On controlling an autothermal fixed-bed reactor at an unstable state—1: Steady-state and dynamic modeling

Abstract Models of distributed chemical reaction systems which are both accurate and wieldy are extremely difficult to obtain. This paper discusses traditional methods for deriving models of fixed-bed reactors, i.e. where the attempt is made to accurately account for steady-state and dynamic characteristics only. It illustrates the development of such models for the complex case of a tubular autothermal reactor with internal countercurrent heat exchange which exhibits multiple steady states for certain ranges of operating conditions. A two-dimensional dynamic model of the reactor is constructed, and then simplified to a linear state-variable form suitable for dynamic analysis by using successively: (i) a double collocation procedure to discretize the equations in both the radial and axial directions; (ii) a linearization technique around a specified steady-state profile; and (iii) the assumption of quasi-steady state for the coolant temperature and for the concentration of the reacting mixture. The dynamic analysis includes evaluation of the eigenproperties of the linearized model. The degree of instability of the reactor is correlated to some design variables and properties of the reaction. The sensitivity of the model to changes in parameters or operating conditions is also investigated. Finally, a shortcoming of the traditional modeling approach with its total emphasis on steady-state and dynamic properties is discussed. It is noted that the internal structure of a model also must be considered carefully if it is to be useful for controller design. A sequel paper discusses this virtually unrecognized point, again using the autothermal reactor system for example purposes.