SLIDE 1
Lecture #9 (Diffusion) Chapra L8
David A. Reckhow CEE 577 #9 1
Updated: 23 October 2017
Print version
Forge Pond project
Continued discussion
Update questions
David A. Reckhow CEE 577 #9 2
EPA 305(b) listing for Forge Pond
Lecture #9 (Diffusion) Chapra L8 David A. Reckhow CEE 577 #9 1 - - PowerPoint PPT Presentation
Lecture #9 (Diffusion) Chapra L8 David A. Reckhow CEE 577 #9 1 - - PowerPoint PPT Presentation
Updated: 23 October 2017 Print version Lecture #9 (Diffusion) Chapra L8 David A. Reckhow CEE 577 #9 1 Forge Pond project Continued discussion Update questions EPA 305(b) listing for Forge Pond David A. Reckhow CEE 577 #9 2
SLIDE 2
SLIDE 3
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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SLIDE 4
Mass Diffusion
David A. Reckhow CEE 577 #9 4
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
SLIDE 5
Fick’s First Law
Mass flux is proportional to the concentration gradient
and a diffusion coefficient
David A. Reckhow CEE 577 #9 5
dx dc D J x − =
SLIDE 6
Bulk Diffusion Coefficient
David A. Reckhow CEE 577 #9 6
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
SLIDE 7
Dispersion
Differences in velocities of parallel flow paths
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SLIDE 8
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
SLIDE 9
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:
David A. Reckhow CEE 577 #9 9
) (
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:
SLIDE 10
Map of Huron/Saginaw System
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Lake Huron
Saginaw Bay
SLIDE 11
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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SLIDE 12
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
David A. Reckhow CEE 577 #9 12
SLIDE 13
Chloride Tracer Model
David A. Reckhow CEE 577 #9 13
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
= = = ′ =
SLIDE 14
To next lecture
David A. Reckhow CEE 577 #9 14