Sensitivity Analysis of the Accident Rate of a Plant by the Generalized Perturbation Theory

Transcription

1 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 esvy Alyss of e Accde Re of Pl by e Geerlzed Perurbo eory E F L D G exer P F Fruuoso e elo F C lv d A C Alv Absrc we dscuss e lco of e Geerlzed Perurbo eory (GP) o e relbly of syse of ree equl roeco cels of dusrl l e fluece of reers suc s e ded re d e flure re over e l ccde re s dscussed rdol eods ve bee used o sudy e fluece of ese reers o e l ccde re wc e syse of dfferel equos derved fro e rkov roc doed s solved for ec vlue of e ded re Fro e soluo of s syse of equos curves for e ccde frequecy deedg o e ded re (drec clculo) re obed However s ossble o ob ese curves by GP fser wy were e clculo effor y be reduced by fcor of u o I ws foud for ded res lower / yer GP clculos w rd d 5 orders of roxos of gve beer resuls ose w s order roxo we cored o drec clculo However for ded res equl or greer / yer e s order roc reseed beer resuls e rd d 5 orders Keywords Ded re Geerlzed Perurbo eory rkov relbly lyss Pl ccde re I I INRODUCION NDURIAL fcles re equed w syses wose sole fuco s o roec e ublc er ersoel d eque gs desrucve effecs cused by ccdes wc rdocve oxc or flble subsces y be relesed o e evroe E F L forer sude Grdue Progr of Nucler Egeerg COPPE Federl Uversy of Ro de Jero Av Horáco cedo Roo G Ro de Jero RJ Brzl e-l: l@uclerufrjbr D G exer Dc sude Grdue Progr of Nucler Egeerg COPPE Federl Uversy of Ro de Jero Av Horáco cedo Roo G Ro de Jero RJ Brzl e-l: dexer@uclerufrjbr P F Fruuoso e elo Professor Grdue Progr of Nucler Egeerg COPPE Federl Uversy of Ro de Jero Av Horáco cedo Roo G Ro de Jero RJ Brzl e-l: fruuoso@uclerufrjbr F C lv Professor Grdue Progr of Nucler Egeerg COPPE Federl Uversy of Ro de Jero Av Horáco cedo Roo G Ro de Jero RJ Brzl e-l: ferdo@uclerufrjbr A C Alv Professor Grdue Progr of Nucler Egeerg COPPE Federl Uversy of Ro de Jero Av Horáco cedo Roo G Ro de Jero RJ Brzl e-l: lv@uclerufrjbr yclly roecve syses re erodclly esed sdby sfey syses wose relbly fgure of er s er e uvlbly s deeds o e flure d rer res of s cosue cels o e es d ece olces osed s well s o e syse logc cofguro However fro e o of vew of sfey e fcles reer relly ers s e ccde (or zrd) re I s bee coo rcce o evlue e l ccde re s e roduc of e frequecy of occurrece of e g eve (lso kow s ded re) by e roecve syse e uvlbly were oe ssues e ler s deede of e forer s s vld ssuo oly f e ded re s low (yclly less /yer) s es o be for os g eves ucler ower ls Nevereless sgfc effec of e ded re o e l ccde re y be foud weever e forer ssues ger vlues s fluece s lredy bee deeced d dscussed for soe secl cses [] [] As rccl exerece s sow we cosder roecve syses y ve u o fve decl cels for e we wll be coverg 9% of cul syses uder curre usge rkov odels ve bee used order o odel e l ccde re by kg o ccou e erdeedece bewee e ded re d e uvlbly of e roecve syse rkov odels cosder e ossbly of erforg rer o e roecve syse bo w e l ole s well s offle I y sces e frs olcy s o llowed Besdes for ose suos were ccde s occurred d e roecve syse dd o erfor roerly rer s o erfored o for e wole l s lredy uder dge s suo s lso odeled ere As ded res y be s g s /yer sesvy lyses o e l ccde re y requre exesve clculos For s reso e geerlzed erurbo eory s bee cosdered s eresg oo for fcg e roble [4] Oe of e dvges of GP s e fc requres referece soluo for e l ccde re d y geere resuls by erurbg oe or ore reers e se e us cosderbly reducg e couer effor GP s eursc eod [5] wdely used by e ucler egeerg couy s for exle recor yscs [6] d erl ydrulcs lyss [7] [8] e ossbly of lyg GP o relbly lyss bsed o rkov odels ws dscussed [9] e bevor of l ccde frequecy s fuco of flure res d syse ded ws lyzed [4] IN:

2 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 everl sudes ublsed e relbly re cofr e orce of deerg e ccde frequecy of l o e bss of flure d ded res [] [] eekg o exed e lco of GP o s roble s work kes sesvy lyss of e ccde frequecy of l equed w syse of ree roeco cels As we re dscussg r cel syse w redudcy s ecessry o cosder e ossbly of occurrece of coo-cuse flures ere re soe odels re coo-cuse flures suc s e bsc reer odel e ulle Greek leer odel d e fcor odel [] I s work we used e fcor odel e reso for coosg s odel s s relvely sle o ob s reer vlues rcce II HE HREE-CHANNEL PROBLE e relbly rbue of eres for roecve syses s er verge uvlbly (U) wc deeds o e cooe (cel) flure re () rer re (μ) u flure robbly durg ece cves () d lso o e uber of rere vlble Fro e o of vew of l sfey lyss e reer ers s e ccde frequecy () gve by e roduc bewee e frequecy of e g eve lso clled ded re () d e verge uvlbly of e roecve syse U(µ) were s cly ssued e ler s deede of e frs However sgfc effec of e ded re o e verge vlbly of e roecve syse c be foud weever e frs ssues ger vlues (>/yer geerl []) s fluece s bee lyzed rcce (eg syses w u o wo redud cels []) us suc cses oe sould wre: U () We ssue ree-cel roecve syse subjec o : F wc es e roecve syse flure occurs weever les cels fl e syse uvlbly wll be odeled by es of rkov c becuse we eed o odel syse rer d lso ureveled cel flures e se rso dgr for e roecve syse w ree decl cels d reveled flures uder : F logc y be see Fgure e reers e rles < j k > sow Fgure rerese: = uber of oerg cels j = uber of fled cels wose flures re ureveled d k = uber of fled cels wose flures re reveled I Fg k rereses e flure re of k cels ve fled due o coo cuses (coo-cuse flures) e rso fro se o se 7 es ll cels ve fled due o cuse e rso re fro se o se es oly oe cel flure s occurred bu ere re dffere wys becuse ere re cels o se As e uber of rere s equl o e uber of cels e rso fro se o se 6 s equl o (- ) eg ec fled cel s ssged rer For e cse of e rso fro se o se 8 ureveled cel flure s ssued s resul of ece bu g rere re vlble <> (-) 4 7 <> <> (-) 5 <> <> (-) 6 (-) (-) <> <> <> <> (-) 8 9 <> Fg e rso dgr for e -cel roecve syse Due o e ssuo of erforg ece oly we e l s ole ses 6 9 d wll o be ke o ccou we evlug e l ccde re s wll be dscussed ler e roc for reg coo-cuse flures s bsed o e odel [] e odel [] s bsed o ul-reer geerlzed reers re reled o e eves kow w e urose of esg drec wy e bsc eve coocuse robbles c be defed s e frco of eves volvg e flure of rculr cooe due o coo cuse e robbly of suleous flure of k d oly k cooes due o coo cuse s gve by []: k k () k were k () k k d sds for e uber of equl roecve syse cels e reer k s subjec o e followg codo: k (4) k As ere re ree equl roecve cels e = d Eq () s wre s: IN: 998-4

3 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 k k k Fro Eq (5) oe c wre: for k = d (5) (6) Pug Eq (6) Eq (5) w k = d oe s: (7) (8) (9) wc re e syse flure res s fuco of reers e e dfferel equo govers e syse bevor s gve by: d d were () s vecor defed s follows: ) ( ) ( ) () ( d (); = rereses e robbly e syse s e - se d s e rso re rx gve by: were: () As s s l vlue roble l codo us be secfed I s cosdered ll cels re lly o so : () As e flure logc s gve by :F so ere us occur les wo cel flures for e syse o fl e l ccde re s gve by []: d (4) Eq (4) kes o ccou o-le rer s fesble As we re o gog o ke s olcy o ccou (s dscussed [4]) e oly e offle rer olcy wll be ke o ccou so Eq (4) y be rewre s: wc y be recs o: P were d d ) 8 ( d (5) (6) (7) (8) e erurbo reers d wll gve us ew ccde re wc c be obed by ylor seres exso: IN: 998-4

4 !! (9) were oe obs fro Eq (6): d () f d f d ; ; () d f ; d f ; d d () e dervves of () w resec o d reers re e soluos of e followg equos: d d () d d (4) d d (5) wose source ers re s follows: (6) ) ) ( (7) l l l ) ( (8) were! w (9) d ) ( () were () w d INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 IN: 998-4

5 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 () () However ccordg o e source recrocy relos [] Eqs () () y be recs o: d d d * * d ( ) ( ) * d d ( ) d () (4) (5) were *() e orce fuco ssoced o e egrl quy s e soluo of e followg equo: d * ( ) * ( ) (6) d Pug Eqs () (5) o Eqs () () resecvely d e resulg equos Eq (9) oe obs: *! ( ) * ( ) d d * ( ) d! * ( ) * ( ) [ d d! * ( )! d ] (7) were e source ers d were defed Eqs (6) (8) Eq (7) s used for erforg e sesvy lyss for e l ccde re Noe e use of e orce coce d of source ers crcerzes e use of e geerlzed erurbo eory III CAE UDIE o use GP for erforg e sesvy lyss o e ccde frequecy of l (usg syse of ree equl roeco cels) e syse ded re d (frco of eves volvg e flure of rculr cooe due o coo cuse) were erurbed e u d used s reseed ble [] [] ble Iu reers Preer ybol Vlue Proof es ervl yr Cel flure re /yr Cel rer re 65/yr Hu flure robbly durg cel rer Probbly of wo cel flures due o coo-cuse flure oreover reer ws vred s follows: = 7 + 5( ) = 5 (8) e referece vlue for reer ws ssued s 8 e vlue ssued for s reseed ble s es we re ssug % robbly of wo suleous cel flures due o coo cuses I e sesvy sudes for ec vlue vros of ccordg o ble were doed s for ec cse sow were dffere ervl for s defed e vlues ese rges re gve ccordg o equo e ls colu of e ble Also referece vlue for e ded re s se s lso sow e ble ble Perurbed ded res Cse Rge (yr - ) Ref (yr - ) Perurbed reer vlue (yr - ) 9 5 +(-); =9 5 +5(-); = (-); =9 4 +5(-); = (-); = (-); = (-); = (-); = (-); = (-); = (-); = (-); =9 esvy clculos usg GP e solvg e syse of dfferel equos of Eq () 6 es sce ere re IN: 998-4

6 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 referece vlues for e ded re d 5 vlues for e reer [Eq (8)] were doed (see ble ) Corvely e resuls reseed [] requred e soluo of e se syse ore 6 es IV REUL AND DICUION Fgure sows e sesvy lyss erfored o e l ccde re for = 75 e curves for e drec soluo d for e erurbos cosderg e frs rd d ff orders exsos ers re dslyed [Eq (7)] Fgs 5 dsly e sesvy lyss for = d 95 resecvely I c be see e resuls volve e reseo of e drec soluo d of e erurbed soluos w dffere ylor exso orders Accde Re (yr - ) Drec s order rd order 5 order 75 Ded Re (yr - ) Fg esvy lyss for = 75 Accde Re (yr - ) Drec s order rd order 5 order 8 Ded Re (yr - ) Fg esvy lyss for = 8 IN:

7 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 Accde Re (yr - ) Drec s order rd order 5 order 85 Ded Re (yr - ) Fg 4 esvy lyss for = 85 Accde Re (yr - ) Drec s order rd order 5 order 9 Ded Re (yr - ) Fg 5 esvy lyss for = 9 I ws foud for ll vlues of e rd d 5 roxo orders were beer for </yer weres for > /yer e s order roxo s beer For < /yer e ccde frequecy s fuco of e ded re creses rdly w e eed o use gerorder ylor seres o rerese e fuco s rge erefore e roces of rd d 5 orders were beer wle e roc of s order ce o ve devo of u o 88% for = / yer Fgure 5 For > / yer e ccde re s los syoc d s dervves of ger orders re close o zero As e roc of s order does o use ese dervves er resuls re beer s rge e roces of rd d 5 orders use ese dervves d erefore ed o crese e devo recg 6% for = 65/yer for e 5 order roc IN:

8 INERNAIONAL JOURNAL OF AHEAICAL ODEL AND EHOD IN APPLIED CIENCE Volue 6 I CONCLUION e urose of s er ws o lyze e sesvy of ree-cel roecve syse cosderg s egrl quy of eres e l ccde re e syse sesvy lyss ws que ssfcory d GP s recoeded GP o erfor sesvy lyses becuse e couol effor s reduced by fcor of I c be see fro e resuls sow e s rd d 5 roxos orders sowed good resuls relo o e drec clculo well-defed ervls s dscussed s bevor olds rue for e oer vlues erefore we recoed e use of GP s ye of roc d oer robles For fuure work suc s e use of u o 5 roeco cels we recoed usg e GP However oe us lyze w roxo o use for e ded re ervls Aoer or feure s e cosdero of cel gg I s or o dscuss e fluece of cel gg o e roecve syse uvlbly d lso l ece olces sgfcly ffec e l ccde re s cosdero s jusfed by e fc e ssuo of cel useful lfe ( s exoel flure es) y be oo resrcve due o l sressg codos A l dscusso o s y be foud elsewere [] [] P F Fruuoso e elo L F Olver d RW Yougblood A rkov odel for e relbly lyss of ul-celed roecve syses cosderg reveled flures d coo-cuse flures by e l odel Proc 9 N ee O Recor Pyscs d erl Hydrulcs Brz Assoc Nucl Eergy Ro de Jero RJ Brzl [] P F Fruuoso e elo D G exer d A C Alv A oe Crlo Evluo of e Accde Re of Pl Equed w Agg gle-cel r Devce o be reseed e 4 Ierol Coferece of Nuercl Alyss d Aled ecs o be eld Rodes Greece 9-5 eeber6 REFERENCE [] F P Lees A geerl relo for e relbly of sgle-cel r syse Relbly Egeerg vol 98 [] L F Olver d J D Arl Neo Ifluece of e ded re d rer re o e relbly of sgle-celed roecve syse Relb Eg vol [] L F Olver R W Yougblood d P F Fruuoso e elo Hzrd re of l equed w wo-cel roecve syse subjec o g ded re Relb Eg d yse fey vol [4] P F Fruuoso e elo A C Alv d F C lv esvy lyss o e ccde re of l equed w sgle roecve cel by geerlzed erurbo eods Als of Nucler Eergy vol [5] A Gd Geerlzed erurbo eory (GP) eods: eursc roc Advces Nucler cece d ecology vol [6] F C lv d A Gd Perurbo ecques for Recor Lfe Cycle Alyss Proc I ocl ee o Advces Recor Pyscs ecs d Couo Prs Frce [7] F C lv d Z D oé Deleo clculos w sc geerlzed erurbo eory Als of Nucler Eergy vol [8] A C Olver F R A L d A C Alv Alco of e Geerlzed Perurbo eory of wo-cel odel for e esvy Alyss of PWR Recor Core ( Poruguese) Proc 7 N ee Recor Pyscs d erl Hydrulcs Ro de Jero Brzl [9] A Gd A Iorce d sesvy lyss ssessg syse relbly IEEE rscos o Relbly vol [] A osle d N u A ul-reer coo-cuse flure odel rs 9 ruc ec I Rec ec (R) Cof Luse wzerld 987 er # 7/ 47-5 [] F C lv Develoe of Geerlzed Perurbo eory (GP) eods d er lco o recor yscs ( Poruguese) Dc dssero Grdue Progr of Nucler Egeerg COPPE/UFRJ Ro de Jero RJ Brzl 989 IN: