Experimental Liquid Density Research Articles

Predicting the phase behavior of fluorinated organic molecules using the GC-SAFT-VR equation of state

Fluorinated molecules such as perfluoroalkanes (PFA), perfluoroalkylalkanes (PFAA), fluoroalkanes, and hydrofluoroethers (HFE) possess attractive physical properties that have resulted in their use in a wide range of applications. However, while there is an abundance of thermophysical data for hydrocarbons in the literature, only limited studies have been performed that report the properties of the corresponding fluorinated species. Predictive approaches are therefore needed to accurately and reliably determine the physical properties of these molecules. The statistical associating fluid theory (SAFT) is a commonly used molecular-based equation of state that in its various forms has been applied to study a wide range of fluid systems. In recent work, several group contribution (GC) SAFT equations of state have been proposed, such as the GC-SAFT-VR equation that combines the SAFT equation for potentials of variable range (VR) with a group contribution approach that uniquely allows for the description of hetero-segmented chains. The GC-SAFT-VR equation has been shown to provide an excellent description of the phase behavior of pure associating and non-associating fluids and their mixtures, with a minimal reliance on fitting the model parameters to experimental data. Specifically, parameters for key functional groups (such as CH3, CH2, CH, CH2=CH, C=O, C6H5, ether and ester, OH, NH2, CH=O, COOH) have been obtained by fitting to experimental vapor pressure and saturated liquid density data for selected low molecular weight fluids and then used to predict the phase behavior of pure fluids and their mixtures without further adjusting the group parameters. To expand upon this effort, here we report parameters for the CF3, CF2, CF, CH2F, CHF2, and CHF functional groups and their cross interactions. The theoretical predictions are compared with experimental data for pure PFAs, PFAAs, and HFEs, as well as binary mixtures of alkanes, alkenes, PFAs, PFAAs, and CO2 in order to test the transferability of the new group parameters. The GC-SAFT-VR approach is found to accurately predict the phase behavior of the systems studied.

Thermodynamic modeling of solubility of hydrogen sulfide in ionic liquids using Peng Robinson-Two State equation of state

In this work, a simple association equations of state, namely Peng Robinson-Two state (PR-TS) association model is applied to model the PVT behavior of pure ionic liquids and solubility of H2S in 12 various imidazolium-based ionic liquids. This equation of state consists of two terms, the Peng-Robinson (PR) equation of state as cubic term for non-specific energy contribution and two-state association model (TSAM) for association energy contribution. First, to obtain the parameters of the PR-TS EoS for pure components, the experimental liquid density of different pure ionic liquids at various temperatures and pressures are correlated and the percent absolute average deviation between the calculated and experimental densities of ionic liquids is about 0.24%. For pure H2S two association schemes are considered as in the presence or not of association behavior. Then, the parameters of the model for these two schemes are correlated by simultaneously optimization of vapor pressure and liquid density data. Following successful application of the model for the pure components the PR-TS EoS is applied to predict the vapor-liquid equilibrium (VLE) of the several H2S + IL binary mixtures with this assumption that in binary mixtures present cross-association or self-association interaction. For binary systems in first approach only one interaction parameter is used and in second approach two binary interaction parameters are applied. The results of the VLE calculation of the H2S + IL systems show that the best accuracy with AAD = 3.40% is obtained when H2S is considered as non-association component and is used two binary interaction parameters for modeling the binary systems. In overall, the results of the present model for pure and binary systems comprise H2S and ILs are in very good agreement with experiments.

The implementation of ion-based ePC-SAFT EOS for calculation of the mean activity coefficient of single and mixed electrolyte solutions

Following our previous work (Journal of Molecular Liquids 221 (2016) 904–913), the modified perturbed chain statistical associating fluid theory (ePC-SAFT) incorporated with Debye-Huckel term has been applied to calculate some thermodynamic properties of single and mixed electrolyte solutions. The applicability of this model has been investigated by calculation of the mean ionic activity and osmotic coefficients of electrolyte solutions as well as the water activity of regarded systems at different temperatures. Firstly, water-ion hydration has been taken into account independently by two individual strategies, i.e. ions can be considered as non-associating and associating compounds distinctly. Afterwards, a new set of ion parameters containing 31 common ions has been estimated using the experimental mean ionic activity coefficients and liquid densities of 78 binary electrolyte solutions in both strategies. The optimized parameters which have been utilized for prediction of single-salt aqueous electrolyte solutions MIACs up to 373.15 K are global and transferable to different salts. Eventually, it can be observed that not only the density of aqueous electrolyte solutions, but also MIACs, osmotic coefficients and water activity of single and mixed salt solutions are satisfactorily calculated by considering ions as association compounds over a wide range of temperature and salt concentration.

Solubility of carbon monoxide in bio-oil compounds

The solubility of carbon monoxide is measured in four different bio-oil compounds (furan, diacetyl, 2-methylfuran, and trans-crotonaldehyde) at temperatures (273.15, 283.15, 298.15, and 323.15K) and pressures up to 8MPa using a static-analytical VLE measurement method. The equipment was validated by measuring the solubility of CO2 in methanol at 298.15K and pressures (P=2.9–5.7MPa). The results were compared with the abundantly available literature values. PC-SAFT, Polar PC-SAFT (PPC-SAFT), and Cubic (SRK, PR) EoS, part of commercial process simulator Aspen Plus V. 8.6, are used here for modelling purpose. The pure component parameters needed for PC-SAFT and PPC-SAFT EoS models, are regressed using the experimental liquid density and vapour pressure data of the pure components. It was observed that furan, 2-methylfuran and diacetyl, having weak dipole moments (μ<1.0D), could be modelled reasonably well without the addition of polar contribution using conventional PC-SAFT, while it is recommended to use PPC-SAFT for the description of a polar compound like trans-crotonaldehyde (μ∼3.67D).It was observed that SRK and PR EoS have similar predictive ability in comparison to PC-SAFT for a mixture of CO with weakly polar compounds in this study. A comparison between the performances of EoS models was made in two ways: first by setting the binary interaction parameter kij to zero, and second by adjusting a temperature-dependent binary interaction parameter (kij). All the models perform with comparable accuracy with adjusted binary interaction parameters. However, due to the large differences between the chemical and physical properties of the compounds in this study, it is challenging to make a general statement on which is the best model.

SAFT-VR modelling of the surface and bulk properties of imidazolium and pyridinium based ionic liquids with ten different anions

Statistical associating fluid theory for potential of variable range has been used to provide an accurate thermophysical properties for 26 imidazolium and pyridinium-based families of ionic liquids (ILs) with different cationic structures combined with [PF6]−, [BF4]−, [NTf2]−, [Cl]−, [dca]−, [Triflate]−, [EtSO4]−, [lactate]−, [C(CN)3]− and [MeSO4]− anions. An appropriate set of molecular parameters were obtained by means of fitting the model predictions to experimental liquid densities over a wide temperature and pressure ranges. The overall absolute average relative deviation (AARD) between the calculated and experimental liquid densities is 0.12% over a wide range of temperature and pressure from 283 to 472K and 0.1–200MPa. The reliability and physical significance of the parameters were tested by calculation of thermodynamic derivative properties including isobaric thermal expansivity and isothermal compressibility of ILs. Moreover, the interfacial surface tension of ILs was calculated by density gradient theory (DGT) coupled with the SAFT-VR model. The results are in excellent agreement with the available experimental data.

Review of the BACKONE equation of state and its applications

ABSTRACTThis paper presents a review of the BACKONE equation of state (EOS) and its various applications in the study of pure fluid and mixtures as refrigerants, working fluids, natural gases and the study of heat pumps, refrigeration cycles, organic Rankine cycles, trilateral cycles and power flash cycles. It also presents an accurate parameterisation of the BACKONE EOS for the low global warming potential working fluid 3,3,3-trifluoropropene (HFO-1243zf). The average absolute deviations (AAD) between experimental vapour pressure and saturated liquid density data from those of the BACKONE EOS are 0.12% and 0.08%, respectively. The BACKONE EOS for HFO-1243zf also predicts thermodynamic data accurately. The AAD between the BACKONE predicted values and experimental data are 0.20% for sub-cooled liquid density and 0.56% for gaseous pressure.

Experimental Study on the Saturated Liquid Density and Bubble Point Pressure for R1234ze(E) + R290

Saturated liquid densities and bubble point pressures of trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) + propane (R290) binary mixture were measured at temperatures from (253.141 to 293.284) K and mole fractions of R1234ze(E) from (0.1746 to 0.8803) using a compact single-sinker densimeter. The standard uncertainties were estimated to be less than 5 mK for temperature, 600 Pa for pressure, 0.003 for mole fraction, and 0.01% for density. The experimental saturated liquid densities were reproduced by the VDNS and our modified Rackett density equations, while the experimental bubble point pressures were represented with the Patel–Teja (PT) equation of state. Good agreement between values of calculation and experiment were found for both saturated liquid densities and bubble point pressures. In addition, saturated vapor and liquid densities of azeotropy point at temperatures T = (258.150, 263.150, 273.150 and 283.150) K were determined.

Vapor–liquid phase equilibrium diagram for uranium hexafluoride (UF6) using simplified temperature dependent intermolecular potential parameters (TDIP)

The properties of uranium hexafluoride (UF6, CAS: 7783-81-5) are of importance to the nuclear industry as a precursor for the enrichment and product spent fuel reprocessing. This work is focused on obtaining the vapor–liquid equilibrium (VLE) curve for UF6 using temperature dependent intermolecular potential parameters (TDIP) as opposed to temperature independent intermolecular potential parameters (TIIP). TDIP indeed improves the simulated vapor–liquid coexistence curve, critical constants, and vapor pressure of UF6. However, both approaches need improvement since the predictions are still far from reproducing experimental saturated liquid density data for UF6.

Prediction of Radon-222 Phase Behavior by Monte Carlo Simulation

Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble are used to determine saturated liquid and vapor densities, vapor pressures, heats of vaporization, and compressibility factors for radon-222 from the normal boiling point to the critical point. An optimized intermolecular potential is developed by fitting parameters to reproduce experimental vapor pressures and the critical temperature. Vapor pressures are reproduced by simulation to within 2.2% of experiment, while the critical temperature and normal boiling point are reproduced exactly within the combined uncertainty of simulation and experimental data. The predictions of simulation are used to evaluate the reliability of reported experimental liquid densities, and those predicted by equations of state. While the predictions of simulation are in agreement with equations of state for the liquid density, significant differences are observed between the predictions of simulation and experiment. These results suggest that previously reported experimental liquid densities for radon-222 may be erroneous.

Extension of the LOPLS-AA Force Field for Alcohols, Esters, and Monoolein Bilayers and its Validation by Neutron Scattering Experiments.

The recently presented LOPLS-AA all-atom force field for long hydrocarbon chains, based on the OPLS-AA force field, was extended to alcohols, esters, and glyceryl monooleate (GMO) lipids as a model lipid. Dihedral angles were fitted against high level ab initio calculations, and ester charges were increased to improve their hydration properties. Additionally, the ester Lennard-Jones parameters were readjusted to reproduce experimental liquid bulk properties, densities, and heats of vaporization. This extension enabled the setup of LOPLS-AA parameters for GMO molecules. The properties of the lipid force field were tested for the liquid-crystalline phase of a GMO bilayer. The obtained area per lipid for GMO is in good agreement with experiment. Additionally, the lipid dynamics on the subpicosecond to the nanosecond time scale is in excellent agreement with results from time-of-flight (TOF) quasielastic neutron scattering (QENS) experiments on a multilamellar monoolein system, enabling here for the first time the critical evaluation of the short-time dynamics obtained from a molecular dynamics simulation of a membrane system.

Development of a novel Peng–Robinson plus association equation of state for industrially important associating compounds

Cubic plus association (CPA) equations of state (EoSs) have found great interest in describing thermodynamic properties of associating fluids. In CPA EoSs, the association contribution proposed by Wertheim is added to cubic EoSs such as Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). In different developments of CPA EoSs, adjusting the pure component properties such as critical temperature and critical pressure in addition to the association parameters is proposed in some works in the literature. In this work, the PR EoS has been extended to water, phenol, and a number of alcohols (methanol up to dodecanol) by addition of the Wertheim association contribution. In contrast to other CPA EoSs, the experimental values of critical properties are used. The energy and co-volume parameters of PR EoS are modified by introducing a correction factor that is correlated as a function of reduced temperature. The results show that this model is capable of reproducing experimental saturated liquid density and vapor pressure data accurately.

Optimized Mie potentials for phase equilibria: Application to noble gases and their mixtures with n-alkanes.

Transferrable force fields, based on n-6 Mie potentials, are presented for noble gases. By tuning the repulsive exponent, ni, it is possible to simultaneously reproduce experimental saturated liquid densities and vapor pressures with high accuracy, from the normal boiling point to the critical point. Vapor-liquid coexistence curves for pure fluids are calculated using histogram reweighting Monte Carlo simulations in the grand canonical ensemble. For all noble gases, saturated liquid densities and vapor pressures are reproduced to within 1% and 4% of experiment, respectively. Radial distribution functions, extracted from NVT and NPT Monte Carlo simulations, are in similarly excellent agreement with experimental data. The transferability of the optimized force fields is assessed through calculations of binary mixture vapor-liquid equilibria. These mixtures include argon + krypton, krypton + xenon, methane + krypton, methane + xenon, krypton + ethane, and xenon + ethane. For all mixtures, excellent agreement with experiment is achieved without the introduction of any binary interaction parameters or multi-body interactions.

Thermodynamic modeling of refrigerants solubility in ionic liquids using original and ϵ*-Modified Sanchez–Lacombe equations of state

Ionic liquids can dramatically improve the efficiency of absorption refrigeration processes due to their negligibly small vapor pressure; where the IL absorbs the refrigerant gas in one stage and subsequently releases the high-pressure gas upon addition of heat. In the current study, phase equilibrium data (P-T-x) of a diverse set of refrigerants in different types of ionic liquids are modeled with the aid of two equations of state based on lattice fluid theory, i.e. Sanchez–Lacombe and ϵ*-Modified Sanchez–Lacombe EOSs. The characteristic parameters of the pure components were determined from a database of 3086 experimental liquid density datapoints for 11 refrigerants and 12 ILs. According to the results obtained by considering the experimental data of 25 binary IL/refrigerant mixtures comprised of 88 isotherms with a total of 658 datapoints, both EOSs can successfully correlate the solubility data with AARDs of %5.773 and %5.771 for SL and ϵ*-Modified SL EOSs, respectively.

Simplified Flory-dimer equation of state for application to non-associating fluids, polymers and their mixtures

A simplified generalized Flory dimer (s-GFD) theory is developed to improve the performance of equation of state (EOS) for long chain molecules. The new EOS is formulated by a combination of the s-GFD theory and perturbed chain statistical associating fluid theory (PC-SAFT). Three pure component parameters are required for nonassociating fluids: the number of segments per molecules (m), the diameter of segments (σ), and the depth of intermolecular potential (ϵ/k). These parameters were obtained by correlating experimental liquid densities and vapor pressures for pure n-alkanes ranging from methane to eicosane. The pure component parameters of polyethylene (PE) were determined by extrapolating the pure component parameters of a series of n-alkanes. Comparisons to other EOSs are made up with the PC-SAFT and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). The proposed equation provides excellent correlation results for vapor pressures and liquid densities, particularly for long chain molecules and for PE of a broad range of molecular weights. The proposed model allows phase equilibrium calculations to be conducted for binary and ternary mixtures of volatile components without requiring the use of binary interaction parameters. Correlations were carried out for equilibrium behaviors of PE solutions by using one adjustable parameter, and the calculated results agreed well with experimental data.

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T 0, characteristic density ρ0, anisotropy factor α, and reduced quadrupolar moment Q*2. The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.

The role of monomer fraction data in association theories—Can we improve the performance for phase equilibrium calculations?

Monomer fraction (fraction of non-hydrogen bonded molecules) data obtained from spectroscopy are available for a few associating compounds. Such data can be used for testing the performance of association models like CPA and SAFT or alternatively be employed in the model development. But how accurate and how useful are such data today and how successful is their use in the context of association models? In this work we attempt to answer these questions in the case of the CPA model and for ethanol. CPA has been already successfully used to describe thermodynamic properties of many ethanol containing mixtures, using an ethanol parameter set that was adjusted to experimental vapor pressure and liquid density data. We present in this work a new parameter set for ethanol which is estimated using experimental vapor pressure, liquid density data as well as the experimental monomer fractions for liquid ethanol. Using both the existing (“old”) and the new parameter sets, we perform an extensive comparison of CPA results for a wide range of ethanol-containing systems, with water and alkanes as well as multicomponent water–ethanol–hydrocarbon liquid–liquid equilibria and hydrate curves with different ethanol content as inhibitor. There are some differences in the performance of CPA with the two sets but on average the results are similar. This may indicate that monomer fraction data are not very useful in this case or that ethanol monomer fraction data are not accurate and both possibilities are discussed.

Equations of state for HFO-1234ze(E) and their application in the study on refrigeration cycle

This paper aims to describe the thermodynamic properties of the HFO-1234ze(E) with the molecular based BACKONE and PC-SAFT equations of state (EOS) that can be easily extended to mixtures. This paper also evaluates the accuracies of the BACKONE, PC-SAFT, and multi-parameter EOSs. For the data used in the construction of the EOS, the average absolute deviations (AAD) between experimental vapour pressures, experimental saturated liquid densities and values from the BACKONE EOS are 0.34% and 0.42%, respectively. The AAD between experimental vapour pressures, experimental saturated liquid densities and those from the PC-SAFT EOS are 0.16% and 1.51%, respectively. The AAD between predicted compressed liquid densities, predicted isobaric heat capacities, predicted pressures in gaseous phase from the BACKONE EOS and experimental data are 0.60%, 2.29%, and 0.99%, respectively. The AAD between predicted compressed liquid densities, predicted isobaric heat capacities, predicted pressures in gaseous phase from the PC-SAFT EOS and experimental data are 1.35%, 2.91%, and 1.84%, respectively. An independent investigation for data used in the construction of the multi-parameter EOS shows that the AAD between experimental vapour pressures, experimental saturated liquid densities, experimental densities in compressed liquid, experimental isobaric heat capacities, experimental pressures in gaseous phase and those from the multi-parameter EOS are 0.55%, 0.17%, 0.07%, 2.21%, and 0.11%, respectively. The BACKONE, PC-SAFT, and multi-parameter EOSs are used in the investigation of a refrigeration cycle using HFO-1234ze(E) as refrigerant for air-conditioning application. The study shows that the relative differences of all investigated characteristics calculated from thermodynamic properties from these EOSs are mostly within 1%. The thermodynamic properties of HFO-1234ze(E), HFO-1234yf, R-134a, R22, and R32 from the most accurate EOSs are used in the investigation of a refrigeration cycle. The results show that the cycle using R1234ze(E) as refrigerant has the highest coefficient of performance.

Accurately modeling benzene and alkylbenzenes using a group contribution based SAFT approach

In recent work, the GC-SAFT-VR equation, which combines the SAFT equation for potentials of variable range (VR) with a group contribution (GC) approach, was proposed. Parameters for key functional groups (such as CH3, CH2, CH, CH2CH, CO, C6H5, ether, ester, OH, NH2, CHO, COOH) were obtained by fitting to experimental vapor pressure and saturated liquid density data for selected low molecular weight fluids and then used to predict the phase behavior of both pure non-associating and associating fluids and their mixtures, generally without adjusting the group parameters to binary mixture data. In the GC-SAFT-VR approach the benzene ring was modeled as a single group (C6H6 for benzene and C6H5, for alkylbenzenes) however, in common with other group-contribution based SAFT approaches, this approach fails to reproduce the correct curvature seen in the experimental liquid density of alkylbenzenes. In this work, to improve upon the model adopted for ring molecules, the benzene ring is explicitly considered through the connectivity of several smaller groups to more accurately capture the π–π interactions. We demonstrate that the improved model better captures the curvature present in the experimental saturated liquid density data of pure alkylbenzenes. Additionally, mixtures of several non-associating and associating fluids with benzene and alklybenzenes are studied.

Molecular simulation of the vapor–liquid phase behavior of cyanides and their binary mixtures

The vapor–liquid phase behavior of binary mixtures containing cyanogen, cyanogen chloride, hydrogen cyanide and acetonitrile is predicted by molecular simulation and compared to experimental data as well as the Peng–Robinson equation of state. Two new molecular force field models are presented for cyanogen and cyanogen chloride, molecular models for the other compounds are taken from preceding work. The parametrization of the present classical molecular interaction models is carried out on the basis of quantum chemical calculations and subsequent fitting to experimental vapor pressure and saturated liquid density data. To validate the present molecular models, vapor–liquid equilibria for the pure cyanides and 14 binary mixtures containing cyanides are calculated and compared with the available experimental data and the Peng–Robinson equation of state. In general, the simulation results are in good agreement with the experimental data.

Adsorption of hydrogen sulphide on Metal-Organic Frameworks

Three new sets of interatomic potentials to model hydrogen sulphide (H2S) have been fitted. One of them is a 3-sites potential (which we named 3S) and the other two are 5-sites potentials (which we named 5S and 5Sd). The molecular dipole of the 3S and 5S potentials is 1.43 D, which is the value usually employed for H2S potentials, while the dipole of the 5Sd is the dipole measured experimentally for the H2S molecule, circa 0.974 D. The interatomic potentials parameters were obtained by fitting the experimental vapour-liquid equilibrium, vapour pressure and liquid density curves. The potential parameters fitted so far for H2S have been obtained applying long-range corrections to the Lennard–Jones energy. For that reason, when a cut and shift of the Lennard–Jones potentials is applied they do not yield the correct results. We employed a cut and shift of the Lennard–Jones potentials in the fitting procedure, which facilitates the use of the new potentials to model H2S adsorption on systems such as Metal-Organics Frameworks (MOFs). We have employed the newly developed potentials to study the adsorption of H2S on Cu-BTC, MIL-47 and IRMOF-1 and the results agree with the available electronic structures calculations. All calculations (both quantum and interatomic potential-based) predict that H2S does not bind to the Cu atoms in Cu-BTC.