Estimation of Time-Variant Parameters with States in Chemical Reactors

Simultaneous estimation of unknown kinetic rate constant and heat of reaction is considered for on-line estimation of concentration in chemical reactors from thermal balance. A first-order reaction is studied to illustrate potential problems threatening this goal when the employed model seeks to estimate time-variant parameters. In particular, identifiability of the unknown parameters is lost when the model allows for time variations in these parameters, even though the true parameters in the process may remain constant. This unidentifiability rules out the popular technique of modeling parameter dynamics as a random walk in order to track time-variant parameters with an Extended Kalman Filter. A new strategy involving decoupled parameter estimation is shown to recover partial identifiability to the extent that when a true parameter settles at a new constant value, this value is estimated without bias. During the transition of the true parameter, the estimate shows bias; however, this bias is small for reasonable choices of the sampling period, allowing satisfactory tracking of slow drifts.