Center for Subsurface Modeling Support USEPA Region III
Robert S. Kerr Environmental Research Laboratory 841 Chestnut Building
U.S. Environmental Protection Agency Philadelphia, PA 19107
P.O. Box 1198
Ada. Oklahoma 74820
EPA
INTRODUCTION TO THE
WELLHEAD ANALYTIC ELEMENT MODEL
June 5 - 7,1995
Philadelphia, Pennsylvania
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INTRODUCTION TO W/iAEM: The Wellhead Analytic Element Model
USEPA Region III
841 Chestnut Building, Philadelphia, PA
Monday, June 5, 1995
1:00-2:15 Introduction
Course objectives, approach
Wellhead Protection overview (Slides)
W/?AEM=GAEP+CZAEM
Digital maps
Capture zone delineation
215-2:30 Break
2:30-4:30 Calculated Fixed Radius- Vincennes, Indiana
CZAEM Tutorial (Basics)
Example 1, Well in uniform flow
Ex. 2, Well near a river
Ex. 3, Critical pumping of well near a river
4.30 Adjourn
Tuesday, June 6
8:30-9:45 W/?AEM Tutorial
I
Introduce Vincennes, Indiana wellfield as case study
Map preparation
GAEP operations
digitizing demo
aquifer data input
file operations
element operations
9:45-10:00 Break
10:00-11:30
11:30-1:00 lunch
1:00-2:15
CZAEM operations
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tracing capture zones
refinement of initial conceptual model using the method of images
2:15-2:30 Break
2:30-4:30 Vincennes Summary (Slide show)
4:30 adjourn
Wednesday, June 7
8:30-9:45 CZAEM Tutorial (advanced)
Ex. 4, Contaminant pump-out system
Ex. 5, Data manipulation and model refinement
Ex. 6, Data file and graphics control
9:45-10.00 Break
10.00-11:15 GAEP Features (advanced)
edititing
options
utilities
11:15 Adjourn
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\ Slide # D-02
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or
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* *_:¦»•;
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^*Ti" y.i^
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l6MV°V,io^.N
Saturated-Unsaturated Zone
Source: Horslsy & Witt«n, Inc., 1691
j Slide # D-04
Water Table Map,
Sand and Gravel Aquifer
Sourc«: USGS, 1984
Slide # D-05
(
>
Water Table Map,
Bedrock Aquifer, Dover,
New Hampshire
Source: GriswoW and Vernon, in press
V
.)
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\ Slide #D-07
OtocMrg*
Buried Valley Aquifer
\ Slide # D-09
Hydrologic Cross-Section-
Edwards Aquifer
Sourcs: Tsxas Water Commission, 1088
Quit Ct»»itKn§i
¦DC
Slide #D-10
ZJ
Plan View-
Edwards Aquifer
Sou res: Tsxas Water Commission, 1988
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4 Slide # D-11
r~
MOUtFEP V«
WELLHEAD
\ PfiOTBCTJOti
Aquifer vs. Wellhead
Protection
Slide # D-12
<*Ap.
ft:
mm
Aquifer vs. WHPA-
Cross-Section
METHODS OF
DELINEATION
Slide # D-14
« Arbitrary Fixed Radius
• Calculated Fixed Radius
• Simplified Variable Shapes
• Analytical Methods
• Numerical Methods
• Hydrogeologic Mapping
Methods of Delineation
J
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WHPA BOUNDARY
e
WHPA Delineation Methods:
Arbitrary (Discretionary)
Fixed Radius
Slide # D-16
WHPA Delineation Methods:
Calculated Fixed Radius
Source: Horsley & Wittan, Inc., 1991
-C®
Slide # D-20
WHPA Delineation Methods:
Combination
W.VL.
-------
Typical Computer Modeling Grid
J*
; 5 B){ |
Si I
... S|
i s" n
.. ,. ^;4^i
_ „;. ¦. #»v% aatv
1 Slide » D-21
Numerical Modeling
Sou ret: HoreJey * WǤn, inc. 1991
l>
LINKING DELINEATION
WITH MANAGEMENT
• Relationship of WHPA Boundaries
to Parcel Boundaries
• Relationship of WHPA Boundaries
to Jurisdictional Boundaries
Slide # D-22
Linking Delineation with
Management
V_
Slide # D-23
WHPA vs. Parcel
Boundaries
Source: Horsley & Witten, Inc., 1991
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r
CANOC RIVER
; Jkovirea .
| Slide # D-24
Aquifer vs. Municipal
Boundaries
1 Slide # D-29
WHPAs in Arid and Semi-
Arid Regions
Source: Horsley ft Wiflen, Inc., 1091
J Slide # D-32
Fence Diagram, Bedrock
Aquifer In Dover,
New Hampshire
Source: Vernon and Griswold. in press
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\ Slide # D-33
Dover, New Hampshire,
Bedrock Aquifer WHPA
Source: Vsmon and Griswold, in prase
SEPA
kCAfmfC
EPA STttWI-CO*
Delineation Of Wellhead
Protection Areas
In Fractured Rocks
DELINEATION OF A REFINED WELLHEAD PROTECTION AREA
FOR BEDROCK PUBLIC SUPPLY WELLS, CHARLESTOWN,
RHODE ISLAND
Doug la* L. B«ath
Ground Water lUaagout Section
O<od tnvironaantal Protection Agency - BI«v lag land
Boston, HaaaechuMtt*
April. 1915
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U.S. Environmental Protection Agency
REQUEST FOR ASSISTANCE
RFA-95-1: FRACTURED CARBONATE ROCK GEOHYDROLOGY
The US EPA Robert S. Kerr Environmental Research Laboratory, Ada,
Oklahoma, is seeking assistance by cooperative agreement with non-
profit organizations (minimum 5% cost sharing required) or by
interagency agreement with Federal Agencies qualified to conduct
research in the geohydrology of fractured carbonate rock aquifers.
The focus of the research should be to summarize, demonstrate, and
extend the understanding of the capture zone concept for pumping
wells as applied to fractured carbonate rock aquifers. It is
anticipated that a balance between computer modeling/scientific
visualization and field observations will be demonstrated in a
cost-effective characterization at a dedicated field site. Insights
are expected as to the significance of preferred flow pathways and
long-term storage zones within capture zones, with particular
attention to aquifer remediation and protection. The project is
anticipated as a three-year project, beginning no later than
October 1, 1995, with the EPA share of the budget not to exceed
$500,000 for the three-year period, pending availability of funds.
Interested sources must request a solicitation package containing
a scope of work, evaluation criteria, and additional instructions
in writing before the response date of April 21, 1995. FAX
requests may be directed to (405) 436-8597. Telephone requests for
the solicitation package or technical information will not be
accepted.
Contact Point:
Stephen Kovash
U.S. Environmental Protection Agency
Robert S. Kerr Environmental Research Laboratory
P.O. Box 1198
919 Kerr Research Drive
Ada, Oklahoma 74820
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Historical
Perspectives
We are pleased to present our readers with the opportu-
nity to read a classical contribution to the historical litera-
ture of ground-water science. We try to highlight the
contributions of the greatest names In our field. Readers
are urged to recommend appropriate contributions to be
Included in this section of GROUND WATER.
Revisiting the Membrane Analog—A Conceptual and
Communication Tool
by Forest Arnold, Roy F. Weston, Inc., 215 Union
Boulevard, Suite 600, Lakewood, Colorado 80228
Abstract
Membrane analogs were used before the advent of com-
puters as physical models of stresses on the water-table surface.
Measurement of the membrane deflection can be related to
equations representing pumping stresses. Although numerical
models using computer techniques have replaced membrane
analogs due to their greater accuracy and versatility, the mem-
brane analog remains an inexpensive way to conceptualize the
effect of different boundary conditions, nearby surface-water
bodies and pumping stresses, and is useful in preparing input
data sets for numerical modeling. The membrane analog is also
a visual way to communicate modeling results and modeling
Scenarios to nonmodelers. A small office-sized membrane
analog can be constructed for less than $25.00 and can be stored
on a shelf or under a desk, for ready access.
Introduction
Membrane analogs were used before computers and
numerical modeling to represent ground-water movements and
stresses. They were set up in engineering labs as large frames
covered with a sheet of latex and a mechanism for precisely
lowering and measuring rods to represent well discharge or
other stresses and discharge points (Todd, 1959; Strack, 1989;
Hansen, 1952). These measurements were quantified and
related to known equations about ground-water mechanics.
Moire pattern techniques were developed using the membrane
analog to represent the superposition of field solutions for
two-dimensional problems (Freeze, 1971; De Josselin de Jong,
1961). Other physical models used before numerical modeling
include: electrical analog models, Hele-Shaw models, and sand
tank experiments (Todd, 1959).
These physical models are no longer used for quantitative
experiments due to the advent of more powerful numerical
techniques. However, the analog models continue to be used as
conceptual and teaching tools. Several limitations to the older
membrane analogs include the following: they were relatively
expensive to set up and took up a lot of space, and the latex
membranes tended to break down over time. The updated
membrane analog described in this paper is smaller, portable,
and made of more durable materials not available then. It fan
be constructed for less than $25.00.
W 1° 'he conceptualization stage of modeling, it is important
m be able to compare different scenarios quickly. Unless one is
an extraordinary draftsman, it is difficult to sketch out three-
dimensional representations of the water-table surface. The
effects of complex boundaries and stresses can be easily repre-
sented in three dimensions on a membrane analog.
The membrane analog is not a quantitative tool, but it can
be scaled to be reasonably accurate in a relative sense. The
membrane grid surface spacing can be measured to represent
distances of drawdown and capture zones. The addition of
more or less pressure to points representing wells will reflect
changes in drawdown and capture zones due to different pump-
ing rates. For more complex sites, calculations with analytical
packages such as Hydropal I and II (Watershed Research, Inc.,
1988) or Walton's Welflo or Conmig (Walton, 1989) will suffice
to properly scale the placement on the membrane surface.
In addition, the membrane analog is very useful for com-
municating model results, possible scenarios, and uncertainties
to nonmodelers. People relate to visual images. The membrane
analog makes modeling concepts visual and makes it easier for
nonmodelers to understand. This allows other colleagues to ask
questions and have input early in the modeling process because
they understand the conceptual framework. This can save time
later and makes the modeling process more approachable.
People who would be put off by the computer and mathemati-
cal modeling can often relate better to the membrane analog
than a complex printout.
Methods and Materials
Materials and Methods of Construction
1. Membrane surface—use white spandex instead of latex,
which is available at fabric stores.
2. Mark the surface with a permanent marker using a % to
l/i inch grid.
3. Stretch the membrane on a needlepoint hoop 14 inches
or bigger. The circular layout avoids corner effects and works
better than a square or rectangular frame. The double hoop
and locking mechanism make it possible to adjust membrane
tension for different problems (see Figure 1).
4. Obtain two to three flexible architect's mlers, or cut a
long one into pieces. They will be used to represent line sinks
and area sinks for rivers and lakes, and for complex geologic
boundaries, mounds, quarries, and mines.
5. Obtain 8-12 blocks of wood of different thicknesses to
support rulers for mounds, area sinks, and other features.
6. Obtain eightpenny or larger nails to represent wells. Use
wood dowels or strips with holes in the wood to represent
spatial placement of wells. The holes in the dowels should
provide enough room to hold the nails in place but allow them
to slide up and down to reflect different pumping rates.
Fig. 1. The membrane analog and equipment for represent-
ing wells and water bodies.
762
Vol 29, No. 5—GROUND WATER—September-October 1991
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Fig. 2. A simulation of simultaneous Injection and pumping
wells.
Fig. 3. A simulation of a complex well field.
Methods of Representing Hydrogeologfc Features
To represent a single pumping or injection well, a pen,
pencil eraser, or nail can be applied to depress the membrane
surface. For pumping wells, the top of the membrane is
depressed, while for injection wells the underside of the mem-
brane is depressed (see Figure 2). The strength of the pumping
can be adjusted by the depth of depression. For multiple wells,
nails in one or more dowels can be used. The strength of the well
can be adjusted by pulling in or out on the nails. For complex
well patterns, use two dowels with a pivot in the middle and
multiple holes (see Figure 3).
Line sinks to represent streams and riven can be repre-
sented by shaping the flexible arichitect's rule into the appropri-
ate stream shape and placing it on the surface of the membrane.
Fishing weights can be placed on the rule to further depress the
line sink or to hold it in place. The effects of a losing stream can
be represented by placing the ruler on wood blocks to support it
underneath the membrane surface, thereby reflecting a mound
(see Figure 4).
Area sinks to represent lakes or wetlands can be repre-
sented by shaping the flexible architect's ruler into the shape of
the lake and placing it on the surface of the membrane. An
influent lake or landfill mound can be represented by placing
the ruler on wood blocks to support it underneath the mem-
brane surface, thereby reflecting the mound shape on the mem-
brane surface (see Figure 4).
A major river with a significant gorge and bluffs nearby
can be represented by a ruler underneath the membrane sup-
ported by blocks to represent the bluffs and a ruler placed
nearby on the membrane to represent the river. Other major
topographic features such as quarries, open pit mines, etc. can
be represented with combinations of the flexible rulers on top
of and underneath the membrane.
Fot aquifers with tight boundaries such as glacial melt-
water channels or alluvial aquifers, the shape can be defined
with rulers and blocks placed underneath the membrane. The
stream is then placed on top, and pumping stresses can be
added as previously described. This makes it possible to see
elongated cones of depressions and the effects of geologic
boundaries on pumping.
For more complex sites with combinations of the different
features previously described, it is best to lay out the boundary
features near the edges and add pumping stresses in the center
to avoid distortions near the frame. Tlie location of an existing
or proposed waste site can be marked with a light thin block of
wood, or a piece of masking tape placed on the membrane. For
problems with unusually high or low hydraulic conductivity, it
Fig. 4. A simulation of a landfill mound, nearby stream, and
multiple pumping wells.
may be necessary to tighten or loosen the tension on the
membrane. This is easily accomplished with the needlepoint
hoop—simply loosen the locking wing nut on the outer of the
two hoops, adjust the tightness of the membrane, and then
tighten to lock the membrane in place.
Summary
Use of the membrane analog can enhance the conceptual
phase of modeling in trying out initial scenarios of the modeling
effort such as cases of multiple stresses near waste sources in
complex terrain with nearby surface-water bodies. This type of
conceptualization is especially important in wellhead protec-
tion, capture well design, and risk assessment
The membrane analog is also useful in communicating
modeling concepts to other colleagues. It makes ground-water
mechanics visual, helping others understand your modeling
results. By laying out a conceptual model on the membrane
analog early in the process, it is possible to match the overall
goals of the modeling with the conceptual design of the
modeler.
Over time, attention to communicating the conceptual
model of different sites will help colleagues to become more
comfortable with complex hydrologic concepts. They will be
more supportive of modeling efforts in the future. The mem-
brane analog takes the modeling out of the "black box" realm
763
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and puts it into perspective as a useful tool with some
limitations.
By using modern materials, some of the drawbacks of the
old membrane analogs have been avoided. The revised mem-
brane analog is inexpensive, portable, and compact. It is easy to
Bet up and take down for formal or informal meetings. It does
not require preprocessors, postprocessing software, complex
configuration files, or supporting hardware like special printers
or digitizers. There is no fee for hardware updates. Just make
Dew pieces from inexpensive materials as the need arises.
We are fortunate to be in an era wilh compute rued numer-
ical methods that allow us to go beyond the limitations of
simple physical models such as membrane and electrical ana-
logs. The need to carefully conceptualize a site for numerical
modeling and the ability to communicate modeling results is
still with us, though. The membrane analog, although an older
tool, can still be a powerful tool to aid in the newer, modern
process of numerical modeling.
Acknowledgments
Special thanks to Otto Strack at the University of
Minnesota for explaining the use of membrane analogs initially
and for providing references and guid ance during development.
Also, thanks to Bruce Olson of the Minnesota Department of
Health for suggestions which led to refining the representation
of complex wells. Thanks to Bob MacNeil of Geraghly and
Miller, Inc., Minneapolis, for helpful comments and enthusi-
asm throughout.
References Cited
De Josselin de Jong, G. 1961. Moire patterns of the membrane
analogy for ground-water movement applied to multiple
fluid flow. Journal of Geophysical Research, v. 66, no. 10.
Freeze, R. A. 1971. Moire pattern techniques in groundwater
hydrology. Water Resources Research, v. 6, no. 2.
Hansen, V. E. 1952. Complicated well problems solved by the
membrane analogy. Transactions, American Geophysical
Union, v. 33, no 6.
Strack, O.D.L W89. Groundwater Mechanics. Prentice-Hall Inc.,
Englewood Cliffs, SJ.
Todd, D. K. 1959. Ground Wale: Hydrology. John Wiley and
Sons, Inc., New York.
Walton, W. C. 1989. Analytical Groundwater Modeling: Flow and
Contaminant Migration. Lewis Publishers. Chelsea, MI.
Watershed Research Incorporated. 1988. Hydropal I and II Inter-
active Hydrogeological Applications. White Bear Lake,
MN.
• • »
Forest D. Arnold is a Hydrogeologist wilh Roy F. Weston,
Inc. in Lakewood, Colorado. He has 13 years of experience work-
ing on surface- and ground-water quality problems. His interests
are in the application ofground-water flow and transport models
for remediation and exposure assessments of hazardous waste
sites.
DENSE, IMMISCIBLE PHASE LIQUID CONTAMINANTS (DNAPLs)
IN POROUS AND FRACTURED MEDIA
a short course sponsored by;
Waterloo Centre for Groundwater Research
An Ontario Centre of Excellence funded bp the Premier's Council on Economic Renewal
October 7 -10,1991
Kitchener, Ontario, Canada
This 4 day course is designed for groundwater and environmental professionals who wish
to team about the theory and practice of investigating and remediating groundwater
contaminated by DNAPLs such as solvents (TCEI, creosotes and PCB oils. The topics
addressed will include the physical behaviour of immiscible fluids in the subsurface, the
behaviour of contaminant vapours in the unsaturated zone, and the nature of contaminant
plumes created below the watettabk by the shut dissolution of fluid residuals. Recent
research in geophysical methods and remedial technologies will also be discussed. This
course is independent of the dissolved organics course offered by the Centre.
To register, or request more information, contact:
Short Courses
Waterloo Centre for Groundwater Research
Lfnii>ersily of Waterloo
Waterloo, Ontario, Canada Telepho ne: (519} 885-1211 ext. 2892
N2L3G1
>;>><>>>. :
1'
fax: (519) 888-4654
764
VoL 29, No. 5—GROUND WATER—September-October 1991
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- SWolUw- rorcUe.^rr
Cxrom^d w*hr FIoka/
Land surface, — Wi«f table Stream —
V
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Equtpotenuai Une—
Figure 3.—Row pattern in uniformly permeable materia! with
constant areal recharge and discharge to symmetrically
placed streams. (Modified from Hubbert, 1940.)
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A, [ \ United States Robert S. Kerr Environmental
l^/p| \ 1 ' Environmental Protection Research Laboratory
Agency Ada OK 74820
Research and Development EPA/600/SR-94/210 December 1994
&EPA Project Summary
Demonstration of the Analytic
Element Method for Wellhead
Protection
Hendrik M. Haitjema, Otto D.L Strack,
and Stephen R. Kraemer
Abstract
A new computer program has been
developed to determine time-of-travel
capture zones in relatively simple
geohydrological settings. The WhAEM
package contains an analytic element model
that uses superposition o( (many) closed
form analytical solutions to generate a
ground-water flow solution. W/iAEM consists
of two executables: the preprocessor GAEP,
and the flow model CZAEM. W/>AEM differs
from existing analytical models in that it can
handle fairly realistic boundary conditions
such as streams, lakes, and aquifer recharge
due to precipitation.
The preprocessor GAEP is designed to
simplify the procedures for getting data into
a ground-water model; specifically it
facilitates the interactive process of ground-
water flow modeling that precedes capture
zone delineation. The flow model CZAEM is
equipped with a novel algorithm to accurately
define capture zone boundaries by first
determining all stagnation points and dividing
streamlines in the flow domain. No models
currently in use for wellhead protection
contain such an algorithm.
This Project Summary was developed by
USEPA's Robert S. Kerr Environmental
Research Laboratory, Ada, Oklahoma, to
announce key findings of the Research
Project that is fully documented in separate
reports and supporting software (See Project
Report ordering information at the back).
Introduction
The delineation of capture zones requires
precise determination of streamlines. In
most numerical methods, such accurate
determin-ation is difficult because the
velocities are computed on the basis of
values of piezometric heads that are known
only at the nodes of a mesh. This deficiency
stimulated the development of a number of
computer models which implement
elementary analytic solutions for ground-
water flow problems. The analytic are
capable of producing more or less
approximate shapes of the boundaries of
capture zones for any given time; e.g., the
USEPA's original wellhead protection model
WHPA. However, even when the velocity
components are known precisely, accurate
determination of the boundaries of capture
zones still requires that both stagnation
points and dividing streamlines are known.
The delineation of capture zones in
complex settings is currently done either
by the use of discrete numerical models or
analytic element models. The discrete
numerical models, such as MODFLOW/
MODPATH of the US Geological Survey,
and analytic element models, such as
Strack'8 MLAEM, require detailed
knowledge of the setting and advanced
modeling expertise to run; and they do not
currently have advanced algorithms for
delineation of capture zones.
The Wellhead Analytic Element Model
(W/iAEM) falls between the two
aforementioned technologies. It does
contain an advanced algorithm for
determining capture zones for any well at
any time based on precise knowledge of
the locations of all stagnation points and
dividing streamlines. It has features that
make the inclusion of open or closed, head-
specified boundaries possible (for example
to model streams), but lacks the power of
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advanced discrete numerical or analytic
H>ment models. The authors believe that
Va newly developed model will serve
ground-water professionals who wish to
determine capture zones in relatively simple
geohydrological settings.
WhAEM consists ot two executables: the
preprocessor GAEP and the flow model
CZAEM (see Figure 1). In order to facilitate
data entry in the computer program CZAEM
(Capture Zone Analytic Element Model), a
separate computer program was developed
called GAEP, (Geographic Analytic Element
Preprocessor). This program makes it
possible for most users not familiar with the
input structure of analytic element models
to concentrate on modeling aspects, rather
than on the intricacies ol preparing input
data files.
WhAEM was developed under a
cooperative agreement between EPA and
Indiana University and the University of
Minnesota.
The Analytic Element Method
The analytic element method was
developed at the end of the seventies by
Otto Strack at the University of Minnesota.
KFor a detailed description of the method,
reader is referred to Groundwater
chanics. O.D.L. Strack, 1989, Prentice
I, while a brief review follows.
This new method avoids the discretization
of a ground-water flow domain by grids or
element networks. Instead, only the
boundaries of the surface water and aquifer
features in the domain are discretized and
entered into the model. Each of these
boundary segments are represented by
closed form analytic solutions—the analytic
elements. The comprehensive solution to a
complex, regional ground-water flow
problem is obtained by superposition of all
analytic elements in the model, from a few
hundred to thousands.
Traditionally, modeling ground-water flow
by use of analytic functions was considered
to be limited to homogeneous aquifers of
constant transmissivity. However, by
formulating the ground-water flow problem
in terms of appropriately chosen discharge
potentials rather than piezometric heads,
the analytic element method becomes
applicable to both confined and unconfined
flow conditions as well as to heterogeneous
aquifers.
The analytic elements are chosen to best
^present certain hydrologic features. For
Stance, stream sections are represented
WhAEM
CZAEM
Figure 1. The modeling process using WMEM.
by line-sinks; lakes or wetlands may be
represented by areal sink distributions.
Streams and lakes that are not fully
connected to the aquifer are modeled by
area sinks with resistance to flow between
surface water and the aquifer.
Discontinuities in aquifer thickness or
hydraulic conductivity are modeled by use
of line doublets (double layers). Other
analytic elements may be used for special
features, such as drains, fractures, and
slurry walls.
The analytic element method differs
fundamentally from most classical numerical
models, for instance:
1. The solution is analytical; no
interpolation is required to compute heads
or velocities at any point in the domain.
This makes the method insensitive to scale,
allowing contour plots and streamlines to
be produced in areas varying in size from
several square feet to hundreds of square
miles.
2. Since the velocity field is calculated
analytically, inaccuracies in capture zone
boundaries and isochrones of travel times
are due solely to approximations made in
the conceptual model and its implementation
in the program; they are not the
consequence of a model grid resolution
and the associated numerical (approximate)
differentiation process.
3. The aquifer is unbounded in the
horizontal plane; there are no artificial model
boundaries that may influence the solution.
WAAEM
Time-of-travel capture zone delineation
is conducted by ground-water flow modeling.
Modeling in this context is an interactive
process of data acquisition, data analysis,
and running a computer model. Initial
modeling results prompt changes in the
conceptual model, which in turn will lead to
new modeling results. In the absence of
definite data, hypothesis testing and
sensitivity analysis will be important aspects
of the modeling process. As a result, the
modeler will usually make frequent changes
to the input data file (an ASCII file of program
instructions) during the modeling process.
WhAEM was designed to facilitate this
process. GAEP greatly improves the
process of data entry, especially when used
2
-------
in combination with USGS topographic
maps and a digitizer (optional). The GAEP
knerated electronic background map
Becomes the template lor "on-screen"
design of the ground-water flow model.
GAEP communicates with the flow solver
CZAEM through an ASCII file that contains
the command script for delineating capture
zones.
Program CZAEM
CZAEM is a single layer model for
simulating steady flow in homogeneous
aquifers. The mathematical framework
underlying the model is based on the Dupuit-
Forchheimer assumption, where the vertical
resistance to flow is negligible, such as for
shallow aquifer flow. The implementation
of the analytic element method in CZAEM is
elementary, supporting only a few basic
analytic elements. These elements can be
used to simulate river boundaries, streams,
lakes, wells, uniform flow, and uniform
infiltration over a circular area.
Line-sinks are used to model river
boundaries, streams, and lakes. Line-sinks
are mathematical functions that simulate a
constant rate of extraction along a line. The
sink densities (strengths) of the line-sinks
the model are determined such that the
Apads at the center of the line-sinks are
¦qua! to specified values (usually chosen to
equal the water levels in the streams or
lakes). The accuracy with which the ground-
water inflow (or outflow) along a stream can
be modeled improves with a finer subdivision
of the stream in line-sink segments.
The well function (Thiem equation) is
used to model wells with given discharge
(pumping rate). Unlike numerical models,
the piezometric head distribution and the
velocity field near a well remain accurate,
since there is no discretization of the aquifer
by a grid or element network.
A special function, the "pond" function, is
used to model areal recharge due to
precipitation. Since CZAEM models steady
state flow, this recharge rate is a yearly
average. The "pond" function is a circular
element with an areal "source" density equal
to the recharge rate. The circular pond
overlays the domain of interest, the well
field and surrounding surface waters, to
simulate the desired aquifer recharge.
The uniform flow function may be used to
replace the combined effects of areal
recharge and surface water boundaries,
similar to the WHPA program. Since
W/iAEM allows the explicit representation
of these boundary conditions, the uniform
flow approximation is less often used in
applications to field problems.
Figure 3. Travel time isochrones for two wells in
a uniform How field.
The computer program CZAEM is an
elementary analytic element model with the
capability to generate capture zones of
wells. The program has the following
modules:
1. AQUIFER, for the input of aquifer data.
2. GIVEN, for the input of uniform flow and
areal recharge.
3. REFERENCE, for the input of the head
at one point in the aquifer.
4. WELL, for the input and implementation
of wdls
5. LINE-SINK, for the input and
implementation of line-sinks.
6. GRID, for the generation of a grid of
piezometric heads to be contoured.
7. PLOT, for piezometric contour plotting.
8. TRACE, for streamline tracing.
9. CAPZONE. for the generation of time-of-
travel capture zones.
10. CURSOR, for cursor controlled
interaction with elements.
11. CHECK, for monitoring the values of
parameters.
12.10, tor binary write and save of solutions.
13. PSET, for sending graphics to output
devices.
Capzone Module
The capzone module has been designed
to define the capture zone boundaries as
well as the travel time isochrones inside
these capture zone boundaries, called
timezones for arbitrary arrangements of
wells arvd line-sinks (stream boundaries).
Rather than merely tracing a number of
streamlines from the well, the capzone
module logic first determines all stagnation
points in the flow domain, determines
whether they are connected to the wells by
streamlines, and uses them as the basis for
defining the capture zone boundaries.
Under multiple well scenarios, one well
may have several different capture zones,
termed subzones. which have their own
travel time isochrones.
Figure 2 illustrates capture zones for five
different wells surrounded by two stream
branches and a tributary (solid lines). The
dashed lines are background map features
for orientation purposes. The capture zones
are pear shaped and of finite extent: the
wells receive all their water from areal
recharge.
In Figure 3, travel time isochrones are
presented tor two wells in a uniform flow
field. Notice that the isochrones wrap all the
way around the well; between the well and
i j
Figure 2. Capture zone envelopes for five wells
in a regional setting defined by streams and
areal recharge.
3
-------
its stagnation point, all travel times between
iero and infinity occur. Also notice that the
rapture zone of the right-hand well wraps
wound the capture zone of the other well,
causing a discontinuity in the residence
times across the latter capture zone
envelope.
Figure 4 shows capture subzones (or a
well near a river. The well is receiving 80%
of its discharge from the far-field and 20%
from the river.
The module CAPZONE has been written
specifically for this project. The source code
(FORTRAN) of this module is available
from USEPA and contains documentation
to facilitate its inclusion in other ground-
water models.
Preprocessor GAEP
The absence of a grid or element network
in analytic element models makes it
unnecessary to translate hydrography data
(stream locations and associated stream
levels) into cell specific data, which is the
main function of preprocessors for numerical
models. In contrast, the stream levels and
geometry are entered into the analytic
element model, through simple commands
which are in an ASCII file. These commands
ban be input directly from the keyboard
(command line mode) or read in from an
ASCII file (batch mode) (see Figure 5). The
line-sinks representing streams and lakes
are represented in the file by their end
coordinates and a specified head at the
center (stream level). The traditional
procedure for creating such an input data
file is to sketch the line-sink layout on a
map, write the stream elevations near these
line-sinks, and use a digitizer to produce
the coordinate pairs listed in Figure 5. The
syntax of the various commands in Figure
5 must be consistent with the requirements
of CZAEM, or one or more errors occur
when the file is read by CZAEM. Any change
in the input data, as part of the interactive
modeling procedure requires editing of the
input file, whereby it is often necessary to
revisit the topographical map and digitize
new line-sinks.
To facilitate this process, the preprocessor
GAEP separates the digitizing activities from
the creation of analytic elements (e.g. line-
sinks) to be included in the input data file for
CZAEM. GAEP, therefore, has two
functions:
1. Creation of a digital map of all streams,
Hakes, wetlands, well locations, and
Figure 4. Subzones for a well near a river. The
dotted lines represent hydraulic head contours.
AQUIFER
BOTTOM 330
THICKNESS 100
PERMEABILITY 350
POROsmr 0.20
RETURN
AOUIFER
REFERENCE 0 656160 410
RETURN
*RainElement
StNKDSK
DSCHARGE
21983 -6183 43881 -94755 <0.00411
RETURN
TablelttemtD: wabash east
UNESINK
HEAD
•13409 -18389 -12778 -10574 3&2 Mil
•12778 -10574 -8046 -5825 396.1 we2
•8046 -5825 4927 -1257 396.8 we3
•6927 -1257 -2322 367 397.2 wM
Figures. Part ol a CZAEM input data file.
background map information (roads, city
boundaries, outlines of surface geological
features, etc.). The surface water features
have associated with them the water levels
as reported on the topographical map
(intersections of elevation contours with the
stream beds).
2. Creation of an input data file for CZAEM
with all aquifer data and all analytic elements
(line-sinks and wells) needed for the model.
The first activity, creation of the digital '
map, is a routine procedure that does not;
require any modeling expertise or
hydrological knowledge. The digital map is
saved on disk for future use by the modeler.
A digital map, as displayed on screen by
GAEP, is reproduced in Figure 6. By pointing
at a feature with the mouse, its name is
displayed for easy identification.
The modeler will use GAEP and a digital
map previously saved on disk to create a
CZAEM input data file. To represent a
stream by line-sinks, the modeler merely
points at the stream with the mouse and
selects it by 'clicking" the mouse button.
By moving the pointer over the stream and
"clicking" on intended line-sink end points,
a string of line-sinks is created with heads
computed at their centers using the stream
elevations stored with the digital map. In
Figure 7, a string of line-sinks is illustrated.
The numbers printed near the line-sinks
represent the average stream elevations
(heads at the center of the line-sinks). GAEP
will also prompt for aquifer data; and when
instructed to create the CZAEM input data
file, write an ASCII file to disk that can be
read directly by CZAEM. In fact, the GAEP
generated input data file will introduce the
data, solve the problem, and create a grid
with piezometric heads. The modeler then
enters the TRACE and CAPZONE modules
in CZAEM to generate capture zone
boundaries.
Conclusions and
Recommendations
The deliverable of this project consists of
an analytic element modeling package for
simulating steady flow in homogeneous
aquifers, with the primary objective to
delineate capture zones in settings with
streams, rivers, lakes, infiltration and wells.
New algorithms have been developed for
the accurate delineation of capture zone
boundaries. These algorithms are
implemented in the computer code CZAEM.
The algorithms make accurate delineation
of capture zone boundaries possible. A
preprocessor program, GAEP, has been
developed to facilitate the entry of field data
into CZAEM. GAEP simplifies the process
of modeling considerably. Specifically,
GAEP separates the time consuming (but
routine) task of digitizing hydrography data
from the creation of conceptual models and
subsequent analytic element input data files.
With GAEP, the modeler is free to
concentrate on interpretation of modeling
results rather than the details of data
modification and entry into CZAEM.
The WhAEM package is documented in
various ways. The primary documentation
is contained in a program manual, which
includes installation instructions, program
descriptions and a tutorial for the integrated
use of GAEP and CZAEM. Reference
manuals for both GAEP and CZAEM are
4
-------
Mouse button 1: add point Keyboard F3: Done; Esc: CANCEL
42l
heads aloni
Kelso Creel
440
470
provided in the W/iAEM manual. A tutorial
(or stand-alone use of the program CZAEM
is availableas a separate document Finally,
both GAEPand CZAEM codes support on-
line help.
The W/iAEM package should only be
used by ground-water hydrologists qualified
to address wellhead protection delineation
problems. W/iAEM is designed to assist
hydrologists in teaming as much as possible
about the geohydrologica! problems they
(ace. Model predictions must always be
interpreted critically, with the simplifying
assumptions in mind. For complex
geohydrological settings, it may be
necessary to apply a more powerful model
than W/iAEM, requiring more experience
from the ground-water (low modeler.
Figure 6: Kelso Creek with elevation marks where contours cross the stream.
Mouse button 1: add point Keyboard F3: Done; ESC: CANCEL
.402.5
13.8
interpolated
line sink head
435.8
figure 7: Line-sinks created along Kelso Creek.
Hendrtk M. Haltjema, Ph.D.. is an
Associate Professor in the School of
Public and Environmental Affairs, Indiana
University, Bloomington, IN 47405.
Otto D.L Strack, Ph.D., is Professor of
Civil and Mineral Engineering, University
of Minnesota, Minneapolis, MN 55455.
Stephen ft Kraemer, Ph.D., Is a
Research Hydrologist for the USEPA ,
Robert S. Kerr Environmental Research
Laboratory, Ada, OK 74820. Dr. Kraemer
served as the USEPA Project Officer for
the cooperative agreement
Hardware requirements:
¦ 386 or 486 PC
• 2.5 MB RAM
• 2 MB hard disk space
• MS compatible mouse
• digitizer (optional)
• printer (optional)
Software requirements:
• MS DOS version 5.0 or higher
• Windows 3.1 (optional)
5
-------
The complete reports are:
CZAEM User's Guide: Modeling Capture Zones of Ground Water Wells Using the Analytic Element Method, EPA/600/R-94/174.
W/iAEM: Program Documentation for the Wellhead Analytic Element Model, EPA/60Q/R-94/210.
For a copy of the reports and associated software, please send a letter of request and one formatted 3.5 inch high density PC
diskette (please specify whether DOS or Windows) to:
Center for Subsurface Modeling Support (CSMoS)
Robert S. Kerr Environmental Research Laboratory
P.O. Box 1198
Ada, OK 74821
The reports are also available from:
National Technical Information Service (NTIS)
5285 Port Royal Road
Springfield, VA 22161
(703) 487-4650
6
-------
CALCULATED FIXED RADIUS
• RECHARGE METHOD
Vincennes, IN
Q = 370,000 ft3/day
N = 0.0032 ft/day (14 in/yr)
R = 6067 ft (1849m)
• VOLUMETRIC METHOD
Q '
71 H H
Vincennes, IN
Q=370,000 ft3/day
H = 30 ft screen
n = 0.2
t = 1825 days (5 yrs)
t = 3650 days (10 yrs)
Rs = 5985 ft (1824 m)
RI0 = 8464 ft (2580m)
(/=£> Q
top of cosing
water level
total depth
screened Interval
H
-------
CALCULATED FIXED RADIUS (CFR) WORKSHEET
What is the average pumping rate at the well
(in m3 per year)? A.
What is the estimate for effective porosity?
(porosity ranges: gravel 0.20-0.40, sand 0.20-0.50,
silt 0.30-0.50, clay 0.30-0.70) B.
What is the average saturated thickness of the aquifer
(in meters)? C.
What average residence time for the contaminant do
you want to calculate (in years)? D.
Multiply A x D = E.
Multiply BxCx3.14 = F.
Divide E / F = G.
Square root G = = CFR (m)
Locate your well on a USGS 7.5 minute map. Set your compass spread to the calculated
radius (CFR) using the scale below. Draw your CFR on the map.
• o.s o
<—i >—' i—t i—i i—i ~r
56
-------
CAPTURE ZONE
WELL IN UNIFORM FLOW
Qo
2Qo
Qo
v_
64. A* *, • ~,
^ Qo — s - — " —:— ^ 7U^ x
. u~~w gx £X £
[>Ccnt-~l^.sk*-vT. &y
, Jt^f rj
-.w* bt
\.^K JLSJZb yfV^-
X - k H 4> - - k H7 confined flow { ] re&t,
'1~ U€-C=£>-V_,
¦ — £ 4>J unconfmed flow
where Q (m3/day) is the well pumping rate, k is the hydraulic conductivity (m/day), H is the
aquifer thickness (m), x is the cartesian coordinate in direction of flow (m), and <}>, (m) is the
hydraulic head at x,. See the CZAEM Users Guide, page 7, for an example of computing Qo
given head observations in the field.
-------
WhAEM Tutorial Script
Load and Start the GAEP Program
^ C:\WHAEM> gaep
Ik press any key to continue
An Example Digital Map
1.
select File module
2.
read digital map
3.
vincenne
import file vincenne.dm
4.
return to the Main module
5.
enter the Digitize module
6.
view the vincennes digital map
7.
zoom in
8.
zoom out
9.
<= =>
cursor controlled pan and sccin
10.
quit the Digitize module
11.
exit the program
Create and Input File for CZAEM
1.
C:\WHAEM> gaep.
2.
select File module
3.
read digital map
4 .
vincenne
import file vincenne.dm
5.
return to the Main module
6.
enter the Element module
7.
select the Linesink command
8:
<= =>
page down, pan,1 scan to set window for Kelson Creek
9.
"mouse"
select Kelso Creek with left mouse button
|
"mouse"
build line-sinks by clicking left mouse button
for end points
w.
save, return to Element menu
12.
select the Well command
13.
<= =>
zoom down, pan & scan to set window for wellfield
14.
"mouse"
select wellfield
15.
"mouse"
position cursor in center of wellfield, click
llOooo
left button
16.
A&7J&&0
set the well discharge in ft*3/day
17.
1
set the well radius in ft
18.
save, return to Element menu
19.
quit, return to Main module
20.
enter the Aquifer module
21.
select the Base command
22.
330
set the base in ft above mean sea level
23.
select the Thickness command
24.
100
set the thickness of aquifer in ft above base
25.
select the Permeability command
26.
350
set the hydraulic conductivity in ft/day
27.
<0>
select the Porosity command
28.
0.2
set the porosity
29.
select the Reference command
30.
0
reference point x coordinate (world coordinates)
31.
656160
reference point y coordinate (world coordinates)
32.
410
reference head in ft above mean sea level
33.
select the Rain command
34.
"mouse"
click the left mouse button at the center of
the near field
m
"mouse"
click the left mouse button to define the rain circle
W.
yes
accept the rain circle
37.
0.0032
set the recharge rate in ft/day
38.
quit, return to the Main
Saving the CZAEM Input Data on Disk
-------
1.
enter the File module
2.
select the SaveElement command
3.
tutorial
save the file tutorial.dat to disk
¦
450000 4280000
define the model origin in world coordinates
¦
quit, return to Main module
P.
exit the program
Model
the Site with CZAEM
1.
C:\WHAEM> cz
activate the CZAEK program
2.
clear the intro screen, display COMMAND
module
3.
swi vincenne.dat switch in the script file
4.
window push
push the current window coordinates into
the buffer
5.
window all
define the new window to include all elements
6.
lay
display the layout of telements
7.
return, to the COMMAND module
8.
window pop
retrieve the last window in buffer
9.
win
display the window coordinates
10.
lay
display the layout of the wellfield
11-
return to the COMMAND module
12.
plot
enter the PLOT module
13.
d
select default contour settings
14.
accept levels, view head contours
15.
return to COMMAND module
16.
trace
enter the TRACE module
17.
lay
view the layout
IB.
"mouse"
set the cursor with the mouse to define
initial position of traceline
19.
trace 380
start trace at elevation 380 ft
V-
menu
return to TRACE menu
W--
set
enter the SET submodule
22.
back on
set backward tracing on
23.
maxstep 100
set the step size to 100 days
24.
mark time 730
mark time on tracelines to 73 0 days
25.
term time 3650
terminate tracelines after 3650 days
26.
ret
return to the TRACE menu
27.
lay
view the layout
26.
"mouse"
move the cursor to the well
29.
wgen 16
release 16 reverse tracelines from well casing
30.
menu
return to the TRACE menu
Hypothesis Testing with GAEP
1.
C:>\WHAEM> gaep
initiage the GAEP program
2.
enter the File Module
3.
select ReadNew command
4.
vincenne
read in the digital map vincenne.dm
5.
quit, return to Main Module
6.
enter the Element Module
7.
view and identify Mantle Ditch
8.
select the Image command
9.
"mouse"
position cursor, click to define image origin
10.
"mouse"
select the image second point, click and define
axis of symmetry
11.
yes
accept image line
.12.
"mouse"
use mouse to open recharge circle, click
h3.
to set
yes
accept recharge circle
14.
0.0032
enter recharge rate in ft/day
15.
405
enter the reference head
16.
view the image and real linesinks
17 .
return to Element menu
18 .
return to Main Module
-------
19. enter File Module
20. select the SaveElement command
21. tu_image save element file to hard disk
22. return to Main Module
23. exit program
^pothesis Testing with CZAEM
1. C:\WHAEM> cz activate the CZAEM program
2. clear intro screen
3. swi vinimage.dat switch in script file for images solution
4. capzone enter the CAPZONE module
5. 400 5 select contour levels for viewing
6. view contours
7. "mouse" position the cursor on the well
8. subzone wait for subzones to be drawn
9. time select for time zones
10. 730 730 3650 wait for timezones to be drawn
11. ret return'to CAPZONE menu
12. ret return to COMMAND menu
-------
CZAEM Tutorial Script
Example 1. Uniform Flow with a Well
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14 .
15.
16.
17.
18 ,
19,
20,
21,
22,
23,
24,
25,
26
!9.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
I
56.
activate the CZAEM program
clear intro menu
enter the AQUIFER module
define hydraulic conductivity in m/day
define porosity
define aquifer thickness in m
define base in m
return to COMMAND module
enter GIVEN module
define uniform flow discharge vector in
mA2/day and angle in degrees from x-axis
return to COMMAND module
enter REFERENCE module
define reference coordinates
solve for the unknowns
win -2000 -2000 2000 2000 define the lower left and upper
right coordinates of the window
fill a grid 50 x 50 with heads
enter the PLOT module
select default levels and plot 20 contours
view head contours
return to the COMMAND module
enter the WELL module
select for given discharge wells
x,y,discharge,radius
return to COMMAND module
solve for the new unknowns
C:\WHAEM> cz
aquifer
perm 6
poro 0.3
thick 100
base 150
ret
given
uni 0.'3015 0
ret
ref
-250 -250 200.5
solve
grid 50
plot
d 20
well
given
0 0 60 0.15
ret
solve
win -500 -500 500 500 zoom in with new window
grid 50
plot
d 20
trace
plot
d 20
"mouse"
trace
ret
map
plot on
curve
-350 150
-350 350
-150 350
-150 150
-350 150
ret
ret
trace
plot
d 20
"mouse"
trace
ret
stop
fill 50x50 grid with heads
enter the PLOT module
select default levels for 20 contours
view head contours
return to COMMAND module
enter the TRACE module
prepare for plot of head contours in background
position cursor for beginning of streamline
start streamline
return to COMMAND module
enter MAP module
turn of map features on
activate curve definition
XfY
finish curve
return to COMMAND module
enter the TRACE module
position cursor for beginning of streamline
start streamline
return to COMMAND module
exit the program
Example 2. Well Near A River
1. C:\WHAEM> cz
-------
2.
3.
aquifer
4.
perm 5
5.
thick 50
£.
base 0
|
poro 0.25
P
ret
9.
given
10.
uni 0.5 30
11.
ret
12.
linesink
enter the LINESINK module
13.
head
select head specified line-sinks
14.
-1500 1500 -600 1300
32
xl,yl, x2, y2, head
15.
-600 1300 -200 900 33
16.
-200 900 200 500 34
17.
200 500 500 200 35
18.
500 200 500 -800 37.5
19.
500 -800 800 -1000 38
20.
800 -1000 1100 -1000
39
21.
1100 -1000 1500 -1800
40
22.
ret
23.
win -1500 -1500 1500
1500
24.
layout
view the layout
25.
return to the COMMAND module
26.
ref
27.
-2000 4000 40
28.
solve
29.
grid 50
30.
plot
31.
d
32.
33.
return to the COMMAND module
M-
check
enter the CHECK module
m.
head 1 1
display head at point (1,1)
W6.
head -2000 5000
display head at point (-2000,5000)
37.
ret
38.
win -1000 -1000 1000
1000
39.
well
40.
given
41.
0 0 1500 0.3
42.
ret
43.
solve
44.
save
enter the SAVE module
45.
sol
46.
ex2.sol
47.
grid 50
48.
plot
49.
d
50.
view the head contours
51.
return to COMMAND module
52.
ref
53.
1 1 37.1828
54.
solve
55.
grid 50
56.
plot
57.
34 4
58.
view the head contours
59.
return to COMMAND module
60.
ref
fc-
-2000 5000 39.7540
P
solve
53.
grid 50
64.
plot
65.
26 2
66.
view the head contours
67.
return to COMMAND module
-------
68.
69.
70.
71.
I
75.
76.
77.
78.
read •
sol
ex2.sol
trace
plot
d
backward on
wgen 20
ret
stop
enter READ module
set backward tracing on
well generate 20 streamlines
return to COMMAND module
exit the program
------- |