Binary interaction coefficients of the Redlich—Kwong equation of state

A direct relationship between the binary interaction coefficients, k_ij and c_ij proposed by Chueh and Prausnitz, and Zudkevitch, for modifying the original mixing rules of the Redlich—Kwong equation of state is presented. Values of k_ij are evaluated by means of two methods for binary vapor—liquid equilibrium data for five systems at a total of thirty-two isothermal conditions. The calculated results from k_ij value obtained by minimizing Σ|ΔP| values are preferable to those obtained by minimizing Σ|Δy| values. The effect of temperature on k_ij for the systems investigated is shown and discussed.     

Predicting NRTL parameters for binary hydrocarbon mixtures for calculating liquid—vapor equilibriums of multicomponent systems

The parameters of the NRTL method are fitted, for binary hydrocarbon systems, on the activity coefficients calculated by the Flory—Hildebrand method with binary coefficients l_ij of deviation from the geometric mean assumption for cohesive energy densities (NRTL-FH parameters). For aromatic saturated hydrocarbon mixtures, the l_ij coefficients are correlated to the products δ_iδ_j of solubility parameters. The predicted NRTL-FH parameters are used in calculations of bubble pressures and vapor phase compositions of binary hydrocarbon mixtures and of ternary mixtures with at least two hydrocarbon components. The NRTH-FH method is compared to the Chao—Seader and the zero l_ij-Flory-Hildebrand methods for many hydrocarbon systems, and gives the best results among these three predictive methods. The introduction of the non zero l_ij coefficients is an improvement in regards to the case with zero l_ij coefficients, particularly for the cycloparaffin-aromatic hydrocarbon mixtures. The NRTL-FH method is also compared to the NRTL-EXP method (parameters fitted on experimental data), and results obtained with the two methods are satisfactory for binary and ternary mixtures.     

Excess enthalpy data for the ternary system methane—ethylene—carbon dioxide by flow calorimetry

Excess enthalpy data for the ternary system methane – ethylene – carbon dioxide was obtained utilizing an isothermal flow calorimeter. The measurements were made at three temperatures: 293.15, 305.15 and 313.15 K and pressures of 1.114, 1.520 and 3.445 MPa (11, 15 and 34 atm). The determination of excess enthalpies for the binary systems methane—ethylene, ethylene—carbon dioxide and methane—carbon dioxide has been reported in three preceeding articles, respectively: Gagné et al., 1985; Ba et al., 1979 and Barry et al., 1982a. The binary interaction coefficients k_ij obtained for these systems have been utilized as initial values for the optimization procedure leading to the k_ij for the ternary system. For the case of the ternary system studied in this investigation, two types of binary interaction coefficients k_ij have been determined from experimental data: k_ij independent of temperature and pressure and k_ij adjusted as function of temperature and pressure. Experimental data were compared with the predictions from Benedict—Webb—Rubin and Redlich—Kwong equations of state. In both cases, the coefficients k_ij dependent on temperature and pressure led to better prediction of excess enthalpies.     

Measurement of enthalpies of mixing in gaseous phase for the binary system carbon dioxide – hydrogen sulphide by an isothermal flow calorimeter

Enthalpies of mixing for the binary system carbon dioxide – hydrogen sulphide were measured by means of an isothermal flow calorimeter at temperatures of 293.15. 305.15 and 313.15 K. For the first isotherm, excess enthalpy measurements were made at pressures of 0.507, 1.013 and 1.419 MPa. For the last two isotherms, these measurements were performed at pressures of 0.507, 1.013 and 1.520 MPa. The experimental data were treated by the same techniques described for the systems previously studied (Barry et al., 1982a, 1982b, 1982c). Two types of binary interaction coefficients k_ij have been utilized for the prediction of experimental data from equations of state: coefficients k_ij independent of temperature and pressure, and k_ij's adjusted as function of temperature and pressure. A better prediction of the excess enthalpy experimental data was obtained from the latter series of binary interaction coefficients.     

A modified heil-prausnitz equation for excess gibbs energy

An equation for the Gibbs excess energy, similar to that of Heil-Prausnitz, is derived on the basis of the lattice theory of fluids. This equation takes into account both the enthalpic and entropic contributions to G^E for liquid mixtures, and in addition uses the α_ij parameter of Renon-Prausnitz. It is compared in the one- and two-parameter forms with the analogous equations of Wilson, NRTL and Heil-Prausnitz for 44 binary liquid-vapour systems, and with the NRTL equation for 2 ternary liquid-liquid systems. Rules are given for calculating the α_ij parameter. Methods are also reported for predictive calculations of the binary interaction parameter g₁₂ based on the properties of the pure fluids.     

Description of the mutual solubilities of fatty acids and water with the CPA EoS

Data for the mutual solubilities of fatty acid + water mixtures are scarce and so measurements for seven fatty acid (C₅‐C₁₀, C₁₂) + water systems were carried out. This new experimental data was successfully modelled with the cubic plus association EoS. Using data from C₆ to C₁₀ and the Elliot's cross‐associating combining rule a correlation for the k_ij binary interaction parameter, as a function of the acid chain length, is proposed. The mutual solubilities of water and fatty acids can be adequately described with average deviations inferior to 6% for the water rich phase and 30% for the acid rich phase. Furthermore, satisfactory predictions of solid‐liquid equilibria of seven fatty acids (C₁₂‐C₁₈) + water systems were achieved based only on the k_ij correlation obtained from liquid–liquid equilibria data. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Phase behaviour of CO2 -bitumen fractions

The phase behaviour of Cold Lake bitumen and its five fractions (or “cuts”) saturated with carbon dioxide is examined. The two lightest fractions (bp < 510°C) were clear liquids, whereas the third and fourth fractions were dark and viscous, i.e. much like the whole bitumen. The fifth fraction was a glass-like solid, with a softening temperature of approximately 100°C. The vapour-liquid equilibrium (VLE) data for the bitumen and bitumen fractions saturated with CO₂ were collected at temperatures from 25 to 150°C and pressures up to 10 MPa. Experiments were also performed at conditions under which pure CO₂ exists as a liquid. The VLE and LLE data were correlated with the Peng-Robinson equation of state by modeling each bitumen fraction as one pseudocomponent whose critical properties and acentric factor were estimated from correlations available in the literature. The CO₂-solubility and density data were used to develop generalized correlations for the critical pressure and the binary interaction parameter (k_ij) in terms of molar mass and critical temperature. The model was subsequently used to predict the solubility of CO₂ in the whole bitumen which was represented as a 5-component mixture. A correlation for Cut i-Cut j binary interaction parameter (k_ij) was developed in terms of temperature and the difference in hydrocarbon molar masses. The average deviation in the predicted and experimental CO₂-solubility in the whole Cold Lake bitumen was less than 7%.     

Model for phase equilibria correlation and prediction. Characteristics and application to binary liquid—vapor and binary,ternary and quaternary liquid—liquid equilibria

A new model for the excess Gibbs energy has been developed. The model has three binary parameters. The presence of the third parameter, k_ij, the power of the composition, gives to the model an extraordinary flexibility. The model has been widely tested for different types of equilibria, such as binary liquid-vapour equilibria, both isothermal and isobarid; as well as on liquid-liquid equilibria, binary, ternary and quaternary, for both correlation and prediction. Results obtained for the average errors were always lower than those obtained by the Van Laar, Wilson and UNIQUAC models, and even by a three parameter model such as NRTL.     

Excess molar enthalpies of ternary and constituent binary systems {1,2-dichloropropane+2-propanol+2-butanol} at T=298.15 K

Ternary excess molar enthalpies at T=298.15 K and P=101.3 kPa for the system of {1,2-dichloropropane+2-propanol+2-butanol} and their constituent binary systems {1,2-DCP+2-propanol}, {1,2-DCP+2-butanol}, and {2-propanol+2-butanol} have been measured over the whole composition range using an isothermal micro-calorimeter with flow-mixing cell. All of the binary and ternary systems, including three pseudobinary systems, show endothermic behavior except for the binary mixture {2-propanol+2-butanol}, which shows small exothermicity. The Redlich-Kister equation was used to correlate the binary H _{m, ij} ^E data, and the Morris equation to correlate the ternary H _{m, 123} ^E data. Comparisons between the Morris and Radojkovi equations for the prediction of H _m,123 ^E have been also made. The experimental results have been qualitatively discussed in terms of self-association, isomeric effect and chain length among molecules.     

Ternary and constituent binary excess molar enthalpies of {1,2-dichloropropane + 2-pentanol + 3-pentanol} at T=298.15K

Excess molar enthalpies for the ternary system of {1,2-dichloropropane (1,2-DCP)+2-pentanol+3-pentanol} and their constituent binary mixtures {1,2-DCP+2-pentanol}, {1,2-DCP+3-pentanol}, and {2-pentanol+3-pentanol} have been measured over the whole range of composition using an isothermal micro-calorimeter with flow-mixing cell at T=298.15 K and atmospheric pressure. The experimental excess molar enthalpies of all the binaries and ternary mixture, including three pseudo-binary mixtures, are positive (endothermic effect) throughout the mole fraction range, except for the binary mixture {2-pentanol+3-pentanol} in which shows a small negative values over the entire composition range. The experimental binary H _{m, ij} ^E data were fitted to Redlich-Kister equation, and the Cibulka and the Morris equations were employed to correlate the ternary H _{m, 123} ^E data. Several empirical equations for predicting ternary excess enthalpies from constituent binary mixing data have been also examined and compared. The experimental results have been qualitatively discussed in terms of molecular interactions.     

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.     

High-pressure gas solubility in multicomponent solvent systems for hydroformylation. Part I: Carbon monoxide solubility

High-pressure gas-solubility data of carbon monoxide (CO) in various solvents like n-hexane, propylene carbonate, dimethylformamide, 1-dodecene, n-dodecanal and n/iso-tridecanal was measured for temperatures between 295 K and 364 K and pressures up to 17 MPa. The experiments were performed in a high-pressure variable-volume view cell applying the synthetic method. The binary systems investigated were correlated using the perturbed chain statistical associating fluid theory (PC-SAFT). A temperature-independent binary interaction parameter k_ij was fitted to solubility data. Based on this, to CO solubility in mixtures of n-dodecanal and 1-dodecene with various molar compositions of the two liquids (3:1, 1:1, 1:3) were predicted. CO-solubility measurements for these systems confirmed that PC-SAFT is able to accurately predict the ternary data based on the knowledge of the binary subsystems, only.     

Strengths and limitations of SAFT for calculating polar copolymer–solvent phase behavior

Statistical associating fluid theory (SAFT) is used to calculate the cloud-point behavior of poly(ethylene-co-methyl acrylate) (EMA) copolymers (0–41 mol % methyl acrylate) in ethane, propane, butane, ethylene, propylene, 1-butene, chlorodifluoromethane, and dimethyl ether at temperatures to 250°C and pressures to 2,600 bar. Poor agreement is obtained between calculated and experimental data if the pure component EMA parameters used in SAFT are calculated using mixing rules that average polyethylene (PE) and poly(methyl acrylate) (PMA) parameters. Therefore, two of the three pure component parameters for all of the EMA copolymers are fixed to the values reported for PE and the third parameter, u^o/k, for the copolymer containing 31 mol % methyl acrylate (EMA₃₁) is determined by fitting the EMA₃₁-butane cloud-point curve. The value for (u^o/k)_PMA is then obtained using a mixing rule and the values of u^o/k for all of the EMA copolymers are calculated. A good fit of all of the copolymer–solvent cloud-point curves is obtained using a temperature-independent mixture parameter, k_ij. With this method of calculation it is possible to correlate cloud-point data with the SAFT equation of state if a small amount of experimental data are available. © 1996 John Wiley & Sons, Inc.     

Interaction model for the critical pressures of aliphatic hydrocarbon mixtures

An interaction model is proposed for the prediction of the critical pressures of multicomponent aliphatic hydrocarbon mixtures which may include methane. This model utilizeg a series consisting of terms of increasing order which has been truncated beyond the fifth interaction term. After a number of algebraic manipulations, the excess critical pressure for these multicomponent mixtures has been represented as follows The nonmethane interaction coefficients A_ij, B_ij, C_ij and β_ijk and the methane interaction coefficients A_1j, B_1j, C_1j, D_1j and β_1jk have been expressed as functions of the critical pressure parameter, π_ij. The resulting relationships permit the evaluation of these interaction coefficients for a multicomponent system and from its composition, the critical pressure of the mixture is calculated. The critical pressures of several binary and multicomponent aliphatic hydrocarbon mixtures have been calculated and have been compared with experimental values. For 99 binary methane-free mixtures representing 11 systems, the average deviation is 3.23%. For 46 binary mixtures representing six methane systems, the average deviation becomes 4.41 %. For 36 multicomponent aliphatic hydrocarbon mixtures containing from three to six components, the average deviation is found to be 3.18%.     

Equilibre entre vapeur et liquide pour le système azote-argon-methane

A forced recirculation apparatus has been used to measure the vapor-liquid equilibrium compositions for the nitrogen-argon-methane system at 123.4d'K. A modified Redlich-Kwong equation of state with the incorporation of binary interaction constants k_ij and temperature-dependent characteristic constants Ω_a and Ω_b have been successfully employed to represent the data. Equilibrium ratios obtained from the equation of state are compared with the experimental values. The average absolute deviations are 1.62%, 1.67% and 7.57% for the components nitrogen, argon and methane respectively.     

Extending the range of COSMO‐SAC to high temperatures and high pressures

The range of the predictive Gibbs energy of solvation model, COSMO‐SAC, is extended to large ranges of density, pressure, and temperature for very nonideal mixtures by combining it with an equation of state (EOS) using the Wong‐Sandler mixing rule. The accuracy of isothermal vapor‐liquid equilibria (VLE) calculations based on using the predictive COSMO‐SAC model and separately the correlative NRTL model is compared, each combined with three different forms of the Peng‐Robinson equation of state. All the models considered require the value of the EOS mixing rule binary parameter k_ij. The NRTL model also requires three other parameters obtained from correlation low pressure VLE data. The PRSV + COSMO‐SAC model is showed, with its one adjustable parameter obtained from low temperature data leads good predictions at much higher temperatures and pressures. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1806–1813, 2018     

An extension of the group contribution method for estimating thermodynamic and transport properties. Part IV. Noble gas mixtures with polyatomic gases

Earlier work on the group contribution method applied to Kihara potentials is extended to noble-polyatomic gas mixtures for the calculation of second virial cross coefficients, mixture viscosities and binary diffusion coefficients of dilute gas state using a single set of gas group parameters. Previously estimated parameter values for pure gas groups by our work [Oh, 2005; Oh and Sim, 2002; Oh and Park, 2005] were used. Assuming that noble-polyatomic gas mixtures examined are chemically dissimilar, a group binary interaction coefficient, k _{ij, gc} , was assigned to each interaction between noble-polyatomic gas groups, and 25 group binary interaction parameter values (k _{He-H2, gc} , k _{He-N2, gc} , k _{He-CO, gc} , k _{He-CO2, gc} , k _{He-O2, gc} , k _{He-NO, gc} , k _{He-N2O, gc} ; k _{Ne-H2, gc} , k _{Ne-N2, gc} , k _{Ne-CO, gc} , k _{Ne-CO2, gc} , k _{Ne-O2, gc} ; k _{Ar-H2, gc} , k _{Ar-N2, gc} ; k _{Ar-CO, gc} , k _{Ar-CO2, gc} , k _{Kr-O2, gc} ; k _{Kr-H2, gc} , k _{Kr-N2, gc} , k _{Kr-CO, gc} , k _{Ar-CO2, gc} ; k _{Xe-H2, gc} , k _{Xe-N2, gc} , k _{Xe-CO, gc} , k _{Xe-CO2, gc} ) were determined by fitting second virial cross coefficients data. Application of the model shows that second virial cross coefficient data are represented with good results comparable to values predicted by means of the corresponding states correlation. Reliability of the model for mixture viscosity predictions is proved by comparison with the Lucas method. And prediction results of binary diffusion coefficients are in excellent agreement with literature data and compared well with values obtained by means of the Fuller method. Improvements of the group contribution model are observed when group binary interaction coefficients are adopted for mixture property predictions.     

Interaction parameters in ternary polystyrene solutions at high temperature

A combination of dilute solution viscometry and Rayleigh light scattering has been used to evaluate experimentally the interaction parameters χ_ij in solutions comprising tetralin (1), polystyrene (2) and 3-methyl cyclohexanol (3). The measurements were carried out at 371.5 K, where binary solutions of the polymer in 3-methyl cyclohexanol are under θ-conditions and tetralin is a thermodynamically good solvent for polystyrene. For polymer-solvent interaction, values of χ₁₂ = 0.40 ± 0.01 and χ₂₃ = 0.50 were obtained. The solvent-solvent interaction parameter χ₁₃ was composition dependent, having limiting values of 0.52 and 0.73 at X₁ = 0 and X₁ = 1, respectively, where X₁ is the mol fraction of liquid 1 in binary mixtures of liquids (1) and (3).     

High voltage coefficient piezoelectric materials and their applications

The piezoelectric d_ij coefficient is often regarded in materials science as the most important figure of merit of piezoelectric performance. For many applications, the piezoelectric g_ij coefficient which correlates to voltage output and sensitivity of a piezoelectric material can be considered of equal or increased importance, however is often an overlooked parameter in materials science literature. The aim of this review is to highlight the importance of this parameter and to provide insight into the mechanisms that drive a high piezoelectric voltage coefficient in single crystal, polycrystalline, and composite form. For bulk ceramics, special attention is given to tetragonal systems due to the availability of electrical and crystallographic data allowing for a clear structure-property relation. Orthorhombic and rhombohedral systems are mentioned and specific cases highlighted, however investigating structure-property relations is difficult due to the lack of crystallographic datasets. Composite materials have been the forefront of high g_ij piezoelectric materials over the decades and are therefore also considered in both ceramic-matrix and polymer-matrix form. An overview of applications in medical, energy, fishing and defence industries where a high g_ij is desirable are considered and the scientific and commercial considerations that must be made for the transition from laboratory to industry are discussed from the perspective of integrating new piezoelectric materials into sonar devices.     

Cyclic voltammetric study of polyselenide ions in fused potassium thiocyanate solvent

The study of the electrochemical oxidation and reduction of polyselenide ions in fused KSCN by cyclic voltammetry indicates two oxidation and two reduction reactions. The following consecutive reaction schemes are consistent with the observations:

Emf measurements of the cell Pt/Se^2?_n, KSCN|KSCH, Ag₂S/Ag at constant polyselenide concentration fit the empirical equation E=E′ + klog(n-1) where the constants are E′ = ?0.4058 V and k=0.5071 V.