Phase equilibria calculations with a modified redlich-kwong equation of state

A modified Redlich-Kwong equation of state for pure substances in the liquid-vapour coexisting phase region is suggested in which the fugacity coefficients of the two phases are equated and the resulting relationship is solved by assuming ω_b to be temperature dependent while ω_a remains constant. A generalised correlation for ω_b is found with the acentric factor as a parameter. This approach is compared with the other two possible modifications, i.e. when ω_a is a funtion of temperature while ω_b is constant, and when both ω_a and ω_b are temperature dependent. Comparison revealed the excellent attainment of the equilibrium conditions when the proposed method is applied. Predicted volumetric properties and isothermal enthalpy departures of the liquid and vapour as well as the saturation vapour pressures are also compared which reveal the adequacy of the new modification. With the application of the mixing rules, the proposed modified equation is successfully applied to VLE calculations for binary mixtures of different complexities.     

THE MODIFIED PGR EQUATION OF STATE: PURE-FLUID PREDICTIONS

The Park-Gasem-Robinson (PGR) equation of state (EOS) has been modified to improve its volumetric and equilibrium predictions. Specifically, the attractive term of the PGR equation was modified to enhance the flexibility of the model, and a new expression was developed for the temperature dependence of the attractive term in this segment-segment interaction model.

The predictive capability of the modified PGR EOS for vapor pressure and saturated liquid and vapor densities was evaluated for selected normal paraffins, normal alkenes, cyclo-paraffins, light aromatics, argon, carbon dioxide, and water. The generalized EOS constants and substance-specific characteristic parameters in the modified PGR EOS were obtained from pure component vapor pressures and saturated liquid and vapor molar volumes. The calculated phase properties were compared with those of the Peng-Robinson (PR), the simplified-perturbed-hard-chain theory (SPHCT), and the original PGR equations. Generally, the performance of the proposed EOS (%AAD of 1.3, 2.8, and 3.7 for vapor pressure, saturated liquid, and vapor densities, respectively) was better than the SPHCT and original PGR equations in predicting the pure fluid properties.     

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.     

Fluid-phase equilibria in binary systems containing an ionic liquid. Application of the Percus-Yevick-van der Waals equation of state

Following some simplifications to reduce the computational effort, the Percus-Yevick-van der Waals equation of state is used to calculate the isothermal total pressure of a binary liquid system containing one volatile nonelectrolyte liquid and one nonvolatile ionic liquid. Pure-component parameters a and b are found from pure-component enthalpy-of-vaporization and liquid-density data. The single binary parameter a₁₂ is obtained from Henry's constant for the nonelectrolyte in the ionic liquid. For 10 binary systems, calculated total pressures are in good agreement with experiment although in a few systems observed total pressures are slightly higher than those calculated in the region where the ionic liquid is dilute. Brief attention is given to a few binary systems with a miscibility gap.     

Application of a New Gibbs Energy Equation to Model a Distillation Tower for Production of Pure Ethanol

A steady‐state equilibrium‐stage model based on MESH equations was proposed to simulate saline extractive distillation columns. The interaction parameters between each component of water‐CaCl₂ and ethanol‐water were obtained from mean ionic activity coefficients and vapor‐liquid equilibrium (VLE) experimental data. Additionally, the interaction coefficients for the ethanol‐CaCl₂ pair were fitted to experimental VLE data which were reported by Nishi for the ethanol‐water‐CaCl₂ system. It should be noted that adjustable parameters between each pair were considered to be temperature dependent. The results confirmed that the proposed model could accurately predict the experimental vapor‐liquid equilibrium data for ethanol‐CaCl₂‐water systems. Finally, the validated model was coded using MATLAB software and was solved using the Wang‐Henke method, including the VLE and enthalpy models.     

Effect of water on the solubilities and mass transfer coefficients of gases in a heavy fraction of fischer-tropsch products

The effects of water on the solubilities, C^*, and volumetric mass transfer coefficients, k_La, for CO, H₂, CH₄ and CO₂ in a heavy fraction of Fischer-Tropsch liquid were examined at elevated pressures and temperatures at different mixing power inputs. For these gases, higher solubilities were measured in the hydrocarbon mixture saturated with water than those obtained in the hydrocarbon free of water. The k_La values for the four gases were slightly affected by the presence of dissolved water in the hydrocarbon mixture; and they were strongly dependent on the power input per unit liquid volume. Two empirical correlations for k_La as a function of turbine speed and pressure are proposed.     

Generalized treatment for the vapor pressure behavior of polar and hydrogen-bonding compounds

The vapor pressure behavior of 25 polar compounds, including water and a number of alcohols, has been analyzed and subjected to a generalized treatment using the relationship, for a total of 1343 experimental measurements presented in the literature and covering the range included between their respective triple points and critical points. For each of these compounds, the parameters of this equation were established using a nonlinear regression numerical technique. The parameters resulting from this regression reproduce vapor pressures for all these polar compounds with an average deviation of 0.44 percent (1343 points). To extend the application of this vapor pressure relationship, the original parameters of these polar substances were correlated with their respective basic physical properties M, T_c, P_c and T_b. The resulting generalized parameters reproduce vapor pressures with an average deviation of 1.44 percent (1343 points) for all these polar and hydrogen-bonding compounds. This generalized correlation can be applied for the reliable prediction of vapor pressures for polar substances for which inadequate information is available.     

Simultaneous liquid–liquid and vapour–liquid equilibria predictions of selected oxygenated aromatic molecules in mixtures with alkanes,alcohols, water,using the polar GC-PC-SAFT

Phase equilibria of oxygen-bearing aromatic compounds, hydrocarbons and water mixtures are of essential interest in many processes using feeds originating from biomass. The strong non-ideal thermodynamic behavior of these systems sometimes results in immiscibility with both water and alkanes.To address this problem, the GC-PPC-SAFT equation of state [Tamouza et al., 2004; Nguyen-Huynh et al., 2008a] is extended to some selected components: phenol, alkyl-phenols, alkyl-benzoates, benzaldehyde and anisole. However, as in these multifunctional compounds, the proximity of polar functional groups may result in a lack of transferability of the parameters from the monofunctional homologous species, some parameters have been adapted in view of physical arguments. Next, liquid–vapour and liquid–liquid equilibria of mixtures with n-alkanes were evaluated, using a predictive method for the binary interaction parameters (k_ij) [Nguyen-Huynh et al., 2008b]. Finally, mixtures with other associating compounds, as alcohols and water have also been considered.In all cases, both correlations and predictions are qualitatively and quantitatively satisfactory. The relative deviations obtained on bubble pressure of vapor–liquid equilibria are 4–8%, that is comparable to those obtained on previously investigated systems.     

A modified van der Waals type equation of state

A cubic equation of the van der Waals type is presented with the critical compressibility factor taken as substance dependent. Input requirements are Pitzer's acentric factor and the critical temperature and pressure. Parameter b is treated as independent of temperature, and the temperature dependence of parameter a is given by an expression similar to that proposed by Soave. A test on vapour pressure is presented for more than one hundred substances and on liquid density for 65 substances and comparisons are given with results of Soave's and Peng-Robinson's equations. Representation of vapour pressure, particularly at low pressures, and of the liquid density has been improved. The equation is restricted to non-associating compounds.     

Aspects of vapor pressure osmometry

Three aspects of vapor pressure osmometry were examined: drop size, solute volatility, and the constancy of the calibration factor. It was shown that there is a drop size effect which is dependent on the solute concentration. Solutes having vapor pressures as low as 0.3 mm Hg under the operating conditions were found to give unsatisfactory results. The calibration factor was determined using eight compounds in the molecular weight range of 128 to 883 in chloroform, toluene, and methyl ethyl ketone at several temperatures; a small but significant dependence of the calibration factor on molecular weight was demonstrated. The results fitted, with a high degree of accuracy, the relation log M?_n = a + b log (ΔV/C)_{C = 0}, where a and b are constants for a given solvent/temperature combination. However, measurements with standard polystyrene samples, using extrapolations of this relationship to higher molecular weights, revealed considerable discrepancies in results for the one compound under different solvent/temperature combinations.     

The controlling quantity in cubic equations of state for phase equilibrium calculations

It has been demonstrated that the vapor—liquid equilibrium values calculated from the modified Martin equation and the Clausius equation are identical to those obtained from a properly modified van der Waals equation of state. The reason for this observation is explained in this work in terms of the role of Ω_a (= aP_c/r²T) at specified state conditions. It is the controlling quantity in VLE calculations when simple van der Waals-type equations of state together with the conventional mixing rules are used. Thus, equations capable of yielding identical values of Ω_a give identical equilibrium values. The evidence and the mathematical proof of the relationship required for defining such a role for Ω_a are presented.     

Prediction of partial molal volumes of normal fluid mixtures

Partial molal volumes of normal fluid mixtures in the liquid state were evaluated by means of a modified Redlich-Kwong equation of state. Molal volumes and vapor pressures of pure saturated liquids were used for evaluating the two parameters of the equation. These parameters were treated as temperature dependent. Partial molal volumes of six binary systems were satisfactorily predicted in this investigation. Satisfactory compressibility factors for pure liquids at high pressures were also obtained by the proposed method.     

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.     

Taking advantage of available cubic equations of state

All available simple cubic equations of state (EOS) are developed for specific representations. An effort has been made to take advantage of these existing equations for binary vapor-liquid equilibrium (VLE) as well as density calculations by assigning different EOS to different components of the mixture under consideration. A four-parameter cubic equation was used for combining the equations in the calculation. The effect of substance-dependent Ω_ac on vapor-liquid equilibrium calculations was further investigated, using two sets of mixing rules. A criterion for selection of equations for VLE calculation by means of the proposed approach was suggested. The improvement in the prediction of liquid volumes for binary mixtures based on the fitting of pure component liquid volumes was very satisfactory.     

Hydrolysis of triacylglyceridesin the presence of tin(IV) catalysts

Tin(IV)-based compounds (mono-n-butyltin hydroxide oxide (a), di-n-butyl-oxo-stannane (b), di-n-butyl tin dilaurate (c) and tin oxide (d)) were used as catalysts in the hydrolysis of triacylglycerides (TGs). The effects of the nature and amount of the catalysts, the nature of the TGs, the temperature and reaction time were evaluated. Compared with the usual industrial processes, these systems showed excellent activities at mild temperatures and pressures, and low amounts of catalyst (ca. 0.3% w/w_oil). Fatty acid (FA) conversions of ca. 97% were obtained at 180 °C, 4 h at oil:water:catalyst a molar ratio of 1:24:0.01 and, using soybean oil.     

Vapor-liquid equilibria of carbon dioxide+n-propanol at elevated pressure

High-pressure vapor-liquid equilibrium data were measured for the binary mixtures of CO₂+n-propanol at various isotherms (313.15–343.15 K). The vapor and liquid compositions and pressures were measured in a circulation-type apparatus. To facilitate easy equilibration, both vapor and liquid phases were circulated separately in the experimental apparatus and the equilibrium composition was analyzed by an on-line gas chromatograph. The experimental data were compared with literature results and correlated with the Peng-Robinson (PR) equations of state using the Wong-Sandler mixing rules. Calculated results with PR EOS showed good agreement with our experimental data.     

基团对应状态法(CSGC)用于纯物质饱和蒸气压的估算

将对应态原理与基团贡献法相结合,引入拟临界性质的概念,提出基团对应状态法(Correspounding State with Group Contribution,简称CSGC)。并将其与Riedel方程相结合用于饱和蒸气压的估算,提出新的蒸气压估算方程(CSGC-PR方程)。88种基团的参数由包括饱和烃、不饱和烃、环烃、芳烃、含氧化合物、含硫化合物、含氮化合物、含卤化合物等350种物质5255个饱和蒸气压实验数据关联获得。新模型的估算精度优于现有的对应状态法,不仅对于高碳数分子有良好的估算精度,并对非极性物质能较好地外推高压下的饱和蒸气压。     

Study of Water Layers Adsorbed on Na- and Ca-Montmorillonite by the Pulsed Nuclear Magnetic Resonance Technique

The pulsed magnetic resonance technique was applied to the measurement of the longitudinal (T₁) and transversal (T₂) relaxation time of water molecules adsorbed by Na- and Ca-Montmorillonite, In the Na-clay the water was adsorbed as a monomolecular layer whilst in the Ca-clay, the bimolecular layer was formed under specified water vapor pressures. The effect of paramagnetic centers (Fe³⁺) was corrected and the samples were studied between + 30°C and ?80°C. The main contribution to T₁ was the “inter” contribution of protons diffusing from one water molecule to another whilst T₂ results from simultaneous rotational (intramolecular) and diffusional (intermolecular) contributions. The proton diffusion coefficient and the life-time of a proton on one specified water molecule is derived from T₁ inter. The calculated value at 298°C is equal to 10^?7 times the life-time in liquid water, suggesting a dissociation degree 10⁷ times higher in the adsorbed state than in liquid water. This increase in the dissociation degree as well as the reported activation energies are in good agreement with experimental data obtained from conductimetric and dielectric measurements performed previously.     

High-pressure vapor-liquid equilibrium measurement for the binary mixtures of carbon dioxide+n-butanol

High-pressure vapor-liquid equilibrium data for the binary mixtures of CO₂+n-butanol were measured at various isotherms of (313.15, 323.15, 333.15 and 343.15) K, respectively. The equilibrium compositions of vapor and liquid phases and pressures at each temperature were measured in a circulation-type equilibrium apparatus. To facilitate easy equilibration, both vapor and liquid phases were circulated separately in the experimental apparatus and the equilibrium composition was analyzed by an on-line gas chromatograph. The experimental data were compared with literature results and correlated with the Peng-Robinson (PR) equations of state using the Wong-Sandler mixing rules. Calculated results with the PR EOS showed good agreement with our experimental data.     

立方型状态方程用于液体过量体积的计算

用 SRK、PR 和 YU-LU 三个立方型状态方程对常压下的液体混合过量体积进行了关联计算,涉及的体系包括非极性、弱极性、水及羧酸等强极性混合物。对于对称的非极性、弱极性、极性流体混合物获得了良好的结果,但这种计算方法不适用于含水或羧酸的体系。