Fatigue life analysis of production risers

OTC 5468

Fatigue Life Analysis of Production Risers

by C.M. Larsen, Norwegian Inst. of Technology, and E. Passano, SINTEF

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UNIVERSITEIT

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Copynght 1987 Offshore Technology Conference

This paper was presented at the t 9th Annual OTC in Houston. Texas, April 27-30. 1 987.The material is subject to correction by the author, Permission

copy s restricted to an abstract of not more than 300 wordS

ABSTRACT

When calculating fatigue 'life of a marine struc-ture, several strategies are available. The dynamic analysis can be carried out in the time domain or fre-quency domain; fatigue damage in one seastate can be

found by using a "rain-flow" technique or statistical methods, and fatigue damage during life-time can be found by using short-term results in different ways. Furthermore, wave force model, current effects and

operational data can be considered differently in the ana lys i s.

The purpose of the present paper is to discuss various strategies as applied on a tensioned marine riser, and to present results from a Fatigue life ana-lysis of a production riser On a tension-leg platform in a typical North Sea environment. The main conclu-sion of this study is that frequency domain methods seem to give adequate accuracy, and that the effect of simultaneously acting waves and current should be considered. Results from long-term fatig'Je analysis indicate that the extreme seastates (significant

w.. .height larger than 10 meters) give a negligible contribution to fatigue damage.

INTRODUCT ION

Exploration of commercial petroleum fields in deep water and reduced oil prices have increased the

interest in floating production systems. One of the most critical components for such systems is the

marine riser. Traditionally, such risers have been steel pipes suspended from the seabed installation and tensioned by a heave compensating system. During the 'last decade, flexible risers have also entered the scene, and are today often believed to be the future riser type for most floating production systems. However, many advantages still exist for the tensioned steel riser compared to its flexible cumpetitor, and when using a tension-leg platform (TLP), its largest drawback - namely the heavy and expensive heave com-pensating system - is reduced to a minimum. The com-bination of tensioned steel risers and TLPs is there-fore likely to be seen in future deepwater Fields.

References and illustrations at end of paper

Production risers have to meet all structural requirements defined by operators and authorities. Consequently an acceptable fatigue capacity during the riser's lifetime must be documented, which points out the need for a reliable procedure for fatigue life calculation. The purpose of this paper is to discuss various methods for this type of analysis, and to pre-sent results from a fatigue life study of a production riser under North Sea conditions.

Dynamic analysis of marine risers have been studied by several authors during the last two decades. /1/, ¡2/, /3/. Time domain and frequency domain methods

have been compared ¡./ and sophisticated methods for improving the linear frequency domain solution tech-nique have been published /5/, /6/. Most authors

have, however, concentrated on the dynamic analysis, which is in fact only the first step in a complete

fatigue life study. The intention of this work is therefore not only to discuss methods for response analysis, but to see how different analyses can be used to obtain acceptable accuracy when applied in a fatigue life calculation.

The present work will deal with wave and current loads according to Morisons well-known formula. This means that lift forces, lock-in vibrations /7/ and more sophisticated hydrodynamic load models /8/, ¡9/

will not be discussed.

In many cases effects from different hydrod'ynamic

load models, wave theories and current/wave com-binations are easily illustrated by using results from regular wave analyses. Such results are presented in

a separate section of this paper and are meant to

illustrate basic physical behaviour of a riser and the relative importance of sorne key parameters for riser response. All results used in the fatigue life analy-sis are found by using stochastic analyses.

All fatigue damage calculations in the present work are based upon the Mirter-Paltagren hypothesis for

fati-gue damage accumulation, which is the only practical way of handling stress cycles of stochastic nature.

ALTERNATIVE METHODS FOR FATIGUE LIFE ANALYSIS

DriamJc respflSe

The stochastic nature of ocean waves and the fact

that wave effects give the most important

loads on a

marine riser, make it necessary to perform some

kind

of

stochastic

analysis

when

calculating

structural

response

of

risers.

Two

alternative families of

methods are

then available,

namely frequency domain

and time domain methods.

The most important

differen-ces between these methods are as

follows:

The frequency domain method must be linear with

respect

to structural

stiffness

as

the method

always

is

based upon

linear superposition

of

load effects.

Non-linear load effects such as

quadratic drag

/4/

and

wave and current

com-bination /5/ can however be considered.

Even

the fact that the quadratic drag term in general

can give loads at multiple frequencies (2w.

3w,

4w . ..

where w is the wave frequency)

can be

included by using convolution techniques /10/.

The structural response will be represented by a

spectrum, which means that the statistical

pro-perties

of

the

response

are

known, and

the

response process (time history) will

always be

Gaussian.

Consequently, non-symmetric response

i.e.

due to non-symmetric wave loading close to

mean

water

level,

can

not

be

correctly

described.

The

frequency domain methods normally compare

favourably witn time domain methods with regard

to computing tine,

however, calculation of

con-volution terms may be very costly.

The time domain methods are to some extent more

cenerai than che frequency domain methods as ali

'jpss

of

structural

non-iinearities

can be

accounted for.

Such refinements will, however,

'ncrease computing

time

and hence

costs,

and

must

therefore

be

justified

by

the

need

for

inoroved accuracy.

The time domain methods can rot easily include

-

treauericy

depencent

stiffness,

mass

or

load

parameters

as

is

the

case

in

the

frecuency

domain.

This point is not important for m3rine

risers,

but

is certainly for marine structures

with

larger

diameters

for

which

a

frequency

Jependant added mass term is oresenc.

Wave cads car, be

better

described

in

titre

aonain than

n frequency domain.

This comment

rs valid for the following effects:

-

tne unsymmetric effect when current and waves

are combined

-

variation of wet surface (load area) of the

riser due to varythg sea surface elevation in

'ees.

-

tact that a specific riser cross sectrcr

riì

rove eno hence not stay

in a pcsiticn

,,here wave

nducec velocities and

ecceTera-tra

tar: h

C5l,::iated

:ndependartiy

cr'

r-se

c'soacemerts.

non-lir:ear wave theories

- locO

tr,ebrres

mascO on a more

aecailec

deseriptrcn of fluid/structure :nteractron

The "a' dsadv.antmge o

the time domain methods

's

omet one

result will

conca-

as a esmonse

rat'.'.

From a sratistcs' acint o

vie'w.j

this time history represents only one sample

among many

possible

samples

in

the

actual

environment condition (wave spectrum, current,

etc.).

From this sample statistical parameters

have

to

be

estimated.

The

accuracy

of

such

estimates is strongly dependent on the length of

the simulation period.

On the other hand, the

time

history

can

represent

a

non-Gaussian

response type.

This

is

important

if one can

show that other probability distributions give a

better

description

of

the

response

than

the

Gaussian

distribution.

Alternative

distribu-tions

can then be used

for calculating both

fatigue damage and extreme response.

Short-term fatigue

From a stochastic analysis in frequenc

domain it

is possible to calculate fatigue damage in two

dif-ferent ways.

In both cases the calculation will start

from a stress spectrum found for the actual cross

sec-tiori of the riser.

The alternatives are:

Accept the Gaussian process to be narrow-banded

and hence use the Rayleigh distribution for the

stress peaks and stress ranges.

The

distribu-tion parameter

is

found by integration of

the

stress spectrum, and from the spectrum moments

the cycle frequency (number of cycles per unit

time) can be found.

For a narrow-banded process

this frequency is found as the zero uperossing

Frequency.

The fatigue damage per unit time in

the actual seastate can then be calculated.

The

damage can be found by using a closed-form

solu-tion or numerical

integration depending ori

how

the actual S-N curve is defined.

/11'.

From

the

stress

spectrum

one

can generate

a

stress history by using Fast Fourier Transform

(FFT).

This computation is very fast even for

long time histories, and gives a general

broad-banded Gaussian process.

Fatigue damage can then

be calculated

by a "rain-flow" technique.

Note

that this strategy gives a sample for the

fati-gua damage and not a statistically correct value

as is the case for the first method.

A

suffi-ciently long simulation time must therefore be

used. This method makes

it possiOle to

investi-gate

the

effect

from

the

bandwidth

of

the

response.

Th

time domain results can also be handled in two

different ways as Follows:

Direct use of the calculated stress histories by

using the 'rain-flow" technique.

Select a probability distribution and estimate

its parameters on the basis of the time history,

and calculate fatigue damage by integrating the

probability distribution versus the S-N-curve in

the

standard way.

The simplest way of

per-forming this analysis is to estimate the standard

deviation IRMS) and assume a Rayleigh

distribu-tion

For description of

tre stress range

sta-tistics.

rhe

average cycle

frequency can be

estimated

directly

from

the

sammle

(time

history) or my estimating the zero up-crossing

period from the mean value and variance of the

extremes.

The last procedure is consistent with

the use of Rayleigh aistribution as the cycle

frequenc1

tner

is

icentical

to

trC

zero

um-crossng

"aouenc

(narrow-hand assumption).

2 FATIGUE LIFE ANALYSIS OF PRODUCTION RISERS

LonqtermfatiqUe ana lis

When determining the strategy for accumulating fatigue damage over the structure's lifetime, one has

to consider all relevant environmental and operational conditions that the marine riser will meet. Opera-tional conditions will not be discussed further here,

but it should be noted that variation of top tension, installation and workover conditions might be impor-tant also for the fatigue evaluation.

Normally, the environmental data are given by some type of wave and current statistics. The wave sta-tistics can be given as a joint frequency distribution of significant wave height (H5) and zero up-crossing, peak or average wave period (Ti, Ip or Tav), based

directly on measurements (scatter diagram") or

derived from an established statistical distribution. /12/. A minor number of 'representative seastates" are also often used which in fact is ari attempt to repre-sent the often more than loo seastates in the "scatter

diagram' by 10-15 seastates with defined H5, Tz and

d& ion. Such representative seastates can be derived

fr.., the joint frequency distribution by establishing the marginal distribution for H5 and using the average wave period at each level. Use of these seastates may however, give different results compared to the total scatter diagram as the energy distribution along the frequency axis in fact will be different for the two cases.

Current data are often found as a numerically defined distribution for current speed at some levels. In some cases direction distributions are also given,

but statistical data for simultaneous occurance of

waves and current has so far not been published. This makes it difficult to include current effects in a

correct way for systems where the combined wave and current effect is important. In the present work current is included in some cases in order to

illustrate the load effects. No attempt is, however, made to include current in a correct way when

esti-mating long-term fatigue damage.

If a frequency domain method is used for all

seastates, and stochastic linearization as described

in /5/ is carried Out, the transfer function for riser

Ci )nse will become dependant on the wave condition and must hence in principle be established for each condition. This will of course lead to increased com-puting time compared to use of one transfer function for all seastates. One should therefore introduce the term "iteration block" which means a block of

seasta-tes for which one transfer function is used for

response calculation. Computing time will then be

more determined by the number of iteration blocks than by the number of seastates. Proper selection of such iteration blocks will therefore be an important part of a long-term fatigue analysis.

Finally it should be mentioned that it is possible

to use different methods for dynamic analysis and

short term fatigue calculation for different classes of seastates. It is possible to use frequency domain

methods for i.e. wave heights smaller than 10 meters and then proceed with time domain methods for higher waves. This can be done in order to have a uniform accuracy For all seastates, but should only be used if the large wave seastates are important for the final results. The duration of extreme seastates is one key

p 'meter in this discussion.

f'

...ii..,-,

3 LARSEN & PASSANO OTC 5468

CASE STUDY DEFINITION

A tension-leg platform in 350 m waterdepth was selected for the present study. Design principles for this platform are given in /13/, and the main geometry and transfer function for surge motions are presented in Figure 1.

The riser subjected to analysis is a 20" gas export

riser shown in Figure 2. Key data for weight, geometry etc. are presented in Table 1. Table 2 gives results from an eigenvalue analysis. The five lowest eigenfrequencies from a two-dimensional analysis are

given.

Long-term wave statistics were established using data and probability functions from /12/. A complete joint frequency distribution for H5 and the spectrum peak period T was generated, later referred to as the "scatter diagram". The marginal distribution for Hs is shown in Table 3, where the associated values for

and seastate duration are given.

In order to simplify this study, the fatigue analy-sis is performed without considering directional sta-tistics for waves and current, short-crested waves or any direction dependant response. Consequently, waves and current are always assumed to come from the same direction, and fatigue life is calculated at a point

on the riser cross section where dynamic bending stresses are highest. This simplification makes

abso-lute fatigue life estimates conservative, but should

not alter any conclusions concerning relative

effects.

A stress concentration factor (SCF) of 1.0 was

used, which means that the weakest point of the riser is assumed to be at a weld between the riser pipe and the coupling. A somewhat higher value might have been selected ,14/, and would have reduced the calculated fatigue life by a factor of (1/SCF)' for the selected S-N-curve.

The fatigue capacity of the riser is assumed to be defined by the "D-curve" recommended for high quality butt welds by Det norske Ventas /15/. This curve is shown in Figure 3. Normally, an endurance limit is assumed at 2 108 cycles. For the present study the S-N curve was extrapolated beyond this value, assuming that the endurance limit does not exist.

REGULAR WAVE ANALYSIS

Regular wave analyses reported in this section were performed using a computer program based on a

two-dimensional finite element model /16/. A linear time integration method is used for the dynamic analysis, but non-linear drag forces are accounted for. Several models for wave kinematics are available. These are illustrated in Figure 4, and are briefly described as

follows:

Integration of wave forces to mean water level. This is consistent with the linear wave theory

and is identical to the wave model normally applied in a frequency domain analysis. Use of surface value for wave potential in the wave crest. This model gives unsymmetrical dynamic loads, both with respect to the force integral and local forces.

Parallel move of wave potential to actual wave surface. This model gives a globally syrn-metrical load time history (integration of wave forces along the riser), but locally the wave forces will be unsymmetrical.

5th order Stoke wave theory as described in

/17/.

Figure 5 shows typical results from a regular wave study using the different wave models. Envelope cur-ves showing maximum and minimum bending stresses along the upper part of the riser are drawn.

Wave model i gives a symmetrical response, while unsymmetrical responses are found for the other models. This result is by no means astonishing, but a consequence is that while wave models 2, 3 and 4 give larger maximum response, stress range results are seen to be less effected. This follows from the fact that maximum negative and positive stresses do not appear at the same position for these wave models.

Results are summarized in Table 4, where it is seen at wave models 2 and 3 - which often are used in

time domain stochastic analyses - give reduced stress range compared to 1 and 4. Model i is applied in fre-quency domain methods, while 4 should be regarded as the most realistic wave model. A careful conclusion is therefore that wave models 2 and 3 should not be used in a fatigue study as they can lead to unconser-vative results. Model i is also seen to give too

small values for stress range compared to 4, but seems to be the best alternative among models based on the linear wave theory. For analyses aimed at estimating extreme responses, the conclusion is that models 2 and 3 are better than 1, and model 3 seems to be the best alternative as these results are closest to results from 5th order Stoke wave.

Figure 5 gives maximum stress range in the wave

zone for increasing wave height and Variation of some important parameters. The solid curve gives results for the drag coefficient C0 = 0.8, while the upper and lower curves give results for C0 = 1.0 and 0.6 respectively. Results are also indicated for current in combination with waves, and use of 5th order Stoke

ory. The following conclusions can be drawn:

i. Variation in stress range due to wave theory is insignificant for wave heights less than 10

meters for the present period.

2. For moderate wave heights, the response

variat'on due to a ± 25% variation of C0 is

less than the effect of current with velocity of 0.5 ms1.

Figures 7 and 8 present similar results from 9

second wave period, which is close to the second eigenperiod for the riser. Stress range results are presented both for the wave zone and at riser

mid-point. Drag coefficient, current velocity and wave theory are varied. The response is here seen to he very sensitive to current velocity, and the reason for this is obvious: For this frequeo-y, damping is

nportant. At the riser mid-point, drag forces will

tend to become damping forces and hence reduce the response. Current will increase damping due to the quadratic drag term. Consequently, increasing current is seen to decrease riser response. in the wave zone, however, drag forces act as external exciting forces.

'rent

hill

increase these forces, and consequently increase the response. The main conclusion is that

430

FATIGUE LIFE ANALYSIS OF PRODUCTION RISERS OTC 5468

the riser is much more sensitive to current variation

at this frequency, and that a 25% variation of the drag coefficient has only minor influence on riser response. The marginal distribution for wave height

(Table 3) shows that wave cases with significant energy around 9 seconds are quite frequent. It is

therefore believed that current effects can be impor-tant when calculating fatigue life of a riser.

Some analyses were performed where the riser

posi-tion in the wave potential was updated due to riser

displacements during the analysis. The effect of this updating was found to be insignificant except for

extreme waves, and therefore not of interest for fati-gue analyses.

SHORT-TERM FATIGUE ANALYSES

The remaining analyses were carried out with a com-puter program system for analysis of tensioned marine

risers. Both time domain and frequency domain analy-ses including stochastic linearization are available, as well as several alternative methods for calculating the resulting fatigue life.

Short-term fatigue results for four seastates are presented in Figure 9. Fatigue life in years is

plotted versus significant wave height. Wave periods are selected according to the marginal distribution

(Table 3).

Frequency domain results are obtained by using the closed form solution, and time domain results are

found by "rain-flow" counting of stress cycles.

Simu-lation time has been 8 - 10 minutes, and wave forces are integrated to mean water level. Results from riser cross sections in the wave zone and at mid-point are

given.

In general, good agreement between time and fre-quency domain results is found, and fatigue damage per

unit time (inverse of fatigue life) is seen to

increase dramatically with increasing wave height. Two samples are given from time domain simulation for H5 = 8.5 m. Results from these samples are com-pared in Table 5. The scatter is seen to be

signi-ficant, which indicates that the simulation period should have been somewhat longer. The fatigue life has greater variation between samples than the standard

deviation of the response process does.

An attempt was therefore made to estimate the fati--gue life directly from the statistical properties of

the time series. The Rayleigh distribution was assumed for the stress maxima and, consistent with

this, the number of cycles was derived from the zero up-crossing frequency. This will be correct for a narrow-banded process, and will otherwise introduce inaccuracies that will be small for a "not too

broad-handed' process. The fatigue life is calculated both from each sample and from the mean process variance and zero uo-crossng period. The results are pre-sented in Table 6 together with results from the other applied methods.

Finally stress histories were generated by FFT from

the frequency domain stress spectrum, and fatigue damage was calculated using the "rain-flow" technique.

The fatigue life is shown in Table 7 for stress histories with between 2048 (2'') and 32768 (2S) time

stt of 0.25 seconds. It is seen that the effect of using more than 8192 (2') time steps is minute.

The two methods assuming that the response process

is narrow-banded, and the two methods with no such

assumption, may now be compared (Table 6). The

narrow-banded assumption seems to be slightly

conser-vat ive.

Table 8 gives results from a short investigation on effects from drag coefficient variation, wave theory and current. Fatigue life in the wave zone is seen to increase for decreasing drag coefficients, while the opposite effect is found for the riser mid-point. This observation is the same as previously pointed out for the regular wave case.

Three time domain results for the same wave con-lition are given in Table 8. The wave time histories have been identical for these simulations, which means that result variation from one simulation to another is due to different wave theory and current, and is

not m statistical variation. From the table it is se that using wave theory i (integration to mean wate level) gives shorter fatigue life than theory 2 (parallel move of potential) in the wave zone. This

confirms the conclusion stated on the basis of regular wave analysis, which means that wave theory 2 should not be used for fatigue analyses. It is also observed that fatigue life at riser mid-point is unaffected by the applied wave theory. It is also seen that the variation due to wave theory is of the same order of magnitude as the effect from 25% variation of the drag coefficient.

Current velocity for the presented case was

1.0 ms'

at sea surface, and this current gives a reduction of fatigue life in the wave zone almost identical to the increase caused by changing the wave theory from i to 2. The effect at riser mid-point is, however, completely different, as fatigue life here is seen

to be more

than doubled. This confirms the

observation previously made for the regular wave case.

LONG-TERM FATIGUE ANALYSIS

:ique life for the riser based on long-term wave statistics is presented in Table 9. Note that all

waves are assumed to attack the structure from the same direction, which makes the absolute values conser-vative. From the table it can be observed that the actual riser will experience larger fatigue damage in the wave zone than at mid-depth, which is a

con-sequence of the selected top tension level.

5 different strategies for long-term fatigue accu-mulation are applied:

Use of complete scatter diagram, 15 iteration h 1 oc k s

Use of complete scatter diagram, transfer func-tion established at diagram center of gravity

and applied for all seastates (1 iteration

block)

Use of marginal distribution (Table 3), trans-fer function established for each individual seastate (17 iteration blocks)

Marginal distribution, 4 iteration blocks Marginal distribution, I iteration block '-'mpliting time involved will be closely related to

th imber of applied iteration blocks.

5 LARSEN & PASSANO OTC 5468

The results indicate that use of the marginal distribution will underestimate fatigue damage (overestimate fatigue life) in the wave zone, while the opposite effect is seen for the riser mid-point.

It can also be observed that by refining the analysis, the fatigue life tends to decrease in the wave zone, while an increase is seen for the mid-point. As the wave zone is the most critical part of the riser this means that simplified use of long-term statistics tends to give results on the non-conservative side. The trend in these results also leads to the conclu-sion that when refining the analysis by increasing the number of iteration blocks, one should rather use the full "scatter diagram" than the marginal distribution.

Figures 10 and li present the relative importance of seastates when long-term fatigue is calculated, and absolute values of fatigue damage for various

strate-gies. Results from marginal distribution and "scatter diagram" are given both in the wave zone and at the riser mid-point. The tendency for all these curves is

identical

maximum contribution to fatigue damage will come from seastates with Ii = 4 - 5 meters.

seastates with Hs > 10.0 meters give an insigni-ficant contribution to fatigue damage.

An important consequence of this observation is that the need for refined time domain analysis methods involving structural non-linearities is not seen when dealing with fatigue analysis. Even if results from

linear frequency domain methods have significant errors for large waves, the duration of these

seasta-tes is so short that the influence on the total

result becomes insignificant. One can in fact neglect all seastates with Ks > 10 m and still include more than 95% of the fatigue damage.

CONCLUDING REMARKS

From the case study, the following conclusions can be drawn:

Regular wave analysis

The influence from current can be significant. Current will increase stress range in the wave

zone, but reduce the response at riser

mid-point.

Modified linear wave theories of type 2 and 3 should not be applied in time domain analysis in connection with fatigue calculation as these models will give unconservative results.

Short-term fatigge

Frequency domain analysis using stochastic linearization shows good agreement with time domain analysis.

The wave force model seems to represent a signi-ficant uncertainty to the analysis.

The most rational way of calculating fatigue damage from a tie aornain simulation, is to

estimate statistrcal parameters for the

response, and not to use a "rain-flow" technique directly on the stress time history.

Use of the narrow-band assumption when calcu-lating fatigue damage from stress spectra gives slightly conservative results compared to

Long-term fatigue

Use of a marginal distribution for Ns can give significantly different results compared to use of a joint frequency distribution for and Tp. For the present case, the marginal distribution gave unconservative results.

Several iteration blocks have to be used in order to obtain reliable results.

The main contribution to fatigue damage of the

actual riser came from seastates with

= Tn.

Seastates .dth Hs > 10.0 m give an insignificant contribution to fatigue damage.

SuqqestiOns for further work

Combine current and wave statistics in order to perform a _{long-term fatigue analysis including}

all directional effects.

Improve load model by incorporating experimental results and/or fullscale measurements in time domain analysis.

Use of other probability distributions than Rayleigh to fit time domain results.

Estimation of extreme response on the basis of similar statistical methods.

oscillatory flow at hign ?eynlds number". Jour-r,l cf Shin Research, V' 21. No .. Des. 1977.

TABLE . EY DATA FOR RISER

-3,

r' '

- ,

'i'

/10/ Borgman, L.E.

"Statistical Models for Ocean Waves and Wave For-ces" in Advances in Hydrosc'ience, Vol. 8, pp. 139-181, Academic Press, 1972.

/11/ Olufsen, A. , Fames, K.A. and Fergestad, D. "FAROW", a computer program for dynamic response analysis and fatigue life estimation of offshore structures exposed to ocean waves. Theory Manual STF71.A86040 SINTEF, Trondheim 1986.

/12/ Haver, S. and Nyhus, K.A.

"A wave climate description for long-term response calculations", OMAE, Tokyo 1986. /13! Larsen,C.M., White, M., Fylling, 1.3. and

Nordsve; N.:

"Non-linear static and dynamic behaviour of ten-sionleg platform tethers", OMAE, New Orleans

1984.

/14/ "Mandatory design based on fatigue analysis", ASME, Section VIII, Division 2, Appendix 5. /15/ Rules for the design, construction and

inspec-tion of offshore structures, Appendix C. Dat norske Ventas, 1977.

REFERENCES

/1/ Thucker, T.C. and Murtha, J.P.

"Non-deterministic analysis of marine risers, OTC 1770, 1973.

/16/ Larsen, C.M.

"RISANA", a computer program for marine riser analysis. User's manual, Division of marine structures, NIH, 1986.

/17/ Skjeldbreia, L. and Nendrichson, 3.:

"Fifth order gravity theory". Proceedings of Conference on Coastal Engineering, Chapter 10,

/2/ Morgan, G.W. and Peret, J.. 1961.

"Applied mechanics of marine riser systems, Petroleum Engineer", Oct. 1974 - Nov. 1975.

/3/ Larsen, CM.: Glcbal data

"Marire riser analysis'. Norwegian Maritime

Research, 4/1976. Total riser length 367.5 m

Total weight in air (incl.gas

'4/ Leira, S..). and Remseth, S.R. con te rit 220.4 tons

"A comparison of lnear and non-linear methods far dynamic analysis of narine risers",

BOSS' 85, Deift University of Technology.

Total weight in position - 30.0 tons

Riser cross section

/5/ Krolikcwski, P. and Gay, T.A.:

"An imoroved hneanzation technisue for fre- Outer diameter 50.8 cm

quency domain riser analysis", OTC 3777, 1980. Wall thickness 2.22 cm

Density, gas content 0.1673 kg/dm3

6! Leira, S.J. and Olufaeri, A.: Density, riser material

"Bipianar linearization of drag forces with (incl.couplings etc.> 10.97 kg/dm' application to riser 3nlySiS", OTC 5100, 1986. Unit submerged weight 0.1922 t/m

'7/ Larsen, C.M. and Bech, A.:

"Stress anaiysis of marine risers under lock-in condition", OMAS, Iokyo, 1966.

Buovanc'/ zone

Length of zone 300 m

.eì

Kj3sen, S.P. aro

kre, A.S. Buoyancy cross section area 0.583 m2 "Summary of experiments performed with wave for- Density of buoyancy material 0.420 kg/dm ces on a vertcal pile rear tre free surface". Equivalent outer diameter 1.037 m PR-51-511017-01-87 MARINIEK, crondhem, Norway. mit submergea weight irmol. riser -0.1607 t/m

'9.

Srpkay. T.:

L ire and transverse forces on cylinders ir

Added nass coeffcient: 1.0 for riser and buoyancy zone

TABLE 5 SHORT TERM FATIGUE RESULTS, FATIGUE LIFE AND STANDARD DEVIATIONS Current Wave case C D Wave theory velocity at surface

ms'

o max MPa ¿a max MPs 1.0 1 0.0 33 66 H = 15 ni 1.0 2 0.0 33 61 T 13,7 sec 1.0 3 0.0 42 63 1.0 4 0.0 50 72 H = 10 m 1.0 2 0.0 24 43 T = 9 sec 1.0 4 0.0 36 50 0.8 2 0.0 20 38 1.0 2 0.4 30 47 1.0 2 1.0 44 55 Eigenvalue no. Eigenfrequency rad.s1 Frequency

s1

Periods 1 0.3419 0.0544 18.4 2 0.7030 0.1119 8.9 3 1.091 0.1737 5.8 4 1.508 0.2401 4.2 5 1.956 0.3113 3.2

Standard deviation, MPs Fatigue life, years

H = 8.5 m

S

Freq.dom. Time dom. Diff. Freq.dom. Time doni. Diff.

T = 9.5 sec result samples result samples

Wave zone 5.860 5.804 -1.0 56 55 -1.8 6.241 +6.5 41 -27.0 Riser 5.020 5.005 -0.3 105 112 +7.0 mid-point 5.106 +1.7 95 -9.5 H5 = 8.5 ni Tz =3.5 sec Wave zone Riser mid-point Frequency domain, closed-form solution 56 105 Frequency domain, Rain-flow technique on generated stress histories

57 112 Time domain, 55 112 Rain-flow technique 2 samples 41 95 Time domain, 61 98 Estimation from statistical parameters 49 99 Time domain,

Estimation from mean statistical prameters 64 99 a State no H5 ni Tp S Duration, 20 years hour i 0.5 6.60 31828 2 1.5 8.42 45969 3 2.5 9.54 39119 4 3.5 10.40 ₂₆₈₈₁ 5 4.5 11.14 15968 6 5.5 11.79 8452 7 6.5 12.38 4055 8 7.5 12 . 93 ₁₇₈₃ g 8.5 13.40 712 10 9.5 13.94 274 li 10.5 14 .40 ₉₇ 12 11.5 14.85 32 13 12.5 15.28 10 14 13.5 15.69 3 15 14.5 16.09 0.8 16 15.5 16.47 0.2 17 16.5 16.85 0.05

TABLE 3. MARGINAL DISTRIBUTION FOR H5 BASED ON JOINT TABLE 6. FATIGUE LIFE IN YEARS

PROBABILITY DISTRIBUTION OF Hs AND Tp COMPARISION OF DIFFERENT METHODS FOR

(REF /14/) CALCULATING FATIGUE LIFE.

7 LARSEN & PASSANO

_{DIC 5468}

TABLE 2. RESULTS FROM EIGENVALUE ANALYSIS TABLE 4 RESULTS FORM REGULAR WAVE ANALYSIS. WAVE THEORY VARIED

35 30.5 o 2.0 -J 0.0 (2 (2 24 300 250 200 153 100 53 C

Table 8

SHORT TERM FATIGUE RESULTS.

FATIGUE LIFE IN YEARS

00 1.0 2.0

FEOU5NCY DSi

Figure 1 P 3torrn geometry and surge transfer function

1.3 2.0

0EQU5C QiS

434

TABLE 9. RESULTS FROM LONG-TERM FATIGUE ANALYSIS

235 tons

Riser geometry rn)

25

Buoyancy material

103.7

Figure 2 Riser geometry

t20" gas rser)

Riser cross section (cm)

H5 = 8,5 m

Frequency dom.results

Time dom. samples, CD = 1.0

identical wave history

T

= 9,5 sec

CD = 0.8

CD = 1.0

Wave

theory i

theory 2

Wave

Wave theory

2 + Current

Wave zone 7D 56 55 78 57

Riser

mid-point

95 105 112 112 282

H5=8.Sm

Tzg.5seC

Wave zone

Number of time steps

= 0.25 sec

Fatigue life,

years

211 = 2048

212 =

4096

213 =

8192

214 = 16384

21

= 32768

62 56 57 57 57

Estiroated fatigue life, years

Scatter

15 blocks

diagrani

i block

Marginal

17 blocks

distribution

4 blocks

i block

Wave zone 396 472 539 555 658

Riser

mid-poi rit

617 542 742 721 635

FATIGUE LIFE ANALYSIS OF PRODUCTION RISERS OTC 5468

TABLE 7 SHORT-TERM FATIGUE RESULTS. RAIN-FLOW TECHNIQUE APPLIED TO STRESS HISTORIES GENERATED FROM FREQUENCY DOMAIN RESULTS

;tress ange, 1000

loo

lo

tog o, MPa

Parameters: k = 3.0

log10A = 12.18

Wave k inematic model:

102 iO

io4

iO

io6

iü

N

Numbers of cycles to failure

Figure 3

Applied S-N curve

/15/

C

= 1.0

CM = 2.0

Bending stress IMPa)

-30

-20

-10

s 10 20 30 40

Meters

435

Figure 4

Alternative models for wave potential

Level for max

a

Integration to mean water level

Parallel move of wave

potential

MWL

y

LARSEN & PASSANO OTC 5468

Integration to mean water level

)1l

5th order Stoke theory 14)

Parallel move of potential (2)

Wave type 2 in combination with

Use of surface potential in wave crest 13)

current 1.0 m s1

at surface level

Figure 5

Bending stress envelope curves in wave zone, kinematic model varied

Wave height :

15.0 m

Wave period : 13.7 sec

steepness

20

No upper end morions

Use of surface value in wave

5th order Stoke wave

crest theory

._,V4VS,*s r.,.. '7'W S.c'.anttr'r'.2r t.Th= -60 50 40

10-o MPa v = 1.0 ms1

/

/

o Stoke 5th order, C0 = 0.8

//

A Current included, CD = 0.8

/

0/

Wave period 13.7 sec

/

v=O.,5ms

/

/

z...

7...

v0.5rns

,

0.4 A -

LOrrs

4 6 8

FATIGUE LIFE ANALYSIS 0F PRODUCTION RISERS OTC 5468

.\3..r

m

ure 7

axmurrt

. .-'ie

rio v.terDn

e .Th't, crìc cernet.

:...r'enZ ariec MPa C0= 1.0

50 -

0.8 o Stoke, C0 = 1.0 D A Current included 2 4 6 8 10 Wave height, m = 1.0

- °D

CD = 0.8

CD =0.6

O 6 8 10 12 14 Wave height, m

Figure 6 Maximum stress range n wave zone, wave height, wave

theory and drag coefficlent varied.

Current effect illustrate

r.Pa

Figure 8 Maxmum stress range in wave zone, wave height, theory and drag coefficient varied.

C0= 1.0 Current effect illustrated

C...= 08

30

Stcke 5r, order. C =

U

0.04-C C

o

2 0.03

C) 0.02 -0.01 0.00

o'

0.04 C C)

>

0.03 o, C C C, C E 0.01 0.00 o 1000 500 Figure 9

RISER MIDPOINT

5 10 15 20

Marginal distribution, H5 (m)

- linearization for each seastate

four iteration block

---I:nearizarion at center of gravity

for marginal distribution

'igure 10 Results from long term fatigue analysis using

the marginal distribution

Fatigue life

years

A

\

10 15 20

Marginal distribution, H5 Im)

Frequency domain results:

--

Riser mid-point

Wave zone Time domain samples:

A

Riser mid-point

0 Wave zone

Fatigue life versus significant wave height, frequency domain and time domain results

437

0.04-C C

>-o

2

0.03-C) C

002

0.01 0 00

0.06-WAVE ZONE

0.05.

0.01 0.00 o 5 10 15 20

Full scatter diagram, Hs (m) 15 iteration blocks

diagram,

linearization at center of gravity

marginal distribution, linearization for each seastate

Figure 11 Results from long term fatigue analysis using scatter diagram O

I

/

RISER MIDPOINT

5 10 15 20

Full scatter diagram, H

(m)

LARSEN & PASSANO OTC 5468

o

'O.04,

!"

0.03 0.02