Chemical systems are characterized by very complicated dynamics. For example, in a commercial chemical reactor, one may face unknown kinetics, multi-phase flow, difficult mass and thermal transport and a complex coupling of all these mechanisms in an irregular domain. Therefore, reaction engineers have studied idealized problems in the past, with the hope of obtaining useful rules of thumb. Because the dynamics of chemical systems are often dominated by only a few "master" spatial structures, the construction of low dimensional, nonlinear dynamic models from purely empirical estimations is possible. The PI plans to develop a spatial and temporal correlation technique for the identification and construction of canonical distributed evolution equations of the master modes. Because such canonical equations contain only a few coefficients, general reactor dynamic theory will be developed using bifurcation theory to encompass and classify all dynamic phenomena in distributed parameter chemical reactors. Specifically, reactor responses like growing hot-spots, creeping reaction zones, spinning instabilities of propagating fronts, etc. will be connected to specific classes of distributed disturbances in the theory. The growth and propagation of these instabilities will be mathematically delineated in a general reactor stability theory. Preliminary results suggest that the methodology can also be used to successfully control reactor dynamics and patterns without an explicit model. The technique permits model updating on-line, including adjustments on the order of the model, thus overcoming some robustness issues. Parallel experimental studies will be carried out to confirm the dynamic patterns predicted by the theory and to verify the resultant control schemes.//
