High pressure isotherms

The high pressure isotherms (P/P0 0.01 to 0.95) could be fitted with normal success to any one of several isotherm equations, and, in fact four procedures were tested. The first was the standard BET method (6), using 16.1 sq. meters per gram as the area of the nitrogen molecule at 77.6°K (14). 

Low- and high-pressure isotherms of pure vanadium [125], and high-pressure isotherms of V-0.5at.%C at 298K showing the a, a... 

Jain, R. K., and Simha, R., High-pressure isotherms of polyethylene crystals, J. Polym. Sci. Polym. Lett. Ed., 17, 33-37 (1979a). 

High pressure isotherms of I(N2), n(CH4) and IIKCO2) sorbed in silicalite-1 at 25 C. (O) low pressure (corrected isosteric points) ( ) high pressure. Continuous line is Langmuir-Freundlich fit. 

One practical problem in using Eq. (28) to calculate qi as a complete function of nf is that the procedure requires very high pressure isotherm data at the higher temperatures [12]. 

For PSA simnlation, high-pressure isotherm data are needed. The high-pressure N2/CH4 isotherms for purified clinoptilolite and Mg-exchanged clinoptilolite are shown in Figures 10.43 and 10.44, respectively. An equilibration time of 2 h was used for each data point of the CH4 isotherms. The N2/CH4 selectivity reflects molecular sieving. 

The three general states of monolayers are illustrated in the pressure-area isotherm in Fig. IV-16. A low-pressure gas phase, G, condenses to a liquid phase termed the /i uid-expanded (LE or L ) phase by Adam [183] and Harkins [9]. One or more of several more dense, liquid-condensed phase (LC) exist at higher pressures and lower temperatures. A solid phase (S) exists at high pressures and densities. We briefly describe these phases and their characteristic features and transitions several useful articles provide a more detailed description [184-187]. 

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

The working temperature, 77 K, is well below the triple point of krypton, 116 K, but if the solid is taken as the reference state the isotherm shows an unusually sharp upward turn at the high-pressure end. The usual practice, following Beebe, is therefore to take p° as the saturation vapour pressure of the supereooled liquid (p° = 2-49 Torr at 77-35 K and 27-5 Torr at 90-2 K). 

Deviation from the standard isotherm in the high-pressure region offers a means of detecting the occurrence of capillary condensation in the crevices l>etween the particles of a solid and in any mesopores present within the particles themselves. A convenient device for detecting deviations from the standard is the t-plot . In the next section the nature and uses of t-plots will be discussed, together with a,-plots, a later development from them. As will l>e shown, both of these plots may l>e used not only for the detection of capillary condensation in mesopores, but also for showing up the presence of micropores and evaluating their volume. 

Condensable Hquids also are recovered from high pressure gas reservoirs by retrograde condensation. In this process, the high pressure fluid from the reservoir produces a Hquid phase on isothermal expansion. As the pressure decreases isotherm ally the quantity of the Hquid phase increases to a maximum and then decreases to disappearance. In the production of natural gas Hquids from these high pressure wells, the well fluids are expanded to produce the optimum amount of Hquid. The Hquid phase then is separated from the gas for further processing. The gas phase is used as a raw material for one of the other recovery processes, as fuel, or is recompressed and returned to the formation. 

If the power requirement of the gaseous diffusion process were no greater than the power required to recompress the stage upflow from the pressure on the low-pressure side of the barrier to that on the high-pressure side, then the power requirement of the stage would be Z RTLq (1 /r) for the case where the compression is performed isotherm ally. The power requirement per unit of separative capacity would then be given simply by the ratio... 

Birch, F. (1978), Finite Strain Isotherm and Velocities for Single-Crystal and Polycrystalline NaCl at High Pressures and 300 K, J. Geophys. Res. 83, 1257-1268. 

The chapter on equation-of-state properties provides the basic approaches used for describing the high-pressure shock-compression response of materials. These theories provide the basis for separating the elastic compression components from the thermal contributions in shock compression, which is necessary for comparing shock-compression results with those obtained from other techniques such as isothermal compression. A basic understanding of the simple theories of shock compression, such as the Mie-Gruneisen equation of state, are prerequisite to understanding more advanced theories that will be discussed in subsequent volumes. 

Isotherm measurements of methane at 298 K can be made either by a gravimetric method using a high pressure microbalance [31], or by using a volumetric method [32]. Both of these methods require correction for the nonideality of methane, but both methods result in the same isotherm for any specific adsorbent [20]. The volumetric method can also be used for measurement of total storage. Here it is not necessary to differentiate between the adsorbed phase and that remaining in the gas phase in void space and macropore volume, but simply to evaluate the total amount of methane in the adsorbent filled vessel. To obtain the maximum storage capacity for the adsorbent, it would be necessary to optimally pack the vessel. 

However, in the non-isothermal case the pressure is also high at low injection rates. This is because slow injection gives time for significant solidification of the melt and this leads to high pressures. It is clear therefore that in the non-isothermal case there is an optimum injection rate to give minimum pressure. In Fig. 5.28 this is seen to be about 3.0 x 10 m /s for the situation considered here. This will of course change with melt temperature and mould temperature since these affect the freeze-off time, //, in the above equations. 

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