Sphere Chain Equation Of State Research Articles

Prediction of CO2 solubility in electrolyte solutions using the e-PHSC equation of state

The aim of this work is to provide a reliable model to predict CO2 solubility in formation brines using an equation of state (EoS). In this regard, the electrolyte perturbed hard sphere chain equation of state (e-PHSC) was utilized to describe the solubility of carbon dioxide in aqueous electrolyte solutions. Using the ion-specific parameters and a binary interaction parameter between ions and CO2, CO2 solubilities in single electrolyte solutions (NaCl, KCl, CaCl2, MgCl2, Na2SO4, and K2SO4) were calculated. Then the model capability was evaluated for CO2 solubility in mixed-electrolyte solutions. Obtained results prove that e-PHSC EoS can be used for the prediction of CO2 solubility in mixed electrolyte solutions without any additional adjustable parameters. Finally, the predictive capacity of the e-PHSC EoS was explored for two synthetic formation brines up to 423 K. The result shows that the CO2 solubility in formation brines can be efficiently predicted using e-PHSC EoS.

Corrigendum to “Density and isothermal compressibility of ionic liquids from perturbed hard -sphere chain equation of state” [J. Mol. Liq. 174 (2012) 52–57

Abstract After a careful reconsideration of the article (S. M. Hosseini, M. M. Papari, J. Moghadasi, Journal of Molecular Liquids, 174 (2012) 52–57), several typos are appearing in some of the key equations of this article which would not allow the readers to utilize the underlying equation of state for the calculation of volumetric properties of pure ionic liquids without any problem. Regarding this, Erratum is presented to fix this issue.

Modelling of wax deposition by perturbed hard sphere chain equation of state

This article presents a model to predict the wax appearance temperature (WAT) and the quantity of wax deposition in eight different n-alkane mixtures using a correlative technique. The perturbed hard sphere chain equation of state (PHSC EoS) was employed in conjunction with the multi-solid model to describe the liquid-liquid and solid-liquid equilibria. The results are compared with experimental data. The results showed that PHSC EoS for some mixture of n-alkanes can perceptibly outperform the sole solid solution theory, improving the modelling of wax deposition quantities and wax appearance temperature by giving predictions closer to experimental values.

Thermodynamic modeling of hydrogen solubility in a series of ionic liquids

In this study, the Perturbed Hard Sphere Chain Equation of State (PHSC EoS) has been employed to predict the hydrogen solubility in a series of ionic liquids. As ionic liquids have no vapor pressure and no critical parameters and as hydrogen is a light molecule which behaves like a perfect gas, simple cubic equations of state cannot be used for modeling of H2 + ionic liquid mixture. Three main parameters of non-cubic PHSC EoS, i.e. (r) the number of segments per molecule, (σ) the distance between two molecules at zero potential and (ε) well-depth of potential between two non-bonded units have been calculated by regression of the experimental Pressure-Volume-Temperature (PVT) data points. The hydrogen solubility decreases with increasing temperature in [BMIM][BF4], [BMIM][C8SO4], [EMIM][EtSO4], [MDEA][Cl], and [N4,1,1,1][Tf2N], but inverse temperature effect is observed in [BMIM], [BMPY], [EMIM] and [HMIM][Tf2N] as well as [BMIM][MeSO4]. The binary interaction parameter which has been obtained from fitting of the equation of state with experimental hydrogen absorption data shows both the usual and the opposite trend of temperature effect as well.

Renormalization group corrections to the modified perturbed hard sphere chain equation of state for vapor liquid equilibria and interfacial tension of pure and binary mixtures

The interfacial tensions of pure fluids and binary fluid mixtures are described following an investigation of phase behavior. A modified version of the perturbed hard sphere chain (PHSC) equation of state (PHSC-CL EOS) is developed by applying the chain length dependence contribution to the PHSC EOS. The density gradient theory (DGT) is combined with the proposed model to account for both the phase equilibria and the interfacial tension. The influence parameter, the only input of the DGT with EOS to calculate the interfacial tension of the fluid, is considered an adjustable parameter for each fluid. The PHSC-CL EOS accurately describes the vapor liquid equilibria (VLE) and interfacial tensions of fluids away from the critical region. It is combined with a renormalization group theory to consider the contribution of long range fluctuations in the near critical region. The calculation procedure is based on White's work and the phase space cell approximation is adopted for mixtures. The VLE and interfacial tensions are obtained with good agreement to experimental data for linear alkanes, cyclo hexane, benzene, toluene, carbon dioxide, and their binary mixtures.

Thermodynamic modeling of CO2 absorption in 1-butyl-3-methylimidazolium-based ionic liquids

There are a number of methods to capture the carbon dioxide; among them ionic liquids are the recent magical solvents as gas absorption agents. To understand and predict the phase behavior of CO2+ionic liquid mixtures, a convenient thermodynamic model such as an equation of state is required. In this study, Perturbed Hard Sphere Chain Equation of State (PHSC) has been selected to model CO2 absorption in a series of ionic liquids including 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4], 1-butyl-3-methylimidazolium hexafluorophosphate [BMIM][PF6], 1-butyl-3-methylimidazolium methylsulfate [BMIM][MeSO4], 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl−mide) [BMIM][Tf2N]. Three molecular-based parameters, i.e. hard-sphere diameter, the non-bonded interaction energy and the number of segments per molecule have been employed as scaling constants. It is the advantage of PHSC EoS that works satisfactorily by regression of only one binary interaction parameter. The binary interaction parameter is enhanced with rising temperature due to the lower interaction of CO2 with ionic liquids.

Thermodynamic modeling of wax disappearance temperature in n-alkane mixtures by perturbed hard sphere chain equation of state

In this study, the perturbed hard sphere chain equation of state (PHSC EoS) has been used for the prediction of the wax disappearance temperature (WDT) in n-alkane mixtures. The PHSC EoS can thermodynamically predict the properties of high-molecular-weight compounds and chain-like molecules. The WDT of binary and ternary n-alkane mixtures have been predicted thermodynamically without using any fitting parameter. The liquid and solid phases are described by PHSC EoS based on multi-solid phase theory. The results have shown that the PHSC EoS is capable to predict the WDT of a n-alkane mixture by reasonable accuracy in comparison with experimental data.

Prediction of CO2 solubility in ionic liquids with [HMIM] and [OMIM] cations by equation of state

The discovery of various ionic liquids which can effectively absorb CO2 from flue gases motivated us to study the phase behavior of carbon dioxide with ionic liquids. A convenient thermodynamic model such as an equation of state is required for predicting structure–property relationship. In this study, Perturbed Hard Sphere Chain Equation of State (PHSC) has been selected to model CO2 absorption in a series of ionic liquids including 1-hexyl-3-methylimidazolium tetrafluoroborate [HMIM][BF4], 1-hexyl-3-methylimidazolium hexafluorophosphate [HMIM][PF6], 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [HMIM][Tf2N], 1-octyl-3-methylimidazolium tetrafluoroborate [OMIM][BF4], 1-octyl-3-methylimidazolium hexafluorophosphate [OMIM][PF6] and 1-octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [OMIM][Tf2N]. Using three molecular-based parameters plus regression of only one binary interaction parameter is sufficient for PHSC EoS to achieve noticeable modeling purposes.

A perturbed hard sphere chain equation of state for refrigerants

The present work shows a successful extension of a recently developed modified perturbed hard sphere equation of state to liquid refrigerants. Our objective is the prediction of a reliable model to describe the volumetric properties of refrigerants. In this regard, we have applied our previously developed equation of state to R12, R13, R13b1, R22, R23, R32, R123, R124, R134a, R141b, R142b, R143a, R170, R218, R227ea, R290, R1150 and R1270. Two temperature dependent parameters which are universal functions of the reduced temperature and just one adjustable parameter that can be calculated by fitting to a few experimental data exist in this equation of state. Boiling point constants are utilized as scaling factors. In order to evaluate the model, we compared the predicted densities to the literature data. This led to very encouraging results. The results of four other equations of state are presented for comparison. Our results seem to be promising in view of application to mixtures of refrigerants and long-chain hydrocarbons. In this respect the paper can be regarded as a necessary step towards the prediction of the mixture behavior of refrigerants and the effect of the presence of the lubricant oil in the mixture.

Sorption of methane in a series of Zn-based MOFs studied by PHSC equation of state

Adsorption and storage of gaseous methane as a clean fuel for cars has always attracted the attention of researchers. One of the most famous porous absorbents which has been used for separation and storage of several gases is called metal organic framework (MOF). These kinds of absorbents have been intensely studied in recent years. In this study, the experimental data related to methane adsorption on and desorption from five absorbents, namely, MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 have been adopted. Then, the methane sorption has been modeled by applying Perturbed Hard Sphere Chain Equation of State (PHSC EoS). PHSC equation of state has three molecular-based parameters, r, σ and ɛ; which are the number of segments per molecule, the hard-sphere diameter and the non-bonded interaction energy, respectively. These three parameters have been calculated using the group contribution (GC) method. The amount of methane uptake in the adsorbents has been obtained through gas-absorbents phase equilibrium calculations at temperature 298K and various pressures up to 90×105Pa. Finally, results have been compared with the experimental data to show the precision of PHSC equation of state in predicting the methane sorption trend.

Hydrogen storage in a series of Zn-based MOFs studied by PHSC equation of state

One of the most famous porous adsorbents used for separation and storage of several gases is metal organic framework (MOF). In this study, the experimental data related to hydrogen adsorption on and desorption from five adsorbents including MOF-5, MOF-177, MOF-200, MOF-205 and MOF-210 is adopted. Then, the hydrogen sorption is modeled by applying Perturbed Hard Sphere Chain Equation of State (PHSC EoS). PHSC equation of state has three molecular-based parameters, namely, the number of segments per molecule, the hard-sphere diameter and the non-bonded interaction energy, respectively. The amount of hydrogen uptake in the adsorbents is obtained through gas-adsorbents phase equilibrium calculations at temperature 77 K and various pressures up to 80 × 105 Pa. Finally, the result is compared with the experimental data to show the precision of PHSC equation of state in predicting the hydrogen sorption trend.

Sorption of CO2, C2H2 and C2H4 in HOF-1a studied by PHSC equation of state

Acetylene is a byproduct of modern ethylene production by cracking of hydrocarbons. There are extensive research efforts to exchange solvent extraction and hydrogenation methods for removing acetylene from ethylene with cost-effective membrane separation technology. Recently, the first Hydrogen-bonded Organic Framework (HOF) has been established to examine its capacity for acetylene uptake. In this study, Perturbed Hard Sphere Chain equation of state (PHSC) has been selected to obtain volumetric data for CO2, C2H2 and C2H4 sorption on HOF-1a system. Three molecular-based parameters including hard-sphere diameter (σ), the non-bonded interaction energy (ɛ) and number of segments per molecule (r) have been employed as scaling constants and calculated using group contribution (GC) method. High capacity of HOF-1a has been demonstrated for C2H2/C2H4 separation. C2H2 and C2H4 coupling effects in the mixed gas sorbed in HOF-1a, have been extracted from PHSC EoS for mixture sorption. The sorption of acetylene decreases in the presence of ethylene while sorption of ethylene increases in the presence of acetylene. HOF-1a has high capacity to sorb C2H2 as an impurity in industrial gas separation, but its low selectivity causes the loss of ethylene which makes it economically detrimental.

Calculation of the Density and Activity of Water in ATPS Systems for Separation of Biomolecules

In this study, the perturbed hard sphere chain equation of state is utilized to calculate the activity of water in binary and ternary solutions of polyethylene glycol (PEG), salt and water. The liquid density of the binary and ternary solutions is also predicted. To estimate the water activity in PEG–water binary systems, a linear correlation is obtained for the binary interaction parameter between water and PEG. Then, using this correlation and without introducing any additional binary parameters, the water activities are predicted in ternary solutions of water, salt and PEG with different molecular weights (MW). Our results show that the mean absolute average relative deviation (AARD %) of water activity for binary PEG–water solutions in 298 K is 0.73 %. In addition, the water activity in ternary solutions of water and two PEGs with different MW is predicted within 0.31 % AARD %. Furthermore, the AARD % for prediction of water activities in binary PEG–water solutions over the temperature range 308–338 K is 0.41 %. Also, the water activities of aqueous two-phase systems are predicted with AARD % = 0.64 %. In this regard, no adjustable parameters were correlated between salt and PEG. Finally, liquid densities were predicted in binary solutions of water–PEG and ternary solutions of water–PEG–salt.

Application of PHSC equation of state in prediction of gas hydrate formation condition

In this work the modified perturbed hard sphere chain equation of state (PHSC), coupled with Van der waals Platteuw model, has been used for prediction of gas hydrate formation (dissociation) conditions. The PHSC EOS has been modified using association and electrostatic contributions. In order to evaluate the capability of the PHSC EOS, the hydrate formation conditions of various pure as well as mixed gases in the presence and absence of the thermodynamic inhibitors such as methanol, ethanol, mono ethylene glycol(MEG), NaCl, KCl and CaCl2 have been studied. In the absence of inhibitors, the pure gas hydrate formation conditions have been predicted within 3.4% absolute average relative deviation. The hydrate formation condition of gas mixtures have been predicted within AARD 4.6%. In the presence of organic inhibitors and single electrolyte 6.1% and 5.8% AARD has been observed respectively. A total of 102 systems have been studied; our results showed that the PHSC EOS is capable of prediction of hydrate formation condition with reasonable absolute average relative deviation (AARD) from experimental data.

Precipitation of lutein and co-precipitation of lutein and poly-lactic acid with the supercritical anti-solvent process

The supercritical anti-solvent (SAS) process has been used to re-crystallize lutein from ethyl acetate solutions. The influence of several process parameters (pressure, temperature, initial concentration, CO 2 and solution flowrates) on the particle size and morphology have been studied. The results have been compared to these obtained with other carotenoids (β-carotene and lycopene) with similar operating conditions, and have been interpreted with the aid of a phase equilibrium model based on the perturbed hard sphere chain equation of state. Large differences in particle size have been observed between the experiments performed in the two-phase and the single-phase regions of the vapor–liquid phase diagram. A change in the particle morphology, from agglomerated microparticles to polygonal crystals, has been observed when the CO 2/solution flow ratio was increased or the initial concentration was decreased. As a result of the precipitation, the purity of the lutein has been increased from 75% to over 90%. The co-precipitation of lutein with poly-lactic acid (PLA) has also been studied. A reduction in the particle size with the polymer/drug ratio has been observed, down to a minimum diameter of 1–5 μm.

Molecular dynamics simulations of real systems: application to chloro-fluoro-hydrocarbons and polymers

The present paper reports the results obtained from MD calculations on the following systems: (1) chloro-fluoro-hydrocarbons (CFHs) of widespread use in the refrigerant industry (e.g., R22, R32, R123, etc.) and (2) selected polymers of industrial applications. In the case of CFHs, force field and quantum-mechanical techniques were employed in molecular modeling and for the calculation of geometrical and chemico-physical parameters. The Connolly surface algorithm, corrected for quantum-mechanical effects, was used in the evaluation of molecular surfaces and volumes. From these data, the parameters of the perturbed hard sphere chain equation of state, V* and A*, were obtained. The third parameter, E*, was calculated from extensive MD simulations under NPT conditions. For polymers, a more complicated preliminary procedure was necessary to model realistic amorphous polymeric chains. The Lattice Fluid equation parameters were then calculated from thorough MD simulations both under NVT and NPT conditions. The predicted thermophysical properties of both classes of substances are then discussed and compared with the relevant experimental data, were available.

A perturbed hard sphere chain equation of state for applications to hydrofluorocarbons, hydrocarbons and their mixtures

The evaluation of thermodynamic properties of pure hydrofluorocarbons and hydrocarbons, and their binary mixtures is considered. A modification of the perturbed-hard-sphere-chain equation of state is applied to these compounds and tested on a large database of refrigerants, hydrocarbons and their mixtures, with reference to both volumetric and equilibrium properties. The ability of the proposed model to reproduce experimental values is discussed. First, the theoretical background of the model is revisited in order to obtain a predictive method for the ‘a priori’ calculation of the values of parameters which reflect the size, shape and interaction energy of the molecule (three parameters for each pure component). Expressions to predict these values as a function of molecular quantities are presented and it is shown that the proposed model can be reliably used for calculating the properties of pure refrigerants and hydrocarbons,starting from the Bondi volume and surface area values, and the vapor pressure curve (2% errorin the PVT behavior at worst). Then, the extension to mixtures is addressed. Attention is focusedon the evaluation of binary interaction parameters ( k ij ) for systems of refrigerant–refrigerant, hydrocarbon–refrigerant and hydrocarbon–hydrocarbon type. Vapor–liquid equilibrium data of eighteen binary systems at several temperatures have been regressed, with errors in pressure ranging below 2% for refrigerant and below 1% for hydrocarbons when using a single value of k ij for each binary pair, independent of temperature.

Effect of pressure on solid-liquid equilibrium for the system carbon dioxide/n-decane/n-octacosane

Solid-liquid saturation lines (pressure vs temperature for a saturated solution of given composition) were determined for n-octacosane in mixtures of n-decane and carbon dioxide. The carbon dioxide content of the solutions ranged from 0 to 90 mol %, at pressures up to 25 MPa. The data were correlated by means of the perturbed hard sphere chain equation of state. The equation of state requires three pure component constants for each component plus three binary interaction parameters. Two of the interaction parameters were obtained from binary data. The third was adjusted to fit the ternary data. The correlation was satisfactory for carbon dioxide contents up to 80 mol %. For higher carbon dioxide levels the octacosane solubility predicted by the correlation was consistently low.