1. CONTAMINANT TRANSPORT MECHANISMS

2. ADVECTION PROCESSES Seepage velocity Advective flux
K hydraulic conductivity
n effective porosity
h hydraulic head
Advective flux h h1 h2 vx x1 x X2

3. DIFFUSION AND DISPERSION PROCESSES
Fick’s first law
fx = mass flux [M/L2/T]
Dd diffusion coefficient [L2/T]
h hydraulic head C C1 C2 fx x1 x X2

4. STOCHASTIC SIMULATION OF ADVECTION DIFFUSION PROCESSES
Use a large number of particles
Predict their position using
Determine their position and
distribution at t=tfinal
v=0.15 m/h
Dd= m2/h

5. ADVECTION DISPERSION EQUATION FOR SOLUTE TRANSPORTz
Mass conservation
Min-Mout=Accumulation dz y dx dy x

6. ADVECTION DISPERSION EQUATION FOR SOLUTE TRANSPORT (ctd)
Complete formulation
1-D formulation
Analytical solutions exist sometimes for both complete and 1-D formulations (e.g. BIOCHLOR)

7. ADSORPTION EFFECTS Sorption
association of a contaminant with a solid material
adsorption = association with the surface of the solid
absorption = association within the solid
S = f(C) the amount of absorbed contaminant is a function of C
S=KdCb
The transport equation becomes
If b=1 then

8. ADSORPTION AND FIRST-ORDER DECAY EFFECTS
Transport and adsorption
The combination of the two equations yields
where R is the retardation factor

9. ADSORPTION ISOTHERM Freundlich adsorption isotherm Consider a simple
S=KdCb
Consider a simple
experimental setup
L=1cm
Darcy flux q=0.27cm/h
Porosity n=0.3
Cin is measured and given
Cout is measured and given
q,Cin
q, Cout
L=1cm

10. ANALYTICAL SOLUTION (2-D CASE)
Hypotheses
no advection in y-direction
constant vx velocity
conservative substance
pulse source
Example
2 wells ( (3.7, 0.2), (4.9,-2.8) )
tracer is injected at (0,0)
determine vx, Dx, Dy,

11. ANALYTICAL SOLUTION (2-D CASE)
Use the Excel Solver (obviously) to minimize the differences between observations and measurements

12. WRAP-UP
The equations of contaminant transport may be derived from mass conservation principles
Diffusion, dispersion and advection have “discrete” meaning
Simple formulations and “optimization”/ calibration procedures may be used to determine physical parameters