Effectiveness factor for a hollow-fiber biofilm reactor at maximum substrate consumption

In this work, a model was proposed to evaluate the effectiveness factor of a hollow-fiber biofilm reactor (HFBR) for optimum biofilm densities, to achieve a maximum substrate consumption rate. The effectiveness factor was calculated for selected lumen concentrations using a cell-density-dependent effective diffusion coefficient, Monod biokinetics adapted for maintenance, and a minimum substrate concentration concept for biofilm activity in the model, a different approach from that in the literature. The solution of the continuity equation revealed an optimum biofilm density and active biofilm thickness, corresponding to a maximum substrate consumption rate within the biofilm. The optimum biofilm density decreased with increasing lumen substrate concentrations, while the maximum substrate consumption rate and active biofilm thickness parabolically increased, as experimentally observed in the literature. Meanwhile, an interesting descending trend of the effectiveness factor at optimum biofilm density was observed at low lumen substrate concentration and biofilm thickness values for different radial flow rates.