Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008

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1 Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn Abstract Marne rser s an mportant component for the offshore ol platforms. Rser falure results n cessaton of producton and may lead to spllage and polluton. The deepwater rsers under cyclc load due to ocean current experence sgnfcant gue damage. Ths paper focuses on the fundamental gue analyss phlosophy of the deepwater rsers, coverng the dscusson of dfferent sources of cyclc load, S-N curves and combnaton of gue damages. Besdes the determnstc approach, the rsk based gue analyss s also studed n the probablstc feld. 1. Introducton Ol and natural gas have been produced from offshore locatons snce 1950s. At that tme all the platforms were fxed platforms whch were sttng on the seabed. Wth the ol exploraton and producton move to the deeper water, the other types of ol platform, such as tenson-leg platforms, floatng producton system (FPS) become more popular (See Fgure 1). Fgure 1 Fxed platform and Floatng producton system Rsers are the structure systems whch connect the platforms at the ocean surface and the structures on the seabed. The man functon of the rser system s to convey flud (crude 1

2 ol or the natural gas) between wells and platforms. Typcally the rsers are made of steel or ttanum ppe wth an outer dameter less than 30 nches and a wall thckness less than 1 nch (See Fgure 2). Wth the producton movng nto deeper water, the rsers become longer and longer, usually are about 3,000 ~ 6000 feet, and the longest ones are over 10,000 feet. The rsers are prone to be vbrated under the exctaton of current flow due to ther slenderness and low-dampng ratos. The sustan vbraton may cause gue damage whch may lead to cessaton of producton or spllage and polluton to the ocean. In ths paper, the basc steps of rser gue analyss were outlned. The procedures to estmate the probablty of gue falure usng Monte Carlo smulaton were ntroduced also. Fgure 2 Rsers 2 Rser Fatgue Analyss 2.1 Two types of components Generally the gue lfe conssts of two phases: crack ntaton and crack propagaton. For the un-welded components, such as the seamless ppes, the crack ntaton perod takes over 95% of the total gue lfe. And the gue strength ncreases wth materal tensle strength. For the welded jonts, the ntal cracks, such as the welded toes, always present. The crack propagaton perod represents the bulk of the total gue lfe. The crack propagaton rate s dependent on the propertes of base materal, envronment and other factors, so there s no consstent trend between gue strength and materal tensle strength. 2.2 Fatgue crteron and S-N curves The gue crteron s represented by D DFF 1 where D = Accumulated gue damage, estmated by Palmgren-Mner rule DFF = Desgn gue factor, whch depends on the safety classes, see Table 1. 2

3 Table 1 Classfcaton of Safety class and DFF values Safety class Defnton DFF Low Where falure mples low rsk of human njury and mnor 3.0 envronmental and economc consequences Normal Where falure mples rsk of human njury, sgnfcant 6.0 envronmental polluton or very hgh economc or poltcal consequences Hgh Where falure mples hgh rsk of human njury, sgnfcant envronmental polluton or very hgh economc or poltcal consequences 10.0 If approprate, fracture mechancs may be used to analyze the rser gue. However, the S-N curves based approach s commonly used whch correlates the number of stress cycles to falure and a constant stress range. N = a S m log( N ) = log( a) m log( S ) N: Number of stress cycles to falure S: Constant stress range a, m : Emprcal constants obtaned from experments 2.3 Fatgue loads Rser gue analyss should consder all relevant cyclc load effects, such as (a) Frst order wave effects (b) Second order floater moton (c) Vortex nduced vbraton (d) Thermal and pressure nduced stress cycles (e) Collsons (f) Fabrcaton and nstallaton loads (g) Others cyclc loads. Typcally, frst order wave effects, second order floater moton, and vortex nduced vbraton have relatvely larger contrbuton to rser gue. Ths paper wll focus on the analyss of gue due to the frst order wave effects and second order floater moton. The frst order wave effects s also called wave frequency effects, whch ncludes wave frequency floater motons and drect wave loadng on rsers. Second order floater moton means low frequency (the frequency s much lower than the natural frequency) response of floater motons, so also called low frequency effects. 3 Long-term gue damage due to wave frequency and low frequency effects The general approach for estmate the wave frequency and low frequency gue damage takes the followng procedures. 3

4 (a) Dvde all sea current state data nto a number of representatve blocks; (b) Use a sngle sea state to represent all the sea-state wthn one block. The probabltes of occurrence for all sea-states wthn the block are lumped to the selected sea-state. Here should be noted that, the selected sea-state should gve equal or greater damage than all the orgnal sea-state wth the block. (c) The long-term gue damage s equal to the weghted summaton of all short-term gue damage, expressed as D N = s = 1 D P n whch D : Long-term gue damage N S : Number of sngle sea-state, number of blocks of sea-state D : Short-term gue damage P : Sea-state probablty Table 2 and Table 3 gve an example of the scattered sea states and the lumped sea states. Table 2 shows the probablty of scatted sea states whch are grouped by wave heght ( H s ) and wave perod ( T p ). For example the sea state havng wave perod Tp = 8 ~ 10 sec. and wave heght H s = 1.00 ~ meters accounts for 4.74% of total occurrence. Note that ths table s uncompleted. It does not nclude the sea states havng perod 4~6 sec. All the scattered sea states were lumped and represented by 7 representatve sea states, whch are summarzed n Table 3. H se s the effectve wave heght for each representatve sea state, whch wll gve equvalent gue damage compared to all the scattered sea state n that bn. Calculate the short term gue damage for each lumped sea state, weghed by the sea state probablty and the fnal summaton wll gve the long term gue damage. 4

5 Table 2 Scattered sea states (uncompleted) Table 3 Lumped sea states 4 Short Term Fatgue -S-N Curves Approach The S-N curves approach s the general practce to calculate the short term gue n the rser ndustry. Besdes the lnear S-N curves, the blnear S-N curves represent the expermental data better and are frequently used. So here the method of usng the blnear S-N curves and the Mner-Palmgren rule to estmate the accumulated gue damage are ntroduced. 4.1 Blnear S-N curves N a1 S = a2 S m1 m2 S > S S S sw sw As same as the lnear S-N curves, N s the number of stress cycles to falure, for a constant stress range S. a, a and m, m are emprcal constants obtaned from experments. The basc defnton of blnear S-N curves s showed n a log-log scaled plot, see Fgure 3. 5

6 Fgure 3 Defnton of Blnear S-N curves (log-log scales) 4.2 Mner-Palmgren rule Palmgren-Mner rule s used for accumulaton of gue damage caused by varable stress ampltudes. The basc equaton s D = n( S ) N( S ) When n ( S ) s the number of stress cycles wth stress range S ; and N ( S ) s the number of stress cycles to falure wth stress range S. For a gven tme T, the accumulated gue damage can be obtaned from the followng equaton, Tf S sw V m Tf 2 D = S f fs( s) ds a 0 2 V m1 s( s) ds + S a S sw 1 In whch, f = Mean frequency of stress cycles V f s (s) = Probablty densty functon for stress cycles The above equatons consttute the basc formulatons for accumulated gue damage under statonary envronmental condtons 6

7 5 Fatgue Stress The gue stress consdered for rsers s the prncple stress wth a thckness correcton factor. 5.1 Thckness correcton factor S S = 0 t SCF t ref k Where: S 0 = Nomnal stress range SCF = Stress concentraton factor k t t ref than a reference wall thckness t t = t = Thckness correcton factor. Apples for ppes wth a wall thckness t greater norm norm 0.5 t corr before after t ref = 25mm nstallaton nstallaton t norm = Nomnal ppe wall thckness t = Corroson allowance, assumng lnear corroson loss corr 5.2 Nomnal stress The nomnal stress component of ppes s a lnear combnaton of the axal and bendng stresses gven by σ ( t) = σ ( t) + σ ( θ, t) a Te ( t) Axal stress: σ a ( t) = π ( D t ) t M D t Bendng stress: σ ( ) M ( θ, t) = M y ( t)sn( θ ) + M Z ( t)cos( θ ) 2I In whch, D s the outer dameter. T e s the effectve tenson. M y and M Z are the bendng moments about the local y and z axes, I s the moment of nerta. See Fgure 4. The stress vares along the crcumference, so at least 8 ponts along the crcumference needs to be analyzed to dentfy the most crtcal locaton. 7

8 Fgure 4 Cross-secton of rsers 6. Uncertantes of Fatgue Estmate and Monte Carlo Smulaton Many factors assocate wth rser gue analyss, ncludng the nput varables (such as drag coeffcent, ppe wall thckness, etc.), are stochastc n nature. These uncertantes need to be studed and the probablstc models for all stochastc varables should be set up based on lterature, experence and data analyss. If lackng of nformaton, the values n Table 4 may be used. Table 4 Stochastc varables After approprate probablstc models obtaned for all the stochastc varables, Monte Carlo smulaton can be used to get the rsk based gue estmaton. The advantage of Monte Carlo smulaton s that gven accurate probablstc models any desred level of accuracy can be acheved by ncreasng the number of teraton. The basc steps of the Monte Carlo smulatons are outlned as followng, (1) Establsh the probablstc model (mode type, mean and standard devaton) for each ndependent basc nput varables; 8

9 (2) Samplng probablty dstrbuton to obtan pont estmate for each ndependent nput varable; (3) Calculate dependent and then output varables; (4) Do loop for sets 2-3 (typcally more than 100,000 tmes for satsfed accuracy); (5) Post-process results to obtan probablstc dstrbuton of the output. 7. Summary (1) Fatgue damage estmaton s crtcal mportant for rser desgn and analyss. Unfortunately, the procedures and consderatons are very complex. (2) Blnear S-N curves and Mner rule are the typcal approach. (3) Fatgue damage and gue lfe can be estmated by usng the mean value of the nput varables. (4) Probablty of gue falure can be estmated by the stochastc model of the nput varables and Monte Carlo smulaton. 8. Reference DNV, 2005, Rser gue, DNV-RP-F204 Sen, T.K., Probablty of gue falure n steel catenary rsers n Deep Water, Journal of Engneerng Mechancs, Sep