Estimation of second-order derivative thermodynamic properties using the crossover cubic equation of state

In this research, we apply the crossover cubic equation of state (XCubic EOS) [1] to the calculations of thermodynamic second-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, the Joule–Thomson coefficient, and speed of sound). This equation of state is used to calculate those properties of pure systems (carbon dioxide, normal alkanes from methane to propane). We show that, over a wide range of states, the equation of state yields each property with a much better accuracy than the original PT equation of state and near the critical region, represents the singular behaviour well.     

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.     

Modification of the Peng–Robinson equation of state for helium in low temperature regions

Helium shows the nearest behaviour to ideal gas in the room conditions. In contrast, thermodynamic behaviour of helium in the critical region, in which its liquefaction is possible, is extremely complicated. The equation of state (EOS), which is in common use for helium, is the modified Benedict–Webb–Rubin (MBWR) EOS developed by McCarty and Arp which is a 13th-order equation with 32 substance-dependent parameters. MBWR is a complicated EOS and its use is time consuming. In this work, the modified Peng–Robinson EOS introduced by Feyzi et al. is customised with 10 adjustable parameters for helium in the temperature range of 2.20–15.20 K and pressures up to 16 bar. The proposed EOS is able to predict the properties of helium in the vapour–liquid equilibrium (VLE) conditions and in the single gas-phase region. In addition, a temperature-dependent correlation for constant pressure heat capacity of helium from very low up to normal temperatures is proposed. The liquefaction process of helium, which is being done by cooling it to very low temperatures by passing through a Joule–Thomson valve, is predicted by the proposed EOS. Very accurate results are observed.     

Extended Veytsman statistics for the solid–fluid transition in the framework of lattice fluid

Lattice fluid can describe a vapor–liquid transition but not a solid–fluid transition. In this work, we propose a simple and analytic term which yields a solid–fluid transition when coupled with a lattice based equation of state (EOS). The proposed term is derived based on the two assumptions that (1) solid can be considered as highly associated phase affected by strong attractive force and (2) this force is distinct from the conventional attractive forces yielding a vapor–liquid transition. To formulate these assumptions, we extend Veytsman statistics by modifying its density dependency. The derived term was combined with a quasi-chemical nonrandom lattice fluid theory (QLF) developed by the authors. The combined model was found to require only two parameters besides 3 QLF parameters for physical properties calculation of three phases. When tested against equilibrium properties of 8 components, the combined model was found to closely reproduce melting pressure, sublimation pressure, and vapor pressure, but underestimate solid density as well as heat of melting at the triple point temperature. It was found that the present approach can yield a solid–liquid transition at all temperatures.     

A crossover lattice fluid equation of state for pure fluids

A lattice fluid model is one of the most versatile, molecular-based engineering equations of state (EOS) but, in common with all analytic equations of state, the lattice fluid (LF) EOS exhibits classical behaviour in the critical region rather than the non-analytical, singular behaviour seen in real fluids. In this research, we use the LF EOS and develop a crossover lattice fluid (xLF) equation of state near to and far from the critical region which incorporates the scaling laws valid asymptotically close to the critical point while reducing to the original classical LF EOS far from the critical point. We show that, over a wide range of states, the xLF EOS yields the saturated vapour pressure data and the density data with much better accuracy than the classical LF EOS.     

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Vibrational and thermodynamic properties of β-HMX: a first-principles investigation

Thermodynamic properties of β-HMX crystal are investigated using the quasi-harmonic approximation and density functional theory within the local density approximation (LDA), generalized gradient approximation (GGA), and GGA + empirical van der Waals (vdW) correction. It is found that GGA well describes the thermal expansion coefficient and heat capacity but fails to produce correct bulk modulus and equilibrium volume. The vdW correction improves the bulk modulus and volume, but worsens the thermal expansion coefficient and heat capacity. In contrast, LDA describes all thermodynamic properties with reasonable accuracy, and overall is a good exchange-correlation functional for β-HMX molecular crystal. The results also demonstrate significant contributions of phonons to the equation of state. The static calculation of equilibrium volume for β-HMX differs from the room-temperature value incorporating lattice vibrations by over 5%. Therefore, for molecular crystals, it is essential to include phonon contributions when calculated equation of state is compared with experimental data at ambient condition.     

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.     

Caloric properties of mixtures of refrigerants R22 / R114

The nonazeotropic refrigerant mixture chlorodifluoromethane (R22) and 1,2-dichlorotetrafluoroethane (R114) has been frequently suggested as a working fluid in cooling systems and heat pump applications. However, especially for mixtures exact and reliable measurements of the caloric properties are often missing, so that calculations with equations of state yield results of great uncertainty. In spite of the CFC-ozone problem of this mixture it can be considered as an exemplary mixture to set up accurate equations of state.

Therefore measurements with an isenthalpic throttle calorimeter were carried out for three different compositions of the mixture. The measured isenthalps could be reproduced within the experimental accuracy by polynomials. Together with the specific heat capacity of the pure components the measurements lead to several caloric properties in the liquid-, vapour- and critical region. The caloric properties can also be calculated by equations of state (EOS). It turned out that the results obtained from Bender's EOS with interaction parameters fitted to the experiments lead to a good agreement with the experimental data.     

Application of the crossover lattice equation of state for fluid mixtures

In previous work, we developed the crossover lattice equation of state (xLF EOS) for pure fluids and the xLF EOS yielded the saturated vapour pressure and the density values with a much better accuracy than the classical LF EOS over a wide range. In this work, we extended xLF EOS to fluid mixtures. Classical composition-dependent mixing rules with only adjustable two binary interaction parameters same as the LF EOS are used. A comparison is made upon experimental data for fluids mixtures in the one- and two-phase regions. The xLF EOS shows more improved representations than the LF EOS, especially in the critical region.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Improvements to a new equation of state for pure components

In a recent work [Fluid Phase Equilib. 194–197 (2002) 401], Kedge and Trebble presented a non-cubic equation of state (EOS) including a near-critical correction term. The evaluation of that equation was limited initially to matching fluid properties of methane. In this work, we investigate the impact of incorporating a Carnahan–Starling (CS) repulsive term [J. Chem. Phys. 51 (2) (1969) 635] into the non-cubic equation. The CS term improves the fit of the critical isotherm and it is shown to improve the fit of the entire PVT space. Anomalies in the fit of temperature dependence in the EOS parameters in the near-critical region are also reduced. We also demonstrate in this work how the new correction term serves to flatten the top of the vapor–liquid coexistence curve. The new term is compared to the exponential term in Soave’s modification of the BWR equation (SBWR) [Ind. Eng. Chem. Res. 34 (1995) 3981] which achieves a similar effect in a slightly different way.     

Thermodynamic equilibrium of adsorbed phases

The types of phase equilibrium behavior for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on the lattice gas theory are investigated. The equilibrium conditions were obtained by solving the isofugacity equations between adsorbed phases. It is observed that the investigated EOS can predict complex behavior for adsorbed phases such as the existence of azeotropes, and retrograde and double retrograde phase transition phenomena, that are analogous to those found in bulk phase equilibrium. Furthermore, it was possible to find systems that presented phase equilibrium between two dense adsorbed phases, analogously to liquid–liquid equilibrium for bulk phases. Experimental data would be necessary to confirm the types of adsorbed phase behavior predicted by the calculations presented.     

缔合马丁-侯状态方程I 方程的建立

An associating MH equation of state (AMH EOS) is developed on the basis of the MH equation of state by incorporating the chemical association into it, a constant evaluation method is proposed for the AMH EOS. The AMH EOS is used to calculate thermodynamic properties of water, some alcohols and carboxylic acids, good results are obtained. It shows that the constant evaluation method is feasible.     

Modelling the volumetric properties of ionic liquids using a modified perturbed hard-sphere-chain equation of state

In this paper, a modified perturbed hard-sphere-chain equation of state (EOS) by Eslami [H. Eslami, Fluid Phase Equilib. 216 (2004) 21–26], is applied for modelling the thermodynamic properties of some ionic liquids (ILs). Two reliable scaling constants are used to determine two temperature-dependent parameters in the proposed EOS. The unique adjustable parameter that is reflecting the number of segments per molecule, r, compensates the uncertainties in the calculated temperature-dependent parameters. The reliability of the proposed EOS has been checked by comparing the results with 1561 experimental data points for 18 ILs over a broad range of pressures and temperatures. The overall average absolute deviation is 0.35%. A comparison of the predicted results, using the present EOS with the results of some previous models, indicates that the determined results of this EOS are in more accordance with experimental data than those.     

Crossover SAFT equation of state for pure supercritical fluids

A crossover statistical associating fluid theory (SAFT) equation of state (EOS) is used to fit the parameters of eight common pure supercritical fluids (water, ammonia, carbon dioxide, R134a, ethane, propane, ethene and propene) and calculate their thermodynamic properties. Over a wide range including the critical region, the EOS reproduces the saturated pressure data with an average absolute deviation (AAD) of about 1% and the saturated densities with an AAD of about 2%. In the one-phase region, the EOS represents the experimental values of pressure with an AAD of about 1–3%. The results are satisfactory.     

Description of self-diffusion coefficients of gases,liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T_c and the experimental critical pressure P_c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.     

A new three-parameter cubic equation of state for calculation physical properties and vapor–liquid equilibria

A new three-parameter cubic equation of state is presented by combination of a modified attractive term and van der Waals repulsive expression. Also a new alpha function for the attractive parameter of the new EOS is proposed. The new coefficients of alpha function and the other parameters of the attractive term are adjusted using the data of the saturated vapor pressure and liquid density of almost 60 pure compounds including heavy hydrocarbons. The new EOS is adopted for prediction of the various thermophysical properties of pure compounds such as saturated and supercritical volume, enthalpy of vaporization, compressibility factor, heat capacity and sound velocity. Following successful application of the new EOS for the pure components, using vdW one-fluid mixing rules, the new EOSs are applied to prediction of the bubble pressure and vapor mole fraction of the several binary and ternary mixtures. The accuracy of the new EOS for phase equilibrium calculation is demonstrated by comparison of the results of the present EOSs with the PT, PR, GPR and SRK cubic EOSs.