Compressibility factor generalized correlations

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 ... 

A disadvantage of the generalized compressibility-factor correlation is its graphical nature, but the complexity of the functions Z° and Z1 precludes their general representation by simple equations. However, we can give approximate... 

The relative simplicity of the generalized virial-coefficient correlation does much to recommend it. Moreover, the temperatures and pressures of most chemical-processing operations lie within the region where it does not deviate by a significant amount from the compressibility-factor correlation. Like the parent correlation, it is most accurate for nonpolar species and least accurate for highly polar and associating molecules. 

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... 

Figure 3.16, drawn specifically for the compressibility-factor correlation, is also used as a guide to the reliability of the correlations of residual properties based on generalized second virial coefficients. However, all residual-property correlations are less precise than the compressibility-factor correlations on which they are based and are, of course, least reliable for strongly polar and associating ... 

The generalized correlations of Pitzer provide an alternative to the use of a cubic equation of state for the calculation of thermodynamic properties. However, no adequate general method is yet known for the extension of the Pitzer correlations based on the compressibility factor to mixtures. Nevertheless, Z, as given by... 

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... 

Since the acentric factor is here so small, the two- and three-parameter compressibility-factor correlations are little different. Both the Redlich/Kwong equation and the generalized compressibility-factor correlation give answers very close to the experimental value of 185(atm). The ideal-gas equation yields a result that is high by 14.6 percent. 

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. 

As with the generalized compressibility-factor correlation, the complexity ol the functions (H f/RZ. H Y/RZ. (S /R, and S Y/R preclude then general representation by simple equations. However, the correlation for Z basec on generalized virial coefficients and valid at low pressures can be extended U the residual properties. The equation relating Z to the functions and ia derived in Sec. 3.6 from Eqs. (3.46) and (3.47) ... 

Generalized correlations find widespread use. Most popular are correlations of die kind developed by Pitzer and cowoikers for the compressibility factor Z and for the second virial coefficient B. ... 

As with the generalized compressibility-factor correlation, tire complexity of tire fuirc-tioirs (H f/RTc, (H f/RTc, S f/R, and (Sy/R precludes tlreir geireral representation by simple equations. However, tire generalized secoird-virial-coefficientcorrelationvalid at low pressures fonrrs the basis for airalytical correlations of tire residual properties. The equation relating B to the functions aird 5 is derived iir Sec. 3.6 ... 

Mole fraction, species i, vapor phase Compressibility factor = FV/RT Critical compressibility factor s PcVc/RTc Functions, generalized compressibility-factor correlation Partition function... 

Generalized correlations for the compressibility factor, Z, as well as analytical expressions, based on the second virial coefficients, have been developed by Pitzer et a/. The correlation for Z takes the form ... 

Pitzer s Generalized Correlations In addition to the corresponding-states coorelation for the second virial coefficient, Pitzer and coworkers [Thermodynamics, 3d ed., App. 3, McGraw-Hill, New York (1995)] developed a full set of generalized correlations. They have as their basis an equation for the compressibility factor, as given by Eq. (2-63) ... 

Working with generalized correlations for the compressibility factor. 

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