Critical compression

The critical compressibility factor is estimated using the Lee and Kesler equation (1975) ... 

The critical pressure, critical molar volume, and critical temperature are the values of the pressure, molar volume, and thermodynamic temperature at which the densities of coexisting liquid and gaseous phases just become identical. At this critical point, the critical compressibility factor, Z, is ... 

Critical Compressibility Factor The critical compressibility factor of a compound is calculated from the experimental or predicted values of the critical properties by the definition, Eq. (2-21). 

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. 

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). 

If no value of Zra is available or derivable, the critical compressibility factor can be used in Eq. (2-84) as originally proposed by Rackett. Use of Z increases the average error to about 3.0 percent. 

Hence there must be one relation involving pc, Tc and Vc which is independent of the parameters a and b. This relation defines the critical compressibility factor Zc ... 

Estimating the critical density IE, ln(Pc7Pc) No consistency test is available for ln(pc7Pc), but for the original Van der Waals equation and the modified VdW equations discussed in this chapter the critical compressibility factors, Zc(VdW) = Pc/(pcRTc), are equal to 3/8 and (a2 - l)/(4a), respectively. In the latter case,... 

Gaseous paraffins and olefins with low molecular weight and short chain length have relatively high critical compression ratios. Their octane numbers must all be well above 100. Normal paraffins have the lowest octane numbers of any of the members of their... 

The engine data for the normal olefins, pentenes to octenes inclusive, are recorded in Table IX. The data are stated as octane numbers or critical compression ratios. The table is fragmentary, the work being still incomplete, but it is sufficiently complete to show the trends. 

The boiling point, refractive index, and density of the olefin derivative of any paraffin were shown, by use of Table III, to stand in the onier of their olefin type. Table X contains the engine data of the olefin derivatives of 2-methylpentane and 3-methylpentane, recorded in the order of their olefin type. No consistent relations between octane numbers or critical compression ratios are obvious—but the blending octane numbers of these branched olefins, as measured by both the research and Motor methods, do generally stand in the order of their type. Two olefins of type III form exceptions, the exceptions being in one case too high and in the other case too low. 

Aromatic hydrocarbons have exceptionally high engine characteristics. The Research octane numbers of all aromatic hydrocarbons thus far measured are above 100. Those measured by the Motor method are a little lower, but in all cases are above 95. The critical compression ratios at 600 revolutions per minute and 212° F., jacket temper-... 

This datum constitutes, or is partly derived from, an extrapolated, octane number based on critical compression ratios, measurement of which is not limited to the octane range as defihed (0-100). 

The blending octane members of the first five members of the monoalkylbenzenes as measured by the Motor method show alternation. The same is true for the four mono-butylbenzenes, as the butyl group is telescoped on the aromatic nucleus. This is also true of their critical compression ratios (Table XI). 

One of the most fundamental elements of molecular structure is chain length. It serves to fix the hydrocarbon s position on its own subseries curve and thus becomes a factor in determining its physical constants. It also is a major factor in determining the hydrocarbon s rate of combustion and hence its octane number and critical compression ratio. 

The double bond functions in a very analogous manner. It too interrupts effective chain length and determines the principal point of oxidative attack. In a manner quite analogous to the methyl group, through changes in the combustion velocity, the double bond also alters the octane number and critical compression ratio. 

Hydrocarbon Structure Olefin Type Research Octane No. Motor Octane No. Blending Octane No. (Research) Blending Octane No. (Motor) Critical Compression Ratio (600/212° F.) Critical Compression Ratio (600/350° F.)... 

The aromatic hydrocarbons form a unique case of cyclic structure. The benzene ring, like the methyl group and double bond, exerts a powerful influence upon the properties of any hydrocarbon of which it is a part. All aromatic hydrocarbons have high boiling points, high densities, and high refractive indices. They also have high octane numbers and critical compression ratios. 

Table 2.4 displays critical constants Tc, Pc, Vc and critical compressibility factor Zc for a number of common gases. (Accurate determination of the critical point is experimentally challenging, and quoted values are generally uncertain in the final decimal.) One can see from the table that many common gases (including N2, 02, and CH4) are actually supercritical fluids ( permanent gases ) under ambient temperature conditions, incapable of liquefaction by any applied pressure whatsoever. (Aspects of cryogenic gas-liquefaction techniques are discussed in Section 3.6.3.)... 

The Redlich-Kwong equation gives a somewhat better critical compressibility (Zc = 0.333 instead of 0.375 as results from the Van der Waals equation), but is still not very accurate for the prediction of vapour pressures and liquid densities. 

The above equations were obtained from twenty non-polar gases including inert gases, hydrocarbons and carbon dioxide (but not hydrogen and helium). Hence, possible errors can be as large as 20%. The maximum pressure corresponds to a reduced density of 2.8. In the above equations, Zc represents the critical compressibility factor. The value of gamma is calculated using Eqn. (3.4-26). 

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