The starting point for this study was an incident in an industrial pla
nt, where the ammonia synthesis reactor became unstable with rapid tem
perature oscillations (limit cycles) in the range from about 300 degre
es C to 500 degrees C. A simple dynamic model reproduces this behavior
In industry a steady-state van Heerden analysis is often used to anal
yze the stability, but a more careful analysis for this reactor system
reveals that instability occurs when there still is a positive steady
-state margin, namely as a pair of complex conjugate poles cross the i
maginary axis (Hopf bifurcation). This is consistent with the observat
ions where the instability manifests itself as oscillations rather tha
n extinction of the reaction. This somewhat unusual behavior can be ex
plained by the presence of an inverse response for the temperature res
ponse through the reactor beds combined with the positive feedback cau
sed by the preheater.