Analysis and modeling of temperature patterns in adiabatic catalytic reactors.

摘要

Adiabatic catalytic reactors are known to form localized temperature patterns during their operation. We examine different mechanisms for pattern formation in uniformly active catalytic reactors.;In the first part, we consider an adiabatic down-flow packed-bed reactor and develop a three dimensional two-phase mathematical model that accounts for the variation of local interphase heat and mass transport coefficients with local fluid velocity. The steady-state behavior of the one-dimensional (transversely uniform) solutions is analyzed in detail. It is found that up to five steady-states can exist for Lef (ratio of thermal to mass diffusivity) ≥ 1, while for Lef 1, there can be as many as eleven 1-D uniform solutions. The stability of these 1-D solutions with respect to two and three dimensional transverse perturbations is analyzed. We find that the uniform solution can become unstable to small transverse perturbations and lead to transversely non-uniform velocity, concentration and temperature profiles, corresponding to maldistributed flows and localized hot spots. The size of the parameter region in which transverse non-uniformities exist increases monotonically with increasing interphase transport resistances. Spectral methods are used to follow numerically the bifurcating non-uniform solutions. Finally, the results are summarized in terms of some guidelines for minimizing the occurrence of maldistributed flows and hot spots in down-flow adiabatic packed-bed reactors.;In the second part, a two-phase system of n-particles in an adiabatic catalytic reactor with a well-mixed fluid phase is considered. The stability of the uniform state in the solid phase was examined with respect to small perturbations to determine the possibility of non-uniform states. The linear stability analysis revealed that steady non-uniform patterned states emerge from the unstable middle branch of the uniform state of the particles. For a fixed set of kinetic constants, the range of fluid flow-rate corresponding to the stable patterned states increases with increased heat and mass transfer resistances between the phases or with decreased heat conduction between the solid particles. These transport limited stable patterns can only exist within the region of multiple solutions of the homogeneous states. Analogous results are also presented using one-dimensional continuum model for the solid phase in the catalytic reactor.