毕业设计（论文）专用纸frommanysourcestoasingledestination.Iftheshortestpathbetweenanytwopointsisastraightline,thentheleast-costpathisthepathofleastresistance.Least-costpathanalysisusesthecostweighteddistanceanddirectionsurfacesforanareatodetermineacosteffectiveroutebetweenasourceandadestination.CriteriaforAnalysis:
Acostpathconsistsofsequentiallyconnectedlinksthatprovidetherouteforeachcelllocationtoreachasourcecell.Acostpathdistance(orcostdistance)fromanycelltoasourcecellistheaccumulativecostofalllinksalongthepathforthecelltoreachthesourcecells.Therearemanypossiblepathstoreacheachsourcecell,andtherearemanypathstoreachthemanysourcecells.Thereisoneleast-costpath,dependinguponthemodelcriteria.TofindtheleastcostpathforaproposedroutepipelinebetweentwoSabkhasinShaybahfield(SabkhaA&SabkhaB).Todothatwewillhavetokeeptheconstructioncostdown,minimizingsluggingandbackpressureofoilandalsoavoidsurfacefacilities.Thefollowingobjectivesaretobeconsidered;Theleast-costpathshouldbeprimarilycomposedoflandwithashallowslopebecausesteepterrainwillincreasetheoperatingcost.Thelongerthepath,thehighertheconstructioncosts;therefore,thedistancebetweenthetwositesneedstobeconsidered.ThefirststeptowardsleastcostpathanalysisistheconversionofcontourdatatoDigitalElevationModel(DEM)usuallydonethroughArcGISSpatialAnalystExtension.TheDEM(digitalelevationmodel)isarasterversionofthecontourdata.ThesourceofcontourdataisSurveyingServicesDivision(SSD)ofSaudiAramco.DerivingSlopeMap:
37毕业设计（论文）专用纸TheSlopehelpstoidentifythemaximumrateofchangeinsurfacevalueoveraspecificdistance,anditisexpressedindegreesorpercentage.CalculatingtheslopeisoneofmanyfunctionsofthespatialanalysttoolandthisfunctionwasusedtoderiveaslopemapfromDEM.Fig2:SlopeMapReclassSlopeMap:
TheSlopemapwasreclassifiedonascaleof1to10.Thedarkershadesrepresentareasofshallowslope,areaswhereconstructioncostswillbelessexpensive.Theresulthelpstodifferentiatetheslopeclassesandhenceprovideanopportunitywhenchoosinglocation.Fig3:ReclassMapCreatingTotalCostLayer:
Thedarkershadesindicateareasthroughwhichitwillbelesscostlytoconstruct.Thisisanexampleofaversionoftotalcost.Wecanconsidervariouscombinationsofcontributingfactors,therebycreating38毕业设计（论文）专用纸severaltotalcostsurfacealternatives.CostDistanceandCostDirectionAnalysis:
Fig5:CostDistanceFig6:CostDirectionOncetotalcostlayeriscreated,weneedtoderivecostdistanceandcostdirectionsurface.Onesurfaceisincreasingcostsaswetravelfartherawayfromthesource.Theothersurfacemodelisincreasingcostsdependingonthedirectionwearetraveling.Bothofthesesurfacesactasinputstocalculatetheleast-costpath.TheCostDistancelayerrepresentshowcostsaccumulateaswemovefurtherawayfromtheoneoftheSabkhas.Thecostdistancelayertakesintoaccountdistancemeasurementsfromthesourceandthevaluesofthetotalcostlayerforeachlocationonthemap.Thecostdirectionlayertakesintoaccountthetotalcostlayeranddeterminesthebearingtothe39毕业设计（论文）专用纸easiest(leastcostly)pathbacktothesource.Whencombined,theselayersarelikeanobstaclecourse.Thefartherawayyouare,themoreitcostsyouintime,money,orefforttoreachthegoal.Least-CostPath:
Theleast-costpathdistancefromacelltoasourcecellisthesmallest(orleast)costdistanceamongallcostpathdistancesfromthecelltothesourcecells.Forshortestorleast-costpathanalysis,weidentifyatleasttwopointsorlocations:thesourceandthedestination.UsingArcGISspatialanalystwecanFig7:Source&DestinationPointsFig8:LeastCost-Pathgenerateleastcostpathasshownaboveandalsotheshortestpathfromthesourcetothedestinations.Theresultsindicatetheoptimumroutebetweentwopoints.Theseroutesarefurtherutilizedinthepetroleumindustryforrunning40
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