Theory Of Corresponding States Research Articles

Application of the Corresponding-State Law to the Parametrization of Statistical Associating Fluid Theory (SAFT)-Type Models: Generation and Use of “Generalized Charts”

Most of the Statistical Associating Fluid Theory (SAFT) and cubic equations of state (EoS) for nonassociating pure components obey the three-parameter corresponding-state law, meaning that the knowledge of three component-specific properties is a prerequisite to apply an EoS to a given pure species. Here, the methodology used to attribute values to EoS parameters is called “parameterization procedure”. In this Article, it is shown that generalized charts, derived from the corresponding-state theory, can be used advantageously to parametrize SAFT models. SAFT EoS is a well-established class of models frequently used for process simulation. Depending on the EoS parameter set selected, most of SAFT EoS are likely to predict unrealistic phenomena (mainly, the presence of multiple critical points and three-fluid phase equilibrium regions in pure-component phase diagrams). Generalized charts can be used to detect whether such unrealistic phenomena affect pure-component phase diagrams in the temperature and pressure domains of interest. As a second application, it is proposed to parametrize SAFT EoS in the same spirit as cubic EoS: the three SAFT input parameters are fixed in order to exactly reproduce the experimental critical temperature, critical pressure, and one point of the vaporization curve through the acentric factor. It is shown that the procedure is simple to implement and opens the door to a large industrialization of SAFT EoS (i.e., the possibility to determine SAFT input parameters for any compound using a universal and univocal method).

A New Surface Tension Equation for Refrigerants

This study presents a new formula for the surface tension prediction of refrigerants. As a first step, an analysis of the available experimental surface tension data for refrigerants was performed. The experimental data were collected, after a careful literature survey, for the following pure fluids: R11, R12, R13, R13B1, R14, R21, R22, R23, R32, R113, R114, R115, R123, R124, R125, R134, R134a, R141b, R143a, R152a, R218, R227ea, R236ea, R236fa, R245ca, R245fa, R365mfc, and R1234yf. Then, the experimental data were regressed with the most reliable semi-empirical correlating methods based on the corresponding-states theory existing in the literature. As a final step, to minimize the deviation between the predicted data and the experimental data and to find the optimal equation for experimental data regression, a (μ + λ)-evolution strategy was adopted. After a careful statistical analysis of the results, a new formula based on the corresponding-states principle with improved representation of the experimental results was found and proposed.

Estimation of Surface Tension of Molten Carbonate Mixtures by the Theory of Corresponding States

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A new generalized corresponding-states equation of state for the extension of the Lee–Kesler equation to fluids consisting of polar and larger nonpolar molecules

The Lee–Kesler equation of state for the thermodynamic properties of small nonpolar fluids is extended to all fluids consisting of polar and larger nonpolar molecules, based on the general corresponding-states theory for highly nonspherical fluids. The thermodynamic functions are represented by an analytical equation of state. The results for polar fluids are substantially better than those obtainable from other currently available methods, while the results for nonpolar fluids are equivalent to and mostly better than those obtained by the Lee–Kesler method. The input data required are the critical temperature, the critical volume, the acentric factor and the aspherical factor, which is related to the critical compression factor; the critical volume is therefore required in the present method. The method developed in this work shows good accuracy for 15 representative nonpolar, polar, hydrogen bonding and associating fluids and provides a simple method for industrial applications. Average deviations for the compressibility factor, the heat capacity and the speed of sound for six nonpolar and nine polar fluids from the new equation of state are 0.74%, 2.1% and 2.3%, which are about 8 times smaller than those obtained from the Lee–Kesler equation (about 5.6%, 17% and 29%, respectively).

A Predictive Method for Estimating the Minimum Dynamic Critical System Pressure Required to Disperse Blowing Agent in Polystyrene

A predictive method for estimating the minimum dynamic critical system pressure required to disperse the blowing agents in molten polystyrene has been introduced based on the relationship between dynamic and equilibrium solubility determined using the Theory of Corresponding States. This method can be used to estimate the minimum dynamic system pressure required to disperse new blowing agent systems as a function of temperature and blowing agent concentration in the foam extrusion line. A brief discussion on the effect of dynamic system pressure on the cellular structure, skin, quality, and the pressure drop calculations through the foam extrusion line will be given.

Xenon melting: Density functional theory versus diamond anvil cell experiments

We performed two-phase ab initio density functional theory based molecular dynamics simulations of Xe melting and demonstrated that, contrary to claims in the recent literature, the pressure dependence of the Xe melting curve is consistent with the corresponding-states theory as well as with the melting curve obtained earlier from classical molecular dynamics with a Xe pair potential. While at low pressure the calculated melting curve is in perfect agreement with reliable experiments, our calculated melting temperatures at higher pressures are inconsistent with those from the most recent diamond anvil cell experiment. We discuss a possible explanation for this inconsistency.

Application of New, Modified BWR Equations of State to the Corresponding-States Prediction of Natural Gas Properties

The accurate description of mixtures includes both single-phase (bulk) properties and the location of phase equilibrium boundaries, e.g., properties that depend upon partial molar properties. In order to estimate these properties, many variants of corresponding-states theory have been developed, especially for nonpolar mixtures such as those found in natural gas systems, In this work we have developed two new, modified BWR equations of state for two natural gas components (n-pentane and n-heptane) and used these equations in a reformulated (Teja-like) Lee–Kesler model. The reformulated model has been tested on bulk-phase properties of hydrocarbon systems, in both the pure and the mixed states. Results have been obtained using the original Lee–Kesler model, the extended corresponding-states theory, and the multifluid corresponding-states principle using several combinations of reference fluids chosen from this and previous equation of state studies. Details of the new equations of state and theoretical comparisons are reported.

Thermodynamics of the lower critical threshold line in solutions of cyclic and linear poly(dimethylsiloxane)s in tetramethylsilane

The main features of the critical line in presure-temperature-composition space for mixtures containing either a linear or a cyclic poly(dimethylsiloxane) (PDMS) in tetramethylsilane (TMS) are predicted through the use of the Patterson modification of Prigogine's corresponding-states theory, which incorporates the cell model of a liquid together with a simple van der Waals dependence of the configurational energy on volume. Two main kinds of critical lines are obtained: one is a continuous line for those mixtures with a small chain-length difference between the components, leading to a fairly good prediction of the liquid-vapour critical temperatures of the pure substances; and the other is a broken line for mixtures with a large chain-length difference between the polymer and solvent, indicating the occurrence of a lower critical threshold temperature ( LCTT) at low polymer concentrations. A full set of temperature and pressure reduction parameters for both linear and cyclic oligomers and PDMS are reported, and are used as the basis for all the calculations with no adjustment whatsoever. It is predicted that the system of minimum chain length to show an LCTT is that containing a PDMS of 24 skeletal bonds, compared to the methane-hexane system in the n-alkanes, thus giving an insight into the more flexible and more expanded nature of the PDMS series. Results for the interaction parametert χ 1 confirm that any difference in chemical nature between TMS and the PDMS series may be largely ignored since the structural term c 1 τ alone can account for the LCTT behaviour.

Thermodynamics of poly(ethylene oxide)-poly(methyl methacrylate) blends: prediction of miscibility based on the corresponding-states theory

The compatibility of the poly(ethylene oxide)-atactic poly(methyl methacrylate) (PEO-aPMMA) system has been studied using Patterson's theory of polymer-polymer miscibility. Specific volumes and thermal pressure coefficients for both polymers have been accurately determined; the characteristic parameters V∗, T∗ and P∗ are obtained from the experimental results. Experimental heat-of-mixing data were used to calculate the interaction energy between the two components. The shape of the curve of χ 12 V* 1 versus temperature indicates that PEO-aPMMA mixtures are miscible in the liquid state over all the composition and temperature range explored.

Non-equilibrium molecular dynamics simulations of structured molecules

Corresponding-states theories fail to predict the large difference observed between n-butane and isobutane viscosities at similar reduced conditions. To investigate the molecular cause of these structural effects upon viscosity, nonequilibrium molecular dynamics simulations of Lennard-Jones site-site models representing n-butane and isobutane are performed over much of the density range for which experimental data are available. Simulated viscosities at zero shear agree very well with experimental data over the entire density range. Site size, non-equilibrium molecular alignment and molecular geometry are the primary factors causing both the similarities and differences between the isomers' viscosity and rheology.

Olefin-vapor conductivities below 0.1 MPa at 220?680 K

A curve has been fitted to measurements on the thermal conductivities of olefin vapors at 220–680 K, which is based on the corresponding-state theory. Measurements have been made on the thermal conductivity of non-1-ene at 303–372 K.

Theory of dynamic shear viscosity and normal stress coefficients of dense fluids

On the basis of the nonlinear evolution equation for the stress tensor derived from the kinetic equation for dense simple fluids, we examine the shear rate and frequency dependence of the shear viscosity and normal stress coefficients. An analytic expression for nonlinear shear viscosity has been obtained, which is in agreement with nonequilibrium molecular dynamic simulation results. Based on the material functions obtained in the analysis, a theory of rheological corresponding states is developed by showing that there exists a set of reduced material functions which depend on the reduced shear rate, reduced frequency, reduced static normal coefficients and limiting values of the reduced imaginary parts of dynamic normal stress coefficients. It is also shown that the dynamic normal stress coefficients can change its sign as the critical value of the frequency is crossed.

A test of the mean density approximation for Lennard-Jones mixtures with large size ratios

The mean density approximation for mixture radial distribution functions plays a central role in modern corresponding-states theories. This approximation is reasonably accurate for systems that do not differ widely in size and energy ratios and which are nearly equimolar. As the size ratio increases, however, or if one approaches an infinite dilution of one of the components, the approximation becomes progressively worse, especially for the small molecule pair. In an attempt to better understand and improve this approximation, isothermal molecular dynamics simulations have been performed on a series of Lennard-Jones mixtures. Thermodynamic properties, including the mixture radial distribution functions, have been obtained at seven compositions ranging from 5 to 95 mol%. In all cases the size ratio was fixed at two and three energy ratios were investigated, ɛ22/ɛ11=0.5, 1.0, and 1.5. The results of the simulations are compared with the mean density approximation and a modification to integrals evaluated with the mean density approximation is proposed.

Group contributions to activity coefficients from the hard sphere expansion corresponding states theory

A new method has been developed for predicting liquid activity coefficients in ternary mixtures from group contributions. In this method, activity coefficients are obtained from the excess Gibbs free energy of mixing at constant temperature and pressure. In calculating this excess function, the constituent and mixture Gibbs free energies are each represented by an expansion about a pure reference fluid in powers of ratios of hard-sphere diameters and molecular attraction parameters. When the pure component differs from the reference by a single structural group, these ratios represent, respectively, the size contribution and the attraction contribution of this group to the thermodynamic property of the pure fluid. Contributions of intermolecular repulsion to the excess Gibbs free energy are calculated directly from hard-sphere equations of state for the mixture and pure components. The effect of polar contributions calculated by a Pade approximant is also examined. Results indicate that the method developed from the hard-sphere expansion corresponding-states theory is useful for predicting activity coefficients in ternary mixtures when unlike-pair interaction parameters are fitted to binary activity coefficient data. Furthermore, the method shows promise in providing a theoretical basis for applying group contributions to activity coefficients.

A relation between the critical properties of aqueous salt solutions and the heat capacity of the solutions near the critical point using a single-fluid corresponding-states theory

The effects of added salts on the heat capacity of water at constant pressure are extremely large near the critical point of water. A corresponding-states theory for the heat capacity of aqueous salt solutions is proposed. This theory is based on the assumption that the major effect of the salt is to shift the critical point of the water in the solution. Since the water has an infinite heat capacity at constant pressure at the critical point, this shift causes the very large effects observed. Tests of this theory with the available data on NaCl show that the theoretical predictions are surprisingly accurate. The heat capacity of the solution is predicted with an average error of ± 0.7 per cent and a maximum error of 3.4 per cent at temperatures from 320 to 600 K, molalities from 0.1 to 3.0 mol·kg −1, and at a pressure of 17.7 MPa. A similar equation for the enthalpy of the solutions is not accurate, and there are insufficient data in the literature to test the corresponding equations for thermal expansivity, compressibility, and the difference between heat capacities at constant pressure and at constant volume. Since the equation has been tested only for NaCl solutions at temperatures below the critical point, there is a pressing need for more experimental results. The theory predicts very large effects on the heat capacity of any solution of a strong electrolyte near the critical point of the solvent and that these effects can be predicted from a knowledge of the critical temperature and critical pressure of the solutions.

Thermodynamic properties from corresponding states theory

Abstract A corresponding states approach has been applied to the two-constant equations of state by Wilson, Soave, Peng—Robinson, Hamam et al., Lu et al., Simonet—Behar, and Chaudron et al. in order to obtain the equivalent shape-factor correlations. The correlations derived are compared with the Leach—Leland corresponding-states theory. Different fluid approximations for mixtures have been applied to the various corresponding states approaches. The resulting computation methods have been applied to calculate saturation properties of pure fluids and separation factors in binary mixtures for some fluids commonly encountered in natural gas and petroleum refining operations. Finally it is shown that the binary interaction parameters depend only on the fluid approximation and not on the specific form of the potential.

Second Virial Coefficients of Gas Mixtures Containing Simple Fluids and Heavy Hydrocarbons

The University of California, Berkeley, estimates fugacity coefficients at advanced pressure in gas streams containing small amounts of heavy hydrocarbons, such as n-heptane, the largest, mixed with excess methane, nitrogen, hydrogen, or other simple fluids (N/sub 2/, Ar, CH/sub 4/, CO, H/sub 2/). The calculations - based on the tuncated virial equation of state - require virial coefficients that are found by correlations useful for mixtures containing large molecules, where normal-fluid corresponding-state theory is inapplicable. Structural data fom vapor pressure and from reasonable correlations concerning enthalpy of vaporization are determinants for such calculations. New experimental studies are in progress to test the proposed correlations for highly asymmetric systems.

Sorption of solutes by poly(ethylene oxide). II. Benzene at finite concentrations

We have determined the activity of benzene in poly(ethylene oxide) over concentration ranges from 0 to 20 wt-% from 70° to 150°C using gas–liquid chromatography. The results are well corelated by the corresponding-states theory of Prigogine and Flory. Comparison between our results and those obtained by other workers using a “static” method indicate good agreement, except at very low benzene concentrations.

On the calculation of heats of mixing of compressed gases by the corresponding-states theories of mixtures

Heats of mixing are calculated with the corresponding-state theory of mixtures for CH 4-N 2 and CH 4-Ar and compared with experimental values. The one-fluid model gives a better agreement than the two-fluid model.

Compressibilities of the Molten Alkali Nitrates and Silver Nitrate at High Pressure

The densities of the pure molten salts LiNO3, NaNO3, KNO3, RbNO3, and AgNO3 were determined by the piston—cylinder method at pressures up to 9000 atm. The temperature covered by the measurements was from just above the liquidus curves up to about 500°C. The results were related to the corresponding-states theory of fused salts. In the case of LiNO3, deviation from the corresponding-states law was ascribed to anion—anion contact.