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

244 Pages·2017·2.98 MB·English

by  Goltz

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AnalyticalModeling
ofSoluteTransport
inGroundwater
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Analytical Modeling of Solute Transport
in Groundwater
UsingModelstoUnderstandtheEffectofNaturalProcesses
onContaminantFateandTransport
MarkGoltzandJunqiHuang
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Copyright©2017byJohnWiley&Sons,Inc.Allrightsreserved
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LibraryofCongressCataloging-in-PublicationDataappliedfor:
Names:Goltz,Mark,1951-author.|Huang,Junqi,1956-author.
Title:Analyticalmodelingofsolutetransportingroundwater:usingmodels
tounderstandtheeffectofnaturalprocessesoncontaminantfateand
transport/MarkGoltzandJunqiHuang.
Description:Hoboken,NewJersey:JohnWiley&Sons,2017.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2016054299|ISBN9780470242346(cloth)|ISBN9781119300274(epub)
Subjects:LCSH:Groundwaterflow–Mathematicalmodels.|
Groundwater–Pollution–Mathematicalmodels.
Classification:LCCGB1197.7.G652017|DDC628.1/61–dc23LCrecordavailable
athttps://lccn.loc.gov/2016054299
Coverimage:courtesyofJunqiHuang
Coverdesign:Wiley
Setin10/12ptWarnockbySPiGlobal,Chennai,India
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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v
Contents
ListofSymbols xi
Preface xv
Acknowledgments xvii
AbouttheCompanionWebsite xix
1 Modeling 1
1.1 Introduction 1
1.2 Definitions 3
1.3 ASimpleModel–Darcy’sLawandFlowModeling 3
(cid:2) 1.3.1 Darcy’sLaw 3 (cid:2)
1.3.2 FlowEquation 5
1.3.3 ExampleApplicationofDarcy’sLawandtheFlowEquation 8
1.3.4 NoteofCaution–KnowModelAssumptionsandApplicable
Conditions 9
1.3.5 Superposition(ForaFullerDiscussionofSuperpositionAppliedto
GroundwaterFlow,SeeReillyetal.,1984) 13
1.3.6 ExampleApplicationofthePrincipleofSuperposition 13
References 16
2 ContaminantTransportModeling 19
2.1 Introduction 19
2.2 FateandTransportProcesses 19
2.2.1 Advection 19
2.2.2 Dispersion 20
2.2.3 Sorption 22
2.2.4 ChemicalandBiologicalReactions 24
2.3 Advective–Dispersive–Reactive(ADR)TransportEquation 25
2.3.1 ReactionSubmodel 27
2.3.2 SorptionSubmodel 28
2.3.2.1 LinearEquilibrium 28
2.3.2.2 Rate-LimitedSorption 28
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vi Contents
2.4 ModelInitialandBoundaryConditions 29
2.4.1 InitialConditions 30
2.4.2 BoundaryConditions 31
2.5 Nondimensionalization 32
References 35
3 AnalyticalSolutionsto1-DEquations 37
3.1 SolvingtheADREquationwithInitial/BoundaryConditions 37
3.2 UsingSuperpositiontoDeriveAdditionalSolutions 38
3.3 Solutions 40
3.3.1 AnaModelToolSoftware 40
3.3.2 VirtualExperimentalSystem 41
3.4 EffectofAdvection 41
3.5 EffectofDispersion 43
3.6 EffectofSorption 48
3.6.1 Linear,EquilibriumSorption 48
3.6.2 Rate-LimitedSorption 51
3.6.2.1 First-OrderKinetics 51
3.6.2.2 Diffusion-Limited 57
3.7 EffectofFirst-OrderDegradation 60
3.8 EffectofBoundaryConditions 64
(cid:2) 3.8.1 EffectofBoundaryConditionsonBreakthroughCurves 64 (cid:2)
3.8.2 Volume-AveragedResidentConcentrationVersusFlux-Averaged
Concentration 66
References 68
4 AnalyticalSolutionsto3-DEquations 71
4.1 SolvingtheADREquationwithInitial/BoundaryConditions 71
4.2 UsingSuperpositiontoDeriveAdditionalSolutions 72
4.3 VirtualExperimentalSystem 72
4.4 EffectofDispersion 73
4.5 EffectofSorption 78
4.5.1 Linear,EquilibriumSorption 78
4.5.2 Rate-LimitedSorption 80
4.6 EffectofFirst-OrderDegradation 83
5 MethodofMoments 87
5.1 TemporalMoments 87
5.1.1 Definition 87
5.1.2 EvaluatingTemporalMoments 88
5.1.3 TemporalMomentBehavior 88
5.1.3.1 Advective–DispersiveTransportwithFirst-OrderDegradationand
LinearEquilibriumSorption 88
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Contents vii
5.1.3.2 Advective–DispersiveTransportwithFirst-OrderDegradationand
Rate-LimitedSorption 97
5.2 SpatialMoments 102
5.2.1 Definition 102
5.2.2 EvaluatingSpatialMoments 103
5.2.3 SpatialMomentBehavior 104
5.2.3.1 Advective–DispersiveTransportwithFirst-OrderDegradationand
LinearEquilibriumSorption 104
5.2.3.2 Advective–DispersiveTransportwithFirst-OrderDegradationand
Rate-LimitedSorption 105
References 120
6 ApplicationofAnalyticalModelstoGainInsightinto
TransportBehavior 121
6.1 ContaminantRemediation 121
6.2 BordenFieldExperiment 124
References 127
A SolutiontoOne-DimensionalADREquationwithFirst-Order
DegradationKineticsUsingLaplaceTransforms 129
(cid:2) Reference 132 (cid:2)
B SolutiontoOne-DimensionalADREquationwith
Zeroth-OrderDegradationKineticsUsingLaplace
Transforms 133
Reference 135
C SolutionstotheOne-DimensionalADRinLiterature 137
References 140
D UserInstructionsforAnaModelToolSoftware 141
E UsefulLaplaceTransforms 145
E.1 LaplaceTransformsfromvanGenuchtenandAlves(1982) 145
Reference 148
F SolutiontoThree-DimensionalADREquationwith
First-OrderDegradationKineticsforanInstantaneousPoint
SourceUsingLaplaceandFourierTransforms 149
References 151
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viii Contents
G SolutiontoThree-DimensionalADREquationwith
Zeroth-OrderDegradationKineticsforanInstantaneous
PointSourceUsingLaplaceandFourierTransforms 153
References 155
H SolutionstotheThree-DimensionalADRinLiterature 157
References 160
I DerivationoftheLong-TimeFirst-OrderRateConstantto
ModelDecreaseinConcentrationsataMonitoringWellDue
toAdvection,Dispersion,EquilibriumSorption,and
First-OrderDegradation(Three-DimensionalInfiniteSystem
withanInstantaneousPointSource) 161
J ApplicationofAris’MethodofMomentstoCalculate
TemporalMoments 163
K ApplicationofModifiedAris’MethodofMomentsto
CalculateSpatialMomentsAssumingEquilibrium
Sorption 165
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L ApplicationofModifiedAris’MethodofMomentsto
CalculateSpatialMomentsAssumingRate-Limited
Sorption 167
L.1 ZerothSpatialMoment 168
L.2 FirstSpatialMoment 168
L.3 SecondSpatialMoment 168
M DerivationofLaplaceDomainSolutionstoaModel
DescribingRadialAdvective/Dispersive/SorptiveTransport
toanExtractionWell 171
References 173
N AnaModelToolGoverningEquations,InitialandBoundary
Conditions,andSourceCode 175
N.1 Model101 175
N.2 Model102 176
N.3 Model103 178
N.4 Model104 179
N.5 Model104M 180
N.6 Model105 182
N.7 Model106 184
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Contents ix
N.8 Model107 185
N.9 Model108 187
N.10 Model109 189
N.11 Model201 191
N.12 Model202 193
N.13 Model203 195
N.14 Model204 197
N.15 Model205 200
N.16 Model206 201
N.17 Model207 203
N.18 Model208 206
N.19 Model301 207
N.20 Model302 210
N.21 Model303 212
N.22 Model304 215
N.23 Model305 217
N.24 Model306 220
N.25 Model401 222
N.26 Model402 223
N.27 Model403 225
N.28 Model404 227
(cid:2) N.29 Model405 229 (cid:2)
N.30 Model406 232
Index 235
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xi
ListofSymbols
a Dispersivityintheithdirection[L]
i
b Characteristiclengthofimmobileregion[L]
B Heightofaconfinedaquifer[L]
C Dissolvedcompoundconcentration[M-L−3]*
C Flux-averageddissolvedconcentration[M-L−3]*
f
C Initialdissolvedcompoundconcentration[M-L−3]*
i
C (r) Dissolvedconcentrationinanimmobileregionatcoordinate
im
r[M-L−3]*
C Inputdissolvedcompoundconcentrationorcharacteristic
0
(cid:2) dissolvedconcentration[M-L−3]* (cid:2)
C Volume-averagedresidentconcentration[M-L−3]*
̃r
C Dimensionlessconcentration= C∕ [–]
C
0
D Diffusionordispersioncoefficient[L2-T−1]
D Dispersioncoefficientintheithdirection[L2-T−1]
i 𝜆L
Da orDad Damköhlernumberfordegradation= [–]
I I 𝛼x v
Das Damköhlernumberforsorption= [–]
I v
erfc(x) Complementaryerrorfunctionofargument(x)[–]
f(s) Laplacetransformoffunctionf(t)
F(p) Fouriertransformoffunctionf(x)
H(t) Heavisidestepfunction[–]
h Hydraulichead[L]
∇h H√ydraulicgradient[–]
i −1
J Massflux[M-L−2-T−1]
→−
J Massfluxvector[M-L−2-T−1]
K Hydraulicconductivity[L-T−1]
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xii ListofSymbols
k Sorptiondistributioncoefficient[M-M−1solid]/[M-L−3
d
liquid]*
k First-ordersorptionrateconstant[T−1]
f
k Zeroth-orderrateconstant[M-L−3-T−1]*
0
L Columnlengthorcharacteristiclengthscale[L]
m orM Inputmass[M]
0
m jthabsolutespatialmoment[M-Lj−2]*
j
m jthabsolutetemporalmomentofaconcentrationversustime
j,t
breakthroughcurve[M-L−3-Tj+1]*
p Fouriertransformvariable[L−1]
vL
Pe Pecletnumber= [–]
D
x
Q Flowrate[L3-T−1]
Q Extractionwellpumpingrate[L3-T−1]
→−w
q SpecificdischargeorDarcyvelocityvector[L-T−1]
r Radialcoordinate[L]
𝜌 k
R Retardationfactor=1+ b d [–]
𝜃
r Radiusofcontaminatedzone[L]
b
r Wellradius[L]
w
s Laplacetransformvariable[T−1]
S Sorbedconcentration[M-M−1solid]
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S (r) Sorbedconcentrationinanimmobileregionatcoordinate
im
r[M-M−1solid]
s Drawdownatlocationi[L]
i
S Specificstorage[L−1]
s
t Timevariable[T]
t Durationofinputconcentrationpulse[T]
̃s
t Dimensionlesstimevariable= vt∕ [–]
→− L
v Pore,seepage,orlinearvelocityvector[L-T−1]
v Pore,seepage,orlinearvelocity[L-T−1]
v Averageporevelocityofgroundwaterinthex-direction
x
[L-T−1]
x,y,z Cartesiancoordinates[L]
x̃ Dimensionlessdistancevariable= x∕ [–]
L
𝛼 First-orderdesorptionrateconstant[T−1]
𝜌 k
𝛽 b d [–]
𝜃
𝛿(x) Diracdeltafunctioninonedimension[L−1]
𝛿(x,y,z) Diracdeltafunctioninthreedimensions[L−3]
𝜃 Watercontent=porosityinthesaturatedzone(volumeof
voidspacepervolumeofporousmedium)[–]
𝜆 First-orderdecayrateconstant[T−1]
𝜇 jthspatialmomentaboutthemeanforj≥2[Lj]
j
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