Scaling in Series for Constant-Density Fluids

The general scaleup relationships in Tables 3.1-3.3 are made specific for scaling in series by setting = 1 and Sl = S. The results are Srs = S for Reynolds number, Sap = for a turbulent pressure drop, and Sap = for a laminar pressure drop. 

For turbulentflow in tubes, a series scaleup by a factor of 2 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, 2nRL, 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 (see Chapter 5). There should be no problem with heat transfer if the pressure drop is acceptable. The input of power by the pump, 2 AP, increases dramatically upon series scaleup, as. The power per unit volume of fluid increases 

To study the series scaleup of a packed bed, take ratios for the large and small reactors of Equation 3.21. Due to the additive term, there is no simple scaleup relationship, but simple relationships emerge in the limits of high and low particle Reynolds numbers. Set Sp = I and Sp = S for a series scaleup to obtain 

The pressure drop across a packed bed in laminar flow scales like the pressure drop across an open tube in laminar flow. In the turbulent limit, the Ergun equation predicts 

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