OTC 5531

Dynamic Aspects of Offshore Riser and Mooring Concepts by H.J.J. van den Boom, J.N. Dekker, and A.W. van Elsiicker, Maritime Research Inst. Netherlands

Copyright 1987 Offshore Technology Conference

This paper was presented at the 19th Annual OTC in Houston, Texas, April 27-30, 1987. to copy is restricted to an abstract of not more than 300 words.

ABSTRACT . . .

Up to very recently the design of mooring sys- tems and flexible risers lacked an adequate approach to account for dynamic effects in the extreme load assessment. Usually the design concept was based on the extreme positions of the floating structure. Recent research has indicated that the dynamtc amp1ificati0n the in the lines and risers can be of the same order of magnitude as the cO-calLed quasi static values- u s 0 it has been concluded that the dynamic effects in the mooring system can affect the low frequency motions of the structure by the increase of virtual stiffness and damping.

In this paper newly developed 3D computational procedures are presented, describing the motion, tension and bending moment along a flexible pipe or a mooring line. Also correlations with model test data are discussed.

1. INTRODUCTION

The growth the number amongst the structures and the trends towards cheaper technology as a result of low oil prices, puts high demands on the design of the mooring arrangement.

Important parameters in this respect are the large the structure, deep and

waters and the required rOund-the-~ear workability.

The wide variety of mooring systems may be il- lustrated by the existence of shallow and deep water single point moorings d t h temporarily or permanent- ly moored tankers, clump weight systems used for guyed towers and wire moorings of s&-submersible crane vessels.

The current design procedures mostly include a dynamic motion analysis of the moored object. This provides extreme positions of the structure. From the static load excursion characteristics of the mooring system, the mooring line tensions at these extreme positions can be found.

References and illustrations at end of paper

The material is subject to correction by the author. Permission

In this so-called quasi-static mooring analy- sis, all other phenomena having an effect on the maximum line load are taken account In an overall safety factor, as required by the certifying authorities* Typical values are OperatiOnaf and

Experimental and theoretical research have shown that high frequency oscillations (in the wave frequency range) of the upper end of a mooring line can generate significant dynamic amplification of the line loads.

These dynamic effects are depending on: - frequency of oscillation - amplitude of oscillation - line mass - pretension hydromechanic line

Van Sluijs and Blok [5] have found from a sys- tematic series of forced oscillation model tests, that the ratios of maximum dynamic tension and maxi- mum quasi static tension depend strongly on the fre- quency of oscillation. This ratio is enhanced by increasing oscillation amplitude, increasing pre- tension and reduction of line mass.

Knowing the importance of dynamics for mooring systems, a similar behaviour is to be expected for related "line-type" configurations such as flexible risers, pipe bundles etc. The additional parameters concerning dynamic effects in these cases are the direct wave forces and the bending stiffness. The traditional theoretical approach to solve the dyaam- ic behaviour of cablelriser systems is based on semi-analytical techniques. Geometrical non-lineari- ties are neglected to reduce the equations to dif- ferential equations which could be solved. Perturba- tion techniques were applied with success but are restricted to certain areas [ 3 ] .

A more general approach to the problem was provided by discretization techniques* The line is assumed to be composed of a limited number of di8- Crete elements* These elements can have physical properties of their own. The thus formed system of partial differential equations describing the vari- ables along the line, could be replaced by equatians of motion in an earth-bound system of coordinates.

2 RISER, MOORING, DYNAMICS OTC 5532

The most successful methods are well-known as the lumped mass method (M) and the finite element method (FEM).

In this paper a LMM-technique and the resulting algorithm (named DYNFLX) are presented. The valida- tion of this approach has been obtained by use of the results of an extensive research program. This study was carried out by the Maritime Research Institute Netherlands (MARIN), on behalf of the Netherlands Marine Technological Research (MaTS) program (Figure 1). This program was sponsored by the following parties:

- Dutch Ministry of Economic Affairs - Gusto Engineering C.V. - Heerena Engineering Service B.V. - MARIN - Shell Internationale Petroleum Maatschappij B.V. - Van Rietschoten h Houwens B.V.

2. THEORY

Basic approach ------- ----- The mathematical model for the simulation of

the three dimensional behaviour of flexible lines is an extension of the lum ed mass method used for mooring chains and wires fZ]. The spacewise discret- ization of the line is obtained by lumping the mass and all forces to a finite number of nodes.

To derive the governing equations of motions for the j-th lumped mass, Newton's law is written in global coordinates (Figure 2).

J The added inertia matrix can be derived from the normal and tangential fluid inertia coefficients by directional transformations:

F (r) = T (r)Ax.(T)lRj- Tj-l(~)&j-l(~)f~S,l ( 3 ) -T j -3

where :

- X.) "Yj=(&j+l -J T.(T)

R instantaneous length of segment j=Ro,(l+) EA 4

-t

Assuming that all nodal force contributions are formulated in terms of node positions, velocities and accelerations the motions of the nodes may be approximated by a finite difference method known as the Houbolt scheme [3]:

or:

To derive consistent segment tensions and dis- placements, a Newton-Baphson iteration using the additional constraint equation for the constitutive stress-strain relation is applied:

[mj(r)l = anj[~nj(~)] + atj[htj(~)] . . . . (2) where a and atj represent the nornal and tangen- tial addled mass:

2 anj = P (cIn - 1) 1114 D. E

J j 2

atj = P (cIt - 1) v14 Dj ej [ A ] , [Atj] : directional transformation matrices

The nodal force vector F contains the following - j

internal and external force components:

a. segment tension FT(~) b. shear forces due to bending rigidity FS(r)

c. fluid forces Ff(T) d. sea floor reactive forces Fr(r) e. buoyancy and weight Fw f. buoy forces Fb(T) g. tether forces FTT(T)

Since the tangential stiffness of the line, represented by its modulus of elasticity EA is an

magnitude higher than the stiffness in normal direction, the tension is taken into account in the solution procedure direct [4]

The tension vector on the j-th node results from the tension and orientation of the adjacent line segments

- Tk+l (T) = 90) - [A$~(~)]-~A~(T) . . . . . (7)

For each time step the system of equations (7) S ould be solved until acceptable convergence of P' T (T+AT) is obtained. The initial tentative tension can be taken equal to the tension in the previous step. Each node j is connected to the adjacent nodes j-l and j+l, hence equation (7) represents a tridi- agonal (Nx3) system. Such equations may be effi- ciently solved by the so-called Thomas algorithm.

---------- Fluid forces

The fluid forces acting on the submerged part of the line originate from line motions (fluid reac- tive forces) and water particle motions due to waves and current. Dividing the forces into velocity and acceleration dependent parts, the total element force may be approximated by the relative motion concept known as the Morison formulation:

Ff - ~ P C ~ ~ D ~ ! L ~ ~ ~ ( ~ ) I uj(~)I + 1 1 4 n P ~ ~ j~:ej;j (8)

Since the inertia part of the fluid reactive forces is already accounted for in the left hand side of equation (1) ?nd the current velocity is assumed to be constant, u only consists of the Water accelera- tion due to Waves*

The element relative velocities and accelera-

406

OTC 5531 VAN DEN BOOMIDEKKERJVAN ELSACKER 3

ti0ns are taken equal to the average values of the values at the subsequent nodes* The inertia and drag force shape coefficients for slender cylindrical elements may be formulated in normal and tangential components. For this reason the fluid forces in DYNFLX are computed in a local system of coordi- nates.

U(T) = [NT)]~(T) - . . . . . . . . . . . ( 9) where :

U = velocity vector in local coordinates

[ a ] = directional transformation matrix

U m velocity vector in global coordinates

Note that for both tangential and normal fluid forceq the same reference area (DE) and volume ( ~ 1 4 ~ R) are used.

After computation of the element fluid forces in local coordinates S e , the global force compo- nents are found from:

. . . . . . . . . . -fe (10)

The node forces are readily derived from the element fluid forces :

112 % (5e + %e j j j-1 The direction of the current is defined by the

horizontal angle pc between the current vector and the x-axis:

V,, = VC COS P, Vcy = VC sin pc . . . . . . . . . . . (11) VC, = 0

To calculate the instantaneous orbital veloci- ties and accelerations of the water particles due to wave action use is made of the Volterra series for- mulation which represents a linear filtering of the specified wave train [7] :

m

vj(t) - 1 \(T) G(~-T) dT . . . . . . . (12) -m

where :

V = orbital velocity hV = impulse response function for V C = input wave train

The impulse response function can be found from the frequency dependent transfer function $(U) = V(U)/C(U) by inverse Pourier transform:

m 1 iwr dw

X -i;; 1 Hv(u> e , , (13) -m

Orbital velocities and accelerations at an arbitrary position (X, z) , are formulated according to small amplitude (linear) wave theory.

The advantage the VOlterra series is that simulatiOns can be carried Out on mea- mred wave records as well as on synthetic wave records.

Bendis moments and shear forces

For the derivation of the bending moments and the shear forces it is assumed that the bending

moment in the j-th node is acting in the plane through the elements j-l and j (Figure 3). According to slender beam theory this bending moment can be written as a linear function of the angle between the successive elements.

. . . . . . . . d4j = 4j - 4j-1 (14)

with 2 4 = -D .l.//2~1

J j j . . . . . . . . ( 15) 4 - = D 1 l2 1 /ZEI j-1

. . . . . . . . and BMj = -D R = D R j j j-1 j-1

(16)

(l4) yields:

BM R BM R A-.i+AkL . . . . . . d4j = 2EI 2EI . . ( 1 7 )

j j-1

or :

BM = d$ j/ (& + . . . . . . j

..(18) j LE= jql

Knowing the co-ordinates of the nodes in 3-D the angle d+ between the successive elements j-l and j is found from the scalar product of the element

d + j = a r c c o s ( ( a - b ) / l a l / b l ) . . . . . . (19) -j -j -j -j with: a = x . - x

= G? -j -~+1 -j

The direction of the bending moment vector is p e r pendicular a and b and given by their vector product:

. . . . . . . . . . . . . . Ej " % ( 2 0 )

The shear force vector for element j-1 is now given by:

. . . . . -j-l (21)

where:

d = m x a -j -j -j

gj = !!!j-l Zj The force components acting on the j-th node are now readily found from the shear force vectors of the adjacent elements:

. . . . . . . . . . . F a gj-l - zj (22) *j

From the bending moment the bending stress and the bending radius are derived direct. In case of a clamped end condition use is made of an extra fic- tive element which remains in the original orienta- tion of the end element. At the top of the line the motions of this element result from the floater motions.

Sea f loor forces

In vertical direction sea floor contact is sim-

4 RISER, MOORING. DYNAMICS oY.2 5531

ulated by means of a linear spring system for each node. Instabilities due to large impacts are pre- vented by adding a critical damping.

Buoys and Tether

When the line contains large volumes fixed in orientation, the force formulations as presented in subsection "Fluid forces" cannot be applied. There- fore an additional direction fixed formulation for fluid forces on such components is optional. Toe wire or tether application can be applied as linear springs from any node in arbitrary direction.

To1 motions -- -----m-

The upper-end position of the line is derived from the motions in six degrees of freedom of a vessel attached to the line. Phase shifts between vessel motions, top motions and direct wave forces are accounted for.

3. VERIFICATION

The development of the computer algorithms pre- sented in Figure 1 has been undertaken in continuous relation with extensive model testing programs both for module building and integrated validation. The validation has been focussed on specific applica- t ions :

- mooring systems and floaters [2] - rigid risers [6] - flexible risers. Mooring systems and floaters

In the 1984 mooring line dynamics study [2] extensive tests have been carried out for determina- tion of fluid reactive force coefficients of chains and wires.

Model tests utilizing harmonic upper-end forced oscillations of the line at five frequencies for eleven combinations. The water depths ranged from 75 m to 608 m. Chains, steel wires and chain-wire combi-lines were investigated (Table 1). For these tests, which were carried out according to Froudels law of similitude, use was made of steel studless chain and wire. The scale ratios ranged 'from 19 to 76. It should be noted that the chain links of the 1.0 and 2.0 mm chain were cut at one side. The EA- values were derived from tension-elongation tests (Table 2).

The oscillation tests were carried out in the 220 m X 4 m X 4 m and the 240 m X 18 m X 8 m basins of MARIN. During the tests the forced oscillation, generated by means of a mechanical large stroke os- cillator, was measured by means of a potentiometer. The upper-end line tension and vertical angle were measured by means of a two-component force trans- ducer while the tension at the anchor point was mea- sured by means of a ring-type force transducer. The motions of the line were recorded by underwater video. The measured tensions were directly compared with the computed results. Moreover comparisons were carried out on the basis of the Dynamic Tension Amplification (DTA) defined as amplification of the maximum total quasi-static tension, i.e. the static tension at the maximum excursion.

For the 300 m water depth cases typical results

are presented in Figures 4 and 5.

Results of the mentioned study clearly showed that in practical situations the dynamic behaviour may contribute to the maximum tension significantly. Important parameters are the non-linear static load- excursion, the low frequency ("pre-") tension and the amplitude and frequency of the exciting upper- end oscillation.

The prime dynamic tension increase originated from the normal drag forces related to large global (first mode) line motions at the middle sections. Long periods of slackness even at low frequencies of osciLlation occurred due to "flying" of the line under the influence of gravity and drag only. With increase frequency the drag and inertia equalled gravity forces resulting in an "elevated equilibri- um" of the line and normal motions in the upper section yielding lower DTA-values.

Inertia became of importance at higher wave frequencies especially for steel wires and multi- component lines.

A good correlation between measured and calcu- lated line tensions was found during the harmonic oscillation tests for the wide range of situations investigated. Because of the non-linear phenomena involved, the ultimate vaLidation of the developed computer program was carried out by means of model tests in irregular waves. A model of a floating structure was moored by means of two parallel lines and a tensioning weight.

During the tests the motions of the structure were measured by means of an optical tracking device while the upper-end mooring line tensions and angles were meazured by means of two-component strain- gauges. The fairlead motions derived from the mea- sured motion at deck level were used as input to DYNFLX. This procedure enabled a deterministical comparison between experimental and numeric tension records.

Results for the semi-submersible and the barge (defined in Table 3) in irregular waves with a sig- nificant height of 13.0 m and a mean period of 15.5 s are given in Figures 4 and 5. In order to show the contribution of the dynamic behaviour, the computer simulations were repeated for 80 per cent reduced line diameters thus reducing drag (80%) and added inertia (96%).

Since in the basic approach to the extreme loading assessment it was assumed that motions fo the floating structure are not affected by the dynamic mooring forces some additional analyses were performed. To this end the dynamic tension records resulting from bi-harmonic top oscillations, combin- ing a typical low frequency oscillation with a wave frequency response, were investigated.

The low frequency energy in the bi-harmonic result was studied by removing the high frequency tension components by means of lorpass filtering. This result was compared with the tension due to the low frequency oscillation are given in Figure 6.

The change of restoring forces experienced by the floating structure is illustrated by an increase in amplitude of low frequency tension and a phase shift. Dividing the tension record in an in-phase and quadrature phase component, it is clear that the dynamic behaviour of the mooring line may increase both the effective mooring stiffness and the low

presented in Figure 7.

OTC 5531 VAN DEN BOOM/DEKKER/VAN ELSACKER 5

The riser was manufactured at MARIN to scale 1 to 30.5 having the correct weight, mass and outer dimensions. The bending stiffness was approximated through a proper choice of the material and was checked by a bending test.

frequency damping. The latter can be of the same order of magnitude as the potential and viscous fluid damping acting on the vessel's hull directly and is therefore important for the low frequency behaviour of the mooring structure.

Flexible risers ------------- The newly developed DYNFLX program was sub-

jected to several verification tests based on com- parison with well-known analytical solutions. In addition to this, it was decided to carry out a correlation study between calculations and model tests for a so-called "lazy-wave flexible riser"

Furthermore, buoyancy rings were fitted in order to reach the appropriate shape of the "lazy- wave" configuration.

The riser top was subjected to forced harmonic oscillations in X, y and z direction with constant amplitude for a number of frequencies.

- location 3 are sensitive for changes in inertia coefficients CIn and CIt. Apparently, the effect of increasing c ~ ~ / c ~ ~ increases for higher frequencies. - Results for locations 2 and 3 are sensitive for changes in the normal drag coefficient of the arch, $,. The effect of a $, modification seems to be reduced for higher frequencies.

- Results for locations 2 and 3 Prove to be insensi- tive to changes in the tangential drag coefficient

C ~ t

To establish meaningful correlation results, it was essential that the DYNFLX model discretization closely approximated the tank model. This was easily achieved for mass and flexibility, while for the hydrodynamic coefficients of smooth cylindrical parts of the riser well-known values were taken from literature.

I

The arch, however, including the buoyancy beads as well as two transducers, was identified as main area of uncertainty. Since this part of the riser is also represented in the mathematical model by means of cylindrical mem- bers with an equivalent diameter, it is implicitly assumed that the influence of the buoyancy beads on drag and inertia in normal and tangential direction can be described by a single parameter. Therefore it was felt appropriate to investigate the sensitivity of calculation results for separate variations in the individual hydrodynamic coefficients CDn, CDt , CIn and CIt.

For the correlation study the oscillations in z direction were chosen as representative for the test model behaviour, since this component introduces significant tension and bend radius variations at the instrumented locations.

In Figure 8 some calculated and measured mean values for bending and tension are presented. On the basis of the fair agreement found, it was concluded that the geometry and material properties of the discretization correspond with the tank model.

The results of the parameter variations are also presented in Fig. 8. Apart from the complex nature of the problem, interpretation was hampered by:

- Standard deviations for signals at locations 2 and 3 are small compared to the mean values.

- The rate of change in bending moments at the in- strumented locations is large. Hence, approxima- tion by a discretized model may lead to noticeable differences.

4. CONCLUS1 ONS

The following major conclusions were drawn from the research programs presented in this paper:

Dynamic behaviour of mooring lines occurs in many practical off shore mooring situations and strongly increases the maximum line tensions. Dynamic components of mooring line tension may affect the low frequency motions of the moored structure by increase of the virtual stiffness and damping of the system. The hydromechanic properties of both mooring lines and riser systems are of prime importance for motion, tension and bending behaviour. The presented Lumped Mass Method does provide a cost effective and accurate approach to predicting the motions and internal loads of 3-D mooring and riser systems under random top excitation, waves and current.

5. ACKOWLEDGEMENT

The authors are indebted to the mentioned sponsors of the research programs of the Netherlands Marine Technological Research (MaTS) for their kind permission to make use of the results from these programs.

NOMENCLATURE

amplitude, material area cross-section added inertia, vector buoyancy per unit length vector bending moment hydrodynamic drag coefficient hydrodynamic inertia coefficient current

D = line diameter d = water depth, vector

dc = volumetric diameter E Young's modulus e - subscript; element, vector F = force in global co-ordinates F. = nodal force vector T~ = force in local coordinates g = gravitational acceleration H =water depth, frequency domain transfer

function h = impulse response function I = second moment of sectional area j = subscript: node number k iteration index L = length

Nevertheless, some trends were deduced from the R = line segment length M , line mass

6 RISER, MOORImCt , DYNAMICS OTC 5531 1 I l

= inertia matrix 121 - time dependent added inertia matrix N - node n = subscript: normal direction R = radius r = horizontal distance in wave direction,

bending radius S a shear force T - tension, period of oscillation TT = tether tension t = subscript: tangential direction, time U relative fluid velocity in local co-

ordinates U = relative fluid velocity in global co-

ordinates V = velocity W = subscript: weight, wave X - displacement, input record

* excursion vector (x,y,z) j - output record x,y,z = 3-D system of coordinates

l a = angle B = angle E = element strain

= wave elevation A = transformation matrix X - scale factor !J = angle P = fluid density U = standard deviation T = time

= segment length error = segment error vector ..., Jtj, ..., JtN) = length error derivative matrix [a~/8~] obtained from equations (5) and (6)

W = angular frequency of oscillation, wave frequency

Q = transformation matrix

REFERENCES

1. Bathe, K. and WiLson, E.L.: "Numerical methods in finite element analysisff, Prentice Hall, Englewood Cliffs, 1976.

2. Boom, H.J.J. van den: "Dynamic behaviour of mooring lines", BOSS-Conference, Delft 1985.

3. Polderdijk, S.H.: "Response of Anchor Lines to Excitation at the Top", BOSS Conference, Delft, 1985.

4. Ractliffe, A.T.: "Dynamic response of catenary risers", RINA Int. Symposium on Floating Pro- duction Systems, London, 1984.

5. Sluijs, M.F. van and Blok, J.J.: "The Dynamic behaviour of mooring lines", OTC paper 2881, Houston, 1977.

6. Sun Yi-Qing and Boom, H.J.J. van den: "Dynamic behaviour of marine risers", Offshore China '85, Guangzhou, 1985.

7. Wheeler, J.D. : "Method for calculating forces produced by irregular waves", Journal of Petroleum Technology, March 1970.

+ = line angle

TABLE 1-TEST SITUATIONS FOR MOORING STUDIES PERFORMED

I

Situation Situation Situation 1 !:::076 m 1 3 I 1 9/14/17 1 I

Chain D=0.076 m

Chain D=0.152 m

TABLE 2-MOORING LINES PROPERTIES AS MODELLED

Water depth 75 m

X = 19

I Model chains I Prototype chain l

Situation 1

Situation 2

W (~/m)l dC (m) I EA (~*10~)1

Water depth 150 m

X = 38

Situation 4

Situation 5

Water depth 300 m

X = 76

Water depth 608 m

X = 76

Situation 7/12/15

Situation 81 131 16

7

TABLE 3-MOORED FLOATER CHARACTERtSTlCS

Designation

Length Beam Depth Draft Displacement weight Centre of gravity above base Transverse metacentric height Transverse gyradius in air Longitudinal gyradius in air Natural periods:

Surge (sit. 12/15) (sit. 13/16)

€leave

Roll (free-floating) (sit. 12/15) (sit. 13/16)

Pitch (free-floating) (sit. 12/15> (sit. 13/16)

Fig. 1-RkD programs on moorlng and rImr dynamics.

rear

1983

1984

Symbol

L B D T - A - KG

2 lryy

Tx

Tz

To

T0

~ I

RESPONSIBILITY

Unit

m m n m t m

i s

S

8

S

1985 DYNRIS

* Wave forces Preprocessing and postprocessing

* CRAY veraion

DYNFLX (VM-VII-8)

- PlaTS (IROI

1986

1987

Magnitude

MARIN

Semi-sub

117.0 85.0 64.7 22.8 46,360 21.5 4.4 36.0 38.0

217.0 104.0

23.0

50.9 46.9 47.9

39.9 38.4 35.1

3D mathematical

INDUSTRY

Barge

230.0 57.5 26.5 7.6 87,750

- - -

357.0 173.0

- 10.4 10.4 10.. 3 - - -

model ' Bending stiffness Wave forces Flexible riser model tests

* Publication m 8 7

- DYNLINE (VM-V-5)

* 20 mathematical model ' Oscillating tests * Harmunic tests Irregular tests Publication BOSS 1985

1

DYNAFA

* Fatigue analysis * Vectorisation

I

L I l F

'I I EXTENSION DYNnX

(VM-IX-81

* Torsion ' Advanced access and application systematic model testa Validation

-l

Delivery to sponsors

Delivery sponsors: to

SIPM,KSEPL Gusto/sBn HeeremaDluewater RLH -IN

- - DYNPIPE

* Bending stiffness Rigid riser tests Publication China 1985

--

ILSX naow 17

a l -

.% 0 = L * vr

. .- m

. . -

Y' jo! ; 0 'C-

1 WAVE [ M1

T 5. 10' (reduced I

I I I 0 200 400

Time [S]

Irregular wave resu l t s f o r barge (s i tuat ion 16)

- 0 200 400

Time [S]

Irregular wave resu l t s f o r semi-sub ( s i tua t ion 13)

[M] 7

200 -

100 -

X Line discret izat ion [M]

0 0.5 1 .O 1.5 w [rad/s]

Harmonic osc i l l a t ion resu l t s

Fig. 5-Discretizatkm, DTA-values, and irregutar wave results for S'ituations &/10113/16.

5

X-TOP [M] 0

-5

--- 0 100 200 0 100 200 0

loo Time [ S ] 255 Resu l t s f o r wl + w2 a f t e r low pass f i l t e r i n g Resu l t s f o r wl

Pig. 6-81-harmonic simulation results.

Mom. t ransducer

Fig. 7-General test arrangement flexible riser.

41 5

MEAN VALUES BENDING ~JIOMENT I I MEAN VALUES TENSION I E x p e r i m e n t 1 E x p e r i m e n t

-----m DYNFLX

-m- -m--

FLEXIBLE RISER PARAMETER VARIATIONS

w i n r a d / s

Fig. 8-Flexible riser correlation results.