Bifurcation analysis of a two-dimensional catalytic monolith reactor model

We present a complete bifurcation analysis of a general steady-state two-di mensional catalytic monolith reactor model that accounts for temperature an d concentration gradients in both axial and radial directions and uses Danc kwerts boundary conditions. We show that the ignition/extinction characteri stics of the monolith are determined by the transverse Peclet number (P = R -2(u) over bar /LDm, ratio of transverse diffusion to convection time) and the transverse Thiele modulus (phi (2)(s) = 2Rk(s)(T-0)/D-m, ratio of trans verse diffusion to reaction time). When phi (2)(s) much less than 1, igniti on occurs at P values of order B phi (2)(s) and the monolith behaves like a homogeneous reactor with simultaneous ignition/extinction of the surface a nd the fluid phase. However, when phi (2)(s) much greater than 1, surface i gnition occurs very close to the inlet (or for very short residence times c orresponding to large values of P) to a maximum surface temperature of B/(L e(f))(a) (a = 1/2 for flat velocity and a = 2/3 for parabolic velocity prof ile) while the fluid-phase conditions are still close to the inlet values. In this fast reaction, mass transfer controlled regime, the fluid temperatu re reaches the adiabatic value (and the mean exit conversion is close to un ity) only when the P values are of order unity or smaller. We show that the behavior of the monolith is bounded by two simplified models. One of them is the well-known convection model and the second is a new model which we c all the short monolith (SM) model. The SM model is described by a two-point boundary value problem in the radial coordinate and has the same qualitati ve bifurcation features as the general two-dimensional model. We also show that when the fluid Lewis number is less than unity(Le(f) < 1), there exist bifurcation diagrams of surface temperature versus residence time containi ng isolated solution branches on which the surface temperature exceeds the adiabatic temperature. Finally, we present explicit analytical expressions for the ignition, extinction and hysteresis loci for various models and als o for the fluid phase conversion and temperature in the fast reaction (mass transfer controlled) regime. <(c)> 2001 Elsevier Science Ltd. All rights r eserved.