Perturbed-chain Statistical Associating Fluid Theory Research Articles

Modeling Viscosity of Ionic Liquids with Electrolyte Perturbed-Chain Statistical Associating Fluid Theory and Free Volume Theory

Viscosity is one of the most important physical properties when developing ionic liquids (ILs) for industrial applications such as CO2 separation. The viscosities of ILs have been measured experimentally, while the modeling work is still limited. In this work, the electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) was combined with the free volume theory (FVT) to model the viscosities of pure ILs and IL mixtures up to high pressures and temperatures, in which the ePC-SAFT was used to calculate the density as inputs for modeling the viscosity of ILs with FVT. The ILs under consideration contain one of the IL cations [Cnmim]+, [Cnpy]+, [Cnmpy]+, [Cnmpyr]+, or [THTDP]+ and one of the IL anions [Tf2N]−, [PF6]−, [BF4]−, [tfo]−, [DCA]−, [SCN]−, [C1SO4]−, [C2SO4]−, [eFAP]−, Cl–, [Ac]−, or Br–. In total, 89 ILs were considered combined with a thorough literature survey of the available experimental viscosity data and evaluation. The comparison with the available experimental viscosities s...

Solid–Liquid–Gas Equilibrium of Methane–n-Alkane Binary Mixtures

In this work, a solid-phase thermodynamic model is coupled with the Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), and Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equations of state (EoS) to model the solid–liquid–gas equilibrium (SLGE) of binary methane (CH4) mixtures with normal alkanes (n-alkanes). The mixtures considered include n-alkanes from n-C6H14 up to n-C36H74. The predictive capabilities of each combined model are validated against available experimental data and vary substantially as the asymmetry of the binary mixture, with respect to the size of the molecules involved, increases. Several aspects of the models, such as the use of binary interaction parameters (BIPs) fitted to experimental vapor (or gas)–liquid equilibrium (VLE/GLE) data and the importance of specific terms of the solid-phase model, are studied to showcase their effect on the accuracy of the calculations. In this way, modifications on the basic combined models are applied. A specific volume translation strat...

Measuring and modeling thermodynamic properties of aqueous lysozyme and BSA solutions

A novel approach towards modeling proteins in aqueous solutions by applying perturbed-chain statistical associating fluid theory (PC-SAFT) is proposed in this work. Lysozyme and bovine serum albumin (BSA) were chosen as model proteins due to a vast database available in literature. However, the huge majority of these literature data had been measured at certain ionic strengths, which is disadvantageous in order to derive pure-component parameters for proteins. Thus, in a first step within this work osmotic coefficients of dialyzed lysozyme and of dialyzed BSA in pure water were measured at 298.15 K. The data were very different for dialyzed and non-dialyzed solutions and further showed a strong dependence on pH and ionic strength. In a second step, the pure-component parameters of lysozyme and BSA were adjusted to the measured osmotic coefficients and to solution densities of dialyzed lysozyme or dialyzed BSA. PC-SAFT explicitly takes into account the complex association behavior between protein and water as well as among the proteins. Therefore, the number of protein association sites of one protein was determined from the sum of association sites of the single amino-acid constituents of a protein available from previous work (Ind. Eng. Chem. Res 50 (2011) 141–151). Similarly, the two PC-SAFT parameters “segment number” and “segment diameter” of a protein were summed or averaged from the single amino-acid constituents. This approach allowed modeling densities and osmotic coefficients of protein solutions with reasonable accuracy compared to experimental data.

Surface tension of droplets and Tolman lengths of real substances and mixtures from density functional theory

The curvature dependence of interfacial properties has been discussed extensively over the last decades. After Tolman published his work on the effect of droplet size on surface tension, where he introduced the interfacial property now known as Tolman length, several studies were performed with varying results. In recent years, however, some consensus has been reached about the sign and magnitude of the Tolman length of simple model fluids. In this work, we re-examine Tolman's equation and how it relates the Tolman length to the surface tension and we apply non-local classical density functional theory (DFT) based on the perturbed chain statistical associating fluid theory (PC-SAFT) to characterize the curvature dependence of the surface tension of real fluids as well as mixtures. In order to obtain a simple expression for the surface tension, we use a first-order expansion of the Tolman length as a function of droplet radius Rs, as δ(Rs) = δ0 + δ1/Rs, and subsequently expand Tolman's integral equation for the surface tension, whereby a second-order expansion is found to give excellent agreement with the DFT result. The radius-dependence of the surface tension of increasingly non-spherical substances is studied for n-alkanes, up to icosane. The infinite diameter Tolman length is approximately δ0 = -0.38 Å at low temperatures. For more strongly non-spherical substances and for temperatures approaching the critical point, however, the infinite diameter Tolman lengths δ0 turn positive. For mixtures, even if they contain similar molecules, the extrapolated Tolman length behaves strongly non-ideal, implying a qualitative change of the curvature behavior of the surface tension of the mixture.

Carbon dioxide solubilities in tricyanomethanide-based ionic liquids: Measurements and PC-SAFT modeling

This work reports the measurements of the solubility of carbon dioxide (CO2) in three tricyanomethanide based ionic liquids (ILs) constituted by different cations: 1-butyl-3-methylimidazolium, 1-butyl-4-methylpyridinium, 1-butyl-1-methylpyrrolidinium in order to investigate the effect of the cation on the solubility. The solubility of CO2 have been determined using high-pressure variable volume cell in a range of temperature from T = (292.13–367.85) K and pressure up to 121.6 bars. A high solubility of CO2 in the 1-butyl-4-methylpyridinium tricyanomethanide was observed in comparison with the other cation. It was found that the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) may be used to represent with good accuracy the experimental data of CO2 solubility in tricyanomethanide based ionic liquid.

Mutual Influence of Furfural and Furancarboxylic Acids on Their Solubility in Aqueous Solutions: Experiments and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) Predictions

Furan compounds are of mounting global interest due to their biorenewable nature and their potential to replace petroleum-based compounds as feedstocks in manufacturing. In this work the solubilities of furfural and the furancarboxylic acids 2-furoic acid (FA), 5-formyl-2-furancarboxylic acid (FFA), and 2,5-furandicarboxylic acid (FDCA) in aqueous solutions and organic solvents were investigated experimentally and by modeling with perturbed-chain statistical associating fluid theory (PC-SAFT). The PC-SAFT pure-component parameters of the solutes FA, FFA, and FDCA and one binary parameter between each solute and each solvent were adjusted to fit experimentally determined solubilities of each solute in each organic solvent or in water. Pure-component parameters of furfural were fitted to experimental density data and vapor-pressure data, and a binary interaction parameter was fitted to capture the solubility behavior of furfural in water. Modeling of pH effects enhanced predictions of the mutual influences ...

Thermodynamic Modeling of Multicomponent Liquid–Liquid Equilibria in Ionic Liquid Systems with PC-SAFT Equation of State

This work is a continuation and extension of previously published study showing that the perturbed-chain statistical associating fluid theory (PC-SAFT) is an efficient and robust approach for calculating thermodynamic properties of the mixtures containing ionic liquids (ILs) [J. Phys. Chem. B 2012, 116, 5002–5018]. The modeling strategy presented in the original paper was based on application of infinite dilution activity coefficients of molecular solutes in ILs (γ∞) to calculate binary corrections for the PC-SAFT combining rules. In this work, the idea is further investigated, in particular extended to a broader spectrum of pure fluids (the model parametrization is provided for almost 100 ILs), and evaluated based on a large compilation of liquid–liquid equilibrium (LLE) data, including more than 400 distinct and diverse ternary systems and a number of higher systems. Three PC-SAFT modeling strategies are proposed and systematically reviewed in order to elucidate an effect of γ∞ data on the quality of LL...

Oil desulfurization using deep eutectic solvents as sustainable and economical extractants via liquid-liquid extraction: Experimental and PC-SAFT predictions

The reduction of the sulfur content in crude oil is of utmost importance in order to meet the stringent environmental regulations. Thiophene and its derivatives are considered key substances to be separated from the crude oil. In previous works, six deep eutectic solvents (DESs) based on tetraethylammonium chloride, tetrahexylammonium bromide and methyltriphenylphosphonium bromide as hydrogen bond acceptors (HBAs) and polyols (ethylene glycol and glycerol) as hydrogen bond donors (HBDs) were successfully applied for the extraction of thiophene from {n-alkane + thiophene} mixtures via liquid-liquid extraction. One of the objectives of this work was to study the effect of the aliphatic hydrocarbon type/length (e.g. n-hexane vs n-octane) on the extraction performance of the same DESs. Extraction performance was evaluated by the selectivity and the thiophene distribution coefficient. Based on new experimental data, higher selectivities and lower thiophene distribution coefficients were obtained when thiophene was extracted from n-octane instead of n-hexane. Another objective was to predict the phase behavior of the ternary systems {n-alkane + thiophene + DES} using Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). The PC-SAFT “pseudo-pure component” approach was applied, in which a DES was considered as a pseudo-pure compound (not a mixture). The pure-component parameters of the DESs were obtained by fitting to liquid density data, which were measured at temperatures between 298.2 K and 323.2 K. Binary interaction parameters were fitted to experimental binary LLE data for the systems {n-alkane + DES} and {thiophene + DES} at 298.2 K and atmospheric pressure, while the LLE data of the ternary systems {n-alkane + thiophene + DES} were fully predicted. It was found that the distribution coefficients and selectivity of the ternary systems containing DESs could be qualitatively well predicted using this model.

Phase Equilibrium Study of the Ternary System CO2 + H2O + Ethanol At Elevated Pressure: Thermodynamic Model Selection. Application to Supercritical Extraction of Polar Compounds

The purpose of this study is to select an appropriate thermodynamic model among the ones available in commercial process simulators for representing the phase behavior of the carbon dioxide + ethanol + water system. The following versions of the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) cubic equations of state (EoS) were considered: Panagiotopoulos-Reid, modified Panagiotopoulos-Reid, Huron-Vidal-NRTL, Modified Huron-Vidal (MHV2-UNIFAC), Predictive Soave-Redlich-Kwong (PSRK) and Volume-Translated Peng–Robinson (VTPR). The Polar Perturbed-Chain SAFT EoS deriving from the Statistical Associating Fluid Theory (PPC-SAFT) was also selected for the present investigation. This study highlighted that the optimal thermodynamic models for the application of interest have to be chosen among the VTPR, PSRK and MHV2-UNIFAC EoS. Once identified a suitable thermodynamic model for the CO2 + ethanol + water ternary system, it has been possible then to simulate the extraction process of polar compounds from natural products and to discuss how water influences the process efficiency.

Viscosity Prediction for Petroleum Fluids Using Free Volume Theory and PC-SAFT

In this study, free volume theory (FVT) in combination with perturbed-chain statistical associating fluid theory is implemented for viscosity prediction of petroleum reservoir fluids containing ill-defined components such as cuts and plus fractions. FVT has three adjustable parameters for each component to calculate viscosity. These three parameters for petroleum cuts (especially plus fractions) are not available. In this work, these parameters are determined for different petroleum fractions. A model as a function of molecular weight and specific gravity is developed using 22 real reservoir fluid samples with API grades in the range of 22 to 45. Afterward, the proposed model accuracy in comparison with the accuracy of De la Porte et al. with reference to experimental data is presented. The presented model is used for six real samples in an evaluation step, and the results are compared with available experimental data and the method of De la Porte et al. Finally, the method of Lohrenz et al. and the method of Pedersen et al. as two common industrial methods for viscosity calculation are compared with the proposed approach. The absolute average deviation was 9.7 % for free volume theory method, 15.4 % for Lohrenz et al., and 22.16 for Pedersen et al.

Equation-Oriented Approach for Handling the Perturbed-Chain SAFT Equation of State in Simulation and Optimization of Polymerization Processes

The perturbed-chain SAFT (PC-SAFT) equation of state (EOS) is a very popular and promising model for fluids. Resolution of the PC-SAFT EOS is generally conducted by subroutine-based calculations that involve logical conditions. This approach can lead to nonsmoothness and convergence issues when used with gradient-based solvers in an equation-oriented (EO) framework. In this paper, we propose a novel EO approach for the PC-SAFT EOS embedded in large flowsheet optimization. First, the mathematical structure of the PC-SAFT EOS is analyzed through a digraph. It reveals that for polymerization systems, resolution of the PC-SAFT EOS is coupled not only by phase equilibrium but also by the polymerization kinetics. This feature strongly motivates implementation of both EOS resolution and process optimization in a complete EO framework. A novel EO approach is proposed for selecting the appropriate root of the PC-SAFT EOS by incorporating thermal stability criteria to eliminate the undesirable roots. Numerical exam...

Light-scattering data of protein and polymer solutions: A new approach for model validation and parameter estimation

The development of separation processes for polymers or proteins from aqueous solutions requires a high amount of experimental effort, including phase-equilibrium data such as solid-liquid, liquid-liquid or vapor-liquid equilibria. This effort can be reduced by means of thermodynamic models. This work presents a new method for parameter estimation and validation of thermodynamic models by means of static-light-scattering (SLS) measurements. In this work the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was used to predict directly the SLS data (Rayleigh ratio) of macromolecular solutions. In a first step, SLS data were measured for binary water/polyethylene glycol (PEG molecular weight ranging from 2000 to 12000 g/mol) mixtures and for binary water/lysozyme mixtures. Applying pure-component PC-SAFT parameters from literature, the SLS data of these binary mixtures were successfully predicted with PC-SAFT. In a second step, one binary interaction parameter between lysozyme and PEG was adjusted to new experimental SLS data of buffered PEG/lysozyme/water solutions with PEG6000 concentration of 20 g/L. Finally, SLS data for buffered ternary PEG/lysozyme/water solutions with PEG of different molecular weights (2000–12000 g/mol) and different concentrations (1–50 g/L) were accurately predicted with PC-SAFT. Thus, (1) the proposed approach allows predicting SLS data, and (2) the method provides an access to the estimation of model parameters by means of experimental SLS data, which are accessible with much less effort than experimental phase-equilibrium data.

In-situ determination of crystallization kinetics in ASDs via water sorption experiments

Amorphous solid dispersions (ASD) are intended to improve the bioavailability of poorly water-soluble active pharmaceutical ingredients. However, the development of long-term stable ASDs is often limited by the unwanted crystallization of the incorporated active pharmaceutical ingredient. Robust detection and quantification of crystal formation - especially at temperatures and humidites relevant for long-term storage tests - are essential for understanding crystallization phenomena. In this work, the crystallization kinetics in spray-dried nifedipine/poly (vinyl acetate) ASDs was investigated by measuring the time-dependent water sorption behavior at constant storage conditions. By coupling these experiments with thermodynamic predictions of the water sorption in amorphous and crystallized ASDs using the Perturbed-Chain Statistical Associating Fluid Theory, the amount of crystallized nifedipine as function of time could be determined in-situ just by weighing the ASD samples and without any calibration. The experimental findings were validated by X-ray diffraction measurements. Metastable ASDs with nifedipine contents between 70 wt% and 90 wt% were investigated at relative humidities between 60% RH and 90% RH and in a temperature range between 30 °C and 40 °C. Storage at high temperature and at high RH, and high nifedipine contents dramatically increased the crystallization rates.

Evaluation of Thermodynamic Models for Predicting Phase Equilibria of $$\hbox {CO}_{2}$$ CO 2 + Impurity Binary Mixture

For the design and operation of $$\hbox {CO}_{2}$$ capture and storage (CCS) processes, equation of state (EoS) models are used for phase equilibrium calculations. Reliability of an EoS model plays a crucial role, and many variations of EoS models have been reported and continue to be published. The prediction of phase equilibria for $$\hbox {CO}_{2}$$ mixtures containing $$\hbox {SO}_{2}$$ , $$\hbox {N}_{2}$$ , NO, $$\hbox {H}_{2}$$ , $$\hbox {O}_{2}$$ , $$\hbox {CH}_{4}$$ , $$\hbox {H}_{2}\mathrm{S}$$ , Ar, and $$\hbox {H}_{2}\mathrm{O}$$ is important for $$\hbox {CO}_{2}$$ transportation because the captured gas normally contains small amounts of impurities even though it is purified in advance. For the design of pipelines in deep sea or arctic conditions, flow assurance and safety are considered priority issues, and highly reliable calculations are required. In this work, predictive Soave–Redlich–Kwong, cubic plus association, Groupe Europeen de Recherches Gazieres (GERG-2008), perturbed-chain statistical associating fluid theory, and non-random lattice fluids hydrogen bond EoS models were compared regarding performance in calculating phase equilibria of $$\hbox {CO}_{2}$$ -impurity binary mixtures and with the collected literature data. No single EoS could cover the entire range of systems considered in this study. Weaknesses and strong points of each EoS model were analyzed, and recommendations are given as guidelines for safe design and operation of CCS processes.

Standard Gibbs Energy of Metabolic Reactions: III The 3-Phosphoglycerate Kinase Reaction.

The glycolytic pathway is one of the most studied metabolic pathways to date. This work focuses on determining the standard Gibbs energy of reaction (ΔRg0) of the first adenosine triphosphate-yielding reaction step of glycolysis, namely, the 3-phosphoglycerate kinase (PGK) reaction. Trustworthy values of ΔRg0 are required for thermodynamic approaches to determine single reaction conversions or even fluxes of metabolic reactions. In literature, the observed ΔRg0,obs values are usually determined directly from the experimental equilibrium composition data without accounting for the nonideality of the reaction mixture. That is the reason why the observed ΔRg0,obs values do not present consistent standard data as they are a function of the concentration, pH, and pMg. In this work, a combination of experimentally determined equilibrium composition data and activity coefficients of the reacting agents was used to determine ΔRg0 values for the temperatures 303, 313, and 323 K at pH 7. The activity coefficients were predicted with the thermodynamic model electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT). The ePC-SAFT parameters were taken from literature or fitted to new experimental osmotic coefficients. At 313.15 K, a value for ΔRg0 of −16.2 ± 0.2 kJ/mol was obtained. This value is about 4 kJ/mol less negative than what is usually considered as an accepted standard value. The reason behind this discrepancy was found to be the activity coefficients of the reacting agents, which dramatically influence the equilibrium position of the PGK reaction. On the basis of the temperature-dependent ΔRg0 values, the standard enthalpy of reaction was determined and found to be ΔRh0 = −49 ± 9 kJ/mol.

Pervaporation performance of crosslinked PVA membranes in the vicinity of the glass transition temperature

This work investigates the pervaporation performance of crosslinked poly (vinyl alcohol) (PVA) membranes for ethanol dehydration near the glass transition. The solubility of water and ethanol mixture in the membranes was measured as a function of feed composition and sorption temperature, and the data was modelled by perturbed-chain statistical associating fluid theory (PC-SAFT). Importantly, this approach allows the solubility of the two components to be determined individually. Model results show that the heat of sorption of water and ethanol was constant across the temperature range. Water permeance generally decreased when operational temperature increased, indicating a solubility-controlled transport behavior. The permeance also increased when water feed concentration increased. Activation energy analysis provided more insights about the influence of membrane properties on the mass transport mechanism. At 90 wt% ethanol feed composition, the apparent activation energy (Ea) for water permeation changed from 9.6 kJ mol−1 when temperature was < 70 °C to − 9.1 kJ mol−1 when temperature was > 80 °C. When the feed composition decreased to 80 wt% ethanol, a transition was observed at a lower temperature range (60–65 °C). These changes were related to changes in the activation energy of diffusion, given the heat of sorption was constant. The permeability of ethanol was lower due to its larger molecular size, but a similar transition was observed for the 80 wt% ethanol case.

Vapor - liquid equilibrium of the carbon dioxide/methane mixture at three isotherms

Experimental vapor – liquid equilibrium data for the CO2/CH4 mixture have been measured at 293.13 K, 298.14 K and 303.15 K, with emphasis on the mixture critical area. The maximum estimated standard uncertainties are 3 mK in temperature, 2 kPa in pressure and 0.0008 in mole fraction. The scaling law of statistical thermodynamics has been fitted to the critical region data of each isotherm and very good estimation of the critical point is achieved with a maximum uncertainty of 10 kPa in critical pressure and 0.0009 in critical molar composition. The measurements have been validated against experimental data taken from the literature, where available, and against the prediction of the GERG-2008 model. The Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) Equations of State using the classic van der Waals one fluid mixing rules, the perturbed chain statistical association fluid theory (PC-SAFT) and the Universal Mixing Rule – Peng Robinson (UMR-PRU) model have been fitted to the data of each isotherm with very satisfactory results. UMR-PRU yields the lowest deviation, especially concerning the critical point area, with an overall absolute average deviation (AAD) of 0.18% in bubble point pressure and 0.43% in CO2 mole fraction of the vapor phase. In the critical points, UMR-PRU results in an average % AAD equal to 1.55 in critical pressure and 0.99 in the critical point composition.

Modeling of physical properties and vapor – liquid equilibrium of ethylene and ethylene mixtures with equations of state

Ethylene (C2H4) is one of the most important compounds for the chemical and petrochemical industry, since it has found extensive use in the production of polymers, functionalized hydrocarbons and many other basic and intermediate products. As a result, significant amounts of ethylene are being transported, mainly through pipelines, from the site of production to the relevant industrial areas for exploitation and conversion to products of higher value. Accurate knowledge of the physical properties of the chemical systems involved, as well as the conditions for which two or more phases are formed, is a key aspect to the design and operation of a safe and optimal transportation process. In this work, the capability of three different Equations of State (EoS) in predicting the various physical properties (density, heat capacity, speed of sound, Joule-Thomson coefficient, and isothermal compressibility coefficient) of pure ethylene was assessed. The EoS considered include the Peng-Robinson (PR), the Perturbed Chain – Statistical Association Fluid Theory (PC-SAFT), and the SAFT with the Mie potential of variable range (SAFT-VR Mie) EoS, all of them in their original forms, with respect to the parameterization procedure. Furthermore, the vapor - liquid equilibrium (VLE) of pure ethylene and binary ethylene mixtures with hydrocarbons (CH4, C2H6, C3H6, C3H8, 1-C4H8) and gaseous components (H2, CO2) was calculated and the binary interaction parameters (BIPs) were regressed to optimize the performance of each EoS. Finally, the VLE of ternary mixtures with the components mentioned above and ethylene was predicted using the optimized BIPs. Most of the physical properties of pure C2H4 are predicted with relatively high accuracy by PC-SAFT and SAFT-VR Mie EoS, with none being clearly superior to the other. Both SAFT EoS are more accurate than PR in predicting the pure C2H4 physical properties overall. For phase equilibrium predictions, SAFT-VR Mie is overall the most accurate EoS, but when BIPs are used, the performance of all EoS is of comparable accuracy.

Mutual Impact of Phase Separation/Crystallization and Water Sorption in Amorphous Solid Dispersions.

The molecular integration of poorly water soluble active pharmaceutical ingredients (APIs) in a suitable polymeric matrix is a possible approach to enhance the dissolution behavior and solubility of these APIs. Like all newly developed pharmaceutical formulations, these formulations (often denoted as amorphous solid dispersions (ASDs)) need to undergo storage stability tests at defined relative humidity (RH) and temperature conditions. In a previous work ( Int. J. Pharm. 2017 ; 532 , 635 - 646 ), it was shown that thermodynamic modeling can be successfully used to predict the long-term stability of ASDs against API crystallization and moisture-induced amorphous-amorphous phase separation (MIAPS). This work in turn demonstrates the prediction of water sorption in ASDs accounting for the potential occurrence of API crystallization and MIAPS. The water sorption and phase behavior of ASDs containing the APIs felodipine and ibuprofen incorporated in three different hydrophilic polymers poly(vinylpyrrolidone), poly(vinyl acetate), and poly(vinylpyrrolidone-co-vinyl acetate) at the conditions 25 °C/60% RH and 40 °C/75% RH were predicted using the perturbed-chain statistical-associating fluid theory (PC-SAFT). The predictions were successfully validated via two-year-lasting water sorption experiments. It was shown that crystallization of the API and MIAPS on the one hand and water sorption in the ASDs on the other hand dramatically influence each other and that this behavior can even be quantitatively predicted by PC-SAFT, which already provides valuable insights at early stages of formulation development.

Thermodynamic Modeling and Simulation of Biodiesel Systems at Supercritical Conditions

Biodiesel is becoming a promising fuel in many markets in the world for being a renewable energy source and for not requiring significant adaptation in existing diesel engines. It is biodegradable and its polluting gas emissions are less harmful to the environment. Transesterification is used for the biodiesel synthesis at supercritical conditions using triacylglycerols and solvents in a heterogeneous reaction. The Peng–Robinson (PR), the volume-translated Peng–Robinson (VT-PR), and the perturbed chain statistical associating fluid theory (PC-SAFT) equations of state were using to predict the fluid phase behavior of systems containing solvents and components present in the synthesis of biodiesel at supercritical conditions. Two pure component parameters for the VT-PR equation, N and k3, and the five pure component parameters for the PC-SAFT equation, m, σ, and e as well as the associating parameters κAiBj and eAiBj, were predicted based on the vapor pressures and the saturated liquid volumes. Results were...