COMPARISON OF A PAIR OF THREE PARAMETER EQUATIONS OF STATE

The lattice fluid (LF) equation of state derived by Sanchez and Lacombe from a lattice model is compared to the empirical Peng-Robinson (PR) equation for normal alkane fluids ranging from methane to heptadecane in molecular weight. With respect to vapor pressure predictions, the equations are both good. The LF equation is superior, especially for higher molecular weight fluids, to the Peng-Robinson equation in predicting saturated liquid densities. For carbon numbers less than 6, the PR equation predicts heats of vaporization more accurately, whereas for carbon numbers greater than 9 the LF equation is more accurate than the PR one for temperatures lower than about 95% of critical.     

AN IMPROVED PENG-ROBINSON EQUATION OF STATE WITH A NEW TEMPERATURE DEPENDENT ATTRACTIVE TERM

An improved form of the Peng-Robinson cubic equation of state has been proposed. The temperature dependence of the attractive term has been modified so as to accurately represent vapor pressures of several fluids with large acentric factors from triple point to close to the critical point. The prediction of saturated liquid volume is also improved by introducing volume translation term in the equation of state. Comparisons of theoretical results with experimental data are made for the vapor/liquid phase equilibria of 44 pure fluids including nonpolar, polar and associating fluids. Our results show that the modified Peng-Robinson equation of state can represent accurately saturated vapor pressures of the fluids investigated in this paper, and it is more accurate than the Peng-Robinson equation of state and its earlier modifications due to Stryjek and Vera (1986) and Twu et al. (1995rpar;. Incorporation of the volume translation term in the equation of state has been found to improve the accuracy of saturated liquid volume significantly.     

Prediction of the infinite-dilution partial molar volumes of organic solutes in supercritical carbon dioxide using the Kirkwood-Buff fluctuation integral with the hard sphere expansion (HSE) theory

Two thermodynamic models were used to predict the infinite dilution partial molar volumes (PMVs) of organic solutes in supercritical carbon dioxide: (1) the Kirkwood Buff fluctuation integral with the hard sphere expansion (HSE) theory incorporated (KB-HSE fluctuation integral method) and (2) the Peng-Robinson equation of state with the classical mixing rule. While an equation of state only for pure supercritical carbon dioxide is needed in the KB-HSE fluctuation integral model, and thus, there is no need to know the critical properties of solutes, two molecular parameters (one size parameter σ₁₂ and one dimensionless parameter α₁₂) in the KB-HSE fluctuation integral model are determined to fit the experimental data published on the infinite dilution PMVs of solutes. The KB-HSE fluctuation integral method produced better results on the infinite dilution PMVs of eight organic solutes tested in this work than the Peng-Robinson equation of state with the classical mixing rule.     

PREDICTION OF MOLAR VOLUMES, VAPOR PRESSURES AND SUPERCRITICAL SOLUBILITIES OF ALKANES BY EQUATIONS OF STATE

A generalized cubic equation of state which can represent all the cubic equations is introduced and thermodynamic property relations for it are presented. Five cubic equations of states with respective mixing rules are used to predict molar volumes and vapor pressures of pure alkanes (from methane till n-tritriacontane) and solubilities of solid wax components (high molecular weight alkanes) in supercritical solvents. They are the RK (Redlich-Kwong), MMM (Mohsennia-Modarress-Mansoori), RM (Riazi-Mansoori), PR (Peng-Robinson), and SRK (Soave-Redlich-Kwon) equations of state. The experimental data necessary to compare the equations of state are taken from the literature. It is demonstrated that the SRK equation of state is more accurate for predicting vapor pressures of alkanes. The RM equation of state is shown to be more accurate for predicting molar volumes of saturated and sub-cooled liquid alkanes as well as molar volumes of alkanes in their supercritical condition. For the solubility of wax components in supercritical solvents it is shown that the MMM equation of state gives the least AAD% for the 270 data points of 10 binary systems studied consisting of a high molecular weight alkane and supercritical ethane and carbon dioxide.     

Solubility of hinokitiol in supercritical fluids; measurement and correlation

Supercritical fluid technology has been an alternative for purification and separation of biological compounds in cosmetic, food, and pharmaceutical products. Solubility information of biological compounds in supercritical fluids is essential for choosing a supercritical fluid processes. The equilibrium solubility of hinokitiol was measured in supercritical carbon dioxide and ethane with a static method in the pressure range from 8 to 40MPa and at temperatures equal to 313.2, 323.2 and 333.2 K. The experimental data were correlated well by Peng-Robinson equation of state and quasi-chemical nonrandom lattice fluid model.     

Application of the kirkwoodbuff solution formalism and the hard sphere expansion method with the modified mean density approximation to predict solubility of solutes in supercritical fluids

The Kirkwood-Buff solution theory to give the relations between macroscopic thermodynamic properties and the fluctuation integrals (G_ij) was utilized to predict solubility of solutes in supercritical fluids. The solvent-solute fluctuation integral (G₂₁) in the derivation for solubility of solute is expressed in terms of the solvent-solvent fluctuation integral (G₁₁) using the hard sphere expansion (HSE) conformal solution method with the modified mean density approximation (MMDA) where the scaling factor (R₁₂) represents the ratio of the first peak heights of the radial distribution functions for the mixture and the reference fluid having the mean density determined from the mean density approximation (MDA). The values of R₁₂ were evaluated by considering it as an adjustable parameter and solving the Ornstein-Zernike equation with the hypernetted chain (HNC) closure, and were compared. It is shown that solubility can be evaluated with an equation of state for pure supercritical fluid, three molecular parameters, and the scaling factor (R₁₂) without knowledge of critical properties of solutes, which can not be measured precisely for some organic solids. This model based on the molecular theory leads to better results in solubility calculations than both the Peng-Robinson equation of state with the classical mixing rule and the previous method with the original MDA instead of the MMDA. It might be due to the superiority of the MMDA over the original MDA.     

A comparison among three equations of state in predicting the solubility of some solids in supercritical carbon dioxide

Equations of state play an important role in chemical engineering designs, and they have assumed an expanding role in the study of the phase equilibria of fluids and fluid mixtures. In this report, a modified Peng-Robinson equation of state by Danesh et al., a modified Peng-Robinson equation of state by Gasem et al., and the Mansoori-Mohsen Nia-Modarress equation of state are used to predict the solubility of some solids in supercritical carbon dioxide. The systems studied were binary mixtures containing supercritical carbon dioxide with Ascorbic acid, Ascorbyl palmitate, Butyl hydroxyl anisole, Dodecyl gallate and Propyl gallate. Interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in each calculation is displayed.     

IMPROVING CUBIC EQUATIONS OF STATE FOR HEAVY RESERVOIR FLUIDS AND CRITICAL REGION

It is shown that by considering the “b” parameter in a cubic equation of state (EOS) as acentric factor/temperature-dependent, liquid densities especially for heavy compounds and the region near the critical point can be estimated more accurately. The proposed equation can also be used for accurate estimation of critical compressibility factors of different compounds, Although the method is applied to Peng-Robinson equation of state (PR-EOS), it can be used for any other cubic equation of state. The proposed method is particularly useful for phase equilibrium calculations of reservoir fluids. The proposed equation requires critical temperature, critical pressure and acentric factor as the input parameters. The proposed equation of stale estimates properties of liquids, vapor-pressure and critical compressibility factors with greater accuracy for pure compounds and mixtures as well as light and heavy compounds found in reservoir fluids.     

Rheology of PVAc–MMT–STAB

Polyvinyl acetate (PVAc) is considered to be an acceptable environmental friendly adhesive, and montmorillonite (MMT) is a cheap and accessible natural nano-mineral. In this work, MMT was first organically activated by octadecyl trimethyl ammonium bromide (STAB). The intercalated nano-composite, MMT–STAB, was then polymerized with VAc. The influence of various additions of MMT–STAB on the rheology of PVAc–MMT–STAB was analysed using the power-law function equation and the Cross–Williamson model viscous equation. The results showed that MMT–STAB was able to improve the rheology of PVAc. The PVAc and PVAc–MMT–STAB all were pseudo-plastic non-Newtonian fluids, with a flow index (i) of 0.93. The apparent viscosity (η), fluid consistency (Ï), characteristic time of materials (ζ), zero shear viscosity (η ₀), weight average molecular weight (M _w), number average molecular weight ( M _n) and the solid content (O), all increased with increasing additions of MMT–STAB as a result of the polymerization process. All properties, apart from ζ, showed a maximum with the addition of 2.0 wt%. The limiting viscosity (η _∞) was 0 mPa s for all samples of PVAc or PVAc–MMT–STAB. Their storage stability was found to be excellent. The reasonable addition of MMT–STAB in polymerization was found to be no more than 2.0 wt% of VAc. In addition, both PVAc and PVAc–MMT–STAB exhibited the normal stress effect (or Weissenberg effect), also known as the 'pole-climbing phenomenon'.     

Calculation of pure compound saturated enthalpies and saturated volumes with the PRSV equation of state. Revised k1 parameters for alkanes

The Stryjek-Vera (1986a) modification of the Peng-Robinson (1976) equation of state has been used to predict heats of vaporization, enthalpies of saturated phases and saturated volumes for pure compounds ranging in molecular complexity from diatomic gases to compounds showing polarity and association. Heats of vaporization at the normal boiling temperature are reproduced within 2% for the majority of the compounds tested. Similar results were obtained for the enthalpy of the saturated phases. Revised k₁ parameters of the PRSV equation of state are reported for alkanes. An empirical correction has been developed for calculating saturated liquid volumes from the liquid volumes given by the PRSV equation of state. For the range of reduced temperatures from 0.5 to 0.99, deviations from experimental values are smaller than 4%. Saturated vapor volumes calculated from the PRSV equation of state were found to be satisfactory for most technical calculations.     

Synthesis of 9‐(4‐nitrophenylsulfonyl)‐9H‐carbazole: Comparison of an impedance study of poly[9‐(4‐nitrophenylsulfonyl)‐9H‐carbazole] on gold and carbon fiber microelectrodes

In this study, 9‐(4‐nitrophenylsulfonyl)‐9H‐carbazole (NPhSCz) monomer was chemically synthesized. The monomer characterization was performed by Fourier transform infrared spectroscopy, ¹H‐NMR, and melting point analysis. Two different electropolymerizations of NPhSCz were studied on a gold microelectrode (Au electrode) and carbon fiber microelectrodes (CFMEs) in a 0.1M sodium perchlorate (NaClO₄)/acetonitrile solution. The electropolymerization experiments were done from 1 to 4 mM. The characterizations of two different modified electrodes of poly[9‐(4‐nitrophenylsulfonyl)‐9H‐carbazole] [poly(NPhSCz)] were performed by various techniques, including cyclic voltammetry, scanning electron microscopy–energy‐dispersive X‐ray analysis, and electrochemical impedance spectroscopy (EIS). The effects of the initial monomer concentrations (1, 2, 3, and 4 mM) were examined by EIS. The capacitive behaviors of the modified electrodes were defined via Nyquist, Bode magnitude, Bode phase, and admittance plots. The variation of the low‐frequency capacitance (C_LF) and double‐layer capacitance (C_dl) values are presented at different initial monomer concentrations. Poly(NPhSCz)/CFME was more capacitive (C_LF = 6.66 F/cm² and C_dl ≈ 28 mF) than the Au electrode (C_LF = 6.53 F/cm² and C_dl ≈ 20 mF). An equivalent circuit model of R[QR(CR)(RW)](CR), (R: Current, Q: Constant phase element, C: Double layer capacitance, W: Warburg impedance), was used to fit the theoretical and experimental data. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

A novel equation of state (EOS) for prediction of solute solubility in supercritical carbon dioxide: Experimental determination and correlation

Solubility data of organophosphorous metal extractants in supercritical fluids (SCF) are crucial for designing metal extraction processes. We have developed a new equation of state (EOS) based on virial equation including an untypical parameter as BP/RT, reduced temperature and pressure for prediction of solute solubility in supercritical carbon dioxide (SC CO₂). Solubility experimental data (solubility of tributylphosphate in SC CO₂) were correlated with the two cubic equations of state (EOS) models, namely the Peng–Robinson EOS (PR‐EOS) and the Soave–Redlich–Kwong EOS (SRK‐EOS), together with two adjustable parameter van der Waals mixing and combining rules and our proposed EOS. The AARD of our EOS is significantly lower than that obtained from the other EOS models. The proposed EOS presented more accurate correlation for solubility data in SC CO₂. It can be employed to speed up the process of SCF applications in industry.     

Expanded ensemble Monte Carlo simulations for the chemical potentials of supercritical carbon dioxide and hydrocarbon solutes

We carry out expanded ensemble Monte Carlo simulations in order to calculate the chemical potentials of carbon dioxide as solvent and those of hydrocarbons as solutes at supercritical conditions. Recently developed adaptive method is employed to find weight factors during the simulation, which is crucial to achieving high accuracy for free energy calculation. The present simulation method enables us to obtain chemical potentials of large solute molecules dissolved in compressed phase from a single run of simulation. Simulation results for the excess chemical potentials of pure carbon dioxide at 300, 325 and 350 K are compared with experimental data and values predicted by the Peng-Robinson equation of state. A good agreement is found for high pressures up to 500 bar. The chemical potentials of hydrocarbon solutes dissolved in carbon dioxide at infinite dilution are predicted by simulation. Less than eight intermediate subensembles are required to gradually insert (or delete) hydrocarbon solute molecules from methane to noctane into dense CO₂ phase of approximately 1.0 g cm⁻³.     

A FOUR-PARAMETER EXTENSION OF MODIFIED LEE-KESLER EQUATION OF STATE

A modified Lee-Kesler equation of state has been proposed to improve the accuracy for the subcooled and saturated liquid regions of normal fluids. It is further extended to polar fluids by the addition of a fourth parameter X. The extended equation has been found to be reliable over a wide vapor and liquid regions for polar fluids and it is easy for computer use. Fourteen kinds of normal fluids and twelve kinds of polar fluids have been tested. The total average absolute deviations for the normal fluids and polar fluids are 0.79% and 1.68% over the range of T_r = 0.3 to 4 and P_r - 0.01 to 10.     

A MODIFIED PENG-ROBINSON EQUATION OF STATE

A modified form of the Peng-Robinson equation of state is proposed. This equation shows its greatest advantage in the predictions of the volumetric properties in the single-phase region for mixtures, while it performs as good as original Peng-Robinson equation for the predictions of thermodynamic properties of pure components, and vapor-liquid equilibria of mixtures. Also the equation gives apparently more realistic Joule-Thomson inversion curves than both the SRK and PR equations.     

Difference in the rates of evaporation and condensation in the presence of an inert gas

On the basis of experimental data on the non-steady-state evaporation and the subsequent condensation of vapors of a substance on a flat cooled surface in the presence of an inert gas, the existence of the molecular and convective regimes of the condensation of vapors depending on the ratio of the molecular weights of the components of a gas-vapor mixture is found for the first time. It is shown that the kinetics of the evaporation-condensation processes differs: if the molecular weight of a vapor M _A is more than the molecular weight of an inert gas M _B, evaporation occurs in the molecular regime and condensation takes place in the convective regime; if M _A is less than M _B, the regimes of the processes change to the opposite ones. The results of experiments performed using ethyl acetate-air, ethanol-air, carbon tetrachloride-air, methanol-air, water-air, and water-helium systems are in satisfactory agreement with the results calculated by the proposed equation. Procedures for studying the dynamics of condensation and evaporation are described.     

Electrocoated Films of Poly(N-Methylpyrrole-co-2,2′-Bithitiophene-co-3-(Octylthiophene)), Characterizations,and Capacitor Study

N-Methylpyrrole (N-MPy), 2,2′-bithiophene (BTh), and 3-(Octylthiophene) (OTh) were electrocopolymerized in 0.2 M NaClO₄/CH₃CN on glassy carbon electrode (GCE). The resulting terpolymers of N-MPy, BTh and OTh in different initial monomer feed ratios such as [N-MPy]₀/[BTh]₀/[OTh]₀ = 1/1/1 and 1/2/5 were characterized by cyclic voltammetry (CV), Fourier-transform infrared attenuated total reflectance spectroscopy (FTIR-ATR), scanning electron microscopy (SEM), energy-dispersive X-ray analysis (EDX), and electrochemical impedance spectroscopy (EIS). The capacitive behaviors of the modified electrodes were defined via Nyquist, Bode-magnitude, Bode-phase, and Admittance plots. The equivalent circuit model of Rs(C _dl1 (R ₁ (QR ₂ )))(C _dl2 R ₃ ) was performed to fit the theoretical and experimental data. The low-frequency capacitance (C_LF) were obtained from initial monomer concentrations of 50 mM as C_LF = ～2.34 × 10^?4 mFcm^?2 for P(N-MPy), C_LF = 5.06 × 10^?4 mF cm^?2 for P(BTh), C_LF = 5.07 m F cm^?2 for P(OTh), and C_LF = ～3.78 m Fcm^?2 for terpolymer for [N-MPy]₀/[BTh]₀/[OTh]₀ = 1/1/1. The terpolymer may be used as energy storage devices.     

Solubility of propane in N-formyl morpholine

N-formyl morpholine (NFM) is a solvent that has been used to separate acid gases from gas streams. An advantage of NFM is the high solubility of acid gases compared with the low solubility of light hydrocarbons. The solubility of the light hydrocarbons in NFM is important, as the hydrocarbons constitute a loss to the process, and result in hydrocarbon emissions to the atmosphere. However, there are only a few experimental data sets dealing with the solubility of hydrocarbons in NFM. To provide data to be used in the design of plants in the natural gas processing industry, the solubility of propane (C₃H₈) in NFM was measured at 298.15, 313.15, and 343.15 K at pressures up to 20.15 MPa. The Peng-Robinson equation of state was employed to correlate the experimental data and to obtain binary interaction parameters. The binary interaction parameters were used to obtain the parameters of the Krichevsky-Ilinskaya equation and Henry's law constants for propane were calculated. Henry's law constants for propane were compared with those of hydrogen sulphide, carbon dioxide, methane, and ethane in NFM.     

Measurement and correlation of vapor-liquid equilibria of the binary carbon dioxide-chloroform mixture system

Binary vapor liquid equilibrium data of the carbon dioxide+chloroform system were measured at five isotherms from 310.13 K to 333.32 K. A circulating type apparatus with on-line gas chromatography was used in this study. The experimental data were correlated by classical Peng-Robinson equation of state using van der Waals one fluid mixing rules and the multi-fluid nonrandom lattice fluid (MF-NLF) equation of state.