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Summary of Selected Computer Programs 

Produced by the U.S. Geological Survey for 

Si mulation of Ground-Water Flow and Quality 

l 9 9 4 

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SUMMARY OF SELECTED COMPUTER PROGRAMS PRODUCED 

BY THE U.S. GEOLOGICAL SURVEY FOR SIMULATION OF 

GROUND-WATER FLOW AND QUALITY, 1994 

By Charles A. Appel and Thomas E. Reilly 

U.S. GEOLOGICAL SURVEY CIRCULAR 1104 
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary 

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director 

UNITED STATES GOVERNMENT PRINTING OFFICE: 1994 

Free on application to the 

USGS Map Distribution 

Box 25286, MS 306 

Denver Federal Center 

Denver, CO 80225 

(303) 236-7477 
CONTENTS 

Abstract............................................................................................................................ 1 

Introduction...................................................................................................................... 1 

Purpose and Scope..................................................................................................... 4 

Sources of Reports and Computer Programs ............ .'................................................ 4 

Summary List of Computer Programs ... . .. ... . .. . .. . .. .. .. . .. . .. . .. . .. . .. .. .. . . . .. . .. . .. .. . ... . . . .. . .. .. . . . .. . .. . 5 

Individual Descriptions of Computer Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

Summary and Closing Remarks . . .. . .. . .... .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . ... . .. .. . .. . .. . . . .. . ... .. . .. .. . .. .. . . . . . 84 

References........................................................................................................................ 85 

Appendix.......................................................................................................................... 94 

TABLES 

Table 1. Summary table of use of U.S. Geological Survey Models for simulation of 

ground-water flow and water quality in the U.S. Geological Survey operational 

program (as of late 1992)........................................................................................ 3 

iii 
On the cover: 

Background - The experimental apparatus of Darcy ( 1856), used in the empirical 

determination of the basic momentum balance equation for ground water, known as 

Darcy's law. 

Foreground- A two-dimensional flow net (DaCosta and Bennett, 1960). 

Artwork by Joan Rubin and Leslie Robinson 

iv 
SUMMARY OF SELECTED COMPUTER PROGRAMS PRODUCED 

BY THE U.S. GEOLOGICAL SURVEY FOR SIMULATION OF 

GROUND-WATERFLOW AND QUALITY, 1994 

By 

Charles A. Appel and Thomas E. Reilly 

ABSTRACT 

A summary list of computer models that simulate ground-water flow and quality is presented. 

The list contains a brief description of each model program, its numerical features, a qualitative 

expression of the number of past applications, the reference for the report documenting the program, and where to obtain a copy. Reports included in the list have been published or developed 

by the U.S. Geological Survey, and contain listings of the computer programs, although in a few 

cases, the program is so long that a listing was not included in the report, but a copy of the program 

is available on request. 

INTRODUCTION 

Numerical models provide a powerful aid in understanding and assessing ground-water 

systems. The U.S. Geological Survey (USGS) has contributed significantly to the development 

and use of models for the analysis of ground-water problems. Two reports had previously 

documented the status of ground-water modeling in the USGS, Appel and Bredehoeft (1976) and 

Appel and Reilly (1988). Because developments in the field have taken place since that time, 

additional computer programs have been published. This report gives information on selected 

computer programs published or developed by the USGS or by the USGS in cooperation with 

Federal, State, and local agencies for modeling flow, quality, and solute or heat transport in groundwater systems. The information for each program includes the reference, a brief description of the 

field conditions that the program can simulate, the numerical approximation procedures used, an 

indication of the extent of past field applications of the program by USGS personnel, and where to 

obtain copies of the report and, in some cases, the computer code. 

The list of programs is organized by general modeling category. Information on each program 

is separated by one solid horizontal line. In many cases a program is based on or related to another 

program. The parent program is listed first and followed by the related programs. Three solid lines 

mark the end of the list of those programs related to a parent computer program. In a few cases, 

however, a program listed under one category was derived from a program in another category; for 

example, some of the programs listed in the "Freshwater-Saltwater" category are modifications to 

ground-water flow programs described in the category "Flow-Saturated." Also, some programs 

could be included under other categories; for example, the programs by Grove and Stollenwerk 

( 1984) and Lewis, Voss, and Rubin ( 1986) are models for the transport of fluids that are affected 

by physical and chemical processes. Both of those programs could have been included in the 

"Chemical Mass Transfer" category instead of the category of "Solute Transport" in which they are 

contained in this report. Although several flow models that account for surface-water interaction 

1 
are listed as having been derived from some parent flow model, we have listed the coupled groundand surface-water flow model of Swain and Wexler ( 1993) separately even through it represents a 

coupling of the ground-water flow model of McDonald and Harbaugh (1988) and a surface-water 

flow model of Schaffranek, Baltzer, and Goldberg (1981). This choice was made to bring attention 

to the fact that it is the only case in which the surface-water formulation is based on a 

comprehensive set of unsteady flow equations, which are subject only to the limitations inherent in 

a one-dimensional formulation of streamflow. The intent of these examples is to indicate that a 

potential user should thoroughly evaluate the programs in all related categories to choose the most 

appropriate numerical tool. The category titles are generalized and are not intended to be allinclusive. 

Depending on the nature of the problem, more than one computer program may apply. In some 

cases, the choice of program may reflect more the individual's familiarity with a particular 

approach than the superiority of the approach. In other cases, the choice of program may definitely 

reflect the level of approximation required; for example, if field data indicate a thick zone of 

brackish water that separates strictly fresh water from strictly salt water, then the choice of a 

program that assumes the zone is an interface may result in a lesser level of approximation than 

would a solute-transport program that includes consideration of the density variations in the zone. 

Many computer programs for the simulation of ground-water flow and quality are listed herein. 

Some of these programs are listed for historical reasons or because they represent specialized 

aspects of either physics or chemistry. Additionally, many areas of ground-water flow and 

chemistry are the subjects of multiple investigations, in which related programs are developed in 

an attempt to refine and (or) perfect the methods currently available; therefore, some aspects of 

ground water can be simulated by more than one model listed in this report. Although the reports 

that document the programs have been reviewed and approved, not all parts of every program have 

necessarily been thoroughly tested, and a user bears the ultimate responsibility for assuring that a 

program does, in fact, what is claimed. Confidence in a program increases with good agreement 

between program results and known solutions to problems closely related to those for which the 

program is intended to solve. 

As an indication of models that are currently "popular," a poll was made in late 1992 of model 

usage in the U.S. Geological Survey's operational program. The models being used at that time 

are listed in table 1. This listing provides general information on usage. However, new codes or 

specialty codes may not be included (or may be under represented) in this table simply because of 

the available utility of the codes at the start of these projects and the scope of the current projects 

being undertaken. Associated with many of the computer programs discussed in this report are 

acronyms. Appendix 1 gives a list of those acronyms and the full name of the corresponding 

program and the appropriate reference(s). 

2 
TABLE 1. Summary table of use of U.S. Geological Survey Models for simulation of groundwater flow and water quality in the U.S. Geological Survey operational program (as of late 1992) 

Model Name 

Number of Projects 

Using the Model 

AQUIFEM-SALT (Voss, 1984b) ................................................................................ 4 

AX (Rutledge, 1991 ) ................................................................................................... 1 

BALANCE (Parkhurst and others, 1982) ................................................................. 10 

HST3D (Kipp, 1987) .................................................................................................. 8 

INTERCOMP (INTERCOMP, 1976; INTERA, 1979) .............................................. 2 

MOC (Konikow and Bredehoeft, 1978; Goode and Konikow, 1989) ........................ 8 

MOD FE (Torak, 1993a, b; Cooley, 1992) .................................................................. 4 

MODFLOW (McDonald and Harbaugh, 1988) ...................................................... 165 

MODFLOWP (Hill, 1992) .......................................................................................... 8 

MODPATH (Pollock, 1989) ...................................................................................... 54 

NETPATH (Plummer and others, 1991) ................................................................... 29 

PHREEQE (Parkhurst and others, 1980; revised, 1990) .......................................... 36 

PHRQPITZ (Plummer and others, 1988) ................................................................... 2 

SHARP (Essaid, 1990) ............................................................................................... 8 

SOLMINEQ (Kharaka and others, 1988) ................................................................... 3 

SUTRA (Voss, 1984a) .............................................................................................. 12 

TRACY (Dunlap and others, 1984) ............................................................................ 2 

Trescott-3D (Trescott, 1975) ....................................................................................... 1 

Variable Density Flow (Kuiper, 1985) ........................................................................ 1 

VS2D (Lappala and others, 1987) .............................................................................. 8 

WATEQF (Plummer and others, 1976; revised, 1984) .................. ~ .......................... 11 

WATEQ4F (Ball and Nordstrom, 1991) ................................................................... 20 

3 
Purpose and Scope 

This report makes available a moderately comprehensive list of computer programs that have 

been produced by the U.S. Geological Survey for simulation of ground-water flow and quality. 

The main criterion used in compiling the list is that the program must be documented in a published 

report that includes a listing of the computer program, although in a few cases, the program is so 

long that a listing was not included in the report, but a copy of the program is available on request. 

Sources of Reports and Computer Programs 

For those reports not available from a cooperating State agency, an indication is given from 

which of the following Federal sources the report and computer program can be obtained: 

U.S. Geological Survey 

NWIS Program Office 

437 National Center 

Reston, VA 22092 

(703) 648-5695 

NTIS, U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

703) 487-4650 

U.S. Geological Survey Open-File Reports and Water-Resources Investigations 

Reports, can be purchased from: 

USGS ESIC--Open-File Report Section 

Box 25286, MS 517 

Denver Federal Center 

Denver, CO 80225-0046 

(303) 236-7476 

U.S. Geological Survey Water-Supply Papers, Professional Papers~ Bulletins, 

Circulars, and Techniques of Water-Resources Investigations, can be purchased 

from: 

USGS Map Distribution 

Box 25286, MS 306 

Denver Federal Center 

Denver, CO 80225 

(303) 236-7477 

4 
SUMMARY LIST OF COMPUTER PROGRAMS 

Page 

Flow-Saturated: 

Two-dimensional finite difference (Trescott, Pinder, and Larson, 197 6) . . . . . . . . . . . . . 9 

Direct matrix-solver using D4 node ordering (Larson, 1978) ......................... 10 

Conjugate-gradient matrix solver (Manteuffel, Grove, and 

Konikow, 1983) .......................................................................................... 10 

Approximate surface-water interaction (Ozbilgin and Dickerman, 1984) ....... 10 

Head-dependent flux procedure along model boundary (Hutchinson, 

Johnson, and Gerhart, 1981) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

Two-dimensional finite element, steady state (Kuniansky, 1990) . . . . . . . . . . . . . . . . . . . . . . . 12 

Two-dimensional finite element Galerkin (including river accounting 

procedure) (Dunlap, Lindgren, and Carr, 1984)............................................. 12 

Two-dimensional finite element (kinematic equation representing 

river flows) (Glover, 1988) ............................................................................. 13 

Two-dimensional finite element (including transient leakage effects) 

(Cooley, 1992; Torak, 1993a, b)...................................................................... 14 

Cylindrical coordinates (Finite-element Galerkin) (Reilly, 1984) . . . . . . . . . . . . . . . . . . . . . 16 

Pre- and post -processor (Pucci and Pope, 1987) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

Axisymmetric finite difference (well bore/aquifer) (Rutledge, 1991)................. 17 

Two-aquifer system (Finite-element Galerkin) (Mallory, 1979)......................... 18 

Quasi-three dimensional aquifer system (Finite difference) (Weeks, 1978) ..... 19 

Three-dimensional finite difference (Bredehoeft, 1992) . ... . .. . . . . . . .. . .. . .. . .. . . . . . . .. . . . .. . 20 

Three-dimensional finite difference (Trescott, 197 5; Trescott and 

Larson, 197 6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

Include head-dependent sources/sinks (Torak, 1982)....................................... 22 

Include conversion from confined to unconfined flow, recharge to any 

layer, and other modifications (Helgesen, Larson, and Razem, 1982) ..... 22 

Include transient leakage in confining layers and added program to compute 

sensitivity of parameter changes (Torak and Whiteman, 1982) ............... 23 

Include transient leakage from confining layers, change method of 

handling confining-bed and aquifer pinchouts, reduce computer 

memory needed (Leahy, 1982) ................................................................... 23 

Approximate land subsidence induced by pumping (Meyer and 

Carr, 1979) .................................................................................................. 24 

Three-dimensional finite difference (include transient leakage from 

confining layers, "cube" input capability) (Posson and others, 1980)......... 24 

Improve treatment of boundaries, revise code to run on CRA Y -1 computer 

(Hearne, 1982) . . .. . .. . .. . .. . .. . .. . ... . .. . .. . .. . .. . . .. . .. . .. . . . . . . . .. . ... . .. . .. . .. . . . .. . . . . .. . .. . . . .. . . . .. . 25 

Three-dimensional finite-difference (McDonald and Harbaugh, 1988)... .. . .. .. . . . .. . 26 

Preconditioned conjugate gradient matrix solvers (Kuiper, 1987) ................... 27 

Statistical processor (Scott, 1990) . .. . .. . .. . . .. . .. . .. . . .. . .. . . . . .. . .. . .. . .. . .. . . . . . . . . . . . . .. . . . .. . . . .. 27 

Read and write geographical information system (GIS) files (Orzol and 

McGrath, 1992)......................................................................................... 28 

5 
Page 

Calculation of water budgets (Harbaugh, 1990) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 28 

Aquifer compaction (Leake and Prudic, 1991)................................................. 29 

River routing and accounting (Miller, 1988) .................................................... 29 

Handling narrow canyons and faults and layer pinchouts (Hansen, 1993). ... .. . 30 

Stream-aquifer relations (Prudic, 1989)............................................................ 30 

Calculation of pathlines (Pollock, 1989, 1990) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 

Preconditioned conjugate-gradient matrix solver 2 (Hill, 1990) ...................... 31 

Parameter estimation (Hill, 1992). ... .. . ..... ... .. . ... .. . .. . .. . ...... .. . .. . .. . .. . ..... .. . .. .. . .. ... .. . 32 

Generalized finite-difference formulation (Harbaugh, 1992)........................... 33 

Cylindrical flow to a well (Reilly and Harbaugh, 1993b) . . .. . .. . . . . .. . .. .. . .. .. . .. ... .. . 34 

Alternative of different interblock transmissivity conceptualizations 

(Goode and Appel, 1992).......................................................................... 34 

Simulate horizontal-flow barriers (Hsieh and Freckleton, 1993) ..................... 35 

Rewetting dry cells (McDonald, and others, 1992) ......................................... 35 

Simulate transient leakage from confining units (Leake, Leahy, and 

Navoy, in press).......................................................................................... 36 

Two-dimensional--parameter estimation (Cooley and N aff, 1990) . . .. .. . .. . .. .. . .. .. . 37 

Coupled ground-water and surface-water flow (Swain and Wexler, 1993) ....... 38 

Flexibility in representing surface water system (Swain, 1993)....................... 39 

Soil moisture accounting program coupled to a two-dimensional 

unconfined-confined aquifer system (Reed, Bedinger, and Terry, 1976) ..... 39 

Flow-Variably saturated: 

Two-dimensional (Lapp ala, Healy, and Weeks, 1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 

Simulation of trickle irrigation (Healy, 1987) . . .. . .. . ... . .. . .. . .. . .. ... ... . . . .. . .. . .. .. .. . .. . .. 42 

Two-dimensional diffusion (Ishii, Healy, and Striegl, 1989) ................................ 42 

Solute transport-Saturated: 

One-dimensional finite-difference method (equilibrium-controlled sorption 

and irreversible-rate reaction) (Grove and Stollenwerk, 1984) ................... 44 

Two-dimensional method of characteristics (advective transport, dispersion, 

and decay and equilibrium-controlled sorption or ion exchange) 

Ko~ikow and Bredehoeft, 1978; Goode and Konikow, 1989) ........................ 44 

Front tracking (advective transport only) (Garabedian and 

Konikow, 1983) .......................................................................................... 46 

Two constituent solute transport, including density-dependent flow 

Stanford and Konikow, 1985)................................................................... 46 

Two-dimensional finite-element Galerkin method (advective transport, 

dispersion, sorption, ion exchange, equilibrium chemistry) (Lewis, 

Voss, and Rubin, 1986).................................................................................... 4 7 

Dual porosity flow and transport (nonreactive advective transport and 

dispersion in fractures, diffusion between fractures and rock) 

(Glover, 1987) .................................................................................................. 47 

6 
Page 

Solute transport-Variably saturated: 

Two-dimensional (Healy, 1990).. ... ... . .. ... ... . .. . ... . .. . .. . .. . .. . ... .. . .. . .. . ..... .. . . . ... . . . .. . . . .. . . . .. 49 

Solute and heat transport-Saturated: 

Three-dimensional finite-difference method (INTERCOMP, 1976) .................. 50 

Include water table, recharge, equilibrium controlled adsorption and 

irreversible-rate reaction (INTERA, 1979) .. ... . ...... .. . .. . ... ...... .. . .. .. . .. . .. . .. . . . .. . . . .. .. 50 

Three-dimensional finite-difference method (Kipp, 1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 

Flow-Saturated freshwater/saltwater: 

Two-dimensional areal (Sharp interface) (Mercer, Larson, and 

Faust, 1980) . . .. . . . .. .. . ... . .. . .. . .. . .. . ... ... ... . .. . .. . .. ...... .. ........ .. . . .. . .. . .. .. . .. . .. ... .. . .. . .. .. . .. .. . 53 

Two-dimensional areal (Sharp interface) (Voss, 1984b)..................................... 54 

Three-dimensional (Sharp interface) (Guswa and LeBlanc, 1985) ..................... 55 

Three-dimensional (Sharp interface) (Sapik, 1988) ............................................ 55 

Three-dimensional (Sharp interface) (Essaid, 1990) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 

Three-dimensional (Variable density) (Weiss, 1982) .......................................... 57 

Three-dimensional (Variable density) (Kuiper, 1985) ......................................... 58 

Three-dimensional (Variable density and multiaquifer wells) (Kontis and 

Mandie, 1988) . .. . .. . .. . .. . .. .. . .. . .. . ... . .. . .. . .. . .. ..... ... .. . .. . .. . .. . .. . . .. . .. .. . .. . .. . . . ... .. . .. . .. .. . . . .. . 58 

Heat transport: 

Two-dimensional single-and two-phase (Faust and Mercer, 1977)...................... 60 

Two-dimensional single phase (liquid) (Mercer and Pinder, 1975) ..................... 60 

Three-dimensional (single phase-liquid) (Reed, 1985) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 

Three-dimensional (multi phase) (Hayba and Ingebritsen, in press)..................... 62 

Solute or heat transport-Saturated and unsaturated: 

Two-dimensional finite-element Galerkin method (fluid-density dependent 

advective transport, dispersion, equilibrium controlled adsorption, 

zero-order production or decay) (Voss, 1984a) ............................................ 64 

Aquifer management: 

Two-dimensional saturated flow (Lefk.off and Gorelick, 1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

Three-dimensional saturated flow (Puig and Rolon-Collazo, in press)............... 67 

Chemical mass balance: 

Mass balance and electron conservation (Any elements, specified phases) 

(Parkhurst, Plummer, and Thorstenson, 1982) ................................................ 68 

Characterization of natural waters (Bodine and Jones, 1986) . .. .. . .. . .. . .. . . . .. . . . .. . .. . 69 

Mass balance reaction models satisfying specified constraints (Plummer, 

Prestemon, and Parkhurst, 1991) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

7 
Page 

Aqueous speciation: 

Speciation of major and some minor elements in 0-100 °C temperature range 

(Truesdell and Jones, 1973, 1974) ................................................................... 72 

FORTRAN IV version (Plummer, Jones, and Truesdell, 1976; 

revised, 1984).............................................................................................. 73 

Expands thermodynamic data base and adds trace elements (Ball, 

Nordstrom, and Jenne, 1980) ...................................................................... 74 

Adds uranium (Ball, Jenne, and Cantrell, 1981)............................................... 75 

Expanded personal computer, FORTRAN version of W ATEQ4F (Ball and 

Nordstrom, 1991)........................................................................................ 75 

Chemical mass transfer: 

System CaO-Mg0-Na20-K20-C02-H2S04·HCI-H20 (Plummer, Parkhurst, 

and Kosiur, 1975)............................................................................................. 77 

Mineral and water/gas interactions at low temperatures (Subject to 

thermodynamic constraints-any elements, specified phases), 

(Parkhurst, Thorstenson, and Plummer, 1980; revised, 1990) .. . ... . . .. . ... . . .. . .. ... . 78 

Interactive program for forming data input (Fleming and Plummer, 1983) ..... 79 

Incorporate Pitzer's equations for brines (Plummer and others, 1988) . . . . . . . . . . . . 80 

Speciation of major and many minor elements with mineral and water 

interactions in 0-350 °C temperature range (Kharaka and Barnes, 1973) .. 81 

Updated program (Kharaka and others, 1988).................................................. 81 

Processor to create and modify input (DeBraal and Kharaka, 1989) . . ... . . .. . . . ... 82 

Nonideal solid-solution aqueous-solution reactions (Glynn, 1991a)................... 83 

8 
INDIVIDUAL DESCRIPTIONS OF COMPUTER PROGRAMS 

FLOW-SATURATED 

Two-Dimensional Finite Difference 

Program Documentation: 

Trescott, P.C., Pinder, G.F., and Larson, S.P., 1976, Finite-difference model for aquifer 

simulation in two dimensions with results of numerical experiments: Techniques of 

Water-Resources Investigations of the United States Geological Survey, book 7, chap. 

C1, 116 p. 

Description: 

This model simulates steady and nonsteady ground-water flow in an irregularly shaped 

aquifer that can be a confined or unconfined aquifer or both. The transmissive 

properties of the aquifer may be heterogeneous and anisotropic, although the principal 

directions of anisotropy must be aligned with the grid and the anisotropy ratio must be 

constant, and the storage coefficient may be heterogeneous. The model simulates well 

discharge; recharge that can differ spatially, but not with time; leakage from a confining 

bed or streambed in which the effects of storage are considered; and evapotranspiration 

as a linear function of depth to water. Specified head and specified flux boundaries can 

be simulated. 

Numerical features: 

The grid is block centered and rectangular with variable spacing in each direction. 

Finite difference numerical approximations are used. The resulting matrix problem is 

solved by an iterative procedure; the user has a choice of selecting one of three solution 

algorithms: line successive overrelaxation, iterative alternating direction implicit, and 

the strongly implicit procedure. Mass balances are computed for each time step and as 

a cumulative volume of water from each source and each type of discharge. 

Past applications: 

Up to a few years ago, this was one of the most-used flow models for two-dimensional 

problems. See McDonald and Harbaugh (1988), which is one of the reports listed as 

"Flow-Saturated--Three-dimensional finite difference," for a newer code that contains 

most of the capabilities of this program. 

Availability: 

Report is available from the USGS Map Distribution. Computer program and report 

are available from NWIS. 

9 
Related program: 

Larson, S.P., 1978, Direct solution algorithm for the two-dimensional ground-water 

flow model: U.S. Geological Survey Open-File Report 79-202, 22 p. 

Most significant change to original program: 

A direct-matrix-solver program that assumes the D4 (alternating diagonal) nodeordering scheme is presented. For moderate-sized grids, this solver can be 

computationally more efficient than iterative matrix methods. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Manteuffel, T.A., Grove, D.B., and Konikow, L.F., 1983, Application of the conjugategradient method to ground-water models: U.S. Geological Survey Water-Resources 

Investigations Report 83-4009, 24 p. 

Most significant change to original program: 

A conjugate-gradient matrix solution procedure is presented for the two-dimensional 

ground-water flow problem. Application to a field problem of this method as compared 

with the iterative alternating direction implicit procedure (IADIP) and the strongly 

implicit procedure (SIP) methods showed the conjugate gradient method to compare 

favorably with IADIP but less satisfactorily with SIP. The main advantage of the 

conjugate gradient method is that it does not require the use of iteration parameters. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Ozbilgin, M.M., and Dickerman, D.C., 1984, A modification of the finite-difference 

model for simulation of two-dimensional ground-water flow to include surface-ground 

water relationships: U.S. Geological Survey Water-Resources Investigations Report 

83-4251, 98p. 

10 
Most significant change to original program: 

The Trescott, Pinder, and Larson (1976) two-dimensional finite-difference program is 

based on the assumption that the water level in streams that are in hydraulic connection 

with an aquifer are not appreciably affected by the flow between those streams and the 

aquifer. Because the Ozbiligin and Dickerman ( 1984) program related stream 

discharge to the depth of water in the stream at that place (by using the Manning 

formula), it accounts for changes in stream-water level associated with changes in 

stream discharge resulting from flows between the aquifer and the stream. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Hutchinson, C.B., Johnson, D.M., and Gerhart, J.M., 1981, Hydrogeology of well-field 

areas near Tampa, Florida, Phase !--Development and documentation of a twodimensional finite-difference model for simulation of steady-state ground-water flow: 

U.S. Geological Survey Open-File Report 81-630, 129 p. 

Most significant change to original program: 

The original program assumed that model-grid boundaries are places where either the 

head or the fluxes across the boundary are specified. This report described a headcontrolled flux condition for the model grid boundary that allows both head and flux to 

change. Two assumptions are made - that at some distance beyond the model grid, 

the head is constant and equals the head in an overlying source zone and that the 

transmissivity, confining-bed leakance, and source-zone head are constants in the strip 

between the model-grid and the constant-head boundaries. The storage properties of 

the aquifer and the confining bed in the strip are neglected. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

11 
Two-Dimensional Finite Element 

Program Documentation: 

Kuniansky, E.L., 1990, A finite-element model for simulation of two-dimensional 

steady-state ground-water flow in confined aquifers: U.S. Geological Survey OpenFile Report 90-187, 77 p. 

Description: 

This report described a finite-element model that can be used to simulate twodimensional steady-state ground-water flow in either isotropic or anisotropic aquifers. 

The principal axes of anisotropy can vary in direction over the modeled area, and the 

transmissivity can vary spatially, but not with changes in head. Constant head, constant 

flux, and head-dependent flux boundary conditions can be simulated. 

Numerical features: 

The computer program is based on the Galerkin finite-element technique and it uses 

triangular elements. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Two-Dimensional Finite-Element Galerkin 

Program Documentation: 

Dunlap, L.E., Lindgren, R.J., and Carr, J.E., 1984, Projected effects of ground-water 

withdrawals in the Arkansas River Valley, 1980-99, Hamilton and Kearny Counties, 

southwestern Kansas: U.S. Geological Survey Water-Resources Investigations Report 

84-4082, 168 p. (Pages 27 to 168 contain documentation for the program developed by 

J. V. Tracy.) 

Description: 

This model simulates steady and nonsteady two-dimensional ground-water flow in an 

irregularly shaped confined or unconfined aquifer. The transmissive and storage 

properties of the aquifer may be heterogeneous. The model accounts for gains and 

losses from the river flow in each reach based on the incoming river and tributary flows 

and the gain from or loss to the aquifer in the reach. With an estimate of river discharge, 

12 
the river stage is computed for each reach by using an input stage-discharge relation 

given for each reach. The river/aquifer gains and losses are calculated as a function of 

streambed area, riverbed leakance values, and the head gradient between the river and 

the aquifer. Evapotranspiration from ground water is estimated by using monthly 

values of precipitation, applied water rate, evapotranspiration demand, the moisture 

capacity of the soil zone, and depth of root zone. Well discharges can vary monthly. 

Specified flux and specified head boundaries can be simulated. 

Numerical features: 

A "regular" finite-element grid is used in the simulation. A "regular" grid is defined as 

a region subdivided by a given number of columns that do not have to be parallel or the 

same length but that have an equal number of elements. The effect is of a deformed 

rectangular grid. Applying the Galer kin method results in an associated matrix problem 

that is solved by using a direct method. Mass balances from all sources are computed 

for each time step and as a cumulative volume for each source from the start of the 

simulation. 

Past applications: 

Several field problems. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Two-Dimensional Finite Element (kinematic equation representing river flows) 

Program Documentation: 

Glover, K.C., 1988, A finite-element model for simulating hydraulic interchange of 

surface and ground water: U.S. Geological Survey Water-Resources Investigations 

Report 86-4319, 90 p. 

Description: 

This model couples the equation of two-dimensional ground-water flow with the 

kinematic equation approximation for one-dimensional open-channel flow. Darcy's 

law for vertical flow through a semipermeable streambed is used to couple the groundwater flow and streamflow equations. The transmissive and storage properties and 

distributed recharge/discharge of the aquifer can vary by element, as can the streamchannel properties. Elements can be grouped together into user-defined property zones 

for ease of varying the magnitudes of those properties. The program can simulate 

perched streams, streamflow diversions, springs, recharge from irrigated acreage, and 

evapotranspiration. 

13 
Numerical features: 

Triangular elements are used to approximate the aquifer, and one-dimensional linear 

elements located along the sides of the aquifer elements are used to approximate the 

stream network. The stream depth, stream velocity, and aquifer head are approximated 

throughout the stream/aquifer system as varying linearly within elements and are 

continuous between adjacent elements. The program assumes that the changes in 

hydraulic head are small and that the aquifer transmissivity does not change. 

Modifications to the program are outlined for the case where the aquifer transmissivity 

changes with hydraulic head. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Two-Dimensional Finite Element (including transient leakage effects) 

Program Documentation: 

Torak, L.J., 1993a, Model description and user's manual; Part 1 of A MODular finiteElement model (MODFE) for areal and axisymmetric ground-water-flow problems: 

U.S. Geological Survey Techniques of Water-Resources Investigations, book 6, chap. 

A3, 136 p. 

Cooley, R.L., 1992, Derivation of finite-element equations and comparisons with 

analytical solutions; Part 2 of A MODular finite-Element model (MODFE) for areal 

and axisymmetric ground-water-flow problems: U.S. Geological Survey Techniques 

of Water-Resources Investigations, book 6, chap. A4, 108 p. 

Torak, L.J., 1993b, Design philosophy and programming details; Part 3 of A MODular 

finite-Element model (MODFE) for areal and axisymmetric ground-water-flow 

problems: U.S. Geological Survey Techniques of Water-Resources Investigations, 

book 6, chap. A5, 243 p. 

Description: 

MOD FE was developed to provide solutions to ground-water flow problems based on 

the governing equations that describe two-dimensional and axisymmetric-radial flow in 

porous media. The documentation is divided into three parts. 

14 
Part 1 is the user's manual in which the hydrologic features and simulation capabilities 

of MOD FE are described. Descriptions are given for preparing hydrologic data to 

characterize aquifer properties and boundary conditions by zone. Examples of data 

input and model output are provided to demonstrate the different types of ground-water 

problems that are solved by using the simulation capabilities of MOD FE. Guidelines 

for designing the finite-element mesh and for node numbering and determining 

bandwidths are given to instruct users in the appropriate application of MOD FE to 

ground-water problems. 

In Part 2, the finite-element equations are derived by minimizing a functional of the 

difference between the true and approximate hydraulic head, which produces equations 

that are equivalent to those obtained by either classical variational or Galerkin 

techniques. Spatial finite elements are triangular with linear basis functions, and 

temporal finite elements are one dimensional with linear basis functions. Comparisons 

of finite-element solutions with analytical solutions are given for five example 

problems. 

Part 3 contains descriptions of subroutines, programming details and program structure 

diagrams. Descriptions of subroutines that execute the computational steps of the 

modular-program structure are given in tables that cross-reference the subroutines with 

particular versions of MOD FE. Programming details of linear and nonlinear 

hydrologic terms are provided. Structure diagrams for the main programs show the 

order in which subroutines are executed for each version and illustrate some of the 

linear and nonlinear versions of MOD FE that are possible. Computational aspects of 

changing stresses and boundary conditions with time and of mass balance and error 

terms are given for each hydrologic feature. Program variables are listed and defined 

according to their occurrence in the main programs and subroutines. Listings of the 

main programs and subroutines are given. 

Numerical features: 

Aquifer geometry, flow boundaries, and variations in hydraulic properties are 

represented by triangular elements or element sides in a finite-element mesh. Time 

variations in hydraulic response are represented by one-dimensional elements. Linear 

coordinate functions are used to approximate the head distribution within elements. 

The finite-element matrix equations are solved by using either a direct symmetric 

Doolittle method of triangular decomposition or an iterative method that uses the 

modified, incomplete Cholesky, conjugate-gradient method. The direct method can be 

efficient for small- to medium-sized problems (less than about 500 nodes), and the 

iterative method generally is more efficient for larger-sized problems. 

Simulation capabilities and uses of MOD FE are transient or steady-state conditions, 

nonhomogeneous and anisotropic flow where directions of anisotropy change within 

the model region; vertical leakage from a semiconfining layer that contains laterally 

nonhomogeneous properties and elastic storage effects; point and areally distributed 

sources and sinks; specified head (Dirichlet), specified flow (Neumann), and head15 
dependent (Cauchy-type) boundary conditions; vertical cross-section and 

axisymmetric cylindrical flow; confined and unconfined (water-table) conditions; 

partial drying and resaturation of a water-table aquifer; conversion between confinedand unconfined-aquifer conditions; and nonlinear head-dependent fluxes (for 

simulating line, point, or areally distributed sources and sinks). Aquifer stresses and 

boundary conditions can be changed on a time-step basis, or a stress-period basis or 

both. Hydraulic properties and boundary conditions can be input by zone. 

Past applications: 

This is a new program that has been used in a few field studies. 

Availability: 

Reports are available from the USGS Map Distribution. Computer program and reports 

are available from NWIS. 

Cylindrical Coordinates 

Program Documentation: 

Reilly, T.E., 1984, A Galerkin finite-element flow model to predict the transient 

response of a radially symmetric aquifer: U.S. Geological Survey Water-Supply Paper 

2198,33 p. 

Description: 

This computer program was developed to evaluate radial flow of ground water at a 

pumping well, a recharge basin, or an injection well. It is capable of simulating 

anisotropic, inhomogenous, confined, or pseudo unconfined (constant saturated 

thickness) conditions. 

Numerical features: 

The program is based on the Galer kin finite-element technique. It uses linear triangular 

elements and a backwards finite difference in time. 

Past applications: 

Several. 

Availability: 

Report is available from the USGS Map Distribution. Computer program and report 

are available from NWIS. 

16 
Related program: 

Pucci, A.A., Jr., and Pope, D.A., 1987, Preprocessor and postprocessor computer 

programs for a radial-flow, finite-element model: U.S. Geological Survey Open-File 

Report 87-680, 69 p. 

Most significant change to original program: 

This program serves as a preprocessor by: generating a triangular finite-element mesh 

from minimal data input, producing graphical displays and tabulations of data for the 

mesh, and preparing an input data file. The postprocessor has the ability to produce 

graphical output for simulation and field results and to generate statistics for comparing 

the simulation results with observed data. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Axisymmetric Finite-Difference (well bore/aquifer) 

Program Documentation: 

Rutledge, A.T., 1991, An axisymmetric finite-difference flow model to simulate 

drawdown in and around a pumped well: U.S. Geological Survey Water-Resources 

Investigations Report 90-4098, 33 p. 

Description: 

This computer program was developed to simulate drawdown in and around a pumped 

well. It provides a tool that is useful for analyzing some aquifer test data that are 

complicated by features not handled by analytical methods. Aquifer properties that can 

be simulated include confined (leaky or nonleaky) conditions, unconfined conditions, 

vertical-horizontal anisotropy, and vertical variation in hydraulic conductivity and 

specific storage. The model requires horizontal uniformity of hydraulic conductivity, 

specific yield, and specific storage. Well properties that can be simulated include wellcasing storage, hydraulic head loss across the well screen, and hydraulic head variation 

along the length of the well bore that results from pipe-flow friction and nonuniform 

velocity. The program allows for partial well penetration and for multiple screened 

intervals. 

17 
Numerical features: 

The program is based on the finite-difference technique. Because the time derivative 

approximation used is the forward-difference (explicit) in time, an upper limit on the 

time-step length is needed to assure numerical stability. The program allows an early 

time-step size and a larger later time-step size. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Two-Aquifer System 

Program Documentation: 

Mallory, M.J., 1979, Documentation of a finite-element two-layer model for simulation 

of ground-water flow: U.S. Geological Survey Water-Resources Investigations Report 

79-18, 347 p. 

Description: 

Theoretical development of the model represented by this program is from Durbin 

(1978). The program simulates steady and nonsteady ground-water flow in an 

irregularly shaped two-aquifer system. The areal extent of the two aquifers does not 

have to be coincident. The transmissive and storage properties of the aquifer can differ 

spatially but are assumed to be isotropic. Discharge and recharge can be varied 

spatially and with time. Evapotranspiration is treated as a linear function of depth to 

water. The vertical hydraulic conductivity of the confining layer is assumed to be a 

constant, its thickness can differ spatially, and the changes in confining layer storage 

are assumed to be negligible. 

Numerical features: 

The program uses the Galerkin finite-element method and approximates the time 

derivative by backwards finite-difference formulation. The region to be modeled is 

subdivided into triangles, and the head is assumed to vary linearly in any one triangle. 

The associated matrix problem is solved by using the PSOR (point iterative successive 

over-relaxation method). 

Past applications: 

A few field applications. 

18 
Availability: 

Report is available from NTIS (PB-80-140-932). 

Quasi-Three-Dimensional Aquifer System (Finite Difference) 

Program Documentation: 

Weeks, J.B., 1978, Digital model of ground-water flow in the Piceance Basin, Rio 

Blanco and Garfield Counties, Colorado: U.S. Geological Survey Water-Resources 

Investigations 78-46, 108 p. 

Description: 

The computer program capability is "quasi-three-dimensional" in that it simulates a 

three-dimensional multiaquifer system by assuming horizontal flow in the aquifers and 

vertical flow through the confining layers that separate the aquifers. The program 

simulates steady and nonsteady ground-water flow in an irregularly shaped flow system 

that consists of aquifer layers and confining layers. Changes in storage in the confining 

layers are assumed to be negligible. The transmissivity and storage coefficient of each 

aquifer layer and the confining layer leakance values can differ spatially. Uniform 

recharge to each layer and distributed discharge can be simulated. Specified head 

boundaries can be simulated in the uppermost aquifer. 

Numerical features: 

The planar area of the irregularly shaped flow region is divided into a rectangular blockcentered grid that permits variable grid spacing. Finite-difference numerical 

approximations reduce the equations of ground-water flow in each aquifer to a matrix 

problem that can be solved by using IADIP (the iterative alternating-direction implicit 

procedure). The computational procedure essentially is to treat the aquifer system as a 

sequence of two-dimensional flow models coupled by terms that represent flow 

(leakage) through intervening confining beds. The leakage at a node in a particular 

layer is based on, among other things, the difference in head in the layer during the 

current iteration and the most recently computed heads for the nodes in the overlying 

and underlying layers vertically in line with the subject node. Outflows to the specified 

head boundaries are computed for each time period and as a cumulative volume of 

water. 

Past applications: 

Many. 

19 
Remarks: 

This program is a revision and adaptation for the Piceance Basin of a program 

developed by J.D. Bredehoeft in 1969 and described in Bredehoeft and Pinder (1970); 

the latter program was used widely before about 1980. See McDonald and Harbaugh 

(1988) for a newer code that has more capabilities. 

Availability: 

Report is available from NTIS (PB-284-341). 

Three-Dimensional Finite-Difference 

Program Documentation: 

Bredehoeft, J.D., 1992, Microcomputer codes for simulating transient ground-water 

flow-In two and three space dimensions: U.S. Geological Survey Open-File Report 

90-559, 73 p., diskette in pocket. 

Description: 

This report is the documentation for a code for solving two- and quasi-threedimensional formulations of the general ground-water flow equation. The code is 

written in FORTRAN 77 and was developed to be a simple basic code that could run 

on a variety of small computer systems. Specified head and specified flux boundaries 

can be simulated. The transmissivity is assumed to be isotropic and not change with 

head, but it can vary spatially. One value is assumed to be representative of the storage 

coefficient of all aquifers, and the effects of storage in the confining layers are assumed 

to be negligible. The leakance values (vertical hydraulic conductivity divided by the 

thickness of the leaky confining layer) can vary spatially for each confining layer. 

Recharge/discharge can be simulated and can vary spatially. 

Numerical features: 

The flow region is considered to be divided into blocks in which the medium properties 

are assumed to be uniform. Block-centered finite-difference numerical formulations 

are used. The associated matrix problem is solved by using the SIP (strongly implicit 

procedure) iterative technique. A total mass balance and the rate of flow in the system 

are computed and printed at user selected times. 

Past applications: 

Limited. 

20 
Availability: 

Report is available from the USGS EIC--Open-File Report Section. The report 

includes a source diskette that contains the two- and three-dimensional programs and 

data sets that correspond to the test problems described in the report. 

Three-Dimensional Finite-Difference 

Program Documentation: 

Trescott, P. C., 197 5, Documentation of finite-difference model for simulation of threedimensional ground-water flow: U.S. Geological Survey Open-File Report 75-438, 

32p., 

Trescott, P. C., and Larson, S. P., 1976, supplement to Open-File Report 75-438-

Documentation of finite-difference model for simulation of three-dimensional groundwater flow: U.S. Geological Survey Open-File Report 76-591, 21 p. 

Description: 

Steady and nonsteady flow are simulated in an irregularly shaped three-dimensional 

flow region. The flow system can be fully confined, or the uppermost zone can be an 

unconfined aquifer. Hydraulic conductivities may be heterogeneous and anisotropic 

(restricted to having the principal directions alined with the grid axes and the anisotropy 

ratios fixed for each layer), and the storage coefficient may be heterogeneous. The 

model simulates well discharge from any layer and recharge to the uppermost layer that 

can vary spatially (but not with time). Specified head and specified flux boundaries can 

be handled. For some flow systems that are characterized by alternating layers of 

"high" and "low" hydraulic conductivities, a modified three-dimensional formulation 

is available that exploits essentially horizontal flow in "aquifer" layers and essentially 

vertical flow (assuming storage in confining beds is not significant) in "tight" layers to 

give approximate solutions for less computational effort. 

Numerical features: 

The flow region is considered to be divided into blocks in which the medium properties 

are assumed to be uniform. Block-centered finite-difference numerical approximations 

are used. In plan view, the discretization is formed by dividing the area by two sets of 

parallel lines that may be variably spaced and the sets of lines are mutually 

perpendicular. In the vertical direction, the real conditions are approximated by a set 

of parallel layers. The resulting matrix problem is solved by using the SIP (the Strongly 

Implicit Procedure) iterative scheme. Mass balances are computed for each time step 

and as a cumulative volume from each source and type of discharge. 

21 
Past applications: 

Many field problems. 

Remarks: 

During the 1970's and early 1980's, one of the most -used models for three-dimensional 

flow problems. See McDonald and Harbaugh (1988) for a newer code that has more 

capabilities. 

Availability: 

Reports are available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Torak, L. J., 1982, Modifications and corrections to the finite-difference model for 

simulation of three-dimensional ground-water flow: U.S. Geological Survey WaterResources Investigations Report 82-4025, 30 p. 

Most significant changes to original program: 

This report describes corrections to be made and extends the application of the Trescott 

three-dimensional program to simulations that involve leaky rivers, evapotranspiration 

as a linear function of depth to water, and discharge to drains and springs. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Helgesen, J.O., Larson, S.P., and Razem, A.C., 1982, Model modifications for 

simulation of flow through stratified rocks in eastern Ohio: U.S. Geological Survey 

Water-Resources Investigations Report 82-4019, 109 p. 

Most significant changes to original program: 

The changes are as follows: The calculation for vertical leakage between adjacent 

aquifer layers allows for the case in which a lower aquifer converts from confined to 

unconfined conditions; a head-dependent function was added to simulate spring 

discharge from the top layer and interaction between leaky streams and the aquifer layer 

immediately below the top layer; recharge from precipitation to any layer can be 

simulated; water-budget calculations are made for each layer; and spring flow from the 

top aquifer can recharge the next lower aquifer. 

22 
Past Applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Torak, L.J., and Whiteman, C.D., Jr., 1982, Applications of digital modeling for 

evaluating the ground-water resources of the "2,000-foot" sand of the Baton Rouge 

area, Louisiana: Louisiana Department of Transportation and Development, Office of 

Public Works Water Resources Technical Report 27, 87 p. 

Most significant change to original program: 

The most significant changes were the simulation of transient-leakage effects in 

confining layers, and the addition of a program to quantify the effect of making selected 

changes in aquifer-parameter values on computed heads. The program gives estimates 

of the percentage change in parameter values that would reduce the sum of the squares 

of the differences between observed and computed heads. 

Past applications: 

Few. 

Availability: 

Report is available from: 

Louisiana Department of Transportation and Development 

Water Resources Section 

P.O. Box 94245 

Baton Rouge, LA 70804-9245 

Related program: 

Leahy, P.P., 1982, A three-dimensional ground-water flow model modified to reduce 

computer-memory requirements and better simulate confining-bed and aquifer 

pinchouts: U.S. Geological Survey Water-Resources Investigations Report 82-4023, 

59p. 

Most significant changes to original program: 

Modifications are presented that permit the simulation of confining-bed and aquifer 

pinchouts without the use of artificial hydraulic parameters, reduce the computermemory requirements for aquifer systems that have complex external boundary shapes, 

and include the capability to approximate transient leakage from confining layers. 

23 
Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section 

Related program: 

Meyer, W.R., and Carr, J.E., 1979, A digital model for simulation of ground-water 

hydrology in the Houston area, Texas: Texas Department of Water Resources Report 

LP-103, 27 p. (Appendix, 107 p.) 

Most significant change to original program: 

Land subsidence induced by ground-water extraction can be approximated. Different 

storage coefficients are used for elastic and inelastic compression of two clay layers. 

The choice of storage coefficient depends on the current head relative to the "critical 

head" associated with the maximum effective stress to which the clays have been 

previously subjected. 

Past applications: 

Few. 

Availability: 

Report and computer program are available from: 

Texas Water Development Board 

TNRIS 

P.O. Box 13231 

Austin, TX 78711 

Three-Dimensional Finite-Difference 

Program Documentation: 

Posson, D.R., Hearne, G.A., Tracy, J.V., and Frenzel, P.F., 1980, A computer program 

for simulating geohydrologic systems in three dimensions: U.S. Geological Survey 

Open-File Report 80-421, 795 p. 

24 
Description: 

This program has the same basic capabilities as Trescott's (1975) except that (1) this 

program uses "cube" input commands that allow the modeler to change aquifer 

parameters oy zones that are believed to have uniform values and reinitialize the model 

with few input records; (2) a data-swapping procedure between the central memory and 

the peripheral storage devices exploits the nature of the SIP (strongly implicit 

procedure) matrix-solving technique by solving for heads at a subset of blocks at any 

one time, this data-swapping procedure allows simulations to be run that involve more 

blocks than can be handled by the approach of having all the problem variables in 

central memory at one time; and (3) in flow systems characterized by aquifer layers, 

separated by tight "confining" layers, the effects of storage in the confining layers is 

approximated. 

Numerical features: 

They are the same as for Trescott's (1975) except that an analytical/numerical 

approximation is included for transient leakage from the confining beds. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Hearne, G.A., 1982, Supplement to the New Mexico three-dimensional model: U.S. 

Geological Survey Open-File Report 82-857, 90 p. 

Most significant changes to original program: 

The computer program, which was discussed in Posson and others ( 1980), was changed 

to allow representation of more than one head-dependent flow boundary in each cell, to 

improve the program stability and convergence by making the calculation of flow at 

such boundaries more implicit, and to allow the program to execute on a CRA Y -1 

computer. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

25 
Three-Dimensional Finite-Difference 

Program Documentation: 

McDonald, M.G., and Harbaugh, A.W., 1988, A modular three-dimensional finitedifference ground-water flow model: Techniques ofWater-Resources Investigations of 

the United States Geological Survey, book 6, chap. Al, 586 p. 

Description: 

The model (referred to as MODFLOW) simulates steady and nonsteady flow in an 

irregularly shaped flow system in which aquifer layers can be confined or unconfined 

or both. Flow from external stresses, such as flow to wells, areal recharge, 

evapotranspiration, flow to drains, and flow through river beds, can be simulated. 

Hydraulic conductivities or transmissivities for any layer may differ spatially and be 

anisotropic (restricted to having the principal directions aligned with the grid axes and 

the anisotropy ratio between horizontal coordinate directions is fixed in any one layer) 

and the storage coefficient may be heterogeneous. The model requires input of the ratio 

of vertical hydraulic conductivity to distance between vertically adjacent block centers. 

Specified head and specified flux boundaries can be simulated as can a head-dependent 

flux across the outer boundary of the model that allows water to be supplied to a 

boundary block in the modeled area at a rate proportional to the current head difference 

between a "source" of water outside the modeled area and the boundary block. 

Numerical features: 

The flow region is considered to be divided into blocks in which the medium properties 

are assumed to be uniform. The plan view rectangular discretization results from a grid 

of mutually perpendicular lines that may be variably spaced. In the vertical direction, 

zones of varying thickness are transformed into a set of parallel "layers." The associated 

matrix problem is solved by using either the SIP (Strongly Implicit Procedure) or the 

SSOR (slice-successive overrelaxation). Mass balances are computed for each time 

step and as a cumulative volume from each source and type of discharge. 

Past applications: 

Widely used. 

Remarks: 

This is the most-used numerical model in the U.S. Geological Survey for ground-water 

flow problems. An efficient contouring program is available (Harbaugh, 1990a) to 

visualize heads and drawdowns output by the model. 

Availability: 

Report is available from the USGS Map Distribution. Computer program and report 

are available from NWIS. 

26 
Related program: 

Kuiper, L.K., 1987, Computer program for solving ground-water flow equations by the 

preconditioned conjugate gradient method: U.S. Geological Survey Water-Resources 

Investigations Report 87-4091, 24 p. 

Most significant changes to original program: 

A preconditioned conjugate-gradient method is given for the solution of the finitedifference approximating equations generated by the modular flow model. Five 

preconditioning types may be chosen-three different types of incomplete Choleski, 

point Jacobi, or block Jacobi. Either a head change or residual error criteria may be 

used as an indication of solution accuracy and iteration termination. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Scott, J.C., 1990, A statistical processor for analyzing simulations made using the 

modular finite-difference ground-water flow model: U.S. Geological Survey WaterResources Investigations Report 89-4159, 218 p. 

Most significant changes to original program: 

The report described the computer program MMSP (Modular Model Statistical 

Processor). By using MMSP, data input or output from the modular model 

MODFLOW can be used to calculate descriptive statistics, generate histograms, make 

logical comparisons between data arrays, generate new data arrays by operating on 

specified data arrays, and prepare data files that can be used to graphically display some 

of the model results. 

Past applications: 

Several. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

27 
Related program: 

Orzol, L.L., and McGrath, T.S., 1992, Modifications of the U.S. Geological Survey 

modular, finite-difference, ground-water flow model to read and write geographical 

information system files: U.S. Geological Survey Open-File Report 92-50, 202 p. 

Most significant changes to original program: 

The report documented the design and use of the program MOD FLOW ARC which is 

an enhanced version ofMODFLOW that can transfer data directly between ARC/INFO 

software and the ground-water flow model. ARC/INFO can be used to process data that 

is in a nongridded form into the gridded form required for input to the ground-water 

model, and to graphically display and edit the gridded data sets. 

Past applications: 

Several. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Harbaugh, A.W., 1990b, A computer program for calculating subregional water 

budgets using results from the U.S. Geological Survey modular three-dimensional 

finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 

90-392, 46 p. 

Most significant changes to original program: 

This report describes the computer program ZONEBUDGET that uses cell-by-cell flow 

data saved by the U.S. Geological Survey modular three-dimensional finite-difference 

ground-water flow model. ZONEBUDGET calculates water-budgets for subareas 

within the modeled region, as defined by the user. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available form NWIS. 

28 
Related program: 

Leake, S.A., and Prudic, D .E., 1991, Documentation of a computer program to simulate 

aquifer-system compaction using the modular finite-difference ground-water flow 

model: Techniques of Water-Resources Investigations of the United States Geological 

Survey, book 6, chap. A2, 68 p. 

Most significant changes to original program: 

Removal of ground water by pumping from aquifers may result in compaction of 

compressible fine-grained beds that are within or adjacent to the aquifers. Compaction 

of the sediments and resulting land subsidence may be permanent if the head declines 

result in vertical stresses beyond the previous maximum stress. The process of 

permanent compaction is not routinely included in simulations of ground-water flow. 

This computer program was written for use with the U.S. Geological Survey modular 

finite-difference ground-water flow model, to simulate storage changes from elastic 

and inelastic compaction. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS Map Distribution. Computer program and report 

are available from NWIS. 

Related program: 

Miller, R.S., 1988, User's guide for RIV2-A package for routing and accounting of 

river discharge for a modular, three-dimensional, finite-difference, ground-water flow 

model: U.S. Geological Survey Open-File Report 88-~. '?33 p. 

2'\.\~ 

Most significant changes to original program: 

This computer program was developed to provide an accounting for river discharge by 

river reach. The program limits the maximum leakage from a river to the aquifer by 

considering the river discharge available and assuming that the maximum effective 

downward head difference is the difference in elevation between the stream stage and 

the streambed bottom. The user needs to specify the stream stage for each stream reach, 

and the stage is assumed to not vary with stream discharge. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

29 
Related program: 

Hansen, A.J., Jr., 1993, Modifications to the modular three-dimensional finitedifference ground-water flow model used for the Columbia Plateau regional aquifersystem analysis, Washington, Oregon, and Idaho: U.S. Geological Survey Open-File 

Report 91-532, 162 p. 

Most significant changes to the original program: 

Changes are described that permit flow between layers to be simulated without the use 

of artificial hydraulic parameters, and the simulation of canyons and other flow barriers 

(for example, faults) that are much narrower than a grid cell. 

Past applications: 

Recently published. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Prudic, D.E., 1989, Documentation of a computer program to simulate stream-aquifer 

relations using a modular, finite-difference, ground-water flow model: U.S. Geological 

Survey Open-File Report 88-729, 113 p. 

Most significant changes to original program: 

This computer program was written for use in the modular finite-difference groundwater flow model to account for the amount of flow in streams and to simulate the 

interaction between surface streams and ground water. This package is not a true 

surface-water flow model but rather is an accounting program that tracks the flow in 

one or more streams that interact with ground water. The program limits the amount of 

ground-water recharge to the available streamflow. The stream stage in each river 

reach is computed by using the Manning formula under the assumption that the stream 

channel is rectangular. The program permits two or more streams to merge into one 

with flow in the merged stream equal to the sum of the tributary flow and also permits 

diversions from streams. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

30 
Related programs: 

Pollock, D.W., 1989, Documentation of computer programs to compute and display 

pathlines using results from the U.S. Geological Survey modular three-dimensional 

finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 

89-381, 188 p. 

Pollock, D., W., 1990, A Graphical Kernel System (GKS) version of computer program 

MODPATH-PLOT for displaying path lines generated from the U.S. Geological 

Survey three-dimensional ground-water flow model: U.S. Geological Survey OpenFile Report 89-622, 49 p. 

Most significant changes to original program: 

This particle-tracking program was developed to compute three-dimensional path lines 

on the basis of output from steady-state simulations obtained with the U.S. Geological 

Survey modular three-dimensional finite-difference ground-water flow model. The 

package consists of two FORTRAN 77 computer programs-MODPATH, which 

calculates pathlines, and MODPATH-PLOT, which presents results graphically. 

MODP ATH uses a semianalytical particle-tracking scheme. The method is based on 

the assumption that each directional velocity component varies linearly within a grid 

cell in its own coordinate direction. This assumption allows an analytical expression to 

be obtained that describes the flow path within a grid cell. Given the initial position of 

a particle anywhere in a cell, the coordinates of any other point along its path line within 

the cell, and the time of travel between them, can be computed directly. 

Past applications: 

Widely used. 

Remarks: 

This is a very powerful tool for determining pathlines in flow models. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Hill, M.C., 1990, £reconditioned Conjugate-Gradient 2 (PCG2)-A computer program 

for solving ground-water flow equations: U.S. Geological Survey Water-Resources 

Investigations Report 90-4048, 43 p. 

31 
Most significant changes to original program: 

This report described and documented two preconditioned conjugate-gradient methods 

(a modified incomplete Choleski factorization and a least-squares polynomial 

preconditioner) that can be used for the solution of the system of linear equations in the 

U.S. Geological Survey modular three-dimensional finite-difference ground-water 

flow model. 

Past applications: 

Many. 

Remarks: 

This efficient matrix solver is gaining acceptance as a good altemati ve to the standard 

solvers as more people gain experience with it. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Hill, M.C., 1992, A computer program (MODFLOWP) for estimating parameters of a 

transient, three-dimensional, ground-water flow model using nonlinear regression: 

U.S. Geological Survey Open-File Report 91-484, 358 p. 

Most significant changes to original program: 

When this new version of the U.S. Geological Survey modular, three-dimensional, 

finite-difference, ground-water flow model (MOD FLOW) is combined with the new 

Parameter-Estimation Package, which also is documented in Hill (1992), it can be used 

to estimate parameters by nonlinear regression. The new version of MOD FLOW is 

called MODFLOWP and functions nearly identically to MODFLOW when the 

Parameter-Estimation Package is not used. Parameters are estimated by minimizing a 

weighted least-squares objective function by either the modified Gauss-Newton 

method or a conjugate-direction method. The following MOD FLOW model input 

parameters can be estimated: transmissivity and storage coefficient of confined layers; 

hydraulic conductivity and specific yield of unconfined layers; verticalleakance; 

horizontal and vertical anisotropy; hydraulic conductance of the River, StreamflowRouting, General-Head Boundary, and Drain Packages; areal recharge rates; maximum 

evapotranspiration; pumpage rates; and the hydraulic head at constant-head boundaries. 

Any spatial variation in parameters can be defined by the user. Data used to estimate 

parameters can include independent estimates of parameter values, observed hydraulic 

heads or temporal changes in hydraulic heads, and observed gains and losses along 

32 
head-dependent boundaries (such as streams). Model output includes statistics for 

analyzing the parameter estimates and the model; these statistics can be used to 

quantify the reliability of the resulting model, to suggest changes in model construction, 

and to compare results of models constructed in different ways. 

Past applications: 

Recently published. 

Remarks: 

Hill ( 1994) describes five computer programs that use results from MODFLOWP to ( 1) 

produce data sets that can be used to create two graphs commonly used to test weighted 

residuals that are important in analyzing regression results, (2) calculate linear 

confidence and prediction intervals, (3) test the validity of one of the assumptions of the 

method used to calculate linear confidence and prediction intervals. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Harbaugh, A.W., 1992, A generalized finite-difference formulation for the U.S. 

Geological Survey modular three-dimensional finite-difference ground-water flow 

model: U.S. Geological Survey Open-File Report 91-494, 60 p. 

Most significant changes to original program: 

The U.S. Geological Survey's three-dimensional finite-difference modular groundwater flow model MOD FLOW assumes that model nodes are in the center of cells and 

that transmissivity is constant within a cell. On the basis of these assumptions, the 

model calculates coefficients, called conductances, that are multiplied by head 

difference to determine flow between cells. Although these are common assumptions 

in finite-difference models, other assumptions are possible. This option to the model 

program allows conductance to be part of the input data rather than calculating it. This 

option allows the user to calculate conductance outside of the model. The user thus has 

the flexibility to define conductance by using any desired assumptions. 

Past applications: 

New program. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

33 
Related program: 

Reilly, T.E., and Harbaugh, A.W., 1993b, Source code for the computer program and 

sample data set for the simulation of cylindrical flow to a well using the U.S. Geological 

Survey modular finite-difference ground-water flow model: U.S. Geological Survey 

Open-File Report 92-659, 7 p., diskette in pocket. 

Most significant changes to original program: 

The computer program documented in this report serves as a preprocessor to the U.S. 

Geological Survey model MODFLOW by creating the input data file needed to 

implement an axisymmetric conceptualization for simulation of flow to a well. The 

theory involves the conceptualization of a system of concentric shells that are capable 

of reproducing the large variations in gradient in the vicinity of the well by decreasing 

their area in the direction of the well. The theory and logic of the computer program, 

as well as an example of the use of the preprocessor, are described in Reilly and 

Harbaugh (1993a). The preprocessor generates a data set that is to be used with the 

General Finite-Difference Package (Harbaugh, 1992) of the U.S. Geological Survey 

modular finite-difference ground-water flow model. 

Past applications: 

New. 

Availability: 

Report (which contains the program on diskette) is available from either the USGS 

ESIC--Open-File Report Section or NWIS. 

Related program: 

Goode, D.J., and Appel, C.A., 1992, Finite-difference interblock transmissivity for 

unconfined aquifers and for aquifers having smoothly varying transmissivity: U.S. 

Geological Survey Water-Resources Investigations Report 92-4124, 79 p. 

Most significant change to original program: 

The interblock transmissivity calculated by the modular finite-difference model of 

McDonald and Harbaugh (1988) is a weighted harmonic mean. This report described 

changes to that model to incorporate alternative interblock transmissivity functions for 

the cases of linear spatial variation of transmissivity in a confined aquifer and either 

uniform hydraulic conductivity or hydraulic conductivity that varies linearly with 

distance in an unconfined aquifer. 

Past applications: 

New. 

34 
Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Hsieh, P. A., and Freckleton, J. R., 1993, Documentation of a computer program to 

simulate horizontal-flow barriers using the U.S. Geological Survey modular threedimensional finite-difference ground-water flow model: U.S. Geological Survey 

Open-File Report 92-477, 32 p. 

Most significant changes to original program: 

The horizontal-flow-barrier (HFB) package simulates thin, vertical, low-permeability 

geologic features that impede the horizontal flow of ground water. These geologic 

features are approximated as a series of HFB' s conceptually situated on the boundaries 

between pairs of adjacent cells in a finite-difference grid. Two key assumptions 

underlie the HFB package-the width of the barrier is negligibly small in comparison 

to the horizontal dimensions of the cells in the grid and the barrier has zero storage 

capacity. 

Past applications: 

New program. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

McDonald, M.G., Harbaugh, A.W., Orr, B.R., and Ackerman, D.J., 1992, A method of 

converting no-flow cells to variable-head cells for the U.S. Geological Survey modular 

finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 

91-536, 99 p. 

Most significant changes to original program: 

The original model, MODFLOW, could simulate the de saturation of variable-head 

model cells, which resulted in their conversion to no-flow cells, but could not simulate 

the resaturation of cells. This report described an option that was added to MOD FLOW 

to allow cells to convert from no-flow to variable head; this process is called "wetting" 

a cell. Examples of situations for which the wetting capability is useful are the recovery 

of water levels when pumping wells are turned off, and the mounding that can occur in 

response to irrigation applied to the land surface above an aquifer. This wetting 

capability also is very useful in situations where cells incorrectly go dry (convert to no 

35 
flow) as part of the iterative solution process. During the iterative solution process, 

heads in some cells may decrease to less than their final values, which may cause such 

cells to go dry. The new wetting capability allows such cells to convert back to wet. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Related program: 

Leake, S.A., Leahy, P., and Navoy, A.S., in press, Documentation of a computer 

program to simulate transient leakage from confining units using the modular finitedifference ground-water flow model: U.S. Geological Survey Open-File Report 94-59. 

Most significant changes to original program: 

The computer package TLKl represents a new method of simulating transient leakage 

from confining beds. The method incorporated into the TLKl package is a solution of 

integrodifferential equations that describe flow at the upper and lower boundaries of 

confining units. The package is applicable to confining units in which flow is nearly 

vertical, confining unit properties do not vary vertically, the specific storage of the 

confining unit does not vary with head, and the confining unit is bounded below by an 

aquifer and above by an aquifer or a specified-head boundary. The TLKl package can 

not simulate transient leakage in a confining unit bounded on top or bottom by an 

impermeable boundary. 

The TLKl package allows simulation of transient leakage without use of additional 

model layers to simulate flow in the confining units. Use of this package for some 

problems is more accurate and less computationally intensive than use of model layers 

to simulate confining units. 

Past applications: 

New program. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

36 
Two-Dimensional--Parameter Estimation 

Program Documentation: 

Cooley, R.L., and Naff, R.L., 1990, Regression modeling of ground-water flow: 

Techniques of Water-Resources Investigations of the U.S. Geological Survey, book 3, 

chap. B4, 232 p., diskette in pocket. 

Description: 

Regression procedures are used to solve for one or more of the following parameters: 

transmissivity, vertical hydraulic conductance (hydraulic conductivity divided by 

thickness) of sediments that underlie a stream or of an aquitard that overlies or underlies 

the aquifer, areally distributed recharge or discharge values, specific discharges normal 

to segments of the model boundary, and hydraulic heads at segments of the model 

boundary. This regression is based on steady-state observed heads, prior estimates of 

the regression parameters and their reliability, and known fluxes into or out of the 

aquifer. 

Numerical features: 

A rectangular grid is formed by two sets of mutually parallel and variably spaced lines. 

In this report, the intersections of the grid lines are called nodes, and the intra grid areas 

bounded by four adjacent nodes are called cells. The flow parameters, such as 

transmissivity, vertical hydraulic conductance, and distributed recharge and discharge, 

are assumed to be constant within a cell. Aquifer properties are characterized by zones, 

which are made up of a collection of cells. An integrated finite-difference method is 

used to develop a discrete form of solution of the flow equation. Various statistics 

associated with the regression analysis are computed. 

Past applications: 

Several. 

Remarks: 

An application of a preliminary version of the program, with modifications, was 

described in Garabedian (1986). Cooley (1993) described changes to the computer 

code that allow any model parameters to be transformed to natural logarithms and that 

improve the procedure for computing the parameter that is used to damp changes in the 

values of model parameters for each iteration of the solution method. In addition, 

instructions are given on how to input prior information on parameters separately from 

the set of initial parameter values. 

Availability: 

Report is available from the USGS Map Distribution. The computer program is 

contained on a diskette that comes with the report. 

37 
Coupled Ground-Water and Surface-Water Flow Model 

Program Documentation: 

Swain, B.D., and Wexler, E.J., 1993, A coupled surface-water and ground-water flow 

model for simulation of stream-aquifer interaction: U.S. Geological Survey Open-File 

Report 92-138, 162 p. 

Description: 

The program couples the ground-water flow model MOD FLOW with the surface-water 

flow model BRANCH to form a package called MODBRANCH. MOD FLOW is a 

modular three-dimensional finite-difference ground-water model (McDonald and 

Harbaugh, 1988, see description under "three-dimensional finite-difference"), and 

BRANCH (Schaffranek, Baltzer, and Goldberg, 1981) is a one-dimensional finitedifference model used to simulate the unsteady flow in a single open network of reaches 

composed on interconnected channels. The "linkage" between the aquifer and the 

surface-water models is a term that corresponds to the flow (commonly referred to as 

the "leakage") across the streambed between the stream and the aquifer in response to 

a difference in heads in the two places. BRANCH is based on a comprehensive set of 

unsteady flow equations and, within the limitations inherent in a one-dimensional 

formulation of streamflow, can accommodate a variety of open-channel flow problems. 

Numerical features: 

The BRANCH code was modified (to form BRANCH') to allow it to be called from 

MODFLOW. The surface-water time-step size selected in using BRANCH' must be 

such that the ground-water time step is an integral multiple of the surface-water time 

step. The leakage flow rates between the stream and the aquifer calculated by using 

BRANCH' are averaged over an entire ground-water time step and used in 

MOD FLOW as the leakage for the time step. The aquifer head used at each BRANCH' 

time step is linearly interpolated from heads calculated by using MODFLOW at the 

beginning and end of its time step. This approach necessitates multiple interactions 

between BRANCH' and MODFLOW for each MODFLOW time step. The authors 

reported that while this approach may not be as numerically stable at high leakage rates 

as the implicit calculation of leakage in MODFLOW, it is needed to maintain mass 

balance between the two models. 

Past applications: 

New program. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

38 
Related program: 

Swain, E. D., 1993, Documentation of a computer program (Streamlink) to represent 

direct-flow connections in a coupled ground-water and surface-water model: U.S. 

Geological Survey Water-Resources Investigations Report 93-4011, 62 p. 

Most significant change to original program: 

The program Streamlink allows direct-flow connections to be simulated among the 

MODFLOW ground-water model, the channel stage RIVER package (see McDonald 

and Harbaugh, 1988), the flow-routing stream package (see Prudic, 1989) and the 

unsteady open-channel model BRANC~ by using the MOD BRANCH coupling 

program. Two of the new connections are useful in modeling direct inlet/outlet 

between channels and the lakes or wetlands when the lakes or wetlands are represented 

by a high-conductivity aquifer block. Four other connections allow the three channel 

packages to connect to each other, thus modeling different sections of a channel 

network with various methods. The appeal of this flexibility in channel representation 

is that for some field problems, computation time can be reduced significantly by using 

the simpler packages for some of the channel sections without incurring a loss in 

accuracy. 

Past applications: 

New program. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Soil Moisture Accounting Program Coupled to a Two-Dimensional Unconfined/Confined 

Aquifer System 

Program Documentation: 

Reed, J.E., Bedinger, M.S., and Terry, J.E., 1976, Simulation procedure for modeling 

transient water-table and artesian stress and response: U.S. Geological Survey OpenFile Report 76-792, 173 p. 

Description: 

The program (called SUPERMOCK) was designed to simulate transient stress and 

response of an aquifer system that consists of a confined aquifer overlain by a watertable aquitard; climatic conditions and soil and vegetative properties, as well as the 

hydraulic properties of the aquifer system, must be taken into consideration. This 

aquifer system can be in various degrees of hydraulic connection with streams and 

lakes. The model has three components-a soil-moisture accounting component that 

39 
computes changes in soil-moisture storage and recharge and discharge from the zone of 

aeration to the water table; a vertical-flow component that computes the altitude of the 

water table in the fine-grained water-table aquitard that overlies the confined aquifer; 

and a horizontal flow component that computes accretion to the confined aquifer and 

its nonsteady heads. Simulated stresses on the confined aquifer include changes in 

stream stage, withdrawal by wells and infiltration or evapotranspiration or both, 

through the fine-grained zone above the confined aquifer. 

Numerical features: 

The grid is a rectangular array of nodes, which are at the intersection of two sets of 

mutually perpendicular lines (rows and columns). The spacing of nodes can differ in 

either direction. Data on properties of the aquifer and boundary conditions are specified 

at each node. Finite-difference numerical approximations are used. The resulting 

matrix problem is solved by using the ADIP (alternating-direction implicit procedure). 

Past applications: 

A few field applications. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

40 
FLOW-VARIABLY SATURATED 

Two-Dimensional 

Program Documentation: 

Lappala, E.G., Healy, R.W., and Weeks, E.P., 1987, Documentation of computer 

program VS2D to solve the equations of fluid flow in variably saturated porous media: 

U.S. Geological Survey Water-Resources Investigations Report 83-4099, 

184p. 

Description: 

Simulates isothermal, two-dimensional movement of liquid water in variably saturated 

porous media. The mathematical model of this physical process is developed by 

combining the law of conservation of fluid mass with a nonlinear form of Darcy's law. 

The resultant mathematical model, or flow equation, is written with total hydraulic 

potential as the dependent variable. This allows straightforward treatment of saturated 

and unsaturated conditions. In addition, the model can simulate "difficult" nonlinear 

problems, such as those caused by infiltration into dry soils and by discontinuities in 

permeabilities and porosities. 

Numerical features: 

The model can analyze problems in one and two dimensions with planar or cylindrical 

geometries. The spatial derivatives in the flow equation are approximated by central 

differences written about grid-block boundaries. Time derivatives are approximated by 

a fully implicit backward scheme. Nonlinear storage terms are linearized by an implicit 

Newton-Raphson method. Nonlinear conductance terms, boundary conditions, and 

sink terms are linearized implicitly. Relative hydraulic conductivity is evaluated at cell 

boundaries by using full upstream weighting, the arithmetic mean, or the geometric 

mean of values from adjacent cells. Saturated hydraulic conductivities are evaluated at 

cell boundaries by using distance-weighted harmonic means. The linearized matrix 

equations are solved by using SIP (the strongly implicit procedure). 

Past applications: 

Several. 

Remarks: 

Some additional modifications to the computer program VS2D are described in Healy 

(1990), which is listed in the section "Solute Transport--Variably Saturated." 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

41 
Related program: 

Healy, R.W., 1987, Simulation of trickle irrigation, an extension to the U.S. Geological 

Survey's computer program VS2D: U.S. Geological Survey Water-Resources 

Investigations Report 87-4086, 61 p. 

Most significant changes to original program: 

A method for use with VS2D is presented for simulating water movement through 

unsaturated porous media in response to a constant rate of application from a surface 

source. Because the rate at which water can be absorbed by soil is limited, the water 

will pond; therefore, the actual surface area over which the water is applied may change 

with time and, in general, will not be known beforehand. An iterative method is used 

to determine the size of this ponded area at any time. This method will be most useful 

for simulating trickle irrigation and may be of value for simulating movement of water 

in soils as a result of an accidental spill. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Two-Dimensional Diffusion 

Program Documentation: 

Ishii, A.L., Healy, R.W., and Striegl, R.G., 1989, A numerical solution for the diffusion 

equation in hydrogeologic systems: U.S. Geological Survey Water-Resources 

Investigations Report 89-4027, 86 p. 

Description: 

This program provides a numerical solution of the linear diffusion equation in one or 

two dimensions in cartesian or cylindrical coordinates. Applications of the program 

include molecular diffusion, heat conduction, and fluid flow in confined ground-water 

systems. The flow media may be anisotropic and heterogenous. 

Numerical features: 

The model uses a block -centered finite-difference method. The resulting matrix 

equation is solved by the method of preconditioned conjugate gradients. The model 

allows the specification of various boundary conditions for any number of stress 

periods. 

42 
Past applications: 

Very few. 

Remarks: 

The report describes application of the model to a hypothetical two-dimensional field 

situation that involves gas (methane in this case) diffusion in the unsaturated zone. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

43 
SOLUTE TRANSPORT--SATURATED 

One-Dimensional Finite-Difference Method 

Program Documentation: 

Grove, D.B., and Stollenwerk, K.G., 1984, Computer model of one-dimensional 

equilibrium-controlled sorption processes: U.S. Geological Survey Water-Resources 

Investigations Report 84-4059, 58 p. 

Description: 

A numerical solution to the one-dimensional solute-transport equation with 

equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. 

Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without 

equal valence. 

Numerical features: 

General equations that describe transport and reaction processes are solved by finitedifference methods; nonlinearities are accounted for by iteration. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Two-Dimensional Method of Characteristics 

Program Documentation: 

Konikow, L.F., andBredehoeft, J.D., 1978, Computer model of two-dimensional solute 

transport and dispersion in ground water: Techniques of Water-Resources 

Investigations of the United States Geological Survey, book 7, chap. C2, 90 p. 

Goode, D.J., and Konikow, L.F., 1989, Modification of a method-of-characteristics 

solute-transport model to incorporate decay and equilibrium-controlled sorption or ion 

exchange: U.S. Geological Survey Water-Resources Investigations Report 89-4030, 

65 p. 

44 
Description: 

This model simulates solute transport in flowing ground water. It is applicable to oneor two-dimensional problems that involve steady-state or transient flow. The model 

computes changes in concentration over time caused by the processes of advective 

transport, hydrodynamic dispersion, mixing or dilution from fluid sources, and the 

following types of chemical reactions: first-order irreversible-rate reaction, such as 

radioactive decay; reversible equilibrium-controlled sorption with linear, Freundlich, 

or Langmuir isotherms; and reversible equilibrium-controlled ion exchange for 

monovalent or divalent ions. The first type of reaction is accounted for by an 

exponential decay term applied directly to the particle concentration. The second and 

third types of reactions are incorporated through a retardation factor, which is a function 

of concentration for nonlinear cases. Gradients of fluid density, viscosity, and 

temperature are assumed not to affect the velocity distribution. However, the aquifer 

may be heterogeneous and anisotropic. 

The model has been evolving since its first release in the report by Konikow and 

Bredehoeft (1978). The updated model is reflected in the Goode and Konikow (1989) 

report, and both reports are required for a complete documentation. 

Numerical features: 

The model couples the ground-water flow equation with the solute-transport equation. 

The digital computer program uses the IADIP (iterative alternating-direction implicit 

procedure) to solve a finite-difference approximation to the ground-water flow 

equation and the method of characteristics to solve the solute-transport equation. The 

model uses a particle-tracking procedure to represent convective transport and a twostep explicit procedure to solve a finite-difference equation that describes the effects of 

hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This 

explicit procedure has several stability criteria, but the consequent time-step limitations 

are automatically determined by the program. 

Past applications: 

Widely used. 

Remarks: 

This is one of the most-used models for solute-transport problems. Complete 

documentation of the current version of this model requires the Konikow and 

Bredehoeft (1978) report and the report by Goode and Konikow (1989). 

Availability: 

The Konikow and Bredehoeft (1978) report is available from the USGS Map 

Distribution. The Goode and Konikow ( 1989) report is available from the USGS ESIC 

Open-File Report Section. Computer program and both reports (including updates to 

the program) are available from NWIS program office. 

45 
Related program: 

Garabedian, S.P., and Konikow, L.F., 1983, Front-tracking model for convective 

transport in flowing ground water: U.S. Geological Survey Water-Resources 

Investigations Report 83-4034, 55 p. 

Most significant change to original program: 

Unlike the original program this program does not represent dispersion and dilution. 

The model tracks representative water or tracer particles, initially located along 

specified lines, as they move in response to the ground-water velocity field. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Sanford, W.E., and Konikow, L.F., 1985, A two-constituent solute-transport model for 

ground water having variable density: U.S. Geological Survey Water-Resources 

Investigations Report 85-4279, 88 p. 

Most significant change to original program: 

This model was developed to simulate advective solute transport and dispersion of 

either one or two constituents in ground water in a cross-sectional plane where the 

density and viscosity of one constituent is a function of concentration. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

46 
Two-Dimensional Finite-Element Galer kin Method 

Program Documentation: 

Lewis, F.M., Voss, C.l., and Rubin, Jacob, 1986, Numerical simulation of advectivedispersi ve multisolute transport with sorption, ion exchange and equilibrium chemistry: 

U.S. Geological Survey Water-Resources Investigations Report 86-4022, 165 p. 

Description: 

This model simulates fully saturated two-dimensional transient, or steady-state, areal or 

cross-sectional, constant-density ground-water flow and multisolute transport. The 

options for transport under the condition of local equilibrium are linear sorption and up 

to two aqueous complexations and binary ion exchange and a single complexation 

reaction that involves one of the exchanging species. 

Numerical features: 

This model, SATRA-CHEM, is a modified version of the computer program SUTRA 

(Voss, 1984a). A finite-element Galerkin method is used for spatial approximations of 

the dependent variable and backwards finite-difference method for its time derivative. 

Hydraulic conductivities of each element can be anisotropic and variable in direction 

and magnitude. Boundary conditions and source/sink terms can vary with time. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Dual-Porosity Flow and Transport 

Program Documentation: 

Glover, K. C., 1987, A dual-porosity model for simulating solute transport in oil shale: 

U.S. Geological Survey Water Resources Investigations Report 86-4047, 88 p. 

Description: 

This model simulates three-dimensional flow and advective transport and 

hydrodynamic dispersion in an aquifer that has parallel fractures separated by 

nonfractured rock with significant porosity and negligible hydraulic conductivity. The 

flow and transport are assumed to take place primarily in the fractures with the potential 

for the exchange of solute between fluid in the fracture and the nonfractured rock by 

47 
molecular diffusion. Such diffusion is simulated by including a source-sink term 

developed from the analytical solution for the problem of mass transfer from two 

parallel, constant-concentration boundaries into the intervening material. 

Numerical features: 

By using the finite element Galerkin procedure, the differential equations that describe 

flow and mass transport are approximated by a system of linear equations. The system 

of equations are solved by selected forms of Gauss elimination. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

48 
SOLUTE TRANSPORT--VARIABLY SATURATED 

Two-Dimensional Finite-Difference Method 

Program Documentation: 

Healy R.W., 1990, Simulation of solute transport in variably saturated porous media 

with supplemental information on modifications to the U.S. Geological Survey's 

computer program VS2D: U.S. Geological Survey Water-Resources Investigations 

Report 90-4025, 125 p. 

Description: 

This report documents VS2DT, which simulates two-dimensional solute transport in 

porous media under variably saturated conditions. The program is an extension of the 

U.S. Geological Survey's computer program VS2D (Lappala, Healy, and Weeks, 

1987), which simulates water movement through variably saturated porous media. The 

extension consists of four new subroutines and slight modifications to existing routines. 

VS2DT may be a useful tool in studies of water quality, ground-water contamination, 

waste disposal, or ground-water recharge. 

Numerical features: 

VS2DT uses a finite-difference approximation to the advection/dispersion equation, as 

well as the nonlinear water-flow equation (based on total hydraulic head). It can 

simulate problems in one, two (vertical cross section), or three dimensions (axially 

symmetric). The porous media may be heterogeneous and anisotropic, but principal 

directions must coincide with the coordinate axes. Boundary conditions for flow can 

take the form of fixed pressure heads, infiltration with pending, evaporation from the 

soil surface, plant transpiration, or seepage faces. An extension to Healy's (1987) 

program also allows simulation of infiltration from trickle irrigation. Boundary 

conditions for solute transport include fixed solute concentration and fixed mass flux. 

Solute source/sink terms include first-order decay, equilibrium partitioning to the solid 

phase (as described by Langmuir or Freundlich isotherms), and ion exchange. The 

design of the program is modular, so that programmers can easily modify subroutines 

and functions to apply the model to particular field, laboratory, or hypothetical 

problems. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

49 
SOLUTE AND HEAT TRANSPORT--SATURATED 

Three-Dimensional Finite-Difference Method 

Program Documentation: 

INTERCOMP Resource Development and Engineering, Inc., 1976, A model for 

calculating effects of liquid waste disposal in deep saline aquifers: U.S. Geological 

Survey Water-Resources Investigations Report 76-61, 263 p. 

Description: 

A transient, three-dimensional model was developed to solve the three coupled 

governing equations for pressure, mass and heat transport. Although this program was 

initially developed to simulate certain aspects of waste injection into confined saline 

aquifers, it also is suitable for other applications that involve significant spatial 

variation in temperature and solute mass. 

Numerical features: 

The model is a finite-difference solution to the pressure, energy, and mass-transport 

equations. Equation parameters, such as viscosity and density, are allowed to be 

functions of the dependent variables of the equations. Multiple-user options allow the 

choice of three dimensional cartesian orr and z radial coordinates; various finitedifference methods; iterative and direct matrix solution techniques; restart options; and 

various provisions for output display. 

Past applications: 

Limited. 

Remarks: 

See Kipp ( 1987) for a current model of similar capabilities. 

Availability: 

Report is available from NTIS (PB-256 903/AS). 

Related program: 

INTERA Environmental Consultants, Inc., 1979, Revision of the documentation for a 

model calculating effects of liquid waste disposal in deep saline aquifers: U.S. 

Geological Survey Water-Resources Investigations Report 79-96, 

79p. 

50 
Most significant changes to original program: 

The additions and modifications in this revision include a free water surface, vertical 

recharge, equilibrium-controlled linear adsorption, and a first-order irreversible rate 

reaction. These, plus additional modifications, make this model more adaptable to 

general hydrologic problems and those that involve waste disposal with simple 

chemical reactions. 

Past applications: 

Several. 

Remarks: 

See Kipp ( 1987) for a current model of similar capabilities. 

Availability: 

Report is available from NTIS (PB-80 122 542). Computer program and report are 

available from NWIS. 

Three-Dimensional Finite-Difference Method 

Program Documentation: 

Kipp, K.L., Jr., 1987, HST3D-A computer code for simulation of heat and solute 

transport in three-dimensional ground-water flow systems: U.S. Geological Survey 

Water-Resources Investigations Report 86-4095, 517 p. 

Description: 

The Heat- and Solute-Transport Program (HST3D) simulates ground-water flow and 

associated heat and solute transport in three dimensions. This program is a descendant 

of the computer codes developed by INTERCOMP Resource Development and 

Engineering Inc. ( 1976) and revised by INTERA Environmental Consultants, Inc. 

(1979). HST3D may be used for analysis of such problems as those related to 

subsurface-waste injection, landfill leaching, saltwater intrusion, freshwater recharge 

and recovery, radioactive-waste disposal, hot-water geothermal systems, and 

subsurface-energy storage. The three governing equations are coupled through the 

interstitial pore velocity; the dependence of the fluid density on pressure, temperature, 

and solute-mass fraction; and the dependence of the fluid viscosity on temperature and 

solute-mass fraction. The solute-transport equation is for only a single solute species 

with possible linear-equilibrium sorption and linear decay. 

51 
Numerical features: 

Finite-difference techniques are used to discretize the governing equations by using a 

point-distributed grid. The flow-, heat- and solute-transport equations are solved, in 

turn, after a partial Gauss-reduction scheme is used to modify them. The modified 

equations are more tightly coupled and have better stability for the numerical solutions. 

Two techniques are available for solution of the finite-difference matrix equations. One 

technique is a direct-elimination solver, in which equations are reordered by alternating 

diagonal planes. The other technique is an iterative solver, in which two-line 

successive overrelaxation is used. 

Past applications: 

Several. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

52 
FLOW-SATURATED FRESHW ATERJSALTWATER 

Two-Dimensional Areal 

Program Documentation: 

Mercer, J.W., Larson, S.P., and Faust, C.R., 1980, Finite-difference model to simulate 

the areal flow of saltwater and freshwater separated by an interface: U.S. Geological 

Survey Open-File Report 80-407, 88 p. 

Description: 

The model is capable of simulating ground-water flow of saltwater and freshwater 

separated by an interface. The partial differential equations are integrated over the 

thicknesses of freshwater and saltwater, which results in two equations that describe the 

flow characteristics in the areal domain. The program is designed to simulate such 

time-dependent problems as those associated with the development of coastal aquifers 

and can treat water-table or confined conditions with steady-state leakage of fresh 

water. The program generally will be most applicable to the analysis of regional aquifer 

problems in which the zone between saltwater and freshwater can be considered to be 

a surface (sharp interface). 

Numerical features: 

The equations are approximated by using finite-difference techniques. The resulting 

algebraic equations are solved for the dependent variables, freshwater and saltwater 

heads using an iterative solution method. 

Past applications: 

Few field problems. 

Remarks: 

See Essaid ( 1990) for an updated three-dimensional model (SHARP) with similar 

capabilities. 

Availability: 

Report is available from the USGS ESIC--Open-File Reports Section. Computer 

program and report are available from NWIS. 

53 
Two-Dimensional Areal 

Program Documentation: 

Voss, C.I., 1984b, AQUIFEM-SALT-A finite-element model for aquifers containing 

a seawater interface: U.S. Geological Survey Water-Resources Investigations Report 

84-4263, 37 p. 

Description: 

This is an areal ground-water model that simulates head changes in and movement of 

only the freshwater in an aquifer. The freshwater and saltwater are assumed not to mix 

because they are separated by an effectively sharp interface. Vertical hydrostatic 

equilibrium in the freshwater and saltwater is assumed, and the model ignores any time 

lag that may result from transient horizontal saltwater flow as the interface attempts to 

readjust to a new hydrostatic equilibrium elevation. Parts of the freshwater lens may 

be confined above and below by less permeable units. 

Numerical features: 

A Galerkin finite-element formulation is used. 

Past applications: 

Few field problems. 

Remarks: 

This model is a modification to AQUIFEM, which is described by Pinder and Voss 

( 1979). The computer code was prepared by George Pinder, Emil Frind, Peter Trescott, 

and Clifford Voss. Copies of that report may be obtained from: 

AQUIFEM-SALT 

U.S. Geological Survey 

431 National Center 

Reston, VA 22092 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

54 
Three-Dimensional (Sharp interface) 

Program Documentation: 

Guswa, J.H., and LeBlanc, D.R., 1985, Digital models of ground-water flow in the 

Cape Cod aquifer system, Massachusetts: U.S. Geological Survey Water-Supply Paper 

2209, 112 p. 

Description: 

This model is a modification of the three-dimensional ground-water flow model 

described in Trescott (1975) and Trescott and Larson (1976). The modifications are 

based on the assumptions that the zone between fresh and saline ground water can be 

treated as an interface, that the saline-water zone is static, and that the flow system is 

in a state of dynamic equilibrium. Because the pressure in such a flow field must be 

continuous across the assumed interface, a relation can be written between the 

freshwater head and the elevation that must be satisfied at each point of the interface, 

which depends on the equivalent freshwater head along the seabed and the density 

difference between the freshwater and saline water. The computational scheme used 

requires that the starting head values be sufficiently large to define an interface position 

that is seaward of and deeper than the real interface position. During an iteration 

sequence, the calculated interface moves landward and upward until it is in balance 

with the freshwater flow system. The transmissivity of those zones that are calculated 

to be below the interface are assumed to be zero for computational purposes because 

the saline water is assumed to be static. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS Map Distribution. 

Three-Dimensional (Sharp Interface) 

Program Documentation: 

Sapik, D.B., 1988, Documentation of a steady-state saltwater-intrusion model for threedimensional ground-water flow, and user's guide: U.S. Geological Survey Open-File 

Report 87-526, 174 p. 

55 
Description: 

This report describes changes made to Trescott's ( 197 5) three-dimensional finitedifference ground-water flow program so that a steady-state sharp interface between 

freshwater and saltwater can be simulated. The model simulates flow only in the 

freshwater region and incorporates a Ghyben-Herzberg type approximation to locate 

the freshwater/saltwater interface. 

Past applications: 

Very few. 

Availability: 

Report is available from the USGS ESIC--Open-File Reports Section. 

Three-Dimensional (Sharp Interface) 

Program Documentation: 

Essaid, R.I., 1990, SHARP-A quasi-three-dimensional finite-difference simulation 

model for freshwater and saltwater flow in layered coastal aquifer systems: U.S. 

Geological Survey Water-Resources Investigations Report 90-4130, 181 p. 

Description: 

This model is a quasi-three-dimensional, numerical, finite-difference model that 

simulates freshwater and saltwater flow separated by a sharp interface in layered coastal 

aquifer/confining unit systems. SHARP facilitates regional simulation of coastal 

ground-water conditions in layered systems and includes the effects of saltwater 

dynamics on the freshwater flow system. 

Numerical features: 

The model accommodates multiple layered aquifers separated by confining units. Each 

aquifer is handled as a single layer with hydraulic properties that can vary spatially. 

The leakance (the ratio of vertical hydraulic conductivity to bed thickness) of confining 

layers also can vary spatially. The uppermost aquifer of the system may be confined, 

unconfined, or semiconfined with an areally distributed recharge. Temporal variations 

in recharge and pumping are accounted for by multiple pumping periods. The boundary 

conditions that may be simulated in the model are prescribed flux boundaries, constant 

freshwater and (or) constant saltwater-head boundaries, and leaky head-dependent 

boundaries in the uppermost aquifer. The program is written in FORTRAN 77. 

56 
Past applications: 

Although this is a new program, it has already been applied in a variety of field cases. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Three-Dimensional (Variable Density) 

Program Documentation: 

Weiss, Emanuel, 1982, A model for the simulation of flow of variable-density ground 

water in three dimensions under steady-state conditions: U.S. Geological Survey 

Open-File Report 82-352, 59 p. 

Description: 

The computer program associated with this model is a preprocessor for the constant 

density three-dimensional ground-water flow model by Trescott (1975). This 

preprocessor enables simulation of variable density flow fields, where the density is 

known throughout the three-dimensional flow field and is assumed to be constant in 

time (the density distribution does not change as a result of the movement of the fluid). 

Information on the density distribution and elevation of the layers is processed by the 

preprocessor, and the output from the preprocessor is calculated sources and sinks that 

when entered into the Trescott code will simulate the variable density flow field. 

Included in the report is a computer program for calculating ground-water density from 

aquifer depth, temperature, and dissolved solids concentration. 

Numerical features: 

The information required for the program's operation is aquifer elevation, thickness, 

and ground-water density. The report contains two FORTRAN programs that are used 

to generate the necessary flow-model input The model is based on the same threedimensional finite-difference scheme as the Trescott (1975) model. 

Past applications: 

Very few field problems. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

57 
Three-Dimensional (Variable Density) 

Program Documentation: 

Kuiper, L.K., 1985, Documentation of a numerical code for the simulation of variable 

density ground-water flow in three dimensions: U.S. Geological Survey Water 

Resources Investigations Report 84-4302, 80 p. 

Description: 

This is a numerical program for the simulation of variable density time-dependant 

ground-water flow in three dimensions. The ground-water density, although variable 

in space, is assumed to be approximately constant in time and known. The integrated 

finite difference grid elements in the program are rectangular when viewed from the 

vertical direction, but their top and bottom surfaces follow the curvature of the geologic 

strata in the modeled area. 

Numerical features: 

The program uses the integrated finite difference method. The SIP (strongly implicit 

procedure), SOR (successive overrelaxation), and eight different PCG (preconditioned 

conjugate gradient) methods are used to solve the approximating matrix equations. 

Past auplications: 

Very few field applications. 

Remarks: 

The theoretical development, on which the numerical code is based, is described in 

Kuiper (1983). 

Availability: 

Report is available from the USGS ESIC--Open-File Reports Section. Computer 

program and report are available from NWIS. 

Three-Dimensional (Variable Density and Multiaquifer wells) 

Program Documentation: 

Kontis, A.L., and Mandie, R.J., 1988, Modification of a three-dimensional groundwater flow model to account for variable water density and effects of multiaquifer 

wells: U.S. Geological Survey Water Resources Investigations Report 87-4265, 78 p. 

58 
Description: 

This report described changes made to the constant density three-dimensional groundwater flow model of Trescott (1975) that allow it to be used for variable density flow 

fields in which the spatial distribution of the fluid density is assumed not to change with 

time. The report also described changes made to simulate wells open to more than a 

single aquifer. 

Numerical features: 

In addition to describing the variable-density and multiple-well modifications to the 

Trescott model, two new computer programs were described. Those programs compute 

ground water and pure water density and dynamic viscosity and the horizontal and 

vertical hydraulic conductances and variable density input data for the Trescott model. 

A SSOR (slice-successive-over-relaxation) matrix solver is described. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

59 
HEAT TRANSPORT 

Two-Dimensional Single- and Two-Phase 

Program Documentation: 

Faust, C.R., and Mercer, J.W., 1977, Version 1-A finite-difference model of twodimensional, single- and two-phase heat transport in a porous medium: U.S. 

Geological Survey Open-File Report 77-234, 84 p. 

Description: 

The model can simulate two-dimensional (areal) flow of compressed water, two-phase 

mixtures, and super-heated steam over a temperature range of 10 to 300 °C. The model 

can handle the conversion from single-phase to two-phase flow. The dependent 

variables solved for are pressure and enthalpy. The aquifer is assumed to be underlain 

and overlain by impermeable layers that allow only conduction of heat. The aquifer 

permeability, porosity, and thickness can vary spatially. The permeability can be 

anisotropic in each block, but the principal directions must be aligned with the 

coordinate axes. 

Numerical features: 

The modeled area is divided into rectangular grid blocks (with nodes at the block 

centers) in which the fluid and aquifer properties are assumed to be uniform. 

Past applications: 

Limited. 

Remarks: 

It was recognized that the model would require some sophisticated changes and 

additions before a complicated field problem could be simulated; consequently, the 

model was considered to be a research tool only. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Two-Dimensional Single-Phase 

Program Documentation: 

Mercer, J.W., and Pinder, G.F., 1975, A finite-element model of a two-dimensional, 

single-phase heat transport in a porous medium: U.S. Geological Survey Open-File 

Report 75-574, 115 p. 

60 
Description: 

This program simulates the two-dimensional areal equations of ground-water flow and 

heat transport. The program solves for aquifer pressures and temperatures and allows 

vertical flow of heat and liquid through an overlying confining bed. An areally 

distributed heat function may be used to approximate a heat source below the aquifer. 

Numerical features: 

The Galerkin finite-element method is used. The basic shape of the elements are 

quadrilaterals, but the sides may be curved, depending on the degree of polynomial 

used to describe the side. Linear, quadratic, and cubic basis functions are available. 

The elements are designed to allow the basis functions on different sides of the same 

element to be polynomials of different degrees. Backward or central differences are 

used for time derivative. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Three-Dimensional 

Program Documentation: 

Reed, J.E., 1985, Digital model for simulating steady-state ground-water and heat flow: 

U.S. Geological Survey Water-Resources Investigations Report 85-4248, 134 p. 

Description: 

This model simulates the three-dimensional equation of ground-water and single-phase 

heat flow by convective flow and conduction. The thermal conductivity of the saturated 

rock materials and the volumetric specific heat for the fluid are assumed constants. The 

heat flows accounted for are geothermal heat flow, conduction to the land surface, 

convection from recharge from precipitation, and convection to or from fixed-head 

boundaries. Because the model assumes that fluid density is constant, buoyancy effects 

caused by fluid-density variations that result from temperature differences are not 

considered. 

Numerical features: 

The program is based on separate finite-difference approximations of the ground-water 

flow equation and of the convective-dispersive heat-flow equation. The ground-water 

61 
flow and heat flow models are interdependent because hydraulic conductivity in the 

ground-water flow model is a function of temperature and convective flow in the heatflow model is a function of ground-water flow. The ground-water flow and heat-flow 

models use block-centered, finite-difference approximations. The hydraulic 

conductivity and porosity can vary from block to block. The program uses an iterative 

procedure that alternately solves the ground-water flow and heat-flow equations 

improving the estimate of convective flux after solution of the ground-water flow 

equation and improving the estimate of hydraulic conductivity after solution of the 

heat-flow equation. Time of travel is determined by particle tracking through the 

modeled region. 

Past applications: 

Limited. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Three-Dimensional 

Program Documentation: 

Hayba, D.O., and Ingebritsen, S.E., in press, The computer model HYDROTHERM, A 

three-dimensional finite-difference model to simulate ground-water flow and heat 

transport in the temperature range of 0 to 1,200 °C: U.S. Geological Survey WaterResources Investigations Report 94-4045. 

Description: 

The HYDROTHERM model simulates the flow of pure water and heat in a porous 

medium. The model allows for spatial and temporal variations of permeability, 

porosity, and thermal conductivity. HYDROTHERM incorporates pure-water 

equations of state that cover the temperature range of 0 to 1 ,200 °C and pressures from 

0.5 bars to 10 kbars. The governing equations are expressions of mass and energy 

conservation that are posed in terms of pressure and enthalpy. The advantage of 

pressure and enthalpy as the dependent variables is that they uniquely specify the 

thermodynamic state of the fluid under both single- and two-phase conditions. Major 

assumptions are that the rock matrix can be treated as a porous medium; that the water 

and rock are in thermal equilibrium; and that capillary pressure is negligible. The 

intrinsic permeability can be anisotropic in each block, but the principal directions are 

assumed to be aligned with the coordinate axes. Rock density and specific heat are 

assumed to be constants. 

62 
Numerical features: 

The modeled region can be represented using cartesian or radial coordinate 

systems. The governing equations for the model require values for fluid densities, 

viscosities, and temperature. HYDROTHERM uses a bicubic interpolation routine to 

derive, for any given pressure-enthalpy pair, values of density, viscosity, and 

temperature, as well as the local gradients of those values with respect to pressure and 

enthalpy. For a fully three-dimensional model, the numerical solution technique used is 

slice-successive overrelaxation embedded in a Newton-Raphson iteration. The report 

describes five example problems solved using HYDROTHERM to demonstrate the 

thermodynamic range and multi-dimensional performance of the model. 

Past applications: 

New. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

63 
SOLUTE OR HEAT TRANSPORT--SATURATED AND UNSATURATED 

Two-Dimensional Finite-Element Galerkin Method 

Program Documentation: 

Voss, C.I., 1984a, A finite-element simulation model for saturated-unsaturated, fluiddensity-dependent ground-water flow with energy transport or chemically-reactive 

single-species solute transport: U.S. Geological Survey Water-Resources 

Investigations Report 84-4369, 409 p. 

Description: 

The model may be employed for areal and cross-sectional modeling of saturated 

ground-water flow systems and for cross-sectional modeling of unsaturated zone flow. 

Solute-transport simulation that uses SUTRA may be employed to model natural or 

man-induced chemical species transport, which includes processes of solute sorption, 

production, and decay, and may be applied to analysis of ground-water contaminant 

transport problems and aquifer restoration designs. In addition, solute-transport 

simulation with SUTRA may be used for modeling of variable density leachate 

movement and for cross-sectional modeling of saltwater intrusion in aquifers, with 

either dispersed or relatively sharp transition zones between freshwater and saltwater. 

SUTRA energy-transport simulation may be employed to model thermal regimes in 

aquifers, subsurface heat conduction, aquifer thermal energy storage systems, 

geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic 

convection systems. 

Numerical features: 

The model employs a two-dimensional hybrid finite-element and integrated-finitedifference method to approximate the governing equations that describe the following 

simulated interdependent processes: fluid density-dependent saturated or unsaturated 

ground-water flow and either transport of a solute in the ground water, in which the 

solute may be subject to equilibrium adsorption on the porous matrix, and both firstand zero-order production or decay, or transport of thermal energy in the ground water 

and solid matrix of the aquifer. 

Past applications: 

Many. 

Remarks: 

A graphical postprocessor developed by Souza ( 1987) is available for use with the 

computer code. This postprocessor facilitates interpretation of the simulation results. 

64 
Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report (including an update to the program) are available from NWIS. 

65 
AQUIFER MANAGEMENT 

Two-Dimensional Saturated Flow 

Program Documentation: 

Lefkoff, L.J., and Gorelick, S.M., 1987, AQMAN-Linear and quadratic programming 

matrix generator using two-dimensional ground-water flow simulation for aquifer 

management modeling: U.S. Geological Survey Water-Resources Investigations 

Report 87-4061, 164 p. 

Description: 

AQMAN provides a link between a modified version of the two-dimensional groundwater flow model of Trescott, Pinder, and Larson (1976) and any optimization program 

that expects an input file written in MPS (Mathematical Programming System) format. 

AQMAN uses the modified Trescott ground-water flow model to solve the basic 

ground-water flow equation to determine aquifer responses to the stresses that cannot 

be controlled because of physical limitations or either legal or socioeconomic demands 

(the unmanaged stresses) and that can be controlled (the managed stresses). A 

management problem is to determine the distribution of pumping and (or) recharge that 

minimizes or maximizes some user-specified objective function while satisfying userspecified constraints on the ground-water hydraulic conditions. AQMAN creates a data 

file written in MPS format that contains all the hydrologic information and 

management objectives needed by an optimization program to solve the management 

problem. MPS format is required by most standard linear and quadratic programming 

optimization packages. 

Numerical features: 

The spatial discretization of the aquifer is that used by the Trescott, Pinder, and Larson 

( 197 6) program. AQMAN requires that the management time periods, during which a 

particular decision variable is constant or a particular set of constraints apply, are equal 

in duration. AQMAN is written to handle either a linear or quadratic objective function. 

Various types of constraints can be defined for pumping and (or) recharge rates and on 

ground-water heads, gradients, and velocities. AQMAN assumes that the relation 

between aquifer stress and water-level response is essentially linear, that is, that linear 

superposition of solutions to the transient ground-water flow equation is appropriate. 

Past applications: 

Few. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

66 
Three-Dimensional Saturated Flow 

Program Documentation: 

Puig, J.C., and Rolon-Collazo, L.I., in press, User's manual for AQMAN3D-A 

mathematical programming system dataset generator for aquifer management using the 

U.S. Geological Survey modular three-dimensional finite-difference ground-water 

flow model: U.S. Geological Survey Open-File Report 92-481. 

Description: 

The computer code AQMAN3D provides a link between the U.S. Geological Survey 

modular three-dimensional finite-difference ground-water flow model, MODFLOW 

(see McDonald and Harbaugh, 1988), and any standard optimization program that uses 

MPS (Mathematical Programming System) input format. The program creates the 

input fields that will be used by the optimization program. The relation between 

AQMAN3D and MODFLOW is comparable to the relation between AQMAN (see 

Lefkoff and Gorelick, 1987) and the two-dimensional ground-water flow model of 

Trescott, Pinder, and Larson (1976), except that AQMAN3D permits applications to 

three-dimensional problems as opposed to the two-dimensional problem limitation of 

AQMAN. 

Numerical features: 

The user of AQMAN3D must be familiar with the MODFLOW code (see McDonald 

and Harbaugh, 1988) and documentation and should be familiar with the AQMAN 

documentation (see Lefkoff and Gorelick, 1987) to understand the basic concepts of 

aquifer-management modeling and problem formulation for linear and quadratic 

programming. One of the main differences between AQMAN3D and the AQMAN 

code is that AQMAN3D has three-dimensional capability. 

Past applications: 

This is a new code. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

67 
CHEMICAL MASS BALANCE 

Mass Balance and Electron Conservation 

Program Documentation: 

Parkhurst, D.L., Plummer, L. N., and Thorstenson, D. C., 1982, BALANCE-A 

computer program for calculating mass transfer for geochemical reactions in ground 

water: U.S. Geological Survey Water-Resources Investigations Report 82-14, 29 p. 

Description: 

BALANCE is a FORTRAN computer program designed to help define and quantify 

chemical reactions between ground water and soluble mineral assemblages. Given the 

chemical concentrations of various elements in water samples from two points along a 

flow path, together with the chemical compositions of a set of minerals, organic 

substances, or gases that are presumed to be the only, or at least dominant, potential 

reactive phases in the system, this program calculates the mass transfer (amounts of 

selected phases that dissolve or precipitate) necessary to account for the observed 

changes in element concentrations between the two water samples. Additional 

constraints can be included in the problem formulation to account for mixing two endmember waters with or without mineral-water interaction, redox reactions, and in a 

simplified form, isotopic composition. 

Numerical features: 

The number of potential reactive or product phases must equal the number of elements, 

except for mixing problems, in which case the number of reactive or product phases 

must be equal to the number of elements minus one. If oxidation reduction is 

considered, then an additional phase may be added. BALANCE solves a set of 

simultaneous linear equations that mathematically represent the conservation of mass 

for selected elements, conservation of electrons, and conservation of isotopic species. 

Past applications: 

Many. 

Remarks: 

The purpose of BALANCE is to derive balanced reactions of the form: 

Initial Water+ Reactant Phases -7 Final Water+ Product Phases 

A "reaction model" is defined by the user-selected phases and the calculated amount of 

each phase necessary to satisfy this equation. Because the BALANCE models are not 

constrained by any thermodynamic criteria, the output may imply reactions that are not 

thermodynamically possible. Plummer, Parkhurst, and Thorstenson ( 1983) discussed 

methods for identifying reaction models that can be eliminated from consideration 

because they do not satisfy available thermodynamic, petrographic, mineralogic, or 

isotopic information. 

68 
Availability: 

Report is available from NTIS (PB-82 255 902). Computer program and report are 

available from NWIS. 

Characterization of Natural Waters 

Program Documentation: 

Bodine, M.W., Jr., and Jones, B.F., 1986, THE SALT NORM-A quantitative 

chemical-mineralogical characterization of natural waters: U.S. Geological Survey 

Water-Resources Investigations Report 86-4086, 130 p. 

Description: 

The SALT NORM is the quantitative ideal equilibrium assemblage that would 

crystallize if the water evaporated to dryness at 25 °C and 1 bar pressure under 

atmospheric partial pressure of C02. This assemblage is called ideal, in part, because 

certain liberties are necessarily inherent in the selection of the particular normative 

salts; for example, because the standard chemical potentials of many compound salts 

that are not found as minerals are unknown, those were excluded as possible normative 

salts. The SALT NORM is a computer program written in FORTRAN IV that 

quantitatively distributes 18 selected solutes (Mg, Ca, Na, K, Li, NH4, Sr, Ba, Cl, S04, 

HC03, C03, F, Br, I, N03, B, P04) reported from an analysis into normative salts that 

are assigned from 63 selected possible normative salts to allow only stable associations 

on the basis of the Gibbs phase rule, available free energy values, and observed lowtemperature mineral association. 

Examination of over 500 salt norms calculated from water analyses that represent a 

wide range of concentrations and hydrochemical settings has suggested that certain key 

phases or assemblages are characteristic of solute origin. 

Past applications: 

Few. 

Remarks: 

Normative analysis of ground waters was used as an aid in the interpretation of the 

origin and evolution of waters in the Rustler Formation in southeastern New Mexico by 

Bodine and Jones (1990) and the Madrid Basin in Spain by Jones and Llamas (1989). 

69 
Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Computer 

program and report are available from NWIS. 

Mass Balance Reaction Models That Satisfy Specified Constraints 

Program Documentation: 

Plummer, L.N., Prestemon, B.C., and Parkhurst, D.L., 1991, An interactive code 

(NETPATH) for modeling net geochemical reactions along a flow path: U.S. 

Geological Survey Water-Resources Investigations Report 91-4078, 227 p., and 

diskette in pocket. 

Description: 

NETP ATH is an interactive FORTRAN 77 computer program used to interpret net 

geochemical mass balance reactions between an initial and final water along a 

hydrologic flow path. Given the chemical and isotopic data for two points on a flow 

path, NETP ATH determines every possible geochemical mass balance reaction model 

that indicates the masses of plausible minerals and gases that must enter or leave the 

initial water along the flow path to define exactly a set of selected elemental, electron 

transfer, and isotopic constraints observed in a final (evolutionary) water. The 

calculations are of use in interpreting geochemical reactions, mixing proportions, 

evaporation and (or) dilution of waters, and mineral mass transfer in the chemical and 

isotopic evolution of natural environmental waters. If sufficient isotopic data are 

available, then Rayleigh distillation calculations are applied to each mass balance 

model that satisfies the constraints to predict carbon, sulfur, and strontium isotope 

compositions at the end point and an adjusted 14c content that is useful for radiocarbon 

dating. 

Numerical features: 

The number of potential reactive or product phases must be at least as great as the 

constraints (except for the case of mixing). Constraints can be chemical elements, 

expression of electron conservation, or conservation of a particular isotope of an 

element. 

If there are many more phases than constraints, then the total number of reaction models 

can be very large. Long computation times may be required to find all possible models. 

The total number of reaction models can be reduced by either deleting unnecessary 

phases or designating them for dissolution or precipitation only and then including 

appropriate forcing conditions for phases. For a phase to be "forced" means that every 

reaction model considered must contain that phase. 

70 
Past applications: 

Many. 

Remarks: 

NETP ATH combines information on mineral saturation indices with mass balance 

modeling to identify and quantify mineral reactions in the system. This interactive 

program allows the user to build a file that contains chemical and isotopic data for each 

water; runs the water analyses through a modified version of the speciation model, 

WATEQF (Plummer, Jones, and Truesdell, 1976); and uses output from the speciation 

step and the user's selection of two (or three) water analyses, chemical and isotopic 

mass balance constraints, and a set of plausible reactions to construct a set of possible 

chemical evolution models. 

Availability: 

Report (including diskette) is available from the USGS ESIC--Open-File Report 

Section and NWIS. The diskette contains source and executable code. 

71 
AQUEOUS SPECIATION 

Speciation of Major and Some Minor Elements in 0 to 100 °C Temperature Range 

Program Documentation: 

Truesdell, A. H., and Jones, B.F., 1973, W ATEQ-A computer program for calculating 

chemical equilibrium of natural waters: National Technical Information Service PB220 464, 77 p. 

Description: 

This model calculates the distribution of inorganic aqueous species (that is, free ions 

and complexes) of major and important minor elements in low temperature natural 

waters. The thermodynamic data base included in the program contains equilibrium 

constants for about 150 reactions. Input to the program includes the chemical analysis 

results for 20 selected solutes (Ca, Mg, Na, K, Cl, S04, HC03, Fe, H2S, C03, Si02, 

NH4, B, P04, Al, F, N03, Li, Sr, and Ba), and field measurements of the water 

temperature and pH. Measurements of Eh and dissolved oxygen, as well as some other 

trace element analyses, may be included. 

A mass balance equation can be written for each analyzed constituent that relates the 

sum of the concentrations of the free ions and complexes to the total concentration 

measured for that constituent. By means of experimentally developed equilibrium 

constants, the law of mass action relates the chemical activities of the various ion pairs 

to the activities of the complexes that involve that constituent. Taken together, the mass 

balance and the equilibrium relations form a set of nonlinear equations that involve the 

unknown concentrations of free ions and complexes. These are nonlinear because the 

activities are equal to the product of the concentration and an activity coefficient, where 

the activity coefficient depends on the ionic strength, which is a measure of the total 

concentration of charged ions in solution. Aqueous activity coefficients are calculated 

by using a novel extended form of the "extended Debye-Hiickel equation," which 

contains two ion-specific parameters instead of one. The inclusion of the second 

parameter allows a more accurate calculation of activity coefficients beyond the 0.1 

ionic strength limit usually considered by the traditional extended De bye-Hiickel 

equation. 

The program output is typical of a speciation code. It includes concentrations and 

thermodynamic activities of aqueous species, major ion activity ratios that can be used 

to help determine the water-rock reactions that may be controlling water compositions, 

and mineral-saturation indices that express the state of disequilibrium of the water with 

respect to various mineral phases. 

72 
Numerical features: 

A method of successive approximation called the continued fraction method is used 

with the activity coefficients calculated from ionic strengths updated at each iteration. 

When the mass balance for the anions is within 0.5 percent of the analytical values, the 

iteration is stopped. The program was written in PL/1 for IBM 360 computers. 

W ATEQ was one of the first-generation programs developed for general use that uses 

the method of successive approximation to solve equilibrium problems in aqueous 

geochemistry (Nordstrom and others, 1979). 

Past applications: 

Many. 

Remarks: 

The methodology (everything but the computer listing) also was published in: 

Truesdell and Jones ( 197 4). 

A series of computer programs have been developed based on this original W ATEQ 

model that have added to, or otherwise modified, the thermodynamic data base and 

chemical species considered or changed the mathematics used to approximate the 

solution to the set of nonlinear equations. However, the Truesdell and Jones (1974) 

paper remains important because of its description of the basic methodology. See Ball 

and Nordstrom ( 1991) for a newer code that uses the same general methodology but has 

an expanded and improved thermodynamic data base. 

Availability: 

Report that includes computer program listing is available from NTIS (PB-220 464). 

Truesdell and Jones (1974) is available from NWIS. 

Related program: 

Plummer, L.N., Jones, B.F., and Truesdell, A.H., 1976, WATEQF-A FORTRAN IV 

version of W ATEQ-A computer program for calculating chemical equilibrium of 

natural waters: U.S. Geological Survey Water-Resources Investigations Report 76-13, 

70 p. (Revised 1984). 

Most significant changes to original program: 

W ATEQ, which was originally written in the PL/1 language, is reprogrammed in 

FORTRAN IV. With a few exceptions, the thermochemical data, speciation, activity 

coefficients, and general calculation procedure for this version of the program is 

equivalent to the original version. W A TEQF includes 14 species of manganese and 

computes saturation data for 21 manganese minerals. A value for pEcan now be set by 

the dissolved oxygen relation of Sato (1960) and by S04=1s=. In addition to the DebyeHtickel equation, the Davies equation can be used to calculate the activity coefficients. 

73 
The carbon-bearing species are computed from titration alkalinity, carbonate alkalinity, 

or total carbon in solution. The computational method of convergence on mass balance 

for anions has been improved. 

Past applications: 

Many. 

Remarks: 

This is a widely used program. The Ball and Nordstrom (1991) code refined and 

supplemented the thermodynamic data base and has improved capabilities. Either 

Truesdell and Jones (1973) or (1974) are needed to understand the basic methodology. 

A modified version of W A TEQF is included in the NETPATH program (Plummer, 

Prestemon, and Parkhurst, 1991). 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Original report 

(PB-261 027) and magnetic tape of original computer program (PB-261 026) are 

available from NTIS. 

Related program: 

Ball, J.W., Nordstrom, D.K., and Jenne, E.A., 1980, Additional and revised 

thermochemical data and computer code for W ATEQ2--A computerized chemical 

model for trace and major element speciation and mineral equilibria of natural waters: 

U.S. Geological Survey Water-Resources Investigations Report 78-116, 109 p. 

(Second printing, 1981.) 

Most significant changes to original program: 

This program expands and revises W A TEQ to include consideration of ion association 

and solubility equilibria for 10 selected elements (Ag, As, Cd, Cs, Cu, Mn, Ni, Pb, Rb, 

and Zn). Certain polysulfides and additional complexes of Br, I, and bisulfides have 

been added, as have various metastable solids, sparingly soluble salts, and several 

complexes of major ions. The complete program is in the PL/1 language and is a 

corrected and revised extension of the original WATEQ program (Truesdell and Jones, 

1973, 1974). 

Past applications: 

Many. 

Remarks: 

Ball, Jenne, and Nordstrom (1979) should be read to understand this program because 

it describes the functions of various parts of the computer program and the changes in 

74 
logic made to the W ATEQ chemical model. The report by Nordstrom and others 

(1984) refined and supplemented the thermodynamic data base. See also Nordstrom 

and others (1990). 

The report by Ball, Nordstrom, and Zachmann (1987) described WATEQ4F, which is 

a FORTRAN 77 version ofW ATEQ2 that has been adapted for operation on a personal 

microcomputer with math coprocessor and professional FORTRAN compiler. Limited 

data-base revisions are made that include the addition of several ion pairs. An updated 

version ofWATEQ4F is described in Ball and Nordstrom (1991). 

Availability: 

Report is available from NTIS (PB-80 224 140). 

Related program: 

Ball, J.W., Jenne, E.A., and Cantrell, M.W., 1981, WATEQ3-A geochemical model 

with uranium added: U.S. Geological Survey Open-File Report 81-1183, 81 p. 

Most significant changes to original program: 

Procedures for the calculation of the speciation of uranium solutes and the activity 

products of uranium solid phases have been added to the W A TEQ2 chemical model, 

and an error in the W ATEQ2 program has been corrected, as well as a few problems 

with the previous text. 

Past applications: 

Few. 

Remarks: 

The program WATEQ4F, which was described by Ball and Nordstrom (1991), includes 

the capabilities of the W ATEQ3 model. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related program: 

Ball, J.W., and Nordstrom, D.K., 1991, User's manual for WATEQ4F, with revised 

thermodynamic data base and test cases for calculating speciation of major, trace, and 

redox elements in natural waters: U.S. Geological Survey Open-File Report 91-183, 

189 p., and diskette in pocket. 

75 
Most significant changes to original program: 

The report states that it replaces Ball, Nordstrom, and Jenne (1980), Ball, Jenne, and 

Cantrell (1981), and Ball, Nordstrom, and Zachmann (1987), as the primary reference 

and user's manual for W ATEQ4F. The entire library of reactions and thermodynamic 

data used in WATEQ4F is included in this report. Previously, Ball, Nordstrom, and 

Zachmann (1987) was the principal documentation for a FORTRAN 77 version of 

W ATEQ2 that was designed to run on a personal microcomputer. This report 

supersedes that report and reflects the following primary changes in the model: the 

addition of Se, U, five Fe, Mn, and Ba carbonate reactions and the Feel+ and SrSO~ 

complexes to the model calculations; revision of the user options for the control of 

redox calculations; significant revision of the thermodynamic data base, from 

Nordstrom and others (1990); and inclusion of the entire WATEQ4F data base in the 

report. 

Past applications: 

Many. 

Remarks: 

As of 1993, this version of the WATEQ-generated ion-association models has the most 

complete and current library of reactions and thermodynamic data. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. Report and 

computer program (on diskette) are available from NWIS. 

76 
CHEMICAL MASS TRANSFER 

Program Documentation: 

Plummer, L.N., Parkhurst, D.L., and Kosiur, D.R., 1976, MIX2-A computer program 

for modeling chemical reactions in natural waters: U.S. Geological Survey WaterResources Investigations Report 75-61, NTIS Report PB 251 668,73 p. 

Description: 

MIX2 utilizes an aqueous model akin to W ATEQ and constraints of mass and electrical 

balances to compute the pH and equilibrium distribution of .inorganic species in 

solution as a result of net reaction in the system-CaO-MgO-Na20-K20-C02-H2S04-

HCl-H20. The system is assumed to be closed in the sense that the mixing calculations 

do not reflect changes in mass of the constituent or constituents in mixtures because of 

the exchange or interaction with adjacent systems. In addition, MIX2 allows for 

mineral precipitation along the reaction path in maintaining a fixed ion activity product 

in solution for a given mineral. 

Numerical features: 

MIX2 is written in FORTRAN IV. A successive approximation method is used to 

calculate the distribution of the aqueous species that is similar to that used in W ATEQ 

(Truesdell and Jones, 1974), except that MIX2 uses cation and anion mass balances to 

determine convergence. 

An iterative approach is used in finding the pH of a solution that, through convergence 

on mass balance in the aqueous model, will result in perfect electrical neutrality. In 

estimating the number of moles of a specified mineral to be dissolved or precipitated to 

bring the solution to equilibrium with a specified mineral and accompanying mass and 

charge balance, an iterative cyclic approach also is used. 

Past applications: 

Many. 

Remarks: 

The program, PHREEQE, which is described in Parkhurst, Thorstenson, and Plummer 

( 1980), is considered to be a replacement for MIX2. 

Availability: 

Report is available from NTIS (PB-251 668/AS). Computer program and report also 

are available from NWIS. 

77 
Mineral and Water/Gas Interactions at Low Temperatures 

Program Documentation: 

Parkhurst, D.L., Thorstenson, D.C., and Plummer, L.N., 1980 PHREEQE-A 

computer program for geochemical calculations: U.S. Geological Survey WaterResources Investigations Report 80-96, 195 p. (Revised 1990.) 

Description: 

PHREEQE is a FORTRAN 77 computer program that models geochemical reactions. 

The program calculates the following quantities during a reaction simulation: hydrogen 

ion activity (pH), relative electron activity, total concentration of elements, the 

amounts of minerals (or other phases) transferred into or out of the aqueous phase, the 

distribution of aqueous species, and the relative saturation of the aqueous phase with 

respect to specified mineral phases. PHREEQE can simulate several types of reactions, 

which include addition of reactants to a solution, mixing of two waters, and titrating one 

solution with another. In each of these cases, PHREEQE can simultaneously maintain 

the reacting solution at equilibrium with multiple specified mineral phases. 

With step-by-step manipulation by the user, PHREEQE can be used to analyze the 

progress of a reaction in a geochemical system in which an irreversible reaction is 

occurring. Reaction progress is measured by locating the intersection of the reaction 

path with mineral phase boundaries (specified by the user as the plausible phases 

present) and in defining the reaction paths across the mineral stability fields between 

the mineral phase boundaries. The revised 1990 report includes a new thermodynamic 

data base that is consistent with the data published by Nordstrom and others (1990). 

The data base includes data on 19 elements, 133 aqueous species, and 43 minerals. 

Numerical features: 

Because of the nonlinear nature of the problem of determining a distribution of species 

that simultaneously satisfies electron neutrality, conservation of electrons, mass 

balance for each element, mineral equilibrium, and the mass action equation, numerical 

convergence to a solution is not assured, although most problems attempted have been 

solved. Problems that involve oxidation/reduction processes are more likely to cause 

such convergence difficulties because the equilibrium concentrations of some species 

can vary dramatically from a fully/oxidizing to a fully/reducing environment. 

PHREEQE uses a continued fraction scheme to calculate species distribution and a 

modified Newton-Raphson iterative technique for pH, pE, and mass transfer estimates. 

Past applications: 

Many. 

78 
Remarks: 

The geochemical reaction model PHREEQE has been used with ground-water flow and 

solute-transport models to simulate a variety of problems that involve the combined 

effects of complex chemical processes and the physical processes of advection and 

dispersion. Sanford and Konikow (1989) used PHREEQE in conjunction with a twoconstituent solute-transport model (MOCDENSE) that allows for variable density 

fluids to study calcite dissolution and related porosity changes in coastal freshwater/ 

saltwater mixing zones in carbonate aquifers. Engesgaard and Kipp ( 1992) described 

a one-dimensional multiple species geochemical reaction transport model, MST1D. 

MST1D iterates sequentially between solving the transport equations by means of an 

implicit finite-difference method and solving a set of nonlinear algebraic equations that 

describe chemical mass transfer and aqueous speciation by using PHREEQE. Glynn, 

Engesgaard, and Kipp (1991) discussed a geochemical reaction mass-transport model 

PHREEQM. PHREEQM decouples geochemical reaction transport into three stepsadvection, application of PHREEQE to calculate chemical equilibration, and 

simulation of the dispersion process by mixing the contents of each cell with that of its 

adjacent cells by using mixing factors calculated as a function of aquifer dispersivity 

and molecular diffusion. 

Availability: 

Original PHREEQE report is available from NTIS (PB-81 167 801). Revised (1990) 

computer program and revised report are available from NWIS. The report and 

computer program for PHRQINPT (Fleming and Plummer, 1983) are provided by 

NWIS as companions to the report and program for PHREEQE. 

Related program: 

Fleming, G.W., and Plummer, L.N., 1983, PHRQINPT-An interactive computer 

program for constructing input data sets to the geochemical simulation program 

PHREEQE: U.S. Geological Survey Water-Resources Investigations Report 83-4236, 

108 p. 

Most significant changes to original program: 

PHRQINPT facilitates formulation of the input data file to PHREEQE. It interactively 

asks the user for values of variables required by PHREEQE, explains the meaning and 

significance of each variable when required, and internally checks to make sure that 

values entered are valid. 

Past applications: 

Many. 

79 
Availability: 

Report is available from the USGS ESIC--Open-File Reports Section. The report and 

computer program are provided by NWIS as companions to the report and computer 

program for PHREEQE. 

Related program: 

Plummer, L.N., Parkhurst, D.L., Fleming, G.W., and Dunkle, S.A., 1988, A computer 

program incorporating Pitzer's equations for calculation of geochemical reactions in 

brines: U.S. Geological Survey Water-Resources Investigations Report 88-4153, 

310 p., two diskettes in pocket. 

Most significant changes to original program: 

This report described PHRQPITZ, which makes geochemical calculations in brines and 

other electrolyte solutions of high concentrations by using the Pitzer virial-coefficient 

approach for activity-coefficient corrections. Reaction/modeling capabilities include 

calculation of aqueous speciation and mineral-saturation index, mineral solubility, 

mixing and titration of aqueous solutions, irreversible reactions and mineral-water mass 

transfer, and reaction path. The program has been adopted from PHREEQE. 

(Parkhurst, Thorstenson, and Plummer, 1980). The report described how PHRQPITZ 

can be used to simulate the reaction path that corresponds to the evaporation of 

seawater. 

Past applications: 

Few. 

Remarks: 

The diskettes included with the report contain a machine-readable copy of the 

PHRQPITZ source code and of the source code to the interactive input program 

PITZINPT. 

Availability: 

Report (including diskette) is available from the USGS ESIC--Open-File Report 

Section and NWIS. 

80 
Speciation of Major and Many Minor Elements With Mineral and Water Interactions 

in the 0 to 350 °C temperature range 

Program Documentation: 

Kharaka, Y.K., and Barnes, Ivan, 1973, SOLMNEQ-Solution-mineral equilibrium 

computations: U.S. Geological Survey Computer Contribution, National Technical 

Information Service PB-215 899, 81 p. 

Description: 

SOLMNEQ is a computer program written in PL/1 for the IBM 360 computers. It 

computes the equilibrium distribution of 162 inorganic aqueous species generally 

present in natural waters over a temperature range from 0 to 350 °C from the reported 

concentrations of Ca, Mg, Na, K, Ag, AI, Ba, Cu, Fe, Hg, Li, Mn, Pb, Sr, Zn, Cl, S04, 

HC03, Si02, As(OH)4, P04, F, H3B03, NH3, C03, N03, and pH; Eh is optional. The 

state of reaction of the aqueous solution with respect to 158 minerals also are computed 

by means of saturation indices. 

Numerical factors: 

A method of successive approximations is used in which convergence is based on the 

mass balance for the anions. 

Past applications: 

Many. 

Remarks: 

Because the temperature range of the SOLMNEQ data base goes considerably higher 

than the other speciation programs of the Water Resources Division, it is the most 

suitable choice for "hot" waters. Logic of the program was developed in part from 

W ATEQ (Truesdell and Jones, 1973, 1974) and W ATCHEM (Barnes and Clark, 1969). 

See Kharaka and others ( 1988) for an updated and improved version of this model. 

Availability: 

Report is available from NTIS (PB-215 899). 

Related program: 

Kharaka, Y., Gunter, W.D., Aggarwal, P.K., Perkins, E.H., and DeBraal, J.D., 1988, 

SOLMINEQ.88-A computer program for geochemical modeling of water-rock 

interactions: U.S. Geological Survey Water-Resources Investigations Report 88-4227, 

420p. 

81 
Most significant changes to original program: 

This report updates the computer model SOLMNEQ. This version, which was renamed 

SOLMINEQ.88 (SOLution MINeral EQuilibrium, 1988), is written in FORTRAN 77 

and has an improved algorithm for faster execution. This version has a revised 

thermodynamic data base, more inorganic (260) and organic (80) aqueous species and 

minerals (220), and computed pH and mineral solubilities at subsurface temperatures 

and pressures. New modeling options have been added to SOLMINEQ.88 that can be 

used to study the effects of boiling, mixing of solutions, and partitioning of gases 

between water, oil and gas phases. SOLMINEQ.88 has mass-transfer capabilities that 

can be used to study the effects of ion exchange, adsorption/desorption, and dissolution/ 

precipitation of solid phases. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

Related Program: 

DeBraal, J.D., and Kharaka, Y.K., 1989, SOLINPUT-A computer code to create and 

modify input for the geochemical program SOLMINEQ.88: U.S. Geological Survey 

Open-File Report 89-616, 140 p. 

Most significant changes to original program: 

This report documented SOLINPUT, which is an interactive computer program 

designed to create and modify input files for the geochemical code SOLMINEQ.88. 

Past applications: 

Many. 

Availability: 

Report is available from the USGS ESIC--Open-File Report Section. 

82 
Non-ideal Solid-Solution Aqueous-Solution Reactions 

Program Documentation: 

Glynn, P.D., 1991a, MBSSAS-. A code for the computation of Margules parameters 

and equilibrium relations in binary solid-solution aqueous-solution systems: 

Computers and Geoscience, v. 17, no. 7, p. 907-966. 

Description: 

MBSSAS (Margules parameters and equilibrium relations in Binary ,Solid-Solution 

Aqueous-Solution systems) is a FORTRAN program that can be used in calculating 

thermodynamic equilibrium, stoichiometric saturation, and pure-phase saturation states 

in binary solid-solution aqueous-solution systems. "Binary" is used here to mean twocation single-anion solid solutions. The results of these calculations can be used to 

construct phase diagrams and to model mineral-water reactions in natural and 

contaminated systems. 

Past applications: 

New. 

Remarks: 

Geochemical mass-transfer and mass-transport codes commonly ignore mineral 

impurities and defects and assume the minerals behave as constant -composition solids. 

MBASSAS can be useful in estimating the effects of mineral impurities on mineral 

solubility calculations made by programs like PHREEQE and to estimate the 

equilibrium partitioning between isotopically pure minerals and common minerals 

(Glynn, 1991b). 

Availability: 

Computer program is available from NWIS. 

83 
SUMMARY AND CLOSING REMARKS 

The computer programs listed in this report have been published or developed by the U.S. 

Geological Survey and solve problems that concern the physics and chemistry of ground water. 

Some programs are included for either historical purposes or documentation of a specific method. 

Thus, not all programs are being widely used. Some programs have been released so recently that 

the statements on past applications cannot indicate the potential usefulness of these programs. A 

few programs have been or are being used in many studies and have been so noted. 

84 
REFERENCES CITED 

Appel, C.A., and Bredehoeft, J.D., 1976, Status of ground-water modeling in the U.S. Geological 

Survey: U.S. Geological Survey Circular 737, 9 p. 

Appel, C.A., and Reilly, T.E., 1988, Selected reports that include computer programs produced by 

the U.S. Geological Survey for simulation of ground-water flow and quality: U.S. 

Geological Survey Water-Resources Investigations Report 87-4271, 64 p. 

Ball, J.W., Jenne, E.A., and Cantrell, M.W., 1981, WATEQ3-A geochemical model with 

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Ball, J.W., Jenne, E.A., and Nordstrom, Darrell K., 1979, WATEQ2-A computerized chemical 

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Ball, J.W., and Nordstrom, D.K., 1991, User's manual for WATEQ4F, with revised 

thermodynamic data bases and test cases for calculating speciation of major, trace, and 

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with diskette in pocket. 

Ball, J.W., Nordstrom, D.K., and Jenne, E.A., 1980, Additional and revised thermochemical data 

and computer code for WATEQ2--A computerized chemical model for trace and major 

element speciation and mineral equilibria of natural waters: U.S. Geological Survey 

Water-Resources Investigations Report 78-116, 109 p. (Second printing, 1981.) 

Ball, J.W., Nordstrom, D.K., and Zachmann, D.W., 1987, W ATEQ4F-A personal computer 

FORTRAN translation of the geochemical model W ATEQ2 with revised data base: 

U.S. Geological Survey Open-File Report 87-50, 108 p. 

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__ , 1990, normative analysis of ground waters from the Rustler Formation associated with the 

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85 
__ , 1993, Supplement 1 --Modifications to the computer code for nonlinear regression solution 

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86 
__ , 1991 b, Effect of impurities in gypsum on contaminant transport at Pinal Creek, Arizona, in 

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U.S. Geological Survey Water-Resources Investigations Report 89-4030, 65 p. 

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Hansen, A.J., Jr., 1993, Modifications to the modular three-dimensional finite-difference groundwater flow model used for the Columbia Plateau regional aquifer-system analysis, 

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__ , 1990b, A computer program for calculating subregional water budgets using results from 

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__ , 1990, Simulation of solute transport in variably saturated porous media with supplemental 

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Hearne, G.A., 1982, Supplement to the New Mexico three-dimensional model: U.S. Geological 

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87 
Helgesen, J.O., Larson, S.P., and Razem, A. C., 1982, Model modifications for simulation of flow 

through stratified rocks in eastern Ohio: U.S. Geological Survey Water-Resources 

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Hill, M.C., 1990, ~reconditioned Conjugate-Gradient 2 (PCG2)-A computer program for solving 

ground-water flow equations: U.S. Geological Survey Water-Resources Investigations 

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__ , 1992, A computer program (MODFLOWP) for estimating parameters of a transient, threedimensional, ground-water flow model using nonlinear regression: U.S. Geological 

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__ , 1994, Five computer programs for testing weighted residuals and calculating linear 

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horizontal-flow barriers using the U.S. Geological Survey modular three-dimensional 

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Hutchinson, C.B., Johnson, D.M., and Gerhart, J.M., 1981, Hydrogeology of well-field areas near 

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INTERA Environmental Consultants, Inc., 1979, Revision of the documentation for a model 

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INTERCOMP Resource Development and Engineering, Inc., 1976, A model for calculating effects 

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89-4027' 86 p. 

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Kharaka, Y.K., Gunter, W.D., Aggarwal, P.K., Perkins, E.H., and DeBraal, J.D., 1988, 

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420p. 

Kipp, K.L., Jr., 1987, HST3D-A computer code for simulation of heat and solute transport in 

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88 
Kontis, A.L., and Mandie, R.J., 1988, Modification of a three-dimensional ground-water flow 

model to account for variable water density and effects of multiaquifer wells: 

U.S. Geological Survey Water-Resources Investigations Report 87-4265, 78 p. 

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__ , 1985, Documentation of a numerical code for the simulation of variable density groundwater flow in three dimensions: U.S. Geological Survey Water-Resources Investigations 

Report 84-4302, 80 p. 

__ , 1987, Computer program for solving ground-water flow equations by the preconditioned 

conjugate gradient method: U.S. Geological Survey Water-Resources Investigations 

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Kuniansky, E.L., 1990, A finite-element model for simulation of two-dimensional steady-state 

ground-water flow in confined aquifers: U.S. Geological Survey Open-File Report 90-187, 

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Lappala, E.G., Healy, R.W., and Weeks, E.P., 1987, Documentation of computer program VS2D 

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Larson, S.P., 1978, Direct solution algorithm for the two-dimensional ground-water flow model: 

U.S. Geological Survey Open-File Report 79-202, 22 p. 

Leahy, P.P., 1982, A three-dimensional ground-water flow model modified to reduce computermemory requirements and better simulate confining-bed and aquifer pinchouts: 

U.S. Geological Survey Water-Resources Investigations 82-4023, 59 p. 

Leake, S.A., Leahy, P., and Navoy, A.S., in press, Documentation of a computer program to 

simulate transient leakage from confining units using the modular finite-difference groundwater flow model: U.S. Geological Survey Open-File Report 94-59. 

Leake, S.A., and Prudic, D.E., 1991, Documentation of a computer program to simulate aquifersystem compaction using the modular finite-difference ground-water flow model: 

Techniques of Water-Resources Investigations of the United States Geological Survey, 

book 6, chap. A2, 68 p. 

Lefkoff, L.J., and Gorelick, S.M., 1987, AQMAN-Linear and quadratic programming matrix 

generator using two-dimensional ground-water flow simulation for aquifer management 

modeling: U.S. Geological Survey Water-Resources Investigations Report 87-4061, 164 p. 

Lewis, F.M., Voss, C.l., and Rubin, Jacob, 1986, Numerical simulation of advective-dispersive 

multisolute transport with sorption, ion exchange and equilibrium chemistry: U.S. 

Geological Survey Water-Resources Investigations Report 86-4022, 165 p. 

Mallory, M.J., 1979, Documentation of a finite-element two-layer model for simulation of groundwater flow: U.S. Geological Survey Water-Resources Investigations Report 79-18, 347 p. 

Manteuffel, T.A., Grove, D.B., and Konikow, L.F., 1983, Application of the conjugate-gradient 

method to ground-water models: U.S. Geological Survey Water-Resources Investigations 

Report 83-4009, 24 p. 

McDonald, M.G., and Harbaugh, A.W., 1988, A modular three-dimensional finite-difference 

ground-water flow model: Techniques of Water-Resources Investigations of the United 

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89 
McDonald, M.G., Harbaugh, A.W., Orr, B.R., and Ackerman, D.J., 1992, A method of converting 

no-flow cells to variable-head cells for the U.S. Geological Survey modular finitedifference ground-water flow model: U.S. Geological Survey Open-File Report 91-536, 

99p. 

Mercer, J.W., Larson, S.P., and Faust, C.R., 1980, Finite-difference model to simulate the areal 

flow of saltwater and freshwater separated by an interface: U.S. Geological Survey OpenFile Report 80-407, 88 p. 

Mercer, J.W., and Pinder, G.F., 1975, A finite-element model of a two-dimensional, single-phase 

heat transport in a porous medium: U.S. Geological Survey Open-File Report 75-574, ll5 p. 

Meyer, W.R., and Carr, J.E., 1979, A digital model for simulation of ground-water hydrology in the 

Houston area, Texas: Texas Department of Water Resources Report LP-103, 27 p. 

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Miller, R.S., 1988, User's guide for RIV2-A package for routing and accounting of river 

discharge for a modular, three-dimensional, finite-difference, ground-water flow model: 

U.S. Geological Survey Open-File Report 88-345, 33 p. 

Nordstrom, D.K., Plummer, L.N., Langmuir, D., Busenberg, Eurybiades, May, H.M., 

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Nordstrom, D.K., Plummer, L. N., Wigley, T.M.L., Wolery, T.J., Ball, J.W., Jenne, E.A., Bassett, 

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Nordstrom, D.K., Valentine, S.D., Ball, J.W., Plummer, L.N., and Jones, B.F., 1984, Partial 

compilation and revision of basic data in the WATEQ programs: U.S. Geological Survey 

Water-Resources Investigations Report 84-4186, 40 p. 

Orzol, L.L., and McGrath, T.S., 1992, Modifications of the U.S. Geological Survey modular, 

finite-difference, ground-water flow model to read and write geographical information 

system files: U.S. Geological Survey Open-File Report 92-50, 202 p. 

Ozbilgin, M.M., and Dickerman, D.C., 1984, A modification of the finite-difference model for 

simulation of two-dimensional ground-water flow to include surface-ground water 

relationships: U.S. Geological Survey Water-Resources Investigations Report 83-4251, 

98 p. 

Parkhurst, D.L., Plummer, L. N ., and Thorstenson, D.C., 1982, BALANCE-A computer program 

for calculating mass transfer for geochemical reactions in ground water: U.S. Geological 

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Parkhurst, D.L., Thorstenson, D.C., and Plummer, L.N., 1980, PHREEQE-A computer program 

for geochemical calculations: U.S. Geological Survey Water-Resources Investigations 

Report 80-96, 195 p. (Revised 1990.) 

Pinder, G.F., and Voss, C.I., 1979, AQUIFEM-A finite-element model for aquifer evaluation 

(Documentation): Department of Water Resources Engineering, Royal Institute of 

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90 
Plummer, L.N., Jones, B.F., and Truesdell, A.H., 1976, WATEQF-A FORTRAN IV version of 

W A TEQ-A computer program for calculating chemical equilibrium of natural waters: 

U.S. Geological Survey Water-Resources Investigations Report 76-13, 70 p. (Revised 

1984.) 

Plummer, L.N., Parkhurst, D.L., Fleming, G.W., and Dunkel, S.A., 1988, A computer program 

incorporating Pitzer's equations for calculation of geochemical reactions in brines: U.S. 

Geological Survey Water-Resources Investigations Report 88-4153, 310 p., and two 

diskettes in pocket. 

Plummer, L.N., Parkhurst, D.L., and Kosiur, D.R., 1976, MIX2-A computer program for 

modeling chemical reactions in natural waters: U.S. Geological Survey Water-Resources 

Investigations Report 75-61, National Technical Information Service Report PB-251 668, 

73 p. 

Plummer, L.N., Parkhurst, D.L., and Thorstenson, D.C., 1983, Developmentofreactionmodels for 

ground-water systems: Geochimica et Cosmochimica Acta, v. 47, p. 665-686. 

Plummer, L.N., Prestemon, E.C., and Parkhurst, D.L., 1991, An interactive code (NETPATH) for 

modeling net geochemical reactions along a flow path: U.S. Geological Survey WaterResources Investigations Report 91-4078, 227 p., with diskette in pocket. 

Pollock, D.W., 1989, Documentation of computer programs to compute and display pathlines 

using results from the U.S. Geological Survey modular three-dimensional finite-difference 

ground-water flow model: U.S. Geological Survey Open-File Report 89-381, 188 p. 

__ , 1990, A Graphical Kernel System (GKS) version of computerprogramMODPATH-PLOT 

for displaying path lines generated from the U.S. Geological Survey three-dimensional 

ground-water flow model: U.S. Geological Survey Open-File Report 89-622, 49 p. 

Posson, D.R., Hearne, G.A., Tracy, J.V., and Frenzel, P.F., 1980, A computer program for 

simulating geohydrologic systems in three dimensions: U.S. Geological Survey Open-File 

Report 80-421, 795 p. 

Prudic, D.W., 1989, Documentation of a computer program to simulate stream-aquifer relations 

using a modular, finite-difference, ground-water flow model: U.S. Geological Survey 

Open-File Report 88-729, 113 p. 

Pucci, A.A., Jr., and Pope, D.A., 1987, Preprocessor and postprocessor computer programs for a 

radial-flow, finite-element model: U.S. Geological Survey Open-File Report 87-680,69 p. 

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programming system dataset generator for aquifer management using the U.S. Geological 

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Geological Survey Water-Resources Investigations Report 85-4248, 134 p. 

Reed, J.E., Bedinger, M.S., and Terry, J.E., 1976, Simulation procedure for modeling transient 

water-table and artesian stress and response: U.S. Geological Survey Open-File Report 76-

792,173 p. 

Reilly, T.E., 1984, A Galerkin finite-element flow model to predict the transient response of a 

radially symmetric aquifer: U.S. Geological Survey Water-Supply Paper 2198, 33 p. 

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91 
__ , 1993b, Source code for the computer program and sample data set for the simulation of 

cylindrical flow to a well using the U.S. Geological Survey modular finite-difference 

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Rutledge, A.T., 1991, An axisymmetric finite-difference flow model to simulate drawdown in and 

around a pumped well: U.S. Geological Survey Water-Resources Investigations Report 

90-4098, 33 p. 

Sanford, W.E., and Konikow, L.F., 1985, A two-constituent solute-transport model for ground 

water having variable density: U.S. Geological Survey Water-Resources Investigations 

Report 85-4279, 88 p. 

__ , 1989, Simulation of calcite dissolution and porosity changes in saltwater mixing zones in 

coastal aquifers: Water Resources Research, v. 25, no. 4, p. 655-667. 

Sapik, D.B., 1988, Documentation of a steady-state saltwater-intrusion model for threedimensional ground-water flow, and user's guide: U.S. Geological Survey Open-File 

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singular and interconnected channels: U.S. Geological Survey Techniques of WaterResources Investigations, book 7, chap. C3, 110 p. 

Scott, J.C., 1990, A statistical processor for analyzing simulations made using the modular finitedifference ground-water flow model: U.S. Geological Survey Water-Resources 

Investigations Report 89-4159, 218 p. 

Souza, W.R., 1987, Documentation of a graphical display program for SUTRA finite-element 

simulation model: U.S. Geological Survey Water-Resources Investigations 

Report 87-4245, 122 p. 

Swain, B.D., 1993, Documentation of a computer program (Streamlink) to represent direct-flow 

connections in a coupled ground-water and surface-water model: U.S. Geological Survey 

Water-Resources Investigations Report 93-4011, 62 p. 

Swain, B.D., and Wexler, E.J., 1993, A coupled surface-water and ground-water flow model for 

simulation of stream-aquifer interaction: U.S. Geological Survey Open-File Report 

92-138, 162 p. 

Torak, L.J., 1982, Modifications and corrections to the finite-difference model for simulation of 

three-dimensional ground-water flow: U.S. Geological Survey Water-Resources 

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Torak, L.J, 1993a, Model description and user's manual, Part 1 of A MODular Einite-Element 

model (MOD FE) for areal and axisymmetric ground-water-flow problems: U.S. 

Geological Survey Techniques of Water-Resources Investigations, book 6, chap. A3, 

136 p. 

__ , 1993b, Design philosophy and programming details, Part 3 of A MODular Einite-Element 

model (MODFE) for areal and axisymmetric ground-water-flow problems, part 3: U.S. 

Geological Survey Techniques of Water-Resources Investigations, book 6, chap. AS, 

243 p. 

Torak, L.J., and Whiteman, C.D., Jr., 1982, Applications of digital modeling for evaluating the 

ground-water resources of the "2,000-foot" sand of the Baton Rouge area, Louisiana: 

Louisiana Department of Transportation and Development, Office of Public Works, Water 

Resources Technical Report 27, 87 p. 

92 
Trescott, P. C., 197 5, Documentation of finite-difference model for simulation of three-dimensional 

ground-water flow: U.S. Geological Survey Open-File Report 75-438, 32 p. 

Trescott, P.C., and Larson, S.P., 1976, Supplement to Open-File Report 75-438-Documentation 

of finite-difference model for simulation of three-dimensional ground-water flow: U.S. 

Geological Survey Open-File Report 76-591, 17 p. 

Trescott, P.C., Pinder, G.F., and Larson, S.P., 1976, Finite-difference model for aquifer simulation 

in two dimensions with results of numerical experiments: Techniques of Water-Resources 

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__ , 197 4, W A TEQ-A computer program for calculating chemical equilibrium of natural 

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solute transport: U.S. Geological Survey Water-Resources Investigations Report 84-4369, 

409p. 

__ , 1984b, AQUIFEM-SALT-A finite element model for aquifers containing a seawater 

interface: U.S. Geological Survey Water-Resources Investigations Report 84-4263, 37 p. 

Weeks, J.B., 1978, Digital model of ground-water flow in the Piceance Basin, Rio Blanco and 

Garfield Counties, Colorado: U.S. Geological Survey Water-Resources Investigations 

78-46, 108 p. 

Weiss, Emanuel, 1982, A model for the simulation of flow of variable-density ground water in three 

dimensions under steady-state conditions: U.S. Geological Survey Open-File Report 82-

352, 59 p. 

93 
\0 

..j:::. 

Appendix 1. List of acronyms used to identify selected computer programs, and the report to which they refer. 

Acronym Full Name Reference 

AQMAN Linear and quadratic programming matrix generator using two- Lefkoff, L. J., and Gorelick, S.M., 1987 

dimensional ground-water flow simulation for aquifer management modeling 

AQMAN3D A mathematical programming system dataset generator for aquifer Puig, J. C., and Rolon-Collazo, L. 1., 

management using the U.S. Geological Survey modular three- in press 

dimensional finite-difference ground-water flow model 

AQUIFEM-SALT A finite-element model for aquifers containing a seawater inter- Voss, C. 1., 1984b 

AX 

BALANCE 

HOTWTR 

HST3D 

HYDROTHERM 

INTERCOMP 

MBSSAS 

face 

An axisymmetric finite-difference flow model to simulate drawdown in and around a pumped well. 

A computer program for calculating mass transfer for geochemical 

reactions in ground water 

Three-dimensional finite-difference model for ground-water flow 

and single phase (liquid) heat transport 

A computer code for simulation of heat and solute transport in 

three-dimensional ground-water flow systems 

A three-dimensional finite-difference model for ground-water 

flow and multi phase heat transport in the temperature range of 0 to 

1,200°C 

A model for calculating effects of liquid waste disposal in deep 

saline aquifer 

Margules parameters and equilibrium relations in Binary .S.olid-

.S.olution Aqueous-.S.olution systems 

Rutledge, A. T., 1991 

Parkhurst, D. L., Plummer, L. N ., and 

Thorstenson, D. C., 1982 

Reed, J.E., 1985 

Kipp, K. L., 1987 

Hayba, D.O., and Ingebritsen, S.E., in 

press 

INTERCOMP, 1976; INTERA, 1979 

Glynn, P. D., 1991a 
\0 

Vl 

Acronym 

MMSP 

MOD BRANCH 

MOC 

MOCDENSE 

MOD FE 

MOD FLOW 

Full Name 

A statistical processor for analyzing simulations made using the 

modular finite-difference ground-water flow model 

Reference 

Scott, J. C., 1990 

A coupled surface-water and ground-water flow model for simula- Swain, E. D., and Wexler, E. J., 1993 

tion of stream-aquifer interaction 

Computer model of two-dimensional solute transport and dispersion in ground water 

A two-constituent solute-transport model for ground water having 

variable density 

A MODular Einite-Element model (MODFE) for areal and axisymmetric ground-water-flow problems 

A modular three-dimensional finite-difference ground-water flow 

model 

Konikow, L. F., and Bredehoeft, J. D., 

1978; Goode, D. J., and Konikow, L. F., 

1989 

Sanford, W. E., and Konikow, L. F., 1985 

Torak, L. J., 1993a, band Cooley, R. L., 

1992 

McDonald, M. G., and Harbaugh, A. W., 

1988 

MOD FLOW ARC Modifications of the U.S. Geological Survey Modular, finite-dif- Orzol, L. L., and McGrath, T. S., 1992 

ference, ground-water flow model to read and write geographical 

information system file 

MODFLOWP A computer program for estimating parameters of a transient, Hill, M. C., 1992 

three-dimensional, ground-water flow model using nonlinear 

MOD PATH 

NETPATH 

regression 

Computer programs to compute and display pathlines using results 

from the U.S. Geological Survey modular three-dimensional 

finite-difference ground-water flow model 

An interactive code for modeling net geochemical reactions along 

a flow path 

Pollock, D. W., 1989, 1990 

Plummer, L. N., Prestemon, E. C., and 

Parkhurst, D. L., 1991 
Acronym 

PHREEQE 

PHRQINPT 

PHRQPITZ 

RADFLOW 

RADMOD 

\0 

0"1 

SALT NORM 

SATRA-CHEM 

SHARP 

SOLINPUT 

SOLMINEQ 

SOLMINEQ.88 

Full Name 

PHREEQE-A computer program for geochemical calculations 

An interactive computer program for constructing input data sets 

to the geochemical simulation program PHREEQE 

A computer program incorporating Pitzer's equations for calculation of geochemical reactions in brines 

A Galerkin finite-element flow model to predict the transient 

response of a radially symmetric aquifer 

Computer program for the simulation of cylindrical flow to a well 

using the U.S. Geological Survey Modular Finite-Difference 

Ground-Water Flow Model 

A quantitative chemical-mineralogical characterization of natural 

waters 

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry 

A quasi-three-dimensional finite-difference simulation model for 

freshwater and saltwater flow in layered coastal aquifer systems 

A computer code to create and modify input for the geochemical 

program SOLMINEQ.88 

Solution-mineral equilibrium computations 

A computer program for geochemical modeling of water-rock 

interactions 

Reference 

Parkhurst, D. L., Thorstenson, D. C., and 

Plummer, L. N., 1980 (Revised editionAugust 1990) 

Fleming, G. W., and Plummer, L. N., 

1983 

Plummer, L. N., Parkhurst, D. L., 

Fleming, G. W., and Dunkle, S. A., 1988 

Reilly, T. E., 1984 

Reilly, T. E., and Harbaugh, A. W., 1993b 

Bodine, M. W., Jr., and Jones, B. F., 1986 

Lewis, F. M., Voss, C. 1., and Rubin, 

Jacob, 1986 

Essaid, H. 1., 1990 

DeBraal, J.D., and Kharaka, Y. K., 1989 

Kharaka, Y. K., and Barnes, Ivan, 1973 

Kharaka, Y., Gunter, W. D., Aggarwal, 

Pradeep K., Perkins, E. H., and DeBraal, 

J.D., 1988 
Acronym 

SUPERMOCK 

SUTRA 

SUTRAPLOT 

Trescott-2D 

Trescott-3D 

\0 TRIAG -.) 

VS2D 

VS2DT 

WATCHEM 

WATEQ 

WATEQF 

WATEQ2 

Full Name 

Simulation procedure for modeling transient water-table and artesian stress and response 

Reference 

Reed, J. E., Bedinger, M. S., and Terry, 

J. E., 1976 

A finite-element simulation model for saturated-unsaturated, fluid- Voss, C. I., 1984a 

density-dependent ground-water flow with energy transport or 

chemically-reactive single-species solute transport 

A graphical display program for SUTRA Finite-Element Simulation Model 

Finite-difference model for aquifer simulation in two dimensions 

Finite-difference model for simulation of three-dimensional 

ground-water flow 

A finite-element model for flow in a two-aquifer system 

Computer program VS2D to solve the equations of fluid flow in 

variably saturated porous media 

Simulation of solute transport in variably saturated porous media 

Chemical properties of ground water 

Souza, W. R., 1987 

Trescott, P. C., Pinder, G. F., and Larson, 

S. P., 1976 

Trescott, P. C., 1975; Trescott, P. C., and 

Larson, S. P., 1976; Torak, L. J., 1982 

Mallory, M. I., 1979 

Lappala, E. G., Healy, R. W., and Weeks, 

E. P., 1987 

Healy, R. W., 1990 

Barnes and Clark, 1969 

A computer program for calculating chemical equilibrium of natu- Truesdell, A. H., and Jones, B. F., 1973; 

ral waters Truesdell, A. H., and Jones, B. F., 1974 

A FORTRAN IV version of W ATEQ, A computer program for 

calculating chemical equilibrium of natural waters 

Additional and revised thermochemical data and computer code 

for W ATEQ2--A computerized chemical model for trace and 

major element speciation and mineral equilibria of natural waters 

Plummer, L. N., Jones, B. F., and 

Truesdell, A. H., 1976 (Revised edition 

January 1984) 

Ball, J. W., Nordstrom, D. K., and Jenne, 

E.A., 1980 
\0 

00 

c * 

U1 

c;") 

-o 

Cl 

.. 

..... 

\,() 

\,() 

.p. 

I 

I..N 

Cl 

..... 

I 

Cl 

-....J 

-....J 

co 

Cl 

..... 

Cl 

0'\ 

Acronym 

WATEQ3 

WATEQ4F 

ZONEBUDGET 

Full Name 

A geochemical model with uranium added 

Revised thermodynamic data base and test cases for calculating 

speciation of major, trace, and redox elements in natural waters 

A computer program for calculating subregional water budgets 

using results from the U.S. Geological Survey modular threedimensional finite-difference ground-water flow model 

Reference 

Ball, J. W., Jenne, E. A., and Cantrell, 

M. W., 1981 

Ball, J. W., and Nordstrom, D. K., 1991 

Harbaugh, A. W., 1990 


SELECTED SERIES OF U.S. GEOLOGICAL SURVEY PUBLICATIONS 

Periodicals 

Earthquakes & Volcanoes (issued bimonthly). 

Preliminary Determination of Epicenters (issued 

monthly). 

Technical Books and Reports 

Professional Papers are mainly comprehensive scientific 

reports of wide and lasting interest and importance to professional 

scientists and engineers. Included are reports on the results of 

resource studies and of topographic, hydrologic, and geologic 

investigations. They also include collections of related papers 

addressing different aspects of a single scientific topic. 

Bulletins contain significant data and interpretations that are 

of lasting scientific interest but are generally more limited in scope 

or geographic coverage than Professional Papers. They include the 

results of resource studies and of geologic and topographic 

investigations, as well as collections of short papers related to a 

specific topic. 

Water-Supply Papers are comprehensive reports that 

present significant interpretive results of hydrologic investigations 

of wide interest to professional geologists, hydrologists, and 

engineers. The series covers investigations in all phases of 

hydrology, including hydrogeology, availability of water, quality 

of water, and use of water. 

Circulars present administrative information or important 

scientific information of wide popular interest in a format designed 

for distribution at no cost to the public. Information is usually of 

short-term interest. 

Water-Resources Investigations Reports are papers of an 

interpretive nature made available to the public outside the formal 

USGS publications series. Copies are reproduced on request 

unlike formal USGS publications, and they are also available for 

public inspection at depositories indicated in USGS catalogs. 

Open-File Reports include unpublished manuscript 

reports, maps, and other material that are made available for 

public consultation at depositories. They are a nonpermanent form 

of publication that may be cited in other publications as sources of 

information. 

Maps 

Geologic Quadrangle Maps are multicolor geologic maps 

on topographic bases in 7.5- or 15-minute quadrangle formats 

(scales mainly 1:24,000 or 1:62,500) showing bedrock, surficial, 

or engineering geology. Maps generally include brief texts; some 

maps include structure and columnar sections only. 

Geophysical Investigations Maps are on topographic or 

planimetric bases at various scales; they show results of surveys 

using geophysical techniques, such as gravity, magnetic, seismic, 

or radioactivity, which reflect subsurface structures that are of 

economic or geologic significance. Many maps include 

correlations with the geology. 

Miscellaneous Investigations Series Maps are on planimetric or topographic bases of regular and irregular areas at 

various scales; they present a wide variety of format and subject 

matter. The series also includes 7 .5-minute quadrangle photogeologic maps on planimetric bases that show geology as interpreted 

from aerial photographs. Series also includes maps of Mars and 

the Moon. 

Coal Investigations Maps are geologic maps on topographic or planimetric bases at various scales showing bedrock or 

surficial geology, stratigraphy, and structural relations in certain 

coal-resource areas. 

Oil and Gas Investigations Charts show stratigraphic 

information for certain oil and gas fields and other areas having 

petroleum potential. 

Miscellaneous Field Studies Maps are multicolor or blackand-white maps on topographic or planimetric bases for 

quadrangle or irregular areas at various scales. Pre-1971 maps 

show bedrock geology in relation to specific mining or mineraldeposit problems; post-1971 maps are primarily black-and-white 

maps on various subjects such as environmental studies or 

wilderness mineral investigations. 

Hydrologic Investigations Atlases are multicolored or 

black-and-white maps on topographic or planimetric bases 

presenting a wide range of geohydrologic data of both regular and 

irregular areas; principal scale is 1:24,000, and regional studies are 

at 1:250,000 scale or smaller. 

Catalogs 

Permanent catalogs, as well as some others, giVmg 

comprehensive listings of U.S. Geological Survey publications are 

available under the conditions indicated below from the U.S. 

Geological Survey, Map Distribution, Box 25286, Bldg. 810, 

Federal Center, Denver, CO 80225. (See latest Price and 

Availability List.) 

"Publications of the Geological Survey, 1879-1961" may 

be purchased by mail and over the counter in paperback book form 

and as a set of microfiche. 

"Publications of the Geological Survey, 1962-1970" may 

be purchased by mail and over the counter in paperback book form 

and as a set of microfiche. 

"Publications of the U.S. Geological Survey, 1971-1981" 

may be purchased by mail and over the counter in paperback book 

form (two volumes, publications listing and index) and as a set of 

microfiche. 

Supplements for 1982, 1983, 1984, 1985, 1986, and for 

subsequent years since the last permanent catalog may be 

purchased by mail and over the counter in paperback book form. 

State catalogs, "List of U.S. Geological Survey Geologic 

and Water-Supply Reports and Maps For (State)," may be 

purchased by mail and over the counter in paperback booklet form 

only. 

''Price and Availability List of U.S. Geological Survey 

Publications," issued annually, is available free of charge in 

paperback booklet form only. 

Selected copies of a monthly catalog "New Publications 

of the U.S. Geological Survey" are available free of charge by 

mail or may be obtained over the counter in paperback booklet 

form only. Those wishing a free subscription to the monthly 

catalog "New Publications of the U.S. Geological Survey" should 

write to the U.S. Geological Survey, 582 National Center, Reston, 

VA 22092. 

Note.-Prices of Government publications listed in older 

catalogs, announcements, and publications may be incorrect. 

Therefore, the prices charged may differ from the prices in 

catalogs, announcements, and publications. 
Appel and Reilly-SUMMARY OF SELECTED COMPUTER PROGRAMS PRODUCED BY THE U.S. GEOLOGICAL SURVEY