Acta Mech SinDOI 10.1007/s10409-011-0400-9

RESEARCH PAPER

Dynamic analysis of an oshore pipe laying operationusing the reel method

Marek Szczotka

Received: 24 August 2010 / Revised: 15 September 2010 / Accepted: 15 September 2010The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag Berlin Heidelberg 2011

Abstract A system designed for a rigid and flexible pipelaying purposes is presented in the paper. Mathematical andnumerical models are developed by using the rigid finite el-ement method (RFEM). The RFEM is an ecient solutionin the time domain. Static and dynamic problems related topipe installation are solved by taking the advantage of simpleinterpretation and implementation of the method. Large de-formations of the pipe during spooling and when it is reeledout at sea are considered. A material model implementedis used to take into consideration nonlinear material proper-ties. In particular, the full elasto-plastic material characteris-tics with hardening and Bauschinger eect are included. Dy-namic analyses are performed and the results attached in thiswork demonstrates how the sea conditions influence the ma-chinery and pipeline, assuming a passive reel drive system.The influence of several other operational parameters on dy-namic loads is verified. An active system, implemented as apart of the mathematical model, improves the system perfor-mance. Some results are presented as well.

Keywords Oshore pipeline installation Reel vessel Large elasto-plastic deformations

M. Szczotka (

)University of Bielsko-Biaa, Willowa 2,43-309 Bielsko-Biaa, Polandand AXTech AS, Verftsgt. 10, P.O. Box 2008,6042 Molde, Norwaye-mail: marek.szczotka@axtech.no

1 Introduction

Exploration of under seabed natural resources requirespipelines, risers and other communication and transporta-tion systems [1]. As exploration increases, the natural re-sources are more and more exhausted. Distributed fields anddeep water installations are generating new requirements forpipelines and other oshore systems. Companies are invest-ing large resources in order to design, install and operatepipelines. Large percentage of the total cost is the materialcost. Due to large forces and significant deformations duringthe installation and operation, usually high strength materialsare used, which are expensive [2,3].

The largest pipes are used as oil and gas transportlines. Usually they are installed on seabed using a lay barge,equipped with a special structure called the stinger. Installa-tion methods are today well standardised and introduced tothe oshore practice. However, each new construction re-quires an individual approach, due to the specific, uniqueproject requirements. In spite of the existence of generalpurpose finite element method (FEM) packages, the industrystill developes and uses special FEM built for the purposemodels. FEM packages remains the main analysis tool andmethod, and many dierent problems related to installationand operation are solved [2]. In a conceptual project phase,the application of general, commercial FEM packages maynot be suitable in terms of time and resources. Ecient, sim-plified special purpose models are also developed in order tosupport control systems, especially if they allow for the real-time simulations.

Many dierent methods are used in pipeline construc-tion. Most frequently used methods utilise a lay barge, which

2 M. Szczotka

has to be transported to the location. Then, having somesupport provided by other vessel, it can work as a factory.Lay barges are almost always used for large pipeline con-struction (diameters over 20, sign means inch pipe). Thefirst pipe lay barges were used in the Gulf of Mexico in the1940s and 1950s. Initially, those systems used S-lay method.Since then, with water depth increase, many barges havebeen equipped with an adjustable, vertical lay ramp, found-ing a J-lay technique. An overview can be found in severalbooks Refs. [25].

The lay method assumed in the paper is the reel method,which has several advantages. The first one is related tothe prefabrication, which is performed onshore. Therefore,costly oshore support is very limited and it depends lesson the weather conditions. The whole spooling is arrangedonshore (in a spool base). This makes the method very com-petitive in a financial frame. The second advantage lies inthe high laying rate. The reel method is especially eectivewhen small and medium diameter pipes must be laid, in afew shorter lines. A typical reel lay vessel is shown in Fig. 1.

Fig. 1 Typical vessel configuration for reel lay method

A mathematical model of the reel, pipe, lay ramp andvessel has been worked out. The main goal is to performa dynamic analysis of the system, operated at the roughsea. The drive system considered is a passive, back tension,which provides a braking force. The pipeline is unreeledby the use of a traction force, generated by a tensioner. Asthe vessel moves on waves, large inertia forces may occur,causing an unstable reel behaviour. An active drive system,which has similar power as the passive one, has been sim-ulated, too. A good improvement in the equipment perfor-mance has been achieved.

As the dynamic model is considered, pipe vibrations,together with lay ramp oscillations can be simulated. An-other approach to the problem has been presented in Ref. [6],where the so-called quasi-dynamic model was developed andused. In the mentioned paper, the pipe behaviour was cal-culated in the inner quasi-static loop, determining the pipeshape and reaction forces acting on the reel. Only the dynam-ics of the reel has been solved, neglecting the vibrations ofthe pipe. In this paper, the RFEM, described in Ref. [7], hasbeen extended in order to take into account dynamics of thesystem with material nonlinearities (elasto-plastic character-istics), large deformations and contacts. The performanceof the equipment and the influence of the pipe dynamics is

studied by the model and software developed, when the lay-ing vessel is operated on sea waves.

The calculation results presented in the paper have beenobtained from an own computer programme RTPV, which isbased on developed mathematical models. It allows forcesacting on the pipe as well as on the equipment to be deter-mined in an easy way. The conceptual studies can be per-formed, which may conclude the ability of given vessel tosafely perform the construction work in specified weatherconditions.

2 Mathematical model for dynamic analysis

2.1 Pipelay vessel motion

An example pipelay vessel is presented in Fig. 1 (http://www.wartsila.com). This particular system has two reels,and a lay ramp, equipped with tensioners. Although theships movement caused by sea waves is spacious, this paperassumes that the critical behaviour of the system is causedby heave, surge and pitch. Therefore the system consideredis planar. The assumption about planar motion is consistentwith a practical experience.

Dynamic analysis of an oshore pipe laying operation using the reel method 3

The response of a vessel to the ocean waves can be cal-culated by the application of ship theory and several sim-ulation tools are used, for example WAMIT, VERES [8,9].Both regular and irregular wave theories are in use, howeverirregular waves describe much better a real sea state. One ofthe simplest method to simulate the irregular wave, used alsoin this work, is summation of sinusoidal wave components.The linear, long crested wave model is defined by

(t) =Nw

j=1

Rj sin( jt + j), (1)

where (t) is the height of wave surface elevation, Nw is thenumber of wave components, Rj is the Rayleigh distributedrandom amplitude, Rj =

2S ( j) j, j = j j1,

S () is the wave spectrum, j is the random phase (with uni-form distribution).

The ship response to the assumed wave, consider-ing given vessels response amplitude operators (RAO) is aknown function of time

xS = f (t, (t),RAO()) , (2a)

yS = f (t, (t),RAO()) , (2b)

S = f (t, (t),RAO()) , (2c)

where xS , yS , S are surge, heave and pitch of the vessel,respectively.

2.2 Kinetic and potential energy of the system

The pipe is discretized by means of the rigid finite elementmethod (RFEM) [7]. In its principle, the body (a beam) isdivided into n + 1 rigid elements with appropriate mass andinertia properties, connected by n massless spring-dampingelements, representing stiness and damping properties. Themain advantage of the method is its simple interpretationand easy implementation. The RFEM can not compete withstandard finite element method (FEM). The reason for thisis a poor level of stress and deformation details, especiallywhen geometric details have to be analysed. However, for aglobal analysis of deformations, dynamics and modal anal-ysis, RFEM has been successfully verified by many exper-iments [7]. Considering a beam model presented in Fig. 2,the equations of motion of the system are derived using thismethod.

Fig. 2 Pipe discretized by rigid finite elements

In the classic RFEM method, the coecient of bendingstiness of spring-damping element, can be calculated fromthe simple relation [7]

cB =EIl

, (3)

where E is the Young modulus of elasticity, I is the secondmoment of inertia of cross-section of a beam, l is the ele-ment length.

Each rigid element has one degree of freedom with re-spect to previous element: i = ii1. The resulting bend-ing moment due to spring-damping element deformation, isgiven as

MB = cB(i i1) , (4)where i1 and i are rotation angles of rigid elements at-tached to the spring-damping element.

However, due to the elasto-plastic material model con-sidered, the method diers from the above description. In-ternal forces due to material deformations are assumed asnon-potential forces and are treated as external loads. Thesecomponents are then added to the right side vector of theequations of motion, described later.

The mass and moment of inertia, mi, Ii as well as theelement length li, are assigned when performing the discreti-sation. The properties of the reel are assigned to the elementnumber n. Assuming that each element has its mass centre

4 M. Szczotka

in the half element length, the location of the mass of theelement i can be obtained from equations bellow

xC,i = xS +i

j=0

l(i)j cos( j) , (5a)

yC,i = yS +i

j=0

l(i)j sin( j) , (5b)

where i = S +i

j=0 j, l

(i)j =

l j, for j < i,

l j/2, for j = i.The Lagrange second order equations are used in order

to derive dynamic equations of the system

ddtTk Tk+Vk= Qk, for k = 0, 1, , n, (6)

where T , V are the kinetic and potential energy, Q is the nonpotential, generalised force.

The kinetic energy of i-th rigid finite element equals

Ti =12

mi(x2C,i + y

2C,i

)+

12

Ii2i , (7)

and after dierentiating relations (5) with respect to time andsubstituting into Eq. (7), one obtains

Ti =12

mi{x2S 2xS

i

j=0

l(i)j j sin( j)

+

[ i

j=0

l(i)j i sin( j)]2+

[ i

j=0

l(i)j i cos( j)]2

+y2S + 2ySi

j=0

l(i)j j cos( j)}+

12

Ii2i . (8)

After some transformations, the Lagrange operatork(Ti) = ddt

Tik Tik

can be written as

k(Ti) = mi[yS l

(i)k cos(k) xS l(i)k sin(k)

+l(i)k

i

j=0

l(i)j j cos(k j)

+l(i)k

i

j=0

l(i)j 2j sin(k j)

]+ k,iIii, (9)

where k,i is the Kronecker delta, k i.For the whole system (RFEi, i = 0, 1, , n), the fol-

lowing summation has to be performed

T =n

i=0

Ti, (10)

and the operator k takes the form

k(T ) =n

i=k

k(Ti)

= yS cos(k)n

i=k

mil(i)k xS sin(k)

n

i=k

mil(i)k

+

n

i=k

mil(i)k

i

j=0

l(i)j j cos(k j)

+

n

i=k

mil(i)k

i

j=0

l(i)j 2j sin(k j) + Ikk,

for k = 0, 1, , n. (11)Finally, the form convenient for implementation is con-

sidered

k(T ) =n

j=0

ak, j j cos(k j)

xS Ak sin(k) + yS Ak cos(k)

+

n

j=0

2j bk, j sin(k j), (12)

where Ak =n

i=kmil

(i)k , bk, j =

ni=max{k, j}

mil(i)k l

(i)j , ak, j = bk, j +

k, jIk.The potential energy, taking into account Eq. (2b), can

be expressed as following

V =n

i=0

mig(yS +

i

j=1

l(i)j sin( j)), (13)

where g is the standard gravity acceleration.Having Ak defined as in Eq. (12), one obtains

Vk= Akg cos(k), for k = 0, 1, , n. (14)

2.3 Generalised forces

Generalised forces Qk, arising from external forces andmoments, have to be defined. Consider the force F =[Fx Fy

]T, given in the global coordinate system, applied

on the rigid finite element i, as shown in Fig. 3. The coordi-nates of point of force application, in the global coordinatesystem, are

Fig. 3 External force F applied on RFEi

Dynamic analysis of an oshore pipe laying operation using the reel method 5

xF = xS +i

j=0

di, j cos( j + i, j), (15a)

yF = yS +i

j=0

di, j sin( j + i, j), (15b)

where ai and bi are the coordinates of the point of applicationin the local coordinate system

di, j =

l j, for j < i,

a2i + b2i , for j = i,

i, j =

0, for j < i,

arctan(bi/ai), for j = i.

Having applied the relation

Qi = FxxFi+ Fy

yFi, (16)

and expressing the force F using the normal and tangentialcomponents Ni and Ui (Fig. 3), one can write

Fx = Ni sin(i) Ui cos(i), (17a)

Fy = Ni cos(i) Ui sin(i). (17b)After simple transformations, the generalised force due

to the external force F applied on RFEi is obtained in theform

Qk(F ) = Uidi,k sin(k i + i,k)Nidi,k cos(k i + i,k), (18)

where k = 0, 1, , i.The relation (18) is applied to all contact forces, which

acts between pipeline elements and reel or lay ramp struc-ture, Fig. 4. Thus, the following are defined:

(1) generalised forces Q(r)k due to reel-pipe contact loads

F(n j)r , j = 1, 2, , p, p is the number of elements con-tacting with the reel,

(2) generalised forces Q(l)k due to pipe-lay ramp contact,

(3) generalised force Q(reel)k calculated as

Q(reel)0 = p

j=1

F(n j)r dj cos( j n r, j) +nD

i=1

MDi , (19)

where dj, r, j are defined similar to Eq. (15), nD is the num-ber of reel drives, MDi is the drive torque.

Fig. 4 Contact, streightener and tensioner forces

For the pipeline model used in this work (based on oneDOF elements), the only internal forces are bending mo-ments caused by element deformations. Usually, when thelinear elastic material properties are considered, one can usean approach based on potential energy of spring-damping el-ements SDE. In this paper, large deformations with elasto-plastic material model are considered, therefore bending mo-ments have to be included dierently. Bending moments dueto the pipe deformation are assumed to be non-potential gen-eralised moments, which are considered on the right side ofthe equations of motion as

Qk(Mj) = Mj( j1, j, j, j1), (20a)Qk(Mj+1) = Mj+1( j, j+1, j, j+1), (20b)

where Mj( j1, j, j, j1) is the bending moment, calcu-lated from the elasto-plastic material model, acting in SDE j.

During the spooling process, plastic deformations candevelop in the pipe material. In order to eliminate permanentplastic deformation from the product (before it leaves thevessel when laying on seabed), the lay ramp has a straight-ener. This component is modelled by a set of springs withrollers. If the element reaches certain location on the lay

6 M. Szczotka

ramp, it is guided by these springs through rollers. The plas-tic deformations are removed, and the pipe becomes straight.The spring element with stiness k(r)j , shown in Fig. 4, repre-sents one of such a roller. After similar transformations, thegeneralised force Qk(S j) due to normal force S j, is given bythe equation

Qk(S j) = S jd(i)j,k cos( k (i)j,k

), (21)

where j = 1, 2, , nS , nS is the number of rollers, S j = jk

(r)j is the j-th force due to roller spring deformation, j

is the spring deformation, = S + t, t is the lay rampinclination, d(i)j,k and

(i)j,k are defined in Eq. (15) and depend

on local coordinates of contact point between j-th roller andi-th finite element.

The tension force P0 ensures that the pipes tip is slid-ing along the lay ramp with the assumed velocity vL. Thenormal force N0, applied at the tip of RFE0, keeps the pointE on a desired path. Both forces have to be added to thesystem as generalised forces, which yields to

Qk(P0,N0) = P0l0 sin(t k) + N0l0 cos(t k),for k = 0, 1, , n. (22)

Forces P0 and N0 are two additional unknown reactionforces, which are calculated from constraint equations, to-gether with the equations of motion.

2.4 Constraint reactionsrigid lay ramp

Constraint reactions, ensuring desired motion of the pipe el-ement 0, in the case when the lay ramp is treated as a per-fectly rigid body (part of the vessel body), are derived in thissection. Consider that the point E has the speed equal tovL = vL(t) and it remains on the path defined by the lay rampinclination angle t. The following constraint equations areformulated

[vL(t)]2 =[x(D)E]2+[y(D)E]2,

y(D)E = tan(t)x(D)E + b,

(23)

where x(D)E =n

i=0li cos(i S ), y(D)E =

ni=0

li sin(i S ), arethe coordinates of the point E in the deck coordinate system{D}.

The accelerated form of Eq. (23) can be written as

n

i=0

ili sin(i S )

=vL(t)

1 + tan2(t) S

n

i=0

li sin(i S )

+

n

i=0

(i S )2li cos(i S ), (24a)

n

i=0

ili cos(i S )

=tan(t)vL(t)1 + tan2(t)

+

n

i=0

(i S )2li sin(i S )

+S

n

i=0

li cos(i S ), (24b)

0 = 0. (24c)

Equations (24a) and (24b) allows the forces P0 and N0to be determined. Equation (24c) ensures that RFE0 remainsparallel to the lay ramp guide axis. An additional, unknownreaction moment M0 is solved from Eq. (24c).

2.5 Constraint reactionsflexible lay ramp

The inclination angle t is considered to be an additionaldegree of freedom. This angle takes into account lay rampdeformation. The constraint equations are slightly dierentnow. Let a(L) and b(L) to be the coordinates of the origin ofthe system {L} (see Fig. 2) which is assigned to the lay ramp.Having defined the constraints in the local coordinate system{L} asx(L)E = vL(t), y

(L)E = 0, (25)

where x(L)E = x(L)0 +

ni=0

li cos(it), y(L)E = y(L)0 +n

i=0li sin(i

t), are the coordinates of the reel centre in {L}, and perform-ing simple calculations for determination of derivatives y(L)Eand x(L)E , the following equations can be obtained

t[a(L) sin() b(L) cos()] +

n

i=0

(t i)li sin(i t)

= vL +n

i=0

(i t)2li cos(i t)

+S[a(L) sin() b(L) cos()]

(t S )2[a(L) cos() + b(L) sin()], (26a)n

i=0

(i t)li cos(i t) + t[a(L) cos() b(L) sin()]

=

n

i=0

(i t)2li sin(i t)

+S[a(L) cos() b(L) sin()]

+(t S )2[a(L) sin() + b(L) cos()], (26b)0 t = 0, (26c)where = t S .

Equation (26c) plays the same role as Eq. (24c). Thus,unknown forces P0, N0 and reaction moment M0 are nowdetermined.

2.6 Equations of motion

Having considered relations (12), (14), (18)(21) and con-straints (24) or (26), the equations of motion of the systemwith constraint equations can be presented as follows

Dynamic analysis of an oshore pipe laying operation using the reel method 7

A q + C X = f ,

C T q = U ,(27)

where Al,s = [al,s cos(l s)]l,s=0,1, ,n, An+1,s=0,1, ,n = 0,An+1,n+1 = It, It is the lay ramp moment of inertia, q =[0 1 n t]T, X = [P0 N0 M0 MR]T, f =Q e G , Q = nk

i=1Q (i)(F i) + Q (M) +

nSj=0

Q ( j)(S j) +

Q (reel), Gl=0,1, ,n = gAl cos(l), el=0,1, ,n = Al(xS sin(l) yS cos(l))

nj=02j bl, j sin(l j), en+1 = mtdt cos(t +t)+

mtdt cos(t + t ){xS + yS

}, Gn+1 = mtgdt cos(t + t ), nk is

the number of elements in contact, C and U are constraintcoecient matrices defined by Eq. (26), mt is the lay rampmass, dt, dt , t are constants depending on the ramp centreof gravity location, MR is the additional torque applied onthe reel.

Equations (27) are valid if the lay ramp angle is consid-ered as additional degree of freedom. In the case when incli-nation angle t is constant during analysis, one could simplyremove the last component of the vector q with related rowin system matrixes and generate constraint matrices C andU according to Eqs. (24). Moreover, the number of com-ponents of the vector X may vary during simulation. Thedesign of reel drive system ensures that

0 0, at any time t. (28)Thus, if Eq. (28) is not fulfilled, the reel speed 0 = 0

and the reaction moment MR has to be applied. The associ-ated constraint equation for its determination is

0 = 0. (29)

The system is solved by the application of the RungeKutta method with constant time step h [10]. Before a dy-namic analysis of the system can be performed, a few staticand quasi-static pre-analyses should be done. The mathe-matical model presented has been implemented in an owncomputer programme RPTV.

3 Numerical simulations

3.1 Definition of load cases

Several input data sets are examined, in order to test the sys-tem in various conditions. The main parameters of the sys-tem are provided in Table 1. Two pipe sizes are considered:4 and 12, with unit masses 16 kgm1 and 128 kgm1.All numerical simulations presented have been performedwith the same integration step h = 0.001 s. The numberof elements assumed in all cases (including dierent pipesizes) is n = 250, where element length li = 1.0 m, fori = 1, 2, , n 1. Such a discretisation of the pipeline as-sumed provided both good numerical eectiveness and suf-ficient results quality.

Table 1 Main parameters of the system

Name Value

Vessel length/m 110

Reel storage capacity/t 2 500

Reel external diameter/m 26

Reel inertia (loaded)/(ktm2) 300Lay ramp mass/t 50

Lay ramp length/m 20

Lay ramp head radius/m 8

Lay ramp inclination/() 60

Table 2 presents assumed sea conditions. An influenceof dierent motion components and amplitudes on the sys-tem behaviour is explored. Data set A has no pitch motion.The sea state is built-up in the first 9 seconds. The reel isaccelerated form n = 0 at the initial time up to the nominalspeed during the first two seconds of the analysis.

Table 2 Sea conditions, load cases

Load case Heave/m Surge/m Pitch/()Ty = 6 s Tx = 8 s T = 7 s

A 1 1 0

B 0 0 1

C 1 1 2

D 2 2 3

The parameters describing laying speed, back tensionforce and the lay ramp flexibility are specified in Table 3. Apassive back tension drive system is considered. The level ofback tension force Ft, can be adjusted by the operator duringreeling out. However, in all simulation examples, the backtension is assumed constant and equal to 20 t or 70 t. Thelaying speed vL is assumed to be constant, too (after the reelspeed reaches the nominal value at t = 2 s). The symbol depicts the rigid lay ramp model, while the stiness assumedin load cases C3, C4 and C6 allows for a small angular de-formation of the ramp under the tension force.

Each plot has a legend, where assumed load case is de-fined, i.e. the symbol AC1 presents the simulation result per-formed with sea waves A from Table 2 and parameters C1from Table 3, etc.

Table 3 System settings assumed during laying

Configuration Ft/t vL/(ms1) ct/(MNmrad1)C1 20 0.25 C2 70 0.25 C3 20 0.25 600

C4 70 0.25 600

C5 70 0.50 C6 70 0.50 600

8 M. Szczotka

3.2 System performance with various parameters

All configurations of the wave parameters listed in Table 2are simulated with setting C1. The results are presented inFig. 5 (time course of the pipe tension force) and Fig. 6 (reelangular velocity). Course AC1, obtained when the pitch am-plitude equals zero, illustrates the insignificance of surge andheave motion (when the rigid lay ramp is used in the analy-sis). The pipe tension forces, as well as the reels speed arealmost unchanged, when the pitch angle of the vessel equalszero.

Fig. 5 Pipe tension eect of sea waves

The highest dynamic force in the pipeline has been ob-tained for the sea condition BC1. The pitch amplitude of 1assumed is relatively small, and it generates less accelerationof the reel in the first phase of simulation. But the dynamictension force is the largest among the analysed. For biggerpitch amplitudes, the first wave produces higher reel acceler-ation, loosing the pre-tension in the pipeline. For the highestpitch angle (set D in Table 2), the reel rotation is large at thebeginning of the analysis and a slack pipe is obtained. Dueto low back tension force assumed (20 t ), the reel rotates dueto its inertia. As described in Sect. 2.6, the speed of reel isconstrained (0 0), which ensures that no spooling-in ispossible. Clearly, the level of back tension force assumed isnot enough.

The amount of back tension can be adjusted, depend-ing on the product type, which is laid to the seabed. Theback tension can also improve the reel performance, whenappropriately selected. Figures 7 and 8 present the result ofchanging the back tension force from 20 t to 70 t. The seaconditions B and D are considered as the most representa-tive cases for the real operations. Now, the courses for Btboth 20 t and 70 t demonstrate that the resulting pipe ten-sion force in condition D is quite dierent. This example(DC2) shows that changing the tension can result in worseand dangerous situations. The value of 20 t is too small, but

70 t generates high peaks. Among analysed load cases, thebest combination of sea condition and back tension level hasbeen achieved for the condition BC2. The reel speed doesnot reach zero in this case (Fig. 8, green dashed line), how-ever the speed is far from a constant level (desired value).

Fig. 6 Reel speed, eect of sea waves

Fig. 7 Pipe tension, eect of back tension change

Next results concern the influence of lay ramp flexibil-ity. Assume the sea condition B and setting C1 as well asC3 (rigid or flexible ramp, back tension Bt = 20 t). Figure9 shows lay ramp deformation angle t and deformationspeed. The period of lay ramp vibration is determined byvessel motion (vessel heave and surge motion can becomemore important now). High frequency oscillations are gen-erated due to contact forces and some pipe vibrations. Theresult in Fig. 10 shows the eect of lay ramp flexibility onthe pipeline tension force. It is very beneficial to introducea flexible element into the ramp supporting structure. Peakdynamic tension forces are much smaller than those of the

Dynamic analysis of an oshore pipe laying operation using the reel method 9

system with the rigidly supported structure. Similar eectsare obtained for any other combination of the input data.However, the flexible lay ramp can not eliminate the surg-ing problem, which is clearly visible in Fig. 11. A similarcharacter of the angular velocity indicates the reel instability(partially as a derivative of low back tension level).

Fig. 8 Reel speed, eect of back tension change

Fig. 9 Lay ramp deformation and deformation velocity

Next consider the system with dierent laying speedsvL. Figure 12 presents the maximum tension force, obtainedwhen laying speed vL = 0.25 ms1 and vL = 0.5 ms1, forboth rigid and flexible lay ramp models. The results are ob-tained for load combinations: DC2 vs. DC5 and DC4 vs.DC6 (all 4 pipe). In every case, higher speed generateshigher dynamic loads. It happens due to higher dierencebetween reel velocity and pipeline laying speed defined bythe constraint reaction.

Fig. 10 Pipe tension, rigid vs. flexible lay ramp

Fig. 11 Reel speed, rigid vs. flexible lay ramp

Fig. 12 Peak tension forces when changing laying speed

10 M. Szczotka

All the results presented on proceeding plots concern a4 steel pipe. When a 12 pipe is considered, the results aresignificantly dierent. Figure 13 presents the tension forceand the reel speed for 4 and 12 pipe, assuming the loadcase BC2. Due to higher dynamic inertia forces, peak val-ues of the tension force are larger for the 12 pipe. Havingthe results for dierent pipe sizes, it may be concluded thatthe parameters, which allow us to keep the reel speed above0, when the 4 pipe is installed, do not ensure the same fordierent pipe sizes.

Fig. 13 Results for 4 and 12 pipes: (upper) pipe tension force,(lower) reel rotational speed

The last example in this section is to compare the dy-namic eects of the pipe. In Ref. [6] the problem was solvedby using a combination of a quasi-static (for the pipe itself)and dynamic analysis (reel motion). Only the equation ofmotion of the reel was integrated, considering pipe forcesacting on reel as the result of the static analysis, performedin each integration step. The quasi-static model is repre-sented by the following system of equations

F (q ) = 0 , (30a)

G (X ) = 0 , (30b)

Ir(r + S ) = Mr(t, q , X ), (30c)

where Eqs. (30a) and (30b) are the static equilibrium equa-tions and the constraint equations (solved by the Newtonmethod), Ir is the reel moment of inertia, Mr is the result-ing moment acting on the reel, Eq. (30c) is solved by thenumerical integration.

The results (time histories of the pipe tension force) arepresented in Fig. 14, and show how the pipe dynamics caninfluence the level of tension force. Smaller pipes (flexible)can be calculated with both models. Very similar courseshave been obtained for 4 pipe (upper plot in Fig. 14). Heav-ier and stier pipe, due to the base motion involved, gener-ates higher dynamic loads, and the reel rotates dierently.Therefore, when performing the calculations with the fulldynamic model defined in Eq. (27), a notable increase ofpeak tension force occurs. In the case when a pipe of largesize is analysed, or when the laying vessel moves signifi-cantly (higher sea state), the full dynamic model should beapplied.

Fig. 14 Pipeline tension forces obtained with full and quasi-dynamic models, (upper) pipe size 4, (lower) pipe size 12

Dynamic analysis of an oshore pipe laying operation using the reel method 11

It is demonstrated by the number of examples that itis not possible to maintain relatively constant speed of thereel, considering passive, constant braking moment. The ax-ial tension in the pipeline is very high and may be dangerous(for the personnel, equipment and product). It seems natu-ral to implement a modification to the reel drive system, thatwould enable a compensation of the vessel motions due towaves.

3.3 Active reel drive system

If the passive reel drive is replaced by an active one, the sys-tem can work very dierently. The results presented in thissection have been obtained from the model with a control-lable back tension. The amount of energy available on thevessel defines the operational limit for the equipment. Whenthe sea is too wavy, the requested pipeline tension can not bemaintained, therefore drive control relaxes the tension, us-ing the energy to maintain the speed of the reel constant, ifpossible. The control system is based on a digital PID con-troller, which obtains the control error calculated as the dif-ference between theoretical (joystick signal) and measuredreel speeds. A few electric motors, which speed and torqueis controlled by a frequency converter, can be applied. Inaddition, a feed forward PD controller can be added, withvessel pitch speed as the disturbance signal [11].

Figure 15 presents two surfaces. The upper one hasbeen obtained for the passive while lower for the active reeldrive. Courses of the pipeline tension, for two conditionsindicated in Fig. 15, are plotted in Fig. 16. The value ofroot mean square (RMS) (Ft) = f (Hz, Tz), presented on thevertical axis, has been calculated as

RMS(Ft) =

T

0

[Ft(t) F(0)t

]dt

T, (31)

where T is the total simulation time (T = 32 s), F(0)t is thenominal pipe tension at time t = 0, in the example assumedas F(0)t = 130 t.

Fig. 15 Passive vs. active drive, RMS

Quite a few simulations have been performed in orderto obtain the plot presented in Fig. 15. Significant waveheight is considered between 2.5 m Hz 5.0 m and sig-nificant wave period 6.0 s Tz 12.0 s. The active systemcan work with a relatively constant pipe tension and a con-stant angular velocity of the reel, up to waves Tz = 7.0 swhen Hz = 5.0 m, and up to Tz = 6.0 s with Hz = 2.5 m (theRMS 10 t ). If the vessel has to operate on high sea statewith short wave periods, the level of requested tension has tobe decreased.

Fig. 16 Passive vs. active drive, time courses of Bt

The improvement in resulting dynamic tension force isquite significant. If the drive system can adjust the back ten-sion Bt automatically, the vessel motion is greatly compen-sated. On a small and moderate wave sizes, there would be asimilar behaviour as if the sea would be calm. The lay speedcan also be significantly higher, if the energy installed is bigenough (or sea conditions are not demanding).

4 Conclusion

The mathematical model of the pipe laying machinerymounted on a vessel has been developed, as well as a com-puter analysis tool. It is used to simulate various conditionsand configurations. The results could be useful when plan-ning an installation work, defining a new equipment speci-fications, etc. On the basis of models and software devel-oped, one can find out how big forces are generated on thestructural members, and what loads act on the pipe. Largedeformations of the pipe are taken into account. The mate-rial characteristics used, together with mathematical model,give the possibility to include plastic deformations in thestatic and dynamic analyses. In the examples attached, plas-tic deformations are generated during the spooling, and later,

12 M. Szczotka

when the pipeline is reeled out at the destination.The pitch motion of the vessel strongly aects the per-

formance of the reel and the whole system. Heave and surgedo not influence significantly dynamics of the system, ex-cept the cases when flexible lay ramp is included. Somereduction of tension force peaks could be achieved by theflexibility in the lay ramp design. It has been illustrated thatthe passive drive system does not work very well on a roughsea. The full dynamic model, developed within this work,shows quite similar results to those obtained from the quasi-static model from Ref. [6]. However, when larger and heav-ier pipes are analysed, inertia becomes significant and thefull dynamics model (27) should be used. Similarly, if thelay ramp has a flexible connection, the model (27) allow usto take its vibrations into account. Another important fea-ture of the dynamic model is the simulation time. The fulldynamic analysis is approximately eight to ten times fasterthan the quasi-static one. The reason for this dierence areconvergence diculties in the Newton method applied whensolving the Eqs. (30).

The model presented is applied to verify the perfor-mance of the equipment dedicated to laying of oshorepipelines. Both passive and active reel drive systems canbe analysed. Using the simulation method, the parametersof such a control system can be examined. The amount ofrequired energy can be easily calculated, too. For the de-fined power available, one can obtain a map representing theability of the equipment and the vessel given, to perform theinstallation work safely during specified sea conditions.

Acknowledgements The author wishes to thank Company AX-

Tech AS, Molde, Norway, for valuable discussions. The paper wassupported by the Polish Ministry of Science and Higher Education(N N502 464934).

References

1 Sloan, E.: Oshore Hydrate Engineering Handbook. SPEMonograph, vol. 21 (2000)

2 Bai, Y., Bai Q.: Subsea Pipelines and Risers. Elsevier (2005)3 Kyriakides, S., Corona, E.: Mechanics of Oshore Pipelines.

Volume 1 Buckling and Collapse. Elsevier (2007)4 Palmer, A.C., King R.A.: Subsea Pipeline Engineering. 2nd

edn. PennWell Corporation (2008)5 Guo, B., Song, S., Chacko, J., et al.: Oshore Pipelines. Else-

vier (2005)6 Szczotka, M., Maczynski, A., Wojciech S.: Mathematical

model of a pipelay spread. The Archive of Mechanical En-gineering LIV 1, 2746 (2007)

7 Wittbrodt, E., Adamiec-Wojcik, I., Wojciech S.: Dynamics ofFlexible Multibody Systems. Rigid Finite Element Method.Springer (2006)

8 Neuman, J.N., Sclavounos, P.D.: The computation of waveloads on large oshore structures. In: Proceedings of 5th In-ternational Conference on the Behaviour of Oshore StructuresBOSS 88, June 21-24, Trondheim, Norway (1988)

9 Fathi, D., Ho, J.R.: ShipX Vessel Responses (VERES). The-ory Manual. Marintek AS, Norway (2004)

10 Press, W.H., Flannery, B.P., Teukolsky S.A., et al.: Numeri-cal Recipes in C: The Art of Scientific Computing. CambridgeUniversity Press (1992)

11 Szczotka, M.: Pipe laying simulation with an active reel drive.Ocean Engineering 37, 539548 (2010)

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