Modeling of an aerobic biofilm reactor with double-limiting substrate kinetics: bifurcational and dynamical analysis

A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behaviour of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. (J. Biotechnology, 2008;135;295-303) is extended to embody key features of the phenomenology of the granular-supported biofilm: biofilm growth and detachment, gas-liquid oxygen transport, phenol and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady state conditions and stability, and local dynamic behaviour have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gas-liquid mass transfer coefficient, biofilm detachment rate and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady state scenario with trans-critical and saddle-node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is smaller than 10% of the saturation level the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate.