Critical compression factor

The first term wt = (l+2rc)1/2 of the power series w defined in Eq. (6-10) plays a special role within the interaction model in that it represents a perfect gas phase. If Vo, pc, Tc and R represent the molar volume of a compound, the critical pressure and critical temperature of the system and the gas constant, then the product pcV0 is reduced to llw of the product RTC due to the interaction between the particles in the system. Taking into account an empty (free) volume fraction in the critical state, the critical molar volume is written as Vc = V(). Consequently, a dimensionless critical 

From a data collection with 349 experimental values for the critical compression factor (Reid et al., 1987) obtained with organic and inorganic compounds and elements, a mean value of Zc = 0.2655 is obtained with a standard deviation of a = 0.0346. 

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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,... 

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 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). 

Zra is an empirically derived constant from data. A good approximation for Zra is the critical compressibility factor. The error found in the use of this method averages less than 2%... 

The critical pressure P = PoAso/q2 is more difficult to evaluate. In the earlier literature there is a large spread of values [17]. The recent MC simulations of Orkoulas and Panagiotopoulos [52] yield P c = 8 x 10-5 near the lower limit of earlier estimates, along with a critical compressibility factor of Zc — PJ(pcTc) = 0.024 which is one order of magnitude lower than observed for nonionic fluids (e.g., Zc = 3/8 = 0.375 for the van der Waals fluid). 

The equations given predict vapor behavior to high degrees of accuracy but tend to give poor results near and within the liquid region. The compressibility factor can be used to accurately determine gas volumes when used in conjunction with a vitial expansion or an equation such as equation 53 (77). However, the prediction of saturated liquid volume and density requires another technique. A correlation was found in 1958 between the critical compressibility factor and reduced density, based on inert gases. From this correlation an equation for normal and polar substances was developed (78) ... 

Equation (6-17) can be easily adapted for the critical state, if p is substituted with the critical pressure, pc, obtained with Eq. (6-12) and if W/ in the exponent is substituted with w, e. This takes into account the absence of a pure translational energy contribution in the critical state. On the contrary, an additional negative term, the critical compression factor Zc = -w,lw, is introduced in the exponent, taking into account the decrease in diffusion velocity caused by attraction between the particles. As a result the following equation gives the coefficient of self-diffusion in the critical state ... 

Critical Compressibility Factor. The critical compressibility factor, Za of a van der Waals gas is given by... 

Thus, we can test whether a gas behaves as a van der Waals gas by seeing whether its critical compressibility factor is equal to 0.375. 

Figure 5.4-1 shows a generalized compressibility chart for those fluids having a critical compressibility factor of 0.27. Conditions for both gases and liquids are illustrated, although in our discussions here we only consider estimation of z for gases. Note the increasing deviations from ideal gas behavior as pressures approach Pc O-e-, when Pr 1). 

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

The compilations of CRC (1-2), Daubert and Danner (3), Dechema (15), TRC (13-14), Vargaftik (18), and Yaws (19-36) were used extensively for critical properties. Estimates of critical temperature, pressure, and volume were primarily based on the Joback method (10-12) and proprietary techniques of the author. Critical density was determined from dividing molecular weight by critical volume. Critical compressibility factor was ascertained from application of the gas law at the critical point. Estimates for acentric factor were primarily made by using the Antoine equation for vapor pressure (11-12). 

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