The Peclet number

The Peclet number deals with diffusion processes in fixed-bed reactors, - you could say 'it is the Bo number for packed TFRs'. But there is one difference between packed and 'normal' TFRs: in packed beds you have to take also in account that the fluid molecules ('particles') are diffusing 'additionally' in a radial direction, as they are permanently colliding with the fixed bed particles. The Peclet number for radial diffusion Pe_rad is defined as:

Pe_rad= (u*d)/D_rad

where d = particle diameter, u = linear flow velocity and D_rad = radial diffusion cofficient (which is remarkable higher than the normal molecular diffusion coefficient). Typical values for Pe_rad are in practice about 11 (and should be kept in this sector).

A bit more important is the axial Peclet number Pe_ax, which is defined as:

Pe_ax= (u*d)/D_ax

where D_ax = axial diffusion cofficient. For flows of gases in beds with ball shaped particles Pe_axtakes values of 1.6 to 2.3 ( i.e. about 2).


And here an application example:

As you see from the definitions the relation between Peclet- and Bodenstein- number is:

Bo = Pe_ax* L/d

For the series of CSTRs ('cascade') we found:

n = Bo/2

therefore we can write: n = 0.5 * (Pe_ax* L/d)
with Pe_ax= 2

we get: n = L/d

this means that the height of a fixed bed that equals one vessel (step) of the 'cascade model' (cf. plates in destilling column technics) has the value of (about) the particle diameter. Values cited in literature for L/d are in the range from 5 to 50, so that in the worst case of 50 the height of the bed (equivalent to one 'step') for a catalyst pellet of e.g. 5 mm diameter should be 25 cm (maximum). Compare: heights of beds are in practice more than 1m.

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