The continuum heterogeneous biofilm model with multiple limiting substrate Monod kinetics

Observed (net) rate of biomass growth as a function of ammonium substrate concentration at two different oxygen concentrations. At low oxygen concentration the net growth rate reaches a plateau when oxygen is consumed completely. At high oxygen concentration the growth rate increases continuously with ammonia concentration. However, when the concentration of ammonium exceeds the value of 13.84g of N/m³, oxygen becomes the limiting substrate.

We describe a novel procedure to estimate the net growth rate of biofilms on multiple substrates. The approach is based on diffusion-reaction mass balances for chemical species in a continuum biofilm model with reaction kinetics corresponding to a Double-Monod expression. This analytical model considers a heterogeneous biofilm with variable distributions of biofilm density, activity, and effective diffusivity as a function of depth. We present the procedure to estimate the effectiveness factor analytically and compare the outcome with values obtained by the application of a rigorous numerical computational method using several theoretical examples and a test case. A comparison of the profiles of the effectiveness factor as a function of the Thiele modulus, ϕ, revealed that the activity of a homogeneous biofilm could be as much as 42% higher than that of a heterogeneous biofilm, under the given conditions. The maximum relative error between numerical and estimated effectiveness factor was 2.03% at ϕ near 0.7 (corresponding to a normalized Thiele modulus ϕ*=1). For ϕ<0.3 or ϕ>1.4, the relative error was less than 0.5%. A biofilm containing aerobic ammonium oxidizers was chosen as a test case to illustrate the model's capability. We assumed a continuum heterogeneous biofilm model where the effective diffusivities of oxygen and ammonium change with biofilm position. Calculations were performed for two scenarios; Case I had low dissolved oxygen (DO) concentrations and Case II had high DO concentrations, with a concentration at the biofilm-fluid interface of 10gO₂/m³. For Case II, ammonium was the limiting substrate for a biofilm surface concentration, C_Ns, ≤13.84g of N/m³. At these concentrations ammonium was limiting inside the biofilm, and oxygen was fully penetrating. Conversely, for C_Ns>13.84g of N/m³, oxygen became the limiting substrate inside the biofilm and ammonium was fully penetrating. Finally, a generalized procedure to estimate the effectiveness factor for a system with multiple (n>2) limiting substrates is given. Biotechnol. Bioeng. 2014;111: 2252-2264.