Uptake nonisothermal systems

The apparent simplicity of this approach is, however, deceptive. For measurement of intracrystalline diffusion the method works well when diffusion is relatively slow (large crystals and/or low diffusivity), but when sorption rates are rapid the uptake rate may be controlled by extracrystalline diffusion (through the interstices of the adsorbent bed) and/or by heat transfer. The intrusion of such effects is not always obvious from the shape of the uptake curve, but it may generally be detected by changing the sample quantity and/or the sample configuration. It is in principle possible to allow for such effects in the mathematical model used to interpret the uptake curves (Fig. 2), and indeed the modeling of nonisothermal systems has been studied in considerable detail [8-12]. However, any such intrusion will obviously diminish the accuracy and confidence with which the intracrystalline diffusivities can be determined. 

In a nonisothermal system there are two effects the temperature dependence of the equilibrium adsorbed phase concentration at the adsorbent surface and the temperature dependence of the diffusivity. The latter effect may be eliminated by reducing the size of the concentration step over which the uptake curve is measured, but the former effect is independent of step size. 

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]...

The problem of nonisothermal uptake under conditions such that the main resistance to mass transfer is the diffusional resistance of the particle bcd/ b rather than the intraparticle resistance, is similar and the expression for the uptake curve may be derived in the same way. The response of the system to a step change in sorbate concentration is described by the following set of equations ... 

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