Methane critical point

Five critical points for the methane-n-hexane system in the temperature range of 198 to 273 K measured by Lin et al. (1977) are available. By employing the Trebble-Bishnoi EoS in our critical point regression least squares estimation method, the parameter set (k , kb) was found to be the optimal one. Convergence from an initial guess of (ka,kb=0.001, -0.001) was achieved in six iterations. The estimated values are given in Table 14.8. 

Figure 6.13 Relief map of the electron density for methanal (formaldehyde) in the molecular plane. There is a bond critical point between the carbon and the oxygen nuclei, as well as between the carbon nucleus and each hydrogen nucleus. No gradient path or bond critical point can be seen between the two hydrogen nuclei because there is no point at which the gradient of the electron density vanishes. There is no bond between the hydrogen atoms consistent with the conventional picture of the bonding in this molecule.

Figure 6.16 Molecular graphs for some molecules in their equilibrium geometries. A bond critical point is denoted by a black dot. The molecule HCCH is ethyne, H2CO is methanal, and H2CCH2 is ethene. [Adapted with permission from Bader [1990], Fig. 2.8.]...

Figure 3. The critical points of selected pure compounds. Water (374.0 °C and 217.8 atm) and methane (-82.6 °C and 45.4 atm) are offscale...

Table 9.1. Physical properties of hydrogen, methane, and n-heptane at the triple point, the boiling point and the critical point, and under standard conditions...

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. 

When the temperature exceeds the critical temperature of one component, the saturation envelope does not go all the way across the diagram rather, the dew-point and bubble-point lines join at a critical point. For instance, when the critical temperature of a mixture of methane and ethane is minus 100°F, the critical pressure is 750 psia, and the composition of the critical mixture is 95 mole percent methane and 5 mole percent 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. 

When pressure is less than the critical pressures of both components, the bubble-point and dew-point lines join at the vapor pressures of the pure components at either side of the diagram. When the pressure exceeds the critical pressure of one of the components, the bubble-point line and the dew-point line join at a critical point. For instance, a mixture of 98 mole percent methane and 2 mole percent ethane has a critical temperature of minus 110°F at a critical pressure of 700 psia. 

When the pressure of interest exceeds the critical pressures of both components, the phase envelope exhibits two critical points. For instance, mixtures of methane and ethane exhibit critical points at 900 psia and minus 62°F and at 900 psia and 46°F. 

Figure 2-27 gives the saturation envelope for mixtures of methane, propane, and n-pentane at the same temperature as Figure 2-26 but at a higher pressure. The bubble-point and dew-point lines join at a critical point. The critical point gives the composition of the mixture, which has a critical pressure of 1500 psia and a critical temperature of 160°F. 

The critical point of a specific mixture of methane and propane occurs at 1040 psia at this temperature, dot 5. The dew-point and bubble-point lines of the ternary intersect the methane-propane side of the diagram at the composition of this critical point. 

Above this pressure, dot 6, all mixtures of methane and propane are single phase. Thus only the methane-n-pentane binaries have two-phase behavior, and only the methane-n-pentane side of the ternary diagram can show a bubble point and a dew point. The bubble-point and dewpoint lines of the saturation envelope do not intercept another side of the diagram, rather the two lines join at a critical point, i.e., the composition of the three-component mixture that has a critical pressure of 1500 psia at 160°F. 

The densities of methane liquid and gas in equilibrium along the vapor-pressure line are given below. Estimate the density of methane at its critical point of - 116.7°F. 

Phase behavior of multicomponent reservoir fluids is similar. Reservoir gases, which are predominately methane, have relatively small phase diagrams with critical temperatures not much higher than the orSiranempnatiire of nietfiahe. The critical point is"fairdown the left slope of the envelope. 

The Lw-H-V line has no upper pressure or temperature limit because the pure methane (or nitrogen) vapor-liquid critical points (at 191 and 126 K respectively) are far below the quadruple point Qi. Such low critical temperatures prevent intersection of the vapor pressure line with the Lw-H-V line above 273 K to produce an upper quadruple point. 

Although the proposed mechanism is consistent for photolysis of iodine in helium, nitrogen and methane (24), substantive deviations were present at low densities and especially near the critical point of ethane. As Figure 3 shows, the quantum yields at these low densities are consistently below one, the value expected in this high diffusivity regime where kd k i. 

The examples presented in this work by no means cover the subject of the C-H bond activation on a spectrum of catalytic media. Interaction of methane with the small clusters discussed here obviously cannot pretend to fully mimic catalytic centers in reality. Nevertheless, they seem to justify drawing generalized conclusions regarding the mechanism of catalytic activation in terms of electron withdrawal or donation to the interacting hydrocarbon molecule. A variety of properties contribute consequently to the emerging scheme (electronic density redistribution, geometry evolution in critical points, energetical factors, vibrational analyses) which substantially increases credibility of the conclusions. 

Fio. 3.7. Planar projections of molecular graphs of hydrocarbon molecules generated from theoretical charge distributions. Bond critical points are denoted by black dots. Structures 1 to 4 are normal hydrocarbons from methane to butane, 5 is isobutane, 6 is pentane, 7 is neopentane, and 8 is hexane. The remaining structures are identified in Table 3.2. The structures depicted in these diagrams are determined entirely by information contained in the electronic charge density. 

Fig. 7.4. Representations of the Laplacian distributions of methane and methylfluoride. The figures in (a) are displays of the zero envelope of V p(r), those in (b) of the atomic graphs. The envelope encompassing the inner shell charge concentration on carbon appears as a small sphere. The envelopes of the bonded maxima in the VSCC of carbon also encompass the protons in CH and CH3F. There is a transfer of charge from C to F in CHjF and the bonded maximum along the C F axis is reduced to the small region lying between the C nucleus and the envelope on F. An atomic graph displays the connectivity of the critical points in a VSCC. The carbon nucleus is denoted by a solid cross, the positions of the remaining nuclei by open crosses. There is a bonded maximum, a (3, — 3) critical point in — V p, at each of the four vertices.

We consider these two types simultaneously because they share their distinctive feature. That feature is an interruption in the critical locus where two liquid phases appear over a short range of compositions before the critical locus reappears as a liquid-liquid critical point. Unlike low-temperature LL behavior, varying the pressure has a strong impact on type IV or V liquid-liquid-equilibria, (LLE) making it appear or entirely disappear over a remarkably narrow range of pressures. Systems that exhibit type IV behavior include methane -I- 1-hexene and benzene -I- polyisobutylene, the only polymer solution mentioned by van Konynenburg and Scott. Peters has also speculated that methane and ethane mixed with alkylbenzenes will form type II-rV solutions, in contrast to the I, III, V solutions of the n-alkanes.f ... 

The points Ci and are the critical points of pure methane and ethane, respectively. The line connecting these two points, which is the intersection of the bubble point and dew point surfaces, is the critical locus. This is the set of critical points for the various mixtures of methane and ethane. The black curve connecting points A and Ci is the vapor pressure curve of pure methane, and the violet curve connecting points B and C2 is the vapor pressure curve of pure ethane. 

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