Modeling biofilm and floc diffusion processes based on analytical solution of reaction-diffusion equations

Biofilm modeling is often considered as a complex mathematical subject. This paper evaluates simple equations to describe the basic processes in a biofilm system with the main aim to show several interesting applications. To avoid mathematical complexity the simulations are carried out in a simple spreadsheet. Frequently, only the solution for zero-order reaction kinetics of the reaction-diffusion equation is used (better known as half-order kinetics). A weighted average of the analytical solutions for zero- and first-order reactions is proposed as basic and useful model to describe steady-state (in biofilm composition) biofilm reactors. This approach is compared with several modeling approaches, such as the simple solution for zero-order reaction and more complex ones (i) direct numerical solution for the diffusion equations, (ii) 1-D AQUASIM and (iii) 2-D modeling. The systems evaluated are single and multiple species biofilms. It is shown that for describing conversions in biofilm reactors, the zero-order solution is generally sufficient; however, for design purposes large deviations of the correct solution can occur. Additionally, the role of diffusion in flocculated and granular sludge systems is discussed. The relation between the measured (apparent) substrate affinity constant and diffusion processes is outlined.