Various aspects of the behaviour of fixed bed reactors
supporting highly exothermic reactions, relevant to stable
-optimal design and control, have been studied using detailed mathematical models.
In order to establish the form of the simplest basic
structure, two methods of describing radial heat transfer in
two dimensional packed beds have been examined. It is shown
that a lumped parameter single phase heat transfer model
which implicitly incorporates the heterogeneous structure can account not only for the radial heat flux associated with both the fluid and solid phases but is also the more appropriate formulation since it allows the important reaction rate limitations due to intraparticle mass transfer to be properly estimated. Using this two dimensional, heterogeneous dynamic model of the reactor it has been possible to evaluate a simpler one dimensional formulation. It is shown that the latter gives an adequate-description of the dynamic behaviour of the system, provided that the overall heat transfer coefficient between the fluid and the coolant is suitably defined, and may, therefore, be used for general studies of reactor performance.
Consideration has been-given to the response of the
reactor to sinusoidal perturbations of the inlet conditions.
It has been found that at certain frequencies of oscillation
temperature runaway may develop before a safe quasi-stationary state is reached. A detailed examination of this behaviour has shown that in addition to the non-linear effects the difference in the speeds of propagation of the concentration and temperature waves along the reactor as a result of the heterogeneity of the system is also very significant.
The effect of both cocurrent and countercurrent cooling
of a single reactor tube has been examined. The behaviour
for perturbations in coolant temperature is similar to that
for inlet temperature and indicates potential difficulties
in the design of control systems.
A mathematical model of a multitubular reactor with
crossflow cooling has been developed and used to identify some of the problems which may arise in these systems. In
particular, considerable interaction between the individual
reactor tubes occurs when significant conversion of the reactant takes place. This causes tubes in different parts
of the bundle to exhibit different behaviour and with countercurrent cooling this may give rise to multiple steady states due to the feedback of heat within the system.
A technique has been developed for predicting regions
of parametric sensitivity and temperature runaway in heterogeneous fixed bed reactors. The relationship between this form of instability and that due to multiple states of the catalyst pellet has been demonstrated. Application of this method to both the design and control of a reactor is discussed and it is shown that it provides an insight as to the behaviour of the system since it makes possible the establishment of a relationship between local and global reactor stability and the operating variables.