The MBR Book: Principles and Applications of Membrane

which affords the operator complete control over the SRT. The death rate constant
accounts for endogenous metabolism, that is, the utilisation by cells of stored materials,
and the presence of extracellular polymerics (Section 2.3.6.5) associated with the
biomass. k e also accounts for grazing of the biomass by predatory organisms, as previously
discussed. k e for conventional activated sludge and anaerobic processes is
typically in the range 0.04–0.075/day (Gu, 1993; Metcalf and Eddy, 2003), and
takes similar values for MBRs (Fan et al., 1996; Wen et al., 1999). Experiments by Huang
et al. (2001) showed that the endogenous decay in an MBR is higher (0.05–0.32/day)
than for an ASP (0.04–0.075/day).
2.2.4.2 Sludge yield
Y obs, the observed yield (g/(g/day)), is always lower than Y due to the effects of cell decay
(k e). The relationship between Y obs and Y is governed by the SRT, � x, and is defined by:
Y
obs
(2.5)
where f d is the fraction of the biomass that remains as cell debris, usually
0.1–0.15 g VSS/g substrate (Metcalf and Eddy, 2003). Observed yields (Y obs) are
approximately 0.6/day for conventional aerobic processes and an order of magnitude
lower for anaerobic ones. Y obs is used to calculate the amount of heterotrophic sludge
that will be produced by a biological system (P x,het) for a given flow rate (Q m 3 /day):
Px, het �YobsQ( S�Se) (2.6)
The observed yield is the increase in biomass from heterotrophic cells only.
Nitrification sludge and non-biodegradable solids also impact on the total daily sludge
production. P x is the total sludge yield from substrate degradation and derives from the
heterotrophic sludge yield (P x,het) and the nitrification sludge yield (P x,aut). The sum of
all solids generated each day the non-biodegradable solids can be accounted for by:
X �( TSS �VSS)
Q
0
Y f k Yu
� �
1�ku1�ku e x
(2.7)
The sludge production from biodegradation in an MBR can, in principle, be reduced to
zero by controlling SRT (� x), k e and Y. The change in � x has by far the greatest impact
on sludge production (Xing et al., 2003) and mixed liquor suspended solids (MLSS).
Past experience allows designers to set a desired MLSS concentration (X g/m 3 ). The
MLSS then affects sludge production, aeration demand (Section 2.2.5) and membrane
fouling and clogging (Section 2.3.6). Using a design MLSS and SRT the aeration tank
volume can be calculated by obtaining the mass of solids being aerated, and then using
the MLSS to convert that mass to the volume which those solids occupy:
( P � X )u
V �
X
x 0 x
d e x
e x
Fundamentals 43
(2.8)