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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)