oxygen profile in streams - marmara Üniversitesi...
TRANSCRIPT
![Page 1: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/1.jpg)
Oxygen Profile in Streams Assoc. Prof. Kozet YAPSAKLI
![Page 2: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/2.jpg)
Oxygen depletion in streams
![Page 3: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/3.jpg)
Two mechanisms are known to contribute oxygen to surface waters:
dissolution of oxygen from the atmosphere (reaearation)
production of oxygen by algal photosynthesis
Oxygen level in surface waters
![Page 4: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/4.jpg)
Oxygen deficit is represented mathematically by
𝐷 = 𝑐𝑠 − 𝑐
For constant equilibrium conditions, i.e. Cs does not change, the rate of change in the deficit:
𝑑𝐷
𝑑𝑡= −
𝑑𝑐
𝑑𝑡
The deficit increases at the same rate that oxygen is used
The dissolved oxygen deficit is the main driving force for reaeration
Oxygen Deficit
![Page 5: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/5.jpg)
DO sag definitions
![Page 6: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/6.jpg)
Streeter-Phelps Model*
Mass Balance for the Model
Not a Steady-state situation
rate O2 accum. = rate O2 in – rate O2 out + produced – consumed
rate O2 accum. = rate O2 in – 0 + 0 – rate O2 consumed
Kinetics
Both reoxygenation and deoxygenation are 1st order
* Streeter, H.W. and Phelps, E.B. Bulletin #146, USPHS (1925)
![Page 7: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/7.jpg)
The oxygen deficit in a stream is a function of
Oxygen utilization
Reaeration
𝑑𝐷
𝑑𝑡= 𝑟𝐷 + 𝑟𝑅
rD=Rate of BOD exertion
rR=Rate of reaeration
Sag Curve
![Page 8: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/8.jpg)
Kinetics for Streeter-Phelps Model
• Deoxygenation
L = BOD remaining at any time
dL/dt = Rate of deoxygenation equivalent to rate of BOD removal
dL/dt = -k1L for a first order reaction
k1 = deoxygenation constant, f’n of waste type and temp.
kLdt
Ld
][
C
C
t
dtkL
dL
0 0
ktkt eLLeL
Lorkt
L
L 0
00
ln
![Page 9: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/9.jpg)
Developing the Streeter-Phelps
Rate of reoxygenation = k2D
D = deficit in D.O.
k2 = reoxygenation constant*
2
3
21
)20(21
2
025.19.3
H
vk
T
Where
– T = temperature of water, ºC
– H = average depth of flow, m
– ν = mean stream velocity, m/s
D.O. deficit
= saturation D.O. – D.O. in the water
There are many correlations for this. The simplest one, used here, is from O’Connor and Dobbins, 1958
![Page 10: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/10.jpg)
or
![Page 11: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/11.jpg)
Combining the kinetics
OR
Net rate of change of oxygen deficiency, dD/dt
dD/dt = k1L - k2D
where L = L0e-k1t
dD/dt = k1L0e-k1t - k2D
![Page 12: Oxygen Profile in Streams - Marmara Üniversitesi …mimoza.marmara.edu.tr/~kyapsakli/enve202/Lecture4...Oxygen deficit is represented mathematically by 𝐷= 𝑠− For constant](https://reader031.vdocuments.us/reader031/viewer/2022030800/5b09b8a17f8b9a5f6d8e60bb/html5/thumbnails/12.jpg)
Integration and substitution
tk
o
tktko eDeekk
LkD 221 )(
12
1
tk
oc
tk
o
eLk
kD
DkeLkdt
dD
1
1
2
1
21 0
o
oc
Lk
kkD
k
k
kkt
1
12
1
2
12
)(1ln
1
The last differential equation can be integrated to:
It can be observed that the minimum value, Dc is achieved when dD/dt = 0:
, since D is then Dc
Substituting this last equation in the first, when D = Dc and solving for t = tc: