A simple approach to highly sensitive tubular reactors

The steady state operation of a long tubular fixed-bed reactor in which a single highly exothermic reaction is occurring is analyzed. To avoid temperature runaways, such reactors must be operated so that their temperature rises $\Delta T$ are small fractions of the adiabatic temperature rise $\Delta T_{{\text{ad}}} $ . So here asymptotic methods based on $\Delta T/\Delta T_{{\text{ad}}} \ll 1$ are used to determine the radial temperature and concentration profiles. A simple one-dimensional (z only) reactor model is then derived by substituting these asymptotically correct radial profiles into the full two-dimensional reactor equations and then averaging in r. By comparing with numerical solutions of the two-dimensional reactor equations, it is found that the one-dimensional model accurately simulates the two-dimensional equations, even in the highly sensitive runaway region. It is also shown that a runaway criterion derived from the model accurately predicts the runaway transition of the original two-dime...

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