Temperatur critical

However, if the liquid solution contains a noncondensable component, the normalization shown in Equation (13) cannot be applied to that component since a pure, supercritical liquid is a physical impossibility. Sometimes it is convenient to introduce the concept of a pure, hypothetical supercritical liquid and to evaluate its properties by extrapolation provided that the component in question is not excessively above its critical temperature, this concept is useful, as discussed later. We refer to those hypothetical liquids as condensable components whenever they follow the convention of Equation (13). However, for a highly supercritical component (e.g., H2 or N2 at room temperature) the concept of a hypothetical liquid is of little use since the extrapolation of pure-liquid properties in this case is so excessive as to lose physical significance. 

To use Equation (10b), we require virial coefficients which depend on temperature. As discussed in Appendix A, these coefficients are calculated using the correlation of Hayden and O Connell (1975). The required input parameters are, for each component critical temperature T, critical pressure P, ... 

Equations (2) and (3) are physically meaningful only in the temperature range bounded by the triple-point temperature and the critical temperature. Nevertheless, it is often useful to extrapolate these equations either to lower or, more often, to higher temperatures. In this monograph we have extrapolated the function F [Equation (3)] to a reduced temperature of nearly 2. We do not recommend further extrapolation. For highly supercritical components it is better to use the unsymmetric normalization for activity coefficients as indicated in Chapter 2 and as discussed further in a later section of this chapter. 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

The critical temperature of methane is 191°K. At 25°C, therefore, the reduced temperature is 1.56. If the dividing line is taken at T/T = 1.8, methane should be considered condensable at temperatures below (about) 70°C and noncondensable at higher temperatures. However, in process design calculations, it is often inconvenient to switch from one method of normalization to the other. In this monograph, since we consider only equilibria at low or moderate pressures in the region 200-600°K, we elect to consider methane as a noncondensable component. 

Figure 4-12. Vapor-liquid equilibria for ethane-n-heptane at 6.9 bars. Ethane is treated as a condensable component even though its critical temperature is 305.4 K.

Large errors in the low-pressure points often have little effect on phase-equilibrium calculations e.g., when the pressure is a few millitorr, it usually does not matter if we are off by 100 or even 1000%. By contrast, the high-pressure end should be reliable large errors should be avoided when the data are extrapolated beyond the critical temperature. 

TC = critical temperature, K PC = critical pressure, bars VC = critical volume, cm /g-vol... 

PNOTE - MOOIEIEO PARA tETEPS INCLUDING CRITICAL TEMPERATURE PRESSURE VOLUME OtPOLP MOMENT,... 

Tj. is the reduced temperature, T is the critical temperature, is the critical pressure, and is the modified Rackett parameter as given in the supplemental table for pure-component properties. 

MEAN RADIUS OF GYRATION OF COMPONENT I I A I. CRITICAL TEMPERATURE OF COMPONENT I (DEGREES K). TEMPERATURE OF MIXTURE (DEGREES Kl. 

Very often the choice is not available. For example, if reactor temperature is above the critical temperature of the chemical species, then the reactor must be gas phase. Even if the temperature can be lowered below critical, an extremely high pressure may be required to operate in the liquid phase. 

Phase separation in this way is most effective if the light key component is significantly above its critical temperature. If a component is above its critical temperature, it does not truly condense. Some, however, dissolves in the liquid phase. This means that it is bound to have an extremely high K value. 

The temperature of the phase split is well above the critical temperatures of both hydrogen and methane, leading to large K values. On the other hand, the K values of the benzene, toluene, and diphenyl are very low, and hence the assumption of a sharp split in Example 4.2 was a good one. 

The average error is about 2% for tbe critical temperatures and pressures. The error increases with molecular weight and can reach 5%. 

The estimation of the three parameters —pseudo-critical temperature, pseudo-critical pressure, and the acentric factor— should be done using the same method because these constants should be coherent. 

T = pseudo-critical temperature of the mixture P = pseudo-critical pressure of the mixture Xr — reduction group for the property ij/, for example (/ for enthalpy... 

Normal boiling point K Standard specific gravity Molecular weight kg/lunol Liquid viscosity at 100°F mm /s Liquid viscosity at 2iO F mm /s Critical temperature K Critical pressure bar... 

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