Perturbed Chain Statistical Association Fluid Research Articles

Experimental measurement and thermodynamic/intelligent modeling of yellow 2 G solubility in supercritical carbon dioxide with/without co-solvent

In this study, the solubility of an azo dye, Yellow 2 G, was investigated in supercritical CO2, both with and without co-solvents (methanol and dimethyl sulfoxide (DMSO)), spanning temperatures from 308 to 338 K and pressures from 10 to 34 MPa. The supercritical solubility of Yellow 2 G ranged from 0.052×10−6 to 0.559×10−6 mole fractions, while in the presence of methanol and DMSO, it varied from 0.5×10−6 to 5.92×10−6 and 0.46×10−6 to 4.6×10−6, respectively. Co-solvents significantly increased supercritical solubility, with over a 9-fold increase with methanol and more than a 7-fold increase with DMSO. Semi-empirical models, Peng-Robinson (PR), Soave Redlich Kwong (SRK), Perturbed-Chain Statistical Associating Fluid (PCP-SAFT), and quadrupolar cubic plus association theory (qCPA) equations of state, and a multilayer perceptron (MLP) neural network were used to assess the solubility data. Among the semi-empirical models, the Khansary model for the binary system and the Jouyban and Soltani-Mazloumi models for the ternary system demonstrated the highest conformity. Among models based on equations of state, the PCP-SAFT model demonstrates the highest accuracy in correlating solubility data for both binary and ternary systems. Notably, the accuracy of the SRK model in correlating solubility data for the binary system matches that of PCP-SAFT. The proposed MLP neural network provided highly accurate estimations of Yellow 2 G solubility in both binary and ternary systems, achieving an accuracy of over 99 %.

Crossover description of transport properties for some hydrocarbons in the supercritical region

In the present study, by defining new representative equations based on the transport crossover functions stemming from the application of renormalization group theory to the transport phenomena, as well as using Perturbed Chain Statistical Associating Fluid equation of state to calculate equilibrium quantities and their partial derivatives in and out of the critical regions (up to 2ρc) to obtain thermal conductivity and diffusivity of some hydrocarbons. The results show that in the critical regions a good consistency with the available literature data is obtained, the AAD% of both thermal conductivity and diffusivity of the studied hydrocarbons ranged from 1.5% to 5%.

Thermodynamic and transport properties of binary mixtures containing N-Ethylethanamine and (C5 − C9) 1-Alkanol: PC-SAFT model

ABSTRACT Thermodynamic and transport properties for the binary mixtures of N-Ethylethanamine (EEA) with 1-pentanol up to 1-nonanol at temperatures 298.15 K, 308.15 K, and 318.15 K were reported in this study. Calculation of the excess molar volumes exhibits that the considered mixtures have a negative deviation from the Raoult’s Law. Deviation from ideality increases as the alkyl chain increases. Strong molecular interactions occur in the above binary mixtures due to the formation of hydrogen bonds, dipole-dipole interactions and dispersive forces. Obtaining results were analysed to gain information about the liquid structure in the binary mixtures. The investigation has shown that increasing the alcohol chain length reinforces the strength of intermolecular forces between EEA and 1-alkanol. The perturbed chain statistical association fluid theory (PC-SAFT) with the correlative ability was implemented to the densities of the binary mixtures, and outcomes of this theory indicate that the agreement between experimental data and calculated values is reasonable. Maximum deviation was found for the binary mixtures EEA + 1-hexanol with the absolute average deviation of 0.016.

New modified PC-SAFT pure component parameters for accurate VLE and critical phenomena description

The theory of Perturbed Chain Statistical Associating Fluid (PC-SAFT) is largely applied in many industrial fields. It requires three parameters: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By convention, they are determined by fitting vapor pressure and liquid density data. However, the shortage behind these parameters adopted by their respective authors is that they give excessive values of critical temperatures and critical pressures, which are crucial to forecasting vapor-liquid critical pressure and composition of the mixture at high pressures and temperatures.In this paper, a new approach is proposed to evaluate PC-SAFT parameters of different substances from diverse chemical families. Good fits of saturation pressure and vapor densities values of 94 pure substances are obtained, with an overall AARD of 0.89% and 1.50% respectively.The proposed method requires as input the critical pressure (Pc), the critical temperature (Tc), and the acentric factor (ω). By using these parameters, PC-SAFT estimates with accuracy the critical properties of pure compounds as well as the successful prediction of vapor-liquid equilibria for many non-associating binary systems at critical regions including mixtures containing ammonia, comparing with other literature values. But the limitation of this method is reflected in underestimated liquid densities.

Prediction of vapor pressure and density for nonaqueous solutions of the ionic liquid 1-ethyl-3-methylimidazolium ethyl sulfate using PC-SAFT equation of state

The experimental data on density and vapor pressure for nonaqueous solution of ionic liquids are important not only for the design and optimization of chemical processes, but also from the theoretical perspective to predict physical properties and modeling under different conditions. In this study, the vapor pressure for nonaqueous solutions of the ionic liquid, 1-ethyl-3-methylimidazolium ethyl sulfate [EMIM][ES] in some polar organic solvents, i.e. 1-propanol, ethanol and methanol, in dilute region of the ionic liquid concentration were measured by the use of isopiestic method at 298.15 K. In this regard, the Perturbed Chain Statistical Association Fluid equation of state (PC-SAFT) is used for prediction of the vapor pressure and density of the investigated systems. The obtained results from the PC-SAFT equation of state provide reliable and accurate predictions with the absolute average deviations (AAD), 0.01 and 0.084 for density and for vapor pressure , respectively.

Theoretical and experimental study of physicochemical behavior of binary mixtures: SAFT and PC-SAFT models

The type and magnitude of interactions between diisobutyl ketone (DIBK) and a homologous series of 2-alkanols (2-propanol up to 2-pentanol) are studied in this paper using density and viscosity data. Studies have been carried out in a wide range of temperature (293.15 K to 323.15 K), atmospheric pressure, and in the entire range of composition. The calculated excess molar volumes of the above-mentioned systems are positive, and the viscosity deviations are negative. For the correlation of the density values of binary systems, the statistical association fluid theory (SAFT) and perturbed chain statistical association fluid theory (PC-SAFT) have been used, and the output of two models are compared by average absolute deviation. The results show that the PC-SAFT model is more efficient. Densities and viscosities reported for binary systems along with applied models are all novels, and so far no reports have been investigated in the scientific papers. PC-SAFT and SAFT models were applied to model the densities of binary mixtures containing Diisobutyl ketone and 2-alkanol at various temperatures. Results show that models provide satisfactory outcomes and PC-SAFT model produces better results.

Evaluation of Gas Hydrate Formation Temperature for Gas/Water/Salt/Alcohol Systems: Utilization of Extended UNIQUAC Model and PC-SAFT Equation of State

Naturally occurring gas hydrates are of great importance as a strategic energy source. Hydrates affect coastal sediment stability, global climate change, and ocean carbon cycling. It is vital to understand the thermodynamic conditions of gas hydrates to control/manage and inhibit hydrate formation. A variety of equations of state (EOSs) have been utilized to model the thermodynamic behaviors of gas hydrates. In this study, the perturbed chain statistical association fluid theory (PC-SAFT) equation of state combined with van der Waals and Platteuw model is employed to determine the clathrate hydrate formation temperature of pure gases (e.g., methane, ethane, propane, isobutane, carbon dioxide, and hydrogen sulfide) and binary and ternary systems of hydrate gases. In addition, the gas hydrate formation conditions are investigated where methanol, ethanol, glycerol, NaCl, KCl, CaCl2, and MgCl2 as inhibitors are present. The UNIQUAC model is utilized in this work to obtain the hydrate formation conditions in s...

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.

Measurement, correlation and thermodynamic modeling of the solubility of Ketotifen fumarate (KTF) in supercritical carbon dioxide: Evaluation of PCP-SAFT equation of state

Solubility measurement of desired solid component(s) represents a primary and crucial step of feasibility study on production process of a nanoparticle drug through supercritical fluid (SCF) technology. Ketotifen fumarate (KTF) is an effective anti-histamine and anti-inflammatory drug with a wide spectrum of applications in treatment and prevention of a variety of mucosal and skin allergies. In this research, for the first time, solubility of KTF was determined experimentally in supercritical carbon dioxide (SC-CO2) at different temperatures in the range 308.2–338.2 K and different pressures in the range 120–300 bar. Obtained in mole fraction, KTF solubility was in the range of 0.211 × 10–4 to 10.766 × 10–4. To predict solubility of the solid solute drug in supercritical fluid, experimental data modeling was successfully accomplished by using two different groups of models, i.e. six density-based empirical models, namely Chrastil, Khansari, Bartle, Spark and Bian models, and two equations of state (EoS), namely Peng-Robinson (PR) and Perturbed-Chain Statistical Associating Fluid (PCP-SAFT). Results of analysis of variance (ANOVA) indicated the Peng-Robinson model as the model of choice for predicting solubility of KTF in SC-CO2. Using correlation results, the heat of drug-CO2 solvation and that of drug vaporization were approximated as 223.77 and 0.09577 kJ/mol, respectively.

Modelling the solubility of H2S and CO2 in ionic liquids using PC-SAFT equation of state

The Perturbed Chain Statistical Association Fluid Theory (PC-SAFT) is used to investigate the solubility of carbon dioxide (CO2) and hydrogen sulfide (H2S) in several methylimidazolium bis (trifluoromethylsulfonyl) imide ionic liquids (ILs) or [Cnmim][NTf2] where n=2, 4, 6, and 8. The pure component parameters of the ILs are estimated by fitting to experimental density data and binary solubility data of acid gases in ILs reported in literature. Two strategies are examined to model the ILs. In the first strategy, the ILs are treated as neutral molecules. In the second strategy, the ILs are modelled as two charged ions: imidazolium cation [Cnmim]+ and bis (trifluoromethylsulfonyl) imide anion [NTf2]−. For each strategy, four different self association schemes are examined: non-associating, 2-site, 3-site, and 4-site schemes. The inclusion of self-association of the IL improves the calculated acid gas solubility. The 4-site association scheme with two donors and two acceptors provided the best results for almost all the investigated acid gases-IL binary systems, with an AARD of 2.76%–6.62% for H2S-ILs systems and 1.54%–4.98% for CO2-IL systems. Using these parameters, the solubility of ternary systems of CO2 and H2S in C8mimNTf2 IL is successfully represented, with an AARD of 6.24% for CO2 and 7.99% for H2S, without the need for binary interaction parameters. The high pressure density of ILs and the binary solubility of CO2-ILs at high pressure is also represented with reasonable accuracy. The inclusion of the electrolyte term in the second strategy improves the high pressure density and solubility results as well as the predictive capability of the model by allowing for the examination of the effect of using different cation-anion combinations.

High-temperature, high-pressure viscosities and densities of toluene

Toluene viscosities and densities, measured with a windowed, variable-volume, rolling-ball viscometer/densimeter (RBVD), are reported at temperatures from 296–535K and pressures to 300MPa. The combined expanded uncertainty in the reported viscosities and densities are 4.0% and 0.8% of the measured values respectively, each with a coverage factor, k=2. Densities obtained with the RBVD exhibit an average absolute percent deviation (ΔAAD) of 0.20% against densities calculated with the Lemmon and Span Equation of State. Viscosities obtained with the RBVD exhibit ΔAAD values of less than 4.0% for data from 18 of 20 available literature sources for high pressure data. The reported viscosities are generally in good agreement with calculated viscosities from the reference equation of Avgeri et al. The reported toluene viscosities extend the available database from 423–535K and 40–300MPa. Toluene viscosities are also reasonably correlated with the empirical Tait equation that allows for reliable interpolation of the data. Free Volume Theory (FVT) matches the reported viscosities to within 3.4% ΔAAD using FVT parameters fit to a viscosity data set limited to 373K and using densities calculated with the Perturbed–Chain Statistical Association Fluid Theory (PC-SAFT). An improved fit of the viscosity data is obtained if temperature-dependent, FVT parameters are used. The challenge remains to predict the temperature dependence in the FVT parameters from first principles.

Experimental and modeling asphaltene precipitation in presence of DBSA using PC-SAFT EOS

ABSTRACTAsphaltene precipitation and subsequent deposition in production tubing and topside facilities present significant cost penalties to crude oil production. Therefore, it is highly desirable to predict their phase behavior and the efficiency of dispersants in preventing or delaying deposition. Very few studies have been carried out on the molecular interactions between asphaltenes and different dispersants. As a result, the mechanisms by which dispersants stabilize asphaltenes are still open to discussion. The authors introduced a new method to characterize asphaltenes in perturbed chain statistical association fluid theory equation of state (EOS; perturbed-chain statistical association fluid theory EOS [PC-SAFT-EOS]) and correctly model the effect of dodecyl benzene sulfonic acid (DBSA) dispersant on the thermodynamic behavior of asphaltenes. Using the filtration method the effect of the ionic dispersant (DBSA) on asphaltene precipitation for different concentrations of n-heptane was measured experimentally, then modeled through PC-SAFT EOS. In the approach only the hard-chain and the dispersion terms are taken into consideration, and PC-SAFT parameters were calculated based on Gonzales et al. (2007) based on molecular weight (Mw) and aromaticity factor (γ). Additionally, the model could correctly predict the amount of asphaltene precipitation upon addition of DBSA dispersant.

Solid–liquid phase equilibria of binary hydrocarbon mixtures predicted by Lattice Cluster Theory

The solid–liquid equilibrium (SLE) of hydrocarbon mixtures is highly relevant in petroleum and chemical industry. The formulation of thermodynamic models with a high accuracy in predicting solid–liquid phase behavior is an essential and also a challenging topic. In this publication, the authors applied Lattice Cluster Theory for predicting the SLE of these mixtures. The model takes into account the molecular structure of the pure components, which is a priori known. Using the LCT in the incompressible formulation, an analytical calculation method with a high predictive power for SLE, where the molecular structures of the components are underlying, could be provided. The binary interaction parameter could be estimated using enthalpy of mixing data taken from the literature. The quality of the LCT in modeling the heat of mixture is similar to the quality of the physical based equation of state, the Perturbed Chain–Statistical Association Fluid Theory equation of state (PC–SAFT). The predictive power of the model is investigated using four different solutes (n-dodecane, n-hexadecane, n-eicosane and n-tetracosane) having different chain lengths in the solvent n-hexane. The SLE calculation is based on the properties of the pure components. In the case of n-eicosane, a large scatter of the experimental data in the literature occurs. Therefore, differential scanning calorimetry experiments at very low heating rate were performed.

A Modeling Framework for Predicting and Correlating Viscosities of Liquids in Wide Range of Conditions

This communication reports a modeling framework for estimating viscosities in a wide range of conditions that couples the critical point-based revised perturbed chain statistical association fluid theory equation of state (CP-PC-SAFT EoS) and the modified Yarranton–Satyro correlation (MYS), yet is generalized by SAFT molecular parameters. The proposed approach requires as an input just critical constants and the triple point liquid densities, while the same triplet of MYS parameters can predict viscosities of wide variety of compounds including n-alkanes (from methane and until n-octadecane), various aromatic and nonaromatic hydrocarbons, and oxygenated organic substances. In addition, it can yield particularly accurate predictions for saturated and single-phase viscosities of asymmetric mixtures. Consequently, this modeling framework is characterized by an enhanced predictive character.

Evaluation of thermodynamic properties of fluid mixtures by PC-SAFT model

Densities and viscosities of binary mixtures of methyl isobutyl ketone (MIK) with polar solvents namely, 2-propanol, 2-butanol and 2-pentanol, were measured at 7 temperatures (293.15–323.15 K) over the entire range of composition. Using the experimental data, excess molar volumes VmE, isobaric thermal expansivity αp, partial molar volumes V¯m,i and viscosity deviations Δη, have been calculated due to their importance in the study of specific molecular interactions. The observed negative and positive values of deviation/excess parameters were explained on the basis of the intermolecular interactions occur in these mixtures. The Perturbed Chain Statistical Association Fluid Theory (PC-SAFT) has been used to correlate the volumetric behavior of the mixtures.

Modeling the Solubility of Nitrogen Dioxide in Water Using Perturbed-Chain Statistical Associating Fluid Theory

NO2 is one of the important components in flue gas from combustion in power plants, which together with CO2 and SO2 pollute the atmosphere if released and cause the undesired acid rains. NO2 reacts immediately with H2O upon dissolution, which prevents direct measurements on the physical phase equilibria of the chemical system. Modeling this reacting system is a challenging task due to the complexities arising from the heterogeneous nature of the chemical reaction, the multiple components that are involved in the phase equilibria, ionic dissociation in water, self- and cross-associations among the molecules, and multiple chemical reactions that may occur before reaching the physicochemical equilibria. Therefore, efforts on modeling this NO2/H2O system have been made so far with no satisfactory progress. In this work, we propose a complete model of the system using Perturbed Chain Statistical Associating Fluid Theory (PCSAFT) equation of state (EOS). The model is found to be able to calculate the solubility curves of NO2 in water at various pressures and temperatures, which provide a strong foundation for a later application in flue gas sequestration into aquifers.

Experimental determination and theoretical modeling of the vapor–liquid equilibrium and densities of the binary system butan-2-ol + tetrahydro-2H-pyran

Isobaric vapor–liquid equilibrium (VLE) data have been measured for the binary system butan-2-ol+tetrahydro-2H-pyran at 50, 75, and 94kPa and over the temperature range from 339 to 370K using a vapor–liquid equilibrium still with circulation of both phases. Mixing volumes were also determined at 298.15K and atmospheric pressure with a vibrating tube densimeter. According to experimental results, the zeotropic mixture exhibits slight positive deviation from ideal behavior over the experimental range. The excess molar volumes (v˜E) of the system are positive over the whole mole fraction range. The VLE data of the binary mixture satisfy the Fredenlund's consistency test and were well-correlated by the Wohl, nonrandom two-liquid (NRTL), Wilson, and universal quasichemical (UNIQUAC) equations for all of the measured isobars. The v˜E, in turn, were satisfactorily correlated using a second order Redlich–Kister equation.The theoretical modeling of the measured VLE and v˜E data has been carried out using the polar perturbed chain statistical association fluid theory (PPC-SAFT) equation of state. In this molecular based approach, butan-2-ol was described as a polar auto-associating molecule, while tetrahydro-2H-pyran is treated as polar molecule. Molecular interactions between these two components have been approximated in terms of a hetero-association theory. It is demonstrated that a common set of parameters is able to simultaneously reproduce with good agreement both phase equilibrium and excess molar volumes measurements.

Development and Application of an Asphaltene Deposition Tool (ADEPT) for Well Bores

Asphaltenes often tend to deposit in reservoirs, flow lines, separators, and other systems along production lines causing significant production loss due to restricted oil flow or damages caused to the units and instruments used along the flow lines. Asphaltenes are typically stable in the oil; however, changes in conditions such as temperature or pressure or compositional changes can trigger the phase separation and resultant deposition of these asphaltenes on the surfaces encountered along the flow. Hence, it is required to be able to forecast the possibility of precipitation of asphaltenes for given operating conditions and quantify the amount of deposition. In this work, the development of an asphaltene deposition tool (ADEPT) that can predict the occurrence and calculate the magnitude and profile of asphaltene deposition in a well bore is discussed. The simulator consists of a thermodynamic module and a deposition module. The thermodynamic module uses the Perturbed Chain Statistical Associating Fluid Theory (PC SAFT) equation of state to describe the phase behavior of oil, which is first characterized by using thermodynamic properties such as saturation points and asphaltene onset pressure data and physical properties such as the density of the oil. The deposition module is then used along with input from the thermodynamic module to calculate magnitude of asphaltene deposition along the length of well bore/pipe lines. The mathematical model used in the deposition module is first benchmarked and validated by comparing the simulation results against the experimentally measured asphaltene deposition flux in a capillary scale deposition experiment. The simulator was then used to study deposition in two field cases, for which measurements of asphaltene deposition profile were reported in the literature. This study demonstrates the development and application of a simple yet comprehensive simulator that can be easily integrated with other commercial flow simulators, facilitating quick calculations of the change in the asphaltene deposition profile and magnitude with change in operating conditions as the production continues. It is shown that the simulator enables operators to perform quick sensitivity studies and map out operating envelopes to avoid potential risk zones.

“Vapor–liquid” equilibrium measurements and modeling for the cyclohexane + n-hexanoic acid binary system

To simulate cyclohexane to cyclohexanol oxidation reactors, the acquisition and modeling of vapor–liquid equilibria of the key components, under the process conditions, are essential. n-Hexanoic acid is a co-product of the reaction. Vapor–liquid equilibrium data are reported for the cyclohexane + n-hexanoic acid binary system at four temperatures: 413, 423, 464 and 484 K. All measurements have been carried out using an apparatus based on the “static-analytic” method, with two ROLSI™ pneumatic capillary samplers. The generated data are successfully correlated using two equations of state, the Peng–Robinson (PR) and the Perturbed Chain Statistical Association Fluid Theory (PC-SAFT). Both models are capable of representing the experimental data, but the PC-SAFT EoS uses less binary interaction parameters.

Computation and modeling of tricritical phenomena in ternary and quaternary mixtures using the Perturbed Chain—Statistical Associating Fluid Theory equation of state

Tricritical points (TCPs), contained in two-phase holes in three-phase surfaces, are of great importance in industrial applications of near-critical and supercritical technology because they occur in a range of temperatures, pressures and compositions where the technological processes are carried out. Their predictions are also important for mapping the transitions between different types of fluid phase behavior, when using molecular parameters in theoretical thermodynamic models, since these parameters take into account the different molecular interactions in the phase transition. In ternary systems, the tricritical point (TCP) has zero degrees of freedom; in other words, it exists only at a unique condition of pressure, temperature and composition. On the other hand, in quaternary systems, the tricritical state has one degree of freedom, and a line of tricritical points may exist. In this work, a theoretical procedure was developed and implemented using the theoretical, non-cubic Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) for computing and predicting the tricritical points of various ternary systems with single tricritical points, and tricritical lines of quaternary systems (involving n-alkanes, branched alkenes, alcohols, water, carbon dioxide, nitrogen and hydrogen sulfide) without fitting the binary interaction parameter. The results were compared with experimental tricritical data obtained from literature and an excellent agreement was obtained within a range of temperatures and pressures of practical interest in engineering.