Distributed parameter estimation and identification for system with fast and slow dynamics: A tubular,fixed-bed catalytic reactor to form styrene

A simple and efficient on-line scheme is developed to estimate temperature and compositions along a packed bed reactor in which styrene is being produced by the dehydrogenation of ethylbenzene. Slowly varying catalyst activity is also identified. The system is distributed in time and axial position and is nonlinear in the states: temperature and nine compositions. The dehydrogenation rate is augmented with a catalyst activity parameter which is assumed to undergo a long-term exponential decay.Since the decline in catalyst activity is slow when compared to state dynamics, a quasi-steady-state approach is used to derive a state filter equation neglecting process state dynamics and assuming spatially uncorrelated measurements and model uncertainty. For this filter, temperature measurements are available from four locations along the reactor and compositions are measured only at the reactor exit. A second dynamic, Kalman filter is used to identify the slowly varying catalyst activity.The two filters, one for distributed, steady-state, state estimation and the other for dynamic catalyst activity identification, are tested by computer simulation using measurements with added white noise. Several cases for numbers of sensors and noise levels are studied. The overall scheme is efficient and useable for on-line implementation. The steady-state filter is readily extended to distributed systems in more than one spatial variable such as reactor models with axial and radial dependencies. For steady-state or static models, multiple measurements yield significant improvements in the quality of the optimal estimates. Internal measurement locations allow for the subdivision of the spatial domain for the problem and improved profile estimates.