(582be) Bifurcation Analysis of a Two-Dimensional Homogeneous Reactor Model

We present a comprehensive bifurcation analysis of a full two-dimensional, steady-state homogeneous reactor model with a focus on the dependence of ignition-extinction and hysteresis loci on the reactor design and operation parameters. The mathematical model consists of a pair of partial differential equqations with Danckwerts type boundary conditions and with parabolic/flat velocity profile and heat transfer at the wall.

We show that the hysteresis behavior of the full two-dimensional model is bounded by three limiting models: the two-dimension convection model (which ignores axial heat and mass diffusion), the one-dimensional axial dispersion model (which ignores radial gradient) and the short tube model (which ignores axial gradients), when taking limit values of transvers and axial Thiele moduli or Peclet numbers.

For adiabatic case with parabolic velocity profile, we show that multiple ignition and extinction points can exist even for a single step exothermic reaction, and the types of bifurcation diagrams are classified by hysteresis and double limit varieties. When multiple ignitions exist, the first ignition takes place near the reactor wall due to the boundary layer generated by slow local convection, while the second ignition occurs at the center of the tube, depending on the relative contribution of radial thermal and mass diffusion. For adiabatic case with a flat velocity profile, only axial gradient is important thus there’s only one ignition. The system can exhibit complex hysteresis behaviors when heat transfer occurs at the wall and when the heat and mass transfer rates in the radial direction are not equal. When the residence time is taken as the bifurcation variable, there exist bifurcation diagrams containing isolated solution branches (isolas) even in the adiabatic case when the Lewis number is less than unity.