UNITED STATES DEPARTMENT OF THE INTERIOR GEOLOGICAL SURVEY RESTON, VIRGINIA 22092 GW Branch September 7, 1978 Code 4351 5016 GROUND WATER BRANCH TECHNICAL MEMORANDUM NO. 78.09 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, POStatus of Digital Models to Simulate Solute Transport in Ground Water