Low model order approximations of continuously stirred biofilm reactors with Monod kinetics

Design of controllers and optimization of plants using biofilm reactors require dynamic models and efficient methods of simulation. Continuously stirred biofilm reactors (CSBRs) are useful model units in modeling a variety of different types of biofilm reactors. Often the reaction kinetics in the biofilm is described by a Monod expression. With standard modeling assumptions the equations describing the fast dynamics of a CSBR will then, for each substrate, be one nonlinear partial differential equation coupled with one linear ordinary differential equation. Here, it is shown how a few nonlinear ordinary first order differential equations, which may be solved with standard integration methods, can be used as a close approximation for both dynamic responses and steady state solutions. These low order models can conveniently be used in simulation software and for controller design.