Characteristic Dimensionless Numbers for Reactor Design

To understand the relative importance of different rate processes such as reaction, mixing, diffusion, or dispersion, knowledge of the relevant timescales of these processes is invaluable. The ratios of such timescales form a set of dimensionless quantities. While we cannot possibly give an exhaustive account here (the reader is referred to reactor design texts), we mention the most important dimensionless quantities. 

The ratio of reactor and reaction timescale is the (dimensionless, of course) Damkohler number of the first kind Da] = k-t (for a first-order reaction). In a 

Other factors limiting the overall rate can be external or internal mass transfer, or axial dispersion in a fixed-bed reactor. Pertinent dimensionless numbers are the Biot number Bi, the Damkohler number of the second kind Dan, or the Bodenstein number Bo (Eqs. (5.46)—(5.48)]. 

Dan = timescale of pore diffusion/timescale of reaction = (L2 x kal)/De(( (5.46) Bi = external mass transfer/intemal mass transfer = (kfx RJ/Dgff (5.47) Bo = convective mass transfer/dispersive mass transfer = (u x k)/D L (5.48) 

As a general rule, the longest timescale always dominates the overall rate process. 

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