1. Final Project
I. Calibration
Drawdown Prediction
Particle Tracking
Presentation of Results

2. Final Project

3. Particle Tracking

4. FLOW NETS
The streamfunction, 
(from Hornberger et al., 1998)

5. A flow net consists of equipotential lines and streamlines.
(from Hornberger et al., 1998)
A flow net consists of equipotential lines and streamlines.

6. (used to trace flow lines)
Particle Tracking
(used to trace flow lines)
distance = velocity x time

7. Particle Tracking (used to trace flow lines) Groundwater flow model
MODFLOW
Note: need to input
effective porosity, ne
Darcy’s law
v = KI / ne
Particle tracking code
MODPATH,
Path3D

8. Particle tracking simulates advection of
contaminant “particles”.
Transport models (e.g., MT3D) simulate
advection, dispersion and chemical reactions.
Retardation caused by linear adsorption reactions
can be simulated using particle tracking, since
the velocity can be adjusted: vc = v/Rd
Rd is the retardation coefficient.

9. Steps in Particle Tracking
Need to interpolate velocities from nodal
point values since particle tracking is done
in a continuous coordinate system.
Need to track the movement of the particles
in the computed velocity field.

10. Interpolation Schemes
Linear (MODPATH, Path3D)
Bilinear
Reverse distance (FLOWPATH)

11. Tracking
distance = velocity x time
dx/dt = vx
dx = vx dt

12. Tracking Schemes Semianalytical (MODPATH) Euler (FLOWPATH)
Runge Kutta (Path3D)
Taylor Series (WHPA)

13. Profile Models
(e.g., the Toth Problem) z
h = c x + zo x z x

14. Profile Models The profile should be oriented parallel to flow.
Axisymmetric profiles (useful to simulate pumping)
Slice orientation and layer orientation

15. Layer Orientation Profile – unconfined aquifer 2D confined aquifer
for homogeneous, anisotropic aquifers
 We can simulate a profile by
using 1 confined layer in MODFLOW.

16. Problem 6.1a
Specified head cells
Active cells
MODFLOW computes fluxes between specified head cells and active cells.
MODFLOW does not compute fluxes between specified head cells; you need to compute those manually.

17. active cells with injection wells
Qp= Q1 + Q2 Q1 Q2
active cells with injection wells
Active cells
In problem 6.1b, you use injection wells to simulate
recharge to the profile. Calculate the injection rate
as the net flux into each of the cells in the top row.

18. Problem Set 6 illustrates:
Use of a confined MODFLOW layer to simulate an
unconfined aquifer in profile view.
Procedure for switching from specified head
to specified flux boundary conditions.

19. Problems dealing with the water table
In a profile model or a 3D model, the water table
typically forms the upper boundary of the model.
In transient problems the water table fluctuates and the
position of the water table is unknown.
MODFLOW
utilizes the Dupuit assumptions
to calculate the water table in unconfined layers.
Recharge typically occurs to the top active cell.

20. Alternatives to MODFLOW for water table problems
Finite element codes with deformable elements allow
the element to deform as the water table moves.
Codes that incorporate the unsaturated zone.

21. Models that incorporate the unsaturated zone
solve for the position of the water table by locating
where pressure head (hp) equals zero.
h = z + hp = z + p/g
Total head = elevation head + pressure head
2D USGS codes for flow in partially saturated media
(unsaturated zone and saturated zone)
VS2DTI (for water and solutes)
VS2DHI (for water and heat)
Other codes include: SUTRA, HYDRUS and many others.

22. Example problem run with VS2D Infiltration into a cross section
Possible seepage face
Example problem
run with VS2D
Infiltration into
a cross section
with a slope
low K
layer
perched water
Pressure
head = 0
defines
the water
table

23. Flow through
a dam