Adiabatically operated fixed-bed catalytic reactors

A simplified procedure for design is to assume that both tj and — AH/Cp are constant. If, then, eqn. (60) (the heat conservation equation) is divided by eqn. (59) (the mass conservation equation) and integrated, one immediately obtains 

Because the adiabatic reaction path is linear, a graphical solution, also 

It is often necessary to employ more than one adiabatic reactor to achieve a desired conversion. The catalytic oxidation of SOj to SO3 is a case in point. In the first place, chemical equilibrium may have been established in the first reactor and it would be necessary to cool and/or remove the product before entering the second reactor. This, of course, is one good reason for choosing a catalyst which will function at the lowest possible temperature. Secondly, for an exothermic reaction, the temperature may rise to a point at which it is deleterious to the catalyst activity. At this point, the products from the first reactor are cooled prior to entering a second adiabatic reactor. To design such a system, it is only necessary to superimpose on the rate contours the adiabatic temperature paths for each of the reactors. The volume requirements for each reactor can then be computed from the rate contours in the same way as for a 

The existence of radial temperature and concentration gradients means that, in principle, one should include terms to account for these effects in the mass and heat conservation equations describing the reactor. Furthermore, there should be a distinction between the porous catalyst particles (within which reaction occurs) and the bulk gas phase. Thus, conservation equations should be written for the catalyst particles as well as for the bulk gas phase and coupled by boundary condition statements to the effect that the mass and heat fluxes at the periphery of particles are balanced by mass and heat transfer between catalyst particles and bulk gas phase. A full account of these principles may be found in a number of texts [23, 35, 36]. 

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