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Environmental Hydrogeology

by: London Stiedemann III

Environmental Hydrogeology HYDR 412

London Stiedemann III
GPA 3.83

James Osiensky

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James Osiensky
Class Notes
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This 19 page Class Notes was uploaded by London Stiedemann III on Friday October 23, 2015. The Class Notes belongs to HYDR 412 at University of Idaho taught by James Osiensky in Fall. Since its upload, it has received 56 views. For similar materials see /class/227873/hydr-412-university-of-idaho in Environmental Science & Engineering at University of Idaho.

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Date Created: 10/23/15
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I Hu d qunm arrmud Elq n 39Ftu addit39s C 3 HR eu ltult w rnieq InL11 l5 1 conced39n k39u Sadhd39 w m c n 3 nc q dw m he duu39h39un 939 AMPComm quot0m Puck s c rs l ha and 1M 5 vsHon a c cn39hnudx39 q d cunh d quh39m R quotbus 11 concennion3 F q u usxk5 shnw to spa and 39anc an be hoe 11 us quq39hnn known as ka tutu L ua S39 AS A 9C F ltmn ConA39V5 Bi A z BA 3 a c w a us n cinema In a uus mace Tkt Mums n ccnccd39rnM39un a we Sdu h uniH hmc 32 dC QMCS kow 39UN anten39kh39um 3x1 Qv 3 BVIf hc akahum K Figure 8 Man balanca in a cubic element In Ipuce Freeze and Cherry 1979 Transport Equet1ona from Freeze and cherry 1979 Refer to F1gure B A oonaervat1on of mass statement for the e1ementa1 volume cute shown in figure 8 for a nonreactive tracer in Net rate or change Flux of tracer Flux of solute or mass of tracer out or the 1nto the element wltmn the element element The average 11near ground water velocity given by V qn where e is the apea1r1c discharge and n is the porosity has three components Vx 7 and V2 The concentratmn C or a tracer is defined as the mass or traoer per unlt volume of solutmn Therefore the maaa or tracer per unit volume or a porous mea1um ls equal to the porosity time the concentration no Fur a homogeneous medium porosity n is a constant and anC n Lo 3X 3x The ma a or tracer transported in the xdlrectxon by the two mechanisms at solute transport can be represented b Transport by advectian VxnCdA Eq 1 Transport by dispersion nnxggda Eq 2 where Dx 15 the dispersion coefficient in the x dlrecticn dA 1a the urosaaectlonal area or the cubic element If Fx represents the total mass of tracer per unit cross sectional area transported in the xdirectlon per unit time then Fx vxnc nnxgr Eq 3 39 The negative Sign before the dispersive term indicates er that the tracer moves toward the znne or low concentration We can write similar expressions fur the y and 2 directions as r vync nny Eq u Pz Vznc nnz Eq 5 The total amount of tracer entering the cubic element from all three directinns is F xdydz Fydxdz dexdy Eq 6 where dx dy and dz are the dimensions of the cubic element The total amount of tracer leaving the cubic element in all three directienu 13 SF 3F 3F rxa axdzdy Fy3 yzdydxdz Ff may Eq7 The partial derivatives indicate the spatial change of tracer mass in the direction specified The difference between the amount entering and the amount leaving the cubic element is BF 22 WV 32 dxdydz Eq 8 For a nonreactive tracer the difference between the flux into the element and the flux out of the element is equal to the amount 1 tracer accumulated in the element The rate of msss change in the element is n dedydz Eq 9 If we combine Eq 3 Eq h Eq 5 and Eq 8 and cancel porosity n and the element dimensions ox dy dz from both sides we 7 3 3A 37 BC vxcl 37vyC 33vzc 33 Eq 10 a 30 a QC 3 SC 7mx ax a y um 5mm Fox39 a homogeneous medium the dispersion coefficients Dx Dy and D2 do not vary through space and Eq 10 becomes 32c 2 2 mm was D fz 3 3 i 3 BC wxm avyzvyc Ema R an 11 If the velocity v is steady and uniform 1e if it does not vary through time or space Eq 11 becomes 0 1 m a c m o x 2 Dxax Yay Zaz Eq 12 lt7 an sle ltI e m A 1 so 12 is the threedimensional sovection dispersion equation for a nonreactive tracer where gradient The equation commonly is written as g div 1 grad c v grad 0 Eq 13gt div rcpresents the divergence and gran represents the The advectiondispersion equation is subject to the following a 1 ns assumptions and 1 In onedimension where direction uf ground water flaw limit t n contaminants are soiuoie in water The fluid properties density and viscosity are independent or salute contamsnant concentration The fluid is incompressible The cuerricients or molecular diffusion and mechanical mixing are additive V qnw where w is an empirical exponent which is very nearly one in granular materials The solute is nonreactive the advectiondispersion equation is written 30 a2 as 3 DL3 v 3 Eq 1h BL is the longitudinal dispersion coefficient in the x direction The twodimensional form of the advectiondispersion equation for steady flow in the x direction and dispersion in the x directions is written as n 2 2 DL DT v Eq 15 where BL is the longitudinal dispersion coefficient in the direction of ground water flow and DT is the transverse dispersion coefficient e Conllnuuus supply 0 lmcev cl concenlrallon Co oller limelo HH Oulllow win Ian ul concentvinmn nller mm a quurl s 390 Time gt D V bleakimughiz Flrsl uppmronce i EH95 039 dispersmn 390 Time gt 1 er CCo C Lunglludinal dispersion ol 5 mm p in Ihlouqh u culumn oi pomus medium I Culumn w n nu il my ii a cumin iupplv a lace may lime to b sleplunclinnvae uacer inpul ralalion c lelalive lracal nncenlrnlinn in oulllow hum column dice iii an and solid line lluci al muchmlcll disparsion and molacular diuusiun a concanualiun pro le in ma column al valinus limes Freeze and Cherry 1979 E n a 2 n s TM Boundquot madlong raga th IN Hm hq undiu m 9d m the tab m haw Q on easenhc Mnh Ml a Cl e 411 T u Gunu rh39ua k dunnu 1 dc hutc tauh 393 com c t gt h a munhuh39n d Maul 4quot than us uv T u M anl eununh39dnn Q 3mg o t I o m cmuuhcm o 43 a hnu n W quotm Fer 1M awndu candIFuw 1m sown 1 satamtn vu um 39quothv cdvu hon an nux e unan 1 c Vt 1 L1 6 F a it P quotTAM whuu uk ht aquaAux urr und39um w n k n 0 th n Is h dudnu n un hut wpdk T 15 a nun mnc Gw uhhk DL 05 un lu Anya nunod 19 Is u xqanenhd uud oq Qquot In quv sham PORUSITY F1 re 1 Conceptual representation of the mat msco ic scale as applied to the description of a porous medium after Gillham and Cherry 1982 05mm 2 s0 Q J Crass suchum Emotirmnul warm in m lluluatinn or Dzmy aw ngruzn AFI N ERIEquot at fan mien Gussanc i a url 17 uymd humansmy m Innamg munm Hamdgnnnus Invrnni Homagenmui An snrmnic 1 1 Hemoqanaaus lsnuowc inningMann Ammlmm gure a Few 905mm mmbinlhnn no hnmlmv 3rd amnwy 391 c lt T a K a 6 a z 1 d Kn 4 Flgllrl L IIInan amtIn lawn manageer me mummw Averu re velocilge oprgd average pathIines in representative volume 000000 Actual pa 39rlines o a O o o o o a G o a 0 00 00 000000 00 D 0 50435quot 0000528 ooouc D 009 o O W 0 08 7 Q o 000000 0 New 6 Translation of ini g convechve transport Actual transport convection dispersion Q II C H II B l concent39a on distribution g I C Y 153 C I 2 We 5 QX Vvlp k k rl39 I a 013 91 Fig 3 After Preeza and Cherry 1979 l bending 0f stream39 nes variable poresize velocity pro le wifhin pore around grains Fig 4 Causes Of microscopic variations in ve39locity after Kinzelbach 1936 0 E 0 I ELL 2 I Do I ADVECTIVE 1 DISPERSION I 39 I r 1 39 DIFFUSION 4 I 0 I Illlllll l llllllll l IIIIHH 1 Hull I 1111 D 001 DJ I ID I O FTHIIII I up LONGIYUDINAL DISPERSION cosmcxsm Cruzs DaIMOLEcuLAR DIFFUSION cosFrnanmcm2s AVERAGE SOLUYION VELOCITY cms 5 u mansvsnss DISPEHSKJN wemmsm ngs Dg MOLECULAR DIFFUSION mEFFlCIENYan2s v AVERAGE39SOLLIYION VELOCIYV cm a AVERAGE DIAMEYER or we PARVICLES an 4 DwFusxm common 391 SOLID LINE I EouAnou uzr l I I IHHII I l 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