2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty...

download 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgsæter)

of 170

Transcript of 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty...

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    1/170

    Xu`jog} D/ @kcxu`}

    Dae`kjoc goe Arujdjyjoc un`Aflxna}` R}aephujao af Ajk goeCgx poe`} Poh`}ugjouz

    Un`xjxfa} un` e`c}`` af rnjkaxarnjg` eahua}

    U}aoen`jd+ Ahuam`} =22>

    Oa}s`cjgo Pojv`}xjuz af Xhj`oh` goe U`hnoakaczFghpkuz af Jofa}dgujao U`hnoakacz+ Dgun`dgujhx+goe @k`hu}jhgk @ocjo``}joc

    E`rg}ud`ou af @ocjo``}joc Hzm`}o`ujhxOA$35:7 U}aoen`jd

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    2/170

    =

    OUOP

    Oa}s`cjgo Pojv`}xjuz af Xhj`oh` goe U`hnoakacz

    Eahua}gk un`xjxfa} un` e`c}`` af rnjkaxarnjg` eahua}

    Fghpkuz af Jofa}dgujao U`hnoakacz+ Dgun`dgujhx+goe @k`hu}jhgk @ocjo``}joc

    E`rg}ud`ou af @ocjo``}joc Hzm`}o`ujhxOA$35:7 U}aoen`jd

    h =22> Xu`jog} D/ @kcxu`}/

    JXMO JXMO :3>$>=$537$7=82$5 .r}jou`e v`}xjao*JXMO JXMO :3>$>=$537$7=87$7 .`k`hu}aojh v`}xjao*JXXO 7028$>7>7 JUL ]`ra}u =22>$>$S

    Eahua}gk un`x`x gu OUOP+ =22>9=63

    R}jou`e mz Ugrj} Puu}zll

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    3/170

    Xpddg}z

    Un` uarjh af unjx un`xjx jx arujdjyjoc un` aflxna}` r}aephujao af ajk goe cgxao g egz$ua$egz mgxjx/ Arujdjygujao jx mgx`e ao g dae`k af un` r}aephujao/

    E`xjcojoc xphn r}aephujao dae`kx jx v`}z hadrk`~ goe hngkk`ocjoc+ goe gxg }`xpku dae`kx sjkk gksgzx m` xpmi`hu ua xad` poh`}ugjouz jo r}ghujh`/

    Jo unjx un`xjx g egug$e}jv`o grr}aghn ua r}aephujao dae`kjoc goe dae`kpregujoc jx xpcc`xu`e/ Xjdrk` dae`k xu}phup}`x g}` jof`}}`e f}ad amx`}vg$ujaox af d`gxp}`e r}aephujao+ daujvgu`e mz un` haoh`rux af xzxu`d je`ouj$hgujao goe g e`xj}` fa} dae`kx snjhn g}` xphj`oukz ghhp}gu` snjk` m`joc`gxjkz xakv`e opd`}jhgkkz/ G r}aephujao dae`k o``ex ua m` pregu`e r`}j$aejhgkkz ua }``hu hngoc`x jo }`x`}vaj}x goe s`kkx/ Pregujoc dae`kx gcgjoxuamx`}vgujaox af }`h`oukz d`gxp}`e egug e`xh}jmjoc oa}dgk ar`}gujaox jx xpc$

    c`xu`e+ daujvgu`e mz g e`xj}` fa} go pregujoc xhn`d` snjhn }`wpj}`x kjuuk`npdgo jou`}v`oujao goe ea`x oau }`wpj}` f}`wp`ou geejujaogk `~r`}jd`oug$ujao+ fa} joxugoh` jo un` fa}d af s`kk$u`xux/

    Un` xpcc`xu`e grr}aghn ua dae`k$pregujoc jx mgx`e ao rg}gd`u`} `x$ujdgujao gcgjoxu r}aephujao egug xu`ddjoc f}ad oa}dgk ar`}gujaox/ Gxegug e`xh}jmjoc oa}dgk ar`}gujaox dgz ngv` kas jofa}dgujao haou`ou+ rg$}gd`u`}x `xujdgu`e jo unjx dgoo`} dgz m` xpmi`hu ua xjcojhgou poh`}ugjouz/Maauxu}grrjoc jx haoxje`}`e gx g d`gox af `xujdgujoc poh`}ugjouz jo uu`erg}gd`u`}x/ D`unaex fa} un` `~rkjhju u}`gud`ou af xphn poh`}ugjouz mgx`e

    ao Daou`$Hg}ka gogkzxjx g}` jov`xujcgu`e/ D`unaex fa} `xujdgujoc kaxu ra$u`oujgk ep` ua poh`}ugjouz+ }`xpku gogkzxjx+ `~hjugujao rkgoojoc goe hnaaxjocghujv` e`hjxjao vg}jgmk`x g}` xpcc`xu`e/

    Xjoh` poh`}ugjouz sjkk o`v`} m` hadrk`u`kz `kjdjogu`e jo r}ghujh`+ xad`d`unae jx o``e`e ua gegru ua poh`}ugjouz sn`o jdrk`d`oujoc hngoc`x jo r}a$ephujao xpcc`xu`e mz arujdjygujao/ Daujvgu`e mz nas ar`}gua}x jdrk`d`ouxphn hngoc`x jo r}ghujh`+ go ar`}gujaogk xu}gu`cz grr}aghn jx xpcc`xu`e uakjol arujdjygujao sjun jdrk`d`ougujao goe daojua}joc mz ju`}gujv`kz jdrk`$d`oujoc xdgkk`} hngoc`x snjk` daojua}joc r}aux goe haoxu}gjoux/

    Un` dae`kx haoxje`}`e g}` kas jo hadrk`~juz+ snjhn dgz xjdrkjfz e`xjco$

    j

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    4/170

    jj Xpddg}z

    joc goe pregujoc dae`kx goe dgz }`eph` opd`}jhgk jxxp`x/ Xjoh` un` xpc$c`xu`e d`unaex }`kz ao d`gxp}`d`oux+ un` xphh`xx af un` xpcc`xu`e d`unaexsjkk e`r`oe ao d`gxp}`d`ou wpgkjuz/ Gkxa+ gkunapcn un` d`unaex xpcc`xu`e

    ea oau }`wpj}` `~aujh d`gxp}`d`oux+ un` xpcc`xu`e d`unaex hapke m`o`uf}ad geejujaogk joxu}pd`ougujao ao xad` `kex/ Un` d`unaex xpcc`xu`e ua$c`un`} haoxujupu` g oav`k+ xu}phup}`e grr}aghn ua arujdjygujao af aflxna}`ajk goe cgx r}aephujao jo un` r}`x`oh` af poh`}ugjouz/

    Dae`kjoc d`unaex g}` grrkj`e ua }`gk$sa}ke r}aephujao egug f}ad usaaflxna}` ajk `kex/ Jdrk`d`ougujao af un` xpcc`xu`e d`unaex g}` xupej`e mzxjdpkgujaox gcgjoxu go gogkac af ao` af un` `kex haoxje`}`e/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    5/170

    R}`fgh`

    J sapke `xr`hjgkkz kjl` ua ungol dz usa xpr`}vjxa}x Ua} G}o` Iangox`o goeAkgv Xkprrngpc/ J gd c}gu`fpk fa} Ua} G}o` fa} cjvjoc dz g zjoc xug}u goe

    cpjejoc d` gkaoc dz rgun/ Unjx un`xjx ngx c}`gukz m`o`u`e f}ad Akgvxjoxjcnu joua un` r}ghujhgk xje` af aflxna}` ajk goe cgx r}aephujao goe njxjooavgujv` je`gx/

    Jo geejujao ua dz xpr`}vjxa}x+ unjx un`xjx sapke oau ngv` m``o raxxjmk`jo jux r}`x`ou fa}d sjunapu un` vgkpgmk` ejxhpxxjaox sjun goe f``emghl f}addgoz sa}ljoc r}ghujujao`}x jo un` ajk goe cgx joepxu}z/ J sapke kjl` ua ungolGogxugxjax Xjgdax+ @xr`o Ngkva}x`o goe un`j} hakk`gcp`x gu XuguajkNze}axah`x jo Xgoexkj fa} un`j} gxxjxugoh` jo amugjojoc goe jou`}r}`ujoc egug/ Jsapke kjl` ua ungol G}` Diggvguu`o+ L}jxujo N`xu`upo goe Dg}ug Ep`gxE`y gu XuguajkNze}ax }`x`g}hn h`ou`} jo Ra}xc}poo fa} xujdpkgujoc ejxhpx$xjaox+ goe J sapke `xr`hjgkkz kjl` ua ungol Vjeg} Gkxuge fa} njx xprra}u/J sapke kjl` ua ungol Iano$Da}u`o Caengvo goe R`uu`} Uoe`k goe un`j}hakk`gcp`x gu XuguajkNze}ax }`x`g}hn h`ou`} jo U}aoen`jd fa} un`j} gxxjx$ugoh` jo amugjojoc goe jou`}r}`ujoc egug/ J sapke kjl` ua ungol Ngox$R`uu`}Mj`l`}+ Mi}o M}joc`egk goe un`j} hakk`gcp`x gu GMM @ongoh`e Ajk R}aeph$ujao fa} un`j} vgkp`e f``emghl/ J gkxa sapke kjl` ua ungol dz hakk`gcp`x guun` joxujupu` af @ocjo``}joc Hzm`}o`ujhx/

    J sapke kjl` ua ghloask`ec` un` ]`x`g}hn Hapohjk af Oa}sgz+ XuguajkNz$e}a+ goe GMM fa} fpoejoc unjx }`x`g}hn/

    J gd joe`mu`e ua dz cj}kf}j`oe Jo`x fa} un` kav`+ xprra}u goe `ohap}gc`$d`ou xnaso ua d` ep}joc un` hap}x` af unjx sa}l+ goe J gd c}gu`fpk fa} un`xprra}u xnaso ua px mz ap} fgdjkj`x/

    U}aoen`jd+ Ahuam`} =22> Xu jog} D/ @kcxu`}

    jjj

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    6/170

    jv R}`fgh`

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    7/170

    Haou`oux

    Xpddg}z j

    R}`fgh` jjj

    7 Jou}aephujao 7

    7/7 Daujvgujao / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 7

    7/= ]`kgu`e sa}l / / / / / / / / / / / / / / / / / / / / / / / / / / / 8

    7/8 Xpddg}z goe un`xjx av`}vj`s / / / / / / / / / / / / / / / / / / >

    7/8/7 Rpmkjhgujaox / / / / / / / / / / / / / / / / / / / / / / / / 77

    7/8/= Dgjo haou}jmpujaox / / / / / / / / / / / / / / / / / / / / 7=

    7/5 Oaugujao goe e`ojujaox / / / / / / / / / / / / / / / / / / / / / 7=

    = R}`kjdjog}j`x 7:

    =/7 R}amk`d e`xh}jrujao / / / / / / / / / / / / / / / / / / / / / / / 7:

    =/= Dgun`dgujhgk r}`kjdjog}j`x / / / / / / / / / / / / / / / / / / / =7

    8 Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae kx fa} aflxna}`ajk goe cgx r}aephujao arujdjygujao =0

    8/7 Jou}aephujao / / / / / / / / / / / / / / / / / / / / / / / / / / / / =6

    8/7/7 R}ja} sa}l / / / / / / / / / / / / / / / / / / / / / / / / / =6

    8/7/= Av`}vj`s / / / / / / / / / / / / / / / / / / / / / / / / / =68/= Un` }`kgujaoxnjr m`us``o r}aephujao arujdjygujao+ dae kx

    goe egug / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / =3

    8/8 R}aephujao egug9 G hgx`$xupez / / / / / / / / / / / / / / / / / =:

    8/8/7 Fj`ke e`xh}jrujao / / / / / / / / / / / / / / / / / / / / / 82

    8/8/= ]guja m`us``o s`kk u`xux goe uaugk d`gxp}`e }gu`x / / / 82

    8/8/8 Egug / / / / / / / / / / / / / / / / / / / / / / / / / / / / 87

    8/8/5 Amx`}vgujaox / / / / / / / / / / / / / / / / / / / / / / / 87

    8/8/0 Ejxhpxxjao / / / / / / / / / / / / / / / / / / / / / / / / / 8>

    8/8/6 Hngkk oc`x jo r}aephujao arujdjygujao / / / / / / / / / 8:

    v

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    8/170

    vj Haou`oux

    8/5 Haohkpxjao / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 52

    5 R}aephujao arujdjygujao< xzxu`d je`oujhgujao goe poh`}$

    ugjouz xujdgujao 575/7 Jou}aephujao / / / / / / / / / / / / / / / / / / / / / / / / / / / / 5=

    5/7/7 R}amk`d fa}dpkgujao / / / / / / / / / / / / / / / / / / / 5=

    5/= Dae`kjoc fa} r}aephujao arujdjygujao poe`} poh`}ugjouz / / / 58

    5/=/7 Kahgk r}aephujao dae`kx fa} arujdjygujao / / / / / / / 58

    5/=/= @xujdgujoc rg}gd`u`} poh`}ugjouz / / / / / / / / / / / 55

    5/=/8 Xpddg}z / / / / / / / / / / / / / / / / / / / / / / / / / 50

    5/8 Xzoun`ujh `~gdrk`x goe g hgx` xupez / / / / / / / / / / / / / / 50

    5/8/7 R}aephujao dae`k / / / / / / / / / / / / / / / / / / / / 56

    5/8/= Opd`}jhgk xakpujao af un` rg}gd`u`} `xujdgujao r}amk`d 53

    5/8/8 Rnzxjhgk loask ec` jo rg}gd`u`} `xujdgujao / / / / / 53

    5/8/5 G xzoun`ujh `~gdrk` / / / / / / / / / / / / / / / / / / / 5:

    5/8/0 Hgx` xupez9 R}aephujao egug f}ad g Oa}un X`g ajk `ke 08

    5/8/6 ]`xpkux / / / / / / / / / / / / / / / / / / / / / / / / / / 08

    5/8/3 Ejxhpxxjao / / / / / / / / / / / / / / / / / / / / / / / / 0:

    5/5 Haohkpxjao / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 62

    0 Ajk goe cgx r}aephujao arujdjygujao< kaxu rau`oujgk ep` uapoh`}ugjouz 67

    0/7 Jou}aephujao / / / / / / / / / / / / / / / / / / / / / / / / / / / / 6=

    0/7/7 R}ja} sa}l / / / / / / / / / / / / / / / / / / / / / / / / / 60

    0/7/= R}amk`d fa}dpkgujao / / / / / / / / / / / / / / / / / / / 60

    0/= @xujdgujoc un` kaxx ep` ua poh`}ugjouz / / / / / / / / / / / / / 60

    0/=/7 E`ojujaox / / / / / / / / / / / / / / / / / / / / / / / / 66

    0/=/= @xujdgujoc un` rau`oujgk af r}aephujao arujdjygujao / 63

    0/=/8 @xujdgujoc kaxu rau`oujgk ep` ua poh`}ugjouz / / / / / / 63

    0/=/5 Ejxhpxxjao / / / / / / / / / / / / / / / / / / / / / / / / / 63

    0/8 Grrkjhgujaox / / / / / / / / / / / / / / / / / / / / / / / / / / / / 6>

    0/8/7 Jou}aephujao / / / / / / / / / / / / / / / / / / / / / / / / 6>

    0/8/= Xzoun`ujh `~gdrk` / / / / / / / / / / / / / / / / / / / / 3=

    0/8/8 Hgx` xupez9 Oa}un X`g `ke / / / / / / / / / / / / / / / 3=

    0/8/5 ]`xpkux / / / / / / / / / / / / / / / / / / / / / / / / / / 30

    0/8/0 Ejxhpxxjao / / / / / / / / / / / / / / / / / / / / / / / / / 30

    0/5 Haohkpxjaox / / / / / / / / / / / / / / / / / / / / / / / / / / / / 30

    0/0 Gkca}jundx / / / / / / / / / / / / / / / / / / / / / / / / / / / / 3>

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    9/170

    Haou`oux vjj

    6 G xu}phup}`e grr}aghn ua arujdjyjoc aflxna}` ajk goe cgxr}aephujao sjun poh`}ugjo dae`kx 3:

    6/7 Jou}aephujao / / / / / / / / / / / / / / / / / / / / / / / / / / / / >2

    6/7/7 R}ja} sa}l / / / / / / / / / / / / / / / / / / / / / / / / / >26/7/= R}amk`d fa}dpkgujao / / / / / / / / / / / / / / / / / / / >8

    6/= R}aephujao arujdjygujao poe`} poh`}ugjouz / / / / / / / / / / >8

    6/=/7 G xu}phup}`e grr}aghn ua arujdjygujao sjun poh`}ugjodae`kx / / / / / / / / / / / / / / / / / / / / / / / / / / >8

    6/=/= Ar`}gujaogk xu}gu`cz / / / / / / / / / / / / / / / / / / / >5

    6/=/8 ]`xpku gogkzxjx / / / / / / / / / / / / / / / / / / / / / / :2

    6/=/5 G haxu!m`o`u grr}aghn ua `~hjugujao rkgoojoc / / / / :7

    6/8 Hgx` xupez / / / / / / / / / / / / / / / / / / / / / / / / / / / / :5

    6/8/7 Fj`ke e`xh}jrujao / / / / / / / / / / / / / / / / / / / / / :56/8/= D`unae / / / / / / / / / / / / / / / / / / / / / / / / / / :0

    6/8/8 ]`xpkux / / / / / / / / / / / / / / / / / / / / / / / / / / :>

    6/8/5 Ejxhpxxjao / / / / / / / / / / / / / / / / / / / / / / / / / :>

    6/5 Haohkpxjao / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 772

    3 Arujdjygujao af aflxna}` ajk goe cgx r}aephujao poe`} po$h`}ugjouz< ghujv` e`hjxjao vg}jgmk`x 777

    3/7 Jou}aephujao / / / / / / / / / / / / / / / / / / / / / / / / / / / / 77=

    3/7/7 R}`vjapx Sa}l / / / / / / / / / / / / / / / / / / / / / / 77=3/7/= R}amk`d Fa}dpkgujao / / / / / / / / / / / / / / / / / / / 778

    3/= Hnaaxjoc ghujv` e`hjxjao vg}jgmk`x / / / / / / / / / / / / / / / / 778

    3/8 Hgx` xupez / / / / / / / / / / / / / / / / / / / / / / / / / / / / 776

    3/8/7 Fj`ke E`xh}jrujao / / / / / / / / / / / / / / / / / / / / / 776

    3/8/= D`gxp}`d`oux px`e goe s`kk uzr`x / / / / / / / / / / / 77>

    3/8/8 R}aephujao arujdjygujao / / / / / / / / / / / / / / / / / 77:

    3/8/5 Dae`kjoc / / / / / / / / / / / / / / / / / / / / / / / / / 7=7

    3/8/0 Jdrk`d`ougujao / / / / / / / / / / / / / / / / / / / / / / 7=>

    3/8/6 ]`xpkux / / / / / / / / / / / / / / / / / / / / / / / / / / 7=:3/8/3 Ejxhpxxjao / / / / / / / / / / / / / / / / / / / / / / / / / 7=:

    3/5 Haohkpxjaox / / / / / / / / / / / / / / / / / / / / / / / / / / / / 75=

    > Haohkpxjaox goe xpcc`xujaox fa} fp}un`} sa}l 758

    >/7 Haohkpxjaox / / / / / / / / / / / / / / / / / / / / / / / / / / / / 758

    >/7/7 G egug$e}jv`o grr}aghn ua r}aephujao dae`kjoc goedae`k pregujoc / / / / / / / / / / / / / / / / / / / / / / 758

    >/7/= Go `~rkjhju u}`gud`ou af poh`}ugjouz jo r}aephujao ar$

    u jd jy g u ja o / / / / / / / / / / / / / / / / / / / / / / / / / 7 5 0

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    10/170

    vjjj Haou`oux

    >/7/8 Go ar`}gujaogk xu}gu`cz grr}aghn ua kjol arujdjygujaosjun jdrk`d`ougujao goe daojua}joc / / / / / / / / / 753

    >/= Ej}`hujaox fa} fp}un`} sa}l / / / / / / / / / / / / / / / / / / / / 753

    >/=/7 Jou`c}gujao af r}aephujao dae kx sjun rnzxjhx$mgx`ex jd p kg u a } x / / / / / / / / / / / / / / / / / / / / / / / / / 7 5 3

    >/=/= Ghujv` e`hjxjao vg}jgmk`x / / / / / / / / / / / / / / / / / 75>>/=/8 Xpmx`g s`kkx / / / / / / / / / / / / / / / / / / / / / / / / 75>>/=/5 Hadrg}joc gku`}ogujv` d`unaex af `xujdgujoc poh`}$

    ugjouz / / / / / / / / / / / / / / / / / / / / / / / / / / / 75>>/=/0 Un` m`o`u af xjock $}gu` s`kk u`xux / / / / / / / / / / / 75>>/=/6 Un` vgkp` af }`ephjoc d`gxp}`d`ou poh`}ugjouz / / / / 75:>/=/3 Haoxu}gjou poh`}ugjouz / / / / / / / / / / / / / / / / / / 75:

    >/=/> ]`x`}vaj} dae`kjoc / / / / / / / / / / / / / / / / / / / / 75:>/=/: Xupezjoc un` kjol ua }`x`}vaj} dgogc`d`ou / / / / / / / 702>/=/72 Dgogcjoc u}goxj`oux jo ar`}gujaogk xu}gu`cj`x / / / / / 702>/=/77 @~rkajujoc xnpueasox fa} dae`k pregujoc / / / / / / / 702

    G Egug r}`r}ah`xxjoc 707

    Mjmkjac}grnz 708

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    11/170

    Hngru`} 7

    Jou}aephujao

    7/7 Daujvgujao

    Jo un` aflxna}` r}aephujao af ajk goe cgx+ ajk+ cgx+ sgu`} goe raxxjmkz aun`}hadrao`oux g}` r}aeph`e f}ad g opdm`} af r}aephujao s`kkx+ m`fa}` r}a$eph`e pjex g}` }apu`e un}apcn rjr`x gx dpkujrngx` as ua g r}ah`xxjocfghjkjuz fa} x`rg}gujao/ R}aephujao jo un` haou`~u af aflxna}` ajk goe cgx`kex hgo m` haoxje`}`e un` uaugk apurpu af r}aephujao s`kkx/

    Jo unjx un`xjx r}aephujao arujdjygujao jx e`o`e gx un` dgun`dgujhgkr}amk`d af egjkz dg~jdjygujao af r}aux un}apcn hnaaxjoc g hngoc` jo e`hj$xjao vg}jgmk`x xpmi`hu ua g r}aephujao dae`k goe r}aephujao haoxu}gjoux/ Uaxakv` un` r}aephujao arujdjygujao r}amk`d c`o`}gkkz }`wpj}`x pxjoc opd`}j$hgk arujdjygujao u`hnojwp`x/ R}aephujao arujdjygujao jx xad`ujd`x }`f`}}`eua gx r}aephujao rkgoojoc .Mj`l`}+ Xkprrngpc goe Iangox`o+ =223g*/ Un`dgun`dgujhgk xakpujao af un` r}aephujao arujdjygujao r}amk`d }`wpj}`x gr}aephujao dae`k+ xad` `wpgujao snjhn `~r}`xx`x un` }`kgujaoxnjr m`us``ohngoc` jo e`hjxjao vg}jgmk`x goe hngoc` jo r}aephujao+ maun sjun }`xr`huua r}aux goe haoxu}gjoux/ G r}aephujao dae`k uzrjhgkkz r}`ejhux hngoc` jo

    }gu`x af ajk+ cgx+ sgu`}+ goe raxxjmkz aun`} hadrao`oux af r}aephujao gx fa}joxugoh` hnal` ar`ojocx a} cgx$kjfu }gu`x hngoc`/

    Un` daxu haddao r}ghujh` jo joepxu}z jx go `ocjo``}joc grr}aghn uar}aephujao dae`kjoc+ jou`c}gujoc e`ugjk`e goe hadrk`~ }xu$r}johjrk`x dae$`kx goe `drj}jhgk `wpgujaox jo hadd`}hjgk xjdpkgua}x7+ afu`o un}apcn oaegkgogkzxjx .M`ccx+ =228*/ Arujdjygujao gkca}jundx `jun`} wp`}z xjdpkgua}xej}`hukz .Sgoc+ =228*+ a} xjdpkgua} r}`ejhujaox g}` gcc}`cgu`e jo r}a~z$dae`kx snjhn g}` un`o wp`}j`e mz arujdjygujao gkca}jundx .Ygock+ C}gf goe

    7

    Ao` xphn xjdpkgua} jx R]AXR@] mz R`u}ak`pd @~r`}ux+ sss/r`u`~/had

    7

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    12/170

    = Jou}aephujao

    Gk$Ljogoj+ =226*/

    Un` hadrk`~juz af r}aephujao dae`kjoc jx g l`z hngkk`oc` jo r}aephujaoarujdjygujao fa} g opdm`} af }`gxaox9

    R}aephujao jx ejhpku ua dae`k ep` ua un` xn`g} hadrk`~juz af un`xzxu`dx haoxje`}`e+ xjoh` r}aephujao hgo xrgo g kg}c` opdm`} af s`kkxgoe as kjo`x goe g kg}c` gdapou af xp}fgh` goe xpmxp}fgh` r}ah`xx`wpjrd`ou/

    Un` aflxna}` r}aephujao af ajk goe cgx e`gkx fa} g kg}c` rg}u sjun dgozpjex+ afu`o jo ejfl`}`ou rngx`+ asjoc un}apcn un` xgd` rjr`+ snjhnjx g hadrk`~ goe ejhpku rnzxjhgk r}ah`xx ua dae`k/

    D`gxp}`d`oux af aflxna}` ajk goe cgx r}aephujao g}` afu`o joghhp}gu`+`jun`} ep` ua un` ejhpkuz af ghhp}gu`kz d`gxp}joc dpkujrngx` as+ a}ep` ua g kghl af hgkjm}gujao goe dgjou`ogoh` af d`gxp}`d`ou `wpjr$d`ou/

    R}aephujao hngoc`x ep` ua hngoc`x jo s`kkx goe }`x`}vaj}x+ fa} joxugoh`ep` ua e`rk`ujao/

    Goaun`} l`z hngkk`oc` jo r}aephujao arujdjygujao jx dae`k pregujoc+ pr$egujoc dae`kx ua ghhapou fa} po$dae`k e hngoc`x jo r}aephujao/ Jf po$

    dae`k`e hngoc`x }`wpj}` r}aephujao arujdjygujao ua pregu` e`hjxjao vg}j$gmk`x gu jou`}vgkx af nap}x a} egzx+ un`o xad` d`unae fa} dae`k dgjou`ogoh`gu un`x` jou`}vgkx jx gkxa o`h`xxg}z/ Hngkk`oc`x jo dae`k pregujoc dgz m`kjol`e ua hngkk`oc`x jo dae`kjoc+ gx ujd`kz dae`k pregujoc dgz m` da}`hngkk`ocjoc sjun joh}`gxjoc dae`k hadrk`~juz/

    Z`u goaun`} hngkk`oc` jo r}aephujao arujdjygujao jx opd`}jhgk goe ar$ujdjygujao jxxp`x/ Gx r}aephujao dae kx dgz o``e ua m` }`$xakv`e r`}ngrxdgoz ujd`x ao un` ujd`xhgk` af nap}x a} egzx gx rg}u af dae`k pregujoc goer}aephujao arujdjygujao+ `hj`ohz af un` opd`}jhgk xakv`} jx jdra}ugou/ Ju jx

    gkxa jdra}ugou ungu dae`kx hgo m` xakv`e jo g dgoo`} snjhn jx opd`}jhgkkz}ampxu/ Un` xu}phup}` af un` r}aephujao dae`k dgz dgl` un` r}aephujao ar$ujdjygujao r}amk`d oao$haov`~+ snjhn dgz dgl` opd`}jhgk arujdjygujao afdae`k`e r}aephujao hngkk`ocjoc/ Un` hngkk`oc` af opd`}jhgk jxxp`x jx kjol`eua dae`k hadrk`~juz+ gx da}` hadrk`~ dae`kx dgz m` da}` hngkk`ocjoc uaxakv` goe da}` r}ao` ua jxxp`x af opd`}jhgk xugmjkjuz goe haov`~juz/

    G haou}ak grr}aghn ua r}aephujao arujdjygujao jx gkxa raxxjmk`+ snjhnhgo haoxje`} r}aephujao arujdjygujao gx g haou}akk`} snjhn mgx`e ao am$x`}vgujaox dge` f}ad d`gxp}`d`oux guu`drux ua gku`} e`hjxjao vg}jgmk`x xa

    ungu r}aux joh}`gx`/ Xphn g haou}akk`} sapke xujkk o``e ua m` mgx`e ao

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    13/170

    7/=/ ]`kgu`e sa}l 8

    g r}aephujao dae`k/ Un` dae`kx px`e jo haou}ak g}` afu`o jof`}}`e f}adegug+ goe un` xupez af xphn d`unaex jx un` uarjh af xzxu`d je`oujhgujao.Kipoc+ 7:::*/ Xzxu`d je`oujhgujao ngx m``o fapoe ua afu`o ghnj`v` njcn

    r`}fa}dgoh` sjun v`}z xjdrk` dae`kx goe pregujoc af xphn dae`kx jx af$u`o xjdrk` .C`v`}x+ =226*/ Un` r}ar`}uj`x af dae kx fapoe sjun xzxu`dje`oujhgujao daujvgu` unjx un`xjx+ gx un`z ngv` un` rau`oujgk ua gee}`xxun` hngkk`oc`x jo dae`kjoc+ dae`k pregujoc goe opd`}jhgk jxxp`x fgh`e jor}aephujao arujdjygujao/

    7/= ]`kgu`e sa}l

    Xzxu`d je`oujhgujao jo un` m}age`xu x`ox` e`gkx sjun jof`}}joc ezogdjhgkdae`kx f}ad egug .Kipoc+ 7:::*/ Xim`}c+ Yngoc+ Kipoc+ M`ov`ojxu`+ E`kzao+Cka}`oo`h+ Nigkdg}xxao goe Ipejuxlz .7::0* ejvje`x dae`kx joua snju`$ma~+mkghl$ma~ a} c}`z$ma~ e`r`oejoc ao sn`un`} un j} xu}phup}` jx mgx`e aornzxjhgk }xu r}johjrk x+ `drj}jhjxd a} g hadmjogujao+ }`xr`hujv`kz/ Xzxu`dje`oujhgujao jx xad`ujd`x e`o`e da}` og}}askz gx rp}`kz `drj}jhgk mkghl$ma~ dae`kjoc+ snjk` jo unjx un`xjx un` u`}d jx px`e ghha}ejoc ua un` m}age`}e`ojujao/ Xzxu`d je`oujhgujao ugl x g r}gcdgujh vj`s af un` hnajh` afdae`k xu}phup} + x``ljoc dae`k xu}phup}`x jo g u}jgk$goe$`}}a} fgxnjao snjhnhgo m` }`kgujv`kz `gxjkz uu`e ua egug z`u e`xh}jm` amx`}vgujaox sjun xp$

    hj`ou ghhp}ghz/ @drngxjx jx pxpgkkz ao l``rjoc un` opdm`} af rg}gd`u`}xua m` uu`e kas snjk` jou}aephjoc xad` rnzxjhgk loask`ec` ua ghnj`v` }`$wpj}`e r`}fa}dgoh` .Xim`}c `u gk/+ 7::0*/ Jo unjx un`xjx xugujh dae`kx sjunrg}gd`u`}x ungu vg}z sjun ujd` ua }``hu hngoc`x jo }`x`}vaj} goe s`kk g}`haoxje`}`e+ mpu un` d`unaeakacz px`e jx jop`oh`e mz xzxu`d je`oujhgujao/

    Jo r}ghujh` goz dae`k sjkk o``e xad` geipxud`ou ua dguhn amx`}vgujaoxep` ua xu}phup}gk dae`k `}}a}x a} po$dae`k`e ejxup}mgoh`x/ Rg}gd`u`} `xuj$dgujao jx g r}ah`ep}` m`kaocjoc ua un` xzxu`d je`oujhgujao eadgjo snjhnhadrg}`x un` d`gxp}`e goe dae`k`e apurpu af g xzxu`d fa} g x`u af upojoc

    egug goe geipxux rg}gd`u`}x+ pxpgkkz sjun g k`gxu$xwpg}`x opd`}jhgk xakv`}+poujk d`gxp}`e goe dae`k`e apurpu dguhn gx hkax`kz gx raxxjmk`/ Fa} ju uam` raxxjmk` ua e`u`}djo` rg}gd`u`}x ua m` uu`e pojwp`kz+ un`}` o``ex uam` xphj`ou jofa}dgujao haou`ou jo un` upojoc egug x`u/ Jf un` jofa}dgujaohaou`ou jo r}aephujao egug jx kas+ da}` ungo ao` x`u af uu`e rg}gd`u`}vgkp`x dgz e`xh}jm` un` upojoc x`u `wpgkkz s`kk goe rg}gd`u`} poh`}ugjouzdgz }`xpku/ Jofa}dgujao haou`ou jo egug hgo m` joh}`gx`e mz jou}aephjocvg}jgujao jo e`hjxjao a} ejxup}mgoh` vg}jgmk`x+ a} `~hjugujao+ mpu `~hjugujaoafu`o ngx go gxxahjgu`e haxu snjhn dgz dgl` `kjdjogujoc rg}gd`u`} poh`}$

    ugjouz jdr}ghujhgk/ Ep` ua poh`}ugjouz+ ju jx sje`kz }`hacojy`e ungu g dae`k

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    14/170

    5 Jou}aephujao

    jx af kjuuk` px` jf oa wpgkjuz ugc jx guughn`e ua ju snjhn e`xh}jm`x poh`}ugjouzgoe jx ugl`o joua ghhapou sn`o un` dae`k jx px`e jo r}ghujh` .Hgdrj goeS`z`}+ =220*/

    R}aephujao arujdjygujao jx }`kgu`e ua un` uarjh af }`gk$ujd` arujdjygujaojo r}ah`xx haou}ak+ haou}akk`}x snjhn guu`dru ua dg~jdjy` `haoadjh vgkp` mzhnaaxjoc x`urajoux xpmi`hu ua g dae`k goe haoxu}gjoux/ ]`gk$ujd` arujdjyg$ujao pxpgkkz haoxje`} oaokjo`g} xu`gez$xugu` r}ah`xx dae`kx goe jx pxpgkkzjdrk`d`ou`e sjun xgdrkjoc ujd`x jo un` }goc` af nap}x+ goe dae`k rg}gd`$u`}x g}` pxpgkkz pregu`e pxjoc rg}gd`u`} `xujdgujao .@oc`kk+ =226*/ E`u`}$djojoc un` k`v`k af ghhp}ghz }`wpj}`e jo dae`k goe rg}gd`u`} `xujdgu`x goee`u`}djojoc un` m`o`u af jdr}avjoc ghhp}ghz g}` haoxje`}`e ar`o wp`xujaoxfa} }`x`g}hn jo }`gk$ujd` arujdjygujao .Fa}m`x+ Dg}kjo goe Zjr+ =220*/

    F}j`edgo .7::0* xugu`x ungu g hngkk`oc` ua }`gk$ujd` arujdjygujao jo un`r}ah`xx joepxu}j`x jx ungu un` px` af xu`gez$xugu` r}ah`xx dae`kx r}`v`ouxun` f}`wp`ou }`$x`uujoc af ug}c`ux jo xdgkk`} xu`rx goe ungu e`ugjk`e ghhp}gu`dae`kx goe hadrk`~ xjdpkgujaox g}` }`wpj}`e ua r`}fa}d }`gk$ujd` arujdjyg$ujao/ F}j`edgo .7::3* rajoux apu ungu }`gk$ujd` arujdjygujao jx mgx`e aodae`kx snjhn hgo m` jovgkjegu`e mz x`v`}gk hj}hpdxugoh`x+ fa} joxugoh` vja$kgu`e dae`kjoc gxxpdrujaox a} d`gxp}`d`ou `}}a}x/ Ju jx xu}`xx`e ungu hao$u}ak xhn`d`x g}` }`wpj}`e ua fpohujao r`}f`hukz gu haoxu}gjoux a} }jxl m`jocup}o`e afl+ gx ar`}gua}x g}` pohadfa}ugmk` sjun ar`}gujoc poe`} xphn hao$

    ejujaox+ z`u jf un` dae`k jx joghhp}gu` fa} goz }`gxao }`gk$ujd` arujdjygujaosjkk oau fpohujao r`}f`hukz gu haoxu}gjoux goe un` arujdgk x`urajou hgkhpkgu`emz }`gk$ujd` arujdjygujao jx oa kaoc`} arujdgk jo r}ghujh`/

    Gx rg}gd`u`} `xujdgujao jx haoxje`}`e rg}u af }`gk$ujd` arujdjygujao+hngoc`x jo x`urajoux dge` mz }`gk$ujd` arujdjygujao sjkk jop`oh` ghhp$}ghz af rg}gd`u`} `xujdgujao/ Jo hn`djhgk `ocjo``}joc+ `~r`}jd`ougk e`xjcongx haoxje`}`e rkgoo`e `~hjugujao ua }`eph` rg}gd`u`} poh`}ugjouz/ Hkgxxj$hgk arujdpd `~r`}jd`ougk e`xjco haoxje`}x un` jofa}dgujao haou`ou af egugx`ux sjunapu haoxje`}joc un` haxu af r`}fa}djoc `~r`}jd`oux+ xpcc`xujoc `~$

    r`}jd`oux ua }`eph` ha}}`kgujao m`us``o uu`e rg}gd`u`}x .R}juhng}e goeMghao+ 7:3>*/ ]`h`oukz+ Zjr goe Dg}kjo .=228* ngv` r}arax`e go `~r`hu`er}au grr}aghn snjhn s`jcnx haxux af `~r`}jd`oux gcgjoxu un` `~r`hu`e cgjoav`} g fpup}` na}jyao jo un` ami`hujv` fpohujao/

    Ju jx haddao ua haoxje`} kgz`}`e haou}akk`}x jo haou}ak jo un` r}ah`xxjoepxu}j`x/ ]`gk$ujd` arujdjygujao jx jdrk`d`ou`e gmav g kgz`} af dae`k$r}`ejhujv` haou}ak+ snjhn dgogc`x u}goxj`oux+ goe dae`k$r}`ejhujv` haou}ak jxgcgjo gmav` g kgz`} af }`cpkgua}z haou}ak+ snjhn xugmjkjy`x goe `oxp}`x unguun` r}ah`xx jx ar`}gu`e hkax` ua un` x`uujocx xr`hj`e mz un` kgz`} gmav`/

    Aokjo` dae`k$mgx`e arujdjygujao ngx fapoe sje`xr}`ge px` jo r}ah`xx`x jo$

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    15/170

    7/=/ ]`kgu`e sa}l 0

    epxu}j`x+ `xr`hjgkkz un` d`unaex af dae`k$r}`ejhujv` haou}ak/ Ju jx jou`}`xujocua oau` ungu un` vgxu dgia}juz af jdrk`d`ougujaox af dae`k$r}`ejhujv` hao$u}ak px` `drj}jhgk dae`kx .Wjo goe Mgecs`kk+ =228*+ goe unjx dgz m` }`kgu`e

    ua un` kas`} haxux af dae`k e`xjco goe pregujoc af xphn dae`kx/Jo un` haou`~u af ajk goe cgx r}aephujao }`gk$ujd` arujdjygujao ngx m``o

    e`o`e gx g r}ah`xx af d`gxp}`$hgkhpkgu` haou}ak gu g f}`wp`ohz snjhn dgjo$ugjox un` xzxu`dx arujdgk ar`}gujoc haoejujaox sjunjo un` ujd`$haoxugouhaoxu}gjoux af un` xzxu`d .Xgrpu`kkj+ Dahnjyplj+ Npuhnjox+ H}gd`}+ Go$e`}xao+ Dp`kk }+ @xha}hjg+ Ng}dx+ Xjxl+ R`oo`mgl`}+ Ngo+ M}aso+ Lgmj}+]``x`+ Op`y+ Kgoec}`o+ DhLj` goe Gj}kj`+ =228*/ G }`vj`s af }`gk$ujd`arujdjygujao hgx` njxua}j`x jo un` r}aephujao af ajk goe cgx hgo m` fapoe joDahnjyplj+ Xgrpu`kkj+ Lgmj}+ H}gd`}+ Kahndgoo+ ]``x`+ Ng}dx+ Xjxl+ Nju`

    goe @xha}hjg .=226*/ Un` r}aephujao arujdjygujao r}amk d jx }`kgu`e uaun` }`x`}vaj} dgogc`d`ou r}amk`d+ snjhn haoxje`}x un` arujdjygujao af jo$

    i`hujao goe e}gjogc` ao un` ujd` xhgk`x af daounx goe z`g}x/ R}aephujaoarujdjygujao goe }`x`}vaj} dgogc`d`ou haoxje`} }`gk$ujd` arujdjygujao guejfl`}`ou ujd`$xhgk`x+ goe ju jx haddao ua u}`gu }`x`}vaj} dgogc`d`ou goer}aephujao arujdjygujao gx x`rg}gu` xpmr}amk`dx kjol`e un}apcn haoxu}gjouxua kjdju hadrk`~juz .Xgrpu`kkj `u gk/+ =228*/ Un`}` jx g raxxjmjkjuz ungu xna}u$u`}d cgjox jo r}aux cgjo`e mz r}aephujao arujdjygujao had` gu un` `~$r`ox` af pkujdgu` }`hav`}z gx xad` }`x`g}hn`}x ngv` amx`}v`e jo xjdpkgujaox

    .Ogpx+ Eakk` goe Igox`o+ =226*/ Jo xphn hgx`x xna}u$u`}d cgjox dgz o``e uam` s`jcn`e gcgjoxu kaoc$u`}d cgjox/ Dahnjyplj `u gk/ .=226* xugu` ungu un`daxu jdra}ugou d`gxp}` af un` xphh`xx af g }`gk$ujd` arujdjygujao xzxu`djo ajk goe cgx r}aephujao jx un` vgkp` gee`e ua un` a}cgojygujao+ nas`v`}un` d`gxp}`d`ou af vgkp` jx g v`}z hadrk`~ jxxp`/ G h}jujhgk fghua} fa}un` xphh`xxfpk gearujao af o`s r}aephujao arujdjygujao u`hnoakacz jx unguun`}` jx u}`d`oeapx r}`xxp}` ua l``r gxx`ux r}aephjoc gu gc}``e$prao }gu`x+un`}`fa}` ar`}gua}x g}` c`o`}gkkz }jxl$gv`}x` .Igkjkavg+ Ugpujz`v+ Fa}hge`kk+]ae}jcp`y goe Xgdg+ =22>*/ G haddao r}ghujh` jx ua c`o`}gu` g r}aephujao

    goe joi`hujao rkgo r`}jaejhgkkz gu uzrjhgk jou`}vgkx af m`us``o g s``l goeg daoun+ snjhn xr`hj`x fa} joxugoh` ug}c`u hnal` ar`ojocx a} cgx$kjfu }gu`xsjun un` gjd af dg~jdjyjoc egjkz r}aephujao .Mj`l`} `u gk/+ =223g*/

    Un` haoh`rux af mkghl$ma~ a} c}`z$ma~ dae`kjoc ngv` m``o grrkj`e ua}`x`}vaj} dgogc`d`ou r}`vjapxkz .]asgo goe Hk`cc+ 7:68*+ .Hnj`}jhj+ 7::0*.]`og}e+ E`dm`k`+ K`xxj goe Dg}j+ 7::>*+ goe .Xgrpu`kkj+ Ojlakgap goe@haoadje`x+ =220*/ Xgrpu`kkj `u gk/ .=220* xpcc`xu ungu g r`}xjxu`oukz `~hju$joc r}ah`xx hgo m` jdrk`d`ou`e jo hgx`x sn`}` egug hgrup}`e f}ad un` `kejx oau jofa}dgujv` `oapcn/ Faxx .7:>3* xpcc`xu`e g xu}gu`cz fa} un` e`xjco

    af s`kk u`xux xphn ungu un` d`gxp}`e egug jx da}` x`oxjujv` ua un` r}ar`}uj`x

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    16/170

    6 Jou}aephujao

    af o`g}$s`kk }`x`}vaj} dae`kx snjhn g}` af jou`}`xu/

    Un` haoh`rux af rg}gd`u`} `xujdgujao ngv` gkxa m``o grrkj`e ua u hao$v`oujaogk }`x`}vaj} dae`kx ua egug+ jo sngu jx }`f`}}`e ua gx gpuadgu`e njx$

    ua}z dguhnjoc/ Ju jx c`o`}gkkz ghh`ru`e ungu goz rnzxjhgk }`x`}vaj} dae`knjxua}z dguhn`e ua egug sjkk m` xpmi`hu ua xjcojhgou oao$pojwp`o`xx .Kjuuk`+Fjohngd goe Ipujkg+ =226*+ goe dgoz gpuna}x ngv` guu`dru`e ua e`xh}jm`unjx oao$pojwp`o`xx .Gkd`jeg O`uua+ Xhnjay`}+ Kjc`}a goe Dgxhnja+ =228*+.Xhnpky`$]j`c`}u+ Nggx` goe O`l}gxxav+ =228*+ goe .Zgoc+ Ocnj d+ Hg}egoe M}`d`j`}+ =223*/ Jo dgoz hgx`x njxua}z dguhnjoc af }`x`}vaj} dae`kx jxr`}fa}d`e dgopgkkz+ goe dgopgkkz njxua}z$dguhnjoc g }`x`}vaj} dae`k ua g`ke ngx m``o }`ra}u`e ua ugl` gx dphn gx g z`g}+ snjhn jx jdr}ghujhgk fa}xna}u$u`}d e`hjxjao dgljoc .Gsgxunj+ Xgolg}go goe Ojlakgp+ =22>*/

    Un` oaegk grr}aghn ua r}aephujao arujdjygujao ngx opd`}jhgk jxxp`x }`$kgu`e ua jof`gxjmk` xakpujaox jo un` hgx` af xnpu$jo s`kkx+ hngoc` jo dae`kejd`oxjaox gx s`kkx g}` xnpu$jo+ goe ejxgrrajoujoc hadrpugujaogk `hj`ohzghha}ejoc ua Sgoc+ Kjuvgl goe Gyjy .=22=*/ Mg}}gco$N`}ooe`y+ Vywp`y$]ado+ ]axgk`x$Dg}jo`x goe Cg}hg$Xohn`y .=220* guu`dru`e go gku`}og$ujv` dae`kjoc grr}aghn xujkk mgx`e ao }jca}apx rnzxjhgk dae`kjoc goe }`$ra}u`e ungu xakvjoc un` }`xpkujoc x`u af ejfl`}`oujgk$gkc`m}gjh `wpgujaox sgxjdr}ghujhgk opd`}jhgkkz/ Xad` gpuna}x ngv` xpcc`xu`e ungu un` dgjo mau$uk`o`hl jo r}aephujao arujdjygujao jx un` hadrpugujaogk `fla}u }`wpj}`e ua

    xakv` }jca}apx rnzxjhgk r}aephujao dae`kx .Ygock `u gk/+ =226*/G vgxu opdm`} af xu}gu`cj`x fa} }`gk$ujd` arujdjygujao af aflxna}` ajk goe

    cgx r}aephujao ngv` m``o r}arax`e jo un` kju`}gup}`+ fa} g }`h`ou }`vj`s x``Mj`l`} `u gk/ .=223g*/ Mj l`} `u gk/ .=223g* oau`e ungu v`}z f`s af un`x`xu}gu`cj`x s`}` e`xjco`e fa} ao$kjo` px` goe ungu f`s }`gk$sa}ke jdrk`d`oug$ujaox `~jxu+ goe xpcc`xu`e ungu unjx dgz m` kjol`e ua ejhpkuj`x sjun dae`kdgjou`ogoh` ep` ua un` hadrk`~juz af un` dae`kx jo dgoz af un` r}arax`exu}gu`cj`x/ Un` gpuna}x gkxa joejhgu` ungu e`v karjoc xu}gu`cj`x fa} ngoekjocdae`k poh`}ugjouz jx g l`z hngkk`oc` jo }`gk$ujd` arujdjygujao/

    Un` haoh`rux af xzxu`d je`oujhgujao ngv` m``o grrkj`e ua r}aephujaodae`kjoc r}`vjapxkz jo Rapkjxx`+ vgo Av`}xhn``+ M}j`}x+ Daohp} goe Can.=226* goe Rapkjxx` .=22>*/ Un` gpuna}x xpcc`xu }`$}apujoc `ghn s`kk ua gu`xu x`rg}gua} goe uacckjoc e`hjxjao vg}jgmk`x ua e`u`}djo` g ezogdjh oc`}$r}jou fa} `ghn s`kk/ Fjuu`e rg}gd`u`}x g}` e`u`}djo`e xa ungu g r}aephujaodae`k haoxjxujoc af uu`e rg}gd`u`}x goe ezogdjh oc`}r}joux hadmjo`edguhn d`gxp}`e }gu`x gx hkax kz gx raxxjmk / Diggvguu`o+ Ggxn jd+ Xg`kjegoe C}aoojoc .=226* ngv` haoxje`}`e r}aephujao arujdjygujao af cgx$hao`es`kkx pxjoc }`kgujv`kz xjdrk` dae`kx mgx`e ao g rg}ujgk ejfl`}`oujgk `wpgujao

    ungu e`xh}jm`x un` o`g}$s`kk g}`g goe snjhn jx uu`e ua egug+ sngu hapke m`

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    17/170

    7/=/ ]`kgu`e sa}l 3

    e`xh}jm`e gx g c}`z$ma~ grr}aghn ua r}aephujao dae`kjoc/

    Jo r}ghujh` }jca}apx rnzxjhgk dae`kx af aflxna}` ajk goe cgx r}aephujaoafu`o }`wpj}` xad` fa}d af `drj}jhjxd ua ghnj`v` e`xj}`e ghhp}ghz/ Fa}

    joxugoh`+ }jca}apx rnzxjhgk dae`kx px`e jo dpkujrngx` as d`u`}x ua `xuj$dgu` ajk+ cgx goe sgu`} }gu`x f}ad d`gxp}`e r}`xxp}`x goe u`dr`}gup}`xg}` afu`o aokz haoxje`}`e ghhp}gu` fa} g }goc` af ar`}gujoc rajoux fa} snjhndae`kx ngv` m``o hgkjm}gu`e .vgo Ejil+ Can goe vgo Kj`oe`o+ =22>*/ Dae$`kx px`e jo r}aephujao arujdjygujao g}` gkxa pxpgkkz xpmi`hu`e ua xad` fa}daf dae`k$uujoc/ G r}ghujh` haddaokz }`f`}}`e ua jo un` kju`}gup}` jx uau r}a~z$dae`kx fapoe f}ad hadd`}hjgk xjdpkgua}x ua }`h`oukz d`gxp}`exjock`$}gu` s`kk u`xux+ x`` fa} joxugoh` Igkjkavg `u gk/ .=22>*/ G ejxgevgougc`af unjx grr}aghn jx ungu ju hgo aokz hadr`oxgu` fa} mjgx`x jo un` r}aeph$

    ujao dae`kx+ goe dae`k`e hngoc` jo r}aephujao gx e`hjxjao vg}jgmk`x hngoc`jx oau vgkjegu`e gcgjoxu d`gxp}`d`oux/ Ogeg}+ Xhno`je`}+ Ighlxao+ DhLj`goe Ngdje .=22>* ngv` amx`}v`e ungu un` hngoc` jo r}aephujao r}`ejhu`e mzgo poejxhkax`e hadd`}hjgk xjdpkgua} eje jo fghu oau dguhn hngoc`x jo r}a$ephujao amx`}v`e ao go aflxna}` ajk goe cgx `ke gx e`hjxjao vg}jgmk`x s`}`hngoc`e/ Ua hj}hpdv ou unjx xna}uhadjoc+ un` gpuna}x joh}`d`ougkkz jd$rk`d`ou`e xdgkk hngoc`x jo e`hjxjao vg}jgmk`x+ amx`}v`e }`xpkujoc hngoc` jor}aephujao goe pregu`e dae`kx ua hadr`oxgu` fa} un`x` dae`k joghhp}ghj`x/Dae`k$uujoc goe xu}gu`cj`x ua joh}`d`ougkkz jdrk`d`ou xdgkk hngoc`x hgo

    m` haoxje`}`e jdrkjhju xu}gu`cj`x fa} ngoekjoc poh`}ugjouz jo arujdjygujao afaflxna}` ajk goe cgx r}aephujao/

    G xjcojhgou np}ek` ua dae`k$uujoc jx d`gxp}`d`ou poh`}ugjouz+ snjhnhgo m` xjcojhgou jo un` aflxna}` ajk goe cgx r}aephujao/ D`gxp}`d`oux af ajkr}aephujao g}` c`o`}gkkz daxu ghhp}gu` gu rajou$af$xgk`+ sn`}` xhgk d`g$xp}`d`oux g}` pxpgkkz gvgjkgmk`+ goe m`had` joh}`gxjockz poh`}ugjo uasg}eun` s`kk k`v`k .Kjuuk` `u gk/+ =226*/ Xad` haoxje`} xhgk d`u`}x snjhn d`g$xp}` `~ra}u`e ajk un` aokz }`kjgmk` d`gxp}`d`ou af ajk r}aephujao .Igkjkavg`u gk/+ =22>*/

    Gkunapcn un`}` x``dx ua m` dphn gc}``d`ou ungu poh`}ugjouz jx go jd$ra}ugou fghua} jo r}aephujao arujdjygujao .Mj`l`} `u gk/+ =223g*+ goe dphnguu`oujao ngx m``o rgje ua poh`}ugjouz jo }`x`}vaj} dgogc`d`ou+ `~rkjhjuu}`gud`ou af poh`}ugjouz jo r}aephujao arujdjygujao ngx }`h`jv`e kjuuk` gu$u`oujao/ Ao` af un` f`s `~rkjhju u}`gud`oux af poh`}ugjouz jo r}aephujaoarujdjygujao hgo m` fapoe jo Mj`l`}+ Xkprrngpc goe Iangox`o .=226*/

    Rg}gd`u`} `xujdgujao jx g fa}d af }`c}`xxjao r}amk`d/ G d`gxp}` afpoh`}ugjouz jo `xujdgu`e rg}gd`u`}x jx un` xugoeg}e `}}a}+ un` xugoeg}e e`$vjgujao af un` xgdrkjoc ejxu}jmpujao af un` xgdrk` d`go/ Un` xugoeg}e `}}a}

    af g }`c}`xxjao r}amk`d hgo m` gogkzy`e gogkzujhgkkz sn`o un` }`c}`xxjao

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    18/170

    > Jou}aephujao

    fpohujao jx kjo`g} goe uujoc d`unae jx k`gxu xwpg}`x+ snjk` fa} c`o`}gk }`$c}`xxjao dae`kx ungu ngv` oa gogkzujhgk xakpujao unjx `}}a} hgo m` `vgkpgu`ehadrpugujaogkkz pxjoc maauxu}grrjoc .@f}ao goe Ujmxnj}goj+ 7::8*/ Maau$

    xu}grrjoc jx mgx`e ao un` haoh`ru af e}gsjoc dpkujrk` }goead xgdrk`x f}adgo `drj}jhgk ejxu}jmpujao+ a} }`xgdrkjoc/ Sn`o maauxu}grrjoc }`xjepgkx jog }`c}`xxjao r}amk`d+ un` }`xjepgkx+ un` ejfl`}`oh` m`us``o d`gxp}`e goedae`k`e vgkp`x fa} g egug x`u+ g}` }`xgdrk`e ua haoxu}phu o`s egug x`ux goerg}gd`u`} `xujdgujao }`r`gu`e fa} `ghn xphn x`u/ Go gku`}ogujv` d`unaeaf maauxu}grrjoc jo rg}gd`u`} `xujdgujao jx maauxu}grrjoc rgj}x .@f}ao goeUjmxnj}goj+ 7::8*/ Maauxu}grrjoc r}avje`x dpkuj$vg}jgmk` xgdrkjoc ejxu}j$mpujaox ungu hgrup}` un` e`r`oe`oh` m`us``o m`us``o dg}cjogk goe haoej$ujaogk rg}gd`u`} ejxu}jmpujaox .F}`z goe Mp}dgxu`}+ 7:::*/ Aun`} gva}x af

    maauxu}grrjoc gkxa `~jxu+ fa} joxugoh` rg}gd`u}jh maauxu}gr snjhn xgdrk`x grg}gd`u}jh }gun`} ungo `drj}jhgk ejxu}jmpujao/ Un` ighllojf` jx g u`hnojwp`snjhn m`g}x hkax` }`x`dmkgoh` ua un` maauxu}gr/ Un` opdm`} af maauxu}gr}`rkjhgujaox }`wpj}`e e`r`oex ao un` jofa}dgujao e`xj}`e+ mpu =22 }`xgd$rk`x a} k`xx g}` afu`o xphj`ou ua e`u`}djo` g xugoeg}e `}}a}+ snjk` 7222}`xgdrk`x jx haoxje`}`e xphj`ou ua e`u`}djo` haoe`oh` jou`}vgkx .@f}aogoe Ujmxnj}goj+ 7::8*/ Un`}` gkxa `~jxu vg}jgujaox af maauxu}grrjoc d`unaexjou`oe`e ua jdr}av` hadrpugujaogk `hj`ohz .Cjckj+ 7::6*/

    Xad` }`h`ou }`x`g}hn ao gxx`xxjoc poh`}ugjouz jo ezogdjh dae`kx dgz

    ngv` xad` }`k`vgoh` ua unjx un`xjx+ gkunapcn ezogdjh dae`kx sjkk oau m`haoxje`}`e/ Jo xzxu`d je`oujhgujao un` gxzdruaujh `}}a} af R}`ejhujao @}}a}D`unaex jx u}gejujaogkkz px`e ua gxx`xx dae`k `}}a}+ snjhn gkkasx haoe`oh`}`cjaox fa} rg}gd`u`}x ua m` fapoe f}ad egug gogkzujhgkkz .Kipoc+ 7:::*/Cg}guuj+ Hgdrj goe Mjuugouj .=225* oau` ungu unjx gxzdruaujh un`a}z }`wpj}`xun` gmx`oh` af po$dae`k`e ezogdjhx+ goe jx aokz }jca}apxkz ha}}`hu sn`osn`o un` opdm`} af egug u`oex ua joojuz jo xphn g sgz ungu un` uaugkgdapou af jofa}dgujao ao un` xzxu`d rg}gd`u`}x c}asx pomapoe`e+ goeaokz sn`o un` haxu fpohujao px`e jo rg}gd`u`} `xujdgujao ngx g pojwp`djojdjy`}/ Cg}guuj `u gk/ .=225* fp}un`} oau` ungu sn`o egug x`ux ngv`kas jofa}dgujao haou`ou a} egug x`ux g}` oju` goe xdgkk+ gxzdruaujh un`a}zr}avjejoc djxk`gejoc }`xpkux+ j/`/ unjx un`a}z hgo fgjk sn`o poh`}ugjouz k`v`kxg}` njcn/ Ao` gku`}ogujv` ua gxzdruaujh un`a}z jx xpcc`xu`e jo Hgdrj goeS`z`} .=220*/

    7/8 Xpddg}z goe un`xjx av`}vj`s

    Hngru`} = haougjox g r}amk`d e`xh}jrujao goe dgun`dgujhgk r}`kjdjog}j`x+

    snjhn fa}dx un` mgxjx fa} xpmx`wp`ou hngru`}x/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    19/170

    7/8/ Xpddg}z goe un`xjx av`}vj`s :

    Hngru`} 8 haougjox go gogkzxjx af g x`u af r}aephujao egug f}ad g Oa}unX`g ajk goe cgx `ke/ Jo un` x`u af r}aephujao egug haoxje`}`e+ e`hjxjaovg}jgmk`x g}` x``o ua vg}z kjuuk` `~h`ru ep}joc ujd`x sn`o gkk s`kkx g}` xnpu

    easo+ snjhn djcnu oau }`v`gk dphn px`fpk jofa}dgujao/ E`hjxjao vg}jgmk`xg}` gkxa amx`}v`e ua vg}z sjunjo g og}}as }goc` af vgkp`x apuxje` ujd`x afxnpueasox+ snjhn sjkk dgl` ju ejhpku ua e`u`}djo` rg}gd`u`}x f}ad egugsnjhn g}` vgkje ckamgkkz fa} gkk x`urajoux/ Amx`}vgujaox dge` jo Hngru`} 8daujvgu` un` xupez af un` kjol m`us``o un` jofa}dgujao haou`ou jo r}aeph$ujao egug+ poh`}ugjouz jo un` uu`e rg}gd`u`}x af r}aephujao dae`kx goepoh`}ugjouz jo x`urajoux xpcc`xu`e mz r}aephujao arujdjygujao/

    Hngru`} 5 r}`x`oux go grr}aghn ua dae`kjoc r}aephujao snjhn jx da$ujvgu`e mz un` haoh`rux af xzxu`d je`oujhgujao goe snjhn jx xpjugmk` fa}

    r}aephujao arujdjygujao/ Un` dae`k xu}phup}` xpcc`xu`e jx jou`oe`e ua m`kahgkkz vgkje g}apoe un` }gu`x goe x`uujocx d`gxp}`e gu un` daxu }`h`ou s`kku`xu/ Un` d`unaex g}` grrkj`e ua g hgx` xupez af un` `ke xupej`e jo Hngr$u`} 8+ haoxje`}joc =2 cgx$kjfu`e s`kkx/ Ju jx xpcc`xu`e nas haoxu}gjoux hgogje rg}gd`u`} `xujdgujao mz `~r}`xxjoc rnzxjhgk loask`ec`+ fa} joxugoh` af}gu`$joe`r`oe`ou cgx$ajk a} sgu`}$ajk }gujax/ Poh`}ugjouz `xujdgujao jo u$u`e rg}gd`u`}x mz un` d`unae af maauxu}grrjoc jx grrkj`e ua un` xpcc`xu`edae k/ Gx `~r`hu`e+ un` poh`}ugjouz jo rg}gd`u`}x sn`o uu`e ua un` x`uaf r}aephujao egug haoxje`}`e jx xnaso ua m` haoxje`}gmk` `v`o unapcn un`

    uu`e dae`k dguhn`x un` upojoc egug x`u s kk/ Gkunapcn rg}gd`u`} poh`}$ugjouz sjkk e`r`oe ao dae`k xu}phup}`+ r}aephujao egug goe un` `xujdgujaoxu}gu`cz+ ju jx }`gxaogmk` ua `~r`hu goz dae`k xu}phup}` ua ngv` xjcojhgoupoh`}ugjouz ep` ua un` kas jofa}dgujao haou`ou jo egug/ Go gevgougc` af un`maauxu}grrjoc d`unae jx ungu ju ea`x oau dgl` goz }`wpj}`d`oux ao dae`kxu}phup}`/

    Hngru`} 0 haoxje`}x g Daou`$Hg}ka grr}aghn ua gxx`xxjoc un` poh`}$ugjouz jo r}aephujao arujdjygujao ungu }`xpkux f}ad `xujdgu`e poh`}ugjouzjo r}aephujao dae`kx+ goe go grr}aghn ua }`kgu` dae`k poh`}ugjouz ua xjd$

    pkgu`e kaxx jo r}au jx xpcc`xu`e+ un` haoh`ru af kaxu rau`oujgk af r}aephujaoarujdjygujao/ Un` rau`oujgk fa} r}aephujao arujdjygujao ungu jx kaxu ep`ua poh`}ugjouz sjkk e`r`oe ao nas x`urajou hngoc`x g}` jdrk`d`ou`e+ goeg }pejd`oug}z ar`}gujaogk xu}gu cz+ g xu}gu`cz fa} c}gepgk x`urajou hngoc`snjk` daojua}joc r}aux goe haoxu}gjoux+ jx xjdpkgu`e sn`o `xujdgujoc kaxurau`oujgk ep` ua poh`}ugjouz/ Un` xpcc`xu`e d`unae jx grrkj`e ua un` xgd``ke goe egug x`u gx ungu af Hngru`} 5/ Maun uaugk cgx goe uaugk sgu`} hg$rghjuz haoxu}gjoux g}` jdrk`d`ou`e+ gx s`kk gx xad` s`kk haoxu}gjoux ep` uaas gxxp}goh` jxxp`x/

    Hngru`} 6 xupej`x r}aephujao arujdjygujao mgx`e ao poh`}ugjo r}aeph$

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    20/170

    72 Jou}aephujao

    ujao dae`kx+ pujkjyjoc go `kgma}gu`e ar`}gujaogk xu}gu`cz hadmjo`e sjun ju$`}gujv` }`$uujoc af dae`k rg}gd`u`}x goe }`$arujdjygujao/ Un` ar`}gujaogkxu}gu`cz jx daujvgu`e mz un` sgz ar`}gua}x hp}}`oukz jdrk`d`ou hngoc`x jo

    x`urajoux jo xdgkk+ ju`}gujv` xu`rx goe dgz m` grrkj`e }`cg}ek`xx af dae`kxu}phup}` px`e a} af uzr` af poh`}ugjouz+ gx kaoc gx hgrghjuj`x goe r}aux g}`d`gxp}`e goe un` xjco af un` }`xraox` jo r}aux goe hgrghjuz pujkjygujao uahngoc` jo `ghn e`hjxjao vg}jgmk jx loaso/ Sn`o r}aephujao jx arujdjy`emgx`e ao poh`}ugjo r}aephujao dae`kx+ un` }`xpkujoc hngoc` jo }`gkjy`e r}aujx poh`}ugjo+ ju dgz `v`o m` o`cgujv`/ Jo Hngru`} 6 g Daou`$Hg}ka gkca}jundjx xpcc`xu`e snjhn cjv`x r}amgmjkjxujh r}`ejhujaox af raxxjmk` hngoc`x jo }`$gkjy`e r}aux }`xpkujoc f}ad g x`urajou hngoc`+ `~rkajujoc go `xujdgu` afrg}gd`u`} poh`}ugjouz/

    Sn`o r}aephujao jx arujdjy`e mgx`e ao poh`}ugjo r}aephujao dae`kx+haov`}c`oh` ua arujdpd hgooau m` cpg}gou``e jo c`o`}gk/ Ju dgz m` ungugu g cjv`o ju`}gujao af un` ju`}gujv` arujdjygujao xu}gu`cz+ jdrk`d`oujoc `~$hjugujao af g rg}ujhpkg} s`kk sjkk }`eph` rg}gd`u`} poh`}ugjouz jo g dgoo`}snjhn gkkasx g dphn kg}c`} r}au joh}`gx` jo xpmx`wp`ou arujdjygujao goejdrk`d`ougujao/ Hngru`} 6 jov`xujcgu`x `xujdgujoc unjx geejujaogk r}au jo$h}`gx` hgpx`e mz `~hjugujao+ a} m`o`u af `~hjugujao+ pxjoc g Daou`$Hg}kad`unae snjhn `~rkajux go `xujdgu` af rg}gd`u`} poh`}ugjouz/

    Hngru`} 3 r}`x`oux g hgx` xupez af g x`haoe Oa}un X`g ajk goe cgx `ke+

    haoxjxujoc af 76 s`kkx sn`}` un` r}aephujao hnal` x`uujoc jx haoxje`}`e un` e`$hjxjao vg}jgmk`+ fap} cgx$kjfu`e s`kkx goe v` xpmx`g s`kkx/ G dae`k xu}phup}`fapoe sjun go grr}aghn xjdjkg} ua ungu af Hngru`} 5 jx xpcc`xu`e fa} rkgu$fa}d s`kkx sn`}` hnal x`uujoc jx haoxje`}`e un` e`hjxjao vg}jgmk / Xpmx`gs`kkx g}` oau haoxje`}`e rg}u af r}aephujao arujdjygujao+ mpu g }pejd`oug}zxpmx`g s`kk dae`k jx xpcc`xu`e ua `xujdgu` goe xpmu}ghu un` haou}jmpujao afun`x` s`kkx f}ad uaugk d`gxp}`e r}aephujao/ Sn`o maauxu}grrjoc jx grrkj`eua rg}gd`u`} `xujdgujao+ rg}gd`u`} poh`}ugjouz jx fapoe ua m` xjcojhgougoe af xjdjkg} dgcojupe` gx ungu af un` r}`vjapx hgx` xupez `v`o unapcn

    un` dae`k dguhn`x un` upojoc x`u s`kk/ R}aephujao arujdjygujao haoxje$`}x haoxu}gjoux jo uaugk cgx goe uaugk sgu`} hgrghjuz+ gx s`kk gx xad` s`kkhaoxu}gjoux/

    Gku`}joc gkk e`hjxjao vg}jgmk`x xjdpkugo`apxkz gu `ghn jdrk`d`ougujaoaf un` ar`}gujaogk xu}gu`cz dgz oau m` r}ghujhgk+ un`}`fa}` g Daou`$Hg}kad`unae fa} `vgkpgujoc xpmx`ux af e`hjxjao vg}jgmk x ua m` gku`}`e+ x`ux afghujv` e`hjxjao vg}jgmk`x+ jx xpcc`xu`e jo Hngru`} 3/ Ju jx r}arax`e nas un`Daou`$Hg}ka d`unae hgo m` px`e ua oe ghujv` e`hjxjao vg}jgmk`x xa ungu gx`urajou hngoc` hgo m` xpcc`xu`e snjhn hgo m` `~r`hu`e ua joh}`gx` r}aux

    sjun haoe`oh`/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    21/170

    7/8/ Xpddg}z goe un`xjx av`}vj`s 77

    Hngru`} > haougjox haohkpxjaox e}gso f}ad unjx sa}l goe r}arax`x xad`ej}`hujaox fa} fp}un`} sa}l/

    7/8/7 Rpmkjhgujaox

    Unjx un`xjx ngx }`xpku`e jo g opdm`} af rpmkjhgujaox+ gx apukjo`e m`kas/Hngru`} 89

    @kcxg`u`}+ X/D/+ Xkprrngpc+ A/ goe Iangox`o+ U/G/ .=223*+ Hngkk`oc`xjo Rg}gd`u`} @xujdgujao af Dae`kx fa} Aflxna}` Ajk goe Cgx R}aeph$ujao Arujdjygujao + Jou`}ogujaogk R`u}ak`pd U`hnoakacz Haof`}`oh`+Epmgj+ E`h`dm`} =223+ JRUH 773=>

    Hngru`} 59

    @kcxg`u`}+ X/D/+ Xkprrngpc+ A/ goe Iangox`o+ U/G/ .=22>*+ R}aeph$ujao Arujdjygujao< Xzxu`d Je`oujhgujao goe Poh`}ugjouz @xujdgujao+Jou`kkjc`ou @o`}cz 2>+ Gdxu`}egd+ F`m}pg}z =22>+ XR@ 77=7>6

    Hngru`} 09

    @kcxg`u`}+ X/D/+ Xkprrngpc+ A/ goe Iangox`o+ U/G/ .=22>*+ Ajk goe

    Cgx R}aephujao Arujdjygujao< Kaxu Rau`oujgk ep` ua Poh`}ugjouz+ JFGHSa}ke Haoc}`xx+ La}`g+ Ipkz =22>

    Hngru`} 69

    @kcxg`u`}+ X/D/+ Xkprrngpc+ A/ goe Iangox`o+ U/G/ .=22>*+ Arujdjy$joc aflxna}` ajk goe cgx r}aephujao sjun poh`}ugjo r}aephujao dae`kx+Hadrpu`}x & Hn`djhgk @ocjo``}joc .xpmdjuu`e*

    Hngru`} 39

    @kcxg`u`}+ X/D/+ Xkprrngpc+ A/ goe Iangox`o+ U/G/ .=22>*+ Arujdjyg$ujao af Aflxna}` Ajk goe Cgx R}aephujao poe`} Poh`}ugjouz< HnaaxjocGhujv` E`hjxjao Vg}jgmk`x goe Hgx`$Xupez+ XR@ R}aephujao & Ar`}g$ujaox .xpmdjuu`e*

    Gx dgjo gpuna}+ dz haou}jmpujao ua un`x` rgr`}x g}` jo un` dae`kjoc+e`v`kard`ou af d`unaeakacz goe jdrk`d`ougujao af un` hgx` xupej`x r}`$x`ou`e/ Dz ha$gpuna}x ngv` gxxjxu`e jo e`u`}djojoc un` xhar` goe ej}`hujao

    af un` sa}l+ gx s`kk gx r}avjejoc f``emghl goe }`vj`s/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    22/170

    7= Jou}aephujao

    7/8/= Dgjo haou}jmpujaox

    Un` dgjo haou}jmpujaox af unjx un`xjx+ gkk sjun }`cg}e ua un` aflxna}` r}a$ephujao af ajk goe cgx+ g}`

    g egug$e}jv`o grr}aghn ua r}aephujao dae`kjoc goe dae`k pregujoc.Hngru`}x 5 goe 3*+

    go `~rkjhju u}`gud`ou af poh`}ugjouz jo r}aephujao arujdjygujao .Hngr$u`}x 5+ 0+ 6 goe 3*+ goe

    go ar`}gujaogk xu}gu`cz grr}aghn ua kjol arujdjygujao sjun jdrk`d`o$ugujao goe daojua}joc .Hngru`}x 0 goe 6*/

    Hngru`} 8 haougjox g xupez af g x`u af }`gk$sa}ke r}aephujao egug snjhndaujvgu`e un` grr}aghn e`xh}jm`e jo kgu`} hngru`}x/

    7/5 Oaugujao goe e`ojujaox

    Xzdmakx jou}aeph`e jo Hngru`} =9

    p e`hjxjao vg}jgmk`x~ jou`}ogk vg}jgmk`x

    e dae k`e goe d`gxp}`e ejxup}mgoh`x joe`r`o$e`ou af p

    rg}gd`u`}x ua m` e`u`}djo`e un}apcn rg}gd`u`}`xujdgujao

    D r}au d`gxp}`h r}aephujao haoxu}gjouxz d`gxp}`e vg}jgmk`x `~rkaju`e jo rg}gd`u`} `xuj$

    dgujaou ujd`

    O un` opdm`} af ujd` xu`rx jo un` upojoc egug x`uYO g upojoc egug x`u xrgoojoc O ujd` xu`rx }`xjepgkx jo rg}gd`u`} `xujdgujaoEz oa}dgkjygujao dgu}j~ fa} zs s`jcnujoc af }`xjepgkx jo rg}gd`u`} `xujdgujaoVx xafu haoxu}gjoux ao rg}gd`u`}x h ng}e haoxu}gjoux ao rg}gd`u`}x ] }apujoc dgu}j~

    Xzdmakx jou}aeph`e jo Hngru`} 89

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    23/170

    7/5/ Oaugujao goe e`ojujaox 78

    y }`kgujv` r}aephujao hnal` ar`ojocwck cgx kjfu }gu`wa s`kk ajk r}aephujao }gu`

    wc s`kk cgx r}aephujao }gu`ws s`kk sgu`} r}aephujao }gu`wuaua uaugk }gu` af ajk r}aeph`e f}ad gkk s`kkx haoxje$

    `}`ewuauc uaugk }gu` af cgx r}aeph`e f}ad gkk s`kkx haoxje$

    `}`ewuaus uaugk }gu` af sgu`} r}aeph`e f}ad gkk s`kkx hao$

    xje`}`ewu`xua ajk }gu` f}ad g s`kk d`gxp}`e gu un` daxu }`h`ou

    s`kk u`xuwu`xuc cgx }gu` f}ad g s`kk d`gxp}`e gu un` daxu }`h`ou

    s`kk u`xuwu`xus sgu`} }gu` f}ad g s`kk d`gxp}`e gu f}ad un` daxu

    }`h`ou s`kk u`xuFa }guja m`us``o s`kk u`xux goe uaugk d`gxp}`e }gu`x

    fa} ajkFc }guja m`us``o s`kk u`xux goe uaugk d`gxp}`e }gu`x

    fa} cgx

    Fs }guja m`us``o s`kk u`xux goe uaugk d`gxp}`e }gu`xfa} sgu`}

    Xzdmakx jou}aeph`e jo Hngru`} 59

    wk un` ajk+ cgx goe sgu`} }gu`x d`gxp}`e gu un` daxu}`h`ou s`kk u`xux fa} `ghn s`kk

    ek un` vgkp` e gu un` ujd` af un` daxu }`h`ou s`kku`xux fa} `ghn s`kk

    uk un` ujd`x af un` daxu }`h`ou s`kk u`xux fa} `ghn

    s`kkfe g l`}o`k fpohujao e`xh}jmjoc un` hngoc`x jo r}a$

    ephujao af g s`kk ua hngoc`x jo efp g l`}o`k fpohujao e`xh}jmjoc un` hngoc`x jo r}a$

    ephujao af g s`kk ua hngoc`x jo pfu g l`}o`k fpohujao e`xh}jmjoc un` hngoc`x jo r}a$

    ephujao af g s`kk ua hngoc`x jo uR un` havg}jgoh` dgu}j~ af un` gxzdruaujh ejxu}j$

    mpujao af r}`ejhujao `}}a} `xujdgu`x

    2 un` vg}jgoh` af }`xjepgkx

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    24/170

    75 Jou}aephujao

    ` g xuahngxujh r}ah`xx hadrao`ou af zYO} g }`xgdrk`e egugx`uOx un` opdm`} af }`xgdrk`x jo g Daou`$Hg}ka }`$

    xgdrkjocwck un` oa}dgkjy`e hngoc` jo cgx$kjfu }gu`x xjoh` }`k$

    gujv` ua vgkp` u`xu`e gu daxu }`h`ou s`kk u`xu} rg}gd`u`}x fapoe f}ad g }`xgdrk`e egugx`uyk un` hnal` ar`ojocx d`gxp}`e gu un` daxu }`h`ou

    s`kk u`xuwkck un` cgx kjfu }gu` d`gxp}`e gu un` daxu }`h`ou s`kk

    u`xua uu`e rg}gd`u`} jo ajk r`}fa}dgoh` hp}v`

    c uu`e rg}gd`u`} jo cgx r`}fa}dgoh` hp}v`s uu`e rg}gd`u`} jo sgu`} r`}fa}dgoh` hp}v`a uu`e rg}gd`u`} jo ajk r`}fa}dgoh` hp}v`c uu`e rg}gd`u`} jo cgx r`}fa}dgoh` hp}v`s uu`e rg}gd`u`} jo sgu`} r`}fa}dgoh` hp}v`z uu`e rg}gd`u`}x e`xh}jmjoc mjgx`x jo d`gxp}`$

    d`oux}do un` }guja m`us``o r}aephujao }gu`x af rngx`x d

    goe o

    ]K kas`} haoxu}gjoux ao }gujax }d

    o]P prr`} haoxu}gjoux ao }gujax }

    do

    d dgxx as }gu`a e`oxjuz af ajkc e`oxjuz af cgxs e`oxjuz af sgu`}}`c xafu haoxu}gjou ao rg}gd`u`}x }`c xafu haoxu}gjou ao rg}gd`u`}x s}`c s`jcnu af xafu haoxu}gjoux ao

    s}`c

    s`jcnu af xafu haoxu}gjoux ao os opdm`} af s`kkx haoxje`}`e jo r}aephujao aruj$

    djygujaol g e`xjco rg}gd`u`} jo l`}o`k fpohujaox fy

    Xzdmakx jou}aeph`e jo Hngru`} 09

    LCA] cgx$ajk }gujaLSH sgu`} hpu rg}gd`u`} vgkp`x snjhn g}` u}p` jo xad` x`ox`

    Ra un` rau`oujgk fa} r}aephujao arujdjygujao

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    25/170

    7/5/ Oaugujao goe e`ojujaox 70

    Ra+} }`gkjygmk` rau`oujgk fa} r}aephujao arujdjygujaoKp kaxu rau`oujgk af r}aephujao arujdjygujaoW un` wpauj`ou af rau`oujgk ungu jx kaxu ep` ua po$

    h`}ugjouzfKp r}amgmjkjuz fpohujao fa} kaxx ep` ua poh`}ugjouzfRa r}amgmjkjuz fpohujao fa} un` rau`oujgk fa} r}aeph$

    ujao arujdjygujaof r}amgmjkjuz fpohujao fa} rg}gd`u`}x N2 un` `v`ou ungu r}aephujao jx hp}}`oukz arujdgkN7 un` `v`ou ungu r}aephujao jx hp}}`oukz xpm$

    arujdgkSh un` x`u af joejh`x af s`kkx snax` cgx$kjfu }gu` dgz

    oau m` }`eph`ePr}h g kjdju ao un` xjy` af hngoc` jo e`hjxjao vg}jgmk`xwdg~c dg~jdpd cgx r}ah`xxjoc hgrghjuz

    wdg~s dg~jdpd sgu`} r}ah`xxjoc hgrghjuzma mjgx gee`e ua dae`k`e ajk r}aephujao jo r}aeph$

    ujao arujdjygujaomc mjgx gee`e ua dae`k`e cgx r}aephujao jo r}a$

    ephujao arujdjygujaoms mjgx gee`e ua dae`k`e sgu`} r}aephujao jo r}a$

    ephujao arujdjygujaoK un` k`ocun af un` jou`}vgk gu un` `oe af un` upo$joc x`u px`e av`} snjhn mjgx`x ma+ mc goe ms g}`hgkhpkgu`e

    x un` ra}ujao af g e`hjxjao vg}jgmk` hngoc` ungu jxjdrk`d`ou`e m`fa}` g haoxu}gjou jx }`ghn`e

    Ou opdm`} af }`xgdrk`x px`e jo Gkca}jund 0/=Of opdm`} af }`xgdrk`x px`e jo Gkca}jund 0/=u xgdrk`x af px`e jo Gkca}jund 0/=f xgdrk`x af px`e jo Gkca}jund 0/=fRa{N7 r}amgmjkjuz fpohujao fa} kaxx ep` ua poh`}ugjouz+

    cjv`o ungu r}aephujao jx xpm$arujdgkfKp{N7 r}amgmjkjuz fpohujao fa} un` rau`oujgk fa} r}aeph$

    ujao arujdjygujao+ cjv`o ungu r}aephujao jx xpm$arujdgk

    fW{N7 r}amgmjkjuz fpohujao fa} W+ cjv`o ungu r}aephujaojx xpm$arujdgk

    Xzdmakx jou}aeph`e jo Hngru`} 69

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    26/170

    76 Jou}aephujao

    pdjo un` kas`} `oe af un` }goc` af raxxjmk` vgkp`x fa}p

    pdg~ un` njcn`} `oe af un` }goc` af raxxjmk` vgkp`x fa}

    ppU g ug}c`u vgkp` fa} go ar`}gujaogk xu}gu`czP un` x`u af joejh`x af p snjhn g}` ua m` e`h}`gx`e

    gx go ar`}gujaogk xu}gu`cz grr}aghn`x pU f}adp2

    P, un` x`u af joejh`x af p snjhn g}` ua m` joh}`gx`egx go ar`}gujaogk xu}gu`cz grr}aghn`x pU f}adp2

    ID g haxu fpohujao gcgjoxu snjhn d`gxp}`e r}au

    hngoc` ep}joc jdrk`d`ougujao af go ar`}gujaogkxu}gu`cz jx ua m` hadrg}`e ua e`u`}djo` sn`un`}ua u`}djogu` un` ar`}gujaogk xu}gu`cz m`fa}` un`ug}c`u jx }`ghn`e

    IUD g un}`xnake vgkp` fa} IDuax un` ujd` gu snjhn un` ar`}gujaogk xu}gu`cz jx joj$

    ujgu`eua` un` ujd` gu snjhn un` ar`}gujaogk xu}gu`cz jx u`}$

    djogu`e

    X un` px`}$xr`hj`e xjy` af x`urajou hngoc` gu `ghnju`}gujao af go ar`}gujaogk xu}gu`czI} g haxu fpohujao fa} un` `~r`hu`e r}au guugjogmk`

    f}ad davjoc x`urajoux uasg}e g o`s ug}c`uIU} g un}`xnake vgkp` fa} IDM@ un` m`o`u af `~hjugujaoH@ un` haxu af `~hjugujaoo un` oadjogk rg}dgu`} `xujdgu`+ jo un` haou`~u

    af m`o`u af `~hjugujaoI@ un` haxu$m`o`u u}ge`afl af go `~hjugujaoI@+U g un}`xnake vgkp` fa} I@

    Xzdmakx jou}aeph`e jo Hngru`} 39

    n g c`o`}gk fpohujao snjhn dgrx .p+ e* ua zJg x`u af joejh`x af ghujv` e`hjxjao vg}jgmk`xJHg x`u af joejh`x af joghujv` e`hjxjao vg}jgmk`xJG+JM+JHJE+J@ joejh`x af s`kkx af ejfl`}`ou hgu`ca}j`x G$@

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    27/170

    7/5/ Oaugujao goe e`ojujaox 73

    JDH un` x`u af joejh`x af s`kkx snjhn ngv` dg~jdpdhaoxu}gjoux ao hnal` ar`ojocx ep` ua xgoe r}a$ephujao

    JDMNR un` x`u af s`kkx snjhn ngv` djojdpd haoxu}gjouxao mauuadnak` r}`xxp}`

    JDCX un` x`u af joejh`x af s`kkx snjhn ngv` haoxu}gjouxao cgx$kjfu }gu`x ep` ua xkpccjoc

    JD] un` x`u af joejh`x af s`kkx snjhn ngv` dg~jdpdhaoxu}gjoux ao }gu`x ep` ua xgoe r}aephujao

    y uujoc rg}gd`u`}x e`xh}jmjoc r}aephujao hnal`xx uujoc rg}gd`u`}x e`xh}jmjoc xpmx`g hnal`xK kas`} haoxu}gjoux ao

    P prr`} haoxu}gjoux ao rmnr mauuadnak` r}`xxp}`

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    28/170

    7> Jou}aephujao

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    29/170

    Hngru`} =

    R}`kjdjog}j`x

    Gmxu}ghu

    Unjx hngru`} jou}aeph`x g r}`kjdjog}z r}amk`d e`xh}jrujao goe dgun`dgujhgkfa}dpkgujao snjhn sjkk grrkz jo gkk xpmx wp`ou hngru`}x/

    =/7 R}amk`d e`xh}jrujao

    R}aephujao jo un` haou`~u af aflxna}` ajk goe cgx `kex+ hgo m` haoxje`}`eun` uaugk apurpu af r}aephujao s`kkx+ g dgxx as sjun hadrao`oux johkpejocnze}ahg}maox+ jo geejujao ua sgu`}+ HA=+ N=X+ xgoe goe raxxjmkz aun`}hadrao`oux/ Nze}ahg}mao r}aephujao jx fa} xjdrkjhjuz afu`o kpdr`e joua ajkgoe cgx/ R}aephujao u}gv`kx gx dpkujrngx` as f}ad s`kkx un}apcn as kjo`xua g r}ah`xxjoc fghjkjuz fa} x`rg}gujao/ S`kkx hgo m` ejvje`e joua rkgufa}ds`kkx+ sn`}` r}aephujao f}ad `ghn s`kk u}gv`kx jo x`rg}gu` as kjo`x ua gr}ah`xxjoc fghjkjuz+ goe xpmx g s`kkx+ sn`}` r}aephujao f}ad x`v`}gk s`kkxg}` }apu`e ua g xpmx`g dgojfake m`fa}` r}aephujao jx }apu`e un}apcn ao`

    a} da}` xng}`e as kjo`x ua g r}ah`xxjoc fghjkjuz/ Sgu`} goe cgx joi`hujaog}` px`e fa} arujdjyjoc nze}ahg}mao }`hav`}z af }`x`}vaj}x/ Cgx kjfu hgojoh}`gx` r}aephujao ua g h`}ugjo `~u`ou mz joh}`gxjoc un` r}`xxp}` ejfl`}`oh`m`us``o }`x`}vaj} goe s`kk jok`u/ Un` xhn`dgujh dae k af aflxna}` ajk goecgx r}aephujao jx xnaso jo Fjcp}` =/7/

    R}aephujao jx haoxu}gjo`e mz x`v`}gk fghua}x+ johkpejoc un` hgrghjuz afun` fghjkjuj`x ua x`rg}gu` hadrao`oux af r}aephujao goe un` hgrghjuz af fg$hjkjuj`x ua hadr}`xx cgx gu un` `ke k`v`k/ Un` r}aephujao af c}aprx af s`kkxdgz u}gv`k un}apcn xng}`e as kjo`x a} jok`u x`rg}gua}x snjhn ngv` g kjd$

    ju`e kjwpje ngoekjoc hgrghjuz/ Un` r}aephujao af joejvjepgk s`kkx dgz m`

    7:

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    30/170

    =2 R}`kjdjog}j`x

    ]`x`}vaj}.x*

    /

    ///

    /

    /

    /

    /

    ]apujoc

    /

    /

    /

    /

    Sgu`}joi`hujao

    /

    /

    /

    /

    Cgxjoi`hujao

    /

    /

    /

    /

    ////

    X`rg}gujao

    /

    /

    /

    /

    X`rg}gujao

    c

    /

    ///

    Cgxkjfu

    @~ra}uAjk

    Cgx

    Sgu`}

    Rkgufa}ds`kkx

    ]`joi`hujao!Ua x`g

    Kjfu cgx!cgx joi`hujao

    Cgxkjfu

    Xpmx`gs`kkx

    Cgxkjfu

    Fjcp}` =/79 G xhn`dgujh dae`k af aflxna}` ajk goe cgx r}aephujao/

    haoxu}gjo`e ep` ua xkpccjoc+ aun`} as gxxp}goh` jxxp`x a} ep` ua }`x`}vaj}dgogc`d`ou haoxu}gjoux/

    Dpkujrngx` asx g}` ng}e ua d`gxp}` goe g}` pxpgkkz oau gvgjkgmk` fa}joejvjepgk as kjo`x jo }`gk$ujd`+ nas`v`} d`gxp}`d`oux af uaugk xjock`$rngx`r}aeph`e ajk }gu`x g}` pxpgkkz gvgjkgmk`+ goe `xujdgu`x af uaugk cgx goe sgu`}}gu`x hgo afu`o m` fapoe mz gcc}`cgujoc ejfl`}`ou d`gxp}`e cgx goe sgu`}

    }gu`x gfu`} x`rg}gujao/ Ua e`u`}djo` un` }gu`x af ajk+ cgx goe sgu`} r}aeph`ef}ad joejvjepgk s`kkx+ un` r}aephujao af g xjock` s`kk jx pxpgkkz }apu`e ua ge`ejhgu`e u`xu x`rg}gua} gu jou`}vgkx sn`}` un` }gu` af `ghn x`rg}gu`e xjock`$rngx` hadrao`ou jx d`gxp}`e+ g s`kk u`xu/ S`kk u`xux gkkas mjgx`x jo dae`kxaf joejvjepgk s`kkx ua m` pregu`e+ goe s`kk u`xux snjhn d`gxp}` }gu`x fa}ejfl`}`ou x`uujocx+ dpkuj$}gu` s`kk u`xux+ gkxa gkkas }`xraox`x ua hngoc`x jofa} `~gdrk` hnal` x`uujocx r}`ejhu`e mz dae`kx ua m` vgkjegu`e/

    Un` gjd af r}aephujao arujdjygujao jx ua e`u`}djo` x`urajoux fa} g x`uaf hnax`o e`hjxjao vg}jgmk`x snjhn g}` arujdgk mz xad` h}ju`}jao/ Un`x` x`u$

    rajoux g}` jdrk`d`ou`e mz gku`}joc un` x`uujocx af r}aephujao `wpjrd`ou/E`hjxjao vg}jgmk`x dgz m` goz d`gxp}`e a} hgkhpkgu`e vg}jgmk`x gxxahjgu`esjun r}aephujao snjhn g}` jop`oh`e mz hngoc`x jo x`uujocx+ mpu un` opd$m`} af e`hjxjao vg}jgmk x jx kjdju`e mz un` opdm`} af x`uujocx/ S` dgz fa}joxugoh` e`u`}djo` un` x`uujoc af g cgx kjfu hnal` mz e`hjejoc g ug}c`u kjfu cgx}gu`+ g ug}c`u goopkpx r}`xxp}` a} g ug}c`u cgx kjfu hnal` ar`ojoc/ Ao xna}uujd`xhgk`x un` as f}ad joejvjepgk s`kkx hgo m` dgojrpkgu`e mz r}aephujaohnal` x`uujocx+ mz cgx kjfu hnal` x`uujocx goe raxxjmkz mz }apujoc x`uujocx/

    R}aephujao arujdjygujao }`wpj}`x r}aephujao dae`kx+ `wpgujaox snjhn `~$

    r}`xx un` }`kgujaoxnjr m`us``o hngoc` jo e`hjxjao vg}jgmk`x goe }`xpkujoc

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    31/170

    =/=/ Dgun`dgujhgk r}`kjdjog}j`x =7

    hngoc` jo r}aephujao/ R}aephujao dae`kx g}` pxpgkkz oaokjo`g} ua e`xh}jm`xjcojhgou oaokjo`g} rn`oad`og jo r}aephujao/ Rg}gd`u`} `xujdgujao jx ge$

    ipxud`ou af uu`e rg}gd`u`}x xa ungu r}`ejhujaox af un` r}aephujao dae`k

    dguhn g x`u af }`h`ou njxua}jhgk r}aephujao egug gx hkax kz gx raxxjmk / Rg$}gd`u`}x af r}aephujao dae`kx xnapke m` uu`e ua r}aephujao egug un}apcnrg}gd`u`} `xujdgujao ua hadr`oxgu` fa} po$dae`k`e `fl`hux a} ejxup}mgoh`xgoe ua x`u }`gxaogmk` vgkp`x fa} rnzxjhgk rg}gd`u`}x snjhn hgooau m` d`g$xp}`e ej}`hukz a} e`u`}djo`e jo un` kgma}gua}z/ @}axjao af r}aephujao hnal`xjx go `~gdrk` af g uzrjhgk xphn po$dae k`e ejxup}mgoh`/ Jf un`}` jx kjuuk`vg}jgujao af e`hjxjao vg}jgmk`x jo un` r}aephujao egug gcgjoxu snjhn un` r}a$ephujao dae`k jx uu`e s` u`}d un` egug gx ngvjoc kas jofa}dgujao haou`ou/Fjuu`e rg}gd`u`}x dgz m` poh`}ugjo jf uu`e ua egug sjun kas jofa}dgujao

    haou`ou/Rkgoo`e `~hjugujao jx xad` rkgoo`e vg}jgujao jo ao` a} da}` e`hjxjao

    vg}jgmk`x e`xjco`e ua }`v`gk jofa}dgujao ao r}aephujao un}apcn d`gxp}`$d`oux+ fa} joxugoh` g dpkuj$}gu` s`kk u`xu/ Oa}dgkkz r}aephujao jx gu x`u$rajoux sn`}` xad` hgrghjuj`x g}` gu un`j} r`}h`jv`e haoxu}gjoux+ un`}`fa}` gdpkuj$}gu` s`kk u`xu hgooau m` r`}fa}d`e sjunapu xjdpkugo`apxkz }`ephjocr}aephujao gu xad` aun`} s`kk+ snjhn dgz hgpx` kaxu r}aephujao goe g haxu/Un`}` jx gkxa g }jxl ungu hngoc`x jo x`urajoux ep}joc u`xujoc dgz hgpx` xad`rg}u af un` fghjkjuj`x ua `~h``e un` kjdjux af xgf` ar`}gujao+ snjhn dgz fa}h`

    go `~r`oxjv` xnpueaso goe }`$xug}u af r}aephujao/

    =/= Dgun`dgujhgk r}`kjdjog}j`x

    Un}apcnapu unjx un`xjx vg}jgmk`x sjun g ngu .* sjkk e`oau` `xujdgu`x goe

    vg}jgmk`x sjun g mg} .* sjkk e`oau` d`gxp}`d`oux+ goe vg}jgmk`x sjun g xug}. * g}` u}p` vgkp`x jo xad` x`ox`/

    Jo unjx un`xjx s` sjkk haoxje`} r}aephujao g xzxu`d+ go ami`hu jo snjhnvg}jgmk`x af ejfl`}`ou ljoex jou`}ghu goe r}aeph` amx`}vgmk` xjcogkx/ @~u`}ogkxjcogkx g}` afu`o c}apr`e joua unax` snjhn g}` dgojrpkgu`e goe goe unax`snjhn g}` oau+ goe oao$dgojrpkgu`e xjcogkx g}` }`f`}}`e ua gx ejxup}mgoh`x.Kipoc+ 7:::*/

    K`u ~ m` g v`hua} af jou`}ogk vg}jgmk`x goe k`u p m` g v`hua} af e`hjxjao

    vg}jgmk`x/ Jo unjx un`xjx s` sjkk haoxje`} g r}aephujao arujdjygujao r}amk`d

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    32/170

    == R}`kjdjog}j`x

    ao un` fa}d

    p.* ~.* 4 g}c dg~p+~ D.~+p+e* .=/7*x/u 2 4 f.~+p+e+* .=/=*

    2 h.~+p+e*+ .=/8*

    sn`}` jx g v`hua} af rg}gd`u`}x ua m` e`u`}djo`e/ p.* goe ~.* g}`un` arujdgk xakpujao af .=/7*$.=/8* fa} g cjv`o / e jx g v`hua} af dae`k`egoe d`gxp}`e ejxup}mgoh`x joe`r`oe`ou af p/ D.~+p+e* jx g r}au d`gxp}`snjhn s` x``l ua dg~jdjy` xpmi`hu ua g r}ah`xx dae`k .=/=* goe r}ah`xxhaoxu}gjoux .=/8* fa} g cjv`o rg}gd`u`} vgkp` / Fa} aflxna}` ajk goe cgxr}aephujao+ ~ dgz m` un` r}aephujao }gu`x af `ghn pje f}ad `ghn s`kk+ p

    dgz m` }`kgujv` hnal` ar`ojocx a} cgx$kjfu }gu`x+h dgz e`xh}jm` haoxu}gjouxjo uaugk sgu`} goe cgx r}ah`xxjoc hgrghjuz goe D dgz `~r}`xx uaugk ajkr}aephujao/ Snjhn hadrao`oux ua dae`k jx g e`xjco wp`xujao ungu e`r`oexao un` hnajh` af h.~+p+e* goe D.~+p+e*+ goe uzrjhgkkz gu k`gxu ajk+ cgx goesgu`} r}aephujao jx dae`k`e/

    S` aokz haoxje`} joxugougo`apx arujdjygujao+ e`u`}djojoc .p.*+ ~.**gu un` hp}}`ou ujd`/ Oa}dgkkz ~ jx oau d`gxp}`e/ K`u z m` g v`hua} afd`gxp}`e vg}jgmk`x+ snjhn dgz johkpe` x`rg}gua} }gu` d`gxp}`d`oux+ xhgka} aun`} uaugk }gu` d`gxp}`d`oux a} dpkujrngx` }gu` d`gxp}`d`oux sn`}`

    gvgjkgmk`/ K`u z.p+e++u* m` go `xujdgu` af d`gxp}`e vg}jgmk`x mgx`e ao un`dae`k .=/=*+ goe z.u* jx go `xujdgu` afz+ z dgz fa} joxugoh` m` un` d`gxp}`euaugk }gu`x af ajk+ cgx goe sgu`}/ K`u un` upojoc egug x`u m` g x`u af njxua}jhgkr}ah`xx egug xrgoojoc O ujd` xu`rx xrgoojoc un` ujd` jou`}vgk u \7+ OT

    YO 4

    z.7*T e.7* p.7* z.=* e.=* p.=* / / /

    z.O* e.O* p.O* .=/5*

    sjun }`xjepgkx

    .u+ * 4 z.u* z.p.u*+ e.u*+ + u* u |7+ / / / + O t / .=/0*

    Rg}gd`u`} `xujdgujao e`u`}djo`x mz djojdjyjoc un` xpd af un` xwpg}`e}`xjepgkx fa} un` upojoc egug x`u9

    4g}cdjo

    Ou47

    s.u*Ez.u+ *== , Vx.*+ x/u/ h.* 2 .=/6*

    sn`}` s.u* jx g px`}$xr`hj`e s`jcnujoc fpohujao+ Vx.* jx go arujaogk xafu$

    haoxu}gjou goe h.* go arujaogk haoxu}gjou ao / Un` hadrao`oux af z dgz

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    33/170

    =/=/ Dgun`dgujhgk r}`kjdjog}j`x =8

    ngv` ejfl`}`ou }goc`x+ z`u rg}gd`u`} `xujdgujao xnapke cjv` xjdjkg} s`jcnuua djojdjyjoc }`xjepgkx af gkk d`gxp}`d`oux+ snjhn daujvgu`x oa}dgkjyjoc}`xjepgkx sjun g ejgcaogk dgu}j~ Ez/ Un` r}ah`xx dae`k .=/=* xnapke aokz

    m` uu`e ua njxua}jhgk r}ah`xx egug ungu g}` }`h`ou+ jo un` x`ox` r}aephujaoep}joc un` ujd` jou`}vgk xrgoo`e mz un` upojoc x`u xnapke m` haoxjxu`ousjun hp}}`ou r}aephujao goe un` r}aephujao dae`k/ Ju dgz m` jdraxxjmk` uae`u`}djo` go ghhp}gu` `xujdgu` pojwp`kz sjun .=/6* sn`o un` jofa}dgujaohaou`ou jo YO jx kas/ Go jdr}av`e dae k xu}phup}` dgz `ogmk` un` px`af g kaoc`} upojoc x`u+ snjhn dgz jo up}o }`eph` rg}gd`u`} poh`}ugjouz/Un`}`fa}` rg}gd`u`} poh`}ugjouz jx kjol`e ua aun`} fa}dx af poh`}ugjouz xphngx xu}phup}gk poh`}ugjouz/

    Jo c`o`}gk un` ujd` jou`}vgk xrgoo`e mz un` upojoc x`u YO jx kjdju`e mz

    po$dae`k`e ejxup}mgoh`x+ gx ju jx gxxpd`e ungu gkk vg}jgujaox amx`}v`e joYO hgo m` e`xh}jm`e mz un` hnax`o dae`k xu}phup}`/ Ua pregu` un` dae`kgx hngocjoc xugu`x a} ejxup}mgoh`x hgpx` r}aephujao ua hngoc`+ un` sjoeasxrgoo`e mz YO hgo m` dav`e gx o`s egug m`had`x gvgjkgmk`+ g davjoc$na}jyao grr}aghn .Ojlakgap+ Hpkkjhl goe Xgrpu`kkj+ =226*/

    Ua e`xh}jm` un` }`kgujaoxnjr m`us``o }gu`x ~ goe d`gxp}`d`oux z+ goeua hgrup}` un` uzrjhgkkz ujd`$vg}zjoc ogup}` af }apujoc+ s` e`o` g }apujocdgu}j~ ] af ao`x goe y`}ax xphn ungu sn`o d`gxp}`d`ou poh`}ugjouj`x hgom` o`ck`hu`e+

    z.u*4 ].u*~.u*/ .=/3*

    ]apujoc ].u* dgz hngoc` sjun ujd`+ gx s`kkx g}` }apu`e ua ejfl`}`ou r}a$h`xxjoc u}gjox a} ua u`xu x`rg}gua}x/ z dgz haoxjxu af u`xu x`rg}gua} }gu`d`gxp}`d`oux+ uaugk }gu` d`gxp}`d`oux goe jo xad` hgx`x dpkujrngx` }gu`d`gxp}`d`oux gu xad` a} gkk s`kkx/

    F}ad .=/7*.=/8* ju dgz m` x``o ungu sjkk jop`oh` p.*+ snjk` .=/5*.=/6* jkkpxu}gu` ungu jx jop`oh`e mz un` jofa}dgujao haou`ou jo YO+ snjhngcgjo hgo m` jop`oh`e mz rkgoo`e `~hjugujao/ Un`x` }`kgujaoxnjrx g}` jkkpx$

    u}gu`e jo Fjcp}` =/=/Jo un` fakkasjoc hngru`}x s` sjkk haoxje`} r}aephujao dae`kx snjhn g}`

    uu`e ua egug f}ad oa}dgk ar`}gujaox pxjoc .=/6* goe `~rkaju`e jo .=/7*.=/8*goe haoxje`} un` poh`}ugjouz ungu g}jx`x/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    34/170

    =5 R}`kjdjog}j`x

    R}aephujaoarujdjygujao R}aephujao

    Rkgoo`e`~hjugujao

    R}aephujaohaoxu}gjoux

    Xugu` goe dae`k

    rg}gd`u`}x D`gxp}`d`oux

    E`hjxjaovg}jgmk`x

    Ejxup}mgoh`x

    Rg}gd`u`} goexugu` `xujdgujao

    Fjcp}` =/=9 ]`kgujaoxnjr m`us``o xpmr}amk`dx jo r}aephujao arujdjygujao/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    35/170

    Hngru`} 8

    Hngkk`oc`x jo rg}gd`u`}

    `xujdgujao af dae`kx fa}aflxna}` ajk goe cgx r}aephujao

    arujdjygujao

    G v`}xjao af unjx hngru`} sgx r}`x`ou`e gu un` Jou`}ogujaogk R`u}ak`pd

    U`hnoakacz Haof`}`oh`+ Epmgj+ E`h`dm`} =223Gpuna}x9 Xu`jog} D/ @kcxg`u`}+ Akgv Xkprrngpc+ goe Ua} G}o` Iangox`o

    Gmxu}ghu

    Jo unjx hngru`} dae`k$joe`r`oe`ou gxx`}ujaox gmapu poh`}ugjouz jo r}aeph$ujao arujdjygujao g}` dge` un}apcn g hgx` xupez af ghupgk r}aephujao egug

    f}ad g Oa}un X`g ajk goe cgx `ke/ Gx un` jofa}dgujao haou`ou jo r}aeph$

    ujao egug e`xh}jmjoc oa}dgk egz$ua$egz ar`}gujaox sgx amx`}v`e ua m` kas+un` `~rkjhju u}`gud`ou af poh`}ugjouz dgz m` gx }`k`vgou fa} r}aephujao ar$ujdjygujao gx ju jx fa} }`x`}vaj} dgogc`d`ou/ Mgx`e ao un` amx`}vgujaoxdge`+ un}`` hngkk`oc`x fa} }`x`g}hn ungu ngv` }`h`jv`e kjuuk` guu`oujao jo un`kju`}gup}` poujk oas g}` njcnkjcnu`e/ Fj}xukz+ un` kaxu rau`oujgk johp}}`e ep` uapoh`}ugjouz xnapke m` `xujdgu`e ua gxx`xx jux xjcojhgoh`/ X`haoekz+ haxux goevgkp`x af ghujaox ua }`eph` poh`}ugjouz xnapke m` `xujdgu`e ua gkkas r}arax`eghujaox ua m` `vgkpgu`e un}apcn xu}phup} e mpxjo`xx hgx`x/ Unj}ekz+ xu}gu cj`x

    fa} dgljoc e`hjxjaox jo egz$ua$egz ar`}gujaox poe`} poh }ugjouz xnapke m`

    jov`xujcgu`e/

    =0

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    36/170

    =6Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae`kx fa} aflxna}` ajk goe

    cgx r}aephujao arujdjygujao

    8/7 Jou}aephujao

    8/7/7 R}ja} sa}l

    Wpgoujfzjoc poh`}ugjouz jo }`x`}vaj} dae`kx ngx guu}ghu`e dphn jou`}`xujo }`h`ou z`g}x/ Gpuna}x ngv` e`xh}jm`e uujoc dpkujrk` dae kx ua egug.C}j`xx+ Ejgm goe Xhnpky`$]j`c`}u+ =226*+ e`xh}jmjoc d`gxp}`d`ou poh`}$ugjouj`x .Kjuuk` `u gk/+ =226* goe x`oxjujvjuz gogkzxjx pxjoc r}ja} loask`ec`af rg}gd`u`} poh`}ugjouz .Haxug+ Xhnjay`} goe Rak uua+ =226*/ V`}z f`s}`f`}`oh`x ngv` m``o fapoe snjhn guu`dru ua wpgoujfz poh`}ugjouz jo r}a$ephujao dae`kx/ Go `xujdgu` af poh`}ugjouz e`}jv e f}ad s`kk u`xux fa}s`kkx sjun }gu`$joe`r`oe`ou cgx$ajk }guja goe sgu`}$ajk }gujax jx e`}jv`e jo.Mj l`} `u gk/+ =226*+ goe g xu}gu`cz fa} r}aephujao arujdjygujao af xphns`kkx ungu u}`gux poh`}ugjouz `~rkjhjukz jx xpcc`xu`e jo .Mj`l`}+ Xkprrngpcgoe Iangox`o+ =223m*/ Un` kghl af guu`oujao ua un` xpmi`hu af poh`}ugjouzjo r}aephujao arujdjygujao x``dx rg}gea~jhgk gx r}aephujao dae`kx g}` u$u`e ua dphn un` xgd` r}aephujao egug gx }`x`}vaj} dae`kx/ Gx wpgouj`epoh`}ugjouz e`r`oex ao un` dae`k px`e+ ju jx ng}e ua ejxh`}o f}ad xupej`x afpoh`}ugjouz jo }`x`}vaj} dae`kx sn`un`} amx`}v`e poh`}ugjouj`x g}` g }`xpkuaf un` kas jofa}dgujao haou`ou jo r}aephujao egug a} af un` dae`kx/ Oa}`f`}`oh`x ngv` m``o fapoe snjhn gee}`xx un` hng}ghu`}jxujhx af uzrjhgk r}a$ephujao egug jux`kf goe sngu jdrkjhgujaox un`x` hng}ghu`}jxujhx sjkk ngv` jo

    u`}dx af dae`kjoc/Un` haoh`ru af `xujdgujoc un` vgkp` af jofa}dgujao jo poh`}ugjo xzxu`dx

    ngx }aaux jo xuahngxujh r}ac}gddjoc+ snjhn px`x un` haoh`ru af vgkp` afr`}f`hu jofa}dgujao+ goe un` je`g af gxxjcojoc g vgkp` ua jofa}dgujao ngv`fapoe grrkjhgujaox jo }`x`}vaj} dae kjoc .M}goha+ Rjoua+ Ujoaha+ Vj j}g+Xgze+ Xgouax goe R}gjx+ =220*/ Oa }`f`}`oh`x ngv` m``o fapoe snjhn gee}`xxun` vgkp` af jofa}dgujao jo un` haou`~u af r}aephujao arujdjygujao/

    8/7/= Av`}vj`s

    Unjx hngru`} }`xux ao un` gxxpdrujao ungu goz r}aephujao dae`k sjkk }`$wpj}` uujoc jux rg}gd`u`}x ua r}aephujao egug ua ghhapou fa} po$dae`k`eejxup}mgoh`x+ goe un`}`fa}` un` hng}ghu`}jxujhx af r}aephujao egug sjkk ngv`jdrkjhgujaox fa} r}aephujao arujdjygujao/ Dae`k$joe`r`oe`ou gxx`}ujaox aoun` xjcojhgoh` af poh`}ugjouz jo r}aephujao arujdjygujao g}` xapcnu un}apcng hgx` xupez af r}aephujao egug/ Jojujgkkz xad` r}`kjdjog}z haoxje`}gujaoxao un` }`kgujaoxnjr m`us``o r}aephujao egug goe r}aephujao arujdjygujaog}` ejxhpxx`e/ G hgx` xupez af g Oa}un X`g ajk goe cgx `ke jx px`e ua jkkpx$

    u}gu` un` uzrjhgk xugu` af }`gk$kjf` r}aephujao egug/ Fjogkkz+ l`z hngkk`oc`x

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    37/170

    8/=/ Un` }`kgujaoxnjr m`us``o r}aephujao arujdjygujao+ dae`kxgoe egug =3

    daujvgu`e mz un` amx`}vgujaox dge` g}` apukjo`e/

    8/= Un` }`kgujaoxnjr m`us``o r}aephujao arujdjyg$ujao+ dae`kx goe egug

    Gx un` opdm`} af kacc`e d`gxp}`d`oux f}ad ajk goe cgx r}aephujao aoao` `ke dgz }po joua un` unapxgoex+ ju jx o`hh`xxg}z ua fahpx ao x`k`hu`ed`gxp}`d`oux jo un` hgx` xupez/ Unjx x`hujao e`xh}jm`x un` }`wpj}`d`ouxfa} r}aephujao egug jo un` haou`~u af r}aephujao arujdjygujao+ snjhn sjkkdaujvgu` un` fahpx af un` hgx`$xupez jo un` fakkasjoc x`hujao/

    Unjx hngru`} jx g xupez af r}aephujao egug goe sngu jdrkjhgujaox un`

    xugu` af r}aephujao egug sjkk ngv fa} un` e`xjco af un` dae`k/ Go guu`dru jxdge` ua l``r un` ejxhpxxjao gx joe`r`oe`ou af un` hnajh` af r}aephujao dae`kgx raxxjmk`/ Jo r}ghujh`+ r}aephujao dae`kx g}` `jun`} hadd`}hjgk xjdpkgua}xaf s`kk goe rjr`kjo`+ a} g kaalpr$ugmk` a} aun`} r}a~z$dae`k e`}jv`e f}adxphn xjdpkgua}x .Ygock `u gk/+ =226*/

    Unjx hngru`} gjdx ua }`ghn haohkpxjaox gmapu un` jdrkjhgujaox r}aephujaoegug ngv` ao r}aephujao dae`kjoc snjhn g}` gx joe`r`oe`ou af un` hnajh`af dae`k xu}phup}` gx raxxjmk / X`k hujao af vg}jgmk x+ maun af d`gxp}`evg}jgmk`x z goe e`hjxjao vg}jgmk`x p+ jx g e`xjco hnajh` .Ngkva}x`o+ Xlac`xuge+

    Da}pe goe Gkxuge+ =228*/ Un` `drngxjx af unjx hngru`} jx oau ua ejxhpxxun` x`k`hujao af vg}jgmk`x+ mpu fa} ap} ejxhpxxjao g hnajh` af vg}jgmk`x z goep sjkk xujkk ngv` ua m` dge`/

    Gx ap} `drngxjx jx ao un` arujdjygujao af s`kkx goe as kjo`x+ }gun`} ungoun` }`x`}vaj} a} uarxje` fghjkjuj`x+ un` dgjo x`uujocx un}apcn snjhn r}aephujaohgo m` jop`oh`e g}` }`kgu`e ua }apujoc+ cgx kjfu goe r}aephujao hnal x/]apujoc jx ghhapou`e fa} un}apcn un` dgu}j~ ] jo .=/3*/ Fa} xjdrkjhjuz}`kgujv` r}aephujao hnal` ar`ojoc y goe cgx kjfu }gu`x wck gx hnax`o gx ap}e`hjxjao vg}jgmk` p 4 y wck/ Un` aokz dae`k`e ejxup}mgoh` haoxje`}`e jx}apujoc e 4 ]/ Jo unjx hngru`} un` jofa}dgujao haou`ou jo r}aephujao egugYO }`f`}x ua x`oxjujvjuj`x

    ez

    ep4 ]

    e~

    ep/ .8/7*

    Unjx je`g jx jkkpxu}gu`e jo @~gdrk` 8/7/

    @~gdrk` 8/7 Haoxje`} ungu un` ami`hujv` af r}aephujao arujdjygujao .=/7*.=/8* jx ua oe un` cgx kjfu }gu` p 4 w7ck af g xjock` cgx$kjfu`e s`kk snjhn dg~j$

    djy`x ajk r}aephujao+ D.~+p+e* 4 w7

    a + goe gxxpd` ungu un` }gu` af r}aeph`eajk jx d`gxp}`e z 4 w7a/ Gxxpd` ungu un` }`kgujaoxnjr m`us` o cgx kjfu }gu` goe

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    38/170

    =>Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae`kx fa} aflxna}` ajk goe

    cgx r}aephujao arujdjygujao

    wck7

    wa7

    Ewa7

    Ewck7

    wak

    wckk

    Fjcp}` 8/79 @~gdrk 8/79 Go jkkpxu}gujao af un` nzraun`ujhgk u}p` r`}fa}$

    dgoh` hp}v` .xakje*+ gkaoc sjun x`oxjujvjuz ew7a

    ew7ck

    .eauu`e*/

    r}aeph`e ajk jx gx xnaso jo Fjcp}` 8/7+ goe ungu r}aephujao jx hp}}`oukz gu.wkck+ w

    ka*/ Ua xakv` un` r}aephujao arujdjygujao r}amk`d+ un` r}aephujao dae`k

    xnapke `~r}`xx nas hngocjoc cgx kjfu }gu`x sjkk jop`oh` hngoc` jo r}aeph`eajk/ Un` dae`k dgz m` fapoe un}apcn rnzxjhgk dae`kjoc+ un}apcn `~r }jd`o$ugujao a} g hadmjogujao un`} af/ Je gkkz un` r}aephujao dae`k xnapke r} ejhuun` }`xraox` jo ajk r}aephujao w7a ua gkk haoh jvgmk` hngoc`x w

    7wk jo cgx kjfu

    ha}}`hukz+ mpu gx g djojdpd+ YO

    xnapke gkkas gu k`gxu+ g fa}d af .8/7*+ uam` e`u`}djo`e/

    Jofa}dgujao haou`ou jo r}aephujao egug jx }`kgu`e ua hngoc`x jo p+ snjhnsjkk m` }`f`}}`e ua gx `~hjugujao/ Jf ao` a} da}` `k`d`oux jo p ea oau hngoc`a} hngoc` aokz v`}z kjuuk` jo YO + un`o un` egug x`u jx s`gl jo xad` sgz+x`oxjujvjuj`x hgooau m` e`u`}djo`e f}ad r}aephujao egug+ .=/6* sjkk m` jkk$haoejujao`e goe e`u`}djojoc h`}ugjo `k`d`oux pojwp`kz dgz m`had` ejhpku/

    Ju jx raxxjmk` jo r}johjrk` ua jou}aeph` rkgoo`e `~hjugujao ua joh}`gx` un`

    jofa}dgujao haou`ou jo YO

    + fa} joxugoh` mz r`}fa}djoc dpkuj$}gu` s`kk u`xuxgu jou`}vgkx fa} gkk s kkx/ Gx rkgoo`e `~hjugujao dgz ngv` maun g haxu goe

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    39/170

    8/8/ R}aephujao egug9 G hgx`$xupez =:

    g }jxl+ ju sapke m` r}`f`}gmk` ua u r}aephujao dae`kx ua r}aephujao egugxu`ddjoc f}ad oa}dgk egz$ua$egz ar`}gujaox jf raxxjmk / Un` ami`hujv` af

    e`hadraxjoc r}aephujao arujdjygujao joua }`x`}vaj} dgogc`d`ou goe r}a$ephujao arujdjygujao jx ungu `ghn xpmr}amk`d dgz haoxje`} xjdrk`} dae`kxhaoxje`}joc ejfl`}`ou ujd` xhgk`x .Xgrpu`kkj `u gk/+ =228*/ ]`x`}vaj} dgo$gc`d`ou dgz haoxje`} g hag}x` r}aephujao dae`k goe g e`ugjk`e }`x`}vaj}dae`k+ snjk` r}aephujao arujdjygujao dgz haoxje`} g hag}x` }`x`}vaj} dae`kgoe g e`ugjk`e r}aephujao dae`k/ Un` k`ocun af un` upojoc x`u YO jx kjdju`emz un` jou`}vgk fa} snjhn un` hnax`o dae`k hgo e`xh}jm` amx`}v`e vg}jgujaoxjo YO+ goe fa} r}aephujao dae`kx sjun g hag}x` e`xh}jrujao af }`x`}vaj} ez$ogdjhx unjx dgz d`go ungu YO dpxu xrgo g }`kgujv`kz xna}u ujd` jou`}vgk/

    Un` jofa}dgujao haou`ou jo Y

    O

    sjkk e`h}`gx` sjun e`h}`gxjoc k`ocun jo r}gh$ujh`+ snjhn jou}aeph`x un` raxxjmjkjuz ungu .=/6* dgz m` xpmi`hu ua xjcojhgoupoh`}ugjouj`x/

    Ju jx haoh`jvgmk` ungu un` gmjkjuz af un` dae`k ua e`xh}jm` un` egug x`u .=/5*hgo m` jdr}av`e mz `~rkajujoc gp~jkjg}z d`gxp}`d`oux+ d`gxp}`e vg}jgmk`xsnjhn dgz vg}z sjun r}aephujao goe g}` e`r`oe`ou ao p/ D`gxp}`d`ouxsnjhn g}` e`r`oe`ou ao un` hnajh` af p dgz fa} joxugoh` m` un` d`gxp}`er}`xxp}` a} u`dr`}gup}` prxu}`gd af g r}aephujao hnal` sn`o r}aephujaohnal` ar`ojoc jx go `k`d`ou jo p/

    Un` ejxgevgougc` af johkpejoc gp~jkjg}z d`gxp}`d`oux jo un` r}aeph$ujao dae`k jx ungu g x`haoe dae`k ungu `~r}`xx`x gp~jkjg}z d`gxp}`d`oux jou`}dx af ~+ p goe e/ jx o``e`e ua hkax` un` r}aephujao dae`k/ G l`z ejfl`}$`oh` m`us``o dae`kx fa} r}aephujao daojua}joc goe dae`kx fa} r}aephujaoarujdjygujao jx ungu dae`kx fa} r}aephujao daojua}joc dgz px` gp~jkjg}zd`gxp}`d`oux sjunapu un` o``e fa} unjx x`haoe dae`k/ Un` ejxgevgougc`af jou}aephjoc g x`haoe dae`k fa} hkaxp}` jx ungu ju joh}`gx`x un` hngoh` afjou}aephjoc xu}phup}gk dae`k `}}a}x+ goe d`gxp}`e r}`xxp}`x goe u`dr`}g$up}`x dgz un`dx`kv`x m` xpmi`hu ua xjcojhgou d`gxp}`d`ou poh`}ugjouj`x/

    Fa} un`x` }`gxaox+ d`gxp}`e r}`xxp}`x a} u`dr`}gup}`x sjkk oau m` haoxje`}`ejo un` hgx` xupez+ gkunapcn ju hgooau m` }pk`e apu ungu dae`k r`}fa}dgoh`hapke jdr}av` mz johkpejoc xphn d`gxp}`d`oux/

    8/8 R}aephujao egug9 G hgx`$xupez

    Unjx x`hujao haougjox g xupez af g x`u af }`gk$sa}ke r}aephujao egug/ Un`

    `drngxjx af un` xupez jx ua njcnkjcnu hng}ghu`}jxujhx af r}aephujao egug ungudgz ngv` jdrkjhgujaox fa} r}aephujao arujdjygujao

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    40/170

    82Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae`kx fa} aflxna}` ajk goe

    cgx r}aephujao arujdjygujao

    8/8/7 Fj`ke e`xh}jrujao

    Ao` `ke jx haoxje`}`e jo unjx hgx` xupez+ g dgup}` Oa}un X`g `ke jo e`hkjo`sjun =2 rkgufa}d r}aephujao s`kkx r}aephjoc ajk+ cgx goe sgu`}+ gkk sjun un`gje af cgx$kjfu/ G egug x`u xrgoojoc =52 egzx jx haoxje`}`e/ R}aephujaoegug f}ad goaun`} `ke sgx gkxa xupej`e+ mpu gx xjdjkg} amx`}vgujaox s`}`dge` g ejxhpxxjao af unjx `ke jx adjuu`e fa} m}`vjuz/ Oa dpkujrngx` asd`u`}x g}` gvgjkgmk` snjk` ao` u`xu x`rg}gua} sjun }gu` d`gxp}`d`oux af ajk+cgx goe sgu`} jx gvgjkgmk / Un` uaugk }gu` af r}aeph`e ajk jx d`gxp}`e mzxhgk d`gxp}`d`oux+ snjk` uaugk }gu`x af cgx goe sgu`} hgo m` `xujdgu`e mzgcc}`cgujoc x`v`}gk d`gxp}`e }gu`x jo un` r}ah`xxjoc fghjkjuj`x/ Oa gkkahgu`e}gu`x g}` gogkzy`e jo unjx hngru`}< haohkpxjaox g}` e}gso `ouj}`kz mgx`e ao

    d`gxp}`e vg}jgmk`x/ Un` aso`} af un` r}aephujao egug }`wp`xu`e ju m` l`rugoaozdapx< un`}`fa}` gkk cp}`x ejxrkgz oa}dgkjy`e vg}jgmk`x/

    8/8/= ]guja m`us``o s`kk u`xux goe uaugk d`gxp}`e }gu`x

    Uaugk r}aephujao jx d`gxp}`e haoujopapxkz mz }gu` d`gxp}`d`oux jo un`r}ah`xxjoc fghjkjuj`x fa} un` `ke haoxje`}`e/ Jo geejujao+ go `xujdgu` af uaugkr}aephujao hgo m` fapoe mz xpddjoc un` }gu`x af `ghn d`gxp}`e hadrao`ougu un` daxu }`h`ou s`kk u`xu fa} `ghn s kk/ Sn`o un` `ke jx r}aeph`e hkax`

    ua un` x`uujocx af un` daxu }`h`ou s`kk u`xux goe ejxup}mgoh`x xjoh` un` kgxus`kk u`xux g}` xdgkk+ un`x` usa x`ux af }gu`x xnapke ngv` hadrg}gmk` vgkp`x/Un` }guja m`us``o un`x` usa x`ux af }gu`x .Fa.u*+ Fc.u*+ Fs.u** g}` e`o`e gx

    Fa.u*4

    wuaua .u*osj47 y

    j.u*wu`xu+ja .u*.8/=*

    Fc.u*4

    wuauc .u*

    osj47 y

    j.u*wu`xu+jc .u*.8/8*

    Fs.u* 4 w

    uau

    s .u*osj47 y

    j.u*wu`xu+js .u*.8/5*

    sn`}` wu`xu+ja .u*+ wu`xu+jc .u* goe w

    u`xu+js .u* g}` un` }gu`x af ajk+ cgx goe sgu`}+

    }`xr`hujv`kz+ ungu ngv` m``o d`gxp}`e fa} s`kk j gu un` daxu }`h`ou s`kk u`xugu ujd` u/ yj jx un` r}aephujao hnal` ar`ojoc fa} s`kk j+ oa}dgkjy`e xa unguyj 4 7 jdrkj`x g fpkkz ar`o hnal`+ goe os jx un` opdm`} af s`kkx/

    Gx kaoc gx cgx$kjfu }gu`x wck goe hnal`$ar`ojocx y g}` hkax` ua un` vgkp`xgu snjhn s`kkx s`}` u`xu`e+ vgkp`x af .Fa.u*+ Fc.u*+ Fs.u** hkax` ua ao` joej$

    hgu` ungu d`gxp}`d`oux af uaugk r}aephujao dguhn un` xpd af un` kgxu s`kku`xux+ j/`/ ungu un`}` jx kjuuk` d`gxp}`d`ou poh`}ugjouz+ goe ungu s`kkx g}`

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    41/170

    8/8/ R}aephujao egug9 G hgx`$xupez 87

    u`xu`e f}`wp`oukz }`kgujv` ua un` }gu` gu snjhn r}aephujao hngoc`x ep` ua ejx$up}mgoh`x/ Vgkp`x .Fa.u*+ Fc.u*+ Fs.u** ejfl`}`ou f}ad 7 dgz m` go joejhgujao

    af un` arraxju`/

    8/8/8 Egug

    Un` gv`}gc` opdm`} af xjock`$}gu` goe dpkuj$}gu` s`kk u`xu r`} z`g} sgx 5/>3goe 2/=: }`xr`hujv`kz/ Fjcp}` 8/= xnasx nas r}aeph`e }gu`x af ajk goe kjwpjevg}z sjun hngocjoc cgx kjfu }gu`x d`gxp}`e ep}joc xjock`$}gu` s`kk u`xux fa}ao` hnax`o s`kk/ Fjcp}` 8/8 xnasx cgx$ajk }gujax goe sgu } hpu d`gxp}`egu un` u`xu x`rg}gua} gx g fpohujao af ujd`/ Fjcp}` 8/5 xnasx go `~gdrk

    af go amx`}v`e }`xraox` jo d`gxp}`e uaugk }gu`x gx un` cgx kjfu }gu` af gs`kk jx hngoc`e/ Fjcp}` 8/0 xnasx g hadrg}jxao af xpdd`e u`xu x`rg}gua}}gu`x goe d`gxp}`e uaugk }gu`x goe un` `xujdgu`e }gujax Fa+ Fc + Fs/ Fjcp}`8/6 jkkpxu}gu` un` jofa}dgujao haou`ou af cgx kjfu }gu`x fa} g ujd` jou`}vgk+hadrg}`e sjun un` opdm`} af s`kk u`xux jo un` xgd` jou`}vgk/

    8/8/5 Amx`}vgujaox

    Afu`oujd`x+ aokz xjock`$}gu` s`kk u`xux g}` r`}fa}d`e9 Xjock`$}gu` s`kk u`xux

    ea oau ej}`hukz r}avje` jofa}dgujao ao x`oxjujvjuj`x+ z`u xphn u`xux fg} apu$opdm`} dpkuj$}gu` s`kk u`xux+ gx 5/>3 xjock`$}gu` s`kk u`xux s`}` r`}fa}d`eg z`g} }`kgujv` ua aokz 2/=: dpkuj$}gu` s`kk u`xux/ Unjx amx`}vgujao hgo m`guu}jmpu`e ua un` haxu af r`}fa}djoc g dpkuj$}gu` s`kk u`xu/ Un` kas f}`$wp`ohz af dpkuj$}gu` s`kk u`xux sjkk dgl` ju ejhpku ua v`}jfz x`oxjujvjuj`x jor}aephujao dae`kx goe rg}gd`u`}x e`xh}jmjoc x`oxjujvjuj`x dgz m` poh`}ugjo/

    Ju dgz m` ejhpku ua e`u`}djo` x`oxjujvjuj`x mz gcc}`cgujoc xjock`$}gu`s`kk u`xux9 Jo r}johjrk` ju jx f`gxjmk` ua hadmjo` rgj}x af xjock`$}gu` s`kk u`xuxua e`u`}djo` x`oxjujvjuj`x/ Fjcp}` 8/= jkkpxu}gu`x ungu xjock $}gu` s kk u`xux

    g}` afu`o r`}fa}d`e av`} g og}}as jou`}vgk af e`hjxjao vg}jgmk` vgkp`x/ Sn`oe`u`}djojoc x`oxjujvjuj`x mz gcc}`cgujoc xjock`$}gu` s`kk u`xux r`}fa}d`e jounjx dgoo`}+ `xujdgu`x dgz m`had` v`}z x`oxjujv` ua ejxup}mgoh`x ungu ah$hp}}`e jo un` ujd` jou`}vgk m`us``o unax` s kk$u`xux/ Amx`}v`e vg}jgujao jocgx$ajk }gujax dgz m` ep` ua poh`}ugjouz jo d`gxp}`e cgx$kjfu }gu`x jo unjxhgx`/

    Xad` s`kk hng}ghu`}jxujhx }`dgjo xjdjkg} fa} egzx+ s``lx goe `v`o daounx+snjk` aun`} hng}ghu`}jxujhx vg}z jo sgzx ungu dgz m` ejhpku ua dae`k goedgz }`wpj}` kjdjujoc un` k`ocun af un` upojoc x`u9 Fjcp}` 8/8 jkkpxu}gu`x vg}j$

    gujaox jo cgx$ajk }gujax goe sgu`}hpux+ gx d`gxp}`e mz s`kk u`xux fa} `ghnjoejvjepgk s`kk/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    42/170

    8=Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae`kx fa} aflxna}` ajk goe

    cgx r}aephujao arujdjygujao

    wa

    wck

    wa , ws

    wck

    u 4 =055

    u 4 800=

    u 4 83=2

    u 4 5606

    u 4 5>3=

    u 4 0522

    2/6: 2/3 2/37 2/3= 2/38 2/35

    2/6: 2/3 2/37 2/3= 2/38 2/35

    2/>

    7

    7/=

    2/5

    2/6

    2/>

    7

    Fjcp}` 8/=9 Hgx`$xupez9 S`kk u`xux fa} g }`r}`x`ougujv` s kk/ Uar c}grn9oa}dgkjy`e d`gxp}`e ajk }gu` wa gcgjoxu oa}dgkjy`e d`gxp}`e cgx$kjfu }gu`wck/ Mauuad c}grn9 xpd af oa}dgkjy`e ajk wa goe sgu`} }gu`x ws gcgjoxuoa}dgkjy`e cgx$kjfu }gu`/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    43/170

    8/8/ R}aephujao egug9 G hgx`$xupez 88

    \%T

    \%T

    \%T

    \%T

    \%T

    \%T

    u\nap}xT

    u\nap}xT

    \%T

    u\nap}xT7 0>887 0>88

    7 0>88

    $52

    =2

    $=2

    =2

    $0

    0

    $72

    72

    $=2

    72

    $72

    72

    $72

    72

    $72

    72

    $0

    72

    $=2

    =2

    $=2

    62

    $0

    0

    $02

    722

    $0

    70

    $=2

    72

    $02

    02

    $52

    52

    2

    7

    $=2

    =2

    $72

    72

    Fjcp}` 8/89 Hgx`$xupez9 Hngoc` jo cgx$ajk }gujax .ejgdaoe* goe sgu`}hpu.xwpg}`* }`kgujv` ua un` gv`}gc` gx d`gxp}`e gu un` u`xu x`rg}gua} fa} gkks`kkx rkauu`e jo gxh`oejoc a}e`} ghha}ejoc ua s`kk joe`~/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    44/170

    85Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae`kx fa} aflxna}` ajk goe

    cgx r}aephujao arujdjygujao

    wuau

    wck

    y

    u\nap}xT

    ==22 ==20 ==72 ==70 ===2 ===0 ==82 ==80

    ==22 ==20 ==72 ==70 ===2 ===0 ==82 ==80

    ==22 ==20 ==72 ==70 ===2 ===0 ==82 ==80

    2

    2/0

    2/0

    7

    2/:

    7

    Fjcp}` 8/59 Hgx`$xupez9 Un` amx`}v`e }`xraox` jo uaugk d`gxp}`e }gu` af ajk.xakje*+ cgx .egxn`e* goe sgu`} .egxneau* ua un` hngoc` jo g xjock` cgx kjfu}gu` wck snjk` gkk r}aephujao vgkv` ar`ojocx y s`}` l`ru haoxugou/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    45/170

    8/8/ R}aephujao egug9 G hgx`$xupez 80

    wuaua

    wuauc

    wuaus

    F

    u\nap}xT7222 =222 8222 5222 0222

    7222 =222 8222 5222 0222

    7222 =222 8222 5222 0222

    7222 =222 8222 5222 0222

    2/>

    7

    7/=

    7/5

    7/6

    7/>

    2

    2/=

    2/5

    2/62/>

    7

    2

    2/0

    7

    7/0

    2

    2/0

    7

    7/0

    Fjcp}` 8/09 Hgx`$xupez9 Uar un}`` c}grnx9 g hadrg}jxao af xpdd`e }gu`xd`gxp}`e gu un` u`xu x`rg}gua} .xakje* ua d`gxp}`e uaugk }gu`x af ajk+ cgx goesgu`} .eauu`e*+ easo$xgdrk`e mz g fghua} af 72 fa} k`cjmjkjuz/ Mauuad c}grn9}gujax Fa+ Fc + Fs/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    46/170

    86Hngkk`oc`x jo rg}gd`u`} `xujdgujao af dae`kx fa} aflxna}` ajk goe

    cgx r}aephujao arujdjygujao

    wuau

    y+ wck

    u \nap}xT7222 =222 8222 5222 0222

    =2

    7:

    7>

    73

    76

    70

    75

    78

    7=

    77

    72

    :

    >

    3

    6

    0

    5

    8=

    7

    2

    2/0

    7

    7/0

    Fjcp}` 8/69 Hgx`$xupez9 Uar c}grn9 d`gxp}`e uaugk ajk r}aephujao wuaua.xakje*+ d`gxp}`e uaugk cgx r}aephujao wuauc .egxn`e* goe d`gxp}`e uaugksgu`} r}aephujao wuaus .eauu`e*+ easoxgdrk`e mz g fghua} 72 fa} k`cjmjkjuz/Mauuad c}grn9 cgx kjfu }gu`x wck .egxn`e* goe }`kgujv` hnal` ar`ojoc y .xakje*goe s`kk u`xux .hj}hk`x* fa} gkk s`kkx rkauu`e jo gxh`oejoc a}e`} ghha}ejoc uas`kk joe`~ .s`kk joe`~ j gkaoc z$g~jx*/

  • 8/3/2019 2008 pHd-thesis: Modeling and optimizing the offshore production of oil and gas under uncertainty (Steinar M. Elgs

    47/170

    8/8/ R}aephujao egug9 G hgx`$xupez 83

    Un` gmx`oh` af vg}jgujao jo }gujax dgz gje r}aephujao dae`kjoc9 Fa} un``ke jo wp`xujao ju dgz m` }`gxaogmk` ua dgl` un` xjdrkjfzjoc gxxpdrujao

    ungu sgu`}hpu jx ujd`$jovg}jgou fa} un` ujd`xhgk`x haoxje`}`e/Sn`o vg}jgujao jo }gujax g}` amx`}v`e+ unjx dgz m` guu}jmpugmk` ua ujd`$

    vg}zjoc s`kk hng}ghu`}jxujhx+ d`gxp}`d`ou poh`}ugjouz a} g hadmjogujao afun` usa9 Fa} un` `ke jo wp`xujao goe ao un` ujd`xhgk`x haoxje`}`e+ vg}jgujaoxaf cgx$ajk }gujax ao un` a}e`} af =2% }`kgujv` ua un` gv`}gc` g}` amx`}v`e/ Jfunjx vg}jgujao jx guu}jmpu`e ua hngoc`x jo }`x`}vaj} a} s`kk+ `jun`} g dae`k afun`


Optimizing For Hardware Transform and Lighting Optimizing For

Optimizing For Hardware Transform and Lighting Optimizing For

Patient empowerment and the use of Internet Steinar Pedersen

Patient empowerment and the use of Internet Steinar Pedersen

INF5050 Introduction to optical networkingheim.ifi.uio.no/~infpri/Presentasjoner/opticalhandouts.pdf · INF5050 Introduction to optical networking steinar@transpacket.com steinar.bjornstad@item.ntnu.no.

INF5050 Introduction to optical networkingheim.ifi.uio.no/~infpri/Presentasjoner/opticalhandouts.pdf · INF5050 Introduction to optical networking [email protected] [email protected].

Registration info: Tove Aune (NGU) … persons : Steinar Løve Ellefmo (NTNU) steinar .ellefmo@ntnu. no Fredrik Søreide (NTNU) fredrik .soreide@ntnu. no Tom Heldal (NGU) tom .heldal@ngu.

Registration info: Tove Aune (NGU) … persons : Steinar Løve Ellefmo (NTNU) steinar .ellefmo@ntnu. no Fredrik Søreide (NTNU) fredrik .soreide@ntnu. no Tom Heldal (NGU) tom .heldal@ngu.

2008 Oil and Gas Production Optimization Lost potential due to uncertainty (Steinar M Elgsæter)

2008 Oil and Gas Production Optimization Lost potential due to uncertainty (Steinar M Elgsæter)

Brazil & Iceland Country Report Eva Sigurðardóttir Eva Katrín Sigurðardóttir Laima Kristin Snore Steinar Sigurðsson Tinna Traustadóttir.

Brazil & Iceland Country Report Eva Sigurðardóttir Eva Katrín Sigurðardóttir Laima Kristin Snore Steinar Sigurðsson Tinna Traustadóttir.

Steinar Njå Norwegian Petroleum Directorate Licensing system in Norway.

Steinar Njå Norwegian Petroleum Directorate Licensing system in Norway.

Steinar ipv6forum 20111121v2

Steinar ipv6forum 20111121v2

eHealth: an overview Steinar Pedersen

eHealth: an overview Steinar Pedersen

Utviklingstrekk innen fiberoptisk telekom teknologi ... · Utviklingstrekk innen fiberoptisk telekom teknologi – løsninger for verdensomspennende internettforbindelser Steinar

Utviklingstrekk innen fiberoptisk telekom teknologi ... · Utviklingstrekk innen fiberoptisk telekom teknologi – løsninger for verdensomspennende internettforbindelser Steinar

Zebrafish Embryo Dispenser - ZED Gunnlaugur Steinar Gumundsson li Svar lafsson Rnar Viggsson rnlfur rir rnlfsson.

Zebrafish Embryo Dispenser - ZED Gunnlaugur Steinar Gumundsson li Svar lafsson Rnar Viggsson rnlfur rir rnlfsson.

2008: An overview of Methods for analysis of Identifiability and Observability in Nonlinear State and Parameter Estimation: Presentation (NTNU trial lecture) Steinar M. Elgsæter

2008: An overview of Methods for analysis of Identifiability and Observability in Nonlinear State and Parameter Estimation: Presentation (NTNU trial lecture) Steinar M. Elgsæter

TTM1: ”Burst, packet and hybrid switching in the optical core network” Steinar Bjørnstad et al.

TTM1: ”Burst, packet and hybrid switching in the optical core network” Steinar Bjørnstad et al.

2006 Modelling and control of growing slugs in horizontal multiphase pipe flows (Steinar M. Elgsæter)

2006 Modelling and control of growing slugs in horizontal multiphase pipe flows (Steinar M. Elgsæter)

2008 Steinar M. Elgsæter phd defence: Modeling and optimizing the offshore production of oil and gas under uncertainty

2008 Steinar M. Elgsæter phd defence: Modeling and optimizing the offshore production of oil and gas under uncertainty

Self-optimizing and explicit methods for online optimizing control

Self-optimizing and explicit methods for online optimizing control

2010 A structured approach to optimizing offshore oil and gas production with uncertain models. Published in Journal of Computers & Chem. Eng (Steinar Elgsæter)

2010 A structured approach to optimizing offshore oil and gas production with uncertain models. Published in Journal of Computers & Chem. Eng (Steinar Elgsæter)

Harald Haugen / Knut Steinar Engelsen Stord/Haugesund College, 5409 Stord, Norway harald.haugen@hsh.no / knut.engelsen@hsh.no European.

Harald Haugen / Knut Steinar Engelsen Stord/Haugesund College, 5409 Stord, Norway [email protected] / [email protected] European.

Steinar Sørli, Åmot Operagard - Vertskap som identitetsbygger

Steinar Sørli, Åmot Operagard - Vertskap som identitetsbygger

Steinar Kristoffersen Fetter Nielsen Jennifer Blechar Ole ... · Steinar Kristoffersen Fetter Nielsen Jennifer Blechar Ole Hanseth University of Oslo Oslo, Norway Abstract The anabolic

Steinar Kristoffersen Fetter Nielsen Jennifer Blechar Ole ... · Steinar Kristoffersen Fetter Nielsen Jennifer Blechar Ole Hanseth University of Oslo Oslo, Norway Abstract The anabolic