Steady state and dynamic mathematical models of the fixed bed catalytic reactor have been developed for exothermic (or isothermal) reactions which may involve consecutive and parallel steps. At the steady state, it is shown that
a one-dimensional model gives an adequate description of the system for most purposes, provided that the overall effective heat transfer coefficient between the fluid and coolant is suitably evaluated.
The models, which are of the continuum type, take account of the heterogeneous nature of the system by modifying the rates of reaction and heat generation at each point in the bed to allow for the effects of transport processes
on the performance of individual catalyst pellets. The models of the catalyst pellet have been formulated initially in a fully distributed form, taking account of transport resistances around and within the particles, and are then simplified by lumping the thermal resistance at the boundary between solid and fluid. These simplified models of the pellet are found to give excellent
results over all controlling regimes for practical ranges of the system parameters, and are capable of very rapid solution.
The proposed dynamic model of the reactor is one dimensional and has been used to examine the basic transient characteristics of the system. It is demonstrated that some unexpected difficulties may arise in attempting to
control the reactor. In particular, very high peak temperatures may occur when the inlet temperature is reduced. These are specifically associated with the heterogeneous nature of the model.
A method has been developed which is capable of determining the ranges of fluid conditions over which multiple steady states are possible for the catalyst pellet, and it is shown how this may be extended to enable local and global
stability to be related under steady and transient operating conditions. Whereas previous work on non-uniqueness in reacting systems has been concerned either
with single catalyst pellets, or with quasi-homogeneous reactors subject to axial diffusion effects, the present work enables, for the first time, reactor stability to be studied in terms of the behaviour of the catalyst pellets,
Without reference to axial diffusion, which is likely to be unimportant in most practical systems.