Scaleup at constant pressure drop

For laminar flow of a Newtonian fluid, scaleup at constant pressure drop is identical to scaleup with geometric similarity. For constant pressure drop in turbulent flow, the reactor diameter increases somewhat faster, than for scaleup with... 

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. 

The same result is obtained when the fluid is compressible, as may be seen by substituting Sr = Si = S into Equations (3.40) and (3.41). Thus, using geometric similarity to scale isothermal, laminar flows gives constant pressure drop provided the flow remains laminar upon scaleup. The large and small reactors will have the same inlet pressure if they are operated at the same outlet pressure. The inventory and volume both scale as S. 

Applying these factors to the 5= 128 scaleup in Example 5.10 gives a tube that is nominally 125 = 101 ft long and 1.0495 = 4.1 inches in diameter. The length-to-diameter ratio increases to 298. The Reynolds number increases to 85005 = 278,000. The pressure drop would increase by a factor of 0.86 j jjg temperature driving force would remain constant at 7°C so that the jacket temperature would remain 55°C. 

SOLUTION Now, AT = 107°C. Scaling with geometric similarity would force the temperature driving force to increase by = 1.9 as before, but the scaled up value for AT is now 201°C so that the coolant temperature would drop to —39°C, technically feasible but undesirable. Scahng with constant pressure forces an even lower coolant temperature. A scaleup using a sheU-and-tube reactor is feasible but scaling with constant heat transfer should be considered. 

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