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AccountingforResistanceto3DFlownear

HorizontalWellsorGalleriesina

Dupuit-ForchheimerModel

HenkM.Haitjema

May28,2006

Introduction

Asdrillingtechniquesimprove,horizontalwellsandradialcollectorwellsarebecomingmoreeconomical.Thesewellsareparticularlysuitableforshallowhighlypermeableaquifersinwhichtraditionalverticalwellshavelowyieldsduetothelimiteddrawdownthatcanberealizedinsidethewell.Horizontalwellsorradialcollectorwellshavesigni cantlyhigherwellscreenexposuretotheaquiferandcanproducelargequantitiesofwaterunderonlymoderatedraw-downconditions.Radialcollectorwellsmayhavetheirhorizontalwellscreens(laterals)pushedunderneathanearbystream,furtherincreasinggroundwaterproduction.

Bothforpurposesofthedesignofthesewellsasforthepurposeofwellheadprotectionitisnecessarytocalculatethegroundwaterin owrateintothesewellsandidentifythesourcesofthatwater.Thegroundwater owproblemnearhorizontalwellsorradialcollectorwellsisdistinctlythree-dimensionalinnature,withallthreecomponentsof ow(qx,qyandqz)beingofequalimportance.Dupuit-Forchheimermodels,whichignoreresistancetovertical ow(qz)seeminappropriateforrepresenting ownearthesewells.However,ifitissu cienttodeterminetheproductionrateofahorizontalwellorradialcollectorwell,insteadofaccuratelydepictingthe3D ow eld,aDupuit-Forchheimermodelmaybeusedprovidedthatitsomehowaccounts,ifonlyapproximately,fortheresistancetovertical ow.IfsuchaDupuit-Forchheimermodelcouldbeconstructeditmayalsobeusedtodistinguish(quantitatively)betweenthevarioussourcesfromwhichthewaterisobtained,whichisofimportanceforcapturezonedelineationinthecontextofwellheadprotection.

Resistancetoconverging owonahorizontalwellInFigure1(a)averticalsectionoverahorizontalwellorgalleryisdepictedwithitscenteratadistancehabovethebaseofacon nedaquifer.Forthe

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