Calculated Vapor Pressures Research Articles

The Laboratory Characterization of Jet Fuel Vapor and Liquid

Jet fuel (Jet A, Jet A1) was characterized using two gas chromatographic techniques. Headspace gas chromatography (HS-GC) was used to determine component partial pressures and total vapor pressures by measuring vapor densities in equilibrium with the liquid fuel. Component partial pressures and total vapor pressures were also derived from analysis of the neat jet fuel liquid by determining liquid component mole fraction and using this result with Raoult's law to calculate vapor pressure. Measurements of some of the fuel vapor samples were made at 40, 50, and 60 °C and at vapor volume-to-liquid volume (V/L) ratios of 274 and 1.2, representing, respectively, a nearly empty (2.9 kg/m3) and a half-filled (364 kg/m3) center wing tank (CWT) in a Boeing 747-100 series aircraft. The temperatures and V/L ratios were chosen to cover the range of conditions that could exist in the CWT under some aircraft operations. Measurements of other fuel vapor samples were made at the individual fuel flash point temperatures (V/L = 1.2). Characterization of the liquid fuels was done by simple injections of the neat liquids onto a temperature-programmed gas chromatograph. Results from the liquid analyses were used to calculate fuel vapor properties for comparison with the HS-GC results. Results from both characterization methods were used to predict fuel flammability by calculating fuel-to-air (F/A) mass ratios for jet fuels under different use conditions. These F/A ratio results were compared with ratios determined for the fuels at their flash points.

An Aqueous Phase Equilibrium Calculation Algorithm

AbstractA multiphase chemical equilibrium algorithm is developed which can be used with aqueous systems. The algorithm uses an average chemical potential for each species as a reference chemical potential. Incipient phases can be identified and their proximity to appearance can be determined through their tangent plane distance. Illustrative examples include the calculation of CaSO4 solubility and the calculation of vapour pressures above an SO2‐NaCl‐H2O system, including the prediction of a three‐phase equilibrium. The algorithm proved robust and versatile. The appearance of incipient phases was easily tracked. Future work needs to be done to optimize damping/acceleration coefficients in the calculations.

An improved model for ternary nucleation of sulfuric acid–ammonia–water

A revised homogeneous ternary nucleation model in H2O–H2SO4–NH3 vapors is presented. The model is based on a self-consistent version of classical nucleation theory with a rigorous treatment of nucleation kinetics. The calculation of equilibrium vapor pressures is completely revised and the effect of H2O–H2SO4 hydration is considered in detail. Compared to earlier models, the new model is able to predict nucleation rates over a wider range of temperatures and trace gas concentrations. A considerable dependence on relative humidity is found. The critical clusters corresponding to significant nucleation rates typically contain less than ten molecules and consist almost exclusively of H2SO4 and NH3.

Numerical calculation of psychrometric properties on a calculator

Simple and precise equations for calculation of saturation vapour pressure in three different temperature ranges are presented in the paper. Input parameters required for calculation of psychrometric properties are wet- and dry-bulb temperatures, dew point and dry-bulb temperatures and relative humidity and dry-bulb temperature. In this paper, the equations used for computing saturation vapour pressure may also be used for determining dew point temperature for the entire pressure range.

The non-random distribution of free volume in fluids: non-polar systems

In local composition models the focus is, usually, on the distribution of molecules or molecular segments and not on the distribution of the free volume of the system. At conditions, however, where the free volume is a significant percentage of the total volume of the system, as in the case of critical or supercritical conditions, its non-random distribution may not be negligible even for non-polar substances. In this work an attempt is made to account for the non-random distribution of the free volume in fluids and their mixtures. The classical quasi-chemical approach is used in connection with the lattice fluid model. The basic formalism is first developed for pure fluids and subsequently extended to multi-component mixtures by preserving its simplicity. The model is used for the calculation of vapour pressures and orthobaric densities of representative non-polar fluids and for the calculation of compositions and densities of liquid and vapour phases at equilibrium in mixtures of non-polar fluids. These calculations are compared with experimental data and with the corresponding calculations of the original lattice fluid model.

Predictors of cardiac events after major vascular surgery: role of clinical characteristics, dobutamine echocardiography, and beta-blocker therapy

Isobaric and isothermal experimental data for the system Methyanol + Methylacetate were analysed using the LIQFIT- and the PXFIT-methods, respectively, and were compared with usual reductions of vapour-liquid equilibrium (VLE) data. The Redlich-Kister equation was selected for describing the excess Gibbs energy as a function of composition. The results obtained with the different methods (the values of the coefficients as well as the mean absolute differences between experimental and calculated vapour pressures, vapour compositions and the extrapolated activity coefficients at infinite dilution) are virtually in complete agreement.

A new quartic equation of state

A new quartic equation of state (EOS) is presented, which consists of the repulsive term of CCOR EOS and the attractive term of PT EOS, coupled with new parameters, the general forms of which are given for non-polar substances. The new EOS can be solved algebraically like a cubic EOS. Calculated vapor pressures, specific volumes and evaporation enthalpies are compared with experimental data and with that calculated by CCOR EOS and PT EOS for a variety of fluids. In low temperature region, the new quartic EOS produces more reliable results than commonly-used cubic EOS. One important character of the new EOS is that it is capable of calculating specific volume of solid and sublimation pressure. The vapor–liquid equilibria (VLE), including volume properties, of binary mixtures are also well presented by the new EOS with van der Waals one-fluids mixing rules containing one adjustable parameter.

Pressure Dependence of Liquid Vapor Pressure: An Improved Gibbs Prediction

A new model for the vapor phase of a pressurized liquid called "the cluster model"' which is originally introduced in this work, along with an accurate equation of state for the liquid phase called the LIR, is used to derive an accurate equation for the vapor pressure of liquid as a function of externalpressure. The chemical potential of both phases have been found to be in good agreement with experiment. The calculated vapor pressure is compared with the Gibbs prediction. Wehave found that the Gibbs prediction is accurate at-low external pressures and is reasonable at moderate pressures, but has a significant deviation at high external pressures. The calculated vapor pressure is used to obtain the vaporization enthalpy in terms of the external pressure. The physical interpretations for pressure dependence of both the vapor pressure and enthalpy of vaporization are also given. Compared to the temperature dependence, the pressure dependence of vapor pressure is insignificant.

Thermodynamic properties for model compounds of coal-liquids and their mixtures — measurements and calculations

Thermodynamic properties were calculated with various cubic equations of state for the model compounds of coal liquids and their mixtures. These properties included vapor pressure, molar volume, excess volume, excess enthalpy, and vapor–liquid equilibrium. Liquid densities were also measured in this work for bicyclohexyl and mixtures of quinoline+tetralin to complement the experimental data of importance to coal liquefaction processes. The Patel–Teja equation of state yielded better results for calculations of vapor pressures and liquid molar volumes. The values of binary interaction parameter k a12 as determined from different types of mixture properties were compared and examined for their reliability. The results showed that excess volumes were capable of serving as a reliable data basis for determination of the binary interaction parameter.

Mixing rules for excess free energy models

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Global renormalization calculations compared with simulations for square-well fluids: Widths 3.0 and 1.5

A recently developed “global” renormalization group theory for calculating thermal properties of fluids both near and to far from the critical point is applied to molecules that interact via a square-well potential. Calculations of gas-liquid coexistence curve densities and vapor pressures are compared with results of recently reported Monte Carlo simulations for hard spheres that interact with square-well potentials of range 3σ (σ=hard core diameter) and with both Monte Carlo and molecular dynamics simulations for square-well potential of range 1.5σ. Additionally, values for the effective critical point exponent βe are calculated for both square wells as a function of temperature distance from the critical point. © 2000 American Institute of Physics.

A compressed liquid density correlation

A new correlation is developed for calculation of the compressed liquid density of pure compounds and mixtures. This correlation is used together with the Hankinson–Thomson (COSTALD) correlation of saturated liquid density and the Riedel equation for the calculation of vapor pressures. The range of application of this correlation is quite wide; from freezing point temperature to critical point temperature and from saturation pressure to 500 MPa. The average of error for the prediction of the compressed liquid volume of 31 compounds consisting of 3324 experimental data points is 0.77% with −0.24% bias from the experimental data. For mixtures, the average of error for the prediction of the compressed liquid volume of 13 mixtures consisting of 2101 experimental data points is 1% with −0.22% bias from the experimental data. The comparison with other correlations shows that the new correlation is somewhat better and quite reliable to very high pressures.

The aqueous solubility of trichloroethene (TCE) and tetrachloroethene (PCE) as a function of temperature

Using a flexible Au bag autoclave and a precision high-pressure liquid chromatography pump to control pressure, the liquid–liquid aqueous solubilities of TCE and PCE were measured as a function of temperature from 294 to 434 K (at constant pressure). The results were used to calculate the partial molal thermodynamic quantities of the organic liquid aqueous dissolution reactions: Δ Ḡ soln, Δ H̄ soln, Δ S̄ soln and Δ C̄ p soln. Calculated values for these quantities at 298 K for TCE are: Δ Ḡ soln=11.282 (±0.003) kJ/mol, Δ H̄ soln=−3.35 (±0.07) kJ/mol, Δ S̄ soln=−49.07 (±0.24) J/mol K, and Δ C̄ p soln=385.2 (±3.4) J/mol K. Calculated values for these quantities at 298 K for PCE are: Δ Ḡ soln=15.80 (±0.04) kJ/mol, Δ H̄ soln=−1.79 (±0.58) kJ/mol, Δ S̄ soln=−59.00 (±1.96) J/mol K and Δ C̄ p soln=354.6 (±8.6) J/mol K. These thermodynamic quantities may be used to calculate the solubility of TCE and PCE at any temperature of interest. In the absence of direct measurements over this temperature range, the Henry's Law constants for TCE and PCE have been estimated using the measured aqueous solubilities and calculated vapor pressures.

Second virial coefficients and the arsenic vapor-condensed phase equilibrium

The published temperature-pressure-vapor density data for As can be fit to 1.07% with two-parameter second virial coefficients for As2 and As4. In contrast to the assumptions of previous analyses of the As system, the vapor already shows significant departure from ideality at 975 K and 5.5 atm. One set of these virial coefficients is used along with the SGTE database with a few small adjustments to obtain a self-consistent description of the vapor-condensed phase equilibria. The calculated vapor pressure agrees with the experimental data to within 1% between 790 and 1000 K, where experimental data are most closely established, and is in agreement with the experimental scatter between 1000 and 1200 K. The thermodynamic data established in this fitting are then used to calculate the vapor pressure up to 1600 K.

Subatmospheric Vapor Pressures for Fluoromethane (R41), 1,1-Difluoroethane (R152a), and 1,1,1-Trifluoroethane (R143a) Evaluated from Internal-Energy Measurements

Vapor pressures were evaluated from measured internal-energy changes ΔU (2) in the vapor+liquid two-phase region. The method employed a thermodynamic relationship between the derivative quantity (∂U (2)/∂V) T , the vapor pressure p σ, and its temperature derivative (∂p/∂T)σ. This method was applied at temperatures between the triple point and the normal boiling point of three substances: fluoromethane (R41), 1,1-difluoroethane (R152a), and 1,1,1-trifluoroethane (R143a). In the case of R41, vapor pressures up to 1 MPa were calculated to validate the technique at higher pressures. For R152a, the calculated vapor pressure at the triple-point temperature differed from a direct experimental measurement by less than the claimed uncertainty (5 Pa) of the measurement. The calculated vapor pressures for R41 helped to resolve discrepancies in several published vapor pressure sources. Agreement with experimentally measured vapor pressures for R152a and for R143a near the normal boiling point (101.325 kPa) was within the experimental uncertainty of approximately 0.04 kPa (0.04%) for the published measurements.

Predicting the High-Pressure Phase Equilibria of Binary Mixtures of n-Alkanes Using the SAFT-VR Approach

The phase behavior of selected alkane binary mixtures is studied using SAFT-VR, a version of the statistical associating fluid theory for potentials of variable attractive range (SAFT). We treat the n-alkane molecules as chains formed from united-atom hard-sphere segments with square-well potentials of variable range to describe the attractive interactions. We use a simple relationship between the number of carbon atoms in the n-alkane molecule and the number of segments in the united atom chains in order to predict the phase behavior of n-butane with other n-alkanes. The calculated vapor pressures and saturated liquid densities of the pure components are fitted to experimental data from the triple point to the critical point. These optimized parameters are rescaled by the respective experimental critical points and used to determine the critical lines and phase behavior of the mixtures. We use the Lorentz-Berthelot combining rule for the unlike interactions. We predict the phase behavior of n-butane + n-alkane binary mixtures, concentrating mainly on the critical region. The gas-liquid critical lines predicted by SAFT-VR for the n-alkane mixtures are in excellent agreement with the experimental data, and improve significantly on the results obtained with the simpler SAFT-HS approach where the attractive interactions are treated at the mean-field level.

Correlations for Direct Calculation of Vapor Pressures from Cubic Equations of State

Vapor pressures computed from nine cubic equations of state (EOS's) of the van der Waals form are correlated in corresponding states form using the linear Pitzer principle and a simple temperature function anchored at the critical point. The results strongly suggest that cubic equations of state do not conform to the usually assumed linear dependence of fluid properties on acentric factor. The failure of three-parameter cubic equations of state to predict the exact vapor pressure consistent with a specified acentric factor is analyzed, and new correlations are presented for the characteristic parameter in Soave's cohesion function that minimize this intrinsic error over a wider range of acentric factors. Soave's direct procedure for calculation of vapor pressures from EOS is found to be more accurate than all other approximate methods by at least 1 order of magnitude. However, the leading coefficient in Soave's equations is shown to be inconsistent with the limiting slope of the vapor pressure curve predicted by the equations of state. New direct expressions are developed that eliminate this inconsistency and give good representation of vapor pressures with fewer adjustable coefficients.

Vapor−Liquid Equilibria of the Three Binary Systems: Water + Tetraethylene Glygol (TEG), Ethanol + TEG, and 2-Propanol + TEG

Vapor−liquid equilibrium and liquid density were measured for the three binary systems water + tetraethylene glycol (TEG), ethanol + TEG, and 2-propanol + TEG at 298.15 K. The experimental apparatus employed for the vapor−liquid equilibrium measurement was based on a flow method, and that for the liquid density was a vibrating tube method. The activity of water showed the negative deviation from Raoult's law, while that of ethanol was almost proportional to the mole fraction of ethanol. For the 2-propanol + TEG system, the positive deviation could be seen. The liquid density for water + TEG showed the negative excess volume for the whole range of the mole fraction. The experimental data were correlated with the Peng−Robinson (PR) equation of state using the mixing rule proposed by Wong et al. and Orbey et al. The calculated vapor pressures showed good reproducibility for the three binary systems. The calculated density was not shown for the water + TEG system.

Application of cubic equations of state to the fit of vapor pressures of pure components

A simplified technique is proposed for the application of cubic equations of state (EOS) to the calculation of vapor pressures of pure compounds and the method can be adapted to any EOS capable of predicting coexisting vapor and liquid phases. The procedure approximates vapor pressures using the zero-pressure liquid fugacity in the low temperature range, allowing a direct estimation of the parameters of a temperature cohesion function α( T r ). Estimation of the whole vapor pressure curve, from low temperatures to the critical point, is possible using minimal information about saturation states. The technique proposed here is illustrated for a generalized form of the cubic EOS.

Group contribution equation of state based on the lattice fluid theory: Alkane–alkanol systems

A new group-contribution equation of state (EOS) is proposed and applied to phase equilibrium calculations. The EOS is based on the generalized van der Waals theory and combines the Staverman–Guggenheim combinatorial term of lattice statistics with an attractive lattice gas expression. The EOS is applied to vapor–liquid equilibrium (VLE) calculations in systems containing pure hydrocarbons, alcohols, and their binary mixtures. These systems cover a wide range of situations, including nonpolar and polar compounds of different sizes and mixtures ranging from nearly-ideal to azeotropic behavior. Using VLE data for pure substances and binary mixtures of linear hydrocarbons, the parameters of linear alkane groups (CH 3 and CH 2) were simultaneously fitted. For pure linear alkanes up to C 12, calculated vapor pressures deviate less than 1.7% from the experimental values. Predicted vapor pressures of eight heavy hydrocarbons (from C 14 to C 28) are in satisfactory agreement with experimental data. The parameters for other groups (branched alkanes and alcohol groups) were fitted sequentially, using data for pure compounds and binary mixtures only containing the characteristic group being estimated and linear alkane groups. Satisfactory predictions of the vapor pressures of pure substances and bubble pressures of binary mixtures were obtained.