eder associates consulting engineers, p. c. · e h 0 eder associates consulting engineers, p. c. U. S. MAIL File #497-8 February 14, 1992 Mr. Michael A. Gifford Remedial Project Manager

e h 0eder associatesconsulting engineers, p. c.

U. S. MAILFile #497-8

February 14, 1992

Mr. Michael A. GiffordRemedial Project ManagerWaste Management Branch - 5HS-11United States EnvironmentalProtection Agency

Region 5230 South Dearborn StreetChicago, IL 60604

RE: Groundwater Modeling. National Presto Industries,Inc. Site. Eau Claire, Wisconsin

Dear Mr. Gifford,

The enclosed copy of the Flowpath User's Manual is being submittedto USEPA and WDNR as discussed in our telephone conversation ofFebruary 13, 1992. We have found this groundwater model to be acost-effective method of evaluating aquifer remediation time framesthat may be possible under various groundwater pumpage scenarios.It also provides capture zone width data similar to the Capturemodel used for the on-site groundwater phased Feasibility Study forthe NPI site.

We are proposing that Flowpath be used in the NPI site FeasibilityStudy to aid in evaluating off-site groundwater remedialalternatives. Please advise if there are any questions or concernsabout the use of Flowpath. We currently anticipate that themodeling would be performed in March 1992.

Very tru

William M. WarrenVice President

WMW/ccEnclosure

cc: J. Boettcher, WDNRR. Nauman, NPI (w/o enclosure)G. Rozmus, Eder Associates (w/o enclosure)

#L0214.mg

315 W. HURON STREET. SUITE 240. ANN ARBOR, MICHIGAN 481O3 • (313) 663-2144 • FAX (313) 747-6530

n Version 3

user's manual

.Waterloohydrogeologicsoftware

FLOWPATHVersion 3.0

Two-dimensional Horizontal Aquifer Simulation Model

developed by:

Thomas Franz&

Nilson Guiguer

Waterloohydrogeologicsoftware

We are pleased to announce /the relocation of our Toronto and Waterloo office*effective September 20, 1991 to:

37 Watersdown CrescentWhrtby, OntarioCanada LlR 1Z1Tel. (416)404-0991^Fax (416) 404-1570 ^~

200 Candtewood CrescentWaterloo, OntarioCanada N2L 5Y9Tel. (519) 746-1798"*-Fax (519) 746-1798

Table of ContentsLICENSE AGREEMENT ........................................................................... l

I. Copyright Notice ....................................................................................... ln. Warranty ................................................................................................ lHI. Disclaimer ............................................................................................... lIV. Governing Law ........................................................................................ 1Introduction ................................................................................................... 2How to Contact Waterloo Hydrogeologic Software ..................................... 3FLOWPATH Training and Consulting ........................................................ 3Acknowledgements ....................................................................................... 4

CHAPTER I. GETTING STARTED .................................................. 51.1 Hardware Requirements And Hardware Options ................................ 51.2 Backup Copies ......................................................................................... 51.3 How To Obtain 3 1/2-inch Diskettes ...................................................... 71.4 How to Install FLOWPATH on Your System ........................................ 71.5 How to Change Printer and Plotter Configuration ............................... 7

CHAPTER II - THEORETICAL BACKGROUND .................................... 92.1 Two-Dimensional Steady-State Flow ..................................................... 92.2 Velocities ....................................................................i........................... 102.3 Pathline Calculation .............................................................................. 102.4 Travel Times ........................................................................................... 112.5 Time-Related Capture Zones And Wellhead Protection Areas ............ 11

CHAPTER IH . NUMERICAL IMPLEMENTATION ............................ 133.1 Flow Equation ......................................................................................... 13

3.1.1 Confined Aquifers ....................................................................... 143.1.2 Unconfined Aquifers .................................................................. 163.1.3 Leaky Aquifers ............................................................................. 173.1.4 Surface Water Bodies ..................................................................... 183.1.5 Infiltration and Evapotranspiration .............................................. 213.1.6 Boundary Conditions ...................................................................... 213.1.7 Solution Method .............................................................................. 23

3.2 Velocity Calculation ................................................................................ 243.3 Particle Tracking .................................................................................... 26

3.3.1 Pathline and Travel Time Calculation .......................................... 263.3.2 Velocity Interpolation ..................................................................... 273.3.3 Automatic Step Control.................................................................. 283.3.4 Capture Mechanism and Pathline Termination ........................... 293.3.5 Release Radius ................................................................................ 303.3.6 Time-Related Capture Zones and Wellhead Protection Areas ..... 30

CHAPTER IV - USING FLOWPATH ..................................................... 314.1 General Overview ................................................................................... 314.2 How to Run FLOWPATH ....................................................................... 314.3 Active Keys And Mouse Functions ........................................................ 314.4 Screen Layout ......................................................................................... 32

4.4.1 Desktop............................................................................................ 324.4.2 Data Menu ...................................................................................... 324.4.3 Run Menu ........................................................................................ 334.4.4 Output Menu ........„....„.„....„„.„„.„....................,.....:..................... 34

4.4.5 Info Menu ........................................................................................ 344.5 How to ..................................................................................................... 35

4.5.1... Generate a Data Set ................................................................... 35Finite Difference Grid, Pumping and Injection Wells ...................... 35Domain Boundary and Hydraulic Boundary Conditions ................. 36Aquifer Properties (Hydraulic Conductivities and Porosity) ........... 36Aquifer Thickness and Aquifer Bottom Elevation ............................ 36Areal Recharge and Evapotranspiration Rates ................................ 37Pathline Specifications ....................................................................... 37

4.5.2 ... Modify a Data Set ....................................................................... 37Finite Difference Grid And Pumping And Injection Wells .............. 38Domain Boundary And Hydraulic Boundary Conditions ................. 38Aquifer Properties (Hydraulic Conductivities And Porosity) .......... 38Aquifer Thickness And Aquifer Bottom Elevation ........................... 39Areal Recharge And Evapotranspiration Rates ............................... 39Pathline Specifications ....................................................................... 39

4.5.3 . Rename A Data Set .................................................................... 394.5.44.5.54.5.64.5.74.5.84.5.9

Delete A Data Set ....................................................................... 39Read from and Store onto Directories and Disks ...................... 40Finish a Session .......................................................................... 40Calculate a Hydraulic Head Distribution ................................. 40Calculate Average Linear Groundwater Velocities .................. 41Calculate Steady-State and Time-Related Groundwater Path-

lines- .......................................................................................................... 414.5.10 ... Calculate Time-Related Capture Zones and Wellhead Pro-tection Areas ............................................................................................ 424.5.11... Obtain an Echoprint of Your Data Sets (Logbook) ................. 424.5.12 ... Produce Graphical Output ....................................................... 43

Screen Graphics .................................................................................. 43Printer and Plotter Graphics ............................................................. 43Graphics via HPGL files .................................................................... 44

4.5.13 Produce ASCII File of Head Values ............................................. 444.6 The CAD Environment .......................................................................... 44

4.6.1 Finite Difference Grid And Wells .................................................. 45Adding Grid Lines .............................................................................. 46Adding Wells ....................................................................................... 46Erasing Grid Lines ............................................................................. 47Erasing Wells ...................................................................................... 47Changing Pumping Rates .................................................................. 47

4.6.2 Domain Boundary And Boundary Conditions .............................. 47Defining Boundaries .......................................................................... 48Undoing Boundaries ........................................................................... 49Defining Constant Head Nodes ......................................................... 49Defining Flux Nodes ........................................................................... 49

Defining Surface Water Body Nodes ............................................ 50Viewing Nodal Values ................................................................... 50Erasing Specified Nodal Values ................................................... 50Changing Nodal Values ................................................................ 50

4.6.3 Aquifer Properties (Hydraulic Conductivities And Porosity)....... 51Denning Heterogeneities ................................................................... 51Viewing Material Properties .............................................................. 52

4.6.4 Aquifer Thickness And Aquifer Bottom Elevation ....................... 524.6.5 Areal Recharge And Evapotranspiration Rates ............................ 534.6.6 Pathline Specifications ................................................................... 54

Specifying Particles Released at Wells ............................................. 54Specifying Individual Particles .......................................................... 55Checking Particle Releases at Wells ................................................. 55

CHAPTERV -EXAMPLE .................................................................. 565.1 Description .............................................................................................. 56

CHAPTER VI - CODE VALIDATION „.„......„„.......„...„..„........„.......-.. 596.1 Uniform Flow Test Case ......................................................................... 596.2 Test Case 2 - Comparison with Numerical Models ............................... 62

6.2.1 Hydraulic Head Distribution ........................................................ 626.2.2 Pathlines and Travel Times ........................................................... 63

6.3 Test Case 3 - Comparison with Semi-Analytical Model ....................... 696.4 Conclusions ............................................................................................. 71

REFERENCES ..« ........«........«........«........«........-.w...w........«........ «......«. 72

Table of FiguresGrid definition .................................................................................................. 13Block definition .................................................................................................. 14Definition of block dimensions .......................................................................... 16Schematic representation of an unconfined aquifer ......................................... 16Schematic representation of a leaky aquifer .................................................... 18Leakage from surface water bodies ................................................................... 20Correction for area ratios ................................................................................... 20Definition of grid boundaries ............................................................................. 21Boundary Types..............................................!................................................... 22Constant flux boundary ..................................................................................... 22Velocity locations ................................................................................................ 25Velocity interpolation ......................................................................................... 27Automatic time step control .............................................................................. 28Capture and release radius ............................................................................... 29Physical domain for the example ...................................................................... 56Grid for example ................................................................................................. 57Hydraulic head distribution for example .......................................................... 57Velocity distribution for example ...................................................................... 58Time-related capture and injection zone for example ...................................... 58Grid for test case 1 ............................................................................................. 60Equipotentials for test case 1 ............................................................................ 60Pathlines for test case 1 ..................................................................................... 61Particle travel times for test case 1................................................................... 61Grid for test case 2 ............................................................................................. 64Aquifer properties for test case 2 ...................................................................... 64Equipotentials for test case 2 (FLOWPATH) ................................................... 65Equipotentials for test case 2 (PLASM) ............................................................ 65Equipotentials for test case 2 (MODFLOW)..................................................... 66Equipotentials for test case 2 (FLOWPATH's own contouring) ...................... 66Pathlines for test case 2 (FLOWPATH) ............................................................ 67Pathlines for test case 2 (GWPATH) ................................................................. 67200-day capture and injection zone for test case 2 -FLOWPATH ................... 68200-day capture and injection zones for test case 2 - GWPATH ..................... 68Pathlines for test case 3 (FLOWPATH) ............................................................ 70Pathlines for test case 3 (RESSQ) ..................................................................... 70

LICENSE AGREEMENTI. Copyright NoticeThis software is protected by both Canadian copyright law and international treatyprovisions. Therefore, you must treat this software JUST LIKE A BOOK, with thefollowing single exception. Waterloo Hydrogeologic Software authorizes you to makearchive copies of the software for the sole purpose of backing-up our software andprotecting your investment from loss.

By saying "JUST LIKE A BOOK", Waterloo Hydrogeologic Software means, forexample, that this software may be used by any number of people and may be freelymoved from one computer location to another, so long as there is NO POSSIBILITYof it being used at one location while it is being used at another. Just like a book can'tbe read by two different people in two different places at the same time.

II. WarrantyWith respect to the physical diskettes and documentation enclosed herein, WaterlooHydrogeologic Software warrants the same to be free of defects in materials andworkmanship for a period of 30 days from the date of purchase. In the event of noti-fication of defects in material or workmanship, Waterloo Hydrogeologic Software willreplace the defective diskettes or documentation. The remedy for breach of thiswarranty shall be limited to replacement and shall not encompass any other damages,including but not limited to loss of profit, and special, incidental, consequential, orother similar claims.

III. DisclaimerNeither the developeKs) of this software nor any person or organization acting onbehalf of him (them) makes any warranty, express or implied, with respect to thissoftware; or assumes any liabilities with respect to the use, or misuse, of this software,or the interpretation, or misinterpretation, of any results obtained from this software,or for damages resulting from the use of this software.

W. Governing LawThis license agreement shall be construed, interpreted, and governed by the laws ofthe Province of Ontario, Canada.

Waterloo Hydrogeologic Software

Introduction

Welcome to FLOWPATH!FLOWPATH is a powerful and easy-to-use tool for two-dimensional numerical aquiferanalysis. FLOWPATH allows you to calculate steady-state hydraulic head distrib-utions, groundwater velocities, pathlines, travel times, capture zones and wellheadprotection areas.

FLOWPATH features a fully menu-driven integrated environment. Even an inexpe-rienced user will find it easy to perform aquifer simulations of professional quality.FLOWPATH is leading groundwater modeling into a new era: with its computer aideddesign (CAD) capabilities, it makes numerical modeling more efficient than ever before.

FLOWPATH has been developed by experienced hydrogeologic modelers and has beenrigorously tested by users on all levels. As a result of detailed data checking, input offaulty data is almost entirely eliminated.

Due to sophisticated dynamic memory management and efficient solution techniques,FLOWPATH can handle problem sizes that would normally require mini- ormainframe-computers: up to 10,000 nodes, over 100 wells, over 100 different aquifermaterials, etc.FLOWPATH satisfies the most demanding post-processing needs. An extensivegraphics package allows direct output to the screen, a printer, a plotter or a file.

FLOWPATH is easy to install. The graphics card, screen type, the presence of a mathco-processor and extended memory are detected automatically. A math co-processorwould mainly speed up computations; extended memory in conjunction with anappropriate extended memory driver (Lotus-Intel-Microsoft LIM) will also reducerun-time effectively by reducing disk access.We are convinced that you will enjoy FLOWPATH's numerous features. We would liketo hear your comments and suggestions. Please call us or write to Waterloo Hydro-geologic Software.

FLOWPATH

How to Contact Waterloo Hydrogeologic Software

If, after reading this manual and using FLO WPATH.youwouldlike to contact WaterlooHydrogeologic Software with comments or suggestions, you can write a letter to :

Waterloo Hydrogeologic Software37 Watersdown Crescent 200 Candtewood CrescentWhitby, Ontario Waterloo, OntarioCanada L1R 121 Canada N2L 5Y9Tel. (416) 404-0991 Tel. (519) 746-1798Fax (416) 404-1570 Fax (519)746-1798

You can also telephone usat(EJO)74g 1709. To help us handle your problem as quicklyas possible, have these items ready before you call or include them in a detailed problemreport letter (use form at the back of the manual):

* Product name and version number.* Product serial number.* Computer make and model number.* Operating system and version number.* Total free RAM.* Number of free bytes on your hard disk.

FLOWPATH Training and Consulting

Training for the use of FLOWPATH and the interpretation of FLOWPATH's resultscan be arranged by contacting Waterloo Hydrogeologic Software. Consulting chargesapply.Waterloo Hydrogeologic Software also offers expert consulting services for mostnumerical modelling problems concerning groundwater flow and mass transport. Forfurther information please call or write.


AcknowledgementsThe authors would like to express their gratitude to the following persons for theirtime in reviewing the manual and their advice and encouragement during thedevelopment of FLOWPATH: Dr. Robert W. Cleary, Christopher Neville, ReneeTherrien, Dr. Bernhard Kueper, Dr. Emil 0. Frind and Dominique Guyonnet.

FLOWPATH

CHAPTER I - GETTING STARTED

1.1 Hardware Requirements And Hardware Options

To run FLOWPATH you need the following minimum system configuration:

* 640Kb RAM, with at least 500Kb free.

* A floppy drive (51/4-inch floppies or31/2-inch diskettes)for software installation.

* A hard drive, with at least 2Mb free. -.'

* A graphics card (Hercules, CGA, EGA, VGA; others available upon request atadditional charge) and a suitable monitor.

* DOS 2.0 or higher.

The following options make the use of FLOWPATH more convenient or efficient; theyare, however, not required :

* A Microsoft or compatible mouse.

* A math co-processor.

* Extended memory.

* A printer with graphics capabilities.

* A plotter.

If you have any problems with your particular system configuration, please make surethat you followed the installation instructions precisely (section 2.4). If the problemis still not resolved, contact Waterloo Hydrogeologic Software.

1.2 Backup Copies

The three distribution disks that come with this manual are formatted for standard5 V4-inch disks, 360Kb disk drives, and can be read by IBM PCs and compatibles.Before you do anything else, make backup copies of these three disks and store the


originals and backups in a safe place. Use your original disks only to make work orbackup copies, since there is a replacement charge if you erase or damage the originaldisks. Take the following steps to make backups :

* Get three new or unused floppy disks.* Boot up your computer.

* At the system prompt, type DISKCOPY A: B: and press ENTER. Themessage INSERT SOURCE DISKETTE IN DRIVE A: will be displayedon your screen. Remove your system disk (if you booted from the A: floppydrive) from drive A: and put distribution disk 1 into drive A:.

* If your system has two floppy disk drives, your screen will also say INSERTDESTINATION DISKETTE INTO DRIVE B:. In that case you'll need toremove any disk in drive B:, replacing it with a blank disk. If your systemonly has one floppy drive, then you'll be swapping disks in drive A:. Justremember that the distribution disk is the source disk, and the blank diskis the destination disk.

* If you haven't done it already, press ENTER. The computer will startreading from the source disk in drive A:.

* If you have a two-drive system, it will then write out to the destinationdisk in drive B: and continue reading from A: and writing to B: until thecopying is complete. If you have a one-drive system, you'll be asked to putthe destination disk in A:, then the source disk, then the destination diskand so on and so forth until it's finished.

* When copying is completed, remove the distribution disk (source) diskfrom drive A: and put it away. Remove the copy (destination) disk fromdrive B: and label it "FLOWPATH Disk #1".

* Repeat the preceding process with the second and third distribution disksand the other two blank floppies.

FLOWPATH

1.3 How To Obtain 3 1/2-inch Diskettes

If you want to obtain FLOWPATH on 3 1/2-inch diskettes (formatted for 720Kb forIBM PC's), send your original 5 1/4-inch disks back to Waterloo Hydrogeologic Soft-ware. You will then receive the 3 1/2-inch version of FLOWPATH for a nominal fee tocover shipping and handling.

1.4 How to Install FLOWPATH on Your System

. iYou must install FLOWPATH in your hard disk in order to run it. Make sure you haveat least 1 Mb of free space in the hard disk before installing FLOWPATH. In thefollowing it is assumed that drive A: in your system can read the FLOWPATH dis-tribution diskettes; if that is not the case just substitute A: by B:.

* Change the default drive to A: and insert FLOWPATH disk 1.

* Type FPINSTAL and press ENTER.

* Wait to be prompted to insert FLOWPATH disk 2. Replace disk 1 withdisk 2 and press ENTER.

* Repeat the preceding procedure for disk 3.

* Now you are prompted to install the printer and plotter drivers for yoursystem.

1.5 How to Change Printer and Plotter Configuration

You do not need to reinstall FLOWPATH in order to change the printer or plotterconfiguration. Just type FPSETUP at the FLOWPATH directory. Follow theinstructions that will appear in your screen. FLOWPATH supports the followingprinters for graphics output:

8 Waterloo Hydrogeologic Software

* EPSON FX* EPSON EX* EPSON LX* EPSON RX* EPSON MX* EPSON LQ* HP LaserJet

* HP DeskJet* IBM Proprinter

* IBM QuietWriter U* NEC 24 pin

* Okidata 9 pin

* Panasonic 9 pin

* Panasonic 24 pin

* Roland 9 pin

* Roland 24 pin

* Star 9 pin

* Star 24 pin

* Toshiba P321

* Toshiba P341

* Toshiba P351If your printer is not compatible with any one of the above, FLOWPATH supplies twoadditional generic drivers for 9 pin and 24 pin printers which you can try.

FLOWPATH also supports HP plotters or fully compatibles.

FLOWPATH

CHAPTER II - THEORETICAL BACKGROUND

2.1 Two-Dimensional Steady-State Flow

The governing equation for two-dimensional, steady-state flow in heterogeneous,saturated, anisotropic, porous media, is:

where: •/

7"« • 7"w = principal components of the transmissivity tensor (Li2!*1)

h = hydraulic head (L)

Q(x*y} = volumetric fluxes of sinks (-) and sources (+) per unit surfacearea of aquifer. This term can represent pumping/injectionwells, evapotranspiration, infiltration, and leakage fromsurface water bodies or over- and underlying aquifer-aquitardsystems (LT1)

. :t,y = Cartesian coordinates

The components of the transmissivity tensor are given by:T — hJf T — hJT (2)

where:

b = saturated thickness for unconfined aquifers, or aquiferthickness for confined aquifers (L)

^« * Ky, = principal components of the hydraulic conductivitytensor (LT1)


2.2 Velocities

The relationship between the properties of the porous medium, the hydraulic gradientand the groundwater flux is given by Darcy's law:

3A _ dh_ (3)* aBx y W9y

where:

qMtqy = components of the Darcy flux in the directions x and y (LT1)

The components of the average linear groundwater velocity are given by:

v =£- v =^ (4>

where:

9 = effective porosity for flow (dimensionless)

2.3 Pathline Calculation

Pathlines provide a clear visual description of the groundwater flow regime. In asteady-state flow field with no areally distributed recharge, pathlines coincide withstreamlines.

The two-dimensional characteristic equation of a pathline is given by :(5)

)

where p is a vector containing the xty coordinates of the pathlines, p(Xo,y0) defines thestarting point of the pathline (initial condition), v is the average linear groundwatervelocity and r is time.

FLOWPATH 11

2.4 Travel Times

As a by-product of the pathline integration in equation (5), the travel time of a fluidparticle is obtained from:

t= • • - C6)

where di is an infinitesimal time increment corresponding to the spatial increment vdtand tQ is initial time.

2.5 Time-Related Capture Zones And Wellhead Protection Areas

The capture zone of a pumping well is defined by the entire recharge area of the well.A time-related capture zone is the surface or subsurface area of an aquifer that providesrecharge to the well discharge within a specified time.

According to the US EPA guidelines (1987), one way of delineating a wellhead pro-tection zone is to find the "Zone of Contribution". This zone is equivalent to what hasbeen defined above as a time-related capture zone. Time levels of interest rangebetween 50 days and several years.

A large number of dissolved organic chemicals, bacteria and viruses adsorb to theaquifer material. Adsorption causes the contaminants to move slower than thegroundwater. Linear, isothermal adsorption can be accounted for by introducing aretardation factor R in equation (5):

where p4 is the bulk density of the aquifer material, 9 is the effective porosity and Kd

is the partitioning coefficient. Equation (5) can be re-written as:

fJ ,at

where v" = v/R.


This leads to a smaller wellhead protection area than in the case of a conservativechemical (e.g. chloride). It is therefore economical to account for the effect of adsorptionin the process of delineating wellhead protection areas. However, in most cases it isnot known a priori which chemicals or microbes the wellhead should be protected for.Looking at the sensitivity of the size of the wellhead protection area with respect tothe retardation coefficient can, however, provide useful information about the behaviorof the aquifer system. A retardation mechanism has therefore been implemented inFLOWPATH.

FLOWPATH 13

CHAPTER III - NUMERICAL IMPLEMENTATION

3*1 Flow Equation

A finite difference method is employed to solve the governing equation (1) for two-dimensional steady-state horizontal flow. The finite difference method has beencommonly used in groundwater modeling (e.g. Finder and Bredehoeft, 1968; Prickettand Lonnquist, 1971; Kinzelbach, 1986; McDonald and Harbaugh, 1984). In equation(1) the partial differentials dx and By are approximated by finite lengths Ax and Ay.The aquifer is subdivided (discretized) into a number of blocks with side lengths of Axand Ay and thickness b. Thus the governing equation takes the form of a fluid massbalance formulated for an ensemble of finite volumes of the aquifer. The two-dimensional formulation neglects any vertical gradients of hydraulic heads andvelocities.A rectangular grid is superimposed over the map of the groundwater system to dis-cretize the system into grid cells that are small compared to the spatial extent of theentire aquifer. In the limiting case for an infinite number of cells (i.e. for infinitelysmall grid spacings Ax and Ay) the solution approaches the exact solution. Theintersections of the grid lines are called nodes; they are referenced with a column (i )and a row (/ ) co-linear with the x and y directions, respectively (figure 1).

column i

row 11 >

j o r y

IJ

ij-1

node

i or x

Figure 1 - Grid definition


FLOWPATH uses a block-centered finite difference scheme. Aquifer properties (hy-draulic conductivities, porosity, aquifer thickness, aquifer bottom elevation) aredefined for each block and can vary from block to block. Figure 2 shows the blockrepresentation corresponding to node ij of figure 1.

Figure 2 - Block definition

3.1.1 Confined Aquifers

Considering an internal node ij in a confined aquifer, the finite-difference form ofequation (1) may be written as:

1

where:

!„

Ax..,

(9)• +

i.;-l/2

, 7"^ = aquifer transmissivities between nodes ij and i - IJ, and

nodes ij and i + IJ, respectively. These values are taken asthe weighted harmonic mean between the transmissivities ofblocks [(i,/);(*-1,7)1 and [(ij);0' •*• 1,7)1 :

•

FLOWPATH 15

b,j = aquifer thickness of block ij (L)

K^ = hydraulic conductivity of block ij in* direction (LT1)

*»ij-w * 7 " W i a s aquifer transmissivitics between nodes 1,7 and f , 7 - I , and

nodes 1,7 and 1,7 +1 , respectively. These values are takenas the weighted harmonic mean between the transmissivitiesofblocks [(i,7);(i,;-l)l and WJWJ + DJ-

T».j = *».A,

JTW = hydraulic conductivity of block i,/ in y direction (LT1)

AZjj = length of block ij inx direction (L)

Ax,_int> , Axi + w>> s distance between nodes i,j and /-IJ ; and nodes 1,7 andi + l,y , respectively (L) (figure 3)

Ayit> = length of block i,; in y direction (L) (figure 3)

= distance between nodes i,j and ij - 1 ; and nodes ij and1,7 •*• 1 , respectively (L) (figure 3)

~ hydraulic head at node 1,7' (L)

= volumetric fluxes of sinks (•) and sources (+) per unit surfacearea of aquifer at node ij. This term can represent pum-ping/injection wells, evapotranspiration, infiltration, andleakage from surface water bodies or over- and underlyingaquifers. For pumping or injection wells, FLOWPATH auto-matically divides the total flow rate of the well by the blocksurface area ArÂy^ to obtain the flux at node i,7 (LT1)


j o r y

tor x

Figure 3 - Definition of block dimensions

3.1.2 Unconfined Aquifers

For unconfined aquifers the saturated thickness biti is a function of the hydraulicheads, A priori, both the hydraulic heads and the saturated thickness are unknown.Mathematically, this leads to non-linear behavior. An initial guess for the saturatedthickness is required in order to estimate the aquifer transmissivities 7^ and Tn^ .

An iterative scheme must be used to calculate the hydraulic head distribution, updatethe transmissivities and check if the discrepancy between the previously estimatedsaturated thickness and the updated one is greater than a specified tolerance (see alsosection 3.1.7).

Saturated thicknessUnconfinedaquifer -

Figure 4 - Schematic representation of an unconfined aquifer

FLOWPATH 17

The directional transmissivities between adjacent nodes T. , 7L are cal-**l * laj "l J » 1/3

ciliated by multiplying harmonic averages of hydraulic conductivities by geometricaverages of saturated thickness (Butler, 1957).

where:

BTij = aquifer bottom elevation at node ij (figure 4). i

K* K* = hydraulic conductivities between blocks ij and i + IJ ; and^•l&j * JîJ*!/*

blocks i j and ij + l .respectively.

(ID

»'•>*« K».t £yttj +! -f- K^&yi.j

3.1.3 Leaky Aquifers

A leaky aquifer condition such as the situation shown in figure (5) is simulated byintroducing exchange fluxes with the overlying and the underlying aquifers as source-or sink-terms. The exchange terms are formulated according to Darc/s law; thus, theflow between neighboring aquifers is proportional to their head-difference. Let H^

and H^ be the constant hydraulic head in the overlying and underlying aquifers,

respectively. Then the steady-state flux exchanged between these aquifers and themodelled aquifer at node i,j is represented as:


where L,(J and L^ are the leakage factors for the overlying and the underlyingaquifers, respectively. The leakage factors are defined as:

(13)

where Kn and AT/, , are the hydraulic conductivities, and d, <L are the thicknesses'•/ *™«/ ij ^jof the overlying and underlying aquitards respectively.

1

h

tfi

~

H2

1

Q___

Ns^7

=

MlK. * ': ^1 (H -hj wwrtying aqljir«r

j d,

/ / / r~} / A |/////ov«n>inQ«qui(ani

. ' * * modtU«d tquttor« . • * • *

* * • " « ° *— ,' ; • 1> • • • *- ' -•

undttrtying •quttcrK'» (H-h)

I

Figure 5 - Schematic representation of a leaky aquifer

3.1.4 Surface Water Bodies

The flux induced by infiltration or exfiltration from surface water bodies is accountedfor by adding a head-dependent in(out)flux q^ to the source or sink term QttJ . By

assuming that the rate of flow through a streambed is directly proportional tostreambed area, hydraulic conductivity of the streambed, and head difference betweenthe aquifer and the stream (figure 6), this flux can be represented by:

FLOWPATH 19

is the elevation of the river or lake bottom, //P is the surface water table elevationin the river or lake at node ij . Note that the effect of partial penetration of a surfacewater body is neglected and the head in the stream or lake is assumed to remainconstant. Z,, is a leakage factor defined at each streambed node:w

K, • U5)- '•'

where:

K, = hydraulic conductivity of the river or lake bed (LT1)

dr = thickness of the river or lake bed (L)

R* = correction factor for ratio of surface areas of finite difference*ublock and river or lake in the block (figure 7).

The correction factor for the area ratio R^ is employed because the leakage area AttJ

of the river or lake bed within a block ij maybe smaller than the area of the blockitself (Ax.jAy.j) . Thus, the correction factor is written as:

A,;


impervious

water taWe _2

Jfc

semi pervious

datum

surface water1

'• Q

« .

. Hr

1

table elevation___ wnrtartahl*

i

h

i

' , riuw/1a

i

BR

' i

bottorr

•

Figure 6 - Leakage from Surface Water Bodies (after Kinzelbach, 1986}

RiverArea A..

Block i,j

Figure 7 • Correction for Area Ratio

Note that the flux q, in equation (13) remains constant as long as the groundwater^jtable lies below the river or lake bottom. However, if the groundwater table lies above

FLOWPATH 21

the river bottom, the flux becomes a function of the head difference between the aquiferand the surface water body; this results in a non-linearity in the system and iterationis necessary (see section 3.1.7).

3.1*5 Infiltration and Evapotranspiration

Surface infiltration or evapotranspiration remain constant throughout the simulation,independent of the hydraulic heads. Infiltration and evapotranspiration rates aredefined as flow rates per unit aquifer surface area. They are added directly to thesource/sink term Q^ in equation (9).

3.1.6 Boundary Conditions

The boundary conditions are specified at the center of a block (figure 8) for any typeof boundary condition.

Figure 8 - Definition of grid boundaries

Three types of boundary conditions can be defined: constant head node, no-flux (i.e.impermeable boundary), and constant flux boundary (figure 9).


no-flux boundary flonMBnMiMd boundvy oomtanf-fluK boundary

column I

Figure 9 • Boundary types. i

By default, all blocks outside the modeled region are assigned zero transmissivities,thus forming an impermeable boundary around the whole domain. All blocks insideof an impermeable region do not contribute to flow. These default conditions, however,can be redefined by specifying a constant-flux boundary as a flow per unit length ofboundary per unit thickness of aquifer ( q at figure 10). Internally this flow rate ismultiplied by the length of the block (half space between two successive nodes) andby the total saturated thickness of the aquifer and then added to the source or sinkterm Qu in equation (9).

Figure 10 • Constant-flux boundary

FLOWPATH 23

3.1.7 Solution Method

By writing an equation of the same form as equation (9) for every node of the finite-difference grid, a large set (NX*NY) of simultaneous algebraic equations is obtainedand must be solved for the unknown heads. There are many methods available forsolving such systems. FLOWPATH uses the modified iterative alternating directionimplicit method (IADI) because of its small memory requirements. The method wasoriginally developed by Peaceman and Rachford (1958) and is described in detail byPrickett and Lonnquist (1971). A predictor-corrector method is also included forimproved convergence.

The IADI technique is an iterative technique; iterations required for solving non-linearproblems, such as the ones arising due to free watertable aquifers, surface water bodies,leakage, etc., are therefore automatically accounted for.It can be shown that the systems of equations for groundwater flow are always diag-onally dominant. For such systems the IADI method is unconditionally stable (Kin-zelbach, 1986). The behavior of the iterative solution has to be monitored. For everyiteration the solution is checked against a convergence criterion. It is assumed thatconvergence is achieved if, for every node, the discrepancy between the current valuehfj* and the previous value h£f is less than 0.2 percent of the maximum head differencein the system:

I,***1 — I,0**h"> *'•> <0.2%(17)

The number of iterations is limited to a maximum of 100.The described convergence criterion and the maximum number of iterations, however,are only suggested default values that can be altered to the specific needs of anyparticular problem. It is strongly recommended not to change the default values toavoid premature termination of the hydraulic head calculation which would causeerroneous results.


3.2 Velocity Calculation

The internodal components of the Darcy flux qt and q, are obtained by differentiationof the calculated hydraulic heads :

*•>.,*,-*•

49tii.M = K,

where:

Ayii>+w = distance between nodes/,/ and i + !,./; and nodes/,/ and/, y + 1,respectively (L)

c conductivities between nodes /,/ and i-f I,/ at xdirection; and nodes / ,/ and ij + 1 at y direction, respectively.These values are taken as the weighted harmonic meanbetween the hydraulic conductivities of adjacent blocks:

From the Darcy fluxes the pore velocities are calculated'as:

q q,tû (19)

where:

FLOWPATH 25

0ij+i/2 = effective porosities between nodes ij and i + IJ ; and nodesij and i"J + l , respectively. These values are taken as theweighted arithmetic mean between the porosities of adjacentblocks:

(20)i + 1/2,;

8.

This formulation yields a discrete distribution of internodal velocities as shown infigure 11.

internodal velocities

block i.j

Figure 11 • Velocity locations


3.3 Particle Tracking

3.3.1 Pathline and Travel Time Calculation

Equation (5) is written in discretized form as an explicit time-stepping scheme:

with v* = v/R

where Ar is the time increment, vvv, are the upstream components of the average

linear groundwater velocity, R is the retardation factor, and x,y are the pathlinecoordinates.

The plus-sign in equation (21) corresponds to a forward tracking mode, the minus-signcorresponds to a reverse tracking mode. By using forward tracking, one can predictthe location of a particle at a future time; by using reverse tracking one can determinewhere a particle, whose present location is known, came from.

The travel times are obtained from a simple summation of all time increments :

r=r 0+lAr (22)where f is the total travel time, and 4, is the initial time level.

The pathlines obtained with this upstream weighted Eulerian time integration schemeare piecewise linear. The quality of the Euler integration is a function of the length ofthe spatial step As :

(23)

The accuracy of the velocity v at the current particle location strongly affects thequality of the pathline calculation. An interpolation scheme has to be used to processthe discrete velocity field obtained from equation (19). In order to guarantee smoothand accurate pathlines, the spatial steps have to be small in areas where large changesin the direction and magnitude of the velocity field occur and they can be larger inareas of more uniform flow. These accuracy requirements are reflected in the automaticadjustment of the spatial and temporal increments.

FLOWPATH 27

3.3.2 Velocity Interpolation

The internodal velocities v^ +iaj , v w are defined at discrete points. In order tocalculate accurate and smooth pathlines the velocity components must be calculatedat any location in the domain. The velocity vector at an arbitrary particle location iscalculated from a weighted average of the four nearest discrete velocity components.A scheme proposed by (Soell, 1988) has been modified to allow for irregular grid spacingand heterogeneous aquifers (figure 12). The weights are inversely proportional to thedistance between the current particle location and the points at which the velocitycomponents are defined:

i?'"' ''

i- (24)

where rvr>( are the distances of the particle from the /-th velocity vector, and vvv>(

are the velocity components defined at discrete locations on the finite difference grid.

Figure 12 • Velocity interpolation


3.3.3 Automatic Step Control

A predictor-corrector method is used to control the time step : using the velocitycomponents at the current particle location jr^.y^, a tentative partide location jcJWW,<y^wis computed from equation (21). At the new location the new velocity components areevaluated and can now be used to check the accuracy of the tentative step by performinga "reverse" step from the tentative particle location:

'y^-v, Ar (25)

Note that this relationship holds for the forward tracking mode. For reverse tracking,the "reverse" particle location is obtained by exchanging the'minus-signs in equation(25) with plus-signs.The discrepancy d between the original particle location JcoUly0tf and the "reverse"particle location jc^^y^ is calculated from (

r~T (26)

The discrepancy d has to be smaller than a specified accuracy criterion e. e is expressedas a percentage of the average grid spacing ds :

(27)

new

x ,ynew' new

Xoldy old

Figure 13 - Automatic time step control

FLOWPATH 29

If the discrepancy d exceeds the accuracy criterion £ the tentative particle location isrejected and the tune increment is reduced by 50 percent. This procedure is repeateduntil the pathline accuracy satisfies the error tolerance. In a relatively uniform flowfield the discrepancy d is small; if the discrepancy d is smaller than 0.5e, the tentativeparticle location becomes a pathline coordinate and the time increment is doubled. Inall other cases the time increment does not change.

3*3.4 Capture Mechanism and Pathline Termination

Particles are followed until they are discharged either by singularities or leave thedomain.

,iIn the direct vicinity of singularities such as pumping or injection wells, the interpo-lation scheme in equation (24) is not valid; it produces an artificial stagnation pointin the center of the well. If a particle approaches a pumping well (forward tracking)or an injection well (reverse tracking) closer than 30 percent of the grid spacing directlyadjacent to the well center, then the pathline calculation for that particular particleis terminated. The pathline ends at the well coordinates.

dy1

dy2

reloa&« anacaptureradius

dx1 dx2

r - 0.3' Min(dxl.dx2,dy1,dy2)

Figure 14 - Capture and release radius

To avoid particle oscillations around a stagnation point, the pathline computation isterminated if a particle's velocity is near zero. A particle could also oscillate around"weak" singularities that occur in areas of strong recharge events or near surface water


bodies such as lakes, etc. With the automatic step control mechanism described insection 3.3.3, such oscillations lead to decreasing spatial steps; the pathline calculationis terminated if the step length falls below 0.5 percent of the average grid spacing.

3.3.5 Release Radius

Injection zones and capture zones are obtained by releasing a number of imaginaryparticles on a circle around an injection well (forward tracking) or a pumping well(reverse tracking), respectively, approximating the well perimeter. The radius of therelease circle is a function of the grid spacing directly at the well (due to velocityinterpolation problems at singularities; see section 3.3.4). The velocity interpolationscheme implemented in FLOWPATH gives accurate velocities at a distance equal orgreater than 0.3 times the distance between the well and the nearest grid intersection.This distance is used as the release radius (figure 14).

3.3.6 Time-Related Capture Zones and Wellhead ProtectionAreas

Time-related capture zones are calculated as a set of pathlines originating on a circlearound the well of interest. The pathlines are only calculated up to the specified timelevel. The last time increment is adjusted such that the specified time level is reachedprecisely. Travel times are calculated according to equation (22).A wellhead protection area that is based on time of travel, is equivalent to a time-relatedcapture zone. As stated above, many chemicals, bacteria and viruses adsorb to theaquifer material. If the wellhead protection area is to be designed for a specific con-taminant, a retardation factor can be used to delineate the wellhead protection zonemore accurately. In general, the time-related capture zone and the resulting wellheadprotection area are smaller for sorbing solutes than for conservative ones and theassumption of conservative chemical behaviour leads to a conservative estimate forthe size of the required wellhead protection zone.

FLOWPATH 31

CHAPTER IV - USING FLOWPATH

4.1 General Overview

FLOWPATH has been designed to make numerical modeling accessible to hydro-geologists who have not had any previous formal training in numerical methods andcomputers in general. FLOWPATH's level of sophistication should also appeal to anexperienced modeler. Waterloo Hydrogeologic Software developed an integratedenvironment in combination with CAD-graphics; you will find these features in allIBM-PC programs by Waterloo Hydrogeologic Software.

4.2 How to Run FLOWPATH

The current directory must be the directory where FLOWPATH has been installed onyour hard drive. Type "fp" to run FLOWPATH.

4.3 Active Keys And Mouse Functions

At all stages in a session, the following keys on your keyboard are active :* <return>;* <F3>;*<Esc>;

* cursor (arrow) keys.Only when numerical or text input is required, the number or letter keys also becomeactive. All other keys have no meaning and are ignored by FLOWPATH.The keys listed above have the following meaning :

* <return> : execute an option;* <F3> : execute an option (equivalent to <return>);* <Esc> : escape from currently active procedure or window;* <F1> : display help for currently active procedure or window;* cursor keys : move cursor and/or highlight an option in a menu.


Note: If for any mason you cant continue In your session and FLOWPATH does notrespond to any keyboard Input, press <Esc>. You will then be kicked back onto theprevious level; this should usually allow you to restart the desired procedure.

If you have a Microsoft compatible mouse, the mouse buttons emulate the followingfunctions :

* left button or right button* both buttons together* mouse movements

: same as <return> or <F3>;: same as <Eso;: same as cursor (arrow) keys.

4.4 Screen Layout

The integrated environment consists of four major parts : the desktop, the CAD-graphics for data manipulation, the execution level for computation and the post-processing graphics.

4.4.1 Desktop

The desktop gives you access to four menu options in the top bar. You have to use thecursor (arrow) keys or the mouse to highlight one of the displayed options. By pressing<return> or one of the mouse buttons the desired option is selected and executed. Atthe bottom of your screen you «*" see a status line for brief explanations, error mes-sages, warnings, etc. Drop-down menus (also called "pop-up menus") display moreoptions.

4.4.2 Data Menu

RunFLOUFRIH

Output Info

yBenaneDeleteChange dirQuit

FLOWPATH

[Generate][Modiry][Rename]

[Delete]

[Change dir]

[Quit]

...generate a new data set.

...modify an existing data set.

...rename an existing data set (all files associated with the oldname, including data and result files).

...delete an existing data set (all files associated with the oldname, including data and result files).

...change current directory to the specified (existing) directory;data will be read from and/or written to the selected directory.

...ends a session and returns you to DOS.

4.4.3 Run Menu

Bata?IO«PfiIH

Output Info

VelocitiesPathlinesCapture 2one

The following options are available :

[Steady State Flow][Velocities][Pathlines][Capture Zone]

...calculates a steady-state hydraulic head distribution,

...calculates average linear groundwater velocities.

...calculates pathlines.

...calculates time-related capture zones (wellheadprotection areas) and time-related particle paths.


Select the desired option from the menu. A window containing all complete data setswill pop-up. Highlight and select the data set of interest.If the results for the option of your choice were already calculated, a warning will bedisplayed. You will then be asked to either cancel the procedure or overwrite theexisting results.After the calculation is finished, the results will be displayed on the screen.

4.4*4 Output Menu,i

You can output to screen, printer, plotter, or to a HPGL-file.

[Grid][Equi potentials][Velocities][Pathlines][Capture Zone]

[Logbook]

...output finite difference grid and well locations.

...output steady-state hydraulic head distribution.

...output average linear groundwater velocities.

...output steady-state or time-related pathlines.

...output steady-state or time-related capture zones (wellheadprotection areas) and injection zones.

...produces an echoprint of all significant input data; the echo-print will be directed to the screen and a file (fh.log; m standsfor the name of the selected data set); screen output can beinterrupted by using the <Pause> key.

4.4.5 Info Menu

This menu contains a copyright notice.

FLOWPATH 35

4*5 How to...

4.5.1... Generate a Data Set

Select [Generate] in the [Data] menu (see section 4.4.2). Input a new file name. Anerror message will be displayed in the status line in case the operation was unsuc-cessful.A pop-up window will appear on the right of the [Data] menu; the following optionswill be displayed:

. 1[Grid and Wells][Domain Boundary][Aquifer Properties][Thickness/Elevation][Recharge Rates][Pathlines]

Each one of these options stands for the generation of an entire data file. You have togenerate each file starting with the first one in the above listYou will then be prompted for some general information such as unit system, default(background) values of your particular system, etc. Then the program loads the CADinput menus, where you can refine the data. The CAD environment is described inmore detail in section 4.6.

Finite Difference Grid, Pumping and Injection Wells

Select [Grid and Wells]. Select the unit system of your choice : English or S.I. units.In the following menu you will be asked to set up a "default" grid. You have to specifythe number of grid lines in both the x and the y direction, as well as the minimum and

x and y coordinates. FLOWPATH will then generate a grid with these overalldimensions and a uniform grid spacing.


You will then be transferred into the CAD environment, where you can alter the grid(i.e. add or erase grid lines), add and erase wells and specify pumping or injectionrates. A detailed description of the CAD environment can be found in section 4.6.

Domain Boundary and Hydraulic Boundary Conditions

Select [Domain Boundary]. You will then be transferred into the CAD environment(see section 4.6).

Aquifer Properties (Hydraulic Conductivities and Porosity)

Select [Aquifer Properties]. In the following menu you will be asked to enter "default"values for the hydraulic conductivities in the i- and y-direction and the aquifer porosity.FLOWPATH will then generate an aquifer with the defaults as background values.You will then be transferred into the CAD environment, where you can define het-erogeneities such as high or low permeability lenses (section 4.6).

Aquifer Thickness and Aquifer Bottom Elevation

Select [Thickness/Elevation]. You have to specify if you want to simulate a confinedor unconfined aquifer.If you select an unconfined aquifer, you will be asked to specify the elevation of theaquifer bottom. In the CAD environment you are allowed to specify spatially varyingbottom elevations. You do not have to specify the saturated thickness for the unconfinedaquifer, FLOWPATH will solve for the thickness iteratively.If you select a confined aquifer, you will have to specify if the aquifer is leaky ornon-leaky; for the leaky aquifer you have to input the values of the hydraulic headsin the under- and overlying aquifers, the conductivities of the separating aquitardsand the thickness of the modeled aquifer. You win then be transferred into the CADenvironment, where you can define aquifer thicknesses different from the defaults.

FLOWPATH 37

Area! Recharge and Evapotranspiration Rates

Select [Recharge Rates]. You will then be asked to enter default values for infiltrationand evapotranspiration rates.

You will then be transferred into the CAD environment, where you can define infil-tration and evapotranspiration rates different form the background.

Pathline Specifications

Select [Pathlines]. You will immediately be transferred to the CAD environment.

4.5.2 ... Modify a Data Set

•gig Bun OUTPUT Wefen-rat?WansIieleaCnangHirQuit

Current oirtctOHJ •iMl^TRl'J!! If im^tl!

E

X^====

CSRZIZBpoHITDura.EXRtffUNIKEionucs:

==„, . "MTTja

:

^H

Select [Modify] in the [Data] menu. Select the desired data set from the figure.Note: You can only modify complete data sets (!.•• all files must exist)!

A pop-up window will appear on the right of the [Data] menu; the following optionswill be displayed (the items are described in detail in section 4.5.1):

Waterloo Hydro*eologic Software

JUNPR1HOutput Info

Generate

DeleteChange dirQuitDorain touxanflquifer PropertyIhickness/BottonBecharge RatesPathlines

[Grid and Wells][Domain Boundary] *'

[Aquifer Properties][Thickness/Elevation][Recharge Rates][Pathlines]

Finite Difference Grid And Pumping And Injection Wells

Select [Grid and Wells]. You will then be transferred into the CAD environment.Nott: You cannot modify tr» unit system or ovtrall dimensions of th« grid !

Domain Boundary And Hydraulic Boundary Conditions

Select [Domain Boundary]. You will then be transferred into the CAD environment.

Aquifer Properties (Hydraulic Conductivities And Porosity)

Select [Aquifer Properties], You will then be transferred into the CAD environment.Nott: You cannot modify th« default aquifer properties!

FLOWPATH 39

Aquifer Thickness And Aquifer Bottom Elevation

Select [Thickness/Elevation]. You will then be transferred into the CAD environ-ment.

Note : You cannot modify the default value* for thickness or bottom elevation. Youcannot change a confined aquifer to an unconflnsd or vlca versa.

Area! Recharge And Evapotranspiration Rates

Select [Recharge Rates]. You will then be transferred into the CAD environment.Note: You cannot modify the default values. ';

Pathline Specifications

Select [Pathlines]. You will then be transferred into the CAD environment.

4.5.3 ... Rename A Data Set

Select [Rename] in the [Data] menu. A window containing all complete data setswill pop-up. Highlight and select the data set you wish to rename. You will then beprompted to type a new file name. An error message will be displayed in the statusline in case the operation was unsuccessful.

Note : all existing result files will also b« renamed.

4.5.4 ... Delete A Data Set

If you want to delete an entire data set along with all existing result files, select[Delete] in the [Data] menu. A window containing all complete data sets will pop-up.Highlight and select the data set you wish to delete. You will be prompted to confirmthat you really want to delete this data set. After you have confirmed, the data set willbe erased.


Not*: 1) All existing result file* of the same data set will also be erased.2) If you delete only one of the data files by using the DOS "del** or "erase"commands, you will not be able to modify the remaining data Hies of thesame set and you will not be able to access any of your result files usingFLOWPATH.3) If you run out of space on your disk drive, FLOWPATH will terminate wtthan error message; If you nave more than 30 data sets In the same directory,you will be asked to delete some of your data sets. If you want to keep allof your data sets, move some of them to a different directory or drive usinga DOS command or any utility of your choice.

4.5.5 ... Read from and Store onto Directories and Disks

Select [Change dir] in the [Data] menu; you will then be prompted for the path ofthe new directory. If the new directory does not exist or if the specified drive is notresponding, etc., an error message will be displayed in the status line and the directorywill not be changed. After you finish your FLOWPATH session, you will automaticallybe returned to the directory from which you started FLOWPATH.

4.5.6 ... Finish ;. Session

Select [Quit] in the [Data] menu.

4.5.7 ... Calculate a Hydraulic Head Distribution

Select [Steady-State Flow] in the [Run] menu. A window containing all completedata sets will pop-up. Highlight and select the data set for which you want to calculatethe hydraulic head distribution.

If the hydraulic head distribution was calculated previously, a warning will be dis-played. You will then be asked to either cancel the procedure or overwrite the existingresults.During execution, the maximum hydraulic head correction in the system will be outputto screen for each iteration of the solution algorithm.

FLOWPATH 41

After the calculation is finished, the results will be displayed on the screen. By default,ten equipotentials will be drawn.

4.5*8 ... Calculate Average Linear Groundwater Velocities

Select [Velocities] in the [Run] menu. A window containing all complete data setswill pop-up. Highlight and select the data set for which you want to calculate theaverage linear groundwater velocities.

If the velocity distribution was calculated previously, a warning will be displayed. Youwill then be asked to either cancel the procedure or overwrite the existing results.The results will be displayed on the screen.

4.5.9 ... Calculate Steady-State and Time-Related GroundwaterPathlines

Select [Pathlines] in the [Run] menu. A window containing all complete data setswill pop-up. Highlight and select the data set for which you want to calculate thehydraulic head distribution.

If the pathlines were calculated previously, a warning will be displayed. You will thenbe asked to either cancel the procedure or overwrite the existing results.In the next screen menu you will be asked if you want time-related or steady-statepathlines. If you select "steady-state" the particle pathlines will be calculated untilthe particles are discharged over a domain boundary or by a receptor (e.g. a hydraulicsink). Time-related pathlines will only be displayed up to a distance associated withthe selected time level.The results will be displayed on the screen.


4.5.10... Calculate Time-Related Capture Zones and WellheadProtection Areas

Select [Capture Zone] in the [Run] menu. A window containing all complete dataseta will pop-up. Highlight and select the data set for which you want to calculate thehydraulic head distribution.If time-related capture zones were calculated previously, a warning will be displayed.You will then be asked to either cancel the procedure or overwrite the existing results.As for the pathline calculation, in the next screen menu you will be asked if you wanttime-related or steady-state capture zones: If you select "steady-state1* the particlepathlines will be calculated until the particles are discharged over a domain boundaryor a receptor (e.g. a hydraulic sink). You can specify if you want capture zones (wellheadprotection zones) or injection zones or both. Hie calculated pathlines describe thesteady-state capture zone or injection zone of the pumping or injection well, respec-tively. Time-related capture zones will only be displayed up to a distance associatedwith the selected time level.The results will be displayed on the screen.

4.5.11 ... Obtain an Echoprint of Your Data Sets (Logbook)

Select [Logbook] in the [Output] menu. A window containing all complete data setswill pop-up. Highlight and select the data set for which you require an echoprint. Yourinput data will then be printed to the screen (interrupt screen scrolling with the<Pause> key) and also be saved in the file fri.log ffrT stands for the name of the selecteddata set). You can print this file by specifying TRINT m,LOGM at the DOS prompt.

FLOWPATH 43

4.5.12 ... Produce Graphical Output

Data BuiFLOUPfllH

Info

fluipotennaisVelocitiesPathlinesCapture Zone

Graphical output can be directed to the screen, a printer, a plotter or a file.Select [Output]. A pop-up menu with the available types of graphical output willappear on the screen. At this point, the following options are available:[Grid], [Equipotentials], [Velocities], [Pathlines], [Capture Zones].After you selected the type of graphics you want, a window containing all completedata sets will appear allowing you to specify the data set of interest. Finally, fromanother pop-up window you select where you would like to direct the graphics. Youhave the choice between screen, hardcopy output on a printer or plotter, and outputto a file with standard HPGL language commands.

Screen Graphics

FLOWPATH has a built-in graphics library for previewing results in graphical formon the screen. The graphics card of the computer is automatically detected.

Printer and Plotter Graphics

If you select printer or plotter, you must have previously installed an appropriateprinter or plotter (see section 1.5)! FLOWPATH checks automatically if an outputdevice has been installed before graphics are sent to the printer/plotter ports.


Graphics via HPGL files

HPGL-files can be post-processed by printers and plotters using appropriate softwarepackages (including e.g. PRINTAPLOT from Insight Development Corp.). HPGL filesare also useful for importing graphics into standard word-processing packages.

4.5.13 Produce ASCII File of Head Values

An ASCII file containing X,Y coordinates and head values for each finite differencenode is automatically generated. This file has the extension ".DAT*. These files areuseful for producing contour maps of hydraulic head distribtutions using standardcontouring software (for example SURFER from GOLDEN Software Inc.) or if aprintout of hydraulic head values is required.

4.6 The CAD Environment

The CAD (Computer Aided Design) environment is one ofFLOWPATrTs most powerfulfeatures. It allows fast and easy setup of complicated problems and at the same timeallows the user to visually inspect his actions. Errors that occur frequently during theinput of data are thus virtually eliminated.In order to run a problem, a data set must be completed. A complete data set is a dataset that contains grid and well data, boundary and boundary condition data, aquiferproperties, aquifer thickness and bottom elevations, recharge rates and pathlinespecifications.For the CAD environment, a Microsoft (or compatible) mouse is strongly recommendedsince it simplifies and speeds up many of the required tasks (e.g. moving around onthe screen) that otherwise have to be done by using the cursor keys.In all CAD environments the following keys are active : <Return>, <Eso and thecursor keys; if you have a mouse, the left and the right button of the mouse emulate<Return>, both buttons pressed at the same time emulates <Eso. Note: If for anyreason the program does not respond, press <Esc>; <Esc> will not cause loss of data,but usually terminate any currently active procedure.

FLOWPATH 45

4.6.1 Finite Difference Grid And Wells

Select [Grid and Wells] in the [Modify] or [Generate] menu; if you already havespecified the default values (see section 4.5.1.1) you will be transferred to the CADenvironmentThe following options are displayed on the right hand side of the screen:

[Horiz Line] ...add a horizontal grid line;[Vert Line] ...add a vertical grid line;[Pumping Well] ...define pumping well parameters;[Injection Well] ...define injection well parameters; ..[Erase Line] ...erase a horizontal or vertical grid line;[Erase Well] ...erase a pumping or injection well;[View Well] ...display coordinates, pumping or injection rates of wells;[Save & Redraw] ...save all input parameters to file (fh.grd) and redraw the screen

image (remain in CAD environment);

[Exit & Save] ...save all input parameters to file (fii.grd) and exit to main menu;

[Quit] ...abandon all changes since the last save and exit to main menu.To execute one of the above options highlight the desired option by moving the bar(use cursor keys up or down) and press <Return>; you can also use the mouse tohighlight and click the left mouse button to execute the highlighted option. The cursor(a cross) will be positioned approximately in the center of the domain; move the cursor(press cursor keys or move the mouse) to move the grid line, well or cursor.The maximum resolution of the cursor movements depends on the resolution of yourgraphics adapter. You can accelerate the cursor movements by pressing <+> or <•>.Note that the spatial resolution of the cursor movements decreases as you accelerate;this could be critical if you are trying to position a well, erase a well or erase a gridline (see below). The precision of the cursor movements will be displayed on top of thedomain window.


Adding Grid Lines

The grid can be made up of up to 100 grid lines in the x-direction and 100 grid linesin the y-direction. Thus, the maTimiim number of unknown hydraulic head values is10,000. To add grid lines follow these steps:

1) select [Horiz Line] or [Vert Line];2) move to the desired position (you can check the coordinates on the screen!);3) press <Return> or click one of the mouse buttons;4) repeat steps 1) to 3) to add more lines or press <£so to finish.

Note: The accuracy of the hydraulic head field Increases with the, grid resolution. A finergrid will normally give results of a better quality; there Is, however, a trade-off withcomputer time requirements. For best results the grid spacing should change gradually.The grid spacing should not Increase by more than about 50 percent for two adjacentcells. Also an aspect ratio must be respected: a grid eel! shall not be more than 10 timesbigger tn one direction than In the other.

Adding Wells

Up to 100 pumping and 100 injection wells can be specified. To position a well andinput the pumping or injection rate follow these steps:

1) select [Pumping Well] or [Inject Well];2) move to the desired position and press <Return>; note that wells can only be

defined on grid intersections. If you fail to place the well directly on a grid node,FLOWPATH will ask you to either add another grid line or will automaticallymove the well to the nearest grid node;

3) after you have pressed <Retura>, a window will pop up and you will be asked toinput the pumping or injection rate Q. You can move the window to any positionin the domain in case it obstructs your view;

4) repeat steps 1) to 3) to add more wells or press <Eso to finish.Note:The accuracy of the hydraulic head solution Is a function of the grid spacing;especially In the vicinity of large gradients (velocities), a good resolution of the spatialdomain Is required. It Is therefore recommended to refine the grid In the vicinity of wells.

FLOWPATH 47

Erasing Grid Lines

1) select [Erase Line];2) move directly on top of the line to be erased (press <-> to increase the precision

of the cursor movements if necessary);3) repeat steps 1) and 2) to erase more lines or press <Eso to finish.

Erasing Wells

1) select [Erase Well];

2) move directly on top of the well to be erased (press <-> to increase the precisionof the cursor movements if necessary);

3) repeat steps 1) and 2) to erase more wells or press <Eso to finish.

Changing Pumping Rates

1) erase the well (select [Erase Well]);2) define a new well (select [Pumping Well] or [Inject Well]) with a new pumping

rate.

4.6.2 Domain Boundary And Boundary Conditions

Select [Domain Boundary] in the [Modify] or [Generate] menu; you will imme-diately be transferred to the CAD environment.The following options are available:

[Draw Boundry] ...define a geometrically irregular domain boundary orimpermeable zones inside the domain;


[Undo Boundry]

[Constnt Head][Specifd Flux][River/Lake][Erase]

[View]

[Save &Redraw]

[Exit & Save][Quit]

...recovers the grid with all previously defined parameters wherea boundary has been drawn;

...define constant head nodes;

...define flux boundary nodes;

...define a surface water body node;

...erase a constant head node, specified flux node or surface waternode;

...display constant head, specified flux or surface water bodyparameters;

...save all input parameters to file (fh.bdy) and redraw the screenimage (remain in CAD environment);

...save all input parameters to file (m.bdy) and exit to main menu;

...abandon all changes since the last save and exit to main menu.

Defining Boundaries

In order to define an irregular boundary you have to overlay parts of the aquifer witha shaded pattern. To do this you have to:

1) select [Draw Boundry];2) move the cursor to a corner of the area that you want to define as a boundary,3) move to the opposite corner an press <Retura> or click one of the mouse buttons;

the redefined area will appear shaded on the screen;4) repeat steps 2) and 3) to draw another boundary or press <Eso to finish.

You can define a rather smooth boundary if your grid spacing is sufficiently small.Note: boundaries are by default Impermeable (no-flux) boundaries.

FLOWPATH 49

Undoing Boundaries

In order to recover an area of the aquifer that you may have declared as part of theboundary by mistake, follow these steps:

1) select [Undo Boundry];2) move the cursor to a corner of the area that you want to recover;3) move to the opposite corner and press <Retura> or click one of the mouse buttons;

the grid will appear in the redefined area;4) repeat steps 2) and 3) to recover more or press <Esc> to finish.

Defining Constant Head Nodes

1) select [Constnt Head];2) move the cursor to the grid node that you want to define as a constant head node;3) press <Return> or click one of the mouse buttons;4) input the hydraulic head value H in the pop-up window;5) repeat steps 2) to 4) to define more constant head nodes or press <Esc> to finish.

Defining Flux Nodes

1) select [Specifd Flux];2) move the cursor to the grid node that you want to define as a flux node;3) press <Retura> or click one of the mouse buttons;4) input the flux value q in the pop-up window;5) repeat steps 2) to 4) to define more flux nodes or press <Esc> to finish.

Note: the flux value q Is defined as the flowper unit aquifer thickness and untt length of boundary (units LVT/L*) (see section 3.1.6).


Defining Surface Water Body Nodes

1) select [River/Lake];2) move the cursor to the grid node that you want to define as a surface water body

node;3) press <Return> or click one of the mouse buttons;4) input the water table elevation of the surface water body (WT), the bottom ele-

vation of the river or lake (B) and the leakage factor of the river or lake bed (L);5) repeat steps 2) to 4) to define more river/lake nodes or press <£so to finish.

Not«: the leakage factor is defined In section 3.1.3. • >

Viewing Nodal Values

1) select [View];2) move the cursor onto the node you want to examine; a pop-up window will display

all input data;3} repeat step 2) for other nodes or finish with <£so.

Erasing Specified Nodal Values

1) select [Erase];2) move the cursor onto the node you want to erase;3) press <Return> or click on of the mouse buttons;4) repeat steps 2) and 3) to erase more nodes or finish with <Eso.

Changing Nodal Values

1) Erase the node;

FLOWPATH 51

2) Define a new node.

4.6.3 Aquifer Properties (Hydraulic Conductivities And Poros-ity)

Select [Aquifer Properties] in the [Modify] or [Generate] menu; you will imme-diately be transferred to the CAD environment.The following options are available:

[Property Box] ...define heterogeneities (hydraulic conductivities and porosity);[View Proprty] ...view aquifer properties;

[Save &Redraw] ...save all input parameters to file (fh.prp) and redraw the screenimage (remain in CAD environment);

[Exit & Save] ...saveallinputparameterstofile(fii.prp)andexittomainmenu;

[Quit] ...abandon all changes since the last save and exit to main menu.

Defining Heterogeneities

FLOWPATH can handle up to 100 different user-specified aquifer materials. To definehydraulic conductivities and porosities different from the default (background) values,follow these steps:

1) select [Property Box];2) move the cursor to a corner of the area you would like to redefine;3) press <Return> (or click one of the mouse buttons);4) move the cursor to the opposite corner of the area to be redefined; a "rubberbox"

will be drawn;5) press <Return> or click one of the mouse buttons; the area of the "rubberbox"

will appear white;


6) a pop-up window will appear,7) input the material number (if you have not denned any other materials than the

default, input "2"); material numbers have to be in consecutive numbers;8) input the hydraulic conductivities and the porosity for material #2;

9) press <Return> or one of the mouse buttons after each entry,10) the redefined area will be filled in;11) finish pressing <Esc> twice or redefine another area.

If a previously defined material appears several times, you can speed up the redefi-nition of aquifer properties:

1) follow the above steps 1) to 6);2) input the material number associated with the properties you have defined pre-

viously;3) FLOWPATH will assign the appropriate properties and fill in the redefined area;4) finish by pressing <Esc> twice or redefine another area.

Viewing Material Properties

1) select [View Proprty];2) move the cursor to the desired position in the domain; as you move, the material

properties at the current position is displayed.

4.6.4 Aquifer Thickness And Aquifer Bottom Elevation

Select [Aquifer Properties] in the [Modify] or [Generate] menu; you will imme-diately be transferred to the CAD environment.

The following options are available:

FLOWPATH 53

[Thk/Bttm Box]

[View][Save ARedraw]

[Exit & Save][Quit]

...define aquifer thickness or bottom elevations different fromdefault values;

...view aquifer thickness or bottom elevation;

...save all input parameters to file (m.thk) and redraw the screenimage (remain in CAD environment);

...save all input parameters to file (m.thk) and exit to main menu;


Spatially varying aquifer thicknesses or aquifer bottom elevations are assigned thesame way as different aquifer properties. Follow the steps outlined in section 4.6.3 toredefine thickness or bottom elevation.

4.6.5 Areal Recharge And Evapotranspiration Rates

Select [Recharge Rates] in the [Modify] or [Generate] menu; if you already havespecified the default values you will immediately be transferred to the CAD envi-ronment.

The following options are available:

[Rate Box]

[View Rate]

[Save &Redraw]

[Exit & Save][Quit]

...define infiltration and evapotranspiration rates different fromthe default values;

...view infiltration and evapotranspiration rates;

...save all input parameters to file (fh.qar) and redraw the screenimage (remain in CAD environment);

...save all input parameters to file (m.qar) and exit to main menu;



Spatially varying injection and evapotranspiration rates are assigned the same wayas different aquifer properties. Follow the steps outlined in section 4.6.3 to redefinethickness or bottom elevation.

4.6.6 Pathline Specifications

Select [Pathlines] in the [Modify] or [Generate] menu; you will immediately betransferred to the CAD environment.

The following options are available: •.'

[Well Release][Forward]

[Reverse]

[Erase][View Wells]

[Save &Redraw]

[Exit & Save][Quit]

...specify particles released on a circle at wells;

...define release locations of individual particles travelling for-ward in time;

...define release locations of individual particles travellingbackward in time;

...erase particles;

...display number of particles released at a well, well coordinatesand well discharge;

...save all input parameters to file (fh.par) and redraw the screenimage (remain in CAD environment);

...save all input parameters to file (fh.par) and exit to main menu;


Specifying Particles Released at Wells

1) select [Well Release];2) move the cursor directly on top of the desired well (use <-> to increase the precision

of the cursor movements if necessary);

3) press <Return> or click one of the mouse buttons;

FLOWPATH 55

4) enter the number of particles in the appearing pop-up window;5) repeat steps 2) to 4) for another well or press <Eso to finish;

The particles will he released on a circle with a radius of 0.3 times the distance to thenearest grid line.

Specifying Individual Particles

To define start positions of individual particles (forward or reverse tracking) followthese steps: .,

!)• select [Forward] or [Reverse];2) move the cursor to the desired release coordinates;3) press <Return> or click one of the mouse buttons;4) repeat steps 2) and 3) for another particle or finish with <Eso;

Checking Particle Releases at Wells

To find out how many particles have been specified for any particular well, follow thesesteps:

1) select [View Well];2) move the cursor directly on top of the well of interest (press <-> to increase the

cursor precision); the well specifications will pop-up;3) repeat 3) or press <Esc> to finish;


CHAPTER V - EXAMPLE

5.1 Description

An example is included on the distribution disks. We suggest that you display theresults, modify the data sets and re-run the problem to get familiar with FLOWPATH'sfeatures.The physical domain is shown in figure 15. The domain is irregular, several hydraulichead and flux values are specified. A river enters the domain at the left boundary andexits at the right. Three production wells nearby the river withdraw water from theaquifer. An injection well is located in the top half of the domain Groundwater flowoccurs mainly from the left to the right of the domain. The aquifer is heterogeneousand anisotropic. Distributed area! recharge and evapotranspiration are specified. Thevalues for aquifer properties, distributed recharge and boundary conditions can beviewed by specifying "View" under [Modify] (section 4.5.2).The grid and the hydraulic head distribution are shown in figures 16 and 17 respec-tively. Figure 18 shows the velocity the velocity distribution in the domain. It can benoticed that large velocities occur in the vicinity of the river and the wells. Figure 19reveals that the production wells receive most of their recharge from the river.

lcnp«nn«abt« boundary

Figure 15 • Physical domain for the example

FLOWPATH 57

*!• *Mi

1)

t Cwt W

Figure 16 • Grid for example

Figure 17 - Hydraulic head distribution for example


M Mtf •*•

IUI-M

n*

Figure 18 - Velocity distribution for example

M ••••r M«

f*m

TIM,

Figure 19 - Time-related capture and injection zones for example

FLOWPATH 59

CHAPTER VI - CODE VALIDATION

FLOWPATH is validated against PLASM (Prickett and Lonnquist, 1971) and MOD-FLOW (McDonald and Harbaugh, 1984) for the hydraulic head distribution andRESSQ (Javandel and Tsang, 1986) and GWPATH (Shafert 1987) for the pathlinesand travel times. Additionally, a simple uniform flow case is used to check thenumerical model. For all test cases, rectangular domains are chosen because thenumerical and semi-analytical models mentioned above cannot handle irregularboundaries.

•}B.I Uniform Flow Test Case

For this first test case, the domain is of rectangular shape with side lengths of 2000meters in the x-direction and 1500 meters in the y-direction. It is overlain by a gridwith 21 grid lines in the x-direction and 16 grid lines in the y-direction yielding a gridspacing of 100 meters (figure 20). A constant hydraulic head value of 102 meters isspecified along the left boundary (for x=0m). Similarly, the hydraulic head along theright boundary (for x-2000m) is set at a constant value of lOOmeters. The boundariesat the bottom and the top of the domain are impermeable. The aquifer is confined andnon-leaky. No area! recharge or evapotranspiration occur over the domain. The aquiferis homogeneous and isotropic (Ka = Kn = 100 m/d, 6 = 0.25) and is 25 meters thick.

The resulting hydraulic head distribution is described by a planar surface with agradient of i = -10"3 in the x-direction and no gradient in the y-direction. The equipo-tentials are therefore equidistant lines running parallel to the y-axis (figure 21). Thepathlines are straight lines running parallel to the x-axis (perpendicular to theequipotentials) (figure 22). The uniform average linear groundwater velocity in thex-direction is:

-K.i -(lOOK-O.OQl) .. nA ., (28)v-=~e~=——633——""'-0.4m*.

v =0 (29)7


Thus, within a time period of 2500 days a particle travels a distance of 1000 metersin the x-direction. Fathline "A" in figure 23 is calculated in a forward mode and pathline"B" is calculated in a reverse mode.

1M IM

n*.-urc

Figure 20 • Grid for test case 1

n*UM

Figure 21 • Equipotentials for test case 1

FLOWPATH 61

Figure 22 - Pathlines for test case 1

•r MM

Figure 23 - Particle travel times for test case 1


6*2 Test Case 2 - Comparison with Numerical Models

In the second test case scenario the domain is a square with side lengths of 1400 feet:One pumping well and one injection well are active. The discharge of the pumpingwell is 125,000 gpd and the recharge rate of the injection well is 100,000 gpd. Thereare no area! recharge or discharge components.The aquifer is confined and non-leaky. The aquifer properties are isotropic and non-homogeneous; a low conductivity lens with Ka=Kn= 3 ft/d and a porosity of 0.3 islocated between the two wells (figure 24). In the remaining area of the domain theaquifer has a hydraulic conductivity of 30 ft/d and a porosity of 0.3. The aquiferthickness is 25 feet everywhere. Since the aquifer is nonhomogeneous, a numericalmodel must be used.The boundaries along the top and the bottom of the domain are impermeable(streamlines); the left and the right domain boundaries are constant head boundarieswith a hydraulic head value of 50 feet and 45 feet, respectively. The finite differencegrid is shown in figure 25.

6.2.1 Hydraulic Head Distribution

The equipotential surfaces obtained from simulation runs using PLASM, MODFLOWand FLOWPATH are shown in figures 26 to 28. The hydraulic head distributionsobtained from these three models are contoured with the contouring package "Surfer"by Golden Software. All three contour maps are in excellent agreement.FLOWPATH features its own contouring package (in the [Output] menu); the contourmap obtained from this contouring algorithm is shown in figure 29. FLOWPATH'scontouring routine is based on an algorithm found in (Kinzelbach, 1986). It employsa linear interpolation between four adjacent head values; the contour map obtainedfrom this algorithm represents the data without smoothing them. "Surfer", however,uses higher order interpolations and interpolation weights according to the inversedistance between the interpolation point and the discrete data point (i.e. the calcul? tedpoint value at a grid node). The graphical appearance of the interpolated imagesobtained from "Surfer" and FLOWPATH are therefore slightly different, even thoughthey were produced from the same original data. From a mathematical and a physicalstandpoint, however, a linear interpolation such as the one employed by FLOWPATHrepresents the actual data better since no smoothing post-processing is done. If the

FLOWPATH 63

spatial distribution of a functional relationship is unknown, the best estimate for afunction value between to known points is a straight line; other interpolation functionsmay produce artifacts. If smoother hydraulic head contours are desired, the finitedifference grid must be refined.

6.2.2 Pathlines and Travel Times

The pathlines, capture zones and injection zones obtained from FLOWPATH arecompared to the output from GWPATH (Shafer, 1987). The hydraulic head distributionrequired for GWPATH has been produced with PLASM; output from PLASM had tobe post-processed to match the format requirements of GWPATH.The pathlines from both models (figure 30 and 31) are in good agreement. Differencesoccurring between some individual pathlines arise from the two different interpolationschemes, different release and capture radii and different time-stepping schemes inthe two models. The effect of the low-conductivity lens between the two wells is morepronounced in FLOWPATH's pathlines whereas GWPATH appears to dampen thecontrast between the two aquifer media.The overall dimensions of the time-related (200 days, no adsorption) capture andinjection zones are also in good agreement (figures 32 and 33). For a good definitionof these zones, a very large number of pathlines has been released at the wells (200particles per well).


Ittt-

0.14k-

0,«k-

O.W*.

0.00k.

—— (

1 ' 1

1 ——

—— I 1 ——

, i

1 ' \0.00k 0.2M O.Kk 0.14k \ffll 140k

Figure 24 - Grid for test case 21400

K.30IUUVPW..0.3

Q.125000 flpo

Pw-.QJ

Q» 100000 gpa

1400

i:II

Figure 25 - Aquifer properties for test case 2

FLOWPATH 65

1400.00

1200.00

1000.00

90000

MO 00

400 OO

30000

0.00 >-,-<• ,/JJ,0.00 2OO.OO 4OO.OO 600.00 BOO.OO 1000 00 1200.00 1400 00

Figure 26 - Equipotentials for test case 2 (FLOWPATH-contoured with "Surfer")uoooo

1200.00

1000.00

600 00

60000

40000 •

20000

0.000.00 200.00 4OO.OO 400.00 800.00 100000 1200.00 14OO.OO

Figure 27 - Equipotentials for test case 2 (PLASM-contoured with "Surfer")


140000

1200.00

1000.00

000.00 •

600.00 -

40OOO -

200.00 •

0.000.00 200.00 400.00 tOO.OO 800.00 1000.00 1200.00 1400.00

Figure 28 - Equipotentials for test case 2 (MODFLOW-contoured with "Surfer")

a.oak000k 02N 09«k t4Clt

Figure 29 - Equipotentials for test case 2 (FLOWPATH's own contouring)

FLOWPATH 67

0.00*-

0.00* Q.2M

Figure 30 - Pathlines for test case 2 (FLOWPATH)

Figure 31 - Pathlines for test case 2 (GWPATH)


ton.

O.SA-

0.2W-

aooi\ ' 1

tak

Figxore 32 - 200-day capture and injection zones for test case 2 (FLOWPATH)

Figure 33 - 200-day capture and injection zones for test case 2XGWPATH)

FLOWPATH 69

6.3 Test Case 3 • Comparison with Semi-Analytical Model

A single well in a homogeneous aquifer under uniform flow conditions is selected forthe last test case scenario. The pathlines for this case are compared to results fromRESSQ (Javandel and Tsang, 1986). RESSQ is a semi-analytical model. The velocityMeld is calculated from superposition of analytical solutions for confined aquifers.Pathlines are obtained from a particle tracking technique. The analytical flow solutionsare valid for aquifers of infinite extent; RESSQ cannot handle boundary conditions atfinite distances.

The aquifer is isotropic and homogeneous (Ka = K7J= 100 m/d, 6 = 0.25), confined andnon-leaky, with a thickness of 10 meters. There is no areal infiltration or evapotran-spiration over the domain. The aquifer thickness is 10 meters. The pumping rate ofthe well is 500 m3/d; the average linear groundwater velocity of the background flowfield is 0.137 m/d (50 m/year). The background flow occurs uniformly from the left tothe right.

In the RESSQ simulation the aquifer is of infinite extent. In the FLOWPATH simu-lation, boundary conditions have to be specified along all boundaries of the domain.The domain dimensions are chosen to be 2000 by 2000 meters, with impermeableboundaries at the top and bottom of the domain and constant head nodes at the leftand right boundary. For the given aquifer properties, the hydraulic head differenceacross the domain (in x-direction) must be 1.39 meters to yield the same backgroundvelocity as for the RESSQ simulation.

The pathlines obtained from FLOWPATH and RESSQ are shown in figures 34 and35. Despite the different boundary conditions, the agreement between the two solutionsis very good. The top and bottom domain boundary in the FLOWPATH simulationcoincides with a streamline thus forcing adjacent streamlines to run parallel to theboundary (figure 34). Pathlines originating at locations further away from theboundary are not influenced by this boundary condition as strongly. Therefore, thepathlines of those particles that are captured by the well are less affected and producealmost identical results compared to the semi-analytical RESSQ model. In general,the discrepancy between an analytical infinite model and a bounded numerical solutionincreases for smaller domains due to the boundary effect.


2.00k

UOk-

0.40k

-0.40k-

•12* - -

-2.00k-120k -0.40k 0.40k 120k 2.00k

Figure 34 - Pathlines for test case 3 (FLOWPATH)

-toot

Figure 35 - Pathlines for test case 3 (HESSQ)

FLOWPATH 71

6.4 Conclusions

The three described test cases demonstrate that the results obtained from numericalsimulations with FLOWPATH are in good agreement with results from other analyticaland numerical models. It is concluded that FLOWPATH's numerical implementationsolves the mathematical equations describing groundwater flow and advective particlemovement correctly.


REFERENCES

Butler, S.S., 1957. Engineering Hydrology. Prentice Hall, Englewood Cliffs, NJ.Golden Software Inc., 1987. Surfer version 3.0.Javandel, L, Tsang, C.-F., 1986. Capture-zone type curves : a tool for aquifer cleanup.Ground Water, 24(5).Kinzelbach, W., 1986. Groundwater Modelling • An introduction with sample programsin BASIC. Elsevier Science Publishers, Amsterdam.

McDonald, M.G., Harbaugh, A., 1984. A modular three-dimensional finite-differenceground-water flow model. U.S. Geological Survey, Reston, Virginia.

Peaceman, D.W., Rachford, D.D., 1955. The numerical solution of parabolic andelliptical difference equations. Jour. Soc. Industrial and Applied Mathematics, 3(11),28-41.

Pinder, G.F., Bredehoeft, J.D, 1968. Application of the digital computer for aquiferevaluation. Water Resour. Res., 4(5), 1069-1093.

Prickett, T.A., Lonnquist, C.G., 1971. Selected digital computer techniques forgroundwater resource evaluation. Bull. 55, El. State Water Surv., Urbana.

Shafer, J.M., 1987. Reverse pathline calculation of time-related capture zones innonuniform flow. Ground Water, 25(3).

Soell, T.. 1988. Berechnungsverfahren zur Abschaetzung anthropogener Tempera-turanomalien im Grundwasser. Eigenverlag des Instituts fuer Wasserbau der Uni-versitaet Stuttgart, PhD Dissertation.United States Environmental Protection Agency, 1987. Guidelines for delineation ofwellhead protection areas. Office of Water, Office for Ground-Water Protection,Washington, D.C., EPA 440/6-87-010.

Index

2-D flow equation, 9

active keys, 31,44add

constant head nodes, 49flux nodes, 49grid lines, 46heterogeneities, 51irregular boundaries, 48particles, 54surface water nodes, 50weDs,46

adsorption, 11alternating directions, 23aquifer properties, 36aquifer property, 38area ratio

surface water bodyareal recharge, 21, 39

data generation, 37

backup copies, 5bottom elevation, 36boundary, 38

domain, 36boundary condition, 21, 36, 38

constant head, 21flux, 22impermeable, 22

CADsee Computer Aided Design

capture mechanism, 29capture zone, 11, 30

delineation, 11time-related, 11wellhead protection area, 11

changeboundary nodes, 50pumping rates, 47

change directory, 33,40Computer Aided Design, 44

areal recharge, 53bottom elevation, 52boundaries, 47grid and wells, 45particles, 54pathlines, 54

thickness, 52conductivity, 36, 38confined aquifer, 14

data generation, 36contour maps, 44convergence, 23copyright, 1

Darcy*s law, 10data input, 44data menu, 32data set

delete, 39generate, 35modify, 37rename, 39 •;using directories, 40

defaultaquifer properties, 36aquifer thickness, 36areal recharge, 37evapotranspiration, 37grid, 35infiltration, 37

delete data files, 33desktop, 32directories, 33, 40disclaimer, 1distributed recharge, 21

echoprint, 34, 42erase

boundary nodes, 50grid lines, 47irregular boundaries, 49particles, 54wells, 47

escape, 32Euler integration, 26evapotranspiration, 21, 39

data generation, 37example, 56

finite difference, 13block, 14confined aquifer, 14evapotranspiration, 21grid line, 13

Index

infiltration, 21leaky aquifer, 17node, 13surface water body, 18unconfined aquifer, 16

forward tracking, 26

generatearea! recharge, 53constant head nodes, 49data set, 35flux nodes, 49end lines, 46heterogeneities, 51particles, 55surface water nodes, 50thickness, 52well particles, 54wells, 46

generate data, 33governing law, 1graphics, 43grid, 35, 38grid line, 13GWPATH, 59

hardwareoptions, 5printers and plotters

see printer, plotterheterogeneities, 51

IADI.23importing graphics, 44infiltration, 21, 39injection well, 35,38installation, 7integrated environment, 32interpolation scheme, 26

lake, 18leakage factor, 18,19leaky aquifer, 17

data generation, 36License Agreement, 1logbook, 34, 42

menu, 32

MODFLOW, 59m

areal recharge, 53boundaries, 48boundary nodes, 50data set, 37grid, 46heterogeneities, 51particles, 55thickness, 52well particles, 54wells, 46

modify data, 33mouse, 31,44

. inode, 13non-linearity, 16, 21, 23

output, 43ASCII, 44capture zone, 34equipotentials, 34file, 44grid, 34HPGL,44pathlines, 34plotter, 43printer, 43screen, 43velocities, 34

pathlineaccuracy, 28capture mechanism, 29characteristic equation, 10data generation, 37data modification, 39numerical calculation, 26particle step, 28predictor-corrector, 28release radius, 30theory, 10travel time, 11

PLASM, 59plotter, 7,43porosity, 36, 38post-processing, 43printer, 7, 43

Index

pumping well, 30, 35, 38

quit FLOWPATH, 33, 40

release radius, 30rename data files, 33RESSQ, 59retardation factor, 11reverse tracking, 26river, 18run FLOWPATH

capture zones, 42hydraulic heads, 40numerical calculation, 31patnUnes, 41velocities, 41wellhead protection areas, 42

run menu, 33

screen, 32, 43solution, 23solver, 23spatial step, 26stability, 23stepping scheme, 28streamline, 10surface water body, 18

thickness, 36, 39time-stepping, 26transmissivity, 9,15,17travel time, 11

numerical calculation, 26

unconfined aquifer, 16unit system, 35user interface, 32

see Computer Aided Design

validation, 59velocity, 10, 24

interpolation, 27view

aquifer properties, 52areal recharge, 53bottom elevation, 53boundary nodes, 48, 50particles, 55

pumping rates, 45thickness, 53

warranty, 1Waterloo Hydrogeologic Software, 3well, 35, 38wellhead protection area

delineation, 11numerical calculation, 30

wellhead protection zonesee capture zone

word-processing, 44

zone of contribution, 11

UNITED STATES ENVIRONMENTAL PROTECTION AGENCYREGION 5

\ I V 77 WEST JACKSON BOULEVARDCHICAGO, IL 60604-3590

REPLYTO THE ATTENTION OF:

FEB 13 1992Mr. Richard NaumanProject CoordinatorNational Presto Industries, Inc3925 North .Hastings WayEau .ClairfiWisconsin 54703

t^- Uown.vpf Hal e Sanitary District No. 1 Payment Request No. 16

Dear Rich:

I have received your letter dated February 4r 1991 and attachmentsregarding costs incurred by Hallie Sanitary District No. 1(District) . It is the Agency's position that National PrestoIndustries, Inc. (NPI) take the initiative to resolve disputes overthe appropriateness of costs incurred by the District relative tothe provisions of the March 8, 1991 Administrative Order forRemedial Action. The fact that the District did not receive a copyof your February 4th letter suggests that NPI has not attempted toresolve these cost issues with the District. In order tofacilitate such discussions, I am providing a copy of your letterto David Meier, Hallie Town Chairman and District Commissioner.

NPI and National Defense Corporation (NDC) are reminded that theOrder requires prompt payment of all undisputed costs incurred bythe District , including James Nyre ' s contractual , mileage andexpense costs. Undisputed costs constitute a significantpercentage of the December 30, 1991 invoice from the District andwitholding payment of these legitimate costs is not justified.

Sincerely,

MichaelRemedial Project Manager

cc: David Meier, Town of Hallie, w/enc.Jim Boettcher, WDNR, w/enc.

Printed on Recycled Paper

Documents

eder associates consulting engineers, p. c. · e h 0 eder associates consulting engineers, p. c. U. S. MAIL File #497-8 February 14, 1992 Mr. Michael A. Gifford Remedial Project Manager