Determination of kinetic parameters in fixed-film bio-reactors: an inverse problem approach

Processes employing bio-films are increasingly used nowadays for wastewater purification, because they are perceived to be highly efficient compared to the physical or chemical methods of treatment. Mathematical modelling of some of the bio-film processes is not always straightforward, however. A case in point is the fixed-film bioreactors, which have a microbial film attached to a solid inert packing material. The problem is mainly due to the difficulty in obtaining proper kinetic information about the biological reactions taking place in the bio-films. Some attempts have been reportedly made to determine these experimentally but the outcome is not wholly satisfactory. An alternative methodology is proposed in the present work, which makes use of a novel optimization method to evaluate the bio-kinetic parameters, in the course of the solution of an inverse problem with the aid of measured data of fractional conversion of the substrate. In this context, the importance of using a rigorous mathematical model to obtain an accurate estimate of the kinetics is emphasized. Also highlighted is the need to account for the variation of the bio-film thickness in the reactor and its dependence on the organic and the hydraulic loading rates.