Wastewater Calculations - Mathematics and Statistics for the Environment - page 698

Y
Q

Y = (24.64)

obs

1 +

ct

where
Y obs = Observed yield in the system with recycle (mg/mg).
Y = Maximum yield coefficient over finite period of log growth (mg/mg).
Q ct = Mean of all residence times based on solids in aeration tank and in secondary clarifier
(days).

24.7.1.13.1 Process Design and Control Relationships
The specific substrate utilization rate (closely related to F/M ratio, which is widely used in practice)
can be computed by

r
X

su

U = (24.65)

( ) =

QS − S SS

X

−

o o

U = (24.66)

VX θ

The net specific growth rate can be computed by

1
θ c

=− YU K (24.67)

d

The flow rate of waste sludge from the sludge return line will be approximately

VX
X

Q = θ (24.68)

wt

cr

where X r is the concentration of sludge in the sludge return line (mg/L).

24.7.1.13.2 Sludge Production
The amount of sludge generated per day can be calculated by

P x = Y obs Q ( S o - S )(8.34) (24.69)

where
P x = Net waste activated sludge (VSS) (kg/day, lb/day).
Y obs = Observed yield (g/g or lb/lb).
Q = Influent wastewater flow (m 3 /day, MGD).
S o = Influent soluble BOD concentration (mg/L).
S = Effluent soluble BOD concentration (mg/L).
8.34 = Conversion factor [(lb/MG):(mg/L)].

24.7.1.13.3 Oxygen Requirements
The theoretical oxygen requirement to remove the carbonaceous organic matter in wastewater for an
activated biosolids process is expressed by Metcalf & Eddy (1991) in SI units and the British system:

Mass of Oper dayTotal mass of BODused
2

= − 1.42(mass of organismswasted, P x )

u