7 Dissolved Oxygen
Introduction Oxygen SaturationBiochemical Oxygen DemandReaerationStreeter-Phelps EquationNitrificationSediment Oxygen DemandPhotosynthesis and RespirationExpanded Streeter-Phelps EquationArtificial Re-aeration
Dissolved Oxygen
Important for aquatic healthDO standards typically 5 to 6 mg/L
Redox chemistryAffects release of chemicals bound to sedimentsAnaerobic conditions => H2S
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
++
+−−+−
+++−
++−=
−
TxTxSTx
TxTx
TxxSTcs
⎥⎦
⎤⎢⎣
⎡−−−−
=)1)(1(
)1)(/1(),(),,(
θθ
wv
wvss p
pppSTcpSTc
])15.273/(1016961.2)15.273/(108407.38575.11exp[ 253 +−+−= TxTxpwv
285 10436.610426.1000975.0 TxTx −− +−=θ
Standard Methods (1995)
Cs (T, S, p)
T=0o 10 20 30Effect of p (S=0)
p = 1 atm (z=0) 14.6 11.3 9.1 7.6p = 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 7.7S = 10 13.6 10.6 8.6 7.2S = 35 11.4 9.0 7.4 6.2
Processes affecting DO
BOD (-)
Re-aeration (+/-)
P(+)/R(-)Inflow (+/-)
SOD (-)
Biochemical Oxygen Demand
Organic wastes are food for microorganisms
Oxygen consumed in processSelf-purification (bio-degradation) in natural watersBiological stage of WWT
Other chemicals exert oxygen demandC2H6O2
NaHSO3
Theoretical Oxygen Demand
43
3222 )2
323
2()
45
43
24(
POdH
cNHOHdcanCOOdcbanPNOHC dcban
+
+−−+=+−−++
OHHNOONH 2223 23
++=+ +−
−− =+ 322 21 NOONO
Carbonaceous BOD (CBOD)
Nitrogenous BOD (NBOD)
IssuesDifferent types of wastesSome not labileRates vary (nitrification)
Practical Measures of Oxygen Demand
BODTraditional water quality measureCumbersome and time-consuming
CODEasy to measure
TOCState variable in WQ models
Traditional BOD
Practical measure of O2 “debt”How much DO would decrease due to respiration of organic wastes
BOD Jar TestObserve the decline of DO over time (e.g. 5 days)Extrapolate to “ultimate” demandUsed for wastewater and natural waters
BOD Jar Test
PrecautionsNo photosynthesisEnough initial O2
Adequate dilution (WW)Enough microorganismsNon toxic sampleOnly carbonaceous BOD
[DO]
time
y5 = BOD5
yu = BODu
y(t)
0
0 5 days
)1( 1tKeLy −−=
155
1 KeL
L −−=
2011 )20( −= TKK θ
047.1~;5.01.0~)20( 11 θ−− dK
In rivers
sdr KKK +=
hwK ss /=
Other Measures of BOD
CODEasy to measureMuch quicker
TOCState variable in WQ models
Relationship to BOD (Metcalf & Eddy)BOD5/COD ~ 0.4 to 0.8BOD5/TOC ~1.0 to 1.6
Stream Reaeration
Water side controlFlux F ~ DO deficitPiston velocity [LT-1]
kL ~ kw
Reaeration rate [T-1]Ka = K2 = kw/h
TheoriesStagnant FilmSurface Renewal
H c
csδzw
h F=kL(cs-c)
δ = zw
Stream Reaeration
Stagnant FilmkL = D/zw
Surface Renewalzw ~ (Dt)0.5
t ~ h2/Ez ~ h/uzw ~ (Dh/u)0.5
kL ~ (Du/h)0.5
Ka ~ (Du/h3)0.5
H c F=kL(cs-c)
csδzw
h
Stream Reaeration Formulae
u in m/s, h in m, T=20o
5.1
5.093.3h
uKa =O’Connor-Dobbins (1958)
Churchill et al. (1962
Owens & Gibbs (1964)
67.1
0.5h
uKa =
85.1
67.03.5huKa =
Kovar, 1976
0.10.30.40.50.60.8
1
2Dep
th (f
t.)
34568
10
20
3040 O'Connor
Owens
.05
0.5
5
10
105
Churchill
50100
1
50
0.2
Velocity (ft./sec.)
0.3 0.4 0.6 0.8 1 2 3 4 5 6
0.1
Figure by MIT OCW.
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-
0.2430.60
1-D Analysis(Streeter-Phelps, 1925)
Continuity
lqAuxt
A=
∂∂
+∂∂ )(
Mass Transport
)()()()( eiL rrAxcAE
xAuc
xAc
t++
∂∂
∂∂
=∂∂
+∂∂
BOD (c = L)
LKr ri −=
ALqre /ll=
∫=x
xudx
0 )(τ
ALLq
LKdxdLu r
)( −+−= ll
)( LLLKddL
r −+−= lντ
[ ] { }])(exp[1)(
)(exp)( τνν
ντντ +−−
+++−= r
rro K
KL
KLL l
DO (c = c)LKr di −=
)(/ ccKAcqr sae −+= ll
Accq
ccKLKdxdcu sad
)()(
−+−+−= ll
)()( ccccKLKddc
sar −+−+−= lντ
ccs −=∆
]})(exp[])({exp[)()(
]})(exp[1{))((
])(exp[)(
τντν
ν
τν
τυτ
+−−+−⎥⎦
⎤⎢⎣
⎡+
−−
+
+−−++
++−∆=∆
arr
ora
d
aar
dao
KvKK
LL
KKK
vKvKvK
LKK
l
l
Streeter-Phelps-additional comments
cmin and xmin can be calculated analyticallyMultiple sources handled by superposition or re-initialization at stream confluencesProcedures for anoxic conditionsNeglect of longitudinal dispersion?Additional terms
Nitrification
(2)(32/14) = 4.5743
3222 )2
323
2()
45
43
24(
POdH
cNHOHdcanCOOdcbanPNOHC dcban
+
+−−+=+−−++
OHHNOONH 2223 23
++=+ +−
−− =+ 322 21 NOONO (0.5)(32/14) = 1.14
Theoretical (upper bound) NBOD
NNONNHNOrgNBOD −+−+−= 23 14.1)(57.4
TKN = total Kjeldalh nitrogenTKNNBOD 57.4≅
[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
Sediment Oxygen Demand (SOD)
“BOD in sediments”Significant downstream from outfalls or following algal bloomsSB = 0.1 to 1 g/m2-dre = SB/h
Oth order process0.1 to 1 mg/L-d (h = 1 m)
SOD (cont’d)
Measuredin situ with benthic flux chambersin lab with core
Calculated from organic carbon content of settled solids Calibrated from oxygen modelComplication: extraneous sources
Benthic Flux Chambers
Zebra Mussels
Algal Photosynthesis and Respiration
Photosynthesis (primary production) => fixation of CO2 by autotrophic bacteriaReverse is respiration6CO2 + 6H2O C6H12O6 + 6O2
P/R (cont’d)
Limitations on primary production:LightTemperatureNutrients
Time and space dependentDiurnal variationDepth variation
P(t)
Pm
Pa
24 hf0 t
ma PfPπ24
2= f = photoperiod (hrs)
EPA (1985)
Curve A
Curve B
Wyman Creek, CalifAugust 6, 1962
Average 10.1 MG/L
River Ivel, EnglandMay 31, 1959
Average 10.4 MG/L
7
8
9
10
11
12
13
0600 06000900 1200N 1500 1800 2100 2400 0300Hours
Dis
solv
ed O
xyge
n M
G/L
Figure by MIT OCW.
Estimation of P/R
In situ measurements w/ Light & Dark Bottles
LKt
ccR d
dark
to −⎥⎦⎤
⎢⎣⎡ −
= mg/L-d; L = ultimate BOD of filtered sample
dark
ot
light
ot
tcc
tcc
tP ⎥⎦⎤
⎢⎣⎡ −
−⎥⎦⎤
⎢⎣⎡ −
=)(
P(t) is averaged over time t. t = 24 hrs => Pa;
t< 24 h => fit to diurnal variation using f
Pm
t24 hf
Pa
0
Estimation of P/R (cont’d)
Calibrate to observed diurnal variation in P(t) using estimated Ka
“Delta” Method (Chapra and DiToro, 1979)
Correlate with chlorophyll-a
aChlP −= 25.0
aChlR −= 025.0
Expanded Streeter-Phelps Eqs*
hRP
hSccccKLKLK
ddcu B
saNNr)()()( −
+−−+−+−−= lντ
CBOD NBOD* Reaeration Lat Inflow SOD P/R
[ ] { }])(exp[1)(
)(exp)( τνν
ντντ +−−
+++−= r
rro K
KL
KLL l
])(exp[)( ττ vKLL NNoN +−=
Expanded S-P (cont’d)
{ }
{ }
{ }
{ })])(exp[1)(
)/(
])(exp[])(exp[)(
])(exp[1))((
])(exp[])(exp[)(
])(exp[
τνν
τντν
τννν
ν
τντνν
ν
τν
+−−+−−
−
+−−+−−
+
+−−++
+
+−−+−⎥⎦
⎤⎢⎣
⎡+
−−
++−∆=∆
aa
B
aNNa
NoN
aar
d
arr
ora
d
ao
KK
HSRP
KKKK
LK
KKKLK
KKK
LL
KKK
K
l
l
Expanded S-P (cont’d)Lateral BOD sources w/o significant inflow
ALq
Lrdll= 0=υ ux /=τ
[ ]
{ }
[ ] [ ]
[ ])/exp(1
)/exp()/exp()(
)/exp(1
)/exp()/exp()(
)/exp()/exp()/exp(
uxKK
HSRP
uxKuxKKKK
LKuxK
KKLK
uxKuxKKK
LK
uxKuxKKK
LKuxK
aa
B
arrra
rdda
ar
rdd
aNNa
NoN
arra
odao
−−⎟⎟⎠
⎞⎜⎜⎝
⎛ −−−
−−⎭⎬⎫
⎩⎨⎧
−−−−+
−−−−
+
⎭⎬⎫
⎩⎨⎧
−−−−
+−∆=∆
Artificial Reaeration
Open water bodies (direct transfer, turnover, fountains)Hydropower stations (inject to turbine intake, downstream aeration)