Simplified Equations for Effectiveness Factors in Anaerobic Biofilms

The diffusion effects occuring in a biofilm in which a consecutive bioreaction takes place are studied theoretically, and effectiveness factors $\left(\mathrm{Ef}\right)\text{,}$ which evaluate the effect of the diffusion rates on substrate decomposition rates, are represented by a simple algebraic relation expressed in terms of normalized substrate bulk concentrations (B) and normalized characteristic biofilm parameters. On the other hand, the overall decomposition rates of the substrates can be expressed by a Monod‐type equation for the substrate bulk concentration. The apparent half velocity constants in the Monod‐type rate equation are affected by the diffusion and biochemical reaction rates of the substrates. The ratio of the apparent half velocity constants to the corresponding specific half velocity constants (λ) is related to $\mathrm{Ef}\text{.}$ The relationship is expressed in the following equation: $\mathrm{Ef}=(1+B)/(\lambda +B)\text{.}$ The applicability of these theoretical relations is experimentally demonstrated in volatile fatty acids decomposition. This equation may be rationally used for the design and/or performance of biofilm reactors.