Uptake heat transfer limitations

Transient uptake rate measurements are subject to intrusion of heat transfer hmitations, especially in batch measurements at low pressures. Membrane permeation, frequency response, and ZLC measurements should not be subject to serious heat transfer limitations but, especially in frequency response and ZLC, there is always a danger of intrusion of extracrystalline resistances to mass transfer, although in principle these can be eliminated by reducing the sample size and ensuring that the crystals within the sample are dis-... 

FIGURE 6.15. Experimental uptake curves for CO2 in 5A zeolite crystals at 273 K showing limiting case of heat transfer control [Eq, (6.70)]. Note that the rate of approach to equilibrium is faster in the thin bed as a result of the greater surface area-volume ratio. Curve (b) shows a case where the heat transfer limited uptake curve lies (fortuitously) close to the ideal curve for isothermal diffusion except in the initial region. (From ref. 20, with permission.)... 

Van Campen et al. [31] developed models describing the rate of moisture uptake above RH0 that consider both the mass transport of water to the solid substance and the heat transfer away from the surface. For the special case of an environment consisting of pure water vapor (i.e., initial vacuum conditions), the Van Campen et al. model is greatly simplified since vapor diffusion need not be considered. Here, only the rate at which heat is transported away from the surface is assumed to be an important factor in limiting the sorption rate, W. For this special case, an expression was derived to express the rate of moisture uptake solely as a function of RHj, the relative humidity of the environment, and RH0. 

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

Fig. 2 Experimental uptake curves for CO2 in 4A zeolite crystals showing near isothermal behavior in large (34 and 21.5 Jim) crystals (D 9 x 10 cm s at 371 K and 5.2 X 10 cm s at 323 K). The solid lines are the theoretical curves for isothermal diffusion from Eq. 2 with the appropriate value of Ddr. The uptake curves for the small (7.3 jim) crystals show considerable deviation from the isothermal curves but conform well to the theoretical nonisothermal curves with the values of Dc estimated from the data for the large crystals, the value of p calculated from the equilibrium data, and the value of a estimated using heat transfer parameters estimated from uptake rate measurements with a similar system under conditions of complete heat-transfer control. The limiting isothermal curve is also shown by a continuous line with no points. From Ruthven et al. [8]...

Figure 4.8 shows some experimental uptake curves for the adsorption of CO2 in a 5A zeolite which agree very well with equation (4.39) expressing rates of adsorption limited by heat transfer. 

Figure 4.8 Experimental uptake curves for CO2 on 5A zeolite demonstrating the limiting behaviour of heat transfer control. Adsorption temperature 273 K. Figures on curves represent various adsorbate pressures which relate to differing effective heat capacities. Curve 1,4.3 -3.6 torr curve 2, 20-17 torr curve 3,68 - 63 torr curve 4,234 - 204 torr.

More detailed uptake rate studies carried out with larger crystals and with a range of different crystal sizes, however, showed no evidence of any surface barrier.(7-9) For diffusion of propane and n-butane in laboratory synthesized 5A crystals the uptake results show reasonably close agreement with the NMR.(10) However, for some other systems such as benzene-NaX the NMR diffusivities were still much higher. The uptake rates were, however, close to the limit of the experimental technique so the possible intrusion of extraneous heat or mass transfer resistances could not be unequivocally excluded. 

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