Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in...

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Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model
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Page 1: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Source Terms

• Constant Concentration

• Injection Well

• Recharge

May be introduced at the boundary or inthe interior of the model

Page 2: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Q

Constant Concentration(Z&B, p. 283)

cs

at boundary

e.g., NAPL source area

Page 3: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Injection Well

Qcs

well

Page 4: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Recharge

R, cs

Mass Flux = R (x y) cs

Page 5: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Problem Set #3Source Terms and Chemical Reactions

• Constant Concentration

• Injection Well

• Recharge

• retardation• 1st order decay

Page 6: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Problem Set #3Two Layers

This screen shows aconstant concentrationsource. Contours ofhead are also shown.

Confined layers

Page 7: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Note the water table

Flow field for anunconfined upper layerwith areal recharge anda recharge source cell.

Page 8: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Problem Set #3

0.0

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Time

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Parts 1 and 2: Producebreakthrough curves underdifferent assumptions aboutthe source term and chemicalreactions.

Page 9: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Problem Set #3 – Part 3 - Remediation

TVD Solution

Numerical error causedby high Peclet number

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Page 10: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

0.0

12.0

24.0

36.0

48.0

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0.0 0.6 1.2 1.8 2.4 3.0

Time

Layer 2

Concentration vs. Time at pumping well

Central Finite Difference Solution

Page 11: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Problem Set #3 – Part 3 - Remediation

TVD Solution

Numerical error causedby high Peclet number

0.0

10.0

20.0

30.0

40.0

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time

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Page 12: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Courant Numberx

tvCr

Cr < 1

Peclet Numberx

D

xvPe

Pe < 4

Page 13: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

Pumping well isrepresented by 4 nodes

50 m grid

Page 14: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

0.0

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Time (years)

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100 m grid spacingPeclet number = 5

50 m grid spacingupper left node in the pumping complexPeclet number = 2.5

TVD solution

Page 15: Source Terms Constant Concentration Injection Well Recharge May be introduced at the boundary or in the interior of the model.

100 m grid 50 m grid – near centerof pumping compex

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Time

Concentration vs. Time at pumping well

0

10

20

30

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0.0 0.6 1.2 1.8 2.4 3.0

Time

Concentration vs. Time at pumping well

TVD Solution