Applied Contaminant Transport Modeling
Second Edition
Chunmiao Zheng and Gordon D. Bennett
Preface
Preface to the FIRST Edition
1.1 Solute Transport and the Role of Simulation
1.2 A Historical Perspective
1.2.1 Pre-1960s Era
1.2.2 Post-1960s Era
1.3 About This Book
1.4 A Note on Computer Software
PART I CONCEPTS and Techniques
2 Darcy’s Law and Advective Transport
2.1 Average Particle Velocity and Time of Travel
2.2 Generalization of Darcy’s Law and Equation of Groundwater Flow
2.3 Advective Transport
2.3.1 Mass-Balance Considerations and the
Eulerian Approach to Advective Transport2.3.2 The Particle Tracking Approach to Advective Transport
Further Reading and Problems
3 Dispersive Transport and Mass Transfer
3.1 Introduction
3.2 Microscopic Dispersive Processes
3.2.1 Mechanism of Hydrodynamic Dispersion
3.2.2 The Analogy between Dispersive Transport
and Molecular Diffusion3.2.3 Dispersive Flux and Dispersion Coefficient
in Two Dimensions3.2.4 Dispersive Flux and Dispersion Coefficient
in Three Dimensions3.2.5 Porosity in Solute Transport Calculation
3.3 Macroscopic Dispersion
3.4 Development of the Advection-Dispersion Equation
3.5 Advective-Diffusive Systems
Further Reading and Problems
4 Transport with Chemical ReactionS
4.1 Introduction
4.2 Equilibrium-Controlled Sorption
4.2.1 Sorption Isotherms and the Representation of
Sorption in Transport Equations4.2.2 Ion Exchange
4.3 Kinetic Sorption
4.4 First-Order Irreversible Reactions
4.5 Monod Kinetic Reactions
4.6 Multi-species Kinetic Reactions
4.6.1 Instantaneous Reactions
4.6.2 Multiple Monod Kinetics
4.6.3 First-Order Parent-Daughter Chain Reactions
4.7 Reactions in a Dual-Domain System
Further Reading and Problems
5 Mathematical Model and Analytical SolutionS
5.1 Mathematical Model of Solute Transport
5.1.1 Governing Equations
5.1.2 Initial Conditions
5.1.3 Boundary Conditions
5.1.4 Solution of the Mathematical Model
5.2 Analytical Solutions
Further Reading and Problems
6 Simulation of Advective Transport
6.1 Introduction
6.2 Particle Tracking Method
6.2.1 Velocity Interpolation
Velocity Interpolation in Finite-Difference Flow Models
Velocity Interpolation in Finite-Element Flow Models
6.2.2 Tracking Schemes
Semianalytical Scheme
Numerical Schemes
6.2.3 Effect of Spatial Discretization
Weak Well
Distorted Vertical Discretization
6.3 Capture Zone Delineation
6.3.1 Two-Dimensional Steady-State Flows
6.3.2 Three-Dimensional Steady-State Flows
6.3.3 Transient Flows
6.4 Evaluation of Travel Times
6.4.1 Contaminant Arrival/Breakthrough Distribution
6.4.2 Cleanup Times
6.4.3 Residence Times and Geochemical Evolution
6.5 General Particle Tracking Codes
Further Reading and Problems
7 Simulation of Advective-Dispersive Transport
7.1 Introduction
7.2 Eulerian Methods
7.2.1 Finite-Difference Method
Spatial and Temporal Discretization
Solution of Finite-Difference Equations
Artificial Oscillation and Numerical Dispersion
A Two-Dimensional Example
General Finite-Difference Codes
7.2.2 Finite-Element Method
A One-dimensional Example
General Finite-Element Codes
7.2.3 Finite Element versus Finite Difference
7.3 Lagrangian Methods
7.3.1 Random Walk Method
Treatment of Advection and Dispersion
Treatment of Sorption and First-Order Reactions
Evaluation of Concentrations
Advantages and Limitations
General Random Walk Codes
7.4 Mixed Eulerian-Lagrangian Methods
7.4.1 Method of Characteristics (MOC)
Initial Particle Allocation
Concentration Change due to Dispersion
Cell and Particle Concentration Updates
Particle Insertion and Deletion
Application to an Example Problem
7.4.2 Modified Method of Characteristics (MMOC)
7.4.3 Hybrid Method of Characteristics
7.4.4 General Mixed Eulerian-Lagrangian Codes
7.5 Total-Variation-Diminishing (TVD) Methods
7.5.1 The ULTIMATE Scheme
Third-Order Approximation
Universal Flux Limiter
Comparison between TVD and Other Solution Schemes
General TVD Codes
Further Reading and Problems
8 Simulation of Nonequilibrium Processes
and Reactive Transport8.1 Introduction
8.2 Nonequilibrium Sorption
8.3 Dual-Domain Mass Transfer
8.4 Multi-species Kinetic Reactions
8.4.1 Simultaneous Solution
8.4.2 Operator Splitting
8.5 Coupled Transport and Geochemical Modeling
8.6 General Reactive Transport Codes
8.7 A Case Study – Modeling Natural Attenuation
8.7.1 Site Description
8.7.2 Modeling Approach
8.7.3 Numerical Model
8.7.4 Discussion of Results
Further Reading and Problems
PART II FIELD APPLICATIONS
9 A Framework for Model Applications
9.1 The Model Application Process
9.2 Defining Goals
9.3 Data Collection and Conceptual Model Development
9.4 Selection of a Computer Code
9.5 Building a Contaminant Transport Model
9.6 Model Calibration and Sensitivity Analysis
9.7 Prediction and Uncertainty
9.8 Keys to Successful Model Applications
Further Reading and Problems
10 Building a Contaminant Transport Model
10.1 Getting Started
10.1.1 Present Understanding of the Flow System
10.1.2 Dimensions of Analysis
10.1.3 Domains of Simulation
10.2 Spatial Discretizations
10.2.1 Horizontal Nodal Spacing
10.2.2 Vertical Discretization
10.3 Temporal Discretizations
10.4 Initial Conditions
10.5 Boundary Conditions
10.5.1 Use of the Specified Concentration Condition
10.5.2 Use of the Specified-Mass-Flux Condition
10.5.3 Role of Flow Model Boundary Conditions
in Solute Transport10.5.4 Comparison Between Flow and Transport
Boundary Conditions10.5.5 A Note On Scale Difference in Flow and
Transport Simulation10.6 Sources and Sinks
10.6.1 Types of Sources and Sinks
10.6.2 Concentrations of Sources and Sinks
10.7 Data Management
10.7.1 Preprocessing and Postprocessing
10.7.2 Geographic Information System (GIS)
Further Reading and Problems
11.1 Data Needs in Transport Modeling
11.2 Flow Parameters
11.2.1 Hydraulic Conductivity
11.2.2 Storage Coefficient and Specific Yield
11.3 Transport Parameters
11.3.1 Porosity
11.3.2 Dispersivity
11.4 Chemical Parameters
11.4.1 Sorption Constants
11.4.2 Kinetic Reaction Rates
12 Model Calibration and Sensitivity Analysis
12.1 Basic Concepts of Model Calibration
12.1.1 The Calibration Process
12.1.2 Calibration, Verification and Validation
12.1.3 The Nonuniqueness Problem
12.2 Assessment of Model Calibration
12.2.1 Statistical Measures of Goodness-of-Fit
12.2.2 Other Considerations in Assessing Model Calibration
12.2.3 Presentation of Calibration Results
12.3 Calibration by Trial-and-Error
12.3.1 Procedure and Limitation
12.3.2 Case Studies
12.4 “Automated” Calibration
12.4.1 Can Calibration Be Automated?
12.4.2 Techniques for Automated Parameter Identification
Estimation of Parameter Values
Determination of Parameter Structures
12.4.3 A Case Study
12.5 Sensitivity Analysis
12.5.1 Sensitivity Coefficients
12.5.2 Procedure for Sensitivity Analysis
Further Reading and Problems
13.1 Introduction
13.2 Types and Sources of Uncertainty
13.3 Methods for Evaluating Uncertainty
13.3.1 Sensitivity Analysis
13.3.2 Monte Carlo Method
Basic Concepts
Generation and Sampling of Parameter Distribution
Procedure and Example of Monte Carlo Simulation
13.3.3 First-Order Error Analysis
13.4 Managing Uncertainty
13.4.1 Reduction of Uncertainty
13.4.2 Decision-Making Under Uncertainty
Further Reading and Problems
14 Contaminant Transport Modeling: Case Studies
14.1 Modeling Contaminant Migration from a Landfill
at the Borden Site in Canada14.1.1 Site Description
14.1.2 Historical Perspective
14.1.3 Two-Dimensional Modeling
Model Setup
Sensitivity Analysis
Close-Fit Simulation
14.1.4 Three-Dimensional Modeling
14.2 Evaluating Remedial Alternatives at a Superfund Site
in New Jersey14.2.1 Site Description
14.2.2 Remedial Objectives
On-Site Source Control Remedy
Off-Site Areas of Attainment
14.2.3 The Modeling Approach
Estimation of Number of Pore Volumes Required for Cleanup
Estimation of Cleanup Time
Flow Simulation and Calibration
Particle Tracking
14.2.4 Evaluation of Alternatives
No-Action Alternative (Source Control Only)
Interceptor Drain Alternative
Interceptor Drain and Extraction Well Alternative
Accelerated Cleanup Alternative
A Comparison of Alternatives
14.3 Assessing Aquifer Susceptibility to Contamination
at an Agricultural Field in Wisconsin14.3.1 Site Description
14.3.2 Groundwater Flow Model
14.3.3 Particle Tracking and Assessment of Aquifer Susceptibility
14.3.4 Transport Modeling and Evaluation of Long-Term Impacts
Simulation Objectives and Approach to the Uncertainty Analysis
“Grand Mean” Contamination Predictions
Expected Values and Variances of the Model Predictions
14.4 Application of the Dual-Domain Mass Transfer Approach
to the MADE Site in Mississippi14.4.1 Site Description
14.4.2 The MADE-2 Tracer Test
14.4.3 Spatial Discretization and Boundary Conditions
14.4.4 Assignment of Hydraulic and Transport Properties
14.4.5 Simulation Results for the Kriged Hydraulic
Conductivity Field14.4.6 Simulation Results for the Fractal Hydraulic
Conductivity Field14.4.7 Comparison and Discussion
14.4.8 Sensitivity of Dual-Domain Model Parameters
PART III ADVANCED TOPICS
15 Simulation of Density-Dependent Flow
and Transport Equation15.1 Introduction
15.3 The Relationship Between Solute Concentration
and Water Density15.4 The Solute Transport Equation
15.5 General Solution Sequence
15.6 Sharp Interface Approach
15.7 General Variable-Density Codes
15.8 A Case Study – Seawater Intrusion Modeling
15.8.1 Background
15.8.2 Cross-sectional Simulations
15.8.3 Three-dimensional Simulation
Further Reading and Problems
16 Simulation of Flow and Transport
in the Vadose Zone16.1 Introduction
16.2 Basic Concepts of Vadose Zone Hydrology
16.3 Flow Equation for Partially Saturated Conditions
16.4 Solute Transport under Partial Saturation
16.4.1 Basic Transport Equation
16.4.2 Implications of Partial Saturation for Dispersive Transport
16.4.3 Dual-Domain Systems
16.5 Extension to the Air Phase
16.5.1 Air-Water Partitioning
16.5.2 Air-Phase Transport
16.6 General Variably Saturated Codes
16.7 An Illustrative Example
Further Reading and Problems
17 Optimal Management of Groundwater Quality
17.1 Introduction
17.2 The Simulation-Optimization Approach
17.3 Optimization Techniques
17.3.1 Linear Programming
17.3.2 Genetic Algorithms
Basic Procedures
Application to Remediation Design
General GA-Based Codes
17.3.3 Simulated Annealing
17.3.4 Tabu Search
17.4 Optimal Management Examples
17.4.1 A Hypothetical Example
Effect of Well Numbers
Effect of Aquifer Heterogeneity
17.4.2 A Field Example
Site Description and Background
Flow and Transport Simulation Models
Steady-State Pumping Strategy
Dynamic Pumping Strategy
Further Reading and Problems
Appendix A Darcy’s Law and Variable-Density
Flow EquationAppendix B Application of Stream Functions
to Groundwater FlowsAppendix C Groundwater Modeling Software
