Course 8 BoundaryConditions S1 2014

5/26/2018 Course 8 BoundaryConditions S1 2014

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Geological Engineering Department

Faculty of Engineering

Groundwater ModelingBoundary Conditions

Dr. Doni Prakasa Eka Putra


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Boundary conditions

(After Freeze and Cherry, 1979)


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Three basic types of Boundary Conditions

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.


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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.


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Natural and Artificial Boundaries

BOUNDARY TYPE NATURAL

EXAMPLES

ARTIFICIAL USES

CONSTANT Fully Penetrating SurfaceWater 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 Distant Boundary (Line of

unchanging hydraulic head

contour)

Springs (drains)

Evapotranspiration

Leakage From a Reservoir

or Adjacent Aquifer


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Hydrologic Features as Boundaries

Boundary can be assigned to hydrologic featuresuch 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


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Ground-water / Surface-water Interaction

Hydraulic head in aquifer can be equal to elevation ofsurface-water feature or allowed to leak to the surface-water feature

Usually defined as a Constant-Head or SpecifiedHead Boundary or Head-dependent flow boundary

If elevation of SW changes, as with streams, elevation ofthe boundary condition changes


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How a stream could interact

with the ground-water

system

T.E. Reilly, 2000


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No-Flow Boundary

Hydraulic conductivity contrasts between units Alluvium on top of tight bedrock

Assume GW does notmove across this

boundary Can use ground-water divide or flow line


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Understanding natural systemAlluvium

Clay, Silt

Sandy materials

Shale

Groundwater Divide

Water table

River


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Conceptualizing groundwater system

Groundwater Divide

No Flow

River

Specified HeadRecharge

K1

K2

K3

K2

No Flow

Model area


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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)


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DIRICHLET

Constant 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.

Implications:

Supply Inexhaustible, or Drainage Unfillable


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Example: Constant Head

Example of Potential Problems Which May Result

From Misunderstanding / Misusing a Constant

Head Boundary

If heads are fixed at the ground surface to

represent a swampy area,


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Example: Constant Head

and an open pit mine is simulated by defining

heads in the pit area, to the elevation of the pit

bottom,


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Example: Constant Headthe use of constant heads to represent the swamp

will substantially overestimate in-flow to the pit.This is because the heads are inappropriately

held high, while in the physical setting, the

swamp would dry up and heads would decline,

therefore actual in-flow would be lower. The

swampy area is caused by a high water table. It is

not an infinite source of water.


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Example: Constant HeadLesson: Monitor the in-flow at constant head

boundaries and make calculations to assureyourself the flow rates are reasonable.


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Note ground-water divide shifts after

developmentmay or may not be a good no-flow

BC

T.E. Reilly, 2000


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Example: Specified Head


From Misunderstanding / Misusing a Specified

Head Boundary

When a well is placed near a stream, and the

stream is defined as a specified head,


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the drawdown may be underestimated, if the

pumping is large enough to affect the stream

stage. The specified flow boundary may supply

more water than the stream caries,


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and drawdowns should be greater, for the given

pumping rate. The stream stage, and flow rate,

should decrease to reflect the impact of the

pumping.

G i i i


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Lesson: Monitor the in-flow at specified head

boundaries. Confirm that the flow is low enough

relative to the streamflow, such that stream

storage will not be affected.

G l i l E i i D t t


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NEUMANN

No 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 toproduce 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.

G l i l E i i D t t


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Example: SPECIFIED FLOW


From Misunderstanding / Misusing a Specified

Flow Boundary

In this example, the model represents a simple unconfined

aquifer with one well. Two cases are presented:

1) an injection well, and

2) a withdrawal (pumping) well.

G l i l E i i D t t


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Injection Well: If the injection flow is too large,

calculated heads may be above the ground

surface in unconfined aquifer models.



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Withdrawal Well: If the withdrawal flow is too

large, calculated heads may fall below the bottom

of the aquifer, yet the model may still yield water.



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Lesson: Monitor calculated heads at specified

flow boundaries to ensure that the heads are

physically reasonable.



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Example: NO FLOW

Example of Potential Problems Which May ResultFrom Misunderstanding / Misusing a No Flow

BoundaryWhen a no flow boundary is used to represent a ground

water divide, drawdown may be overestimated, andalthough the model does not indicate it, there may be

impacts beyond the model boundaries.



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Example: NO FLOW

Simplified model with no-flow boundary

representing the ground-water divide.



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Example: NO FLOWUse of a no-flow boundary in this manner may cause

problems: When a ground water divide is defined as a no-flow boundary, the flow system on the other side of the

boundary cannot supply water to the well, therefore

predicted drawdowns will be greater than would be

experienced in the physical system. The no-flow boundary

prevents the ground water divide from shifting, implying

there drawdown is zero on the other side of the divide.



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Example: NO FLOW

Lesson: Monitor head at no flow boundaries used

to represent flow lines or flow divides to ensure

the location is valid even after the stress is

applied.



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CAUCHY

Head Dependent Flow

Head Dependent Flow:

H1= Specified head in reservoir

H2= Head calculated in model

Implications:If H

2

is below AB, q is a con stant and AB is the seepage face, but

model may contin ue to calculate increased flow.

If H2rises , H1doesn' t change in the model, but i t m ay in the f ield.

If H2is less than H1, and H1r ises in the phys ical sett ing, then inf low is

underest imated.

If H2is greater than H1, and H1r ises in the phy sical sett ing, then

inf low is overest imated.



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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 f ield geometry varies s o transm issiv i ty wi l lvary w ith head (i.e., this is a no nlinear co nd it ion ). If the water table is

at the ground su rface or high er, water should f low out o f the model, as

a spr ing o r r iver, bu t the mod el design may not al low that to occu r.



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g g g p


Seepage Surface

Seepage Surface: The saturated zone intersects theground 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 n either a head or f low l ine.Often seepage faces c an be neglected in large scale models.



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g g g p


Boundary Condition Exercise

Example:An oceanic island in a humid climate; permeable

materials are underlain by relatively impermeable bedrock



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g g g p



Example:An alluvial aquifer associated with a medium-

sized river in a humid climate; the aquifer

is underlain and bounded laterally by bedrock of low

hydraulic conductivity



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g g g p



Example:An alluvial aquifer associated with an intermittent

stream in an arid climate; the aquifer is underlain and

bounded laterally by bedrock of low to intermediate

hydraulic conductivity



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Example:A western valley with internal drainage in an arid

region; intermittent streams flow from surrounding

mountains towards a valley floor; a part of valley floor is

playa



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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

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Course 8 BoundaryConditions S1 2014

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