1. Transport Modeling in Groundwater

2. Components of a Mathematical Model Governing Equation
Boundary Conditions
Initial conditions (for transient problems)
In full solute transport problems, we have two
mathematical models: one for flow and one for transport.
The governing equation for solute transport problems is the advection-dispersion equation.

3. Conceptual Model
A descriptive representation
of a groundwater system that incorporates an interpretation of the geological, hydrological, and geochemical conditions, including information about the boundaries of the problem domain.

4. Problem with contaminant source
Homogeneous, isotropic aquifer
Groundwater
divide
Groundwater
divide
Impermeable Rock
2D, steady state

5. Processes to model
Groundwater flow
Transport
Particle tracking: requires velocities and a particle tracking code calculate path lines
(b) Full solute transport: requires velocites and a solute transport model calculate concentrations

6. Processes we need to model
Groundwater flow
calculate both heads and flows (q)
Solute transport – requires information on flow (velocities)
calculate concentrations
v = q/n = K I / n
Requires a flow model and a solute transport model.

7. Groundwater flow is described by Darcy’s law.
This type of flow is known as advection.
Linear flow paths
assumed in Darcy’s law
True flow paths
The deviation of flow paths from
the linear Darcy paths is known
as dispersion.
Figures from Hornberger et al. (1998)

8. In addition to advection, we need to consider two other processes in transport problems.
Dispersion
Chemical reactions
Advection-dispersion equation
with chemical reaction terms.

9. Allows for multiple
chemical species
Dispersion
Chemical
Reactions
Advection
Source/sink term
Change in concentration
with time
is porosity;
D is dispersion coefficient;
v is velocity.

10. advection-dispersion equation
groundwater flow equation

11. advection-dispersion equation
groundwater flow equation

12. Flow Equation:
1D, transient flow; homogeneous, isotropic,
confined aquifer; no sink/source term
Transport Equation:
Uniform 1D flow; longitudinal dispersion;
No sink/source term; retardation

13. Flow Equation:
1D, transient flow; homogeneous, isotropic,
confined aquifer; no sink/source term
Transport Equation:
Uniform 1D flow; longitudinal dispersion;
No sink/source term; retardation

14. Models Parameters Initial Concentration: Page 224
Dispersion: Page 227/228