isothermal VLE data for SC CO2 (1)+ o-toluidine (2). Thus, the main purpose of the present work is to experimental study of the VLE properties (solubility, PTxy relationship) of o-toluidine (one of the technologically important compound) in the SC CO2 needs for variety industrial applications. The measurements were made at four selected isotherms of (313.15, 333.15, 353.15, and 373.15) K over the pressure range from (1.24 to 31.44) MPa. A high-temperature and high-pressure optical cell has been used to measure of the phase equilibrium properties (PTxy) of the binary CO2 (1)+ o-toluidine (2) mixture. The combined expanded absolute and relative uncertainty of the temperature, pressure, and the phase concentration measurements at 0.95 confidence level with a coverage factor of k = 2 is estimated at 0.15 K, 0.2 %, and 3 %, respectively. The critical point parameters of the mixture in the PC−TC projection have been estimated using the measured VLE data. The shape of the critical curve behavior indicates that CO2 (1) + o-toluidine (2) mixture belongs to the Type III according to the Konynenburg and Scott classification. PR and PC-SAFT equation of state (EoS) were successfully applied to model the phase equilibria (qualitative point of view) for the SC CO2 (1) + o-toluidine (2) mixture at the measured experimental temperatures. From a quantitative point of view, the best choice (among the models used) was PR EoS. The critical curves predicted with PR and PC-SAFT EoS confirmed that the mixture is classified as Type III phase behavior.

Water content in CO2–CH4 mixtures: New saturation setup and measurements using a quartz-crystal microbalance.

This study presents experimental data on water content in CO2, methane, and their mixtures. A new saturation process was developed using a PVT cell connected to a variable-volume cylinder filled with deionized water. Dry gas with a known composition was injected into the cylinder, and the temperature and pressure conditions were adjusted accordingly. The water content of the saturated gas was then analyzed using a quartz-crystal microbalance (QCM). Various mixtures with different CO2 and methane mole ratios were investigated at different pressures for a given temperature. The PC-SAFT and CPA equations of state were applied to correlate the moisture data. The association scheme employed included 2B, 3B, and 4C types, considering the cross-association between water and CO2. The results for pure methane showed that the water content increased as the pressure decreased across all pressure ranges. However, for pure CO2 above 70 bar, the water content increased due to the condensation behavior of CO2. The same trend was observed for mixtures, where the water content increased with increasing pressure for CO2 mole fractions above 0.74. For all the systems studied, the PC-SAFT and CPA equations of state successfully correlated the water content data using a single constant binary interaction parameter and considering the cross-association between water and CO2.

Viscosity of imidazolium ionic liquids and mixtures of ILs from entropy scaling using the PC-SAFT and ePC-SAFT equations of state

Entropy scaling is a promising method for the development of engineering models for transport properties of ionic liquids (ILs). Here we present two entropy scaling models for the viscosity of ionic liquids and their mixtures at various temperatures and pressures: 1) a molecular-based approach treating each IL as one pure species and using the PC-SAFT equation of state (EoS); and 2) treating each ion as a separate species and using the ePC-SAFT EoS. Both approaches were correlated to viscosity data of 12 ionic liquids from the imidazolium cation class and three different anions comprising 4233 data points with overall average absolute deviations (%AARDs) of less than 8 % over a wide range of temperature and pressures. The ion-based approach was better able to correlate IL viscosity at low temperatures and/or high pressure (to 4011 bar) than the molecular approach. The functional entropy-scaling coefficients for both models were regressed as linear functions of molecular weight, which allowed good prediction of another nine ionic liquids not in the training set. Interestingly, both approaches well predict the viscosity of binary mixtures of imidazolium ionic liquids. In addition, the effect of various reference viscosities and comparison with the Peng-Robinson EoS was performed.

Isothermal vapor–liquid equilibria of binary mixtures containing (methanol, or propan-1-ol, or water, or acetonitrile) and 1-ethyl-3-methylimidazolium thiocynate ionic liquid: Measurements and modeling

Ionic liquid vapor–liquid equilibrium (VLE) measurements were performed on binary systems for1-ethyl-3-methylimidazolium thiocynate [EMIM][SCN] (2) + {methanol, or propan-1-ol or water or acetonitrile}(1) at range temperatures between 273.15 and 363.15 K. Experiments were undertaken at pressures between 15 Pa and 255 kPa using a static device. The reported data were successfully correlated by means of two models, namely NRTL or COSMO-RS, and the PC-SAFT equation of state. While results obtained in this study indicate that the phase behavior of systems involving the ionic liquid and alcohols, water or acetonitrile can be accurately described by these three models, it was found that experimental data may be represented with higher accuracy with PC-SAFT than NRTL and COSMO-RS models.