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RECOMMENDED PRACTICE

DET NORSKE VERITAS

DNV-RP-F203

RISER INTERFERENCE

APRIL 2009

FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, prop-erty and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification and consultancyservices relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out researchin relation to these functions.DNV Offshore Codes consist of a three level hierarchy of documents:— Offshore Service Specifications. Provide principles and procedures of DNV classification, certification, verification and con-

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Recommended Practice DNV-RP-F203, April 2009 Contents –

AcknowledgementsThis Recommended Practice has been developed in close co-operation with the Norwegian Deepwater Programme (NDP).It has been sponsored by Norsk Hydro, Statoil, BP, Cono-coPhilips, ExxonMobil, Total, and Shell. It has been a part of

the Joint Industry Project called “Management of Riser Con-tact” sponsored by Conoco, BP, Chevron, Texaco and Exxon-Mobil carried out by Aker Kværner and Det Norske Veritas.All contributions are highly appreciated.

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Recommended Practice DNV-RP-F203, April 2009 – Contents

DET NORSKE VERITAS

Recommended Practice DNV-RP-F203, April 2009

CONTENTS

1. INTRODUCTION .................................................. 71.1 General .....................................................................71.2 Objective...................................................................71.3 Scope and Application.............................................71.4 Definitions ................................................................71.5 Abbreviations...........................................................81.6 Main Symbols ..........................................................81.7 Organisation of Document......................................8

2. DESIGN APPROACH ........................................... 82.1 General .....................................................................82.2 Design Principles .....................................................92.3 Design Parameters for Compliant

Configurations .........................................................92.4 Design Parameters for Top-Tensioned

Riser Arrays .............................................................9

3. HYDRODYNAMIC INTERACTION................ 103.1 General ...................................................................10

3.2 Mean Force in Steady Current ............................ 103.3 Drag Amplification due to VIV............................ 113.4 Models for Hydrodynamic Interaction

in Global Analysis ................................................. 11

4. RISER CLEARANCE ASSESSMENT.............. 124.1 General ................................................................... 124.2 Quasi-Static Analysis ............................................ 124.3 Dynamic Analysis .................................................. 124.4 Wake Instability Analysis..................................... 124.5 Clearance Acceptance Criterion.......................... 12

5. REFERENCES..................................................... 13

APP. A INTRODUCTION TO HYDRODYNAMIC INTERACTION PHENOMENON .................................. 15

APP. B ANALYSIS CONSIDERATIONS ................... 17

APP. C LOCAL IMPACT STRESS ANALYSIS OF STEEL PIPES ............................................................. 20

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1. Introduction1.1 GeneralA more accurate methodology for assessing riser interferencehas become increasingly more important when oil and gasexploration moves to deeper water. The risk of interferencebetween marine risers increases with increasing riser length. Historically, the general design practice is that riser collisionsare not allowed under normal or even extreme conditions. Thepresent document considers analysis procedures and designcriteria for riser interference assessment.

1.2 ObjectiveThe overall objective of this document is to recommend amethodology for engineering analysis, and to provide rationaldesign criteria and guidance for assessment of riser interfer-ence. Riser interference comprises complex physical phenomena,not yet fully understood, and research is ongoing. The aimherein is to achieve and document the industry consensus asper today.

1.3 Scope and ApplicationThe scope of work is first of all to propose a framework for fea-sible analysis strategy and practical design procedures withfocus on how to assess if the risers collide or not. Whenever theterminology “risers” is used in this document it generally alsoapplies for all types of riser systems e.g. umbilicals, flexiblerisers, Steel Catenary Risers (SCRs) and Top-Tensioned-Ris-ers (TTRs).In order to derive a complete framework for feasibility andpractical design procedures, the following topics need to beconsidered:

— overall framework and design approach— safety philosophy— environmental conditions and loads— analysis strategies and hydrodynamic interaction models— acceptance criteria and fundamental requirements.

The safety philosophy and design principles adopted in DNV-OS-F201 /5/ apply. However, any recognised code consideringthe set of limit states discussed herein is in principle accepta-ble. The basic principles are in agreement with recognisedcodes and reflect state-of-the-art industry practice and latestresearch.In view of high uncertainties in interference predictions, nocalibration of safety factors is applied. Instead, conservativeenvironmental modelling and analysis are applied; reference ismade to DNV-OS-F201 /5/ and API RP 2RD /1/. A formal cal-ibration is neither feasible nor optimal with the present level ofexperience.This Recommended Practice formally supports and complieswith DNV-OS-F201 /5/. It is recognised to be a supplement torelevant National Rules and Regulations.

1.4 DefinitionsAccidental Loads: Loads acting on the riser system, due to asudden, unintended and undesirable event. Typical accidentalevent has an annual probability of occurrence less than 10-2.Clearance: Sufficient minimum spacing between risers is doc-umented.Coating: Sheeting on the outside of the riser used to protect theriser from damages caused by the surroundings. Compliant Configuration: A unified term for riser/umbilicalconfigurations being a catenary or e.g. free hanging, pliantwave, lazy wave, steep wave, etc.Computational Fluid Dynamics (CFD): Numerical methods

which aim to model and solve all physics involved by solvingthe coupled equations of the structure and the fluid. Failure: An event causing an undesirable condition, e.g. lossof component or system function, or deterioration of functionalcapability to such an extent that the safety of the unit, person-nel or environment is significantly reduced.Fatigue: Cyclic loading causing degradation of the material.Force Coefficients: Non-dimensional coefficients for the dragand lift force as function of relative spacing.Global Analysis: Herein referred to as analysis of forcedresponse of floater and risers due to waves and current.Hydrodynamic Interaction: Interaction effects due to the pres-ence of other structures located nearby in the fluid; e.g., thedownstream riser located in the wake of an upstream riser willbe affected by the upstream one. Impact Angle: The angle between the relative velocity vectorand the line between the cylinder (riser) centres at time andlocation of impact; also known as kissing angle.Impact Event: One impact event is defined as one collisionevent governed by the gross riser motion. Each impact eventmay involve several successive stress peaks, typically 4-5 fora straight hit and 1-2 for a kissing event. Impact Velocity: Referred to as the relative velocity between tocolliding risers at the time of impact. Herein denoted as Urel.Limit State: The state beyond which the riser or part of the riserno longer satisfies the requirements laid down to its perform-ance or operation. Examples are structural failure (rupture,local buckling) or operational limitations (stroke or clearance).Line Impact: Assumes the ideal case where the longitudinalpipe axes are parallel at impact.Load: Refers to physical influences which cause stress, strain,deformation, displacement, motion, etc. in the riser. Load Effect: Response or effect of a single load or combinationof loads on the structure, such as bending moment, effectivetension, stress, strain, deformation, etc.Numerical Fluid Flow Models: Direct force and fluid flow esti-mation from a CFD solver. Operation, Normal Operation: Conditions that are part of rou-tine (normal) operation of the riser system. Point Impact: Assumes the case where the pipe axes are non-parallel resulting in a small contact area at impact.Reduced Velocity: Non-dimensional velocity parameter usedfor assessing VIV due to the vortex shedding force. Riser Array: Riser system consisting of vertical or near verticaltop-tensioned risers. Typically up to 20 risers distributed in acluster. Riser Interference: Minimum spacing between risers is lessthan acceptance criteria. Riser Tensioner System: A device that applies a tension to theriser string while compensating for the relative vertical motion(stroke) between the floater and riser. Safety Factors: Partial safety factors, which transform thelower fractile resistance to a design resistance. Screening Analysis: Used to frame the problem in order toidentify if analysis and methods that is more advanced shouldbe employed. Side-by-Side Arrangement: See Figure 1-1Staggered Arrangement: See Figure 1-1Strakes: Helical structural elements attached outside the riserto suppress VIV response.Tandem Arrangement: See Figure 1-1. Undisturbed Fluid Flow Model: Analysis approach disregard-

DET NORSKE VERITAS


ing hydrodynamic interaction effects. Vortex Induced Vibrations (VIV): Resonant vibrations causedby vortex shedding.Wake Induced Oscillations (WIO): Motion of downstreamriser due to fluid elastic instabilities when located in the wakeof an upstream riser. Weight/Diameter Ratio: Defined as submerged weight per unitlength divided by the outer diameter; WS/D. This ratio maychange considerably due to marine growth.

Figure 1-1Tandem, Staggered and Side-by-Side Arrangements

1.5 Abbreviations

1.6 Main Symbols

1.7 Organisation of DocumentThe documents is organised as follows:Section 2 contains the design approach including designparameters and design principles. Section 3 provides an introduction to the hydrodynamic inter-action phenomenon including wake induced instabilities.Available modelling approaches accounting for hydrodynamicinteraction in a global analysis tool are discussed. Section 4 contains a description and discussion of the proce-dures and methodologies involved in a riser clearance assess-ment.Section 5 contains the basic references used in the document.Appendix A provides and introduction to the hydrodynamicinteraction phenomenon in general. Available methods to esti-mate the force coefficients applied to describe the hydrody-namic interaction effects have been introduced. Appendix B provides an introduction to different analysis con-siderations, such as a description of hydrodynamic interactionmodels including application areas which are suitable forimplementation in a global analysis tool. Appendix C contains an introduction to local impact stressanalysis and requirements regarding modelling issues.

2. Design Approach2.1 GeneralThe individual risers are generally subjected to loading fromwaves, current and forced wave-frequency and low-frequencyfloater motions. Whether collision between two adjacent riserswill occur or not, depend on many factors such as:

— loading environment— riser spacing at floater and seafloor terminations— riser configuration and riser tension— floater offset involving intact conditions as well as acci-

ALS Accidental Limit StateAPI American Petroleum InstituteCFD Computational Fluid DynamicsDNV Det Norske VeritasFD Frequency-DomainFEM Finite Element MethodFLS Fatigue Limit StateLF Low FrequencyLRFD Load and Resistance Factor DesignLTD Linearized Time-DomainNDP Norwegian Deepwater ProgramNLTD Non-Linear Time-DomainRP Recommended PracticeSCF Stress Concentration FactorSCR Steel Catenary RiserTD Time-DomainTLP Tension Leg PlatformTTR Top Tensioned RiserULS Ultimate Limit StateVIV Vortex Induced VibrationsWF Wave FrequencyWIO Wake Induced Oscillations2D Two-dimensional 3D Three-dimensional

Tandem Arrangement

Staggered Arrangement

Side-by-Side Arrangement

On-coming flow

On-coming flow

On-coming flow

CD drag force coefficientCL lift force coefficientD diameterE Young’s modulusRE Reynolds numberUrel relative impact velocityV0 free-stream current velocityV* local inflow velocityVd wake deficit velocityVR reduced velocity

(defined with frequency given in Hertz)VWR reduced velocity based upon local inflow velocity in

wakeVrel relative inflow velocityVw current velocity in wakeWs submerged weightε turbulent kinetic energyθ impact angleρ fluid (water) densityΔσ stress rangeσy Yield stress ω angular frequency ωn fundamental angular frequency

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dental scenarios such as one or multiple mooring line fail-ures

— marine growth— hydrodynamic interaction comprising shielding, wake

instabilities and VIV— use of VIV suppression devices, e.g. strakes— riser operation, e.g. variation in density of conveyed flu-

ids, drilling/completion/workover operations— accidental load scenarios; e.g. loss of pre-tension or loss of

buoyancy— different static/dynamic properties of the risers due to dif-

ferences in mass, diameter, effective weight, applied top-tension or effective tension distribution, etc.

Possible riser interference is a key design issue for deep waterfloating installations that might be decisive for the choice offloater concept, station-keeping system as well as riser systemlayout. Riser interference should therefore be addressed inearly stages of the design process. A design target weight/diameter ratio is often specified toachieve similar behaviour of adjacent riser systems. Note thatweight/diameter ratio can be significantly influenced bymarine growth. This is in particular important for small diam-eter light weight risers. The design target weight/diameter ratioshould hence be checked with and without accounting formarine growth.

2.2 Design Principles

2.2.1 GeneralTwo fundamentally different design strategies apply:

— no collisions allowed— collisions allowed.

These design philosophies set different requirements to loadeffect analyses as well as acceptance criteria. Hydrodynamicinteraction is a key issue that needs to be adequately accountedfor in the load effect analyses for both alternatives. Assessmentof structural interaction will in addition be required if colli-sions between risers are allowed.The engineering efforts required to qualify a riser system forstructural impact is hence substantially more demanding com-pared to a no collision criterion. However, the cost savings dueto relaxation of the no collision design philosophy in extremeand/or accidental loading scenarios may be significant. Collisions are normally not acceptable in the following scenar-ios:

— in buoyancy sections for example for compliant configu-rations

— between risers and mooring lines— between risers and other structures such as mid water arch

and pontoons not specially design for handling contacts— between risers with unprotected external lines such as kill

and choke lines on drilling/workover risers or piggy backumbilicals.

2.2.2 No collision allowedSufficient spacing between adjacent risers should be docu-mented for all critical load cases. The load cases shouldinclude normal operation, extreme conditions as well as iden-tified accidental scenarios. Due regard should be given to hydrodynamic interaction in theglobal load effect analyses.

2.2.3 Collision allowedInfrequent collision may be allowed provided that the conse-quences are evaluated and found acceptable. The differentloading conditions should be classified depending on probabil-ity of occurrence. This means that collisions may be allowed in

temporary, accidental and extreme conditions. Collisions inpermanent conditions are normally not allowed. It should bedocumented that the structural integrity is not endangered; i.e.sufficient fatigue and ultimate capacity as well as wear resist-ance should be ensured. This should generally be done by combining qualification test-ing and design calculations. Static load effect analysis can be used for assessment of thecontact load in pure static interference scenarios; e.g. interac-tion between flexible riser and umbilicals in current conditionswith no VIV. Testing may be required in the event that no cal-culations are available to document that the structures can sus-tain the contact load considering the local geometry of thecontact area. Please see Appendix C for guidance on local impact analysis,strategy and principles for vertical steel risers.

2.3 Design Parameters for Compliant ConfigurationsFor risers arranged in compliant configurations the followingcan be considered to mitigate riser interference or reduce theload effects due to contact:

— grouping of risers with similar static/dynamic properties,e.g. weight/diameter ratios

— increased wear resistance by e.g. increased outer sheath inbell mouth, I-/J-tube and floater interface area

— design of adjacent system configurations allowing for risercrossing with different vertical positions

— horizontal and vertical staggering of adjacent riser config-urations

— separation of the risers with different vertical hang-offangles

— separation of the risers with different azimuth hang-offangles

— cleaning of risers to remove marine growth if necessary— adjusting the cross-current configuration stiffness by mod-

ifying the effective tension through buoyancy and/orweight distribution.

To avoid damage on risers due to mooring line failures it isnormally not allowed that a mooring line crosses above theriser in any condition.

2.4 Design Parameters for Top-Tensioned Riser ArraysTTRs operated from SPAR and TLP platforms are arranged inclusters of vertical- or near vertical risers denoted riser arrays. Thenumber of individual risers in a riser array may be 20 or more. Top-tension and riser spacing are the primary design parame-ters to mitigate riser interference. The cost related to increasedtop-tension and/or riser spacing at floater terminations may bevery high. Other proposed design changes to mitigate riserinterference or to reduce load effects due to contact are:

1) Grouping of risers with similar static/dynamic properties,e.g. weight/diameter ratios.

2) Cleaning of risers to remove marine growth.3) Introduction of bumpers or coating along critical areas of

the risers to reduce the load effect due to collision.4) Synchronisation of the tensioners to give equal pay-out or

equal effective length for all risers in a riser array.5) Introduction of spacer frames to keep the risers apart at

critical locations.

Operational aspects may limit the applicability of the thirdapproach, while the first and second seem more feasible fromthat point of view. Further development is needed to establishthe last two described alternatives as feasible design strategies.

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Conclusions from model tests are that ensuring equal payoutfor the risers by connecting them to a common frame can beapplied to reduce the probability of collision in steady current/14/. Equal effective length i.e. that the riser length plus the payoutlength of the tensioner system is equal for all risers, was inves-tigated in /20/.

3. Hydrodynamic Interaction3.1 GeneralAssessment of hydrodynamic interaction is a generic issue forload effect analyses related to riser interference evaluations.The importance of the interaction effects is strongly systemdependent and should be evaluated on a case by case basis. Significant effort has been applied to investigate hydrody-namic interaction in steady current; see e.g. the work of Huse/12/ & /13/, Huse & Kleiven /14/ or Kavanagh et al. /16/, whileless information is available regarding interaction effects dueto wave loading; see e.g. Duggal & Niedzwecki /6/ & /7/. In addition, numerous experiments to study hydrodynamic inter-action for arrays of cylinder sections are performed; for an over-view, reference is made to Blevins /2/ and Zdravkovich /33/. Clashing between SCRs has been investigated by Fontaine etal. /9/. Fernandes et al. /8/ present experiments with flexiblejumpers exposed to current. In both cases clashing caused bywake effects were observed. Experimental results on hydrody-namic interaction due to combined loading from waves, cur-rent and floater motions seems to be lackingOne may distinguish between three different kinds of physicalexcitation forces on a downstream riser located in the wake ofan upstream riser:

— a broad band buffeting force due to oncoming turbulentflow and vortices shed from the upstream riser, which willinduce broad band buffeting vibrations

— a periodic vortex shedding force causing high frequencyVIV with limited amplitude

— a time averaged mean force, which varies depending uponthe location in the wake.

These loading mechanisms will in general depend on Reynoldsnumber as well as turbulence level in the incoming fluid flow.Kalleklev et.al. /15/ showed that hydrodynamic interaction onthe upstream riser conservatively can be ignored, and hencethe upstream riser can be treated as an isolated riser. Full atten-tion will therefore be given to hydrodynamic interactioneffects on the downstream riser.As outlined above, the physical load mechanisms on a pair ofadjacent risers are complex. The most important effects of rel-evance for assessment of riser interference are:

— reduced mean forces on downstream risers due to shield-ing effects tending to bring the risers closer

— VIV effects on mean forces on upstream and downstreamriser in terms of drag magnification.

The non-linear force field generated by the upstream riser mayin addition lead to the following hydrodynamic interactioneffects:

— wake instability motions of downstream riser— multiple static equilibrium positions of downstream riser.

The wake instability motions are typically large amplitudemotions caused by the position dependent force field due to theupstream riser.Fundamental research is needed to fully understand these loadmechanisms and how they interact with each other. It is there-fore required to introduce simplifications supported by rationalconservative assumptions in practical riser interference analy-ses.

3.2 Mean Force in Steady CurrentThe hydrodynamic loading on downstream riser will be influ-enced by the wake field generated by upstream riser. Theeffects on mean forces on the downstream riser are:

— reduced mean drag force due to shielding effects— lift force due to the velocity gradients in the wake field.

The mean drag and lift coefficients will hence depend on therelative distance between the risers. The mean force coeffi-cients are most conveniently described in a local coordinatesystem with x-axis in the incoming fluid flow direction, and they-axis in the transverse direction. The origin is located in thecentre of the upstream riser, see Figure 3-1.

Figure 3-1Coordinate system for description of drag- and lift-coefficients on downstream riser

V0 is defined as the free-stream current velocity which is thevelocity on the upstream riser. Examples of mean drag and lift force coefficients on a cylinderlocated in the wake of another cylinder of equal diameter aregiven Figure 3-2 and Figure 3-3 as function of relative spacingbetween the cylinders. The spacing has been normalised by thediameter of cylinders.

Figure 3-2Mean drag force on cylinder in a wake [Wu et al. /28/]

x

yV0

Vw (x, y)

Vd (x, y)

-0.20

0.05

0.30

0.55

0.80

1.05

1.30

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0

y/D [-]

CD [-

]

X/D = 2X/D = 5X/D = 10X/D = 15X/D = 20X/D = 25

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Figure 3-3Mean lift force on cylinder in a wake [Wu et al. /28/]

A significant shielding effect is seen when the risers are close.Furthermore, it is seen that the mean lift force is directedtowards the wake centre line meaning that it will try to push theriser towards the centre of the wake. For further details, reference is made to Appendix A andAppendix B.

3.3 Drag Amplification due to VIVRepresentative drag amplification is based on the estimatedVIV amplitude A normalised by the diameter D. Severalexpressions for the increase in drag coefficient with vibrationexist in literature. The expression presented by Vandiver /25/is recommended:

As a conservative estimate, a value slightly on the high side isrecommended for the upstream riser. For the downstream riser,it is conservative to apply a lower bound value for the dragamplification due to VIV. This will tend to bring the meanposition of the risers closer to each other. Thus, separate VIV assessments for the upstream- and down-stream risers are required prior to the global riser interferenceanalysis. A state-of-practice VIV assessment tool should beapplied, see e.g. /23/ or /26/. The upstream riser should con-servatively be treated as an isolated riser. The VIV response onthe downstream riser should in general be based on the localinflow velocity at a mean position being representative for theVIV response. Note that very limited information is available regarding VIVbehaviour of a riser located in the wake of an upstream one. Aconservative lower bound VIV response should therefore beapplied for the downstream riser. It is recommended to use noVIV on the downstream riser as a first estimate.Strakes are commonly used to suppress VIV of risers. In exper-iments with two adjacent risers, Huse & Kleiven /14/ observedthat VIV motions almost disappeared for both risers whenattaching strakes. A typical amplitude of one diameter for ris-ers without strakes reduced to one tenth of a diameter for riserswith strakes. Also low frequency, stochastic and chaoticmotion disappeared. Another significant observation from the tests was that the ris-ers were kept in mechanical contact after clashing due tochanges in the force field.

3.4 Models for Hydrodynamic Interaction in Global Analysis

3.4.1 GeneralThis section provides an introduction to formulation of rele-vant hydrodynamic interaction models in global load effectanalysis computer codes. Alternative formulations are availa-ble with significant variations with regard to computationalefforts, accuracy, generality etc. It is focused on establishing aload model which aims to account for the major physical phe-nomena relevant for a riser interference assessment. The purpose of global riser analysis is to predict global struc-tural response, e.g. bending moments, effective tension, dis-placements and curvature, in a stationary environmental loadcondition. Such analyses are normally performed by tailormade finite element computer codes using a global cross-sec-tional description; i.e. 3D beam elements with specified bend-ing-, axial- and torsional properties are used for modelling.Reference is made to e.g. DNV-OS-F201 /5/ for further details.The hydrodynamic interaction models discussed in the follow-ing can be implemented by means of a 2D strip model. Thismeans that hydrodynamic interaction forces are computed in anumber of ‘strips’ over the entire water column. The interac-tion forces will therefore depend on the relative distancebetween the risers in each strip. A static or dynamic approach may be applied depending on thepurpose of the analyses. A dynamic approach is required tocapture possible WIO response.It is noted that linearization of the external loading as requiredby frequency-domain techniques, is not applicable to hydrody-namic models incorporating interaction effects from adjacentrisers. Obviously, a time-domain formulation is required tocapture the interaction effects.The strip model is applicable to linearized (LTD) as well asnon-linear (NLTD) time-domain analyses. The main differ-ence between these approaches is that the structure is linear-ized at the static equilibrium position in a LTD formulationwhile a fully non-linear structural representation is applied inthe NLTD formulation.

3.4.2 Undisturbed fluid flowA first approach is often to ignore hydrodynamic interaction.This approach may be applied for the first screening to identifyif riser interference is a potential problem or not.This approach may also be applicable if the area of hydrody-namic interaction is very small compared to the overall lengthof the riser; e.g. interaction between compliant risers with dif-ferent hang-off angles or interaction with mooring lines.The undisturbed fluid flow models should not be applied tointeraction analyses of clusters of top-tensioned risers exposedto current loading.

3.4.3 Numerical fluid flow modelComputational Fluid Dynamics (CFD) can be applied to solvethe viscous flow around two or more adjacent risers in eachstrip. Numerical fluid flow models allow for an advanceddescription of hydrodynamic loading including interactioneffects from adjacent risers. Due to the enormous computa-tional efforts involved, the CFD approach is presently notapplicable in practical global riser interference analyses.

3.4.4 Parametric mean force modelHydrodynamic interaction effects between adjacent risers areaccounted for by introduction of mean drag- and lift force onthe downstream riser as a function of distance from theupstream riser. This parametric representation of the interac-tion forces, which is derived in e.g. Blevins /2/, has gained con-sensus throughout the literature, and has been applied inanalysis of heat exchangers and power cables since 1970.

(3.1)

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0

y/D [-]

CL [

-]

X/D = 2X/D = 5 X/D = 10 X/D = 15X/D = 20X/D = 25

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

65.022043.11'D

ACC DD

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Relevant drag and lift coefficients need to be established bymodel tests or 2D numerical calculations (e.g. CFD) for theactual cross-sectional configuration. The parametric force model is straightforward to implement inglobal time domain dynamic analysis software by means of a2D strip approach. This model will in principle capture possi-ble WIO response.For further details, reference is given to Appendix B.

3.4.5 Parametric wake field modelA semi-empirical static wake formulation to account for thehydrodynamic interaction between individual risers in steadycurrent was proposed by Huse /11/, /12/ & /13/. Essentially, the model is based on an analytical expression ofthe wake field behind a riser in steady current. The inflow to ariser situated in the wake can hence be computed at any loca-tion. The drag force on the downstream riser can subsequentlybe computed taking shielding effects into account. No lift forceformulation is presently available in the model. As for parametric mean force model, a 2D strip model can beused for static analysis. However, WIO response cannot bedescribed due to no lift force formulation.For further details, reference is given to Appendix B.

4. Riser Clearance Assessment4.1 GeneralHistorically, the design criterion against riser interference typ-ically comprises assessment of the required spacing to avoidcollision, see e.g. API RP 2 RD /1/. The first step is to determine whether collisions are likely tooccur or not considering floater offset and current loading. At first, the static deflection due to free-stream current loadingmay be calculated for each riser in the array, neglecting anyhydrodynamic interaction between them. If the static deflec-tion is less than the minimum spacing between the risers innominal static condition, one can for TTRs conclude that riserinterference is not a possible scenario and no further analysisis necessary.Refined analyses taking possible hydrodynamic interactioneffects into account is required if the initial assessment revealsthat the interaction effects are significant.

4.2 Quasi-Static Analysis

4.2.1 General The quasi-static analysis should include floater offset and cur-rent loading. The omni-directional values for environmentalloading and vessel offsets should be applied for all directionsfrom 0 to 360 deg in steps of typically 5-10 deg.For certain system it can be difficult to assess whether thestructures cross or not by looking at the configuration inextreme current. Less severe current conditions may lead tomore severe interference scenarios and should hence be con-sidered. The worst scenario, i.e. combination of floater offset and cur-rent loading, should be subject for dynamic analysis account-ing for wave loading if required. Note that possible drag amplification due to VIV needs to beaccounted for as described in the previous chapter.

4.2.2 Undisturbed flow analysisStatic analysis of upstream and downstream riser can forundisturbed flow analysis be performed separately. If the results from the undisturbed flow analysis indicate that

the hydrodynamic interaction effects are of importance, shield-ing analysis should be performed.

4.2.3 Shielding analysisStatic analyses using the parametric wake field model fordescription of hydrodynamic interaction is denoted quasi-static shielding analysis.Streamlined computations require that the wake field model isimplemented in the FE analysis software. However, any com-puter software for non-linear static analysis of slender struc-tures can be applied using the following iterative scheme forassessment of shielding effects:

1) Compute static upstream riser configuration.2) Compute static downstream riser configuration under

incoming current loading.3) Compute resulting inflow on downstream riser consider-

ing shielding effects from the upstream riser.4) Re-calculate downstream riser configuration considering

resulting inflow as current loading.5) Repeat steps 3-4 until convergence is achieved.

This approach requires that separate computer models areestablished for the upstream and downstream risers. Thedescribed procedure is a slightly modified version of theapproach described by Kavanagh et al. /16/. Shielding effects can in principle be accounted for by modifi-cation of the drag coefficient or resulting inflow (i.e. currentloading) on the downstream riser. It has however been experi-enced that modification of current loading on the downstreamriser is the most straightforward approach to handle in practicalcalculations.

4.3 Dynamic AnalysisSimplified assessment of dynamic effects due to waves andfloater motions may be based on separate dynamic analyses ofthe upstream and downstream risers. As an approximation, the converged inflow on the downstreamriser (see item 4.2.3) may be applied to represent mean currentloading on the downstream riser in such analyses.

4.4 Wake Instability AnalysisPresent experience on the wake instability phenomenon fromlaboratory and field measurements is limited. Based on available information, wake instability is not consid-ered relevant for compliant configurations. However, it cannoton a general basis be excluded as a possible phenomenon forvertical riser arrays.Possible wake induced instabilities should be evaluated if thequasi-static shielding analysis reveals hydrodynamic interac-tion effects along a significant part of the risers. Dynamic analyses using the parametric mean force model fordescription of hydrodynamic interaction allows for evaluatingpossible wake induced instabilities. A tailor-made softwareapplication with the parametric mean force model implementedis however required for such analyses. This is because simulta-neous dynamic analysis of the upstream and downstream risersis required for application of the parametric mean force.There is presently no consistent theoretical formulation allow-ing for combining the parametric mean force model with load-ing due to waves and floater motions.

4.5 Clearance Acceptance CriterionSince the parametric wake model is applicable for the far wakeregion (greater than about two diameters behind the upstreamcylinder /16/), the behaviour of the flow in the near wakeregion cannot be adequately described as it is a highly non-lin-ear phenomenon.

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Another issue is that the VIV response of the adjacent risers isnot included in the clearance assessment analyses. The maxi-mum VIV displacement can be in the order of one diameter foreach riser.The minimum spacing criterion is selected such that it accountfor possible VIV on both cylinders. In Figure 4-1, Δ is definedas the distance between the outside of the cylinders.With this background, a minimum clearance of two times theouter diameter is recommended for risers with equal outerdiameters. The sum of the outer diameters is recommended asacceptance criterion in case of different outer diameters.Hence, to avoid collision the minimum spacing is givenby . This criterion does not reflect any “safety fac-tor.

Figure 4-1Minimum spacing criterion

5. References

21 DD +≥Δ

/1/ API RP 2 RD “Design of Risers for Floating Production Systems (FPSs) and Tension Leg Platforms (TLP’s)”

/2/ Blevins, R.D. (1994) ‘Flow induced vibrations’, Krieger publishing company, 1994.

/3/ Blevins, R.D. (2005) ‘Forces on and Stability of a Cylinder in a Wake’, Journal of Offshore Mechanics and Arctic Engineering, Vol 127, pp 39-45.

/4/ Cooper, K.R. & Wardlaw, R.L. (1971) “Aeroelastic instabilities in wake” Proceedings International Symposium on Wind Effects on Building and Structures, Tokyo, Paper IV, pp. 647-655.

/5/ DNV-OS-F201 “Dynamic Risers”

/6/ Duggal, A.S., Niedzwecki, J. M. (1993a) “An Experimental Study of Tendon/Riser Pairs in Waves”, OTC paper no. 7239.

/7/ Duggal, A.S., Niedzwecki, J. M. (1993b) “Regular and Random Wave Interaction with a Long Flexible Cylinder”, OMAE 1993.

/8/ Fernandes, A.C., Rocha, S.D., Coelho. F.M., Jacob, B.P., Queiroz, J.V., Capanema, B., Merino, J.A. (2008) “Riser Clashing Induced by Wake Interference” OMAE2008-57639

/9/ Fontaine, A.C., Capul, J., Rippol. T., Lespinasse, P. (2007) “Experimental and Numerical Study of Wake Interference and Clashing between Steel Catenary Risers”, OMAE2007-29149.

/10/ Hori, E. (1959) “Experiments on Flow around a Pair of Parallel Circular Cylinders” Proceedings 9th Japan National Con-gress for Applied Mechanics, pp. 231-234.

/11/ Huse, E. (1987). “Drag in Oscillatory Flow Interpreted from Wake Considerations.” Offshore Technology Conference, OTC paper no. 5370.

/12/ Huse, E. (1993) “Interaction in Deep-Sea Riser Arrays”, OTC paper no. 7237.

/13/ Huse, E. (1996) “Experimental Investigation of Deep Sea Riser Interaction”, OTC paper no. 8070.

/14/ Huse, E., Kleiven, G. (2000) “Impulse and Energy in Deepsea Riser collisions Owing to Wake Interference” OTC paper no. 11993.

/15/ Kalleklev, A.J., Mørk, K.J., Sødahl, N., Nygård, M.K. Horn, A.M. (2003) “Design Guideline for Riser Collision” Offshore Technology Conference, OTC paper no. 15383.

/16/ Kavanagh, W.K., Imas, L., Thompson, H. & Lee, L. (2000) “Genesis Spar Risers: Interference Assessment and VIV Model Testing” OTC paper no. 11992.

/17/ Li, Y. & Morrison, D.G. (2000) “The “Colliding Participating Mass”. A Novel Technique to Quantify Riser Collisions”, OMAE 2000.

/18/ Price, S.J. (1975) “Wake Induced Flutter of Power Transmission Conductors” Journal of Sound and Vibration, Volume 38, pp. 125-147.

/19/ Price, S.J. & Piperni, P. (1987) “An Investigation of the Effect of Mechanical Damping to Alleviate Wake-Induced Flutter of Overhead Power Conductors.” Journal of Fluid and Structures, Volume 2. pp. 53-71.

/20/ Rustad, A.M., Larsen, C.M. & Sørensen, A.J (2008). ”FEM Modelling and Control for Collision Prevention of Top Tensioned Risers.” Journal of Marine Structures, Vol 21, No 1, pp 80-112.

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/21/ Sagatun, S.I., Herfjord, K. & Holmås, T. (2002) "Dynamic Simulation of Marine Risers Moving Relative to Each other due to Vortex and Wake Effects." Journal of Fluid and Structures.

/22/ Schlichting, H. (1968) “Boundary Layer Theory”, McGraw Hill Book Company Inc, New York.

/23/ Shear7 (2002) “Shear7 Program Theoretical Manual” Draft - for Version 4.2 dated March 25, 2002.

/24/ Sumer, B.M. & Fredsøe, J. (1997) “Hydrodynamics Around Cylindrical Structures” Advanced Series on Ocean Engineering, Volume 12. World Scientific Publishing Co. Pte. Ltd.

/25/ Vandiver, J.K. (1983) “Drag Coefficients of Long-Flexible Cylinders.” Offshore Technology Conference, OTC 4490.

/26/ Vivana (2000) “Deep Water Analysis Tools - DEEPER. Task 2.1 - part 1. VIVANA - Theory Manual” Marintek Report No. 513102.21.01, dated 2000-02-02.

/27/ Wardlaw, R.L. & Cooper, K.R. (1973) “A wind tunnel investigation of the steady aerodynamic force on smooth and stranded twin bundled power conductors for the Aluminium Company of America” National Research Council of Canada, LTR-LA-117.

/28/ Wu, W., Huang, S. & Barltrop, N. (1999). “Lift and Drag Forces on a Cylinder in the Wake of an Upstream Cylinder.” OMAE, St. John’s.

/29/ Wu, W., Huang, S. & Barltrop, N. (2001a). “Multiple Stable/Unstable Equilibria of a Cylinder in the Wake of an Upstream Cylinder.” OMAE, Rio de Janeiro.

/30/ Zdravkovich, M.M. (1977) “Review of Flow Interference Between Two Circular Cylinders in Various Arrangements” Journal of Fluids Engineering, Volume 99, pp. 618-633.

/31/ Zdravkovich, M.M. (1980). “Aero-dynamics of two parallel circular cylinders of finite height simulated at high Reynolds number” Journal of Wind Engineering and Industrial Aerodynamics, Volume 60, pp. 59-71.

/32/ Zdravkovich, M.M. (1987) “The Effect of Interference between Circular Cylinders in Cross Flow” Journal of Fluids and Structures, No. 1, pp. 239-261.

/33/ Zdravkovich, M.M. (2003). “Flow Around Circular Cylinders.” Volume 2 Applications, Oxford University Press.

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APPENDIX A INTRODUCTION TO HYDRODYNAMIC INTERACTION PHENOMENON

In order to evaluate the fluid-elastic instability and hydrody-namic interaction of the riser pair, an essential prerequisite isthe knowledge of the fluid forces on the risers as function ofrelative distance between the risers.The first systematic measurements of surface pressure distri-bution around one of the two parallel cylinders in various stag-gered arrangements was carried out by Hori /10/. Horicalculated drag and lift coefficients from the surface pressuremeasurements, and from his results Zdravkovich /30/ plottedthe resultant interference force coefficient as shown inFigure A-1. The interference effects are proportional to thevectors shown.

Figure A-1 Interference force coefficients [Zdravkovich /30/]

A direction of the interference force coefficient from right toleft indicates that the drag at that position is less than for thesingle cylinder, while the opposite direction means that thedrag is greater than for a single cylinder. The upward directionin the upper half and downward direction in the lower half ofthe figure indicate a repulsive, positive lift force while theopposite directions in the corresponding halves indicate a neg-ative lift force. All possible arrangements of the two cylinders are classifiedinto regions by taking into account whether the drag force isgreater or less than for the single cylinder and whether the liftforce is positive, negative or negligible. The upstream cylindercan be located in three regions:

1) Negligible lift forces and reduced drag forces.2) Small repulsive lift force and reduced drag force.3) Repulsive lift force and increased drag force.

The downstream cylinder can be located, in addition to theabove three, in the following regions:

4) Negligible lift force and increased drag force. This is asmall region and beyond it there is no interference.

5) Negligible lift force and decreased drag force. This is adominant region for the downstream cylinder.

Note that the above classification is repeated as given inZdravkovich /30/. In the fifth region, at least the part closest tothe wake centre-line and to the upstream cylinder, the lift forceshould be classified as negative and not negligible. Alterna-tively, a sixth region could have been introduced in betweenregion one and five with a decrease in drag and an attractive ornegative lift force.

The Reynolds number is defined by:

where V is the current velocity, D is the cylinder diameterand ν is the kinematic viscosity. The Reynolds number for offshore risers with typical diameterof 0.3 m and a current velocity of 1-2 m/s will be between0.3E + 06 and 0.6E + 06 which corresponds to what is calledpost-critical or super-critical flow regime, see Figure A-2.

Figure A-2 Drag coefficient as function of Reynolds number, [Sumer & Fredsøe/ 24/]

Figure A-2, which is valid for a single cylinder in uniformflow, indicates that the drag force is strongly depending on theflow conditions and the Reynolds number. It is hence expectedthat the Reynolds number effects are at least equally importantfor the hydrodynamic interaction in riser arrays as well. ForReynolds number larger than 1.0E + 06, the wake is disorgan-ised and turbulent, which will affect the drag and lift coeffi-cient for the downstream riser significantly. Most of the experiments and models tests have been performedfor low or moderate Reynolds number below the criticalregime, but some results have been found in literature consid-ering higher Reynolds number. A few preliminary findingshave been reported in the following.Hori /10/ performed his experiments, which are referred to inFigure A-1, in air with a Reynolds number in the order of1.0E + 04, i.e. in the sub-critical flow regime. In the post-crit-ical flow regime the wake behind a single cylinder narrowscompared with the sub-critical regime /30/. This will cause asimilar contraction of the interference boundary in the case oftwo staggered cylinders.According to Cooper & Wardlaw /4/ the wake instabilityboundary moves closer to the upstream cylinder and its wakeaxis as well. Figure A-3 shows the lift and drag coefficient variation typical forthe sub-critical state of flow measured by Zdravkovich /30. Fig-ure A-4 shows the lift and drag coefficient variation typical forthe post-critical state of flow compiled from the measurements ofWardlaw and Cooper /27/ presented in Zdravkovich /32/. It isobserved that the measured forces on the downstream cylinderare almost identical to those in the sub-critical state of flow.

(A.1)ν

VDRE =

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Figure A-3 Force coefficients measured in sub-critical state of flow: (a) lift co-efficient and (b) drag coefficient [Zdravkovich /32/]

Figure A-4 Force coefficients measured in post-critical state of flow: (a) dragcoefficient and (b) lift coefficient [Zdravkovich /32/]

Note that the experiments performed for higher Reynoldsnumber e.g. /4/ and /18/ typically in the post-critical flowregime is performed for stranded cables and not for smoothcylinders. Zdravkovich /31/ verified the findings for strandedcables when the flow was simulated by surface roughnessaround a pair of cylinders. It is noted from the figures in the Sec.3 that the upstream riserexperiences a positive lift force and a reduction in the dragforce when being close to the downstream riser. In addition, itis observed that the interaction effects on the upstream riserdiminish rapidly when the relative distance between the risersincreases. Hence, it will be conservative to ignore the interac-tion effects on the upstream riser for the purpose of a riserinterference assessment.

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APPENDIX B ANALYSIS CONSIDERATIONS

B.1 Strip FormulationA 2D strip model for the hydrodynamic excitation forcesshould be applied for the load functions on the 3D risers.Assuming piecewise constant conditions along the riser, con-ventional strip theory can be applied dividing the two risersinto equal number of strips. The strip mesh for the load formu-lation can be defined relatively coarse. Typically, a coarsermesh than the one applied in order to calculate the globalresponse of the risers can be applied. However, the mesh den-sity should be fine enough to ensure a proper description of theloads acting along the riser.

B.2 Parametric Wake Field ModelA semi-empirical static wake formulation to account for thehydrodynamic interaction between individual risers in steadycurrent was proposed by Huse /11/, /12/ & /13/. The parametricwake field formulation is based on the turbulent wake expres-sions of Schlichting /22/. The deficit velocity field in the wakeof a circular cylinder is given by:

where xs and b are defined as

The deficit velocity field Vd(x, y) is described in a local xy co-ordinate system with x-axis in the current direction and originin centre of the cylinder. The other parameters involved are:

D- cylinder diameterV0- free-stream current velocityCD- drag coefficientk1, k2- empirical constants

where k1 = 0.25 and k2 = 1.0 for a smooth cylinder. The result-ing inflow on a downstream riser at position (x1, y2) is hencegiven by:

This principle has been extended to multiple riser arrays byHuse /12/, who proposed a scheme for calculation of resultinginflow on a riser influenced by the wakes of several upstreamrisers.The inflow velocities and wake fields for all upstream risersare computed sequentially in current flow direction startingwith the far most upstream riser. Based upon correlation withexperiments Huse /12/ recommends to apply RMS (Root MeanSquare) summation of the individual wake fields from allupstream risers to compute the resulting wake field. The main advantages of the parametric wake field model are:

— the formulation is simple to implement in standard FEriser analysis tools without significant increase in compu-tation time and it allows for arbitrary depth variation of thecurrent loading along the riser;

— the computational procedure is well documented for two-riser systems;

— the formulation is applicable to multiple riser arrays, and

— it allows for assessment of shielding effects in steady cur-rent without making use of dedicated software.

The main limitations of the model may be summarised as:

— the formulation is static, which means that the model is notapplicable for prediction of impact velocity and collisionintensity;

— the turbulent wake model is applicable to the far wakefield only, i.e. the model is not considered valid when therelative distance between adjacent risers is less than twodiameters, and

— the load formulation does not include a lift force formula-tion which is considered essential for describing the insta-bilities in the wake. Note that in recent studies Blevins /3/has included a lift force formulation.

B.3 Parametric Mean Force ModelA parametric force model requires that the force coefficientsare derived as functions of relative riser spacing. The drag andlift coefficients should be established by model tests or 2Dnumerical calculations (e.g. CFD) for the actual cross-sec-tional configurations. The dynamic formulation outlinedbelow is applicable to two-riser systems in steady current. The co-ordinate system applied in the load formulation and theconfiguration of two cylinder sections in steady current aregiven in Figure B-1.

Figure B-1 Time-averaged properties of the turbulent wake of a cylinderwith a downstream cylinder in the wake

V0 is the free-stream current velocity and i.e. inflow velocityon the upstream riser. The inflow velocity on the downstreamriser, Vw, is adjusted due to shielding effects e.g. by makinguse of the generic drag coefficient approach as describedbelow or the parametric wake field model outlined in the sec-tion above. The x-coordinate is taken as the longitudinal direc-tion with respect to the incoming fluid flow, and the y-coordinate in the transverse direction. The origin is located inthe centre of the upstream riser. A parametric representation of the hydrodynamic loading ontwo-riser systems, which has gained consensus throughout theliterature, is derived in e.g. Blevins /2/. The time averagedmean fluid forces on the downstream cylinder may bedescribed by:

where r is the fluid density, an d are the local mean drag

(B.1)

(B.2)

(B.3)

( )2

693.0

02,⎟⎠

⎞⎜⎝

⎛−

= by

s

Dd e

xDC

VkyxV

sD

Ds

DxCkb

CDxx

1

4

=

+=

dw VVV −= 0

(B.4)

x

yV0

Vw (x, y)

Vd (x, y)

( )γγρ

γγ

sincos21

sincos

2LDrel

LDx

CCDV

FFF

−=

−=

( )γγρ

γγ

cossin21

cossin

2LDrel

LDy

CCDV

FFF

+=

+=

DC LC

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and lift coefficients. The other parameters are defined in theforce diagram shown in Figure B-2.

Figure B-2 Force diagram

The relative inflow velocity Vrel is defined as

where and are the structural velocity in x- and y-direc-tions, and V* is the local inflow velocity. The local inflowvelocity V* is defined as the free-stream current velocity V0 forthe upstream riser and for the downstream riser as the localwake velocity Vw after accounting for shielding effects. Perdefinition the local inflow velocity is parallel to the x-axis. Inthe following V* is used as the local inflow velocity to indicatethat the relations yields for both the upstream and downstreamriser. V0 or Vw will be used when the relations yields forupstream or downstream riser only.From the force diagram the following relations can be out-lined:

Further, the mean drag and lift coefficients for the downstreamriser can be related to the free-stream velocity V0 by:

and the fluid forces may be rewritten as:

The force coefficients are tabulated as functions of relativespacing between upstream and downstream riser, CD(x, y) andCL(x, y). The local inflow velocity in the wake is needed in order to cal-culate Vrel for the downstream riser. It might be estimatedusing the approach of Price & Piperni /19/:

where CDG is a generic drag coefficient and CD(x, y) is the drag

coefficient of the downstream cylinder influenced by the wake.The main advantages of the parametric mean force model are:

— the formulation is simple to implement in standard FEriser analysis tools, and it allows for arbitrary depth varia-tion of the current loading along the riser

— the instantaneous hydrodynamic loading on the individualrisers is expressed by a parametric formulation as functionof relative position of the adjacent riser

— the formulation allows for re-use of results from advancedCFD calculations and/or model tests in practical designanalyses. With a comprehensive database, it is possible tocover a wide range of two-riser systems

— the effects from strakes or other VIV suppression devicesmay be included by means of results from model tests, and

— the load formulation has gained consensus throughoutmost of the literature.

The main limitations of the model may be summarised as:

— the formulation is impractical for extension to multipleriser arrays or more complex load cases (e.g. WF excita-tion)

— the force coefficients depend on Reynolds number, i.e. itis necessary to obtain databases for a range of Reynoldsnumber.

B.4 Estimating the Force CoefficientsThe force coefficients applied to describe the hydrodynamicinteraction effect between a pair of risers can be derived frome.g. dedicated CFD analysis or laboratory tests or from othernumerical methods such as the free-streamline method. It is generally necessary to establish a database of the meandrag and lift forces on the downstream cylinder as function ofrelative spacing from the upstream one. Figure B-3 shows typical locations of the downstream riserwhere the upstream cylinder is located in the origin, x-axispoints longitudinal in the current direction and y-axis trans-versely to the current direction. The downstream cylinder islocated at different locations in the wake of the upstream one.In this illustrative example, the force coefficients are estab-lished for 28 different arrangement.

Figure B-3 Mesh of locations where force coefficients generally should be es-timated

Note that both the drag and lift force are symmetric around thewake centreline, and it is only necessary to estimate the coef-ficient on one side. Generally, the mesh should be denser forsmaller spacing where the hydrodynamic interaction effectsare most pronounced. As illustrated the mesh can be coarser farout and down in the wake. In between the locations given in the database, the force coef-ficients are based upon either linear or more advanced interpo-lation. It is recommended to apply linear interpolation for tworeasons:

(B.5)

(B.6)

(B.7)

(B.8)

(B.9)

Fx

Fy

FD FL

Vrel

xV &−*

y&− γ

γ

( ) 22* yxVVrel && +−=

x& y&

relVxV &−

=*

cos γ

relVy&−

=γsin

20

2

20

2

;VVCC

VVCC w

LLw

DD ==

( )( )yCxVCVVDVF LwD

wrelx && +−= 2

20

21 ρ

( )( )xVCyCVVDVF wLD

wrely && −+−= 2

20

21 ρ

( ) ( )DG

Drel C

yxCVyxV ,, 0=

x

y

Typically > 20D

Typi

cally

> 4

D

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— the gross riser displacement is assumed unaffected bylocal variations

— uncertainties of each of the known values are quite signif-icant; e.g. it depends on the level of accuracy when esti-mating it, but also on the Reynolds number, roughness etc.

It is generally recommended that the force coefficients should

be estimated from the wake centreline and 4 diameters in trans-verse direction. In longitudinal direction, typically 20 to 25diameters should be sufficient as an upper boundary. The forcecoefficient should also be estimated with as low spacing aspossible, e.g. a lower boundary of 1.5-2 diameters centre-to-centre distance should be applied.

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APPENDIX C LOCAL IMPACT STRESS ANALYSIS OF STEEL PIPES

C.1 GeneralLocal non-linear dynamic analyses should be performed inorder to capture the local dynamics of the riser at an impact.The result of the analyses should be the peak stresses, stressranges and typically number of stress peaks in one collisionevent. The analysis should be performed for a range of differ-ent relative impact velocities and impact angles, /15/.The resulting load effects further depend on the pipe-walldeformation properties. The “participating mass”, see e.g. Li &Morrison /17/, depend strongly on the impact duration and willnormally be implicit in the solution and not an input-parame-ter.The strategy for calculation of the collision induced loadeffects depend on the type of impact, such as:

— line impact— point impact.

In addition, the effect of coating and strakes should be consid-ered if relevant. Coating is effective in reducing the stresseseven for small thickness’ typical for corrosion protection. Thereduction in stresses in the pipe due to the coating is reducedwith an increasing stiffness of the coating.The peak stresses and stress-ranges for one specific impactneed to be determined based on detailed finite element analy-sis. The response can be strongly dominated by local dynam-ics, and a quasi-static approach is in general not sufficient.

C.2 Response SurfaceBased on finite elements analysis, a response surface for stresscomponent s may be derived as function of relative impactvelocity and impact angle as follows:

The form of the response surface will typically take the shapeof a 2nd order polynomial in the plane of impact angle andstress response. In the plane of impact velocity and stressresponse, the relation will be approximately linear. Figure C-1shows a response surface plotted in a 3D diagram.For determining this response surface, a series of finite ele-ment analyses need to be carried out. The analyses can be lim-ited to series of analyses with given impact velocity for threedifferent impact angles. A 2nd order curve through these threepoints can then be established.

Figure C-1 Response surface for a given point in the pipe

C.3 Requirements to Finite Element Model The extent of the 3-D element model should be large enoughsuch that the local dynamics giving the peak stresses is notimpaired by boundary conditions. Generally, a half joint,applying symmetry conditions, will be sufficient. The type of element should either be shell or solid volume ele-ments with contact modelling between the impacting surfaces,see Figure C-2. The mesh density should be fine enough to capture the localdynamics as well as giving the proper measure for the shellbending stresses in the pipe wall. Generally, sensitivity analy-ses should be performed in order to verify the model. Contact modelling should be made with a method, whichimplies little sensitivity to the peak stresses. A Lagrange mul-tiplier technique meets this criterion, as this solves the equa-tion defining no intrusion between the two contacting surfaces.Other methods, like the “penalty stiffness” method may beapplied if the selected contact spring stiffness is documented toyield satisfactory contact stresses. A conservative approach for mass modelling is to apply theentire mass as an equivalent mass to the outer cross-section.More detailed and less conservative way of applying themasses may be done as long as they are properly documented.The time stepping procedure needs to be sufficient small toprovide reliable results for the peak stresses. Typically, the risetime for the peak stresses at the area of impact is in the orderof 1 millisecond. A convergence study should be performed in order to evaluatethe expected accuracy of the results in the applied model. Thistype of time-domain non-linear dynamics are fairly time con-suming, the mesh density needs for practical purposes to belimited to a level that gives satisfactory results. Generally, the models should be run with a refinement in alldirections. Examples of this are shown in Figure C-3, startingwith fairly coarse meshes, and gradually refining the meshes inlongitudinal and circumferential directions.

Figure C-2 FE model of production riser with connector (top) and without connector (bottom)

(C.1)( )θσ ,,nrelUΔ

0 0,2 0,4 0,6 0,8 1

1,2 1,4 1,6 1,8 2

0 16,875

33,75 50,625

67,5 0

100

200

300

400

500

600

Stressrange [MPa]

Urel,n [m/s] Impact angle [deg]

Shell elements for entire pipe.

Contact elements on surface.

Shell elements for entire pipe.

Solid elements for connector, one layer of shell on inside.

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Figure C-3 Examples of convergence studies

C.4 Special Case ImpactAs a special case, the riser-riser line impact problem assumesthat the risers are effectively impacting in a straight, paralleland co-planar configuration. The derivation assumes a simpli-fied analytical ring model as follows:

— the two risers may be considered as a simple mass-spring-mass system

— the assessment can be based on elastic ring and beam the-ories

— the impact force is assumed to act as a point load— linear elastic response may be assumed for the vast major-

ity of realistic line-like collisions.

The required input to the analyses is as follows:

— mass per unit length incl. added mass for the risers, i.e. m1and m2

— mean diameter and wall thickness t for the risers;— combined contact stiffness kc representing the cross-sec-

tional force-deformation characteristics of the risers dur-ing the impact, and

— relative velocity of risers prior to the impact Urel.

According to assumption 1, the impact force per unit length pis given by; see e.g. Li & Morrison /17/:

The contact stiffness kc may be evaluated directly fromassumption 2 & 3.

Where is the mean diameter, E is Young’s modulus andindices 1 and 2 indicating riser 1 and riser 2.The pipe wall stress may be evaluated using the followingexpression:

where C is a correction factor accounting for the ring thick-ness. C = 0.72 applies for the mid-wall and should be used forfatigue purposes and C ≈ 0.74-0.80 corresponds to the maxi-mum tensile inner fibre stress at the ring.

3

2

1

(C.2)

(C.3)

(C.4)

D

relc Umm

mmkp

)( 21

21

+=

( )

13

2

2

3

1

1

8332

32

−

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛

−=

tD

tDEkc π

π

D

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛⋅=

tD

tpCσ

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