Lec12

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