2024年4月28日发(作者：)

第

23

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9

期

2019

年

9

月

Article ID

：

1007-7294(2019)09-1099-11

船舶力学

Journal of Ship Mechanics

Yol.23 No.9

SQM

Transient Pipe Tension Influence on Dynamic Positioning

Control During S-Lay Installation

AI Shang-mao 1, LIU De-peng1, LI Peng1,2, MA Gang1

(1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China; 2. CNOOC CENER

Tech Company Oil Production and Service Branch, Tianjin 300457, China)

Abstract

：

Traditionally, dynamic positioning (DP) capability and tensioner capability of a laying ves­

sel are calculated by static tension while the dynamic effects are either ignored or taken into account

by empirical load amplification factors. A coupled dynamic model of normal S-lay was developed to

simulate the closed-loop automatic control process integrating with DP controller. The model suffi­

ciently takes account of the pipeline-rollers contact and the coupling between the pipeline and the

controlled surface vessel. By conducting dynamic simulation in time domain and comparing the results

achieved, significant coupled dynamic behaviours of applied DP thrust forces are observed, which of­

fers very intuitive evidences of the transient tension effects concerning DP capacity assessment. And

tensioner capacity based static results of the tension force would be overestimated.

Key words: S-lay

；

coupled analysis

；

transient tension

；

dynamic positioning

CLC number: O35 Document code

：

A doi: 10.3969/.1007-7294.2019.09.007

0 Introduction

S-type pipelay operations in deepwater are much more complicated than those in shallow

water, and put greater demands on the laying equipment. Normal pipelay starts after comple­

tion of the start-up operation when the start-up head touches down on the seabed. Deepwater

installation vessels typically require a dynamic positioning (DP) system due to its good perfor­

mance and the simplified operation procedures for the station-keeping.

The governed parameters for an S-lay configuration include the pipe material properties,

tension at the pipelay vessel, stinger shape (curvature radius and roller positions), departure

angle and water depthY1]. Among these parameters, tension at the vessel is the only parameter

that can be manipulated during the installation by adjusting the vessel position or the holding

force of tensioners. The free spanning part from the touchdown point to the stinger gets longer

when the water gets deeper. This will make the free spanning pipeline heavier. In order to main-

Received date: 2019-03-09

Foundation item: Supported by the National Natural Science Foundation of China (Grant No.51979050);

the Natural Science Foundation of Heilongjiang Province of China (Grant No. E2017029)

Biography

：

AI Shang-mao(1978-), male, associate professor;

LIU De-peng(1994-), Ph.D. student;

LI Peng(1984-), senior engineer, corresponding author, E-mail: lipeng9@.

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tain the sagbend configuration, a large tension force has to be applied to the pipe in order to

secure a safe bending radius. Also, when the stinger guides the pipe as it bends from horizon­

tal to the inclination, a more curved stinger is required to guarantee that the pipe does not reach

the end of the stinger for the steepest expected departure angle@2].

To avoid losing the pipeline, the applied tension of the pipeline must be less than the work­

able tension limitation of tensioners. Additionally, the thrusters of a dynamic positioning (DP)

system must have the capability to compensate for the external tension forces of pipe acting

on the vessel. Traditionally, DP capability and tensioner capability of a laying vessel are cal­

culated by static tension while the dynamic effects are either ignored or taken into account by

empirical load amplification factors. This representation lacks the detailed understanding of dy­

namic interactions between the pipe and the DP station-keeping. A dynamic simulation in time-

domain coupled with DP controller is significant to identify limiting environmental operation

conditions and to analyze any risk associated with thruster saturation or thruster failures@3A.

Some researchers have already emphasized the dynamic effect of the vessel motion on

the spanning pipeline, such as Clauss et al (1992)[4] and Gong et al (2014)[5]. However, it is

worth mentioning that the dynamic effective tension is still relative to the DP thrust force, be­

cause the DP system must compensate for the horizontal drag force of the pipeline. The purpose

of this study is to analyze the transient tension effect when integrating S-lay operations with

DP demand, since deepwater S-lay operations are a closed-loop automatic control process.

1 Numerical model of the pipeline

A variety of techniques and methods have been developed for decades to analyse the re­

sponse of marine pipelay system in a dynamic sea environment. the state-to-art computation

programs coupled by increasing computer capacity have provided sufficient accuracy of pre-

Fig.1 Lumped-mass discretization model of the S-lay simulation

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AI Shang-mao et al: Transient Pipe Tension Influence on …1101

diction and simulation in spite of existence of uncertainties due to pipe-soil interaction. Here­

in, the code orcaflex is chosen to implement S-lay analysis because of its friendly interface

with Matlab environment, which allows us to use a limited range of OrcaFlex’s facilities for

adding the dynamic positioning (DP) tasks.

In the global coordinate system

(XYZ),

the ending point $〇 of the pipeline anchors on the

flat seabed, while the point

PN

contacts with the tensioner at the other end as shown in Fig.1.

The axial stiffness of the line is modeled by simple spring elements between nodes, and bend­

ing is modeled by rotational springs. The pipeline is discretized into

N

elements

(Ek,

'=1 …%)

by N+1 lumped-mass nodes (P(, (=0■••%).

The lumped-mass of each element is concentrated on the nodes while the tension and the

bending are modelled by extensional and rotational springs. The nonlinear stress-strain rela­

tionship of the pipeline is characterized by a load-dependent path of moment-curvature. In the

Orcaflex, the Ramberg-Osgood formula is used, which has the following expression

(

1

)

where ! and — are the pipe curvature and moment, and are the pipe curvature and mo­

ment at the nominal yield stress, , and . are the Ramberg-Osgood equation coefficient and

hardening exponent.

The effective tension at the mid-point of line segment can be calculated as

T

e

=T

2

+(

1_2

")(P〇A〇_P

(

A

()

(S)

where

Tw

is the function relating axial strain to wall tension,

Pt

and P〇 are the internal and ex­

ternal pressure respectively; and 3〇 are the internal and external cross-section areas of the

stress annulus respectively; and " is Poisson’s ratio. The upward contact forces between pipe

and seafloor are included in the model while friction effects are neglected.

In practical situations, some of the rollers may miss the pipe contact, resulting in more

concentrated forces acting on a fewer number of rollers. If astern/ahead loading acts on the ves­

sel, the rollers can be simplified to a rigid line. Thus the stinger contact search becomes point-

wise and depends on the minimum distance 4 shown in Fig.1.

2 Controlled motion equation of pipelay vessel

2.1 Motion equations in time domain

The vessel response to waves is a sophisticated kinematics and dynamics issue. Potential

flow theory and the viscous flow empirical formula can be used to forecast the responses of

the vessel under the effect of waves, wind and current. When the pipelay vessel is considered

to be a rigid body, the motion equation in time-domain can be expressed by

⑶

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where ! i& the instant vessel displacement vector, !2 ■*. for the surge, sway, heave,

roll, pitch and yaw of the vessel, respectively. MF, MF and KF are structural mass matrix,

hydrodynamic added mass matrix, and total system stiffness matrix respectively. CF is the mem­

ory effects of the fluid field.

The exciting force F! on the right hand side including the environmental load, propulsion

forces in DP system and the pipeline reaction force acting on the vessel is written as

⑵

L

F!?F$ (%)+F$ (%)+F&'(%)+FWI+FDP

⑷

（F!

⑷

⑷

where F*' and F

bc

are the sea current and wind force, which are dependent on the aerodynam­

ic coefficients achievable by model tests. F=> is the total thrust forces of the dynamic position­

. , . ... .

ing system; F+ is the total reaction force of the pipeline acting on the vessel and comprises of

a few roller-pipe contact forces and the tension force at the top of the pipeline.

The standard procedure for performing pipelay dynamic analysis consists of two stages. A

static analysis is first applied with only the static components of the environmental loadings.

The initial equilibrium positions of the vessel are defined as the static positions of the ends of

pipelines. The governing motion equations of the pipeline are highly non-linear, and should

be solved iteratively using an incremental correction approach.

The dynamic solution of Eq.(3) may contain spurious high frequency response, a feature

inherent in the finite element method. The generalized-a integration scheme has controllable

numerical damping which is desirable since it removes this spurious, non-physical high fre­

quency response. This numerical damping also leads to much more stable convergence and

hence allows for longer time steps and much faster simulations.

2.2 PID controller and thrust allocation

The thrust forces confine a vessel to pinpoint in a certain permitted range. The Proportion-

Integration-Differentiation (PID) controller is herein adapted to control the pipelay vessel mo­

tions. The total thrust forces F=> in the PID controller consist of three components: surge, sway

and yaw forces, formulated as

F

dp

(e )?KP "+K. f

sdt+

KD

where

(5)

is the vessel position error,"

尸，

K. and K/ represent proportional gain coeffi­

cient, integral gain coefficient and differential gain coefficient. The function of the PID con­

troller takes instant position ! as input, and outputs the magnitude of thrust force. An effec­

tive way for filtering the oscillatory components of motion is Kalman-Filter^.

After the thrust system receives the commanded force signal, thrusters produce proper

forces and moment to compensate for the environmental loads. Considering a marine vessel e­

quipped with 6 azimuth thrusters, the generalized force vector is given by

FDP?$87

⑵

7

(

6

)

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AI Shang-mao et al: Transient Pipe Tension Influence on1103

The vector u contains the magnitude of the force produced by each individual thruster,

. .

冲

th ...

is the azimuth of the ! thruster, and the ! column of the matrix is given by

. . T

(!!) = [ cos!! 9 sin!! 9 -"#! cos!! +/$! sin!! ] (7)

th

where (!, ’#!) is the location of the ! thruster. The quadratic programming (QP) method is

used for the optimal thrust allocation algorithm.

2.3 Coupled solution with transient tension

The pipelay model comprises three distinct components: the vessel9 the pipeline and a set

of connecting contact springs. In this numerical simulation, all forces are not assumed to be

feedforward terms but transient forces coupled with the PID controller. The vertical compo­

nent of pipe reaction force acting on the vessel is passively compensated by the pipelay ves­

sel restoring forces; the horizontal tension of the spanning pipeline is left to active control by

the vessel motion control system.

The S-lay simulation is developed from integrating a marine systems simulator (MSS),

which contains guidance, navigation, and control blocks for real-time simulation by using Mat-

lab librariesS7T. Based on the framework of MSS, the pipeline, vessel and DP system are inte­

grated into a closed loop. And the flowchart of the simulation code for pipelay vessel motion

controlled by DP system is summarized in Fig.2.

Fig.2 Flowchart of MSS code for vessel motion controlled by DP system

3 Cases studies

3.1 Parameters and conditions

Major particulars of the DP pipelay vessel are summarized in Fig.3 and Tab.1 (obtained

from Yuan et al[8] and Sun et al[9]). There are seven azimuth thrusters in the pipelay vessel,

thrusters #1 and #2 are main thrusters with downgraded maximum thrust 734 kN in the aft of

the vessel. Five retractable thrusters are optimized for bollard pull, and the maximum thrust

of each retractable thruster is 530 kN. Assuming the vessel is fully actuated, the available con­

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trol input is the vessel thruster data limited to surge, sway and yaw.

Tab.l Major particulars of ‘HYSY 201’

Parameters

Length overall

Breadth molded

Depth molded

Operational draught

Values

204.65 m

39.20 m

14.00 m

7.4 m

Parameters

Tensioner

AUR winch

Loaded displacement

Values

2

x

200

t

400 t

59 014.895 t

^

g1

、&1

81m

®T

©

.r...............

f

丄

©

丄

50.5m I

®

T

^

乂

46m

vL/

II

Fig.3 Arrangement site of the thrusters of HYSY201

All studied cases are performed on a pipelay operation in 1 500 m water depth. The prop­

erties and input parameters of the laying pipeline are listed in Tab.2, and environmental con­

ditions are shown in Tab.3. An idealized fixed stinger is connected to the stern for launching

the pipe into the water at a suitable curvature. The pipeline is laid from 6.2 m below the main

deck level at the stern of the barge for the radius of 110 m. There are 20 rollers mounted on the

stinger section as shown in Fig.4, in which the rollers are numbered from up to down. It should

be pointed out that the aim of performing such cases is to investigate the coupling or transient

effect on operation simulation integrating DP demand; the capability of HYSY201 is not our

focus, since the realistic parameters of the stinger structure and rollers position equipped on

the HYSY201 are very different from the present model.

Tab.2 Pipe properties and parameters in studied cases

Pipe properties and parameters

Steel modulus of elasticity

Weight per-unit-length in air

Steel outside diameter

The coefficient a and "

Steel wall thickness

Yield stress

Poisson! s ratio

Total upstretched length

Vertical distance between two ends

Horizontal distance between two ends

Seabed stiffness

Roller stiffness

Number of elements

Element size

207 000 MPa

4 296.78 N/m

60.96 cm

0.002, 25.58

3.048 0 cm

448.00 MPa

0.3

2 558 m

1 506.2 m

1 842 m

100 kN/m

3.5x106 N/m

320

2 m in overbend zone, 10 m in the other zones

Values

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AI Shang-mao et al: Transient Pipe Tension Influence on …

1105

Tab.3 Environmental conditions in studied cases

Conditions

Wind

Wave

Linear sheared current

Direction

Astern

Astern

Astern

Description

16 m/s wind (10 min average) speed

!"=2.0 m, #$=6.0 s, JONSWAP type with

a peak enhancement factor y of 3.3

%=1.2 m/s at sea surface

Fig.4 Arrangement position of the rollers in the pipelay simulation

3.2 Transient results and discussions

Firstly two transient coupled simulations are implemented by using the different PID co­

efficients. Fig.5 shows the contact results between rollers and pipeline in the case with high PID

coefficients, indicating that Rollers 17 and 20 are not in contact with the pipe. The time-his­

tory results of vessel surge motion and the top tension shown in Fig.6 demonstrate that differ­

ent PID coefficients lead to different vessel motion, and the DP controller is efficient to keep

the vessel around the target position. Few varieties of the statistical tension are observed from

both cases with low PID coefficients and high PID coefficients. The reason is that both of the

vessel motions are still very small compared to the water depth.

500 i

400

{

§

)

S

JO

J

P

2

U

O

U

i Max

I Min

oo

3

oo

2

oo

1

u

—

寸

•O'scr'-OOGNO — (Nrn

寸

>/^^〇卜〇〇

Fig.5 Statistic value of contact spring forces acting on 20 rollers of stinger

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(

M

-

麵

J

X

9400.0 9600.0

Time (s)

(a) Tension at the top of the pipeline TN

8000.0 9000.0

Time (s)

(b) Surge motion

Fig.6 Comparison of time history results between low PID and high PID case

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AI Shang-mao et al: Transient Pipe Tension Influence on

1107

In the following, the dynamic contribution is discussed based on the results with low PID

coefficients. Here a ratio defined by (Max-Mean)/Mean is used to investigate the dynamic con­

tribution for bending stress and tension force of the pipeline.

The maximum bending stress in the overbend and the sagbend sections is shown in Fig.7.

The maximum bending stress in the overbend section predicted from the coupled analysis dif­

fers from mean value by the ratio of 1Q

〜

2Q. It can be concluded that the coupled dynamic

approach has little dynamic effect on the stress safety assessment of pipes compared to the static

state approach, since the overbend stress is much larger than the other part. The large variations

of bending stress are observed in the lift-off point zone (about 200%) and touchdown zone

(9.28%).

0.6

5000

-Maximum value

Mean value

S 4000

3000

(u 2000

1000

400

800

200

Arc length (m)

1600

2000

2400

Fig-8

Time history statistics results of effective tension along arc length

2400.0 ■

Low PID

2000.0

-

Mean

Max

Min

1361.2

2104.8

456.1

1600.0 -

1200.0

800.0 -

400.0

7000.

7200. 0

7400. 0

Time (s)

7600.07800. 0

8000

Fig-9 Time histories of transient tension force (!

〇

) at the bottom end of the pipeline

with low PID coefficient

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Fig.8 demonstrates the pipe effective tension and dynamic contribution along the whole

arc length. Large variations of the dynamic tension are observed, the ratio at most positions

exceeds 37%. At the touchdown zone the ratio rises to 60.4%. Thus the dynamic contribution

is significant for the effective tension.

Lastly it is necessary to investigate the transient tensions of two pipe-ends, since the two

tensions are directly related to the tensioners and DP system. According to statistics value of

in Fig.1), the dynamic maximum tension of the

the tension at the top end of the pipe (Point

PN

high PID case is 44.3% higher than the mean value (shown in Fig.6a). It is noted that this tran­

sient tension force TN exceeds nominal allowance tension capacity 4 000 kN of the blocked

tensioners. On the other hand, the dynamic effect of the tension force T。（shown in Fig.9) is

also remarkable, with 66.5% larger than the mean value.

4 Conclusions

Simultaneous prediction of the transient tensions on the structural, motion response and

DP force provides useful insights into S-lay operations in this study. The numerical model in­

tegrates the major aspects related to normal deepwater S-lay operation including the structural

behaviour of the pipe, a roller-pipeline interaction, the DP forces via a PID controller and

Kalman filter, and the loose coupling between the pipe structural response and the vessel mo­

tion response. The major contributions of this study are summarized as follow:

(1) A PID controller and Kalman Filter are integrated into the pipelaying motion equations

in time domain. This coupling approach can be used to effectively predict the pipeline transient

tension, surface vessel motion and required thrust force of the controller simultaneously to en­

sure operation safety.

(2) Numerical simulation results showed that the dynamic contributions are more signifi­

cant for the tension force at the top of the pipeline than for the stress and strain of the pipeline

structure. Tensioner capacity based static results of the tension force would be overestimated.

(3) Numerical simulation results offer very intuitive evidence of transient pipe tension ef­

fects on deepwater S-lay DP thrust. A coupled analysis approach in deep water is therefore rec­

ommended for the prediction of DP thrust forces to compensate the horizontal pipe tension.

References

[1] Bai Y, Bai Q. Subea pipelines and risers (1st ed)[M]. Norway: Elsevier Science Ltd., 2005.

[2] Yun H D, Peek R R, Paslay P R, Kopp F F. Loading history effects for deep-water S-lay of pipelines[J]. Journal of Off­

shore Mechanics and Arctic Engineering, 2004, 126: 156-163.

[3] Armaoj"lu E, Monti P. Advantages of using a time-domain approach for dynamic positioning (DP) pipelay studies[C]// In:

Proceedings of the 33rd International Conference on Ocean, Offshore and Arctic Engineering. San Francisco, California,

USA, 2014.

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AI Shang-mao et al: Transient Pipe Tension Influence on *1109

[4] Clauss G F, Weede H, Riekert T. Offshore pipe laying operations-Interaction of vessel motions and pipeline dynamic stress-

es[J]. Appl. Ocean Res., 1992, 14: 175-190.

[5] Gong S，Xu P, Bao S, Zhong W, et al. Numerical modeling on dynamic modeling of deepwater S-lay pipeline!】]. Ocean

Eng., 2014, 88: 393-408.

[6] Cadet O. Introduction to Kalman filter and its use in dynamic positioning systems[C]// Dynamic Positioning Conference.

Houston

，

USA

，

2003.

[7] Fossen T I. Handbook of marine craft hydrodynamics and motion control[K]. John Wiley & Sons Ltd, 2011.

[8] Yuan F, Guo Z, Li L, Wang L. Numerical model for pipeline laying during S-lay[J]. Journal of Offshore Mechanics and

Arctic Engineering, 2012, 134: 21703(1-9).

[9] Sun L，Zhu X，Li B，Ma W. Comparison of time domain simulation and steady state capability analysis of dynamic posi­

tioning^]// Proceedings of the 25th International Ocean and Polar Engineering Conference. Kona

，

Hawaii

，

USA

，

2015.

s

型铺管瞬态张力对动力定位控制的影响

艾尚茂刘德鹏李鹏

u

，马刚1

(1.哈尔滨工程大学船舶工程学院，哈尔滨150001# 2.中海油能源发展采油服务公司，天津300457)

摘要：

铺管船动力定位能力和张紧器能力通常基于静态管线张力或者采用一定动力放大系数进行评估，忽略了管线张

力动态的影响。本文集成PID动力定位控制和卡曼滤波，充分考虑管线-辊筒接触及管线-铺管船耦合，发展了一种S型

铺管作业的闭环自动控制数值模型。时域数值结果对比分析表明：动力定位推力动态耦合效应显著，亦证明了管线张力

的瞬态效应对深水S型铺管作业动力定位评估影响深远，且基于静态管线张力评估张紧器能力将会高估。

关键词

：S型铺管；耦合分析；瞬态张力；动力定位

中图分类号：

O35

文献标识码

：A

基金项目：

国家自然科学基金项目（51979050);黑龙江省自然科学基金项目（E2017029)

作者简介

：艾尚茂（1978-)，男，哈尔滨工程大学副教授；

刘德鹏（1994-)，男，哈尔滨工程大学博士研究生；

李鹏（1984-)，男，中海油能源发展采油服务公司高级工程师；

马刚（1984-)，男，哈尔滨工程大学副研究员。