Approximate characteristics of a moving temperature front in an fixed-bed catalytic reactor. The case of vanishing thermal front propagation velocity

A method is developed to determine parameters of a reactor model, which exp licitly define a set of states in an adiabatic tubular fixed-bed reactor wi th vanishing propagation velocity of the thermal front. The vanishing front propagation velocity constitutes the definition of a steady state in the r eactor from the point of view of the dynamics of the process. Therefore the knowledge of the parameters mentioned above is crucial for a general chara cteristics of the propagation process of the thermal front in the reactor. It is found that the position of the temperature and conversion profiles in the reactor is uniquely determined by the value of a single parameter chos en (e.g., the feed temperature or the mixture flow rate in the reactor). Th e variation in this parameter leads to the propagation of the reaction fron t until a different steady state is established or the reactor is extinguis hed altogether. A simultaneous bifurcation analysis reveals that, over the multiplicity reg ion, only three steady states can exist of which two are stable and one is unstable. Consequently, all steady states associated with high conversion d egrees (y similar to 1) and vanishing front propagation velocity, independe ntly of their position within the reactor, from the standpoint of bifurcati on analysis represent steady states located on the upper stable branch of t he bifurcation diagram. No reasons thus exist to differentiate between thes e states. An approximate method is proposed for evaluating the range of inl et temperatures over which steady states with zero propagation velocity app ear in the reactor.