The MBR Book: Principles and Applications of Membrane

occurs from the surrounding air to the bulk liquid via a liquid/air interface (as for a
TF or rotating biological contactor (RBC)).
The oxygen requirement to maintain a community of micro-organisms and
degrade BOD and ammonia and nitrite to nitrate can be found by a mass balance on
the system (Metcalf and Eddy, 2003):
(2.17)
where m o is the total oxygen required (g/day). The first term in Equation (2.17) refer to
substrate oxidation, the second refers to biomass respiration, the third refers to nitrification
and the final term refers to denitrification. Certain terms thus disappear from the
expression depending on whether or not the system is nitrifying and/or denitrifying.
2.2.5.2 Mass transfer
Mass transfer of oxygen into the liquid from air bubbles is defined by the overall liquid
mass transfer coefficient (k L m/s) and the specific surface area for mass transfer
(a m 2 /m 3 ). Because of the difficulties associated with measuring k L and a, the two are
usually combined to give the volumetric mass transfer coefficient k La (per unit time).
The standard method accepted for determining k La in clean water is detailed in ASCE
(1992). The rate of oxygen transfer into a liquid can be determined by:
(2.18)
where C and C* are the dissolved and saturated oxygen concentration values in kg/m 3 .
For pure water and equilibrium conditions C is found using Henry’s Law. This can be
converted to process conditions by the application of three correction factors (�, �
and �) which account for those sludge properties which impact on oxygen transfer
(Section 2.2.5.3):
OTR
process
(2.19)
Aeration also provides agitation to ensure high mass transfer rates and complete
mixing in the tank. There is thus a compromise between mixing, which demands larger
bubbles, and oxygen dissolution, which demands small, indeed microscopic, bubbles
(Garcia-Ochoa et al., 2000). Consequently oxygen utilisation, the amount of oxygen
in the supplied air which is used by the biomass, can be as low as 10%, and decreases
with increasing biomass concentration (Equation (2.25)). This can be quantified by
the standard aeration efficiency (kg O 2/kWh):
SAE �
( ) ( ) ( )
m � Q S�S �1.42P �4.33Q NO �2.83Q
NO
o e x x x
OTR � k a( C* �C
cleanwater L )
OTR
�
abw
OTRxV
W
cleanwater
Fundamentals 47
(2.20)
where W is the power demand. The OTR into the mixed liquor can be increased by
using oxygen-enriched air, but this increases costs and is rarely used other than for