Coupled fluid–structure simulations for evaluating a performance of full-scale deepwater composite riser

Ocean Engineering 94 (2015) 19–35

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Coupled fluid–structure simulations for evaluating a performance of full-scale deepwater composite riser L.B. Tan, Y. Chen, Rajeev K. Jaiman n, X. Sun, V.B.C. Tan, T.E. Tay Department of Mechanical Engineering, National University of Singapore, Singapore

art ic l e i nf o

a b s t r a c t

Article history: Received 19 August 2013 Accepted 10 November 2014

A global–local analysis methodology based on fluid–structure coupling is used to investigate the mechanical responses of both composite and steel risers. Since the design of the riser system can be a daunting task, involving hundreds of load cases for global analysis, semi-empirical fluid load models are considered for the reduced order computations of full-scale riser models. The structural performance of composite risers under real sea current conditions is investigated systematically and discussed with regard to the practical concerns in full-scale settings. The failure envelops of internal liners are found to be within that of the composite layers, which reveals that the liner is the weakest link for composite riser design. Results show that the composite risers can be more prone to vortex-induced vibration (VIV) due to their lower structural frequencies. In the present study, the composite riser yields 25.5% higher RMS strains than the steel riser. Placement of buoyancy modules along the riser may be critical for the design against VIV, and our results show that the modules are not recommended at the top region of the riser, especially if a top-sheared current is expected. Instead, it is preferable to implement them at the bottomhalf portion of the riser and as a continuously buoyed region rather than short discrete buoys separated with gap spaces. Composite risers with different metallic liners are studied, and the titanium liner riser is found to be favourable over the steel and aluminum liner risers. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Carbon fiber reinforced polymer (CFRP) Vortex-induced vibration (VIV) Global–local analysis Composite riser Fluid–structure interaction (FSI) Failure envelopes

1. Introduction Carbon fiber reinforced polymer (CFRP) materials have drawn an attention from offshore industry due to their high specific strength and good structural durability. Material properties ranging from stiffness, corrosion resistance and damping may be tailored easily in a composite system than other traditional metallic systems (Ochoa and Salama, 2005; Ochoa, 2006). The weight reduction attainable using a composite riser is substantial and can lead to huge cost savings. However, it also brings about new challenges in the design and analysis of such risers in harsh ocean environment. In particular, it is vital to assess their performances in terms of strength and durability in real sea conditions. Composite materials are introduced into offshore applications about two decades ago as interests in deepwater oil reserves grew exponentially (Wang et al., 1993). Due to the weight of traditional steel risers that restricted their use in greater water depths, prototype production and drilling composite risers are developed. Studies show that the decrease in payload can translate to cost savings due to decreasing platform size and mooring pretension. The assessment of these composite risers (with single and dual casings) targeted

n

Corresponding author. E-mail address: [email protected] (R.K. Jaiman).

http://dx.doi.org/10.1016/j.oceaneng.2014.11.007 0029-8018/& 2014 Elsevier Ltd. All rights reserved.

water depths of 1000–1660 m (Ochoa, 2006; Salama, 1986, 1997; Tamarelle and Sparks, 1987; Andersen et al., 1997; Karayaka et al., 1998). Very little work has been done on the evaluation of coupled global–local performance in the context of composite risers subjected to vortex-induced vibrations. In the first study of present work, the mechanical responses of full-scale 1500 m steel and composite risers under the Gulf of Mexico current profile are evaluated. The application of composite risers can provide cost-savings in terms of using a lower top-tension capacity rig or in minimizing the use of buoyancy modules. However, the lower transverse stiffness and lower tension within the composite riser result in lower structural frequencies which can lead to a susceptibility of composite riser to vortex-induced vibration (VIV). With the more uniform riser tension distribution, there is a greater tensioning range that can be applied to the risers to mitigate VIV without a potential risk of a pull-out or disengagement at the bottom of the riser connecting to the well. On the contrary, if the riser is under-tensioned against VIV, a larger portion of the riser may be affected due to the more uniform riser tension distribution. For oil production in deep waters, steel risers typically require buoyancy modules to provide enough tension along the riser and prevent them from failing due to self-weight. The main purposes of keeping the entire riser in tension are to control its deflection and to prevent buckling due to axial compression (Kim, 2007). Buoyancy modules are preferred over large platform rigs for maintaining

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tension, owing to the high cost of rigs and their poorer ability to provide better tension distribution within the riser compared to buoys. The buoy materials are typically made of closed-cell polyurethane foam or silica beads embedded within a matrix material, with equivalent densities lower than that of sea water, and have high enough compressive modulus so as to resist against the hydrostatic pressure exerted by the deep waters. The VIV response of risers with buoyancy modules are recently shown to exhibit an existence of nonlinear interaction of frequencies which are not a multiple of the frequency associated with either bare or buoyant regions (Rao et al., 2013). An expression is also proposed to predict the winner of the excitation competition between bare and buoyant segments for a given buoyancy coverage. As the water depth of interest is 1500 m for our work, we investigate the mechanical performance of these long steel risers with and without buoys and on how the modules should be placed for design against VIV fatigue damage. The results of riser dynamics are covered in the second study, and will be useful for oil production sites that are close to this water depth as engineers decide between using higher strength steels, risers with buoyancy modules or composite risers. It is also important to assess how the composite riser will perform under real sea current conditions located at different parts of the world, as contrasted with studies based on simple linear or sheared currents (Song et al., 2011; Xu et al., 2008). In the third study, three current profiles obtained from regions in the North Sea, Gulf of Mexico and Shetland are used. The design profiles are obtained from Faltinsen (1990) and Rustad (2007) and dimensioned for 1500 m water depth. The current magnitudes are slightly scaled

such that the maximum is 1.2 m/s. This yields a Reynolds number upper range of around 3.65
105. It is found that the distribution pattern of lock-in riser lengths for the eigenmodes is characteristic of the incident current profile and riser structure properties, and may be used as an indicator of the severity of riser vibration. The tube body of the composite riser joint is usually a hybrid material system design in which the axial load and hoop pressure are carried by helically wound carbon- or glass-fiber plies, while leakage prevention is achieved through the use of liners (Johnson et al., 1999). The primary function of an internal liner is to prevent the leakage from the annulus, and the material should be highly resistant against material wear, chemical corrosion and adhesively compatible with the composites. Typical internal liner materials include thermoplastic polymers, synthetic rubbers and structural metals (steel and titanium). Composite production risers have been developed to satisfy the same requirements as conventional steel risers on the Magnolia TLP in the Gulf of Mexico (GoM) at about 1500 m water depth. The initial wall design has two inner liners, steel and rubber, and modified later by adding a secondary steel liner between rubber liner and structural composite layers (Ochoa, 2006). For the design of composite risers, finding a suitable liner material for reduction of riser vibration and fatigue damage is important. In the last study, aluminum-, steel- and titanium-liner composite risers are evaluated. In this paper, parametric studies for riser dynamics are reported and the factors for VIV mitigation are discussed systematically. Accurate prediction of VIV has proved to be challenging, owing to nonlinear fluid forces and feedback between the riser motion and the fluid-flow (Blevins, 2001). Fully-coupled fluid–

Table 1 Geometries and material properties of composite riser.

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

structure simulations can be employed to model the coupled fluid–structure response and forces (Jaiman et al., 2009). This paper, however, utilizes a semi-empirical reduced-order modeling for the forces imposed by the periodic vortex shedding on vibrating cylindrical riser. These forces are applied to predict the vortex-induced vibration of elastic riser structure subjected to ocean current. The main objectives are to: 1. compare the dynamical performances of the composite riser with conventional steel risers under the Gulf of Mexico current (Nowlin et al., 2001); 2. investigate the responses of steel risers with attached buoyancy modules and how best to place them along the riser to mitigate VIV; 3. assess the coupled fluid–structure dynamics of composite risers under real current profiles of different locales; and 4. investigate the performances of composite risers with different metallic liners.

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Table 3 Global riser specifications. Composite riser Geometry Riser length 1500 m Internal diameter 0.28 m Outer diameter 0.32067 m Properties Ez ¼54.37 GPa Er ¼71.68 GPa Eθ ¼ 11.99 GPa Gzr ¼22.89 GPa Grθ ¼ 3.43 GPa Gzθ ¼ 3.25 GPa νzr ¼0.27 νrθ ¼0.30 νzθ ¼ 0.36 ρriser ¼2293 kg/m3 ρseawater ¼1026.52 kg/m3 Axial stiffness (Ez*A)¼ 1.0432 GN Bending stiffness (Ez*I) ¼11.816 M Nm2 Steel riser Geometry Riser length Internal diameter Outer diameter Properties E ¼200 GPa Axial stiffness (Ez*A)¼ 1.4476 GN

1500 m 0.28 m 0.296 m ρriser ¼ 7925 kg/m3 Bending stiffness (Ez*I) ¼15.021 M Nm2

2. Modeling approach A combined global–local methodology is used for the riser analysis. Both local and global analyses are performed using a finite element software AbaqusTM. A literature survey of composite risers (Andersen, 1997; Sparks and Odru, 1988; Baldwin and Newhouse, 1997; Salama et al., 2002) facilitated the selection of suitable composite materials, stack orientation, layer thicknesses, and riser geometric dimensions for our model (See Table 1). A homogenization scheme, based on the classical laminate theory (CLT), is used to extract the equivalent single-layer transverse isotropic properties of the riser (Jones, 1998; Sun et al., 2013). Subsequent global analyses of the full-scale composite riser are modelled using PIPE32H beam elements assigned with the equivalent anisotropic properties (See Table 3) obtained from the homogenization scheme. The global analyses use a force-based model for the prediction of static and dynamic VIV responses of the deep-sea risers. The fluid–structure coupling is performed by applying the hydrodynamic forces, with force coefficients established from the semiempirical data, onto the riser structure. An automation script interface is developed to help generate the Abaqus input file for the analyses. The interface allows user specification of riser geometry, material properties, Strouhal number, the lock-in

Table 2 Hashin composite failure criteria. 1. Matrix tensile (MT) failure for σ 22 þ σ 33 40
Z1 failure σ2 þ σ σ σ2 þ σ2 ðσ 22 þ σ 22 Þ2 þ 23 2 22 33 þ 12 2 13 ¼ Y T2 S23 S12 o 1 no failure MT ¼1 if element fails by this mode, otherwise, MT ¼0 2. Matrix compressive (MC) failure for σ 22 þ σ 33 o 0   
 2 Z1 2 σ2  σ σ σ2 þ σ2 YC  1 σ22 YþC σ 33 þ ðσ 22 þ2σ 33 Þ þ 22 2 22 33 þ 12 2 13 ¼ 2S23 4S23 S23 S12 o1 MC ¼1 if element fails by this mode, otherwise, MC ¼ 0 3. Fiber tensile (FT) failure for σ 11 Z 0
 2 2 Z1 failure σ þ σ2 σ 11 þ 12S2 13 ¼ XT 12 o 1 no failure FT ¼1 if element fails by this mode, otherwise, FT¼0 4. Fiber compressive (FC) failure for σ 11 o 0  2
Z 1 failure σ 11 ¼ Xc o 1 no failure FC ¼1 if element fails by this mode, otherwise, FC ¼0

failure no failure

bandwidth, density of seawater, the static and dynamic drag and added mass coefficients, the current profile along the riser, the boundary conditions for riser ends, the applied top-tensioned load and internal and external pressures to the riser. The finite element analysis, conducted in three dimensional (3D) space, takes into account geometric and mass variation along the riser. The AbaqusTM module, Aqua, used for the riser analyses allows implementation of fluid inertia, buoyancy, drag and lift effects of structures immersed in a fluid environment. In the static analysis, the top-tensioned load and the form drag are applied consecutively to the pinned riser. The transverse drag per unit length on the riser is applied via the use of the Morison drag equation (Blevins, 2001). The riser deflection, bending strains and axial stresses due to both tension load and drag are then obtained. The static analysis is followed by a modal analysis of the bowed riser due to the static drag. Galerkin modal analysis is applied to the equation of motion of the slender elastic structure of beam elements responding to the fluid forces. The effects of structural damping and added mass are considered in the eigen-analysis and outputs of mode shapes and modal curvatures and their associated eigen-frequencies are obtained. The 3D analysis will result in modes that come usually in matched pairs, due to near symmetry of the riser in the two directions perpendicular to the riser axis. The automated script reads in the eigen-analysis results, picks up the unique modes, and then determines the lock-in modes for each element of the riser based on the current profile applied, the lock-in bandwidth specified, and the structural frequencies obtained from the eigenvalue analysis. The vortex-shedding or Strouhal frequency, fs, is empirically correlated to the flow velocity normal to riser axis, U, the hydrodynamic diameter of the cylinder, D, and the Strouhal number by fs ¼StU/D, where the Strouhal number, St, is related to the Reynolds number (Blevins, 2001; Sumer, 1997) and usually taken to be between 0.18 and 0.22. Lock-in occurs when the applied flow velocity induces vortex-shedding frequencies that approach the natural frequencies of the riser to result in resonance in vibrations occurring at close to the natural frequencies. For determination of the velocity ranges where vortex-shedding will be in resonance with an eigen-frequency of the member, the reduced velocity parameter, Vr, is used where Vr ¼U/fiD and fi is an eigen-frequency of the member and the other symbols have their usual meanings. The reduced velocities for in-line and cross-flow responses may range from 1.0oVro3.7 and 3.7oVro11,

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respectively (Sumer, 1997). These values vary with literature (Blevins, 2001; Det Norske, 2010a) and further depends on the Scruton number, a stability parameter that is related to the damping and vortex-shedding force in the member. The interface script calculates the range of reduced velocities attained by each element along the riser which thence determines if the particular element falls into the excitation zone or the non-excitation zone. For elements that fall within the excitation zone, they will be automatically applied with the dynamic lift and drag forces for vortexinduced vibration (VIV) analysis. The harmonic force excitation technique (Blevins, 2001) is used to model and predict VIV responses whereby the Strouhal frequencies (due to the input current profile) along the riser span are used for the harmonic excitation for lift, while twice the Strouhal frequencies are used for dynamic drag. For our analysis of 1500 m composite riser with outer diameters of around 0.32 m, the expected Reynolds number is around 3
105. Hence, the value of St¼0.2 is used throughout our analyses. The VIV step is conducted in time-domain with a total analysis time of 180 s to ensure that the riser has attained resonance on its structural frequencies. The typical first excitation mode of the riser is around 0.25 Hz which is 4 s. Singularity of the response is prevented by applying fluid and structural damping to the riser to ensure convergence of the analyses. In order to determine the required dynamic force coefficients for the VIV step, the script computes the estimation of riser displacement amplitudes, Ay/D, from the reduced velocities calculated for each of the modes. The formulas and charts used are according to DNV-RP-C205 (Det Norske, 2010a). A chart replotted from RP-C205 is shown in Fig. 1a. Based on the particular current profile, riser material and diameter, the number of excited elements for each mode is calculated, and the dominant and weak modes are identified through knowing which modes have the greatest number of elements excited. The maximum cross-flow riser displacement is given by the sum of the amplitude of the dominant cross-flow

mode and half the amplitude values of weaker cross-flow modes (Det Norske, 2010a). Mathematically, it is given as     Ay Ay 1 Ay ¼ þ ð1Þ D D dom: 2 D weak The in-line riser displacement amplitude, Ax/D is approximated from the plot given in Fig. 1b (Det Norske, 2010b) which gives a coarse prediction of the relation between Ay and Ax at different cross-flow mode numbers. The obtained reference riser displacements are then used for the tuning of dynamic force coefficients. For the dynamic VIV analysis, at least two iterations of finite element computations are needed in order to tune the dynamic cross-flow and in-line force coefficients to attain the same resulting riser amplitudes as provided by the DNV empirical response models. These coefficients usually have larger values then the static ones due to drag amplification caused by VIV. For this analysis step, the bowed configuration of the riser, due to form drag, is brought over from the previous step. The analysis for the time-domain VIV step is run with the time step increment of Δt¼0.01s. Drag and fluid inertia forces are applied to the riser span via the Morison drag and fluid inertia equations (Blevins, 2001; Abaqus, 2012) as given in (2) and (3): In-line/Cross-flow drag force per unit length of riser

1=2 1 F D ¼ ρC D DΔvn Δvn :Δvn sin ðωs t Þ 2

ð2Þ

Inertia force per unit length of riser  1 F I ¼ ρπ D2 C M af n  C A apn 4

ð3Þ

where CD is the in-line or cross-flow coefficient, Δvn is the relative transverse velocity of the fluid with the riser, ωs is the vortexshedding frequency, CM is the transverse fluid inertia coefficient, CA the transverse added-mass coefficient, afn the transverse component of the fluid acceleration, and apn is the transverse component of the riser acceleration. The inline forces are made to oscillate at twice the Strouhal frequencies (i.e. 2ωs) while the cross-flow forces oscillate at the Strouhal frequencies. The dynamic force coefficients used are constant over time. The static transverse drag, added mass and fluid inertia coefficients used are 0.6, 1.0, and 2.0, respectively. A similar harmonic model, with the same values of coefficients, was also used by Kim (2007) for his riser study using beam elements in Abaqus. The vibration in a structure is damped by the surrounding fluid. The hydrodynamic damping used is based on the Morison formulation of the drag force that incorporated a drag coefficient. The damping factor, ξf , is given by (Blevins, 2001; Le Cunff et al., 2002)

ξf ¼

2 ρD2 Ay ω CD 3π m D ωn

ð4Þ

For small-amplitude vibration, the drag coefficient may be given by CD ¼(fD/U)(3π3/2)[v/(πfD2)]1/2, where U is the amplitude of the velocity oscillation and v is the kinematic fluid viscosity. Setting the velocity amplitude U¼ ωAy and the oscillation frequency to natural frequency, f¼fn ¼ ωn/2π gives the fluid damping per unit length of the riser as (Blevins, 2001) !1=2 π ρD2 v ξf ¼ ð5Þ 2 m π f D2

Fig. 1. (a) Cross-flow A/D as a function of reduced velocity. (b) Ratio of Ax/Ay at different cross-flow modes.

This damping is utilized by DeepVIV™ (2008) and also by Le Cunff et al. (2002). Several other damping expressions are also reported by Brouwers (1982). For the dynamic step, the fluid modal damping for the excited modes are calculated according to the equations above and implemented in the coupled analysis. For the elements with the reduced velocities falling outside the curve in Fig. 1a or elements that fall outside the lock-in frequency bandwidth, the equivalent force

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

coefficients will be zero. The results of riser displacements, axial stresses and section curvatures over the entire analysis time are then obtained for the evaluation of root-mean-square (RMS) strains, section moments and tension values. For the riser models with discontinuous geometries due to additions of buoyancy modules, the related transition drag and inertia loading on exposed areas are also taken into account (Abaqus, 2012). Wave loading is currently not implemented for the riser analyses. The procedures for global riser analysis are shown in Fig. 2. The local FE model of a 10 m composite riser joint is next developed using 18000 C3D8R linear brick solid elements with reduced integration scheme, and with details of individual plies (titanium liner and composite layers) and their stacking orientations (see Table 1). The material failure envelopes, consisting of a combination of pressure, axial tension and bending moment, are then generated by results from multiple local model simulations of load cases. The maximum moment, tension and pressure (MTP) values obtained from global analysis are then plotted onto the respective

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failure envelopes. The consideration of bending moment is important in VIV analysis because the contribution from vibrational modes may be significant, and the value differs from one riser system to another and for distinct environmental loading conditions. The maximum combined loading states are then evaluated to achieve a better prediction of riser conditions (Kim, 2007). The Hashin failure criteria (Hashin, 1980) are programmed into the USDFLD subroutine in AbaqusTM as a basis for development of the failure envelopes, and in determining the failure locations, failure modes and plies within the multiple-layered riser joint in the local model. The four Hashin failure modes considered in our riser analyses are given in Table 2 where σij denote the stress components. XT, YT, XC and YC denote allowable tensile and compressive strengths in the respective material directions. S12, S13 and S23 are the shear strengths. The values of these parameters are given in Table 1. The MTP values plotted onto the failure envelopes help determine if the riser design exceeds the failure limits after incorporating a safety factor. This similar global–local technique was also utilized by Kim (2007) in his riser study. The admissible stress is usually taken as 0.67 of the yield strength (Sevillano et al., 2013; American Petroleum Institute (API), 1993).

3. Validation of VIV model

Fig. 2. Global modeling process flowchart.

For the global analysis, the VIV response of the riser model is first validated using field experimental data to establish the parameters for the fluid–structure coupling. Jaiswal and Vandiver (2007) and Vandiver et al. (2006) performed a series of composite riser tests that was carried out offshore of Miami, near the Gulf Stream. The experiment utilized a glass fiber composite pipe, 150.2 m long and 0.0363 m in outer diameter. The pipe was lowered into the seawater with a railroad wheel (328.5 kg in seawater) attached at the bottom end to provide tension. Strain gauges along the pipe are used to measure in-situ strains experienced during VIV when the pipe is being dragged in seawater by a vessel. Simulation cases of varying shear current profiles are conducted for our model validation work. The results are presented in an earlier publication by Chen et al. (2013) and shown in

Fig. 3. Validation of time-based model against experimental data and Shear7™ results; RMS bending strains (left), time history of normalized amplitude (right-top), and motion trajectories (right-bottom).

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Fig. 3. The RMS strains from our in-house model are shown by the red-dashed curve. In general, the in-house model gives similar trends as those predicted by Shear7™, and matches reasonably well against the experimental data. This validation exercise helps to ascertain the methodology used, and provides a confirmation of reference values of the modeling parameters for the appropriate fluid–structure coupling.

higher density of the steel riser, a much higher top-tension load is required which resulted in higher tensile stresses to the top portion of the riser than at the bottom. As reported by Chen

4. Parametric studies With the model validated, numerical studies are conducted on a full-scale 1500 m riser with pinned–pinned boundary conditions applied to both ends of the riser. The vertical riser is modeled with 1500 1-D PIPE32H elements. Table 3 shows the global modeling information for the composite and steel risers used for the parametric studies. As the composite materials are highly anisotropic between the in-plane and out-of-plane orientations, the transverse isotropic properties of the composite riser are used for the global analyses. These equivalent riser properties (including equivalent density) obtained from the multi-ply local analyses (Jones, 1998; Sun et al., 2013) already include the effects the titanium liner, composite layers, and the anti-corrosion layer. Ez represents the modulus in the riser axial direction, while Er and Eθ are modulus in the radial and hoop directions respectively. 4.1. Assessment of steel and composite risers In order to compare the mechanical performance of the CFRP composite riser with conventional steel risers, two cases of global riser analyses are performed under the Gulf of Mexico current profile which is given in Section 4.3. Both risers have an internal diameter of 0.28 m. The steel riser has an applied top-tension load of 867.2 kN and a thickness of 8 mm while the composite riser, with a thickness of 20.335 mm, has a top-tension load of 375 kN. The load is chosen such that when the riser is tensioned with the applied load at the top end, the entire riser will be in tension with the bottom end experiencing a tensile stress of not more than 20 MPa. Since the riser weight increases with water depth, deeper water and heavier riser necessitates higher top tension to be applied, as was the case for the steel riser. It is also noted that with the applied current drag, the bottom tension will typically increase, in this case, to about 45 MPa for the steel riser. Table 4 shows the parameters used in the study. The results for Cases 1 and 2 are presented here while another steel versus composite riser study is reported in a previous publication by Chen et al. (2013). Fig. 4a shows the resulting riser deflection due to current drag and top-tension load. The composite riser deflected much more than the steel riser due to its lower modulus (and hence lower stiffness). The hydrodynamic diameter of the composite riser is also greater than the steel riser which resulted in greater drag to the former. The composite riser has a maximum deflection of 13.33 m at 556 m from the riser bottom while the steel riser has a deflection of 9.88 m at 488.5 m from the bottom. Fig. 4b shows the tension distribution on the riser. Both cases do not have buoyancy modules along the riser span. Due to the

Fig. 4. (a) Static riser deflection due to top-tension and form drag (Cases 1–2). (b) Tension along riser due to top-tension and drag (Cases 1–2).

Table 4 Specifications for steel versus composite risers study. Cases Inner diameter (ID) (m)

Outer diameter (OD) (m)

Riser thickness (m)

Current (m/s)

1 2

0.32067 0.296

0.020335 0.008

Gulf of Mexico 375.0 (max.@ 1.2 m/s) 867.2

0.28

Top-tension applied (kN)

Material

Static drag coeff. (Cd)

Composite 0.6 Steel

Ends boundary conditions

Pin

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et al. (2013), the top portion of the riser could experience much higher axial stress than the lower portion of the riser, depending on the riser density and thickness and of the current and wave conditions it experiences. For the case of the Gulf of Mexico current, the top end of the steel riser is experiencing about 145 MPa while the bottom end is around 45 MPa. In general, the heavier steel riser develops a greater difference in tension distribution along the riser. For composite risers with lower density, the distribution of riser tension exhibits nearly constant behavior. The magnitudes of axial stresses are also much lower than those obtained from the steel riser, despite the composite riser having a greater deflection. With the more uniform riser tension distribution, there is greater tensioning range that can be applied to the risers to mitigate VIV. If sensors are embedded within the riser structure, operators could monitor the riser vibrations and vary the top-tension more effectively to avoid resonance and hence increase the fatigue life. Eigenvalue analysis is next performed for the extraction of frequencies. The structural frequencies are compared with the Strouhal frequencies to determine the modes and locations of the riser where

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lock-in excitation will occur. In most situations, resonance of a string occurs from superposition of vibration waves (Kim, 2007, Sparks, 2002). When a wave sent from one end is reflected back and forth and is in-phase with subsequent waves caused by a periodic excitation, the vibration amplitude increases significantly. Fig. 5 shows the distribution of the excited modes and the excited length for each mode. The lighter composite riser requires a lower top-tension load to enable bottom tension to the riser. However, the lower transverse stiffness ((Ez*I)comp ¼ 11.816 M Nm2, (Ez*I)steel ¼ 15.021 M Nm2) and lower tension within the composite riser resulted in lower structural frequencies that make it more prone to VIV. The more significant modes for the steel riser are modes 3–7 (0.257–0.593 Hz) while those for the composite riser are modes 5–10 (0.254–0.509 Hz) whereby almost at least one-third of the riser is being excited. The much stiffer steel riser excited lower modes while the composite riser experienced more modes and higher modes to be excited which eventually corresponds to higher RMS strains and stresses for the riser. With this regard, the composite riser materials should be able to withstand a very high number of fatigue cycles without catastrophic failure and be resilient against large strains-induced damage, due to the higher modes and modal curvatures experienced. Alternatively, fixtures may be designed to restrict the vibration amplitudes or to raise the stiffness of the riser so as increase the structural frequencies. A steel/composite/steel riser structure is an example whereby the steel plates help increase the

Fig. 5. Potentially excited modes and length contributions (Cases 1–2).

Fig. 6. RMS strains along riser span (Cases 1–2).

Fig. 7. (a) Displacement–time plot at 1050 m riser height (Cases 1–2). (b) Normalized amplitude plots at 450 m riser height (Cases 1–2).

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structural frequencies while the sandwiched composite material help reduce overall density of the riser. There is usually high hoop strength for composite risers due to the filament winding procedure used in creating the CFRP cylinders. It is recommended that the winding angle be increased so as to improve the transverse stiffness of the cylinders to mitigate the effects of VIV. Fig. 6 shows the RMS strains along the riser span. It is observed that the composite riser experiences 25.5% higher RMS strains than the steel riser and the higher values occur near the top and bottom of the riser. Chen et al. (2012) also investigated the effect of varying riser tension and stiffness, based on time-domain analysis, and concluded that modal amplitudes may be larger at regions with lower tension. Kim (2007) also concluded in his study that severe local loads tend to be at the bottom of the riser near to the stress joint at the well, and at the mean water level whereby waves act across the riser. Appendix A provides the values of normalized displacement amplitudes and RMS values for comparison. The tension factor, a ratio of the applied top tension to the total effective weight of the riser is also provided in the Appendix. It is noted that despite the steel riser having lower displacement amplitudes and RMS strains than the composite riser, its RMS stresses are much higher due to the higher modulus of steel. The plots of transient riser displacements at the riser height of 1050 m and normalized amplitudes plots of Ay/D against Ax/D at 450 m are shown in Fig. 7. Fig. 8 shows the maximum MTP values plotted onto the failure envelopes of the composite and steel riser joints. The steel material has yield strength of 464.5 MPa and two curves are provided to depict failure boundaries for riser joints of 8 mm and 10 mm thicknesses. Two other envelope curves based on the failure of composite layup and titanium liner are plotted. Unlike

Fig. 8. MTP values from global analyses plotted onto failure envelopes of riser joints (Cases 1–2).

isotropic materials, failure of the riser wall does not occur in a concurrent manner, since it consists of multiple material systems, i.e. composite and steel. It is seen that the curve of the titanium liner falls completely within that of the composite layup, suggesting that the liner material is the weakest link for the composite riser design. Kim (2007) also reported that regardless of loading scenarios, considerable amount of loads are transferred from the termination of a joint to the steel liner. As a result, the derived failure envelopes for composite riser will show a smaller failure envelope for the metallic liner (i.e. the liner will yield first), followed by matrix cracking and fiber fracture in the composite later on. Fig. 8 shows that if tension failure is the primary consideration, then a steel riser of 8 mm thickness would provide the same threshold as the liner of the composite riser. However, a steel riser of 10 mm thickness will be required to attain the same strength as the composite riser against pressure failure. Both Kim’s (2007) and our conclusion reveals that it may be possible to extend the use of composite joints to locations that are subjected to more intense loads, such as in stress joints where steel joints are currently utilized. 4.2. Effects of buoyancy modules on steel risers As discussed in the preceding section, long and thick steel risers would require greater applied top-tension. This raises cost due to increased requirement for higher tension capacity of the platform rig. Further, excessively long steel risers could also fail due to its own weight. Buoys can be used to resolve the issue and their placements along the riser may be critical for design against VIV and fatigue damage. In this study, the effect of buoyancy modules on steel risers is investigated. Table 5 shows the parametric cases involved in the study of buoyed risers. The length, outer diameter, density and modulus of the buoyancy modules are provided in the table. The tube-in-tube modeling technique in AbaqusTM is used, whereby the buoyancy element is fitted over the riser element so that individual riser and buoy properties can be applied. Buoyancy and drag effects due to the added buoy modules are included. For simplicity, the buoy elements are constrained rigidly to the riser for this study, although slippage between elements may be modeled. For the study, the outer diameter of the buoy is twice the riser diameter and the effective density of the buoy material is 500 kg/m3. The steel risers have a thickness of 17 mm and the static drag coefficient used is 0.6. The incident current profile is top-sheared with a current magnitude of 1.2 m/s at the bottom of the riser that rises steadily up to 2.4 m/s at the top of the riser. Fig. 9a–b show the riser model with distributed buoys and with five 36 m buoys located at the bottom end of the riser. Cases 3–6 compare the mechanical responses of a bare riser to a riser with distributed buoys, and buoys at bottom and top portion of the riser respectively. For the distributed buoy riser, thirty buoyancy modules, each 6 m long, are uniformly distributed at 42 m apart from one another, over the entire span of the riser.

Table 5 Specifications for buoyancy modules study. Cases Inner diameter (ID) (m) 3 4 5 6

0.28

Outer diameter (OD) (m)

0.314

Riser thickness Current (m/s) (m)

0.017

1.2–2.4 (top sheared)

Top-tension applied (kN) 1825.0 1256.9 1256.9 1256.9

Material Buoy distribution

Steel

Buoy diameter & properties

No – Yes (30B, 6 m span, 42 m gap) Yes (5B (BOT), 36 m span, 2xriserOD, 500 kg/m3, 42 m gap) 1.5 GPa Yes (5B (TOP), 36 m span, 42 m gap)

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

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Fig. 9. (a) Riser with distributed buoyancy modules. (b) Riser with five long buoys at one of the ends.

For the latter two cases, five long buoys 36 m each and 42 m apart are situated at the bottom and top of the riser respectively. All three cases have exactly 180 m of the riser covered with buoyed material (12% coverage). The addition of the buoyancy modules reduced the amount of required top-tension from 1460.2 kN to 1256.9 kN so as to achieve the same tension at the riser bottom end. Fig. 10a shows the plot of riser deflection due to current drag and top-tension. Intuitively, the riser with no buoys resulted in a lower deflection due to a smaller hydrodynamic diameter. The buoyancy modules have a larger hydrodynamic diameter that will induce greater current drag and riser deflection. The maximum deflections are 25.95 m, 27.79 m, 27.19 m and 27.27 m for the bare riser, distributed buoys, bottom five buoys and top five buoys cases respectively. The distributed buoys case resulted in the greatest riser deflection, while the other buoyed riser cases resulted in slightly lower deflections. The maximum deflections are located at 707.8 m, 698.25 m, 722.25 m and 662.25 m from the top of the riser, respectively for Cases 3–6. The results show that when buoys are evenly distributed, a slight upward shift of the maximum deflection location is expected due to the buoyancy effect of the buoys. For buoys situated at the bottom, the location of maximum riser deflection will be shifted downwards. While buoys at the top of the riser will shift the peak riser deflection location slightly upwards. Fig. 10b shows the tension distribution along the risers due to both top-tension load and current drag. Due to the higher density of steel, the resulting axial stress distribution is a sloped line and utilization of buoys shifted the gradient of the tension line to make it more vertical. The tensile stresses at the top of the riser are about 250 MPa. It is observed that placement of buoys at only a portion of the riser will effectively cause a kink in the stress distribution plot. The buoyed regions will experience a more constant tension distribution, whereas the regions with only the bare riser exhibit a greater linear variation of tension along the riser. Also observed is that riser regions within the wrapped buoys

experience lower stresses due to numerical constraints affixing the buoy elements to the riser elements. This provided slightly greater stiffness to these regions and as a result the inner riser elements experienced lower stresses. In contrast, the riser elements near buoy edges experienced slightly greater stress due to stress concentration effects. Lastly, it is shown that the riser with buoys located at the top, will experience greater overall tension, while the riser with buoys at the bottom will experience lower overall tension along the riser. The eigenvalue analysis is conducted prior to the VIV step. Fig. 11 shows the distribution of the excited modes and their extent of influence over the riser span. With the large hydrodynamic diameters of the buoy modules, the resulting Strouhal frequencies at the buoyed regions will be lower given the same current magnitude, as dictated by fs ¼StU/D. If same top-tension load is applied, then the added tension from the buoys will raise structural frequencies of the riser that will in turn lower the reduced velocities for the various modes. From our study, with the Strouhal frequencies largely reduced at the buoyed regions, considerable segments of the riser are correspondingly excited at lower modes. As a result, the riser with distributed buoys has a more spread out number of excitable modes than the riser with no buoys. For the riser with distributed buoys, modes 10–14 (0.870– 1.22 Hz) have a more dominant excitation length contribution, while modes 10–14 (0.852–1.269 Hz), and modes 8–13 (0.717– 1.144 Hz) are for the cases with buoys at the bottom and top of the riser, respectively. Fig. 12 shows the RMS strains along the riser span. The riser with distributed buoys performed worse than the no buoys case, as seen by the larger RMS strains. This corroborated with results from the tension distribution plot (Fig. 10b) and eigenvalue analysis which show that the buoyed riser has an overall lower tension and also a more gradual pick-up in harmonic frequencies which resulted in higher modal curvatures to be excited within the riser and hence higher RMS strains. Numerous spikes along the RMS plot are also observed which correspond to values obtained

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Fig. 11. Potentially excited modes and their length contributions (Cases 3–6).

Fig. 12. RMS strains along riser span (Cases 3–6).

Fig. 10. (a) Static riser deflection due to top-tension and form drag (Cases 3–6). 10 (b) Tension along riser due to top-tension and drag (Cases 3–6).

from riser elements near the edges of buoyancy modules that are rigidly constrained to the steel riser. This is expected since additional buoy drag and inertia on the constrained edges (geometric discontinuity) will result in greater localised bending strains. Intuitively, the higher the modal section curvatures occurring along the riser, the greater will be the amplification of strains at the buoy edges. The riser elements that are wrapped within the buoy elements generally also yielded higher RMS strains. Although the Strouhal frequencies are lowered at the buoyed regions, the current drag on the buoys (due to the high flow velocities applied)

has resulted in significantly higher RMS strains to the riser at these regions. The peak RMS strains for Cases 4 (626.6 με) and 5 (738.8 με) are close while that for Case 6 (buoys at top of riser) gives much higher RMS strains of 937.1 με. The higher RMS strains for Case 6 are due to the top-sheared current incident on the riser. Estimations of the strain amplification factors are obtained by normalizing the spike values with values at the immediate unbuoyed riser parts. The factors obtained for Cases 4 and 5 are between 1.7 and 2.2, while those obtained for Case 6 have an upper value of around 2.4, especially for the topmost buoy. The strain amplification, in general, depends on exact local geometry of the buoys or joints, and also on how they are attached to the riser. The values presented herein serves to merely illustrate the effects of buoys on the riser. The study shows that having long or large buoys at the top of the riser is detrimental to its fatigue life if a top-sheared current is expected to be incident on the vertical riser. A riser with buoys designed to be at the bottom yields about the same maximum RMS strains as one with distributed buoys along the span of the riser. Our analysis shows that if additional riser tension is required via buoyancy modules, and high top-layer currents are expected, then such modules may be situated at the bottom-half portion of

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

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Fig. 13. Normalized amplitude plots at 450 m (left), and 900 m (right) riser heights (Cases 3–6).

Fig. 14. MTP values from global analyses plotted onto failure envelopes of riser joints (Cases 3–6).

the riser, and as a continuously buoyed region instead of short discrete buoys separated with gap spaces. Appendix A provides the normalized displacement amplitudes and RMS values for comparison. The maximum RMS values are obtained with consideration of the effects due to the implementation of the buoyancy modules. It is noted that the maximum displacement amplitude and maximum RMS value may occur at different locations, since for a small displacement the riser may experience high RMS strains at the regions close to the buoyancy modules. Fig. 13 compares the A/D plots taken at the riser height of 450 m and 900 m. Although the same current profile is incident on the riser, differences in the locations and distribution of the buoyancy modules resulted in plots with slightly different shapes. Notably, Cases 3 and 6 have a figure "8"-shaped profile at 450 m while Case 5 has a flipped “C”-profile at 900 m. Fig. 14 shows the maximum MTP values plotted onto the T–P and M–T failure envelopes of the 17 mm thickness steel riser joint. The failure envelopes detail the combinations of applied tension, moment and pressure loads where the riser will fail. The steel material has a yield strength of 464.5 MPa. The figures show that despite the amplification effects on the buoyed risers, the MTP values are within the failure envelope although the bending moments yielded a slightly lower safety factor of 2.5 compared to the safety factor for tension which is 3.78. 4.3. Effects of current profiles on riser responses It is expected that the current profiles incident on the riser span has direct effect on riser response. Atadan et al. (1997) reported parametric studies on the riser response due to effects of riser

flexural rigidity and ocean currents and concluded that a larger current magnitude will increase the riser displacements. In this study, three current profiles are used. The Ormen Lange profile, adapted from Herfjord et al. (2002) and Norsk Hydro (2001), is taken from a one-year return period current profile for the Ormen Lange field that is located in the Storegga region off mid-Norway, close to Norwegian Seas. The Gulf of Mexico profile is obtained from Nowlin et al. (2001), which exhibits a “necking” at around 400 m due to loop eddy currents in the top layer. Deep water reserves in this region are far larger than shallow water fields, and the average production is twelve times that of shallow fields (Baud et al., 2002). The bidirectional current is a linearly sheared current with opposite current directions at sea surface and seabed. It is found west of Shetland that is due to a residual warm flow northeast-ward in the upper layer and a southwestern cold flow in the lower layer (Rustad, 2007). The linear bidirectional shear current is introduced to investigate riser behaviors for a wider range of environmental conditions. It is noted that the Shetland profile has a uniform shear gradient (current change per unit riser length) while the other two profiles have varying shear gradients along the riser. The carbon-fiber reinforced composite risers have a thickness of 20.335 mm and the same internal diameter of 0.28 m as the steel risers, assuming the same flow/production capacity. The applied top-tensioned load is 375 kN and is such that a small bottom-tension of around 30 MPa will be experienced by the risers’ lower end. Table 6 shows the parameters used in the study and Fig. 15 shows the profiles of the different currents incident along the riser span. The resulting riser deflections due to current drag on the top-tensioned risers are shown in Fig. 16.

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L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

Table 6 Specifications for current profiles study. Cases Inner diameter (ID) (m)

Outer diameter (OD) (m)

Riser thickness Current (m/s) (m)

7 1 8

0.28

0.32067

0.020335

Ormen Lange (max.@ 1.2 m/s) Gulf of Mexico (max.@ 1.2 m/s) Shetland (max. @ 1.2 m/s)

Top-tension applied (kN)

Material

Static drag coeff. Ends boundary (Cd) conditions

375.0

Composite 0.6

Pin

Fig. 15. Ormen Lange, Gulf of Mexico and Shetland current profiles.

The Ormen Lange current induces the greatest riser deflection of 20.32 m, at around 675 m from the riser’s top end, due to the overall higher current drag. The Gulf of Mexico current induces a maximum riser deflection of 13.33 m, but at the lower portion of the riser, at around 973.5 m from the riser’s top end. The location for maximum riser deflection is directly related to the current profile incident on the riser and the drag coefficient used. The riser deflection profiles indicate that the Ormen Lange current is more detrimental towards riser static deflections since a large portion of its deflection curve lies beyond the deflection curve for Gulf of Mexico (GoM). It is also observed that despite the GoM profile having a larger current magnitude near the bottom of the riser than the Ormen Lange, this does not translate to a significant increase in riser deflection for the portion of 1200 m to 1500 m below seawater surface. The Shetland current profile produced an “S” shaped deflection with the maximum riser deflection of 6.18 m occurring at 1222.5 m from the riser’s top end. The local maxima occurring at the top portion of the riser is 5.65 m at 277.5 m from the riser’s top end. Despite having equal current magnitudes from the mid-span, the bottom maxima will be higher due to the linear varying tension along the riser with the bottom portion of the riser having less tension than the top due to the weight acting on the riser. Eigenvalue analysis is next performed for the extraction of frequencies for the riser model. The structural frequencies are compared with the Strouhal frequencies to determine the modes and locations of the riser where lock-in excitation will occur. Fig. 17 shows the spread of the potentially excited modes and the excited length of the riser for each mode. The 3D analysis will result in modes that come in matched pairs thus the results presented in Fig. 17 are

Fig. 16. Static riser deflection due to top-tension and form drag (Cases 7, 1 and 8).

Fig. 17. Lock-in modes and their length contributions (Cases 7, 1 and 8).

for the unique modes, while the RMS strains will usually depict more modes due to consideration of strains from both the cross-flow and inline directions. The Shetland profile resulted in a more spreaded

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

contribution of modes while the Gulf of Mexico profile resulted in a more skewed distribution, with a larger portion of the riser being excited at mode 5–10 (0.25–0.51 Hz). The Ormen Lange profile resulted in a significant portion of the riser being excited at three

Fig. 18. RMS strains along riser span (Cases 7, 1 and 8).

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distinct eigen-frequencies of mode 6–8 (0.37–0.5 Hz). The spread of excited modal frequencies depends largely on the range and how sheared the current profiles are and also on the specified lock-in bandwidth (25% lock-in bandwidth is used in our case). Fig. 18 shows the RMS strains obtained along the 1500 m composite riser from the dynamic VIV step. Appendix A shows the compilation of maximum normalized displacement amplitudes, A/D, and the RMS stresses and strains for the cases. The profiles of RMS strains along the riser are directly influenced by the incident current applied on them. The Shetland profile generated the greatest RMS strains with high values occurring at the riser’s ends. The maximum RMS strain of 577.7 με and RMS stress of 33.51 MPa was generated near the bottom of the riser. High RMS strains are observed at the mid-span of the riser due to very low current drag at this region. It is noted that the case with the highest static riser deflection does not necessarily result in highest RMS bending strains, as observed from Appendix A and Fig. 16. The number and extent of contributing modes play a part on the resulting RMS strains and stresses. The Shetland current condition resulted in higher structural modes to be excited due to lower drag experienced at the mid-span. The higher modal curvatures and high drag at the riser’s ends contributed to the corresponding higher RMS values. The riser tension distributions revealed that the Shetland profile induces the lowest tension in the riser among the three cases. The Gulf of Mexico and Ormen Lange profiles generated maximum RMS strains of 314.2 με and 422.5 με respectively at the top of the riser. Their corresponding maximum RMS stresses are 18.22 MPa and 24.51 MPa. Fig. 19 shows the normalized amplitude plots of Ay/D against Ax/D at 300 m and 1200 m riser height. It is observed that the applied current conditions have a direct impact on the shapes of the amplitude–time curves and normalized A/D responses. For the

Fig. 19. Normalized amplitude plots at 300 m (left), and 1200 m (right) riser heights (Cases 7, 1 and 8).

Fig. 20. MTP values from global analyses plotted onto failure envelopes of riser joints (Case 7, 1 and 8).

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L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

case with the Shetland current, the plot obtained at 300 m and 1200 m of the riser appear to be reflections of each other along the Ay/D ¼0 and Ax/D ¼0 axes (See Fig. 19). This is because the transient cross-flow and in-line displacements at the bottom and top of the riser are moving in opposite directions due to the bidirectional current profile applied to the riser. The overall area encompassed by both the plots is about the same. With the Ormen Lange current, the bottom portion of the riser encompassed a larger area than the top portion of the riser, where the encompassed area has somewhat an inverted triangular shape. For case with Gulf of Mexico current, the two plots seemed to encompass the least areas out of the three cases. The maximum moment, tension and pressure (MTP) values extracted from the global analyses are next plotted on the failure envelopes obtained from detailed local analysis of the riser joint. Fig. 20 shows the two envelope curves based on the failure of composite layup and titanium liner of the CFRP composite riser. It is seen that the curve of the titanium liner falls completely within that of the composite layup, suggesting that the liner is relatively vulnerable. This is because the liner is stiffer than the composite layup and it bears considerable loads especially when the riser section is subjected to bending and axial tension. In order to fully utilize the strength of composite layup, it is suggested that a softer, fatigue and wear resistant material may be used for the liner. The extreme design condition assuming that maximum moment, tension and pressure occurs at the same time and location is used to plot the points. It is seen that the points fall below the region for liner yielding and the design provides a good safety margin to compensate the localized stress concentration arising from joint connectors and metal-composite interface (MCI).

Fig. 21. Tension along riser due to top-tension and drag (Cases 9–11).

Table 7 Bulk liner and equivalent riser properties.

4.4. Composite risers with different metallic liners

Aluminum liner E ¼70 GPa Equivalent composite riser Ez ¼ 41.537 GPa νzr ¼ 0.256 Gzr ¼ 17.766 GPa ρ ¼ 1870.57 kg/m3

ν ¼0.35

ρ¼ 2700 kg/m3

Er ¼58.772 GPa νrθ ¼ 0.306 Grθ ¼ 3.244 GPa

Eθ ¼ 11.425 GPa νzθ ¼ 0.377 Gzθ ¼ 3.071 GPa

Composite materials are not expected to possess perfect fluid tightness, and usually additional liners are used as barriers against

Steel liner E ¼210 GPa

ν ¼0.30

ρ¼ 7750 kg/m3

Equivalent composite riser Ez ¼ 74.257 GPa νzr ¼ 0.265 Gzr ¼ 30.821 GPa ρ ¼ 3071.26 kg/m3

Er ¼92.067 GPa νrθ ¼ 0.304 Grθ ¼ 3.31 GPa

Eθ ¼ 12.052 GPa νzθ ¼ 0.353 Gzθ ¼ 3.13 GPa

Titanium liner E ¼120 GPa

ν ¼0.33

ρ¼ 4500 kg/m3

Equivalent composite riser Ez ¼ 53.263 GPa νzr ¼ 0.265 Gzr ¼ 22.368 GPa ρ ¼ 2292.56 kg/m3

Er ¼70.708 GPa νrθ ¼ 0.304 Grθ ¼ 3.285 GPa

Eθ ¼ 11.754 GPa νzθ ¼ 0.364 Gzθ ¼ 3.108 GPa Fig. 22. Lock-in modes and their length contributions (Cases 9–11).

Table 8 Specifications for metallic liners study. Cases Inner diameter (ID) (m)

Outer diameter (OD) (m)

Riser Current (m/s) thickness (m)

9 10 11

0.28

0.32067

0.020335

Top-tension applied (kN)

Gulf of Mexico 255.83 (max @ 1.2 m/s) 594.91 375.00

Material

Composite (Al liner) Composite (steel liner) Composite (Ti liner)

Static drag coeff. (Cd)

Ends boundary conditions

Riser orientation

0.6

Pin

Vertical

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

Fig. 23. Static riser deflection due to top-tension and form drag (Cases 9–11).

Fig. 24. Comparison of RMS strains between codes (Cases 9–11).

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the fluids. The bonding between liner and structural composite laminate is critical, since debonded areas are vulnerable to failure due to stress build up at the interface (Ochoa, 2006). In order to contain the fluid in the interior safely, design community has adopted the concept of internal metal and/or polymeric liners (Ochoa and Salama, 2005). The design should minimize the loads directed to the liners since the composite structure is supposed to undertake most of the mechanical loads. The Magnolia composite riser project reported the manufacture and qualification of composite riser joints with titanium liners. The joints were subjected to one million cycles of rotating bending fatigue. The joint did not fail illustrating the robustness of the design. The design was selected for the demonstration of composite risers in the Gulf of Mexico on Magnolia Field at about 1500 m depth (Ochoa and Salama, 2005). With regard to the mechanical performance, information on static deflections and RMS values from VIV analyses will provide insights on how each composite riser with different metallic liners will respond. For this study, aluminum, steel and titanium liners of 5 mm thickness each are separately combined with the 20-ply composite layer and an anti-corrosion layer of thicknesses 13.335 mm and 2 mm respectively. The schematic of the multilayer riser is given in the inset of Fig. 21. The liner properties and the equivalent riser properties are provided in Table 7. In general, the steel liner has both the highest modulus and density. Table 8 shows the parameters used for the study. The Gulf of Mexico current with a peak magnitude of 1.2 m/s is used across the three cases. The applied top-tension load is such that the bottom of the riser experiences the same magnitude of tension. The analysis is for vertical top-tensioned risers that have pinned–pinned end conditions. No buoys are implemented since the composite risers are much lighter than steel ones. It is observed from Table 8 that the composite riser with steel liner requires a top-tension load of 594.9 kN while the one with aluminum liner requires the least top-tension of 255.8 kN to exact same magnitude of tension at the riser bottom. Fig. 21 shows the axial stress distribution on the risers due to top-tension and current drag. The stress distributions are generally linearly-varying despite the irregular profile of the Gulf of Mexico current. This observation was also reported by Kim (2007) who additionally commented that most composite risers will experience insignificant amount of bending moment cause by static current drag and tension because of the long lengths of the riser. The risers yielded different stress gradients due to different equivalent modulus and density. The composite riser with steel liner has the least constant axial stress distribution along the riser due to larger mass while the riser with aluminum liner yielded the most constant axial stress distribution. Fig. 22 shows the distribution of the excited modes and the excited riser length for each mode. The 25% bandwidth is used for all the cases

Fig. 25. MTP values from global analyses plotted onto failure envelopes of riser joints (Cases 9–11).

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L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

analyzed. The distribution pattern is a characteristic signature of the Gulf of Mexico current profile applied to the riser, as already noted in Section 4.3. This characteristic of mode-length signatures may be used as a coarse qualitative indicator on the severity of riser vibration caused by different current profiles. From the mode-length distribution plot, the greater and higher the number of modes and lengths expected to be excited, the more severe the vibration the riser will expect to experience. The distribution pattern and frequencies are very similar for the three cases, with modes 5–10 (0.249–0.54 Hz) having greater excitation length contributions. Fig. 23 shows the static deflection of the risers after application of top-tension and current drag. As the hydrodynamic and strength diameters are the same for the three cases, the extent of riser deflection is entirely due to the effective riser stiffness and overall tension within the riser. The riser with steel liner has the lowest deflection of 11.59 m while the riser with aluminum liner has the highest deflection of 14.83 m. The locations of maximum deflection are 919.5 m, 973.75 m and 943.25 m from the top of the riser for Cases 9, 10 and 11 respectively. For the context of the applied GoM current, stiffer and greater tensioned risers will shift the maximum deflection location downwards away from the midspan, while a less-stiff riser will shift the location towards the midspan. It is noted that a change of the liner from steel to aluminum material, with other parameters constant, will result in a 28% increase in maximum riser deflection. The maximum RMS strains and stresses obtained from the timebased VIV step are given in Appendix A. Comparison of RMS values with another in-house frequency-based VIV solver and with the commercial Shear7™ software shows that the presented results provides the same trend and conclusions as from other solvers, despite having predictions of slightly lower values. Fig. 24 shows the plot of maximum RMS strains among the three codes. All codes predicted the location of maximum RMS strains to be at the top one-tenth portion of the riser. Although the riser with aluminum liner yielded highest RMS strains of 472.5 με, its corresponding RMS stress is the lowest due to lower equivalent moduli for the aluminum liner riser. In contrast, although the steel liner riser has the lowest maximum RMS strains of 304.6 με, its RMS stresses are the highest. The titanium liner riser yielded neither highest stresses nor strains. It has about 20% lower RMS strains than the aluminum liner riser and 10% lower RMS stress than the steel liner riser. For design against fatigue failure, aluminum has the lowest fatigue S–N curve making it the weakest material out of the three in terms of fatigue strength. There is typically no endurance limit for aluminum alloys meaning that any increase in stress amplitudes experienced by the material will be sensitive to its resulting reduction in fatigue life. Steel and titanium alloys have endurance limits which means that any stress amplitude fluctuations below these thresholds will effectively not have an effect on fatigue life of the component (Boyer, 2006). Practically, the liner thickness and riser designs should ensure that the admissible cyclic stresses are below their endurance limits. The high yield strength of steel (464.5 MPa) and titanium (410 MPa) make them better candidates for liner material. The lower density of titanium alloys ( 40% lighter than steel) and their hardness and resistance to wear and corrosion make them a better choice over steel if price is not a factor. Fig. 25 shows the MTP values plotted onto failure envelopes of composite risers with different metallic liners. The figures show that the MTP values are within the failure envelopes although pressure values yielded a lower safety factor of 1.75. The riser displacement–time and normalized amplitude plots are similar to those presented in Section 4.3, where the Gulf of Mexico current is also applied. As previously concluded, these plots are most affected by the incident current profile, tension distribution along the riser, and the riser ends boundary conditions. These factors also influence the distribution pattern of excited modes along the riser span.

5. Conclusions The global–local analysis approach is developed to investigate the coupled fluid–structure responses of 1500 m steel and composite risers. The results from the coupled fluid–structure scheme match reasonably well with the experimental data from the fullscale riser tests which ascertains the methodology used. The validation exercise allows us to set the values of the model and numerical parameters, and leads to the choice of the appropriate coupling model. The performance of composite risers under several real current conditions are investigated which shows the Shetland current profile inducing the greatest RMS strains of 577.7 με. The distribution pattern of the excited riser lengths for each mode is a characteristic of the incident current profile and may be used as an indicator of severity of riser vibration. The failure envelopes of the internal liners fall within that of the composite layers, which reveals that the liner is the weakest link for composite riser design. Our results reveal that the composite riser may be more vulnerable to vortex-induced-vibration (VIV) and hence fatigue damage. The composite riser sees greater number of modes and higher modes being excited, given the same environmental conditions, due to its lower eigenfrequencies. This inadvertently translates to high RMS strains. In our study, the composite riser yielded 25.5% higher RMS strains than the steel riser. A conclusion is that the prospective riser material should withstand a very high number of fatigue cycles without catastrophic failure and be resilient against large-strain induced damage. A suggestion to increase the fiber-winding angle for riser cylinders may help improve its transverse stiffness for better load bearing and raise eigenfrequencies so as to mitigate VIV. It is found that the composite risers have a relatively constant distribution of tension. This implies that locations for riser failure might be more dispersed, making localized enhancements difficult. Active VIV suppression devices may have to be considered to dynamically seek out and attenuate high localized strains. Buoyancy modules have large hydrodynamic diameters that induce large current drag on the riser but also reduced the Strouhal frequencies which allow lower structural modes to be excited. Our results show that partial implementation of buoys along the riser will cause kinks in the initial linear riser tension distribution. The modules are also not recommended at the top of the riser if high toplayer currents are expected, unless structural restraints are used. Instead, they are better implemented at the bottom-half portion of the riser and as a continuously buoyed region instead of short buoys separated by gap spaces. High bending strains can occur at buoy edges and the stress concentration problem may be mitigated using buoys with more gradual tapers or improved attachment methods to reduce force transfer to the riser. Longer modules with smaller diameters are also preferred over short larger diameter ones for the mitigation of VIV. The titanium liner riser yielded 20% lower RMS strains than the aluminum liner riser and 10% lower RMS stress than the steel liner riser. The lower density of titanium alloys and their wear and corrosion resistance make them a better choice over steel.

Acknowledgements The authors gratefully acknowledge the support from Singapore A*STAR (Agency for Science, Technology and Research) through the project no. 1123004033 for MIMO (Materials Innovation for Marine & Offshore Applications).

Appendix A See Table A1.

L.B. Tan et al. / Ocean Engineering 94 (2015) 19–35

Table A1 Normalized displacements and RMS values for all cases. Cases Max Ay/D

Max Ax/D

Max. RMS strains (με)

Max. RMS stress (MPa)

Riser material

Top-tension factor (TTF)

*#1 #2 ∧ 3 ∧ 4 ∧ 5 ∧ 6 *7 *8 þ9 þ10 þ11

0.353 0.216 0.230 0.249 0.228 0.219 0.331 0.366 0.390 0.314 0.355

314.2 250.3 380.8 626.6 738.8 937.1 422.5 577.7 472.5 304.6 384.9

18.22 50.05 76.16 125.32 147.77 187.42 24.51 33.51 19.63 22.62 20.50

Composite Steel Steel Steel Steel Steel Composite Composite Composite Composite Composite

1.0491 1.1802 1.1334 0.7806 0.7806 0.7806 1.0491 1.0491 1.0735 1.0305 1.0491

1.085 0.622 0.795 0.889 0.818 0.759 1.034 1.186 1.185 0.954 1.085

# Composite versus steel riser. Steel risers with buoyancy modules. * Effect of current profiles. þ Composite risers with different metallic liners.

∧

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