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.     

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%.     

Modeling of Nitrogen and Carbon Dioxide Solubility in Alternative Fuels at High Pressures Using the Soave‐Redlich‐Kwong Equation of State

In this paper, the Soave‐Redlich‐Kwong equation of state with quadratic mixing rule has been tested for correlation of vapor‐liquid equilibria (VLE) at high pressures in the binary nitrogen + dimethyl ether, dimethyl ether + methanol, nitrogen + methanol, carbon dioxide + dimethyl ether and carbon dioxide + methanol systems. The interaction parameters k_ij were evaluated for each binary pair and used for prediction of VLE in the ternary nitrogen + dimethyl ether + methanol and carbon dioxide + dimethyl ether + methanol systems at high pressures. The results of correlation and prediction are discussed.     

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.     

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.     

Correlation of K-factors for mixtures of hydrogen and heavy hydrocarbons

K-factors for hydrogen-heavy hydrocarbon mixtures are becoming increasingly important in new industrial applications, particularly in coal liquefaction. When equations of state such as Soave's are used to fit hydrogen-heavy hydrocarbon binary data, unrealistic binary interaction parameters k_ij are required because equilibrium ratios are not sensitive to k_ij for highly asymmetric binary systems containing a highly supercritical component.Reliable representation of experimental results can be obtained by modifying the composition dependence of the covolume parameter b for the mixture. The modification introduces a binary parameter E_Hj which has a physically reasonable size. Upon adjusting E_Hj to fit the binary data (setting k_ij = 0), good results are obtained for seven hydrogen-heavy hydrocarbon binaries.     

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.     

Untersuchung des binären Diffusionskoeffizienten in Argon/Neon‐Gemischen mittels einer Loschmidt‐Zelle kombiniert mit holografischer Interferometrie

Binary diffusion coefficients D_ij were determined for mixtures of argon and neon over the entire composition range using a Loschmidt cell at 293.15 – 333.15 K and 1 – 10 bar. Before the measurements, the different pure gases were added into the two half‐cells of the Loschmidt cell. After connecting both half‐cells, the change in partial molar density, or rather in the refractive index has been detected simultaneously as a function of position and time within each half‐cell using holographic interferometry. The binary diffusion coefficients obtained for the upper half‐cell show systematic deviations from literature data. In contrast, the data measured in the lower half‐cell are in excellent agreement with literature. Within the measurement uncertainty, the product of the molar density of the mixture and D_ij is not affected by the pressure.     

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.     

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     

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.     

Excess volume and excess enthalpy of binary mixtures composed of 1,2-dichloropropane and 1-alkanol (C5-C8)

The excess molar volumes and excess molar enthalpies at T=298.15 K and atmospheric pressure for the binary systems {CH₃CHClCH₂Cl (1)+CH₃(CH₂) _n?1OH (2)} (n=5 to 8) have been determined over the whole range of composition from the density and heat flux measurements using a digital vibrating-tube densimeter and an isothermal calorimeter, respectively. The measured excess molar volumes of all binary mixtures showed positive symmetrical trend with values increasing with chain length of 1-alkanol. Similarly, excess enthalpy values of all binary mixtures showed skewed endothermic behavior with values increasing with chain length of 1-alkanol. The maxima of excess molar enthalpy values were observed around x₁=0.65 with excess enthalpy value ranging from 1,356.8 J/mol (1-pentanol) to 1,543.4 J/mol (1-octanol). The experimental results of both H _m ^E and V _m ^E are fitted to a modified version of Redlich-Kister equation using the Padé approximant to correlate the composition dependence. The experimental H _m ^E data were also fitted to three local-composition models (Wilson, NRTL, and UNIQUAC). The correlation of excess enthalpy data in these binary systems using UNIQUAC model provides the most appropriate results.     

Temperature dependence of interaction parameters in electrolyte NRTL model

The electrolyte NRTL model captures the electrolyte solution nonideality over the entire concentration range with two binary interaction parameters. Here, the temperature dependence of the binary parameters is formulated with a Gibbs‐Helmholtz expression containing three temperature coefficients associated with Gibbs energy, enthalpy, and heat capacity contributions. We show the Gibbs energy term is correlated to the excess Gibbs energy of aqueous single electrolyte systems at 298.15 K. With the Gibbs energy term identified, the enthalpy term is correlated to the excess enthalpy at 298.15 K. With the Gibbs energy term and the enthalpy term identified, the heat capacity term is correlated to the excess heat capacity at 298.15 K. Once the temperature coefficients are properly quantified by regressing data of mean ionic activity coefficient, excess enthalpy, and heat capacity at 298.15 K or the equivalents, the model provides a comprehensive thermodynamic framework to represent all thermodynamic properties of electrolyte solutions. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1244–1253, 2016     

The refined e-NRTL model applied to CO2–H2O–alkanolamine systems

The electrolyte NRTL (e-NRTL) model by Chen (1982) and Chen and Evans (1986) is perhaps the most commonly used activity coefficient based thermodynamic model for industrial systems. It has been shown by Bollas et al. (2008) that the original e-NRTL model is inconsistent for systems with multiple cations and/or anions, in the same work the model equations for the so-called refined e-NRTL model were given. In this work the refined e-NRTL model is applied to CO₂–H₂O–alkanolamine systems. The interaction parameters of the refined e-NRTL model are regressed to partial pressure of CO₂, binary vapour–liquid-equilibrium, freezing point depression data and excess enthalpy data. The model is in the end used to predict partial pressures and speciation for the CO₂–H₂O–MEA and CO₂–H₂O–MDEA systems.     

Modeling thermodynamic properties of aqueous single‐solute and multi‐solute sugar solutions with PC‐SAFT

The Perturbed‐Chain Statistical Association Fluid Theory is applied to simultaneously describe various thermodynamic properties (solution density, osmotic coefficient, solubility) of aqueous solutions containing a monosaccharide or a disaccharide. The 13 sugars considered within this work are: glucose, fructose, fucose, xylose, maltose, mannitol, mannose, sorbitol, xylitol, galactose, lactose, trehalose, and sucrose. Four adjustable parameters (three pure‐sugar parameters and a k_ij between sugar and water that was allowed to depend linearly on temperature) were obtained from solution densities and osmotic coefficients of binary sugar/water solutions at 298.15 K available in literature. Using these parameters, the sugar solubility in water and in ethanol could be predicted satisfactorily. Further, osmotic coefficients and solubility in aqueous solutions containing two solutes (sugar/sugar, sugar/salt) were predicted (no additional k_ij parameters between the two solutes) reasonably. The model was also applied to predict the solubility of a sugar in a solvent mixture (e.g., water/ethanol) without additional fitting parameters. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4794–4805, 2013     

Prediction of Henry's law constants by matrix completion

Methods for predicting Henry's law constants H_ij are important as experimental data are scarce. We introduce a new machine learning approach for such predictions: matrix completion methods (MCMs) and demonstrate its applicability using a data base that contains experimental H_ij values for 101 solutes i and 247 solvents j at 298 K. Data on H_ij are only available for 2661 systems i + j. These H_ij are stored in a 101 × 247 matrix; the task of the MCM is to predict the missing entries. First, an entirely data-driven MCM is presented. Its predictive performance, evaluated using leave-one-out analysis, is similar to that of the Predictive Soave-Redlich-Kwong equation-of-state (PSRK-EoS), which, however, cannot be applied to all studied systems. Furthermore, a hybrid of MCM and PSRK-EoS is developed in a Bayesian framework, which yields an unprecedented performance for the prediction of H_ij of the studied data set.