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7 Dissolved OxygenIntroduction
Oxygen Saturation
Biochemical Oxygen Demand
ReaerationStreeter-Phelps Equation
Nitrification
Sediment Oxygen Demand
Photosynthesis and Respiration
Expanded Streeter-Phelps EquationArtificial Re-aeration
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Dissolved Oxygen
Important for aquatic health DO standards typically 5 to 6 mg/L
Redox chemistry
Affects release of chemicals bound tosediments
Anaerobic conditions => H2S
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Oxygen Saturation
]})15.273/(101407.2
)15.273/(754.10107674.1[)15.273/(10621949.8
)15.273/(10243800.1)15.273/(10642308.6
)15.273/(10575701.1103934411.1exp{),(
23
2411
31027
52
++
++
+++
++=
Tx
TxSTx
TxTx
TxxSTcs
=
)1)(1(
)1)(/1(),(),,(
wv
wv
ssp
pppSTcpSTc
])15.273/(1016961.2)15.273/(108407.38575.11exp[ 253 ++= TxTxpwv
285 10436.610426.1000975.0 TxTx +=
Standard Methods (1995)
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Cs (T, S, p)T=0o 10 20 30
Effect of p (S=0)
p = 1 atm (z=0) 14.6 11.3 9.1 7.6
p = 0.89 (1000m) 12.9 19.9 8.0 6.7p = 0.79 (2000m) 11.4 8.8 7.1 5.9
Effect of S (p=0)
S = 0 PSU 14.6 11.3 9.1 7.7
S = 10 13.6 10.6 8.6 7.2
S = 35 11.4 9.0 7.4 6.2
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Processes affecting DO
BOD (-)
Re-aeration (+/-)
P(+)/R(-)
Inflow
(+/-)
SOD (-)
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Biochemical Oxygen DemandOrganic wastes are food formicroorganisms Oxygen consumed in process
Self-purification (bio-degradation) innatural waters
Biological stage of WWT
Other chemicals exert oxygen demand C2H6O2
NaHSO3
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Theoretical Oxygen Demand
43
3222 )2
3
2
3
2()
4
5
4
3
24(
POdH
cNHOHdca
nCOOdcba
nPNOHC dcban
+
++=+++
OHHNOONH 22232
3++=+ +
=+322 2
1NOONO
Carbonaceous BOD (CBOD)
Nitrogenous BOD (NBOD)
Issues
Different types of wastes Some not labile
Rates vary (nitrification)
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Practical Measures of Oxygen Demand
BOD Traditional water quality measure
Cumbersome and time-consuming
COD
Easy to measure
TOC State variable in WQ models
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Traditional BOD
Practical measure of O2debt How much DO would decrease due to
respiration of organic wastes
BOD Jar Test Observe the decline of DO over time (e.g.
5 days) Extrapolate to ultimate demand
Used for wastewater and natural waters
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BOD Jar TestPrecautions
No photosynthesis
Enough initial O2
Adequate dilution (WW) Enough microorganisms
Non toxic sample
Only carbonaceous BOD
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[DO]
time
y5 = BOD5
yu =
BODu
y(t)
0
0 5 days
)1(1tK
eLy
=15
5
1K
e
LL
=
2011 )20(
=TKK
047.1~;5.01.0~)20( 11 dK
In rivers
sdr KKK +=
hwK ss /=
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Other Measures of BOD
COD Easy to measure
Much quicker
TOC State variable in WQ models
Relationship to BOD (Metcalf & Eddy) BOD5/COD ~ 0.4 to 0.8
BOD5/TOC ~1.0 to 1.6
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Stream ReaerationWater side control
Flux F ~ DO deficit
Piston velocity [LT-1]
kL ~ kw
Reaeration rate [T-1]
Ka
= K2
= kw
/h
Theories
Stagnant Film
Surface Renewal
H
c
cszw
h F=kL(cs-c)
= zw
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Stream ReaerationStagnant Film
kL = D/zw
Surface Renewal
zw ~ (Dt)0.5 t ~ h2/Ez ~ h/u
zw ~ (Dh/u)0.5
kL ~ (Du/h)0.5
Ka ~ (Du/h3)0.5
H
c
F=kL(cs-c)
cszw
h
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Stream Reaeration Formulae
u in m/s, h in m, T=20o
5.1
5.093.3h
uKa = OConnor-Dobbins
(1958)
Churchill et
al. (1962
Owens &Gibbs
(1964)
67.1
0.5
h
uKa =
85.1
67.03.5
h
uKa =
Kovar, 19760.1
0.3
0.4
0.50.60.8
1
2Depth
(ft.)
3
456
8
10
20
30
40O'Connor
Owens
.05
0.5
5
10
105
Churchill
50100
1
50
0.2Velocity (ft./sec.)
0.3 0.4 0.6 0.8 1 2 3 4 5 6
0.1
Figure by MIT OCW.
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Other formulationsRate of Energy Dissipation (Tsivoglou
& Wallace, 1972)
Melching and Flores (1999)
uSuL
LSTH ==
/
Pool and Riffle Reaeration Coefficient
Ka
CV
Q < 0.56 517(uS)0.524Q-0.242 0.61
Q > 0.56 596(uS)0.528Q-0.136 0.44
Channel Control
Q < 0.56 88(uS)0.313H-0.353 0.59
Q > 0.56 142(uS)0.333H-0.66W-
0.243
0.60
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1-D Analysis
(Streeter-Phelps, 1925)
Continuity
lqAu
xt
A=
+
)(
Mass Transport
)()()()(eiL rrA
x
cAE
xAuc
xAc
t++
=
+
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BOD (c = L)
LKr ri =ALqre /ll=
=x
xu
dx
0)(
A
LLqLK
dx
dLu r
)( += ll
)( LLLKd
dLr
+=l
[ ] { }])(exp[1)(
)(exp)(
+
+++= r
r
ro KK
LKLL l
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DO (c = c)LKr di =
)(/ ccKAcqr sae += ll
A
ccqccKLK
dx
dcu sad
)()(
++= ll
)()( ccccKLKd
dcsar ++= l
ccs =
]})(exp[])({exp[
)()(
]})(exp[1{))((
])(exp[)(
++
+
+
+++
++=
ar
r
o
ra
d
a
ar
d
ao
KvK
K
LL
KK
K
vKvKvK
LKK
l
l
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Streeter-Phelps-additional comments
cmin
and xmin
can be calculatedanalytically
Multiple sources handled by
superposition or re-initialization atstream confluences
Procedures for anoxic conditions
Neglect of longitudinal dispersion?
Additional terms
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Nitrification
(2)(32/14) = 4.5743
3222 )
2
3
2
3
2
()
4
5
4
3
24
(
POdH
cNHOHdca
nCOOdcba
nPNOHC dcban
+
++=+++
OHHNOONH 22232
3++=+ +
=+ 3222
1NOONO (0.5)(32/14) = 1.14
Theoretical (upper bound) NBOD
NNONNHNOrgNBOD ++= 23 14.1)(57.4
TKN = total Kjeldalh nitrogenTKNNBOD 57.4
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[DO]
CBOD
NBOD
0
time0
Time scale for NBOD ~ 10 days => often insignificant in rivers
If important, separate CBOD & NBOD analyses required
May be better to include nitrogen species as state variables
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Sediment Oxygen Demand (SOD)
BOD in sediments
Significant downstream from outfalls orfollowing algal blooms
SB = 0.1 to 1 g/m2-d
re = SB/h
Oth order process
0.1 to 1 mg/L-d (h = 1 m)
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SOD (contd)Measured
in situwith benthic flux chambers
in lab with core
Calculated from organic carbon contentof settled solids
Calibrated from oxygen modelComplication: extraneous sources
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Benthic Flux Chambers
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Zebra Mussels
Algal Photosynthesis and
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Algal Photosynthesis and
Respiration
Photosynthesis (primary production) =>fixation of CO2 by autotrophic bacteria
Reverse is respiration
6CO2 + 6H2O C6H12O6 + 6O2
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P/R (contd)Limitations on primary production:
Light
Temperature
Nutrients
Time and space dependent
Diurnal variation Depth variation
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P(t)
Pm
Pa
24 hf0 t
ma Pf
P24
2= f = photoperiod (hrs)
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EPA (1985)
Curve A
Curve B
Wyman Creek, Calif
August 6, 1962
Average 10.1 MG/L
River Ivel, England
May 31, 1959
Average 10.4 MG/L
7
8
9
10
11
12
13
0600 06000900 1200N 1500 1800 2100 2400 0300
Hours
DissolvedO
xygenMG/L
Figure by MIT OCW.
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Estimation of P/RIn situ measurements w/ Light & DarkBottles
LKt
cc
R ddark
to
= mg/L-d; L = ultimate
BOD of filtered sample
dark
ot
light
ot
t
cc
t
cc
tP
=)(
P(t) is averaged over time t. t = 24 hrs => Pa;
t< 24 h => fit to diurnal variation using f
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Pm
t24 hf
Pa
0
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Estimation of P/R (contd)
Calibrate to observed diurnal variationin P(t) using estimated Ka
Delta Method (Chapra and DiToro, 1979)
Correlate with chlorophyll-a
aChlP = 25.0
aChlR = 025.0
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Expanded Streeter-Phelps Eqs*
h
RP
h
S
ccccKLKLKd
dc
u
B
saNNr
)(
)()(
+++=
l
CBOD NBOD* Reaeration Lat Inflow SOD P/R
[ ] { }])(exp[1)()(exp)(
+
+++=
rr
ro KK
L
KLL
l
])(exp[)( vKLL NNoN +=
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Expanded S-P (contd)
{ }
{ }
{ }
{ })])(exp[1)(
)/(
])(exp[])(exp[)(
])(exp[1))((
])(exp[])(exp[)(
])(exp[
++
++
+
++++
++
+
++=
a
a
B
aN
Na
NoN
a
ar
d
ar
r
o
ra
d
ao
KK
HSRP
KKKK
LK
KKK
LK
KKK
LL
KK
K
K
l
l
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Expanded S-P (contd)Lateral BOD sources w/o significant inflow
ALqLrd
ll= 0= ux/=
[ ]
{ }
[ ] [ ]
[ ])/exp(1
)/exp()/exp()(
)/exp(1
)/exp()/exp()(
)/exp()/exp()/exp(
uxK
K
HSRP
uxKuxKKKK
LKuxKKKLK
uxKuxKKK
LK
uxKuxKKK
LKuxK
a
a
B
ar
rra
rdd
a
ar
rdd
aN
Na
NoN
arra
od
ao
+
+
+=
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Artificial ReaerationOpen water bodies (direct transfer,turnover, fountains)
Hydropower stations (inject to turbine
intake, downstream aeration)
Recommended