Perturbed-chain Statistical Associating Fluid Theory Equation Of State Research Articles

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...

The friction theory for modeling the viscosities of deep eutectic solvents using the CPA and PC-SAFT equations of state

Deep Eutectic Solvents (DESs), as recently introduced green solvents, are interesting for different fields and applications. Most of the known DESs have high viscosities, which change dramatically with temperature. Therefore, the viscosity of a DES is most often one of the vital physical properties which must be known accurately. Because of the strong non-ideal interactions between the constituents, as well as the dramatic changes of DES viscosity with temperature, modeling and predicting the viscosities of DESs over wide ranges of temperatures is very challenging. In this study, a viscosity approach is used and implemented into two advanced association equations of state for different families of deep eutectic solvents. The cubic plus association (CPA) and the perturbed chain-statistical associating fluid theory (PC-SAFT) equations of state (EoSs), which are two powerful models to handle associating compounds, have been coupled with the friction theory, which is itself among the successful theoretical viscosity models of literature. Twenty-seven different types of DESs, for which density and viscosity data are available in open literature, were considered. A large density databank, consisting of 590 density data over wide ranges of temperatures and pressures, together with a large viscosity databank covering 253 viscosity data over wide ranges of temperatures at atmospheric pressure were collected. The resulting friction theory models with the CPA and PC-SAFT EoSs were checked against experimental data and their deviations were found to be the same and equal to 4.4%. Such accuracy showed the promising capability of both models. By changing the hydrogen bond donor types for a fixed hydrogen bond acceptor, the accuracies of the models were also shown to be good with respect to experimental values. In addition, both models perfectly followed the trends of changing ratios of hydrogen bond donors to hydrogen bond acceptors. The viscosity-temperature trend of the different DESs was also successfully modeled.

Asphaltene precipitation modeling with PR and PC-SAFT equations of state based on normal alkanes titration data in a Multisolid approach

Reservoir fluid Asphaltenes show different precipitation behavior during titration with different normal paraffins, reminding a polydisperse nature. In this respect, the precipitated Asphaltene is increased with decreasing the solvent carbon number. Titration experimental data can be used to improve the precipitation model flexibility. In this study, an improved thermodynamic model is developed to calculate the Asphaltene precipitation conditions. The main focus of this work is on the maximum use of experimental data to increase the accuracy of Asphaltene precipitation calculation using perturbed chain statistical associating fluid theory (PC-SAFT) and Peng-Robinson (PR) equations of state (EOS) (including volume shift) in a Multisolid framework. To do so, at first, PR and PC-SAFT Asphaltene parameters are regressed to bubble point pressure, precipitation onset pressure and the amount of precipitated Asphaltene using the published experimental data on titration of dead oil using normal pentane as a solvent in atmospheric conditions. Afterwards, to follow the polydisperse behavior, the Asphaltene component is divided into three pseudo-components based on the precipitating solvents and the calculations are repeated to adjust the parameters of the EOSs of the new Asphaltene parts. Finally, the results for monodisperse and polydisperse Asphaltene are compared with experimental date of two types of Mexican crude oil samples from reliable published literature and the modeling results with statistical associating fluid theory for the potentials of variable attractive range (SAFT-VR) used by Buenrostro-Gonzalez et al. [1]. The maximum and minimum deviations from the experimental data to calculate the weight percent of the precipitated Asphaltene after dilution are obtained by PR EOS for monodisperse and by PC-SAFT EOS for polydisperse Asphaltene. For one of the oil samples the maximum and minimum mean percent deviation by PR and PC-SAFT EOSs are 9.1079 and 1.7279, respectively, while for the other oil sample they are 3.6674 and 1.0845, respectively.

Uncertainty assessment of equations of state with application to an organic Rankine cycle

ABSTRACTEvaluations of equations of state (EoS) should include uncertainty. This study presents a generic method to analyse EoS from a detailed uncertainty analysis of the mathematical form and the data used to obtain EoS parameter values. The method is illustrated by comparison of Soave–Redlich–Kwong (SRK) cubic EoS with perturbed-chain statistical associating fluid theory (PC-SAFT) EoS for an organic Rankine cycle (ORC) for heat recovery to power from the exhaust gas of a marine diesel engine using cyclopentane as working fluid. Uncertainties of the EoS input parameters including their corresponding correlation structure, are quantified from experimental measurements using a bootstrap method. Variance-based sensitivity analysis is used to compare the uncertainties from the departure function and the ideal-gas contribution. A Monte Carlo procedure propagates fluid parameter input uncertainty onto the model outputs. Uncertainties in the departure function (SRK or PC-SAFT EoS) dominate the total uncertainties of the ORC model output. For this application and working fluid, SRK EoS has less predictive uncertainty in the process model output than does PC-SAFT EoS, though it cannot be determined if this is due to differences in the data for parameter estimation or in the mathematical form of the EoS or both.

Stabilized density gradient theory algorithm for modeling interfacial properties of pure and mixed systems

Density gradient theory (DGT) allows fast and accurate determination of surface tension and density profile through a phase interface. Several algorithms have been developed to apply this theory in practical calculations. While the conventional algorithm requires a reference substance of the system, a modified “stabilized density gradient theory” (SDGT) algorithm is introduced in our work to solve DGT equations for multiphase pure and mixed systems. This algorithm makes it possible to calculate interfacial properties accurately at any domain size larger than the interface thickness without choosing a reference substance or assuming the functional form of the density profile. As part of DGT inputs, the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was employed with the SDGT algorithm. PC-SAFT has excellent performance in predicting liquid phase properties as well as phase behaviors. The SDGT algorithm with the PC-SAFT EoS was tested and compared with experimental data for several systems. Numerical stability analyses were also included in each calculation to verify the reliability of this approach for future applications.

Phase Behavior and Densities of Propylene + Hexane Binary Mixtures to 585 K and 70 MPa

In this study, we report phase behavior data for propylene + hexane mixtures at temperatures of 295 to 468 K and pressures to 5.5 MPa and high-pressure mixture density data at temperatures of 295 to 584 K and pressures to 70 MPa. Both the phase behavior and density data are simultaneously determined using a variable volume, high-pressure view cell that is coupled with a linear variable differential transformer. The phase behavior and mixture density data are modeled with the Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), modified Sanchez–Lacombe (MSL), and perturbed-chain statistical associating fluid theory (PC-SAFT) equations of state (EoS). The PC-SAFT and MSL EoS provide the best fit of the phase behavior data with a nonzero value of 0.028 for kij. Likewise, the PC-SAFT EoS provides the best fit of the high-pressure mixture density data, though the PC-SAFT equation slightly overpredicts the solution density and the calculated densities are relatively insensitive to changes in kij from zero to 0.028.

Modeling the liquid–liquid equilibrium of petroleum fluid and polar compounds containing systems with the PC-SAFT equation of state

A critical test for the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS) is the modeling of systems containing petroleum fluid and polar compounds. In this work, two approaches are proposed for the simplified PC-SAFT EOS to obtain the necessary pure component parameters for the characterized non-associating pseudo-components of petroleum fluids. New pure component parameters of mono-ethylene glycol (MEG) are obtained by considering the liquid–liquid equilibrium (LLE) data of MEG with normal hydrocarbons in the estimation process and a simple binary interaction scheme of MEG with pseudo-components is proposed. These new parameters are applied to model LLE of the systems of petroleum fluid+MEG with or without water. The results show that the simplified PC-SAFT EOS yields promising predictions of the key mutual solubility of these systems: 15–18% overall deviations for the systems of petroleum fluid+MEG and 23–25% overall deviations for the systems of petroleum fluid+MEG+water. The two approaches are further studied in a more theoretical manner to show the relationship between the solubility of petroleum fluid in the polar phase and the PC-SAFT parameter segment diameter.

High-Temperature, High-Pressure Volumetric Properties of Propane, Squalane, and Their Mixtures: Measurement and PC-SAFT Modeling

This study reports the high-temperature, high-pressure density data for propane, squalane, and their binary mixtures for five compositions at temperatures to 520 K and pressures to 260 MPa. The density measurements are obtained with a floating-piston, variable-volume, high-pressure view cell. From the density data, the isothermal and isobaric excess molar volumes upon mixing are computed. For the mixture compositions studied here, the excess volume is mostly negative, showing a minimum at 0.6550 mole fraction of propane and becomes less negative as the propane concentration increases. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) provides good representation for the experimental data. A mean absolute percent deviation (δ) of 1.4% is obtained with the PC-SAFT EoS when using propane and squalane pure component parameters fit to density data at high-temperature, high-pressure conditions.

Comparison of Cubic-Plus-Association and Perturbed-Chain Statistical Associating Fluid Theory Methods for Modeling Asphaltene Phase Behavior and Pressure–Volume–Temperature Properties

The tendency of asphaltene, the heaviest and most polarizable component of crude oil, to deposit and block wellbores and pipelines can potentially lead to production loss and significant cost of remediation. Asphaltenes constitute a particular interest in oil production because of the lack of understanding of their molecular structure and the mechanisms by which they precipitate and deposit. Because prevention is far less expensive than removal, a better understanding of asphaltene precipitation and deposition phenomena is of great importance for the oil industry. Precipitation, which is a necessary but not sufficient condition for deposition, requires accurate modeling of asphaltene phase behavior with respect to variations in the temperature, pressure, and composition. Over the past decade, cubic-plus-association (CPA) and perturbed-chain statistical associating fluid theory (PC-SAFT) equations of state (EOSs) have been proposed for modeling complex systems, such as asphaltenic crude oils. In this work, a comparison between CPA and PC-SAFT EOSs is presented to illustrate their potential and limitations on the prediction of asphaltene phase behavior and pressure–volume–temperature (PVT) properties of crude oils over a range of pressures and temperatures. With an optimized characterization, both EOSs are able to give acceptable predictions of the phase behavior and asphaltene precipitation tendency. However, PC-SAFT is superior in the prediction of derivative thermodynamic properties, especially at high pressures.

Technical equation of state models for heat transfer fluids made of biphenyl and diphenyl ether and their mixtures

Complete thermodynamic models were developed for the estimation of thermodynamic properties of biphenyl (C12H10, CAS number 92-52-4), diphenyl ether (C12H10O, CAS number 101-84-8), and of their mixtures. These compounds are used as heat transfer fluids, both in the liquid and in the vapor phase, especially in the eutectic formulation (commercially known mainly as Therminol® VP-1 and Dowtherm® A). In particular, these fluids are adopted as thermal energy carriers in concentrated solar power plants using parabolic troughs linear concentrators. The developed models are based on the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) and on the improved PRSV (iPRSV) technical equations of state (EoS), complemented by the Wong–Sandler mixing rules. The models’ performance is discussed and their predictions compared with experimental data. It is proven that, from an engineering viewpoint, sufficiently accurate predictions can be obtained with both models. The model based on the PC-SAFT EoS is overall more accurate, but its mathematical complexity could play a significant role if computation time is an issue. On the other hand, the iPRSV-based model could be the solution of choice for applications requiring maximum computational efficiency such as, e.g., the process-level simulation of parabolic troughs solar collectors.

Thermodynamic Study of Binary Mixtures of 1-Butyl-1-methylpyrrolidinium Dicyanamide Ionic Liquid with Molecular Solvents: New Experimental Data and Modeling with PC-SAFT Equation of State

This work is concerned with thermodynamic properties of binary mixtures composed of 1-butyl-1-methylpyrrolidinium dicyanamide ionic liquid (IL) and the following molecular solvents: n-heptane, benzene, toluene, ethylbenzene, thiophene, 1-butanol, 1-hexanol, and 1-octanol. This is the very first time when experimental data on liquid-liquid equilibrium (LLE) phase diagrams and excess enthalpies of mixing (H(E)) for these systems are reported. An impact of the molecular solvent structure on LLE and H(E) is discussed. Furthermore, modeling of the properties under study is presented by using perturbed-chain statistical associating fluid theory (PC-SAFT). The equation of state is used in purely predictive and semipredictive mode. The latter one involves temperature-dependent binary corrections to combining rules employed in the PC-SAFT model determined on the basis of infinite dilution activity coefficients. The results shown indicate that such an approach can serve as an interesting modern thermodynamic tool for representation of thermodynamic data for complex ILs-based systems.

On petroleum fluid characterization with the PC-SAFT equation of state

The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state has shown promising results for describing complex phase behaviors and high pressure properties of various systems. It has been proposed as an alternative to the classical cubic equations of state in the petroleum industry. It is, however, far from a simple task to develop a sophisticated oil characterization method for the PC-SAFT EOS. In this work, in order to answer some fundamental questions of developing new characterization methods for PC-SAFT, six methods are proposed to estimate the model parameters by combining the well-behaved correlations of homologous series with the PNA contents and/or by using different fitting approaches. Along with different options in characterization procedure, the performance of these methods is investigated on PVT calculations, i.e. predicting the saturation pressure and density of 80 petroleum fluids over wide temperature, pressure and composition conditions. These options include the molar composition distribution, the specific gravity correlation, the number of pseudo-components, the estimation method of PNA contents and the binary interaction parameters. Two candidate methods are showing better overall performance than the others, with deviations less than 6.0% and 1.3% of saturation pressure and density, respectively. These two methods are further studied for predicting more complete sets of PVT data, i.e. constant mass expansion, differential liberation and separator test, of three petroleum fluids. The results are promising if compared to those available in the literature.

PC-SAFT modeling of asphaltene phase behavior in the presence of nonionic dispersants

This study introduced a new method to characterize asphaltenes in PC-SAFT equation of state (EOS) and correctly model the effect of nonionic dispersants on the thermodynamic behavior of asphaltenes. Our approach is to combine microscale parameters from Molecular Dynamics (MD) simulations with Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) to develop a comprehensive model that enables the prediction of macroscopic behavior such as the amount and onset of asphaltene precipitation at various pressures, temperatures, and fluid compositions. More specifically, association parameters were considered for asphaltene molecules and determined by equating the Gibbs energy of association calculated by PC-SAFT EOS to the one obtained from MD simulations. A correlation was derived to relate the association energy parameter (ɛAB) of asphaltenes to the molar weight of their aromatic cores. Our model showed that asphaltene association energy is affected by temperature and solvent type and is inversely proportional to the solubility parameter of the medium. The hetero-segment approach in PC-SAFT EOS was adopted to accurately characterize asphaltene molecules and their non-association parameters in PC-SAFT were determined based on the molecular weight and aromaticity factor of asphaltenes. Moreover, the average aggregation number of asphaltene nanoaggregates was calculated using the Wertheim association theory. This model was applied to predict asphaltene precipitation envelopes for three different live crude oils and showed excellent agreement with experimental data in the literature. Additionally, the model could correctly predict the amount of asphaltene precipitation upon addition of nonionic dispersants.

Densities and viscosities of the mixtures (formamide + 2-alkanol): Experimental and theoretical approaches

Densities and viscosities of binary liquid mixtures of formamide (FA) with polar solvents namely, 2-PrOH, 2-BuOH, 2-PenOH, 2-HexOH, and 2-HepOH, have been measured as a function of composition range at temperatures (298.15,303.15,308.15,313.15)K and ambient pressure. From experimental data, excess molar volumes, VmE and viscosity deviations Δη, were calculated and correlated by Redlich–Kister type function. The effect of temperature and chain-length of the 2-alkanols on the excess molar volumes and viscosity deviations are discussed in terms of molecular interaction between unlike molecules. The statistical associating fluid theory (SAFT), and perturbed chain statistical associating fluid theory (PC-SAFT) were applied to correlate and predict the volumetric behavior of the mixtures. The best predictions were achieved with the PC-SAFT equation of state. Also the Peng–Robinson–Stryjek–Vera equation of state has been used to predict the viscosity of binary mixtures.

Liquid Densities of Xylene Isomers and 2-Methylnaphthalene at Temperatures to 523 K and Pressures to 265 MPa: Experimental Determination and Equation of State Modeling

Experimental density data for o-xylene, m-xylene, p-xylene, and 2-methylnaphthalene, are reported at pressures (P) to 265 MPa and temperatures (T) to 525 K using a variable-volume, high-pressure cell. The reported data agree to within ±0.4% of available literature data. o-Xylene has the largest densities and p-xylene has the smallest densities in the P–T range investigated in this study although the 525 K isotherms for all three aromatics virtually superpose at high pressures. The aromatic densities are modeled using the Peng–Robinson (PR), high-temperature, high-pressure, volume-translated Peng–Robinson (HTHP VT-PR), and perturbed chain statistical associating fluid theory (PC-SAFT) equations of state (EoS). Generally, the PC-SAFT EoS gives the best predictions of the HTHP density data with mean absolute percent deviations (δ) within 1.0%, even though the pure-component parameters are fitted to low-pressure vapor pressure and saturated liquid density data. δ decreases to 0.4% for calculations with a new set of PC-SAFT parameters obtained from a fit of the HTHP experimental density data obtained in this study.

Effect of Isomeric Structures of Branched Cyclic Hydrocarbons on Densities and Equation of State Predictions at Elevated Temperatures and Pressures

The cis and trans conformation of a branched cyclic hydrocarbon affects the packing and, hence, the density, exhibited by that compound. Reported here are density data for branched cyclohexane (C6) compounds including methylcyclohexane, ethylcyclohexane (ethylcC6), cis-1,2-dimethylcyclohexane (cis-1,2), cis-1,4-dimethylcyclohexane (cis-1,4), and trans-1,4-dimethylcyclohexane (trans-1,4) determined at temperatures up to 525 K and pressures up to 275 MPa. Of the four branched C6 isomers, cis-1,2 exhibits the largest densities and the smallest densities are exhibited by trans-1,4. The densities are modeled with the Peng-Robinson (PR) equation of state (EoS), the high-temperature, high-pressure, volume-translated (HTHP VT) PREoS, and the perturbed chain, statistical associating fluid theory (PC-SAFT) EoS. Model calculations highlight the capability of these equations to account for the different densities observed for the four isomers investigated in this study. The HTHP VT-PREoS provides modest improvements over the PREoS, but neither cubic EoS is capable of accounting for the effect of isomer structural differences on the observed densities. The PC-SAFT EoS, with pure component parameters from the literature or from a group contribution method, provides improved density predictions relative to those obtained with the PREoS or HTHP VT-PREoS. However, the PC-SAFT EoS, with either set of parameters, also cannot fully account for the effect of the C6 isomer structure on the resultant density.

Thermodynamic properties of binary mixtures containing N,N-dimethylformamide + 2-alkanol: Cubic and statistical associating fluid theory-based equation of state analysis

Densities and viscosities of mixtures of N,N-dimethylformamide with 2-propanol, 2-butanol, 2-pentanol, 2-hexanol, and 2-heptanol have been measured as a function of composition range at T=(298.15, 303.15, 308.15, 313.15)K and atmospheric pressure. Excess molar volumes VmE and viscosity deviations Δη were calculated and correlated by the Redlich–Kister type function. The statistical associating fluid theory (SAFT), and perturbed chain statistical associating fluid theory (PC-SAFT) were applied to correlate and predict the volumetric behavior of the mixtures. The best predictions were achieved with the PC-SAFT equation of state. Also the Peng–Robinson–Stryjek–Vera (PRSV) equation of state (EOS) has been used to predict the binary viscosities.

Thermodynamic Modeling of Aqueous Ionic Liquid Solutions Using PC-SAFT Equation of State

In this work, an equation of state has been utilized for thermodynamic modeling of aqueous ionic liquid (IL) solutions. The proposed equation of state is a combination of perturbed chain statistical associating fluid theory (PC-SAFT) equation of state and mean spherical approximation (MSA) term. In this model, the ion-based approach has been used to adjust the model parameters. The ion parameters have been estimated through simultaneous fitting to experimental mean ionic activity coefficient and liquid density data of strong electrolytes. Using adjusted ion parameters, osmotic coefficients, mean ionic activity coefficients, liquid densities, apparent molar volume, and water activity of several ILs, assumed as chainlike electrolytes, have been calculated. Results show that PC-SAFT, in combination with the MSA term has acceptable accuracy for prediction of density, apparent molar volume, and activity coefficient of ILs. The average deviations of predicted mean ionic activity coefficients, liquid densities, water activity, and apparent molar volume are 6.43, 0.86, 0.033, and 8.20%, respectively.

Perturbed-Chain SAFT as a Versatile Tool for Thermodynamic Modeling of Binary Mixtures Containing Isoquinolinium Ionic Liquids

This contribution reports a recapitulation of our experimental and modeling study on thermodynamic behavior of binary systems containing N-alkylisoquinolinium ionic liquids (ILs) based on bis(trifluoromethylsulfonyl)imide anion, [CniQuin][NTf2] (n = 4,6,8). In particular, we report isothermal vapor-liquid equilibrium (VLE) phase diagrams and molar excess enthalpies of mixing (H(E)) for binary mixtures of [C8iQuin][NTf2] IL with various organic solutes including benzene, toluene, thiophene, pyridine, and butan-1-ol. The measured VLE data represented simple homozeotropic behavior with either negative or positive deviations from ideality, depending on polarity of the solute, temperature, and mole fraction of IL. In turn, the obtained data on H(E) were negative and positive for the mixtures containing aromatic hydrocarbons or thiophene and butan-1-ol, respectively, in the whole range of IL's concentration. All of the measured and some previously published data regarding phase behavior of [C8iQuin][NTf2] IL were analyzed and successfully described in terms of perturbed-chain statistical associating fluid theory (PC-SAFT). The methodology used in this work was described by us previously. In general, the proposed modeling results in VLE diagrams, which are in excellent agreement with experimental data. In the case of H(E), the results obtained are good as well but not so satisfactory such as those for VLE. Nevertheless, they seem to be very promising if one take into account the simplicity of the utilized molecular model against significant complexity of IL-based systems. Thus, we concluded that PC-SAFT equation of state can be viewed as a powerful and robust tool for modeling of systems involving ILs.

Prediction of Phase Behavior for the System Methane-Carbon Dioxide- Hydrogen Sulfide-Water with the PR and PC-SAFT Equations of State

In this work, we present the predicted multiphase behavior (vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria) for a quaternary mixture containing methane, carbon dioxide, hydrogen sulfide, and water. The capabilities of the PR (Peng-Robinson) and PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equations of state (EoS) to predict the phase behavior exhibited by this mixture were compared and analyzed. The computer algorithm used for isothermal multiphase flash calculations is based on the minimization of the Gibbs energy along with stability analysis to find the most stable state of the system. The binary interaction parameters used with the PR EoS for modeling this system were taken from the literature whereas the interaction parameters for the PC-SAFT were obtained from the regression of binary vapor-liquid equilibrium data. The results obtained differ from each other and demonstrate different capabilities and accuracies of the present thermodynamic models in the predictions.