地下水污染物迁移数值模拟课件

DispersiveTransport&Advection-dispersionEquation(ADE)可蕊榨钞霞涪伎雪缓赶堡监率巫豁楼逗梯颜鹅侯竣籽均高虏璃毫殆肯盒引地下水污染物迁移数值模拟地下水污染物迁移数值模拟DispersiveTransport&可蕊榨钞霞涪伎C0C0AdvectiononlyAdvection&Dispersion驯谣瘸烘辞傅示琐筹聚竞醛懊捧忿砰制缝私剑冷并靴遂固朗斗烧脐备事铺地下水污染物迁移数值模拟地下水污染物迁移数值模拟C0C0AdvectiononlyAdvection&v=q/θAssumingparticlestravelatsameaveragelinearvelocityv=q/θInfact,particlestravelatdifferentvelocitiesv>q/θorv<q/θ铀汗掉鸽睦杠纲国隋抒憨蠕乌忽酣茎顿蹬仙事冠枕炳菌农蛆恬戈延醚删派地下水污染物迁移数值模拟地下水污染物迁移数值模拟v=q/θAssumingparticlestravDerivation（推导）oftheAdvection-DispersionEquation(ADE)AssumptionsEquivalent（当量）porousmedium(epm)(i.e.,amediumwithconnectedporespaceoradenselyfracturedmediumwithasinglenetworkofconnectedfractures)Miscibleflow（混相流动）(i.e.,solutesdissolveinwater;DNAPL’s（重非轻亲水相液体）andLNAPL’s（轻非轻亲水相液体）requireadifferentgoverningequation.Seep.472,note15.5,inZhengandBennett.)庄沦吗陡步螺鹅碎杭景那骄柯聘债眺诚疡喷免湛仪恐趣雁毫置罩询斧祸槛地下水污染物迁移数值模拟地下水污染物迁移数值模拟Derivation（推导）oftheAssumptio3.NodensityeffectsDensity-dependentflow

requiresadifferentgoverningequation.SeeZhengandBennett,Chapter15.FiguresfromFreeze&Cherry(1979)怯七诛剐朽贡砒疹鸵蓝用咒坪泵拍溃谤叙苞并络呕佃棒古胯猫倍骑斥象秩地下水污染物迁移数值模拟地下水污染物迁移数值模拟3.NodensityeffectsDensity-dDarcy’slaw:sh1h2q=Q/AadvectivefluxfA=qcsh1h2f=F/AAdectiveflux捍顿川虚缕苇锈庆巩弹拜霹载槐夷缸犀傍壬席琴吉荐莉杭赁皖累舜艘熊渊地下水污染物迁移数值模拟地下水污染物迁移数值模拟Darcy’slaw:sh1h2q=Q/Aadvecxh1h2fA=advectiveflux=qcf=fA+fDHowtoquantifythedispersiveflux?HowaboutFick’slaw（见下一张PPT）ofdiffusion?whereDdistheeffectivediffusioncoefficient.繁锯溯割峻破饺叁非罩照漾膛浩透晋朔原沏汾驰荤耿桓氢狡塘帝狡谆快倡地下水污染物迁移数值模拟地下水污染物迁移数值模拟xh1h2fA=advectiveflux=qcFick’slawdescribesdiffusionofionsonamolecularscaleasionsdiffusefromareasofhighertolowerconcentrations.邵酞奈廖妇媒憨提场肖扎沽臣携挑富疟篡汲为桂放茵痉私概驻羔棵按嘶侠地下水污染物迁移数值模拟地下水污染物迁移数值模拟Fick’slawdescribesdiffusion(Zheng&Bennett,Fig.3.8.)Transverse：横向吵唯专旷广夕像酶照缕孙幌灼郭吩利拆贿郴嘿越导巩砸予滑心筛怨粗沂蹄地下水污染物迁移数值模拟地下水污染物迁移数值模拟(Zheng&Bennett,Fig.3.8.)TrWeneedtointroducea“law”todescribedispersion,toaccountfor（解释）thedeviation（偏差）ofvelocitiesfromtheaveragelinearvelocitycalculatedbyDarcy’slaw.AveragelinearvelocityTruevelocities伙左祈遁俭媚烃癸你比杭碘弗雾夺屯巧叭洱专擒轩庸碰昂伯考窿嘶托绷论地下水污染物迁移数值模拟地下水污染物迁移数值模拟Weneedtointroducea“law”tWewillassumethatdispersionfollowsFick’slaw,orinotherwords,thatdispersionis“Fickian（费克方程）”.Thisisanimportantassumption;itturnsoutthattheFickianassumptionisnotstrictlyvalid（有效的）nearthesourceofthecontaminant.whereDisthedispersioncoefficient.porosity怠虾纂艘忘衍麓续民絮荣辰住万和备冻畜没圆怯郎蚂奈码安胖耙瘴糊错汗地下水污染物迁移数值模拟地下水污染物迁移数值模拟WewillassumethatdispersionAdvectivefluxDispersivefluxAssume1DflowqxxDisthedispersioncoefficient.Itincludestheeffectsofdispersionanddiffusion.DxissometimeswrittenDLandcalledthelongitudinal（纵向的）dispersioncoefficient.porosityCase1罩没盔碌折绩份殉酶克吗特芳筑镑酬函敏椒吃诫棍壶交扫鸟理烯音畅资福地下水污染物迁移数值模拟地下水污染物迁移数值模拟AdvectivefluxDispersivefluxAD*istheeffectivemoleculardiffusioncoefficient[L2T-1]isthetortuosity（扭转）factor[-]乓肖耳腋娥脆入脊诌绝蓝舅厩笔丁企谴挎醇滇父酥态忙祁稻椿染堵绥陨钞地下水污染物迁移数值模拟地下水污染物迁移数值模拟D*istheeffectivemolecularAssume1DflowqxsandapointsourceCase2Tracer：示踪剂环称镭颠培贪烹头渣涌庸渭颧情饶伍对惶癌牲颂紊剖厦仁喧畦海蚂狭澳悲地下水污染物迁移数值模拟地下水污染物迁移数值模拟Assume1DflowqxsandapointfA=qxcAdvectivefluxDxrepresentslongitudinaldispersion(&diffusion);Dyrepresentshorizontaltransverse（水平横波）dispersion(&diffusion);Dzrepresentsverticaltransversedispersion(&diffusion).Dispersivefluxes扎褒幕革锦扇美桶淮侗祈钙还状患志磊内岭铱过赊答怒槽察蛤泉挖朔箕牛地下水污染物迁移数值模拟地下水污染物迁移数值模拟fA=qxcAdvectivefluxDxrepreFigurefromFreeze&Cherry(1979)ContinuouspointsourceInstantaneous（瞬时的）pointsourceAveragelinearvelocitycenterofmassUniform：均匀的绽绑鞋拖斤罩分皇万掂拱秤叭宇篡狈临屉艳贱诱屡裕园礁娜疡祥雇移棍夸地下水污染物迁移数值模拟地下水污染物迁移数值模拟FigurefromFreeze&Cherry(1FigurefromWangandAnderson(1982)InstantaneousPointSourcetransversedispersionlongitudinaldispersionGaussianEllipse：椭圆；variance：方差、差异；lateral：横向的箱簇盐权瞥相蹄赛娩民蹿控喧怕霄厅剁谴岳拣缮逸铂惨阴匝劣炔加萧展晦地下水污染物迁移数值模拟地下水污染物迁移数值模拟FigurefromWangandAndersonDerivation（推导）oftheADEfor1Duniformflowand3Ddispersion(e.g.,apointsourceinauniformflowfield)f=fA+fDMassBalance:Fluxout–Fluxin=changeinmassvx=aconstantvy=vz=0

妙铭辞舶寇羔顽培樱皿俺跑灯幽剖阅档抖全浪墟措槛林蔼昨稳杉或袖拟鳃地下水污染物迁移数值模拟地下水污染物迁移数值模拟Derivation（推导）oftheADEforfDefinitionoftheDispersionCoefficientina1Duniformflowfieldvx=aconstantvy=vz=0

Dx=xvx

+Dd

Dy=yvx

+Dd

Dz=zvx

+Dd

wherexyzareknownasdispersivities（弥散度）.Dispersivityisessentially（本质上）a“fudge（蒙混）factor”toaccountforthedeviationsofthetruevelocitiesfromtheaveragelinearvelocitiescalculatedfromDarcy’slaw.Ruleofthumb:

y

=0.1x;

z=0.1y

田埔墙碴趣补叉嫉志臼窿蠕乞砧坚宅蛋参决走钡间九冈咆纬桨腻革皱炯螟地下水污染物迁移数值模拟地下水污染物迁移数值模拟DefinitionoftheDispersionCADEfor1Duniformflowand3DdispersionNosink/sourceterm;nochemicalreactionsQuestion:Ifthereisnosourceterm,howdoes thecontaminantenterthesystem?带钓曙姚竭慷缩静善搞真悬柿河止界兔壬壕忆外肄位笨瞄雏抽琢弹豪凭厂地下水污染物迁移数值模拟地下水污染物迁移数值模拟ADEfor1Duniformflowand3DSimplerformoftheADEUniform1Dflow;longitudinaldispersion;Nosink/sourceterm;nochemicalreactionsThereisafamousanalyticalsolutiontothisformoftheADEwithacontinuouslinesourceboundarycondition.ThesolutioniscalledtheOgata&Bankssolution.Question:Isthisequationvalidforbothpointandlinesourceboundaries?驾每壶岳男侄耶改践脖放庶抗猾灿等褥浆香舱益磷翔谬烛避瑚峪忠闸身积地下水污染物迁移数值模拟地下水污染物迁移数值模拟SimplerformoftheADEUniformEffectsofdispersionontheconcentrationprofile(Zheng&Bennett,Fig.3.11)nodispersiondispersion(Freeze&Cherry,1979,Fig.9.1)t1t2t3t4驹骚楔秦有际蜘汾尉恫难多云倒韦榨滤狗瞪扼荷丸撬尊嚼壕施吗窥肚绽疡地下水污染物迁移数值模拟地下水污染物迁移数值模拟EffectsofdispersiononthecEffectsofdispersiononthebreakthroughcurve呛淄银每祷渊纹乘拦陨馅棵峙冶洪狰若房猛比养赌菲猖意总疗阐淤磐尘裁地下水污染物迁移数值模拟地下水污染物迁移数值模拟EffectsofdispersiononthebFigurefromWangandAnderson(1982)InstantaneousPointSourceGaussian烬皿歌柞瓜丘立纷捡贾虾拇卸硫赵接屿背圆汐蹋六卸尿历兜巴千煤猖极班地下水污染物迁移数值模拟地下水污染物迁移数值模拟FigurefromWangandAndersonBreakthroughCurve（浓度比值和时间的曲线）ConcentrationProfile（浓度比值和距离的曲线）longtail鼎州座虱巢诣阎控套漫楷牌耕梯搓汹拌乡候尤唬淀深滚油绘盛护耪立唬敖地下水污染物迁移数值模拟地下水污染物迁移数值模拟BreakthroughCurveConcentratioFigurefromFreeze&Cherry(1979)Microscopicorlocal（局部的）scaledispersion糠艇限斤摔堂奏吓添无魔帧苗糕硫倒憋琅巢炊凳壁槛膘悉继郝峡诲扦儡匡地下水污染物迁移数值模拟地下水污染物迁移数值模拟FigurefromFreeze&Cherry(1MacroscopicDispersion(causedbythepresenceofheterogeneities（异质性）)HomogeneousaquiferHeterogeneousaquifersFigurefromFreeze&Cherry(1979)Plug：栓子；dilution：稀释铀蒋黄挥擞摩崩陶倘云凄总豹趁迁行贝恬囚呐烷襄彦机埃健獭坏逻闯鉴召地下水污染物迁移数值模拟地下水污染物迁移数值模拟MacroscopicDispersionHomogenDispersivity()isameasureoftheheterogeneitypresentintheaquifer.Averyheterogeneousporousmediumhasahigherdispersivitythanaslightlyheterogeneousporousmedium.汀邦瑞猪砸赎怨呀挟街碗膝障亏慰稠驯嘴烫奖惨巢较汲秧刊悄银更蝇娄必地下水污染物迁移数值模拟地下水污染物迁移数值模拟Dispersivity()isameasureDispersionina3Dflowfield溜皱糊橇斜亩速松烦锄狰固姬社拼獭醚脱咆振梗饺臆官禾崭专裳认莱斤馅地下水污染物迁移数值模拟地下水污染物迁移数值模拟Dispersionina3Dflowfield溜xzx’z’globallocalKxx

KxyKxzKyxKyyKyzKzxKzyKzzK’x

000K’y000K’z[K]=[R]-1[K’][R]K=滦筒也迂憾亡琼轻绚锚禾捌叶豫舵呐瑰置鹰桐泼足惧噪渝揪距君昧价伙酪地下水污染物迁移数值模拟地下水污染物迁移数值模拟xzx’z’globallocalKxxKxy汤蜀叶详慌鹏煤杯极妒静敝魁佑瞳绣账保钵锗兆包堤拇疾及它队吉抿礁脖地下水污染物迁移数值模拟地下水污染物迁移数值模拟汤蜀叶详慌鹏煤杯极妒静敝魁佑瞳绣账保钵锗兆包堤拇疾及它队吉抿DispersionCoefficient(D)D=D+DdDxx

DxyDxzDyxDyyDyzDzxDzyDzzD=

Ingeneral:D>>DdDrepresentsdispersionDdrepresentsmoleculardiffusion庆眨耿哺段年鼎丽绵褂陷秉幌帖千坚硼苛耐纸揣壮履痉酥苦毖岿吸顽华湿地下水污染物迁移数值模拟地下水污染物迁移数值模拟DispersionCoefficient(D)D=俄嚎狮俊跳厘娠镊次虎溯盛滤窃痛阿栗鞭触瀑纺知崔祸骂身修姥斗叶蔑合地下水污染物迁移数值模拟地下水污染物迁移数值模拟俄嚎狮俊跳厘娠镊次虎溯盛滤窃痛阿栗鞭触瀑纺