Simulating a ceramic membrane bioreactor for the production of penicillin: an example of the importance of consistent initialization for solving DAE systems

Abstract

Computer simulation of membrane bioreactors may give rise to numerical divergence when their operational strategy includes sudden changes in the culture medium. The mathematical model of this type of bioreactor is a system of differential–algebraic equations (DAE). This work illustrates the importance of defining consistent initial conditions for this system. The membrane bioreactor presented here is used for the cultivation of Penicillium chrysogenum, immobilized on the upper face of a flat, porous, ceramic membrane. Substrate comes from the medium stream flowing parallel to the membrane lower face. The cells are preserved from shear–stress damage and are kept in direct contact with air. To enhance penicillin production, the medium is diluted at the end of the trophophase. A consistent set of (new) initial conditions has to be selected at this moment; otherwise, the numerical solvers will not converge. Tests are performed using the codes dassl and radau, with almost identical results.