Modeling of continuous-flow bioreactors with a biofilm with the use of orthogonal collocation on finite elements

The paper discusses mathematical modeling of two types of continuous bioreactors, a continuous stirred tank bioreactor (CSTBR) and a tubular bioreactor with biofilm on inner walls. The method of orthogonal collocation on finite elements (OCFE) was used for the modeling of a microbiological process occurring in the biofilm. Single-substrate Monod and Haldane kinetic models, and double-substrate Haldane–Monod kinetic model were used. The accuracy of the OCFE method was evaluated by comparison with the solution obtained using shooting method (SM). Profiles of substrate concentration, biofilm effectiveness factors, steady state-branches of CSTBR and distribution of substrate concentrations and biofilm thickness along the length of the tubular bioreactor were determined. Steady-state branches of the CSTBR were compared with experimental results from the literature. It was shown that the mathematical model gives good agreement. The efficiency of the OCFE method was demonstrated even for very steep gradients of concentrations in the biofilm.