Rational transfer function models for biofilm reactors

Design of controllers and optimization of plants using biofilm reactors often require dynamic models and efficient simulation methods. Standard model assumptions were used to derive nonrational transfer functions describing the fast dynamics of stirred‐tank reactors with zero‐ or first‐order reactions inside the biofilm. A method based on the location of the singularities was used to derive rational transfer functions that approximate nonrational ones. These transfer functions can be used in efficient simulation routines and in standard methods of controller design. The order of the transfer functions can be chosen in a natural way, and changes in physical parameters may directly be related to changes in the transfer functions. Further, the mass balances used and, hence, the transfer functions, are applicable to catalytic reactors with porous catalysts as well. By applying the methods to a nitrifying trickling filter, reactor parameters are estimated from residence‐time distributions and low‐order rational transfer functions are achieved. Simulated effluent dynamics, using these transfer functions, agree closely with measurements.