Dynamic Response of Deepwater Lazy- Wave Catenary Riser

Transcription

1

2 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 Dnmc Response of Deepwter Lz- Wve Ctenr Rser 1 Abstrct ongcheng L, H Offshore Inc. & Chu Nguen, H Offshore Inc. Lz-wve ctenr rsers hve gned populrt s vble soluton to mprove ftgue nd strength performnce t the touchdown zone of smple ctenr rser. Wth the obectve to provde techncl reference for lz-wve shped rser, ths pper focuses on the stud of lz-wve confgurtons nd dnmc responses when the rser s supported from hgh moton flotng producton pltforms such s sem-submersbles nd FPOs. The stud eplores the behvor of lz-wve rsers wth respect to vret of nput prmeters, such s crtcl curvture rd, hng-off ngle, top tenson nd buonc dstrbuton. A sstemtc pproch to pnpont drvng fctors nd crtcl loctons s dscussed. Equtons re lso presented to provde n nltc nd determnstc pproch to desred lz-wve shpe for further numercl ssessment of strength nd ftgue responses. Introducton The pplcton of lz-wve ctenr rser (LWR) hs been populr n deep wter pplcton due to ts dustble plod on vessel nd ts optons to control dnmc strength nd ftgue response long the rser [1]. Wth help of commercl softwre or self-developed optmzton tools [], current prctces rel on numercl pproches usng trl nd error or tertve procedures to eplore lz-wve rser confgurton [], whch demnds huge effort for optmzton. It s tme consumng nd not cost effectve, especll durng prelmnr screenng stge or rser stud for proect. The chllenge encountered n the optmzton of lz-wve confgurton s ssocted wth the lck of prmeterzed equtons for the confgurtons. 1 Lern more t

3 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 In ths work, confgurton of lz-wve rser s derved nltcll wth two desgn nput optons. The ke fctors for dnmc strength nd ftgue responses re eplored nd epressed s equtons of the lz-wve confgurton prmeters, whch provde nsght nd perspectve n lz-wve rser behvor. Ths work smplfes the rser optmzton process nd cn be used s frmework for lz-wve confgurton desgn. ttc Confgurton of CR nd LWR A smple steel ctenr rser (CR) s consdered cord of unform denst nd cross-secton re hngng on two ends under grvt nd buonc force n wter [4], lthough slght vrton n denst or cross-secton m est due to strkes, mrne growth or specl onts such s tper stress ont. A tpcl CR s chrcterzed b downwrd wet weght long ts length. A lz-wve ctenr rser (LWR) s specl CR wth segment of ts length equpped wth eternl buonc modules, where ts upwrd buonc force n wter s greter thn ts downwrd grvt force nd thus n equvlent negtve grvt force. A tpcl LWR conssts of three segments, ech segment ctenr, nmel the hng-off ctenr (hngng nd umper sectons), the buonc ctenr (lft nd drg sectons) nd the touchdown ctenr, s llustrted n Fgure.1. The buonc ctenr les between the hng-off ctenr nd the touchdown ctenr. A tpcl LWR hs sg bend nd n rch bend. The elevton dfference between the top of the rch bend nd the bottom of the sg bend s termed rch heght. As generl rule of thumb, the buonc force provded b the buonc modules s round twce the self-weght of the steel ppe wth nternl flud. The vrton of the net buonc force from the buonc modules produces hgh-rch, md-rch or low-rch LWR confgurtons, or shped CR[5]. A shped CR s defned s degenerted LWR wth no sg bend or rch bend. Tht s, ts lowest elevton long the hng-off ctenr concdes wth the hghest elevton long the buonc ctenr t ther connecton pont. A sg bend long the hng-off ctenr nd n rch bend long the buonc ctenr dstngush LWR from shped CR. Lern more t

4 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 The equtons n the subsequent sectons ppl to CR, LWR nd shped CR Hngoff Ctenr Buonc Ctenr Touchdown Ctenr Elevton from ebed (ft) Hngoff Locton Hngng ecton Arch Bend Lft ecton Lft Pont Drg ecton Drg Pont Jumper ecton g Bend Touchdown Pont Horzontl Dstnce from Hngoff (ft) Fgure.1 Emple Confgurton of Lz-Wve Ctenr Rser.1 Generl Chrcterstcs of CR As specl CR, the LWR shres some common chrcterstcs of CR such s correltons between curvture, rser mss denst, rc length nd hng-off ngle. A ctenr s governed b hperbolc cosne functon [6] n Equton (1) s llustrted n Fgure.: (cosh 1) ( e e ), (1) where s the curvture rdus of ctenr t ts orgn, snce curvture k or where t orgn 0 gves d d 1 k, () d 1 ( ) cosh d d ds cos, d dssn, () Lern more t

5 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec k. (4) Y Y X T+dT ds β ds d d T ds=mgds O X Fgure. Coordnte stem of Ctenr Curvture Equton () cn be rewrtten s 1 k, cosh ( ) whch dontes the mmum curvture or the lowest curvture rdus long ctenr occurs t the orgn =0. The ctenr curve s smmetrc bout the Y-s n Fgure.. Wthout loss of generlt, the bsolute vlues of X nd Y re used for the equtons n ths pper. The rc length of ctenr from ts orgn cn be obtned from d ds 1 d snh. (5) d The nclnton ngle β suffces d tn snh. (6) d From horzontl equlbrum T cos ( T dt )cos 0, one obtns d ( T cos ) 0, 4 Lern more t

6 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 whch mples constnt horzontl force long ctenr. B defnng horzontl force N nd wet weght per unt length : N T cos const, mg, (7) where m s the wet mss per unt length nd g the ccelerton of grvt, the reltonshp between the horzontl force N nd wet weght per unt length cn be derved usng vertcl equlbrum equton: T sn ds ( T dt )sn 0, or or d( T sn ) ds, d( T cos tn ) ds. (8) ubsttutng () nd (7) nto (8) gves or d d( N ) d d N d d 1 ( ), 5 d d d d 1 ( ). (9) ubsttutng Equton (1) to (9), the reltonshp between the horzontl force N nd wet weght per unt length s obtned: N const, or N. (10) Ths mples tht the curvture rdus t orgn cn be dusted b vrng the horzontl force N or the wet weght per unt length.. Generl Chrcterstcs of Lz-Wve Rser The sttc equlbrum of the LWR llustrted n Fgure. () nd (b) ndctes tht, the resultnt forces t the sg bend B nd the rch bend D re horzontl nd both equl to the horzontl force N t the touchdown pont. In the vertcl drecton, there re no sher forces t ponts B nd D, whch requres sttc equlbrum of the weght of the umper secton BC nd net buonc force of the lft secton CD, s well s the drg secton DE nd the touchdown ctenr EF. In other words, the net buonc force of the lft secton CD lfts the wet weght of the umper secton, nd tht of the drg secton drgs the wet weght of the touchdown secton. Lern more t

7 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 Lft ecton D N N D Drg ecton C E N B Jumper ecton Touchdown Ctenr N () (b) F Fgure. ttc Equlbrum Anlss of the LWR In locl coordnte sstems -B-, u-d-v nd p-f-q, s shown n Fgure.4, the hng-off ctenr ABC, the buonc ctenr CDE nd the touchdown ctenr EF cn be epressed s the followng equtons: where, u p (cosh 1), v (cosh 1), q k (cosh 1). (11) nd k re the curvture rd t ther correspondng orgns B, D, nd F. k Hngoff Ctenr () Buonc Ctenr () Touchdown Ctenr (k) A β θ 1 V u C D v 4 B E s q 5 F p H Fgure.4 Locl Coordnte stems of Ctenr Equtons 6 Lern more t

8 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 Assumng m, m nd mk the wet msses of steel ppes wth nternl flud t unt length of the hng-off ctenr, the buonc ctenr nd the touchdown ctenres, the wet weghts of rser per unt length re m g, F m g, k mk g, (1) where F s the net buonc force from the buonc modules pontng upwrd. Applcton of the dmensons n Fgure.4 to Equton (5), the rc lengths of the umper secton nd the lft secton become, snh The vertcl equlbrum n Fgure. () requres, or. (1) snh (14) Equton (14) mples tht the lengths of the umper secton nd the lft secton re proportonl to ther vertcl weght t unt length. Further dervtons usng Equton (10) gve. (15) mlrl, for the drg secton nd the touchdown ctenr, the followng s true: k. (16) Usull sme mterls nd sme geometrc propertes re utlzed for both the hng-off ctenr nd the touchdown ctenr, tht s k or k Combnton of Equtons (15) through (18) obtns 5, or 4 k. (17) 5. (18) 4. Confgurtons of Lz-Wve Rser For lz-wve confgurton, there re usull two desgn nput optons. One opton gve the lengths of the three ctenres, nd the other the elevtons of the sg bend nd the rch bend. 7 Lern more t

9 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 For desgn nput opton 1, gven the lengths of the hng-off ctenr, the buonc ctenr, ether the wter depth V t the hng-off locton A or the touchdown ctenr length k, the confgurton of the LWR s determned. Wthout loss of generlt, the touchdown ctenr length k s ssumed provded heren, s presented n Equtons (19) through (1). 1 (19) 4 (0) k 5 The totl length of the LWR s therefore (1) Combnton of Equtons (19) through (1) provdes the rc length of the hngng secton: 1 (1 ) 8 k. () On the other hnd, pplcton of Equton (6) to the hng-off locton gves tn cot, () 1 0 where s the gven top hng-off ngle, nd 90 s the nclnton ngle t the hng-off locton, s shown n Fgure.4. ubsttutng Equton () nto Equton () obtns the curvture rdus of the sg bend or the touchdown pont: ( 1 ) tn. (4) ubsttutng Equtons () nd (4) nto Equtons (5), (10) nd (11), one obtns the spred nd heght of the hngng secton: 1 rcsn h(cot ), (cosh 1 1 1). Equtons (11), (1) nd (19) gve the spred nd heght of the umper secton: 1 rcsn h( ), [cosh( ) 1]. Lern more t

10 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 Equton (15) gves the spred nd the heght of the lft secton:, 9. Equtons (16) nd (1) provde the length of the drg secton: ( ). 4 ubsequentl, the curvture rdus t rch bend s the spred nd heght of the drg secton re, 4 4 rcsn h( ), [cosh( 4 4 ) 1], nd the spred nd heght of the touchdown ctenr re 5 rcsn h( ), 4 5. Wth ll the dmensons clculted bove, the sg bend heght s determned b: nd the rch bend heght becomes s, The wter depth V t the hng-off locton cn be checked b V For desgn nput opton, the LWR confgurton cn lso be unquel determned f the sg bend heght s, the rch bend heght nd the wter depth V t the hng-off locton A re provded. trtng wth the heght of the hngng secton 1 V s, Equtons (6) nd (11) gve the curvture rdus t the sg bend s 1. (5) cosh[rcsn h(cot )] 1 The curvture rdus t the rch bend s gven b Equtons (15) nd (5) s Lern more t

11 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec (6) cosh[rcsn h(cot )] 1 The spred of the hngng secton s clculted from Equton (5) s rcsn h(cot ). 1 Gven the rch heght, or the vertcl dstnce between the rch bend nd the sg bend, s. (7) Equtons (15) nd (7) produce the heghts of the umper secton nd the lft secton: ( ) s, 10 ( ) s. ubsequentl, the spreds of the umper secton nd the lft secton re thus rccosh( 1), rccosh( 1). The sme dervtons ppl to the drg secton nd the touchdown ctenr. Gven the rch bend elevton 4 5, (8) Equtons (16) nd (8) eld the heghts of the drg secton nd the touchdown ctenr: Hence ther spreds cn be epressed s 4, rccosh( 1), 5 rccosh( 1). As result, the rc length of ech ctenr cn be clculted usng Equton (5) s follows: 1 4 (snh snh ), (snh snh ), 5 snh. 5 k For both desgn nput optons, the totl horzontl dstnce from the hng-off locton to the touchdown pont s H, the horzontl force t n pont long the LWR nd t touchdown pont s N, (9) k k Lern more t

12 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 nd the top tenson t hng-off locton s Combnton of Equtons (9) nd (0) gves T sn, T N / sn. (0) T sn, or 4 Dnmc Response of Lz-Wve Rser k T sn. (1) k 4.1 Wve nd Drft Moton Response of Lz-Wve Rser The frst order motons n heve, surge nd sw drectons t the hng-off pont A re mnl trnslted nto heve motons t the sg bend B due to the constrnt of the length of the hngoff ctenr nd the drg of the buonc modules t lft pont C, s shown n Fgure 4.1. For emple, the horzontl surfce moton s functon of tme t pont A becomes heve domnted moton t sg bend B due to the moton dfference n mpltude nd phse between A nd C. P A Y R C X B Fgure 4.1 Heve Moton t g Bend due to Horzontl Moton t Hng-Off Pont As opposed to the frst order moton, the reltvel long perod of the second order moton gves the more tme for the LWR to respond globll, especll long the buonc ctenr. The second order motons t the hng-off pont A turn nto both horzontl moton nd heve moton t the sg bend, s shown n Fgure 4.. For emple, horzontl second order moton t the hng-off pont A s followed b domnnt horzontl motons t the lft pont C nd the drg pont E. Ths genertes open nd close movements of the sg bend or the rch bend, 11 Lern more t

13 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 fluctutng curvture rd long LWR, especll t such crtcl loctons s the sg bend B, the rch bend D nd touchdown pont F. Hngoff Ctenr Buonc Ctenr Touchdown Ctenr A A β θ D ud V B uc C ub ue E uf F Fgure 4. Illustrton of econd Order Moton long LWR Techcll, the crtcl loctons for curvture rdus refer to crtcl zones. The locl top pont D m trvel long the buonc ctenr, such tht the ponts ner the rch bend D on the rser tke turns to become the locl top elevton to ccount for tenson vrtons nd secton length dustment durng dnmc motons. In ths sense, the rch bend s ctull zone n length nsted of fed pont, so re the sg bend nd the touchdown pont. The length of these crtcl zones vres wth dnmc motons s well s vessel offsets, s shown n Fgure 4.. At fr offset of 10% wter depth, LWR shpe wth decent rch heght t ner offset m degenerte nto low rch LWR, or even shped CR f fled to optmze the buonc ctenr for lrge offsets. Etreme fr nd ner offset postons should be checked for LWR confgurton to vod undesred bucklng problem of low-rch confgurton, nd to vod locl hgh stress t the rch bend t ner offset. 1 Lern more t

14 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 Crtcl curvtures long LWR re ssocted wth etreme vessel postons under drvng lod condtons nd re functons of the horzontl force N or top tenson T nd hng-off ngle θ s ndcted n Equton (1). A confgurton wth hgher top tenson T or greter hng-off ngle θ gves lrger crtcl curvture rd nd generll provdes better dnmc strength response. Restrcted b vessel plod, sg bend cn lso be dusted for gven top tenson cp. The denst, length nd thckness of the buonc modules re mong other ke prmeters for optmzton of LWR confgurton. Fgure 4. Vrton of LWR Confgurton wth Lrge Offsets 4. trength Response of Lz-Wve Rser Tper stress ont or fle ont s wdel used for stress relef t the hng-off locton, whle other crtcl loctons long LWR hve to rel on the optmzton of the buonc ctenr. The horzontl moton nd the heve moton t the hng-off locton led to n open nd close movement of the sg bend, the rch bend nd the touchdown zone s llustrted n Fgure 4.. The lowest curvture rd t these crtcl loctons governs ther stress response snce stress nd bendng moment re proportonl to curvture, s shown n Fgure 4.4. The hghest stress frequentl occurs t the rch bend where the most crtcl curvture s more lkel when the 1 Lern more t

15 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 lft pont nd the drg pont move out of phse wth the vessel t ner offset poston. On the other hnd, the preference of hgh net buonc force for rch heght optmzton lso results n lower curvture t the rch bend. Other crtcl curvtures occur t the touchdown pont nd the sg bend. For n optmzed LWR, the stress t the touchdown pont nd the sg bend s normll not drvng n strength response, whch s nother feture of the LWR Von Mses / Yeld tress Rto Elevton from ebed (ft) Horzontl Dstnce from Hngoff (ft) Fgure 4.4 trength Response of Hgh Arch Lz-Wve Rser Rser mss denst s nother fctor for LWR optmzton. A lghter rser or smller ncludng nternl flud mproves the strength response t the sg bend nd the touchdown pont s suggested n Equton (1). As equvlent negtve mss long the buonc ctenr where F m g, lower net buonc force F fvors greter curvture rdus, but m result n n undesrble low-rch confgurton t vessel fr offset. For nstnce, the stress response of low-rch lz-wve confgurton wth sg bend nd rch bend elevtons of 900 ft nd 100 ft, respectvel, s shown n Fgure 4.5. Heve moton t the sg bend becomes whppng nd bucklng wve moton between sg bend nd the rch bend, whch results n locl curvture nd stress much hgher thn those otherwse t the sg bend or the rch bend. The structurl nd hdrodnmc dmpng effect s sgnfcntl compromsed n ths cse. 14 Lern more t

16 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec Von Mses tress / Yeld trength Rto Elevton from ebed (ft) Horzontl Dstnce from Hngoff (ft) Fgure 4.5 trength Response of Low Arch Lz-Wve Rser 4. Moton Ftgue Response of Lz-Wve Rser trength response s drven b etreme curvture t crtcl loctons, whle ftgue response s controlled b curvture fluctuton rnge ssocted wth hgher stress rnge. The hghest curvture fluctuton occurs t the sg bend, the rch bend or the touchdown pont. The low ftgue lves occur t these hgh curvture fluctuton zones, s shown n Fgure 4.6. Crtcl ftgue dmge s observed t the touchdown pont nd t the rser hng-off locton. The ftgue dmge t the touchdown zone s drven b sol-structure ntercton under more frequent occurrence of smll stress ccles from low sesttes, whle t the top hng-off secton t s drven b combnton of tenson nd bendng moment from less frequent but hgh stress rnge from hgh sesttes. Three cse studes re presented n ths secton for senstvt of the ftgue response of LWR ttched to n nternll turret-moored FPO. 15 Lern more t

17 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec 010 The frst cse eplores the frst order ftgue senstvt to rch heghts. Three confgurtons wth dfferent rch heghts nmel hgh rch, md rch nd low rch re developed b vrng the length of the buonc ctenr. The vessel plod remns the sme n ll confgurtons wth constnt hng-off ngle nd sg bend elevton. It s observed tht ftgue lfe t the touchdown pont (TDP) mproves wth rch heght. Wth the sme buonc thckness, hgher rch confgurton requres longer buonc ctenr tht provdes more dmpng to motons. The buonc lengths of the three rch heghts re compred n Fgure 4.7, nd ther frst order moton ftgue lves re presented n Tble 4.1. The ftgue lfe of the md-rch confgurton t the TDP mproves slghtl from the low-rch confgurtons, but tht of the hgh-rch confgurton doubled. A hgher rch dverts nd dmps cble wve moton n more fvorble drectons. Ths lso ndctes nonlner redstrbuton of structurl dmpng nd hdrodnmc dmpng between dfferent confgurtons. Mnmum Ftgue Lfe (ers) 1.E+1 1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 1.E+05 1.E+04 1.E+0 1.E+0 1.E+01 1.E Horzontl Dstnce From Hngoff (ft) Ftgue Lfe lck ecton Buonc ecton Elevton bove ebed (ft) Fgure 4.6 Emple of Ftgue Response long Lz-Wve Rser 16 Lern more t

18 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec Elevton from ebed (ft) gbend Archbend g Bend Heght: 400ft Arch Bend Heghts: Low Arch 600ft Md Arch 100ft Hgh Arch 600ft Horzontl Dstnce From Hngoff (ft) Low Arch Md Arch Hgh Arch Buonc 174 ft Buonc 61 ft Buonc 7 ft Fgure 4.7 Buonc Lengths Vrton wth Arch Heghts Rser Confgurton Mnmum Ftgue Lfe t Arch Tpe Arch Heght (ft) TDP (ers) Hgh Arch 100 1,500 Md Arch Low Arch Tble 4.1 Frst Order Moton Ftgue Lfe Vrton wth Arch Confgurtons The second cse compres the frst order ftgue responses to sg bend elevtons. Two confgurtons wth dfferent sg bend elevtons re developed s shown n Fgure 4.8. The hng-off ngle nd rch heght re kept constnt. The lower sg bend confgurton mproves the TDP ftgue lfe b 80%, however decreses the ftgue response t top of the rser b 1%, s compred n Tble 4.. The ftgue lfe ncrese t the TDP cn be ustfed from Equton (1). The lower sg bend confgurton hs longer hng-off ctenr length hence greter hng-off tenson nd smller TDP curvture nd bendng stress rnge. The hgher dnmc tenson fluctuton ner the hng-off locton dversel contrbutes to the ftgue performnce t top of the rser. 17 Lern more t

19 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec Elevton from ebed (ft) Hgh gbend Low gbend Buonc 7 ft Buonc 189 ft Horzontl Dstnce From Hngoff (ft) Lz Wve gbend 400ft Lz Wve gbend 600ft Buonc 10nch Thckness Buonc 10nch Thckness Fgure 4.8 Lz-Wve Confgurton wth Vrng g Bend Elevtons Locton Mnmum Moton Ftgue Lfe (ers) g Bend 400 ft g Bend 600 ft Touchdown Pont 1,500,700 Top Tper tress Jont,400,100 Tble 4. Moton Ftgue Lfe enstvt to g Bend Elevtons The thrd cse stud s bout ftgue response to current lodng. Bckground current nterferences rser moton nd helps dssptng cble wve energ n n ddton to hdrodnmc dmpng. As shown n Fgure 4.9, the TDP ftgue lfe mproves wth ncresed bckground current speed. Bckground current profle should be used wth cuton to reduce conservtveness. Generll, pplcton of bckground profle wth 50% occurrence ncreses TDP ftgue lfe ~ tmes from wthout bckground current dependng on vrton of current drectons nd speeds. 18 Lern more t

20 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec ,000 1,000 Mnmum Ftgue Lfe (ers) 10,000 8,000 6,000 4,000,000 Bse Cse (no bckground current) urfce peed of Bckground Current Profle (knots) Fgure 4.9 Effect of Bckground Current on Moton Ftgue Lfe t Touchdown Pont 5 ummr Consstng of three ctenres, nmel the hng-off ctenr, the buonc ctenr nd the touchdown ctenr, lz-wve rser hs better strength nd ftgue responses thn CR. The buonc ctenr produces effectve hdrodnmc nd structurl dmpng to ttenute cbles wves from vessel motons propgtng long lz-wve rser. The crtcl loctons for strength nd ftgue responses re t the top hng-off locton, the sg bend, the rch bend nd the touchdown pont. Ths work provdes prmeterzed equtons for confgurton optmzton nd strtegc nlss. The dmpng effcenc of the buonc ctenr nd the vrton of the curvture rd t the crtcl loctons n conuncton wth the top tenson nd hng-off ngle re the drvng fctors for lz-wve rser strength nd moton ftgue responses. The horzontl force long the rser s constnt nd functon of net rser wet weght t the hngng secton nd the top hng-off ngle. The curvture t the crtcl loctons s functon of horzontl force nd submerged weght of rser secton, whch drves dnmc response. Dnmc response s senstve to rch heght, sg bend elevton, top hng-off ngle nd bckground current lodng. 19 Lern more t

21 Deep Offshore Technolog Interntonl, Amsterdm, Netherlnds, Dec References [1] Torres, A.L.F.L. et l (00), Lz-wve steel rgd rsers for turret-moored FPO, OMAE 0/OFT-814 [] Jco, B.P. et l (008), nthess nd optmzton of steel ctenr rsers confgurttons through evolutonr computton, 5 th Report for Petrobrs, COPPE/UFRJ [] Edmundo ueroz de Andrde et l (010) Optmzton Procedure of teel Lz Wve Rser Confgurton for pred Moored FPOs n Deepwter Offshore Brzl, OTC 0777 [4] Hugh Howells, (1995). Advnces n teel Ctenr Rser Desgn: Advnces n teel Ctenr Rser desgn, DEEPTEC '95, Aberdeen, Februr 1995 [5] Bn Yue et l, (010) Improved CR Desgn for Dnmc Vessel Applctons, OMAE , Beng, June 010 [6] Lockwood, E.H. (1961) A Book of Curves, Cmbrdge Unverst Press. 0 Lern more t