Perturbed-chain Statistical Associating Fluid Theory Research Articles

Evaluation of the simultaneous presence of SO2 and CO as impurities in the carbon capture and storage technology. CO2/SO2/CO cocapture

From the presented experimental data of two CO2-rich mixtures containing SO2 and CO as impurities of anthropogenic CO2, we evaluated the impact of the simultaneous presence of these impurities on the transport, injection and storage of carbon capture and storage (CCS) technology. We determined the density, vapor-liquid equilibrium and speed of sound of a cocapture mixture (non-purified captured flue gas) [CO2 + 4.93 mol% SO2 + 3.01 mol% CO] and a mixture representative of European emissions (purified) [CO2 + 0.09 mol% SO2 + 1.12 mol% CO], measured from 263 to 373 K and pressures up to 30 MPa for the density and up to 190 MPa for the speed of sound. Using our experimental results, we validated two extended versions of the equation of state for combustion gases (EOS-CG) and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS). From the calculation of selected operational CCS parameters, we concluded that, in the cocapture mixture, SO2 overcomes or compensates for the negative effect of CO, and then this mixture could be a favorable fluid for CCS. The negative effect of CO predominates in the emissions mixture. Differences in the chemical reactivity due to the studied impurities were not considered.

Effects of 2-Butanol Addition on Waste Cooking Oil Biodiesel Density: An Updated Experimental Measurement and Thermodynamic Modeling Study

Biodiesels will become the most popular alternative energy resource to fossil diesels; they can be used alone or blended with an oxygenated additive in any proportion. The properties of biodiesels strongly depend on the type of the fatty acid methyl esters (FAME) that compose them. The main objective of the present work is to investigate the influence of 2-butanol addition on the waste cooking oil biodiesel (WCOB), for this fact, the new experimental density data (952 points) of WCOB + 2-butanol binary mixtures over a wide range of composition [seven compositions; 0 ≤ (WCOB) mole fraction x ≤ 1] between 0.1 and 140 MPa and 298.15 and 393.15 K are presented. The experimental data were correlated using Tait and perturbed chain-statistical associating fluid theory (PC-SAFT) equations of state (EoS), to our knowledge, this is the first time that density measurements for the WCOB + 2-butanol mixture are correlated using the famous PC-SAFT EoS. The Tait equation predicts successfully the density with a global absolute average deviation (AAD) of 0.089%, while the PC-SAFT model correlates well the density with a very small global AAD of 0.223% in each composition. Furthermore, contrary to the Tait equation, the PC-SAFT model can explain some interactions between fluid molecules. From the experimental data, the excess volumes VE have been calculated and fitted using the Redlich-Kister equation with a very small global standard deviation of 7.49 × 10-5 cm3 mol-1, and VE show a positive and symmetric parabolic shape in all composition ranges. Finally, the isobaric thermal expansivity, αp, and the isothermal compressibility, κT, have been derived from the Tait equation and their observed trend was as expected.

Insights into the orientation and hydrogen bond influence on thermophysical and transport properties in choline-based deep eutectic solvents and methanol

The search for new solvents which fulfil the needs of modern times has put the Deep eutectic solvents (DESs) in a leading role given their wide range of applications, versatility, low cost, and minimal environmental impact. For the above reason, it is critical to achieving predictive capabilities and the accurate description of their properties, both macroscopic and microscopic. In this work, DESs based on choline chloride as the hydrogen bond acceptor plus ethylene glycol and glycerol as hydrogen bond donors have been analysed in a mixture with methanol. Densities, excess volume and viscosity were determined by molecular dynamics and predicted by the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). Radial distribution functions and the number of hydrogen bonds derived from molecular simulations confirmed an anticipated bonding network within the liquid, with significant ordering interactions. When methanol is added to the eutectic solvent become incorporated into this structure as a second hydrogen bond donor. Methanol reduces the viscosity, but the eutectic solvents retain their characteristics. The analysis performed in this work could be a valuable feature of the new theory in developing more realistic models of the hydrogen-bonding interaction in deep eutectic solvents.

Estimation of pure component parameters of PC-SAFT EoS by an artificial neural network based on a group contribution method

In this study, we introduced an artificial neural network (ANN), which can represent objects that are difficult to formulate, rather than the integrated model of the group contribution method (GCM), because the integrated model in the existing GCM is no longer able to manage enormous diversification of substances. Hence, a model to estimate the pure component parameters m, σ, and ε of the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was developed. We optimized the structure of the ANN by changing the number of neurons and layers in the hidden layer. In this study, the optimized ANN structure was two hidden layers and 40 neurons. The results confirm that the model can determine the pure component parameters of PC-SAFT EoS, which can estimate the liquid density, saturated vapor pressure, and critical properties. In terms of the critical properties, the estimated results were almost as good or better than those obtained using the GCMs, which are specified for the critical properties. We were able to calculate properties for substances whose parameters were not reported in the literature by using this ANN. The results would be useful for chemical process design, for example, to be incorporated into process simulators.

Prediction of dynamic viscosities of carbon dioxide – organic solvent mixtures with combined equation of state and Eyring theory

This study proposes a method without adjustable parameters for predicting the viscosities of CO2 expanded alkane or 1-alkanol ((1.0–120) MPa, (298−473) K) using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, and the Eyring kinetic theory equation. The accuracy in terms of average relative deviation (ARD) between the calculated results and experimental data was 19% for the present method, 15% for the ASOG-VISCO model, and 37% for the method based on the corresponding state principle. When the Eyring constant k was determined as an adjustable parameter in each system, the accuracy was improved to 12%. The Eyring k in CO2 + alkane and CO2 + alcohol systems were expressed by each linear relationship with the number of carbon atoms in solvent organic compounds.

Modeling the Vapor-Liquid equilibria of binary and ternary systems comprising associating and non-Associating compounds by using Perturbed-Chain Statistical association fluid Theory. Part I

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was implemented for modeling the vapor–liquid equilibrium of binary and ternary systems of carbon dioxide (CO2) + fatty oil, CO2 + ionic liquids (IL), CO2 + perfluoroalkanes, CO2 + HFE-449mec-f, CO2 + water + IL, CO2 + thiophene, and alcohols + thiophene at temperatures between 298.15 and 543.15 K and at pressures up to 200 bar. ILs studied in this work contain 1-octyl-3-methylimidazolium hexafluorophosphate [OMIM][PF6] and N-methyl-2-hydroxyethylammonium propionate [m-2HEA][Pr]. The PC-SAFT pure-component parameters were fitted to the experimental density and vapor pressure data of pure-components. For ILs, only liquid density data were used to obtain pure-IL PC-SAFT parameters, because of the negligible values of the vapor pressure of ILs. Temperature-dependent binary interaction parameters of the binary and ternary systems were fitted to vapor–liquid equilibrium data taken from experimental literature data. These parameters were then used to describe the VLE of other binary and ternary systems. Correlation results of the PC-SAFT were found to be in qualitative agreement with the available experimental data and improved the modeling accuracy of past models in the literature. The overall value of the absolute average relative deviation in pressure (ARDP) and vapor-phase mole fraction (ARDy) of 12.05% and 6.13%, respectively, reveals the goodness of the developed models for modeling the phase behavior of other associating or non-associating mixtures with the same parameters reported in this work.

A modified perturbed chain‐statistical associating fluid theory equation of state for water which includes an association dependent hard sphere diameter

AbstractThe concept of an association dependent hard sphere diameter is introduced as a means to obtain an accurate perturbed chain‐statistical associating fluid theory (PC‐SAFT) equation of state model for water. The new approach is demonstrated to be a step change in accuracy for the representation of pure water properties as compared with standard PC‐SAFT applications. Extension of the approach to mixtures is discussed.

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state.

We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.

Simulation of transient effects in a fuel injector nozzle using real-fluid thermodynamic closure

Numerical predictions of the fuel heating and cavitation erosion location indicators occurring during the opening and closing periods of the needle valve inside a five-hole common rail Diesel fuel injector are presented. These have been obtained using an explicit density-based solver of the compressible Navier-Stokes (NS) and energy conservation equations; the flow solver is combined with two thermodynamic closure models for the liquid, vapour and vapour-liquid equilibrium (VLE) property variation as function of pressure and temperature. The first is based on tabulated data for a 4-component Diesel fuel surrogate, derived from the Perturbed-Chain, Statistical Associating Fluid Theory (PC-SAFT) Equation of State (EoS), allowing for the variation of the physical and transport properties of the fuel with the local pressure and temperature to be quantified. The second thermodynamic closure is based on the widely used barotropic Equation of State (EoS) approximation between density and pressure only and neglects viscous heating. The Wall Adapting Local Eddy viscosity (WALE) LES model was used to resolve sub-grid scale turbulence while a cell-based mesh deformation Arbitrary Lagrangian–Eulerian (ALE) formulation is used for modelling the injector's needle valve movement. Model predictions are found in close agreement against 0-D estimates of the temporal variation of the fuel temperature difference between the feed and hole exit during the injection period. Two mechanisms affecting the temperature distribution within the fuel injector have been revealed and quantified. The first is ought to wall friction-induced heating, which may result to local liquid temperature increase up to fuel's boiling point while superheated vapour is formed. At the same time, liquid expansion due to the depressurisation of the injected fuel results to liquid cooling relative to the fuel's feed temperature; this is occurring at the central part of the injection orifice. The spatial and temporal temperature and pressure gradients induce significant variations in the fuel density and viscosity, which in turn, affect the formed coherent vortical flow structures. It is found, in particular, that these affect the locations of cavitation formation and collapse, that may lead to erosion of the surfaces of the needle valve, sac volume and injection holes. Model predictions are compared against corresponding X-ray surface erosion images obtained from injector durability tests, showing good agreement.

Assessment of the Perturbed Chain-Statistical Associating Fluid Theory Equation of State against a Benchmark Database of High-Quality Binary-System Data

The perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state (EoS) is applied, and its performance is assessed using a reliable free-to-access benchmark thermodynamic database developed by the authors. A total of 200 non-electrolytic binary systems are included in the database, which are divided into nine groups according to the associating character of the components, that is, their ability to be involved in a hydrogen bond. The properties based on which the assessment is performed include two-phase vapor–liquid and liquid–liquid equilibrium, three-phase vapor–liquid–liquid equilibrium, critical point, azeotropic point, enthalpy of mixing, and heat capacity of mixing data. A specific procedure for the calculation of deviations between model predictions and experimental data and for grading the thermodynamic model is applied based on a previously published proposed methodology. The PC-SAFT EoS is implemented with classical mixing rules, no induced association scheme, and no regressed binary interaction parameters. The results are discussed, and specific characteristics of model performance with respect to different families of mixtures are analyzed.

Experimental data and modeling of liquid density, speed of sound, refractive index and derivative properties of ternary mixtures dibutyl ether + 1-butanol + heptane or + methylcyclohexane: Application of PC-SAFT equation of state

Thermophysical properties such as density, (ρ), speed of sound, (u), and refractive index, (nD), experimental data (549 points) are presented in this work at 0.1 MPa and 298.15 K for the following ternary mixtures: dibutyl ether (1) + 1-butanol (2) + heptane (3) and dibutyl ether (1) + 1-butanol (2) + methylcyclohexane (3) and their corresponding binary mixtures. In addition, derivative properties such as excess volume, (VE), deviations in speed of sound, (Δu), isentropic compressibility (ks), deviations in isentropic compressibility, (Δks), and deviations in refractive index, (ΔnD), were calculated from the presented measured data. The Redlich-Kister equation is used to correlate the calculated derivative properties. Therefore, the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) Equation of State (EoS) is used to model the reported experimental data of density, and a good agreement is noticed between the experimental and the modeled data of density for different studied binary and ternary mixtures.

Predicting Deliquescence Relative Humidities of Crystals and Crystal Mixtures.

The presence of water in the form of relative humidity (RH) may lead to deliquescence of crystalline components above a certain RH, the deliquescence RH (DRH). Knowing the DRH values is essential, e.g., for the agrochemical industry, food industry, and pharmaceutical industry to identify stability windows for their crystalline products. This work applies the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) to purely predict the DRH of single components (organic acids, sugars, artificial sweeteners, and amides) and multicomponent crystal mixtures thereof only based on aqueous solubility data of the pure components. The predicted DRH values very well agree with the experimental ones. In addition, the temperature influence on the DRH value could be successfully predicted with PC-SAFT. The DRH prediction also differentiates between formation of hydrates and anhydrates. PC-SAFT-predicted phase diagrams of hydrate-forming components illustrate the influence of additional components on the hydrate formation as a function of RH. The DRH prediction via PC-SAFT allows for the determining of the stability of crystals and crystal mixtures without the need for time-consuming experiments.

Influence of excipients on thermodynamic phase behavior of pharmaceutical/solvent systems: Molecular thermodynamic model prediction

In this work, the influence of polymeric excipients (PEG6000, PEG400, PVPK25, and HPMCE3) on thermodynamic phase behavior of active pharmaceutical ingredients (API) (mesalazine and allopurinol) and its aqueous solution was systematically investigated through experimental measurement and thermodynamic modeling. The API/excipients formulations were prepared by ball milling, and the phase behavior was measured by differential scanning calorimetry (DSC). The results showed that the solubility of API/solvent systems were all increased with higher temperature. Meanwhile, it was found that all four excipients can solubilize mesalazine and allopurinol effectively and the solubilization performance of PVPK25 and HPMCE3 were preferable to PEG. Furthermore, the thermodynamic phase behavior of API in the excipients/water ternary system was predicted by the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), demonstrating good accordance with the experimental results with low average relative deviations (ARDs). This work was expected to provide theoretical guidance for the screening of pharmaceutical formulation excipients.

Transient Cavitation and Friction-Induced Heating Effects of Diesel Fuel during the Needle Valve Early Opening Stages for Discharge Pressures up to 450 MPa

An investigation of the fuel heating, vapor formation, and cavitation erosion location patterns inside a five-hole common rail diesel fuel injector, occurring during the early opening period of the needle valve (from 2 μm to 80 μm), discharging at pressures of up to 450 MPa, is presented. Numerical simulations were performed using the explicit density-based solver of the compressible Navier–Stokes (NS) and energy conservation equations. The flow solver was combined with tabulated property data for a four-component diesel fuel surrogate, derived from the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS), which allowed for a significant amount of the fuel’s physical and transport properties to be quantified. The Wall Adapting Local Eddy viscosity (WALE) Large Eddy Simulation (LES) model was used to resolve sub-grid scale turbulence, while a cell-based mesh deformation arbitrary Lagrangian–Eulerian (ALE) formulation was used for modelling the injector’s needle valve movement. Friction-induced heating was found to increase significantly when decreasing the pressure. At the same time, the Joule–Thomson cooling effect was calculated for up to 25 degrees K for the local fuel temperature drop relative to the fuel’s feed temperature. The extreme injection pressures induced fuel jet velocities in the order of 1100 m/s, affecting the formation of coherent vortical flow structures into the nozzle’s sac volume.

Surfactant Modeling Using Classical Density Functional Theory and a Group Contribution PC-SAFT Approach

Models for surfactants need to incorporate the amphiphilic character of the molecules to describe key properties such as the adsorption at interfaces and the reduction of interfacial tensions. One possibility is to model the surfactant molecules as heteronuclear chains. Therefore, we revisit the heterosegmented density functional theory and present a theory consistent with the group contribution perturbed-chain statistical associating fluid theory equation of state. The model is used to study water/surfactant and water/surfactant/octane systems with surfactants from the group of polyethylene glycol alkyl ethers, a commonly used group of nonionic surfactants. The model parameters are obtained by fitting to pure component data of small surfactants. Binary interaction parameters are required to model the water/alkane subsystem and to account for the polarity of the head groups of the surfactant. The model is able to reproduce the significant enrichment of surfactant molecules at both vapor–liquid surfaces and liquid–liquid interfaces and the corresponding reduction of interfacial tensions. For liquid–liquid interfaces, the competing solubility of the surfactant in both phases has to be taken into account when searching for an optimal surfactant molecule.

High-pressure phase equilibrium and volumetric properties of pseudo-binary mixtures of stock tank oil + methane up to 463K

High-pressure phase equilibrium and volumetric properties of highly asymmetric mixtures related to reservoir fluids are critical to the development of high-pressure and high-temperature (HPHT) reservoirs. However, there is a lack of the relevant data and accurate modeling tools. In this work, we prepared asymmetric pseudo-binary mixtures of methane (CH4) + stock tank oil (STO) and systematically measured their phase equilibrium and densities at temperatures from (298.15 to 463.15) K and pressures up to 140 MPa. The methane mole fraction in these mixtures range from 0.20 to 0.61 for the density measurement, and from 0.20 to 0.81 for the phase equilibrium measurement. From the experimental densities, the isothermal compressibility values, as well as the pseudo-excess volumes, were determined. Moreover, phase envelopes, relative volumes, and liquid volume fractions below the saturation point were also measured. These data are valuable for evaluating and improving thermodynamic models for HPHT reservoir fluids. The experimental results were modeled by the Soave-Redlich-Kwong (SRK) equation of state (EoS), the Peng-Robinson (PR) equation of state, their volume translated versions SRK-VT and PR-VT, and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). For density, SRK and PR gave large deviations of ~18% and ~8%, respectively, as compared with ~3% for PC-SAFT. Inclusion of volume translation reduced their deviations to the same level as that for PC-SAFT. For isothermal compressibility, all the models gave deviations of 20-30%, with PC-SAFT, SRK-VT and PR-VT being slightly better. The excess volumes calculated by SRK, PR and PC-SAFT were similar and close to the experimental values. The deviations in the calculated excess volumes resulted in only ~1% deviations in the calculated densities if the experimentally determined STO densities were used. It was illustrated that the small deviations could be utilized in the excess volume method to accurately estimate the high-pressure live oil densities from the high-pressure STO densities. This excess volume method gave ~1% density deviation on average for all the models, with PC-SAFT giving the smallest maximum deviation. The deviations in calculated saturation pressures were ~5% for all the models with the overall deviation for PC-SAFT being slightly smaller.

Simulation of H2S solubility in three acetate-based ionic liquids using PC-SAFT EoS together with RETM

In current work, Perturbed Chain- Statistical Associating Fluid Theory (PC-SAFT) EoS together with the Reaction Equilibrium Thermodynamic Model (RETM) was employed to correlate H2S solubility in three carboxylate ionic liquids including [emim][Ace], [bmim][Ace] and [hmim][Ace]. The RETM proposes a chemical reaction approach between IL (B) and H2S (A) in the liquid phase. Moreover PC-SAFT EoS contributes for VLE calculations. All the H2S and the investigated ILs, as self-associating components, assumed to follow 2B association scheme.Five adjustable variables of PC- SAFT EoS for pure components were calculated using experimental data of liquid density and vapor pressure. Afterwards, the binary systems were investigated applying RETM. Indeed, two nested loops calculate the liquid phase, total pressure and vapor phase concentrations, respectively. For these systems, AAD% equal to 2.29, 3.09 and 7.65 were obtained for all ILs respectively.

Stability of Pharmaceutical Co-Crystals at Humid Conditions Can Be Predicted.

Knowledge of the stability of pharmaceutical formulations against relative humidity (RH) is essential if they are to become pharmaceutical products. The increasing interest in formulating active pharmaceutical ingredients as stable co-crystals (CCs) triggers the need for fast and reliable in-silico predictions of CC stability as a function of RH. CC storage at elevated RH can lead to deliquescence, which leads to CC dissolution and possible transformation to less soluble solid-state forms. In this work, the deliquescence RHs of the CCs succinic acid/nicotinamide, carbamazepine/nicotinamide, theophylline/citric acid, and urea/glutaric acid were predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). These deliquescence RH values together with predicted phase diagrams of CCs in water were used to determine critical storage conditions, that could lead to CC instability, that is, CC dissolution and precipitation of its components. The importance of CC phase purity on RH conditions for CC stability is demonstrated, where trace levels of a separate phase of active pharmaceutical ingredient or of coformer can significantly decrease the deliquescence RH. The use of additional excipients such as fructose or xylitol was predicted to decrease the deliquescence RH even further. All predictions were successfully validated by stability measurements at 58%, 76%, 86%, 93%, and 98% RH and 25 °C.

Free-Energy-Averaged Potentials for Adsorption in Heterogeneous Slit Pores Using PC-SAFT Classical Density Functional Theory.

This study analyzes the adsorption behavior in two-dimensional heterogeneous slit pores using nonlocal density functional theory based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Both chemical heterogeneity and surface roughness on small atomistic scales are investigated. The solid structure is considered as individual solid interaction sites whereby chemical heterogeneity is introduced through the presence of different solid-fluid sites and molecular roughness by varying the position of the interaction sites in the first solid layers. The effect of both forms of heterogeneity on the adsorption behavior is assessed individually. Effective one-dimensional solid-fluid potentials provide a way to reduce the dimensionality and computational demand of the density functional theory (DFT) calculations. We determine one-dimensional free-energy-averaged (FEA) solid-fluid potentials of methane and n-butane in the low-density limit for solid systems with molecular roughness and chemical heterogeneity. Using this effective one-dimensional solid-fluid potential at any density, we find excellent agreement of adsorption isotherms for both solid descriptions in systems with homogeneous slit pores. Subcritical adsorption isotherms of n-butane in slit pores with surface roughness show deviations at higher pressures due to the formation of fluid layers in the one-dimensional FEA potential. Chemical heterogeneity introduces a shift of the capillary condensation pressure below the saturation pressure of the bulk liquid, which is well described by the free-energy-averaged system.

Vapor- liquid equilibrium for the n-dodecane + phenol and n-hexadecane + phenol systems at 523 K and 573 K

A continuous flow apparatus was applied to measure the phase equilibrium at 523 K and 573 K. The performance of the apparatus was analysed with the determination of vapor pressures of water at the temperatures (T = 453 K and 473 K). The measured water vapor pressures deviated from the literature values less than 1 %. Vapor pressures of n-dodecane, n-hexadecane and phenol were measured at the temperatures (T = 523–623 K) and, the bubble point pressures of n-dodecane + phenol and n-hexadecane + phenol were measured at the temperatures (T = 523 K and 573 K). The measured vapor pressures of the pure components were compared with the literature values. Relative vapor pressure deviated from the literature value less than 2 % for all the measured vapor pressures. The measured vapor pressures value in this work agreed well with the literature, which indicates that the measurement apparatus and the method can produce good-quality data. The measured bubble point pressures for the n-dodecane + phenol and n-hexadecane + phenol systems were modeled with Peng-Robinson and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state and Non-random Two-liquid (NRTL) activity coefficient model. The measured systems were at first modeled with Peng-Robinson and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state without binary interaction parameters. Additionally, the parameters were regressed to optimize the performance of the models. The NRTL activity coefficient model described the behaviour of the measured and the literature data better than the equations of state. Furthermore, the Peng-Robinson equation of state resulted in better predictions than PC-SAFT equation of state even without binary interaction parameters regression. Both equations of state modeled the phase equilibrium behaviour of the system well. The n-dodecane + phenol system showed azeotropic behaviour.