Compressibility corresponding-states correlation

Pitzer s Corresponding-States Correlation A three-parameter corresponding-states correlation of the type developed by Pitzer, K.S. Thennodynamic.s, 3ded., App. 3, McGraw-HiU, New York, 1995) is described in Sec. 2. It has as its basis an equation for the compressibility factor ... 

Clausius/Clapeyron equation, 182 Coefficient of performance, 275-279, 282-283 Combustion, standard heat of, 123 Compressibility, isothermal, 58-59, 171-172 Compressibility factor, 62-63, 176 generalized correlations for, 85-96 for mixtures, 471-472, 476-477 Compression, in flow processes, 234-241 Conservation of energy, 12-17, 212-217 (See also First law of thermodynamics) Consistency, of VLE data, 355-357 Continuity equation, 211 Control volume, 210-211, 548-550 Conversion factors, table of, 570 Corresponding states correlations, 87-92, 189-199, 334-343 theorem of, 86... 

Related Calculations. This illustration outlines various simple techniques for estimating P-V-T properties of gaseous mixtures. Obtain the compressibility factor from the generalized corresponding-state correlation, as shown in step 2. 

Critical compressibility factor - helpful in corresponding state correlations... 

Consequently, the fugacity coefficient can be tabulated in the corresponding-states manner. The corresponding-states correlation for the fugacity coefficient of nonpolar gasesjmd liquids given in Fig. 7.4-1 was obtained using Eq. 7.4-15b and the compressibility correlation (Fig. 6.6-3). 

One of the most interesting applications in this class is the method of Lee-Kesler (LK). The compressibility factor is described by three-parameter corresponding states correlation of the form ... 

According to the corresponding-states correlation, this is also equal to the compressibility factor of carbon dioxide at 35 bar, 348.15 K. The molar volume of carbon dioxide is... 

Huang, Y. H. and J. P. O Connell. 1987. Corresponding states correlation for the volumetric properties of compressed hquids and hquid-mixtures. Fluid Phase Equilibria. 37, 75. 

From S.W. Brelvi t J.P. O Conndl, "Corresponding States Correlations for Liquid Compressibility and Partial Molal Volumes of Gases at Infinite Dilution in Liquids", AIChE J, vl8, 6. ppl239-1243 (1972)... 

The volumetric properties of fluids are represented not only by equations of state but also by generalized correlations. Tbe most popular generalized correlations are based on a three-parameter theorem of corresponding states which asserts that the compressibility factor is a universal function of reduced temperature, reduced pressure, and a parameter CO, called the acentric factor ... 

The definition of w makes its value zero for argon, krypton, and xenon, and experimental data yield compressibility factors for all three fluids that are correlated by the same curves when Z is represented as a function of Tr and Pr. Thus the basic premise of the three-parameter theorem of corresponding states is that all fluids having the same value of w have the same value of Z when compared at the same Tr and Pr. 

Lydersen, Greenkom, and Hougenl developed a general method for estimation of liquid volumes, based on the principle of corresponding states. It applies to liquids just as the two-parameter compressibility-factor correlation applies to gases, but is based on a correlation of reduced density as a function of reduced temperature and pressure. Reduced density is defined as... 

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 ... 

By applying the corresponding states principle, the deviations of the properties of a substance from those of a simple fluid may be correlated in terms of the acentric factor, as described above for vapor pressures (Equation 1.14). The compressibility factor has also been correlated in terms of the acentric factor in the form of a polynomial... 

Since O2 and N2 have the exact same compressibility factor (PcVc/ RTc = 0.292), and no dipole moment, it may not be too much of a surprise that the sound speeds correlate well with the empirical law of corresponding states. This result suggests that N2 and O2 molecules are approximately spherical up to 2.2GPa. 

The principle of corresponding states was the first attempt toward a universal method for correlating thermodynamic properties. This is expressed as following The equilibrium properties that depend on intermolecular forces are related to critical properties in a universal way. In two parameters formulation (van der Waals, 1873), the compressibility factor is a function only of the reduced temperature and pressure ... 

For prediction of vapor density of pure hydrocarbon and nonpolar gases, the corresponding states method of Pitzer et al, is the most accurate method, with errors of less than 1 percent except in the critical region where errors of up to 30 percent can occur. The method correlates the compressibility factor by Eq. (2-75), after which the density can be calculated by Eq, (2-75) ... 

Solution According to the correlation of corresponding states, water and CO2 have approximately the same compressibility factor at the same reduced state. The conditions given for CO2 correspond to the reduced coordinates (see cample2 ... 

These forms of a generalized equation of state only require the critical temperature and the critical pressure as substance-specific parameters. Therefore, these correlations are an example for the so-called tsvo-parameter corresponding-states principle, which means that the compressibility factor and thus the related thermodynamic properties for all substances should be equal at the same values of their reduced properties. As an example, the reduced vapor pressure as a function of the reduced temperature should have the same value for all substances, provided that the regarded equation of state can reproduce the PvT behavior of the substance on the basis of the critical data. In reality, the two-parameter corresponding-states principle is only well-suited to reflect the properties of simple, almost spherical, nonpolar molecules (noble gases as Ar, Kr, Xe). For all other molecules, the correlations based on the two-parameter corresponding-states principle reveal considerable deviations. To overcome these limitations, a third parameter was introduced, which is characteristic for a particular substance. The most popular third parameter is the so-called acentric factor, which was introduced by Pitzer ... 

The principle of corresponding states can be used to express the pressure, tan-perature, and specific volume in terms of reduced variables. Experimental observations reveal that the compressibility factor, Z Equation (2.24), for different fluids exhibits similar behavior when correlated as a function of reduced temperature, T, and reduced pressure, The reduced variables may be defined with respect to some characteristic quantity. For example, they can be defined as follows with respect to critical temperature and critical pressure ... 

EOV EOS theory was developed by formulation of canonical function of the Boltzmann distribution of energies and derivation of thermodynamic pressure. The theorem of corresponding states says that the same compressibility factor can be expected for all fluids when compared at reduced temperature and pressure. A two-parameter correlation for compressibility factor, Z, can be derived using the theorem of corresponding states. EOV EOS obeys the corresponding state principle. Characteristic temperature, pressure, and specific volume used in EOV EOS are tabulated for 16 commonly used polymers. 

The third virial coefficients of pure non-polar gases have also been correlated using a three-parameter corresponding-states model by Orbey and Vera. However, in order to obtain a reliable correlation for the third virial coefficients of both polar and non-polar substances it is again necessary to introduce an additional parameter. Liu and Xiang present a correlation of this kind in which the fourth parameter is the critical compression factor Z, their model is " ... 

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