Tubular Reactor Stability Revisited without the Danckwerts Boundary Conditions

Tubular reactor stability is reconsidered for a wide variety of situations where there is dispersion outside the reactor.A complete set of boundary conditions are proposed from which the Danckwetts boundary conditions arise as a special case. While the multiplicity and stability characteristics are found to be the same as those found with Danckwerts boundary conditions (no dispersion outside the reactor), the stability regjons are assessed to be significantly different via the spectrum (set of eigcnvalues) of associated linear differential operators. Finite stability regions can be determined for both zero and non-zero dispersion outside the reactor by using the maximum principle for parabolic partial differential equations. Such determination only requires knowledge of the steady state concentration and temperature profiles. The maximum principle is also used to establish the global asymptotic stability of a unique steady state. The cases of vanishing and non-vanishing initial residual enthalpy are considered.