To cite this version : Özel, Ali and Sarthou, Arthur and Zeren, Zafer and
Fede, Pascal and Simonin, Olivier and Ghouila, Imen and Chamayou,
Jean-Louis Numerical Simulation of Liquid Injection into an Anisothermal Dense
Fluidized Bed. In: 8th International Conference on Multiphase Flow, ICMF
2013, 26 May 2013 - 31 May 2013 (Jeju, Korea, Republic Of).
OATAO is an open access repository that collects the work of Toulouse researchers
and makes it freely available over the web where possible.
This is an author-deposited version published in : http://oatao.univ-toulouse.fr/
Eprints ID : 11036
Any correspondance concerning this service should be sent to the repository
administrator: staff-oatao@listes-diff.inp-toulouse.fr
1XPHULFDO6LPXODWLRQRI/LTXLG,QMHFWLRQLQWRDQ$QLVRWKHUPDO'HQVH)OXLGL]HG%HG
$2]HO$6DUWKRX==HUHQ3)HGH26LPRQLQ ,*KRXLODDQG-/&KDPD\RX
8QLYHUVLWpGH7RXORXVH,137836,0)77RXORXVH)UDQFH &156,QVWLWXWGH0pFDQLTXHGHV)OXLGHVGH7RXORXVH7RXORXVH)UDQFH ,QHRV&KHPLFDOV/DYpUD6$6&HQWUHGH7HFKQRORJLH%3/DYpUD)UDQFH.H\ZRUGV7ZRIOXLGPRGHOIOXLGL]HGEHGHYDSRUDWLRQOLTXLGLQMHFWLRQ $EVWUDFW )OXLGL]HGEHGVDUHZLGHO\XVHGLQUHDFWLYHLQGXVWULDOSURFHVVHVVXFKDVROHILQVSURGXFWLRQRLOFUDFNLQJRUXUDQLXPIOXRULQDWLRQ EHFDXVH RI WKHLU KLJK HIILFLHQF\ PL[LQJ SURSHUWLHV ,Q VXFK SURFHVVHV WKH FKHPLFDO UHDFWLRQ LV VWURQJO\ GHSHQGHQW RQ WKH WHPSHUDWXUHDQGOLTXLGLVLQMHFWHGLQWRWKHUHDFWRULQRUGHUWRFRROLW7KHH[SHULPHQWDOGDWDRIWKHWLPHHYROXWLRQRIWKHJDV WHPSHUDWXUH LQ DQ DQLVRWKHUPDO GHQVH IOXLGL]HG EHG ZLWK D OLTXLG LQMHFWLRQ SURYLGHG E\ ,1(26 LV ILUVW FRPSDUHG ZLWK WKH UHVXOWV SUHGLFWHG E\ D VLPSOH PRGHO ZLWK DQ DVVXPSWLRQ RI D SHUIHFWO\ PL[HG IOXLGL]HG EHG XQLIRUP VROLG DQG WHPSHUDWXUH GLVWULEXWLRQ LQ WKH EHG 7KH UHVXOWV RI WKLV VLPSOH PRGHO VKRZ WKDW WKH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH LV DFFXUDWHO\ SUHGLFWHG$GGLWLRQDOO\ZHSRLQWRXWWKDWWKHZDOOWREHGKHDWWUDQVIHUSOD\VDFUXFLDOUROHRIWKHJDVWHPSHUDWXUHLQWKHEHG 7KHQZHSHUIRUPHG'QXPHULFDOVLPXODWLRQVWKDWOHWXVLQYHVWLJDWHORFDOLQWHUDFWLRQVEHWZHHQSKDVHVDQGKHDWWUDQVIHUZLWK ZDOO 7KH VLPXODWLRQV VKRZ WKDW WKH OLTXLG HYDSRUDWHV TXLFNO\ DQG WKH WHPSHUDWXUH LV LQ D VDWLVIDFWRU\ DJUHHPHQW ZLWK WKH H[SHULPHQWGDWD 1RPHQFODWXUH 6\PEROV GS GO 3DUWLFOH'URSOHWGLDPHWHU DN 9ROXPHIUDFWLRQRISKDVH N 8N L 0HDQYHORFLW\RISKDVH N 9UL 0HDQUHODWLYHYHORFLW\ EHWZHHQJDVDQGGLVSHUVHG SKDVHV +N (QWKDOS\RISKDVH N 7N 7HPSHUDWXUHRISKDVH N <YDS /LTXLGYDSRXUPDVVIUDFWLRQ FG 1XPEHURIGHQVLW\RIGURSOHWV *O ,QWHUIDFLDOPDVVWUDQVIHU ,JoN 0HDQGUDJIRUFHJDVWR GLVSHUVHGSKDVH 6N LM (IIHFWLYHVWUHVVWHQVRURI SKDVH N ON %XONYLVFRVLW\RISKDVH PN 9LVFRVLW\RISKDVH N 3J *DVSUHVVXUH JL *UDYLW\ TN 'LVSHUVHGSKDVHDJLWDWLRQV WJS ) &KDUDFWHULVWLFUHOD[DWLRQWLPH VFDOH WJO 7 &KDUDFWHULVWLF FRQYHFWLRQGLIIXVLRQKHDW WUDQVIHUWLPHVFDOH 9G L 'ULIWYHORFLW\ 5HS 5H\QROGVQXPEHU 6K 6F %0 6KHUZRRG6FKPLGW6SDOGLQJ QXPEHU 6XEVFULSWV J *DVSKDVH S 3DUWLFOHSKDVH O /LTXLGSKDVH ,QWURGXFWLRQ
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
VDIHW\UHDVRQVRIWKHLQGXVWULDOSURFHVVHVDVZHOO
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
,Q WKH SUHVHQW ZRUN ZH ILUVW XVH D VLPSOH PRGHO WR SUHGLFW WKH WLPH HYROXWLRQ RI WKH WHPSHUDWXUH LQ D JDVOLTXLG±VROLG IOXLGL]HG EHG ZLWK WDNLQJ LQWR DFFRXQW WKH ZDOOWREHG KHDW WUDQVIHU 7KLV PRGHO DOORZV XV WR UDSLGO\ WHVW WKH GLIIHUHQW SDUDPHWHUVRIKHDWWUDQVIHUPRGHOLQJ7KHQZHSHUIRUPHGD QXPHULFDO VLPXODWLRQ RI JDVOLTXLG VROLG IOXLGL]HG EHG E\ XVLQJ WKH (XOHULDQ(XOHULDQ PRGHOLQJ DSSURDFK GHYHORSHG E\ 6LPRQLQ
WR LQYHVWLJDWH WKH ORFDO LQWHUDFWLRQ EHWZHHQSKDVHV7KLVDSSURDFKKDVEHHQDOUHDG\H[WHQVLYHO\ XVHGWRSUHGLFWYDULRXVW\SHVRIGLOXWHDQGGHQVHPXOWLSKDVH IORZV VXFK DV WXUEXOHQW URXQG MHWV 6LPRQLQ SDUWLFOHODGHQ FRQILQHG IORZV +H DQG 6LPRQLQ IOXLGL]HG EHGV %DO]HU HW DO DQG*RELQ HW DO XUDQXLXP IORXUDWLRQ .RQDQ 7KLV PRGHO QRW RQO\ DFFRXQWV IRU SDUWLFOH±SDUWLFOH FROOLVLRQV EXW DOVR IRU WKH GUDJLQGXFHG HIIHFWV RI WKH LQWHUVWLWLDO IOXLG $Q (XOHULDQ QIOXLG PRGHOOLQJ DSSURDFK IRU IOXLGSDUWLFOH WXUEXOHQW SRO\GLVSHUVHG IORZV LPSOHPHQWHG E\ ,0)7 ,QVWLWXW GH 0pFDQLTXHGHV)OXLGHGH7RXORXVHLQWKH1(3781(B&)'Y#7OVH YHUVLRQ 1(3781(B&)' LV D PXOWLSKDVH IORZ
VRIWZDUH GHYHORSHG LQ WKH IUDPHZRUN RI WKH 1(3781( SURMHFW ILQDQFLDOO\ VXSSRUWHG E\ &($ &RPPLVVDULDW j O¶(QHUJLH $WRPLTXH (') (OHFWULFLWp 'H )UDQFH ,561 ,QVWLWXW GH 5DGLRSURWHFWLRQ HW GH 6UHWp 1XFOpDLUH DQG $5(9$13VHHIRUWKHSDUDOOH]DWLRQHIILFLHQF\RIWKHFRGH 1HDXHWDO ([SHULPHQWDO)DFLOLW\ 7KH H[SHULPHQWDO VWXG\ ZDV FRQGXFWHG E\ ,1(26 7KH JHRPHWU\LVDSLORWVFDOHIOXLGL]HGEHGZLWKDGRPHPRXQWHG DW WKH WRS VHH )LJXUH $ PL[WXUH RI QLWURJHQ DQG
QKH[DQH ZLWK WKH WHPSHUDWXUH &R IOXLGL]HG WKH VROLG SKDVH7KHQ OLTXLG SHQWDQH ZLWK D ORZHU WHPSHUDWXUHZDV LQMHFWHGDWWKHVSHFLILFKHLJKWGXULQJ V7KHGHQVLW\DQG YLVFRVLW\ RI WKH IOXLGL]DWLRQ JDV LV NJ P
DQG
u3DV UHVSHFWLYHO\ 7KH VROLG PDVV RI WKH EHG LV
NJ DQGSDUWLFOHVDUHRIDGLDPHWHURI PP7KH GHQVLW\ RI VROLG SDUWLFOH LV NJ P
DQG WKH GHQVLW\ RI OLTXLG SHQWDQH LV DURXQGNJ P
7KH VSHFLILF KHDW FDSDFLW\ RI WKH IOXLGL]DWLRQ JDV VROLG SDUWLFOHV OLTXLG SHQWDQH DQG SHQWDQH YDSRXU LV RI - NJ. UHVSHFWLYHO\'XULQJWKHH[SHULPHQWWKHJDVWHPSHUDWXUHZDV UHFRUGHGDWVHYHUDOORFDWLRQVRIWKHIOXLGL]HGEHG )LJXUH7KHIOXLGL]HGEHGJHRPHWU\ $6LPSOH0RGHO
7R GHWHUPLQH WKH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH LQ WKH EHG D VLPSOH PRGHO LV ILUVW SURSRVHG ZLWK D IHZ DVVXPSWLRQV7KHWHPSHUDWXUHDQGVROLGSKDVHGLVWULEXWLRQLV XQLIRUP LQ WKH EHG 7E 7J 7S ZKHUH 7E LV WKH EHG
WHPSHUDWXUHDQG JUHIHUVWRWKHJDVSKDVH O UHIHUVWRVROLG SKDVH DQG S UHIHUV WR WKH VROLG SKDVH 7KH HYDSRUDWLRQ RFFXUVZLWKLQILQLWHUHDFWLRQUDWHDQGWKHUHLVQRUHDFWLRQRI *DV PL[WXUH 3HQWDQH YDSRXU 3HQWDQH OLTXLG )OXLGL]DWLRQJDVPL[WXUH
7KH ILUVW WHUP RQ WKH OHIWKDQG VLGH UHSUHVHQWV WKH HQHUJ\ VXSSOLHG E\ WKH IOXLGL]DWLRQ JDV 7KH VHFRQG WHUP LV WKH HQHUJ\ WUDQVIHU EHWZHHQ WKH JDV SKDVH DQG OLTXLG SHQWDQH GXH WR WKH HYDSRUDWLRQ 7KH WKLUG RQH LV WKH HQHUJ\ WKDW OHDYHVWKHEHGDQGWKHODVWWHUPLVWKHKHDWIOX[EHWZHHQWKH ZDOO DQG WKH EHG (EHG LV WKH WRWDO HQHUJ\ LQ WKH EHG
P J
P ODQG P RXWDUHWKHPDVVIOX[RIWKHIOXLGL]DWLRQJDVOLTXLG SHQWDQH DQG DW WKH EHG RXWOHW UHVSHFWLYHO\ 7E DQG 7Z DUH WKH EHG DQG WKH ZDOO WHPSHUDWXUH /YDS LV ODWHQW
KHDW RI YDSRUL]DWLRQ RI OLTXLG SHQWDQH FSJ DQG FSO DUH
WKH VSHFLILF KHDW FDSDFLW\ RI WKH IOXLGL]DWLRQ JDV DQG WKH OLTXLG 6ZDOO LV WKH WRWDO VXUIDFH RI WKH ZDOO DQG KZDOO LV
WKH KHDW WUDQVIHU FRHIILFLHQW EHWZHHQ WKH EHG DQG WKH ZDOO 7KHJDVPL[WXUHVSHFLILFKHDW FSJ
LVJLYHQE\ F SJ F
SJ <YDS FSYDS<YDS
ZLWKWKHPDVVIUDFWLRQRIWKHOLTXLGYDSRU <YDS GHILQHGDV
<YDS P O P O P J H[S P O P J PJ7E ª ¬ « « º ¼ » » P O P O P J ZKHUH PJLVWKHWRWDOJDVPDVVLQWKHEHG7KHWHPSHUDWXUH RIWKHEHG 7ELVFDOFXODWHGE\ 7E (EHG PJF SJ PSFS S
$ VNHWFK RI WKH EHG ZDOO LV LOOXVWUDWHG LQ )LJXUH :H DVVXPHWKDWWKHJODVVZRRORIWKHZDOOLVDGLDEDWLF7KHKHDW WUDQVIHU FRHIILFLHQW KZ>:P
.@ PXVWEHPRGHOHGLQWHUPV RI PDQ\ IDFWRUV VXFK DV WKH SDUWLFOH SURSHUWLHV WKH ZDOO HPLVVLYLW\ RU WKH EHG VROLG FRQFHQWUDWLRQ :H WHVWHG WKH GLIIHUHQW ERXQGDU\ FRQGLWLRQV DQG WKH KHDW WUDQVIHU FRHIILFLHQW IRUWKHZDOOWRLQYHVWLJDWHWKHHIIHFWRIWKHKHDWWUDQVIHUGXHWR WKHZDOORQWKHFRROLQJRIWKHEHG7KHUHVXOWVDUHJLYHQLQWKH ODVWVHFWLRQ )LJXUH7KHVFKHPDWLFYLHZRIWKHZDOO 0XOWL)OXLG(XOHULDQ$SSURDFK
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
0DVVDQG0RPHQWXP%DODQFH(TXDWLRQV
7KH PXOWLIOXLG PDVV EDODQFH HTXDWLRQ IRU WKH HDFK SKDVH LVZULWWHQ w wW
DJUJ w w[L DJUJ8NL *O w wWDOUO w w[LDOUO8N L *O w wWDSUS w w[L DSUS8N L ZLWK *OLVWKHPDVVWUDQVIHUEHWZHHQOLTXLGDQGJDVSKDVH
DNUS8N L DUH WKH YROXPH IUDFWLRQ GHQVLW\ DQG PHDQ
YHORFLWLHVRIWKHSKDVH N UHVSHFWLYHO\ 7KHPRPHQWXPEDODQFHHTXDWLRQIRUWKHJDVSKDVHLV w wW
DJUJ8JL w w[MDJUJ8J M8JL DJ w3J w[L DJUJJL w w[M 6JLM ,JoN NzJ¦
*O8VL8JL DQGIRUWKHOLTXLGSKDVH w wWDOUO8OL w w[MDOUO8O M8O L DO w3J w[L DOUOJL w w[M6OLM ,OoJ *O8VL8L 8VL UHSUHVHQWVWKH L WK FRPSRQHQWRIWKHPHDQYHORFLW\RI PDVVSDVVLQJWKURXJKWKHLQWHUIDFHEHWZHHQWKHJDVDQGWKH OLTXLG SKDVH ,W LV DVVXPHG WR EH HTXDO WR WKH PHDQ OLTXLG SKDVHYHORFLW\ 8OL7KHPRPHQWXPEDODQFHHTXDWLRQIRUWKHSDUWLFXODWHSKDVH LV
JUDYLW\ JL WKH HIIHFWLYH VWUHVV WHQVRU 6N LM WKH PHDQ GUDJ
IRUFHEHWZHHQWKHJDVSKDVHWRWKHGLVSHUVHSKDVH ,JoN
(QHUJ\%DODQFH(TXDWLRQV
7KH WUDQVSRUW HTXDWLRQ RI WKH HQHUJ\ LV FRQVLGHUHG IRU WKH WRWDOHQWKDOS\7KHHQWKDOS\EDODQFHRIWKHJDVSKDVHLV w wW
DJUJ+J w w[L DJUJ+J8JL w w[L DJUJ.J w+J w[L § ©¨ · ¹¸ DNUNFSN 7J 7N WJN7 § © ¨ ·¹¸ NzJ¦
*O+V +J DQGIRUWKHOLTXLGSKDVH w wWDOUO+O w w[L DOUO+O8O L w w[L DOUO.O w+J w[L § ©¨ · ¹¸ DOUOFSO 7O 7J WJO7 *O+V +JZKHUH +VLV WKH WUDQVIHU RI WKH HQWKDOS\ IURP WKH OLTXLG
SKDVH WR WKH JDV SKDVH LI WKHUH LV HYDSRUDWLRQ RU IURP WKH JDVSKDVHWRWKHOLTXLGSKDVHLIWKHUHLVFRQGHQVDWLRQ:LWK DQ DVVXPSWLRQ WKH UHDFWLRQ LV GLUHFWO\ UHOHDVHG LQ WKH VXUURXQGLQJJDVWKHPHDQHQWKDOS\SDVVLQJWKURXJKSKDVH LQWHUIDFH LV VHW WR WKH HQWKDOS\ RI WKH HYDSRUDWHG OLTXLG +V +O
7KH WUDQVSRUW HTXDWLRQ RI HQWKDOS\ IRU WKH SDUWLFXODWH SKDVHLV w wW
DSUS+S w w[L DSUS+S8SL w w[L DSUS.S w+S w[L § ©¨ · ¹¸ DOUOFSO 7S 7J WJO7 )UHDF7KHWHUP )UHDFLVHQHUJ\ VRXUFHWHUPGXHWRUHDFWLRQVXFK
DV SRO\PHUL]DWLRQ WKH KHDW H[FKDQJHG GXULQJ WKH SDUWLFOHSDUWLFOHFROOLVLRQ:HQHJOHFWHGWKHKHDWH[FKDQJHG GXULQJ WKH SDUWLFOHSDUWLFOH FROOLVLRQV DQG WKHUH LV QR UHDFWLRQ EHWZHHQ WKH JDV DQG WKH SDUWLFXODWH SKDVH 7KH FRQYHFWLRQGLIIXVLRQ KHDW WUDQVIHU EHWZHHQ WKH GLVSHUVHG SKDVHV DQG WKH JDV SKDVH LV PRGHOHG DFFRUGLQJ WR WKH IROORZLQJWHUP
DNUNFSN7N 7J
WJN 7
DQG .N LV WKH HIIHFWLYH SKDVH GLIIXVLYLW\ LQ WKH HQWKDOS\
HTXDWLRQV7KHWHPSHUDWXUHRIHDFKSKDVHLVFDOFXODWHGE\ +J FSJ 7J 7J +O FSO7O 7O +O 7O +S FS S 7S 7S 7J LV FKRVHQ DV WKH UHIHUHQFH WHPSHUDWXUH DQG WKHQ +JYDS7J DQG +J7J LV HTXDO WR ]HUR FSN LV WKH
VSHFLILF KHDW RI WKH SKDVH N DQG WKH VSHFLILF KHDW RI JDV F SJ
LV D IXQFWLRQ RI WKH ORFDO FRQFHQWUDWLRQ RI OLTXLG YDSRUFDOFXODWHGE\
F SJ <
YDSFSYDS <YDSFSJ
<YDS LV WKH PDVV IUDFWLRQ RI WKH OLTXLG YDSRU DQG WKH
WUDQVSRUWHTXDWLRQRIWKH PDVVIUDFWLRQRIWKHOLTXLGYDSRU LVJLYHQLQWKHQH[WVHFWLRQ (YROXWLRQRI7KH'URSOHW6L]HV 7KHOLTXLGYDSRULVGLVSHUVHGLQWKHJDVSKDVHE\PROHFXODU )LFN¶VODZDQGWXUEXOHQWPRWLRQV7KHWUDQVSRUWHTXDWLRQ RIWKHPDVVIUDFWLRQRIWKHOLTXLGYDSRULV w wW
DJUJ<YDS w w[L DJUJ<YDS8JL w w[L DJUJ'YDS w<YDS w[L § ©¨ · ¹¸ *O<YDS *OZKHUH 'YDSLVWKHPROHFXODUGLIIXVLYLW\FRHIILFLHQWDQGLWLV HTXDOWR u
NJ PV
7R GHWHUPLQH WKH GURSOHW VL]H ZH XVH WKH QXPEHU FG RI
GURSOHWVSHUXQLWYROXPH:LWKDQDVVXPSWLRQRIVSKHULFDO GURSOHWVWKHQXPEHURIGURSOHWVLV
FG
SUOGO
:H QRUPDOL]H WKH QXPEHU RI GURSOHWV ;GE\ WKH LQLWLDO
QXPEHURIGURSOHWV FG FG FG 7KHWUDQVSRUWHTXDWLRQRI FG LVJLYHQE\ w wW DOUOFG
w w[M DOUOFG 8O L w w[L DOUO'YDS W wFG w[L § ©¨ · ¹¸ *OFG ZKHUH 'YDS W LV WKH GLIIXVLYLW\ FRHIILFLHQW GXH WR WKH WUDQVSRUW E\ WKH OLTXLG SKDVH IOXFWXDWLRQV 7KHQ ZH FDQ REWDLQ WKH GLDPHWHU RI WKH GURSOHW E\ WKH IROORZLQJ HTXDWLRQ GO GO FG ZKHUH GOLV WKH LQLWLDO GURSOHW GLDPHWHU :LWK DQ DVVXPSWLRQ RI D LGHDO JDV WKH GHQVLW\ RI JDV UJ LV
JRYHUQHGE\
UJ 3J:J 5J7J
ZKHUH :JDQG 5JDUHWKHJDV PRODUDQGWKHJDVFRQVWDQW
UHVSHFWLYHO\
,QWHUIDFLDO0DVV7UDQVIHU
7KHLQWHUIDFLDOPDVVWUDQVIHUWHUP *O LVDIXQFWLRQRIWKH
PDVV IOX[ RI WKH HYDSRUDWHG OLTXLG DQG WKH QXPEHU RI GURSOHWVSHUXQLWPDVV QO
*O QOGPO
ZKHUH QO LV WKH QXPEHU GHQVLW\ RI GURSOHWV JLYHQ E\ QO DOUOFG DQG GPO GW UHSUHVHQWVWKHYDULDWLRQRIWKHPDVV RIWKHGURSOHW,WLVPRGHOOHGDV GPO GW SGOUO'YDS6K OQ%0
ZLWK GO6K %0 DUH WKH GURSOHW GLDPHWHU 6KHUZRRG DQG 6SDOGLQJQXPEHU7KH6KHUZRRGQXPEHULVGHILQHGE\WKH IROORZLQJFRUUHODWLRQ 6K 5H 6F LI 5H6F ZLWK WKH 6FKPLGW QXPEHU 6F PI UJ'YDS 7KH 6SDOGLQJ QXPEHU WDNHV LQWR DFFRXQW WKH JUDGLHQW RI OLTXLG YDSRU FRQFHQWUDWLRQIURPWKHGURSOHWVXUIDFHWRWKHIUHHVWUHDP %0 <YDS v <YDS VXUI <YDS v DQG <YDS VXUI LV WKH YDSRU FRQFHQWUDWLRQ DW WKH IUHHVWUHDPDQGWKHGURSOHWVXUIDFHUHVSHFWLYHO\7KHPROH IUDFWLRQDWWKHVXUIDFHRIWKHGURSOHWLVJLYHQE\
;YDSVXUI H[S '+YDS0O 5J 7YDS 7O VXUI § © ¨ · ¹ ¸ ª ¬ « « º ¼ » »
7KH OLTXLG YDSRU FRQFHQWUDWLRQ DW GURSOHW VXUIDFH LV SURSRUWLRQDOWRWKHPROHIUDFWLRQDWWKHVXUIDFHDV <YDS VXUI ;YDS VXUI ;YDS VXUI 0J 0O ZLWKWKHPRODUPDVVRIWKHOLTXLG 0ODQGWKHJDV 0J7KH
H[FKDQJH RI WKH HQWKDOS\ '+YDS LV
'+YDS FSYDS7O 7O FSO7O 7O +O 7O ,QWHUIDFLDO0RPHQWXP7UDQVIHU 7KHPHDQGUDJIRUFHEHWZHHQWKHJDVSKDVHWRWKHGLVSHUVH SKDVH N FDQEHPRGHOHGDVIROORZV ,JoN ,NoJ DNUN WJN) 9UL ZLWK WJN) UJ US ¢&'² GS ¢_ YU_² WJN) LVWKHSDUWLFOHGURSOHWUHOD[DWLRQWLPHVFDOH ¢² LVWKH HQVHPEOH DYHUDJH RSHUDWRU RYHU WKH GLVSHUVH SKDVH 6LPRQLQ 7KH PHDQ GUDJ FRHIILFLHQW RI D VLQJOH SDUWLFOHGURSOHW ¢&G² FDQ EH ZULWWHQ DV IXQFWLRQ RI D
SDUWLFOH 5H\QROGV QXPEHU DQG GHILQHG E\ :HQ DQG <X DQG (UJXQ FRUUHODWLRQ 7KH FRPELQDWLRQ RI WZR FRUUHODWLRQVZDVJLYHQE\*RELQHWDO ¢&'² PLQ ¢&' (UJXQ²¢& ' :HQ <X²
LIDN! ¢&':HQ <X² LIQRW ® ° ¯° ZKHUH ¢&' :HQ <X² ¢5HS² > ¢5HS² @D J DQG ¢&' (UJXQ² ¢5HS²ZLWK WKH GHILQLWLRQ RI WKH PHDQ SDUWLFOH 5H\QROGV QXPEHU ¢5HS² DJGN¢_YU_²SQJZKHUH GS LVWKHSDUWLFOHGLDPHWHU
DQG LV WKH YLVFRVLW\ RI JDV UHVSHFWLYHO\ 7KH WHUP ¢_YU_²SUHSUHVHQWV WKH ORFDO LQVWDQWDQHRXV UHODWLYH YHORFLW\ YUL DQG LV HTXDO WR GLIIHUHQFH EHWZHHQ WKH ORFDO
SDUWLFOHGURSOHW YHORFLW\ XNL DQG WKH LQVWDQWDQHRXV JDV
YHORFLW\
XJL ZKLFK LV XQGLVWXUEHG E\ SUHVHQFH RI WKH
SDUWLFOHGURSOHW DW WKH SDUWLFOH SRVLWLRQ 9UL LV WKH
DYHUDJHG RI WKH ORFDO UHODWLYH YHORFLW\ DQG HTXDO WR
¢X!JL XNL² ,W FDQ EH H[SUHVVHG LQ WHUPV RI WKH DYHUDJHG
YHORFLW\EHWZHHQSKDVHVDQGGULIWYHORFLW\ 9G L GXHWRWKH
FRUUHODWLRQ EHWZHHQ WKH LQVWDQWDQHRXV GLVWULEXWLRQ RI GLVSHUVHGSDUWLFOHVGURSOHWVDQGWKHWXUEXOHQFHVWUXFWXUHRI JDV SKDVH 9UL 8NL8JL 9G L7KH GULIW YHORFLW\ 9G L LQ
WKH VSHFLDO FDVH RI SDUWLFOHV VXVSHQGHG LQ KRPRJHQHRXV WXUEXOHQFHFDQEHPRGHOHG'HXWVFKDQG6LPRQLQ
7XUEXOHQFH0RGHOLQJ
7KH HIIHFWLYH VWUHVV WHQVRU 6NLM FRQVLVWV RI WZR SDUWV IRU JDV DQG GLVSHUVHG SKDVHV WKH PROHFXODU YLVFRVLW\ TNLM
DQG WKH 5H\QROGV VWUHVV WHQVRU ¢XNL
XN M
² 7KH 5H\QROGV VWUHVV WHQVRU LV PRGHOHG E\ XVLQJ %RXVVLQHVTOLNH DSSUR[LPDWLRQZLWKLQWURGXFLQJWKHWXUEXOHQWYLVFRVLW\QJ W DQGWKHWXUEXOHQWNLQHWLFHQHUJ\ TJ IRUWKHJDVSKDVH ¢XJL XJL ² Q J W w8JL w[M w8JL w[M ª ¬ « « º ¼ » » TJ Q J W w8JP w[P ª ¬ « º ¼ »
7KH WXUEXOHQW NLQHWLF HQHUJ\ LV GHILQHG E\ TJ
¢XJLcXJLc² DQG WKH WXUEXOHQW YLVFRVLW\ LV JLYHQ E\
%DO]HUDQG6LPRQLQDV QJ W TJ W J W & DN DJ WJN W WJN ) TJN TJ § © ¨ ·¹¸ ª ¬ « « º ¼ » » ZKHUH TJN LVWKHIOXLGGLVSHUVHSKDVHFRYDULDQFH
7KH HIIHFWLYH VWUHVV WHQVRU IRU GLVSHUVH SKDVH KDV WZR FRQWULEXWLRQV DV RI WKH JDV SKDVH 7KH ILUVW FRQWULEXWLRQ
¢XNL
XN M
² LV WKH NLQHWLF VWUHVV WHQVRU WKDW UHSUHVHQWV WKH WUDQVSRUW RI WKH PRPHQWXP E\ WKH SDUWLFOH YHORFLW\ IOXFWXDWLRQV7KHVHFRQGRQH TNLM LVWKHFROOLVLRQDOVWUHVV
WHQVRU WKDW DFFRXQWV IRU GHVWUXFWLRQ DQG H[FKDQJH RI WKH PRPHQWXP GXULQJ LQWHUSDUWLFOH FROOLVLRQV 7KH FRQVWLWXWLYH HTXDWLRQ RI WKH HIIHFWLYH VWUHVV WHQVRU IRU WKH GLVSHUVHSKDVHLV
>
@
ON DN U NGNJ HF TN S ZLWK WKH GLVSHUVH SKDVH DJLWDWLRQV TS WKH UHVWLWXWLRQ FRHIILFLHQW HF WKDW GHWHUPLQHV HQHUJ\ ORVV GXULQJLQWHUSDUWLFOH FROOLVLRQV DQG J LV WKH SDLU FRUUHODWLRQ IXQFWLRQ 7KH VKHDU YLVFRVLW\ LV WKH OLQHDU FRPELQDWLRQ RI WKH FROOLVLRQDO DQG WKH NLQHWLF VWUHVV PV DNUN QN NLQQ N FROO ª¬ º¼ ZKHUH QS NLQ WIS W TIS WS TS DSJIF ª ¬« º ¼» VF WS WF ª ¬ « º ¼ » QFROOS DSJ HF QS NLQ G S TS S § © ¨¨ ·¹¸¸ ZLWK VF
HF HF DQG )F HFHF 7KH FROOLVLRQ VWUHVV RI WKH HIIHFWLYH VWUHVV WHQVRU LV QRW WDNHQLQWRDFFRXQWIRUWKHOLTXLGSKDVH7KH WUDQVSRUW HTXDWLRQV RI SDUWLFOH DJLWDWLRQ DQG IOXLGSDUWLFOH FRUUHODWLRQV DUH EH\RQG RI WKLV VWXG\ IRU IXUWKHULQIRUPDWLRQVHH6LPRQLQ
,Q WKH WUDQVSRUW HTXDWLRQ RI WKH PDVV IUDFWLRQ RI WKH OLTXLG YDSRXU WKH FRUUHODWLRQ EHWZHHQ JDV SKDVH DQG WKH PDVVIUDFWLRQIOXFWXDWLRQVLVPRGHOOHGDVWKHGLIIXVLRQDQG GHILQHG E\ ¢\S XJL ² QJ W 6FW ZLWK WKH 6FKPLGW QXPEHU 6FW HTXDOWR &KDUDFWHULVWLF7LPH6FDOHV
,Q WKH IRUPXODWLRQ RI WKH WUDQVSRUW HTXDWLRQV VHYHUDO FKDUDFWHULVWLF WLPH VFDOHV DUH GHILQHG 7KH WLPH RI LQWHUDFWLRQ EHWZHHQ GLVSHUVH SKDVHV DQG JDV SKDVH IOXFWXDWLRQVRUWKHHGG\SDUWLFOHLQWHUDFWLRQWLPHLVGHILQHG E\ WIS W WW 6FW &E[U ª¬ º¼ ZLWK [U _9U_ N
ZKHUH &E LV D FRQVWDQW HTXDO WR 7KHRUHWLFDOO\ LW FRUUHVSRQGVWRWKH/DJUDQJLDQLQWHJUDOVFDOHRIWXUEXOHQFH VHHQ E\ SDUWLFOHV 7KH SDUWLFOHSDUWLFOH FROOLVLRQ WLPH IRU WKHSDUWLFXODWHSKDVHLV WSF D S J GS TS S § © ¨¨ ·¹¸¸
ZKHUH J DFFRXQWV IRU WKH LQFUHDVH RI WKH SUREDELOLW\ RI
FROOLVLRQV DV WKH VXVSHQVLRQ EHFRPHV GHQVHU /XQ DQG 6DYDJH SURSRVHG WKH FRUUHODWLRQ IXQFWLRQ IRU WKH GLVWULEXWLRQ IXQFWLRQ DV JR DNDN PD[
DN PD[
ZLWK D
DNPD[ PD[LPXP UDQGRP SDFNLQJ RI DQ LGHQWLFDO
VSKHUH SDUWLFOH VXVSHQVLRQ 7KHVH FKDUDFWHULVWLF WLPHV VFDOHVDUHXVHIXOWRGHWHUPLQHWKHGRPLQDQW PHFKDQLVPLQ D VXVSHQVLRQ 7KH FKDUDFWHULVWLF WLPH VFDOH RI WKH FRQYHFWLRQGLIIXVLRQKHDWWUDQVIHULVJLYHQE\ WJN 7 UNFSN OJ GN ¢1X²
ZLWK ¢1X² LV WKH WKHUPDO FRQGXFWLYLW\ RI WKH JDV SKDVH 7KH 1XVVHOW QXPEHU RI WKH GLVSHUVHG SKDVH LV
¢1X² ¢5HS² 3U
)ORZ&RQILJXUDWLRQ
7KH JULG ZDV FRQVWUXFWHG E\ 2JULG DQG LW KDV DSSUR[LPDWHO\ FHOOV 7KH JULG LV XQLIRUP LQ GLUHFWLRQ [ \ '[ '\ P ZLWK '] P DQG ZH UHILQHG JULG FORVH WR WKH LQMHFWLRQ 7KH FRPSXWDWLRQDO JULG LV VKRZQ LQ )LJXUH 7KH WLPH VWHS GXULQJ WKH SUHLQMHFWLRQRIWKHEHGDVZHOODVGXULQJWKHHYDSRUDWLRQLV W\SLFDOO\DERXW 'W u V DQGWKHLQLWLDOKHLJKWRIWKH
EHG LV P 'XULQJ WKH HYDSRUDWLRQ WKH JDV DQG WKH GURSOHWV GR QRW ORFDOO\ UHDFW ZKHQ WKH VL]H RI WKH UHDFWLYH SDUWLFOHV LV VPDOOHU WKDQ D JLYHQ GLDPHWHU WDNHQ DERXW
PP 7KH ZDOO ERXQGDU\ FRQGLWLRQ ZLWK VWDQGDUG ZDOO IXQFWLRQ DFFRXQWLQJ IRU WKH IULFWLRQ DW WKH ZDOO LV XVHG IRU WKH JDV SKDVH )RU WKH SDUWLFOHV DQG WKH GURSOHWV QRVOLS ERXQGDU\FRQGLWLRQLVXVHG)HGHHWDO )LJXUH7KHFRPSXWDWLRQDOGRPDLQ 5HVXOWVDQG'LVFXVVLRQ
7KH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUHV LQ WKH EHG SUHGLFWHG E\ WKH VLPSOH PRGHO DQG WKH H[SHULPHQWDO DW WZR ORFDWLRQV DUH FRPSDUHG LQ )LJXUH :H ILUVW PRGHOHGWKHZDOODVDQDGLDEDWLFWKHRUDQJHOLQH7KH WHPSHUDWXUHGURSLVRYHUHVWLPDWHGDVFRPSDUHGZLWKWKH H[SHULPHQWDO GDWD 7KHQ ZH VHW WKH KHDW WUDQVIHU FRHIILFLHQW KZ WR : P .E\ XVLQJ WKH IROORZLQJ FRUUHODWLRQ
PZOZ G7Z
GW KZ6Z7E 7Z
ZKHUH PZ LV WKH PDVV RI WKH ZDOO DQG ZLWK DQ DVVXPSWLRQRIDXQLIRUPGLVWULEXWLRQRIWKHWHPSHUDWXUH WKURXJK WKH ZDOO $V FRPSDUHG ZLWK WKH UHVXOWV RI WKH FDVHZLWKWKHDGLDEDWLFZDOODVVXPSWLRQWKHWHPSHUDWXUH GURSLVVOLJKWO\LPSURYHGWKHEOXHOLQHEXWIDUIURPWKH H[SHULPHQWDO GDWD 7KH WHPSHUDWXUH HYROXWLRQ RI WKH ZDOOLVDOVRVKRZQLQ)LJXUHE\WKHFXUYH³73DURL´,W FDQ EH VHHQ WKDW WKH ZDOO WHPSHUDWXUH LV FORVHU WR WKH WHPSHUDWXUH PHDVXUHG E\ WKH SUREH WKH FXUYHV 6RQGH 7DQG6RQGH7LQWHUPVRIWKHYDOXHDQGWKHJUDGLHQW )RU WKH ZDOO WHPSHUDWXUH WKH VPRRWK DQG SURJUHVVLYH FRROLQJFDQEHH[SODLQHGE\WKHSURJUHVVLYHLQFUHDVHRI WKHWHPSHUDWXUHJUDGLHQWEHWZHHQWKHZDOODQGWKHEHG
:H FDUULHG RXW WKH VHFRQG SDUDPHWULF VWXG\ E\ PRGHOLQJ WKH ZDOO ZLWKDQ LQILQLWH VL]H7KHUHVXOWVRIWKHFDVH ZLWK WKHLQILQLWHVL]HDQGWKHKHDWWUDQVIHUFRHIILFLHQW KE HTXDO
WR : P
. DUH FRPSDUHG ZLWK SUHYLRXV FDVHV LQ )LJXUH JUHHQ 7KLV H[WUHPH FDVH FDQQRW H[SODLQ WKH GLIIHUHQFHEHWZHHQWKHH[SHULPHQWDOGDWDDQGWKHUHVXOWVRI WKH VLPSOH PRGHO :H FDQQRW REWDLQ DQ\ LPSURYHPHQW RI WKH UHVXOW IRU WKH LQLWLDO FRROLQJ SDUW EXW WKHUH LV DQ LQIOXHQFH RI WKH VL]H RI WKH ZDOO RQ WKH UHOD[DWLRQ SURFHVV W!V ,W LV QRW SUHVHQWHG KHUH EXW DQ DGGLWLRQDO SDUDPHWULF VWXG\ ZDV SHUIRUPHG ZLWK WKH VLPSOH PRGHO ZLWK D KLJKHU KHDW WUDQVIHU FRHIILFLHQW KZ 7KH
H[SHULPHQWDO WHPSHUDWXUH ZDV UHWULHYHG E\ DQ DSSURSULDWH YDOXH RI KZ E\ WXQLQJ +RZHYHU LWV YDOXH LV WRR KLJK WR
EH UHDOLVWLF DQG WKH VPRRWK WHPSHUDWXUH GHFUHDVH RI WKH H[SHULPHQWDOGDWDLVQHYHUREVHUYHG
7KH JDV WHPSHUDWXUH SUHGLFWHG E\ WKH PXOWLIOXLG VLPXODWLRQ DW WKH VHYHUDO ORFDWLRQV LV VKRZQ LQ )LJXUH 7KHKHDWWUDQVIHUFRHIILFLHQWZDVVHW : P
. DQGWKH ZDOO WHPSHUDWXUH ZDV R
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
VROLGPHGLDVXFKDVSUREHFRYHURUWKHZDOO
)LJXUH 7KH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH SUHGLFWHG E\ WKH VLPSOH PRGHO ZLWK DQ DVVXPSWLRQ RI DQ DGLDEDWLF ZDOODQGDFFRXQWLQJIRUWKHFDUERQVWHHODQGWKH H[SHULPHQWDODWWZRORFDWLRQV
)LJXUH 7KH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH SUHGLFWHG E\ WKH VLPSOH PRGHO ZLWK DFFRXQWLQJ IRU WKH FDUERQ VWHHO DQG ZLWK LQILQLWH ZDOO OHQJWK DQG WKH H[SHULPHQWDODWWZRORFDWLRQV
)LJXUH 7KH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH SUHGLFWHG DW VHYHUDO ORFDWLRQV E\ ' VLPXODWLRQ ZLWK WKH KHDWWUDQVIHUFRHIILFLHQWRI KZ : P . DQGWKHZDOO WHPSHUDWXUHRI R . &RQFOXVLRQ
7KH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH LQ DQ DQLVRWKHUPDO GHQVH IOXGL]HG EHG ZLWK D OLTXLG LQMHFWLRQ LV LQYHVWLJDWHGE\DVLPSOHPRGHODQG'(XOHULDQ(XOHULDQ VLPXODWLRQ 7KH VLPSOH PRGHO DVVXPHV WKH XQLIRUP GLVWULEXWLRQ RI VROLG DQG WHPSHUDWXUH LQ WKH EHG DQG WKH UHVXOWV RI WKLV PRGHO DUH LQ D JRRG DJUHHPHQW ZLWK WKH H[SHULPHQWDO GDWD SURYLGHG E\ ,1(26 $GGLWLRQDOO\ UHVXOWV VKRZ WKDW WKH ZDOOWREHG KHDW WUDQVIHU KDV FUXFLDO HIIHFW RQ WKH WLPH HYROXWLRQ RI WKH JDV WHPSHUDWXUH )RU
' QXPHULFDO VLPXODWLRQ ZH WDNH LQWR DFFRXQW WKH ZDOOWREHG KHDW WUDQVIHU ZLWK WKH KHDW WUDQVIHU FRHIILFLHQW KZ WKDW LV EDVHG RQ WKH SDUDPHWULF VWXGLHV RI WKH VLPSOH
PRGHO 7KH VLPXODWLRQ VKRZV WKDW WKH OLTXLG HYDSRUDWHV TXLFNO\DQGWKHWHPSHUDWXUHLVLQDVDWLVIDFWRU\DJUHHPHQW ZLWKWKHH[SHULPHQWGDWD $FNQRZOHGJHPHQWV
7KLV ZRUN ZDV JUDQWHG DFFHVV WR WKH +3& UHVRXUFHV RI &,1(6XQGHUWKHDOORFDWLRQPDGHE\*(1&, *UDQG (TXLSHPHQW 1DWLRQDO GH &DOFXO ,QWHQVLI DQG RI &$/0,3 XQGHU WKH DOORFDWLRQ 3 &DOFXO HQ 0LGL3\UpQpHVVSLSSKS"DUWLFOH!
5HIHUHQFHV
$UL\DSDGL 6 +ROGVZRUWK ': 1RUOH\ &-' %HUUXWL ) %ULHQV & 'LJLWDO [UD\ LPDJLQJ WHFKQLTXH WR VWXG\ WKH KRUL]RQWDO LQMHFWLRQ RI JDVOLTXLG MHWV LQWR IOXLGL]HG EHGV ,QWHUQDWLRQDO -RXUQDO RI &KHPLFDO 5HDFWRU (QJLQHHULQJ9ROXPH,VVXH
%DO]HU %|HOOH DQG 6LPRQLQ@ %DO]HU * %|HOOH $ 6LPRQLQ 2 (XOHULDQ JDVVROLG IORZ PRGHOOLQJ RI GHQVH IOXLGL]HG EHG LQ )/8,',=$7,21 9,,, 3URF ,QWHUQDWLRQDO 6\PSRVLXP RI WKH (QJLQHHULQJ )RXQGDWLRQ SS±
%UXKQV6:HUWKHU- $Q LQYHVWLJDWLRQ RI WKH PHFKDQLVP RI OLTXLG LQMHFWLRQ LQWR IOXLGL]HG EHGV $,&K( -RXUQDO±
*RELQ $ 1HDX + 6LPRQLQ 2 /OLQDV -5 5HLO LQJ 9 6HOR -/ )OXLG G\QDPLF QXPHULFDO VLPXODWLRQ RIDJDVSKDVHSRO\PHUL]DWLRQUHDFWRU,QWHUQDWLRQDO-RXUQDO IRU1XPHULFDO0HWKRGVLQ)OXLGV±
+H - 6LPRQLQ 2 1RQ HTXLOLEULXP SUHGLFWLRQ RI WKH SDUWLFOH SKDVH VWUHVV WHQVRU LQ YHUWLFDO SQHXPDWLF FRQYH\LQJLQ$60()('*DV6ROLG)ORZV
+RXVH3.6DEHULDQ0%ULHQV&/%HUUXWL)&KDQ ( ,QMHFWLRQ RI D OLTXLG VSUD\ LQWR D IOXLGL]HG EHG 3DUWLFOH/LTXLG PL[LQJ DQG LPSDFW RQ IOXLG FRNHU \LHOGV ,QGXVWULDO (QJLQHHULQJ &KHPLVWU\ 5HVHDUFK ±
.RQDQ 1$ 1HDX + 6LPRQLQ 2 'XSRL]DW 0 *HD]LRX7/'XQVWHDG\PXOWLSKDVHVLPXODWLRQRI XUDQLXP WHWUDIOXRULGH SDUWLFOH IOXRULQDWLRQ LQ IOXLGL]HG EHG SLORW LQ <XH * =KDQJ + =KDR & /XR = (GV 3URFHHGLQJV RI WKH WK ,QWHUQDWLRQDO &RQIHUHQFH RQ )OXLGL]HG%HG&RPEXVWLRQ6SULQJHU%HUOLQ+HLGHOEHUJSS ±
.XQLL' /HYHQVSLHO 2 )OXLGL]DWLRQ (QJLQHHULQJ %XWWHUZRUWK+HLQHPDQQ 6HULHV LQ &KHPLFDO (QJLQHHULQJ %RVWRQ
6LPRQLQ2E3UHGLFWLRQ RI WKH GLVSHUVHG SKDVH WXUEXOHQFHLQSDUWLFOHODGHQMHWVLQ3URFWK,QW6\PSRQ *DV6ROLG)ORZV$60()('SS±