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.     

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.     

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.     

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.     

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.     

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.     

Vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions

A systematic investigation on vapor-liquid equilibria (VLEs) of dipolar and quadrupolar fluids is carried out by molecular simulation to develop a new Helmholtz energy contribution for equations of state (EOSs). Twelve two-center Lennard-Jones plus point dipole and point quadrupole model fluids (2CLJDQ) are studied for different reduced dipolar moments micro*2=6 or 12, reduced quadrupolar moments Q*2=2 or 4 and reduced elongations L*=0, 0.505, or 1. Temperatures cover a wide range from about 55% to 95% of the critical temperature of each fluid. The NpT+test particle method is used for the calculation of vapor pressure, saturated densities, and saturated enthalpies. Critical data and the acentric factor are obtained from fits to the simulation data. On the basis of this data, an EOS contribution for the dipole-quadrupole cross-interactions of nonspherical molecules is developed. The expression is based on a third-order perturbation theory, and the model constants are adjusted to the present 2CLJDQ simulation results. When applied to mixtures, the model is found to be in excellent agreement with results from simulation and experiment. The new EOS contribution is also compatible with segment-based EOS, such as the various forms of the statistical associating fluid theory EOS.     

Novel corresponding-states principle approach for the equation of state of isotopologues: H2(18)O as an example

The corresponding-states principle (CSP) has been considered for the development of the equations of state (EOS) of minor isotopologues that are usually unknown. We demonstrate that, for isotopologues of a given molecular fluid, a general extended multi-parameter corresponding-states EOS can be reduced to the three-parameter EOS, utilizing the critical parameters (temperature and density) and Pitzer's acentric factor as correlation parameters. Appropriate general CSP mathematical formalism and equations for constructing the EOS of minor isotopologues are described in detail. The formalism and equations were applied to isotopologues of water and demonstrated that the isotopic effect on the critical parameters and the acentric factor of H(2)(18)O can be successfully calculated from the EOS of H2O and experimental data on the isotope effects (liquid-vapor isotope fractionation factor and molar volume isotope effect). We have also shown that the experimental data on the vapor pressure isotope effect (VPIE) for 18O-substituted water are inconsistent within the framework of thermodynamics with the liquid-vapor oxygen isotope fractionation factor. The novel approach of CSP to isotopologues developed in this study creates a new opportunity for constructing the EOS of minor isotopologues for many other molecular fluids.     

Study on vapor-liquid equilibria and surface tensions for nonpolar fluids by renormalization group theory and density gradient theory

An equation of state (EOS) applicable for both the uniform and nonuniform fluids is established by using the density-gradient theory (DGT). In the bulk phases, the EOS reduces to statistical associating fluid theory (SAFT). By combining the EOS with the renormalization group theory (RGT), the vapor-liquid-phase equilibria and surface tensions for 10 nonpolar chainlike fluids are investigated from low temperature up to the critical point. The obtained results agree well with the experimental data.     

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.     

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.     

Empirical correction to the Peng–Robinson equation of state for the saturated region

This work presents an empirical correction to improve the Peng–Robinson equation of state (PR EOS) for representing the densities of pure liquids and liquid mixtures in the saturated region using the volume translation method. A temperature-dependent volume correction is employed to improve the original PR EOS so that it can match the true critical point of pure fluids. The volume correction is generalized as a function of the critical parameters and the reduced temperature. The volume translation PR (VTPR) EOS with the generalized volume correction accurately represents the saturated liquid densities for different polar and non-polar fluids, including alkanes, cycloparaffins, halogenated hydrocarbons, olefins, cyclic olefins, aromatics and inorganic molecules. The average relative deviations for 91 pure compounds was 1.37%. The generalized VTPR EOS was also used to predict the saturated liquid density of 53 binary mixtures with a relative deviation of 0.98%. The generalized VTPR EOS can also be extended to other materials. The accuracy of the generalized VTPR EOS compares well with other methods and equations of state.     

Quintic equation of state for pure substances in sub- and supercritical range

A new quintic equation of state (EOS) for pure substances and mixtures is proposed. The equation is based on critical parameters and one saturation point. The proposed Q5EOS is a generalisation of many cubic equations of state. Equation Q5 has five parameters, four of which are temperature-independent. The temperature-dependent parameter a is expressed by a relation based on a simple power function. Parameters defining this function can be calculated from saturation data, Boyle temperature and supercritical data.     

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.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

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.     

Prediction of gas condensate properties by Esmaeilzadeh–Roshanfekr equation of state

The Esmaeilzadeh–Roshanfekr (ER) equation of state (EOS) is used to predict the PVT properties of gas condensate reservoir fluids. Three gas condensate fluid samples taken from three wells in a real field in Iran, referred here as SA1, SA4 and SA8, as well as five samples from literature have been used to check the validity of the ER EOS in calculating the PVT properties of gas condensate mixtures. Some experiments such as constant composition expansion (CCE), constant volume depletion (CVD) and dew point pressures are carried out on these samples. In order to have an unbiased comparison between the ER and the Peng–Robinson (PR) equation of state, van der Waals mixing rules are used without using any adjustable parameters (k_ij = 0). Also, no pure component parameters are adjusted. The critical properties and acentric factor for plus-fraction are estimated by the Kesler–Lee, Pedersen et al. and Riazi–Daubert characterization methods. The results of dew point pressure calculations show that the ER EOS has smaller error than the PR EOS. For some mixtures, relative volume, gas compressibility factor and condensate drop-out in CVD and CCE test were also predicted. Comparison results between experimental and calculated data indicate that the ER EOS has smaller error than the PR EOS. The total average absolute deviation was found to be 0.82% and 2.97% for calculating gas compressibility factor and gas specific gravity in CVD test. Also, the total average absolute deviation was found to be 2.06% and 3.42% for calculating gas compressibility factor and relative volume in CCE test.     

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.