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PTS 31.40.10.15

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Page 4

PREFACE

PETRONAS Technical Standards (PTS) publications reflect the views, at the time ofpublication,of PETRONAS OPUs/Divisions.

They are based on the experience acquired during the involvement with the design,construction, operation and maintenance of processing units and facilities. Where

appropriate they are based on, or reference is made to, national and international standardsand codes of practice.

The objective is to set the recommended standard for good technical practice to be appliedby PETRONAS' OPUs in oil and gas production facilities, refineries, gas processing plants,chemical plants, marketing facilities or any other such facility, and thereby to achievemaximum technical and economic benefit from standardisation.

The information set forth in these publications is provided to users for their considerationand decision to implement. This is of particular importance where PTS may not cover everyrequirement or diversity of condition at each locality. The system of PTS is expected to besufficiently flexible to allow individual operating units to adapt the information set forth inPTS to their own environment and requirements.

When Contractors or Manufacturers/Suppliers use PTS they shall be solely responsible forthe quality of work and the attainment of the required design and engineering standards. In

particular, for those requirements not specifically covered, it is expected of them to followthose design and engineering practices which will achieve the same level of integrity asreflected in the PTS. If in doubt, the Contractor or Manufacturer/Supplier shall, withoutdetracting from his own responsibility, consult the owner.

The right to use PTS rests with three categories of users:

1) PETRONAS and its affiliates.

2) Other parties who are authorised to use PTS subject to appropriate contractualarrangements.

3) Contractors/subcontractors and Manufacturers/Suppliers under a contract with usersreferred to under 1) and 2) which requires that tenders for projects, materialssupplied or - generally - work performed on behalf of the said users comply with therelevant standards.

Subject to any particular terms and conditions as may be set forth in specific agreementswith users, PETRONAS disclaims any liability of whatsoever nature for any damage(including injury or death) suffered by any company or person whomsoever as a result of orin connection with the use, application or implementation of any PTS, combination of PTS orany part thereof. The benefit of this disclaimer shall inure in all respects to PETRONASand/or any company affiliated to PETRONAS that may issue PTS or require the use of PTS.

Without prejudice to any specific terms in respect of confidentiality under relevantcontractual arrangements, PTS shall not, without the prior written consent of PETRONAS,be disclosed by users to any company or person whomsoever and the PTS shall be usedexclusively for the purpose they have been provided to the user. They shall be returned afteruse, including any copies which shall only be made by users with the express prior writtenconsent of PETRONAS.

The copyright of PTS vests in PETRONAS. Users shall arrange for PTS to be held in safecustody and PETRONAS may at any time require information satisfactory to PETRONAS inorder to ascertain how users implement this requirement.

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TABLE OF CONTENTS

1

INTRODUCTION ....................................................................................................................... 6

1.1 SCOPE ...................................................................................................................................... 6 1.2 DISTRIBUTION, INTENDED USE AND REGULATORY CONSIDERATIONS ........................ 7 1.3 DEFINITIONS ............................................................................................................................ 7 1.3.1 General definitions ..................................................................................................................... 7 1.3.2 Specific definitions ..................................................................................................................... 7 1.4 ABBREVIATIONS ...................................................................................................................... 7 1.5 SYMBOLS .................................................................................................................................. 8 1.6 CROSS-REFERENCES ............................................................................................................ 8 1.7 SUMMARY OF MAIN CHANGES SINCE PREVIOUS EDITION .............................................. 9 2 METHOD OF ANALYSIS ......................................................................................................... 10 2.1 PROCEDURE .......................................................................................................................... 10 2.2 LOAD CONDITIONS ............................................................................................................... 11 2.3 SPAN MODELLING ................................................................................................................. 12 2.3.1 Simple beam model ................................................................................................................. 12 2.3.2 Finite element model ............................................................................................................... 12 3 EXTERNAL LOAD ASSESSMENT ......................................................................................... 14 4 REDUCED VELOCITY ASSESSMENT .................................................................................. 15 5 STATIC STRESS ASSESSMENT ........................................................................................... 17 6 FATIGUE ASSESSMENT ........................................................................................................ 18 6.1 FLOW-INDUCED VIBRATIONS DUE TO VORTEX SHEDDING ........................................... 18 6.1.1 Conditions for permitting flow-induced vibrations .................................................................... 18 6.1.2 Span response from in-line VIVs ............................................................................................. 18 6.1.3 Preventing cross-flow VIVs ...................................................................................................... 19 6.1.4 Fatigue assessment ................................................................................................................. 19 7 STRAIN-BASED ASSESSMENT............................................................................................. 20 8 REFERENCES ........................................................................................................................ 21 9 BIBLIOGRAPHY ...................................................................................................................... 22 APPENDIX A WORKED EXAMPLE ................................................................................... 26 APPENDIX B PIPELINE STRESSES ................................................................................ 32

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1 INTRODUCTION

1.1 SCOPE

This PTS specifies requirements and gives recommendations for the analysis of spans inoffshore pipelines including risers and provides guidance for such analyses. Aspects

included in this PTS are:

- span analysis methodology;

- design loads to be considered;

- span modelling requirements;

- design equations;

- span acceptance criteria.

Span analysis is necessary to assess the potential for pipeline damage at the location of aspan due to:

- possible external loads from activities in the area of the pipelines. Examples of suchactivities are the anchoring of construction or supply vessels for pipelines in the vicinityof installations and trawling;

- over-stressing and deformations from bending due to weight and hydrodynamic loads;

- fatigue due to vortex-induced vibration (VIV).

NOTES: 1. Operating pressures and temperatures affect the response of a span and also need to beconsidered during a span analysis.

2. Vortex shedding occurs behind a cylinder when subjected to a lateral current. Oscillating forces,both transverse and in-line with the current, are imposed by this vortex shedding and may causesignificant vortex-induced vibrations (VIVs) if the frequency of these forces and the naturalfrequency of the bending cylinder can align. VIVs can occur in the direction of the current (in-line)or perpendicular to the current direction (cross-flow). Analysis of span damage due to fatigue fromcyclic wave loads is not a concern in water depths of 100m or more and is therefore not addressedin this PTS. In shallower waters this should be addressed using accepted methods of determininghydrodynamic forces on cross sections under cyclic loading and accounting for the proximity of theseabed.

Cases where there are significant variations in flow velocity along the length of the span (as

is for instance the case in catenary risers) are not addressed in this PTS.

This PTS can be applied:

! to the design of new pipelines, to provide a design concept which results in theprevention of pipeline span damage at minimum life cycle cost. This requires that allpossible span-related costs are addressed, i.e. seabed preparation before pipelineinstallation (such as seabed levelling) and span correction after construction and/orduring operation;

! for the analysis of spans observed from surveys during construction and pipelineoperations, in order to decide whether they can be (temporarily) accepted or requirecorrection.

Design equations included in this PTS apply to single-pipe pipeline concepts only. Whilst the

basic principles for formulating these design equations apply also to other pipeline conceptssuch as bundles or pipe-in-pipe pipelines, they differ depending on the selected concept.

Other span assessment criteria may be applied if justified, and if approved by the Principal.The minimum requirements are that all load categories listed in this PTS shall be addressed,and the factor of safety on the mean fatigue life shall be at least 10 unless otherwisespecified by the Principal.

This is a revision of the PTS of the same number dated December 1997; see (1.7) regardingthe main changes.

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1.2 DISTRIBUTION, INTENDED USE AND REGULATORY CONSIDERATIONS

Unless otherwise authorised by PETRONAS, the distribution of this PTS is confined toPETRONAS companies and, where necessary, to Contractors and Manufacturers/Suppliersnominated by them.

This PTS is intended for use on offshore pipelines.

When PTSs are applied, a Management of Change (MOC) process should be implemented;

this is of particular importance when existing facilities are to be modified.If national and/or local regulations exist in which some of the requirements may be morestringent than in this PTS, the Contractor shall determine by careful scrutiny which of therequirements are the more stringent and which combination of requirements will beacceptable with regard to the safety, environmental, economic and legal aspects. In allcases the Contractor shall inform the Principal of any deviation from the requirements of thisPTS which is considered to be necessary in order to comply with national and/or localregulations. The Principal may then negotiate with the Authorities concerned, the objectivebeing to obtain agreement to follow this PTS as closely as possible.

1.3 DEFINITIONS

1.3.1 General definitions

The Contractor is the party which carries out all or part of the design, procurement,construction, commissioning or management of a project, or operation or maintenance of afacility. The Principal may undertake all or part of duties of the Contractor.

The Manufacturer/Supplier is the party which manufactures or supplies equipment andservices to perform the duties supplied by the Contractor.

The Principal is the party which initiates the project and ultimately pays for its design andconstruction. The Principal will generally specify the technical requirements. The Principalmay include an agent or consultant authorised to act for, and on behalf of, the Principal.

The word shall indicates a requirement.

The word should indicates a recommendation.

1.3.2 Specific definitions

Span - section of a submerged pipeline not in contact with the seabed over its length.

NOTE: Generally applicable definitions and requirements for pipeline engineering can be found in Appendix B.

1.4 ABBREVIATIONS

SMYS - Specified minimum yield strength

VIV - Vortex-induced vibrations.

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1.5 SYMBOLS

" linear thermal expansion coefficient for the pipeline steel °C-1

# logarithmic decrement of damping of the span in still water -

$ density of the seawater kg/m3

% Poisson's ratio -

& modal damping ratio in still watera frequency factor -b Euler constant -

A cross-sectional area of the steel pipe based on nominal wall thickness m2 d fatigue damage -ID internal pipeline diameter m

E Young's modulus N/m2

f1 first natural frequency of span s-1

G the average gap between the seabed and the bottom of the spanning pipealong the central one-third of the span m

I moment of inertia of the pipe m4 k deflection coefficient calculated in accordance with Equation 5.1 -Kc Keulegan-Carpenter number -

Ks stability parameter -L span length mM bending moment in pipe NmMe effective mass per unit length of pipeline including added mass and mass

of pipe content kg/mn predicted number of stress cycles -Ne effective axial compressive force in pipeline (see Equation 2.1) N

nf number of stress cycles resulting in pipeline failure due to fatigue -

Ni residual axial tension in the pipeline from installation N

OD outside diameter of pipeline including coating(s) mODst nominal outside diameter of the steel pipe m

Pi maximum allowable operating pressure N/m2

'T difference, at the location of the span, between the predicted maximum

pipeline operating temperature and the pipe temperature during installation °C Ts wave period associated with the significant wave s

Vc steady current velocity perpendicular to the pipe, at top of pipe level m/s

Vr reduced velocity -

Vw wave-induced velocity, perpendicular to the pipe at top of pipe level m/s

W force, per unit length of pipeline, resulting from the combinedweight and hydrodynamic loads N/m

y mid-span span deflection due to in-line VIV m

1.6 CROSS-REFERENCES

Where cross-references to other parts of this PTS are made, the referenced section numberis shown in brackets. Other documents referenced in this PTS are l isted in (8).

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1.7 SUMMARY OF MAIN CHANGES SINCE PREVIOUS EDITION

This PTS is a revision of the PTS of the same number dated December 1997. The followingare the main, non-editorial changes.

Old section New section Change

General General Some minor corrections have been made.

1.1 1.1 NOTE 2 clarified regarding deep and shallow water depths.

1.1 1.1 A paragraph has been introduced to the effect that otherspan design criteria may be used if approved by thePrincipal.

2.2 2.2 Table 1 has been reworded.

Return periods (Table 2) have been modified.

2.3.2 2.3.2 Analysis requirements have been modified.

4. 4. Equation 4.4 has been modified.

In Equation 4.5, the definition of # has been changed.

Text has been added after Equation 4.6.5. 5. Note has been added at the end.

6.1.1 6.1.1 This section has been modified substantially.

6.1.2 6.1.2 Equation 6.4 has been added.

6.1.3 6.1.3 Sentence added for clarification.

6.1.4 6.1.4 Clarifications for fatigue curve determination and use ofMiner's rule have been added.

Appendix A Appendix A The example has been reduced in scope and revised toensure that all results are reproducible from the informationgiven, and to make it consistent with the methodologydescribed in the PTS.

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2 METHOD OF ANALYSIS

2.1 PROCEDURE

Figure 1 schematises the recommended procedure for the analysis of spans of submergedpipelines outlined below.

The assessment of possible external loads is the first step of the analysis after thenecessary input data have been collected.

Spans which pass the external load assessment should then be subjected to a preliminaryassessment involving a relatively simple analysis based on conservative assumptions. Inthis analysis spans are considered acceptable if:

- the analysis of reduced velocities indicates that VIVs will not occur and that,consequently, fatigue damage from these vibrations can be ruled out; and

- the calculated maximum combined stresses under the loads defined in this PTSstay within the limits for elastic stresses in Appendix B.

Spans which fail the preliminary assessment may still be acceptable if unacceptabledamage and/or failure of the span can be ruled out with a more detailed assessmentremoving some of the conservatism of the preliminary assessment. Spans subjected to the

detailed assessment are acceptable if:

- the fatigue assessment demonstrates that fatigue damage from vortex-inducedvibrations will not lead to failure during the design or remaining operating lifetime ofthe pipeline or until the span can be corrected; and

- limits for acceptable plastic strain are not exceeded.

NOTE: Spans have traditionally been assessed against the criteria of the preliminary assessment only. Recenthydrodynamic research on the effect of currents and waves on spanning pipelines has, however, providedinformation necessary to cautiously quantify stress fluctuations from vortex-induced vibrations. Similarly, researchon post-elastic behaviour of pipelines demonstrates that straining of the pipeline beyond the elastic limits can bepermitted without impairing the safety of the pipeline.

The requirements, criteria and guidance for each of the above assessments are given in (3)to (7).

(2.2) and (2.3) specify the load conditions and requirements for span modelling to beconsidered for these assessments.

The length of the span is the critical parameter. Span corrections to reduce the span's lengthare normally done by dumping rock or seabed material along the entire span, or providingsupports along the span. Other methods are water jetting of supports to lower the span intothe seabed, or (on sandy seabeds) the placing of artificial seaweed to draw sand into thegap. Requirements for long-term stability should be a main consideration when selectingspan rectification method(s).

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2.2 LOAD CONDITIONSPipeline spans shall be addressed for all phases of the pipeline life cycle. Table 1 showsthese phases with the pipeline condition and design loads which shall be considered forspan analyses.

Table 1 Pipeline conditions and design loads

Phase Pipeline condition Design loads

Construction - empty pipeline - residual lay tension - submerged empty pipeline weight- hydrodynamic loads

- flooded pipeline (see NOTE) - residual lay tension- submerged flooded pipeline- hydrodynamic loads

Hydrotesting - pipeline under testpressure, filled with testmedium

- residual lay tension - submerged pipeline filled with test

medium- hydrodynamic loads- test pressure

Operation - operating condition - residual lay tension - submerged pipeline filled with fluid

- hydrodynamic loads

- pipeline operating pressure - maximum operating temperature

- flooded pipeline (see NOTE) - residual lay tension - submerged flooded pipeline- hydrodynamic loads

NOTE: The flooded pipeline case shall be considered in order to prevent damage in the event of accidentalpipeline flooding.

Loads for calculating maximum stresses or strains for comparison with maximum allowablevalues should be based on:

- the maximum allowable operating pressure for the pipeline;

- maximum pipeline operating temperature predicted at the location of the span;

- maximum fluid density;- design currents and maximum waves associated with the relevant return period.

Loads for calculating whether VIVs can occur and for fatigue damage calculation should bebased on:

- pipeline operating pressure, temperature and fluid density predicted for the location ofthe span under planned operating conditions;

- design currents and significant waves associated with the relevant return period.

The return period for the hydrodynamic loads should be taken as not less than indicated inTable 2.

Table 2 Return periods for hydrodynamic loads

Case Return period

Design of safe spans for thepipeline lifetime

100 years

Assessment following surveyduring construction or operations

1 year if span is discovered and is rectifiedimmediately; or10 years if span will be rectified within one year ofdiscovery except when discovered and rectified asindicated above; or100 years if span will not be rectified.

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2.3 SPAN MODELLING

2.3.1 Simple beam model

Spans in pipelines on an undulating seabed or at a location of local scour or seabeddepression may be modelled as simple beams with fixed-pinned boundary conditions andsubjected to uniform lateral forces along the span from the combined weight and

hydrodynamic loads and to the effective axial compressive force, Ne, see Figure 2.Spans which result from the pipeline being lifted off the seabed due to the presence of rock,boulders, debris, etc. should be modelled in accordance with a model appropriate for thespecific span.

For axially restrained lines, the effective axial compressive force (Ne) should take into

account the pipe contraction from the internal pressure due to the Poisson effect and theexpansion due to temperature differentials. The effective axial compressive force forrestrained lines is:

where:

" is the linear thermal expansion coefficient for the pipeline steel

% is Poisson's ratioA is the cross-sectional area of the steel pipe based on nominal pipe wall

thicknessID is the internal pipeline diameterE is Young's modulusNi is the residual axial tension in the pipeline from installation

Pi is the operating pressure selected in accordance with (2.2)

'T is the difference at the location of the span between the maximum pipelineoperating temperature and pipe temperature during installation.

NOTE: The effective axial force Ne is positive when the force is compressive.

Sagging will cause the length of a spanning pipe to increase and effectively cause the pipeto be tensioned. For pipelines in operation, this results in a decrease in the effective axial

compressive force calculated in accordance with Equation 2.1. The beneficial effect of thistensioning on the permissible span length may be taken into account provided the feed-infrom sections adjacent to the span, caused by the imbalance of axial forces, is alsoconsidered.

Interaction of spans may be neglected if the pipeline length resting on the seabed to theadjacent span is 20 % or more of the length of the span being analysed. The length of thespan should be increased by 0.2 times the length of the adjacent span if this distance isless.

2.3.2 Finite element model

Finite element modelling of the span permits the removal of some of the conservatisminherent with the simplified beam modelling. Finite element modelling enables the pipe-seabed interaction to be modelled to include the beneficial effects of

- additional pipe settlement near the span ends,- span tensioning due to sagging,

- arch action due to sagging (whereby the cross flow frequency is raised), and

- soil damping

to be modelled. As with simple beam models, axial feed-in from pipeline sections adjacent tothe span should also be modelled if the effect of pipe tensioning due to span sagging isincluded in the analysis.

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To account for the above effects a nonlinear analysis for the static loads shall be performed.This shall be followed by linearisation to calculate the vibration modeshapes and naturalfrequencies used in the VIV analysis. Steady-state current loads shall not be included in theloads applied prior to linearisation, unless approved by the Principal. Where contact and/orstick-slip conditions are involved to model pipe-seabed interaction, care shall be taken toensure that such linearisation results in realistic dynamic stiffnesses. For example, in thedetermination of the cross-flow frequency in a span with significant sagging, it shall be

ensured that realistic dynamic stiffness values are used to describe the resistance to axialslip of the pipe at the shoulders of the span. This may require the use of dynamic stiffnessesthat differ from the tangent stiffness given by the static analysis.

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3 EXTERNAL LOAD ASSESSMENT

Except for areas in the vicinity of platforms or other installations, trawling is normally the onlypotential external load to be considered when reviewing permissible spans. The effect of theheight of a span on trawlgear loads shall be addressed. Span heights shall be limited toprevent hooking of trawlgear.

Pipeline stresses and/or strains predicted from external loads shall meet the requirements ofAppendix B. unless it is demonstrated that the likelihood of such loads occurring is small andthe consequences of pipeline failure acceptable.

Spans should not be permitted in areas near platforms where cables or chains for theanchoring of supply vessels may be run frequently.

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4 REDUCED VELOCITY ASSESSMENT

Fatigue damage from both in-line and cross-flow VIVs will be prevented if the marginbetween the frequency of the shedding vortices and lowest natural frequency of the span issufficient to prevent "lock in" of those frequencies. It may be assumed that lock-in will notoccur if:

c wr

n

V +VV = <1.0f OD(

(equation 4.1)

where:

Vr is the calculated reduced velocity

Vc is the steady current velocity perpendicular to the pipe at top of pipe level

Vw is the wave-induced velocity perpendicular to the pipe at top of pipe level

fn is the first natural frequency of the span.

For the calculation of Vr, the wave-induced velocity Vw may be based on the significant

wave.

The contribution of the wave-induced current (Vw) in Equation 4.1 may be ignored for

significant waves with a Keulegan-Carpenter number (Kc) less than 30.The Keulegan-Carpenter number is calculated from:

where:

Ts is the period associated with the significant wave.

The first natural frequency of a simple beam span model subjected to an effective axialcompressive force Ne is:

where:

a is the frequency factorb is the Euler constantI is moment of inertia of the pipeL is the span lengthme is the effective mass of the pipeline (including content and added mass)

per unit length.

Values for the frequency factor a and Euler constant b depend on the end condition of thespan:

End condition Frequency factora

Euler constantb

Pinned – pinned 9.87 1.

Fixed – pinned 15.4 2.05Fixed – fixed 22.0 4.

Fixed-pinned end conditions may be assumed for single spans. Fixed-fixed end conditionsmay only be assumed if validated by the observed support conditions. The supportconditions in the case of multiple spans shall be based on sound engineering judgement.

The mass of displaced volume of (sea)water may be assumed for the added mass whencalculating the effective pipeline mass.

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The effect of VIV may be neglected if both in-line and cross flow VIV are negligible.

In-line VIVs are unlikely to occur also in narrow gaps between the seabed and bottom of thepipeline or if the stability parameter (Ks), reflecting the structural damping of the span,

exceeds 1.8. The possibility of fatigue damage from in-line VIVs may therefore be ignored if:

G/OD ! 0.1 (equation 4.4)

or if

where:

# is the logarithmic decrement of damping of the span in still water, definedat the slope of a plot of the natural logarithm of the free vibration amplitude

as function of the cycle number, or by " = 2 # $ , where $ is the modaldamping ratio

$ is the density of the seawaterG is the average gap between the seabed and the bottom of the spanning

pipe along the central one-third length of the spanKs is the stability parameter.

For most spans, cross flow VIV can be neglected if

In Equation 4.6, the contribution of the wave-induced current Vw may be ignored for

significant waves with a Keulegan-Carpenter number less than 6. However, for long spanswith little damping for which VIV could occur at low Reynolds numbers, the possibility andconsequences of cross flow VIV at lower reduced velocities should be considered based onavailable test data and/or accepted industry guidance.

NOTES: 1. The modal damping ratio $ or logarithmic decrement " includes structural and soil damping, butnot hydrodynamic damping as this is already included in the VIV response function. For smallamplitude vibrations in still water hydrodynamic damping is negligible, so that " may be estimatedfrom observations of small amplitude vibrations in still water. However for non-viscous soil and/orstructural damping the effective damping coefficient is amplitude-dependent. In this case the

value used should be based on the expected VIV vibration amplitude.

2. Soil damping can include energy radiated away from the pipe in the form of elastic waves, as wellas energy absorbed in elastic deformations of the soil itself.

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5 STATIC STRESS ASSESSMENT

Weight and environmental loads shall be determined in accordance with acceptedengineering practices and the resulting bending stresses are then determined. Equivalentstresses shall be calculated taking into account these bending stresses, other axial stressesand the hoop stress and be verified against the criteria for permissible stresses in Appendix

B.For calculating bending stresses in spans subjected to an effective axial compressive force(Ne >0), the maximum bending moment in a span may be approximated by:

End condition Maximum bending moment

Pinned – pinned

Pinned – fixed

Fixed – fixed at support:

at centre of span:

where:

k is the deflection coefficient to be calculated from the following:

For a pipeline in which the effective axial tension is zero, the maximum bending momentmay be calculated from:

End condition Maximum bending moment

Pinned-pinned

Pinned-fixed

Fixed-fixed

NOTE: The pinned-fixed boundary condition is sometimes used as an approximation to represent a partial

restraint against rotation at both shoulders. This approximation, however, leads to high static stressesat the fixed shoulder. The fixed-fixed boundary condition provides a better approximation for the staticstresses if there is partial restraint against rotation at the shoulders. Indeed, as the rotational restraintis increased equally at both shoulders the maximum stress first drops to wL

2 /16. Then, the location of

the maximum stress changes from midspan to the shoulders, and the maximum stress risesasymptotically to the fixed-fixed value.

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6 FATIGUE ASSESSMENT

6.1 FLOW-INDUCED VIBRATIONS DUE TO VORTEX SHEDDING

6.1.1 Conditions for permitting flow-induced vibrations

In-line VIVs may be permitted provided:

- a safety margin of at least 10 (ten) is maintained between the predicted fatigue damageand the fatigue damage at which the pipeline will fail, unless a different safety margin isagreed with the Principal for the specific method of calculation used; and

- they do not occur in risers including the subsea connections to the pipeline resting onthe seabed and at locations where intensification of the fluctuating bending stress mayoccur.

Cross-flow vibrations should not be permitted at reduced velocities beyond the limit ofEquation 4.6. If cross-flow vibrations are expected below this limit, the fatigue damage dueto such vibrations shall be assessed. The fatigue damage due to in-line and cross-flowvibrations need not be combined because they occur at different locations on thecircumference of the pipe (6 and 12 o ’ clock positions for cross-flow, and 3 and 9 o ’ clock

positions for in-line).

NOTES: 1. The above safety margin of 10 reflects the fact that subsea pipelines cannot be inspected for thepresence of fatigue damage.

2. Examples of sources for the intensification of bending stresses are fittings, flanges, mechanicalconnectors and ancillaries welded to the pipeline.

3. The occurrence and amplitude of cross-flow vibrations are difficult to predict. E.g. some modeltests on long spans with essentially zero damping have shown cross-flow vibration starting atreduced velocities around 2. Stresses from cross-flow vibrations can lead to rapid pipeline failure,but for long spans a fatigue analysis should be considered to assess whether limited cross-flowvibrations under extreme circumstances can be tolerated.

6.1.2 Span response from in-line VIVs

Fatigue damage due to in-line flow-induced vibrations shall be assessed if the followingthree conditions are satisfied:

G/OD > 0.1 (equation 6.2);

and

NOTE: In-line VIVs are unlikely to occur if any of these conditions are not met.

As in the reduced velocity assessment (4), the contribution of the wave-induced current inEquation 4.1 may be ignored for significant waves with a Keulegan-Carpenter number ofless than 30.

The following may be assumed for the response of the span from in-line vibrations:

- the span will respond with a frequency equal to the first natural frequency of the span;- the maximum mid-point deflection y of the pipeline span may be obtained from Figure 3

or from Equation 6.4.

y = OD max ( 0.2 – K S /6, 0.15 – K S /9) (equation 6.4)

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The total bending stress range due to in-line VIV oscillations with an amplitude y may becalculated as follows:

End condition Maximum bending stress

Pinned - pinned

Fixed - pinned

Fixed – fixed

where:

ODst is the nominal outside diameter of the steel pipe.

6.1.3 Preventing cross-flow VIVs

Cross-flow VIVs may be assumed not to occur if Equation 4.6 is satisfied. At lowervelocities limited cross flow VIV could occur, but may be accepted if it is shown that this willnot lead to fatigue failure.

6.1.4 Fatigue assessment

The fatigue damage of a span over a given period is determined as follows:

- determine the total time that the span may be subjected to in-line VIVs;

- calculate the natural frequency of the in-line VIV;

- calculate the total number of stress cycles n due to VIVs;

- calculate the stress fluctuation per stress cycle (twice the amount calculated with theequations given in (6.1.2));

- determine from a representative fatigue curve the number of cycles nf that would result

in pipeline failure, considering the effects of internal and external environments, thedefect tolerance criteria at girth welds, including misalignment offset, as well as anyallowable lack of fusion and other defects;

- calculate fatigue damage d = n/nf

The span is acceptable if the fatigue damage, d, does not exceed 0.1.

If d exceeds 0.1, then the span should be corrected within a period during which d does notexceed 0.1.

In the above, the number of cycles nf until fatigue failure should be reduced if the pipeline

has been subjected to other, non-concurrent stress cycles, e.g. from installation, or earlierspanning. Miner's rule may be used to add the fatigue damage from various non-concurrentstress cycles occurring at any given location. In such cases the limit of 0.1 applies to theoverall fatigue damage.

If stress cycles from different sources of loading (e.g. thermal cycles) occur concurrently withVIV and at the same location, then Miner ’ s rule is not applicable. For such cases the actual

combined stress history shall be calculated, and the fatigue damage it produces evaluated,

e.g. by a rainflow counting algorithm. Detailed guidance for such cases is outside the scopeof this PTS .

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7 STRAIN-BASED ASSESSMENT

The static stress assessment (5) may be replaced by a strain-based strength assessmentprovided the bending of the span is restricted by the seabed before:

- bending strain can cause fracture;

- compressive strain can cause wrinkling or buckling of the pipe;

- pipe ovalisation can exceed 2.5 %.

A further requirement for permitting strain is that cyclic plastic straining cannot occur.Variations in operating pressures, temperatures and fluid densities and hydrodynamic loadsshould all be considered when determining the total possible strain cycle.

NOTE: To prevent fracture, the maximum value for the permissible total strain is 0.5 % unless it isdemonstrated that for the selected steel and weld properties a higher value may be used.

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8 REFERENCES

In this PTS reference is made to the following publications:

NOTE: Unless specifically designated by date, the latest edition of each publication shall be used, togetherwith any amendments/supplements/revisions thereto.

PETRONAS STANDARDS

Pipeline & Riser Engineering PTS 20.214

NORWEGIAN STANDARDS

Rules for submarine pipeline systems DNV 1981

Free spanning pipelines DNV-RP-F105

Fatigue strength analysis of offshore steel structure DNV-RP-C203

Issued by:Det Norske Veritas Industri Norge ASPO Box 300, N-1322 H øvik Norway

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9 BIBLIOGRAPHY

NOTE: The following documents are for information only and do not form an integral part of this PTS

1. "Dynamics of marine structures: Methods of calculatingthe dynamic response of fixed structures subject to wave

and current action"; Report UR8 (2nd Edition), CIRIAUnderwater Engineering Group

ISSN: 0 86017 101/9

2. Celant M., Re G., Venzi S., Fatigue Analysis forSubmarine Pipelines, Offshore Technology Conference,Houston, Paper No. 4233 (1982).

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FIGURES

FIGURE 1 SPAN ANALYSIS PROCEDURE

FIGURE 2 SIMPLE FIXED - PINNED SPAN MODEL

FIGURE 3 AMPLITUDE OF IN-LINE MOTION AS A FUNCTION OF KS

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FIGURE 1 SPAN ANALYSIS PROCEDURE

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FIGURE 2 SIMPLE FIXED - PINNED SPAN MODEL

FIGURE 3 AMPLITUDE OF IN-LINE MOTION AS A FUNCTION OF Ks

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APPENDIX A WORKED EXAMPLE

A.1 SCOPE

This worked example illustrates the application of this PTS.

A.2 INPUT DATA

A.2.1 General pipeline data

The worked example is for a span of 30 m length in a 500 mm pipeline carrying oil, in theCentral North Sea.

The span is modelled as a beam-column with fixed-pinned boundary conditions, subject toaxial load and uniform lateral loads along the length of the span.

The pipeline is fully axially restrained.

A.2.2 Pipeline and span data

Table A.1 gives the details of the pipeline under consideration. The table also outlines theparameters defining the span assessed in this worked example.

Table A.1 Data for pipeline and span

Parameter Units Value

Pipeline:Nominal outside diameter of the steelpipe (ODst)

m 0.508

Nominal wall thickness mm 15.88Material grade - API 5L X60Young's modulus (E) MPa 2.07x105

Poisson ratio (%) - 0.3

Steel density kg/m3 7850

Coefficient of thermal expansion (") C-1 11.6x10-6 External corrosion coating - Asphalt enamelCorrosion coat thickness m 0.0065Corrosion coat density kg/m3 1300Concrete coating thickness m 0.1Concrete coating density kg/m3 3000Thickness of marine growth m 0Internal diameter (ID) m 0.4762Outside diameter of pipeline includingcoating(s) (OD)

m 0.721

Design life years 20Span:Span length (L) m 30Water depth m 91.5Marine growth on the pipeline not expectedGap under central part of span as afraction of the overall outside diameter(G/OD)

0.277

Logarithmic decrement of damping of the

span in still water (#)

0.126

Bearing of pipeline degrees 150

A.2.3 Operating and environmental data for fatigue assessment

Table A.2 and Figure A.1 give the significant environmental data and normal pipelineoperating conditions required for fatigue assessment of the span.

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Table A.2 Data for fatigue assessment

Parameter Units Value

Environmental :

Density of sea-water ($) kg/m3 1025

Temperature of sea-water during

installation

°C 4

100-year maximum component of steadycurrent normal to the pipeline

m/s 0.59

Steady current reference height m top of pipeSignificant wave height m 12.8Significant wave period (Ts) s 12.1

Content :Fluid OilContents density kg/m3 870Normal operating temperature °C 25Normal operating contents pressure (Pi) bar 120

A.2.4 Data for stress assessment

Table A.3 contains the maximum environmental conditions and extreme operating

conditions to be used for the stress assessment.Table A.3 Data for stress analysis

Parameters Units Value

Environmental :

Maximum wave height m 23.8

Maximum wave period s 17.1

Content :

Extreme operating temperature °C 30

Extreme operating pressure (Pi) bar 134

A.3 EXTERNAL LOAD ASSESSMENT (3)

For the purposes of this example, external loads are not considered. It is assumed that aseparate analysis has demonstrated that the span can withstand loads from trawlgearpresent in the area.

A.4 REDUCED VELOCITY ASSESSMENT (4)

The preliminary assessment of VIV is carried out in accordance with (4).

A.4.1 Axial load on the span

The effective axial compressive force in a fully restrained pipeline is given by Equation 2.1for the normal operating conditions given in Table A.2. If, to be conservative, the residualinstallation tension is agnored, then the resulting effective axial compressive force is 2.09 x

106 N.

A.4.2 Natural frequency of span

The first natural frequency of a beam-column subjected to an axial compressive force isgiven by Equation 4.3. For a fixed-pinned span, the frequency factor and Euler constant are15.4 and 2.05 respectively. This equation can therefore be rewritten using the data inTable A.1 and the effective axial compressive force as calculated in (A.4.1) to give a firstnatural frequency of 0.575 Hz.

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A.4.3 Wave and current velocity

The wave-induced velocity at the crown of the pipeline is calculated from linear wave theory.This yields a component of wave-induced velocity perpendicular to the pipeline of 0.52 m/sand 2.25 m/s, based on the significant and peak wave data in Table A.2, respectively. Thecurrent velocity perpendicular to the pipe at the top of the pipeline is given as 0.59 m/s.

A.4.4 Limiting criteria for vortex-induced vibrationFrom Equation 4.2 the Keulegan-Carpenter number is found to be 8.7. This exceeds 6 but isless than 30. Therefore the significant wave-induced velocity shall be included in theassessment for cross-flow VIV but not for in-line VIV. This leads to reduced velocities of2.7 for cross-flow VIV, and 1.4 for in-line VIV. Thus, in-line VIV could occur according toEquation 4.1, but no cross-flow VIV would occur according to Equation 4.6.

The possibility of in-line VIV can be ignored if either Equation 4.4 or 4.5 is satisfied. For thisexample, the gap under the span as a fraction of overall outside diameter is 0.277, thereforeEquation 4.4 is not satisfied. In addition, the stability parameter is calculated to be 0.644, soEquation 4.5 is also not satisfied. Therefore an assessment of in-line VIV fatigue damage isnecessary.

A.5 FATIGUE ASSESSMENT (6)

A.5.1 Conditions for permitting flow-induced vibrations (6.1.1)

Cross-flow VIV is not permitted. However, the span has already been shown (A.4.4) to beunlikely to suffer damage from cross-flow VIV. Also, there are no connectors or other fittingsin the vicinity of the span where intensification of the fluctuating bending stress may occur.In-line VIV may therefore be permitted provided it is demonstrated that the fatigue damagedoes not exceed 0.1 during the lifetime of the pipeline.

A.5.2 Span response from in-line VIV (6.1.2)

In-line VIV should be taken into account only if the criteria laid down by Equation 6.1,Equation 6.2 and Equation 6.3 are satisfied simultaneously. All three of these conditions aresatisfied, see (A.4.4), and in-line VIV shall therefore be assessed.

A.5.3 Fatigue assessment (6.1.4)

From Equation 6.4 the amplitude of oscillation is found to be y = 56 MPa, and thecorresponding dynamic stress amplitude is 56 MPa based on formula for the fixed-pinnedcondition in (6.1.2).

For the fatigue life, it is assumed, to be conservative that a girth weld is present where thehighest fatigue loading occurs. The fatigue life of the girth weld is determined fromrecommendations given in DNV-RP-C203, which recommends that two hotspots should bechecked: the cap (toe of the weld) and the root.

For the cap, the possibility of loss of protection by the coating is considered. Therefore theD-curve for seawater with cathodic protection applies. Considering this, and the effect ofmisalignment offset assumed to be 1.6 mm, and the wall thickness effect, leads to a fatiguelife of 324,000 cycles.

For the root, the fatigue curve for air is used, because the oil is non-corrosive. Using the F1curve then leads to a fatigue life of 357,000 cycles.

The hotspot giving the lowest fatigue life governs. Thus the cap governs, giving a fatigue lifeof Nf = 324,000 cycles.

According to the response function in this PTS, in-line VIV occurs whenever the reducedvelocity exceeds 1.0, and the amplitude or fatigue damage rate does not depend on theamount by which the threshold velocity is exceeded (provided it is not exceeded by morethan a factor of 3.5, as indicated by Equation 6.1).

The threshold velocity for in-line VIV is

Vthreshold = OD fn = 0.41 m/s

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Based on the probability distribution for the component of current velocity normal to thepipeline (Figure A.1), this threshold velocity is exceeded 0.028 % of the time. Over thedesign life this amounts to 1 day (86,459 s). Multiplying this by the natural frequency ofoscillation gives an applied number of cycles over the lifetime of the span of N = 49,734;which is 15 % of the number of cycles to failure. This exceeds the allowable fatigue damageratio of 10 % as specified by this PTS [(6.1.1) requires a factor of safety of at least 10 onfatigue life].

A.6 STATIC STRESS ASSESSMENT (5)

A.6.1 Wave and current velocity

The peak wave velocity is calculated from linear wave theory. Based on the maximum wavedata in Table A.3, the peak wave-induced velocity perpendicular to the pipe at the top of thepipeline is 2.25 m/s.

The current velocity perpendicular to the pipe at the top of the pipeline is 0.59 m/s.

The Keulegan-Carpenter number, as given by Equation 4.2 with the wave and currentvelocities for the maximum wave, is therefore 53.4. The Keulegan-Carpenter number isused, along with the Reynolds number and the ratio of span height to overall outsidediameter, to establish hydrodynamic coefficients from DNV 1981 which give the

hydrodynamic forces on the pipeline.A.6.2 Maximum load on span

The maximum load on the span is the greatest combined loading resulting from its ownweight and all hydrodynamic forces throughout the 360° wave cycle. The hydrodynamicloads can be calculated according to DNV 1981. The force per unit length resulting from thecombined submerged weight and hydrodynamic loads on the span is found to be 5620 N/m.

A.6.3 Axial load on the span

The effective axial compressive force is calculated using Equation 2.1, applying theconditions for the extreme load case given in Table A.3. To be conservative, the residual

tension is ignored. The resulting effective axial compressive force is then 2.49 x 106 N.

A.6.4 Static stress assessment

A.6.4.1 Maximum bending moment

The maximum bending moment is calculated using the formula for a pinned-fixed beam

given in (5). The maximum bending moment is equal to 1.66 x106 Nm.

A.6.4.2 Maximum/minimum bending stress

The maximum bending stress is calculated from the bending moment and is 568 MPa. Thebending stress is tensile at the top of the pipe (12 o ’clock position) and compressive at thebottom (6 o’clock position).

A.6.4.3 Axial stress

The mean axial stress is calculated according to Appendix B. Appendix 2, using the meandiameter of the steel pipe. The residual tension, sag-induced tension and feed-in are ignored

in this example. The mean axial stress is !4.6 MPa.

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A.6.4.4 Hoop stress

The mean hoop stress is calculated according to Appendix B. Appendix 2, using the meandiameter of the steel pipe. The hoop stress is 193 MPa.

A.6.4.5 Span assessment

The maximum von Mises stress is calculated according to Appendix B. Appendix 2 to be690 MPa. The span is considered safe if the maximum von Mises stress is less than 90 % ofthe specified minimum yield strength for the steel. The 90 % SMYS limit for this pipelinesteel is 373 MPa, which is exceeded by the maximum von Mises stress. The span thereforefails the preliminary static stress assessment. It is necessary to perform a strain-basedassessment in order to further assess whether the span is acceptable.

CONCLUSION

This span does not satisfy the screening criteria of this PTS. This leaves the followingalternatives:

- Shorten the span length, e.g. by seabed intervention; or

- Perform a more detailed and less conservative assessment [as is allowed according to(1.1), provided the approach is justified and approved by the Principal].

To remove conservatism such a more detailed analysis could address the following:

- For spans that are partially constrained against rotation at both ends, the assumption offixed-pinned boundary conditions for the span may provide a reasonable approximationto the natural frequency. However it is very conservative in the assessment of the staticstresses, and the dynamic stresses for a given amplitude of oscillation. Modelling thepipe as a beam with partial restraint against rotation at each end would remove thissource of conservatism.

- The sag of the span tends to reduce the compressive axial force. Accounting for thisleads to a higher natural frequency and lower stresses due to static loads.

- If the sag is sufficient the span becomes supported by the seabed. In such cases astrain-based assessment may be applied, since the displacements are limited. Howeverall possible sources of strain concentration shall be considered in this case.

- The response function used in this PTS for in-line VIV assumes the full VIV amplitude ofoscillation at the moment the threshold velocity is exceeded. Tests suggest that theamplitudes are smaller near the threshold and reach a maximum only at significantlylarger current velocities.

A number of these sources of conservatism are addressed in DNV-RP-F105.

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Figure A.1 Cumulative distribution function for curent velocity

0.00001

0.0001

0.001

0.01

0.1

1

0 0.1 0.2 0.3 0.4 0.5 0.6

Current Velocity (m/s)

E x c e e d a n c e

P r o b a b i l i t y

The "current velocity" shown is the absolute value

of the component of current velocity normal to thepipeline.

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APPENDIX B PIPELINE STRESSES

Documents

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