1. Subsurface Fate and Transport of Contaminants

2. Contaminant Transport
Describes mechanisms to move contaminants from source to receptor
Important to calculate dose in risk analysis process

3. Solutes in saturated media can be transported by three mechanisms
Diffusion
Advection
Dispersion

4. Diffusion
Diffusion - spreading of solute due to concentration gradient, minor at most GW velocity
Diffusion controlled mass transport occurs if the concentration of a species is greater in one location than an adjacent location (concentration gradient)
Fick’s second law used to calculate flux

5. Advection
Advection - transport with bulk flow of groundwater at average velocity of GW.
Mass added to stream tubes remains in stream tubes, other processes move mass between stream tubes (diffusion, dispersion,
Dominant transport mechanism

6. Dispersion
Mechanical Dispersion - mechanical mixing due to the velocity variations as groundwater moves through tortuous pathways
Solute transport by advection and dispersion requires flow of groundwater to carry solutes along with liquid flow
At most fluid flows advection and dispersion dominates over diffusion

7. Transformation Processes
Sorption
Radioactive decade
Chemical transformation
Volatilization
Colloid transport
Biotic

8. Contaminant Transport
Advection
Conc.
Sorption, Dispersion
Sorption, Dispersion
And Degradation
Time

9. Mathematics Change in mass storage with time =
Mass inflow rate - mass outflow rate + mass production rate

10. Mass Balance qx dz dy dx

11. Mass Balance - (1-Dimensional)
Change in mass storage with time =
Mass in/out due to advection, dispersion, diffusion
and sources and sinks

12. Mass Balance (1-Dimensional)
Divide by xyz and let x > 0
F = mass flux rate of contaminant due to
advection, dispersion, and diffusion, mass area-1 time-1
r = source or sink term

13. Advective Groundwater Flow
Q = vA

14. Groundwater Flow

15. Source or sink terms R (mass/vol-time): Biotic Radioactive Decay
Sorption

16. Solution Requires Definition of parameters
Suitable numerical or analytical solution
Boundary and initial conditions
Analytical solution possible if 1-D, source or sink terms linear, boundary and initial conditions known

17. Solution to Mass Balance Including Advection and Dispersion Only
C = the concentration at time t and distance x
Co = original concentration
L = distance
t = time
erfc = complimentary error function
DL = dispersion coefficient
vx = linear velocity

18. Solution to Mass Balance Including Diffusion Only
C = the concentration at time t and distance x
Co = original concentration
x = distance
t = time
erfc = complimentary error function
D* = effective diffusion coefficient

19. Example – Diffusion Process
Assume Landfill A contains Na+1 = 10,000 mg/l and Ca+2 = 5,000 mg/l and assume Landfill B contains Fe+2 = 750 mg/l and Cr+3 = 600 mg/l. Landfill A has a 6 m clay liner under the waste and Landfill B has 3 m of clay under the waste. Assuming diffusion is the only process affecting solute transport, which of the four species will break through the clay layer in either of the landfills first? How long will that take?

20. Given Given: Effective diffusion coefficients D*: Species D* (m2/sec)
Na+1
1.33E-09
Ca+2
7.05E-10
Fe2+
7.19E-10
Cr3+
5.94E-10

21. Solution
The erfc(z)* function has non-zero values only at z values less than 3. To solve this problem assume times and calculate at edge of clay layer for each case and keep changing the time until z has a value of 3. WHY?
*Z=x/2((D*t)^0.5)

22. Assume Time is 5 years Z > 3 Species Clay layer (m) Conc (mg/l)
D* (m2/sec)
Z=x/2((D*t)^0.5)
Na+1 6
10000
1.33E-09
Ca+2
5000
7.05E-10
Fe2+ 3
750
7.19E-10
Cr3+
600
5.94E-10
Z > 3

23. Increase Time to 10 Years Z > 3 Species Clay layer (m)
Concentration (mg/l)
D* (m2/sec)
Z=x/2((D*t)^0.5)
Na+1 6
10000
1.33E-09
Ca+2
5000
7.05E-10
Fe2+ 3
750
7.19E-10
Cr3+
600
5.94E-10
Z > 3

24. Increase Time to 12 Years Fe+2 will break through first Species
Clay layer (m)
Concentration (mg/l)
D* (m2/sec)
Z=x/2((D*t)^0.5)
Na+1 6
10000
1.33E-09
Ca+2
5000
7.05E-10
Fe2+ 3
750
7.19E-10
Cr3+
600
5.94E-10
Fe+2 will break through first

25. Decrease Time to 11 Years Fe+2 will break through ~ 11 years
Species
Clay layer (m)
Concentration (mg/l)
D* (m2/sec)
Z=x/2((D*t)^0.5)
Na+1 6
10000
1.33E-09
Ca+2
5000
7.05E-10
Fe2+ 3
750
7.19E-10
Cr3+
600
5.94E-10
Fe+2 will break through ~ 11 years

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Last updated April 12, 2017 by Dr. Reinhart