EIGENVALUE SPECTRA AND MODAL CONTRIBUTIONS FOR COUNTERFLOW REACTOR MODELS

Counterflow reactor models fall into three classes of partial diferential equations: hyperbolic, parabolic, and mixed hyperbolic-parabolic. These have been analyzed to determine the behavior of their eigenvalues and their modal contributions. Using an asymptotic analytical technique (WKB theory), hyperbolic p.d.e. systems and mixed p.d.e. systems with characteristics similar to hyperbolic systems were found to have a "defective" internal structure, making them generally undesirable for modeling or control applications requiring low-order models. Parabolic systems, or mixed systems with characteristics similar to parabolic systems, were found to be "well-behaved". Hence. where it is possible to choose the type of model to apply to a specific reactor, the choice of the parabolic form is strongly suggested to mitigate potential structural problems.