We derive a new prediction for thermal
runaway starting from the
alpha model for fixed-bed reactor systems. This method accounts for
thermal resistance internal to the reactor tube and the radial temperature
gradients that result. To showcase our method, we compare its predictions
to other common criteria for thermal runaway using o-xylene oxidation as the example chemistry. Even in systems where
internal heat transfer is negligible, the empirical practical design
criterion for thermal runaway is inaccurate. For cases where internal
heat transfer is relevant, our runaway limit is more stringent than
limits derived from simpler 1-D models. To augment our work, we optimize
the product yield with the thermal runaway constraint using orthogonal
collocation. Using the alpha model, the results illustrate that the
thermal runaway limit can be accurately determined using either numerical
or analytical methods