Numerical Investigation of Resonance Behaviour of a Tubular Packed‐Bed Reactor with Non‐Uniform Activity

Abstract

P acked-bed reactors are commonly designed for use under steadystate operation. However, there are circumstances where the reactor is subject to transient operation, e.g. upstream disturbances, periodic operation, etc. High-temperature excursions may occur when a packed-bed reactor carrying out an exothermic reaction is imposed by a sudden decrease of inlet temperature. This induces a positive concentration wave to move downstream at fl uid fl ow velocity. When the high-concentration wave reaches the reaction front, the heat of reaction produced from the local excess concentration causes the hot spot temperature to increase beyond the adiabatic temperature rise. This phenomenon has been known for many years and is referred to as wrong-way behaviour (Crider and Foss, 1966;Chen and Luss, 1989).When there are periodic disturbances, a similar phenomenon arises that Rovinsky and Menzinger (1992) refer to as differential fl ow instability (DIFI). These authors also found resonance behaviour in this situation. Hot-spot temperature at the resonance frequency is much higher than the adiabatic temperature rise. Yakhnin and Menzinger (1999) extended their investigation of DIFI to situations in which catalyst deactivation occurs alongside the desired chemical reaction. A zone of high activity catalyst followed by a zone of low activity and another zone of high activity was found to accentuate DIFI or, in terms of step-change response, the amplitude of the wrong-way behaviour.Of late, there has been a growing interest in various aspects of packed-bed catalytic reactors with non-uniform activity (Clifford et al., 1998;Cote et al., 1999). In this study, we pursue the investigation of Yakhnin and Menzinger (1999) on the effect of a zone of deactivated catalyst on the amplifi cation of inlet temperature disturbances in packed catalytic beds. The objective was to examine amplifi cation in a packed bed reactor in which the degree of segregation of the bed changes in a regular fashion. Our experimental study of segregated beds has recently appeared (Jaree et al., 2001a,b). Mathematical ModelDimensionless energy and mass balances equations describing a pseudohomogeneous, adiabatic packed-bed reactor are given by the system of partial differential equations below, assuming constant velocity and * Author to whom correspondence may be addressed. E-mail address: rhudgins@uwaterloo.ca transport properties. A standard, fi rst-order, exothermic reaction, A  B, taking place in the reactor is catalyzed by solid catalyst. FlexPDE TM (PDE Solutions Inc., Antioch, CA) was employed for integration.The effects of periodic temperature perturbations at the inlet of a packed-bed catalytic reactor were investigated for a system of non-uniform catalyst activity that could arise through catalyst deactivation. A simplifi ed model consisting of zones of active catalyst and inert packing of similar thermal properties was assumed. Simulations showed that large amplifi cation, expressed as gain, can occur. The largest gain is observed at a resonance frequen...

Selection of simplified models: I. Analysis of model‐selection criteria using mean‐squared error

“…Inevitably, modelling leads to the situation where some parameters and terms that would appear in the “true” model are missing, either by mistake or by design. There are many reasons to choose a simplified model (SM) with fewer parameters and terms than the truly structured complex model (Neto and Cotta, 1992; Talukdar and Basu, 1995; Gray, 1997; Zhang, 1997; Ismail, 2004; Jaree et al, 2004; Forney et al, 2005; Marquardt, 2005). The practical advantages of a parsimonious model often overshadow concerns over the correctness of the model structure.…”