Critical pressure locus

Figure 2. Critical pressure locus for Figure 3. Critical volume locus for CO2 — 1-hexene mixtures. CO2 — 1-hexene mixtures.

Figure 7.4 The Subcritical Fluid Cliromatography range. This occupies the volume in the phase diagram below the locus of critical temperatures, above and below the locus of critical pressures, and is composed mostly of the more volatile mobile-phase component. Reproduced by peimission of the American Chemical Society.

SFC (see Figure 7.6) occurs when both the critical temperature and critical pressure of the mobile phase are exceeded. (The locus of critical points is indicated in Figure 7.2 by the dashed line over the top of the two-phase region. It is also visible or partly visible in Figures 7.3-7.8). Compressibility, pressure tunability, and diffusion rates are higher in SFC than in SubFC and EFLC, and are much higher than in LC. 

Figure 2-10 shows a more nearly complete pressure-volume diagram.2 The dashed line shows the locus of all bubble points and dew points. The area within the dashed line indicates conditions for which liquid and gas coexist. Often this area is called the saturation envelope. The bubble-point line and dew-point line coincide at the critical point. Notice that the isotherm at the critical temperature shows a point of horizontal inflection as it passes through the critical pressure. 

Figure 2-15 shows phase data for eight mixtures of methane and ethane, along with the vapor-pressure lines for pure methane and pure ethane.3 Again, observe that the saturation envelope of each of the mixtures lies between the vapor pressure lines of the two pure substances and that the critical pressures of the mixtures lie well above the critical pressures of the pure components. The dashed line is the locus of critical points of mixtures of methane and ethane. 

Notice that the locus of the critical points connects the critical pressure of ethane, 708 psia, to the critical pressure of methane, 668 psia. When the temperature exceeds the critical temperature of both components, it is not possible for any mixture of the two components to have two phases. 

For binary mixtures of hydrogen sulfide and carbon dioxide, the critical locus extends uninterrupted from the critical point of C02 to that of H2S. The critical point of a binary mixture can be estimated from the next two figures. Figure 3.4 shows the critical temperature as a function of the composition, and figure 3.5 gives the critical pressure. 

Figure 4. Temperature-pressure Figure 5. Critical temperature locus critical locus for CO2 - 1-hexene mixtures.

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. 

In the use of these charts, the pseudoheavy component of the mixture is determined by use of Eq. (14-109). The intersection of the line t — tcl with the locus of criticals determines the critical pressure for component 2. If component... 

One example will serve to underscore the reason for the advantage over Chao-Seader at high pressure. Figure 1 shows the convergence of RKJZ K-values to unity as the mixture critical pressure is approached, for a temperature and composition on the mixture critical locus for the methane-ethane-butane ternary (20). This mixture was chosen in order to check RKJZ apparent critical pressure vs. the 1972 corresponding-states correlation of Teja and Rowlinson (21), which presumably has a better theoretical basis than the RKJZ method. In these comparisons, the Teja and Rowlinson correlation uses two interaction parameters per binary pair, based primarily on fits to binary critical loci the RKJZ method uses Cij = 0 for all binaries, based on binary VLE data. 

Figure 3 was constructed as mentioned previously from Fig. 2 by cross-plotting isotherms of reduced conductivity vs. A. The thermal conductivity data for carbon monoxide were not used. Then from Fig. 3 the values of k for tritium (A = 1.00) were obtained to predict the temperature dependence of the thermal conductivity of tritium along the vapor pressure curve as shown in Fig, 2. Lastly, it may be pointed out that an extension of the Ne data of Ldchtermann P ] to the critical-temperature locus would appear to give some values of the thermal conductivity which would be very near to those predicted for tritium, and would also require an S-shaped curve, which seems improbable in view of the value of T for neon, i.e, 1.247. A curve for the thermal conductivity of Ne predicated upon behavior similar to argon and tritium is also shown. Derivation of the thermal conductivities of the unsymmetrical isotopic species of hydrogen—HT, HD, and DT— is a triviality and can easily be obtained from Fig. 3. Note that de Boer s theory does not distinguish between the behavior of HT and D2 P ]. For the unsymmetric isotope HT the value of A should be computed after Friedmann [ ] as...

The apparatus can be also used to establish the dew point-bubble point locus. The great advantage of Kay s apparatus over most types of apparatus for determining critical properties is that it is relatively simple to operate. However, it does have the disadvantage that the samples are not degassed. This could lead to errors of 0.01 to 0.06 MPa in the critical pressure and up to 1 K in the critical temperature. 

In Class B1 systems branch II of the critical locus spans the entire temperature range from the critical temperature of the heavy component (if this is accessible without decomposition) down to and below the critical temperature of the solvent, as in curves (a) and (b) in Figure 1.9. On raising the pressure at a constant temperature which is above the solvent critical temperature, complete miscibility between the liquid and supercritical fluid phases occurs at the pressure (the critical pressure) corresponding to this temperature on the locus curve. The dew- and bubble-point curves then merge giving a closed loop pressure/composition diagram. 

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

Fig. 5.12 Two different 3-D representations of the phase diagram of 3-methylpyridine plus wa-ter(H/D). (a) T-P-x(3-MP) for three different H2O/D2O concentration ratios. The inner ellipse (light gray) and corresponding critical curves hold for (0 < W(D20)/wt% < 17). Intermediate ellipses stand for (17(D20)/wt% < 21), and the outer ellipses hold for (21(D20)/wt% < 100. There are four types of critical lines, and all extrema on these lines correspond to double critical points, (b) Phase diagram at approximately constant critical concentration 3-MP (x 0.08) showing the evolution of the diagram as the deuterium content of the solvent varies. The white line is the locus of temperature double critical points whose extrema (+) corresponds to the quadruple critical point. Note both diagrams include portions at negative pressure (Visak, Z. P., Rebelo, L. P. N. and Szydlowski, J. J. Phys. Chem. B. 107, 9837 (2003))...

At pressures above the vapor pressure of propane and less than the critical locus of mixtures of methane and n-pentane, for instance 500 psia, dot 4, the methane-propane and methane-n-pentane binaries exhibit two-phase behavior, and propane-n-pentane mixtures are all liquid. Thus the saturation envelope appears as in Figure 2-28 (4). 

Convergence pressures of binary hydrocarbon mixtures may be estimated from the critical locus curves given in Figure 2-16. A similar curve which includes multicomponent mixtures is presented in Figure... 

The critical properties of methane and the weighted-average critical properties of the hypothetical heavy component are plotted on Figure 14-3, and a locus of convergence pressures for that pair is interpolated using the adjacent critical loci as guides. 

Third, plot weight-averaged critical point on Figure 14-3, interpolate a locus of convergence pressures, and read pk at 160°F. 

The critical locus shown in Figure 14.9 is only one (probably the simplest) of the types of critical loci that have been observed. Scott and van Konynen-burg10 have used the van der Waals equation to predict the types of critical loci that may occur in hydrocarbon mixtures. As a result of these predictions they developed a scheme that classifies the critical locus into one of five different types known as types I to type V.1 A schematic representation of these five types of (fluid-I-fluid) phase equilibria is shown in Figure 14.10. In the figure, the solid lines represent the vapor pressure lines for the... 

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