Pseudo critical point

It would be convenient if the critical temperature of a mixture were the mole weighted average of the critical temperatures of its pure components, and the critical pressure of a mixture were simply a mole weighted average of the critical pressures of the pure components (the concept used in Kay s rule), but these maxims simply are not true, as shown in Fig. 3.22. The pseudocritical temperature falls on the dashed line between the critical temperatures of CO2 and SO2, whereas the actual critical point for the mixture lies somewhere else. The solid line in Fig. 3.22 illustrates how the locus of the actual critical points diverges from the locus of the pseudo critical points. 

Although Figure A2 is designed for pure CO, it can also be used for CO -rich mixtures. As was demonstrated by Roberts and Carroll (2015), the pseudo-critical temperature and pressure of a mixture can be estimated using several approaches. However, the simple Kay s rule yields accurate results. These are called the pseudo critical point are calculated as follows ... 

It should be noted that within the operating conditions for both GFR and VHTR, hehum behaves as a compressed gas because these operating conditions way above the critical point or pseudo-critical points at corresponding operating pressures. 

Insufficient information concerning the behavior of mixtures requires that the pseudo critical temperature and pseudo critical pressure be used for most oil mixtures. The pseudo critical point as developed by W. B. Kay may be defined as the molal average critical temperature and pressure of the several materials that constitute a mixture. It may be used as the critical point of a mixture in computing reduced temperatures, pres-... 

The volume of gaseous mixtures may be computed for any condition that is not close to the envelope in the diagram, from the pressure-volume-temperature relations of the hypothetical material C using the pseudo critical point designated as c (Example 5-5). Lines of constant volume are indicated on the diagram. 

It will be noted that the pseudo critical point is different from the actual critical point or the focal point. The pseudo critical temperature (Fig. 5-9) is about 890 F, and the pseudo critical pressure (Mg. 5-12 is about 290 psia. If all of the correlation methods had been perfect, the pseudo critical point would have fallen within the phase envelope. 

At an average pressure of 510 psia and at 902°F, the compressibility factor is about 0.37, but note that an average (rather than the 50 per cent) boiling point must be used for such a wide-boiling mixture and also that the pseudo critical point of Figs. 5-9... 

Example 5-6. Pseudo Critical Point. Critical values for ethane and propane are... 

From all these examples we can conclude that the mixture thermodynamics described by the COSMOSPACE equations is in very good agreement with LMC simulations, unless one is very close to a critical point of phase transition or phase separation. This means the geometrical constraints that arise from neighborhood relations of the surface segments on the pseudo-molecules, i.e., on the cubes in the case of the simulations discussed before, and the lattice constraints are of negligible importance for the mixture thermodynamics over a wide range of concentrations and temperatures. 

To apply the above method to mixtures, it is necessary to know the gas composition in order to calculate the pseudo-eriticals. If data on the composition are not available, it is still possible to approximate a value for Z if the specific gravity of the gas is known. It has been found that if the pseudo-oritioal pressure is plotted as a function of specific gravity for a large number of gases, most points fall on a straight line. Similarly, a plot of pseudo-critical temperature versus... 

Fig. 3.3. Gradient vector field of the electronic charge density for the unstable conflict structure shown in Fig. 3.1(e). The plane shown contains the symmetry axis and is perpendicular to the plane of the nuclei. In the lower portion of the diagram, trajectories terminate at the (3, — 1) critical point between the hydrogen nuclei. In the upper portion, trajectories terminate at the pseudo (3, — 3) critical point at the oxygen nucleus. These two critical points are linked by the pair of trajectories which originate at the central (3, — 1) critical point indicated by the dot This is an unstable intersection of the one-dimensional manifold of this (3, — 1) critical point with the two-dimensional manifold of the (3, — 1) critical point between the protons.

FIGURE 43 Phase diagram obtained for the pseudo-alloy, composed of a-Ce (light grey area) and y-Ce (dark grey area). The grey shades display the fraction of localized electrons. The crosses indicate the calculated (upper cross) and experimental (lower cross) critical points. 

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