Coupling Motion Analysis on a Dynamic-Positioning S-laying

WU Chun-lin,SUN Li-ping,AI Shang-mao,LIU Yan

(College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China)

0 Introduction

As offshore engineering,driven by the need of resource,stepping into deeper ocean,the significant role of pipeline in the transportation of oil and gas can never be more exaggerated.However,installation of pipelines in hostile environment raises an array of serious technical and engineering challenges for installation operations.Pipeline is laid under the effect of gravity,hydrodynamic force,hydrostatic pressure,twisting,bending and friction of seabed and the risk rises sharply with water depth.Several methods have been adopted to guarantee the safety of the pipeline in deep-water and ultra-deep-water,e.g.,S-Lay,J-Lay and Reel-lay[1].Among them,S-lay is most commonly and widely used method.Because of the feature of the laying configuration,the S-lay method shows remarkable superiority in the shallow water and still takes a great share in the market for the deep-water and ultra-deep water installation.

The pipeline resembles an S while installing shown as Fig.1.The entire pipeline is geometrically divided into three parts,namely,sag-bend,overbend and middle segment.The overbend segment is supported by rollers on the stinger and its curvature is the same as the stinger.The sag-bend segment falls freely from the inflection point and extends gradually to seabed.The intermediate segment is the short part between the lift-off point and the inflection point.The segment and middle segment are modeled together as catenary in some works.

Fig.1 The configuration of the S-lay method

During the operation of S-Lay installation,the S-lay system is comprised of many parts that are influenced by each other as shown in Fig.2.The motion of vessel,especially heave and pitch,affects pipeline stress,strain and tension adversely.Meanwhile,because the nonlinear drag force on pipeline increases obviously with water depth,the pipeline in turn has a distinct influence on the vessel motion,which can be referred as:surge,sway,heave,roll,pitch,and yaw,respectively.Mutual effect between vessel and pipeline creates complex coupling issue that sensitively affects pipeline configuration and mechanical property as well as vessel motion.Accordingly,to conduct a research on the couple among pipeline,stinger and vessel and to present an accurate,efficient computational tool is crucial for the design and operation of S-lay installation.

Fig.2 Components and interaction in pipe-lay system

Conventional methods neglect the coupling of the system to realize calculation and to conserve calculation time.Namely simulation for pipeline and vessel are conducted separately.Continuous studies are made to resolve these problems.Recently,emphasis is generally put on the modeling of stinger and the interaction between rollers and pipeline.Yuan Feng et al[2]used beams with nonlinear and large deformations to model the S-lay pipeline considering the influence of ocean currents and seabed stiffness,but stinger is seen as boundary condition and no consideration is made to the separation between pipeline and stinger during calculation.Clauss and Saroukh[3]compared experimental results with numerical simulation to analyze the kinematical characteristic of a pipe-lay system composed of vessel and rigid articulated stinger,pipeline.Rinna[4]analysed the hydrodynamic characteristic of a vessel with a stinger hinged under waterline.This paper put emphasis on calculation of stinger’s total force,when considering modeling of vessel-stinger dynamic interaction.From his work,the vessel motion and stinger’s total force was obtained.Danilo et al[5]successfully simulated the process of pipeline installation using SITUA-Prosim.A generalized contact model was utilized to realize pipeline and stinger contact.Martinez and Goncalves[6]used spring to simulate the boundary condition of rollers and seabed.A numerical model was presented in the paper to analyze pipe stress.

Based on achievements of above works,this paper makes several improvements on tensioner and stinger.The dynamic,nonlinear coupling and elaborate interaction between pipeline,stinger and vessel is fully simulated by a new concept of vessel-pipeline-stinger model which is presented in this paper.Radiation-diffraction theory is adopted to calculate the wave exciting forces and radiation forces on floating bodies;Morison equation is applied to small nondiffracting structures or parts of structures;pipeline is modeled on the basis of lumped-mass theory.The date of a pipe-lay crane vessel,HYSY201,is utilized to contribute to the model the vessel which is controlled by a PID dynamic positioning system.Several simulations are conducted,using the model presented by this paper,to analyze the pipeline’s influence on vessel kinematical and mechanical characteristic and significant results are achieved.

1 Numerical model

1.1 Response equations of crane-lay-vessel

Vessel motion responses in waves are sophisticated kinematics and dynamics issue.Potential flow theory and viscous flow empirical formula can forecast the responses of vessel under the effect of waves,wind and current.For large floating body,such as vessels and platforms,Radiation-diffraction theory is a widely acknowledged tool to simulate interaction between vessel and waves despite of its limitation for only 1st and 2st Stokes Wave[7].Forces for small tubular structures or parts of structures are computed by using Morison Equation.Though this formula is empirical,it is available for 3st or 5st Stokes Wave and stream function to calculate hydrodynamic loads.

The pipe-lay system comprises a number of components which are subject to each other as well as numbers of environment factors,as shown in Fig.2.Interaction forces between vessel and pipeline are exchanged with the stinger,the laying tool on the vessel,and with the tensioner,while wind forces and fluid forces generated by waves and streams act directly on the pipeline,vessel and stinger[8].To be more specific,the pipeline,performing as a medium between environment loads and vessel,adds additional loads to the entire pipe-lay system.

Considering Dynamic-position thrust）,wave exciting force,wave radiation force,wind and current force Fcw,pipeline force,time-domain control equation of crane vessel is:

where ζ is the instant vessel displacement.Structural mass matrix M,hydrodynamic added mass matrixsystem linear damping matrix λ,total system stiffness matrix X are obtained by using potential fluid radiation-diffraction theory.Simultaneous solution can be achieved by Formula(1)to obtain responses of vessel motion under the couple of entire installation system.

The hydrodynamic impulse response function and wave diffraction force can be achieved and formulated by hydrodynamic coefficients and Fourier transform relations in the time domain[9].

Then,the radiation forces are expressed as[9]:

Morison Equation is adopted to calculate forces of small tubular structures or parts of structures.It is the sum of inertia force and drag force[10].

where DSis characteristic drag diameter;Cm,Caand CDrepresent drag coefficient,added mass coefficient,inertia coefficient,respectively;un,u˙nis fluid velocity and acceleration in the transverse direction of tube; ζ˙n, ζ¨nis structure velocity in the transverse direction of tube.

1.2 Dynamic-position of crane-lay-vessel

A nonlinear PID controller is designed to compute the input vector for the vessel in time domain.The function takes vessel instant position ζ as input.The output thrust magnitude is then formulated[11].

where ε=ζ-ζrefis the position error;KP,KI,KDrepresent proportional gain coefficient,integral gain coefficient,differential gain coefficient,respectively.

Fig.3 illustrates the geometrical relation among the vessel position,direction and the defined coordinate axis.In order to confine a vessel to pinpoint in a certain permitted range,surge,sway and yaw must be accurately controlled by the dynamic positioning system.Then the thrust is theoretical assumed to consist of three parts.

Fig.3 Geometrical relation in coordinate for DP

where Txand Tyrepresent thrust in ox and oy direction,Mzis thrust moment in oz rotation.εx,εyand εφis the position error in ox,oy and oz directions,respectively.

1.3 Collision-contact model for rollers

Since pipeline,stinger and rollers are all modeled by utilizing lumped-mass lines which are divided into finite segments[12];special consideration should be taken to simulate the contact between pipeline and rollers.The method assumes spring stiffness and damping values to be constant,and neglects friction.

In this model,lines are pushed apart if they are about to penetrate through one another,and are permitted to separate again after contact.Collision between each line segment and every segment in every other line in the model is first checked.Obviously,to check the whole pipeline from one end to the other for collision is time consuming.Therefore,line collision is only activated within the length of the stinger.The collision check between segment S1 on line L1 and segment S2 on a different line L2 is done as follows.

Let the contact radius of the two segments be r1and r2.The instant spatial distance,d,between the centerlines of the two segments is computed.Ifthen the lines do not in contact and no collision-contact force is applied.Ifthen the lines are in contact.In this case,two equal collision-contact forces are applied to the two segments in opposite direction respectively to keep them apart.Let p1 and p2 be the two points of closest proximity.p1 is on the centerline of segment S1 and p2 is on the centerline of segment S2;u is the unit vector in the direction from p1 towards p2.The magnitude of the collision contact force applied is the sum of a Stiffness Term and a Damping Term:

where k1and k2are the contact stiffness of the two segments;c1and c2are the contact damping values of the two segments.v is the rate of penetration,it is the u-direction component of p1’s velocity relative to p2.If v≤0 then the two segments are moving apart and then no damp-ing force is applied.If v＞0 then the penetration is increasing and damping force is applied.When contact is detected,a force of this magnitude Fcis applied to segment S1,at p1,in direction-u.And the equal and opposite forces are applied to segment S2,at p2,in direction+u.

In this model,the roller is built in V shape as shown in Fig.4.The magnitude of horizontal force and vertical force that react on the pipeline are expressed in equations(11)and(12)respectively.

where N1and N2are support forces reacted by two segments of a roller respectively,θ is the included angle of roller supporting rods.

Fig.4 V shape roller

1.4 Tensioner servo system

The tensioner is modeled on the basis of a PID controlling servo system.The system takes force signals from the interface of the tensioner and pipeline as inputs.A Programmable Logic Controller is brought in to implement control algorithm and then a displacement is outputted by tensioner servo and applied to the interface in the direction of pipe centerline(Giuliana Mattiazzo et al,2009).Under the adjustment of the tensioner servo system,the top tension of pipeline is restricted in a permitted range.The system prevents the pipeline from buckling or damage and keeps installation process safe and steady.

For system with more than one tensioner,this model is available to simulate the behavior of several tensioners simultaneously.The Programmable Logic Controller is designed to process feedback force signals from all the tensioners respectively and output pippipeline displacement for each individual tensioner.The servo system controls tension as shown in Fig.5.

Fig.5 Operating principle of the tensioner servo system

First,a constant object tension T0is set in the Programmable Logic Controller.Let the instant feedback force be Ti.The output displacement produced by tensioner is calculated.

where Tt=Ti-Torepresents tension error which is the difference of Tiand To.The output displacement χ is a vector that applies in direction of the pipeline centerline.KP,KI,KDrepresent proportional gain coefficient,integral gain coefficient,differential gain coefficient,respectively.

Though this model neglects the mechanical components of a real tensioner,it provides an effective access to forecast the behavior of a practical tensioner system.

1.5 Nonlinear elastic hinge joint

Due to material elasticity and connecting type,relative rotation between vessel and stinger exists,especially in dynamic operation.Most work merely assumes that stinger is fixed on stern,neglecting the rotation.The elastic joint model is inspired by the spring contact model.An angular velocity&angle-moment function is defined to control the rotation of stinger.A correction term is added to confine the rotation angle to a specific range.

According to local coordinate system shown in Fig.6,let instant stinger angular displacement be θt,maximum angular displacement limitation be θm.M0is the rotation moment which is adequate to hold the stinger and pipeline in static analysis.The moment applied to the end of stinger is Mtin dynamic simulation in time domain.

Fig.6 Coordinates system for the algorithm

If dθt/dt＜0,

If dθt/dt=0,

If dθt/dt＞0,

where λ represents damping term value;γ represents drag term value.

2 Calculation data

The entire model is consisted of three main parts:vessel,stinger and pipeline.Utilizing the coupled model presented in this paper,a numerical model is built with date from the pipelay crane vessel,HYSY201.

Fig.7 Fixed and local coordinates systems for vessel

The global frame of reference is a right-handed system as shown in Fig.7.GXY is set on the still water surface and its Z-axis GZ must be positive upwards.The local coordinate systems for vessel are described in the vessel separately,and the origin is selected at center of gravity and the axes are in special fixed directions,namely the surge,sway and heave directions.

Directions for waves,current and wind are specified by giving the direction in which the wave is processing,relative to global ax-es.Vessel heading is specified as the direction in which the vessel ox-axis is pointing,relative to global axes.

2.1 Vessel data

Tab.1 Main dimensions of the vessel

Fig.8 Hydrodynamic model and grids of the vessel

The main dimensions of vessel are shown in Tab.1.The vessel model is symmetric about the oxz plane.Whole model includes 3 500 finite elements;grids around bulbous bow and stern are detailed and refined to achieve more accurate results.The hydrodynamic model and grids of the crane-lay-vessel are shown in Fig.8.

2.2 Pipeline data

Optimal data for pipeline in the depth of 3 000 m is gained through previous works.The X65 pipeline’s diameter is chosen as 323.9 mm(12.75 in)and wall thickness is chosen as 38.1 mm(1.5in).Mass per unit length is 184 kg/m.Total length is 4 183 m.Pipeline is modeled on the basis of lumped-mass theory;the data of pipeline’s finite elements are shown in Tab.2.

Tab.2 Finite elements data of pipeline

2.3 Stinger data

Stinger is optimized for the depth of 3 000 m from previous works.Stinger’s length is 110 m and radius is 95 m.Rollers are modeled according to vessel local coordinates system.The coordinates for each roller are shown in Tab.3.The included angle between roller supporting rods,θ,is chosen as 120°.

Tab.3 Roller coordinates

Continue Tab.3

2.4 Environment data

The drag loads due to translational velocity of the sea and air past the vessel are calculated using the standard OCIMF method[13].Detailed environment data is shown in Tab.4.

Tab.4 Data for environment

3 Time-domain calculation results

3.1 Pipeline’s influence on vessel motion

For the reason that surge,sway and yaw of vessel are controlled and confined by the PID dynamic positioning system,this work only focus on analysis of pipeline’s influence on heave,roll and pitch.Figs.9-11 illustrate vessel motion in time domain.These figures make comparison about vessel motion between pipe-lay condition and no pipe condition.Black dotted line suggests pipe-lay condition while grey line represents no pipe condition.Differences between two lines are definitely caused by pipeline under coupling of vessel-pipeline-stinger.Direction of wave,current and wind is set as 0°,90°and 0°respectively.

3.1.1 Vessel motion in z-direction

Fig.9a Vessel heave displacement

Fig.9b Vessel heave velocity

According to Tab.5,the results of heave comparison show that the average of heave descends by 3.43%,namely vessel drought increases because of pipeline weight.Standard deviation of heave displacement descends by 1.61%.Standard deviation of heave velocity descends by 2.17%.It is because that water-plane gains more area since drought in stern and bow increases.The augment in water-plane area enhances vessel’s stability in z-direction.Also,considering couple between pipeline and vessel,pipeline raises total inertia of whole pipe-lay system.When the same force is applied,floater with larger inertia performs better stability.Consistent results are achieved when direction of wave,current,wind is set as 0°,45°,30°,or 180°,135°,150°,or 180°,90°,180°.

Tab.5 Statistics for vessel heave

3.1.2 Vessel motion in x-rotation

Fig.10a Vessel roll displacement

Fig.10b Vessel roll velocity

According to Tab.6,the comparison of roll reveals that roll angle averagely ascends by 3 933.33%.Standard deviation of roll angle ascends by 3 669.79%.Average of roll velocity ascends by 5 406.61%.Standard deviation of roll velocity ascends by 5 392.06%.Obviously,all results indicate that pipeline has a crucial influence on roll of vessel.Although value of roll displacement and velocity is relatively small,absolute amplification of average and Standard deviation is quite tremendous.When installation process encounters extreme environment which cannot be avoided by human factors,potential risk and danger will be magnified seriously.The reason for such a colossal deterioration of roll lies in the drag damping of pipeline.Generally,pipeline measures over thousands of meters in the ocean before it touches the seabed.Long length increases sensitivity of pipeline response to sea current.Accordingly,total current force applied on pipeline will be fairly large.The force will be transferred to vessel because of coupling among pipeline,stinger and vessel.Thus,vessel motion is finally affected.Consistent results are achieved while direction of wave,current,wind is set as 0°,45°,30°,or 180°,135°,150°,or 180°,90°,180°.

Tab.6 Statistics for vessel roll

3.1.3 Vessel motion in y-rotation

Fig.11a Vessel pitch displacement

Fig.11b Vessel pitch velocity

According to Tab.7,the results of pitch comparison show that average pitch angle alters by 1 906.40%,namely heeling aft increases because of moment induced by pipeline weight.Standard deviation of pitch angle descends by 5.15%.Standard deviation of pitch velocity descends by 5.95%.Similarly like heave,the augment in water-plane area enhances vessel’s stability in y-rotation.And considering couple between pipeline and vessel,pipeline raises total inertia of whole pipe-lay system.When the same moment is applied,floater with larger inertia performs better stability.Consistent results are achieved while direction of wave,current,wind is set as 0°,45°,30°,or 180°,135°,150°,or 180°,90°,180°.

Tab.7 Statistics for vessel roll

3.2 Pipeline’s influence on vessel loads

As discussed above,pipeline affects vessel motion adversely since the forces applied on vessel increases due to pipeline behavior.Also,rise in forces makes higher requests for the thrust of the dynamic positioning system.Therefore,detailed analysis about loads acted on vessel must be carried out to verify the conclusion.Considering couple among pipeline and vessel,additional loads is imposed on vessel because of the existence of pipeline.As expressed in formula(1),the sum of two portions,the environment loads which act on vessel indirectly utilizing pipeline as medium and pipeline weight,is altogether defined as pipeline force FP,representing forces and moments in wide sense.The total loads,including wave exciting force,wave radiation forcewind and current force Fcw,pipeline forceacting on the vessel,is defined as FT,also representing forces and moments in wide sense.

First,set direction of wave,current,wind is set as 0°,90°,and 0°.Results are shown in Fig.12a,b,c.

From the Tab.8,FPis 76.07%of FTin x-direction.FPis 69.32%of FTin y-direction.FPin z-rotation is 99.70%of FT.Consistent results are achieved while direction of wave,current,wind is set as 180°,90°,and 180°.

Fig.12a Force in x-direction

Fig.12b Force in y-direction

Fig.12c Moment in z-rotation

Tab.8 Maximum forces on vessel

Set direction of wave,current,wind is set as 0°,45°,and 30°.Results are shown in Fig.13a,b,c.

Fig.13a Force in x-direction

Fig.13b Force in y-direction

Fig.13c Moment in z-rotation

Tab.9 Maximum forces on vessel

Form the Tab.9,it is obvious that FPis 73.93%of FTin x-direction.FPis 71.17%of FTin y-direction.FPin z-rotation is 74.72%of FTin z-rotation.Consistent results are achieved while direction of wave,current,wind is set as 180°,135°,and 150°.

Consequently,using pipeline as medium,the environment loads which act indirectly on vessel and pipeline weight,i.e.Fp,take a major part of the total environment loads that apply on vessel.This indicates pipeline increases the entire loads acting on the vessel and thus a higher standard is required for the dynamic positioning system to control the vessel.Enough attention should be paid to pipeline’s influence on vessel’s mechanical characteristic when simulation is carried out.

3.3 Simulation for tensioner servo system

Pipeline top tension output is shown in Fig.14 in a dynamic simulation in time domain.Object tension is set as 2 600 kN,single Airy is chosen to simulate wave whose significant wave height is 1.2 m and spectral peak period is 12 s.

Fig.14 Top tension output of tensioner servo

Black dotted line—tensioner servo system is not activated;grey line—tensioner servo system is activated with single tensioner;black line—tensioner servo system is activated with double tensioners.

The figure reveals that when tensioner servo system is activated,pipeline top tension oscillates harmonically about the object tension in a specific range after a process of transition.This vibration range can be adjusted by regulating the proportional gain coefficient,integral gain coefficient and differential gain coefficient in equation(13).For system with double tensioners,the effect is enhanced because of the couple between two tensioners.

3.4 Verification of stress of the pipeline

According to the equation(16),the stress of pipeline in over-bend segment can be achieved.[14]

where σais stress of pipeline,E is Young’s modulus,D is outer diameter of pipeline,Rc,is the radius of stinger,fDis design parameter which is chosen as 0.85.

Calculating with the equation(16),the stress of the pipeline is 442.105 MPa.In numerical simulation,the maximum Von Mises stress of pipeline is 434.210 MPa,which is under the Specified Minimum Yield Strength(448.2 MPa)for X65 pipeline according to DNV-OS-F101.The error between calculated result and numerical result is 1.818%.

4 Conclusions

A new concept model for S-lay installation considering couple between vessel-pipelinestinger is presented in this paper.Simulation is conducted under combined environment of wave,current and wind.Vessel is controlled by a dynamic positioning system based on PID theory.Pipeline’s influence on vessel’s mechanical and kinematical characteristic is analyzed.

(1)Three main parts are detailed in this paper to simulate the couple between vesselpipeline-stinger.A collision-contact surface contact algorithm is used to calculate the reacted force of V shape roller on the stinger;a model for the simulation of the tensioner behavior with a PID servo system is designed to effectively limit the pipeline top tension;the stinger and the dynamic positioning vessel are linked with a nonlinear elastic hinged joint.The model is proved to successfully simulate pipeline-stinger contact and separation,tensioner behavior as well as rotation between the vessel and the stinger.In summary,this work presented an improved tool to analyze S-lay installation operations in a more accurate and efficient way.Such tool averts some limitations of conventional method and provides valuable knowledge for the design of safe offshore operations.

(2)Because water depth is large,the draft damping of pipeline performs obviously.The current force acting on pipeline increases sharply with water depth.Considering couple between the pipeline and the vessel,using pipeline as medium,environment loads and pipeline weight affect vessel motion and loads acting on vessel adversely.Under the influence of pipeline,the average roll angle of vessel ascends by more than 30 times,and the average roll velocity of vessel ascends by more than 50 times.Heave and pitch is affected by pipeline in different extent.Forces(moment)act through pipeline,the medium,on vessel take up more than 70%of total environment force acts on vessel in x,y direction and z rotation.This creates additional challenges for dynamic positioning system.All in all,influence of pipeline on vessel considering couple between vessel-pipeline-stinger is crucial to the simulation and analysis of S-lay installation operations.

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