7 Dissolved Oxygen
Introduction
Oxygen Saturation
Biochemical Oxygen Demand
Reaeration
Streeter-Phelps Equation
Nitrification
Sediment Oxygen Demand
Photosynthesis and Respiration
Expanded Streeter-Phelps Equation
Artificial Re-aeration
Dissolved Oxygen
Important for aquatic health
„
DO standards typically 5 to 6 mg/L
Redox chemistry
„
„
Affects release of chemicals bound to
sediments
Anaerobic conditions => H2S
Oxygen Saturation
c s (T , S ) = exp{−1.3934411x10 2 + 1.575701x10 5 /(T + 273.15)
− 6.642308 x10 7 /(T + 273.15) 2 + 1.243800 x1010 /(T + 273.15) 3
− 8.621949 x1011 /(T + 273.15) 4 − S [1.7674 x10 − 2 − 10.754 /(T + 273.15)
+ 2.1407 x10 3 /(T + 273.15) 2 ]}
⎡ (1 − p wv / p)(1 − θp) ⎤
c s (T , S , p) = c s (T , S ) ⎢
⎥
⎣ (1 − p wv )(1 − θ ) ⎦
p wv = exp[11.8575 − 3.8407 x10 3 /(T + 273.15) − 2.16961x10 5 /(T + 273.15) 2 ]
θ = 0.000975 − 1.426 x10 −5 T + 6.436 x10 −8 T 2
Standard Methods (1995)
Cs (T, S, p)
T=0o
10
20
30
14.6
12.9
11.4
11.3
19.9
8.8
9.1
8.0
7.1
7.6
6.7
5.9
S = 0 PSU
S = 10
14.6
13.6
11.3
10.6
9.1
8.6
7.7
7.2
S = 35
11.4
9.0
7.4
6.2
Effect of p (S=0)
p = 1 atm (z=0)
p = 0.89 (1000m)
p = 0.79 (2000m)
Effect of S (p=0)
Processes affecting DO
Re-aeration (+/-)
BOD (-)
P(+)/R(-)
SOD (-)
Inflow
(+/-)
Biochemical Oxygen Demand
Organic wastes are food for
microorganisms
„
„
„
Oxygen consumed in process
Self-purification (bio-degradation) in
natural waters
Biological stage of WWT
Other chemicals exert oxygen demand
„
„
C2H6O2
NaHSO3
Theoretical Oxygen Demand
C n H a Ob N c Pd + (n +
a b 3c 5d
a 3c 3d
− − + )O2 = nCO2 + ( − − ) H 2 O + cNH 3
4 2 4
4
2 2
2
+ dH 3 PO4
3
−
NH 3 + O2 = NO2 + H + + H 2 O
2
NO2
−
1
−
+ O2 = NO3
2
Carbonaceous BOD (CBOD)
Nitrogenous BOD (NBOD)
Issues
„
„
„
Different types of wastes
Some not labile
Rates vary (nitrification)
Practical Measures of Oxygen Demand
BOD
„
„
Traditional water quality measure
Cumbersome and time-consuming
COD
„
Easy to measure
TOC
„
State variable in WQ models
Traditional BOD
Practical measure of O2 “debt”
„
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
BOD Jar Test
Precautions
„
„
„
„
„
„
No photosynthesis
Enough initial O2
Adequate dilution (WW)
Enough microorganisms
Non toxic sample
Only carbonaceous BOD
[DO]
y(t)
y5 = BOD5
yu =
BODu
0
time
0
y = L(1 − e
5 days
− K1t
)
L5
L=
1 − e −5 K1
K 1 = K 1 (20)θ T − 20
K 1 (20) ~ 0.1 − 0.5d −1 ;θ ~ 1.047
In rivers
Kr = Kd + Ks
K s = ws / h
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
Stream Reaeration
cs
zδw
H
h
c
F=kL(cs-c)
Water side control
Flux F ~ DO deficit
Piston velocity [LT-1]
„
kL ~ kw
Reaeration rate [T-1]
„
δ = zw
Ka = K2 = kw/h
Theories
„
„
Stagnant Film
Surface Renewal
Stream Reaeration
Stagnant Film
cs
zδw
H
h
„
kL = D/zw
Surface Renewal
c
F=kL(cs-c)
„
„
„
„
„
zw ~ (Dt)0.5
t ~ h2/Ez ~ h/u
zw ~ (Dh/u)0.5
kL ~ (Du/h)0.5
Ka ~ (Du/h3)0.5
Stream Reaeration Formulae
50
40
30
u in m/s, h in m, T=20o
O'Connor
.05
0.1
3.93u 0.5
Ka =
h1.5
Ka =
5.0u
h1.67
5.3u 0.67
Ka =
h1.85
O’ConnorDobbins
(1958)
Churchill et
al. (1962
Owens &
Gibbs
(1964)
Kovar, 1976
Figure by MIT OCW.
Depth (ft.)
20
10
8
6
5
4
3
0.5
Churchill
1
5
10
2
5
1
0.8
0.6
0.5
0.4
0.3
10
50
0.1
100
0.2 0.3 0.4 0.6 0.8 1
Velocity (ft./sec.)
Owens
2
3 4 5 6
Other formulations
Rate of Energy Dissipation (Tsivoglou
LS
∆H
& Wallace, 1972) T = L / u = uS
Melching and Flores (1999)
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
Q < 0.56
88(uS)0.313H-0.353
0.59
Q > 0.56
142(uS)0.333H-0.66W-
0.60
Channel Control
0.243
1-D Analysis
(Streeter-Phelps, 1925)
Continuity
∂A ∂
+ ( Au ) = q l
∂t ∂x
Mass Transport
∂
∂c
∂
∂
( Ac ) + ( Auc ) = ( E L A ) + A(ri + re )
∂x
∂x
∂t
∂x
BOD (c = L)
ri = − K r L
re = ql Ll / A
ql ( Ll − L)
dL
u
= −K r L +
A
dx
x
dx
τ =∫
u ( x)
0
dL
= − K r L + ν ( Ll − L)
dτ
L(τ ) = Lo exp[− ( K r + ν )τ ] +
νLl
(K r + ν )
{1 − exp[−( K r + ν )τ ]}
DO (c = c)
ri = − K d L
re = ql cl / A + K a (cs − c)
u
q (c − c )
dc
= − K d L + K a (c s − c ) + l l
A
dx
dc
= − K r L + K a (c s − c ) + ν (c l − c )
dτ
∆ = cs − c
K dνLl
{1 − exp[−( K a + v)τ ]}
∆(τ ) = ∆ o exp[−( K a + υ )τ ] +
( K r + v)( K a + v)
+
⎡
Kd
νLl ⎤
L
−
⎢ o
⎥{exp[−( K r + v)τ ] − exp[−( K a + ν )τ ]}
(K a − K r ) ⎣
(K r + ν ) ⎦
Streeter-Phelps-additional comments
cmin and xmin can be calculated
analytically
Multiple sources handled by
superposition or re-initialization at
stream confluences
Procedures for anoxic conditions
Neglect of longitudinal dispersion?
Additional terms
Nitrification
C n H a Ob N c Pd + (n +
a b 3c 5d
a 3c 3d
− − + )O2 = nCO2 + ( − − ) H 2 O + cNH 3
4 2 4
4
2 2
2
+ dH 3 PO4
(2)(32/14) = 4.57
3
−
NH 3 + O2 = NO2 + H + + H 2 O
2
1
−
−
NO2 + O2 = NO3
2
(0.5)(32/14) = 1.14
Theoretical (upper bound) NBOD
NBOD = 4.57(Org − N + NH 3 − N ) + 1.14 NO2 − N
NBOD ≅ 4.57TKN
TKN = total Kjeldalh nitrogen
[DO]
CBOD
NBOD
0
0
time
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 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)
SOD (cont’d)
Measured
„
in situ with benthic flux chambers
„
in lab with core
Calculated from organic carbon content
of settled solids
Calibrated from oxygen model
Complication: extraneous sources
Benthic Flux Chambers
Zebra Mussels
Algal Photosynthesis and
Respiration
Photosynthesis (primary production) =>
fixation of CO2 by autotrophic bacteria
Reverse is respiration
6CO2 + 6H2O Ù C6H12O6 + 6O2
P/R (cont’d)
Limitations on primary production:
„
„
„
Light
Temperature
Nutrients
Time and space dependent
„
„
Diurnal variation
Depth variation
P(t)
Pm
Pa
f
0
2f
Pa =
Pm
24π
24 h
f = photoperiod (hrs)
t
13
Curve A
12
Wyman Creek, Calif
August 6, 1962
Average 10.1 MG/L
Dissolved Oxygen MG/L
11
10
9
River Ivel, England
May 31, 1959
Average 10.4 MG/L
Curve B
8
7
0600
0900
1200N
1500
1800
2100
2400
0300
0600
Hours
Figure by MIT OCW.
EPA (1985)
Estimation of P/R
In situ measurements w/ Light & Dark
Bottles
⎡ c o − ct ⎤
R=⎢
− Kd L
⎥
⎣ t ⎦ dark
mg/L-d; L = ultimate
BOD of filtered sample
⎡ ct − c o ⎤
⎡ ct − c o ⎤
−⎢
P (t ) = ⎢
⎥
⎥
⎣ t ⎦ light ⎣ t ⎦ dark
P(t) is averaged over time t. t = 24 hrs => Pa;
t< 24 h => fit to diurnal variation using f
Pm
Pa
0
f
24 h
t
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
P = 0.25Chl − a
R = 0.025Chl − a
Expanded Streeter-Phelps Eqs*
S B ( P − R)
dc
u
= − K r L − K N L N + K a ( c s − c ) + ν (c l − c ) −
+
dτ
h
h
CBOD NBOD* Reaeration Lat Inflow SOD
L(τ ) = Lo exp[− ( K r + ν )τ ] +
νLl
(K r +ν )
L N (τ ) = L No exp[−( K N + v)τ ]
P/R
{1 − exp[−( K r + ν )τ ]}
Expanded S-P (cont’d)
∆ = ∆ o exp[−( K a + ν )τ ] +
⎡
Kd
νLl ⎤
⎢ Lo −
⎥{exp[−( K r + ν )τ ] − exp[−( K a + ν )τ ]}
(K a − K r ) ⎣
Kr +ν ⎦
K dνLl
{1 − exp[−( K a + ν )τ ]}
+
( K r + ν )( K a + ν )
K N L No
{exp[−( K N + ν )τ ] − exp[−( K a + ν )τ ]}
+
(K a − K N )
(P − R − S B / H )
{1 − exp[−( K a + ν )τ )]}
−
(K a + ν )
Expanded S-P (cont’d)
Lateral BOD sources w/o significant inflow
q l Ll
Lrd =
A
υ =0
τ = x/u
⎧ K L
⎫
∆ = ∆ o exp(− K a x / u ) + ⎨ d o [exp(− K r x / u ) − exp(− K a x / u )]⎬
⎩Ka − Kr
⎭
K N L No
{exp(− K N x / u ) − exp(− K a x / u )}
+
(K a − K N )
⎧ K d Lrd
⎫
K d Lrd
+
[1 − exp(− K a x / u )] − ⎨
⎬[exp(− K r x / u ) − exp( K a x / u )]
Kr Ka
−
(
K
K
)
K
r
r ⎭
⎩ a
⎛ P − R − SB H ⎞
⎟⎟[1 − exp(− K a x / u )]
− ⎜⎜
K
a
⎝
⎠
Artificial Reaeration
Open water bodies (direct transfer,
turnover, fountains)
Hydropower stations (inject to turbine
intake, downstream aeration)