Sources and sinks
1 / 25

Sources and Sinks - PowerPoint PPT Presentation

  • Uploaded on

Boundary Conditions. Based on Slides Prepared By Eileen Poeter, Colorado School of Mines. Sources and Sinks. Types of Boundary Conditions. 1) Specified Head: head is defined as a function of space and time (could replace ABC, EFG)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Sources and Sinks' - maya-saunders

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Sources and sinks

Boundary Conditions

Based on Slides Prepared By

Eileen Poeter, Colorado School of Mines

Sources and Sinks

Types of boundary conditions
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)

Three basic types of boundary conditions
Three basic types of Boundary Conditions


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.

Dirichlet constant head specified head boundaries
DIRICHLETConstant Head & Specified Head Boundaries

Specified Head:

Head (H) is defined as a function of time and space.

Constant Head:

Head (H) is constant at a given location.


Supply Inexhaustible, or Drainage Unfillable

Neumann no flow and specified flow boundaries
NEUMANNNo Flow and Specified Flow Boundaries

Specified Flow:

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.

Cauchy head dependent flow
CAUCHYHead Dependent Flow

  • 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.

Free surface
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.

Seepage surface
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.

Natural and artificial boundaries
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.

Natural hydrologic features as boundaries
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

Natural no flow boundary
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

Note ground water divide shifts after development may or may not be a good no flow bc
Note ground-water divide shifts after development—may or may not be a good no-flow BC

T.E. Reilly, 2000

Practical considerations
Practical Considerations may not be a good no-flow BC

  • Boundary conditions must be assigned to every point on the boundary surface

  • Modeled boundary conditions are usually greatly simplified compared to actual conditions

Sources and sinks1

Sources and Sinks

Sources and sinks2

Sources and Sinks

Wells an internal boundary condition at a point thought of as a stress to the system
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

Flux across the water table free surface boundary
Flux across the Water Table (free surface boundary) of as a stress to the system

  • 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

Estimating water table fluxes
Estimating water table fluxes of as a stress to the system

  • 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

Recharge of as a stress to the system

  • 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

Recharge methods
Recharge Methods of as a stress to the system

  • Water Balance Models

    • With MF either pre-process or code modifications

    • PRMS and GS-FLOW

  • Unsaturated Zone Models

Discharge of as a stress to the system

  • 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

Leakage of as a stress to the system

  • 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)

Ground water surface water interaction
Ground-water / Surface-water Interaction of as a stress to the system

  • 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

How a stream could interact with the ground water system
How a stream could interact with the ground-water system of as a stress to the system

T.E. Reilly, 2000