Forge Pond project Continued discussion Update questions EPA - - PDF document

CEE 577 Lecture #9 10/23/2017 1

Lecture #9 (Diffusion) Chapra L8

David A. Reckhow CEE 577 #9 1

Updated: 23 October 2017

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Forge Pond project

 Continued discussion

 Update  questions

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EPA 305(b) listing for Forge Pond

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Liquid Water Transport

 Advection: unidirectional flow  Diffusion: movement of mass that is not unidirectional

flow; usually movement in an unorganized fashion

 Dispersion  Eddy Diffusion  Molecular Diffusion

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Mass Diffusion

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T=0 T=1 T=2 T=large V1, c1 V2, c2

 

1 2 1 1

c c D dt dc V   

Bulk Diffusion (m2/yr) Concentration Gradient Incorporates molecular movement and interfacial area

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Fick’s First Law

 Mass flux is proportional to the concentration gradient

and a diffusion coefficient

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dx dc D J x  

Bulk Diffusion Coefficient

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V1, c1 V2, c2

c

JA dt dc V  

1 1



1 2

c c dx dc  

dx dc D J x  

) (

1 2 1 1

c c DA dt dc V

c

  

And combining all three: D’ The mixing length



c

EA E  

Similar for Eddy Diffusion

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Dispersion

 Differences in velocities of parallel flow paths

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Embayment Model

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Main Lake (1) Bay (2)

) (

1 2 2 2 1 1 1 1 1 1 1 1

c c E c Q c V k c Q W dt dc V        ) (

2 1 2 2 2 2 2 2 2 2

c c E c V k c Q W dt dc V       W1 W2 Q2 Q1

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Embayment Model with a Conservative Substance

 Conservative substances (s) are those that do not

undergo degradation, thus k=0

 The mass balance on the bay (2), then becomes:

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) (

2 1 2 2 2 2 2

s s E s Q W dt ds V     

1 2 2 2 2

s s s Q W E    

And solving for the bulk diffusion coefficient:

Map of Huron/Saginaw System

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Lake Huron

Saginaw Bay

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Parameters for Saginaw Bay

Parameter Symbol Value

Units

Volume V2 8

109 m3

Depth H2 5.81

m

Surface Area A2 1,376

106 m2

Outflow Q2 7

109 m3/yr

Chloride Conc. s2 15.2

mg/L

Chloride Loading Ws2 0.353

1012 g/yr

Phosphorus Loading Wp2 1.42

1012 mg/yr

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Parameters for Lake Huron

Parameter Symbol Value

Units

Volume V1 3507

109 m3

Depth H1 60.3

m

Surface Area A1 58,194

106 m2

Outflow Q1 161

109 m3/yr

Chloride Conc. S1 5.4

mg/L

Chloride Loading Ws1 ~0

1012 g/yr

Phosphorus Loading Wp1 4.05

1012 mg/yr

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CEE 577 Lecture #9 10/23/2017 7

Chloride Tracer Model

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1 2 2 2 2

s s s Q W E    

 

 

yr m x x x E / 10 2 . 25 4 . 5 2 . 15 2 . 15 10 7 10 353 .

3 9 9 12

    



c

EA E  

 

s cm x yr m x m x m x x A E E

c

/ 10 7 . 4 / 10 48 . 1 10 17 . 10 10 10 52 . 2

2 5 2 9 2 6 3 9

     

 To next lecture

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