Modeling and Simulation of Deepwater Pipeline S-lay

JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING

Modeling and Simulation of Deepwater Pipeline S-lay with Coupled Dynamic Positioning Shangmao Ai1 College of Shipbuilding Engineering, Harbin Engineering University No. 145 Nantong Street, Harbin, 150001, China [email protected] Liping Sun College of Shipbuilding Engineering, Harbin Engineering University No. 145 Nantong Street, Harbin, 150001, China [email protected] Longbin Tao Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde 16 Richmond Street, Glasgow, G11XQ, United Kingdom [email protected] Solomon C. Yim School of Civil and Construction Engineering, Oregon State University Corvallis, OR 97331, USA [email protected]

ABSTRACT Dynamic position (DP) control and pipeline dynamics are the two main parts of the deepwater S-lay simulation model. In this study, a fully coupled analysis tool for deepwater S-lay deployment by dynamically positioned vessels is developed. The method integrates the major aspects related to numerical simulation, including coupled pipeline motion and roller contact forces. The roller-pipe interaction is incorporated in

1

Corresponding author, E-mail: [email protected].

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the S-lay pipeline model using a contact search method based on a lumped-mass (LM) formulation in global coordinates. A proportional-integration-differentiation (PID) controller and a Kalman filter are applied in the vessel motion equation to calculate the thrust allocation of the DP system in time domain. Numerical simulation results showed that the dynamic effects add a significant contribution to the tension, but have little influence on the maximum pipe stress and strain. The dynamic response of the coupled S-lay and DP pipeline deployment system increases the demand on the tensioner load carrying capability as well as the maximum DP thruster power.

1 INTRODUCTION One of the most common methods of submarine pipeline installation for hydrocarbon energy extraction in deep water is the S-lay method. Horizontal firing-lines and parallel workstations for assembly of the pipe joints make this method fast and economical. As shown in Fig.1, deepwater S-lay installation vessels are usually equipped with large capacity machines, such as heavy tensioners and a long stinger, to reach greater depths and handle heavy pipelines. These vessels typically require a dynamic positioning (DP) system to ensure good performance using simplified operating procedures for station-keeping with propellers and thrusters. A conventional mooring system is not often suitable for deepwater installation because the reset speed of its anchors could become slower than the pipeline assembling speed [1]. Modeling of the dynamic behavior of a pipeline during installation is complex due to nonlinearity and coupling with the motion of the installation vessel. Firstly, geometric 2


and material nonlinearities are important due to the slenderness of the pipeline structure and the great arc of reverse curvature in the overbend region. Secondly, alternating impact and separation between the pipeline and the rollers near the end section of the stinger will occur during operations. Finally, the positions of the tensioners and rollers in contact with the pipeline are dependent on the vessel motions controlled by the DP system. It is important to derive the idealized mathematical models taking into account all of the above interactions to comprehensively analyze and accurately predict the pipeline installation process. There are two types of pipelay analysis methods: static and dynamic. Static S-lay installation analysis usually is used to obtain the stinger departure angle, roller heights, initial tension, and pipe stresses and strains in static equilibrium. Static analysis often employs stiffened catenary theory and finite-element (FE) methods. The catenary approach is recommended to improve computational efficiency by neglecting torsional stiffness and interaction with solids [2-4]. However, “geometric limitations” refer to “S” shaped cable profiles and solutions cannot be achieved by closed-form continuous analytical models. Recently, Yuan et al. [5] proposed a simple and efficient predictive numerical model of S-lay, in which the pipeline was separated into four segments according to their (different) mechanical properties. The FE method (see [6] for examples) can take all load effects, including inertial and hydrodynamic force, into account, but the computational effort would be much more significant. On the other hand, dynamic S-lay installation analysis takes vessel hydrodynamic behavior and pipe dynamics into consideration. Traditional dynamic analyses usually 3


employ numerical tools based on uncoupled formulations, where the hydrodynamic behavior of the pipelay vessel is not influenced by the nonlinear dynamic behavior of the spanning pipeline. For instance, most of those analyses usually emphasized the dynamic effect of the vessel motion, especially heave and pitch, on spanning pipeline stress and strain [7-9]. Some studies, e.g. Zhang [10], calculated the detailed pipestinger impact behavior based in the uncoupled formulations. There are a number of dynamic pipeline numerical methods ranging from finiteelement (FE) to finite-difference (FD); most of the models achieve similar accuracies as long as a sufficiently fine discretization grid is used. The lumped-mass (LM) model is a useful simplification of the FE analysis process because of its coding simplicity and computational efficiency. It is well recognized that the design of floating production systems (FPS) for deepwater applications should employ coupled analysis tools, taking into account the interaction of the FPS motions with the hydrodynamic-structural behavior of the cables and risers [11, 12]. Based on this coupled FPS-cable-riser dynamic technology, some fully coupled analysis tools have been developed for the pipelay operation. Jensen [13] developed a nonlinear dynamic partial-differential-equation formulation for J-lay. Silva et al. [14] presented a coupling FE computational tool for mooring-system positioning Slay operation allowing a complete customization of the configuration of lay-barge and stinger rollers. Gong et al. [15] developed the framework of the commercial computer code OrcaFlex to investigate the dynamic S-lay effects, including surface waves, ocean

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currents, pipelay vessel motions, and the impact and contact between the pipeline and stinger rollers. In wave-energy research and development, the LM model and coupling method discussed above are also widely applied in practical design and analysis. Recently, Matthew et al. [16] developed an open-source LM numerical code, MoorDyn, to model the mooring systems of wave energy devices without considering the bending elasticity. Using an orthogonal local coordinate system to describe the element orientation, Masciola et al. [17] tried to extend the capabilities of line dynamics and bending effects into the MAP open-source code, which is a quasi-static module developed for a landbased and floating wind turbine numerical modeling tool - FAST. An optional loosecoupling arrangement between the LM model and the FAST simulator, as defined in Jonkman [18], was used previously in the WEC-Sim, an open-source wave energy converter numerical simulation tool. In this coupled analysis, two sets of equations of motion are solved – one for the floater and one for the appendages. The fairlead forces are updated within each iteration over the time step; and the equation of motion is integrated with an implicit or explicit scheme. In most loose coupling models, including both FAST and WEC-sim, time integration of the floater motion solver often uses a large time step, whereas the mooring line solver uses a shorter time step to ensure stability of the RK2 explicit integrator in MoorDyn. Enhanced refinements of this coupled system is needed in order to balance the accuracy and efficiency of these coupled models. The objective of this study is to develop a fully coupled analysis tool for deepwater S-lay deployment and operations coupled with a closed–loop automatic control DP 5


system of the vessel applicable to both oil recovery and wave energy conversion devices. DP controllers are not easy to integrate into the S-lay coupled numerical tools because, in the past, dynamic pipelay models were proprietary and not available in the public domain. To remove the need for transformations between local and global coordinate systems in the LM model, the formulation proposed in Low and Langley [19] is adopted herein. The rest of this article is organized as follows: first a summary of the mathematical model and analysis algorithms underlying the S-lay simulation controlled by DP is presented in Section 2. Analysis methods including static, coupled and decoupled dynamic solutions are developed in Section 3. Model validation and assessment of the predictive capability of the coupled pipeline-rollers contact and DP control system are presented in Section 4. A comparison of numerical results to static (or decoupled) and dynamic coupled solutions in the form of a case study are shown in Section 5. Finally, conclusions of the coupled analysis demonstrating the dynamic coupled characterization and effects on the response of the system are presented. This work is part of a longterm effort to develop a numerical tool to facilitate and complement the coupled dynamic analysis on floater-cable-pipe system controlled by DP system.

2 MATHEMATIC MODELS Based on Low and Langley’s lumped-mass (LM) formulation, the full coupling model between the pipe response and the vessel motion is descripted in this section. Compared to floater-risers system, some new items are developed for the S-lay 6


simulation including modeling of the nonlinear structural behavior of the pipeline, the full coupled roller-pipeline interaction, and the DP forces via a proportional-integrationdifferentiation (PID) controller and Kalman filter. 2.1 Pipelay Vessel Motion with PID Controller Usually, the time-domain control equation can be represented in six degrees of freedom (DOFs) including fluid memory effects as [MVs  MVa ()]η(t )  CV  η, t   K V η(t )  FV

(1)

where η is the instantaneous vessel displacement vector, with components η1, η2 … η6 representing the surge, sway, heave, roll, pitch and yaw of the vessel, respectively; and MVs and KV are the structural mass/inertia matrix and system stiffness matrix,

respectively. The total external force vector on vessel during DP S-lay operation is FV  FVW 1 (t )  FVW 2 (t )  FVC  FVWd  FVDP (t )  FVL (t )

(2)

which includes the first and second order wave load FVW (= FVW 1  FVW 2 ), wind load FVWd , current loads FVC , propulsion forces FVDP in the DP system and the pipeline reaction force FVL . Eq.2 integrates the pipeline, the vessel and the DP system into a single closed loop. Here the pipeline reaction forces on vessel represent the coupling between the vessel motions and the pipeline dynamics. The pipeline reaction forces are comprised of the tension at the top of pipeline and contact forces with the rollers/vessel motions which are controlled by the propulsion forces of the DP system. Note that the environmental force and the horizontal tension of the pipeline are not assumed to be a feedforward

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term of the DP thrust force but external forces acting on the vessel as described in Eq.(2). Numerical solutions of time-domain transformations of the retardation function R (t) are descripted in detail by Fossen [20] and Ogilvie [21]. The formula are 

MVa ()  MVa ( )   R (t ) cos tdt 0

CV  η, t    R (t   ) η( )d t

(3)

0

where MVa ( ) is the added mass coefficient at frequency ω, and MVa () is a constant, equivalent added mass of the vessel at the infinite frequency. The unidirectional time-domain wave excitation forces (first order FVW 1 and second order FVW 2 ) can be written in the two-term Volterra series as  Nw i t  FVW1 (t )  Re   Aj L( j )e j   j 1  W2 V

F

Nw Nw  Nw Nw i (  ) t i (   ) t  (t )  Re   Aj Ak D( j , k )e j k   Aj Ak S ( j , k )e j k  j 1 k 1  j 1 k 1 

(4)

where L(ωj) represents the linear force transfer functions (LTF); D(ωj, - ωk) and S(ωj, ωk) are difference and sum frequency quadratic force transfer functions (QTF) respectively. ANw is wave amplitude, wave frequency, and wave components. Seakeeping refers to the study of motion of pipelay vessel at zero speed under wave excitation. The tool AQWA-LINE is used to calculate the hydrodynamic characteristics of the vessel in the frequency domain, including added mass, hydro-damping and the transfer functions for wave loads. Thrust forces FVDP confine the vessel to a certain permitted range. The proportion8


integration-differentiation (PID) controller was herein adopted to control the vessel motions. This is the most common approach [22]. The total thrust forces FVDP in the PID controller consist of three parts: surge, sway and yaw forces, formulated as [20] FVDP     K P     K I     dt  K D

d   

(5)

dt

where  =η - ηref is the vessel position error; K , K and K are the proportional, P

I

D

integral, and differential gain coefficient, respectively. Note that K P and K D are associated with the stiffness and damping of the control system. Therefore, they are functions of the desired resonant period and the damping ratio for each degree of freedom.

PID

KP

 m1112  = 0  0 

0 m2222 0

  m11 11   0  , K PID =2 D  0 2  0 m666   0

0 m22 22 0

   m66 66  0

0

(6)

where  and  are the resonant frequency and damping ratio for surge, sway and yaw. The integral term weighted by K I ensures zero error for constant system input and takes care of all constant or slowly varying disturbances. The PID controller takes the instantaneous vessel position η as input, and computes a thrust force magnitude. Fig.2 presents the flow chart of the pipelay vessel motion solution controlled by the DP system. An effective tool to filter out the oscillatory components of motion is the discrete-time Kalman-Filter [20]. That is, the model has state variables associated with the low-frequency motion and other state variables associated with wave-frequency motion and dynamic pipe tension. Once these latter states are estimated by the Kalman Filter, only the low-frequency states are used as 9


feedback signals in the controller. The control allocation problem for a vessel equipped with azimuth thrusters is in general a nonconvex optimization problem to generate commanded forces (surge and sway) and moment (yaw) with minimal power consumption. Iterative solutions are obtained using a quadratic programming algorithm. All of these concentrated forces in Eq.2 are transformed to the geometry center of vessel in the solution process. If the acting point has coordinates  xr , yr , zr T relative to the geometric center of vessel, its position vector in vessel-body coordinates is r  [1  zr5  yr6 ,2  zr4  xr6 ,3  yr4  xr5 ]T

(7)

T L Then, the concentrated forces, expressed by FV ,i = [ Fx , Fy , Fz ] in the local coordinates

can be transformed to the generalized force relative to the vessel-body coordinates as

FVL,i   Fx , Fy , Fz ,  zFy  yFz ,  zFx  xFz ,  yFx  xFz 

T

(8)

where Fx , Fy , Fz are the three components of the concentrated force. 2.2 Pipeline Discretization Formulation The LM formulation adopted herein is developed with reference to a global coordinate system. Mass and loading on each element is concentrated at the end nodes. The axial stiffness of the line is modeled by simple spring elements between the nodes, and bending is modeled by rotational springs. Structural damping effects are neglected, since it is only a relatively small compared to the hydrodynamic damping. The pipeline is divided into N segments by N+1 lumped-mass points (Pi, i=0, …, N). The bottom end of the pipeline is fixed at the anchored point P0 on the flat seabed, while the point PN at the top end in contact with the tensioner on the vessel, as shown

10


in Fig.3. Extensional axial spring stiffness kA and rotational bending spring stiffness kB are defined as k A  EA lk , k B  2 EI  lk  lk 1 

(k  1,

(9)

, N)

where EI and EA are the flexural and extension rigidity, and l is the un-stretched element length. In order to simulate the exact material properties, the Ramberg-Osgood equation is proposed to describe the relationship between stress and strain as in [23],      / E    /  y 



(10)

In Eq.10, the stress is assumed to depend only on the bending moment but not the tension force; then the load-dependent path can be rewritten as a nonlinear momentcurvature relationship  / y  M / M y  M / M y 



(11)

where ED and M are the pipe curvature and moment, respectively,  y and My are the pipe curvature and moment at the nominal yield stress, and and  are the Ramberg-Osgood equation yield offset coefficient and hardening exponent, respectively. In each calculation step, EI is updated according to the relation Eq.11, representing the nonlinear rotational spring. According to multibody dynamics and Kane’s formalism, the nonlinear equation of motion at time t can be expressed as

M sLq(t )  FL  FLA  FLB  FLW + FLH + FLS  FLV

(12)

where q is the displacement vector of the mass points, q1, q2, q3 in the x, y, z direction of

11


point P0, respectively. M sL are the pipe structural mass matrix; FLA and FLB are the nodal force vectors arising from the extensional spring and rotational spring, i.e. the axial force and bending force, derived directly from the potential energy expression in global coordinates in [21]; FLH are the nodal hydrodynamic force including the inertia and drag force vectors based on Morison’s equation; and FLW is the effective weight in water. The vessel reaction force FLV has the same value as FVL acting in the opposite direction, more details are descripted in Section 2.3. FLS represents the contact forces between the pipe and the seafloor. The upward

contact forces are included in the model, while the friction effects are neglected. We assumed that the indentation equals to the pipe diameter D in the initial stage of numerical solution, then all positions are in contact with the seafloor with D>di (as shown in Fig.3, di represents the vertical position vector offset to the baseline). The vertical contact force from the ith element is lumped onto node i as

FLs,i 

1  ks D  li   D  di  2

(13)

where li is the un-stretched length of the ith element, and the vertical force coefficient per unit pipe length is assumed to be a constant expressed by the soil stiffness ks (N/m2/m) and the projected length D. 2.3 Pipeline-Roller Contact Formulation In practical situations, under instantaneous dynamic loading conditions some of the rollers may not be in contact with the pipe, resulting in higher concentrated forces on fewer number of rollers. In this study, the rollers are simplified to a line (see Fig.1 insert). 12


Thus the stinger contact search is based on a pointwise contact assumption which occurs at the “minimum distance”. The first step of the contact search is to find the closest elements to the roller lines; it is an approximate initial search in which the objective is to identify the region of possible contact. This search is based on the current positions of the jth pipe element (Ej linked by nodes Pj-1 and Pj) and the ith roller line, see Fig. 4a. PC and SC are the central points for the element and roller line. The element of the pipeline with minimum distance d min  min PC  SC is identified. At this stage, it is not necessary to determine the elements containing the actual contact points. In the second stage, the identified elements with the smallest distances are used to calculate the common perpendicular between the element line and roller line. The closest points on the jth element with respect to the ith roller line are located using the following orthogonality conditions:

 Q r  Qe    Pj  Pj 1   0  Q r  Qe    SiL  SiR   0

(14)

According to analytic geometry (Fig.4b), the distance between two straight lines on different surfaces is di  Qr  Qe  nT  Pi 1  SiL  , n 

P P

j

 Pj 1    SiL  SiR 

L R j  Pj 1    Si  Si 

(15)

where n is a unit vector from the roller to the element, parallel to  Q r  Q e  . To confirm the contact between the roller and the pipeline, the following two contact conditions must be met:

13


(1) It is assumed that cross-sections of contacting pipes do not undergo any deformation, and roller boxes are simplified to a line, so di cannot be larger than pipe radius D/2, i.e. 0  di  D / 2 . (2) It is necessary to define the appropriate side of the element relative to the roller. The R condition of the upward direction of vector n must meet with n   Si  Pi1   0 .

The above check is performed for every pair of closest points. This search is not restricted only to the element Ej because it is possible that the closest points do not lie on the closest elements found in the first stage due to large deformation of pipeline. If the two conditions are not met, the search moves to the previous or to the next element. Before the contact force is allocated to node i and i-1, the exact contact point needs to be determined. Then, the vertical line location of contact pairs are determined by the following two distances on the lines: 1 T  L L  Si  Q r  sin   n e  n   Pi  Si    P  Q  1  n  n T  P  S L  e r i i  i sin 

(16)

where the element unit direction vector n e and the roller line unit vector n r are defined as ne 

P j  P j 1 P j  P j 1

SiL  SiR , nr  L Si  SiR

(17)

and  is the angle between the roller and the element, and is found by cos   n r T ne . The model of the roller-pipe contact can be decomposed in two components: the linear force-displacement law (Hooke’s Law) and a viscous damping force which is proportional 14


to the relative velocities of particle elements in contact. Assuming the combined damping term is negligible, the contact force of roller line acting on the pipe (FRL) can be calculated by linear stiffness kR,

F RL  k R  0.5D  d   n

(18)

Then the allocated forces on the node Pj and Pj-1 are

F jRL 

Qe  Pj Pj  Pj 1

F RL ,

F jRL  1

Qe  Pj 1 Pj  Pj 1

F RL

(19)

3 ANALYSIS METHOD In the pipelay simulation, the whole model comprises of three distinct components: the vessel, the pipeline and a set of connecting springs. The connecting springs are the links between the pipelay vessel and the pipeline in the global FE model. Decoupled solution and coupled solution are presented here to analyze the coupling effect of the pipeline on DP controller. 3.1 Static Analysis The static equilibrium of S-lay deployment is determined in two stages. At the beginning, initial positions for all the nodes on the line are calculated by using an analytical or catenary equation approximation to provide a good starting point. The top end is fixed at the tensioner location defined by the vessel equilibrium state. A full static analysis of the pipeline is subsequently performed using the NewtonRaphson (N-R) iterative technique. Considering the hydrodynamic drag term FLD , the (vector) static equilibrium equation is 15


FLA  FLB  FLW + FLD +FLS  FLV  0

(20)

Let q represent increments of displacement in an extended iteration step. Then the effective residuals ε for the subsequent iteration is solved by  J  q    f   q 

(21)

f  q   FLA  q  q   FLB  q  q   FLW + FLS  q  q   FLV  q  q 

(22)

J  q  

f  q   K LA  K LB  K SL  KVL q

(23)

where K LA and K BL are the stiffness matrix of the connecting axial springs and rotational springs, respectively. For the ith node, the coefficients of the contact stiffness K SL and K VL , which can be derived from Eq.13 of pipe-seafloor contact forces and Eq.18 of roller-pipe contact forces, can be written as

K

S L ,i

 1  k   D  li   2 S 0

if D  di > 0

(24)

if D  di  0

and K LV,i   k R n i

(25)

3.2 Fully Coupled Dynamic Solution The motion equation of the S-lay system can be written as a coupled formulation in the time domain M  u(t )  C  u(t )  K  u(t )  F

(26)

where  MVS  MVa ()  M=   0 

 C  , C=  V S a  M L  M L   0 0

0 K , K=  V  0  0

0 F (t )  ,F V   0  FL (t ) 

(27)

16


The displacement vector u of the coupled system is represented by P0    u  1 ,2 ,3 ,4 ,5 ,6 , q1 , q2 , q3 , , q3( N 1)    vessel line  

T

(28)

The dynamic analysis is restarted from the equilibrium of the balanced system. Time integration of Eq.26 is carried out by the Wilson-theta implicit scheme [24] associated to the N-R iterative technique. At each iteration of a time step, the effective residuals ε for the subsequent iteration is solved by    J 1  u  f  u 

(29)

6    6  3 f  u   F  ut  u   K   u t  u   M   2 u  u t  2u t   C   u  2u t  u t  (30)  2    

J  u  

f  u  u



F  ut  u  u

K 

6



2

3 M C

(31)



In this study, no iteration is required for the hydrodynamic loads in the generalized forces, so the complete Jacobian of the force terms is calculated as following, K L  KV J  u    V 0 

 6  M K K K K  2 0

V L

S L

A L

(32)

B L

where K VL is obtained by combining Eq.8 and Eq.19. 3.3 Decoupled Solution of DP Control and Pipe Tension To examine the coupled effect on DP controller, a decoupled solution is also developed and analyzed. Here “decoupled” means that a horizontal force H from static analysis of S-laying pipe represents the tensioner action on the pipeline. Then Eq.2 is rewritten in the form FV  FVW  FVC  FVWd  FVDP (t )  H

(33) 17


The horizontal force H of the pipeline is normally represented in terms of a tabulated quasi-static force as a function of vessel displacement. This information is used as a ‘look-up’ table of horizontal drag forces for a given vessel position. Linear interpolation is normally applied between the tabulated values. The horizontal force characteristics can be provided by a static analysis of the S-lay pipe according to the solution of Eq.20. It is important to observe that the vertical component of pipe drag force is not included due to its negligible influence on vessel response. Damping of the low frequency motions due to slender structures cannot be included in decoupled analysis.

4 MODEL VALIDATION AND DEMONSTRATION In this section, the coupled dynamic algorithm is validated and the performance of the controller is demonstrated. 4.1 Validation of Pipeline-Rollers Contact Simulation The test model employed here is a suspended pipeline with one end fixed at the stinger framework and the other end with an applied downward force. The amplitude of downward force of the demonstration model is 1000kN. The stinger framework is prescribed with a harmonic pitch motion ( z  cos 29 t ). Eight support-rollers, fixed on the stinger, arranged at the quarter of circle arc length on average, are presented in Fig.5. The environmental loads are neglected in this test case; and the pipe parameters are summarized in Table 1.

18


The static analysis needs to be calculated by an N-R iteration, in which an arc segment with a radius of 73m is specified as the starting shape of the pipeline. Then the dynamic solution of Eq.12 started from the static configuration with a time step of 0.005s is employed for the integration. Dynamic maximum bending moment results of the roller-pipe contact are presented in Fig.6. Six peaks of bending moments are observed, indicating that the six rollers (from R1 to R6) are in contact with pipe but not R7 and R8. Compared to OrcaFlex [25] results, it is found that the simulation results from the model presented in this study and those of the OrcaFlex are in good agreement at the contact section, indicating that the adopted level of discretization is sufficient. The results at the arc length 112m achieve similar level of matching, with a maximum discrepancy ratio about 8.6%. The difference between the predictions by the model proposed in this study and those of OrcaFlex mainly results from two sources: differences in time integration scheme and nonlinear material model. As shown in Fig.7 small oscillations exist during the time integration, due to a very small clearance. Secondly, nonlinear material models in this study neglect the contribution of the axial force, while the OrcaFlex software employed the more general formulation of Eq.4. Fig. 8 shows the predicted trajectories of the pipe bending stress and strain at arc length 31m of the present study and the OrcaFlex code. The difference can be attributed to the effect of the line clearance (d presented in Eq.18) that report shortest distances between the roller-lines and the segments of pipeline in the model. 4.2 Demonstration of PID Controller Performance 19


Control of the vessel considered is assumed to be fully-actuated with the available control inputs being the vessel thrusters. For demonstration of the capability of the PID controller, the pipelay is not modelled in this performance test. The static initial position of the pipelay vessel is taken as the surface position (30m, -20m), and the heading angle is 90°. Then the PID controller is switched on and it starts to propel the vessel to the desired surface reference position (10m, -10m) with the specified heading angle of

.

The simulation scenario was performed twice, first with no controller and then with a PID controller. Under the condition of no controller, the drift of the vessel was induced by the current and wind loads as well as the drifting forces, not including the wave loads. After the PID controller was applied, the vessel hovers over the targeted stationary position with small oscillations with a maximum amplitude of 0.75m, as shown in Fig.9. As observed, with the control system, the vessel gradually moved from the initial position to the targeted location and became “stationary” after 23 seconds. The time to target position depends on the travel distance and thruster power of the DP system.

5 CASE STUDY 5.1 Parametric Input Description Numerical simulations are performed on a pipelay operation in an 1157m water depth. The HYSY 201 (see [15]) is chosen as the pipelay vessel for deepwater S-lay operation. Pertinent information on HYSY 201 including the ship geometry, particulars, and thruster configuration are presented in Fig.10. The vessel is equipped with seven azimuthing thrusters: two non-retractable main thrusters of 4.5MW in the aft of the 20


vessel that are optimized for propulsion at transit speed, and 5 retractable thrusters optimized for bollard pull. The thruster data and main parameters of vessel are presented in Table 2. Accounting for viscous effects, 3% additional roll damping has been added to the potential roll damping. A PID-controller has been applied with the following controller gains: KP = diag[2.4x106; 2.4x106; 0; 0; 0; 1.0x105]T

(34a)

KD = diag[3.5x107; 3.5x107; 0; 0; 0; 1.5x105]T

(34b)

KI = diag[0.1x104; 0.5x104; 0; 0; 0; 0.2x104]T

(34c)

A fixed stinger is placed in the stern for launching the pipe into the water at a suitable curvature with the radius 110m. The distance from the end to the start of the curvature depends on the curvature, and the first node is assumed to be fixed with springs. There are 21 rollers arranged on the stinger framework. The unsupported arc length between the rollers in the overbend area is taken as 6.0 m. A 24-inch pipeline (D =0.61m) with wall thickness of 30.6mm is selected with upstretched length 2243m. The coefficient α and β are the same as validation case defined in Table 1. A following sea-state is summarized in Table 3. The global coordinate system is defined by the geometric center of vessel. The S-lay deployment initial configuration in the static analysis is shown in Fig.11, where the result of the horizontal tension force is 1234.7kN. 5.2 Dynamic Effect on Pipe Safety Estimations Static analysis and coupled dynamic analysis are carried out to examine the dynamic effect using the theory and algorithm developed in this study under identical 21


environment and operation conditions. Element sizes of the overbend and sagbend sections are set as 2m, and the other element size is 10m. Initial positions for all the nodes on the line are calculated using an analytical catenary equation. The time step of integration is 0.005s. To determine the design value for the top tensioner, it is important to be able to predict accurately the maximum top pipe tension. It is required that the design tensioner capacity be above the maximum predicted top tension with an adequate safety factor. In this study, the permissible small relative axial motion between the pipeline and the tensioner is assumed negligible, and hence modeled a fixed boundary condition of pipe top end. As shown in Fig.12, the maximum pipe tension is 3852kN at the connection point with vessel, which is about 34.5% higher than the static value (2863kN). Thus the designed tensioner capability has to be significantly higher than the static results. Note that the blocked tensioner assumption may lead to some difference with a more appropriate flexible connection condition. Alternative modeling methods of the tensioner could be implemented by adding a nonlinear gap spring to top end of the pipeline [16]; and/or adding a controller [26]. By the same token, it is important to be able to predict accurately the maximum pipeline stress and strain, thus the design pipeline stress and strain can be obtained by applying a safety factor. Based on DNV rules OS-F101 (K 300 Simplified laying criteria), we focus on the change of strain in the overbend and the equivalent stress in the sagbend. Pipe bending stress/strain results in two analysis are presented in Fig.13, which shows the difference between the dynamic and static results. The maximum 22


difference of the strain in overbend section and the stress in sagbend are 1.3% and 4.6%, respectively. As expected, the overbend is a displacement-controlled region, i.e. the strains are controlled by the radius of the stinger; and the sagbend is controlled by the total vessel travel distance. Hence, the coupled dynamic analysis would have a little effect on the deployment of S-lay pipe specified by DNV rules OS-F101, because the pipeline has a little change in the configuration under a small vessel travel distance from the static position in deepwater DP operation. 5.2 Coupling Effect on Controlled Vessel Motions When it comes to deepwater S-lay, the pipe tension forces become one of the unnegligible factors of the DP thrust force prediction. To investigate the S-lay pipeline and DP coupling effect on the results of thrust force allocation, the coupled and decoupled simulations of the dynamic response of the pipe-lay system with identical initial conditions are performed. Three components of the vessel motions with significant response in the following sea-state condition (surge, pitch, as well as pitch induced heave) are examined. Fig.14 shows a comparison of heave, surge, pitch and thrust forces over 1,000s of simulated response time of the numerical simulation after the transient response has subsided. The corresponding statistical data are presented in Table 4. Control allocation results show that seven azimuth thrusters have the same azimuth angles (0° along x axes) and thrust force amplitude, thus only the total thrust force needs to be presented. This is mainly because a following sea-state is not an extreme condition for DP control, the environmental load acted on the vessel is small. 23


Note that significant differences between decoupled and coupled results exist in the vessel mean position and peak values because the decoupled analysis do not include the vertical component of the pipe reaction forces on vessel motion. As can be seen in the Fig14 (c), a high-precision position control (controlled radio is below 1.5m) is obtained by using the given PID gain coefficients, and the surge motions from both simulation methods are noticeably similar. Similar control motion is helpful to compare the thrust forces by reducing the disturbance by the different vessel drifting motion. In the DP operation, the vertical component of pipe tension is passively compensated for by the pipelay vessel restoring forces; only the horizontal component is left to active control by the vessel motion control system. From Fig.14 (d), the maximum thrust forces from decoupled analysis is much larger than that from coupled analysis, because the larger pipe top tension from decoupled analysis is needed to be compensated. The maximum thrust force obtained from the decoupled analysis is about 25% higher than that from the coupled analysis, indicating that the designed DP capability predicted by the decoupled results tends to over-estimate the actual value. On the other hand, the maximum force is larger than the mean value by 29% and 21% for the coupled and decoupled results respectively, proving that the dynamic effect on the thrust force is also significant and dynamic analysis is needed for accurate force prediction. Therefore, a coupled pipeline-roller-DP analysis approach in deep water is recommended for the initial design stage of S-lay system. 24


6 CONCLUSIONS This study integrates the major aspects related to the numerical simulation of deepwater pipeline installation operations performed by dynamically positioned vessels including coupled pipeline motion and roller contact forces. This approach can be used to accurately predict the pipeline tension, surface vessel motion and required thrust force of the controller simultaneously to ensure operation safety. Simultaneous prediction of dynamic influence on the structural, motion response and DP force provides useful insights into S-lay operations. The major contributions of this study are summarized as follow: 

The new dynamic model of the pipe includes the nonlinear relationship between the bending moment and the curvature. The contact force between rollers and pipeline is incorporated in the new model by a contact search method. A PID controller and Kalman Filter are applied in the vessel dynamic equations, which is helpful to simulate the DP system of deepwater operation.



The dynamic model is validated against the OrcaFlex code and the controller performance is demonstrated.



Numerical simulation results showed that the difference between the static tension and the maximum dynamic tension at the top end (tensioner) can be as much as 34.5% larger. It clearly demonstrates that the tensioner capacity analysis is substantially over-estimated by the static analysis which is often applied at the design stage. 25




In contrast to the maximum stress-strain results where the difference between the static and dynamic analysis along the complete length of the pipe appear to be relatively small, because there is little change in pipe shape in deepwater installation by the DP vessel.



Numerical results further revealed that to achieve a similar motion response of the vessel, decoupled analysis overestimates the forces required from the thrusters of the DP system compared to the fully coupled analysis. A coupled analysis approach in deep water is therefore highly recommended for checks of important design cases of DP system. It is noted that a more detailed DP operation capability should include more

general environmental conditions. And it is worth noting that the tensioner plays an important role in maintaining the tensions within a desired range. As part of the extension to the present model development, research effort should be devoted to implement a more realistic modeling of the tensioner in the coupled analysis tool, by using a nonlinear gap spring added to the top end of pipeline.

ACKNOWLEDGMENT This research is supported by China Scholarship Council (No.201606685001) and “the Fundamental Research Funds for the Central Universities” of Harbin Engineering University. And it is also sponsored support by the US Department of Energy Grant. No. DE-EE0006816 for the fourth author is acknowledged.

26


REFERENCES [1] Kyriakides, S., Corona, E., 2007, Mechanics of Offshore Pipelines, Volume 1: Buckling and Collapse. Elsevier, Oxford. [2] Maier, G., Corradi, L., Mazzoli, A., Michelini, R., 1982, “Optimization of stinger geometry for deepsea pipelaying,” Journal of Energy Resources Technology, 104, pp. 294-301. [3] Zhu, D. S., and Cheung, Y. K., 1997, “Optimization of buoyancy of an articulated stinger on submerged pipelines laid with a barge,” Ocean Engineering, 4(24), pp. 301311. [4] Guarracino, F., and Mallardo, V., 1999, “A refined analytical analysis of submerged pipelines in seabed laying,” Applied Ocean Research, 21(6), pp. 281-293. [5] Yuan, F., Guo, Z., Li, L., Wang, L., 2012, “Numerical model for pipeline laying during Slay,” Journal of Offshore Mechanics and Arctic Engineering, 134(2), pp. 021703. [6] Vlahopoulos, N., Bernitsas, M.H., 1990, “Three-dimensional nonlinear dynamics of pipelaying,” Appl. Ocean Res., 12 (3), pp. 112-125. [7] Suzuki, N., and Jingu, N., 1982, “Dynamic behavior of submarine pipeline under laying Operation,” J. Energy Resour. Technol. ASME 104, pp. 313-318. [8] Clauss, G. F., Weede, H., Riekert, T., 1992, “Offshore pipe laying operations interaction of vessel motions and pipeline dynamic stresses,” Applied ocean research, 14(3), pp. 175-190. [9] Tikhonov, V.S., Safronov, A.I., Kamyshev, M.A., Figarov, N.G., 1996, “Numerical analysis of pipeline dynamics in seabed laying,” International Journal of Offshore and Polar Engineering, 6 (3), pp. 212-218. [10] Zhang, X., Yue, Q., Zhang W., Xie, P.,. 2014, "Study on the design of a model experiment for deep-sea S-laying," Ocean Engineering, 84, pp. 194-200. [11] Garrett, D. L., 2005, “Coupled analysis of floating production systems,” Ocean Engineering, 32(7), pp. 802-816. [12] Jacob, B. P., Bahiense, R. D. A., Correa, F. N., Jacovazzo, B. M., 2012, “Parallel implementations of coupled formulations for the analysis of floating production systems, part I: Coupling formulations,” Ocean Engineering, 55, pp. 206-218. [13] Jensen, G. A., Säfström, N., Nguyen, T. D., Fossen, T. I., 2010, “A nonlinear PDE formulation for offshore vessel pipeline installation,” Ocean Engineering, 37(4), pp. 365377. 27


[14] Silva, D. M. L. D., Lima Jr., M. H. A., Jacob, B. P., 2008, “Pipeline-laybarge interaction model for the simulation of s-lay installation,” Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering. Estoril, Portugal. [15] Gong, S., Xu, P., Guo, Z., 2014, “Numerical modelling on dynamic behaviour of deepwater S-lay pipeline,” Ocean Engineering, 88(0), pp. 393-408. [16] Hall, M., and Goupee, A., 2015, “Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data,” Ocean Engineering, 104, pp. 590603. [17] Masciola, M., Jonkman, J., and Robertson, A., 2014, “Extending the capabilities of the mooring analysis program: a survey of dynamic mooring line theories for integration into FAST,” Proceedings of the ASME 33th International Conference on Offshore Mechanics and Arctic Engineering. San Francisco, US. [18] Jonkman, J., 2013, “The new modularization framework for the FAST wind turbine CAE tool,” Proceedings of the 51st AIAA Aerospace Sciences Meeting. Dallas, US. [19] Low, Y. M., and Langley, R. S., 2006, “Time and frequency domain coupled analysis of deepwater floating production systems,” Applied Ocean Research, 28(6): 371-385. [20] Fossen, T.I., 2011, Handbook of marine craft hydrodynamics and motion control. John Wiley & Sons Ltd. [21] T.F. Ogilvie, 1964, “Recent progress towards the understanding and prediction of ship motions,” Fifth Symposium on Naval Hydrodynamics, Bergen, Norway. [22] Bray, D., 2003, Dynamic positioning, Oilfield Publications Limited. [23] Ramberg, W., Osgood, W. R., 1943, “Description of stress–strain curves by three parameters,” Technical Note No. 902, National Advisory Committee for Aeronautics, Washington DC. [24] Clough RW, Penzien J., 1993, Dynamics of structures. 2nd ed. McGraw-Hill. [25] Orcina Ltd., Orcaflex Manual, 2005 [26] Mattiazzo, G., S. Mauro and P.S. Guinzio, “A tensioner simulator for use in a pipelaying design tool.” Mechatronics, 2009. 19(8): pp. 1280-1285.

28


Figure Captions List Fig. 1

Diagrammatic sketch of coupled S-lay roller, pipeline and DP system.

Fig. 2 Fig. 3

Solution procedure of pipelay vessel motion with coupled DP control system. S-lay pipeline idealized lumped-mass discretization model.

Fig. 4

Schematic diagram of contact search between the pipeline and rollers.

Fig. 5

Fig.10

Schematic diagram of validation model with specified system parameters and vertical oscillation time function. Comparison of predicted maximum bending moment along pipeline arc length between coupled S-lay pipeline-roller model and OrcaFlex results. Comparison of roller R1 and the pipeline line clearance time histories between roller-pipeline model and OrcaFlex. Comparison of pipe bending stress-strain trajectories at arc length 31m between roller-pipeline model and OrcaFlex. Vessel motion with PID controller applied: (a) Surge, sway and yaw time histories, and (b) Trajectory on the water surface. Characteristics of HYSY 201 pipelay vessel.

Fig.11

Schematic diagram of S-lay model static configuration.

Fig.12

Representative top-end pipe tensile force time history from coupled roller-pipeline-DP analysis. Pipe maximum bending stress (a) and maximum strain (b) results along pipe arc length. Vessel response time histories: (a) heave, (b) pitch, (c) surge, and (d) total allocated thrust force.

Fig. 6 Fig.7 Fig.8 Fig.9

Fig.13 Fig.14

29


Table Caption List Table 1

Input data for the bending pipe

Table 2

Hull parameters of pipelay vessel HYSY201

Table 3

Environmental condition in the studied case

Table 4

Statistical results of vessel displacement and thrust force

30


Table 1 Input data for the bending pipe Total upstretched length 150m Outer diameter, D

323.9mm

Wall thickness

38.1mm

Number of elements

150

Element size (constant)

1m

Stiffness kR in Eq.11

3.5x106N/m

Yield stress (σy)

350 MPa

Young’s Modulus

207GPa

Yield offset

0.002

Hardening exponent

25.58

31


Table 2 Hull parameters of pipelay vessel HYSY201 Vessel size Length between perpendiculars

185 m

Breadth

39.2m

Draught

9.3m

Displacement

56380 t

Vertical distance between keel and gravity center

14.4m

Radius of gyration for roll

15.7 m

Radius of gyration for pitch

48.7 m

Radius of gyration for yaw

50.8 m

Thrusters Thrust of number 1-2

816kN

Thrust of number 3-7

589kN

Input Electrical Power of number 1-2

4500kW

Input Electrical Power of number 3-7

3200kW

Tensioners

2*200t

32


Table 3 Environmental condition in the studied case Conditions

Direction

Description

Wind

0° along x axes

16m/s wind (10min average) speed

Wave

0° along x axes

Hs=2.0m,Tp=6.0s, JONSWAP type with a peak enhancement factor γ of 3.3

Linear sheared current

0° along x axes

u=1.2m/s at sea surface

Seabed

vertical

Flat seabed, linear soil stiffness 100kN/m3

33


Table 4 Statistical results of vessel displacement and thrust force Value

Analysis method

Coupled Decoupled Mean Difference Coupled Maximum Decoupled Difference Coupled Minimum Decoupled Difference

Surge (m)

Heave (m)

Pitch (deg.)

-0.033 -0.04 21.21% 1.73 1.93 11.56% -1.47 -1.87 27.21%

-0.94 -0.9 -4.26% -0.75 -0.7 -6.67% -1.14 -1.11 -2.63%

-0.12 0 -100.00% 0.35 0.54 54.29% -0.61 -0.55 -9.84%

Thrust (kN) #1-#7 121.74 169.92 39.58% 171.58 214.34 24.92% 51.44 80.61 56.71%

34


wind tensioners

wave

stinger

DP thruster system

current pipe-roller contact

Fig.1 Diagrammatic sketch of coupled S-lay roller, pipeline and DP system.

35


Pipeline Reaction Force

Vessel Motion Solver

Measured Position Vessel Position Resultant Thrust Force

Discrete-Time Kalman-Filter

PID Controller

Thrust Force Allocation

Environmental Forces

Fig.2 Solution procedure of pipelay vessel motion with coupled DP control system.

36


z

PN y pipeline

x

kR

tensioner roller line

No contact Contact seafloor

Pi

D di

baseline kz = ks.D

Pi+1

kA

reference plane

kB



Pi Pi-1 P0 P1

H

Fig.3 S-lay pipeline idealized lumped-mass discretization model.

37


PCJ

Pj

Pj-1

n Qe

L

Si

element j

di,j-1

di,j

di S CI

Qr S iR

(a)

ne

roller i

nr

(b)

Fig.4 Schematic diagram of contact search between the pipeline and rollers: (a) Search for minimum distance between the central point of the roller-line (SC) and the central point of the pipe element (PC), then (b) Calculate the common perpendicular.

38


z (t )  cos( 29 t )

R3

12" pipeline

R2

R1

73 m Roller R7 R8

G=1000kN

Fig.5 Schematic diagram of validation model with specified system parameters and vertical oscillation time function.

39


OrcaFlex coupled pipe-roller model

maximum moment (kN.m)

1200 900 600 300 0 0

40 80 120 arc length (m)

160

Fig.6 Comparison of predicted maximum bending moment along pipeline arc length between coupled S-lay pipeline-roller model and OrcaFlex results.

40


Fig.7 Comparison of roller R1 and the pipeline line clearance time histories between roller-pipeline model and OrcaFlex.

41


0.94 0.92

OcraFlex Coupled pipe-roller model

strain (%)

0.90 0.88 0.86 0.84 0.82 0.80 374.0 374.1 374.2 374.3 374.4 374.5 374.6 stress (MPa)

Fig.8 Comparison of pipe bending stress-strain trajectories at arc length 31m between roller-pipeline model and OrcaFlex.

42


90

angle (degree)

yaw 75

60

45 0

200

400

600

800

1000

displacement (m)

30 sway surge

20 10 0 -10 -20 0

200

400

600

800

1000

time (s) (a)

-10.1

 2 (m)

-10.0

-9.9

-9.8

9.8

10.0

1 (m)

10.2

10.4

(b)

Fig.9 Vessel motion with PID controller applied: (a) Surge, sway and yaw time histories, and (b) Trajectory on the water surface.

43


(a). Lines plane

(b). Thrusters configuration

(c). Geometric mesh

Fig.10 Characteristics of HYSY 201 pipelay vessel.

44


z

wave, wind

x CG (0,0,0)

1175m

current pipe arc length 2243m

H=1234.7kN

X=-1650

Fig.11 Schematic diagram of S-lay model static configuration.

45


top tension (kN)

4,000 2863kN

3,600 3,200 2,800 2,400 2,000 1,600 5000

5200

5400 5600 time (s)

5800

6000

Fig.12 Representative top-end pipe tensile force time history from coupled rollerpipeline-DP analysis.

46


(a)

stress (MPa)

400 coupled solution

320

static solution

240 160 80 0

0

500

1000

1500

2000

2500

0

500

1000 1500 arc length (m)

2000

2500

(b)

strain (%)

0.3 0.2 0.1 0.0

Fig.13 Pipe maximum bending stress (a) and maximum strain (b) results along pipe arc length.

47


(a)

heave (m)

-0.6

decoupled solution

coupled solution

-0.8 -1.0 -1.2 5000

5200

5400

5600

5800

6000

5200

5400

5600

5800

6000

5200

5400

5600

5800

6000

5200

5400 5600 time (s)

5800

6000

(b)

pitch (deg.)

0.6 0.3 0.0 -0.3

(c)

surge (m)

-0.6 5000 3.0 1.5 0.0 -1.5

(d)

total thrust force (kN)

-3.0 5000 1,600 1,200 800 400 5000

Fig.14 Vessel response time histories: (a) heave, (b) pitch, (c) surge, and (d) total allocated thrust force.

48

Modeling and Simulation of Deepwater Pipeline S-lay

Modeling and Simulation of Deepwater Pipeline S-lay

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