United States Environmental Protection Agency Robert S. Kerr Environmental Research Laboratory Ada, OK 74820 Research and Development EPA/600/SR-94/210 EPA Project Summary March 1995 Demonstration of the Analytic Element Method for Wellhead Protection Hendrik M. Haitjema, Otto D.L. Strack, and Stephen R. Kraemer A new computer program has been developed to determine time-of-travel capture zones In relatively simple geo- hydrological settings. The WhAEM package contains an analytic element model that uses superposition of (many) closed form analytical solutions to generate a ground-water flow solu- tion. W/iAEM consists of two executables: the preprocessor GAEP, and the flow model CZAEM. W/iAEM differs from existing analytical models in that it can handle fairly realistic boundary conditions such as streams, lakes, and aquifer recharge due to pre- cipitation. The preprocessor GAEP is designed to simplify the procedures for getting data into a ground-water model; spe- cifically it facilitates the interactive pro- cess 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 well- head protection contain such an algo- rithm. This Project Summary was developed by USEPA's Robert S. Kerr Environ- mental Research Laboratory, Ada, OK, to announce key findings of the Re- search Project that Is fully documented In separate reports and supporting soft- ware (See Project Report ordering In- formation at the back). Introduction The delineation of capture zones re- quires precise determination of stream- 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 imple- ment elementary analytic solutions for ground-water flow problems. These ana- lytic models are capable of producing more or less approximate shapes of the bound- aries of capture zones for any given time; e.g., the USEPA's original wellhead pro- tection model WHPA. However, even when the velocity components are known pre- cisely, 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 com- plex settings is currently done either by the use of discrete numerical models or analytic element models. The discrete nu- merical models, such as MODFLOW/ MODPATH of the US Geological Survey, and analytic element models, such as Strack's MLAEM, require detailed knowl- edge of the setting and advanced model- ing expertise to run; and they do not cur- rently have advanced algorithms for delin- eation of capture zones. The Wellhead Analytic Element Model (W/7AEM) falls between the two aforemen- tioned technologies, ft does contain an advanced algorithm for determining cap- ture zones for any well at any time based on precise knowledge of the locations of all stagnation points and dividing stream- lines, it has features that make the inclu- sion of open or closed, head-specified boundaries possible (for example to model streams), but lacks the power of advanced Printed on Recycled Paper ------- discrete numerical or analytic element models. The authors believe that the newly developed model will serve ground-water professionals who wish to determine cap- ture zones in relatively simple geohydrological settings. W/?AEM consists of two executables: the preprocessor GAEP and the flow model CZAEM (see Figure 1). In order to facilitate data entry in the computer pro- gram CZAEM (Capture Zone Analytic Ele- ment Model), a separate computer pro- gram was developed called GAEP, (Geo- graphic 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. W/jAEM was developed under a coop- erative agreement between EPA and Indi- ana University and the University of Min- nesota. The Analytic Element Method The analytic element method was de- veloped at the end of the seventies by Otto Strack at the University of Minne- sota. For a detailed description of the method, the reader is referred to Ground- water Mechanics, O.D.L. Strack, 1989, Prentice Hall, while a brief review follows. This new method avoids the discretiza- tion 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 rep- resented by closed form analytic solu- tions—the analytic elements. The com- prehensive 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 thou- sands. Traditionally, modeling ground-water flow by use of analytic functions was con- sidered to be limited to homogeneous aqui- fers of constant transmissivity. However, by formulating the ground-water flow prob- lem in terms of appropriately chosen dis- charge potentials rather than piezometric heads, the analytic element method be- comes 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 repre- sented by line-sinks; lakes or wetlands may be represented by areal sink distribu- tions. Streams and lakes that are not fully connected to the aquifer are modeled by WhAEM Figure 1. The modeling process using WhAEM. area sinks with resistance to flow between surface water and the aquifer. Disconti- nuities in aquifer thickness or hydraulic conductivity are modeled by use of line doublets (double layers). Other analytic elements may be used for special fea- tures, such as drains, fractures, and slurry walls. The analytic element method differs fun- damentally from most classical numerical models, for instance: 1. The solution is analytical; no interpo- lation is required to compute heads or velocities at any point in the do- main. This makes the method insen- sitive 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 approxi- mations made in the conceptual model and its implementation in the program; they are not the conse- quence of a model grid resolution and the associated numerical (ap- proximate) differentiation process. 3. The aquifer is unbounded in the hori- zontal plane; there are no artificial model boundaries that may influence the solution. W/7AEM Time-of-travel capture zone delineation is conducted by ground-water flow model- ing. Modeling in this context is an interac- tive process of data acquisition, data analy- sis, 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 as- pects of the modeling process. As a re- sult, the modeler will usually make fre- quent 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 pro- cess of data entry, especially when used in combination with USGS topographic maps and a digitizer (optional). The GAEP generated electronic background map be- comes the template for "on-screen" de- sign 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 simu- lating steady flow in homogeneous aqui- fers. The mathematical framework under- lying the model is based on the Dupuit- Forchheimer assumption, where the verti- cal resistance to flow is negligible, such as for shallow aquifer flow. The imple- mentation of the analytic element method in CZAEM is elementary, supporting only a few basic analytic elements. These ele- ments can be used to simulate river bound- aries, 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 in the model are determined such that the heads at the center of the line- sinks are equal to specified values (usu- ally 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 aqui- fer 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. 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. 4. 5. 6. 2. GIVEN, for the input of uniform fbw and areal recharge. 3. REFERENCE, for the input of the head at one point in the aquifer. WELL, for the input and implemen- tation of wells. LINE-SINK, for the input and imple- mentation of line-sinks. GRID, for the generation of a grid of piezometric heads to be contoured. 7. PLOT, for piezometric contour plot- ting. 8. TRACE, for streamline tracing. 9. CAPZONE, for the generation of time-of-travel capture zones. 10. CURSOR, for cursor controlled in- teraction with elements. 11. CHECK, for monitoring the values of parameters. 12. IO, for binary write and save of solu- tions. 13. PSET, for sending graphics to out- put 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 stagna- tion 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 bound- aries. 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 no- tice that the capture zone of the right- hand well wraps around the capture zone of the other well, causing a discontinuity 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. 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 writ- ten specifically for this project. The source code (FORTRAN) of this module is avail- able from USEPA and contains documen- tation to facilitate its inclusion in other ground-water models. ------- Figure 4. Subzones for a well near a river. The dotted lines represent hydraulic head contours. Preprocessor GAEP The absence of a grid or element net- work 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 numeri- cal models. In contrast, the stream levels and geometry are entered into the ana- lytic element model, through simple com- mands 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 Fig- ure 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 tradi- tional procedure for creating such an in- put data file is to sketch the line-sink lay- out 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 com- mands 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 proce- dure 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 prepro- cessor GAEP separates the digitizing ac- tivities from the creation of analytic ele- ments (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 lo- cations, and background map in- formation (roads, city boundaries, outlines of surface geological fea- tures, etc.). The surface water fea- tures have associated with them the water levels as reported on the topographical map (intersec- tions 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 hydro- logical 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 point- ing at a feature with the mouse, its name is displayed for easy identification. The modeler will use GAEP and a digi- tal 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 us- ing 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 BOTTOM 330 THICKNESS 100 PERMEABILITY 350 POROSITY 0.20 RETURN AQUIFER REFERENCE 0 656160 410 RETURN Rain Element 5INKDISK DISCHARGE 21983 -6193 43881 -24755 -0.00411 RETURN TabletltemlD: wabash east .INESINK 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 aquifer data; and when instructed to cre- ate 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 piezo- metric heads. The modeler then enters the TRACE and CAPZONE modules in CZAEM to generate capture zone bound- aries. 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 de- lineate 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 imple- mented 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. Spe- cifically, GAEP separates the time con- suming (but routine) task of digitizing hy- drography data from the creation of con- ceptual models and subsequent analytic element input data files. With GAEP, the modeler is free to concentrate on interpre- tation of modeling results rather than the details of data modification and entry into CZAEM. The W/iAEM 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 inte- grated use of GAEP and CZAEM. Refer- ence manuals for both GAEP and CZAEM are provided in the WftAEM manual. A tutorial for stand-alone use of the program CZAEM is available as a separate docu- ment. Finally, both GAEP and CZAEM codes support on-line help. The W/iAEM package should only be used by ground-water hydrologists quali- fied to address wellhead protection delin- eation problems. W/iAEM is designed to assist hydrologists in learning as much as possible about the geohydrological prob- lems they face. Model predictions must always be interpreted critically, with the simplifying assumptions in mind. For com- plex geohydrological settings, it may be necessary to apply a more powerful model than WhAEM, requiring more experience from the ground-water flow modeler. Figure 5. Part of a CZAEM input data file ------- Mouse button 1: add point Keyboard F3: Done; Esc: CANCEL A 360 470 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) Figure 6. Kelso Creek with elevation marks where contours cross the stream Mouse button 1: add point Keyboard F3: Done; ESC: CANCEL interpolated line sink head Figure 7. Line-sinks created along Kelso Creek. ------- 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. Stephen R. Kraemer (also the EPA Project Officer see below), is with the U.S. Environmental Protection Agency, Ada, OK 74820 The complete report consists of two volumes, entitled "CZAEM User's Guide: Modeling Capture Zones of Ground Water Wells Using the Analytic Element Method," (Order No. PB95-194189; Cost: $19.50, subject to change) and "WhAEM: Program Documentation for the Wellhead Analytic Element Model," (Order No. PB95-167375; Cost $27.00, subject to change) will be available only from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 Telephone: 703-487-4650 The EPA Project Officer can be contacted at: Robert S. Ken Environmental Research Laboratory U.S. Environmental Protection Agency Ada, OK 74821 United States Environmental Protection Agency Center for Environmental Research Information Cincinnati, OH 45268 Official Business Penalty for Private Use $300 BULK RATE POSTAGE & FEES PAID EPA PERMIT No. G-35 EPA/600/SR-94/210 ------- |