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Abstract

Risers with high-grade steel are widely used in offshore oil and gas industry at present. The extreme weight, lower fatigue and corrosion resistance of steel risers significantly limited the exploitation depths and the production capacity. Nowadays, it is acknowledged that using fibre-reinforced polymer composites to manufacture risers can be a better option. The prototypes of composite risers fabricated and tested confirm that fibre-reinforced polymer composites have an obvious advantage over steel risers on weight saving. Three different approaches are developed here to minimise composite risers’ weights: (1) enhancing the riser with only axial-direction and hoop-direction fibre; (2) off-axis reinforcements are included using an iterative approach of manual inspection and selection and (3) employing the optimisation technique of surrogate-assisted evolutionary algorithm. These design approaches have been applied to eight different material combinations to achieve the minimum structural weight by optimising their laminate configurations. The designs are conducted in accordance with the Standards, considering both local load cases and global – functional as well as environmental loads using ANSYS 15.0. The results show that comparing with steel risers, weight savings achieved by different design approaches and material combinations are different.

Keywords

Composite riser design optimisation surrogate-assisted evolutionary algorithm offshore engineering design of fibre-reinforced polymer composite materials

Introduction

Risers act as a transport component between the sub-sea wellheads and the production platforms by transporting fluids/gas (production riser) or guiding a drilling stem and conducting the drilled fluids upwards (drilling riser). In top-tensioned risers (TTR), a tension is applied at the top to maintain the position vertically and reduce the compressive stresses. Production risers with high-grade steel are widely used in offshore oil and gas industry at present. However, the weight of steel risers limits their length and hence prevents offshore operations from moving into deeper sea. Reducing individual risers’ weight will facilitate the exploitation of natural resources from deeper waters as well as installation of more risers on existing platforms, thereby increasing their production capacities.

It is well known that using fibre-reinforced polymer (FRP) composites instead of steel will lead to weight reduction, thereby providing lower operational costs. Also, FRP composites have advantages in fatigue, corrosion and thermal properties compared with steel, providing additional profits in maintenance costs. Furthermore, the design of composite riser can be tailored according to specific conditions since they have different possibilities in liner materials, composite material combinations, stacking sequences of laminate, as well as fibre orientations. However, the use of composites for offshore risers also introduces challenges and added complexities to design and analysis.

Over the last three decades, several design studies and projects regarding the application of fibre-reinforced composites in the manufacture of pipe segments for offshore risers have been conducted. Initially, Ahlstone¹ patented a drilling riser filament-wound structure including an internal liner made from glass fibres coated with an epoxy resin in 1973. In the 1980s and 1990s, projects which demonstrated and proved the mechanical capacities of the composite riser tube were carried by the Institut Francais du Petrole (IFP) and Aerospatiale of France² and National Institute of Standards and Technology (NIST) Advanced Technology Programs (ATPs).³ In the Heidrun Tension Leg Platform (TLP) (July 2001), a demonstration composite riser joint was installed in three typical locations of a drilling riser string for the first time and operated for about 45 days functionally.⁴ In March 2003, Magnolia Project was subsidised by ChevronTexaco, Kvaerner Oilfield Products and ConocoPhillips,⁵ which found the weakness of steel liner’s pressure integrity.⁶ For more recent projects, thermoplastic composite riser tubes were developed and ±55° reinforced angle layers were included to increase burst resistance.⁷

These prototypes confirm that FRP composites definitely surpass steel in saving weight for risers. However, most of the designs used only the axial and hoop fibre reinforcements and made no attempt to optimise a laminate configuration to minimise structural weight. As one of the main advantages of fibre-reinforced laminate construction is that the reinforcement orientations in individual laminae can be tailored to maximise load-carrying capacity, it appears reasonable that by including composite layers reinforced in the off-axis directions and tailoring the configuration, including the lamination sequence, fibre orientations and thicknesses of individual layers, greater weight savings and, thereby, economic benefits can be achieved.

In this article, a composite riser is designed based on the requirements in the Gulf of Mexico for the extraction of natural resources from a depth of about 2000 m. The laminate configurations (including their inner liners) are optimised for minimum weight using three different design procedures developed specifically for this purpose, namely, conventional design, manually tailored design and surrogate-assisted evolutionary algorithm (SAEA) optimisation design. All the design procedures have been conducted using finite element (FE) program ANSYS 15.0. Three stages are contained in every design procedure, which are local design stage, global analysis stage and structural verification stage. In the stages 1 and 3, elements of solid185-homogeneous and solid185-layered are utilised to model the liner and composite laminate of the local riser section, respectively. Solid185 is a three-dimensional (3D) element, defined by eight nodes having 3 degrees of freedom at each node. The element has plasticity, hyperelasticity, stress stiffening, creep, large deflection and large strain capabilities. The difference between solid185-homogeneous and solid185-layered is that solid185-homogeneous is defined by the orthotropic material properties, while solid185-layered supports anisotropic material properties and the layered section can be defined by ANSYS section commands. In the global analysis, elements of pipe288 are employed to model the whole length of the riser, which is a linear, quadratic or cubic two-node pipe element having 6 degrees of freedom at each node and well-suited for linear, large rotation and/or large strain non-linear applications.

As the configuration of a composite riser is very complex and involves many variables, its design involves three stages, the first of which is the design of the local geometry of the composite tube (lamination sequence and thicknesses of the liner and the composite layers) under local loads. It is necessary to perform the local design first to obtain initial estimates of the geometric configuration of riser’s lamination, as the forces and moments in the riser with global loads are influenced by its large deformations which depend on the sectional geometry of the tube. Once the local geometry is tentatively established, the design proceeds to the second stage which is an analysis of the entire riser with the effect of global loads to determine the pivotal load combinations and locations. In the stage of global analysis, the use of layered elements for a 2 km long riser becomes computationally expensive due to the large number of elements required to satisfy the element aspect ratio constraints of the FE software; hence, pipe288 with effective properties obtained from the local design is employed. The third stage of the design is structural verification to test the riser’s capacity with the effects of combined forces, pressures and moments, as determined from the global analysis. If the factors of safety (FSs) do not meet the design specifications, these sections are redesigned and the entire design process is repeated. Eight different material combinations are studied in this article.

In section ‘Design specifications, approaches and material selection’, design specifications, three design approaches and material selections are introduced. The local and global design results using all three different design approaches are presented in sections ‘Local design of composite riser’ and ‘Global design of composite riser’, respectively. Finally, comparison of results using the three design approaches is presented in section ‘Comparison of results’.

As the depth from which oil or natural gas is extracted increases, longer risers have to be employed which dramatically increases the load on a production platform due to the higher top tension required to support the weight of the risers and the greater power required for extraction. Thus, the benefits due to weight savings offered by composite materials are more apparent and significant for deep-sea applications. Hence, a deep-sea scenario with an extraction depth of about 2000 m is selected for the design study. It should be noted that the proposed design procedure can easily be adapted to risers of different lengths by considering the appropriate load.

Design specifications, approaches and material selection

The load scenarios, load factors for the local loads, environmental and operational loads, and the FSs employed all comply with the American Petroleum Institute (API), American Bureau of Shipping (ABS) and Det Norske Veritas (DNV) recommendations.^8–11

Riser geometry

In offshore engineering terminology, a rigid TTR normally consists of different segments (relatively short pipes with connectors at either end) called ‘joints’. Apart from standard riser joints, a TTR will have a tension joint at its top and a ball/flex connector or stress joint at its bottom. For this article, a TTR system with a stress joint at the bottom is considered.

Since the ball/flex connector and the stress joint occupy only a small portion of the length of the riser and their geometry is more involved due to the requirements for their connections to the rest of the system, standard configurations made of high-strength (HS) steel are assumed for them. This research focuses only on the savings of weight brought by FRP composites for the standard riser joints.

The internal diameter (ID) of the riser joints is fixed at 250 mm. The outer diameter varies from joint to joint depending on the wall thickness of segment determined by the design. Each composite riser joint consists of an inner liner, a composite structural body and an external sacrificial layer (Figure 1).

Figure 1.

Cross section of composite riser joint.

In actual designs, fairings are employed on riser joints to suppress vortex-induced vibrations. In this study, fairings are assumed to be present from the mean sea level up to a depth of 624 m below sea level and their weight is considered in determining the loads. The metallic tension joint at the top and metallic stress joint at the bottom are retained. Since the external liner and sacrificial layers of the composite riser joints have no contribution to load bearing, only their weights are taken into account in the analysis. The total length of the riser is taken to be 1970.1 m.

Design loads

The riser has to be designed to withstand local loads, such as internal and external pressures and tensions, as well as global loads, such as buoyancy, wave, current and platform displacement loads. To identify the load specifications for the design, the riser is considered to be installed on an offshore rig in the Gulf of Mexico as the environmental conditions and typical functional loads on a TTR riser with a length of about 2000 m for this situation are readily available in the literature.^8,9,12–16 It may be noted that the tension to be applied at the top depends on the riser’s weight and geometry.

In general, the design loads can be divided into two categories: local loads, which govern the burst, tension, collapse and buckling capacities of the riser joints (tubular segments) and global loads, which determine the overall structural capacity of the riser. The local loads are considered in the first stage (local design) to determine the laminate configurations (which are rechecked and if necessary changed in the final stage of structural verification), and the global loads are employed in the second (global design) stage.

Local load cases

In terms of the local design, four local load cases (LLCs) are considered:^17,18

LLC 1: burst (internal pressure with end-cap effect is 155.25 MPa);

LLC 2: tension ((1) pure maximum tension force and (2) tension with external pressure. Here, the tension force is based on the risers’ geometries and the fluid inside, and external pressure is 19.5 MPa);

LLC 3: collapse (external pressure is 58.5 MPa); and

LLC 4: buckling (external pressure is 58.5 MPa).

Environmental situations and global load cases for composite riser designs in Gulf of Mexico

As shown in Figure 2, for a TTR, a tension is applied to its top to keep its vertical position and eliminate compressive stresses along its length. Besides the tension force, risers are also subjected to wave and current loads, buoyancy, gravity, hydrostatic pressure, the internal pressure and motions of a floating platform or ship.

Figure 2.

Loads on a top-tensioned riser system.

Environmental loads on a riser system consist of wave loading, current profiles and platform motions. As wave and current loads lead to the movement of a TLP, this movement has to be included in the global load cases (GLCs) and can be expressed as equation (1)^14,19

$S (t) = S_{0} + S_{L} \sin (\frac{2 π t}{T_{L}} - α_{L}) + \sum_{n = 1}^{N} S_{n} \cos [k_{n} S (t) - ω_{n} t + \emptyset_{n} + α_{n}]$ (1)

where $S_{0}$ is the mean displacement of platform, $S_{L} \sin ((2 π t / T_{L}) - α_{L})$ is the low frequency motion of platform, $S_{n} \cos [k_{n} S (t) - ω_{n} t + \emptyset_{n} + α_{n}]$ is the wave frequency motion of platform, $S_{L}$ is the mean displacement of platform of low frequency motion, $T_{L}$ is the period of platform low frequency motion, $α_{L}$ is the phase angle between the low motion and wave (normally equal to 0), $S_{n}$ is the mean displacement of platform of wave frequency motion, k is the wave number, $ω$ is the frequency of wave (rad/s), $\emptyset$ is the initial phase angle of wave and $α$ is the phase angle between the wave frequency motion and wave.

Using equation (1), the TLP displacements in the global analysis are calculated as equations (2)–(4) and are applied in the FE model (transient dynamic analysis) as a dynamic displacement boundary condition.

Condition of 1-year storm

$X = 38.4 + 1.83 \sin (0.0314 t) + 0.656 \cos (- 0.698 t - 1.378)$ (2)

Condition of 100-year hurricane

$X = 115.2 + 6.77 \sin (0.0314 t) + 14.77 \cos (- 0.4486 t - 1.694)$ (3)

Condition of 100-year loop current

$X = 172.7 + 0.61 \sin (0.0314 t) + 0.557 \cos (0.785 t)$ (4)

In addition, the riser also bears other pressures and functional loads. As a conservative way of considering the combination of all the environmental loads is to assume that waves, currents and platform movements all act in the same direction (the environmental heading). This assumption is used for all the events analysed in this study.

The GLCs based on the actual working situations up to a depth of about 2000 m in the Gulf of Mexico employed in the global analyses of all the risers considered in this article, in accordance with the riser design codes and previous riser design projects,^8,9,12–14 are tabulated in Table 1.

Table 1.

Global design load cases for the riser system.

Global load cases	Riser condition	Fluid density (kg/m³)		Internal pressure (MPa)^a		Sea water density (kg/m³)	Design environment	Mean TLP movement (m)	Tension ratio
Global load cases	Riser condition	Annulus	Tubing	Annulus	Tubing	Sea water density (kg/m³)	Design environment	Mean TLP movement (m)	Steel riser	Composite riser
LC1	External pressure test	0	NA^b	0	NA	1030	1-year winter storm	38.4	1.5
LC2	Shut-in pressure test	800	NA	69.0	NA	1030	1-year winter storm	38.4	1.5
LC3	Shut-in with leak^c	800	NA	58.6	NA	1030	1-year winter storm	38.4	1.5
LC4	Shut-in with leak^c under hurricane	800	NA	58.6	NA^b	1030	100-year hurricane	115.2	1.5	2
LC5	Maximum production with leak^c	800	NA	58.6	NA^b	1030	100-year loop current	172.7	1.5	2
LC6	Well killed^d 1	1860	NA	35.7	NA^b	1030	100-year hurricane	115.2	1.2	1.5
LC7	Well killed^d 2	1860	NA	35.7	NA^b	1030	100-year loop current	172.7	1.2	1.5
LC8^e	Shut-in under hurricane	0	800	0	58.6	1030	100-year hurricane	115.2	1.5	1.2 + end effect of external pressure
LC9^e	Maximum production	0	800	0	58.6	1030	100-year loop current	172.7	1.5	1.2 + end effect of external pressure

TLP: Tension Leg Platform.

The internal pressure at the bottom end of the riser is the maximum internal pressure.

NA stands for no tubing.

The load cases with leakage consider failure of the tubing and all pressures are applied to the riser wall.

For the well-killed situation, the production tubing is removed and mud inserted into the whole riser annulus.

For load cases 8–9, the weight of the production tubing is considered.

Selection of materials for composite riser

It is important to ensure that the matrix and fibre reinforcements selected can satisfy the long-term requirements.¹⁷ A production riser used in offshore engineering must ensure fluid tightness. In general, additional liners made with corrosion and abrasion resistant materials are utilised to prevent fluid leakage.²⁰ As the purpose of the liner is to maintain fluid tightness, the loads directed to the liner should be minimised¹⁷ and, when a thermoplastic polymeric liner is used, the same material should be used as the matrix for the fibre-reinforced structural tubular wall to avoid debonding;⁷ when metal liners are used, the manufacturing process should be carefully monitored. In general, an external liner and sacrificial glass fibre layers may be added to prevent corrosion and be against environmental effects brought by seawater, ultraviolet (UV) radiation, and so on.¹⁷

Overall, the FRP composites studied in the present riser design include four different polymer matrix and fibre combinations, while thermoplastic polyether ether ketone (PEEK), steel, and titanium and aluminium alloys are considered for the inner liner. The mechanical properties of the unidirectional laminae (elastic constants and long-term strengths) and the liner selected for the design study are listed in Tables 2 and 3, respectively.

Table 2.

Unidirectional lamina properties.

Composite	Fibre volume	Density ρ (kg/m³)	E₁ (GPa)	E₂ = E₃ (GPa)	G₁₂ = G₁₃ (GPa)	ν₁₂ = ν₁₃	G₂₃ (GPa)	ν ₂₃
AS4-epoxy (938)²¹	0.60	1530	135.4	9.37	4.96	0.32	3.20	0.46
AS4-PEEK (APC2)²²	0.58	1561	131.0	8.70	5.00	0.28	2.78	0.48
P75-epoxy (938)²³	0.60	1776	310.0	6.60	4.10	0.29	2.12	0.70
P75-PEEK (APC2)²⁴	0.55	1773	280.0	6.70	3.43	0.30	1.87	0.69
Composite	$σ_{1}^{T}$ (MPa)		$σ_{1}^{C}$ (MPa)	$σ_{2}^{T}$ (MPa)		$σ_{2}^{C}$ (MPa)	τ₁₂ (MPa)
AS4-epoxy (938)²⁵	1732		1256	49.4		167.2	71.2
AS4-PEEK (APC2)²²	1648		864	62.4		156.8	125.6
P75-epoxy (938)²³	720		328	22.4		55.2	176.0
P75-PEEK (APC2)²⁴	668		364	24.8		136.0	68.0

PEEK: polyether ether ketone.

Subscript 1: fibre direction; subscript 2: in-plane transverse; subscript 3: through-thickness direction; superscript T: tension; superscript C: compression.

Table 3.

Liner material properties.

Liner	Density (kg/m³)	Modulus of elasticity (GPa)	Poisson’s ratio	Yield stress (MPa)	Ultimate stress (MPa)	Elongation at break (%)
PEEK (Victrex)	1300	3.64	0.40		120	50
Steel X80	7850	207	0.3	555	625	5.868
Titanium (Ti-6Al-4V)	4430	113.8	0.342	880	950	14
Aluminium (1953T1)	2780	71	0.3	480	540	7.5

PEEK: polyether ether ketone.

The above liner and composite body materials lead to eight material combinations for this study as listed in Table 4.

Table 4.

Material combinations considered for design.

Configuration	Fibre	Matrix	Liner material
1	AS4	PEEK	PEEK
2	P75	PEEK	PEEK
3	AS4	Epoxy	Steel
4	P75	Epoxy	Steel
5	AS4	Epoxy	Titanium
6	P75	Epoxy	Titanium
7	AS4	Epoxy	Aluminium
8	P75	Epoxy	Aluminium

PEEK: polyether ether ketone.

Design approaches for composite riser

The composite riser design is conducted by three stages: (1) a local design under the four LLCs with layered elements (3D-solid185); (2) a global analysis of the entire composite riser under GLCs with pipe elements (1D-pipe288) to determine the pivotal load combinations and locations and (3) a structural verification of determined pivotal locations with layered elements (3D-solid185) under the critical load combinations.

In this study, the design criterion is the first ply failure which uses maximum stress failure criterion.²⁶ The distribution of only the in-plane stresses in every composite lamina is determined for each load case since the thickness of each individual layer is small and the stresses in the thickness direction are relatively small.¹⁶

Three different design approaches are developed for the local design of a composite riser: (1) the conventional design which is an ‘orthogonal’ method with only hoop and axial reinforcements; (2) the manually tailored design which includes hoop, angular and axial reinforcements and (3) tailored design using population-based SAEA^27,28 for weight optimisation.

All the material system combinations listed in Table 4 are designed using the three procedures to determine the optimum geometries for achieving minimum weight. In all the procedures, the minimum thickness of ply is determined by the first ply failure which uses maximum stress failure criterion.²⁶ Also using the FE model, the investigated configuration’s buckling pressure is determined by an eigenvalue buckling analysis. In order to achieve the minimum weight for the given load cases, both local and global, an iterative procedure is applied to adjust all the design variables until the minimum FS is just above the allowed value.

The design variables and their ranges for the composite riser joints are as follows: (1) t_liner: liner’s thickness (6–12 mm for the PEEK liner and 2–8 mm for the metal liners); (2) t₀: 0° (axial) layers’ thickness (0–2.5 mm); (3) t_θ; ±θ° (angular) layers’ thickness (0–2.5 mm); (4) t₉₀: 90° (hoop) layers’ thickness (0–2.5 mm); (5) ±θ°: ±θ° (angular) layers’ angles (0°−90°) and (6) n-stacking sequence (n₁ = [0/±θ/90], n₂ = [0/90/±θ], n₃ = [±θ/0/90], n₄ = [±θ/90/0], n₅ = [90/0/±θ] and n₆ = [90/±θ/0]) (Figure 3). To optimise the composite riser joint’s geometry, the riser’s structural weight should be minimised with the required conditions which make up the optimisation constraints. Figure 4 shows the flowchart of the steps involved in the design processes, noting that only axial and hoop fibre orientations are considered in the first approach, the other two design approaches consider off-axis fibre orientations, with the optimisation performed by manual examination in the second approach and using SAEA in the third approach.

Figure 3.

Finite element model of composite tube and coordinate system.

Figure 4.

Flowchart for the design process.

For the conventional design approach: (1) initial estimate of composite layers’ thicknesses based on LLC1; (2) adjust composite lamina thicknesses with guessed value of liner thickness based on 3D FE analysis under LLC1; (3) repeat step 2 with different liner thicknesses and (4) repeat steps 2 and 3 for all the LLCs.

For the manually tailored design approach: (1) determine the initial optimum angle and layers’ thicknesses based on LLC1; (2) re-estimate the thicknesses of layers and optimum angle based on 3D FE analysis under LLC1; (3) add the axial layers and determine stacking sequence under LLC2; (4) repeat finite element analysis (FEA) for LLC1 to add hoop layers and determine stacking sequence; (5) repeat steps 3 and 4 until the riser meets the requirements of both LLC1 and LLC2; (6) reduce the thicknesses of angle plies and (7) the design is checked for all the LLCs.

For the SAEA optimisation design approach: (1) create the initial training database through design of experiment (DOE); (2) employ SAEA to determine an ‘optimised’ result; (3) verify the solution from step 2 using FEA, if it fails go to step 5; otherwise, go to step 4; (4) compare the results from step 3 with manually tailored design’s results, if it is better, it is the best results; otherwise, go to step 5; (5) determine and set true constraints, load capacities and objective values to modify the initial training database and (6) repeat the whole procedure until the best results are obtained.

Local design of composite riser

Stage of composite riser’s local design involves design of the composite pipe cross section, that is, determination of the number of plies, stacking sequence, layer thickness, fibre orientation and the liner thickness, required to ensure that the individual segments are able to withstand all four LLCs presented in section ‘Local load cases’. To determine the stress distributions and buckling capacity under all the LLCs, a 3D FE analysis of a local composite riser joint is conducted. During the stage, all the material combinations in Table 4 are designed to yield minimum acceptable margins of safety (FS of just above 1.0) and, thereby, provide minimum structural weights. All the three different approaches (described in section ‘Selection of materials for composite riser’) are employed to achieve the minimum weight of the eight material combinations.

The FE model

Composite tubes’ stress and buckling analyses under the four LLCs are carried out using 3D FE modelling with ANSYS 15.0. Homogeneous isotropic solid elements (3D-solid185-homogeneous) are utilised for the liner and layered solid elements (3D-solid185-layered) for the composite laminate (Figure 3). With rigid body motions constrained, axial displacement of the tube is fixed at one end but free at the other.

Based on convergence studies, there are 50 elements per meter in axial direction and 80 elements in circumferential direction. The tube’s ID is 0.25 m. For the length of the segment modelled, 5 m is used for buckling analysis and 3 m for stress analysis. Substantially, the local design of composite riser comprises of performing stress analysis (LLCs 1–3) and buckling analysis (LLC 4), with different laminate configurations and liner thicknesses, determining their FSs, and changing the laminate configuration and thicknesses either by manual selection or using the optimisation procedure to achieve FS of just over 1.0. For the first three load cases, the FS is defined in terms of stresses and in the buckling case it is defined in terms of the buckling pressure, as given below

$F S_{local load cases 1 - 3} = \frac{σ_{allowable}}{σ_{actual}}$ (5)

$F S_{local load cases 4 - buckling} = \frac{P_{allowable}}{P_{design}}$ (6)

where $σ_{allowable}$ is the allowable stress in LLCs 1–3, $σ_{actual}$ is the actual stress in LLCs 1–3, $P_{allowable}$ is the allowable buckling pressure in LLC 4 and $P_{design}$ is the design buckling pressure in LLC 4.

Results of local design for AS4/epoxy riser with titanium liner

The local design results of AS4/epoxy riser with titanium liner are compared here to demonstrate the effect of different design approaches. The composite risers’ geometries utilising conventional design, manually tailored design and SAEA optimisation are presented in Table 8 (section ‘Comparison of results’). The values of the thicknesses and angles of the liner and the composite layers for the minimum required FS of 1.0 obtained from the three different design approaches are plotted in Figure 5. The labels t_liner, t₀, t₉₀ and t_θ represent the lamina thicknesses of the liner, 0° plies, 90° plies and the off-axis plies, respectively. For the conventional design, there are only 90° (circumferential) and 0° (axial) layers alternatively. Different stacking sequences of the angle plies and axial and circumferential plies were analysed, and it was found that [0/±θ/90] is the most efficient stacking sequences for both manually tailored design and SAEA optimisation design. Contrary to the netting theory’s prediction that the optimum reinforcement angle is ±54.7°, the best reinforcement angle found is ±53° (or ±53.4°), according to the 3D FE analysis.

Figure 5.

Optimum thicknesses and angles of the composite layers and liner from the three designs.

From Figure 5 and Table 8, we can see that the conventional design resulted in a FRP composite laminate thickness of 37.5 mm; the manually tailored design gave a composite laminate thickness of 28.5 mm and the SAEA optimisation yielded a composite laminate thickness of 28.33 mm; and in all cases, the titanium liners are 2 mm. It is seen that compared to the conventional design, both manually tailored and SAEA optimisation designs lead to a 23% weight saving.

For illustration, Figure 6 shows the FS in each composite layer for the conventional, manually tailored and SAEA optimisation designs (layer1 – the most inside composite layer) in the fibre, transverse and in-plane shear directions, obtained for a typical LLC of burst.

Figure 6.

FSs of composite layers under burst load for AS4/epoxy with titanium liner in (a) fibre direction, (b) transverse direction and (c) in-plane shear for conventional design, manually tailored design and SAEA optimisation design.

The FSs for the titanium liner for LLC 1 (burst case) are 1.08, 1.07 and 1.08 for the conventional, manually tailored and SAEA optimisation designs, respectively. It can be seen that for all three design approaches, the transverse stresses are more critical. The min FSs in the fibre direction are 1.74 (layer 1), 1.65(layer 14) and 1.64 (layer 14) for the conventional, manually tailored and SAEA optimisation designs, respectively; the min FSs in the transverse direction are 1.00 (layers 20 and 21), 1.01 (layers 3 and 17) and 1.00 (layers 3 and 17) for the conventional, manually tailored and SAEA optimisation designs, respectively; and about 2.16 (layer 4) and 2.18 (layer 4) in shear for manually tailored and SAEA optimisation design, respectively.

The FSs in each composite layer for the conventional, manually tailored and SAEA optimisation designs under the other LLCs 2–4 have been obtained as well. It is found that the FSs in all the layers for LLCs 2 and 3 are much higher than 1.0, and the FS of buckling (LLC 4) is much larger than 1.0 as well, which means that the burst load (LLC 1) is the most critical LLC for AS4/epoxy composite with titanium liner. Since the FSs in transverse direction are much lower than those in other directions, for this material combination, the most critical failure mode is matrix cracking. Note here, the detailed results for LLCs 2 and 3 are not provided due to space limitations.

Remarkably, the safety margins are much lesser in both manually tailored and SAEA optimisation designs, indicating that they are more efficient. From former study,²⁸ these two design approaches also have similar local load capacity.

Global design of composite riser

This section presents global design of composite risers with the geometries of the composite tubes obtained during the stage of the local design. The two stages in global design are as follows: (1) global analysis of the entire riser with different GLCs and (2) structural verifications of its critical sections identified from global analysis.

The stage of global analysis considers different load combinations, including movement of platform, wave and current loads, buoyancy, hydrostatic and internal pressures, gravity, and top tension force, which are illustrated in Figure 2 and listed in Table 1. In this section, only the extreme conditions (GLC4–GLC9) are considered since the FS for each composite layer and liner that satisfy them will automatically satisfy the less severe global conditions (GLC1–GLC3). The riser’s critical sections and the forces and moments acting on them are identified in this stage. Then, a final structural verification of riser’s pivotal sections with the forces and moments got in global analysis is conducted and discussed.

The FE model

The tension joint (top), stress joint (bottom) and three standard riser joints (around sea level) are subjected to very high stresses. Therefore, they are the same as those in the steel riser, that is, made from high-grade steel (X80) and with the same geometries, including lengths, diameters and thicknesses. For the global analysis, the geometries of all the other (composite) standard riser joints (laminate sequences, ply thicknesses and orientations) are kept the same as determined in section ‘Local design of composite riser’ from manually tailored and SAEA optimisation designs. This entire riser configuration is shown in Figure 7.

Figure 7.

Composite riser configuration for global analysis.

The global design is performed only for manually tailored and SAEA optimisation designs’ configurations of the three most promising material combinations and not for the conventional geometries, since the latter require much higher thicknesses for the same material combinations than the tailored geometries.

During the global analysis, pipe element 288 in ANSYS 15.0 is used to model the entire composite riser. The wave and current loadings are applied by selecting the option ‘ocean loads’ and providing inputs of the water depth (1931.2 m), water density (1030 kg/m³), wave period (GLCs 1–3: 9 s, GLCs 4, 6 and 8: 14 s, GLCs 5, 7 and 9: 8 s), wave height (GLCs 1–3: 9.08 m, GLCs 4, 6 and 8: 23.25 m, GLCs 5, 7 and 9: 2.1 m), wave length, wave theory (airy wave theory), current velocity (GLCs 1–3: 0.36 m/s, GLCs 4, 6 and 8: 1.22 m/s, GLCs 5, 7 and 9: 2.13 m/s), current location, drag coefficient (1.0 and 0.7 for the bare riser joints and joints with fairings, respectively), coefficient of inertia (2.0), and so on. As Pipe288, being a one-dimensional (1D) element, does not have restrictions on its aspect ratio, each element can be quite long and only few numbers of elements are required to model the entire riser (1970.1 m). In this study, only 2127 elements are employed for the entire composite riser in the global analysis. The option of non-linear dynamic analysis is chosen to take the dynamic effects of platform’s movement and environmental loads into consideration. Ball and slip support conditions are applied at the top and the fixed support condition at the bottom of the riser. As the ball and slip supports allow rotations and displacements, the top tension forces and displacements of the platform can be used. The fixed support condition at the bottom is achieved by applying fixed constraints to the elements which simulates a wellhead under the mud-line (Figure 7).

Effective material properties for composite riser tube

Geometric parameters, that is, liner thickness, lamination stacking sequences, fibre orientations and laminate layer thicknesses employed in global analysis are those determined from its local design. In order to model the composite riser using pipe elements, the 3D effective properties for composite riser tube are calculated and utilised.

The classical laminated plate theory (CLT) is effective while investigating thin composite laminates, and for moderately thick laminates, higher-order plate theories are normally utilised to increase the accuracy of analysis. However, the CLT and higher-order plate theories are constrained to two-dimensional (2D) analysis and are improper in calculating 3D properties.²⁹ Therefore, a MATLAB code of 3D laminate property theory^29,30 is created for calculating composite tube’s 3D effective properties.

Table 5 presents the composite tube’s 3D effective properties employed in global analysis, where the axial, hoop and radial directions are referred by subscripts x, y and z. These homogenous constants are based on the 3D lamina and liner material properties presented in section ‘Design specifications, approaches and material selection’ and composite tubular geometries obtained from the local design stage in section ‘Local design of composite riser’.

Table 5.

3D effective properties of composite tubes used in global analysis.

Name	ρ_effective (kg/m³)	E_x_{_tension} (GPa)	E_x_{_bending}^a (GPa)	E_y (GPa)	E_z (GPa)	G_xy (GPa)	G_xz (GPa)	G_yz (GPa)	ν_xy	ν_xz	ν_yz
AS4/PEEK-PEEK liner (0/±52/90)	1513.3	30.40	29.00	50.28	9.59	16.44	2.46	2.75	0.251	0.378	0.284
AS4/PEEK-PEEK liner (0/±51/90)	1512.8	30.56	29.25	55.77	9.58	16.22	2.48	2.76	0.255	0.379	0.286
AS4/epoxy-Ti liner (0/±53/90)	1700.8	40.50	36.50	66.25	12.01	22.84	4.10	4.35	0.275	0.344	0.272
AS4/epoxy-Ti liner (0/±53.4/90)	1700.1	40.62	36.78	66.74	12.00	22.55	4.12	4.36	0.28	0.346	0.275
AS4/epoxy-Al liner (0/±53.5/90)	1599.8	41.40	37.20	64.12	11.92	20.57	4.07	4.28	0.254	0.349	0.293
AS4/epoxy-Al liner (0/±53.4/90)	1599.2	41.58	37.47	64.61	11.92	20.37	4.08	4.29	0.25	0.351	0.295

PEEK: polyether ether ketone.

From static FEA.

It is necessary to note that the effective bending and tension moduli (E_x_{_bending} and E_x_{_tension}) can be significant different for a composite laminate. In this article, in terms of AS4/PEEK with PEEK liner, an average value of 29.7 GPa is utilised, since the distinction between E_x_{_bending} and E_x_{_tension} is smaller than 5%. For the other two material combinations, both E_x_{_bending} and E_x_{_tension} are applied to verify the worst-case scenario because their E_x_{_bending} and E_x_{_tension} are quite different.

GLCs for composite riser

The GLCs are the combinations of different riser conditions and environmental loads. For analysis, the extreme GLCs 4–9 listed in Table 1 are used for analysis since the FSs of their liners and composite layers which satisfy these extreme conditions will satisfy the less severe conditions of the global design.

The environmental situation and platform movement data in Gulf of Mexico used for composite riser design are exactly same as those for steel riser design.^16,31 The coefficient of inertia (C_M) is set to 2.0 for all the joints and the value for C_D (normal drag coefficient) is taken as 1.0 for the bare riser joints and 0.7 for the joints with fairings, respectively, as recommended by design standards.^8,13

The top tensions applied in different GLCs are according to the composite risers’ effective weights. The effective weight of a riser is a function of the density of its different material combinations, wall thicknesses and different contents in the riser. The top tension ratios for different GLCs are given in Table 1.

Results of global analysis for AS4/epoxy riser with titanium liner

As an example, this section presents detailed global design results for the riser with the AS4/epoxy composite with titanium liner analysed using its effective 3D properties with pipe elements for the laminate configuration and thickness combinations which provide the minimum structural weight, as achieved in section ‘Local design of composite riser’ (the stage of local design). The results of global analysis under different GLCs are presented below.

The distribution of internal and external pressures is the functions of riser’s depth for all GLCs (equations (7) and (8)). Since pressure distribution is not dependent on the materials of the risers, they are same for all the design conditions in this article

$P_{internal} = P_{shut - in} + ρ_{internal_fluid} gh$ (7)

$P_{external} = ρ_{sea_water} gh$ (8)

In Figures 8 –10, the distributions of tension, bending and shear are illustrated, which are evaluated from the stage of global analysis for GLC4 to GLC9, respectively. It should be noted that only the magnitudes of tension, bending and shear within composite section (from −44 to −1904 m) are concerned in this study.

Figure 8.

Tension forces for different load cases for (a) manually tailored design and (b) SAEA optimisation design.

Figure 9.

Bending moments for different load cases for (a) manually tailored design and (b) SAEA optimisation design.

Figure 10.

Shear forces for different load cases for (a) manually tailored design and (b) SAEA optimisation design.

From former studies,^28,32 the results of global analysis are slightly different when E_x_{_bending} and E_x_{_tension} are different. Hence, in this article, only the results with worst-case scenario are presented.

Figure 8(a) and (b) shows the distributions of tension force along composite material sections for manually tailored and SAEA optimisation designs, respectively. From Figure 8(a), the maximum tension force is 3378.1 kN (with bending modulus) at the top end of the composite material sections, which occurs under GLC4 for the manually tailored design. As can be seen in Figure 8(b), the maximum tension force is 3373.5 kN (with tension modulus) at the top end of the composite material sections, which occurs under GLC4 for the SAEA optimisation design.

Bending moment distributions along the composite material section are presented in Figure 9(a) and (b) for manually tailored and SAEA optimisation designs, respectively. It is clear in Figure 9(a), for the manually tailored design, the maximum bending moments (with tension modulus) are 59.1 kN m under GLC4 at the top of the composite material region and 72.6 kN m under GLC7 at the bottom of the composite material region. From Figure 9(b), the maximum bending moments (with tension modulus) are 57.7 kN m under GLC4 at the top of the composite material region and 72.8 kN m under GLC7 at the bottom of the composite material region for the SAEA optimisation design.

In Figure 10(a) and (b), the shear force distributions along the composite riser region are demonstrated for manually tailored design and SAEA optimisation design, respectively. Figure 10(a) shows that the maximum shear force (178.5 kN with tension modulus) happens at the bottom of the composite material part under GLC9 for manually tailored design. And in Figure 10(b), the maximum shear force (179.3 kN with bending modulus) happens at the bottom of the composite material part under GLC9 for SAEA optimisation design.

As an example, the stress distributions under GLC4 from ANSYS15.0 have been presented in Figure 11, since GLC4 is one of the three (GLC4, GLC7 and GLC9) most important GLCs. Figure 11(a) and (b) shows the axial stress distributions for manually tailored design and SAEA optimisation design, respectively. Figure 11(c) and (d) shows the hoop stress distributions for manually tailored design and SAEA optimisation design, respectively. It can be seen, under GLC4, the maximum axial stresses are 222 and 204 MPa at the top for the composite riser with manually tailored design and SAEA optimisation design, respectively; the maximum hoop stresses are both 309 MPa at the bottom for the composite riser with manually tailored design and SAEA optimisation design.

Figure 11.

Axial and hoop stress distributions under GLC4 for manually tailored design and SAEA optimisation design: (a) axial stresses for manually tailored design, (b) axial stresses for SAEA optimisation design, (c) hoop stresses for manually tailored design and (d) hoop stresses for SAEA optimisation design.

Based on the above analysis, for all the risers, the internal and external pressures raise with the increasing sea depth (equations (7) and (8)), while the tension forces reduce from top to bottom of the composite riser joints (Figure 8). Meanwhile, at the top or bottom of the composite riser joints section, the maximum bending (Figure 9) and shear (Figure 10) take place. Consequently, composite riser joints at top and bottom can be regarded as the most pivotal locations. To ensure structural integrity, final verification by local stress analysis is conducted based on the load combinations in these critical sections.

Results of structural verifications for AS4/epoxy riser with titanium liner

The pivotal load combinations in the critical locations are gained from the global analysis stage for the different GLCs. In the stage of structural verification, layered solid elements (3D-Solid185) are utilised again to conduct a local analysis of the critical locations with pivotal load combinations. To illustrate, Figure 12 presents the results of structural verifications for AS4/epoxy riser with titanium liner under combined GLC4 at the top section (layer1 – the most inside composite layer). Table 6 shows the identified load combinations for manually tailored and SAEA optimisation designs (GLC4 at the top section).

Figure 12.

FSs of composite layers under LC4_top for AS4/epoxy with titanium liner in fibre direction, transverse direction and in-plane shear for manually tailored design and SAEA optimisation design.

Table 6.

Critical load combinations at the top section under global load case LC4 for AS4/epoxy with titanium liner from global analysis for manually tailored design and SAEA optimisation design.

Load case	Designs	Tension (kN)	Internal pressure (MPa)	External pressure (MPa)	Shear force (kN)	Bending moment (kN m)
4	Manually tailored	3378.1	44.3	0.7	49.8	59.1
	SAEA	3373.5	44.3	0.7	50.7	57.7

SAEA: surrogate-assisted evolutionary algorithm.

For both design approaches, the min FSs of liner are 1.97. The min FSs in the fibre direction are 4.60 (layer 3) and 4.64 (layer 3) for manually tailored and SAEA optimisation designs, respectively; the min FSs in the transverse direction are 1.57 (layer 17) and 1.58 (layer 17) for manually tailored and SAEA optimisation designs, respectively; and about 10.59 (layer 13) and 10.93 (layer 4) in shear for manually tailored and SAEA optimisation designs, respectively.

Similar verifications for other critical locations with critical load combinations have been conducted as well. The min FSs of titanium liner and each AS4/epoxy composite lamina, and the GLCs in which they occur are listed in Table 7.

Table 7.

Minimum FSs for liner and composite layers of the AS4/epoxy with titanium liner with manually tailored design and SAEA optimisation design.

Design approaches	Liner		Composite layers – fibre direction			Composite layers – transverse direction			Composite layers – in-plane shear
Design approaches	FS	LC	FS	Layer	LC	FS	Layer	LC	FS	Layer	LC
Manually tailored design	1.97	LC4_T	4.37	3	LC6_T	1.57	17	LC4_T	3.94	13	LC6_T
SAEA optimisation	1.97	LC4_T	4.34	3	LC6_T	1.58	17	LC4_T	3.95	13	LC6_T

FSs: factors of safety; SAEA: surrogate-assisted evolutionary algorithm.

Minimum FS required: 1.53 for composite layers, 1.74 for PEEK liner and 1.68 for metallic liners.

The results confirm that geometries of composite riser obtained in the stage of local design utilising both manually tailored and SAEA optimisation designs are capable of satisfying global load requirements, as their FSs are just above standards’ requirements.¹¹

Comparison of results

The results from the different design approaches are compared for the three selected material combinations. In Table 8, the stacking sequence, each layer’s thickness (both liner and composite lamina) and structural weight are listed with three different design approaches. Also, the structural weight (170 kg/m) and thickness (25 mm) of a steel riser with the same inner diameter as required to meet the same design requirements³³ are presented in Table 8.

Table 8.

Comparison of local design for composite risers.

Material combination	Design method	Configuration	Thickness (mm)					Structural weight (kg/m)
Material combination	Design method	Configuration	Liner	0°	θ°	90°	Total	Structural weight (kg/m)
Steel		ID = 0.25 m					25.00	169.50
AS4/PEEK-PEEK liner	Conventional design	[liner/90/(0/90)₁₀]	6.00	1.165	0.00	1.85	38.00	52.41
	Manual tailored design	[liner/0₃/(+52.0,−52.0)₅/90₄]	6.00	1.48	1.30	1.64	30.00	39.93
	SAEA optimisation design	[liner/0₃/(+51.0,−51.0)₅/0₄]	6.00	1.24	1.36	1.64	29.88	39.75
AS4/epoxy-titanium liner	Conventional design	[liner/90/(0/90)₁₀]	2.00	1.385	0.00	2.15	39.50	59.56
	Manual tailored design	[liner/0₃/(+53.0,−53.0)₅/90₄]	2.00	1.70	1.64	1.75	30.50	45.71
	SAEA optimisation design	[liner/0₃/(+53.4,−53.4)₅/90₄]	2.00	1.77	1.61	1.73	30.33	45.46
AS4/epoxy-aluminium liner	Conventional design	[liner/90/(0/90)₁₀]	2.00	1.525	0.00	2.25	42.00	60.93
	Manual tailored design	[liner/0₄/(+53.5,−53.5)₅/0₄]	2.00	1.62	1.60	1.88	32.00	45.35
	SAEA optimisation design	[liner/0₄/(+53.4,−53.4)₅/90₄]	2.00	1.62	1.57	1.93	31.90	45.20

PEEK: polyether ether ketone; ID: internal diameter; SAEA: surrogate-assisted evolutionary algorithm.

From Table 8 we can see that the weight saving of riser section achieved using FRP composite materials ranges from 64% to 76% according to different material combinations and design methods. As can be seen in Table 8 and Figure 13, for all three material combinations, manually tailored and SAEA optimisation designs result in similar structural weights (both being significantly lower than the weight obtained using the conventional design) and their stacking sequences are exactly the same. Noticeably, the SAEA optimisation design gives marginally better weight savings (about 1%) than the manually iterated tailored design in every case. The main reason for this is that adding the manually tailored design results to the training database provides more accurate approximations but allows the optimisation procedure to converge to these points using surrogate models.

Figure 13.

Comparison of structural weights obtained from three different designs.

The improved structural weight obtained from the SAEA tailored design comes from small reductions in the overall thicknesses of the composite bodies compared with those from the manually tailored design, as shown in column 8 in Table 8. However, both these designs provide significant improvements in structural weight and thickness (over 20%) over the conventional design, as shown in Figures 13 and 14.

Figure 14.

Comparison of total thicknesses obtained for three designs.

Conclusion

The aim of this study is to demonstrate and quantify the weight savings obtained by tailoring composite riser’s design for deep-water offshore applications. In this article, composite risers are designed using eight different material combinations and their performances investigated, primarily through computational simulations. The results from three different design approaches are compared and it is demonstrated that both tailored designs (manually tailored and SAEA optimisation designs) can offer significantly greater weight savings than the conventional design in all cases. Meanwhile, the design results of FRP composite riser are compared to the conventional steel riser which has the same design requirements and it shows that the significant weight savings can be achieved by utilising FRP composite to replace the high-grade steel. This work and the companion paper shows that although all the composite material combinations considered offer weight savings over the steel riser, it is much more beneficial to use HS rather than high-modulus (HM) carbon fibre reinforcements as their failure modes are different. For HS (AS4) fibre reinforcements, failure is dominated by transverse stresses due to matrix cracking, whereas for HM (P75) fibre reinforcements, it generally occurs in the fibre direction. It may be noted that although this study specifically considers the TTR, other types of composite risers can easily and effectively utilise the same design approaches.

Footnotes

Academic Editor: Ismet Baran

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was funded by Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (BS2014SF013).

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Tailored design of top-tensioned composite risers for deep-water applications using three different approaches

Abstract

Keywords

Introduction

Design specifications, approaches and material selection

Riser geometry

Design loads

Local load cases

Environmental situations and global load cases for composite riser designs in Gulf of Mexico

Selection of materials for composite riser

Design approaches for composite riser

Local design of composite riser

The FE model

Results of local design for AS4/epoxy riser with titanium liner

Global design of composite riser

The FE model

Effective material properties for composite riser tube

GLCs for composite riser

Results of global analysis for AS4/epoxy riser with titanium liner

Results of structural verifications for AS4/epoxy riser with titanium liner

Comparison of results

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References