IBP1023 05 UPDATED FREE SPAN DESIGN PROCEDURE DNV RP …

______________________________ 1 Ph.D., Civil Engineer – Det Norsk Veritas, Norway

IBP1023_05 UPDATED FREE SPAN DESIGN PROCEDURE DNV RP-F105

ORMEN LANGE EXPERIENCES Olav Fyrileiv1, Kim Mørk 1, Muthu Chezhian1

Copyright 2004, Instituto Brasileiro de Petróleo e Gás - IBP This Technical Paper was prepared for presentation at the Rio Pipeline Conference & Exposition 2005, held between 17 and 19 October 2005, in Rio de Janeiro. This Technical Paper was selected for presentation by the Technical Committee of the event according to the information contained in the abstract submitted by the author(s). The contents of the Technical Paper, as presented, were not reviewed by IBP. The organizers are not supposed to translate or correct the submitted papers. The material as it is presented, does not necessarily represent Instituto Brasileiro de Petróleo e Gás’ opinion, nor that of its Members or Representatives. Authors consent to the publication of this Technical Paper in the Rio Pipeline Conference& Exposition 2005 Annals. Abstract

The Ormen Lange gas field is located within a prehistoric slide area with varying water depths from 250 to 1100m. Due to the slide area, the seabed is very uneven including steep slopes and seabed obstacles up to 50 meters tall. The major technical challenges with respect to pipeline design in this area are:

• Extreme seabed topography combined with inhomogeneous soil conditions. • Uncertainties related to current velocities and distribution. • High number of spans including some very long spans. • Deep waters and therefore difficult and costly seabed preparation/span intervention. • Flowlines with large potential to buckle laterally in combination with free spans

In order to minimise span intervention costs, a major testing campaign and research programme has been

conducted in the Ormen Lange project to come up with a design procedure in compliance with the DNV-RP-F105 (DNV, 2002) design philosophy.

The improvements in terms of reduced seabed intervention and rock dumping costs are in the order of several 100 MNOKs. The lessons learned and the improved knowledge will also be a great value for other project dealing with similar free span problems. 1. Introduction

Free span assessment is a complex problem, which requires detailed knowledge in several disciplines such as

Vortex Induced Vibrations (VIV) and direct wave load models, environmental modelling, fatigue calculations, structural response analysis and geo-technical aspects.

The relevant failure modes for free spans are fatigue and local buckling. Fatigue may occur due to accumulated damage from stress cycles caused by VIV and with contributions from direct wave loads in shallow waters. Over-stress (local buckling) due to static bending (weight & current), VIV & wave loads, pressure effects and axial force also needs to be considered. Trawl gear interference analysis can provide limiting conditions, in areas of trawling.

The focus of the presented study will be restricted to VIV aspects of very long free spanning pipelines. The free span vibrations can be classified and analyzed under the following categories:

• Isolated single span - single mode response • Isolated single span - multi-mode response • Interacting multispans - single mode response • Interacting multispans - multi-mode response

The existing design code DNV-RP-F105, can be effectively applied to deal with both single and multiple

spans vibrating predominantly in a single mode. The combination of long spans and high currents may imply that not only the fundamental eigen modes are activated but also higher modes. Such a multi-mode response is not prohibited by the design codes. However, no detailed guidance is provided in the present days design codes about the fatigue damage from multi-mode vibrations.

Rio Pipeline Conference & Exposition 2005

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2. Ormen Lange Free Spans

The Ormen Lange gas field is a typical deep water pipeline project located 120 km west of Kristiansund, off the coast of Norway, see Figure 1. It is situated within a gigantic prehistoric slide area with varying water depths from 800 to 1100m. The field is to be developed with subsea installations, and the gas is to be transported to shore by two 30” multiphase pipelines. Due to the prehistoric slide, the seabed is very uneven including steep slopes and seabed obstacles up to 50 meters tall.

Figure 2 presents a 3D-map view of the Storegga slide with an indication of the development area for the wells/templates at 850 m water depth. The pipeline route from the subsea installations and out of the slide area towards the onshore terminal is also indicated. Figure 3 shows a local view of the uneven seabed in the Development area. The tallest seabed obstacles are up to 50m in height.

Figure 1 - Ormen Lange Field location outside the west coast of Norway.

Figure 2 - Illustration of the Ormen Lange reservoir and Storegga slide area

This paper presents an overview of the activities performed in the project in order to minimise the span

intervention costs by advanced routing and by developing a new design approach to document the integrity of long free spans.

Ormen Lange


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Further, the recent updates of the DNV-RP-F105 regarding the design methodology, response models and acceptance criteria are briefly discussed. This new revision of the Recommended Practice is to be issued during autumn 2005. 3. Free Span Design Aspects

Current design practice for free spanning pipelines is to allow free spans as long as the integrity with respect to potential failure modes are checked and found acceptable, ref. DNV-RP-F105 (DNV,2002).

The uneven seabed will, of course, cause a high number of spans, some of them very long and with a large pipe-seabed gap, see Figure 4 below where all spans longer than 40 meter are plotted. The steep slopes in some areas will also cause challenges for the seabed preparation work and span intervention, e.g. due to rock berm stability problems and several high spans may need costly intervention work. In addition the 100-year extreme value for the near bottom current is above 1.1 m/s. This restricts the allowable span lengths due to VIV and associated fatigue and is motivating efforts to extend the existing practice for allowable spans length while still not compromising the overall safety objective.

Figure 3 - Uneven seabed in the Development area.

In case of very long spans exposed to high current velocities for long duration, the multi-mode behaviour for inline (IL), cross-flow (CF) and CF induced IL needs to be taken into account. This calls for advancements in the design guidelines, in order to provide explicit methodologies to assess multi-spanning pipelines vibrating in multiple modes.


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Figure 4 - Free span distribution for one route stretch

The focus for the free span design, in addition to ensuring the structural integrity of the pipelines, will be to

minimize the seabed preparation and span intervention costs. In the Ormen Lange project this has been done by a combination of:

• Advanced routing activities • Current measurement campaign and current modelling activities • VIV test programme • Updated project specific design guidelines based on test results • Use of reliability analysis for the free spans

3.1. Advanced Routing During the conceptual study and detailed design phase of the Ormen Lange development, several pipeline routes have

been evaluated. Detailed surveys of the possible routes have been performed. For this purpose the autonomous underwater vehicle “Hugin” has played an important role. The detailed mapping of possible routes has made it

possible to optimize the pipeline route. This optimization has further made it possible to avoid several of the longest free spans encountered in early phases of the planning. As an example see the routes checked out in a local area in

Figure 5 below.


5

KP 12

KP 11

KP 8

KP 9

KP 10

N

KP 12KP 12

KP 11KP 11

KP 8KP 8

KP 9KP 9

KP 10KP 10

N

Figure 5 - Local routing alternatives to minimize free spans 3.2. VIV Tests and Design Guideline

A test program was performed at Marintek to gain experience and data with respect to long free span response Marintek (2001, 2002). Details about the test programme are given by Søreide et al (2001). Analysis of the test results, Nielsen (2002a, 2002b) concluded in a calculation procedure on how the interaction between cross-flow (CF) and in-line (IL) VIV response could be treated for long free spans. On this basis, a project specific guideline for long free spans has been developed, built on the design methodology of DNV-RP-F105.

A truss girder served as the support structure for the pipe, see Figure 6. Figure 7 shows the set-up of the test rig with its removable clamp support enabling changes of the

span length. The model scale was 1: 17, and a Froude scaling law was applied. The bending stiffness of the test pipe reflected the bending stiffness of the Ormen Lange pipe, while the tension in the pipeline was adjusted in the tests by a pre-tensioning device. The L/D span length ratio was varied between 145 and 350.

Figure 6 - Model testing rig at Marintek


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By towing the test rig through water in a ship model tank, the vortex induced vibrations were measured for

different flow velocities or reduced velocities as used in the response models. During towing, both the strains at different locations were measured by strain gages and the vertical and horizontal displacements were recorded by use of video.

Figure 7 - VIV test rig with clamp supports.

The multi-mode behaviour of the long free spans can be seen vividly in the model test results conducted at Marintek, (2001, 2002). In Figure 8 the multi-mode behaviour of the free span with an L/D ratio of 215 is shown. The “Y-Displ” and “Z-Displ” denote the displacement in the IL and the CF direction. Figure 8 is based on the displacement measurements during the time window of 454 and 464 seconds. The first 2 CF modes and the first 3 IL modes are active. Similar multi-mode behaviour has been observed in several test cases.

Figure 8 - Multi-mode behaviour of the free spans in model tests.

The identification of the different effects have been directed towards a design procedure for multiple spans VIV, and implemented into the Ormen Lange project guideline (DNV, 2003). 3.3. Update of DNV RP-F105 Response Models

In principle, there is no limitation to the span length in DNV-RP-F105. The basic CF VIV response is, however, based on single mode response and, hence, focuses on short to moderately long spans. For cases of very long spans exposed to high current velocities for long duration, the multi-mode behaviour for IL, CF and CF induced IL needs to be taken into account.

DNV-RP-F105, applies so-called response models to predict the vibration amplitudes due to vortex shedding. These response models are empirical relations between the reduced velocity and the non-dimensional response amplitude. The response models are based on test data and a few hydrodynamic and structural parameters.

The vortex shedding frequency caused by a flow normal to a free span is governed by the Strouhal’s number, the pipe outer diameter and the flow velocity. As the flow velocity and thereby the shedding frequency reach one of the natural frequencies of the span, the span starts to vibrate and the vortex shedding along the span get correlated by the vibration of the span. In this way the vortex shedding frequency and the VIV get locked-in with the natural frequencies of the span over a certain range of flow velocities. The response frequency may differ from the calm water natural frequency, Nielsen (2002) and Larsen (2001). This is related to change in added mass. As the vibration


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amplitude of the span increases, the motion of the pipe will change the relative flow velocity and will therefore at a certain limit have influence on the vortex shedding. In this way the VIV could be considered as a displacement-controlled load.

The response models given in the DNV-RP-F105, were studied for its applicability on long free spans. Based on the results from the model VIV tests conducted at Marintek, the response models which needed to be modified were identified. It was found that the inline response model given in DNV-RP-F105, was indeed very adequate and was able to capture the inline response behaviour of long free spans, even for higher modes.

The CF response model required some modifications, in order to capture the observed VIV response behaviour. Two CF response model options were proposed and tested for their suitability.

Fatigue analysis has also been performed on the stress series measured in the model tests and this has been successfully used to verify and validate the presented computational procedure. Uncertainty in the model test based fatigue estimates has been assessed and sensitivity studies have been carried out. Reasons for deviations and potential problem areas for long free spanning pipelines have been identified.

Figure 9 - CF Response Model from Ormen Lange test Campaign

The main findings from the VIV tests and development of a project specific design guideline may be

summarised as: • Response models for cross-flow have been identified and examined, see Figure 9. • DNV-RP-F105 in-line response model is found to be sufficient and applicable. • Added mass effect has been included to calculate the response cross-flow frequency. • The ratio between fatigue estimates based on the computational method and fatigue estimates based on model

test results agree reasonably well and the deviations are within a quantifiable range. For more details reference is made to Mørk (2003).

3.4. Use of Reliability Analysis

A reliability approach allows dedicated uncertainty modelling, including statistics for natural variability and explicitly accounting for model uncertainties. Such a study has been made in the Ormen Lange project for the free span fatigue issue. This allows a more accurate prediction of the maximum allowable span lengths than is possible based on a design code with safety factors developed for a broader scope of design conditions. Further the reliability analysis gives valuable sensitivity measures that support design modifications and cost optimization.

Different sensitivity studies were performed. Among these were: • Acceptance level (annual probability; system effects) • Pipe (wall thickness) • Effective axial force • Span (length, gap) • Soil (firm, stiff, soft) • Current (distr., depth, direction)

CROSSFLOW MODE 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

VRd

A/D

Response Model

75xx -single span

71xx - single span

72xx - 2 spans symmetric

725x- 2 spans unsymmetric

73xx - 3 spans


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• Response analysis (response curve, eigen frequency, damping, concrete stiffness, static deflection) • SN (air, corrosion, curve) • Damage (allowable, stress amplitude)

In addition the effect of using strakes and monitoring of VIV has been studied. The main observations drawn from this study using probabilistic analysis were:

• Fatigue is governed by 1st and 2nd mode IL VIV • DNV-RP-F105 provide conservative results for operational conditions • The governing uncertainties are related to:

SN curve Eigen frequency stress amplitude

For more details about the reliability analysis see Hagen (2003).

3.5. Design Approach

One of the most important parameters related to free span design is the fundamental or natural frequency of the span:

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅= ⋅

E

eff

effe PS

CLmEICf 2410 1

(1)

Where C1 and C2 are boundary condition coefficients, EI is the bending stiffness. Leff is the effective span length as shown by Fyrileiv and Mørk (2002). me is the effective dynamic mass, PE is the Euler buckling load and Seff the effective axial force:

eeiieff ApApNS +−= (2)

Where N is the true axial force and pi, pe and Ai, Ae are the internal and external pressure and cross sectional area, respectively.

As can be demonstrated the effect on the allowable free span lengths and fatigue caused by the effective axial force can be substantial in pipelines with high temperatures and/or high pressures (HTHP). As such this effect must be accounted for in free span design of most of the flowlines and also in the hot end of export pipelines.

Quite recently Galgoul et al (2004a) claimed that the expression for the effective axial force and the way it is applied in some DNV codes like DNV-OS-F101 and DNV-RP-F105 is wrong. It is argued that the effect of the internal pressure is the opposite of what is given in Eq. (1). However as shown by Fyrileiv et al (2005), when considering the effect of the internal pressure by the concept of effective axial force as shown in the figure below, Eq. (1) is correct.

Figure 10 - Equivalent physical systems – internal pressure

The governing equation of motion for an infinitesimal element of the pipe becomes:

pi

pi

piAi

N


9

0)(2

2

2

2

4

4

=∂∂

+∂∂

−−∂∂

tvm

xvApN

xvEI effii

(3)

The classical solution of this accounting for the boundary conditions is given by Eq. (1). Let us consider the previous equation without the dynamic term (inertia term). Having no external distributed

load but including external and internal pressures will lead to:

02

2

4

4

=∂∂

−∂∂

xvS

xvEI eff

(4)

Solving this equation gives the following critical load, buckling load, for a pinned-pinned boundary condition:

2

2

, LEIApApNS eeiicrcreff

π=+−=

(5)

This shows that there is a clear relationship between how the internal (and external) pressure affects both global buckling and the natural frequencies of a span. For this reason it of outmost importance to predict potential buckling of the pipeline and estimate the release of effective axial force in order to end up with a safe and reliable free span design.

Figure 11 below illustrates a typical design flow for HTHP pipelines. After performing the initial design selecting pipe diameter, wall thickness, material and insulation requirements, it has to be decided whether the pipeline is to be buried or installed exposed at the seabed.

In case the pipeline is to be exposed on the seabed interference with trawl gear and/or on-bottom stability aspects may set requirements to the impact resistance and the weight of the coating. If these requirements can not be met, the pipeline has to be buried.

Any potential global buckling needs to be addressed in order to check the integrity of the pipeline after such an event. Another important aspect is to establish the correct effective axial force as an input to the free span design. This is in line with the recommendations in DNV-RP-F105 (2002) and also the essence of the findings by Galgoul et al. (2004b) addressing the problem of lateral buckling and free span design of flowlines.

After the buckling/expansion and free span design aspects have been solved, the main task is to verify that it is feasible to install the pipeline with the selected method and equipment.

In Figure 12 below an example of a pipeline installed on uneven seabed is shown. Due to the internal pressure and temperature, the pipeline will lift off the seabed at high points and buckle sideways. The effect on the free span lengths and their fatigue lives in this area are strongly influenced by the buckling response.

Besides of the effect caused by global buckling and release of effective axial force, the span deflection will gradually increase as the effective axial force tends towards the critical buckling value. This deflection will release some of the axial force and may also cause the span to vanish as the span height is limited. For these reasons, span response expressions based on linear beam theory can not be applied and must be replaced by for example non-linear FE analysis.


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Figure 11 – Design flow chart for HTHP pipelines

-385

-384

-383

-382

-381

-380

-379

-378

-377

-376

-375

3000 3100 3200 3300 3400 3500 3600KP [m]

Wat

er d

epth

[m]

Seabed

Seabed intervention

Vertical configuration

Lateral configuration

-10

-8

-6

-4

-2

0

2

4

6

8

10

3000 3100 3200 3300 3400 3500 3600

Figure 12 – Release of effective axial force by lateral buckling on uneven seabed (vertical plan with uneven seabed in

upper figure and horizontal plan with lateral buckle in lower figure).

The Ormen Lange pipelines and especially the 30” flowlines to shore are installed in very uneven seabed and with numerous vertical and horizontal curves. These curves acts as initial imperfections and cause the pipelines to buckle laterally at several locations.

Trenching Expansion

Expansion

Check feasibility wrt installation

Routing

Burial

Free Span

Trench/ Protection

Safety evaluations Flow assurance

Material selection Wall thickness design

Trawling

Stability


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This buckling is utilised in the design in order to decrease the effect of the compressive effective axial force caused by temperature and internal pressure, and thereby increasing the acceptable free span lengths and minimise the span intervention costs 3D non-linear FE analysis are used as a basis for the buckling and free span design.

4. Case Study

In order to demonstrate the effects of the activities performed in the Ormen Lange project, a case study of one of the 30” flowlines has been performed. The location studied is on 900 meters close to the templates.

The following cases have been studied:

0 base case – no release of effective axial force due to buckling 1 Release of effective axial force due to buckling 2 Updated long-term distribution of current after extended measurement campaign 3 Updated SN curve due to fatigue testing 4 Updated multimode response calculation

It is assumed that the span is a single, isolated span, i.e. no multi-spanning section, and that the response

quantities such as natural frequencies and mode shapes can be accurately estimated from the beam theory based expressions in DNV RP-F105. This represents of course an approximation but still can be used to easily demonstrate the effect of the different updates made in the Ormen Lange project.

Figure 13 shows the fatigue lives for the different cases as functions of span length. It can easily been seen that the maximum acceptable span length increases significantly from around 35m to 72m when the release of effective axial force due to lateral buckling is accounted for.

The improvements in fatigue life due to updated long-term distribution of current and improved SN curve bring the fatigue curve up to a level (case 3), where the minimum fatigue life becomes higher that the design life (50 years) for all span lengths. The increase in fatigue life with span length when exceeding 100 meters seems unphysical, but is due to the counteracting effects of decreasing frequencies and stress cycles with span length. In the left part of the fatigue curve, the effect of the frequency is most important while in the right part the effect of the stress cycles becomes the dominating one.

In such a case one may be misled to believe that there is no limitation in span length due to fatigue. However, the effect of higher modes due to the Ormen Lange specific guideline has been calculated. As shown in case 4 (solid, black line), the maximum acceptable span length becomes approximately 100 meters for this specific case. The importance of addressing the multi-mode response has been clearly demonstrated.

1

10

100

1000

10000

20 40 60 80 100 120 140

Span Length (m)

Fatig

ue li

fe (y

ears

)

Case 0 - Full SeffCase 1 - Released SeffCase 2 - Updated currentCase 3 - Updated SN curveCase 4 - Multimode calculation

Figure 13 – Fatigue lives as function of span length, single spans.


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5. Challenges and the Way Ahead

While pushing the limit for pipeline free span design but still maintaining a sufficient safety level requires understanding in both physical and probabilistic terms of the phenomena involved. The design philosophy has been to approach the problem from the conservative side by using presumably conservative assumptions and models.

Multispan scenarios have been encountered in the North Sea, Persian Gulf, South East Asia and Gulf of Mexico and free spans have been designed using DNV Guideline 14 with a conservative approach for adding damage from several potential modes or simply not allowing for CF VIV.

The development of free span design criteria used in the industry has, however, mainly been based upon experimental results under 2D conditions using heuristic analysis models. For long spans and in particular multimodal response for multispan scenarios with limited experience, better understanding involving 3D considerations of the IL-CF interaction are required.

It should be noted that long free pipeline spans have some similarities with Steel Catenary Risers (SCR) exposed to low-mode VIV. Standard industry design practice for risers have been to use semi-empirical models for CF and ignoring IL and combined IL and CF VIV. This is a paradox since the in-line component normally dominates the design for pipeline free spans.

Present pipeline design is based on response model for vibration amplitude as function of hydro dynamical, geotechnical and pipeline parameters. This is considered adequate when remaining inside the scope of experience and experimental tests reflected by present codes and guidelines.

For long spans in macro-roughness areas several unresolved issues remain before response model may be fully qualified. This includes the effect of the current boundary layer close to the seafloor, in-homogenous flow along the span or adjacent multiple spans, large scale turbulence and not to mention scenarios with combined wave and current flow. All these issues call for more advanced computational methods. Navier-Stoke solvers are continuously improving but codes capable of reproduce the experimental results with sufficient reliability is not available.

Compared to isolated spans where the mode shapes and frequencies can be quantified based on the free span length, the soil stiffness, bending stiffness, effective axial force and effect from sagging, multispan scenarios is very case specific. This call for more involved guidelines in case many modes may be excited due to high current velocities.

So, in order to expand the scope of existing codes further studies is needed in efficient and reliable computational methods for engineering design that can cover the gap between simple heuristic methods and comprehensive testing campaigns. The Ormen Lange VIV tests represent a step towards increased knowledge of multispan scenarios and to facilitate project specific guidelines. 6. Summary The main findings from the presented free span study of the Ormen Lange pipelines may be summarized as:

• Lateral buckling and associated release of effective axial force needs to be addressed prior to the free span design. This is especially of great importance for flowline and other HTHP pipelines.

• Multi-mode response is important and needs to be considered in the design phase for long single spans as wells as multi-spanning sections.

• Updated project specific design guideline has been developed based on VIV model tests, which provides advanced computational methods to assess long single spans undergoing single mode and multi-mode response.

• The routing becomes very important in order to reduce number of and length of spans. High resolution survey data is needed as a basis for the routing activity.

• Through reliability analysis focus can be put on governing parameters and uncertainties. This again enables case specific optimization of the design and information about where to put the attention during data collection and design phases.

• The main conclusion drawn from this study is that substantial savings in seabed preparation and span intervention costs may be saved by improving the data basis, knowledge and design methodology with respect to long free spans.

DNV-RP-F105 is presently being revised in order to reflect the findings and recommendations from the

Ormen Lange project.


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7. Acknowledgement

These studies were funded by the Ormen Lange license group. Norsk Hydro and its license partners BP, Exxon, Petoro, Shell and Statoil are acknowledged for the permission to publish these results. The model tests were conducted at Marintek and analyses of the model tests results and modal analysis have been performed by Reinertsen Engineering. We express our gratitude and acknowledge their contribution. 8. References DNV-RP-F105, Recommended Practice: Free Spanning Pipelines, March 2002. MARINTEK, Ormen Lange 3D model tests. Marintek report 512326.00.01, March 2001. MARINTEK Ormen Lange 3D Phase II model tests. Marintek report 512352, 2002-07-04. SØREIDE, T. PAULSEN G. AND NIELSEN, F.G., Parameter Study of Long Free Spans, Proc. Of the Eleventh

(2001) International Offshore and Polar Engineering Conference (ISOPE) Stavanger, Norway, 2001 NIELSEN, F.G., A suggested procedure for estimating Vortex Induced Vibrations for long free spanning pipelines.

Norsk Hydro Report 2002a. NIELSEN, F.G., KVARME, S.O. AND SØREIDE, T., VIV response of long free spanning pipelines. 21st International

conference on offshore mechanics and artic engineering, (OMAE), Oslo, Norway, 2002b. MØRK, K.J., FYRILEIV, O., CHEZHIAN, M., NIELSEN, F.G., SØREIDE, T. ,Assessment of VIV Induced Fatigue in

Long Free Spanning Pipelines, 22nd International conference on Offshore Mechanics and Artic Engineering, (OMAE2003-37124), Cancun, Mexico, June 8-13, 2003.

HAGEN, Ø., MØRK, K.J., NIELSEN, F.G., SØREIDE, T., Evaluation of Free Spanning Design in a Risk Based Perspective, 22nd International conference on Offshore Mechanics and Artic Engineering, (OMAE2003-37419), Cancun, Mexico, June 8-13, 2003.

LARSEN, C.M., VIKESTAD, K., YTTERVIK, R. AND PASSANO, E., Empirical model for analysis of vortex induced vibrations – Theoretical background and case studies. Proceedings of 20th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2001, Rio de Janeiro, Brazil.

FYRILEIV, O., MØRK, K.J. AND CHEZHIAN, M, Influence of Pressure in Pipeline Design - Effective Axial Force, 24th International conference on Offshore Mechanics and Artic Engineering, (OMAE2005-67502), Halikidiki, Greece, June 12-16, 2005.

FYRILEIV, O. AND MØRK, K., Structural Response of Pipeline Free Spans based on Beam Theory, Proceedings of OMAE2002, Oslo, Norway, 2002.

DNV Report 2002-0967, rev.2, 'Ormen Lange - Design Guideline for VIV of Long Free Spanning Pipelines', January 2003.

GALGOUL, N.S., MASSA, A.L.L. AND CLARO, C.A., A Discussion on How Internal Pressure is Treated in Offshore Pipeline Design, Proceedings of IPC 2004, Calgary, Canada, 2004a.

GALGOUL, N.S., DE BARROS, J.C.P. AND FERREIRA, R.P., The Interaction of Free Span and Lateral Buckling Problems, Proceedings of IPC 2004, Calgary, Canada, 2004b.

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