Uptake complete heat transfer control

Equation (17) represents the general case of uptake under complete heat transfer control and equation (18) gives the corresponding adsorbent temperature profile. Furthermore, if kg is large compared to h, (s << 1), equation (10) can be approximated as p 3 s and equations (17) and (18) reduce to n... 

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]...

When heat transfer is controlling, the uptake curyes commonly show a rapid initial uptake followed by a slow approach to equilibrium and the observation of a distinct break in an experimental uptake curve therefore provides a useful clue that heat transfer resistance may be important. For all values of the parameters a and the uptake curves in the long time region show a simple exponential approach to equilibrium and so give straight lines when plotted as ln(l-m,/m ) versus t. If the process is substantially isothermal the intercept of such a plot should be 6/ir, and a significant deviation from this value can provide useful evidence of the intrusion of heat transfer effects. However, it is clear from Eq. (6.70) that when / is 1.5 the same intercept will be obtained under conditions of complete heat transfer control. It is therefore not possible to determine unequivocally the significance... 

The extreme case of complete heat transfer control for COj-SA is illustrated in Figure 6.15. For this system diffusion is much faster and even in relatively large crystals the uptake rate is controlled by heat transfer. Uptake curves are essentially independent of crystal size but vary with sample size due to changes in the effective heat capacity and external area-to-volume ratio for the sample. Analysis of the uptake curves according to Eq. (6.70) yields consistent values for the overall heat capacity (34 mg sample C 0.32 and 12.5 mg sample 0.72 cal/g deg.). The variation of effective neat capacity with sample size arises from the increasing importance of the heat capacity of the containing pan when the adsorbent weight is small. 

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