Corresponding-states Methods

Compared to the theory of corresponding states, the reference substance method gives highly accurate results for compounds having sparse experimental data. The corresponding states method gives moderate accuracy for numerous compounds even without actual data. 

Viscosity. A corresponding states method that requires critical pressure, temperature, and dipole moment has been developed for low pressure gas viscosity (221). This method, which includes a group contribution parameter, is also appHcable to gas mixtures. Whereas a group contribution method is not available for dipole moment, the influence this parameter has can be neglected for many species. 

Critical compressibility factors are used as characterization parameters in corresponding states methods (especially those of Lydersen) to predict volumetric and thermal properties. The factor varies from about 0.23 for water to 0.26-0.28 for most hydrocarbons to slightly above 0.30 for light gases. 

The method of Lee and KesleF is the preferred method if the critical temperature and the critical pressure of the hydrocarbon is known or can be reasonably predicted by the methods of the first section. The corresponding states method is shown in equation (2-31) with the simple fluid and correction terms to be calculated from equations (2-32) and (2-33), respectively, for any Tr-... 

For prediction of vapor density of pm e hydi ocaihon and nonpolar gases, tbe corresponding states method of Pitzer et al. is tbe most accurate method, witb errors of less than 1 percent except in tbe critical region where errors of up to 30 percent can occur. Tbe method correlates tbe compressibibty factor by Eq. (2-75), after which tbe density can be calculated by Eq. (2-75) ... 

For pure organic vapors, the Lydersen et al. corresponding states method is the most accurate technique for predicting compressibility factors and, hence, vapor densities. Critical temperature, critical pressure, and critical compressibility factor defined by Eq. (2-21) are used as input parameters. Figure 2-37 is used to predict the compressibihty factor at = 0.27, and the result is corrected to the Z of the desired fluid using Eq. (2-83). 

Sterbacek, Z., Biskup, B. and Tausk, P. (1979) Calculation of Properties Using Corresponding-state Methods (Elsevier). 

For a gas, the effect of pressure on the viscosity depends on the region of P and T of interest relative to the critical point. Near the critical state, the change in viscosity with T at constant pressure can be very large. The correlation of Uyehara and Watson [15] is presented for the reduced viscosity estimated from the corresponding-states method. The critical viscosities of a few gases and liquids are available [15]. These are necessary to calculate the... 

Consider for example, the corresponding states method of Jossi et al. (1962), which is used to correct for the high density ... 

Jossi et al. (1962) presented a generalized correlation for the viscosity of high density fluids as a function of the reduced density via a corresponding states method. This method was discussed earlier. Among the gases that Jossi et al. (1962) used to build their correlation were carbon dioxide, methane, ethane, and propane. This gives us some confidence that this approach should be satisfactory for our acid gas mixtures. 

However, the methods for calculating the density of a supercritical fluid are rather conventional. An equation of state or a corresponding state method can be used. They must be used with caution because the critical region is notorious as a region where the accuracy of density predictions is poor. 

Z. Sterbacek, B. Biskup, and P. Tausk, Calculation of Properties Using Corresponding States Methods, Elsevier, New York, 1979. 

Wilding, W.V. and Rowley, R.L. (1986). A Four Parameter Corresponding States Method for the Prediction of Thermodynamic Properties of Polar and Nonpolar Fluids. Int.J.Thermophys., 7, 525-539. 

The Kesler-Lee correlations for liquid and vapour phase heat capacities of petroleum fluids are used for estimating the respective enthalpies at temperatures of interest. The Lee-Kesler corresponding-states method is used for obtaining estimates of the heats of vaporization and for developing the saturation envelope enthalpies. This method uses the Curl and Pitzer approach and calculates various thermodynamic properties by representing the compressibility factor of any fluid in terms of a simple fluid and a reference fluid as follows ... 

Vapour pressure is a key property in VLB calculations and is thus an important petroleum property. The most common method for prediction of vapour pressures is the corresponding states method. The method requires knowledge of the critical properties and the acentric factor. For petroleum fractions, the Maxwell-BonnelF method is standard. 

Determine AZ Required data from the DIPPR 801 database for this calculation are T, = 645.6 K, P, = 4.25 MPa, and ra = 0.35017. These values are used to determine the reduced conditions and the values of Zg and Zl from the Lee-Kesler corresponding states method as discussed in the subsection on density. 

For higher gas densities, the Lee-Kesler method described below provides excellent predictions for nonpolar and slightly polar fluids. Extended four-parameter corresponding-states methods are available for polar and slightly associating compounds. 

Teja AS, Rice P (1981) Generalized corresponding states method for the viscosities of liquid-mixtures. Ind Eng Chem Fund 20 77-81... 

Many estimation techniques are corresponding-states methods, where the properties of the target fluid are scaled to the properties of a well-known fluid. Scaling factors are often based on the critical temperature and pressure and the acentric factor (which in many cases must be estimated). It is essential to recognize that most correlations were developed for certain classes of fluids, making it dangerous to use them for fluids that are very different from those used to develop the correlation. For example, a correlation developed for nonpolar hydrocarbons should not be applied to a polar fluid such as ammonia or methanol. 

The three approaches mentioned in the previous section may also be used to describe caloric properties (enthalpy, entropy, heat capacity) of mixtures. The same considerations mentioned earlier are also true for the application of mixture equations of state and corresponding-states methods for the prediction of caloric properties. 

Gas viscosity of a single component is calculated from a corresponding state method for CH, CO2, CO and N2 it is calculated by ... 

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