Scaleup with constant heat transfer

Solution Now, Ar=107°C. Scaling with geometric similarity would force the temperature driving force to increase by S = 1.9, as before, but the scaled-up value is now 201°C. The coolant temperature would drop to —39°C, which is technically feasible but undesirable. Scaling with constant pressure forces an even lower coolant temperature. A scaleup with constant heat transfer becomes attractive. 

Determine the reactor length, diameter, Reynolds number, and scaling factor for pressure drop for the scaleup with constant heat transfer in Example 5.12. 

Scaleup with constant heat transfer is theoretically possible with any form of scaleup, provided the wall driving force can be adjusted as shown in Table 10.2. 

Example 5.11 The results of Table 5.1 suggest that scaling a tubular reactor with constant heat transfer per unit volume is possible, even with the further restriction that the temperature driving force be the same in the large and small units. Find the various scaling factors for this form of scaleup for turbulent liquids and apply them to the pilot reactor in Example 5.10. 

A factor of 2 scaleup at constant t increases both u and L by a factor of 2, but the pressure drop increases by a factor of 2 - = 6.73. A factor of 100 scaleup increases the pressure drop by a factor of 316,000 The external area of the reactor, IttRL, increases as S, apace with the heat generated by the reaction. The Reynolds number also increases as S and the inside heat transfer coefficient increases by 5 (see Chapter 5). There should be no problem with heat transfer if you can tolerate the pressure drop. 

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