PROCEEDINGS, Thiry-Third Workshop on Geoherml Reservoir Engineering Snord Universiy, Snord, Cliorni, Jnury 28-30, 2008 SGP-TR-185 FATIGUE LIFE PREDICTION OF A BUTTRESS CASING CONNECTION EXPOSED TO LARGE TEMPERATURE VARIATIONS C. Teodoriu, G. Flcone Texs A&M Universiy 3116 TAMU College Sion, TX, 77843, USA e-mil: clin.eodoriu@pe.mu.edu, gioi.lcone@pe.mu.edu ABSTRACT When he herml sresses induced in geoherml well s csing sring exceed he yield srengh o he csing meril, he igue behvior o he ler cn be deined s low cycle igue (LCF). The connecion hreds in he csing body mpliy he locl sress disribuion nd lower LCF resisnce. A heoreicl pproch is presened o evlue LCF resisnce nd compred wih preliminry resuls rom experimens on lrge dimeer buress connecion. The ler is commonly used in geoherml well compleions. This pper shows h, under exreme lods, he LCF resisnce o he buress hred connecion cn be s low s 10 cycles. INTRODUCTION Over he opering lie o well, is csing sring is generlly subjec o exernl lods h cn be considered s sic or qusi-sic. Curren indusry design sndrds consider he csing sring o be siclly loded, ye i cn be subjec o vrible lods due o chnges in emperure or inernl pressure in geoherml operions. As csing movemen is resriced by he presence o cemen sheh, emperure vriions induce herml sresses in he csing sring, which my become greer hn he meril s yield srengh. Thus, he igue behvior o he csing meril during well s operionl lie cn be clssiied s LCF. The presence o geomericl vriions in he csing body such s he connecion hreds will mpliy he locl sress disribuion, nd reduce he csing s LCF resisnce. The dimeer o he ls csing sring in geoherml well, oen ermed he producion csing, is commonly 9-5/8 inches (Teodoriu, 2005). Such lrge dimeer pipe requires correspondingly lrger surce csing nd 13-3/8 inches dimeer is commonplce in he USA nd Jpn (Bohm, 2000; Joki, 2000; Willimson, 2001). In Europe, mos o he wells drilled o dephs deeper hn 4000 m re compleed wih surce csing dimeers o 18-5/8 inches or greer (Tnzer, 2001). The lrge dimeer o producion csings is consequence o he moun o luids (nd ssocied he) o be pumped rom geoherml wells. The surce csings o deep geoherml wells re exposed o signiicn emperure vriions during drilling, which my ec heir subsequen inegriy. The ollowing heoreicl nd experimenl work ocuses on he igue resisnce o n 18-5/8 inch dimeer csing wih Buress hred connecions. THEORETICAL BACKGROUND Locl Sress/Srin Concep (LSSC) uses he locl sress se o deermine he igue resisnce o merils. LSSC llows he evluion o LCF resisnce o componens hving noches (which c s sress concenrion zones) using he experimenl resuls o unixil smll scle specimens. Csing connecions re known o hve sress concenrion zones due o hred geomery. Clssic igue esimion requires inensive ull scle esing. Figure 1 shows he number o poins used o deermine he sress versus number o cycles o ilure curve (S-N curve) or drill pipes. The pplicion o he locl sress concep reduces he ime nd cos needed or rdiionl sisicl evluion using ull scle specimens. Fig.1. S-N curve or grde D drill pipe, (Wrren e l. 2000)
Two inpu d re required or he pplicion o he LSSC: he experimenl deerminion o he sress/srin curve (/ε curve) nd n evluion o he locl sress disribuion. The sress/srin curve is mesured using pure unixil lod, wih consn deormion cycles. The resuls cn be represened s sress/srin digrm or Wöhler digrm (Teodoriu, 2005). The sress vs. srin dependency cn be wrien using he Rmberg- Osgood correlion (Ulmnu, 2001): 1/ n' ε = ε, e + ε, p = (1) + E K' ε - mpliude o ol srin; ε,e,- elsic srin mpliude; ε,p - plsic srin; - ol sress mpliude; E - Young s modulus; K' - cyclic hrdening coeicien; n' - cyclic hrdening exponen; K', n', E - o be experimenlly deermined. The Wöhler-ype digrm (Teodoriu, 2005, Ulmnu, 2001) cn be drwn using he ollowing equion: ' b ε ( ) ( ) c = ε, e + ε, p = 2 N + ε ' 2 N (2) E is igue srengh coeicien; ε - igue duciliy coeicien; b - igue srengh exponen c - igue duciliy exponen 2N number o cycles o ilure (N semicycles). The experimenl deerminion o, ε, b nd c is required becuse he sress-srin curve diers rom sic o cyclic loding. The b nd c prmeers re meril consns experimenlly deermined, or esimed bsed on csing meril chrcerisics deermined by ensile es. When he exernl lod vriion is slow, he sic sress/srin lod my be used wihou inroducing lrge errors. For exmple, Figure 2 shows comprison beween sic nd cyclic sress-srin curve or 42 CrMo4 seel. Figue deerminion using he locl sress/srin mehod is bsed on he cyclic behvior o merils, on he relionship beween exernl lods nd locl genered sress, nd on he evluion o he sress/srin curve. The resul is represened s Wöhler digrm or sress/srin curve or echnicl crck hving lengh o 0.5 o 1.0 mm. Srin [-] Fig.2. Comprison o sic nd cyclic sress/srin digrms or 42CrMo4/SAE 4142, hrdened (Teodoriu, 2005) The relionship beween locl nd verge sresses nd srins is given by he Neuber equion (Ulmnu, 2001): K 2 = K K ε = S ε e K - ol inensiy cor; K s - inensiy cor or sress; K e - inensiy cor or srin;, ε - locl sress nd locl srin; S, e - verge sress nd verge srin. (3) Using he noion e = S/E, he ollowing equion or he elsic domin cn be wrien: ε E = K S (4) ( ) 2 where E is Young s modulus. The le hnd erm ( α ε α Ε) represens dmge prmeer h, or dieren lods, describes he corresponding dmge. According o Smih e l (Ulmnu, 2001), he dmge prmeer (noed s P SWT ) cn be clculed s ollows: P SWT = ε E (5) The so-clled modiied Wöhler curve o P SWT cn be deermined using he ollowing equion: P SWT Sress [MP] Cyclic 2b b+ c ( 2 N ) + ' ε ' E ( N ) 2 = ' 2 (6) By solving equions 2 nd 4, i is possible o deermine he locl sress nd srin or given lod. Sic
By replcing hem in equion 5, he prmeer P SWT cn be deermined nd he number o semi cycles, N, cn be clculed using equion 6. The inluence o he verge ension on he dmge process mus lso be considered. The ollowing equion cn be used o his im: ( ) = + 0 M m (7) M - correlion coeicien, clculed s: M = ( M + 1) 2 1 m - verge sress; - sress mpliude; M - cor depending on meril chrcerisics. For speciic noch geomeries, he sress concenrion cor cn be clculed using empiricl ormule. The equivlen noch o csing connecion hred cn be modeled by using he so-clled V- or U-ype noch. For he U-ype noch (see Figure 3), he Germn sndrd DIN 471 (1990) provides he ollowing ormul (ssuming bending sress se): K 1,57 = 1,14 + 1,08 = 1,14 + 1,08 = 4,17 r 0,2 m The sress concenrion cor is deined s he mximum sress h occurs in he connecion (commonly he hred roo) vs. he verge sress in he csing body. Fig.4. Geomery nd mesh o 2D inie elemen model o n 18-5/8 inch dimeer csing connecion. Bsed on he FEM nlysis, i ws ound h, or buress connecion, he sress concenrion cor, K T, diers rom ension o compression. This vriion cn be explined by he more ggressive bending on he hred urn or he ensile lod. The dieren wy in which he connecion responds o he lods ws evlued using 3D model, s presened in Figure 5. The deormion o he hred urns under ension lod is dieren rom h under compression lod. The ollowing resuls were obined: K = 3, 51 or ension, K = 2, 73or compression. ( r D Fig.3. Typicl U-ype noch h mimics hreded connecion, DIN 471 (1990) For sndrd hreded connecions (nu nd bol) he sress concenrion cor is considered o be beween 4 nd 10, ccording o (Buch, 1988). NUMERICAL INVESTIGATIONS The Finie Elemen Mehod (FEM) ws used o beer undersnd he sress se in he hreded connecion. The irs gol ws o esime he sress concenrion cors wihin he complee nd incomplee hred urns. Chnges in meril properies due o high emperure were no iniilly considered, s i ws ssumed h he sress concenrion cor is uncion o he geomery only. A 2D model ws used, s presened in Figure 4, s i provided s nd relible resuls. A commercil FEM environmen ws used or his simulion. () (b) (c) Fig.5. The quliive represenion o he deormion o compression loded (), ension loded (b) hreded connecion compred o he non-deormed sus (c) Figure 6 shows hred urns under compression nd ension lods, wih high resuling sresses he hred roo (shown in red). In reliy, he incomplee hred urns presen shrp edges nd hereore higher sress concenrion cors my be expeced.
SY (AVG) RSYS=0 DMX =.169922 SMN =-702.391 SMX =383.632 commonly used grdes o seel pipe. The vlues presened in Tble 1 were clculed using equion (8) nd he ollowing vlues or seel expnsion coeicien, α, nd seel young modulus, E: α = 12.5E-06 1/ 0 C, E = 2.05E05 MP -702.391-461.052-219.714 21.624-581.721-340.383-99.045 TIME=1000 SY (AVG) RSYS=0 DMX =.153252 SMN =-545.063 SMX =636.234 MN 142.294 262.963 383.632 Yield Srengh [MP] 1000 900 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 Temperure [ 0 C] J55 N80 P105 P110 Fig. 7. Yield Srengh o dieren OCTG grdes s uncion o emperure, er Lri (1997) -545.063-413.808-282.552-151.297-20.042 111.213 242.469 373.724 504.979 636.234 Fig.6. Sress disribuion he hred roo or he compression (op) nd ension (boom) lod cses, s simuled wih FEM. THERMAL INDUCED FATIGUE To deermine he inluence o emperure on csing igue, he ollowing ssumpions were mde: The csing cnno move in he cemen sheh. There re no rdil consrins. The induced verge sresses remin in he elsic domin. The induced herml sresses re given by he ollowing equion: S = α E 0 (8) S 0 herml induced sress α - expnsion coeicien, E - Young s modulus, - dierenil emperure o which csing is exposed. Meril properies such s he yield srengh chnge wih emperure. This leds o he c h, eleved emperures, he resisnce o csing is lower hn mbien emperure. Figure 7 shows he yield srengh vriion wih emperure or dieren OCTG grdes (Lri, 1997). Tble 1 shows he emperure vriion h induces herml sresses equl o meril yield srengh or Tble 1. Temperure induced sresses in seel pipe Grde J55 N80 P105 P110 Temp in 0 C 157 222 286 310 Yield srengh (emperure coreced) in MP 392 553 712 771 DISCUSSIONS As shown in Tble 1, ny high-enhlpy geoherml well will cuse plsic deormion even o csing srings mde o high-grde seel. I is lso imporn o noe h, or low-enhlpy geoherml wells wih emperures below 120 0 C, J55 seel-grde pipe is deque. In his cse, he well deph nd he required collpse resisnce re he prmeers h will dice he pproprie selecion o seel grde. Figure 8 shows he modiied Wöhler curve obined rom he LSSC heoreicl model. The y-xis represens he mximum dierenil emperure o which he csing is subjeced. Tble 2 shows he prmeers used or he csing igue esimions. All prmeer re shown in equion 6. Tble 2. Prmeers used or csing igue clculions Prmeer Noion Vlue Consn b -0,079 Consn c -0,869 Young s Modulus E 182000 MP Mximum srin ε 1,78 Tension srengh 720 MP Figure 8 shows h, or exreme emperure vriions, he igue resisnce o he connecions is s low s 10 cycles. I ook 12 cycles o rech rcure wih he ull-scle experimenl ess, corresponding o sress concenrion cor o 4.17.
250.00 200.00 Temperure Vriion [ 0 C] 150.00 100.00 50.00 Mesured 0.00 12 1 10 100 1000 Number o Cycles K=sress concenrion cor, [-] K = 3 K = 4,17 K = 5 Fig.8. Temperure versus cycle curve or 18 5/8 Buress connecion, grde N80 The sress concenrion cor vries rom one ype o connecion o noher, s i is uncion o connecion geomery nd is mnucuring process. The rcure obined during he experimenl invesigions ws loced he zone o imperec hred urns, suggesing h more enion mus be pid during he hred mnucuring process. For high-enhlpy geoherml well producers wih emperures o produced luid beween 100 nd 250 0 C he igue resisnce o he esed N80 Buress connecions vries beween 10 nd 110 cycles. This inormion should be considered or he plnning process o evlue he minimum projec lie ime s well s opimizing he well operions. The hred geomery, especilly he incomplee hred urns inishing ecs srongly he vlue o sress concenrion cor. For exmple lower sress concenrion cor will increse he lie ime o he csing over 1000 cycles, s shown in Figure 7. CONCLUSIONS This pper presened he heoreicl nd experimenl work crried ou o evlue LCF resisnce o n 18-5/8 inch dimeer csing wih Buress hred connecions (ypiclly used in geoherml well compleions). The resuls showed h, under exreme lods, he LCF resisnce o he buress hred connecion cn be s low s 10 cycles. More ull-scle experimenl work is required o exend he vlidiy o he resuls obined wih his sudy o oher ypes o hreded connecions. REFERENCES Bohm, B. (2000), Drilling Geoherml Well ISO, GHC Bullein, December 2000, 12-19. Buch, A., (1988), Figue srengh Clculion, TrnsTech S, Swizerlnd, 1988. Joki, H. (2000), High Angle Direcionl Drilling Tkigmi Geoherml Field, Proceedings World Geoherml Congress 2000, Kyushu-Tohoku, Jpn, My 28-June 10, 2000. Lri, I, Rezisen Colonelor de Bulrne Tube in Sondele Supuse Procesului de Injecioe de Abur Inernl Repor, ICPT Cmpin, 1997 Rgnrs, K., Benediksson, S. (1980) Drilling o 2000 m (6562 ) Borehole or Geoherml Sem in Icelnd, DOE Repor. Tnzer, H., (2001), Developmen o Ho Dry Rock Technology, Geo-He Cener Qurerly Bullein, Vol. 22, No.4, December 2001. Teodoriu, C. (2005) Cerceri privind comporre merilelor s imbinrilor ilee in sondele supuse procesului de injecie de bur, PhD Thesis, Universie Perol-Gze Ploiesi, Romni, 2005. Ulmnu, V., (2001), Verhren zur Lebensduerbschäzung der Tiepumpgesänge nch dem örlichen Konzep, Erdöl Erdgs Kohle, No.4, 2001. Wrren, T.,M., e l. (2000) - Csing Drilling Applicion Design Considerions, presened he 2000 IADC/SPE Drilling Conerence, New Orlens, Lousin. Willimson, K.H. e l.., (2001) Geoherml Power Technology. Proceedings o he IEEE, Vol. 89, No. 12, December 2001. Wicher, J.C. (2001), Geoherml Direc-Use Well or Commercil Greenhouses Rdium Springs, New Mexico, GHC Bullein, December 2001, 1-7. DIN971 (1990) Germn Sndrd DIN 471, Sicherungsringe (Hleringe) ür Wellen, Regelusührung und schwere Ausührung, 1990