Analytical Modeling of Solute Transport in Groundwater: Using Models to Understand the Effect of Natural Processes on Contaminant Fate and Transport

By Mark Goltz and Junqi Huang

Teaches, using simple analytical models how physical, chemical, and biological processes in the subsurface affect contaminant transport

• Uses simple analytical models to demonstrate the impact of subsurface processes on the fate and transport of groundwater contaminants
• Includes downloadable modeling tool that provides easily understood graphical output for over thirty models
• Modeling tool and book are integrated to facilitate reader understanding
• Collects analytical solutions from many sources into a single volume and, for the interested reader, shows how these solutions are derived from the governing model equations

• Language: English
• Publisher: Wiley
• Release date: Feb 8, 2017
• ISBN: 9781119300274

Book preview

Table of Contents

Cover

Title Page

Copyright

List of Symbols

Preface

Acknowledgments

About the Companion Website

Chapter 1: Modeling

1.1 Introduction

1.2 Definitions

1.3 A Simple Model – Darcy's Law and Flow Modeling

Problems

References

Chapter 2: Contaminant Transport Modeling

2.1 Introduction

2.2 Fate and Transport Processes

2.3 Advective–Dispersive–Reactive (ADR) Transport Equation

2.4 Model Initial and Boundary Conditions

2.5 Nondimensionalization

Problems

References

Chapter 3: Analytical Solutions to 1-D Equations

3.1 Solving the ADR Equation with Initial/Boundary Conditions

3.2 Using Superposition to Derive Additional Solutions

3.3 Solutions

3.4 Effect of Advection

3.5 Effect of Dispersion

3.6 Effect of Sorption

3.7 Effect of First-Order Degradation

3.8 Effect of Boundary Conditions

Problems

References

Chapter 4: Analytical Solutions to 3-D Equations

4.1 Solving the ADR Equation with Initial/Boundary Conditions

4.2 Using Superposition to Derive Additional Solutions

4.3 Virtual Experimental System

4.4 Effect of Dispersion

4.5 Effect of Sorption

4.6 Effect of First-Order Degradation

Problems

Chapter 5: Method of Moments

5.1 Temporal Moments

5.2 Spatial Moments

Problems

References

Chapter 6: Application of Analytical Models to Gain Insight into Transport Behavior

6.1 Contaminant Remediation

6.2 Borden Field Experiment

References

Appendix A: Solution to One-Dimensional ADR Equation with First-Order Degradation Kinetics Using Laplace Transforms

Reference

Appendix B: Solution to One-Dimensional ADR Equation with Zeroth-Order Degradation Kinetics Using Laplace Transforms

Reference

Appendix C: Solutions to the One-Dimensional ADR in Literature

References

Appendix D: User Instructions for AnaModelTool Software

Appendix E: Useful Laplace Transforms

E.1 Laplace Transforms from van Genuchten and Alves (1982)

Reference

Appendix F: Solution to Three-Dimensional ADR Equation with First-Order Degradation Kinetics for an Instantaneous Point Source Using Laplace and Fourier Transforms

References

Appendix G: Solution to Three-Dimensional ADR Equation with Zeroth-Order Degradation Kinetics for an Instantaneous Point Source Using Laplace and Fourier Transforms

References

Appendix H: Solutions to the Three-Dimensional ADR in Literature

References

Appendix I: 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)

Appendix J: Application of Aris' Method of Moments to Calculate Temporal Moments

Appendix K: Application of Modified Aris' Method of Moments to Calculate Spatial Moments Assuming Equilibrium Sorption

Appendix L: Application of Modified Aris' Method of Moments to Calculate Spatial Moments Assuming Rate-Limited Sorption

L.1 Zeroth Spatial Moment

L.2 First Spatial Moment

L.3 Second Spatial Moment

Appendix M: Derivation of Laplace Domain Solutions to a Model Describing Radial Advective/Dispersive/Sorptive Transport to an Extraction Well

References

Appendix N: AnaModelTool Governing Equations, Initial and Boundary Conditions, and Source Code

N.1 Model 101

N.2 Model 102

N.3 Model 103

N.4 Model 104

N.5 Model 104M

N.6 Model 105

N.7 Model 106

N.8 Model 107

N.9 Model 108

N.10 Model 109

N.11 Model 201

N.12 Model 202

N.13 Model 203

N.14 Model 204

N.15 Model 205

N.16 Model 206

N.17 Model 207

N.18 Model 208

N.19 Model 301

N.20 Model 302

N.21 Model 303

N.22 Model 304

N.23 Model 305

N.24 Model 306

N.25 Model 401

N.26 Model 402

N.27 Model 403

N.28 Model 404

N.29 Model 405

N.30 Model 406

Index

End User License Agreement

List of Illustrations

Chapter 1: Modeling

Figure 1.1 Differential element of porous media.

Figure 1.2 Conservation of mass through a differential element of porous media.

Figure 1.3 Rectangular culvert filled with sand for example application of Darcy's law and the flow equation.

Figure 1.4 Pumping well in an infinite, confined aquifer.

Figure 1.5 Annular differential element in an infinite, confined aquifer with a pumping well.

Figure 1.6 Conservation of mass through a differential element of porous media where the area of inflow to the element does not equal the area of outflow.

Figure 1.7 Using the principle of superposition to determine the hydraulic conductivity of an infinite homogeneous aquifer with two pumping wells.

Chapter 2: Contaminant Transport Modeling

Figure 2.1 Concentration profile when only advection acts.

Figure 2.2 Spherical zone of immobile water.

Figure 2.3 Conservation of mass for a sorbing chemical moving through a differential element of porous media.

Chapter 3: Analytical Solutions to 1-D Equations

Figure 3.1 Superposition used to develop a first-type finite pulse boundary condition (concentration C0 for duration ts) as the sum of two Heaviside step functions.

Figure 3.2 Output of Model 102 for Table 3.1 virtual column experiment to demonstrate the effect of advection on concentration breakthrough curves at the column outlet. D ≈ 0 m²/min, λ = 0 min−1, kd = 0 m/kg.

Figure 3.3 Output of Model 102 for Table 3.1 virtual column experiment to demonstrate the effect of advection on concentration profiles in space. t = 8 min, D ≈ 0 m²/min, λ = 0 min−1, kd = 0 m/kg.

Figure 3.4 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of dispersion on concentration breakthrough curves at the column outlet. v = 0.1 m/min, λ = 0 min−1, kd = 0 m/kg.

Figure 3.5 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of dispersion on concentration profiles in space. t = 8 min, v = 0.1 m/min, λ = 0 min−1, kd = 0 m/kg.

Figure 3.6 Output of Model 104 for an infinite one-dimensional system to demonstrate how dispersion results in Gaussian concentration profiles in space. t = 8 min, v = 0.1 m/min, λ = 0 min−1, kd = 0 m/kg.

Figure 3.7 Output of Model 104 for an infinite one-dimensional system to demonstrate how dispersion results in asymmetric breakthrough curves. x = 8 m, v = 0.1 m/min, λ = 0 min−1, kd = 0 m/kg.

Figure 3.8 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of sorption on concentration breakthrough curves at the column outlet. v = 0.1 m/min, λ = 0 min−1, D = 0.0001 m²/min, α = INF.

Figure 3.9 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of sorption on concentration profiles in space. t = 10 min, v = 0.1 m/min, λ = 0 min−1, D = 0.0001 m²/min, α = INF.

Figure 3.10 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of sorption kinetics on concentration breakthrough curves at the column outlet. v = 0.1 m/min, λ = 0 min−1, D = 0.0001 m²/min, kd = 0.167 m/kg (R = 2).

Figure 3.11 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of sorption kinetics on concentration profiles in space. t = 15 min, v = 0.1 m/min, λ = 0 min−1, D = 0.0001 m²/min, kd = 0.167 m/kg (R = 2).

Figure 3.12 Output of Model 106 for Table 3.1 virtual column experiment with α = 0.05 min−1, v = 0.1 m/min, λ = 0 min−1, D = 0.0001 m²/min, and kd = 0.167 m/kg (R = 2) to demonstrate the effect of sorption kinetics on concentration profiles in space at (a) an early time (t = 0.5 min, DaI = 0.025) and (b) a long time (t = 150 min, DaI = 7.5).

Figure 3.13 Output of Model 106 for Table 3.1 virtual column experiment with α = 0.15 min−1, v = 0.1 m/min, λ = 0 min−1, D = 0.0001 m²/min, and kd = 0.167 m/kg (R = 2) to demonstrate dual-peaked concentration profiles (a) in space (at time = 21.7 min, DaI = 3.3) and (b) in time (DaI = 3), which result from sorption kinetics.

Figure 3.14 Comparison of breakthrough curves simulated assuming sorption may be described by first-order kinetics (α = 0.05 and 0.0757 min−1) and by diffusion into spherical immobile regions (D/(b²R) = 0.0033 min−1). Table 3.1 virtual column parameter values with v = 0.1 m/min (q = 0.025 m/min), λ = 0 min−1, D = 0.0001 m²/min, and kd = 0.167 m/kg (R = 2). First-order sorption kinetics simulated by Model 106. Diffusion into spherical immobile regions simulated using a numerical code to represent Equations (2.23 a), (2.23c), (2.23d), (2.23e), with ν = 3. Breakthrough curves for (a) t = 0–100 min, and (b) t = 100–200 min.

Figure 3.15 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of first-order degradation on concentration breakthrough curves at the column outlet. v = 0.1 m/min, D = 0.0001 m²/min.

Figure 3.16 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of first-order degradation on concentration profiles in space. t = 10 min, v = 0.1 m/min, D = 0.0001 m²/min.

Figure 3.17 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of sorption on the concentration breakthrough curves at the column outlet of a degrading compound. v = 0.1 m/min, D = 0.0001 m²/min, λ = 0.05 min−1(DaI = 1), α = INF.

Figure 3.18 Output of Model 106 for Table 3.1 virtual column experiment to demonstrate the effect of sorption on concentration profiles in space of a degrading compound. t = 10 min, v = 0.1 m/min, D = 0.0001 m²/min, λ = 0.05 min−1(DaI = 0.5), α = INF.

Figure 3.19 Output of Models 102 (first-type BC at x = 0) and 106 (third-type BC at x = 0) for Table 3.1 virtual column experiment to demonstrate the effect of BC on the concentration breakthrough curves at the column outlet at high Pe. v = 0.1 m/min, λ = 0 min−1, kd = 0 m/kg, D = 0.0001 m²/min (Pe = 2000).

Figure 3.20 Output of Models 102 (first-type BC at x = 0) and 106 (third-type BC at x = 0) for Table 3.1 virtual column experiment to demonstrate the effect of BC on the concentration breakthrough curves at the column outlet at low Pe. v = 0.1 m/min, λ = 0 min−1, kd = 0 m/kg, D = 0.05 m²/min (Pe = 4).

Chapter 4: Analytical Solutions to 3-D Equations

Figure 4.1 Three-dimensional virtual aquifer system.

Figure 4.2 Output of Model 301 for the virtual three-dimensional system (Table 4.1) to demonstrate the effect of longitudinal dispersion on the maximum concentration observed at a monitoring well 1 m downgradient of the rectangular source (x = 1 m, y = 5 m, z = 3 m). Dy = Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0 L/kg, α = INF.

Figure 4.3 Output of Model 301 for the virtual three-dimensional system (Table 4.1) to demonstrate how typical ratios of longitudinal to transverse dispersion and longitudinal to vertical dispersion affect the morphology of a contaminant plume. Dx = 0.1 m²/min, Dy = 0.01 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0 L/kg, α = INF. (a) Plan view (at z = 3 m) and (b) vertical cross section (at y = 5 m) at t = 100 min. All coordinates in meters and note the axes have different scales.

Figure 4.4 Output of Model 306 for Table 4.1 virtual system soil and hydraulic characteristics (θ = 0.25, ρb = 1.5 kg/L, v = 0.1 m/min) and M = 1 mg, Dx = 0.1 m²/min, Dy = 0.01 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0 L/kg, α = INF. (a) Plan view (at z = 0 m) and (b) vertical cross section (at y = 0 m) at t = 100 min. All coordinates in meters and note the axes have different scales.

Figure 4.5 Approximate location of the center of mass in the x-direction as a function of dispersion in the x-direction, Dx (log scale), simulated by Model 304 for Table 4.1 virtual system soil and hydraulic characteristics (θ = 0.25, ρb = 1.5 kg/L, v = 0.1 m/min) and Dy = 0.01 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0 L/kg, α = INF, t = 100 min.

Figure 4.6 Concentration versus time output of Model 304 for Table 4.1 virtual system characteristics to demonstrate effect of transverse dispersion in a three-dimensional system. Dx = 0.1 m²/min, Dy = 0.01 or 0.0001 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0 L/kg, α = INF. (a) Sampling well at x = 10 m, y = 3.1 m, z = 3 m, and (b) sampling well at x = 10 m, y = 2.9 m, z = 3 m.

Figure 4.7 Concentration contours in space simulated by Model 306 for Table 4.1 virtual system soil and hydraulic characteristics (θ = 0.25, ρb = 1.5 kg/L, v = 0.1 m/min) and M = 1 mg, Dx = 0.1 m²/min, Dy = 0.01 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, α = INF. (a) Plan view (at z = 0 m) for kd = 0.0 L/kg (R = 1) at t = 100 min, (b) vertical cross section (at y = 0 m) for kd = 0.0 L/kg (R = 1) at t = 100 min, (c) plan view (at z = 0 m) for kd = 0.167 L/kg (R = 2) at t = 200 min, and (d) vertical cross section (at y = 0 m) for kd = 0.167 L/kg (R = 2) at t = 200 min. All coordinates in meters and note the axes have different scales.

Figure 3.8 Plan view at z = 0 m, t = 200 min, of concentration contours in space simulated by Model 306 for Table 4.1 virtual system soil and hydraulic characteristics (θ = 0.25, ρb = 1.5 kg/L, v = 0.1 m/min) and M = 1 mg, Dx = 0.1 m²/min, Dy = 0.01 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0.167 L/kg (R = 2). (a) α = INF, (b) α = 0.005 min−1. All coordinates in meters.

Figure 4.9 Concentration versus time output of Model 306 for Table 4.1 virtual system soil and hydraulic characteristics (θ = 0.25, ρb = 1.5 kg/L, v = 0.1 m/min) and M = 1 mg, Dx = 0.1 m²/min, Dy = 0.01 m²/min, Dz = 0.0002 m²/min, λ = 0 min−1, kd = 0.167 L/kg (R = 2), α = INF versus α = 0.005 min−1. Sampling well at x = −0.1 m, y = 0 m, z = 0 m.

Figure 4.10 Output of Model 304 for the virtual three-dimensional system (Table 4.1) at t = 200 min and ts = 100 min. Dx