• No results found

Stochastic Event Simulation of Oil Recovery Projects

N/A
N/A
Protected

Academic year: 2022

Share "Stochastic Event Simulation of Oil Recovery Projects"

Copied!
75
0
0

Laster.... (Se fulltekst nå)

Fulltekst

(1)

UNIVERSITY OF OSLO Department of Informatics

Stochastic Event Simulation of Oil Recovery Projects

Master thesis

Ole Morten Thorsø Amundsen

27th October 2005

(2)
(3)

!"#%$&(')*#&($,+.-$/10/&('234657&(')#89&:89#$&;89-7#$/23<2942&

5#&(,2=&(/2>')#84-?'(23&)@#7A&(>B*#&C5D&)&(;&EF-#2&(HGJIK>&EF-2L123

!H/86&)$J#$M89#$&%')#84-?&EN#?A&(?O$&2OM#5<*P#Q/+N-?$A235&R#23?&K&)&(

!S#$&(/'($5?92&T$//@!J23?&T$/&('(*&($/+:-$/10/&('23U*&V57&(')#84&C89#$&C--$&)W2(G

XY623?M23&)Z23&KQ')&($/23<2&(Z!H2&U$/&(/&($/*#$)R?&[E?-7&(?&()R#-$'(&(\89#$/&

$&\'(#8]5?&)V23^-?$PQ'(&_0/#<2J$//C-?$A&()G`%&%Q?'(&($,2L<23&)J84+C57&a/2Q&(

2>&*#&)$3b&*#&((GMcd$PQ'23#=-$A&R?')#84&"-?$A&Re&EF-7&(/&(-$A&()G

IU@-?-'B2#N232a-$/F?Q'(&)\/23$/5QF23d!S#$O?&)2a-?$&(/&(<2%*Q?&RW<23&)$

$32&4!a$&23Q$/HRb'B-f2Ld&g9'(&)')+RJ?h-$/A&)"!S#$i'B/hjkiRld$&)'(*#&)$/+RJ#

-$'(&)(R?'(#89&i=*$#Q%&EF-7&(/&()Rm>57&(&):&*#&)#-7&(HGZ`%&C-?Q?2>&(&)&(

!S#$N23&;8]Q23#N$/&=/23P'L,23';*$/n5&(]224$&:B*5&62923&=&B$+

/23#&(C!ao#J$/&(')*&($,+h-$/10/&('2BG4pU&)A:,23$/5Q?2#?U!S#$i&B'Lq/2F'L/23'

*$5&R+##Qo$/&]5?&T26,23Q?+:23&T&)rD&('2^2312U*$#Q>*$5&)K*&N#s2&

$&)Qf23(GZt\#]&EF-#2323#9-n9!S$#8uV/&(89fvwQ589&($/5&$T23]V$

-HRW#$&(23f+V?&('($/&B/&(O'B-f2L?&EF-D&)&)a?4584&)<2O&[EF-D&)&)(GMXY92Q$mR

23&N841EF8VQ8x-$P'(&)@'B-'(f2Y+s?$#-iyA&(z#-7&($3123s2384&T')$&B&()R

$&)Q'({23&i&2K-?$&(/&(<2*Q&G

(4)
(5)

ƒ„&(@Xd/#?&(Q-423T2&U/Q5P0/&)')2>842/vw/23F…†F‡†?RˆO‰LŠŒ‹BLŽ’‘=“M’‘7”‘mŽLL•H–[‘?—˜F‰/”‘mŽL

”‘7™;š>—L›F(Rb-$/:&)84&)/23&)$V!%…†#†œ?Rl22&]? X"P?ku5D#QF2C2&{!')2C2312VX

k\Qy&)yQ-:k>$2657#Q?2K#_-$/FQ?')23#HR7s'(&($,2L+=?2U22K2k\#Q?

5D&)'(#89&K2&^5O!ž8V+484/2&($Z23&)(GMŸO+45D&)V?!S#$842'(M,23Q&)<2BR8V+

23Q?2#$^:23?&]Q5W0/&(')2(R_IU$?&NŸa KQ/&(5<+#Rbsn2&($(RD8V+:86,23&)$K23?&(U23QF23#$)R

/#?&(o6-$/10/&('2"2389&Tk>?&($&NX>')#Q:2L&{?*<2L&V!M8V+:-$/##$38489

W)G.`%&:23¡k\923h84-?&(89&(<2{')$&)2&:&*#&)W223 8]Qn123&=-$PQ'23#

-$A&)CqA&))G=¢F'(&N23?&(HRb23&NkO#$£RJq2&9--'B123z86?&RbB*#&

5D&)&(=2323f+9$&)k>$/2/23&(;?;&[EP23&(?&(HR!S&(23Q$/N572@')#84&^=&EF-7&(/&(U

f23#239=&EP2&(&)y89F&)m!S#$a2&i#D$&(')*#&($,+#G

Xž8¤>/23Q?&(<2J!`b&(W/CcM$/##$8V*$&R1cM$/!S&(’0/#//23Q?&2BR<2_2&OXY?/23f23Q?2&

!CXY?!S#$/862')(R>¥K?*#&)$/2Y+.!T¦"/G§X{57&(<¨8V+©,23Q?&(@IKQ#Q,2:…†#†?‡y

$&N?Q&]23A?z8T+s84/2&($/"&(#$/&(&NopU&(')&(8]57&($C…††<ªFRH!Z6+#&($"-$/#$23

/23$/HGM`%&i&B&"!b23a23&)>"‡#GZ«K*#&)8]5D&)$K…†#†<ªFG

X=k>¬2©23­8V+„23Q?2#$)RT Kzcb&)2/23&($y®b2L#&(~§IU$/&¡Ÿ\

 KQ/&(5<+#G `%?P]2z¯d*P?p^89&)23mR!S#$]&)-s89&6¡#&223zs$/&(&)*<2

Q8989&($J0/#5ys«K#$/: +P$/I"¢FITGH¢P-D&)'(n+623?PK23`%$&V`%WQ&)/23

° Q?8]Q9±"&)*&({9«K$] +P$V¦^²C¯d&)$+C!S#$JkO&('(#89"89&RWN!S#$M

23&C*#&)$/+=*Q5&"-Q?2KXa#2(GaX\!S&)2$&)-7&(')2&(o?:23?&T?!S#$842#=?sQ?v

#&(,23#>Xa#2>?#{5{-$/2!2%2&(/(GO¯EF-'(2+R?2312K%23&T¢F`¦^XXŒcbR

K³OR#%t\XLR<¯EF-7&(/&(Z4´s1EF8]Q8µcd$P'(&(/Tta-')2Y+#GIU/U23WJ23i¯d$/

IVG¶Ÿ\&($/RH >+P$Rm&(-484&C84W64!S#$8VQnN!S#$U?/2$5Q?23{2323_$&(/&($,*#&(

$&)'(*#&)$35&C2N23&i#DkO&(%2323H$&)&)$/*#&)U$/&('(*&($35&G

Ia2O/2(R#Xlk>N23iQ?&/-D&)'(?23Wd23i8V+V2Q?23$(R<IU$/&>Ÿa?T Q&)5<+#RF!S$

-'LW;2"-?$10/&)')2C!S#$"84&9?q-$@84&Nk>f23z+##Q?$T&)W2WQ8;G4XUB*#&

--$/&(')n2&(=+##Q$fkaB+P>·WQ'L$/&(/-D#?&(U@23?#$#Q?#+4!S&(&)5'L£G

I¸$/&(Q$')&K-#&%!S#$J23&>23?&(M86B+N57&%!S#Q42Z<223-m¹»º#º186,23&)$(Ge#<23+G¶?G

t\#<2L'2\?!S#$/862#VMP'B2&(92Z8V+N-7&($/#£#89&%-#&<223-m¹»º#º1#<23+G¶?G

`%&>-$#$38µ?#QN57&>B*5&OM^$/Q5?&a-$/##$8¼#]2&%$&)#Q?$'(&>-#&

M!J‡G½«*{…†#†<ªFR<Q??V¾#B*"k\&)56/23$/2¿»0B*Bk>LÀGd`%?&U-?-'B2#]Jk>$f223&)4

¾+W23#mRH¾#B*6?y³#$/2$3sÁ#Á:¿ÂpUQ-?'(23&\0B*4')F&CK5D&)&(sk>$/2/23&(:k\&)ÃR

!S#$akO&(5s')#89-2352Y+?ÀG

(6)
(7)

Í Î(Ï

B1ÐHÑlÒbÓSÐ

Ï Ô

‡#G‡ ƒ„292&ycdQ$/-D&y!T¢W23P'L/2':¯J*#&(<2:¢F8]Q23#Õ!C¦^

&)'(*#&)$/+;cd$10/&)')2LÖ×GTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡†

‡#G»… ƒ„2%$&>23& ° <M!b¢P2F'L/23'^¯J*#&)<2K¢F8]Q?n2#N!l¦^D>&v

'(*#&)$/+;cd$10/&)')2LÖ9GCGiGTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡†

‡#G»…PG‡ ¢F?#Q@2&i#7A&(:57&"&EF-#2&(£Ö GCGTGCGCGTGCGTGCGiGTGCGx‡†

‡#G»…PG»… ƒ„12%A&(:&[E?-?#f2L2#-?n=?#Q=57&i'L#&)£ÖCGCGiGTGCGx‡#‡

‡#G

Ä

ƒ„2>-$,23H#<aNkO&T*&ÖØGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡#‡

‡#G¶œ  Kk~/#Q=2%?F')Q84&)<2K57&i$&(£ÖqGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡…

Ù Ú

ÐHÛ_ )ӝ

Ú

ӝÜoÒlÝS ?ÓSÐ

Ï ÍFÞ

…FG‡  KkÕ$/&Z2&O?/2$5Q?23#_?V-$/A&)_5Qf2ž!S$#8~2&Z/23P'L,23'

*$n5&)LÖ GTGCGTGCGiGTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡ª

…FG»… ƒ„2$/&C?')$&23&i&)*&(<233Ö GCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡Á

…FG»…PG‡ ƒ„<+ 'LP#&9/'($/&)23&4&)*&(<2]/8]Q23#z*#&)$T!SQ'23#

/8]Q23#£Ö GTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡Á

…FG

Ä

ƒ„2>F!S#$8423#P&(>,23P'L/2'"&*#&(<2U8VQn2#?\#f*#&"Q3ÖßGx‡Á

…FG¶œ ƒ„W+$&(-?$&(/&(<2U2&iQ')&($/23<2&(ak>f23;-D&)$')&(<23&(3ÖßGCGTGCGiGTGCGx‡à

á â

ОÑbÒlӝÐ

Ï©â УãÝSä

ÍFÔ

Ä G‡  Kk~a23%'L-?2&($&)2Q-ÖiGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGx‡å

Ä G»… ƒ„2>/2F'L/2'"*$5&)a{k\&iB*&Ö GTGCGTGCGCGTGCGTGCGiGTGCGx‡å

Ä GÄ  Kk§$/&^23&i')$&)2&T&*#&)W2K84-?&(89&(<2&(£Ö GTGCGCGTGCGTGCGiGTGCGæ…F‡

Ä GÄ G‡ ƒ„124kO#Q¨.--'B2#Õ!^/'($&23&:&)*#&)<23ç23?&

,23P'L/2'i8]Q23#6!l#H-$PQ'23#=P#4&ÖsGiGTGCGæ…

Ä

Ä

G¶œ  Kk~a23&i#DkO&(ž89P&(H?&)A&)£ÖzGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGæ…#ª

Ä

G¶œ?G‡  k¤8VQ'Ls#ž'Byz¦^Hƒq&(ž$&)'(*#&)$^s9#f*#&)s2384&

-7&($/P£ÖUGTGCGiGTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGæ…#ª

(8)

Ä Ä

G¶œ?G»…FGf‡ ƒ„2¢F`¦^X/XŒcOÖNGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGæ…è

Ä

G¶œ?G»…FG½… ƒ„2>%t\X,Ö GCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGæ…è

Ä

G¶œ?G»…FG

Ä

ƒ„2>³dÖ GCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGæ…#Á

Ä G¶œ?G»…FGeœ  Kké'B]2&O22LP$&)&)$/*#&)M$&(')*#&($5&a5D&\Œv

23$5Q?2&(;#<23N23&i#DkO&(LÖ GTGCGiGTGCGTGCGCGTGæ…#Á

Ä G¶œ?G»…FG½ª ƒ„&(./#Q¨¢F`¦^X/XŒcu.³µ57&;-$&!S&($$/&(

*&($>&22N/2$5?Q?23#O!S$a&B'L=#7kO&(H$&[v

-7&(')2*&(+?Ö GCGCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGæ…#Á

Ä GeœGÄ ƒ„&(s$&^2&i#mkO&(%-&)sÖ§GCGCGTGCGiGTGCGTGCGCGTGæ…#Á

Ä G½ª ƒ„2a23&i#DA&);84P&(nÖ GCGCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGæ…à

Ä G½ªFGf‡ ƒ„2a2&i$&(')*#&($5&T$/&(&)$/*&(U!l2&i#7A&(£ÖÊGCGCGTGæ…å

Ä G½ªFG½… ƒ„2a2&T¦"ž³&(cM$/F?Q')2#;23&BÖ GiGTGCGTGCGCGTGæ…å

Ä G»ªPG»…FGf‡  KkêP&(4q'L#&;Õ23&;-$PQ'23#Õ/2L123&

F')'(Q$3քGCGTGCGCGCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGæ…å

Ä

G»ªPG»…FG½… ƒ„2a-?$PQ')2#4$32&UCk\&UB*#&^r:-23&(Q

!’23&)$&)$/2#@!b23?&CmkO&(’ÖëGCGiGTGCGTGCGCGTG

Ä †

Ä

G½ªFG

Ä

ƒ„2%841EF8]Q?8æ-$/F')&(/?4'(-')2Y+?Ö9GCGiGTGCGTGCGCGTG

Ä ‡

Ä G»ªPGÄ Gf‡  Kk­'B6kO&^&23&)$89&23&K/2L123&"?-$PQ'[v

23ç$23&:!’23&)${-/qçq&kê#akO&(2

5D&)k~841EF8]Q?8æ'(-')2Y+?ÖqGCGTGCGiGTGCGTGCGCGTG

Ä …

Ä

G¶è ƒ„2P&(%2&i8VQn2&(@-$/F?Q')2#=-$/A&)%P#6&Ö GCGCGTG

Ä …

Ä

G¶è?Gf‡ ƒ„2^'(z57&V3y5D#QF2U23?&V-?$&Bz!J23?&]-$PQ'23#

-$A&"8]Q23#LÖ¬GCGCGCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTG Ä œ

ì Î(Ï #Ð7Ühä á£Þ

œGf‡  Kk~$&"23?&Cm-?$')&(>&*#&(#-7&(£Ö×GCGTGCGTGCGCGTGCGiGTGCGTGCGCGTG Ä ª

œG½…  Kk¬%23&"'(84&"'(')Qn2&(£Ö­GCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTG Ä è

Þ íUîžï ä Ï

(äP

áDð

ªFGf‡ ƒ„2&[E?-7&(?&(KNk\&CB*#&BÖ GCGCGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTG

Ä Á

ªFG½…  Kk~$&C¯EF-D&)&)U$&)n2&(@23N2&CcM$/F?Q')2#£Ö GCGiGTGCGTGCGCGTG

Ä à

ªFG

Ä

 Kk~$&i'B-23H&EF-7&(/&(K89-&)84&)W2&(£Ö{GTGCGCGTGCGiGTGCGTGCGCGTG

Ä å

ªFGeœ  Kk~$&C5#89&(<2&EF-7&(/&(K89-&)84&)W2&(£Ö.GCGiGTGCGTGCGCGTGʜ<†

ªFG½ª  Kk~$&i$/T&EF-7&(/&(U84-?&(89&(<2&(£Ö GCGCGTGCGiGTGCGTGCGCGTGʜ<†

ªFG¶è  Kk~$&i#-7&($23N&EF-7&(/&(U84-?&(89&(<2&(£Ö×GCGTGCGiGTGCGTGCGCGTGʜ<†

ªFG½Á  Kk~$&"2L$rs&EF-7&(/&(U84-?&(89&(<2&(£Ö6GCGTGCGCGTGCGiGTGCGTGCGCGTGʜ‡

ªFG¶à ƒ„2K$/&^23&i`l1E?23#;¯E?-7&(?&(3ÖçGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGʜ‡

(9)

ñ ò Ï Ï ìmá

è?G‡  Kk~a23&i'B=jk~$&)-$&)&)W2&(£ÖuGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGʜ Ä

è?G»…  Kk~a23&i&2K-?$&(/&(<2*Q&"$/&(-$/&(&)<23&(Ö{GCGTGCGCGTGCGTGCGiGTGCGʜ#œ

è?G

Ä

ƒ„2>%'(-f2LH&g9'(&)')+?ÖóGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGʜWª

è?G¶œ ƒ„2>%<23&($/ž$23&"!l$&23Q$/£ÖóGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGʜWª

ð ô Ð Ï

<ÝÂÒbÑbÓ

Ï_õ

äPÜh öž

ìžð

ÁFG‡ «K2&(%!S#$a23?&C$/&B?&($>GTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGʜWÁ

ÁFG»… ±i?k>;&($/$#$/>@23&C-?-'B2#xGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGʜWÁ

ÁFG

Ä

³£QF23Q$/&ipU&)*&(-84&)<2 GCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGʜ<à

÷=äPÑbÒlӝÐ

Ï

{øÃÐ74Ûbä

â

ОÑbÒbӝÐ

Ïéâ ÐãJÝSä

ô

ÝÂ<Òbݝ FӝÐ

Ï

Þ_Í

IVGf‡×ƒ„2%23?&T#HA&(:-?$PQ')2#;$3123&C&EF'(Q?92&T841EF8VQ8

-$P'(&){'B-'(f2Y+Ö GCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGæªF‡

IVG½…ùƒ„2d23&%WA&(N-$PQ'23]$32&ak>2{^861EF8]Q8¤-$P'(&)Œv

N'(-')2Y+@'(-£ÖóGiGTGCGCGTGCGTGCGCGTGCGiGTGCGTGCGCGTGCGTGCGiGTGCGæªà

ú â

ОÑbÒlӝÐ

Ï_â

ÐãJÝSäW]ûTüVÛ_äy

ïbï

ݝÓÂ# FӝÐ

Ï ñ7Þ

ô Ú

Òlўý­þNøUÿäP#Ð7äWý

ò

BÐ7=

Ï

Ñ.ÿäP(äW7ÐDÓS

ô

Ð7Ü

ï

ݝä

î

Ӓ[ý

Î(Ï

û

Ñbä

î ñ7Ô

÷ þ9ÓÂÝZÿäP#Ð7äWý

â

Ð)äFNû

â

ÐDÝS

Ú

?

ðHÍ

(10)
(11)

ÇÊÉ;ÆqÉHƼÇ

cl&)848 &)/28423#"-$/#$^2;2&457P#8×z2&4J-$/')&((Rb'BQ&)¡86W+

#D'(#89-?&(a2{'B'(Q23&"&)/2386123&(@'(84&"Q/NA?EF&):#m-$/')&(>!

$16

-7&($

5$/$&(ÂRP!S&($

$10

-D&)$O5$$/&(ÃGI¬'(&)·PQ?&(')&"!H23?MkaO232O84<+{#A&) k\&)$&K/'B$/&(HRWA&)M2312O4$/&B2Y+Tk\#Q?9B*#&U57&(&)4*&($/+9-$/A235&GJ`%Z

5Q?2"&]&E?89-&G"`%&{PE?&)2Y+;!')2#$U!S#$!Q$&T'(Q&)z23&]-?$#552Y+

,23$/5Q?2#?a!S#$>$&(/&($,*#&(i;2&C&"23657&C#*&(;k\&)$K&)/28423&)>2;23&+

-$55f+i#Q?V*&GJXYVQ8;R12_!S#$/8§!$iB*#&)$/2Y+T#5<*F#Q/+i'B$&)]

2_!?-$/10/&('23)GJIUž23?&($&O$/&M!S&k¡5C&B,+i#A&(?bWk>T&)!’2(R&EF-2L123

!ž/86&)$d#$O89#$/&')#89-&[E9#A&)ZB*#&U5D&)'(#89&K89#$/&84-7#$,2L<2BGb`%&+$/&

2JJ#5<*P#Q?+C-$/A235&O]2&\?&(&(N!S#$l&(/'($/5K2&a$i!2&a-$/10/&('23

a*P23m!S#$%?&(#{-Q$/-D#/&()G

´:#/2]!%k>2NX"*&@&($&)¡X"B*#&@57&(&)¡2LQ?#<2]h-D&)$HGz>&)!S&($/&(')&(

23=$,23'(&)Uy23U23&[EF2C$&]&($U2=5&)<2BG]ŸO&)!S#$/&]8V+skO#$/y2i«#$/y >+F?$

I"¢FITRDX%y2U$&(y<+:$&)n2&(y$/23'(&((G>Ia2^ +P$6Xa23&)$&TkO&($/&N86W+RD5?Q?2

CX^#&(q='(#?A&(<23f2Y+o#$/&(&)84&)W2C23?&($&4$/&4;P'(Q89&(<2C2:$/&)!S&($i23?G

´:#,2a!H2&U842&($423?M23&EP2(R?Xd4-$#$d23V2&K +P$>0/#5HGJ`%&U862&($/n

2312Ub;2KB*#&V-$#$>2K'(#/&)$&)y'(#FA&(<2nl;kaK#$3W2&(yQ?&

5<+48T+N23Q?2#$Z6 +P$?G

°

)RP/F')n2&(6#\

CO 2

$/&K?2\')*#&($/&(@5<+{23 23&[EF2(Ržy^?'(#89&T-72&(<23_2^22L+=?$/&(<$&)HG^¯EF-D&)&)C/F')n2&(

23N23?&(&T$/&C/Q--7#&)s')*&($/&(s@23&i&EF-7&(/&(K84P&(ÂG

(12)

&132 54()3#6. #T€879:4<; >‚=#>,Va}"? |~}@#BAm>‚CDFE

`%&986 -Q$-7#/&4i2s-$/*F&4=!,2]h/Q?g9'(&)<2VA'(d5/i!S#$"23&

&)'(/#=84&)$%239?/kO&($>23&)&i2Yk\{!SQ84&)W23H·WQ&)/23#)¹

‡#GK¢F?#Q@2&i#7A&(;57&i&EF-#2&(£Ö

…FG%ƒ„12%A&(:&[E?-?#f2L2#-?n@/#Q:57&"'L#/&(£Ö

HG

 i}l  IJ#T43 #C€ &0)#4‚

K)(‚ +-,V/.0

&132 54()3#6. #T€879:4<; >‚=#>,Va}"? |~}@#BAm>‚CDFE

`%&M84^<H$&J2%'($&(23&d2&d&(&(89&(<23ž!P23?&JA')n5m!S#$H2&d&(')/#

84&)$(GM`%&)&T$&"2&

«&)2Kcd$&)&(<2MLZQ?&R«KcNL ¿è?G»…À

ta:³kÈ¿Âè?Gf‡À

XY<2&($_K123&"!&23Q$/HRXŒÊ¿Âè?GeœWÀ

ta-23H¯Jg9'(&('+#RDta-7&)rç¿ÂèFGÄ À

ƒq&yka<2;23&z&[EF-D&)')23&)¸*Q&(@!C23?&(8 ?­2&($@/F')n2&(„Q')&($,2LW2&)(G

`%&)&V&)&)84&)W2^$/&C*Pf2LH2F#a!S#$>23&C&(')/#:86&($/(R£$&)-$&)&(<262&V$//

-72&(<23]!2&@<*&(/284&)<2{-$10/&)')2(G¡¥K/z,23P'L,23'@/8]Q?n2#qN

#PF=k\+;239As2&V$//7R7$&)-$&)&)W2&( K-$#552Y+6,23$5Q?2#>!JQ'(&)$,v

2L<2Y+#G >&B'Ly23?&(&=84q#<(RJkO&@B*#&k>12{]&)&(&)é2z,k\&)$N23&

·WQ&(,23#>!b23&i-Q$/-D&G

OQPSRTPUO VXW>Y[Z>\^]`_WbacY[d^\feBa*\^]hg%a8ajiXkB\^YQdS_a*]ml

°

*#&)92&>&(,23842#M92&>Q')&($/23<2Y+9&)'($/-?2#?Z!D2&A')n5)R

23?&s$éB*#&)$f2Y+.!U23&y?&('(#©84&)$6k>%&23&)$89&;k>&)2&($$62423

<2&(#$23&@23?{<*#&)/284&)W26-$0/&(')24Õ23?&(${-7#$/2/!S#G`%&;$32&:!^$&23Q$/©!

89#&)+^<*#&)/23&)VVi##-$/10/&('2ž89-D#$,2L<2žV%$/U-D&)$-7&('23f*#&R&(84

6$/&(n123*&(f+:?#;*Q&Rm#$/86+@kO&(5D*#&@‡ªonRHU2&]&[E?-7&(?&(i!M2&]#

&EF-#2323#a*#&($,+=$/=24-?$&(?')2(R=23?&C-72&(<23H$/@23{&(,23842&G

(13)

`%&($/&]&EF/23K&*#&($?rD&($&)<2U#HA&(s&[E?-?#f2L2#=-7#/52&)(G\IK_#HA&(

$&z?rD&($&)<2;¨23&z&[EF-#f2L2#ç-n¨8]Q/2=57&z'(Q?/2384{z(&(¨!S#$6&B'L­#&G

 KkO&)*#&)$(R?2&($/&U$&QQ+]84#$/&%234#&>Q?2#{!S#$d23&frm&)$&(<2O&(&(89&(<23)R

!S#$%&E?89-&¹

¾#'L#vwQ-:$/&(89fvwQ589&($/5&K#H$/RF-n12!S#$/8æ#$>$/?V?-3Ö

¢F?->#$%--D&)a!S#$a23?&Cm2$3/-D$/2L123£Ö

¥86&(;#$%84&)=-n2/!S#$89LÖ

¢F8VQn2hQ23&o?-Q?2=23!V2&orD&($/&(<2@A&(¸?&)*#&)#-?84&)W2;-)R

$&)-7&(')2*&(+RmkO&]#&)2^rD&($/&(<2^$/&(Q?23)RDk>'Lz86B+;57&]'(#89-$/&(zskO&(W2&(

</2^&B'Lq23&)$(G{¯d·WQ*&(<23f+#RH,23P'L,23'{-Q?2"*$/n5&(^84B+y57&{2&($/&(

23",23Q?+T23&%&rm&)')2d2&a*$5&Zd]23&a-?$A2352Y+Gb³£$J&E?89-&R#Q?--D&

2312^!lk\&VQ&)o6&)k¤89&)2Ps!S#$$]23?&V#_kO&()R7kO&]'(Q:$&(?Q'(&]2&

$ &EF-7&(/&(;£º1#$623?&z$z2384&GµIK2&($23f*#&(f+#R%84B+F57&s2&z&)k

84&23P;>84$&"&EF-7&(/*&Rm5?Q?2U$/&(Q?'(&(23&CWQ8]57&($>!#mkO&(&(&)&(mGa`%&

8ê!J23&T&)*&(#-89&(<2^!23&T/23P'L,23'V&)*&(<2i8]Q23#=--'(23#=K!S$

23&iQ/&($>23{57&i5&^24,23QF+23(R5<+=f23&)$?]23&i?-Q?2%*$5&((G

6U|

}!;"}"))4<~#Vm45# €È

/,]BE

Xw2ii@kaB+y2=#@23=$&('L 2&N84z##)GV`b;$/&B'Lo23?&(8;RHk\&{&)&(o23

A=23&¹

cd$PQ'23#;cM$/A&9¿Ãt\-F23&($

Ä

=IU-?-D&)fE@I"À



>&('(*&($35&C>&(&)$/*&(N¿

Ä

GeœG»…À



¦^7ƒh&)ÃR?s¦^ž³&(HR¦^m&)'(*#&)$/+s¢F-7&(&)¡¿Ä G¶œ]v Ä G»ªÀG

XY')#89&6¿Ât\-?2&($>œWÀ



¦^mcM$/')&(T¿œGf‡À

¯EF-D&)&)N¿Ât\-?2&($Kª#À

(14)

 Ä



IK5?#89&(<2K¯JEF-7&(/&()RDIUŸap^¯F‚ê¿ÂªFGeœWÀ



¦^-7&($23{¯E?-7&(?&()Rž¦"cM¯F‚ ¿ÂªFG¶è<À



pK$]¯EF-D&)&)(Rmp^XŒ®_®_¯F‚ ¿ÃªFG½ª#À



`l$/ro¯EF-D&)&)(R7`lIUK¯F‚ ¿ÃªPG»Á#À



`l1E;¯EF-7&(/&((R7`bI>‚"¯F‚ ¿ÃªFGÄ À

`%&&B;C23yQ/&623?&Q')&($/23<2Y+q 23&kÊ&)*&(M*$5&)(RlQ'LéC2323

$&)&)$/*#&)(R7$&)'(*#&)$/+@!'23#$)R$&)'(*#&)$/+;$32&"!l#7k\&))R-$/F')&(/9$3123&"!b23&i$/

éq#HRZ23 5Q23&]0/#<2{$/h-$A&()G.¥?q,23P'L/2'@*$5&({

'($/&)2&y&)*&(<23q¿ Ä GÄ À{!S#$42&z#>-$/F?Q')2#„?¨$&(-7&B123?h23&s8VQn2#?

84<+9289&()RPkO&iV#5?234-$PQ'23#-$/A&GJ`%a-$A&U@2\/2$5?Q?23#

'B;kO&i/23Q??+@23&iQ?'(&($,2L<23&)%!ŒG¿Ã…PG¶œWÀ

ŸO+y/-f22Q?-o*$/n5?&(K232"$&]2&{#Q$/'(&)C!Z2&{#$&(23&)/2iQ?'(&($,2LFv

23&()R?<2]23&)$akO&($%&)*&(ž-$,23)R?23&)$b0/<2a/2$5?Q?23#6k>D89#$/&"'(')Q$3123&(f+

&)'($/57&T2&VQ?'(&($,2L<2Y+s!23&C*$n5&G>³£$K&[E84-&R£23&T-$PQ'23#sy

#?$id&23&($/84&(95<+N23&>-$/F?Q')2#{!723&#FkO&(Z{23&>$#d841EF8]Q8

-$/F')&(/{#$%2$3/-D$/2>'B-'(f2Y+#R£89#/2%2&($/(G

`%&($/&i$&U23&)$a&(&(89&(<23\!l@#£A&)&[E?-?#f2L2#4-$10/&)')2>ak\&)ÃG ° )R

/P'(n123&(„<:

CO 2

$&o2='(#/&)$&)¬&)$&RK23&z23?&(=@84f23&)©23 '(Q?"23&>#?$/&('(*&($/+GM`%&>&EF-D&)&)a/P'(23&){k>f23N23?&$/&(')*&($,+#RFM<

0/&(')2#h&)23'G$/&@Q--7#/&(©')*#&($/&(é5<+¡23&@&[EF-D&)&)689F&)ÃRJ&)-7&(')n+ 23&

#-7&($23N&EF-7&(/&((G

„ƒ …

#M€

#%543

†5#9‚T‡2 /.f‰ˆz }l>6ŠE

`%&=2L$/#&)29$/&B&)${!U2{P'(Q89&(<299ç'(&(89'@$9-?$!S&)#%-7&($/#

k>2q23&@$&By!K,23P'L,23'68VQn2# #$]/-D&)'(/2]&B$/+ /23#&@#O$/&v

'(*&($/+q-$/10/&('23(G@Xw2TT=k>$2/23&)q23;&)$/*&@C5C!S$Th&)*&(<23Q\/Q'(')&(,v

$6k>/q23h!SQ$,23&)$@&)*&(#-.23&y*$/#Q?689F&)4£º1#$623?&z--'(23#

‹

cM$/F?Q')2#;cd$A&($^ŒÂG

`%&s$/&(·WQ$&(89&(<24!S#$9ç#%-$/10/&('2/Q235&@!S#$N2{23&[EF2(R%N2326f29

2"2&9*&($,+o&B$/+z,2L#&)i!a-= &*#&(#-89&(<2BG4`%2C)RbqA&)

CQ?--D&($/&)*&B&(HRM?¡$&)&($,*##$V&)#?&(&($/V23:B*#&@#f*#&)h23&)$C&(,23842&(

57#Q?2"$/&(/&($/*&()RlA&)o'(#89-&EF2Y+s&)23'GNXw2i^2;57&N&23&($/84&(zk>&23&)$T$"2

23¡!SQ?$/23?&($=<*#&)/2;.2&o#A&(HG¼`%?@=,2L#&z$/&)!S&)$$&)­2Õ5W+.#89&z

(15)

#89123&(T5<+]&EF-7&('2L2#JV2PQ?8]5N$Q&()Rk>'L]kO#$/Pd$&B12BR5?Q?2dP&(J?2

#*&C4#PF=&)')$-F23:!l23&CQ')&($,2LW2&)(G\`%?>P'(Q89&(<2K-$&)&(<2^N*#&($,+

rD&($/&(<2^-?$P'(&(?Q$&R7!SP'(Q/4#sQ?'(&)$/2L<2Y+;$&(-?$&(/&(<2L123^!J2&i*$n5&)

]0/#?V2&(8;G

´;+]23?&(J23$/&B223&%/Q&%!789-&)84&)<23?K,23P'L/2'%&*#&(<2Z8]Q23#_23

!S#$8¸#-$PQ'23#"-$A&)(R#-$'(&)(R1')#84&R&EF-7&(/&(Ji84#$/&G_`%&Z--?fv

'B2#:-$*P?&(^#$-'B_+#Q?2^z+PK!d23&)&

‹

cd$PQ')2#;cd$A&)$‘ŒÂG

IU--7&(?fE;٬&)')$57&(>23?&i--'B123=?#$/2?s=&[E84-&"-?Q?2%A&^!S$

2>%#*&(==IU-?-D&)fE=pVG

XOk>D,2L$,2>#&(?&($3+9k>2=/23P'L,23'"&)*#&)<2U/8]Q23#^¿Ãt\-F23&($…ÀR?2&(

<23$/F?Q'(&@23?&;89P&(\!S$N5Q?y23&=-$/FQ?')23#Õ84P&)i¿Ãt\-?23&)$

Ä

ÀGÕ`%&

'B'(Q23#V!S${2&=$&)Qf23{-$&)&)W2&(©2&($/&:84B+57&=!SQéÕIU--7&(?fEéITG

 UB*Pé&EF-?&(¨23&o-$/F?Q')2#„-$/A&RUX9k>U<23$/FQ?'(&oÕ84P&(K!S#$@#

-$'(&){Õ')#89&z¿Ãt\-?23&)${œWÀRJ2&(23?&@&EF-D&)&)489P&(^¿Ãt\-F23&($4ª#ÀT

A+R?XOk>D<23$/FQ?'(&"23&"A'(&i89F?&(M¿Ât\-?2&($è<ÀG

(16)
(17)

“uÉ;Æ$ Ì9É* “*” •*§ÉHƼÇ

G(3 …

#>€ "}–

‰53Kž}@:ˆ5):#6.¤.‡ !@}"#—4/8ˆ‡:4˜

€}@#62

™K)#9‚

6K))‚',""}"(mˆ‡4)/FE

XYTAQ$&\…FGf‡OXH<23&(?C2KQ?/23$23&J2&M-2V!F23&Z/2F'L/23'O"23&Z8]Qn123(R

'(#8V5:290/#W2V,23$/5Q?2#?V?£º#$]-?$A&()Gz`%&5722#8ù&)*&(Vh2&

Q,23$3123HR$&a23?&%/23P'L,23'a*$n5&)J&)A&(4d?-Q?2d*$5&((G_ƒ„&)92&

8]Qn123K,2L$,2^kO&N$3Bkµ!S$#8x23&)&GT`%&{##$/284&)'(?&V23&NQ?23')#84&)

;5Qa2&T?/2$5Q?23#%:-?$A&(%!S#$%&('Ls/8]Q23#HGJIK2&i')#89&

&9z23&{&[E?-7&(?&(T&N!Z23&{8]Q23#^$&N$&({z(&)HRH23&+z'(8]5?&]23

23&"!S#Q?$?&($&):$/&(Q?23)¹d23&C«UcFLVRmta-D&r =XŒK~-?$#552Y+4,23$5Q?2#

=23&i'(=jk~-$/A&G

`%&o/23P'L,23's*$5&)6')Q/&(­©2--D&)$=$&y$&)-$&)&(<2&(¬

23&4n#$38;G6`%?&6#$38óC2Vd'(#89-&23&Rlf2TTWQ&R/yQ$23#q

/23$/2O2389&>*$n5&)Z!S#$Z23&U&EF-D&)&)62&it\I^cM¯F‚]R?`lIM‚"¯F‚¤6`lIUK¯F‚

$&@+q84&)<23&(¡23&EP2(Gh`%&+Õ$&6'(#,23$/Q')2&(é¡23?&@389&@86&($]

23&T23?&($)Rm+#Qy84+&EF-D&)')2(GK`%&T/2F'L/23'C*$/n5?&(%!J23&C&EF-7&(/&(i$/&

'(*#&)$&)¡o'L-F23&($Vª=o23&{$&({zB2#s!\2&{-$PQ'23 -?$A&{"&)&(-f+

'(*#&)$&)o'L-?2&($ Ä ?h-?-D&)fE ITG6IÊA')2*&4#J$&)'(*#&)$/+q-$0/&(')2



cb#n$

¢P2L$Uz¿IU-?-D&)fEp"À4Rdk>'Lç$&62&@#Q?$'(&@!2&@#$-)RO$&#f*#&)çN

&E?89-&"!JN-7#/5&"-QF2%A&^!S#$a2&"*$#Q%/2F'L/2'"*$5&)(G

(18)

-$/A&)(G

(19)

G(šG

œi—Ž‰3Œ@:‘’—$&9&)*&(<23]/&)2T23;--7&(12V#f*#&)q2384&G@´sW+ /Q'L&)*&(<23

B*#&=$&(?+ 5D&)&(89&(<23#&)HRdQ'LéV/&($/2#q!#dk\&)ÃGs`%&@&)*&(<23

&(&)¡2C57&4-?W+P/'BO#?&(TC2i#?&R5?Q?2V'(h57&{23?&($)RJC'L?#&6 2&

/2323&T!d-$/FQ?')23#HR£#$U5?#89&(<2U&*#&)W2^!J23?&V#_A&(:Q&C236?#:'(#,23

¨k ')#84&G~¯J*#&)<23=86B+é'BQ&y23&)$6&)*&(<23@2¡F')'(Q$)G§³#$9&E?89-&R

/&($,236!b@k\&)DO@&)*&(<2')$&(23&)>V-n123&BQ&(@&*#&)W2(R#$O'BQ/&(

23&"289&^!b23&i-23&(Q=&(;&)*&(<2U29'L#&4¿ Ä G»ªFG½…#À[G

RTPSRTPUO q W=ž'xyW>YXYQva9]bd^vwx Ÿyaj_a‰aK¡Qa*uC_ vwd‘¢£Z>\UrF_d^YQu Y)¡QaKŸ ¤¥Zbu>x§¦

_d^YQubrQ\fvwd‘¢£Z>\UrF_d^YQul

³Q')2#ž8]Qn123@>!/2&($>23:/'($/&)23&T&)*&(<2"8]Q23#HR5QF2U'($/A')&(

j&EF52Y+#GlXY!SQ'23m/8]Q?n2#{+##Q@?&(&(@2N&)A?&iVA2&^&2%!b-7#/5&

')&($/#)RFk>'L6#Q$Z'B/&^O&23&)$895?&Gb`%&^WQ8V5D&)$\!_&*#&(<2%'B?2

5D&>&23&)$89&)4{?*')&UM&*#&(<2\84+V#$M86B+V2Z'($/&B2&K2#?&*#&(<2(R

¡2&($V#$/&($]84B+q*$,+ #$]'L?#&Go`%&)&=$/&&(/&(<2na-?$#-7&($,23&)V!>2&

84P&)ÃRF='B?2>57&^32,!')2#$/+489-&)84&)<23&(4k>23@!SQ?')23#78]Q23#HG©¨

G(U|

ª.@€«#C}@2 )3#6.¬5#{/<K)#9‚

6K))‚~T,]/.f­*2 ®

54)m):#%.‡†~:,V¬‡FE

³#$=&B'L~/8]Q?n2#)RkO&h&)~Q-­k>2¬?R"/Q--7#&)+Ri-D#/5&o$&({zB2#

!Uç\$/&(')*&($,+ç-?$10/&)')2BGé>&(-7&B2y2)RZkO&=k>O#&)2{89#$/&=érD&($/&(<2

$&({zB2#)Rbhk>f23q2&6'($/&B/:WQ8]57&($V!%8]Qn123(Rb:-22&($qk>

-$&)&)W2J23/&(f!ŒGb`%?*#&)lQ?l23?&a5f2Y+U23K&(/'($/57&O23?&O&)FPž!Q')'(&(/J!

23&C-$/10/&('2BGOŸO+*$/+P92&i-$552Y+4/23$/5QF23a!l23&i/2F'L/2'i-?Q?2

*$5&)\23?&C/8]Q?n2#Zk>H-$*P?&"rD&($/&(<2&(PF?(G

¯U°²±3³T´ ±:µ·¶¹¸·´K´Uº²»¼´U½¿¾À´š¾Á:¹´j¾ÀëÄÅÆ´‘Ç^¶¶p±DµÈ뽫DŽ¶pÉʱ3½«Á˜Ë·¾¹ÉʳC÷ËÌÁ¥¶¹Éͱ:½wΘÁ:¾¶¹¸·´‘ÏQÁ˜Âp´j¾¹Ã·»·»¼±3¾¹´‘Ð[Ѳ½·±¥Ò*½

Á:¸·´‘Á3ÐM±3ÂK¶¹¸«Á˜¶j¶p¸·´NÉ͹Âp´UÓ3÷ËÍÁ:¹Éʶ¹ÉÍ´‘¾KÁ:¹´@¹´‘»·Âp´‘¾¹´U½¶¹´šÐMÉͽM¶p¸·´N÷½«ÇU´U¹¶pÁ:Éʽ¶ÆÏ:Ô

(20)

G0„ƒ

‚\/.0):4/NE

¢P2Q?+PT23&^$/&(/Q2\!S$#8 2&^8]Q23#dk>2623&UQ&^!_-D&)$'(&)<23&(aO*QFv

5&\J2l#*&(U#PFT89-$&)#V!23&O-$/&B{?N&(/2Y+T!2&a$&({zB2#?

=]-?$A&GMŸO+'LF?N86<+6-D&)$'(&)<23&()R'(#8V5&)@k>23=N#@WQ8]57&($%!

8]Q23#(R2&]-D&Tk>_·WQ'LPf+s$/&)*&Bl23/&(f!ŒG"¦U23&)$^/Q&)(Rž^84&)<23&(

=/&(')2#o‡#G½…FG½…FR?2&T'L#{!-Q?2%*Q&()Rk>m$&j&('2Uf23/&(!b=2&i-$/&B

#$^*Q&{!O2&9-D&)$'(&)<23&()G6³#$"&[E84-&Rž'L#?;2&{Q'(&)$/23<2Y+ &EWv

-7&(')2323#]!£2&%-$PQ'23#]-723&)W2n#$$&(')*#&($,+{-D23&(<2n!2&¦^Wƒh&))R

k>B*#&"T#489-'2O623&K,23$/5Q?2#mGl`%\-$/#-7&($/2Y+4?#Q923&)@&)$/*#&

U6Q&!SQl2Fby?&(<23f!’+F{23&V*$/n5?&(>k>2:2&]#$/&B2&(/2U89-'2U#:23&

*#&)$3HQ')&($/23<2&()G

(21)

Ö ;ÆqÉHÆÈÇ Ö ;ÆØכ•HË

|Ù3 …

#>€ 9

3 ‚

m!‡_a}_T}5!$E

`%&>&)*&(<2\/8]Q?n2#]!72&>-$PQ'23#N-$A&)M$&%*#&)$/+N')#89-&[EmGl`%M'L-Fv

23&)$U%k>$/22&(s2#-Fvwk>HRD?')Q/923&T*#&($_Q?&(UA$//2(RD#&22984$&T

84$&C-7&('(fA'T!S$K&('Lz&)')23#s2$#Q?# Ä G½…{2 Ä G½ªFG%ƒh&T/23$/2U5W+;&)'($42&

/2F'L/23'^*$5&)a2&"#m$&)'(*#&)$/+=/8]Q23#)R?-?-+P?]/'($/&)23&i&*#&(<2(R

23&)h')QC23&9Q&4!\2&(8 2&6¦"Jƒh&)Z´:P&)ÃG6Ia2C23?&4&)qkO&6-QF2Vf2

723#&)23?&($a23&C¦^m³&)=´;F&)ÃGJ`%?&C'L-?23&)$%a892&(42N&EF-V2&

84P&)>ç2&;/2L123&(9!^2&;-$PQ'23HRO5&).#©$/&(/Q24!UIU--7&(?fEéITG

`%\--7&(?fE4'(#<23\2&^&)'(&(/3$,+'(')Qn2#?(RW5/&(#423\'L-F23&($)R

-$&)&)W2{23?&C$/&(/Q2;yŽ:Úf”ÜÛ}Ý@Þ7‰LŠŠ^ßs86&($)G

`%&N&(657&(y23&]2#-Fvwk>o--$/<'Lz!d2^'L-?23&)$"236k>$/23&V&B'L

&)')23#y22]2&)+h$/&#f+q?&(-7&(&)<24¡23&62&($/+q!>23&@5D*#&6nB+#&)$

¿SAQ$&

Ä

G‡À[Gi`%Uk\B+#Ržf2^84&)"2^&(&($U26A ?z/23Q??+s2&{$&(^!M2&

$&(&($/%<23&)$&)/2>2\n2&($Z-D<23)R423&^$/&B?&($a84B+684/&(f!H'LP#&"?k­&)&(-

<23N2&i&)23a&"kaW223{#?R?!S#k>V2&iWa239--7&(?fE@ITG

|ٚG

†K)#9‚

6K))‚à,^i}"(mˆ‡4)/h5# €¼

/,]BE

`%&^WQ8]57&($Z!ž,23P'L,23'*$5&)M!H23?&U-$/FQ?')23#$&U+{8923&)N5<+42&

&(/$/&(o'(#89-&EF2Y+:!M23&V84P&(ÂGi`%&N84/2"84-7#$/23<2U-?$#552Y+=/23$/5QPv

23#i!S#$"23&)&RM$&{23&9'(#?/2LW2(RJQf!S#$8;Rž23$/n&R_$84ÃR_##$/86J

&EF-7#&(<2nb,23$/5Q?2#?(R£ž89-&)84&)W2&(;=23&V--'(23#=>*;$&)-$&[v

&)W2323#a!S#$\Q'(&)$/23<2Y+@!b&('L;2&"/2F'L/2'"?-Q?2a*$/n5&RP$&)-7&(')2*&(+G

(22)

Ä

`%&684 5P0/&('23V!a8V+z/8]Q?n2#i$&N23&âáaÜÚã9:ÚÜÚ½—G=t\#8V5&) k>f23

#d$/; 23$-7#$,2L2#oQ?2f23&(U2&)+z!S#$/8×23&âáaÜړMÃ:Úf™G9`%&6'L?#&)

'(84-&EF2Y+4!8V+89F?&(HQ/&(>23&i,23P'L/2'"*$5&(a/2&(=57&(kiG

â

1ÐHÑlÒbÓSÐ

Ï

ÿ ?ä pU&)A?&(qU23?&N89#Q<2^!Z#l$/&(')*&($/&(q2^&('Lo/'($&23&

289&^/2&(-_¿SB+#R£84W2=&)23'G»À]!S#$%&('L:$/&(/-D&)')23f*#&V¦^mƒq&(M¿ Ä GeœGf‡#R Ä G½ªFG½…#ÀG

ÿäP#Ð7äW lݝä;ÿäP(äWDäP &)&($,*#&)V$&)'(*#&)$35?&{z23?&N#A&(ç¿ Ä G»ªPG‡À#$(R_v

2&($23f*#&(f+#R?!S$&('LsmkO&(ž$&(/-D&)')2*#&)+m¿

Ä

G¶œG½…#À[GO`%>,23$5Q?2#@84B+

57&"'(#?/23$/Q')2&(;!S$#8 2YkO923&)$>/23P'L,23'^*$n5&)(¹

ü\Ð ÝOÿäP(äW7äF

`%&"2323H$/&(&)$/*&(U@23&i#DA&)h¿ Ä GeœG½…FG‡ÀG

ÿäP#ÐwDäWý

ò

У `%&N!S$3')23#z!M232Ll$&(/&($,*#&(C2312C$&N$/&('(*&($35&

¿ Ä GeœG»…PGÄ À[G

â

Ûb )ä

Î(Ï

üVӝÜhä `%&s/&($/2#ç2389&=!C„¦^>ƒq&(ÃR%h$&)!S&)$$/&(.23h@

Þåä?”1—C’‘?•b?&)A&)y2345D&C23&C2389&i!2&TA$/2U#ž$/&(')*&($/&(o;232K#

(23)

Ä Ä

=23?&C&Ra23&i&EF-7#&)W2nm,23$5Q?2#HG

æ î ÓÜ ÒbÜ â 1ÐH#äF(BÓ Ï_õéô ï <Ӓ[ý pU&A&)©23 5D&@2&@*Q&=!23&  572/23&

&)'LN$&(23&)y232&N#b$&)'(*#&)$/+GN`%^"QQf+:892&(:223&N841EFfv

8]Q8ê-?$P'(&(/35?&Vž$&)'(*#&)$/+:-7&(&)y!J2&Tž$GaXw2K86B+;95D&i232

2>a23&"2$3/-D$/2L123@'B-'(2Y+42312Ka23&i8923i!')2#$(G

â

ÝS ?äW Ò

â

ОÑbÒlӝÐ

Ï

`%&Q8Ê!m23&86E?8]Q8 -$PQ'234$23&-D23&(<2n

!b23&Cm23?&"#mkO&()R$&)-7&(')2*&(+G

â ÝS ?äW Ò â ОÑbÒlӝРϩò ÓSÐ Ï pU&)A&(q^23?&]-D$/23#y!Z#b22i84B+s57&

$&)'(*#&)$&)z2>23&i#mkO&(%!SQH-?$PQ')2#='(-')2Y+#R57&)!S$&i-$&)/Q$&V

jk $#-?(G]`%&{&)'(2#sz-$/FQ?')23#z$3123&NU&)A?&(qio&EF-7v

&)W2nD!SQ')2#mG

â ОÑbÒbÓÐ Ï¨Ú Fä `%&($/&"$/&^&)A&(2YkON/2323&)\!S#$O2&UA&(HRbŠ1‘fÞçÚf”Y”˜

Š^èéÞçÚf”Y”˜yê

|ÙU| …

#>€ i}l›

›5_‚O}lT_ T,V/.0D–2 !‡4/2 /.0_/ŠE

pU/'($/&)23&U&)*#&)<23aT/8]Q?n2#{-$/##$38 86B+{57&U89-&(89&(<23&)6\T&(6,2

#$^4'Ls!d-7#<23&)$)Rm$/23&)z5<+:2&]&)*&(<2^289&G>ƒ„&(os&)*#&)<2iU')$&(23&)HR

2>&)$/2&(;<23N23?&T'L£º&(=/2>122&C-D#/2#@'(23&)=5W+=f23%&*#&(<2

2384&Gl`%&O8]Qn123#$ž')n/l23?&(V2$3B*#&)$&)J23&O/2b5<+T-?$P'(&(/^&)*&(<2M5<+C&)*#&)<2BR

k>@23?&&)*&(<23]2s89-7#&{23&4'($/&B2#q!%&kæ&*#&)W2(Gy`%?&(&k>J2&(

5D&@-?Q?2N<2y23&@&*#&(<29·WQ&(Q?&:'('($y23y2&@&)*&(<2{2389&RJN#$/86ÂGz`%&

8]Qn123s&(?Ck>?&(o23&{·WQ&(Q?&9!\&*#&(<2VU&(89-?2Y+z#$^k>&)h@&A&)h&(?Fv

2384&OJ-&)4$dN&)*&(<2Z'BQ?&(Mf2dF23"&):¿#3º"-$/A2[À[GIKNQ/2$32#

!l/'($&23&i&)*&(<23K%#f*#&):=A#Q$& Ä G½…FG

XYVC#5P0/&)')2b#$/&(<2&(C-$#$38984a#Q#&J&D0B*?R+##QT86B+U89-&)84&)W2

/'($/&)23&%&*#&)W2OQ??i^'(#<23$/#')n/(R2&%/2J&($>¿S&($/&¹d¢P84 U?&($3ÀR

@&)*&(<2>'("¿Ã¢F86¯J*#&)<2[ÀRa?k>=623&KA#Q$/&Gd`%&"-$/##$8æ/23<2323&)

23&^¢F84 U&)$Z2nëz(&)d2Z5<+6-/{¢P84¯d*&(<23O23Vf2BGƒ„?&(62&^8{v

Qn1234,2L$,23(RP23&^¢F84 U&)$O-?$P'(&(/&)\23&KA$,2a&)*&(<2BR2&(423&^?&EP2BGM¯M'L

¢F84¯J*#&)W2J'(#<2Ld^-7#W2&($b23"2k>&)$(R<k>'LN')#<2L2&a89-&(89&(<2L2#

!2&C-$P'(&)4#$28u!22&)*&(<2BR£23$/##&)$&);5<+=23?&V¢P84 U?&($)GZ³£$

&E?89-&R?23?&C&*#&)W2Uf2>-$P'(&)&)K84B+57&¹

(24)

Q,23$23#6!b23?&C'L=/2$Q'23Q$/&G

cd$/FQ?')23#=/23$/2>!;#7k\&)ÂG

¯d;!l-n123&BQ;-?$PQ')2#mG

´:!SQ?')23#@&)*&(<23

IK5?#89&(<2&)*#&)<2BG

I /23$/¸'L­!]?')$&23& &)*#&)<23s84B+¨P#ç&¹-ìk\&)"?&($,23#KìfR%ìk\&)

?&($,23#KìfR

. . .

R"ìk\&)_?&($,23#KìfR*ì¶-23&(Qs-?$PQ')2#;&(?KìRDìe&(y!J-$/FQ?')23#KìfG

(25)

-D&)]#2&^'(84-&EF2Y+9!ž2&^89F?&(D23?&^WQ8]57&($a!b/2'23*&K2Y+P-7&(

!_&)*&(<23)G\³#$O&E?89-&RFf!ž84!SQ?')23#O$&2L&(@W2N')'(#Q<2(R?k\&U84#<2\#&2

&)*&(<23"k>'Lyk\#Q?y'(Q&]6-$PQ'23#yf2U!Z4k\&)ÂGU`%Uk\Qs2&(z8{v

-+6'($/&B2{5ìk\&)ž?&($,23#Kì?&*#&)W2U2]23&)$a2389&U?&)23&)$89&)=5W+623&i$&)-$

-D&)$FHG

í/P¹í/PUO q W>rN_ îïYQZb\^] r[u rNkbkb\Ud^x rN_d^YQu YQ¤s]>dUvwx Ÿaj_a`aK¡Qa*u[_v d^u

_W>a™v_YXxWbrQvð_d^x'vdU¢£Zb\^rF_dUYQu Y[¤cYQdU\ñk>ŸyYX]>Zbxç_d^YQu \^YXYNò

\^d„òQa@l

pU&(-7&(?6#s23?&]89#Q<2K!M$&)&($,*#&)"!d#b$/&B'L?&(HRmk>?&(z?&($,234?&)kµ#

k\&)(R>k\&z84B+o0/Q89-¨#­¨r~-23&(Q¨-$PQ'23#HG¤`%&o##$f23894

86123&)862'(_'B'(Q23#>k>_57&]'(Q?&)qy&)')2#zITG‡{?zIVG½…FGiŸ\&(kiR

A#Q$/& Ä GÄ R>{84-&^&E?89-&"!JN-7#/5&"-$PQ'23#@')&($/¨G

³#Q$& Ä GÄ ¹Z¢P2L?$:cd$PQ'23:cd$/A&

³£$/#8Ê23&"#$-HRFk\&"$/&('(#ëz)&^23&"/-7&"!l]84-&U-$/F?Q')2#@-$/A&U!

¯^óK¸·´"ô¥Á˜ËÍ÷´‘¾ ÉʽM¶¹¸·´@´^º·Á:³=»«ËÊ´š¾UÎ3õ«Ó:ë¹´@ö·Ôö[Á˜½¿Ð/ö·Ô÷«Î²Á˜Âp´DÄ«Á3¾À´šÐX±:½MÄ¿±:¶¹¸/¶p¸·´Qø"ÉÊËoùÉÊ´‘ËÍÐ>ú±Ð´UË

û

ö·Ôýü:þ„ÔNÁ:½«Ð¶p¸·´Xø"ÉÍËÿ6´‘ËÊËåú±Ð´‘Ë

û

ö·Ô÷þ)Ò*¸·ÉÍÇS¸%Á˜Âp´Cдš¾¹ÇU¹ÉÍļ´‘ÐËÌÁ¥¶p´UšÔFóK¸«´UÏÁ˜Âp´Q¶p¸·´C±3öpÇU±:³T´[±:µ

¾À¶¹±ÇS¸«Á3¾Æ¶pÉÍÇ@ô¥Á˜ÂpÉÍÁ:Ä·ËÍ´‘¾jÒ*¸·ÉÌÇS¸bÁ:¹´FÓ:ÉÍô:´‘½>¸«´UÂp´"¶p±TÉÊËÍËÊÿ¾Æ¶pÂpÁ˜¶¹´@¶¹¸·´Nÿ¾À´N±:µÐÉ̾¹ÇU¹´U¶¹´F´Uô3´U½¶p¾‘Ô

(26)

23?$&(&i-$/23)R!89$d23{#H?Q/2$/+@&)#?&(&($/ IK$&CŸUG£ Q&)5W+ŒÃG

â Í ¿’ƒh&)ž?&($,23#LÀaXYs2&(˜FÜÚf™6˜Þ -D&)$FHR!SQ$kO&($/&T-&)y:2

2&"2389&(

t1

R

t2

R

t3

?

t4

R$&)-7&(')2*&(+G

â Ù

¿cM23&(Q9-$PQ'23£À`l#&)2&($)RP2&>#?kO&(M-$/FQ?'(&K2Z-n2&BQ{-$/v

Q?')23#=Q<23m2384&

t 0

G

â á

¿Â¦^r£vY-?n2&BQ£À>IU^2&N-$&)/Q$&{!M23?&N#_A&(o$#-?(RHkO&NB*#&9z&EWv

-7#&)W2n+9&)'(?N-$PQ'23HGZta&(2&{‰˜P‘ ™PŠd‘y-&G

XY¡A#Q?$& Ä GeœRJkO&@B*#&=s5?2]89#$/&@?*')&(-$/F?Q')2#¡-?$A&GoŸ\&!S#$&423&

?&($,23#=!kO&( Ä R5D&2Yk\&)&(s289&

t2

?

t3

RkO&T/&(&C232>2&T-?$PQ')2#;#P&(

r:-n123&BQ@-$PQ'236!S#$%V/#$,2>-D&)$P!ž289&RPQ<23DkO&(

Ä

a&)$/2&(=

/235ëz)&(m2&d2323#-$/F?Q')2#HGžƒq&d23&)T-$/F?Q'(&M#i-23&(QiQ<2323&M-$/&(/Q$&

$/#-=2@289&

t 0

R^„-$PQ'23¨#F&)=r~-23&(QHGÈ`%?& /89$4/2Q23#

P'('(Q?$a12a?&($,23#4!žk\&)7œR?12O289&

t4

RF5QF2\23?O289&R<23PV8VQ'L#7\57&(&)

$&)'(*#&)$&):239&)&(-:Q-:-?$&(/Q$/&G

³l#Q$/& Ä Geœ¹Z¢F-7&(')nH'(&C!b23&i/89-fA&(-?$PQ')2#=-$/A&

)±:¶¹´T¶¹¸¿Á¥¶Q¶p¸·´/Ð÷ÂSÁ¥¶pÉʱ3½6±3ÂQËÊ´‘½·Ó˜¶p¸«¾F±˜µj¶¹¸«´/»·ËÌÁ¥¶¹´šÁ˜Ã »·Âp±ÐëDŽ¶pÉʱ3½6É̾Q¾¹±:³T´UÒ*¸¿Á¥¶N´^º²¶¹´‘½«Ð´šÐÔ

óK¸·É̾KÉ;*¶¹¸·´QǑÁ:¾¹´"Éͽb¶¹¸·´š¾À´N´UºÁ:³T»·ËÊ´š¾*Á˜½«ÐM¶¹¸«´QÇ^±:³TÉͽ·ÓT±:½·´š¾UβµÈ±3Â*ÉÊËÍËÍë¾Æ¶pÂpÁ˜¶¹Éͱ:½b»·Ã·Âp»¿±¾À´š¾UÔ

(27)

&)*&(<234Õ<2$PQ'(&423&@')#'(&)-?29!KÕ#ZA&(-$PQ'23#-$A&G ° *&(

2312U23?&($&{9k\Qz--D&($^84!SQ?')2#)Rk\&]kO#Qy-72"$/#-Uz-7&BW

N23?&%-$PQ'239-?$A&G¯M5"Qd23i&[E?-{23&>89F&)N/Q'L"84&)$

d#?&!m23?&,23$/&(2Z!m?')$&23&>&)*&(<23)R?84W"!SQ?2Q$&>&EF-#M$&)n2*#&)+

&B,+@23{89-&(89&(<2BG

|ÙSƒ …

#>€ 9

'#34ª€ÈX4:4­2 #(@X4ª@T— .@/ŠE

ƒh&q$/&qk ')#/&z23ç2& 5D#$/&($=!Tk>2:=Wk>~&A2*&(+¨¸k>2

5D&)/2T'Bq5D&9'L$')2&($/ëz(&)¡C&)5&{/#Q?2#?Tq<23Qf23*&N84P&)(G6³$#8

23^-7#<2"#mRHXK$/&(f+s#z&)84-?$'Bb89F&))Rm89F&)K#*&(y23=89&V5<+z8V+;23QF23#$)R

 KQ/&(5<+#RU©!S$/#8 -$!S&(/#62@«#$/© >+F?$I"¢PI \`%WQ&)/23HRK±i&(f*#&(mR

Ÿ\&($/C4K/8]Q/&(mGdIUF89-&)84&)<2L2#)R###$/23?84l{'B'(Q?n2#B*#&

5D&)&(;#&i5<+=89&i;XOB*&T&)$f*#&(;89F&)a!S$/#8æ2&i84P&(a#f*#&(mG

í/PMPUO cYDî ¢£ZbxyW'YQd^\ xjrQuàrQuªdU\(q a*\U\1Ÿya*xjY)¡QaKŸ d^uàrQd„¡Qa*u

_dU¢ a8k6aKŸyd^YX]l

IUa?&)!Qf2BRP23&U289&K-7&($/PO&2a23N+RW5Q?2%2&($/>$&Uk\&)HGJ`%&"·WQ&),v

23#y23&)q"kÈ8]Q?'Lq#'(q57&N$&)'(*#&)$&)¡5D&]2&{#bk\&)J&*#&)$/+ B+#GN`%

U/23P'L,23'V*$5&C!MQ/Q+:yQ')&($/23<2Y+GTpK&(-7&(@#y2&]Pv

!S#$842#9B*5&a+#Q84B+{-7&('(f!’+9,23$5Q?2#d!S#$M&('L@#kO&(D/&(-$32&(+

#$i84-f+s?$3BkÈ23?&9*Q&("!S$8× &)<23'(d/23$/5QF23y!S#$^23&)8 ÂGN`%&

n2/23&)$N]23?&;&=5&)çé2&=&B/2989#Q<2{!K?!S$8423#HRd{]23&='B&

©2&s&($f+é/2L#&(!Ch-$0/&(')2$&Bëz(23#HG¸¦^&y-7#/5&:?/2$5Q?23#ç!S$

+q-$PQ'23HRM'(#Q5D&;y###$/86O/2$5?Q?23#hk>2éå#†nTvLROª†nR>‡†n

-D&)$')&(<23&()R?!S#$O&E?89-&

p 10 = 1200 Sm 3

R?kiR

p 50 = 2000 Sm 3

RF84&)Q8;RF

p90 = 2500Sm 3

R#HGM«23&R

1Sm 3 ≈ 6.3

5$$&))G

í/PMPpR q W>rN_ªrQŸac_Wba8Ÿa*xjY)¡QaKŸyrNgB\^a Ÿa*vaKŸ¡Qa*vYQ¤ÙrQu`YQdU\fîïa*\^\Hl

`%&o$/&Bh!ik>'L„¨#>kO&(U84B+©$/&('(*&($@#ÃR\2&y$&('LHR892&(HR\

dM$&)&($,*#&)] 23&9A&(h84+o?2V57&9$&(')*#&($/&(HG:`%&84#Q?W2T$&)'(*#&)$35?&

&(-7&(?]#¡/&)*&($3\!')2#$(RbjQqjkiRk\23&)$(Rd<(R-7#$/#f2Y+#RJ84#?#/2T23?&($)G

ܽ ¾À±3³T´TÇU±:³T»«Á:½·ÉÊ´š¾FÉʽ6¶¹¸«´X±:ÉÍËåÉʽ«Ð·Ã«¾Æ¶p¹Ï3ÎÁ3¾FÉʽ)±3Âp¾¹Ñ)ÏÐÂp±"°[Î𶹸«´=³T´šÁ˜½·Éͽ·ÓB±˜µj¶¹¸·´

»¼´UÂSÇ^´‘½3¶pÉÊËÍ´‘¾KÉ̾*Âp´Uô3´UÂS¾À´šÐÔóK¸¿Á¥¶*É;‘ζp¸·´ "!⻿´‘ÂpÇU´U½¶¹ÉÍËÊ´3Î

p 90

βÉ;*¶¹¸·´NËͱ¥Òô¥Á˜ËÍ÷´3ηÁ˜½«Ð

p 10

¸·ÉÍÓ:¸ðÔ

(28)

$&)'(*#&)$35?&i$&)&($,*#&)K!S#$a2&i#mkO&()¹

@ݒäW

Ï

?ÓÜ7ä

Í

³2{/2$5?Q?23#]!S#$N$/&('(*&($35&:#\!S$9&('L©akO&(ÂRZ2&(

$Bk¬!S$8æ23?&(&GO`%?&T/Q8 !b23%k>723&):57&(')#89&i2&"*Q&^!S$a2323

$/&('(*&($35&"#ÃGl³#$\&[E84-&RF!ž23?O*#Q?84&^a/Q89&(=###$/86žR?&EWv

-7&($,23Jk>?&)/2386123&%å#†onVv3RPª†nTvb?;‡B†nµ-7&($/'(&(<2&)J!S#$d2(R<f23&($/2*#&)+R

/&)22

µ

σ

$/&('23+G

@ݒäW

Ï

?ÓÜ7ä

Ù

³¡2&232LO$&(')*#&($5&;$/&(/&($/*&(9A$,2BRM23&)é?/2$5Q?23&@f2

#<2s23&6#Mk\&)(Gy`%N89#Q<2]84B+ 5D&6!SQ5<+h?$3Bk>y!S$/#8 2Yk\

/2'23*&>,23$5Q?2#)RF¢F`¦^XXŒc­¿ Ä GeœG½…FGf‡Àd³.¿ Ä GeœG»…PGÄ À[G`%&K86

frm&)$&)'(&%!S$8 2&($/23f*#&"‡#R<23&)$M295D&)i5Q?2d!S$/#8 2YkOV-?$#55v

f2Y+s/2$5?Q?23#(RmU22"kO&{2K2389&],2L$,23^k>2y2323J#$/&('(*&($35&

?=2&(;f*F&"2>57&)2YkO&(&):2&i#mkO&()R2%2&i23&)$%kaB+;$/#QHG

IUf23&)$2*&4‡TK2$f*FÃR?5D&)k§k\&Tk>ž&[EF-#f2^23&)$123*&]…PRm92K84$&C'(#8Nv

-&Eq#Q?23#HG:IU2&($/23f*#&…:V:*#&)$/+¡FPh&[E84-&6!>?ku'($/&B/;23&

'(84-&EF2Y+i')$&(23&)JU/2$5?Q?23#i84#$/&O$/&(-$/&(/&(<2L2*&\!S#$l2&\Q?'(&)$/2L<2Y+#Gbƒh&

-?2%{,23P'L,23'^*$/n5?&U<23{2a5Q]5F'LW='(/2$Q'2Kf23%/2$5?QFv

23#4!S$/#8 23&)&GZ`%?a'($/&B/&(%')'(Q$')+4!ž2&^&(,23862&()RF5QF2%'(#<2$5?Q?23&)\23

23?&C')#89-&[E?f2Y+:?&(')&T'($/&B/&(>8]Qn12362384&G

á$#ì%#Ù$#Í &

Û_ ?ӝ

Ú

ü{þ

ÎÎâ('

>&B*)£YŠŽL›,+£”‘?›áaÜږ‘’”¼ÚÜÚ.-’‘NˆCÚf”PŽLZTb>-?$#552Y+K,23$5Q?2#"5&(

#4&)*&($D,23P'L,23'*$5&) W3HRWka2&($)R?<)RW89&(/#?O&23'GXw2a&)'($/57&(

23?&62323a84#Q?W2]!>$&)&($,*#&)4¡23&OA&(mG `%?]/2$5?Q?23#¡T#*&(Õ5<+

$&)&)$/*#$>&(&)&($2:&($f+/23#&i!_2&i#D-$10/&)')2(G

á$#ì%#Ù$#Ù & Û_ ?ӝ]ÿ ôTÎ/'

`%&O'(#89-&[EF2Y+i!7$&(/&($,*##$V84-7#$,2L<2b?'B123#$_!?ké8]Q?'L]!2&a#

232^')23Qf+@86B+;57&V$&)'(*#&)$&)HG"¢F84&T#ž')#84-&)2&(s'($&(23&)o4$/#Q?23&

!S#$C&(/'($/5s23?&6'(84-&EF2Y+qV¡&Eq$#:!S$/#8߆:23q‡#Gs`%&6&[E

23?&)+@'(&(=%t\X%=$&BU>&(/&($,*##$t\#84-?&EFf2Y+XY&[E

‹

>&(/Q$/$--7#$/2&(åŒÃG

(29)

á$#fì0#Ù$#á & ò1'

`%&sš>LŽLŠ«‰2-;“ž”PŽŒŠ1‰3•aK³\Rb&)'($/57&(V2&6!S$')2#q#$]-7&($')&(<2L#&!%22LZ$&[v

&)$/*#&)Nk>'L¡84B+ 5D&4$&(')*#&($/&(HG ³¸Ns&B$C$/&(23# 2z%t\X4¿

Ä

G¶œG½…FG½…#ÀR

#$/86+Õ/2$5?Q?23&)HG XY¨23&)$k\#$/(Rk\&z*& ¡'(#?23#/23$/5QF23

k>&($/&UWk>?T23?&^%t\X+P&(?\i#$/86?/2$5Q?23#N!S#$ZK³OG43\I¸,23Q?+9!D23

$&)n2#/-@>5D&)&(;#&C=/Q8986$/ëz)&(@=IK--D&)E:tUG

á$#fì0#Ù$#ì 5

Ð76 #

Ï

Û_äVÐ ÝmäF)äP7äPäP#Ð7äW lݝäTdä{Ñlӝ)1ÓSҞäPÑ:Ð

Ï

Ð

Û_äsÐ7ÓÂÝ6]äPݝÝÂ

'

° f*#&)V23&\PQ?8]5D&)$J!£#<k\&)b23^57&a&)$/23&)HR<?N,23$5Q?2#ž!S#$b23&)$l$&B'LHR

k\&T86B+=/'B&C2&V#QF23'(84&)K!l23&T/2F'L/23'C*Q&(92312K2&)+;Q?8x242&

*Q&4!a2&6232LM$&)&)$/*#&){$&(')*#&($5&o¿$Bk>¡!S$#8ù¢F`¦^XXŒcµ¡K³98%t\X,À[G

XY¡2&($Ck\#$/(Rd*#&)

N W

¿WQ8]57&($T!>#JkO&(3ÀR$/&(')*&($5&6$&(/&($,*#&()R

R = ST OIIP · RF

Ržo/2$5?Q?23#

V 1 , V 2 , . . . , V N W

!S#$U23?&N#l$&(')*#&($5&{!S$

&B'L;k\&)ÂRFkO&T/'B&C5<+

∆ = P N W

i=1 V i R

¿ Ä G‡À

23{&(?sQ-@k>2

∆ · V i

H$/&('(*&($35&"!S#$%#mkO&(

i

‹

¯d$/6ITG£Ÿ\&($/¼ŒÂG

á$#fì0#Ù$#Þ & Ûbä Ï BÛ_Ð7ÒlÝÑ Ú ü{þ ÎÎâ Ï ÑÈÿ ò dä ï äWøwäW1äPѼÐwDäWh(ä<BÓ Ïbõ

Ñlӝ)1ÓSҞÓSÐ

Ï

VøÃÐ74äW Û.Ð7ӝÝ:6VäFݝÝM1äP

ï

äPÓÜ7äPÝSý

'

`%&^/kO&($Z23i23O&)-D&)O#42&K?!S#$/862#]*n5?&GbXw!H2&K&(##$-'B

-D2#?a!b23&i#mk\&)>$&iWk>HR£f23&($/2*#&N‡i/#Q:57&"'L#/&(HR75D&)'BQ?&

299#f+Q?&($6/Q'L.')$')Q89/2L'(&)4232+P/{!^2&:$/&B'L©!^&('L.$&[v

-7&('23*&o#>k\&)^84B+©57&z-7&($/!S$89&(HG  KkO&)*#&)$(R^2?!S#$/862#éh*#&($,+

&EF-7&(/*#&Rb$$/*P2in123&V,2L&]!M23&Nb-$10/&)')2i&*#&)#-89&(<2(Rž$&(·WQ$

&EP23&)f*#&@+P/(G=Ia2V&B$/&)$i/2L#&()Rd2&($/23f*#&4…=kO#Q¡57&4-$/&)!S&)$$&)#&G

Ÿ\2y¢F`¦^X/XŒc.:%t\Xa$&"#f*#&(:2;&B$+6/23#&G

í/PMPÀí q W>a*u`rNŸac_Wba YQd^\ îïa*\U\^v­kBW>r[vwa*]`dUuml

`%&V&)$/2#@2384&)>!2&TmkO&('B?25D&C&)A2*#&)+@?&)23&)$89&)ssPv

*'(&R\23?#Q#¡-?nV84#<2]B*#&=57&(&)çHGzIK<HRd&(-7&(?o#¡2&@Pv

!S#$842#çB*n5&RZkO&y84+é/&)2@&)$/23#ç289&:?/2$5Q?23#N!S#$4&B'L.kO&(

;=< Á:¾¹´‘ÐM±:½b¸·É̾ƶp±:ÂpÉÍÇ?>)ùA@B>0CDjзÁ¥¶SÁ·ÎѲ½·±¥Ò*Éͽ·Ó[¶p¸·´>0CDçÒ*ÉÍËÊːϲÉÍ´UËÌÐ>Á=½·±3¹³XÁ:ËoзÉ;À¶¹ÂpÉÊīö¹Éͱ:½bµÈ±:Â

¶p¸·´>)ù0Ò*Éʶ¹¸«ÉʽÁT¾Æ¶SÁ˜½«Ð«Á˜ÂSÐ>д‘ô²ÉÍÁ˜¶¹Éͱ:½b±˜µÁ:»·»·Âp±HºÉʳXÁ¥¶p´UËÍÏE·Ô F

û

F"!Cþ^εÈÂp±:³­¶p¸·´FËÊÉͽ·´šÁ˜Â*³T´‘Á:½ðÔ

(30)

+qN23&='(&;!"23&)$123*&;…ç¿ Ä GeœG»…ÀRO 89#$&@&23&($/842*#&@-?$P'(&(?Q$&

?#Q=57&i'L#&)HGZXw!/R&(,23842&^k>23m¹

ü{þ

ò

þ×üVӝÜhäzþ{ø

ò

ӝ1)@þ9ÓÝ `%&4/23P'L,23'4-&4q289&N!a2&4*&($/+oA$//2

#DkO&(ÃG

â

Ûb )äzÓ

Ï Ó Ï

äW·? Ý `%&4/2F'L/23'6W2&($,*i5D&2Yk\&)&(¡2&6-&4o2389&(i!

2&i#7k\&))R!’2&($%23&"A$//2#&">5D&)&(s-?&):HG

|1HG

‰‰

'#6:4ª—;X4 2 #(@X4·E

`%&\¦^<³&("84P&(ž23&M')#84-?&)2&d84P&)!S#$ž23&M-$/F?Q')2#HGbXw2b86#&)H23&

#mk\&)>s')#//2>!J/&)*#&)$3b2&($%2384&"?&(-7&(&)<2"=2384&U&)-D&)&)W2

/2F'L/2'"*$5&)(GJ`%?&)+;$/&"&)A?&(s=&('23#

Ä

G»…{=$/&(-7&B2&(;&($/&¹

>&(')*#&($5&mLMQ89&^!J¦^ÃR

V

cd23&(Q;cM$/F?Q')2#=23&R

r p

cd23&(Q;cM$/F?Q')2#=³$3')23#HR

k

´:1EF8]Q8 cd$P'(&(/ta-'(f2Y+#R

r m

¢F#89&"2&($a*$/n5&(%&)&(&):!S#$a2&i$&)-$&)&(<2323#$&¹

þ9ӝÝ

â

ОÑbÒlÓSÐ

Ï

ÿ ?BäJI

r

`%&U-?$PQ')2#9$3123&K2aC#*&(92389&>ZC!SQ?')2#

!b2384&^=-$&)/Q$&G%¦^=-n2&BQ=-$/F?Q')2#=2a&(·WQ

r m

#$

r p

:2

r;-23&(Q6-?$PQ')2#42OZ$&)-$&)&(<2&(;5W+923?&K!SQ'23#

f(t)

¿S&)A2#

ITG»Á#À[G

XY¨&)')2#

Ä GÄ

Gf‡#R%A#Q$/&(

Ä GÄ

Ä

G¶œR%kO&z3Bkë&E?89-&)!i23&s5D&)B*F#$!

-$/FQ?')23#;$32&V::#žA&)HR£&EF')Q42&V841EF8VQ8 -$/F')&(/4'B-'(f2Y+#G

³#Q$& Ä GeœN%N#PF6&E?89-&^!]')#89-&[E-$/F?Q')2#@-$/A&R?<*##f*F]-$/v

Q'23#s$23&RD$/&('(*&($35&C*##Q84&Ts-n2&BQ;-$/FQ?')23#HGK¢F#89&C&(&)84&)<2L$,+

-$/#-D&)$/2&(%!l2&i#mA&(=89F?&(H(¹

+Kä6Š1ÜÚLKa:Úf™s—{‰L”Y™z”1—@Š1‘mG{Xw2C"23&{#kO&(i-$PQ'23 $23&9?

#J$&)'(*#&)$35?&{23##&23&)$C22C&23&($/84&(i23?&9,2L2&R>Š^è #$Š1‘-n123&BQHG

`%12\(RW#&>84+{'(')Qn123&a23?&289&!mk>'L4kO&U'(Q?8]Qn123*&(f+Vk>B*#&

$/&('(*&($&)ym23?&Cm$/&(')*&($5&C#=-23&(QHG

(31)

232L-$/F?Q')2#{$3123&4#$/&(')*&($5&>k>?'($&(&Gd`%&/2L123&!m2&

A&)HRk>M57&6&23&($/84&(¡Vf!>d2&6#dk\&)T8]Q23&)#Qf+z/23$/2&(

-$/FQ?')23#HR#$/&(')*&($/"23?&>84Q<2dB*P"57&(&)4$/&('(*&($&)HGZ´:#$/&%!£23

=/&(')2# Ä G½ªFG½…FG

¦Ur.-?n2&BQ-$/F?Q')2#$23&@]&)A&(Õ23o57&=&EF-7#&(<2na!SQ?')23#

‹

IU$?&TŸKG£ KQ/&(5<+ŒÂG

í/PNMTPUO q W>rN_ªdUvª_Wba Ÿya*xjY)¡QaKŸyrNgb\Ua£Ÿa*vaKŸ¡Qa*v<YQ¤1_W>a YQdU\ eba*\^]l

`%&]$/&('(*&($35&T$&(/&($,*#&("!J23&T#žA&):&)2U5<+:2&V/Q8x!J23?&V$&)'(*#&)$35?&

$&)&($,*#&)"!MH23&C#žkO&((R7&)'($/57&(ys/&(')2# Ä GeœG»…PG%Xw2U84B+=5D&T$/&(')2+

&(?Q'(&)Õ!S$/#8 Ä GeœG»…PG‡#R Ä G¶œ?G»…FGÄ ? Ä G¶œ?G»…FG½…FRl!%23?&(&684P&(]$/&6Q/&(HRZC23

+P&(a23?&i22LH$&)'(*#&)$35&T$/&(/&($/*&(K@23&i#DA&)HG

í/PNMTPpR q W>rN_ªdUvª_WbaO­d^\,P1d^a*\U]RQŠŸyYX]>Zbx§_d^YQuTSrF_a@l

Xw!\2&4·WQ&)/2# kaik>2C23?&4#A&) -n2&BQ -$/FQ?')23# $32&{k\)Rl23?&6Pv

/kO&($ik\Q 5D&9"2$*PJ"2&4&95D*&U l2&{Q8 !O2&4lkO&(i-23&(Q

-$PQ'23#¡$3123&()GoŸ\Q?2]VkO&@B*#&2&($T!')2#$]/Q'LéV-?$PQ')2#h/2L123&()R

23&C?/kO&($U%8]Q'L;84$&"'(84-'(23&)HGdIU:f23#D'(#,23$<2BRkO&CB*#&

23&Vz”"W#ÜÛN˜ÛàáaÜÚ7ˆ\‰3ŠŽLL—L—(”Xڍ4¿Ä G½ª#ÀRN*$5&^&2239;Q--7&($>84f2O292&

#m$&(')*#&($,+#G

XYs23&i!S#k>?RF23?&V841EF8]Q8æ-$P'(&)/4'B-'(2Y+@k>H57&V##$/&(HGO`%&

!SF')QMk>?5D&#42$/+P?C2T&[E?-?n92&K57&(*P#Q$Z!m2&K-?$PQ')2#9$3123&>!H2&

#PA&(HR#k>2{$&(/-D&)')2M23if23d#FkO&(J-23&(Q{-$PQ'23N$32&(Z{$&)'(*#&)$35?&

#"¿IVGf‡À[G©`%&;84f2Vk>a57&:$/&(<2$PQ'(&)©é/&('23 Ä G½ªFGÄ R\?h?23&)$

89&(?23N23&i')#84-?&EFf2Y+!b23&i89F?&(M¿SIVG½…#ÀG

á$#Þ$#Ù$#Í 5

Ð76×Ñ_ÐHäP4 1Ûb

Ï_õ äoÓ

Ï

Û_ä

ï

ОÑbÒbӝÐ

Ï

) ?äsО<<Òb

'

`%&a-$/F?Q')2#C/2323&O$&(-?$&(/&(<23J2&\-?$&(/Q$/&>CjkiR<89##,22&($/(R#T2&

A&(HGJXw!

V

M2&>2323*##Q89&!H$&)&)$/*#&)a$&)'(*#&)$35?&!m2&K?kO&((R

kV

84B+

5D&K$&)'(*#&)$&(¡Š1‘fÞçÚf”Œ”˜

‹

IK$&TŸUG Q&)5W+ŒÃGJƒ„?&(

kV

#£\57&(&(@$/&(')*&($/&(HR 23&V#žkO&(U84B+s6#&($$&(')*#&($"l2^841E:-D23&(<2nÂRDy23&T$&)86?

(1 −k)V

#<l$/&(')*&($/&(92dV&EF-7#&)W2n+i&)'(K/-D&)&(HGd´s23?&(8423'B+#R k\&K&)A&U232a12Z289&

t

!’23&)$M2&U-?n2&BQ9&(42389&R

t plateau

R<23&K-$PQ'23#4

(32)

f(t) = r p e λ(t t plateau )

k>&)$&

λ

92&;'(#,2L<26&(/Q$q22{23&;$&)86

(1 − k)V

ak>a57&

$&)'(*#&)$&)y

t → ∞

¿IVGf‡À[G

I¤'L#&i=2&i-$PQ'23#=/2L123&i86B+=NP'(')Q$%k>&(:-/{:{&k

kO&(ÂRžU2^^2=2&{89#Q<2^!O$/&(')*&($5&R

V

GCXw!O2&{89#Q<2"!Z#

$&)'(*#&)$&)9Q?-]23U2l-D#<2BR

ω,

l84&($ž23V23?&a&)kÕ*Q&\!

kV

R#-?$PQ')2#

k>m')#<23WQ&Š1‘ÙÞçÚf”Y”˜FR?&(/&i2ak>m')#<23PQ?&=Š^èéÞçÚf”Y”˜PG

á$#ÞY#Ù$#Ù &

Û_ ?

ï

1ÐHÑlÒbÓSÐ

Ï

?BäoÑbÐZ6]äoÛ_ 7ä Ð\[

ï

ݝ FäW Ò¨ øÃäW;Ó

Ï

(äWBû

ÓSÐ Ï Ð£ø%ÛbäsÐDӝÝ*6]äPÝÂÝ '

³#Q$& Ä G»ªsQ/2$32&(V2&@f23Q2#!K-?oÕé#OkO&(a2{r.-?n2&BQ

-$/FQ?')23#HGl`%&^/2323&K!H2&U#A&(Z?k>@5<+{23?&K23-6#$-HRP'B&);“M]WF™

ˆO‰3Š(™˜£ŽÃŠ1‘=ˆO‰3Š^KQڍGJ`%&"Fvw2/23&(6'(Q$,*#&"/23$/2T!S$#8 23?&U-7#<2i¿

u, f f (u)

À

?k>N2&!SQ?23Q?$&@&*#&(#-89&(<2{!>23?&@-$PQ'23$32&#*&(23?&=5&)'(&=!

89#$&"&*#&(<2(G

XYV23?&O$/&BëzB123"!23?&\-$/FQ?')23#C-$A&Z'(Q$/$&(<2+i57&(?U8]Q23&)¿S5D2,v

238È#$3-4AQ$& Ä G½ª#ÀR<kO&^--?+N23?&K$/&(Q?23M!S$8È23&>A?EF&(-?$PQ')2#9-$/A&G

`%&9'(Q$,*#&486$/&)

(2)

R_C&(<2'BJ!S#$"5D23 #$3-?Ck>f23 $&)<$o23=23?&9-?$v Q'23#@!SQ')2#mGJIK!’2&($%AN23&^!SQ?')2#

f f (u)

R?2&i'L&(?#&^%84--?

2M2T23?&K2384&>864!ž#Q$  $&(a-$PQ'23#6-$/A&GJXY62&U$/&B£-$/F?Q')2#

-$/A&RPkO&^A=#Q?$&)*&(>2

t w

¿S2_%k\&)’ÀM62&UAQ$&RB*P]$/&(')*&($/&(

ω

ÃG

`%&i-$/FQ?')23#=$32&i2>23a2384&R

f f (u) = f(t w )

Rž¿&(·£GMIVGf‡è<À\

f (t w ) = r p (1 − ω − kV (1 − k)V )

&)'(&6¿')n8æITG¶œWÀ[R2%289&

t > t w

23&i-$/FQ?')23#=$32&"

f (t) = r p (1 − ω − kV

(1 − k)V )e λ(t t w )

¿ Ä G½…#À

¢P2Q?+P]2O$&)Qf2ak\&"?23&^22\2&"89#$&K#7B*PN57&(&);$/&(')*&($/&(HR

ω

RP23&

&)/&($N23&@-?$PQ')2#Õ$23&k>\57&=2NkO&(%/&($/2#¡289&R

t w

R\9&@84#<2

&EF-7&('2BG

(33)

í/PNMTPÀí q W>rN_ªdUv¢ rFi/dU¢£ZB¢ k>ŸyYXx a*vvwd^u` xjrNkbr[x dS_¼žbl

`%&^-$/F')&(/?N-n<2O!ž23?&^#A&)HRF7$?RP/-6#$\2&($)R?89#<2O2\B*#&

23&'B-'(f2Y+N23C-$P'(&)\!m23?&K#&)*&($/&(65<+N2&KkO&((Gd¯EP23&)T2&

&)A2#:y/&(')2# Ä G»…PRD23?&ÙÛ9”"W#ÜÛN˜wۖÞ7‰3ŠŽLL—L—’‘7a:Ž”:Þ?”PŽ’b-•

r m

•bK2& ÛN’‘ÜÝ

ÛN˜Ûó!O2&N841EF8]Q8x23$/-D#$,2"'B-'(f2Y+s!S$/#8ë2&N#l$#U23=f23^-Q?$'L/&($

¿$/&)A&)$/+?ÀR?{23&841EF8]Q8µ#-$P'(&)C'B-'(2Y+]!m2&K$/i2&(f!ŒG`%

&EP23$9!S&(23Q$/&Ck>H'(Q/&T23?&T-$/F?Q')2#=-$/A&"24B*&]:&EP23&)&(  -23&(Q

(34)

#f+4--f+4k>&)

r p > r m

Gd`%?&"-n2&BQ6&(@2384&\Q5P0/&)')2%2]23&"84&U$Q&(

457*&R924&(-7&(?#é23&s84Q<26!^#%57&(h$/&('(*&($&)HR

ω

R\5Q?24!S#$

'(W*&(&(')&T-?Q$-7#&)kO&ik>D$&)&)A?&Tf2BG

c ӝBӝlÝSä

â

ÝS ?äW Ò

í"Ï

Ñ `%&"2384&K!_k>'L@2&"$-@@-$/FQ?')23#@$/#-%57&v

k­23?&C841EF8VQ8æ-?$P'(&(/4'(-')2Y+R

r m

R&)&CAQ$&iIVGeœG

>&(&A?;2&4-?n2&BQ &(mR

t plateau

Rb2:57&{23&{*P5&N-?n2&BQ &(mRl23?&4-$/v Q'23#=$32&^!SQ')2#@!S#$

t > t plateau

57&(')#89&((¹

f (t) = r m e λ m (t t plateau )

¿ Ä GÄ À

λ m

&)2&($/84&(;>57&)!S#$/&G

á$#ÞY#á$#Í 5 ÐA6æ# Ï 6]ä9Ñbä<äW1Ü¡ÓÏ äTÛbä9)B ?ä{ Ï Ñ ï ОÑlÒbÓSÐ Ï ?äN ?øÃäW

ï Ûb BÓÏ_õ Ó Ï Ï äX6×Ð7ӝÝ:6VäFݝÝO F4däPÝSÐA6×Üh î ӝÜoÒlÜ # ï <Ӓ[ý '

IUZ57&)!S#$/&RWk>&(4-/T4C&k„#Fk\&)ÃRW&)-D&)V#923&#$&)'(*#&)$&(mR

ω

R

23?& -?$PQ')2#„$23&z84B+¨5D&o$#&)$#$@&(@2„23&o841EF8]Q8 -$/F')&(/

'B-'(f2Y+#G Xw!]n$/#&($)R^-$PQ'23#¸')#<23PQ?&(;#¸2;-n123&BQ¬?¸23?& *P/5&

-23&(Q=&(;2389&R

t plateau

R&)&(K$&)'B'(Q23#HGMXw!J-$/F?Q')2#;>&))R£kO&V?&(&(

23KA]23?&\'($$&)')2d&[EF-D#?&(<23F!SQ?')23#V!S#$_23?&a-$PQ'23#=¿')n8§IVG½Á#ÀGl³$/2(R

#&K84/2a&(<2!’+N23?&^-$PQ'23#6$23&U2\2&KkO&(m?&($,23#4289&R

t w

RWk>'L@

f ( t w ) = ( r m − λ m ( ω − kV − V m ))

¿ Ä GeœWÀ

k>&)$&

V m

a23&C89#Q<2>!l#m$&)'(*#&)$&)y@23?&i289&^57&)2YkO&(&(:23&irz-?n2&BQ -$/FQ?')23#N?]k>N23U2&\*P/5&\r4-n123&BQ]-$PQ'23#=¿')n8§IVG½ª#ÀGl`%WQ(R

23?&T57&(k¬86E?8]Q8æ'B-'(2Y+-$PQ'23:$23&C22384&

t

!’23&)$-?9=23&

kO&(H2>2389&

t w

f (t) = (r m − λ m (ω − kV − V m )) e λ(t t w )

¿ Ä G½ª#À

|1d

 5#{/  *32 ‡4)_/ !@}"#1‡=‚C):#%. !@}@#®

—4/}4:#0#fe 4:geTBE

XYQ/2$32#?\!_23?&"$&B23#6!l/&^/8]Q23#Mka*#&)= Ä GÄ Gf‡#RFAQ$&

Ä GÄ

?

Ä

G¶œ?G¬³#Q$/&

Ä

G¶èh/k>623&s$&(/Q24!S$#8 ª††#†q/8]Q23#]!S$/#8 23&

A'23*&i#D$&(')*#&($,+;-$10/&)')2  cb#n$>¢P2L$ULG

(35)

Ä

23&i89&B=+4#H-$PQ'23#HG

³£$/#8ù2&@#$-HRdkO&;/&(&@232N23&@Q?'(&)$/2L<23&({$/&@#$&(23&)/2{¡2&  $/Q

k>=-&;!K-$10/&)')2(GéIKç&($f+¡`¦"³b¦ë#$/86+ 84-&)]é&B$/+h$#-mR

$&)n2*#&K23N23&i84#Q?W2a!7$&(')*#&($5&GZ`%&C84Q<2%!b#D$&)'(*#&)$35&C

23&T-n123&BQ:-$/F?Q')2#;$32&T?&)23&)$89&)2&V&(23;#s841EF8]Q?8 -$PQ'23#

'B-'(f2Y+#RQ?--D?9-?n2&BQ=-$/FQ?')23#=>57*#&"232&)*&(ÂG

`%&{'(Q$,*#&{!M23&N-?$A&N^')#$$/&(23&)HRH@2&N-$552Y+;W2&($,*U!O2&

-D&)$')&(<23&>'(Q$,*#&)\#f+{--?&)Jk>&(42iZWk>65DQ?2M23&>&*#&(#-89&(<2

!£23&>-$/A&aQ-N23^2&a2384&aN·WQ&(,23HG?h[cd223^!£2&(/&$/&(/Q2M$&a!SQ$,23&)$

/'(Q/&)sQ?&($K³£QF23Q$/&ipU&)*&(-84&)<2BR£'L-?2&($KÁFGÄ G

ijF½·±¥Ò*Éͽ·ÓQÁNô¥Á:ËÊ÷´"Éʽ>ÁN»¿±3Éʽ¶šÎ¸«±¥Ò ´‘ô:´UšΘÓ3ÉÊô3´‘¾çÁQ¹´šÁ:¾¹±:½«Á:Ä·ËÊ´*Éͽ«ÐÉÌÇUÁ˜¶¹±3Â籘µð¸«±¥Ò1¶p¸·´D»«Â¹±:õ«ËÊ´DÉ;

ÇU÷¹ô3´‘АÎ3Ç^±:½¿¾À´=k3ë´U½¶¹ËÍÏ:Î:¶¹¸·´0lgF!Š»«Â¹±3Ä«Á˜Ä·ÉÍËÍɶÆÏQÉͽ¶¹´‘¹ô¥Á˜Ë«±˜µ¼¶¹¸·´*±:¶¹¸·´‘§ô¥Á˜ËÍ÷´‘¾åÉͽT¶¹¸¿Á¥¶§»·Âp±˜õ«ËÍ´*Òj±:÷ËÌÐ

Ëͱ²±:Ñ[ô3´UÂpÏCÐÉmo´UÂp´U½¶§µÈÂp±:³â¶¹¸·´"±:½·´)ǑÁ˜ËÌÇ^÷ËÌÁ¥¶p´‘Ð=µÈÂp±:³ ¶p¸·´"ÇU±:ËÍËÊ´šÇ„¶pÉʱ3½=±:µo¶¹¸·´@¾ÀÉͳ[÷ËÌÁ¥¶pÉʱ3½«¾

û

½·±Q¾À¶pÁ˜¶¹´‘¾

Ѳ½·±¥Ò*½¿þ^Ô

(36)

³$#8u23&i-$/F?Q')2#@/8]Q23#!  cb#n$>¢P2L$ULG

í/Pbn/PUO q WbrF_Šx rQu g%aªvwrQd^] rNg%YQZM_‡_Wba­vðkbŸa*r[] Y[¤B_Wbask>ŸyYX]>Zbx§¦

_dUYQu`kbŸyYNeb\Ua8vdU¢£Zb\^rF_dUYQu>v§l

IUK{89-&if23D!S&(23Q?$&C!2&V--'B2#mR?#&C'Bs/2Q?+=23?&T&)f2Y+

/23$/5QF23!723?&a*#&($,23'B/-$&(9!m/8]Q?n2#b5<+N&EP2$3'23?

x

2384&\-D#<23 k>2=&(·WQž&(2

y

=57&)2YkO&(&):23?&(8;G

XYhA#Q?$& Ä G½ÁFRb23&)$&@$/&6-22&( *#&($,23'BO&(/2Y+ !S#$9‡ª;2384&{-7#<2T!S$8

57&(#?]239/2L$/2>k>2s')'(#$/?#+6&(·WQ_-'(GeXw2K%23&i&)f2Y+=$&(-?$&(/&(Fv

2L123U&)·PQ?*&)<2^232&N-$PQ'23#z-$A&T!MA#Q$/&

Ä

G½èo¿2L2&]2

90

23?&U2OP#WZ84#$/&K&2&^-$/FQ?')23#6-?$A&À[Gd³#$\23?&^84P&)(RWf2\\6#5Fv

0/&('23f*#&"!S#$\2&(/&T')Q$/*&(>23{B*#&i23&"?#&)/2-7&B6;$$/k\&)$/-$&(HGZ®ž#

2La$&i{2%2{#FPHR5?Q?2%23&+=86B+6#$84+95D&i##$/&(@!b23?&)+=$/&i2

*#&)$/+=&)&R232>(R?#f+84-$/#55?&G

(37)

ÇÆ ” Ë

ƒ‡3 …

#>€ i}l›

'#6:4­!@}@)‚\/†@T,]X4:#!z/$E

`%&($/&>$&\&)*&($89F&)b!S#$&*#&)#-^#F-?$')&()G%¿Âcl$/2nnÀ ° &(84&23$'\ŸO$kav

n;´:23#@\#&"Q?'L:89&)2FmR!’23&)@Q&):A?'(&"!S#$a,23P'L#-?2#a

5D(G=IK23?&($(Rl84-&($)Rb89&)2PhC5/&(¡q!SQ?2Q$&9&(,23842#i!O23&4#

-$'(&)(RPQ6‡†onVv3RFª†nTv冐nTv-7&($/'(&)W2&(Gd`%&K-7&($/'(&)W2&(a$&>#*&(6!S$

]WQ8]57&($a!ž!SQF23Q$/&^2&(>2&^123&(\84N$/&^QF23A&)6k>2-$5D'

'(Q$,*#&)4&)/2386123&(¡!S$/#8 23&@&)#W57#Q$/y*Q&()G ƒ„f23¡23?&@'(#89-&23&,2]!

-D&)$')&(<23&(a!S$a23&"#m-$/F?Q')2#HRPk\&i84B+6,2L$,2%23{8]Qn123&Um-?$')&()GM¥K

]84P&)Dk>&)$&"23&"7-$'(&(>$&"#$/86+{?/2$5Q?23&)

X i ∼ N (µ i , σ i 2 )

R&23&($Œv 84&(95<+42&-D&)$'(&)<23&()R4'(#$/$&)n2&(4k>f234'(#$/$&(23#HR

ρ

RWkO&U84+{?&)*#&)#- 23&i#H-$/'(&)>%!S#k>(¹

Y i = ρY i − 1 + p

(1 − ρ 2 )X i , i = 1, . . . , N

k>&($/&

Y i

M23&U#£-$/'(&U2\289&

i

Gd`%OO$&(-7&B123&(!S$\&B'L@8VQn2#:¿S&B'L

$&({zB2#£À[Rl+P&)s*&($/+¡rD&($/&(<2N#O-$/')&((RZ$&)n2*&423y2&@'($$&)n2#

ρ

G

`%&;#O-$'(&(9$/&=Q5P0/&)')2923 Q'(&)$/23<2Y+#RaÕ86B+$&B123+¡rD&(')2{2&

A>#QF23'(84&@!K23&;?'(#89&@-$A&=/23$/5QF23(RZ9'Bé57&:/&(&(çÕA#Q$/&

œGf‡#Gd`%&"Q')&($,2LW2&)%!_23&^-?$PQ')2#@-?$A&{¿SA#Q$&

Ä

G½è<ÀZ%57&(&(=#$/&B2+

'(&)HGXw2b#5<*F#Qb232l23&O-$'(&Z84P&)P/&(&(')2&(;¿S-D&)$'(&)<23&(]')#$$/&(n123

!



cb#n$U¢W2L$^,À%K2F4#')n2Ry/#Qs57&V84&)k ')#<23$/#&(HR£&(f23&)$

5<+?'($&(V2&"'(#$/$&)n2#4#$a5<+$$k>V23?&^-D&)$')&(<23&^&)*#&))GMŸ\Q?2a2&(

<HR?=$&B2Y+923?&CH-$/')&($&^2$Qf+&)2&($/8423f*#&G

Referanser

RELATERTE DOKUMENTER

It is found how the anaerobic portion of total energy depends on time, and a sprint cross-country skiing scenario is used to study how racing time and recovery depends on

After section target is reached the simulation proceeds further for other drilling activities like tripping out drill string, collecting drill components etc. So, this process

Table 3-1 Relative permeability characteristics of oil-wet and water-wet reservoirs 33 Table 4-1 Petro physical properties of carbonate reservoirs 36 Table 5-1 Reservoir

The system implemented around the weather station is used to retrieve weather data for display on the Windows Store App developed during this thesis work..

In this research work the effect of the CO 2 injection is represented through the changes in the relative permeability curves (i.e. residual oil saturation and the

The high water production in Case 2 after 1000 days, is because when choking the total flow, the production will mainly occur from the zones in the heel section which

The research works presented here cover core flooding and microfluidic studies of the injection of various nanoparticle suspensions (in water and together with other chem- icals)

Observation y t , deterministic simulation ý„ mean stochastic simulation &#34;ý„, and within-period sample statistics for simulations with stochastic residuals only