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Abstract

This manual describes the next-generation of the modular three-dimensional transport model, MT3D, with significantly expanded capabilities, including the addition of, 1) a third-order total-variation-diminishing (TVD) scheme for solving the advection term that is mass conservative but does not introduce excessive numerical dispersion and artificial oscillation; 2) an efficient iterative solver based on generalized conjugate gradient methods and the Lanczos/ORTHOMIN acceleration scheme to remove stability constraints on the transport time stepsize; 3) options for accommodating nonequilibrium sorption and dual-domain advection-diffusion mass transport; and 4) a multi-component program structure that can accommodate add-on reaction packages for modeling general biological and geochemical reactions.

The new modular multispecies transport model, referred to as MT3DMS in this manual, is unique in that it includes the three major classes of transport solution techniques in a single code, i.e., the standard finite difference method; the particle-tracking-based Eulerian-Lagrangian methods; and the higher-order finite-volume TVD method. Since no single numerical technique has been shown to be effective for all transport conditions, the combination of these solution techniques, each having its own strengths and limitations, is believed to offer the best approach for solving the most wide-ranging transport problems with desired efficiency and accuracy.

MT3DMS can be used to simulate changes in concentrations of miscible contaminants in groundwater considering advection, dispersion, diffusion and some basic chemical reactions, with various types of boundary conditions and external sources or sinks. The basic chemical reactions included in the model are equilibrium-controlled or rate-limited linear or non-linear sorption, and first-order irreversible or reversible kinetic reactions. More sophisticated, multispecies chemical reactions can be simulated by add-on reaction packages. MT3DMS can accommodate very general spatial discretization schemes and transport boundary conditions, including: 1) confined, unconfined or variably confined/unconfined aquifer layers; 2) inclined model layers and variable cell thickness within the same layer; 3) specified concentration or mass flux boundaries; and 4) the solute transport effects of external hydraulic sources and sinks such as wells, drains, rivers, areal recharge and evapotranspiration. MT3DMS is designed for use with any block-centered finite-difference flow model, such as the U.S. Geological Survey modular finite-difference groundwater flow model, MODFLOW, under the assumption of constant fluid density and full saturation. However, MT3DMS can also be coupled with a variably saturated or density-dependent flow model for simulation of transport under such conditions.


Introduction

Purpose and Scope

The modular three-dimensional transport model referred to as MT3D was originally developed by Zheng (1990) at S. S. Papadopulos & Associates, Inc., and subsequently documented for the Robert S. Kerr Environmental Research Laboratory of the United States Environmental Protection Agency. In the past several years, various versions of the MT3D code have been commonly used in contaminant transport modeling and remediation assessment studies. This manual describes the next-generation of MT3D with significantly expanded capabilities, including the addition of, 1) a third-order total-variation-diminishing (TVD) scheme for solving the advection term that is mass conservative but does not introduce excessive numerical dispersion and artificial oscillation; 2) an efficient iterative solver based on generalized conjugate gradient methods to remove stability constraints on the transport time stepsize; 3) options for accommodating nonequilibrium sorption and dual-domain advection-diffusion mass transport; and 4) a multi-component program structure that can accommodate add-on reaction packages for modeling general biological and geochemical reactions.

Key Features

The new mass transport model documented in this manual is referred to as MT3DMS, where MT3D stands for the Modular 3-Dimensional Transport model while MS denotes the Multi-Species structure for accommodating add-on reaction packages. MT3DMS has a comprehensive set of options and capabilities for simulating advection, dispersion/diffusion, and chemical reactions of contaminants in groundwater flow systems under general hydrogeologic conditions. This section summarizes the key features of MT3DMS.

MT3DMS is unique in that it includes three major classes of transport solution techniques in a single code, i.e., the standard finite difference method; the particle-tracking-based Eulerian-Lagrangian methods; and the higher-order finite-volume TVD method. Since no single numerical technique has been shown to be effective for all transport conditions, the combination of these solution techniques, each having its own strengths and limitations, is believed to offer the best approach for solving the most wide-ranging transport problems with desired efficiency and accuracy.

In addition to the explicit formulation of the original MT3D code, MT3DMS includes an implicit formulation that is solved with an efficient and versatile solver. The iterative solver is based on generalized conjugate gradient (GCG) methods with three preconditioning options and the Lanczos/ORTHOMIN acceleration scheme for non-symmetrical matrices. If the GCG solver is selected, dispersion, sink/source, and reaction terms are solved implicitly without any stability constraints. For the advection term, the user has the option to select any of the solution schemes available, including the standard finite-difference method, the particle tracking based Eulerian-Lagrangian methods, and the third-order TVD method. The finite-difference method can be fully implicit without any stability constraint to limit transport step sizes, but the particle tracking based Eulerian-Lagrangian methods and the third-order TVD method still have time step constraints associated with particle tracking and TVD methodology. If the GCG solver is not selected, the explicit formulation is automatically used in MT3DMS with the usual stability constraints. The explicit formulation is efficient for solving advection-dominated problems in which the transport stepsizes are restricted by accuracy considerations. It is also useful when the implicit solver requires a large number of iterations to converge or when the computer system does not have enough memory to use the implicit solver.

MT3DMS is implemented with an optional, dual-domain formulation for modeling mass transport. With this formulation, the porous medium is regarded as consisting of two distinct domains, a mobile domain where transport is predominately by advection and an immobile domain where transport is predominately by molecular diffusion. Instead of a single "effective" porosity for each model cell, two porosities, one for the mobile domain and the other for the immobile domain, are used to characterize the porous medium. The exchange between the mobile and immobile domains is specified by a mass transfer coefficient. The dual-domain advective-diffusive model may be more appropriate for modeling transport in fractured media or extremely heterogeneous porous media than the single porosity advective-dispersive model, provided that the porosities and mass transfer coefficients can be properly characterized.

MT3DMS retains the same modular structure of the original MT3D code, similar to that implemented in the U.S. Geological Survey modular three-dimensional finite-difference groundwater flow model, MODFLOW, (McDonald and Harbaugh, 1988; Harbaugh and McDonald, 1996). The modular structure of the transport model makes it possible to simulate advection, dispersion/diffusion, source/sink mixing, and chemical reactions separately without reserving computer memory space for unused options; furthermore new packages involving other transport processes and reactions can be added to the model readily without having to modify the existing code.

As in the original MT3D code, MT3DMS is developed for use with any block-centered finite-difference flow model such as MODFLOW and is based on the assumption that changes in the concentration field will not affect the flow field significantly. After a flow model is developed and calibrated, the information needed by the transport model can be saved in disk files which are then retrieved by the transport model. Since most potential users of a transport model are likely to have been familiar with one or more flow models, MT3DMS provides an opportunity to simulate contaminant transport without having to learn a new flow model or to modify an existing flow model to fit the transport model. In addition, separate flow simulation and calibration outside the transport model can result in substantial savings in computer memory. The model structure also saves execution time when many transport runs are required while the flow solution remains the same. Although this report describes only the use of MT3DMS in conjunction with MODFLOW, MT3DMS can be linked to any other block-centered finite-difference flow model in a simple and straightforward fashion.

MT3DMS can be used to simulate changes in concentrations of miscible contaminants in groundwater considering advection, dispersion, diffusion and some basic chemical reactions, with various types of boundary conditions and external sources or sinks. The chemical reactions included in the model are equilibrium-controlled or rate-limited linear or non-linear sorption, and first-order irreversible or reversible kinetic reactions. It should be noted that the basic chemical reaction package included in MT3DMS is intended for single-species systems. An add-on reaction package such as RT3D (Clement, 1997) or SEAM3D (Widdowson and Waddill, 1997) must be used to model more sophisticated multi-species reactions. MT3DMS can accommodate very general spatial discretization schemes and transport boundary conditions, including: 1) confined, unconfined or variably confined/unconfined aquifer layers; 2) inclined model layers and variable cell thickness within the same layer; 3) specified concentration or mass flux boundaries; and 4) the solute transport effects of external hydraulic sources and sinks such as wells, drains, rivers, areal recharge and evapotranspiration.

Organization of the Report

This report covers the theoretical, numerical and application aspects of the MT3DMS transport model. Following this introduction, Chapter 2 gives a brief overview of the physical-mathematical basis and various functional relationships underlying the transport model. Chapter 3 explains the basic ideas behind the various solution schemes implemented in MT3DMS. Chapter 4 discusses the computer implementation of the numerical solution schemes. Chapter 5 describes the program structure and design of the MT3DMS code, which has been divided into a main program and a number of packages, each dealing with a single aspect of the transport simulation. Chapter 6 provides detailed model input instructions and discusses how to set up a simulation. Chapter 7 describes the benchmark and example problems that were used to test the MT3DMS code and illustrate its applications. The appendices include information on the iterative solver, the computer memory requirements of the MT3DMS model, the interface between MT3DMS and a flow model, several post-processing programs, and tables of abbreviated input instructions.

Acknowledgments

The original MT3D code was developed at S. S. Papadopulos & Associates, Inc. and documented for the U.S. Environmental Protection Agency. The contributions of Charles Andrews, Gordon Bennett and Stavros Papadopulos to the conception and development of MT3D are gratefully acknowledged. The current work was funded, in part, by the U.S. Army Corps of Engineers Waterways Experiment Station (WES) under contract DACA39-96-K-0016 to the University of Alabama. We are indebted to several WES scientists, including Mark Dortch, Mansour Zakikhani, Dave Richards, Jeff Holland and Carlos Ruiz for their encouragement and support. We are grateful to Chris Neville, Daniel Feinstein, T.P. Clement, Marianne Guerin, Norm Jones, Mark Widdowson, and Ying Ouyang for helpful suggestions and discussions, and to Erin Feehley and Diana Sturm for code testing and editorial assistance. We also wish to thank Chris Neville, Mark Dortch, Daniel Feinstein and Erin Feehley who reviewed a draft version of this report and provided many valuable comments. Finally, we acknowledge the contribution of T.-Z. Mai in the Department of Mathematics at the University of Alabama who developed and provided the documentation for the solution routine of the GCG iterative solver (Appendix A).


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Last modified: June 14, 2001