numerical modeling and mechanical analysis of flexible risers

7/24/2019 Numerical Modeling and Mechanical Analysis of Flexible Risers

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Research ArticleNumerical Modeling and Mechanical Analysis of Flexible Risers

J. Y. Li, Z. X. Qiu, and J. S. Ju

College of Water Resources and Civil Engineering, China Agricultural University, Beijing , China

Correspondence should be addressed to J. S. Ju; [email protected]

Received September ; Accepted December

Academic Editor: Cheneng Li

Copyright J. Y. Li et al. Tis is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABAQUS is used to create a detailed nite element model or a -layer unbonded exible riser to simulate the risers mechanicalbehavior under three load conditions: tension orce and internal and external pressure. It presents a technique to create detailednite element model and to analyze exible risers. In FEM model, all layers are modeled separately with contact interaces;interaction between steel trips in certain layers has been considered as well. FEM model considering contact interaction, geometricnonlinearity, and riction has been employed to accurately simulate the structural behavior o riser. Te model includes the maineatures o the riser geometry with very little simpliying assumptions. Te model was solved using a ully explicit time-integrationscheme implemented in a parallel environment on an eight-processor cluster and G memory computer. Tere is a very goodagreementobtained rom numerical andanalytical comparisons, which validates the use o numerical model here. Te results romthe numerical simulation show that the numerical model takes into account various details o the riser. It has been shown that thedetailed nite element model can be used to predict risers mechanics behavior under various load cases and bound conditions.

1. Introduction

Te unbonded exible riser is a pipe composed o severallayers without adhesive agents between the layers. It is widelyused in the deep sea oil industry or its capacity dealing withlarge deormation and displacement due to its lower bendingstiffness comparing with rigid steel risers. Different layers aredesigned or specic unctions. Achieving the advantage oexible risers requires complicated inner structure. One othe correlative disadvantages is the difficulty o understand-

ing the mechanical behavior o the riser particularly underthe very deep water.

Current methods are generally divided into two cate-gories: analytical methods and numerical methods. In thepast decades, researchers have conducted several analyticalworks on this subject. Among the rst pioneers, Knapp []derived the stiffness matrix or a helically armored cablesubjected to tension and torsion. He took into account thecompressibility o the core and the variation in lay angles.Te research on the response o helically armored cablessubjected to tension, torsion, and bending was conducted byLanteigne []. In his study, the inuences o internal radialorces and curvature on the effective exural rigidity were

investigated. Feret and Bournazel [] presented a ormulationor the slip o tendons undergoing bending on assumptionthat armor tendons ollowed a geodesic path once slip tookplace. Kraincanic and Kebadze [,] presented a nonlinearormulation in consideration o the variation o the bendingstiffness due to rictional sliding between layers, and ananalytical model o an unbonded exible pipe was proposed.

However, all the analytical models share many simpliedassumptions inevitably [], which signicantly limit theapplication range o the results. On the other hand, the ana-

lytical models are quite complicated due to the large nonlin-earity o the complex structure []. What is mentioned abovemotivatesmany researchers to study the rened niteelementmodels, which takes into account many details o the realrisers that the analytical model can hardly contain. And thedetailed nite element model can be achieved convenientlybeneting rom the wide use o computers. Bahtui et al.developed a nite element model or unbonded exible riserwith only two structural layers []. However, papers in thiseld are still quite rare.

In this paper, a urther research on the rened nite ele-ment model o -layer unbonded exible riser is conducted.All layers are modeled separately. FEM model considers

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 894161, 7 pageshttp://dx.doi.org/10.1155/2015/894161


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Mathematical Problems in Engineering

Carcass layer

Internal pressure

protection armor

Interlocking pressureprotection armor

Preparatory pressureprotection armor

Antiwear layer

Tension armor 1

Antiwear layer

Tension armor 2

Antiwear layer

Outer sheath

F : en layers riser.

F : Section and model o carcass layer.

contact interaction, geometric nonlinearity, and riction. Temodel includes the main eatures o the riser geometry with

very little simplication. And the mechanical behaviors o theriser under three load conditions are obtained.

2. Finite Element Model

A detailed nite element model developed using ABAQUS

by parametric method is shown in Figure []. en layersare simulated separately considering the contact interaces.Te coefficient o riction between layers is assumed ..Hourglass control is considered in this study.

Te sequence o layers is listed inable .

Te nite element model was created in a global cylin-drical coordinate system with its origin located at the centero the risers bottom. Te model consisted o ten separatecylindrical layers.

Carcass layer was modeled by D -node reduced-integration shell element. Tere were elements and nodes adopted. Its section and interlocking structureshow inFigure .

: Layers o the riser.

Layer ype

Carcass layer

Internal pressure protection armor

Interlocking pressure protection armor

Preparatory pressure protection armor

Antiwear layer

ension armor Antiwear layer

ension armor

Antiwear layer

Outer sheath

As shown inFigure , internal pressure protection armorlayer was modeled by D -node linear brick, reduced-integration element. Tere are elements and nodes or this layer.

Interlocking pressure protection armor and preparatorypressure protection armor layers were composed o channel


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F : Model o internal pressure protection armor layer.

F : Section andmodel o the pressureprotectionarmor layers.

steel strips; they made up the pressure protection armortogether (as shown in Figure ). Both o the layers weremodeled by D -node linear brick, reduced-integrationelement. elements and nodes were used here.

Tereare threeantiwear layers modeledbetween prepara-tory pressure protection armor, tension armor , tensionarmor , and outer sheath. Te model o antiwear layer is

shown in Figure . D -node linear brick, reduced-inte-gration element was selected or the modeling. Tere are elements and nodes in total.

As shown inFigure , two tension armor layers are spi-rally woundF in opposite directions. ension armor con-sisted o steel strips while tension armor consisted o. Both o them were modeled by D -node linear brick,reduced-integration element. Tere are elements and nodes or tension armor and elements and nodes or tension armor .

Figure shows the detailed dimensions o the riserscross section composed o -layer element model. Due tothe complication and scale o the structure, a parametric

F : Model o antiwear layer.

F : Model o tension armor layers.

modeling procedure was adopted. Te model is solved inABAQUS analysis module afer modeling.

3. Material Properties

Te material properties or layers o the exible riser areshown inable .

4. Load Case, Calculation Results,and Analyses

Tree typical loads (tension, internal pressure, and external

pressure) were applied on a . m long riser to demonstratethe accuracy and reliability o the method. Te bottom end othe riser was constrained in all directions while the other endwas totally ree.

.. Load Case : ension. In this case, a kN concentratedload was applied on the ree end o the riser.Figure showsthe axial-deormation o the riser. Te maximum stretchingo the riser in axial direction is . mm, and the elongationis about .%. Te maximum Mises-stress results o eachlayer are listed inable .

As shown inable , stress mostly concentrated at thetension armor layers. Te maximum Mises stress or tension


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: Material properties.

Carcass layer Internal pressure

protection armor

Pressureprotection

armor

Antiwearlayer

ensionarmor

Outer sheath

Steel strip Low-density

polyethylene Steel strip Nylon braid Steel strip

Low-densitypolyethylene

Density (kg/m)

Youngs modulus (GPa) . . .

Poissons ratio . . . . . .

: Maximum Mises stress o each layer.

Carcasslayer

Internalpressure

protectionarmor

Interlockingpressure

protectionarmor

Preparatorypressure

protectionarmor

ensionarmor

ensionarmor

Outersheath

Mises stress (MPa) . . . . . . .

Lay angle for interlocking

pressure protection armor88Outer diameter=

Inner diameter=

armors 30Lay angle for tension

229 mm

178mm

F : Detailed dimensions o the risers cross section.

U, U3+1.935e 03

+1.761e 03

+1.587e 03

+1.413e 03

+1.239e 03

+1.065e 03

+8.914e 04

+7.175e 04

+5.436e 04

+3.696e 04

+1.957e 04

+2.183e 05

1.521e 04

F : Axial-deormation o the riser under tension.

S, Mises

+9.848e + 07

+9.759e + 07

+9.671e + 07

+9.582e + 07

+9.493e + 07

+9.405e + 07

+9.316e + 07

+9.228e + 07

+9.139e + 07

+9.051e + 07

+8.962e + 07

+8.874e + 07

+8.785e + 07

(Avg.: 75%)

F : Mises-stress contour or tension armor under tension.

armor is . MPa. Te result shows good agreement withresult obtained romRecommended Practice for Flexible Pipe[]. It can also be seen that Mises stress in tension armor is slightly greater than that in tension armor due to thedifference in their radii. In order to achieve a better view othe maximum stress distribution, only stress results o tensionarmor are shown inFigure .

Te analytical result rom recommended practice ortensile stress in the tension armor is given by

=

2cos2

, ()

whereis tensile load,is equivalent armor thickness, andis mean diameter o armor.

Te analytical result is . MPa, .% smaller than theaverage simulation result . MPa. Tere is a good agree-ment between the analytical and numerical results. Te ana-lytical method considering the riser is more likely a contin-uous structure, so it cannot take ull account o contact, slip,


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Carcasslayer

Internalpressure

protectionarmor


protectionarmor

Preparatorypressure

protectionarmor

ensionarmor

ensionarmor

Outersheath


CPRESSGeneral_Contact_Domain

+6.761e + 06

+6.198e + 06

+5.634e + 06

+5.071e + 06

+4.507e + 06

+3.944e + 06

+3.381e + 06

+2.817e + 06

+2.254e + 06

+1.690e + 06

+1.127e + 06

+5.634e + 05

+0.000e + 00

F : Contact pressure contour or tension armor under ten-sion.

S, Mises

+1.069e + 08

+1.038e + 08

+1.007e + 08

+9.762e + 07

+9.452e + 07

+9.142e + 07

+8.833e + 07

+8.523e + 07

+8.213e + 07

+7.904e + 07

+7.594e + 07

+7.284e + 07

+6.974e + 07

(Avg.: 75%)

F : Mises-stress contour or nonriction tension armor under tension.

and riction effect between steel strips o the tension armor.However, as it shows in Figure , or discrete structurelike tension armor, stress concentration caused by thesesinteractions between strips could not be ignored.

Extrusion and slip appear between strips when tension isapplied. FromFigure , the distribution o contact pressurecan be observed easily. Te effect o riction makes stress othe strips smaller than that rom nonriction model. Tis canbe easily veried by comparison o Mises stress rom modelwithout riction effect (shown in Figure ) and that rom

U, U1(CSYS-1)

+3.368e 04

+2.410e 04

+1.451e 04

+4.931e 05

4.651e 05

1.423e 04

2.382e 04

3.340e 04

4.298e 04

5.256e 04

6.214e 04

7.173e 04

8.131e 04

F : Radial deormation contour or the riser under internalpressure.

model with riction effect (shown inFigure ). Calculatedstress result decreases by .% when riction is considered.

.. Load Case : Internal Pressure. In this load case, a. MPa internal pressure was applied on the carcass layero the riser. Te radial deormation o the riser shows inFigure (deormation scale actor ). Te results or themaximum Mises stress o each layer are listed in able .It illustrates that the internal pressure transits rom internalstructure to external structure layer by layer through contact.

Under internal pressure, the pressure protection armorlayers (interlocking pressure protection armor layer andpreparatory pressure protection armor layer) are the mainstructures to resist load. Te maximum hoop-stress in thetwo pressure protection armor layers is . MPa as shown

inFigure .Te numerical results are compared with those rom

Lames ormula in elastic mechanics shown as the ollowingequation []:

= 2/2 + 1

2/2 1, ()

whereis the external radius o the cylinder,is the radiuso an arbitrary point o the cylinder, andis the inner radiuso the cylinder.

Te analytical result is . MPa, smaller than thenumerical result . MPa by .%. Contact pressure distri-bution o channel steel stripsis shown in Figure . Te results


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Carcasslayer

Inner pressureprotection

armor


protectionarmor

Preparatorypressure

protectionarmor

ensionarmor

ensionarmor

Outersheath


S, S22(CSYS-1)(Avg.: 75%)

+9.857e + 07

+9.776e + 07

+9.695e + 07

+9.614e + 07

+9.532e + 07

+9.451e + 07

+9.370e + 07

+9.289e + 07

+9.208e + 07

+9.127e + 07

+9.045e + 07

+8.964e + 07

+8.883e + 07

F : Hoop-stress contour or the pressure protection armorlayers under internal pressure.


+1.198e + 07

+1.098e + 07

+9.985e + 06

+8.987e + 06

+7.988e + 06

+6.990e + 06

+5.991e + 06

+4.993e + 06

+3.994e + 06

+2.996e + 06

+1.997e + 06

+9.985e + 05

+0.000e + 00

F : Contact pressure contour or channel steel strips underinternal pressure.

rom thesimulation agree well with the analyticalresultsromXu [].

.. Load Case : External Pressure. Te external pressure is MPa, acting on the outer sheath layer. Te radial deorma-tion o the riser under external pressure is shown in Figure (deormation scale actor ). Te maximum Mises-stressresults o each layer are listed in able . It illustrates that theexternal pressure transits rom external structure to internalstructure layer by layer through contact.

U, U1(CSYS-1)

+5.121e 04

+4.003e 04

+2.885e 04

+1.768e 04

+6.504e 05

4.672e 05

1.585e 04

2.702e 04

3.820e 04

4.937e 04

6.055e 04

7.172e 04

8.290e 04

F : Radial deormation contour or the riser under externalpressure.

S, S22(CSYS-1)

+7.663e + 06

+3.766e + 05

6.910e + 06

1.420e + 07

2.148e + 07

2.877e + 07

3.605e + 07

4.334e + 07

5.063e + 07

5.791e + 07

6.520e + 07

7.249e + 07

7.977e + 07

(Avg.: 75%)

F : Hoop-stress contour or the pressure protection armorlayers under external pressure.

Te external pressure is mostly resisted by the pressureprotection armor layers (interlocking pressure protectionarmor layer and preparatory pressure protection armorlayer). Te maximum hoop-stress in the two pressure protec-tion armor layers is . MPa as shown in Figure . Contactpressure distribution o channel steel strips is shown inFigure .


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+1.046e + 07

+9.591e + 06

+8.720e + 06

+7.848e + 06

+6.976e + 06

+6.104e + 06

+5.232e + 06

+4.360e + 06

+3.488e + 06

+2.616e + 06

+1.744e + 06

+8.720e + 05

+0.000e + 00

F : Contact pressure contour or channel steel strips underexternal pressure.

5. Conclusions

() A detailed nite element model ora -layer unbond-

ed exible riser has been created or the analysis o itsmechanical behavior. It takes into account geometricnonlinearity, contact interaction, and riction.

() From the calculation in ABAQUS, detailed stress anddeormation results o each layer o the riser underthree load cases are obtained. Te calculation resultsshow a satisactory agreement with those rom ana-lytical method. It veries the numerical methods

validation.

() It suggests that the nite element model can be usedto predict mechanical behavior o the riser in otherdifferent load cases. Te numerical model enables

cost-effective parametric investigations, which can inturn lead to improved riser design.

Conflict of Interests

Te authors declare that there is no conict o interestsregarding the publication o this paper.

Acknowledgments

Tis research was supported by National Science Foundationo China () and Beijing Natural Science Foundation().

References

[] R. H. Knapp, Derivation o a new stiffness matrix or helicallyarmored cables considering tension and torsion,InternationalJournal for Numerical Methods in Engineering, vol. , no. , pp., .

[] J. Lanteigne, Teoretical estimation o the response o helicallyarmored cables to tension, torsion, and bending,ransactionsASMEJournal of Applied Mechanics, vol. , no. , pp. , .

[] J. J. Feret and C. L. Bournazel, Calculation o stresses and slipin structural layers o unbonded exible pipes, ASME Journal

of Offshore Mechanics and Arctic Engineering, vol. , no. , pp., .

[] I. Kraincanic and E. Kebadze, Slip initiation and progressionin helical armouring layers o unbonded exible pipes and itseffect on pipe bending behaviour,Journal of Strain Analysis forEngineering Design, vol. , no. , pp. , .

[] E. Kebadze, Teoretical modeling of unbonded exible pipe cross-sections [Ph.D. thesis], South Bank University, London, UK,.

[] J. J.Feret andC. L. Bournazel, Calculation o stresses and slip instructural layers o unbonded exible pipes,Journal of OffshoreMechanics and Arctic Engineering, vol. , no. , pp. ,.

[] A. M. Harte and J. F. McNamara, Modeling procedures or thestress analysis o exible pipe cross sections,Journal of OffshoreMechanics and Arctic Engineering, vol. , no. , pp. , .

[] P. Claydon, G. Cook, P. A. Brown, and R. Chandwani, A the-oretical approach to prediction o service lie o unbondedexi-ble pipes underdynamic loading conditions,Marine Structures,vol. , no. , pp. , .

[] G. Alano, A. Bahtui, and H. Bahai, Numerical derivation oconstitutive models or unbonded exible risers,InternationalJournal of Mechanical Sciences, vol. , no. , pp. , .

[] A. Bahtui, H. Bahai, and G. Alano, A nite element analysisor unbonded exible risers under torsion,Journal of OffshoreMechanics and Arctic Engineering, vol. , no. , Article ID, .

[] ABAQUS Teory Manual, ABAQUS, Version . Documenta-tion, .

[] ISO, Recommended Practice for Flexible Pipe. ISO -:,International Organization or Standardization, London, UK,.

[] Z. L. Xu,Elastic Mechanics, Version , .


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