Estimating spectral properties of the thermal instability in packed-bed reactors

In response to transient perturbations, the packed-bed reactor (PBR) can exhibit dynamic thermal instability in the form of resonant amplification of process disturbances. Based on linearized PBR model we derive estimates of the resonance frequency, the frequency range where amplification takes place and the maximum amplification. We also discuss the velocity of perturbation waves and how nonlinearity of reactor response to finite-size perturbations limits the amplification predicted by the linear analysis.