Perturbed Hard-sphere-chain Equation Of State Research Articles

Evaluation of the perturbed hard-sphere-chain equation of state for calculations of methane hydrate formation condition in the presence of ionic liquids

This work aims to evaluate the performance of the Perturbed Hard-Sphere-Chain (PHSC) equation of state (EoS) for the calculation of methane hydrate formation in the presence of ionic liquids (ILs). The van der Waals and Platteeuw model is utilized to calculate the hydrate dissociation pressure. The performance of the PHSC model is compared to cubic EoSs and the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) model. Two activity coefficient models are used to estimate the water activity in the presence of ILs. The results show that PHSC EoS with an activity coefficient model provides lower average error values (lower than 2%) and changing the activity coefficient models does not have a great effect on reducing the error. Also, the results of cubic-based EoSs are quite remarkable considering their simplicity. The PHSC model can be utilized as a robust and efficient thermodynamic model for hydrate dissociation pressure calculation in the presence of IL.

Prediction of azeotropes position of refrigerant mixtures using the PHSC EoS

The work aims is predict the azeotropes' position in refrigerant mixtures using the Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). The vapor-liquid equilibrium (VLE) of seventeen binary refrigerant mixtures has been correlated using two model-adjustable parameters. The results show that the proposed model can calculate the bubble and dew points of binary systems, accurately. The average ARD value of binary VLE calculations has been obtained 1.28 %. The azeotropes pressure and composition of binary mixtures have been predicted using the PHSC EoS with the average ARD values of 1.043 % and 2.23 %, respectively. The maximum relative deviation has been observed for R717+R125 systems with two azeotropes points; ARDx=12.2 %. The performance of the PHSC EoS has been evaluated by predicting the azeotropes position of ternary mixtures. The PHSC EoS results have been compared to three cubic-based EoSs containing the PR-vdW, PR-BM, and PR-MHV2-NRTL models. The results show that the PHSC EoS can predict the ternary VLE data and azeotropes position satisfactory. The relative absolute deviation does not exceed 1.7 % for the azeotropes pressure. The PHSC EoS can be used as a robust and efficient model for the prediction of the azeotropes' position in binary and ternary refrigerant mixtures. Prediction of azeotropic composition helps us to find promising refrigerant candidates in the pre-design stage of the desired apparatus.

Molecular modeling of systems related to the biodiesel production using the PHSC equation of state

In this study, capability of the Perturbed Hard Sphere Chain (PHSC) equation of state (EoS) is investigated for thermodynamic modeling of binary and ternary systems related to the biodiesel processing. Vapor-liquid, liquid-liquid and solid-liquid equilibria (VLE, LLE and SLE, respectively) in mixtures containing fatty acid alkyl ester, non – polar and polar compounds are investigated. The PHSC model parameters are calculated for both fatty acid methyl ester (FAME) and Fatty acid ethyl ester (FAEE) molecules by fitting on the experimental pure liquid density and vapor pressure data. Using the obtained parameters, the phase behavior of binary systems over wide range of thermodynamic conditions is studied. The average deviation between model calculations and experimental equilibrium data of water + ester, alcohol + ester, ester + ester, hydrocarbon + ester and carbon dioxide + ester systems are about 5.57, 2.42, 0.31, 3.61 and 6.45%, respectively. Furthermore, the capability of the model has then been assessed by prediction of LLE phase behavior of ternary systems. The results show that, the predicted and correlated results are in good agreement with the experimental data. In the case of SLE, the melting and eutectic points of fatty acid ester systems have been predicted over wide range of composition.

Calculation of NaCl, KCl and LiCl Salts Activity Coefficients in Polyethylene Glycol (PEG4000)–Water System Using Modified PHSC Equation of State, Extended Debye–Hückel Model and Pitzer Model

AbstractFor biomolecules and cell particles purification and separation in biological engineering, besides the chromatography as mostly applied process, aqueous two-phase systems (ATPS) are of the most favorable separation processes that are worth to be investigated in thermodynamic theoretically. In recent years, thermodynamic calculation of ATPS properties has attracted much attention due to their great applications in chemical industries such as separation processes. These phase calculations of ATPS have inherent complexity due to the presence of ions and polymers in aqueous solution. In this work, for target ternary systems of polyethylene glycol (PEG4000)–salt–water, thermodynamic investigation for constituent systems with three salts (NaCl, KCl and LiCl) has been carried out as PEG is the most favorable polymer in ATPS. The modified perturbed hard sphere chain (PHSC) equation of state (EOS), extended Debye–Hückel and Pitzer models were employed for calculation of activity coefficients for the considered systems. Four additional statistical parameters were considered to ensure the consistency of correlations and introduced as objective functions in the particle swarm optimization algorithm. The results showed desirable agreement to the available experimental data, and the order of recommendation of studied models is PHSC EOS > extended Debye–Hückel > Pitzer. The concluding remark is that the all the employed models are reliable in such calculations and can be used for thermodynamic correlation/predictions; however, by using an ion-based parameter calculation method, the PHSC EOS reveals both reliability and universality of applications.

Prediction of water vapor sorption in the polymeric membranes using PHSC equation of state

Dehydration of gas streams such as natural gas, flue gas and compressed air is a major process which has applications in the industry. The most common method for the dehydration of gas streams is the sorption method. Recently attention has been given to the use of membranes for the adsorption of water vapor from gas streams. In this study, water vapor sorption in the polymeric membranes including PEBAX-1074, SPEEK, PEO-PBT, NTDA and Nafion-117 has been modeled by using a thermodynamic model named perturbed-hard-sphere-chain (PHSC) equation of state (EoS) at temperatures 20–70 °C. PHSC equation of state is the sum of a hard-sphere-chain term as a reference system and a van der Waals attractive term as a perturbation term. PHSC equation of state for the simple fluids and spherical molecules contains two parameters which are ε, the well depth in molecular potential energy function, and σ, separation distance between segment centers of molecules. While this equation is used for the chain molecules such as polymers, the parameter r, the number of effective hard spheres per molecule is also required. The equilibrium calculations have been performed and results have been compared with the experimental data showing an overall average absolute deviation equal 0.53.

Vapor–liquid and liquid–liquid equilibrium calculations in mixtures containing non-ionic glycol ether surfactant using PHSC equation of state

In this study, vapor–liquid and liquid–liquid equilibrium in mixtures containing glycol ether surfactant, non-polar and polar compounds are calculated using Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). Pure liquid density and vapor pressure of surfactants are used for parameter estimation of glycol ether surfactants. The PHSC parameters are calculated for both ethylene glycol ether and propylene glycol ether surfactants. Glycol ether surfactant molecules are modeled as associating components by considering two association sites for each molecule. The results show that the PHSC model is capable of correlating thermodynamic behavior of binary (polar+surfactant) and (non-polar+surfactant) systems. Upper critical solution temperature (UCST) for hydrocarbon+surfactant and lower critical solution temperature (LCST) for water+surfactant systems are accurately calculated. The critical temperatures and the extent of immiscibility are in good agreement with the available experimental data.

Vapor–liquid phase behavior of the binary systems containing supercritical carbon dioxide

A thermodynamic model based on the perturbation theory is investigated. The perturbed hard-sphere chain (PHSC) equation of state (EOS) is applied to calculate phase behavior of the binary systems containing supercritical carbon dioxide. A calculation program is written. The vapor–liquid phase equilibrium calculation is conducted with the binary systems and a comparison is made between the calculation results and experimental ones. It is shown that the PHSC equation of state can be reliably used for calculating the vapor–liquid phase behavior of carbon dioxide systems when the pressure is very high.

Multiphase multicomponent equilibria for mixtures containing polymers by the perturbation theory

The correlating and predictive capabilities of a thermodynamic model based on the perturbation theory are investigated, with reference to mixtures containing components of different size and molecular interactions. The simplified Perturbed-Hard-Sphere-Chain (PHSC) equation of state is applied to a series of pure polymers, a number of solvents and pure carbon dioxide, and both volumetric and equilibrium properties are considered. The ability of the proposed model to reproduce experimental phase equilibrium data is discussed and tested with reference to binary and multicomponent mixtures, in the presence of vapor–liquid, liquid–liquid and vapor–liquid–liquid equilibria. Attention is focused on the ternary system polystyrene–cyclohexane–carbon dioxide, to test the proposed thermodynamic model in view of simulating supercritical antisolvent-induced fractionation processes. It is shown that the PHSC equation of state can be reliably used for calculating the phase behavior of such a complex system in different conditions.

Lower and Upper Critical Ordering Temperatures in Compressible Diblock Copolymer Melts from a Perturbed Hard-Sphere-Chain Equation of State

The random-phase approximation is combined with the perturbed hard-sphere-chain (PHSC) equation of state for copolymer systems to represent the microphase separation transition in compressible diblock copolymer melts. The PHSC equation of state takes into account the equation-of-state effect that results from differences in compressibility between pairs of segments comprising a diblock copolymer; these differences favor demixing. Upon increasing the temperature of a microphase-separated diblock copolymer melt, theory first predicts an order-to-disorder transition that corresponds to the upper-critical-solution-temperature behavior in the binary blend of parent homopolymers. At conditions where the equation-of-state effect is significant, theory also predicts a disorder-to-order transition at further elevated temperature that follows closely the lower-critical-solution-temperature behavior in the binary blend containing the parent homopolymers. To compare theory with experiment, we obtain the binary intera...

Liquid-liquid equilibria and theta temperatures in binary solvent-copolymer solutions from a perturbed hard-sphere-chain equation of state

The perturbed hard-sphere-chain (PHSC) equation of state for copolymer systems is used to calculate liquid-liquid equilibria for binary solvent/copolymer systems that exhibit simultaneously an upper critical solution temperature (UCST) and a lower critical solution temperature. The PHSC equation of state for copolymer solutions uses those binary parameters that represent liquid-liquid equilibria for the two parent homopolymer solutions. An additional intersegmental parameter is also required to define the interaction energy between a pair of chemically dissimilar segments comprising the copolymer molecule. Theory is compared with experiment for binary copolymer solutions containing poly(styrene-co-α-methylstyrene) random copolymers. Using the same K BC , the intersegmental parameter between styrene and α-methylstyrene segments, theory and experiment show fair agreement for the copolymer-composition dependence of theta temperatures associated with UCST in cyclohexane, methyl cyclohexane, and decalin. A comparison is also made between K BC obtained from the copolymer-solution data and that obtained from the coexistence curve of homopolymer blends containing polystyrene and poly(α-methylstyrene). Data for copolymer solutions require a K BC . that represents interactions more unfavorable than those in homopolymer blends.

Liquid-liquid equilibria for polymer solutions and blends, including copolymers

A simplified perturbed hard-sphere-chain (PHSC) theory is applied to interpret, correlate, and (in part) predict liquid-liquid equilibria (LLE) for polymer solutions and blends, including copolymers. The PHSC equation of state uses a hard-sphere-chain reference system plus a van der Waals attractive perturbation. Three pure-component parameters are obtained from readily available thermodynamic properties. Mixture parameters are obtained using pure-component parameters, conventional combining rules, and one or two binary constants. Theoretical and experimental coexistence curves and miscibility maps show good agreement for selected blends containing polymers and copolymers. For LLE of dilute or semi-dilute solvent/polymer solutions, it is necessary to decrease the pure-component polymer chain length in the perturbation term, probably because the mean-field approximation is not suitable for such solutions.

Equation-of-State Analysis of Binary Copolymer Systems. 3. Miscibility Maps

The perturbed hard-sphere-chain (PHSC) equation of state for copolymer systems is applied to binary polymer mixtures containing random copolymers. Intersegmental parameters are obtained for several pairs of segments, and theoretical miscibility maps are compared with experiment for systems containing two, three, and four kinds of segments. The PHSC equation of state is able to represent immiscibility caused by lower critical solution temperature (LCST) phase behavior as well as that caused by upper critical solution temperature phase behavior. For the system poly(methyl methacrylate)/poly-(acrylonitrile-co-styrene), theory represents the miscibility window caused by LCST behavior where miscibility changes from immiscible → miscible → immiscible as the composition of poly(acrylonitrile-co-styrene) random copolymer becomes rich in acrylonitrile. Using the same set of intersegmental parameters, theoretical miscibility maps and experiment show good agreement for systems containing styrene, acrylonitrile, methyl methacrylate, and cyclohexyl methacrylate.