A New Thiele's Modulus for the Monod Biofilm Model

A new Thiele's modulus, ϕF, was developed to provide a gradual transition between zero and the first order of kinetics, and to accurately calculate the mass transfer flux and the effectiveness factor for the Monod biofilm. Values of the effectiveness factor, calculated using the new Thiele's modulus, were compared with those obtained from numerical solutions and from other published moduli and empirical formulae. The comparison indicated that the new Thiele's modulus was the best modulus for the Monod biofilm model. In addition, another Thiele's modulus, ϕG, was developed for a Monod biofilm, covered with an external water layer. The overall effectiveness factor can also be calculated by using both moduli ϕF and ϕG. The criteria that were proposed for identification were based on the values of ϕF and ϕG, the limiting processes for biomass growth, and substrate conversion. Developed from ϕF, a new parameter Ψ was related uniquely to such features as the depth and shallowness of the generalized substrate concentration profiles inside a Monod biofilm. Criteria were developed to identify the types of concentration distribution inside a Monod biofilm. These methods were used to estimate the substrate flux and the concentration distribution of the biofilms defined in the first benchmark problem (BM1), by a task group of the International Water Association on Biofilm Modeling.