Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equations of state II. Carbon dioxide-heavy n-alkanes

In the present study we present the final development of the Global Phase Diagram-based semi-predictive approach (GPDA), which requires only 2-3 key data points of one homologue to predict the complete phase behavior of the whole homologues series. The ability of GPDA to predict phase equilibria in CO₂-heavy n-alkanes is compared with the equations of state LCVM and PSRK. It is demonstrated that both LCVM and PSRK are more correlative rather than predictive because their parameters are evaluated by the local fit of a considerable amount of VLE experimental data. In addition, these models fail to predict accurately the VLE of systems, which have not been considered in the evaluation of their parameters. They are also particularly inaccurate in predicting LLE and critical lines. In contrast, GPDA is reliable in the entire temperature range and for all types of phase equilibria. It yields an accurate prediction of the global phase behavior in the homologues series and their critical lines. Moreover, increasing asymmetry does not affect the reliability of GPDA; it predicts very accurately even the data of the heaviest homologues of the series.     

Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equations of state IV. Mixtures of chained n-alkanes

The present study compares the ability of two semi-predictive approaches, namely the global phase diagram approach (GPDA) and the predictive Soave-Redlich-Kwong model (PSRK), for describing the experimental data in the binary homologous series of n-alkanes. A method to expand the application of the GPDA model to the heavy n-alkanes, absent in the Design Institute for Physical Property Data (DIPPR) data base, is proposed. Since both models do not implement the binary data of the systems under consideration for evaluation of their parameters, they appear here as entirely predictive. It is shown that both models are reliable in predicting the data of symmetric systems and they yield deviations that do not significantly exceed the possible experimental uncertainties. The robustness and reliability of GPDA in comparison with PSRK becomes evident predicting the data of asymmetric systems. PSRK tends to overestimate the liquid-liquid immiscibility range and as a result it over predicts the phase equilibria pressures and fails to describe the global phase behavior. In contrast, GPDA describes the global phase behavior exactly and yields accurate predictions of both the critical and the sub-critical data even for very asymmetric systems, such as propane—n-hexatetracontane.     

Thermodynamic modeling of PVTx properties for several water/hydrocarbon systems in near-critical and supercritical conditions

Both the equation of state-excess Gibbs energy (EoS/G ^E ) model and the cubic plus association (CPA) equation of state (EoS) are compared in this study with respect to their accuracy in the correlation of PVTx for systems such as water/methanol, water/ethanol, water/benzene, water/toluene, water/methane, water/n-butane, water/n-pentane, water/n-hexane, water/heptane, and water/octane, in supercritical conditions within temperature and pressure ranges of (573–698 K) and (7.0–276.0 MPa), respectively. In the proposed EoS/G ^E model, Peng-Robinson (PR) equation of state, linear combination Vidal-Michelsen (LCVM) and Wong-Sandler (WS) mixing rules in conjunction with UNIQUAC activity coefficient model were used. Correlation of both CPA and EoS/G ^E models was evaluated by comparing the results with the experimental data. Average absolute relative deviation (AARD) for WS, LCVM, and CPA was found to be 2.99, 11.11 and 5.14%, respectively, indicating better correlation of WS model with the experimental data.     

Phase equilibria of carbon dioxide + 1-nonanol system at high pressures

Vapor-liquid-equilibria (VLE) and vapor-liquid-liquid equilibria (VLLE) data for the carbon dioxide + 1-nonanol system were measured at 303.15, 308.15, 313.15, 333.15, and 353.15 K. Phase behavior measurements were made in a high-pressure visual cell with variable volume, based on the static-analytic method. The pressure range under investigation was between 1.15 and 103.3 bar. The Soave-Redlich-Kwong (SRK) equation of state (EOS) coupled with both classical van der Waals and a Gibbs excess energy (G^E) mixing rules was used in semi-predictive approaches, in order to represent the complex phase behavior (critical curve, liquid-liquid-vapor (LLV) line, isothermal VLE, LLE, and VLLE) of the system. The topology of phase behavior is correctly predicted.     

Phase equilibrium of the CO2/glycerol system: Experimental data by in situ FT-IR spectroscopy and thermodynamic modeling

Phase equilibrium experimental data for the CO₂/glycerol system are reported in this paper. The measurements were performed using an in situ FT-IR method for temperatures ranging from 40 °C to 200 °C and pressures up to 35.0 MPa, allowing determination of the mutual solubility of both compounds. Concerning the CO₂ rich phase, it was observed that the glycerol solubility in CO₂ was extremely low (in the range of 10⁻⁵ in mole fraction) in the pressure and temperature domains investigated here. Conversely, the glycerol rich phase dissolved CO₂ at mole fractions up to 0.13. Negligible swelling of the glycerol rich phase has been observed. Modeling of the phase equilibrium has been performed using the Peng–Robinson equation of state (PR EoS) with classical van der Waals one fluid and EoS/G^E based mixing rules (PSRK and MHV2). Satisfactory agreement was observed between modeling results and experimental measurements when PSRK mixing rules are used in combination with UNIQUAC model, although UNIFAC predictive approach gives unsatisfactory representation of experimental behavior.     

Comparison of the performance of the LCVM model (an EoS/GE model) and the PHCT EoS (the Perturbed Hard Chain Theory Equation of State) in the prediction of the Vapor–Liquid Equilibria of binary systems containing light gases

The purpose of this work is to compare two models, which are able to perform Vapor–Liquid Equilibrium (VLE) predictions. The first one, the LCVM model, is an EoS/G^E one and it has been successfully applied in the prediction of the VLE behavior of polar and non-polar systems, as well as, systems of dissimilar component size, such as those containing gases with large n-alkanes. The second one is PHCT, an equation of state based on the perturbed hard chain theory. It has also been successfully applied in binary systems of supercritical fluids and non-polar molecules and in systems containing light gases and large n-paraffins. The comparisons results presented in this paper, proved that the two models are comparable, concerning the ability to predict the VLE, as well as, the volumetric behavior of systems with low to medium component size difference (supercritical fluids with non-polar components up to about 10 carbon atoms). However, as the size difference increases, LCVM performs better, especially in the near critical region of such systems.     

THERMODYNAMIC PROPERTIES OF BINARY LIQUID MIXTURES OF ETHANE AND ETHYLENE WITH METHANE AND THE RARE GASES

Two series of binary liquid mixtures containing either ethylene or ethane have been investigated, at one or more temperatures (usually at the triple-point temperature of the component with the higher melting-point). In the ethylene series liquid-vapour equilibrium and liquid density studies were carried out for mixtures with methane, krypton and xenon; the heats of mixing were also measured for the ethylene + krypton mixtures. In the ethane series, which comprised mixtures with methane, argon, krypton and xenon, all three properties were measured except for the ethane + methane and ethane + argon systems where the enthalpies of mixing were already known. The ethylene + ethane system was also investigated at 161.39 K.

The results have been used to estimate the thermodynamic excess functions G^E , V^E and H^E . The G^E values decrease, within each series, as one moves from the lighter to the heavier rare gas, the values being lower in the ethane series. For the ethane + xenon mixtures both G^E and H^E are negative, showing a weak attraction between the two molecules. The V^E values for the mixtures of hydrocarbons suggest the probable formation of interlocking structures between the two components.

The values of the thermodynamic excess functions have been interpreted in the light of the model of Frisch-Longuet Higgins-Widom for the liquid state.     

Effect of temperature gradient on competitive growth behavior of Si and YSi2 in a Si–Y eutectic alloy prepared by Bridgeman method

The Si–Y eutectic alloy has been prepared by Bridgeman method where the high temperature gradient (G_E) can be obtained by means of double heating combining with liquid metal cooling. The microstructures of longitudinal section and cross section at different G_E have been observed. It can be seen clearly that the YSi₂ phase presents the evolution process of thick banded shape, island shape, reticular shape and fine strip shape as G_E increases from 90 K/cm to 200 K/cm. Based on the interface growth temperature model, it can be concluded that the interface growth temperatures of Si phase and YSi₂ phase both will decrease linearly with increasing G_E while that of eutectic structure will keep a constant of 1485.6 K. Two critical temperature gradients G_EC1 = 52 K/cm and G_EC2 = 111 K/cm have been calculated. Eutectic coupling growth will take the dominant position when the actual G_E is greater than G_EC2. The primary Si phase will begin to form as G_E is smaller than G_EC2 and will be thicker as G_E is smaller than G_EC1. The coupling effect of withdrawal rate and G_E on the microstructures of the Si–Y alloy also has been analyzed comprehensively.     

Liquid—liquid phase splitting—I analytical models for critical mixing and azeotropy

The simultaneous phenomena of critical mixing and azeotropy is discussed. The ability of different models for G^E to predict critical mixing is     

Thermodynamics of associated solutions—I: Alcohol-inert solvent solutions

For alcohol-aliphatic hydrocarbon solutions, the athermal associated solution theory of Wiehe and Bagley is modified by introducing a physical interaction term of the Scatchard—Hildebrand type expression. Good fits between the modified theory and experimental data for the excess Gibbs free energy of mixing, G^E, the excess enthalpy of mixing, H^E, and the excess volume of mixing, V^E are obtained. The parameters involved in G^E and H^E expressions are either a characteristic of the alcohol or calculable using the proposed correlations and pure component properties.     

Thermodynamics of associated solutions—II alcohol-active solvent solutions

The modified Wiehe-Bagley expressions for G^E, H^E and V^E of alcohol-inert solvent solutions are applied to alcolhol-active solvent solutions. Excellent agreement with experimental data is obtained, even for H^E and V^E curves showing a maximum and minimum in the composition plots. The alcohol polymerization equilibrium constant depends both on the alcohol and solvent. The physical interaction parameter is calculable from pure component properties using a proposed correlation equation, which is similar to that for alcohol-inert solvent solutions. The Kretschmer-Wiebe theory for alcohol-active solvent solutions, which has been formulated incorrectly, is rederived. In our theory a chemical linking between the alcohol complex and solvent molecule through hydrogen bonding is considered in addition to the self-association of the alcohol molecules. The rederived expression for G^E fits well with the experimental data. However, the hydrogen bonding strength between the alcohol and active solvent molecules calculated is negative for the systems investigated, which is difficult to be justified.     

Prediction of solid–gas equilibria with the Peng–Robinson equation of state

In many applications related to Supercritical-Fluid (SCF) technology, solids are dissolved in SC fluids. Experimental data are now available for many systems but cannot cover all cases of potential practical interest. The prediction of solid solubilities in SC fluids, often in the presence of co-solvents, is useful for rational design of SCF extraction and related processes. Recently, thermodynamics has made considerable steps towards describing complex systems (gases with polar compounds) at high pressures using the so-called Equation of State/Excess Gibbs Free Energy (EoS/G^E) models. The success of these models is so far restricted to Vapor–Liquid Equilibria (VLE) for which they have been primarily developed and tested. In this work we evaluate such a predictive model, the LCVM EoS, for solid–gas equilibria (SGE) including systems with co-solvents. LCVM is chosen due to its success for VLE of asymmetric systems such as CO₂ with heavy alkanes and alcohols. Successful predictions are obtained for several solids as well as for some systems with co-solvents, but the results are less satisfactory for complex, multifunctional solids. A discussion of several factors, which affect modeling of SGE with cubic EoS, is included.     

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.     

Thermodynamic modeling of vapor-liquid equilibria and excess properties of the binary systems containing diethers and n-alkanes by cubic equation of state

A comparison of the performances of two different approaches of cubic equations of state models, based on a classical van der Waals and mixing rules incorporating theG ^E equation, was carried out for correlation of Vapor-Liquid Equilibria (VLE), H^E and C _P ^E data alone, and simultaneous correlation of VLE+H^E, VLE+C _P ^E , H^E +C _P ^E and VLE+H^E +C _P ^E data for the diethers (1,4-dioxane or 1,3-dioxolane) with n-alkane systems. For all calculations the Peng-Robinson-Stryjek-Vera cubic equation of state (PRSV CEOS) was used. A family of mixing rules for the PRSV CEOS based on the Modified van der Waals one-fluid mixing rule (MvdW1) and two well-known CEOS/G^E mixing rules (MHV1 and MHV2), was considered. The NRTL equation, as the G^E model with linear or reciprocal temperature dependent parameters, was incorporated in the CEOS/G^E models. The results obtained by the CEOS/G^E models exhibit significant improvement in comparison to the MvdW1 models.     

Adsorption kinetics and equilibrium of copper from ethanol fuel on silica-gel functionalized with amino-terminated dendrimer-like polyamidoamine polymers

The adsorption kinetics and equilibrium of silica-gel functionalized with amino-terminated dendrimer-like polyamidoamine (PAMAM) polymers SiO₂-G1.0, SiO₂-G2.0 and SiO₂-G3.0 for Cu²⁺ in ethanol fuel were investigated by using batch method. The results indicated that the all the adsorptions of the three adsorbents followed well the pseudo second-order model. The adsorption isotherms were fitted by Langmuir model, Freundlich model and Dubinin–Radushkevich (D–R) model. The results showed that Langmuir model was more suitable to describe the equilibrium data than the Freundlich model. From the D–R isotherm model, the mean free energy E calculated of the three adsorbents showed that the adsorptions were taken place by physical processes. Thermodynamic parameters, ΔG⁰, ΔH⁰ and ΔS⁰ indicated the Cu²⁺ adsorption to be endothermic and spontaneous with decreased randomness at the solid-solution interface, resulting in their higher adsorption capacities at higher temperature. The effect of generation number of PAMAM polymers loaded on silica-gel, contact time, initial concentration and temperatures on the adsorption capabilities were studied in detail. Moreover, the adsorption mechanism of copper from ethanol fuel was also presumed.     

Solutions of iodic acid in formamide. Thermodynamic properties from electromotive force measurements

Electromotive force measurements on cells without liquid junction have been used to determine pK_a of iodic acid and the standard electrode potentials (E°) of the silver-silver iodate electrode in formamide at 9 temperatures from 5–45°C. The pK_a was evaluated by using the Debye-Huckel theory with an ion-size parameter of 5.5 A°. The change in the standard electrode potentials is given as a function of temperature, t°C by the equation E°_t = 0.2786 - 8.125 x 10^?4(t - 25) - 6.385 x 10^?6(t - 25)² The standard thermodynamic quantities (ΔG°, ΔH°, and ΔS°) for the cell reactions have been evaluated for different temperatures.     

Thermodynamic studies of sodium bromide in 2-propanol—water mixtures (10, 30 and 50 wt.%) from electromotive force measurements

The emf of the cell: Pt|Na(Hg)|NaBr(m), w wt.% 2-propanol—water mixture|AgBr, Ag has been measured with w = 10, 30 and 50 at temperatures of 293.15, 303.15 and 313.15 K in the molality range of NaBr from 0.04 to 0.18 mol kg^?1. From these data the standard emf of the cell has been obtained and by utilizing data from the literature for the E⁰ of Ag/AgBr electrode the standard potential of sodium amalgam electrode has been determined. Mean activity coefficients of NaBr and thermodynamic functions ΔG⁰_t, ΔH⁰_t and ΔS⁰_t for transfer of NaBr from water to 2-propanol—water mixtures have also been calculated. Thermodynamic quantities of transfer have been compared to those for the HBr electrolyte.     

Excess Gibbs free energy of butyl acetate with cyclohexane and aromatic hydrocarbons at 308.15K

Molar excess Gibbs free energies of mixing (C ^E ) for butyl acetate+cyclohexane or benzene or toluene or o- or m- or p-xylene were calculated by using Barker’s method from the measured vapor pressure data by static method at 308.15±0.01 K over the entire composition range. The G ^E values for the binary mixtures containing cyclohexane or benzene are positive; while these are negative for toluene, o-, m- and p-xylene system over the whole composition range. The G ^E values of an equimolar mixture for these systems vary in the order: cyclohexane>benzene>o-xylene>m-xylene>p-xylene>toluene. The G ^E values for these systems were also calculated by Sanchez and Lacome theory using the previously published excess enthalpy and excess volume data. It is found that while values of G ^E from Sanchez and Lacombe theory are in reasonably good agreement with those calculated by Barker method for m-xylene and p-xylene mixtures, agreement is very poor for other systems although they predict the sign of G ^E data except in the case of mixtures containing benzene.     

Pit formation in relation to the etching of aluminium in chloride solutions

The pitting potential,E _p , has been determined by steady-state and linear potential sweep methods.E _p is is shown to be a logarithmic function of the chloride concentration; the form of the function yields information about the equilibria between electrode and electrolyte species atE _p . Values of the enthalpy of activation for the pitting process have been determined by measuring the rate of pit propagation at constant driving potential at a series of temperatures. An ‘ad hoc’ interpretation of the data has been avoided and an attempt made to present the results using a more theoretical approach.