Geoscience Reference
In-Depth Information
VX
QX QX
)
=
TotalmassSSinreactor
θ
c
=
(24.54)
(
+
SS wastingrate
wa
cc
where
θ
c
= Mean cell residence time based on solids in the tank (day).
X
= Concentration of MLVSS maintained in the tank (mg/L).
∆
X
/∆
t
= Growth of biological sludge over time period ∆
t
(mg/ L/day).
V
= Volume of aeration tank (m
3
).
Q
wa
= Flow of waste sludge removed from the aeration tank (m
3
/day).
Q
c
= Flow of treated effluent (m
3
/day).
X
c
= Microorganism concentration (VSS in effluent, mg/L).
The mean cell residence time for system-drawn sludge from the return line would be
VX
QX QX
Q
=
(24.55)
c
(
)
+
wr
r
c
c
where
Q
wr
= Flow of waste sludge from return sludge line (m
3
/d).
X
r
= Microorganism concentration in return sludge line (mg/L).
24.7.1.12.2 Microorganism Mass Balance
The mass balance for the microorganisms in the entire activated biosolids system is expressed as
(Metcalf & Eddy, 1991)
dX
dt
=+
()
−
(
)
V
QX
Vr
QX QX
+
(24.56)
o
g
wa
cc
where
V
= Volume of aeration tank (m
3
).
dX
/
dt
= Rate of change of microorganism concentration (VSS) (mg/L/m
3
/day).
Q
= Flow (m
3
/day).
X
o
= Microorganism concentration (VSS) in influent (mg/L).
X
= Microorganism concentration in tank (mg/L).
r
g
′ = Net rate of microorganism growth (VSS) (mg/L/day).
The net rate of bacterial growth (
r
g
′ ) is expressed as
r
g
′ =
Yr
su
-
K
d
X
(24.57)
where
Y
= Maximum yield coefficient over finite period of log growth (mg/mg).
r
su
= Substrate utilization rate (mg/m
3
).
K
d
= Endogenous decay coefficient (per day).
X
= Microorganisms concentration in tank (mg/L).
Assuming the cell concentration in the influent is zero and steady-state conditions, Equation 24.58
can be used:
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