The suspended solids measured by MLSS are one of the major factors affecting -factor (Germain, 2007). Various correlations between MLSS and -factor are available in literature as illustrated in Fig. 1, where -factor declines exponentially as MLSS increases. The dramatic differences among the correlations suggest that there are other factors strongly affecting -factor. For example, as shown in Fig. 3 here, -factor can change significantly throughout a day even in a same location in a same aeration tank. Therefore, the curves in Fig. 1 can be considered only guidelines. (*Note*: The uncertainty of -factor makes process design an art based on prior experiences along with other uncertainties from oxygen demand, flow rate, membrane fouling tendencies, *etc*.)

The two curves (Gunder, 2001; Krampe, 2003) that give moderate values in the most common MLSS range of 8-12 g/L are commonly taken as guidelines. Based on the two curves, OTE is approximately 0.4 ± 0.1 in typical MBR.

Fig. 1. Alpha-factor as a function of MLSS at somewhat unidentified conditions except MLSS.

The -factor can be also correlated with viscosity. According to Einstein-Stokes equation, diffusivity is inversely proportional to the viscosity of medium. As medium viscosity increases, oxygen diffusion from the rising bubbles is hindered and -factor decreases. Fig. 2 shows the excellent correlation between medium viscosity and -factor (Wagner, 2002). Fig. 3 also shows a correlation from other literature, where the viscosity of mixed liquor was measured at a shear rate of 10 s^{-1}.

Fig. 2. Alpha-factor as a function of viscosity. (reproduced from Wagner, 2002)

Fig. 3. Connection between representative viscosity at a shear rate of 10/s and the determined alpha-factor (Krampe, 2002).

© Seong Hoon Yoon