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, withoutpermissioninwritingfromthepublishers. Althoughallcareistakentoensureintegrityandthequalityofthispublicationandthe informationherein,noresponsibilityisassumedbythepublishersnortheauthorforany 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.