List of Symbols |
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xi | |
Preface |
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xv | |
Acknowledgments |
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xvii | |
About the Companion Website |
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xix | |
1 Modeling |
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1 | (18) |
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1 | (2) |
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3 | (1) |
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1.3 A Simple Model - Darcy's Law and Flow Modeling |
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3 | (13) |
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3 | (2) |
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5 | (3) |
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1.3.3 Example Application of Darcy's Law and the Flow Equation |
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8 | (1) |
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1.3.4 Note of Caution - Know Model Assumptions and Applicable Conditions |
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9 | (4) |
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1.3.5 Superposition (For a Fuller Discussion of Superposition Applied to Groundwater Flow, See Reilly et al., 1984) |
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13 | (1) |
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1.3.6 Example Application of the Principle of Superposition |
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13 | (3) |
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16 | (3) |
2 Contaminant Transport Modeling |
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19 | (18) |
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19 | (1) |
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2.2 Fate and Transport Processes |
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19 | (6) |
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19 | (1) |
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20 | (2) |
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22 | (2) |
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2.2.4 Chemical and Biological Reactions |
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24 | (1) |
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2.3 Advective-Dispersive-Reactive (ADR) Transport Equation |
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25 | (4) |
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27 | (1) |
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28 | (1) |
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2.3.2.1 Linear Equilibrium |
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28 | (1) |
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2.3.2.2 Rate-Limited Sorption |
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28 | (1) |
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2.4 Model Initial and Boundary Conditions |
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29 | (3) |
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30 | (1) |
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2.4.2 Boundary Conditions |
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31 | (1) |
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2.5 Nondimensionalization |
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32 | (3) |
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35 | (2) |
3 Analytical Solutions to 1-D Equations |
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37 | (34) |
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3.1 Solving the ADR Equation with Initial/Boundary Conditions |
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37 | (1) |
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3.2 Using Superposition to Derive Additional Solutions |
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38 | (2) |
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40 | (1) |
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3.3.1 AnaModelTool Software |
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40 | (1) |
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3.3.2 Virtual Experimental System |
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41 | (1) |
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41 | (2) |
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43 | (5) |
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48 | (12) |
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3.6.1 Linear, Equilibrium Sorption |
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48 | (3) |
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3.6.2 Rate-Limited Sorption |
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51 | (13) |
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3.6.2.1 First-Order Kinetics |
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51 | (6) |
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3.6.2.2 Diffusion-Limited |
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57 | (3) |
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3.7 Effect of First-Order Degradation |
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60 | (4) |
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3.8 Effect of Boundary Conditions |
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64 | (4) |
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3.8.1 Effect of Boundary Conditions on Breakthrough Curves |
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64 | (2) |
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3.8.2 Volume-Averaged Resident Concentration Versus Flux-Averaged Concentration |
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66 | (2) |
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68 | (3) |
4 Analytical Solutions to 3-D Equations |
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71 | (16) |
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4.1 Solving the ADR Equation with Initial/Boundary Conditions |
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71 | (1) |
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4.2 Using Superposition to Derive Additional Solutions |
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72 | (1) |
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4.3 Virtual Experimental System |
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72 | (1) |
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73 | (5) |
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78 | (5) |
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4.5.1 Linear, Equilibrium Sorption |
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78 | (2) |
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4.5.2 Rate-Limited Sorption |
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80 | (3) |
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4.6 Effect of First-Order Degradation |
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83 | (4) |
5 Method of Moments |
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87 | (34) |
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87 | (15) |
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87 | (1) |
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5.1.2 Evaluating Temporal Moments |
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88 | (1) |
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5.1.3 Temporal Moment Behavior |
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88 | (14) |
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5.1.3.1 Advective-Dispersive Transport with First-Order Degradation and Linear Equilibrium Sorption |
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88 | (9) |
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5.1.3.2 Advective-Dispersive Transport with First-Order Degradation and Rate-Limited Sorption |
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97 | (5) |
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102 | (18) |
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102 | (1) |
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5.2.2 Evaluating Spatial Moments |
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103 | (1) |
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5.2.3 Spatial Moment Behavior |
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104 | (16) |
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5.2.3.1 Advective-Dispersive Transport with First-Order Degradation and Linear Equilibrium Sorption |
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104 | (1) |
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5.2.3.2 Advective-Dispersive Transport with First-Order Degradation and Rate-Limited Sorption |
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105 | (15) |
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120 | (1) |
6 Application of Analytical Models to Gain Insight into Transport Behavior |
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121 | (8) |
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6.1 Contaminant Remediation |
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121 | (3) |
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6.2 Borden Field Experiment |
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124 | (3) |
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127 | (2) |
A Solution to One-Dimensional ADR Equation with First-Order Degradation Kinetics Using Laplace Transforms |
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129 | (4) |
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132 | (1) |
B Solution to One-Dimensional ADR Equation with Zeroth-Order Degradation Kinetics Using Laplace Transforms |
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133 | (4) |
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135 | (2) |
C Solutions to the One-Dimensional ADR in Literature |
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137 | (4) |
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140 | (1) |
D User Instructions for AnaModelTool Software |
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141 | (4) |
E Useful Laplace Transforms |
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145 | (6) |
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E.1 Laplace Transforms from van Genuchten and Alves (1982) |
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145 | (3) |
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148 | (3) |
F Solution to Three-Dimensional ADR Equation with |
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First-Order Degradation Kinetics for an Instantaneous Point |
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Source Using Laplace and Fourier Transforms 149 References |
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151 | (2) |
G Solution to Three-Dimensional ADR Equation with Zeroth-Order Degradation Kinetics for an Instantaneous Point Source Using Laplace and Fourier Transforms |
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153 | (4) |
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155 | (2) |
H Solutions to the Three-Dimensional ADR in Literature |
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157 | (4) |
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160 | (1) |
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) |
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161 | (2) |
J Application of Aris' Method of Moments to Calculate Temporal Moments |
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163 | (2) |
K Application of Modified Aris' Method of Moments to Calculate Spatial Moments Assuming Equilibrium Sorption |
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165 | (2) |
L Application of Modified Aris' Method of Moments to Calculate Spatial Moments Assuming Rate-Limited Sorption |
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167 | (4) |
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L.1 Zeroth Spatial Moment |
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168 | (1) |
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168 | (1) |
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L.3 Second Spatial Moment |
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168 | (3) |
M Derivation of Laplace Domain Solutions to a Model Describing Radial Advective/Dispersive/Sorptive Transport to an Extraction Well |
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171 | (4) |
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173 | (2) |
N AnaModelTool Governing Equations, Initial and Boundary Conditions, and Source Code |
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175 | (60) |
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175 | (1) |
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176 | (2) |
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178 | (1) |
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179 | (1) |
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180 | (2) |
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182 | (2) |
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184 | (1) |
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185 | (2) |
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187 | (2) |
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189 | (2) |
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191 | (2) |
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193 | (2) |
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195 | (2) |
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197 | (3) |
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200 | (1) |
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201 | (2) |
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203 | (3) |
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206 | (1) |
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207 | (3) |
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210 | (2) |
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212 | (3) |
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215 | (2) |
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217 | (3) |
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220 | (2) |
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222 | (1) |
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223 | (2) |
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225 | (2) |
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227 | (2) |
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229 | (3) |
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232 | (3) |
Index |
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235 | |