Modelling of a nonlinear distributed parameter bioreactor via Orthogonal Collocation method

In this paper, the aim is to develop a reduced model of a non linear distributed parameter system of hyperbolic type using the Orthogonal Collocation Method. The approach consists to approximate the original hyperbolic partial derivative equations describing the plant by a set of ordinary differential equations. The method is detailed for modeling a fixed bed bioreactor without dispertion and illustrated with various analysis showing how to select the appropriate reduced model. The dynamics of the obtained reduced model are compared to a finite difference method. Numerical simulations are included to illustrate the dynamical behaviour of the two classes of models.