VLE calculation of carbon dioxide+n-alkanes binary mixtures with MHV2 mixing rule

Vapor-liquid equilibria for binary and asymetric systems include carbon dioxide+C₁-C₈, C₁₀ are calculated by using the Peng-Robinson-Stryjek-Vera equation of state coupled with the modified MHV2 mixing rule. The modified UNIFAC model is used for determining activity coefficient and excess Gibbs free energy. Calculated equilibrium pressures and mole fractions in vapor phase are compared with the experimental data. The average absolute deviation percent (AAD%)s indicates that the error involved in the application of the MHV2 mixing rule by optimized q₁ and q₂ is less than WS and PRSK mixing rules in most cases.     

Equation of state for the systems containing aqueous salt: Prediction of high pressure vapor-liquid equilibrium

An equation of state (EOS), which is based upon contributions to the Helmholtz energy, is presented for systems containing aqueous electrolyte solutions at high pressure. The Peng-Robinson equation of state is used to provide the Helmholtz energy of a reference system. The electrolyte terms consist three terms containing a modified Debye-Hückel term for long-range electrostatic interactions, the Born energy contribution for electrostatic works and a Margules term for short-range electrostatic interactions between ions and solvents. The binary and ternary interaction parameters of the equation of state are obtained by experimental osmotic coefficient data. Systems that were studied here are (water+ NaCl+SC-CO₂), (water+NH₄Cl+SC-CO₂), (water+Na₂SO₄+SC-CO₂) and (water+methanol+NaCl+SC-CO₂). It is found that the proposed equation of state is able to accurately represent the experimental data over a wide range of pressure, temperature and salt concentration.     

Density correlation of solubility of C. I. disperse orange 30 dye in supercritical carbon dioxide

The solubility of C. I. Disperse Orange 30 (O30) dye in CO₂ has been measured by using a closed-loop (batch) solid-fluid equilibrium apparatus at temperatures between 313 and 393 K and at pressures between 11 and 33 MPa. Kumar and Johnston’s equation based on Chrastil’s concept has been used to describe the experimental solubility data. The solubility versus density plot appears much simpler than the solubility versus pressure plot. The isotherms are nearly straight and parallel to each other, as seen in the previous studies. Peng-Robinson equation of state (PR EOS) has also been used successfully in modeling the dye solubility in supercritical carbon dioxide as a function of pressure or density of the fluid phase. The validity of this method has been verified by the vapor pressure calculation. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Extrema of isochoric heat capacity of water and carbon dioxide

The experimental and predicted loci extrema behavior of the isochoric heat capacity C_v was examined for water and carbon dioxide along the subcritical and supercritical isotherms and along the liquid and vapor isochores. The studies were based on a nonanalytical Helmholtz energy-volume-temperature equation (AVT, fundamental equation of state), the IAPWS-95 formulation for water, and scaling-type crossover equations of state (CREOS). The measured isochoric heat capacity data for these fluids near the critical point were analyzed to study the behavior of loci of C_v maxima and to compare these with predictions by the equations of state. A CREOS was applied to study the behavior of the isochoric heat capacity maxima in the immediate vicinity of the critical point. Good agreement with the CREOS prediction and experimental isothermal C_v maxima loci was observed near the critical point. The basic characteristic points on the C_v extrema loci curves in the P-T and 𝜌-T planes were determined on the basis of detailed analysis of the experimental and prediction of C_v extrema loci behavior. Qualitative explanations are given for the nature of isochoric and isothermal C_v maxima-minima curves. The role of C_v extrema loci behavior in developing high-accuracy equations of state in the supercritical region and in the study of supercritical phase-transition phenomena are discussed.     

Vapor-liquid equilibrium correlations for systems containing amines using a lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of vapor-liquid equilibria (VLE) for binary amine and hydrocarbon mixture at various temperatures. For these mixtures, the consideration of hydrogen bondings in the lattice equation of state clearly improves the prediction for VLE. The amines were divided into four groups due to the different strength of the hydrogen bonding. For all groups, different hydrogen bonding parameters were obtained and evaluated. The effects of varying hydrogen bonding energies for NLF-HB EOS are discussed. For systems containing lower amines, the NLF-HB EOS showed excellent agreement with the experimental data. For the correlation of systems containing tertiary amine molecules, binary interaction parameter had to be involved instead of hydrogen bonding parameters.     

Calculation of pure saturation properties using cubic equations of state

A robust algorithm is outlined for the solution of the classical non-linear isofugacity problem by using equations of state (EOS). The procedure suggested is free of numerical pitfalls from the triple point to the critical point. The combination of differential stability (spinodal curve) and zero pressure reference concepts yields an automatic initialization of the calculations inside a region of convergence where the EOS can always predict pure compound vapor pressures at a given temperature.     

Solubility of chemical warfare agent simulants in supercritical carbon dioxide: experiments and modeling

Solubility data are reported for ethyl phenyl sulfide (EPS) and 2-chloroethyl ethyl sulfide (CEES) in CO₂ at temperatures from 25 to 100 °C. These two sulfide-based compounds are homomorphs for chemical warfare agents (CWAs). Both sulfide–CO₂ mixtures exhibit type-I phase behavior. The maximum in the 100 °C isotherm is approximately 2600 psia for the CEES–CO₂ system and approximately 3400 psia for the EPS–CO₂ system. The Peng–Robinson equation of state (PREOS) is used to model both sulfide–CO₂ mixtures as well as the phase behavior of the 2-chloroethyl methyl sulfide (CEMS)–CO₂ system previously reported in the literature. The Joback–Lydersen group contribution method is used to estimate the critical temperature, critical pressure, and acentric factor for the sulfides. Semi-quantitative estimates of the phase behavior are obtained for the CEES–CO₂ and EPS–CO₂ systems with a constant value of k_ij, the binary interaction parameter, fit to the 75 °C isotherms. However, very poor fits are obtained for the 2-chloroethyl methyl sulfide–CO₂ system regardless of the value of k_ij. On the basis of the high solubility of EPS and CEES in CO₂, supercritical fluid (SCF)-based technology could be used to recycle or recover chemical warfare materials.     

A new correlation for VLE data: Application to binary mixtures containing nitrogen

Recently we proposed simple analytical expressions for the calculation of the equilibrium pressure, as well as the mole fractions of both liquid and vapor phases at the vapor-liquid equilibrium of binary mixtures. They are based on a recently proposed molecular model for the vapor pressure of pure non-polar fluids, which, for a given temperature, only requires as input the values of the two Lennard-Jones molecular parameters and the acentric factor, which are parameters related to the molecular shape of each substance, and whose values are readily available. The mixing rules contain adjustable parameters that must be obtained for each mixture. In this work, we test the applicability of the models for some mixtures containing nitrogen. In particular, we find that the calculation of mole fractions must be performed with particular care in some cases. We show that the model for the pressure clearly improves the results obtained with classical equations of state for most of the mixtures studied.     

Thermodynamic modeling of solubilities of various solid compounds in supercritical carbon dioxide: Effects of equations of state and mixing rules

No one can ever deny the significance of calculations of solubilities of industrial solid compounds in supercritical CO₂ in separation processes. In this work, the Peng-Robinson (PR) and the Esmaeilzadeh-Roshanfekr (ER) equations of state (EoS) along with several mixing rules including the Wong-Sandler (WS), the covolume dependent (CVD) and the van der Waals one (VDW1) and two (VDW2) fluid mixing rules are applied to evaluate the solubilities of 52 mostly used solid compounds in supercritical carbon dioxide. Besides, the Van-Laar excess Gibbs energy (G^ex) model is applied in phase behavior calculations by the WS mixing rule. The optimal values of the proposed thermodynamic model parameters are evaluated using the DE (differential evolution) optimization strategy. The absolute average deviations of the model results from 1776 experimental data points and the optimal values of the adjustable parameters of the model are reported to investigate the capabilities of combinations of each equation of state with different mixing rules in calculations of the solubilities. The results indicate that the combination of the ER EoS with the WS mixing rule leads to more accurate results (AAD = 9.0%) compared with other ones.     

On the information and methods for calculation of Sanchez-Lacombe and group-contribution lattice-fluid equations of state

The algorithms for calculation of densities from Sanchez-Lacombe (S-L) and group-contribution latticefluid (GCLF) equations of state have been put forward, respectively. From the S-L equation of state the relationship between the equation characteristic parameters and critical properties was deduced, and the influence of molecular weight of the polymers on critical properties was investigated. However, for the GCLF equation of state, it was surprising to find that there as many as four roots were found at a saturation temperature and pressure for gases, while still two roots above the critical temperature. For polymers, only two roots could be found. So the formerly accepted consistency between the magnitude of the density and vapor or liquid phase is not applicable yet. A way about how to identify the root and corresponding phase was suggested.     

On the modeling of phase and chemical equilibria by equations of state for systems containing supercritical components and ionic species

A technique of modeling of phase and chemical equilibria by equations of state for systems containing supercritical components and ionic species is considered. Attention is focused on the structure of equation of states with inclusion of non-electrolyte and electrostatic contributions. A hole quasichemical model was applied to illustrate the technique and to show how an EOS can be modified for systems with chemical reactions and electrostatic interactions in the liquid phase. The concentration dependency of the density and dielectric permittivity was taken into account in describing the electrostatic contribution that is required for thermodynamic consistency of the results of modeling. A method of assessing the appropriate relationships for mixtures containing supercritical components is suggested, alongside with the way to estimate the “true” composition of mixtures where ionic species are formed due to chemical reactions. The raised questions are discussed with respect to the following systems: solutions of acid gases in water-alkanolamine mixtures and water-ammonia-carbon dioxide system in a broad interval of temperatures and pressures.     

Modeling of drug solubility in supercritical carbon dioxide using equation of state based on hole theory with molecular surface charge density

Equation of state based on hole theory with molecular surface charge density was developed for the modeling of drug solubility in supercritical carbon dioxide. In the hole theory, the density change of supercritical carbon dioxide can be represented by the number of holes in the system. The molecular interaction energy parameter was estimated using the interactions of segments on the molecular surface given by a quantum calculation using conductor-like screening model. The only one parameter, coordination number around a molecule was fitted to the experimental data of the drug solubility in supercritical carbon dioxide. The solubilities of the eighteen drugs in supercritical carbon dioxide were modeled by the equation of state with the molecular surface charge density. The effect of the molecular pair for the coordination number on the correlated results was investigated. It is found that the results using the fitted parameter of the solute–solute pair coordination number result in the modeling performance better than those of carbon dioxide–solute coordination number. The results of the modeling of drug solubility in supercritical carbon dioxide are compared with the experimental data. The average absolute relative deviation between the experimental and calculated results of the solubility for the drug composed of C, H and O atoms acetylsalicylic acid, benzoic acid, ferulic acid, (S)-naproxen, p-benzoquinone, propyl gallate, salicylic acid and vanillic acid is 0.38 smaller than those for compounds including N, F, I and S atoms, amical-48, benzocaine, caffeine, carbamazepine, (±)-flurbiprofen, methimazole, phenazopyridine, theobromine, theophylline and uracil, 0.59.     

Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part I. Molecular thermodynamic framework

Consistent calculation of fugacities of fluid mixtures remains as one of the most important subjects in contemporary molecular thermodynamics. In practice, equations of state (EOSs) and g^E-models have been used. However, most EOSs are erroneous for condensed phases at high densities and g^E-models are inapplicable for pressuresensitive systems. Recently to remedy the shortcomings in both approaches, there has been a surge of new g^E-EOS mixing rules. By equating any set of EOS and g^E-models, the limitations in both approaches could be resolved significantly. However, the self-consistency in the underlying concept of those mixing rules remains controversial. During the last several years, the present authors proposed a new lattice-fluid EOS and its simplification relevant to phase equilibrium calculations. Without employing any g^E-EOS mixing rule and with only two parameters for a pure component and one adjustable interaction energy parameter for a binary mixture, results obtained to date demonstrated that the EOSs are quantitatively applicable to a great variety of phase equilibrium properties of mixtures, especially, for complex and/or macromolecular systems. In the present article we summarize the EOSs and extended the applications to liquid-liquid Equilibria. In part I, we discussed briefly the molecular thermodynamic aspects of general derivation of the EOS and a brief discussion of applying the EOSs to pure fluids while the illustrative application to various real mixture systems is discussed in part II.     

Measurement and prediction of high-pressure vapor-liquid equilibria for binary mixtures of carbon dioxide + n-octane, methanol, ethanol, and perfluorohexane

We report the measurement of high-pressure vapor-liquid equilibrium data for binary mixtures of carbon dioxide + n-octane, +methanol, and +ethanol systems at 313.14 K and carbon dioxide + perfluorohexane at 303.15-323.15 K. The experimental data were collected using a new simple apparatus for measuring high-pressure vapor-liquid equilibria and correlated using a modified SRK equation with the three-parameter conventional mixing rule proposed by Adachi and Sugie. The SAFT-VR equation of state has also been used to predict the phase behavior and found to be in good agreement with experimental data. For the carbon dioxide + methanol, carbon dioxide + ethanol and carbon dioxide + perfluorhexane systems simple Lorentz-Berthelot combining rules can be used to determine the cross interactions and predict the phase behavior. For the carbon dioxide + n-octane system cross interaction parameters fitted to experimental data are needed in order to capture the non-ideal phase behavior exhibited by this system.     

Polymerization of acrylonitrile in supercritical carbon dioxide

A series of fluorinated diblock copolymers, consisting of styrene (St)-acrylonitrile (AN) copolymer [poly(St-co-AN)] and poly-2-[(perfluorononenyl)oxy]ethyl methacrylate, with various compositions as well as with different molecular weights were synthesized by atom transfer radical polymerization and characterized. Dispersion polymerization of acrylonitrile in supercritical carbon dioxide (scCO₂) at 30 MPa and at 65 °C with this kind of amphiphilic block copolymer as a stabilizer and 2,2′-azobisisobutyronitrile as an initiator was investigated. The experimental results indicated that, in the presence of a small amount of poly(St-co-AN) (5 wt% to AN), spherical particles of polyacrylonitrile (PAN) were prepared with small diameter and narrow polydispersity (d_n = 153 nm, d_w/d_n = 1.12), resulting from the high stabilizing efficiency of this fluorinated block copolymer. Furthermore, the polymerization of AN in scCO₂ under different initial pressures especially under low pressure (<14 MPa) was studied. When the polymerization was carried out around the critical pressure of CO₂ (7.7-7.8 MPa), the PANs with high molecular weight (M_ν ≈ 130,000-194,000) were synthesized at high monomer conversion (>90%) no matter whether the stabilizer was added, compared to those synthesized by dispersion polymerization at 30 MPa. It was also found that the crystallinity of PAN synthesized at 7.7-7.8 MPa was somewhat higher than that synthesized at 30 MPa, while its crystallite size did not change.     

Modeling solubility in supercritical fluids via the virial equation of state

We examine the utility of the virial equation of state (VEOS) for the prediction of the solubility of hexane in supercritical carbon dioxide. We computed virial coefficients up to fourth-order for this mixture at 353.15 K, using Mayer-sampling Monte Carlo applied to established molecular models for carbon dioxide and hexane. At this temperature, neither the third- nor fourth-order VEOS indicate the presence of a critical point for the mixture. However, the VEOS coupled with an ideal-solution treatment for the coexisting subcritical fluid phase (with parameters determined from coexistence data at one pressure) reproduces much of the solubility curve as previously established by Gibbs-ensemble molecular simulation. Comparison of the third- and fourth-order VEOS indicate that the virial treatment is converged at the conditions where it is applied.     

Biodiesel production using supercritical methanol/carbon dioxide mixtures in a continuous reactor

Fatty acid methyl esters (biodiesel) were produced by the transesterification of triglycerides with compressed methanol (critical point at 240 °C and 81 bar) in the presence of solid acids as heterogeneous catalyst (SAC-13). Addition of a co-solvent, supercritical carbon dioxide (critical point at 31 °C and 73 bar), increased the rate of the supercritical alcohols transesterification, making it possible to obtain high biodiesel yields at mild temperature conditions. Experiments were carried out in a fixed bed reactor, and reactions were studied at 150-205 °C, mass flow rate 6-24 ml/min at a pressure of 250 bar. The molar ratio of methanol to oil, and catalyst amount were kept constant (9 g). The reaction temperature and space time were investigated to determine the best way for producing biodiesel. The results obtained show that the observed reaction rate is 20 time faster than conventional biodiesel production processes. The temperature of 200 °C with a reaction time of 2 min were found to be optimal for the maximum (88%) conversion to methyl ester and the free glycerol content was found below the specification limits.     

A comparison between semiempirical equations to predict the solubility of pharmaceutical compounds in supercritical carbon dioxide

The aim of this work is to determine, depending on the operation conditions, which semiempirical equation provides the best fit to solubility data of pharmaceutical compounds in supercritical CO₂. Solubility data from 27 different pharmaceutical solutes were collected from literature and the different density-based models (Chrastil, Adachi-Lu, del Valle-Aguilera, Sparks, Kumar-Johnston, Bartle, Méndez Santiago-Teja) together with the Yu's model and Gordillo's model were employed. The results showed that, in general, Sparks’ equation provides the best fit to the solubility data for this kind of solids in supercritical CO₂. However, at certain specific conditions, the best correlation is obtained using Gordillo's equation. By means of a brief comparison with Peng-Robinson equation of state, semiempirical equations present a more accuracy prediction compared to cubic equations of state, and present no drawbacks such as properties estimation and computational difficulties.     

Solubility of astaxanthin in supercritical carbon dioxide

The solubility of astaxanthin in carbon dioxide was measured under supercritical conditions of a pressure range from 80 to 300 bar, and temperature range from 303 to 333 K, by using a dynamic flow-type. The solubility of astaxanthin increasing from 0.42×10⁻⁵ to 4.89×10⁻⁵ with higher temperature and pressure maintains certain density of supercritical carbon dioxide. The solubility data obtained were applied to the Chrastil model, based on the density of carbon dioxide. The data fitted well with the Chrastil model at most experimental conditions.