Download - oxygen sag curve
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Dissolved Oxygen Depletion
![Page 2: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/2.jpg)
Dissolved Oxygen Sag Curve
![Page 3: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/3.jpg)
Mass Balance Approach
• Originally developed by H.W. Streeter and E.B. Phelps in 1925
• River described as “plug-flow reactor”
• Mass balance is simplified by selection of • Mass balance is simplified by selection of system boundaries
• Oxygen is depleted by BOD exertion
• Oxygen is gained through reaeration
![Page 4: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/4.jpg)
Steps in Developing the DO Sag
Curve
1. Determine the initial conditions
2. Determine the reaeration rate from stream geometry
3. Determine the deoxygenation rate from 3. Determine the deoxygenation rate from BOD test and stream geometry
4. Calculate the DO deficit as a function of time
5. Calculate the time and deficit at the critical point
![Page 5: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/5.jpg)
Selecting System Boundaries
![Page 6: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/6.jpg)
Initial Mixing
Qw = waste flow (m3/s)DOw = DO in waste (mg/L)
L = BOD in waste (mg/L)
Qr = river flow (m3/s)DOr = DO in river (mg/L)Lr = BOD in river (mg/L)
Qmix = combined flow (m3/s)DO = mixed DO (mg/L)La = mixed BOD (mg/L)
Lw = BOD in waste (mg/L)
![Page 7: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/7.jpg)
1. Determine Initial Conditions
a. Initial dissolved oxygen concentration
b. Initial dissolved oxygen deficit
DODOD s −=
rw
rrww
DOQDOQDO
++=
where D = DO deficit (mg/L)
DOs = saturation DO conc. (mg/L)
DODOD s −=
mix
rrww
sQ
DOQDOQDOD
+−=
![Page 8: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/8.jpg)
1. Determine Initial Conditions
DOsat is a function of temperature. Values
can be found in Table 6.9 (Gilbert Masters)
c. Initial ultimate BOD concentration
LQLQ +
rw
rrww
aQQ
LQLQL
++=
![Page 9: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/9.jpg)
2. Determine Reaeration Rate
a. O’Connor-Dobbins correlation
where kr = reaeration coefficient @ 20ºC (day-1)
u = average stream velocity (m/s)
2/3
2/19.3
h
ukr =
u = average stream velocity (m/s)
h = average stream depth (m)
b. Correct rate coefficient for stream temperature
where Θ = 1.024
20
20,
−Θ= T
rrkk
![Page 10: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/10.jpg)
Determine the Deoxygenation Rate
a. rate of deoxygenation = kdLt
where kd = deoxygenation rate coefficient
(day-1)
Lt = ultimate BOD remaining at
time (of travel downstream) ttime (of travel downstream) t
b. If kd (stream) = k (BOD test)
and
tk
tdeLL
−=0
tk
ddeLk
−=0
tiondeoxygenta of rate
![Page 11: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/11.jpg)
3. Determine the Deoxygenation
Rate
c. Correct for temperature
20
20,
−Θ= T
rr kk
where Θ = 1.135 (4-20ºC) or 1.056 (20-30ºC)
![Page 12: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/12.jpg)
4. DO as function of time
• Mass balance on moving element
• Solution is
DkLkdt
dDrtd −=
• Solution is
( ) ( )tk
a
tktk
dr
ad
trrd eDee
kk
LkD
−−− +−−
=
![Page 13: oxygen sag curve](https://reader037.vdocuments.net/reader037/viewer/2022100107/55180ccf4a7959d8108b456e/html5/thumbnails/13.jpg)
5. Calculate Critical time and DO
−−−
=ad
dr
a
d
r
dr
cLk
kkD
k
k
kkt 1ln
1
( )Lk ( ) crcrcd tk
a
tktk
ar
ad
c eDeekk
LkD
−−− +−−
=