Analytical Groundwater Modeling: Theory and Applications using Python

243 Pages·2022·10.261 MB·English

by  Mark Bakker, Vincent Post

Analytical Groundwater Modeling
ThisbookprovidesadetaileddescriptionofhowPythoncanbeusedtogiveinsightintothe
flowofgroundwaterbasedonanalyticsolutions.Startingwithsimpleproblemstoillustrate
thebasicprinciples,complexityisaddedstepbysteptoshowhowone-dimensionalandtwo-
dimensionalmodelsofoneortwoaquiferscanbeimplemented.Steadyandtransientflow
problemsarediscussedinconfined,semi-confined,andunconfinedaquifersthatmayinclude
wells,rivers,andarealrecharge.Specialconsiderationisgiventocoastalaquifers,including
theeffectoftidesandthesimulationofinterfaceflow.
ApplicationofPythonallowsforcompactandreadablecode,andquickvisualizationofthe
solutions.Pythonscriptsareprovidedtoreproduceallresults.Thescriptsarealsoavailable
onlinesothattheycanbealteredtomeetsite-specificconditions.Thisbookisintendedboth
as training material for the next generation of university students and as a useful resource
forpractitioners.AprimerisincludedforthosewhoarenewtoPythonorasarefresherfor
existingusers.
Mark Bakker is a groundwater engineer and a professor at the faculty of Civil Engineer-
ingandGeosciencesoftheDelftUniversityofTechnology.Hehastaughtgroundwaterand
Python classes for more than two decades and is the originator and co-developer of many
Python-basedopen-sourcemodelingtools,includingTimml,Ttim,Pastas,andFlopy.
VincentPostisahydrogeologistwithresearchinterestsincoastalhydrogeologyandground-
water quality. After a career in academia and research he founded Edinsi Groundwater in
2021. Python has become indispensable in his everyday professional life, and he actively
promotesitsuseinhydrogeologybyteachingcoursesanddevelopingPython-basedtools.

Analytical Groundwater Modeling
Theory and Applications using Python
Mark Bakker and Vincent Post
Coverillustration:EvavanAalst.https://www.evavanaalst.com/
Firstpublished2022
byCRCPress/Balkema
Schipholweg107C,2316XCLeiden,TheNetherlands
e-mail:[email protected]
www.routledge.com–www.taylorandfrancis.com
CRCPress/BalkemaisanimprintoftheTaylor&FrancisGroup,aninformabusiness
©2022Taylor&FrancisGroup,London,UK
TherightofMarkBakkerandVincentPosttobeidentifiedasauthorsofthisworkhas
beenassertedinaccordancewithsections77and78oftheCopyright,DesignsandPatents
Act1988.
Allrightsreserved.Nopartofthisbookmaybereprintedorreproducedorutilisedinany
formorbyanyelectronic,mechanical,orothermeans,nowknownorhereafterinvented,
includingphotocopyingandrecording,orinanyinformationstorageorretrievalsystem,
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damage to the property or persons as a result of operation or use of this publication
and/ortheinformationcontainedherein.
LibraryofCongressCataloging-in-PublicationData
Names:Bakker,Mark,author.|Post,Vincent,author.
Title:Analyticalgroundwatermodeling:theoryandapplicationsusing
Python/MarkBakker,FacultyofCivilEngineeringandGeosciences,
TechnicalUniversityofDelft,Delft,TheNetherlands,VincentPost,
EdinsiGroundwater,NederhorstdenBerg,TheNetherlands.
Description:FirstEdition.|BocaRaton:TaylorandFrancis,[2022]|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2021059473(print)|LCCN2021059474(ebook)|ISBN9781138605633
(Hardback)|ISBN9781138029392(Paperback)|ISBN9781315206134(eBook)
Subjects:LCSH:Groundwaterflow–Computersimulation.|Python(Computer
programlanguage)
Classification:LCCGB1197.7.B3362022(print)|LCCGB1197.7(ebook)|
DDC551.4901/13–dc23/eng20220406
LCrecordavailableathttps://lccn.loc.gov/2021059473
LCebookrecordavailableathttps://lccn.loc.gov/2021059474
ISBN:978-1-138-60563-3(hbk)
ISBN:978-1-138-02939-2(pbk)
ISBN:978-1-315-20613-4(ebk)
DOI:10.1201/9781315206134
TypesetinTimesNewRoman
bycodeMantra
Contents
Preface ix
Aboutthisbook xi
Acknowledgement xiii
Authors xv
0 Basicsofgroundwaterflow 1
0.1 Hydraulichead 1
0.2 Darcy’sexperiment 2
0.3 Representativeelementaryvolume 2
0.4 Hydraulicconductivityandporosity 3
0.5 Aquifersandaquitards 4
0.6 Storageandtransientflow 5
0.7 Darcy’slawforgroundwatermodeling 6
0.8 DupuitandForchheimer 7
0.9 Groundwatermodels 7
1 Steadyone-dimensionalflowwithconstanttransmissivity 9
1.1 Flowbetweentworivers 10
1.2 Arealrechargebetweentworivers 13
1.3 Arealrechargebetweenanimpermeableboundaryandariver 18
1.4 Flowthroughtwozonesofdifferenttransmissivities 22
2 Steadyone-dimensionalsemi-confinedflow 25
2.1 Flowfromacanaltoadrainedarea 26
2.2 Flowbetweenalakeandadrainedarea 29
2.3 Flowtoalongriveroffinitewidth 32
2.4 Flowtoariverinatwo-aquifersystem 35
2.5 Arealrechargebetweentworiversinatwo-aquifersystem 39
3 Steadyone-dimensionalunconfinedflowwithvariablesaturatedthickness 43
3.1 Arealrechargebetweenanimpermeableboundaryandariver 44
3.2 Flowoverastepintheaquiferbase 48
3.3 Combinedconfined/unconfinedflowwitharealrecharge 50
vi Contents
4 Steadyone-dimensionalflowincoastalaquifers 55
4.1 Confinedinterfaceflow 56
4.2 Unconfinedinterfaceflow 60
4.3 Combinedconfined/semi-confinedinterfaceflow 64
5 Transientone-dimensionalflow 69
5.1 Stepchangesinsurfacewaterlevel 70
5.2 Periodicchangesinsurfacewaterlevel 77
5.3 Arealrechargebetweentworivers 80
5.4 SolutionswithLaplacetransforms 87
5.5 Unconfinedflowwithvariabletransmissivity 91
6 Steadytwo-dimensionalflowtowells 95
6.1 Radiallysymmetricflowonacircularisland 98
6.2 Wellsnearriversandimpermeableboundaries 102
6.3 Wellsnearaninhomogeneityboundary 108
6.4 Wellsinasemi-confinedaquifer 110
6.5 Wellsinatwo-aquifersystem 113
7 Steadytwo-dimensionalflowtowellsinuniformbackgroundflow 117
7.1 Asinglewellinuniformbackgroundflow 117
7.2 Wellcapturezones 122
7.3 Awellinuniformbackgroundflownearariver 124
7.4 Awellinuniformbackgroundflownearariverwithaleakystreambed 129
7.5 Awellinuniformbackgroundflownearthecoast 134
8 Analyticelementmodelingofsteadytwo-dimensionalflow 137
8.1 Uniformflowandwells 137
8.2 Line-sinksformodelingriversandstreams 144
8.3 Area-sinksformodelingarealrecharge 148
9 Transienttwo-dimensionalflow 151
9.1 Wellsinconfinedandunconfinedaquifers 152
9.2 Wellswithaperiodicdischarge 158
9.3 Wellsinasemi-confinedaquifer 160
9.4 Wellswithwellborestorageandskineffect 164
9.5 Wellsinatwo-aquifersystem 167
10 Steadytwo-dimensionalflowintheverticalplane 171
10.1 Verticalanisotropy 172
10.2 Flowtoapartiallypenetratingstream 174
10.3 Flowoverastepinthebase 181
10.4 Spatiallyvaryingheadatthetopoftheaquifer 185
10.5 Interfaceflowtowardsthecoast 190
10.6 Interfaceflowbelowastripisland 194
vii
A Pythonprimer 199
A.1 Basics 200
A.2 Loopsandifstatements 203
A.3 Thenumpypackageandarrays 205
A.4 Thematplotlibpackageforvisualization 210
A.5 Functions 213
A.6 Thescipypackageforscientificcomputing 216
Numericalanswerstoselectedproblems 219
Bibliography 221
Index 225

Preface
Theimportanceofgroundwaterasawatersupplysourcecanhardlybeoverstated.Ground-
waterexistseverywhereinthesubsurface.Extractionofwaterfromaquiferssupportsliveli-
hoods,agriculture,andavarietyofeconomicactivitiesworldwide.Groundwaterisanintegral
part of the hydrological cycle where it sustains ecosystems, such as wetlands and estuaries,
andprovidesthebaseflowofstreamsandriversofallsizes.Theflowofwaterthroughthe
subsurfaceconstitutesamajor transportpathwayfordissolvedsubstancesand playsakey
roleintheplanetarycycleofmanychemicalelements.
Groundwater resources have come under enormous stress in many parts of the world.
Concerns over the quantity and quality of groundwater are the result of past and ongoing
mismanagement.Overexploitationhasresultedinsignificantloweringofwaterlevels.Unsus-
tainablepumpingincoastalareashasresultedinseawaterintrusion.Andcarelessdisposal
andhandlingofchemicalsatthelandsurfacehasresultedincontaminationthatthreatens
preciousresources.Addressingtheseproblemsispossibleonlywithadequateunderstanding
oftheflowinthesubsurface.
Theinvestigationofgroundwatersystemsreliesfirstandforemostonmeasurements.Due
to the difficulty and costs involved in obtaining these, data is commonly available at a few
pointsonly,whichseverelylimitstheknowledgeofthethree-dimensionalsystemunderinves-
tigation. It is sometimes possible to predict future developments based on measured time
series,butitisrarelypossibletomakepredictionsfrommeasuredtimeseriesfornewinter-
ventionsinthesystemorwhenanthropogenic,environmental,orclimaticchangesalterthe
system’sresponse.
Groundwatermodelsareessentialtogainunderstandingofthebehaviorofgroundwater
systemsandtoevaluatemanagementscenariosthatcannotbetestedatfullscaleinthefield.
Groundwater models, like all models, are simplified versions of a complex reality. It is an
important skill for every modeler to decide how a system can be simplified without losing
theessence.Itisunfortunatelyoftenappealingtoaddcomplexitytomodelsbecauseitexists,
eventhoughitdoesn’taffecttheoutcomesignificantly.
Theessenceofagroundwaterflowproblemiscapturedinasetofequationscalledthemath-
ematical model. Simple models can often be solved analytically. Before the advent of grid-
basedmethods,groundwatersolutionswerenecessarilysimplifieduntiltheycouldbesolved,
forexamplebyderivingananalyticsolutiontothemathematicalmodel.Analyticsolutions
giveinsightintotheflowofgroundwaterthatismoredifficulttoobtainwithgrid-basedsolu-
tions.Itisoftenforgottenthatanalyticsolutionshavebenefitedfromtheadventofcomputer
technology,justlikegrid-basedmethods.Especiallythedevelopmentofhigh-levelprogram-
minglanguagesmakesiteasytoevaluateanalyticsolutionsandvisualizetheirresults.
Modelsplayanimportantroleinsolvingtheformidablewaterproblemsofourplanet,as
theyareusedasinstrumentstobetterunderstand,manage,andprotectourwaterresources.
Theauthorshopethattheknowledgecontainedinthisbookcontributestobetterground-
watermodelsand,ultimately,better-informedmanagementdecisionsinthefuture.