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.     

Modification of Simha–Somcynsky equation of state for small and large molecules

The Simha–Somcynsky equation of state (SS EOS) represents the PVT behavior of polymers quite satisfactorily, but cannot be applied to gases at low pressures. This work proposes a modification of the free volume contribution of the SS EOS to allow representation of gaseous state of low molecular-weight substances by introducing the perturbed hard-chain theory of Beret and Prausnitz into the EOS. In addition to this modification, two universal constants are introduced to the free volume term for better representation of properties of low molecular-weight substances. Characteristic parameters in the modified SS EOS were determined for 44 low molecular-weight substances and 64 polymers. The absolute average deviations (AADs) for critical temperature, critical pressure and vapor pressures were 0.86, 2.38 and 2.01%, respectively, while AAD for critical density and saturated liquid density at normal boiling point were somewhat larger, being 20.46 and 5.30%, respectively. The high performance of the original SS EOS for polymer PVT behavior was maintained in the modified EOS with grand AAD of 0.050% for densities.     

A crossover SAFT-VR equation of state for pure fluids: preliminary results for light hydrocarbons

SAFT is perhaps the most versatile, fundamentally, based engineering equation of state in use today. However, in common with all analytic equations of state, SAFT exhibits classical behavior in the critical region rather than the non-analytical, singular behavior seen in real fluids. Recently, so-called crossover equations of state have been developed which solve this shortcoming by incorporating the scaling laws valid asymptotically close to the critical point while reducing to the original classical equation of state far from the critical point. We have combined the SAFT-VR equation of state with an analytical crossover technique to obtain the SAFT-VRX equation of state. The SAFT-VRX approach combines the accurate low temperature behavior of SAFT-VR with a precise representation of the critical region. Preliminary results are presented for hydrocarbon systems which illustrate the accuracy of the SAFT-VRX approach over the entire fluid phase region.     

Estimation of 2nd-order derivative thermodynamic properties using the crossover lattice equation of state

We apply the crossover lattice equation of state (xLF EOS) [M.S. Shin, Y. Lee, H. Kim, J. Chem. Thermodyn. 40 (2007) 174–179] to the calculations of thermodynamic 2nd-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, Joule–Thompson coefficient, and sound speed). This equation of state is used to calculate the same 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 properties with better accuracy than the lattice equation of state (LF EOS), and near the critical region, represents singular behavior well.     

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 nonparametric scaling equation of state for liquids

A new nonparametric scaling equation of state is suggested. The equation correctly describes the p-ρ-T data and heat capacities of liquids close to the critical vaporization points. It was obtained with the use of the S spinodal and the mixing of scaling fields as a first approximation (asymmetric and nonasymptotic terms were ignored). The new equation was used to approximate the data on ⁴He, C₂H₄, and H₂O in the critical region. The results showed that it correctly described the critical behavior of thermodynamic functions, including isochoric heat capacity, not only in the asymptotic but also over a fairly wide density region at the critical point. The suggested equation of state describes the p-ρ-T data with the same error as the Schofield parametric equation of state. The new equation, however, better reproduces the behavior of heat capacities and is much simpler to use. As distinct from the Schofield equation, the new equation, like classic equations of state, allows the spinodal to be determined from the (?p/?v) _T = 0 condition at T < T _c .     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

A new form of the equation of state for pure substances and its application to oxygen

Schmidt, R. and Wagner, W., 1985. A new form of the equation of state for pure substances and its application to oxygen. Fluid Phase Equilibria, 19: 175–200.A new wide range equation of state is presented and expressed analytically in the form of the free energy as a function of density and temperature. This fundamental equation contains, in addition to pure polynomial and “BWR”-terms, new exponential functions especially convenient for the critical region. To guarantee an effective structure, the combination of the terms of the equation was found by using an optimization method recently developed. As a result, the optimized function for the free energy is capable of representing the thermodynamic surface of oxygen in the range 54 ≤ T ≤ 300 K, 0 < p ≤ 818 bar and 0 < ρ ≤ 41 mol dm^?3 within the experimental uncertainty of the data available. With the exception of very few items of data, this statement is also valid for the whole coexistence curve and the critical region. Extrapolations of this new equation beyond the range of data yield physically meaningful results.     

A crossover cubic equation of state near to and far from the critical region

In this research, we use the Patel–Teja (PT) cubic equation of state [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37 (1982) 463–473.] and develop a crossover cubic model near to and far from the critical region, which incorporates the scaling laws asymptotically close to the critical point and it transformed into original classical cubic equations of state far away from the critical point. This equation of state is used to calculate thermodynamic properties of pure systems (carbon dioxide, normal alkanes from methane to heptane). We show that, over a wide range of states, the equation of state yields the saturated vapour pressure data and the saturated density data with a much better accuracy than the original PT equation of state.     

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.     

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.     

Simple modification of the temperature dependence of the Sanchez–Lacombe equation of state

In this work, the interaction energy term of the Sanchez–Lacombe equation of state (SL EOS) was modified to take into account the temperature dependence of hydrogen bonding and ionic interactions. A simple function was used in the form of the Langmuir equation that reduces to the original SL EOS at high temperature. Comparisons are shown between the ?*-modified SL EOS and the original SL EOS. The ?*-modified SL EOS could represent volumetric data for the group of non-polar fluids, polar fluids and ionic liquids to within an absolute average deviation (AAD) of 0.85%, 0.51%, and 0.054%, respectively whereas, the original Sanchez–Lacombe EOS gave AAD values of 0.99%, 1.2%, and 0.21%, respectively. The ?*-modified SL EOS provides remarkably better PVT representation and can be readily applied to mixtures.     

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.     

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.     

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T ₀, characteristic density ρ₀, anisotropy factor α, and reduced quadrupolar moment Q*². The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.     

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.     

Towards understanding the effect of electrostatic interactions on the density of ionic liquids

In order to have a better understanding on the electrostatic contribution to the thermodynamic property of ionic liquids (ILs), a two-parameter equation of state (EOS) is developed on the basis of hard sphere perturbation theory by accounting for the dispersion interaction with Cotterman et al.’s EOS for L-J fluid and electrostatic interaction with mean spherical approximation (MSA) approach. The EOS is applicable for the density correlation of molecular liquids, and the resulting parameters, viz. Lennard–Jones dispersive parameter ?/k and soft-core diameter σ, can be used to predict the density of molecular mixtures and the corresponding ILs. The results indicate that the density of IL is always about 10% higher than the corresponding stoichiometric molecular mixture with which the IL is produced as an ionic adduct, for example, IL 1-methyl-3-methylimidazolium dimethylphosphate ([MMIM][DMP]) versus equimolar mixture of 1-methylimidazole (MIM) and trimethylphosphate (TMP). Furthermore, the density enhancement of ILs with respect to their corresponding stoichiometric molecular mixtures can be well represented by the electrostatic contribution among ionic species involved.     

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.