Analytical Modeling of Solute Transport in Groundwater

Mark Goltz is a well-known authority in the field of hydrogeology and subsurface contaminant transport and remediation. He is Distinguished Professor Emeritus of Engineering and Environmental Management at the Air Force Institute of Technology, where he conducted research into the fate and transport of groundwater contaminants and contaminated groundwater remediation technologies. He has published numerous works in these areas. Junqi Huang is a hydrologist in the Ground Water and Ecosystems Restoration Division, National Risk Management Research Laboratory, US EPA. He is an experienced hydrogeological modeler, with expertise developing models for groundwater flow and transport, groundwater management, and contaminated groundwater remediation strategies.

• List of Symbols xiPreface xvAcknowledgments xviiAbout the Companion Website xix1 Modeling 11.1 Introduction 11.2 Definitions 31.3 A Simple Model – Darcy’s Law and Flow Modeling 31.3.1 Darcy’s Law 31.3.2 Flow Equation 51.3.3 Example Application of Darcy’s Law and the Flow Equation 81.3.4 Note of Caution – Know Model Assumptions and Applicable Conditions 91.3.5 Superposition (For a Fuller Discussion of Superposition Applied to Groundwater Flow, See Reilly et al., 1984) 131.3.6 Example Application of the Principle of Superposition 13References 162 Contaminant Transport Modeling 192.1 Introduction 192.2 Fate and Transport Processes 192.2.1 Advection 192.2.2 Dispersion 202.2.3 Sorption 222.2.4 Chemical and Biological Reactions 242.3 Advective–Dispersive–Reactive (ADR) Transport Equation 252.3.1 Reaction Submodel 272.3.2 Sorption Submodel 282.3.2.1 Linear Equilibrium 282.3.2.2 Rate-Limited Sorption 282.4 Model Initial and Boundary Conditions 292.4.1 Initial Conditions 302.4.2 Boundary Conditions 312.5 Nondimensionalization 32References 353 Analytical Solutions to 1-D Equations 373.1 Solving the ADR Equation with Initial/Boundary Conditions 373.2 Using Superposition to Derive Additional Solutions 383.3 Solutions 403.3.1 AnaModelTool Software 403.3.2 Virtual Experimental System 413.4 Effect of Advection 413.5 Effect of Dispersion 433.6 Effect of Sorption 483.6.1 Linear, Equilibrium Sorption 483.6.2 Rate-Limited Sorption 513.6.2.1 First-Order Kinetics 513.6.2.2 Diffusion-Limited 573.7 Effect of First-Order Degradation 603.8 Effect of Boundary Conditions 643.8.1 Effect of Boundary Conditions on Breakthrough Curves 643.8.2 Volume-Averaged Resident Concentration Versus Flux-Averaged Concentration 66References 684 Analytical Solutions to 3-D Equations 714.1 Solving the ADR Equation with Initial/Boundary Conditions 714.2 Using Superposition to Derive Additional Solutions 724.3 Virtual Experimental System 724.4 Effect of Dispersion 734.5 Effect of Sorption 784.5.1 Linear, Equilibrium Sorption 784.5.2 Rate-Limited Sorption 804.6 Effect of First-Order Degradation 835 Method of Moments 875.1 Temporal Moments 875.1.1 Definition 875.1.2 Evaluating Temporal Moments 885.1.3 Temporal Moment Behavior 885.1.3.1 Advective–Dispersive Transport with First-Order Degradation and Linear Equilibrium Sorption 885.1.3.2 Advective–Dispersive Transport with First-Order Degradation and Rate-Limited Sorption 975.2 SpatialMoments 1025.2.1 Definition 1025.2.2 Evaluating Spatial Moments 1035.2.3 Spatial Moment Behavior 1045.2.3.1 Advective–Dispersive Transport with First-Order Degradation and Linear Equilibrium Sorption 1045.2.3.2 Advective–Dispersive Transport with First-Order Degradation and Rate-Limited Sorption 105References 1206 Application of Analytical Models to Gain Insight into Transport Behavior 1216.1 Contaminant Remediation 1216.2 Borden Field Experiment 124References 127A Solution to One-Dimensional ADR Equation with First-Order Degradation Kinetics Using Laplace Transforms 129Reference 132B Solution to One-Dimensional ADR Equation with Zeroth-Order Degradation Kinetics Using Laplace Transforms 133Reference 135C Solutions to the One-Dimensional ADR in Literature 137References 140D User Instructions for AnaModelTool Software 141E Useful Laplace Transforms 145E.1 Laplace Transforms from van Genuchten and Alves (1982) 145Reference 148F Solution to Three-Dimensional ADR Equation with First-Order Degradation Kinetics for an Instantaneous Point Source Using Laplace and Fourier Transforms 149References 151G Solution to Three-Dimensional ADR Equation with Zeroth-Order Degradation Kinetics for an Instantaneous Point Source Using Laplace and Fourier Transforms 153References 155H Solutions to the Three-Dimensional ADR in Literature 157References 160I Derivation of the Long-Time First-Order Rate Constant to Model Decrease in Concentrations at a Monitoring Well Due to Advection, Dispersion, Equilibrium Sorption, and First-Order Degradation (Three-Dimensional Infinite System with an Instantaneous Point Source) 161J Application of Aris’ Method of Moments to Calculate Temporal Moments 163K Application of Modified Aris’ Method of Moments to Calculate Spatial Moments Assuming Equilibrium Sorption 165L Application of Modified Aris’ Method of Moments to Calculate Spatial Moments Assuming Rate-Limited Sorption 167L.1 Zeroth Spatial Moment 168L.2 First Spatial Moment 168L.3 Second Spatial Moment 168M Derivation of Laplace Domain Solutions to a Model Describing Radial Advective/Dispersive/Sorptive Transport to an Extraction Well 171References 173N AnaModelTool Governing Equations, Initial and Boundary Conditions, and Source Code 175N.1 Model 101 175N.2 Model 102 176N.3 Model 103 178N.4 Model 104 179N.5 Model 104M 180N.6 Model 105 182N.7 Model 106 184N.8 Model 107 185N.9 Model 108 187N.10 Model 109 189N.11 Model 201 191N.12 Model 202 193N.13 Model 203 195N.14 Model 204 197N.15 Model 205 200N.16 Model 206 201N.17 Model 207 203N.18 Model 208 206N.19 Model 301 207N.20 Model 302 210N.21 Model 303 212N.22 Model 304 215N.23 Model 305 217N.24 Model 306 220N.25 Model 401 222N.26 Model 402 223N.27 Model 403 225N.28 Model 404 227N.29 Model 405 229N.30 Model 406 232Index 235