Corresponding-states Correlation Research Articles

Revisiting the Corresponding-States-Based Correlation for Pool Boiling Critical Heat Flux

A corresponding-states correlation for predicting the critical heat flux (CHF) in pool boiling conditions is proposed, and only requires knowledge of physical property constants of the fluid at any fluid temperature: molar mass, critical temperature, critical pressure, and the Pitzer acentric factor. If a fourth corresponding equation of state (EoS) parameter is added, a more accurate CHF correlation is obtained and matches Kutateladze–Zuber prediction within ±10% in the reduced temperature range of 0.55–0.95. This way, CHF can be easily predicted for any reduced temperature within the range of correlation’s validity by only knowing basic properties of the fluid. Additionally, two corresponding-states correlations for determining the capillary length are proposed and also do not rely on any temperature- and pressure-dependent fluid properties. A simpler correlation only using the Pitzer acentric factor is shown to be imprecise, and a more complex correlation also accounting for the fourth corresponding EoS parameter is recommended. These correlations are fundamental for further developments, which would allow for accurate prediction of CHF values on functionalized surfaces through further studies on the influence of interactions of fluid properties with other parameters, such as wetting and active nucleation site density.

Vaporization enthalpy of silanes fluids: A new correlation based on the corresponding states principle

A new and simple correlation based on the corresponding-states principle is proposed for the relation of the vaporization enthalpy with the temperature for saturated silanes. The primary accepted data for 7 silanes obtained from the most recent version of the DIPPR database are used as reference to define the model. Then predictions are made for other 29 silanes and compared with DIPPR data. The proposed correlation reproduces these data with average absolute deviations (AAD) lower than 1% for 8 silanes, AAD<5% for 30 fluids and AAD<10% for 35. The predictive power of the model is also checked by considering vaporization enthalpy data available for other 9 silanes not included in DIPPR. In this case, the mean AAD is 2%. Comparison with other previously published corresponding-states correlations is made, the here proposed being simpler, accurate, and predictive.

Surface Tension of Liquid Organic Acids: An Artificial Neural Network Model.

An artificial neural network model is proposed for the surface tension of liquid organic fatty acids covering a wide temperature range. A set of 2051 data collected for 98 acids (including carboxylic, aliphatic, and polyfunctional) was considered for the training, testing, and prediction of the resulting network model. Different architectures were explored, with the final choice giving the best results, in which the input layer has the reduced temperature (temperature divided by the critical point temperature), boiling temperature, and acentric factor as an independent variable, a 41-neuron hidden layer, and an output layer consisting of one neuron. The overall absolute percentage deviation is 1.33%, and the maximum percentage deviation is 14.53%. These results constitute a major improvement over the accuracy obtained using corresponding-states correlations from the literature.

Thermodynamic properties of dilute hydrogen in supercritical water

A thermodynamic model is developed to calculate the fugacity coefficients and partial molar volumes of hydrogen at infinite dilution in water at 647.1–2000 K and pure water densities between 0 and 1500 kg m−3. The model is based on the predicted values of DCFI (the dimensionless integral of the infinite dilution hydrogen - water direct correlation). Values of DCFI at low water densities are calculated from accurately known second cross virial coefficients; at high water densities predictions are based on the relations from the theory of a mixture of hard spheres; DCFI values at intermediate water densities are interpolated using a variant of corresponding-states correlation. Predicted values of the hydrogen fugacity coefficients at infinite dilution in water are compared with experimental data and results of the literature equations of state. The included Excel spreadsheet allows calculations provided that values of T, P, ρ1∗, and κT for pure water are entered by a user.

Surface tension of refrigerants: A new correlation using the boiling point as reference

A new general corresponding-states correlation model for the calculation of the surface tension of refrigerants is proposed. The main difference with respect to other models available in the literature is that, in addition to the critical point temperature, the proposed model includes the temperature and surface tension values at the boiling point as input properties to define the reduced (non-dimensional) properties. Only three general adjustable coefficients are needed, which were obtained by a fitting procedure to the data presently available for 80 refrigerants. Averaged absolute deviations below 9.5% are found in all cases, being below 5% for 67 out of the 80 fluids considered. Results for another four corresponding-states models available in the literature are also obtained. The correlation model proposed here gives clearly better overall results, and it is the only one including exclusively temperature and surface tension values as inputs.

New corresponding-states correlation model for the surface tension of refrigerants

A new corresponding-states correlation model for the calculation of the surface tension of refrigerants is proposed. The main difference with respect to other models available in the literature is that this includes the temperature and surface tension values at the triple point as input properties to define the reduced (non-dimensional) properties, and therefore it is applicable to the entire vapour-liquid temperature range in which this property is defined. The model uses the critical point and the triple point temperature of refrigerant R142b as fixed input parameters and four numerical coefficients obtained by a fitting procedure. The adjustable coefficients were calculated by taking into account the data for 33 selected refrigerants for which the surface tension values at the triple point are known. For each fluid the input variables are the critical point temperature, the triple point temperature, and surface tension at the triple point temperature. To check the model's capacity, we used it to calculate the surface tension values of another 50 refrigerants for which the value of this property is not known at the triple point. To do this, we used as input the lowest temperature at which a value of the surface tension is available. In both cases, correlation and prediction, the calculations were done by considering the most up-to-date database presently available for the surface tension of refrigerants. Averaged absolute deviations below 5% were found for 63 of the 83 fluids considered, and only for 4 of them were they greater than 10%. Results for another four corresponding-states models available in the literature were also obtained. That proposed here gave clearly better overall results.

Application of modified Tao-Mason equation of state to refrigerant mixtures

In our previous work, we modified the Tao-Mason EOS [1] to predict the volumetric properties of pure refrigerants [2]. In the present study, we have successfully extended the modified Tao-Mason EOS to refrigerant mixtures. The second virial coefficient, B2(T), and the temperature-dependent correction factor α(T) and van der Waals co-volume b(T) were calculated from a two-parameter corresponding-states correlation along with the enthalpy of vaporization and the molar density, both at the normal boiling point. Then the cross parameters B12(T), α 12(T), and b12(T), were determined with the help of simple combining rules. The constructed Tao-Mason EOS was employed to predict the densities and vapor pressures of several HFC, hydrocarbons and HFO mixtures. The calculated results were compared with literature data. The overall agreement between our results and literature values is remarkable.

Equation of state for mercury: revisited

An analytical equation of state by Song and Mason is developed to calculate the PVT properties of mercury. The equation of state is based on the statistical-mechanical perturbation theory of hard convex bodies and can be written as a fifth-order polynomial in the density. There exists three temperature-dependent parameters in the equation of state; the second virial coefficient, an effective molecular volume, and a scaling factor for the average contact pair distribution function of hard convex bodies. The temperature-dependant parameters have been calculated using corresponding-states correlations based on the surface tension and the liquid density at the normal boiling point. Employing the present equation of state, we have calculated the PVT properties of mercury over a wide range of temperatures and pressures. The average absolute deviation for the calculated density of mercury in the saturation and compressed states is 1.09%.

The Corresponding-States Correlation for the Prediction of Crude Oil Undersaturated Densities

In this work, a corresponding-states correlation is presented for prediction of crude oil density in an undersaturated state. The correlation is the extension of corresponding-states liquid densities correlation. The modified corresponding states liquid densities method for predicting saturated liquid densities was coupled with the Tait equation to predict undersaturated densities. Correlations are proposed for the temperature-dependence of Tait equation parameters. Applying proper mixing and combining rules, we calculated the density of 26 crude-oil samples, mainly from Iranian reservoirs. The mixtures included a variety of compositions including N2, H2S, CO2, and hydrocarbons. The AAD% for the present method is 0.85%.

Extension of Tao-Mason Equation of State to Mixtures: Results for PVTx Properties of Refrigerants Fluid Mixtures

Tao and Mason (J. Chem. Phys. 1994, 100, 9075−9084) developed a statistical-mechanical-based equation of state (EOS) for pure substances. In the present study, we have successfully extended this EOS to fluid mixtures, selecting refrigerant fluid mixtures as the test systems. The considered refrigerant mixtures are R32 + R125, R32 + R134a, R134a + R152a, R125 + R143a, R125 + R134a, R32 + R227ea, R134a + R290, and R22 + R152a. The second virial coefficient, B(T), necessary for the mixture version of the Tao−Mason (TM) EOS, was determined using a two-parameter corresponding-states correlation obtained from the analysis of the speed of sound data and two constants: the enthalpy of vaporization ΔHvap and the molar density ρnb, both at the normal boiling point. Other temperature-dependent quantities, including the correction factor α(T) and van der Waals covolume b(T), were obtained from the Lennard-Jones (12−6) model potential. The cross parameters B12(T), α12(T), and b12(T), required by the EOS for mixtures, ...

Corresponding-States Laws for Protein Solutions

The solvent around protein molecules in solutions is structured and this structuring introduces a repulsion in the intermolecular interaction potential at intermediate separations. We use Monte Carlo simulations with isotropic, pair-additive systems interacting with such potentials. We test if the liquid-liquid and liquid-solid phase lines in model protein solutions can be predicted from universal curves and a pair of experimentally determined parameters, as done for atomic and colloid materials using several laws of corresponding states. As predictors, we test three properties at the critical point for liquid-liquid separation: temperature, as in the original van der Waals law, the second virial coefficient, and a modified second virial coefficient, all paired with the critical volume fraction. We find that the van der Waals law is best obeyed and appears more general than its original formulation: A single universal curve describes all tested nonconformal isotropic pair-additive systems. Published experimental data for the liquid-liquid equilibrium for several proteins at various conditions follow a single van der Waals curve. For the solid-liquid equilibrium, we find that no single system property serves as its predictor. We go beyond corresponding-states correlations and put forth semiempirical laws, which allow prediction of the critical temperature and volume fraction solely based on the range of attraction of the intermolecular interaction potential.

Corresponding-states correlations for estimating partial molar volumes of nonelectrolytes at infinite dilution in water over extended temperature and pressure ranges

Analysis has been made of a large volume of data to obtain the partial molar volumes of aqueous solutes at infinite dilution for temperatures up to 700 K and pressures up to 50 MPa. Values of V 2 ∞ are expressed in terms of the infinite dilution water–solute direct correlation function integral (DCFI) at the conditions of interest reduced by the solute's DCFI at 298.15 K, 0.1 MPa. Empirical equations have been found for the temperature-density dependence of these reduced DCFIs for solute classes of: simple fluids, nonpolar compounds, aromatic compounds, monohydric alcohols, monocarboxylic acids, nitriles, amides, and other organic solutes. A reliable, but less accurate generalization, based on pure water DCFI, has also been developed for the reduced DCFI for solute classes of: simple fluids, nonpolar compounds, polar substances, and compounds containing chemically bonded water. At high densities, the reduced DCFI for all solutes is the same as that for water, which is consistent with the behavior of hard-sphere mixtures.

An analytical equation of state for refrigerant mixtures

We have extended our previous work on the equation of state for refrigerants to their mixtures successfully. The temperature-dependent parameters of the equation of state have been calculated using our previous corresponding-states correlation based on the normal boiling point temperature and the liquid density at the normal boiling point. We have applied a simple combining rule for the normal boiling point constants to extend our previously proposed equation of state to mixtures of refrigerants. In this work the liquid densities of a large number of refrigerant mixtures have been calculated and the results are compared both with experimental data and a recent correlation by Nasrifar et al. (1999). The agreement is good.

Corresponding-states correlation for compressed liquid density of mixtures

Our previous corresponding-states correlation for the prediction of the compressed liquid density of pure substances has been extended to mixtures. The correlation requires the values of critical constants, acentric factor, freezing temperature, liquid density at the freezing point, and an adjustable parameter to determine the saturated liquid densities. The mixtures applied with this correlation are liquefied noble gas and inorganic gas mixtures, mixtures of saturated, aromatic, and aliphatic hydrocarbons, refrigerant mixtures, and mixtures of strongly hydrogen-bonded and polar fluids. The predicted results are compared with the well-known corresponding-states liquid densities by Hankinson et al. and with the correlation recently proposed by Nasrifar et al. It is shown that the present correlation works better than both of them.

An analytical equation of state for refrigerants

The liquid density of halogenated hydrocarbons has been calculated using an analytical equation of state. The temperature-dependent parameters of the equation of state have been calculated using our previous corresponding-states correlation based on the normal boiling point constants. In this work, it is shown that the equation of state for halogenated paraffins could be expressed in terms of the minimum input information, namely the normal boiling point temperature and the liquid density at the normal boiling point. The equation of state has been employed to calculate the liquid density of a great number of refrigerants both at saturation and compressed states, over a wide range of temperatures and pressures. A comparison of the predicted results with experimental data shows that the agreement is quite good.

An Analytical Equation of State for Alkaline Earth Metals

In this work, an analytical equation of state based on statistical mechanical perturbation theory, which was initially developed for normal fluids and can be applied to predict the P–V–T data for saturated liquid alkaline earth metals, is presented. The equation of state is that of Ihm, Song, and Mason, and the temperature-dependent parameters of the equation of state are calculated from a corresponding-states correlation as functions of the reduced temperature. Two scaling constants are sufficient for this purpose, the surface tension and the liquid density at the melting point. The equation of state is used to predict the saturated liquid density of molten alkaline earth metals from the melting point up to 2000 K, for which experimental data exist, within an accuracy of 5%.

Equation of State for Alkaline Earth Metals: Prediction from Boiling Point Constants

A statistical-mechanical analytical equation of state has been employed successfully to molten alkaline earth metals. The temperature-dependent parameters of the equation of state have been calculated using our previously reported corresponding-states correlation based on the normal boiling point parameters as the scaling constants. It is shown that knowledge of just normal boiling temperature and the liquid density at a normal boiling point are sufficient to predict the equation of state of magnesium, calcium, stroncium, and barium from the melting points up to several hundred degrees above their boiling points. A comparison of calculated saturated liquid densities of these metals with experimental ones shows that our predicted results are within a 5% difference of experimental ones.

Corresponding-States Correlation and Prediction of Third Virial Coefficients for a Wide Range of Substances

An extended corresponding-states model is developed that is capable of correlating and predicting the third virial coefficients for a wide range of substances. The present method only requires substance-dependent parameters, such as the critical temperature, critical volume, acentric factor, and aspherical factor, which are based on the simple extended corresponding-states principle. Comparisons with experimental data and existing models show that the present model is more general in that it not only is equivalent to the existing method for nonpolar gases, but also can represent the third virial coefficients of polar substances.

Corresponding-states correlation for the compressed liquid density of metals

Applying the previous correlation for the saturated liquid density of metals, we have developed a corresponding-states correlation for the prediction of their compressed liquid densities. The correlation needs the values of the melting and boiling point parameters of metals plus an adjustable parameter, used to predict the saturated liquid densities. In this work, we have shown that by employing the Tait equation together with the previous correlation, for saturated liquid densities, it is possible to develop an accurate method for the prediction of the compressed liquid density of metals. The agreement of the predicted density values with the experimental ones for alkali metals, mercury, bismuth, tin, and lead over a wide range of temperatures, from melting point up to several hundred degrees above the boiling point, and pressures ranging from the vapor pressure up to 4000 bar, is quite good. From 821 data points examined for the aforementioned metals the average absolute deviation for the calculated densities compared with experiment is 0.72%. The correlation is also examined against a number of existing regularities for the liquid phase.

Corresponding-states correlation for compressed liquid densities

A corresponding-states correlation, originally developed by Iglesias-Silave and Hall for the prediction of the saturated liquid densities, has been extended successfully to the compressed state. The Tait equation has been employed for this purpose and its parameters have been correlated to permit accurate prediction of the liquid densities of compressed fluids. The proposed correlation in this work needs the values of the critical constants, the acentric factor, the freezing temperature, the liquid density at the freezing point, and an adjustable parameter used to determine the saturated liquid densities. If the freezing point parameters are not available, another experimentally available low-temperature datum point may be used instead. Utilizing this correlation, we have calculated the liquid density of a large variety of compounds including liquefied noble gases, a number of inorganic diatomic and polyatomic molecules, saturated, aromatic, and aliphatic hydrocarbons, organic acids, alcohols, and refrigerants. The correlation is also compared with the corresponding-states liquid densities by Hankinson et al. and a recent correlation by Nasrifar et al. It is shown that this correlation is superior to both of them.