lec12
TRANSCRIPT
Lecture 12
Introduction to Environmental Introduction to Environmental EngineeringEngineering
Effect of Organic Wastes on Stream Ecosystems Streeter-Phelps Model – DO sag curve Streeter-Phelps Model – DO sag curve
Many equations and computer programs are available Many equations and computer programs are available today to describe the quality of water in streams, rivers today to describe the quality of water in streams, rivers and lakesand lakes
The most prevalent is the Streeter Phelps equation. The most prevalent is the Streeter Phelps equation. Addition of wastewater (BOD) typically causes a slow Addition of wastewater (BOD) typically causes a slow
decrease in Odecrease in O22, followed by a gradual increase close to , followed by a gradual increase close to
the dissolved oxygen (D.O.) saturation concentrationthe dissolved oxygen (D.O.) saturation concentration
Streeter-Phelps Model
Assumptions of the ModelAssumptions of the Model stream is an ideal plug flow reactorstream is an ideal plug flow reactor steady-state flow and BOD and DO reaction steady-state flow and BOD and DO reaction
conditionsconditions The only reactions of interest are BOD The only reactions of interest are BOD
exertion and transfer of oxygen from air to exertion and transfer of oxygen from air to water across air-water interfacewater across air-water interface
Streeter-Phelps Model
Mass Balance for the ModelMass Balance for the Model Not a Steady-state situationNot a Steady-state situationrate Orate O2 2 accum. = rate Oaccum. = rate O22 in – rate O in – rate O22 out + prod. – cons. out + prod. – cons.
rate Orate O2 2 accum. = rate Oaccum. = rate O22 in – 0 + 0 – rate O in – 0 + 0 – rate O22 cons. cons.
Both reoxygenation and deoxygenation are 1Both reoxygenation and deoxygenation are 1stst order order
rate of deoxygenation = -krate of deoxygenation = -k11CC
kk11= deoxygenation constant, function of waste type and = deoxygenation constant, function of waste type and
temperaturetemperature
Streeter-Phelps Model
rate of reoxygenation = krate of reoxygenation = k22DD
D = deficit in D.O. or difference between D = deficit in D.O. or difference between saturation and current D.O.saturation and current D.O.
kk22 = reoxygenation constant = reoxygenation constant
2
3
21
)20(21
2
025.19.3
H
vk
T
Streeter-Phelps Model
WhereWhere T = temperature of water, T = temperature of water, ººCC H= average depth of flow, mH= average depth of flow, m v = mean stream velocity, m/sv = mean stream velocity, m/s
Oxygen DeficitOxygen Deficit D = S – CD = S – C
D.O. deficit = saturation D.O. – D.O. in the waterD.O. deficit = saturation D.O. – D.O. in the water
Streeter-Phelps Model
Streeter-Phelps Model
Deoxygenation rate is equivalent to BOD of Deoxygenation rate is equivalent to BOD of wastewaste
rro o = k= k11 L Ltt
LLtt = L = Looee-Kt-Kt
LLoo or L = ultimate BOD of the wastewater and or L = ultimate BOD of the wastewater and
stream water mixturestream water mixture
Streeter-Phelps Model
In terms of the deficit with timeIn terms of the deficit with time
tkLez
Dkzkdt
dD
1
21
Streeter-Phelps Model
Substiting and integrating yields the following Substiting and integrating yields the following equationsequations
tko
tktko eDeekk
LkD 221 )(
12
1
tkoc
tko
eLk
kD
DkeLkdt
dD
1
1
2
1
21 0
o
oc Lk
kkD
k
k
kkt
1
12
1
2
12
)(1ln
1
Streeter-Phelps Model
Example:Example: Wastewater mixes with a river resulting in aWastewater mixes with a river resulting in a
BOD = 10.9 mg/L, BOD = 10.9 mg/L, DO = 7.6 mg/LDO = 7.6 mg/LThe mixture has a temp. = 20 The mixture has a temp. = 20 CCDeoxygenation const.= 0.2 dayDeoxygenation const.= 0.2 day-1-1
Average flow = 0.3 m/s, Average flow = 0.3 m/s, Average depth = 3.0 mAverage depth = 3.0 mDO saturated = 9.1 mg/LDO saturated = 9.1 mg/L Find the time and distance downstream at which the Find the time and distance downstream at which the
oxygen deficit is a maximum?oxygen deficit is a maximum? Find the minimum value of DO?Find the minimum value of DO?
Streeter-Phelps Model
Initial Deficit Initial Deficit
DDoo = 9.1 – 7.6 = 1.5 mg/L = 9.1 – 7.6 = 1.5 mg/L
Estimate the reaeration constant Estimate the reaeration constant
12/3
21
20202/1
2/3
2/1
2 day 14.0)0.3(
025.1)/3.0(9.39.3
m
sm
H
vk
Streeter-Phelps Model
Calculate the time at which the maximum deficit Calculate the time at which the maximum deficit is reached, with tis reached, with t
cc::
mdaysdayssmvtx
days
Lk
kkDO
k
k
kkt
cc
o
oc
300,6967.2/400,86/3.0
67.2
9.102.0
)2.041.0(5.11
2.0
41.0ln
)2.041.0(
1
)(1ln
1
1
12
1
2
12
Streeter-Phelps Model
The maximum DO deficit is:
mg/L 1.3
e mg/L) 9.10(41.0
2.0 ))(2.67days(0.2day
2
1
1
1
tkoc eL
k
kD