CONTAMINANT TRANSPORT MECHANICAL ASPECTS ADVECTION

Transcription

1 ONTAMINANT TRANSPORT MEHANIAL ASPETS AVETION Kdh φ dl e aerage linear elci ISPERSION/IFFUSION due ariable adecin ha ccurs in he ransiin ne beween w dmains f he fluid wih differen cmpsiins (diffusin is caused b chemical gradiens) Laer we will lk a sme fundamenal Sme NONMEHANIAL ASPETS : eca & Srpin If we nl cnsider adecin and sar wih a "pin" f maerial wih 000mg/l A pin has n lume s can i hae a cncenrain? S wh d we sa a pin? K 0. cm/sec dh 0 cm dl 00 cm φ 0. Hw lng will i ake fr he maerial me 50cm? Wha will he cncenrain be a ha lcain a ha ime?

2 Hweer cncenrain will decreasse due IFFUSION and ISPERSION In he direcin f flw we cnsider LONGITUINAL ISPERSION: Velci ariain Velci ariain Variain f wihin pres: beween pres: flw pah lenghs TRANSVERSE ISPERSION (nrmal he flw pah): Spliing f flw pahs These phsical miing prcesses are cmbined and referred as "Mechanical ispersin" Mechanical dispersin is relaed aerage pre elci b dispersii () Mechanical ispersin dispersii () unis f lengh increases wih increased heergenei and hus wih rael disance

3 iffusin: Memen f dissled species frm areas f high cncenrain lw cncenrain Fick's Law: Flu F l in pen waer fr cmmn grundwaer ins ~ m /sec * represens in prus media and is reduced due rusi and effecie prsi * ~ m /sec * φe sme sugges τ acual pah direc pah τ Transpr Equains The cmbined mechanical and chemical diffusin prcess is reaed wih a Fick's Law apprach F l l Bu here is Hdrdnamic ispersin epressed as l l l * Sudies indicae scale dependence f dispersii 3

4 ispersiiies a arius scales & measured b arius mehds as cmpiled b San ais e al. Table B in he bk "Grund Waer Tracers" Table B ONTINUE ispersiiies a arius scales & measured b arius mehds frm "Grund Waer Tracers"

5 Break hrugh ures cninuus surce saring a 0 0 iniiall fresh waer L uflw Ne wuld be aerage rael ime his pin. Wh? schemaic / fr nur / ersus lcain a ne ime alng he clumn a arius imes 3 L firs arrial aerage arrial ime 3 cnsan Graph / ersus fr 3 differen imes Graph / a ne lcain as a funcin f ime Mechanical Transpr Equains can be deried b cnsidering an elemenal lume as we did fr he flw equains We leae he deriain a laer curse & cnsider he pracical analical frms l l l l l l l l l l l l cncenrain in fluid Ne differing frm f ime flw equains spaial crdinae dispersin ensr h T h h inersiial elci S reflecs he flw direcin reflecs he direcin ranserse laerall flw reflecs he direcin ranserse ericall flw 5

6 Equain fr mechanical ranspr in - cncenrain in fluid ime spaial crdinae dispersin ensr inersiial elci Analical Sluin fr ranspr in - flw field cninuus surce spreading wihu chemical reacin This is an apprpriae mdel fr ranspr alng a sand clumn I will er esimae a if applied a case wih spreading in he ranserse laeral r erical direcins I will predic he break hrugh cures we lked a earlier c ep c c is he cmplimenar errr funcin 6

7 Errr Funcin Tables are lised in he back f grund waer hdrlg bks WARNING EXEL OES NOT APPROXIMATE THIS AURATEL AT EXTREME VALUES OF BETA Suppse ha surce eners he up gradien end f a clumn A a cninuus cncenrain f 000mg/l K 0. cm/sec dh 0 cm dl 00 cm φ 0. 0 ispersii 5 cm Wha will he cncenrain be a 50 cm afer 000sec? aerage linear elci disance raeled in 000sec? cm 0. Kdh 0cm cm sec 0.05 φ dl cm sec cm d sec sec 50cm B inspecin we knw ha he cncenrain shuld be 0.5* 500mg/l Bu le s carr u he calculain 7

8 Eperimen wih he spreadshee hp://inside.mines.edu/~epeer/_gw/namtrans/d.ls Ne he alues f using nl he firs erm and hen bh erms a imes and lcains where ur inuiin allws u knw he cncenrain. When is use f he secnd erm impran? When des ecel cause i be in errr? Tr nsider her imes. Where and when can u knw he crrec? The secnd erm is impran fr calculaing near he surce. Analical Sluin fr ranspr in - flw field slug surce 3 spreading wihu chemical reacin 8

9 Analical Sluin fr ranspr in - flw field slug surce 3 spreading wihu chemical reacin ( ( X ) 8( π) X M ep 3 IMPORTANT! X disance frm cener f mass Maimum cncenrain will ccur a he cener f mass Where X0 ma 8( π) 3 M Suppse a slug surce eners a unifrm flw field Wih an iniial mass f M 000mg K 0. cm/sec dh 0 cm dl 00 cm φ 0. dispersii 5 cm dispersii /5 dispersii /0 Wha will he cncenrain be a 50 cm direcl dwn gradien afer 000sec? 9

10 S we jus cnsidered an Analical Sluin fr ranspr in - flw field slug surce 3 spreading wihu chemical reacin ( X ) 8( π) 3 M ep X X disance frm cener f mass in each direcin NEXT Analical Sluin fr ranspr in flw field cninuus surce 3 spreading wihu chemical reacin 0

11 Analical Sluin fr ranspr in unifrm flw cninuus surce c 8 () 3 spreading wihu chemical reacin see preius graphic gap c Upper case and Are he surce widh and heigh Analical Sluin fr ranspr in unifrm flw cninuus surce 3 spreading wihu chemical c 8 () reacin If surce is n he waer able such ha spreading is nl dwnward Omi (/) n erms

12 Analical Sluin fr ranspr in unifrm flw cninuus surce 3 spreading wihu chemical reacin If surce is f full erical een in a cnfined aquifer OR if u are far frm a limied een surce in a cnfined aquifer () c hange /8 / Omi erms Suppse a surce cninuusl eners ha unifrm flw field Wih an iniial cncenrain f 000mg/l pause cnsider relainship f mass and cncenrain Mass nc * Vlume Mass/Time nc * Velci * Area nc * Q (Q is discharge) Mass nc * Q * Time Enisin he surce is submerged and emanaes frm a 0.5cm high cm wide ne pause cnsider he characer f he surce gemer 0.05 cm/sec dispersii s 5cm dispersii /5 dispersii /0 Wha will he cncenrain be a 50 cm direcl dwn gradien afer 000sec? pause cnsider he crdinae ssem

13 Wha d u make f he cncenrain relaie he we bained fr he slug surce? Hw much mass eners he ssem in 000sec? M QT AV T Hw wuld u g abu deelping a cnur map f he plume? If u did n knw he dispersiiies hw culd u use his equain esimae hem? Hw migh u se up he prblem if 8g/d arried a he waer able er a m area in an aquifer wih he prperies and cndiins used fr he eample? Analical Sluins fr ranspr pride smhed represenains f plumes Be sure pracice using his pic s eercises View an animain f cnaminan ranspr nsider hw wha u see will affec: ) he predicins u make using he analical sluins ) he cncenrains u bain in samples frm field sies View V NOW ONSIER THE NON-MEHANIAL ASPETS OF ONTAMINANT TRANSPORT 3

14 dn d r eca λn N N e where λ deca cnsan is he naural lg f 0.5 ( λ) T Fr a maerial wih a half-life f rs hw much is lef afer 0 rs? (Hin figure i as a % f iniial mass) N N ( λ ) e λ T

15 I is fen said ha maerial is esseniall gne afer 7 half-lies. Hw much is lef hen? N N ( λ ) e λ T Reardain - Adsrpin Unis K d ml mg R V ρ φ K waer b d Vcnaminan e 5

16 Wha is he Reardain efficien fr a sie wih K d 0.0ml Vwaer R mg Vcnaminan effecie prsi f 0.3 paricle densi f.65 g/cc ρ b Kd φ e Wha is he Reardain efficien fr a sie wih Grund waer elci 0.05 cm/sec naminan elci cm/sec R V ρ b K φe waer d Vcnaminan 6

17 R Equain fr ranspr in - wih eca Reardain Reacin Surce iide 's and V's b R R W( ') HEM λ R φ b φ cncenrain in fluid ime b aquifer hickness spaial crdinae dispersin ensr R reardain i cefficien i inersiial elci W surce fluid flu φ prsi ' cncenrain f surce fluid HEM chemical reacin surce/sink per uni lume f aquifer lambda deca cnsan Analical Sluin fr ranspr in unifrm flw cninuus surce 3 spreading Wih eca 7

18 8 Analical Sluin fr ranspr in unifrm flw c λ λ ep 8 ) ( c 8 () Analical Sluin fr ranspr in unifrm flw unifrm flw cninuus surce 3 spreading wih eca Upper case and Are he surce If R> iide b R unifrm flw cninuus surce 3 spreading wih eca Upper case and A h Are he surce widh and heigh Same mdificains appl fr dwnward & n erical spreading Ne his includes a simplificain f Are he surce widh and heigh Same mdificains appl fr dwnward & n erical spreading which is ignred hen equialen if * Analical Sluin fr ranspr in unifrm flw cninuus surce λ ep ) ( λ λ ep 8 ) ( Analical Sluin fr ranspr in unifrm flw cninuus surce cninuus surce 3 spreading wih eca Upper case and Are he surce widh and heigh c λ c cninuus surce 3 spreading wih eca Upper case and Are he surce widh and heigh widh and heigh ON THE ENTER LINE i.e. 0 If R> iide b R and heigh ON THE ENTER LINE

19 9 Analical Sluin fr ranspr in unifrm flw cninuus surce e seadsa λ ep ) ( λ λ ep 8 ) ( Analical Sluin fr ranspr in unifrm flw cninuus surce cninuus surce 3 spreading wih eca Upper case and Are he surce widh and heigh c cninuus surce 3 spreading wih eca Upper case and Are he surce widh and heigh widh and heigh AT STEA STATE i.e. Mass is decaing as fas as i is being supplied a he surce If R> iide b R and heigh AT STEA STATE Analical Sluin fr ranspr in unifrm flw cninuus surce 3 spreading seadsae ) ( λ λ ep 8 ) ( 3 spreading wih eca Upper case and Are he surce widh and heigh λ ep c widh and heigh STEA STATE ON THE ENTER LINE i.e. Mass is decaing as fas as i is being supplied a he surce i.e. 0 If R> iide b R

20 THINK IN TERMS OF ORGANIING THE ANALTIAL SOLUTIONS IN TERMS OF THE TPE OF SOURE: SLUG OR ONTINUOUS TPE OF SPREAING: 3 TPE OF ONTAMINANT BEHAVIOR: EAING ASORPING (and if s sead-sae? cener-line?) A ranspr mdel fr ur eplrain: hp://inside.mines.edu/~epeer/_gw/namtrans/transprmdel/dpf.0web/pflw/pflw.hml Eplre plume spreading as a funcin f heergenei as represened b K ariain AN lcal heergenei as represened b he inpu dispersii reae grid. Make sure u undersand he sie f he ssem u are wrking wih. Prperies: Run a leas hmgeneus and heergeneus mdel alculae heads hse paricle memen fr flw (his is b randm walk adecing based n Ks and gradien hen randml displacing each paricle based n dispersii) Be aware f he number f paricles u use gien spacing grid sie and ur drawn area Use he same paricles fr he abe cmparisn f hmgeneus and heergeneus mdel hse # das per secnd such ha u will ge ranspr acrss ur grid in a maer f a minue r s (make a rugh esimae f rael ime gien gradien K prsi and disance) Alwas chse shw cener f mass sd deiain bars f paricles and pl he ariance f paricle lcains. Run bh ur hmgeneus and heergeneus mdels wih and wihu lcal dispersin. When u use lcal dispersin make sure i is a reasnable alue. Tr aring he alue. Fr all cases ne he spaial ariance f he paricles. Eplain he resuls. When des i sp pling spaial ariance? Wh? 0