A Thermodynamic Property Model for Fluid Phase Hydrogen Sulfide

A Helmholtz free energy equation of state for the fluid phase of hydrogen sulfide has been developed as a function of reduced temperature and density with 23 terms on the basis of selected measurements of pressure–density–temperature (P, , T), isobaric heat capacity, and saturation properties. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from the triple point temperature (187.67 K) to 760 K at pressures up to 170 MPa. The uncertainty in density calculation of the present equation of state is 0.7% in the liquid phase, and that in pressure calculation is 0.3% in the vapor phase. The uncertainty in saturated vapor pressure calculation is 0.2%, and that in isobaric heat capacity calculation is 1% in the liquid phase. The behavior of the isobaric heat capacity, isochoric heat capacity, speed of sound, and Joule–Thomson coefficients calculated by the present model shows physically reasonable behavior and those of the calculated ideal curves also illustrate the capability of extending the range of validity. Graphical and statistical comparisons between experimental data and the available thermodynamic models are also discussed.     

A Thermodynamic Property Model for Fluid-Phase Isobutane

A Helmholtz free energy equation of state for the fluid phase of isobutane (R-600a) has been developed on the basis of the ITS-90 temperature scale. This model was developed using selected measurements of the pressure–density–temperature (P, , T), isobaric heat capacity, speed of sound, and saturation properties. The structure of the present model consists of only 19 terms in its functional form, which is the same as those successfully applied to our recent modeling of R-290 and R-600, and a nonlinear fitting procedure was used to determine the numerical parameters of the present equation of state. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from 113.56 K (the triple-point temperature) to 573 K, at pressures up to 35 MPa, and at densities up to 749 kg·m^–3. Physically sound behavior of the derived thermodynamic properties over the entire fluid phase is demonstrated. The estimated uncertainties of properties calculated using the model are 0.2% in density, 1% in heat capacities, 0.02% in the speed of sound for the vapor, 1% in the speed of sound elsewhere, and 0.2% in vapor pressure, except in the critical region. In addition, graphical and statistical comparisons between experimental data and the available thermodynamic models, including the present one, showed that the model can provide a physically sound representation of all the thermodynamic properties of engineering importance.     

A Thermodynamic Property Model for Fluid-Phase Propane

A fundamental equation of state for propane (R-290), formulated in terms of the non-dimensional Helmholtz free energy, is presented. It was developed based on selected reliable measurements for pressure-volume-temperature (PVT), isochoric and isobaric heat capacities, speed of sound, and the saturation properties which were all converted to ITS-90. Supplementary input data calculated from a virial equation for the vapor-phase PVT properties at lower temperatures and other correlations for the saturated vapor pressures and saturated vapor- and liquid-densities have also been used. The present equation of state includes 19 terms in the residual part and represents most of the reliable experimental data accurately in the range of validity from 85.48 K (the triple point temperature) to 623 K, at pressures to 103 MPa, and at densities to 741 kg·m^–3. The smooth behavior of the derived thermodynamic properties in the entire fluid phase is demonstrated. In addition, graphical and statistical comparisons between experimental data and the available thermodynamic models, including the present one, showed that the present model can provide a physically sound representation of all the thermodynamic properties of engineering importance.     

Thermodynamic Property Model for Fluid-Phase n-Butane

A Helmholtz free energy equation of state for the fluid phase of n-butane (R-600) has been developed on the basis of the ITS-90 temperature scale. This model has been established on the basis of selected measurements of the pressure–density–temperature (P, , T), isochoric heat capacity, speed of sound, and the saturation properties. The linear structural regression optimization and nonlinear fitting procedure were used to determine the functional form and the numerical parameters of the present equation of state. Based on a comparison with available experimental data, it is recognized that the developed model represents most of the reliable experimental data accurately in the range of validity covering temperatures from 134.87 K (the triple-point temperature) to 589 K, at pressures up to 69 MPa, and at densities up to 745 kg·m^-3. The reasonable behaviors of the derived thermodynamic properties have also been confirmed over the entire fluid phase of n-butane.     

A Generalized Model for the Thermodynamic Properties of Mixtures

A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.     

A Rigorous Thermodynamic Property Model for Fluid-Phase 1,1-Difluoroethane (R-152a)

A new thermodynamic property model for the Helmholtz free energy with rational third virial coefficients for fluid-phase 1,1-difluoroethane (R-152a) was developed. The model was validated by existing experimental data for temperatures from the triple point to 450 K and pressures up to 60 MPa. Reasonable behavior of the second and third virial coefficients was confirmed from intermolecular potential models. The estimated uncertainties are 0.1% in density for the gaseous and liquid phases, 0.4% in density for the supercritical region, 0.05% in speed of sound for the gaseous phase, 2% in speed of sound for the liquid phase, and 1% in specific heat capacities for the liquid phase. From the reasonable behavior of the ideal curves and the third virial coefficients, the model can be assumed reliable in representing the thermodynamic properties not only at states with available experimental data but also at states for which no experimental data are available.     

Thermodynamic properties of methane in the critical region

An equation of state is presented for the thermodynamic properties of methane in the vicinity of the critical point. It incorporates the scaled asymptotic critical behavior predicted theoretically and supplements a global analytic equation of state for methane recently developed by Setzmann and Wagner.     

A New Analytical Model for the Prediction of Vapor–Liquid Equilibrium Densities

A new simple, predictive model for estimating both the vapor and the liquid densities of fluids at the vapor–liquid equilibrium is presented. It is based on the symmetry of the derivatives of the two saturation densities with respect to the temperature, which is a consequence of applying the rectilinear diameter law. No adjustable coefficients are involved, and only two parameters—both with certain physical meaning—have to be calculated for each fluid. The method used for these calculations is straightforward, the required inputs being the critical temperature and density, and the value of the vapor and liquid densities at a reference temperature. The results show that the model is accurate for fluids of different kinds as long as the rectilinear diameter law holds, and that, in general, the accuracy is better than that of the most recent model with no adjustable coefficients.     

Prediction of Critical Properties of Binary Mixtures Using the PRSV-2 Equation of State

The aim of this work is to test the value of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state for predicting the critical behavior of binary mixtures. A procedure adopted by Heidemann and Khalil, based on the Helmholtz free energy, has been followed. The resulting two complex nonlinear equations have been solved simultaneously for the critical temperature and volume, while the critical pressure is calculated from the PRSV-2 equation of state itself. Three forms of binary-interaction parameters have been tried: the zero-type, conventional one-parameter type, and Margules two-parameter type. The optimum values of the binary interaction parameters, based on minimizing the sum of the squares of the relative errors between predicted and experimental critical temperatures, have been calculated for 20 polar and nonpolar systems. The Margules two-parameter type gives the best results, but its mathematical derivation is cumbersome and it requires more computation time. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperatures and pressures agree well with the experimental results, and are always better than those predicted by the group-contribution method. The deviations in the predicted critical volumes using any of the tested binary-interaction parameter types are relatively large compared to those using the group-contribution method.     

Correlation for the Carbon Dioxide and Water Mixture Based on The Lemmon–Jacobsen Mixture Model and the Peng–Robinson Equation of State

Models representing the thermodynamic behavior of the CO₂–H₂O mixture have been developed. The single-phase model is based upon the thermodynamic property mixture model proposed by Lemmon and Jacobsen. The model represents the single-phase vapor states over the temperature range of 323–1074 K, up to a pressure of 100 MPa over the entire composition range. The experimental data used to develop these formulations include pressure–density–temperature-composition, second virial coefficients, and excess enthalpy. A nonlinear regression algorithm was used to determine the various adjustable parameters of the model. The model can be used to compute density values of the mixture to within ±0.1%. Due to a lack of single-phase liquid data for the mixture, the Peng–Robinson equation of state (PREOS) was used to predict the vapor–liquid equilibrium (VLE) properties of the mixture. Comparisons of values computed from the Peng–Robinson VLE predictions using standard binary interaction parameters to experimental data are presented to verify the accuracy of this calculation. The VLE calculation is shown to be accurate to within ±3 K in temperature over a temperature range of 323–624 K up to 20 MPa. The accuracy from 20 to 100 MPa is ±3 K up to ±30 K in temperature, being worse for higher pressures. Bubble-point mole fractions can be determined within ±0.05 for CO₂.     

Thermodynamic properties of methane in the critical region

A scaled fundamental equation is presented for the thermodynamic properties of methane in the critical region. The equation supplements the international formulation for the thermodynamic properties of methane issued by IUPAC.     

Liquid Saturation Density from Simple Equations of State

Several simple equations of state, requiring only two input properties, have been studied in order to determine the liquid saturation density of 144 fluids of different kinds. This study includes old and new simple modifications of the van der Waals equation of state, and the Carnahan–Starling–Yelash–Kraska and Carnahan–Starling–Dieterici equations. The new simple modifications of the van der Waals equation give better overall results than some other more complex proposed equations, especially near the critical point. The recent equation proposed by Eslami including the boiling temperature and density as input parameters was also checked, and was found not to reproduce the critical point, but to give excellent results at intermediate or low temperatures. As a reference, the behavior of the well-known Soave– Redlich–Kwong and Peng–Robinson equations, and the more recent expression proposed by Mohsen-Nia et al. that requires three input parameters were also checked. The latter does not improve the accuracy of the Peng–Robinson equation, and very simple van-der-Waals type equations give better overall results.     

Thermodynamic Properties of Methanol in the Critical and Supercritical Regions

The isochoric heat capacity of pure methanol in the temperature range from 482 to 533 K, at near-critical densities between 274.87 and 331.59 kg· m⁻³, has been measured by using a high-temperature and high-pressure nearly constant volume adiabatic calorimeter. The measurements were performed in the single- and two-phase regions including along the coexistence curve. Uncertainties of the isochoric heat capacity measurements are estimated to be within 2%. The single- and two-phase isochoric heat capacities, temperatures, and densities at saturation were extracted from experimental data for each measured isochore. The critical temperature (T_c = 512.78±0.02K) and the critical density (ρ_c = 277.49±2 kg · m⁻³) for pure methanol were derived from the isochoric heat-capacity measurements by using the well-established method of quasi-static thermograms. The results of the C_VVT measurements together with recent new experimental PVT data for pure methanol were used to develop a thermodynamically self-consistent Helmholtz free-energy parametric crossover model, CREOS97-04. The accuracy of the crossover model was confirmed by a comprehensive comparison with available experimental data for pure methanol and values calculated with various multiparameter equations of state and correlations. In the critical and supercritical regions at 0.98T_c≤ T ≤ 1.5T_c and in the density range 0.35ρ_c ≤ ρ leq 1.65 ρ_c, CREOS97-04 represents all available experimental thermodynamic data for pure methanol to within their experimental uncertainties.     

Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol

In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.     

A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol

A formulation for the thermodynamic properties of ethanol (C₂H₅OH) in the liquid, vapor, and saturation states is presented. The formulation is valid for single-phase and saturation states from 250 to 650K at pressures up to 280MPa. The formulation includes a fundamental equation and ancillary functions for the estimation of saturation properties. The experimental data used to determine the fundamental equation include pressure-density-temperature, ideal gas heat capacity, speed of sound, and vapor pressure. Saturation values computed from the ancillary functions were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Comparisons between experimental data and values computed using the fundamental equation are given to verify the uncertainties in the calculated properties. The formulation presented may be used to compute densities to within ±0.2%, heat capacities to within ±3%, and speed of sound to within ±1%. Saturation values of the vapor pressure and saturation densities are represented to within ±0.5%, except near the critical point.     

An Extended Equation of State Modeling Method II. Mixtures

This work is the extension of previous work dedicated to pure fluids. The same method is extended to the representation of thermodynamic properties of a mixture through a fundamental equation of state in terms of the Helmholtz energy. The proposed technique exploits the extended corresponding-states concept of distorting the independent variables of a dedicated equation of state for a reference fluid using suitable scale factor functions to adapt the equation to experimental data of a target system. An existing equation of state for the target mixture is used instead of an equation for the reference fluid, completely avoiding the need for a reference fluid. In particular, a Soave–Redlich–Kwong cubic equation with van der Waals mixing rules is chosen. The scale factors, which are functions of temperature, density, and mole fraction of the target mixture, are expressed in the form of a multilayer feedforward neural network, whose coefficients are regressed by minimizing a suitable objective function involving different kinds of mixture thermodynamic data. As a preliminary test, the model is applied to five binary and two ternary haloalkane mixtures, using data generated from existing dedicated equations of state for the selected mixtures. The results show that the method is robust and straightforward for the effective development of a mixture- specific equation of state directly from experimental data.     

A Thermodynamic Equation of State For the Critical Region of Ethylene

A fundamental equation of state that describes the behavior of the thermodynamic properties of ethylene in the vicinity of the critical point is formulated. Specifically, a crossover equation of state that takes into account not only the scaling laws at the critical point but also the analytical behavior far away from the critical point is presented. Analysis of different sets of data for the thermodynamic properties is made.     

Prediction of Critical Properties of Mixtures from the PRSV-2 Equation of State: A Correction for Predicted Critical Volumes

The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state (1986) for critical properties of binary mixtures was investigated. The procedure adopted by Heidemann and Khalil (1980) and discussed by Abu-Eishah et al. (1998) was followed. An optimized value for the binary interaction parameter based on minimization of error between experimental and predicted critical temperatures was used. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for several nonpolar and polar systems agree well with experimental data and are always better than those predicted by the group-contribution method. A correction is introduced here to modify the predicted critical volume by the PRSV-2 equation of state, which makes the average deviations between predicted and experimental values very close to or even better than those predicted by the group-contribution method.     

Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region

We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.     

Special Equations of State for Methane,Argon, and Nitrogen for the Temperature Range from 270 to 350 K at Pressures up to 30 MPa

In order to describe the thermodynamic behavior of methane, argon, and nitrogen in the so-called “natural-gas region,” namely, from 270 to 350 K at pressures up to 30 MPa as accurate as possible with equations of a very simple form, new equations of state for these three substances have been developed. These equations are in the form of a fundamental equation in the dimensionless Helmholtz energy; for calculating the pressure or the density, the corresponding equations explicit in pressure are also given. The residual parts of the Helmholtz function representing the behavior of the real gas contain 12 fitted coefficients for methane, 8 for argon, and 7 for nitrogen. The thermodynamic relations between the Helmholtz energy and the most important thermodynamic properties and the needed derivatives of the equations are explicitly given; to assist the user there is also a table with values for computer-program verification. The uncertainties when calculating the density ρ, the speed of sound w, the isobaric specific heat capacity c _p, and the isochoric specific heat capacity c _v are estimated as follows. For all three substances it is Δρ/ρ≤±0.02 % for p≤ 12 MPa and Δρ/ρ ≤ ±0.05% for higher pressures. For methane it is Δw/w≤±0.02% for p≤10 MPa and Δw/w≤+-0.1% for higher pressures; for argon it is Δw/w?-0.1 % for p≤ 7 MPa, Δw/w≤±0.3 % for 7 <p≤30 MPa; and for nitrogen it is Δw/w≤±0.1% for p≤1.5 MPa and Δw/w±0.5% for higher pressures. For all three substances it is Δc _p/c _p≤±1 % and ΔC _v/C _v≤±1 % in the entire range.