An equation of specific substrate utilization rate for immobilized microorganism was derived in consideration of external and internal diffusional resistances and microbial substrate utilization. It was expressed by the Michaelis-Menten equation modified replacing the maximum specific substrate utilization rate to ηpνm and the Michaelis constant to (Km/K+δp) in the case of Cbδp/(Cb+Km/K+δp)2«1.
The experimental results of immobilized ammonium and ferrous iron oxidizing bacteria showed that δp should be considered because ratios of δp to Km were 0.34 and 1.14, respectively. On the other hand, when microorganisms were dispersed in a culture medium, δc could be ignored even in a moderate agitation condition.