I am trying to design a packed bed reactor for a low temperature shift reaction in the conversion of CO to H2 and CO2 using steam. The reactor has a fixed volume of 12cm^3 which was calculated based on the dimensions and weight of the catalyst required. The process is conducted at atmospheric pressure. How do I determine the appropriate/optimal diameter and length of the reactor?
In case of a reactor bed with a fixed cross sectional area (S), the differential molar balance can be written as a function of the reactor differential length as can be seen in equation:
dXa/dz=ra*ρb*s/Fao
ρb – catalyst bulk density.
S – reactor bed constant section area.
z – length of reactor (z axis – axial direction)
The L/D ratio may be 2.5 to 4.5
In case of a reactor bed with a fixed cross sectional area (S), the differential molar balance can be written as a function of the reactor differential length as can be seen in equation:dXa/dz=ra*ρb*s/Faoρb – catalyst bulk density.S – reactor bed constant section area. z – length of reactor (z axis – axial direction)The L/D ratio may be 2.5 to 4.5
To obtain the optimal ratio, the Total Annual Cost (TAC) of the reactor should be minimised. These costs include fabrication costs, pumping costs and catalyst cost
Please look up for reactor costing correlations extant in the open literature.
Hope that helps
L/D is usually assumed. Primarily, it is to avoid inlet and outlet flow effects. Of course, the L/D must not be too large, as possible buckling of the vertically positioned reactor tube has to be taken into account.