1. Boundary Conditions Sources and Sinks Based on Slides Prepared By
Eileen Poeter, Colorado School of Mines
Sources and Sinks

2. Types of Boundary Conditions
1) Specified Head: head is defined as a function of space and time
(could replace ABC, EFG)
Constant Head: a special case of specified head (ABC, EFG) 2) Specified Flow: could be recharge across (CD) or zero across (HI)
No Flow (Streamline): a special case of specified flow where the flow is zero (HI) 3) Head Dependent Flow: could replace (ABC, EFG)
Free Surface: water-table, phreatic surface (CD)
Seepage Face: h = z; pressure = atmospheric at the ground surface (DE)
Found in most ground-water modeling texts.

3. Three basic types of Boundary Conditions
Found in most ground-water modeling texts.
After:
Definition of Boundary and Initial Conditions in the Analysis of Saturated
Gournd-Water Flow Systems - An Introduction, O. Lehn Franke, Thomas E. Reilly,
and Gordon D. Bennett, USGS - TWRI Chapter B5, Book 3, 1987.

4. DIRICHLET Constant Head & Specified Head Boundaries
Head (H) is defined as a function of time and space.
Constant Head:
Head (H) is constant at a given location.
Implications:
Supply Inexhaustible, or Drainage Unfillable
Found in most ground-water modeling texts.

5. NEUMANN No Flow and Specified Flow Boundaries
Discharge (Q) varies with space and time.
No Flow:
Discharge (Q) equals 0.0 across boundary.
Implications: H will be calculated as the value required to produce a gradient to yield that flow, given a specified hydraulic conductivity (K). The resulting head may be above the ground surface in an unconfined aquifer, or below the base of the aquifer where there is a pumping well; neither of these cases are desirable.
Found in most ground-water modeling texts.

6. CAUCHY Head Dependent Flow
H1 = Specified head in reservoir
H2 = Head calculated in model
Implications:
If H2 is below AB, q is a constant and AB is the seepage face, but model may continue to calculate increased flow.
If H2 rises, H1 doesn't change in the model, but it may in the field.
If H2 is less than H1, and H1 rises in the physical setting, then inflow is underestimated.
If H2 is greater than H1, and H1 rises in the physical setting, then inflow is overestimated.
Found in most ground-water modeling texts.

7. Free Surface Free Surface:
h = Z, or H = f(Z)
e.g. the water table h = z
or a salt water interface
Note, the position of the boundary is not fixed!
Implications: Flow field geometry varies so transmissivity will vary with head (i.e., this is a nonlinear condition). If the water table is at the ground surface or higher, water should flow out of the model, as a spring or river, but the model design may not allow that to occur.
Found in most ground-water modeling texts.

8. Seepage Surface
Seepage Surface: The saturated zone intersects the ground surface at atmospheric pressure and water discharges as evaporation or as a downhill film of flow.
The location of the surface is fixed, but its length varies (unknown a priori).
Implications: A seepage surface is neither a head or flowline. Often seepage faces can be neglected in large scale models.
Found in most ground-water modeling texts.

9. Natural and Artificial Boundaries
It is most desirable to terminate your model at natural geohydrologic boundaries. However, we often need to limit the extent of the model in order to maintain the desired level of detail and still have the model execute in a reasonable amount of time.
Consequently models sometimes have artificial boundaries.
For example, heads may be fixed at known water table elevations at a county line, or a flowline or ground-water divide may be set as a no-flow boundary.
Found in most ground-water modeling texts.

10. Natural and Artificial Boundaries
BOUNDARY TYPE
NATURAL EXAMPLES
ARTIFICIAL USES
CONSTANT
Fully Penetrating Surface Water Features
Distant Boundary (Line of unchanging hydraulic head contour) or
SPECIFIED HEAD
SPECIFIED FLOW
Precipitation/Recharge
Flowline
Pumping/Injection Wells
Divide
Impermeable material
Subsurface Inflow
HEAD DEPENDENT FLOW
Rivers
Springs (drains)
Evapotranspiration
Leakage From a Reservoir or Adjacent Aquifer
Found in most ground-water modeling texts.

11. Natural Hydrologic Features as Boundaries
Boundary can be assigned to hydrologic feature such as:
Surface water body
Lake, river, or swamp
Water table
Recharge and evapotranspiration or source/sink specified head
Impermeable surface
Bedrock or permeable unit pinches out

12. Natural No-Flow Boundary
Hydraulic conductivity contrasts between units
Alluvium on top of tight bedrock
Assume GW does not move across this boundary
Can use ground-water divide or flow line

13. Note ground-water divide shifts after development—may or may not be a good no-flow BC
T.E. Reilly, 2000

14. Practical Considerations
Boundary conditions must be assigned to every point on the boundary surface
Modeled boundary conditions are usually greatly simplified compared to actual conditions

15. Sources and Sinks Injection and Pumping Wells
Flux across the Water Table
Leakage

16. Sources and Sinks
Same model options used to represent boundary conditions are used to represent internal sources and sinks
Specified flux for wells
Specified head for lakes, rivers, drains

17. Wells—an internal boundary condition at a point—thought of as a stress to the system
A well is a specified flow rate at a point
Can be pumping or injecting water
Withdrawals or injection may vary in space and time
Node may represent entire thickness of a cell (which often represents an aquifer)
MODFLOW’s MNW package remedies some issues

18. Flux across the Water Table (free surface boundary)
Treated as an internal source or sink (Dupuit assumptions)
May vary with time and space
Array(s) of flux values
Variety of methods for estimating water table fluxes
Directly to/from surface or through unsaturated zone

19. Estimating water table fluxes
Recharge
Infiltrated water that crosses the water table and becomes part of the ground water system
Discharge
Ground water that moves upward across the water table and discharges to the surface or to the unsaturated zone

20. Recharge No one universally applicable method
Traditionally based on percentage of precipitation
Significant spatial and temporal variations
Accommodated by Zones
Rates adjusted during calibration
Often largest unknown

21. Recharge Methods Water Balance Models Unsaturated Zone Models
With MF either pre-process or code modifications
PRMS and GS-FLOW
Unsaturated Zone Models

22. Discharge Evapotranspiration occurs when
Plants remove water from the water table
Direct evaporation from the water table
May be head-dependent (if water-table too far below land surface ET is unlikely)
Varies in space and time

23. Leakage
Movement of water through a layer of material that has a lower hydraulic conductivity
Enters or leaves depending on relative head
Magnitude and direction may vary in time
Source: aquifer, river, or lake
Sink: aquifer, river, lake, drain, springs, or seeps
Type of head-dependent boundary
General head boundaries
Drains (only act as sinks)

24. Ground-water / Surface-water Interaction
Hydraulic head in aquifer can be equal to elevation of surface-water feature or allowed to leak to the surface-water feature
Usually defined as a “Constant-Head” or “Specified Head” Boundary or “Head-dependent flow” boundary
If elevation of SW changes, as with streams, elevation of the boundary condition changes

25. How a stream could interact with the ground-water system
T.E. Reilly, 2000