Status of Digital Models to Simulate Solute Transport in Ground Water

                           UNITED STATES
                    DEPARTMENT OF THE INTERIOR
                         GEOLOGICAL SURVEY
                      RESTON, VIRGINIA  22092

                                                      GW Branch

                                              September 7, 1978
                                                 Code 4351 5016


Subject:  Status of Digital Models to Simulate Solute Transport
          in Ground Water

The purpose of this memorandum is to review the application and
availability of models of solute transport in ground water and of
some related investigative tools.  A number of digital solute-
transport models are available and have been used within WRD.
Each of these models has some unique advantages, disadvantages,
and special limitations for application to field problems.  At
present no model or computer program is best (in terms of accuracy
and efficiency) for all solute-transport problems.  Probably any
model selected will have to be modified to some extent for
efficient application to a particular field problem.

Analogies are sometimes made between ground-water flow models and
ground-water solute-transport models.  Just as flow models can be
used to help analyze and make predictions of changes in hydraulic
head, transport models can do the same for changes in
concentration of a chemical dissolved in ground water.  But some
significant differences must be recognized while planning modeling
portions of investigations.

Although the use of digital ground-water flow models has become
almost routine to many WRD hydrologists, the corresponding use of
solute-transport models is barely beyond the research and
development stage.  The basic equation describing solute transport
in a porous medium is less amenable to a straightforward and
efficient numerical solution than is the ground-water flow
equation.  Also, the field data needed to calibrate a solute-
transport model are not as generally available or readily
obtainable as the data required to calibrate a flow model.  For a
field problem, an accurate definition (or model) of the flow
system is a prerequisite to accurately calibrating a transport
model.  The converse is not true; that is, definition of solute
transport is not normally needed to develop a ground-water flow
model.  For aquifers in which fracture permeability is dominant,
porous media flow models have sometimes been applied successfully.
But because of the great difficulty in defining the velocity field
in fractured rocks, porous media transport models should rarely be
applied to aquifers in which fracture permeability is dominant.

These problems should not discourage the use of solute-transport
models.  But it should be recognized during the planning stages of
a project that significantly more time and effort will be required
by a modeler to properly select, apply, and calibrate a solute-
transport model than is usually required for a flow model.

The selection of a program for a particular problem should be
based on several factors, such as numerical accuracy requirements,
program efficiency (and related computer facilities and costs),
and usability.  The first two factors are related primarily to the
nature of the field problem, availability of data, and the scope
or intensity of the investigation (including time and fiscal
constraints).  The usability of a model depends on the
availability and degree of documentation and on the mathematical
background and experience of the modeler, who will probably prefer
the model that uses a numerical method that he or she best
understands.  The solute-transport models are not black-box tools
and the modeler should have training equivalent to that given in
WRD Training Class G0801.

The following is a summary of the status of WRD digital models of
solute transport in ground water and updates the information in
USGS Circular 737, "Status of Ground-Water Modeling in the U. S.
Geological Survey."  Additional information on specific models can
be obtained from the principal investigators, from the Ground
Water Branch, from Regional ground-water specialists, or from
other experienced users (possible contacts for assistance are
listed for each model).

1.  INTERCOMP model (also called SWIP model)--Although designed
for deep-well-injection problems, this is probably the most
general model available in WRD.  It offers the user many options,
including specifications for the coordinate system (1-D, 2-D, and
3-D Cartesian, or radial coordinates), equations solved (flow
equation only, flow and solute transport, flow and heat transport,
or all three), numerical solution techniques, density and
viscosity dependence, boundary conditions, and variable spacing
for the grid.  But the program is large and may be expensive to
run.  Because the program is based on finite-difference methods,
the user may encounter problems of numerical dispersion and (or)
oscillations.  The program has been modified twice for the Survey
by INTERCOMP since the original users' manual was published.
These modifications make the model more compatible to a wider
range of hydrologic problems than it was originally designed for.
The original version of the program (with first set of
modifications) is available on RE2.  The newest version and input
documentation is being reviewed and should be available by
October 1.  Contacts:  D. Grove, S. Larson, J. Mercer, C. Faust,
L. Konikow.

2.  Characteristics model--This program is well documented and has
been applied successfully to a number of field problems.  It is
set up for 2-D rectangular grid, hydrodynamic dispersion
(coefficient formulated as 2nd rank tensor), constant density,
conservative solute, and transient or steady flow.  Although not
included in the general model, the program had been modified in
previous applications to incorporate first order chemical
reactions and surface-water routing.  Program is available on
Denver MULTICS, but can be placed on IBM.  Program listing, card
deck, and preliminary documentation are available.  Final
documentation scheduled for release in November as TWRI Bk. 7,
Ch. C2.  Contacts: L. Konikow, J. Bredehoeft.

3.  Two dimensions with reactions--Option of finite-difference or
finite-element procedure for 2-D, nonconservative transport, with
steady flow, hydrodynamic dispersion, and rectangular grid.
Chemical reactions limited to first-order irreversible rate
reactions, such as radioactive decay and equilibrium-controlled
ion exchange with a linear adsorption isotherm.  Theoretical
background published, program listing and input specifications
available, detailed-program documentation not yet available.
Contact:  D. Grove.

4.  One dimension with reactions--Galerkin finite-element model
for transport and dispersion of nonconservative solute in
unsaturated or saturated, one-dimensional, steady flow.  Theory
published (1973).  Sufficient instructions for individual program
development are presented in WRD Training Class G0801.  In
development are methods for (1) multi-component systems with
nonlinear kinetics and (2) equilibrium-controlled exchange
simultaneous with classical chemical reactions.  Contacts:
J. Rubin and R. James.

5.  Two-dimensional conservative transport--Galerkin finite-
element model for transient or steady flow, with hydrodynamic
dispersion, constant density, surface-water routing, and
quadrilateral elements.  In development for application to Spokane
Valley, Washington.  Documentation is not yet available.
Contacts:  J. Vaccaro, J. Tracy.

6.  Saltwater interface, 3-D freshwater flow--This model is a
modification of Trescott's 3-D, SIP, ground-water flow model.  The
model assumes no dispersion and no flow in saltwater zone.  If the
interface is located intermediately within a block (or cell) of
the grid, the transmissivity of that block is adjusted
proportionately to a lower value.  Model has been applied to a
problem on Cape Cod, Massachusetts.  A program deck and input-data
documentation are available.  Contacts:  J. Guswa, P. Trescott.

7.  Saltwater interface, 2-D freshwater and saltwater flow--Finite
difference model for sharp interface problem (no dispersion).
Model represents horizontal flow in both freshwater and saltwater.
One-dimensional model working; two-dimensional model in
development.  No documentation available yet.  Contacts:
J. Mercer, J. Tracy, C. Faust.

8.  There are also a number of solute-transport models available
from non-survey sources.  Some may be better suited to certain
specific problems than any of the available Survey projects with
varying degrees of success.  Previous problems with using these
outside programs include a lack of adequate or referenceable
documentation, and the absence of technical consulting support for
questions or problems.

There also are a number of related investigative tools that can be
used independently or in conjunction with digital solute-transport
models for the analysis of aquifer contamination problems.
Following is a brief discussion of some of these.

1.  Analytical solutions to the transport equation--In the drive
to use digital computer models, simple analytical methods are
sometimes overlooked.  A large number of analytical solutions are
available for a variety of boundary and initial conditions.  They
can be applied to a field problem if the geometry, dimensionality,
sources and sinks, and aquifer properties can be appropriately
simplified.  If this can be done, the analytical approach can
provide (1) a very quick solution to the simplified problem, (2) a
first approximation of concentration changes, which can help in
designing a grid for a more detailed and complex numerical model,
and (3) a check on the accuracy of the numerical results.
Contacts: A. Ogata, D. Grove.

2.  Heat-transport models--Where temperature variations are
significant, the use of heat-transport models should be
considered.  In addition to the INTERCOMP model, several others
have been developed within WRD specifically for heat-transport
problems.  Detailed documentation is available for some.
Contacts:  A. Moench, J. Mercer, C. Faust, M. Sorey.

3.  Aqueous chemistry models--These can be valuable tools in
groundwater quality studies and can be used prior to or in
conjunction with the application of a solute-transport model.  For
example, in a situation where several species and chemical
reactions might be of concern, the aqueous chemistry models might
help to eliminate the less significant ones from consideration and
thus minimize the number of reactions necessary to consider in a
solute-transport model.  Two types of chemical models are in use
in WRD.  Users should have geochemical training or experience
equivalent to that present in WRD Training Class G0212.

The first type of chemical model predicts the thermodynamic
distribution of individual ions in solution for a particular water
analysis (equilibrium model).  Equilibrium models can be used to
test the likelihood of occurrence of proposed chemical reactions
by comparing computed saturation for minerals or gases with the
theoretical thermodynamic value.  Contacts: WATEQ--B. Jones;
WATEQF--N. Plummer, B. Jones; WATEQ2--J. Ball, E. Jenne; SOLMNEQ--
Y. Kharaka, R. Bassett.

The second type of chemical model (mass transfer model) can be
used to predict the outcome of proposed chemical reactions.
Applications might include (1) computing chemical effects of
mixing aqueous solutions, (2) testing proposed chemical reactions,
such as redox reactions and ion exchange, (3) predicting amounts
of minerals dissolved or precipitated in reacting systems, and (4)
correcting carbon-14 ages of ground water for effects of chemical
reactions.  Contacts:  MIX2 (and more recently developed
versions)--D. Thorstenson, N. Plummer, D. Parkhurst.

                         (s) Leonard F. Konikow
                         (for) Chief, Ground Water Branch

WRD Distribution:  A, B, S, FO, PO