Scaleup of Isothermal CSTRs

A real continuous-flow stirred tank will approximate a perfectly mixed CSTR provided that tmix h/i and tmix i. Mixing time correlations are developed using batch vessels, but they can be applied to flow vessels provided the ratio of throughput to circulatory flow is small. This idea is explored in Section 4.5.3 where a recycle loop reactor is used as a model of an internally agitated vessel. 

Although experts in agitator design are loath to admit to using such a simplistic rule, most scaleups of conventionally agitated vessels are done at or near constant power per unit volume. The consequences of scaling in this fashion are explored in Example 4.7 

Example 4.7 A fully turbulent, baffled vessel is to be scaled up by a factor of 512 in volume while maintaining constant power per unit volume. Determine the effects of the scaleup on the impeller speed, the mixing time, and the internal circulation rate. 

Solution If power scales as N]D], then power per unit volume scales as N]D], To maintain constant power per unit volume. A/must decrease upon scaleup. Specifically, Nj must scale as When impeller speed is scaled 

A volumetric scaleup by a factor of 512 is quite large, and the question arises as to whether the large vessel wiU behave as a CSTR. The concern is due to the factor of 4 increase in mixing time. Does it remain true that tmix h/i and tmix t If so, the assumption that the large vessel wiU behave as a CSTR is probably justified. The ratio of internal circulation to net throughput—which is the internal recycle ratio—scales as the inverse of the mixing time and will thus decrease by a factor of 4. The decrease may appear worrisome, but if the increase in mixing time can be tolerated, then it is likely that the decrease in internal recycle ratio is also acceptable. 

Solution If power scales as NjDj, then power per unit volume scales as NjDj. To maintain constant power per unit volume, IV/ must decrease upon scaleup. Specifically, Nj- must scale as DJ2 3. When impeller speed is scaled in this manner, the mixing time scales as D2J3and the impeller pumping rate scales as D7/3. To maintain a constant value for t, the throughput Q scales as Dj = S. Results for these and other design and operating variables are shown in Table 4.1. 

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