Mathematical Biosciences and Engineering, 2014, 11(5): 1139-1166. doi: 10.3934/mbe.2014.11.1139.

Primary: 92D25; Secondary: 49N90.

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On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria

1. EAWAG, Swiss Federal Institute of Aquatic Science and Technology, Überlandstrasse 133, P.O. Box 611, CH-8600 Dübendorf,
2. Biophysics Interdepartmental Program and Department, of Mathematics and Statistics, University of Guelph, Guelph ON, N1G 2W1

We investigate the question of optimal substrate removal in a biofilm reactor with concurrent suspended growth, both with respect to the amount of substrate removed and with respect to treatment process duration. The water to be treated is fed externally from a buffer vessel to the treatment reactor. In the two-objective optimal control problem, the flow rate between the vessels is selected as the control variable.The treatment reactor is modelled by a system of three ordinary differential equations in which a two-point boundary value problem is embedded. The solution of the associated singular optimal control problem in the class of measurable functions is impractical to determine and infeasible to implement in real reactors. Instead, we solve the simpler problem to optimize reactor performance in the class of off-on functions, a choice that is motivated by the underlying biological process. These control functions start with an initial no-flow period and then switch to a constant flow rate until the buffer vessel is empty. We approximate the Pareto Front numerically and study the behaviour of the system and its dependence on reactor and initial data.Overall, the modest potential of control strategies to improve reactor performance is found to be primarily due to an initial transient period in which the bacteria have to adapt to the environmental conditions in the reactor, i.e. depends heavily on the initial state of the dynamic system. In applications, the initial state, however, is often unknown and therefore the efficiency of reactor optimization, compared to the uncontrolled system with constant flow rate, is limited.
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Keywords Biofilm; treatment time; optimization.; suspended growth; substrate removal

Citation: Alma Mašić, Hermann J. Eberl. On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria. Mathematical Biosciences and Engineering, 2014, 11(5): 1139-1166. doi: 10.3934/mbe.2014.11.1139

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