United States Robert S. Kerr Environmental

Environmental Protection Research Laboratory

Agency Ada, OK 74820

E AP Project Summary

Research and Development EPA/600/SR-94/210 March 1995

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 of

(many) closed form analytical solutions

to generate a ground-water flow solution. WhAEM consists of two

executables: the preprocessor GAEP,

and the flow model CZAEM. WhAEM

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, OK,

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 streamDemonstration of the Analytic

Element Method for Wellhead

Protection

Hendrik M. Haitjema, Otto D.L. Strack, and Stephen R. Kraemer

lines. In most numerical methods, such

accurate determination 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. These analytic models 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’s 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

(WhAEM) 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 advanced

Updated Ordering

Information on Back

 

 5-16-95
2

discrete numerical or analytic element

models. The authors believe that the newly

developed model will serve ground-water

professionals who wish to determine capture zones in relatively simple

geohydrological settings.

WhAEM consists of 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 of 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. For a detailed description of the

method, the reader is referred to Groundwater Mechanics, O.D.L. Strack, 1989,

Prentice Hall, 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 is 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 represent certain hydrologic features.

For instance, stream sections are represented 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.

WhAEM

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

in combination with USGS topographic

maps and a digitizer (optional). The GAEP

generated electronic background map becomes the template for “on-screen’’ design of the ground-water flow model. GAEP

communicates with the flow solver CZAEM

? hypothesis forming

hypothesis testing

WhAEM

GAEP

CZAEM

Digitizer

PC

Model Building

Flow

Modeling

Figure 1. The modeling process using WhAEM.
3

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 DupuitForchheimer 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 linesinks in the model are determined such

that the heads at the center of the linesinks are equal 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

WhAEM allows the explicit representation

of these boundary conditions, the uniform

flow approximation is less often used in

applications to field problems.

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 wells.

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. IO, for 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 and 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 for two wells in a uniform flow

field. Notice that the isochrones wrap all

the way around the well; between the well

and its stagnation point, all travel times

between zero and infinity occur. Also notice that the capture zone of the righthand well wraps around 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 for 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.

Figure 2. Capture zone envelopes for five wells

in a regional setting defined by streams and areal

recharge

Figure 3. Travel time isochrones for two wells in

a uniform flow field.
4

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 can 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 linesinks.

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, lakes, wetlands, well locations, and 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 linesinks 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 provided in the WhAEM manual. A

tutorial for stand-alone use of the program

CZAEM is available as a separate document. Finally, both GAEP and CZAEM

codes support on-line help.

The WhAEM package should only be

used by ground-water hydrologists qualified to address wellhead protection delineation problems. WhAEM is designed to

assist hydrologists in learning as much as

possible about the geohydrological problems they face. 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 WhAEM, requiring more experience

from the ground-water flow modeler.

Figure 4. Subzones for a well near a river. The

dotted lines represent hydraulic head contours.

Figure 5. Part of a CZAEM input data file

AQUIFER

BOTTOM 330

THICKNESS 100

PERMEABILITY 350

POROSITY 0.20

RETURN

AQUIFER

REFERENCE 0 656160 410

RETURN

*Rain Element

SINKDISK

DISCHARGE

21983 -6193 43881 -24755 -0.00411

RETURN

*TabletltemID: wabash east

LINESINK

HEAD

-13409 -18389 -12778 -10574 395.2 [we1]

-12778 -10574 -8046 -5825 396.1 [we2]

 -8046 -5825 -5927 -1257 396.8 [we3]

 -5927 -1257 -2322 367 397.2 [we4]
5

Hardware Requirements

• 386 or 486 PC

• 2.5 MB RAM

• MS compatible mouse

• digitizer (optional)

• printer (optional)

Software Requirements

• MS DOS version 5.0 or higher

• Windows 3.1 (optional)

Mouse button 1: add point Keyboard F3: Done; Esc: CANCEL

heads along

Kelso Creek

400

410

420

430

440

450

460

470

Figure 6. Kelso Creek with elevation marks where contours cross the stream

430

440

450

Mouse button 1: add point Keyboard F3: Done; ESC: CANCEL

interpolated

line sink head

402.5

413.8

426.3

435.8

440

448.3

454.4

400

410

420

460

470

Figure 7. Line-sinks created along Kelso Creek.
6

Hendrik M. Haitjema is with the School of Public and Environmental Affairs, Indiana

University, Bloomington, IN 47405; Otto D.L. Strack is with the University of Minnesota, Civil and Mineral Engineering, Minneapolis, MN 55455; and the EPA author,

Stephen R. Kraemer (also the EPA Project Officer, see below), is with the Robert S.

Kerr Environmental Research Laboratory, Ada, OK 74820.

The complete set consists of associated software and two reports, entitled (1) “CZAEM

User’s Guide: Modeling Capture Zones of Ground Water Wells Using the Analytic

Element Method,” and (2) “WhAEM: Program Documentation for the Wellhead

Analytic Element Model.”

For a copy of the reports (while supply lasts) 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 preference) to:

Center for Subsurface Modeling Support (CSMoS)

Robert S. Kerr Environmental Research Laboratory

P.O. Box 1198

Ada, OK 74821

Attn: WhAEM

Copies of the reports only are also available from (see ordering information below):

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

Telephone: 703-487-4650

(1) “CZAEM User’s Guide,” (Order No. PB95-194189; Cost: $19.50, subject to

change) and (2) “WhAEM: Program Documentation,” (Order No. PB95-167375; Cost:

$27.00, subject to change). Cost does not include associated software.

The EPA Project Officer can be contacted at:

Robert S. Kerr Environmental Research Laboratory

U.S. Environmental Protection Agency

Ada, OK 74820

• •

United States

Environmental Protection Agency

Center for Environmental Research Information

Cincinnati, OH 45268

EPA/600/SR-94/210

BULK RATE

POSTAGE & FEES PAID

EPA

PERMIT No. G-35

Official Business

Penalty for Private Use $300