Acentric Deviations

Table 2-352 Acentric Deviations from the Simple Fluid Compressibility Factor... 

Three Parameter Models. Most fluids deviate from the predicted corresponding states values. Thus the acentric factor, CO, was introduced to account for asymmetry in molecular stmcture (79). The acentric factor is defined as the deviation of reduced vapor pressure from 0.1, measured at a reduced temperature of 0.7. In equation form this becomes ... 

Although use of an equation based on the two-parameter theorem of corresponding states provides far better results in general than the ideal-gas equation, significant deviations from experiment still exist for all but the simple fluids argon, krypton, and xenon. Appreciable improvement results from the introduction of a third corresponding-states parameter, characteristic of molecular structure the most popular such parameter is the acentric factor , introduced by K. S. Pitzer and coworkers.t... 

Here is the fluid s critical pressure in atm, is the fluid s critical temperature in Kelvins, and u) is the fluid s acentric factor as defined in Poling et al. (2001). With these parameters, the kinetic theory reproduces the viscosities of the 14 investigated normal fluids with a RMS deviation of 2.13 percent. 

Description The acentric factor is used to linearly interpolate within the simple-fluid and deviation terms for the In P values of the reference fluids, which themselves have been correlated with the Wagner vapor pressure equation. 

The acentric factor is used in thermodynamic correlations involving fugacity, compressibility factor, enthalpy, fugacity, and virial coefficients. The computer program PROG21 provides a routine for estimating the vapor pressure, and Table 2-1 shows P of water as a function of temperature. Figure 2-6 shows the vapor pressure of water as a function of temperature to its critical value of 374.2°C. For water, deviations of less... 

The Soave equation uses an additional parameter, the acentric factor, to correlate vapor pressure data. The acentric factor, co, had been deflned in earlier work as a parameter that correlates the deviation of the reduced vapor pressure of a particular compound from that of simple molecules. The reduced vapor pressure is correlated with the reduced temperature as follows ... 

For substances in general, the reduced vapor pressure tends to deviate to varying degrees from this equation. The deviation is accounted for by including the acentric factor in the equation ... 

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... 

If the departure from equation (35) is not too large, it can be treated as a perturbation. The effect of non-central interactions on the second virial coefficient is second order and it is very difficult to distinguish between any of the non-central interactions on the basis of the behaviour of In essence, it is possible to fit the properties of many pure substances to equations based on simple corresponding states and additional terms whose magnitude is proportional to a perturbation parameter that is a measure of the deviation from central forces. One such perturbation parameter is Pitzer s acentric factor. 74,76 another is Rowlinson s In a homologous series the number of carbon atoms in the chain constitutes yet another measure of the perturbation. It can be shown that there is a simple relation between the different factors. ... 

Nonpolar molecules that deviate from spherical shape and small molecules of only moderate polarity are described quite well by the three-constant correlation that utilizes the acentric factor. The acentric factor, therefore, can be viewed as an empirical parameter that encompasses the effect of molecular shape, and to some extent polarity. Molecules in this category constitute the class of normal fluids, and include small molecules such as O2, N, as well many lower hydrocarbons. 

A quantity often used in calculations on real gases is the Pitzer acentric factor, co. Pitzer defined the factor as a means of characterizing deviation from spherical symmetry for use in corresponding state modeP . The acentric factor is obtained from experimental data, as follows co = og P[) —1.0 in which P is the reduced pressure P/P at the reduced temperature of 0.7°C, P being the critical pressure. This definition is consistent with acentric factor values of zero for rare gases. 

In this relation, is a term describing thr compressibility factor of a simple fluid and is a term taking into account the deviation of a real fluid from the behavior of the simple fluid. Additionally, Eq. (2.95) contains the so-called acentric factor o), which will be explained in detail later (Section 2.4.4). As B is only a function of temperature, Eq. (2.95) can also be written as... 

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 ... 

A modification of the corresponding-state principle by introducing a parameter related to the vapor pressure curve is reasonable, because experimental vapor pressure data as a function of temperature are easy to retrieve. Furthermore, the vapor-liquid equilibrium is a very sensitive indicator for deviations from the simple corresponding-state principle. The value Tr = 0.7 was chosen because this temperature is not far away from the normal boiling point for most substances. Additionally, the reduced vapor pressure at Tr = 0.7 of the simple fluids has the value = 0.1 (log = —1). As a consequence, the acentric factor of simple fluids is 0 and the three-parameter correlation simplifies to the two-parameter correlation. 

Figure 3.9 Percent deviation in liquid molar volume at 0.7 as a function of acentric factor (adapted from Firoozabadi, 1988).

---