An invariant manifold approach for CSTR model reduction in the presence of multi-step biochemical reaction schemes. Application to anaerobic digestion

A systematic methodology for CSTR model reduction has been developed for multi-step biochemical reaction schemes. The proposed method neglects the dynamics of the fast steps by projecting the overall system dynamics on the slow-motion invariant manifold of the system. In particular, using reaction invariants in the description of the overall system dynamics, the slow-motion invariant manifold is calculated by solving the pertinent invariance equation via series-solution or singular perturbation techniques. The proposed method is an alternative to the quasi-steady state approximation which does not rely on a priori physical information. The proposed approach is applied to two model reduction problems arising in anaerobic digestion. The results provide a rigorous answer on how to properly eliminate the fast dynamics of the acidogenesis step.