Oxygen transfer limitation in a respirometer

The oxygen uptake process in a respirometer was analyzed by a mathematical model consisting of oxygen transfer accompanied with oxygen consumption reaction. The criterion to avoid an oxygen‐transfer limitation was derived on the basis of the ratio of the maximum biochemical reaction rate to the maximum possible oxygen‐transfer rate. The maximum biochemical reaction is described by the first‐order rate equation, whereas the maximum possible oxygen‐transfer rate is calculated by multiplying the oxygen‐transfer coefficient with the solubility of oxygen in water. An oxygen‐transfer coefficient in a respirometric reactor was estimated as 1.8 h−1, by using the model analysis of an oxygen uptake data from the same reactor. A simplified criterion for a respirometer without oxygen‐transfer limitation is then obtained as XS ≪ 16.51/K1 where X and S represent concentration of biomass and substrate, respectively, and K1 is the first‐order rate constant, (L/mg VSS)/h.