Reactive and Hydraulic Behavior of Permeable Reactive Barriers Constituted by Fe0 and Granular Mixtures of Fe0/Pumice

Procedia Engineering 158 ( 2016 ) 446 – 451

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under the responsibility of the organizing and scientific committees of CNRIG2016 doi: 10.1016/j.proeng.2016.08.470

ScienceDirect

9,,7$/,$1&21)(5(1&(2)5(6($5&+(56,1*(27(&+1,&$/(1*,1((5,1*±

*HRWHFKQLFDO(QJLQHHULQJLQ0XOWLGLVFLSOLQDU\5HVHDUFKIURP0LFURVFDOHWR5HJLRQDO6FDOH

&15,*

5HDFWLYHDQGK\GUDXOLFEHKDYLRURI3HUPHDEOH5HDFWLYH%DUULHUV

FRQVWLWXWHGE\)H

_{DQGJUDQXODUPL[WXUHVRI)H}

_SXPLFH

6WHIDQLD%LODUGL

_{'RPHQLFR,HOR}

_{1LFROD0RUDFL}

_{3DROR6&DODEUz}

_

$EVWUDFW

7KHREMHFWLYHRIWKHSUHVHQWZRUNLVWRDQDO\]HE\PHDQVRIFROXPQWHVWVWKHUHDFWLYLW\DQGK\GUDXOLFORQJWHUPEHKDYLRURIWKH ]HUR YDOHQW LURQ )H_{ DQG RI D JUDQXODU PL[WXUH )H}_{SXPLFH IRU WKH UHPHGLDWLRQ WKURXJK WKH 3HUPHDEOH 5HDFWLYH %DUULHUV}

WHFKQRORJ\RIQLFNHOFRQWDPLQDWHGJURXQGZDWHU7KHUHDFWLYHEHKDYLRUZDVVWXGLHGE\DQDO\]LQJQLFNHOFRQFHQWUDWLRQGDWDWKURXJK DILUVWRUGHUNLQHWLFPRGHOLQRUGHUWRGHWHUPLQHWKHWKLFNQHVVRIDK\SRWKHWLFDO35%DQGLWVYDULDWLRQRYHUWLPH

7KH K\GUDXOLF FRQGXFWLYLW\ EHKDYLRU ZDV VWXGLHG WKURXJK D QXPHULFDOVWDWLVWLFDO JHRPHWULFDO PRGHO GHYHORSHG E\ WKH DXWKRUV ([SDQVLYHLURQFRUURVLRQSUHFLSLWDWLRQRIUHDFWLRQSURGXFWVDQGJDVIRUPDWLRQDUHWKHSURFHVVHVFRQVLGHUHG

‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU/WG

3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJDQGVFLHQWLILFFRPPLWWHHVRI&15,*

.H\ZRUGV&ROXPQWHVWVQLFNHOK\GUDXOLFFRQGXFWLYLW\VWDWLVWLFDOPRGHO

,QWURGXFWLRQ

$ SHUPHDEOH UHDFWLYH EDUULHU 35% UHSUHVHQWV D YDOLG WHFKQRORJ\ IRU VXVWDLQDEOH LQ VLWX UHPHGLDWLRQ RI FRQWDPLQDWHG JURXQGZDWHU $ 35% FRQVLVWV RI D GLDSKUDJP ZDOO ILOOHG ZLWK D UHDFWLYH PDWHULDO LQVWDOOHG SHUSHQGLFXODUO\ WR JURXQGZDWHU IORZ :KHQ FRQWDPLQDWHG JURXQGZDWHU IORZV WKURXJK WKH EDUULHU E\ PHDQV RI LWV QDWXUDOK\GUDXOLFJUDGLHQWFKHPLFDOSK\VLFDORUELRORJLFDOPHFKDQLVPVRFFXU>@

 

&RUUHVSRQGLQJDXWKRU7HOID[

(PDLODGGUHVVVWHIDQLDELODUGL#XQLUFLW

© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

7KH]HURYDOHQWLURQ)H_{LVXVXDOO\XVHGDVUHDFWLYHPHGLXPLQ35%EXWQRWZLWKVWDQGLQJLWVKLJKHIILFLHQF\LQ} FRQWDPLQDQWVUHPRYDOLWFDQEHLQHIILFLHQWLQWKHORQJWHUPEHFDXVHRILWVK\GUDXOLFEHKDYLRU7KHH[SDQVLYHQDWXUH RI)H_{FRUURVLRQSURGXFWV+} IRUPDWLRQGHULYHGE\WKHDQDHURELFFRUURVLRQRI)HDQGPLQHUDOVSUHFLSLWDWLRQDUHWKH SRVVLEOHFDXVHVRIPHGLXPFORJJLQJ$GPL[LQJ)H_{ZLWKDQRQH[SDQVLYHPDWHULDOHJJUDYHO0Q2} SXPLFHDQG VDQGLVDSRVVLEOHVROXWLRQWRVROYHWKLVSUREOHP>@

,Q RUGHU WR UHDFK D WDUJHW FRQFHQWUDWLRQ GRZQVWUHDP D 35% WKH GHWHUPLQDWLRQ RI LWV WKLFNQHVV LV FUXFLDO 7KLV SDUDPHWHUFDQEHGHWHUPLQHGE\LQWHUSUHWLQJFROXPQH[SHULPHQWVGDWDWKURXJKDILUVWRUGHUNLQHWLFPRGHODVVXJJHVWHG E\,75&>@$QRWKHUSRVVLEOHDSSURDFKWRGHWHUPLQHEDUULHUWKLFNQHVVLVWRFDOFXODWHWKHUHPRYDOFDSDFLW\RIWKH UHDFWLYHPDWHULDO>@

,QWKLVSDSHUWKHUHDFWLYHDQGK\GUDXOLFEHKDYLRURI)H_{DQGRIDJUDQXODUPL[WXUHRI)H}_{DQGSXPLFHZDVLQYHVWLJDWHG}

WKURXJKFROXPQWHVWV/RQJWHUPFROXPQH[SHULPHQWVKDYHEHHQFDUULHGRXWXVLQJ)H_{DORQHDQGDJUDQXODUPL[WXUHRI}

)H_{ DQG SXPLFH ZHLJK UDWLR  DQG V\QWKHWLF JURXQGZDWHU FRQWDPLQDWHG E\ QLFNHO DW LQLWLDO FRQWDPLQDQW}

FRQFHQWUDWLRQVRIPJ/PDLQWDLQHGFRQVWDQWIRUDOOWHVWVGXUDWLRQ

7KHVSHFLILFREMHFWLYHVRIWKHSUHVHQWZRUNDUHWRGHWHUPLQHWKLFNQHVVRIWKHEDUULHUXVLQJDILUVWRUGHUNLQHWLF PRGHOWKHGLIIHUHQFHLQWHUPRIEDUULHUWKLFNQHVVDQGOLIHVSDQEHWZHHQDEDUULHUFRPSRVHGUHVSHFWLYHO\E\)H_DQG

E\ D JUDQXODU PL[WXUH )H_{3XPLFH  PRGHOOLQJ WKH K\GUDXOLF EHKDYLRU RI WKH )H}_{ DQG D JUDQXODU PL[WXUH RI}

)H_{SXPLFHWKURXJKDQXPHULFDOVWDWLVWLFDOPRGHO} 0DWHULDOVDQGPHWKRGV 7KHXVHG)H_{LVRIWKHW\SH)(5%/$675,GLVWULEXWHGE\3RPHWRQ6S$0HVWUH,WDO\:KHUHDVWKHXVHG} SXPLFHRULJLQDWHVIURP/LSDUL$HROLDQ,VODQGV6LFLO\,WDO\7KHWZRPDWHULDOVDUHFKDUDFWHUL]HGE\DXQLIRUPJUDLQ VL]HGLVWULEXWLRQ7KHPHDQJUDLQVL]HGLVDSSUR[LPDWHO\PPDQGPPIRUWKHWZRPDWHULDOVUHVSHFWLYHO\ 7KH)H_{SXPLFHPL[WXUHZDVPL[HGDWDZHLJKWUDWLRRI7KHFRQWDPLQDWHGDTXHRXVVROXWLRQZDVSUHSDUHGE\} GLVVROYLQJQLFNHO,,QLWUDWHKH[DK\GUDWHSXULW\LQGLVWLOOHGZDWHULQRUGHUWRREWDLQLQLWLDOFRQFHQWUDWLRQRI PJ/>@

7KH H[SHULPHQWV ZHUH FDUULHG RXW E\ XVLQJ SRO\PHWK\O PHWKDFU\ODWH 300$²3OH[LJODVŒ FROXPQV ZLWK DQ LQWHUQDOGLDPHWHURI“FPDQGDKHLJKWRIFPHTXLSSHGZLWKVDPSOLQJSRUWVORFDWHGDWGLIIHUHQWGLVWDQFHV IURPWKHLQOHWDQGFPIURPLQOHW7KHLQIOXHQWVROXWLRQZDVSXPSHGXSZDUGVIURPDVLQJOH3( ERWWOHE\XVLQJDSUHFLVLRQSHULVWDOWLFSXPS,VPDWHF,60$IORZUDWH4RIPOPLQFRUUHVSRQGLQJWRD 'DUF\YHORFLW\HTXDOWRPGD\ZDVXVHGLQRUGHUWRVLPXODWHDSRVVLEOHLQVLWXILOWUDWLRQYHORFLW\>@ 7KHDTXHRXVFRQFHQWUDWLRQVRI1LZDVPHDVXUHGE\XVLQJDWRPLFDEVRUSWLRQVSHFWURSKRWRPHWU\6KLPDG]X$$± )'XULQJWKHFROXPQWHVWVK\GUDXOLFFRQGXFWLYLW\ZDVGHWHUPLQHGE\XVLQJWKHIDOOLQJKHDGRUFRQVWDQWKHDG SHUPHDELOLW\PHWKRGV>@

7KHLQLWLDOSRURVLW\QRIWKH)H_{SXPLFHPL[WXUHDQGRI)H}_{ZDVHVWLPDWHGWREHDSSUR[LPDWHO\DQG}

UHVSHFWLYHO\ QHJOHFWLQJ IRUWKH PL[WXUHWKHLQWHUQDOSRURVLW\RIWKHSXPLFH $ PDVVRIJRI)H_{DQGJRI}

SXPLFHZDVXVHGWRILOOWKHHQWLUHKHLJKWRIWKHFROXPQFPZKHUHDVWKHFROXPQZLWK)H_{ZDVILOOHGZLWKJXS}

WRDKHLJKWRIFPDQGLQHUWPDWHULDOTXDUW]JUDYHOZDVXVHGWRILOOWKHUHPDLQLQJVSDFH>@

&ROXPQWHVWVUHVXOWV

7KHFRQWDPLQDQWFRQFHQWUDWLRQPDVVSHUXQLWYROXPHPHDVXUHGDWHDFKVDPSOLQJSRUWDWWLPHWQRUPDOL]HGUHVSHFW WRWKHLQIOXHQWFRQFHQWUDWLRQ&W&FDQEHSORWWHGDJDLQVWWKHUHVLGHQFHWLPHIRUHDFKVDPSOLQJWLPHDQGDILUVWRUGHU

NLQHWLFZDVK\SRWKHVL]HGDVIROORZV W N W _H & & _    

ZKHUHN >K_{@LVWKHILUVWRUGHUNLQHWLFFRHIILFLHQW7KLVSDUDPHWHUIRUWKHFROXPQWHVWFRQWDLQHG)H}_{ZDVGHWHUPLQHG}

WKHJUDQXODUPL[WXUHWKHILUVWRUGHUNLQHWLFFRQVWDQWZDVGHWHUPLQHGFRQVLGHULQJWKHWKLFNQHVVRIWKHUHDFWLYHPHGLXP ZKLFKFRQWULEXWHVWRWKHFRQWDPLQDQWUHPRYDOZKLFKYDULHVGXULQJWKHWHVW

,Q)LJXUHDWKHN YDOXHVREWDLQHGDWHDFKVDPSOLQJWLPHDUHSORWWHGDJDLQVWWLPHKIRUWKHFROXPQFRQWDLQLQJ )H_{DQGWKHPL[WXUH)H}_{SXPLFHUHVSHFWLYHO\7KHYDOXHRIN GHFUHDVHVRYHUWLPHZKHQ)H}_{LVXVHGWKLVGHFUHDVHLV}

OHVVPDUNHGIRUWKHJUDQXODUPL[WXUH)LJD

(TXDWLRQFDQEHUHDUUDQJHGWR\LHOGWKHWLPH7UQHFHVVDU\WRPHHWDWDUJHWFRQFHQWUDWLRQ&REMHFWLYH

 OQ  N & & 7 REMHFWLYH U   

7KH WKLFNQHVV RI D 35% PD\ EH FDOFXODWHG EDVHG RQ VLWH VSHFLILF K\GURJHRORJ\ LH VHHSDJH YHORFLW\ YV WKH K\GUDXOLFJUDGLHQWGKGODQGK\GUDXOLFFRQGXFWLYLW\NDQGWKHSURSHUWLHVRIWKHUHDFWLYHPHGLXPLHSRURVLW\Q7KH PLQLPXPEDUULHUWKLFNQHVVIRUUHDFKLQJWDUJHWFRQFHQWUDWLRQ/FDQEHWKHUHIRUHFDOFXODWHGZLWKHTXDWLRQ Q GO GK N 7 Y 7 / _U˜ _{V U}    8VLQJWKHYDOXHVRIN GHWHUPLQHGDWHDFKVDPSOLQJWLPHWKURXJKHTXDWLRQDQGFRQVLGHULQJDWDUJHWFRQFHQWUDWLRQ

&REMHFWLYHHTXDOWRPJ/DVUHTXLUHGE\,WDOLDQ5HJXODWLRQ>@

6LQFHWKHUHDFWLYLW\RIWKHPDWHULDOGHFUHDVHVRYHUWLPHIRUDVHWOLIHVSDQRIWKHUHDFWLYHPDWHULDOWKHWKLFNQHVVRI WKH EDUULHU FDQ EH GHWHUPLQHG DV VKRZQ LQ )LJXUH E IRU WKH WZR GLIIHUHQW UHDFWLYH PHGLD )H_{ DQG WKH PL[WXUH}

)H_{SXPLFH7KHEDUULHUWKLFNQHVVLQFUHDVHVDOPRVWSHUIHFWO\OLQHDUO\RYHUWLPH ZKHQ)H}_{LVXVHG ZKHUHDV IRUWKH}

JUDQXODU PL[WXUH )H_{SXPLFH WKH WUHQG LV VWLOO OLQHDU EXW ZLWK VRPH IOXFWXDWLRQV )LJ E 7KH WKLFNQHVV RI WKH}

)H_{SXPLFHEDUULHUYDULHVIURPDSSUR[LPDWHO\WRPIRUJXDUDQWHHLQJWKHWDUJHWFRQFHQWUDWLRQIRUDERXWDQG} PRQWKVUHVSHFWLYHO\7KHWKLFNQHVVRID)H_{EDUULHUYDULHVIURPDSSUR[LPDWHO\WRPIRUDOLIHVSDQRI}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WKHNLQHWLFFRQVWDQWERIWKHEDUULHUWKLFNQHVVIRUWKH)H_{DQGWKHPL[WXUH)H}_SXPLFH            N  K  7LPHK )H3XPLFH1LPJO )H1LPJO D          WK LFN Q HVV  P 7LPHK )HSXPLFH1LPJO )H1LPJO E

7KHPRGHOSURSRVHGLVGHVFULEHGLQGHWDLOLQ0RUDFLHWDO>@DQGUHIHUVWRDUHDFWLYHPHGLXPFRPSRVHGE\)H_

DORQH 7KH PRGHO VLPXODWHV WKH JDV EXEEOH PRYHPHQW WKH H[SDQVLRQ RI LURQ JUDLQV GXH WR FRUURVLRQ DQG WKH SUHFLSLWDWLRQRILURQFRQWDPLQDQWFRPSRXQGV

7KHUHDFWLYH PHGLXPFRPSRVHGE\)H_{ JUDQXODUSDUWLFOHVDVVXPHGVSKHULFDOLV VFKHPDWL]HGE\D VHTXHQFHRI}

SDUDOOHO OD\HUV SODFHG XSRQ HDFK RWKHU DW D GLVWDQFH LQ WKH IORZ GLUHFWLRQ HTXDO WR WKH )H_{ PHDQ JUDLQ VL]H 7KH}

FRQVWULFWLRQVWKHQDUURZWKURDWWKDWFRQQHFWVWZRSRUHVDUHFUHDWHGE\WKHFRQWDFWRIIRXU)H_{SDUWLFOHVLQGLIIHUHQW}

FRPELQDWLRQV7KHFRQVWULFWLRQVVL]HGLVWULEXWLRQLVREWDLQHGDSSO\LQJWKHJHRPHWULFVWRFKDVWLFPHWKRGSURSRVHGE\ 6LOYHLUD>@DQG6LOYHLUDHWDO>@WRWKH)H_{JUDLQVL]HGLVWULEXWLRQ7KH)H}_{QXPHULFDOJUDLQVL]HGLVWULEXWLRQLVREWDLQHG}

IURPWKHVRLOZHLJKWJUDLQVL]HGLVWULEXWLRQFRQVLGHULQJUHODWLRQRI0XVVRDQG)HGHULFR>@,QRUGHUWRVLPXODWHWKH UDQGRPQHVV RI EXEEOHV DQG FRQVWULFWLRQV SRVLWLRQV D VDPSOLQJ VWRFKDVWLF PHWKRG RQ WKH FXPXODWHG QXPHULFDO GLVWULEXWLRQRIERWKWKHQXPEHUDQGVL]HRIFRQVWULFWLRQVDQGEXEEOHVLVDSSOLHG>@7KHVLPXODWLRQRIJDVEXEEOHV PRYHPHQWLVSHUIRUPHGE\FRPSDULQJHDFKEXEEOHFRQWDLQHGLQWKHLWKOD\HUZLWKWKHFRQVWULFWLRQVFRQWDLQHGLQWKH QH[WLWKOD\HU)LJD 7KHYROXPHRI)H_{FRUURVLRQSURGXFWV9} LURQBFRUURVLRQBSURGXFWVZDVGHWHUPLQHGWKURXJKWKHIROORZLQJODZ FRUURGHG LURQ SURGXFWV FRUURVLRQ LURQ 9 9 B B

K

ZKHUH9LURQBFRUURGHGLVWKHYROXPHRILURQFRQVXPHGLQWKHFRUURVLRQSURFHVVDQGȘLVWKH³UXVWH[SDQVLRQFRHIILFLHQW´ ZKLFK LV DVVXPHG LQ WKH SURSRVHG PRGHO HTXDO WR  ZKLFK LV WKH DYHUDJH YDOXH FDOFXODWHG DPRQJ WKH VSHFLHV GHWHFWHGGXULQJH[SHULPHQWDODFWLYLW\LH*RHWKLWHȘ +HPDWLWHȘ DQG0DJQHWLWHȘ >@

7KHLURQH[SDQVLRQYROXPH9H[SFDQEHFDOFXODWHGDFFRUGLQJHTXDWLRQ

9H[S K ˜ B   

7KHYROXPHRILURQFRUURGHG9LURQBFRUURGHG>FP@ZDVGHWHUPLQHGWKURXJKWKHLURQFRUURVLRQUDWH,URQBFRUURVLRQBUDWH FRQVLGHUHGDPRGHOFDOLEUDWLRQSDUDPHWHULWLVDVVXPHGWKDW)H_{H[SDQVLRQLVXQLIRUPIRUHDFKSDUWLFOHXVLQJHT}  B B B     _ ˜ ˜ ˜ ˜ _)H )H )H FRUURGHG

LURQ W ,URQ FRUURVLRQ UDWH 0

30 9

U  

ZKHUH30)HDQGȡ)HDUHWKHUHVSHFWLYHO\WKHPROHFXODUZHLJKW>JPRO@DQGGHQVLW\>JFP@RIWKH)HWLV

WKHWLPH>GD\@0)HLVWKHPDVVRI)H>J@  D E  )LJD6FKHPHRIFRPSDULVRQEHWZHHQEXEEOHVDQGFRQVWULFWLRQVE6FKHPDWL]DWLRQRIEXEEOHVEORFNHGDQGSDVVLQJDQG6HWLWKRISDUWLFOHV DQGYROXPHDQGVXUIDFHRYHUODSSLQJPRGLILHGE\>@ )H_SDUWLFOHV

,QDQDHURELFFRQGLWLRQLURQFRUURVLRQUHVXOWVLQWKHIRUPDWLRQRIK\GURJHQDFFRUGLQJWKHIROORZLQJHTXDWLRQ  _{ } o   + 2 )H + J 2+ )H   _     _{  } ,QWKLVUHDFWLRQPROHRIK\GURJHQJDVLVJHQHUDWHGIRUHYHU\PROHRILURQFRUURGHGE\ZDWHU.QRZLQJWKHPDVV RI )H_{ XVHG LQ WKH FROXPQ H[SHULPHQWV DQG WKH DYHUDJH LURQ FRUURVLRQ UDWH K\GURJHQ SURGXFWLRQ LV FDOFXODWHG}

DFFRUGLQJWRHTXDWLRQVDQGWKHLGHDOJDVODZ7KHDYHUDJHGLDPHWHURIJDVEXEEOHVGHSHQGVE\DQXPEHURIIDFWRUV HJSUHVVXUHDQGWHPSHUDWXUHDQGLWLVFRQVLGHUHGDPRGHOFDOLEUDWLRQSDUDPHWHU*DVEXEEOHVDUHDVVXPHGVSKHULFDO 7KH ILQDO YROXPH RI SUHFLSLWDWHV JHQHUDWHG GXULQJ FRQWDPLQDQW UHPRYDO ZDV FDOFXODWHG NQRZLQJ WKH PDVV RI FRQWDPLQDQWUHPRYHGDWWKHHQGRIWKHWHVWVGHULYHGE\DPDVVEDODQFHDQGK\SRWKHVL]LQJWKDW1LSUHFLSLWDWHVLQWKH V\VWHPDVWUHYRULWH1L)H 2GHQVLW\HTXDOWRJFPDVGHWHFWHGLQSUHYLRXVVWXGLHV>@,WZDVK\SRWKHVL]HG WKDWWKHYROXPHRISUHFLSLWDWHVLQFUHDVHVOLQHDUO\RYHUWLPHXSWRWKHILQDOYDOXH %DVHGRQWKH.R]HQ\&DUPDQHTXDWLRQWKHK\GUDXOLFFRQGXFWLYLW\NFDQEHFDOFXODWHGDV              W 0 W Q W Q 7 W N V R _    :KHUHQWLVWKHSRURVLW\LQWHUHVWHGE\WKHFRQWDPLQDWHGVROXWLRQIORZDWWLPHWDFFHVVLEOHSRURVLW\0VWLVWKH VSHFLILFVXUIDFHDUHDDWWLPHWHTXDWLRQDQG7LVDWRUWXRVLW\SDUDPHWHU)RUPRGHOOLQJSXUSRVHVLWZDVFRQVLGHUHG WKDWWKHDFFHVVLEOHSRURVLW\QWGHFUHDVHVRYHUWLPHGXHWRLLURQFRUURVLRQSURGXFWVLLFRQWDPLQDQWSUHFLSLWDWHVDQG LLLJDVEXEEOHVDUUHVWHGLQWKHRYHUDOOUHDFWLYHPHGLXPVLQFHJDVEXEEOHVFDQQRWEHFURVVHGE\WKHFRQWDPLQDWHG VROXWLRQWKH\DUHFRQVLGHUHGDVDVROLGKDYLQJDRZQYROXPHDQGVXUIDFHZKLFKFUHDWHVDQREVWUXFWLRQWRWKHIORZ 7KHUHIRUHWKHHIIHFWRISDUWLDOVDWXUDWLRQGXHWRJDVVWRSSLQJZDVFRQVLGHUHGDVDUHGXFWLRQRIDFFHVVLEOHSRURVLW\LQ VDWXUDWHGVRLOV 7KHRYHUODSSLQJYROXPHLVVXSSRVHGWREHUHGLVWULEXWHGXSRQIUHHVXUIDFHV)LJE7KHSUHVHQFHRISUHFLSLWDWHV RQ)H_{VXUIDFHZDVWDNHQLQWRDFFRXQWE\FRQVLGHULQJDXQLIRUPUHGLVWULEXWLRQRIWKHYROXPHRISUHFLSLWDWHVRQWKH)H}_ H[SDQGHGVXUIDFH7KHVSHFLILFVXUIDFH0VWFDQEHGHWHUPLQHGIURPHTXDWLRQ

7KHUHIRUH WKH VSHFLILF VXUIDFH FKDQJHV RYHU WLPH GXH WKH VXUIDFH YDULDWLRQ RI L LURQ FRUURVLRQ SURGXFWV LL SUHFLSLWDWHGFRQWDPLQDQWVDQGLLLDUUHVWHGEXEEOHV$QLQLWLDO)H_{VSHFLILFVXUIDFHDUHDHTXDOWRP}_{JLVXVHGLQ} WKHPRGHO>@:KHUHDV9VWLVWKHRYHUDOOVROLGUHDFWLYHPHGLXPYROXPHLQFOXGLQJWKHYROXPHRIWKHLLURQFRUURVLRQ SURGXFWVLLSUHFLSLWDWHGFRQWDPLQDQWVDQGLLLDUUHVWHGEXEEOHV ,WZDVQHFHVVDU\WRVLPXODWHRQO\WKHEHKDYLRURIWKHILUVWFPRIUHDFWLYHPHGLXPOD\HU[URZV[FROXPQV EHFDXVHFORJJLQJLVXVXDOO\REVHUYHGRQO\DWWKHHQWUDQFH]RQHRI)H_{V\VWHPV>@} )LJXUHVKRZVWKHYDULDWLRQRIK\GUDXOLFFRQGXFWLYLW\QRUPDOL]HGUHVSHFWWRWKHLQLWLDOYDOXHNNDVIXQFWLRQRI WLPHIRUWKH)H_{)LJDDQGWKHPL[WXUH)H}_{SXPLFH)LJE,QWKHILJXUHVWKHYDOXHVGHWHUPLQHGE\PHDQVRI}

SHUPHDELOLW\WHVWDQGWKHUHVXOWVREWDLQHGXVLQJWKHQHZSURSRVHGPRGHODUHVKRZHG7KHWZRUHDFWLYHPHGLDKDYHD GLIIHUHQWK\GUDXOLFEHKDYLRUWKHJUDQXODUPL[WXUHLVDEOHWRSUHVHUYHWKHK\GUDXOLFFRQGXFWLYLW\IRUDSHULRGJUHDWHU WKDQ D EDUULHU FRPSRVHG E\ )H_{ DORQH LQ IDFW IRU WKLV ODWWHU WKH K\GUDXOLF FRQGXFWLYLW\ GHFUHDVHV E\ ILYH RUGHU RI}

PDJQLWXGHDIWHUKDERXWPRQWKV&RQVLGHULQJWKHK\GUDXOLFEHKDYLRURI)H_{DORQH)LJDZKHQRQO\)H}_

H[SDQVLRQRU)H_{H[SDQVLRQDQGSUHFLSLWDWHVIRUPDWLRQDUHFRQVLGHUHGWKHYDULDWLRQRINN}

SURILOHVDUHOLQHDUZLWKWLPH

DQG PRGHO UHVXOWV DUH QRW DEOH WR ILW WKH H[SHULPHQWDO YDOXHV :KHQ )H_{ H[SDQVLRQ PLQHUDO SUHFLSLWDWLRQ DQG JDV}

IRUPDWLRQDUHFRQVLGHUHGWKHPRGHOLVDEOHWRPDWFKLQDPRUHVDWLVIDFWRU\ZD\WKHK\GUDXOLFFRQGXFWLYLW\UHGXFWLRQ REVHUYHGLQWKHFROXPQWHVW>@$FFRUGLQJWR PRGHOUHVXOWVK\GUDXOLFFRQGXFWLYLW\UHGXFWLRQFRXOGEHGXHWR JDV VWRSSLQJGXHWRDUHGXFWLRQLQFRQVWULFWLRQVL]HZLWKGLPHQVLRQORZHUWKDQDYHUDJHJDVEXEEOHGLDPHWHU

  )LJ([SHULPHQWDOGDWDDQGPRGHOUHVXOWVRIWKHUDWLRNNDVIXQFWLRQRIWLPHIRUD)HDQGE)HSXPLFHPL[WXUH 7KHFDOLEUDWLRQSDUDPHWHUVDUHWKHLURQFRUURVLRQUDWHPPRONJ GWKHDYHUDJHJDVEXEEOHVGLDPHWHU PPDQGWKHVWDQGDUGGHYLDWLRQıRILWVIUHTXHQF\GLVWULEXWLRQPP7KHGLVFUHWHIUHTXHQF\GLVWULEXWLRQRIWKH EXEEOHVGLDPHWHUVLVDSSUR[LPDWHGE\D*DXVVLDQGLVWULEXWLRQFKDUDFWHUL]HGE\DPHDQ³P´FDOLEUDWHGLQRUGHUWRILW WKHH[SHULPHQWDOUHVXOWV 7KHPRGHOZDVPRGLILHGIRUPRGHOOLQJWKHK\GUDXOLFFRQGXFWLYLW\RIDJUDQXODUPL[WXUHFRPSRVHGE\WZRPDWHULDOV WKH)H_{DQGDQRWKHUPDWHULDOLQWKLVFDVHSXPLFH)URPWKHJUDLQVL]HGLVWULEXWLRQLQZHLJKWRIWKHPL[WXUHREWDLQHG} IURPWKHJUDLQVL]HZHLJKWGLVWULEXWLRQRIHDFKPDWHULDODQGWDNLQJLQWRDFFRXQWWKHWZRGLIIHUHQWGHQVLWLHVDQGWKH ZHLJKWUDWLRZDVREWDLQHGWKHQXPHULFDOJUDLQVL]HGLVWULEXWLRQ,QWKHFDVHRIDPL[WXUHRIWZRVRLOVWKHQXPEHURI FRQVWULFWLRQVZKLFKDUHUHGXFHGDUHSURSRUWLRQDOWRWKHUDWLREHWZHHQWKHQXPEHURI)H_{SDUWLFOHVDQGWKHSDUWLFOHVRI} WKHRWKHUJUDQXODUPDWHULDO7KHYDULDWLRQRIWKHSRURVLW\DQGRIWKHVSHFLILFVXUIDFHHTWDNHVLQWRDFFRXQWWKLV UDWLR,QWKHPL[WXUH)H_{SXPLFHDGHFUHDVHRIK\GUDXOLFFRQGXFWLYLW\ZDVQRWREVHUYHGWKHSURILOHVREWDLQHGE\WKH} PRGHODQGUHIHUUHGWRWKHRQO\)H_{H[SDQVLRQDQGWR)H}_{H[SDQVLRQDQGSUHFLSLWDWHVIRUPDWLRQDUHDOPRVWVLPLODUGXH} WRWKHQHJOLJLEOHYROXPHRISUHFLSLWDWHVFRPSDUHGWRWKHYROXPHRIYRLGVRIWKHUHDFWLYHPHGLXPDQGWKHFRQVHTXHQWO\ QHJOLJLEOHLPSDFWRQWKHK\GUDXOLFFRQGXFWLYLW\)LJE,QRUGHUWRILWH[SHULPHQWDOUHVXOWVLQSUHVHQFHRIJDVDQ DYHUDJHJDVEXEEOHGLDPHWHUHTXDOWRPPZDVFRQVLGHUHGZKHUHDVWKHVDPHYDOXHRIWKHLURQFRUURVLRQUDWH FDOLEUDWHGLQWKHSUHYLRXVVLPXODWLRQUHIHUUHGWR)H_{DORQHZDV PDLQWDLQHG$FKDQJHRIWKHJDVEXEEOHGLDPHWHU}

UHVSHFW WR WKH )H_{ DORQH FDQ EH GXH WR WKH GLIIHUHQW JUDLQ VL]H GLVWULEXWLRQ DQG WR WKH FRQVHTXHQW YDULDWLRQ RI}

FRQVWULFWLRQVRIWKHPL[WXUHDQGWKLVFKDQJHFDQKDYHDQLPSDFWRQWKHVL]HRILQGLYLGXDOJDVEXEEOHV>@

5HIHUHQFHV

>@ ,75& ,QWHUVWDWH 7HFKQRORJ\  5HJXODWRU\ &RXQFLO 3HUPHDEOH 5HDFWLYH %DUULHU 7HFKQRORJ\ 8SGDWH 35% ,QWHUVWDWH 7HFKQRORJ\  5HJXODWRU\&RXQFLO35%7HFKQRORJ\8SGDWH7HDP:DVKLQJWRQ'&86$

>@6%LODUGL36&DODEUz10RUDFL6LPXOWDQHRXVUHPRYDORI&X,,1L,,DQG=Q,,E\DJUDQXODUPL[WXUHRI]HURYDOHQWLURQDQGSXPLFHLQ FROXPQV\VWHPV'HVDOLQDWLRQDQG:DWHU7UHDWPHQW

>@10RUDFL6%LODUGL36&DODEUz3URJHWWD]LRQHGLEDUULHUHSHUPHDELOLUHDWWLYHSHUODERQLILFDGLDFTXLIHULFRQWDPLQDWLGDPHWDOOLSHVDQWL 5LYLVWD,WDOLDQDGL*HRWHFQLFD

>@ 1 0RUDFL 6 %LODUGL 3 6 &DODEUz )HSXPLFH PL[WXUHV IURP ODERUDWRU\ WHVWV WR SHUPHDEOH UHDFWLYH EDUULHU GHVLJQ (QYLURQPHQWDO *HRWHFKQLFVGRLMHQJH >@10RUDFL0&0DQGDJOLR',HOR$QHZWKHRUHWLFDOPHWKRGWRHYDOXDWHWKHXSSHUOLPLWRIWKHUHWHQWLRQUDWLRIRUWKHGHVLJQRIJHRWH[WLOH ILOWHUVLQFRQWDFWZLWKEURDGO\JUDQXODUVRLOV&DQ*HRWHFK- >@10RUDFL0&0DQGDJOLR',HOR5HSO\WRWKHGLVFXVVLRQE\1LHWDORQ³$QDO\VLVRIWKHLQWHUQDOVWDELOLW\RIJUDQXODUVRLOVXVLQJGLIIHUHQW PHWKRGV´&DQ*HRWHFK- >@10RUDFL',HOR6%LODUGL36&DODEUz0RGHOOLQJ/RQJ7HUP+\GUDXOLF&RQGXFWLYLW\%HKDYLRXURI=HUR9DOHQW,URQ&ROXPQ7HVWVIRU 35%'HVLJQ&DQ*HRWHFK- >@$6LOYHLUD$QDQDO\VLVRIWKHSUREOHPRIZDVKLQJWKURXJKLQSURWHFWLYHILOWHUV,Q3URFHHGLQJVRIWKHWK,&60)(0RQWUHDO&DQDGD >@ $ 6LOYHLUD -U - 'H /RUHQD 3HL[RWR -% 1RJXHWHUD 2Q YRLGVL]H GLVWULEXWLRQ RI JUDQXODU PDWHULDOVWK3DQDPHULFDQ FRQIHUHQFH RQ VRLO

PHFKDQLFVDQGIRXQGDWLRQHQJLQHHULQJ%XHQRV$LUHV$UJHQWLQD >@$0XVVR))HGHULFR$JHRPHWULFSUREDELOLVWLFPHWKRGWRYHULI\ILOWHUVWDELOLW\5LYLVWD,WDOLDQDGL*HRWHFQLFD >@$55XKO0-HNHO'HJDVVLQJJDVUHWHQWLRQDQGUHOHDVHLQ)HSHUPHDEOHUHDFWLYHEDUULHUV-&RQWDP+\GURO Ϭ͘ϬϬϬϬϭ Ϭ͘ϬϬϬϭ Ϭ͘ϬϬϭ Ϭ͘Ϭϭ Ϭ͘ϭ ϭ ϭϬ Ϭ ϱϬϬϬ ϭϬϬϬϬ ϭϱϬϬϬ ϮϬϬϬϬ ϮϱϬϬϬ ϯϬϬϬϬ Ŭͬ ŬϬ ƚ;ŚͿ

EŝϴͲ &ĞϬ_{ͬƉƵŵŝĐĞͲ YсϬ͕ϭŵůͬŵŝŶ}

&Ğ &ĞнƉƌĞĐŝƉŝƚĂƚĞƐ &ĞнWƌĞĐŝƉŝƚĂƚĞƐн'ĂƐ ĞdžƉĞƌŝŵĞŶƚĂůĚĂƚĂ ďͿ