Shallow Water Effects on Surge Motion and Load of Soft Yoke Moored FPSO

China Ocean Engineering , Vol.21 ,No.2 ,pp. 187 - 196C 2007 China Ocean Press , ISSN 0890-5487Shallow Water Effects on Surge Motion and Load of SoftYoke Moored FPSOXIAO Long-fei( 肖龙飞)' , YANG Jian-min(杨建民)and LI Xin(李欣)State Key Laboratory of Ocean Engineering , Shanghai Jiao Tong University ,Shanghai 200030 ,China( Received 29 May 2006 ; accepted 20 March 2007 )ABSTRACTMuch attention should be paid to a large FPS0 moored permanently in an oil field with water depth of only a-bout 20 m , since shallow water effects on the hydrodynamics may bring about collision and damage. A 160kDWTFPSO with a permanent soft yoke mooring system is investigated with various shallow water depths and focuses arethe low frequency surge motion and mooring load. Computation for the FPSO system is made based on linear 3-Dpotential fluid theory and time-domain numerical simulation method. Corresponding model test is carried out in theocean engineering basin of Shanghai Jiao Tong University. It is shown that , in the surge natural period , low fre-quency surge motion and mooring force increase remarkably with the decrease of water depth. Especially , thesmaller the ratio of water depth and draught is , the quicker the increase is. The shallow water effects should betaken into account carefully for determining the design load of a single point mooring system.Key words : FPSO ishallow water ; surge ; sofi yoke mooring system1. IntroductionFPSO ( Floating Production , Storage and Offloading ) has become a very popular solution inoffshore oil exploitations in China( Sun ,2005 ) ,as in the world ( Dominic ,2003 ). Much atten-tion should be paid to a large FPSO moored permanently by a soft yoke mooring system in oil fieldwith water depth of only about 20 m ,such as in the Bohai Bay of China( Liet al. ,2004 ;Xiao etal. , 2006 ) , since the effects of shallow water on FPSO hydrodynamics may make the hull collidethe seabed and mooring system and then bring about damage.Yang et al.( 2002 ) investigated vertical motions and touching seabed of a 300 kDWT FPSOin shallow water through model test and discovered shallow water effects on large FPSO. Li et al.( 2003 ) reported similar conclusions by numerical simulation. Subsequently , the added mass ,damping , natural period and wave-induced loads of FPSO in various shallow water depths are in-vestigated( Xiaoet al. ,2004 ,2005 ;Xie et a中国煤化工2004 ) dscussed shallo .water effects and provided guidance regardingMHCNMH Gating the low frequencymotions of LNG carriers moored in shallow water.* This work was financially supported by the National High Technology and Development Program of China( Grant No+ 2004AA616180 )1 Corresponding althor. E-mail : xiaolf@ sjtu. edu. cn188XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196A 160 kDWT FPSO with a permanent soft yoke mooring system is investigated and the lowfrequency surge motion and mooring force are focused in the present paper. The full loadeddraught of the FPSO is 14.5 m. In order to investigate the shallow water effects on the hydrody-namic performance of FPSO , a number of shallow water depths are considered within a range from16.7 m to43.5 m. Accordingly , the ratio between the water depth and the design draught iswithin a range from 1.15 to3.0. As to the environment condition , only wave condition with H13=4.1 m and T。=8.9 s isconsidered.Computation for the FPSO system is made based on linearly 3-D potential fluid theory andtime-domain numerical simulation method and corresponding model test is carried out in the oceanengineering basin of Shanghai Jiao Tong University in China. The results of surge natural perioddamping , motion and mooring force are given and analyzed in the present paper. Conclusions andsuggestions are also presented , which will be useful for the design of FPSO and single point moor-ing system in shallow water.2. Description of FPSO System and Environments2.1 FPSO VesselThe FPSO is a purpose-built vessel. The maximum storage capacity is 1000000 bbls. Theprincipal particulars are listed in Table 1.Table 1Main particulars of FPSO vesselDesignationSymbolUnitFull loadLength over alln287.4Length between perpendiculars282BreadthB51DepthDm20. 6Mean DraftTnr14.5Displacement199359Centre of gravity above baseKG12.945Centre of gravity forward from midshipLCG4.24Transverse radius of gyration16.53Longitudinal radius of gyrationKyy70.5中国煤化工2.2 Soft Yoke Mooring SystemMHCNMHGThe FPSO is permanently moored by a sont yoke' moorng system , which consists of tower ,yoke , ballast , pendants and support frame. The yoke is designed to interface with the tower andvessel while transmitting mooring forces into the bearing. The particulars and arrangement of themooring另万数据shown in Table 2 and Fig. 1.XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196189Table 2Main particulars of the mooring systemDesignation .UnitValueElevation of tower ( bearing above sea surface )n20Length of yoke35Breadth of yoke ( between 2 universal joints )28Length of pendantWeight of yoke structure .MT412Weight of pendant ( each )70Weight of ballast1500390F.P.L_ 1400036000)>5200Fig. 1. Sketch of the soft yoke mooring system.2.3Environment ConditionIn order to investigate the shallow water effects on the hydrodynamic performance of FPSO ,anumber of shallow water depths h are considered , as shown in Table 3.Table 3W ater depthsh( m)16.718.020.0 .24. 029. 043.5h/T.1.151. 241.381.662.003. 00A typical storm in the Bohai Bay of China with significant wave height H/3 of 4. 1 m andpeak wave period T, of 8.9 s is selected as v中国煤化工gular wave spectrum isJONSWAP with a peak parameter γ of3. For t:MHcNMHGisnowindandcurent.3. Basic Theory3.1 Low Frequency Equations of FPSO MotionTo s8R方熬据roblems of motions and loads of the soft yoke moored FPSO in iregular waves190XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196without wind and current , the time domain equations of motion can be split up into a wave fre-quency and a low frequency part( Wichers , 1988 ). The low frequency part as a function of thelow frequency motion in the horizontal plane can be written as :( m +μμ )成2) +μ12iz+μ+( B1+ B)x2)= F"Wawr0(2)+ Fr1r ,(1 )1从21+(m +μ2p )成2 +μ6+ B22x2= F"(2 )andμ+μoaxt° +(I +μ)成°+ B.;= F"(3 )in which :x;= motion in surge( i=1 ),sway( i=2 ) and yaw( i=6 ) direction ;m J =vessel mass and yaw moment of inertia ;μ: = added mass cofficients ( low frequency limits from potential theory ) ;B; = linear damping coefficient of surge , sway and yaw ;B wdd = linear wave drift damping coffcient of surge ;F"v(2)= low frequency wave drift forces ; .prmor= dynamic mooring forces due to wave and low frequency motions.The added mass can be determined relatively straight forward by means of 3-D potential fluidtheory at low frequencies. The linear hydrodynamic damping cofficient ( still water and wave driftdamping ) can be determined from the data( Wichers , 1988 ). The wave drift force is calculatedby means of a second order impulse response technique by use of the second order wave drift forcetransfer function and the wave train as measured in the basin. The mooring force is calculated bythe coupled dynamic analysis on the soft yoke mooring system.3.2 Wave Frequency Equations of FPSO MotionThe wave frequency equations of motion can be expressed in linear hydrodynamic terms as :S[(M,+u,成'(t)+[K1-T)减(r)r +C,"(1)]= F"wd'(t)+ F"fori =1 ,2....6(4 )where ,x( t ) is the wave frequency motion , C; is the restoring matrix , and M; is the inertia ma-trix. K,( t ) , the retardation function , which denotes the influence of the memory effect on thefree-surface , can be obtained byK(t) =π Jo入(w)cos(ot)do,(5 )Fr"wav('( t ) is the first-order wave force. Accoitn 少.irulse technique ,Fr",end ")( t ) can be derived by the first-order wave forc.YH中国煤化工,w ) as follows :CNMHGFi"nd"()=h(t -τ )m( T )dr.(6)Here ,以T ) is the wave elevation at time T and can be considered as an impulse function & T ).h( t )andf( w ) are a couple of Fourier transformation.XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 1961913.3 Equations of Soft Yoke Mooring SystemThe mooring force and the FPSO motions are coupled dynamically and should be solved sim-ultaneously as an integrated system. There are 3 axis around which the yoke can rotate freely andas a result the yoke motion can be defined by 3 rotating angles. The equations of the dynamics ofsoft yoke mooring system are expressed as follows :pJzi+Bzi=Mz+MRzJnβ+Bβ= Mon +Mxy + Mm + Mgm(7 )Ja+B,c=Mx+Mrawhere :ax β and γ denote roll , pitch and yaw angle of yoke , respectively ;J; and B; are the rotating inertia and damping of yoke ;M: and MRi are the moments around rotating axis due to pendant tension ;My and Mp: are the moments around rotating axis due to the weights of yoke structure andballast.All the variables mentioned above except for the yoke angles are determined by FPSO mo-tions. Therefore , by solving Eq. ( 7 ) , the yoke motion can be obtained , and then the mooringforces can be computed with the equations of dynamic equilibrium of yoke. .4. Computation and Model Test4.1 ComputationBased on the theory mentioned above , the motion and loads of the 160kDWT FPSO in vari-ous environments can be calculated in time domain. The mesh arangement of the wetted surfaceof the FPSO is shown in Fig. 2 with 432 x2 panels.Fig. 2. Meshing of the wetted surfaceof FPSO.L4.2 Model TestModel test is carried out in the wave basin of the State Key Laboratory of Ocean Engineering ,Shanghai Jiao Tong University. The linear scale ratio is chosen as 64. A model of soft yoke moor-ing system is installed. All the models , environments and instruments are carefully calibrated. Anoptical non-contact system with active infrared中国煤化工B in Sweden is used tomeasure the motion of the FPSO model.YHCNMHGFig.3 shows the calibration of one wave case. Fig. 4 shows the rregular wave test of themodels of FPSO and soft yoke mooring system. The time duration of each simulation and modeltest is selected as 1. 5 hours. .192XIA0 Long-fei et al. /China Ocean Engineering ,21(2 ),187- 196Power spctrum densityEnvelope spctrum density。Measured。。Mersud一- Targel .一T anpe宣4中。9。0+01.:2).00.210Froqueney (nds)Frequeney (ads)Fig.3. The target and measured wave spectrums.Fig. 4. Model test of FPSO and softyoke mooring system.5. Results and Analyses5.1 Surge Period and Damping in Various Water DepthsKeeping the stiffness of the mooring system to be constant , surge decay tests are conducted instill water with various water depths. The extinction curves are measured and the natural periodsand damping coeffcients of surge are derived ,as shown in Fig. 5 and Fig. 6.0.05T-92.sμ=0.03694s 930.03www.士Natral Period0.01- + DampingCoef.9c200800 1000 1200.0 12 1.1.6 1.8 2.0 2.Time (田)h/TFig.5. Curve of surge extinctionFig.6. Natural period and damping coef. surgein still water( h=20 m).in various water depths.It is shown that the long natural period and the law damninr inaroace with the decrease of wa-中国煤化工ter depth. Especially , the smaller the ratio of w: the quicker the increaseof the natural period and the damping will be. ......TYHCNMH Gj-- pd means the decrease oflow frequency. Therefore , in combination with the envelope wave spectrum in Fig. 3 ,a conclu-sion can be drawn that the low frequency wave drift force on FPSO will be getting larger in shallo-wer water.5.2 Surge M8ta in Various Water DepthsXIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196193Keeping the stiffness of the mooring system to be constant , irregular wave tests are conductednumerically and experimentally in the same wave condition with various water depths. The surgemotion and mooring force are computed and measured , and spectrums are derived.The calculated and measured time traces of surge motion are compared in Fig. 7. It can be .seen that the agreement is satisfactory. The surge motion is split into LF( low frequency ) part andHF ( high frequency ) part , and the spectrums in various water depths are shown in Fig. 8.1..-.-- . Cal. Surge. Mea. Surge宜-10010002000300040005000Time (s)Fig. 7. Calculated and measured time traces of surge motion.Power spectrua desity(cal culsted)Power spectnum desity(measurd)1400b-16.7m1200b-18.0mb=18.0mb- 20.0m一一一 一be 20.0m........ b-24.0mh-29.0mh-43.5m8006004002000.0.05 .0.10.150.200.05Frequeacy(rnd/s)Fraquency(nad/s)Power spectnum deosityh=16.7mFig.8. LF and HF surge spectrums in0.0hE1Romvarious water depths.0.03 Ib-29.0m .中国煤化工MHCNMHG.000.60.81.01.21.4Frouency(rnd/s)194XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196It is shown that the power of the surge motion is almost the LF part ,and the HF part is negli-gible comparatively , especially in ultra- shallow water. The decrease of water depth of shallow wa-ter leads to enormous increase of the LF response of surge motion while the HF response keeps al-most the same.Although the surge damping increases in shallow water as mentioned before , the surge motionstill increases enormously. It indicates that the low frequency wave drift force on FPSO increasesenormously in shallow water. The great increase of wave drift force may be caused not only by thechange of natural period but also by the nonlinearity of the shallow water waves. Much more atten-tion should be paid to the interaction between nonlinear shallow water waves and FPSO.5.3 Surge Load in Various Water DepthsThe mooring forces in surge direction are calculated and measured , and the spectrums arederived , too. The calculated and measured time traces of surge mooring forces are compared inFig.9 , and they are in satisfactory agreement.1500. Mca. Fx1000500-500-1000-1 50002000300040005000Time (s)Fig.9. Calculated and measured time traces of surge mooring force.The LF part and HF part of mooring force spectrums in surge with various water depths areshown in Fig. 10.As the same trend of surge motion , with the decrease of the water depth in shallow water , theLF response of surge mooring force increases enormously , while the HF response keeps almost thesame except for the water depth of 16.7 m. The LF part almost represent the total mooring force ,and the HF part is negligible comparatively , especially in ultra-shallow water.As the governing response for the design of a single point mooring system , the large mooringforce in surge direction certainly brings about I.MH中国煤化Tication off FPSO in shal-low water.CNMHG.6. Conclusions and SuggestionsThe long natural period and the low damping increase with the decrease of water depth. Es-pecially , 82熬振er the ratio of water depth and draught is ,the quicker the increase of the natu-XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196195ral period and the damping will be. As a result , the low frequency wave drift force on FPSO willbe larger in shallow water.Power specrum dsitylcalculasted)Power spectum densitymeasured)2.5e+7h-16.7mh=18.0mb-18.0m2.0e+7---- h-20.0mh -24.0m........ b-24.0mb=29.0m .--- h-29.0m1.5e+7h-43.5mL.0c+71.0e+7(间)(b5.0c+60.0.150.050.100.20Frequency(rad/i)Frequency(nd/)Power spactrum denaityb=16.7m1.2e+3.一一-- h-18.0mFig. 10. LF and HF surge load spec-b- 20.0mtrums in various water8.0e+2depths.4.0e+2(c.4.60.8.0.2Froquencyrnd1)Through comparisons , the agreement between the numerical and experimental results is satis-factory. The LF part almost represent the total surge motion and load , and the HF part is negli-gible comparatively , especially in ultra-shallow water.With the decrease of the water depth in shallow water , the LF response of surge motion andload increase enormously , while the HF response keeps almost the same. It indicates that the lowfrequency wave drift force on FPSO increases enormously in shallow water. This large amplitudeincrease of wave drift force may be caused not only by the change of natural period but also by thenonlinearity of the shallow water waves. Much more attention should be paid to the interactionmechanism between nonlinear shallow water waves and FPSO.For the design of a soft yoke mooring system , the governing response is undoubtedly thesurge motion and load. In shallow water , especially the ultra-shallow water , the surge motion andmooring force will be very large and it will very seriously effect the single point mooring system ofa large FPSO.Ref中国煤化工MYHCNMH GDominic ,H. ,Steve R. and Roger ,K. ,2003. FPSO-.. ....... .. .... production sector , Offshore ,63(8 ):56 ~57.LI Xin , YANG Jian-min and XIAO Long-fei ,2003. Motion Analysis on a Large FPSO in Shallow Water ,Proc. ofthe 13th ISOPE Conf. , Honolulu , Hawaii ,USA ,Vol 1 ,235 ~ 239.LI Xin , YANG Jian-gin and XIAO Long-fei , 2004. Hydrodynamic Behavior of FPSO under Various Loading inSurvivaP somn Shallow W ater , Journal of Hydrodynamics , Ser. B. ,16( 4 ) :442 ~ 448.196XIAO Long-fei et al. /China Ocean Engineering ,21(2 ), 187- 196Naciri ,M. , Buchner ,B. , Bunnik ,T. ,et al. ,2004. Low frequency motions of LNG carriers moored in shallowwater , Proc. of the 23rd Int. Conf. on OMAE , Vancouver , BC , Canada , Vol.3 , 995 ~ 1006.SUN Wei-zheng , 2005. 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