Global Analysis of a Flexible Riser

J. Marine. Sci. Appl. (2011) 10: 478-484DO: 1.007/511804-011-1094-x4Global Analysis of a Flexible RiserLiping Sun and Bo QiCollege of Shipbuilding and Ocean Engineering. Harbin Engineering Universily, Harbin 150001, ChinaAbstract: The mechanical performance of a flexible riser is more outstanding than other risers in violentenvironmental conditions. Based on the lumped mass method, a steep wave flexible riser configurationattached to a Floating Production Storage and Offloading (FPSO) has been applied to a global analysis in orderto acquire the static and dynamic behavior of the flexible riser. The riser was divided into a series of straightmassless line segments with a node at each end. Only the axial and torsional properties of the line weremodeled, while the mass, weight, and buoyancy were all lumped to the nodes. Four diferent buoyancy modulelengths have been made to demonstrate the importance of mode selection, so as to confirm the optimumbuoyancy module length. The results in the sensitivity study show that the flexible riser is not very sensitive tothe ocean current, and the buoyancy module can reduce the Von Mises stress and improve the mechanicalperformance of the flexible riser. Shorter buoyancy module length can reduce the riser effective tension in aspecific range of the buoyancy module length when other parameters are constant, but it can also increase themaximum curvature of the riser. As a result, all kinds of the riser performances should be taken into account inorder to select the most appropriate buoyancy module length.Keywords: flexible riser; lumped mass method; global analysis; sensitivity studyArticle ID: 1671-9433(2011)04-0478-071 Introductionbetween the numerical results and the analytical solution ones(Bahtui et al, 2008). Zhimin Tan, Peter Quggin and TerryDue to the effect of the ocean environment on oceanSheldrake presented a "state-ofthe-art" dynamic simulationplatforms, the motion characteristics are of diverse kinds, andin time domain of the 3D bending hysteresis behaviors of athere are various requirements for the riser systems. Theflexible riser under offshore environment loads (Tan et al,capability of a flexible riser is different from other risers2009). Based on the Algorithmic Processor Descriptionbecause of its special structure, which consists of severalLanguage (APDL), Jifang Zeng realized the program andlayers of different materials. It is superior to other kinds ofatomization modeling (Zeng, 2009).risers because of its larger bending capability, and it can beapplied to more undesirable environmental conditions.As a lot of detailed and local analysis has been completed bythe anterior studies, this paper adopts the lumped massFlexible risers are slender marine structures which are widelymethod to perform global analysis on the flexible riser;used in deepwater exploration and also to deliver oil andfurthermore, the ocean wave and current loads are simplifiednatural gas from the subsea to surface units. In deep-waterin order to represent the static and dynamic response betterapplications, because of the low bending siffness comparedunder the effect of an ocean environment.to axial and torsional stiffness, flexible risers can suffer largedisplacements, causing them to demand geometrically special2 Mechanical model of a flexible risernonlinear analysis (Kordkheili and Bahai, 2007).Based on the lumped mass method, OrcaFlex is used toFlexible risers have many arrangement forms (Bai and Bai,simulate the flexible riser. The analysis is based on the2005), such as Free Hanging Catenary, Lazy Wave, Steepfollowing assumptions: (1) Geometric property and materialWave, and Pliant Wave (azy S, Steep S). Based on thecharacteristics of the flexible riser units are constant. (2) Thelumped mass method, Wang and Chen(1991)established abottom end of theiser is completely constrained in allnon-linear element dynamic analysis method considering thedirections and rotations. (3) Considering the effect of theflowing of fluid in a pipe, and the results were compared todeadweight and the extemal load of the riser, the analysisformer outcomes (Wang and Chen, 1991), Bahtui et al(2008)belongs to the category of small strain and large deformationaccomplished a detailed finite element analysis of unbondedissues (Zhong, 2007). (4) The Stokes 5th wave is used toflexible risers using ABAQUS, and made a comparisonsimulate the motion of the platform to act as the boundaryReceived date; 2011-01-05.中国煤化工Foundation item: the National Natural Science Fundation of China2.1 The loadTMHCNMHGCorreponding author Emal: suinipiaheue cnO500yIn the presence of waves, the current must be extrapolatedabove the still water level. In this paper it is assumed that the。Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2011.Journal of Marine Science and Application (2011) 10: 478-48479surface current applies to all levels above the water surface.Current direction is specified and does not vary with depth.Speed varies with position (X, Y, Z) according to the formulaas follows:S=s, +(S,-,)x((z- z,)(, -Z,))^(I/Ex)where Ss and S, are the current speed on the surface andseabed, Ex is the power law exponent, Zs is the water surfaceof the Z level, all as specifed in the data, and Zz, is the Z levelof the seabed directly below (X,Y).To calculate the current load, an extended form of Morison'sequation has been used. Morison's equation was originallyFig.1 Model of the fnexible riserformulated for calculating the wave loads on fixed verticalcylinders. There are two force components; one is related to2.3 Building the model of the flexible riserwater particle acceleration (the 'inertia' force) and the otherUsing OrcaFlex to simulate the flexible riser, the bottom endrelated to water particle velocity (the‘drag' force).of the riser is completely constrained in all directions androtations, and the Stokes 5th wave is applied to the platform.The extended form of Morison's equation used in this paperThe displacement of the connection point between FPSO andriser is taken as the boundary condition at the top end of theriser. As the dynamic performance of the flexible riser isFw =(O.a. +C。.0.a,)+5P.V,|4,|C。.Ageometrically non-linear, the results of the frequency domainIn the formula, Fw is the wave force, O is the mass of fluidanalysis are not accurate; time domain analysis is commonlydisplaced by the body, aw is the fluid acceleration relative toused to analyze the performance of flexible riser.earth, C。is the added mass coefficient for the body, a, is thefluid acceleration relative to the body,p is the density of water,Based on the lumped mass method, the riser is modeled as aV, is the fluid velocity relative to the body, Co is the dragline, which is divided into a series of line segments. The linecofficient, and A is the drag area. The term in parentheses issegments only model the axial and torsional properties of thethe inertia force, and the other is the drag force. In flexibleline. The other properties (mass, weight, buoyancy, etc.) areriser analysis, CD varies between 0.7 and 1.2.all lumped to the nodes. The lumped mass model is shown inFig.2 (OrcaFlex User Manual).2.2 Boundary conditionActual PipeDiscretised ModelThe top of the riser was attached to an FPSO, using theresponse amplitude operator (RAO) of the FPSO as theEnd A. Node 1boundary condition at the top end of the riser. The bottom endof the riser is fixed to the seabed; the seabed friction is notSegmentlconsidered here. It is very important to obtain accurate valuesof the RAO amplitude and phase if the dynamics of theNode 2system are to be correctly modeled.The model of the flexible riser is shown in Fig.1. Also, theSegmen23 Segmen2fixed bend siffener at the lower end is modeled as two elasticsolid blocks with no rotation, which are connected at theirinterface. The turret at the top end is modeled as an elasticsolid cylinder connected to the FPSO.Segment3(a) Line model中国煤化工MHCNMH G.480 .Liping Sur, et al. Global Analysis of a Flexble Riserthrough the turret, is 15 degree from the vertical, while theSx.Tosion springin-built angle at the pipeline end manifold (PLEM) is 20VoK +damperyedegree from vertical. The buoyancy elements will be clampedto the flexile riser over a length of 70 m, starting from a pointAxial spring.10 m away from the lower end of the riser.+damperTable 2 The fundamenta! parameters of the riserNx.,NodeBending springscasevalue+dampersTotal length185mXYNz(exial diretion)Pipe inner diameter0.3048m~a,+Pipe overall diameter0.4884mThe density of riser material242.5kg/mDesign pressure55.0 bargDesign temperature87.0C .Bending siffness at 20 C390 kNm^2(b) Detailed representation of Line modelFig.2 The theory of the lumped mass methodAxial tensile siffness907 MNTorsional siffness224KNm^2/deg3 Global analysisRelative gravity1.26Global analysis of the flexible riser is performed to evaluatePer Buoyancy Module Weight674.6kgthe global load effects on the riser. In order to evaluate themud density780kg/mperformance of the riser, the static configuration andThe fundamental parameter of the FPSO is shown as follows.extreme response of displacement, curvature, force, andmoment from environmental effects should be calculated inThe RAO of the FPSO is used as the boundary condition atthe global analysis.the top end of the riser, considering the interaction betweenhe FPSO and flexible riser. The RAO is obtained fromThe global analysis includes two aspects: static analysishydrodynamic calculation.and dynamic analysis. The static analysis can determine theTable 3 The fundamental parameters of the FPSOequilibrium configuration of the system under weight,Length overall /m285mbuoyancy, and drag force. Aditionally, it can also provide astarting configuration for dynamic analysis. In most cases, theBreadth./m63mstatic equilibrium configuration is the best starting point forDepth moulded /m2mdynamic analysis. The dynamic analysis is a time simulationDraft (Fully loaded)./m24.45mof the motion of the model over a specified period of time,Topside weight (operational)./t35,860starting fom the position derived by the static analysis.Mooring systemthe single point mooringThe environment defines the conditions to which the objectsin the model are subiected, and it consists of the current,waves, and seabed. The operating water depth is 91.5m, while4 The results and discussionthe influence by the change of tide has not been considered.4.1 The static analysisThe wave height is 7.3m, and the wave period is 11 seconds.The aim of static analysis is to determine the initial staticThe current data is shown in Table 1.geometryf the flexible riser configuration. The designTable 1 The current velocity of 3 different return periodsparameters to be selected in the static analysis are typicallylength, weight, buoyancy requirements, and location of1 year returm10-year-returm100-year-retumXHseabed touchdown point and subsea buoy. The loads/m:/mrs^considered in the static analysis stage are generally gravity,0.12.24buoyancy, intermal fluid, and current loads.).50.911.241.490.90.770.991.17Afer the static analysis, the Z-axis coordinate of the flexibleriser is shown in Fig.3.The fundamental parameter of the riser is shown in Table 2.中国煤化工The flexible riser has a fixed bend sifener at the lower endMHCNMHGand a sliding bend sifener at the upper end. The in-builtangle of the flange on the connecting pipe, which is running.Liping Sun, et al. Global Analysis of a Flexible Risercurent conditions. The minimum bend radii of the flexible0.025 rriser on the three different current conditions are listed inTable 4, and they are all smaller than the designed minimum。0.020 tones, making them safe. However, the bend radius has anabrupt change in the position of the riser where the structure. 0.015also has an abrupt change. For the three different currents, the0.010 tbend radi of the riser segment which has a buoyancy moduleare almost the same.0.0050255075100125150175200- one hundred years retum160ten years returmFig.8 The curvature of the flexible riser on three differentE 120-current conditions in dynamic analysisThe curvatures of the riser under threshown as Fig.8. The minimum and maximum curvatures of80255075100125150175200the riser on three different current conditions are listed inArc length/mTable 5.-0 one hundred years returm-一 ten years returm一one year returnThe three curves are almost the same, only differing in theFig.6 The effective tension of the flexible riser on threeareas ranging from 0 to 100m and 125m to 185m along thedifferent kinds of current conditions in dynamic analysisarc length of the riser. The riser segments from 0 to 100m arebare, without the buoyancy module; the maximum curvature600in the case of the one-hundred-year retum period current isminimum, while the value on the one-year retum period500 tcurrent condition is the biggest. The riser segments from125m to 185m are wrapped with a buoyancy module, and thei 400maximum curvature value in the case of theone-hundred-year returm period current is the biggest, while， 30on the one-year return period current condition it is minimum.It is clear that the buoyancy module has an effect on the200mechanical performance of the riser. The buoyancy modulemakes the riser less sensitive to the current load.100Fig.9 presents the same trend for the bending moments asFig.8 for the curvature on three current conditions, becausethe bending moment is related to the curvature.-一ten years return -一one year retum一t - one hundred years retum8Fig.7 The bend radius of the flexible riser on three differentTable 5 The minimum and maximum curvatures of theflexible riserCurrentsMinimumMaximum82curvature/ 1mcurvature/ I'nOne year returmperiod0.04255075100125150175200Arc length /mTen years retum :0.027 .中国煤化工One hundred years00.024CNMHGreturmreturm periodMHFig.9 The bending moment of the flexible riser on threedifferent current conditions in dynamic analysis.484 .Liping Sun, et al. Global Analysis of a Flexible RiserKordkheili SAH, Bahai H (2007). Non-linear finite element static5 Conclusionsanalysis of flexible risers with a touch down boundaryBased on the lumped mass method, global analysis of thecondition. Proceedings of the 26th International Conferenceflexible riser has been made. A simplification has also beenon Offshore Mechanics and Arctic Engineering, Califormia,USA, 1-5.performned on the ocean wave and current load. The model ofORCAFLEX Help File and User Manual, available froma flexible riser has been built in order to analyze the dynamicwww.orcina.com.response of the riser on three diferent current conditions. TheTan Zhimin, Quiggin P, Sheldrake T (2009). Time domain simulationeffect of the buoyancy module length of the riser has alsoof the 3D bending hysteresis behavior of an unbonded flexiblebeen considered in this study. The results show that, theriser. Journal of Ofshore Mechanics and Arctic Engineering, 131,flexible riser is not very sensitive to the ocean curent, and the031301-1-8.buoyancy module can reduce the Von Mises stress whileWang Anjiao, Chen Jiajing (1991). Non-linear dynamic analysis offlexible riser. Ocean Engineering, 9(3), 12-22. (in Chinese)improving the mechanical performance of the flexible riser.Zeng Jifang (2009). Mechanical behavior and optimum design ofAlso, the bending moment is reltive to the curvature. Inocean flexible riser. Master thesis, Dalian University ofgeneral, an abrupt change of the structure can induce anZhong Li (2007). Mechanics Characteristic Analysis of DeepTechnology,42- 54. (in Chinese)abrupt change of the mechanical performance.Water Dilling Riser. Oil Dirilling & Production Technology.29(1), 19-21. (in Chinese)A comparison of results of the four risers with different lengthof buoyancy modules demonstrates the importance ofmodule length selection. When other parameters are constant,increasing the buoyancy module length can enhance theLiping Sun was borm in 1962. She is a professor atminimum bend radius of the riser, and it can also reduce theHarbin Engineering University. Her currentresearch interests include deepwater technology.bending moment. However, that is not always reasonable, forit works in a specified range of buoyancy module length. Anextremely long or short buoyancy module will weaken themechanical behavior of the riser.ReferencesBo Qi was borm in 1986. She is a graduate studentAPI SPEC17B (2002). American petroleum institute.of Harbin Engineering University. Her currentAPI 17J (1999)， second edition, Specification for Unbondedresearch interests include drilling risers andFlexible Pipeflexible risers.Bahtui A, Bahai H, Alfano G (2008). A finite element analysis forunbonded flexible risers under torsion. Journal of OfshoreMechanics and Arctic Engineering, vol.130, 041301-1-4.Bai Yong, Bai Qiang (2005). Subsea Pipelines and Risers. ElsevierLtd, USA, 401-402.Chung JS, Cheng BR (1996). Effects of elastic joints on 3-Dnonlinear responses of a deep-oceanpipe: modeling anboundary conditions. International Journal of Ofshore andPolar Engineering, 6(3), 203-211中国煤化工MHCNMH G.