Delft University of Technology
A review on predicting critical collapse pressure of flexible risers for ultra-deep oil and gas production
Li, Xiao; Jiang, Xiaoli; Hopman, Hans DOI
10.1016/j.apor.2018.08.013
Publication date 2018
Document Version
Accepted author manuscript Published in
Applied Ocean Research
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Li, X., Jiang, X., & Hopman, H. (2018). A review on predicting critical collapse pressure of flexible risers for ultra-deep oil and gas production. Applied Ocean Research, 80, 1-10.
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A review on predicting wet collapse pressure of flexible
risers for ultra-deep oil and gas production
Xiao Li∗, Xiaoli Jiang, Hans Hopman
Department of Maritime and Transport Technology, Delft University of Technology
Abstract
Flexible riser is a key enabler for the oil and gas production in ultra-deep wa-ter which transports production fluids between floating production systems and subsea wells. As oil and production heads to water depths in excess of 3000 m, high hydrostatic pressure has been one primary challenge facing the riser operators. Excessive hydrostatic pressure may cause collapse failure of flexible risers and thus predicting the critical collapse pressure is of significant importance to their anti-collapse design. Collapse is a complex phenomenon related to the material properties, the geometry of the pipe and its overall surface topography. Those factors make the prediction of critical pressure of flexible risers challenging. Related prediction approaches of collapse pres-sure of flexible risers have been developed for decades, yet a comprehensive review of their predictive capabilities, efficiency and drawbacks is lacking. This paper reviews the recent advances on collapse studies of flexible risers and highlights the gaps in existing prediction methods, aiming to facilitate the current anti-collapse design of flexible risers and provide a baseline for their future utilization in deeper water expansion.
Keywords: flexible riser, ultra-deep water, collapse failure, critical pressure
1. Introduction 1
As the offshore oil industry continuously moves into ever deeper water, 2
there is an increasing demand for the development and qualification of pro-3
duction riser systems to enable this expansion. Flexible riser, a primary riser 4
∗Corresponding author.
device for floating production, is being required to meet such a demand. 5
Flexible riser is one kind of flexible pipes which transports fluid between 6
subsea facilities and topside structures [1], as shown in Fig. 1. It consists of 7
multiple layers of wound metal bands and extruded polymers. The polymeric 8
layers work as sealing, anti-wear and/ or heat-insulated components while the 9
metallic layers withstand the imposed loads, e.g. radial inward forces, inter-10
nal pressure and axial tension [2,3]. The function and the most commonly 11
used materials of each layer are listed in Table 1 [4,5]. This pipe-like struc-12
ture has been applied to shallow water production over four decades with an 13
established technology owing to the advantages of flexibility and corrosion 14
resistance. However, cost and technical challenges increase significantly with 15
water depth, requiring the development of the flexible riser technology. 16
Fig.1. Flexible riser [6] and its layer configuration [7]
Table 1. Name, material and function of each layer within a typical flexible riser
Layer Material Function
Carcass Duplex steel External pressure resistance
Pressure armour Carbon steel Hoop and radial load resistance Tensile armour Carbon steel Axial and torsional load resistance Inner sheath HDPE, XLPE, PA, PVDF Internal fluid containment
Outer sheath HDPE, PA, TPE External fluid barrier Anti-wear layer PA, PVDF, HDPE Abrasion resistance Insulation layer PP, PVC, PU Thermal insulation
High valued external pressure, which increases about ten atmospheres 17
for every 100 meters of water depth, makes flexible riser vulnerable to be 18
collapsed in deep water fields, especially for the curved portion within the 19
touchdown zone, as shown in Fig. 2 [8]. Anti-collapse capability is usually 20
regarded as an essential qualification factor for those ultra-deep water flexible 21
risers. With flexible risers being contemplated for water depths of nearly 3000 22
meters, their anti-collapse capability may govern riser design and the final 23
production cost [9,10]. 24
Fig.2. Touch down zone during installation [8]
In deep water applications, collapse due to external pressure is one of the 25
challenges to be addressed [11–13]. At present, a comprehensive overview of 26
collapse studies of flexible risers under deep sea environment is lacking. In 27
view of that, this paper is intended to introduce the development of collapse 28
studies of flexible risers and elucidate the limitations of existing available pre-29
diction methods, which is organized as: following the introduction, Section 30
2 clarifies the common collapse types of flexible risers in deep water and the 31
problems lie in standards with regard to the prediction of critical collapse 32
pressure. Section 3 is focused on the existing prediction approaches of criti-33
cal pressure of flexible risers while Section4elaborates the studies related to 34
the factors that affect the collapse resistance of the flexible risers. The final 35
section 5 concludes the work. 36
2. Collapse failure of flexible risers 37
Harsh operating environments in deep/ ultra-deep water fields impose a 38
variety of potential failure modes on flexible risers, such as collapse, burst, 39
lateral buckling/ bird-caging buckling and fatigue, etc. Among those different 40
failure modes, collapse failure is always a primary challenge for riser operators 41
to cope with. The anti-collapse capability of a flexible riser usually influences 42
the pipe wall thickness and governs the manufacturing cost. Additionally, 43
the replacement of a collapsed flexible riser is also very costly. Consider-44
ing that, the understanding of collapse failure and related riser performance 45
characteristics is important for designing reliable flexible riser systems [14]. 46
Collapse of flexible risers refers to radial buckling of the internal carcass 47
structures under external hydrostatic water pressure, as shown inFig. 3. This 48
failure is commonly divided into two types, dry and wet collapse, depending 49
on the annulus conditions of risers [15]. Dry collapse may occur when the 50
outer sheath is intact and all layers within the riser play a role together to 51
resist the collapse. In this scenario, the interlocked carcass and the pressure 52
armor are the main layers for collapse resistance, as they contribute the most 53
to radial stiffness. If the outer sheath is breached, the seawater floods the 54
annulus and then the external pressure acts directly on the inner sheath. 55
This situation, named wet collapse, represents the most extreme loading 56
conditions since the whole external loading is resisted by the carcass alone. 57
Normally, the interlocked carcass is designed to carry the whole full external 58
pressure with no failure. However, other layers, mainly the pressure armor, 59
could also contribute to its collapse resistance by acting as a constraint to 60
the radial displacement of the carcass. 61
According to the latest survey of flexible pipe failure/ damage mechanisms 62
carried out by O’Brien et al. [17], the outer sheath damage remains the 63
most common failure, as shown in Fig. 4. For the sections of flexible risers 64
lying on the seabed, their external sheath may be worn out due to many 65
small movements (see Fig. 5) [18]. This phenomenon increases the risk of 66
wet collapse and therefore requires that carcass layer, the main component 67
for collapse resistance, should be strong enough when facing a wet annulus 68
environment. 69
Various standards have been developed with regard to the design of flex-70
ible risers. Among them, API 17B and 17J are two widely acceptable speci-71
fications that issued by American Petroleum Institute [15,19]. For a flexible 72
riser applied for ultra-deep water production, however, those specifications 73
Fig.3. Collapse failure of the flexible riser [16]
Fig.4. Flexible pipe failure/damage mechanisms [17] Fig.5. Damaged outer sheath [18]
did not provide specific approaches for reference to calculate the critical col-74
lapse pressure of the carcass. In their latest versions (2014), no prescriptive 75
methodology was given to guide the anti-collapse design of the interlocked 76
carcass except a safety factor. It reveals that standardized methods have not 77
been established yet for the anti-collapse design of flexible risers and there-78
fore, how to predict the critical pressure is still a gray area for riser designers 79
[20]. 80
Over-conservative design of the carcass is adopted by riser manufacturers 81
to reduce the latent collapse risks of flexible risers in deep sea environment. 82
However, it leads to a heavier carcass, which needs more pairs of tensile ar-83
mor and payloads of floating vessels to withstand the additional weight. As 84
a result, it increases the costs in production, installation and operation[21]. 85
To improve the ultra-deep water performance of flexible risers, various 86
factors should be considered to address their current design limits. As one of 87
the key factors that generally governs final riser wall thickness, overall weight 88
as well as the costs, the critical pressure of the carcass is thus required to be 89
well-determined with reliable and sophisticated methodologies [22]. 90
3. Prediction approaches of critical pressure 91
Collapse studies have been conducted extensively by many researchers 92
since the inception of the flexible risers around the 1970s [23]. Experiments 93
are the most reliable way to predict the critical pressure of riser products. 94
Although such kind of experiments are costly, they are the foundation to 95
develop related analytical and numerical models. Buckling theories of rings 96
are adopted by researchers to develop the analytical models [14,24,25]. Most 97
of them are limited to simplified ring models due to the complexity of the 98
carcass profile [23]. By contrast, numerical simulation, such as Finite Ele-99
ment Analysis (FEA), has less limitations in modeling the carcass with its 100
actual profile and therefore, becomes a suitable alternative of expensive ex-101
perimental studies. Mostly, the prediction of critical pressure of flexible risers 102
is performed on numerical models, aided by the calibration of experimental 103
tests. 104
3.1. Hydrostatic tests 105
Over the past decades, some experimental programs have been performed 106
to assess the critical pressure of flexible pipes that prepared for deep water 107
environment. Although the experimental tests can be a reliable way to mea-108
sure the critical pressure of the flexible pipes, they require a substantial cost. 109
Besides, specialized hyperbaric chambers for such kind of collaspe tests are 110
quite few in the world [26]. For the most part, the experimental tests have 111
been an approach that help developing and calibrating the corresponding 112
numerical models. Souza [27] performed the collapse tests of flexible pipes 113
at the COPPE/UFRJ Submarine Technology Laboratory. The tests were 114
conducted in a horizontal hyperbaric chamber with a capacity of 10000 psi, 115
as shown in Fig. 6. The samples with two different internal diameters, 4 and 116
8 inches, were placed in that hyperbaric chamber and pressurized to collapse. 117
The curves of loading pressure versus time were recorded to validate the ef-118
fectiveness of her numerical models. Due to the internal diameter limitation 119
of that chamber, all the samples were test with no curvature. The test results 120
showed that the collapse might cause the opening of the interlocked carcass 121
layer but that opening would be negligible when there was a pressure armor 122
inside the pipe structures. 123
Fig.6. Hyperbaric chamber used in Souza’s experimental tests [27]
Since the flexible risers are curved in the touchdown zone, this curvature 124
effect weakens the anti-collapse capability of the riser structures. Clevelario 125
et al. [28] conducted curved collapse tests of flexible pipes to investigate 126
the curvature effect, as shown in Fig. 7. The samples with two different 127
internal diameter, 4” and 6”, were used for both straight and curved tests. 128
The carcass, inner liner and the pressure armor were remained in all the 129
samples while additional tensile armors were added to those curved ones 130
to withstand the axial compression loads generated by the reverse end cap 131
effect [29]. Those curved samples were bent to 1.5 times the storage bending 132
radius (SBR) [30] to investigate their curved collapse behavior under external 133
pressure. These test curvature radii were determined by the global analyses 134
of the test samples (see inFig. 8), which could not be reached in all possible 135
environmental and operational conditions. Each samples curved collapse 136
pressure was recorded and compared with its straight counterpart. The test 137
results showed that the reduction in collapse resistance of the samples caused 138
by curvature effect were higher than 10%, indicating the importance of pipe 139
curvature in the collapse analyses of flexible risers. 140
Fig.7. Curved collapse test samples [28] Fig.8. Global analysis result TDZ bend-ing radius histogram [28]
3.2. Analytical methods 141
Owing to the geometric complexity of the interlocked layer profile, an-142
alytical approach has been limited to highly simplified analytical models, 143
aided by experimental calibration. The main difficulty in using those analyt-144
ical models is always the necessity to determine an equivalent ring thickness 145
or width and, eventually, an equivalent material [31]. The equivalent ring 146
width method, proposed by Pesce et al.[32], is often used for crushing anal-147
ysis where the crushing loads were limited in a small region (shoes region) 148
[33]. For the collapse analysis with external pressure applied onto an “infi-149
nite length” flexible pipe, equivalent thickness is preferable since it is a plane 150
strain issue [34]. Therefore, various equivalent layer methods are developed 151
to provide a proper equivalent thickness for those analytical models. 152
Considering the helicoidal geometry of carcass imposes a directional de-153
pendency on the structural mechanical properties, a fictitious orthotropic 154
shell was built based on the analogy between grids and plates [35], as shown 155
in Fig. 9. This idea was first proposed by Cruz and Dias [36], who took the 156
strip spiral carcass layer as a grid with distinct stiffness in two orthogonal 157
directions. By assuming that both the shell and the carcass have the same 158
stiffness (membrane, bending and torsion), they determined the equivalent 159
properties of that orthotropic shell. 160
This method is often used to study the responses of carcass layer sub-161
jected to axial loads [37–39] or crush [3,40–42] due to the orthotropic me-162
chanical properties of the equivalent shell. Since the carcass layer, however, 163
withstands radial loads, mostly, the treatment of helical carcass wire as a 164
homogeneous ring by discarding its lay angle in collapse studies is more ac-165
Fig.9. Analogy between plates and grids [37]
ceptable to academics. Therefore, the lay angle effect on collapse problems 166
was neglected in the equivalent ring methods, allowing to solve the collapse 167
pressure with analytical ring models [43]. This effect was later investigated 168
by Gay Neto and Martins [34], which evidenced the fact that the lay angle 169
has negligible effect in collapse prediction. 170
In recent years, many equivalent methods were proposed in terms of one 171
property of the carcass, e.g. the cross-section area, the bending stiffness or 172
strain energy [24,44–47]. Area equivalent method [44] was carried out based 173
on the equivalence of cross-sectional areas. One another similar method was 174
to use the actual thickness of the interlocked layers directly but with a frac-175
tion fill coefficient that calculated based on area equivalency [24]. As the ring 176
thickness is simply determined by the cross-sectional area in those methods, 177
the actual material distribution in the carcass profile is neglected. Therefore, 178
it makes the prediction for the critical pressure of flexible pipe less accurate 179
[48]. 180
Considering that collapse of ring-like structures is a bending-dominated 181
problem [43], some equivalent ring methods came forward to build this equiv-182
alency based on the structural bending stiffness. One bending stiffness equiv-183
alence method employed by Loureiro and Pasqualino [45] originates from 184
the above-mentioned equivalent orthotropic shell method, which obtains the 185
equivalent thickness by equating the sectional bending stiffness between the 186
carcass and the ring. Another similar bending stiffness equivalence method 187
proposed by Martins et al. [46] requires the ring model has the same bending 188
stiffness per unit axial length of the carcass. Both of the two methods require 189
the consideration of the minimum moment of inertia when calculating the 190
bending stiffness of the carcass profile. However, those two methods neglect 191
the self-contact issue of the carcass, leading to an overestimation of the ac-192
tual structural bending stiffness. 193
Since most equivalent methods were unable to consider the material 194
elastic-plasticity, Tang et al. [47] proposed a method based on the circumfer-195
ential strain energy equivalence. The thickness of the the equivalent ring was 196
calculated based on the strain energy of the carcass that subjected to a given 197
hoop displacement. That strain energy of the carcass was obtained through 198
numerical model which could account for self-contact issues. In this model, 199
only the hoop strain was generated in the carcass layer due to the applied 200
Dirichlet-type boundary conditions [49]. However, that boundary conditions 201
enhance the structural stiffness of the carcass, lowering its absorbed strain 202
energy. As a result, their equivalent model gave an underestimated predic-203
tion on the critical pressure of the carcass. 204
Table 2 summarizes the common equivalent layer methods and gives an 205
overview towards their own characteristics. To gain an insight of the relia-206
bility of the existing equivalent layer methods, Lloyds Register Energy [50] 207
conducted an investigation on the prediction accuracy of the mathematical 208
models with different equivalent layer methods. The results showed a con-209
siderable variation in the predictions between different equivalent methods, 210
indicating that further development of these methods is needed. 211
Table 2. Summary of existing equivalent ring methods
Equivalent method Authors
Geometric factors Material factors
FEM required Section geometry Initial imperfections Linear elasticity Elastic-plasticity Bending stiffness per unit area Cruz et al.
(1997) Y N Y N N
Bending stiffness per unit length Martins et al.
(2003) Y N Y N N
Area equivalent Zhang et al.
(2003) Y N N N N
Actual interlocked layer thickness (with a faction fill coefficient)
Chen et al.
(2015) Y N N N N
Strain energy equivalent Tang et al.
(2016) Y Y Y Y Y
The analytical models for flexible pipe collapse are developed based on 212
a general ring buckling model [23]. With the help of the equivalent layer 213
methods, an equivalent ring model could be constructed and the differential 214
equation for that bending ring takes the form 215
d2w
dθ2 + w = − M R2
Where θ is the angle along the circumference, M is the bending moment due 216
to the loading, R is the mean radius of the ring, EI is the bending stiffness 217
of the ring. 218
By using this equation, the critical pressure pcr of the ring within the 219
elastic limit can be obtained as 220
pcr = 3EI
R3 (2)
Since the flexible pipe is a concentric structure, Glock [51] presented a 221
closed-form analytical solution for the critical pressure of an elastic cylinder 222
that confined in a rigid cavity 223 pG = E 1 − v2( t D) 11/5 (3)
Chen et al. [24] and Bai et al. [25] both considered the outside layers 224
as a spring support to the inner carcass and thus proposed a formulation to 225
that spring-supported ring model [24] 226 pc= 3EI R3 + 1 4k (4)
Where k is a constant that related to the bending stiffness of both inner liner 227
and pressure armor. 228
However, the above-mentioned equations are built based on elastic col-229
lapse merely. For a flexible riser that applied to deep water environment, it is 230
more likely to be collapsed in the plastic range [24]. Clinedinst [52] suggested 231
that replacing Young’s modulus with a “reduced modulus” to consider the 232
plastic collapse of pipes. This reduced modulus is a function of the stress-233
strain curve of the pipe material and its cross-section. For a rectangular 234
cross-section, the reduced modulus can be expressed as 235 Er = 4Edσdε (√E + q dσ dε)2 (5)
Where dσ/dε is the slope of the stress-strain curve of the material at the 236
stress σ and strain ε caused by the critical load. 237
Timoshenko and Gere [43] regarded the initial yielding pressure pe,y as 238
the plastic collapse pressure of pipes and therefore an equation for critical 239
pressure calculation is given as 240 p2e,y− [σyt R + (1 + 6 w0 t )pe,cr]pe,y+ σyt R pe,cr = 0 (6)
Where σyis the material yield stress, w0 is the maximum initial radial devia-241
tion from a circle, pe,cr is the elastic critical pressure that calculated through 242
Eq.(2). 243
This equation was proposed based on the assumption that defined the 244
buckling pressure as the pressure pe,y at the onset of material yielding in 245
the extreme outer fiber. However, this typically underestimated the critical 246
pressure pc, because fail does not occur until the elastic-plastic boundary has 247
penetrated some way through the wall thickness, as shown inFig. 10[53,54]. 248
Fig.10. Elastic ovalization and plastic collapse curves defining collapse pressure [54]
3.3. Numerical simulation 249
Although the experimental tests could offer the engineers a physically 250
intuitive observation on the anti-collapse performance of flexible pipes, rela-251
tively high cost associated with experiments hinders its wide application in 252
the reality. In this regard, numerical simulation is developed to predict the 253
critical pressure of flexible risers as an alternative. 254
Since the carcass and pressure armor are the main components for pre-255
venting from wet collapse, the other layers, e.g. tensile armors, anti-wear 256
and insulation layers, are generally omitted in the numerical models [31]. 257
Numerical models are often divided into two types: 3D full FE model and 258
equivalent FE models (2D or 3D). The 3D full model refers to modeling the 259
interlocked layers with their actual rolled shapes, as shown in Fig. 11. Such 260
kind of FE models preserve the layer geometric details and therefore can be 261
used to investigate the issues related to stress concentrations [31]. 262
However, those full models might be time-consuming in collapse analyses 263
and thus, simplified FE models were constructed with the combination of the 264
equivalent layer methods. Mostly, those simplified models were presented as 265
2D models and used to investigate the effect of initial geometric imperfec-266
tions, pressure armour on the critical pressure of the carcass. One drawback 267
of using such 2D FE models is that they are unable to deal with the pipe 268
curvature directly. With the regard, some 3D simplified FE models were pro-269
posed. Lu et al. [56] presented a 3D model that treated the interlocked layers 270
are helical strips, as shown inFig. 12. The gap size between the helical strips 271
was calculated from the parameter “fraction fill”. This spring-like FE model 272
was able to deal with the pipe curvature but its reliability depended upon the 273
calibration with sufficient test data. Another 3D simplified FE model were 274
proposed by Gay Neto et al.[31], who simulated the infinitely long curved 275
pipe by constructing a small region of flexible pipe with limited length. This 276
was done with the aid of the displacement coupling and kinematic constraints 277
at the cutting regions. This model was presented to given prediction on the 278
dry collapse pressure of flexible pipes. However, the curved configuration of 279
that model may cause as non-null load in axial direction due to the distribu-280
tion of pressure on the asymmetric external surface. Therefore, determining 281
appropriate boundary conditions to ensure equilibrium in the axial direction 282
is important to that 3D FE model in the dry collapse analyses. 283
Although most FE models exclude the layers above the pressure armor 284
(except the external sheath), there might be a need to investigate the “Bend-285
ing moment effect” that brings by those layers. This effect comes primarily 286
from the tensile armors and plastic layers due to friction, as shown inFig. 13
287
[14]. The bending stresses in those layers gives an harmonic squeeze load 288
intensity with the combination of the global curvature, which will increase 289
the ovality of the inner layers. This effect may cause an impact on the critical 290
pressure of the flexible pipes and related investigations should be carried out 291
further. 292
Fig.11. Details of the carcass profile [55] and the 3D full FE model [34]
Fig.12. 3D simplified model for the three layers of the pipe with curvature [56]
4. Geometric imperfections, manufacturing-related factors and cur-293
vature 294
For a flexible riser that operates in ultra-deep water, its critical pressure 295
is affected by many factors, such as geometric imperfections, work hardening, 296
residual stress and pipe curvature. To ensure the structural safety of flexible 297
risers during installation and operation, a lower bound collapse concept is 298
always adopted to consider the possible worst geometric configuration and 299
material properties [44]. Since the collapse resistance of flexible risers is sen-300
sitive to the geometric imperfections, pipe curvature, manufacturing-related 301
work hardening and residual stress, it is necessary to take those factors into 302
account when conducting such a lower bound collapse prediction [28,44]. 303
Related studies have been carried out by scientists to quantify those factors 304
and introduce them into prediction models. 305
Fig.13. Bending moment effect [14]
4.1. Geometric imperfections 306
4.1.1. Ovality of the cross section 307
Practical pipe structures are manufactured to specified tolerances, and 308
as a result always deviate to some degree from an ideally perfect geomet-309
ric shape [57]. This poses geometric imperfections to practical riser struc-310
tures and brings safety hazards to their ultra-deep water application. Many 311
radial buckling studies of pipe structures have been conducted to investi-312
gate the effect of various geometric imperfections on collapse capacity of 313
pipes[43,58–60]. Those works indicate that the collapse capacity is strongly 314
influenced by initial ovalization and gap as both of them are global imper-315
fections affecting the whole cross-section of pipe structures [61,62]. Once the 316
cross section of the metallic layer is fully yielded, increasing pressure will first 317
compress the pipe uniformly inward and then ovalize it owing to those small 318
nonuniformities [63]. As stated by Kyriakides [57],“when the structure stays 319
elastic it is not imperfection sensitive. By contrast, when in-elasticity sets in 320
it becomes imperfection sensitive”. 321
API 17J defines the ovalization (out of roundness) as: 322
∆ad =
Dmax− Dmin Dmax+ Dmin
(7)
It requires the operators to take initial ovalization into account in their 323
collapse analyses. A minimum ovality of 0.2% should be used if no other 324
data exists [19]. Numerical techniques were employed by researchers to gain 325
an insight into the effect of initial ovalization on riser collapse. Gay Neto and 326
Martins [34] modeled the carcass with a set of initial ovalization and com-327
puted the critical pressure numerically. The finite element models exhibited 328
clear reduction of critical pressure due to the increasing initial ovalization. 329
Considering that API 17B [15] allowed the collapse analyses to take the pres-330
sure armor into account, Malta et al. [64] studied the effects of ovalization 331
on confined collapse modes of carcass with 2D FE models. In their work, 332
the carcass layer was confined within the pressure armor and two types of 333
symmetry initial ovalization condition (singly or doubly) were imposed to 334
the carcass. According to the analysis results, they found the symmetry ini-335
tial ovalization condition did have an impact on the post-buckling behavior 336
(eight/ heart shape collapse mode [65], see Fig. 14) of carcass. The dou-337
bly initial ovalization always caused an eight collapse mode while the singly 338
ovalization interfered the final modes together with the pressure armor thick-339
ness. Although the relationship between critical pressure and collapse modes 340
is still under investigation, some studies [66–68] indicated that the heart 341
shape buckling pattern might yielded a lower critical pressure. 342
Fig.14. Eight shape (left) and heart shape (right) collapse modes [65]
4.1.2. Lay gap 343
Layer gap between the inner sheath and the pressure armor is being paid 344
attention to after more and more researchers considered the pressure amour 345
in their collapse studies [4,69,70]. This imperfection reduces the supporting 346
capacity of pressure armor when facing wet collapse. Two factors may trigger 347
the occurrence of the layer gap: volume change of the aging polymer and 348
extrusion into the adjacent interlocked layers[71]. Although no gap is created 349
during the riser manufacture, the factory acceptance test (FAT) causes a 350
volume loss of the polymer layers during first pressurization of the flexible 351
riser. This leads to some unclosed gap between layers, which will act as 352
the initial gap for subsequent pressure loading of flexible risers and practical 353
operations [72]. 354
Numerical modeling is a main approach to address this issue. An air-355
bag technique was adopted by Axelsson and Skjerve [71] to investigate the 356
sensitivity of collapse pressure on radial gaps between riser layers. In their 3D 357
FE models, the gap was simulated as an airbag layer which would not affect 358
the behavior of the surrounding layers. With the increase of the thickness of 359
this airbag, the critical pressure of the carcass dropped significantly. A similar 360
phenomenon was observed by Gay Neto and Martins [73]. In their work, the 361
loading pressure peaked twice during the radial deflection of the carcass. A 362
lower one was reached prior to the gap closure, followed by another larger 363
collapse pressure after the carcass came in contact with the pressure armor, 364
indicating that a premature radial stiffness reduction to the riser structures 365
was caused by the nonzero initial gap. 366
4.2. Manufacturing-related factors 367
4.2.1. Work hardening 368
Due to the cold work during the carcass manufacturing process, strain 369
hardening may occur, causing a high degree of stress-induced material an-370
isotropy [74]. This cold work makes the material properties varied throughout 371
the formed profile of the carcass strip, as shown in Fig. 15, complicating the 372
collapse behavior of carcass layer along with the geometric anisotropy. 373
Fig.15. Material imperfection induced by cold work [71]
Adopting an average stress-strain curve to represent the non-homogeneous 374
material behavior of the overall wire’s cross-section has been one available 375
way for researchers to incorporate this material imperfection. This approach 376
was first employed by Zhang et al. [44], who provided the equivalent layer 377
a typical stress-strain curve according to the cold work level of the original 378
carcass. However, the authors admitted that the level of cold work was dif-379
ficult to measure directly and depended on “a number of factors related to 380
the design and manufacturing process”. To address this problem, Nogueria 381
and Netto [75] proposed a methodology to estimate the average stress-strain 382
curve of the carcass. They first applied loads to the crown point of a half 383
sectional carcass wire specimen and recorded its load-displacement curve. A 384
corresponding FE model of the specimen was then constructed, attempting 385
to reproduce experimental load-displacement curve by repeatedly adjusting 386
the model’s stress-strain curve. This onerous method was improved by Lac-387
erda et al. [76,77], who simplified the average stress-strain curve as a bi-388
linear curve. This bi-linear curve was decided by three material parameters, 389
Young’s modulus, yield stress and tangent modulus. The Young’s modulus 390
was determined by the linear portion of the load-displacement curve of the 391
test specimen, and the yield stress and the tangent modulus were calibrated 392
by the rest elastic-plastic portion. If a simple bi-linear curve was not able to 393
reproduce the experimental results accurately, a tri-linear curve could also 394
be employed. 395
Using average stress-strain curves is a compromise to the limitation of 396
current techniques on the measurement of cold work level, which means dis-397
carding the geometric details of the carcass profile. To avoid an incorrect 398
predictions of stress concentrations, Axelsson [71] constructed a FE model 399
with the actual carcass profile and applied different stress-strain curves to the 400
corresponding cold formed sections. Considering that there was a relation-401
ship between the steel hardness Hv and yield stress σy which approximately 402
followed the form as below [78–81]: 403
Hv ≈ 3σy (8)
a hardness measurement technique was used to estimate the representative 404
yield strength of the carcass curved sections, helping to define those stress-405
strain curves. 406
4.2.2. Residual stress 407
Residual stress is a factor that may cause earlier onset of plasticity and 408
trigger the early collapse of the flexible riser [82]. It is generated from two 409
stages during the pipe manufacture (see in Fig. 16): one is the roll bend-410
ing stage where the metallic wire experiences a sequence of bending and 411
twisting events; another is the interlocking stage, where the profiled wire is 412
wound onto a bobbin [83]. Owing to the practical difficulties, there is no 413
available post-deformation stress relief operation that could be conducted to 414
the flexible riser products [84]. Those products, therefore, contain unknown 415
magnitude of residual stress in the cross-section of their armor wires. 416
Fig.16. Manufacture process of carcass layer [85]
Estimating the residual stress accurately is of great importance since the 417
plastic yielding is caused by the summation of applied stress and residual 418
stress [86], but how to achieve that is a tough task. Numerical approaches 419
are adopted by some researchers to make the first attempt. Tang et al. 420
[87] simulated the cold-forming process of the carcass wire with FE software 421
MARC and obtained the distribution of residual stress along the carcass 422
profile. Those residual stresses were then input into an identical model in 423
ANSYS for the collapse analyses. Although the numerical results showed the 424
residual stresses cause a significant decrease (nearly 8%) on collapse pressure, 425
the lack of test data made it less persuasive. 426
To facilitate the stress analyses of flexible risers, an establishment of 427
preliminary studies for the measurement techniques of residual stress is re-428
quired. Conventional destructive methods such as hole-drilling [88] are no 429
longer applicable as they are unable to measure the stress distribution along 430
the interlocked layer profile. By contrast, non-destructive approaches are 431
gaining popularity among researchers for their advantages of determining 432
the stress state in-situ on the manufactured risers. Fernando et al. [84] 433
first used the x-ray diffraction method to measure the distribution of resid-434
ual stress in pressure armor. This method evaluated the magnitude of the 435
residual stress by measuring the changes in the spacing of the lattice planes 436
between pre- and post-manufactured pressure armor wires [89]. However, 437
this method could only measure the stress state near the armor surface and 438
failed to give a correct evaluation on the magnitudes of stresses along the 439
wires cross-section. In this regard, another measurement technique, the Neu-440
tron Diffraction method, was adopted in their later research [90] for its large 441
penetration depth [91]. This technique, as shown in Fig. 17, was similar to 442
x-ray diffraction but due to its different scattering properties (neutrons in-443
teract primarily with the nuclei of atoms), additional information could be 444
obtained [92]. With the aid of the neutron diffraction method, three orthogo-445
nal strains (hoop, axial and radial based on riser coordinate) at gauge points 446
in the wires cross section were measured, and thus the residual stress distri-447
bution on the whole wire section was depicted. Despite the limited gauge 448
points was unable to cover all localized hot spots on the wire cross section, 449
this technique performed a potential way to measure the residual stress in 450
the interlocked layers within a manufactured flexible risers. 451
Fig.17. Neutron diffraction technique [90]
4.3. Curvature effect 452
During deep-water installation and operation, the flexible risers experi-453
ence bending within the touchdown zone. This bending condition may affect 454
the structural stability of flexible risers for service in such extreme water 455
depth and lead to curved collapse with the combination of external hydraulic 456
pressure. Since the curvature affects many factors, such as the changes in 457
void fraction of carcass layers and gap between layers [28], this makes curved 458
collapse an issue that is still not fully addressed in the literature. 459
The complexity of curvature effect poses barriers to analytical approach 460
and limits most curved collapse studies to finite element methods. Efforts 461
were made by Loureiro [93] to develop the analytical model of riser curved wet 462
collapse. A treatment of curvature as an additional ovalization was adopted 463
in his analytical model, stemming from the bending study of Brazier [94] 464
and Guarracino [95] on thin cylindrical tubes. This additional ovalization 465
was induced by the ovalized inner sheath since pipes undergoes a progres-466
sive flattening during bending due to the Von Karman effect [96]. Although 467
bending a carcass alone without reaching its MBR (minimum bending ra-468
dius) did not introduce high stresses [71], it had to withstand the ovalizing 469
pressure imposed by the inner sheath and thus gains some additional oval-470
ization. Based on the ovalization pressure equation given by Brazier, this 471
additional ovalization was worked out by the author. Finally, a new initial 472
ovalization was obtained by adding it to the straight-pipe initial ovalization, 473
transforming the curvature effect into an initial geometric imperfection issue. 474
This analytical model was examined by the author and other researchers [50] 475
with different FE models. Those work indicated that it could be a feasible 476
way to consider the curvature effect though some differences on the prediction 477
of the collapse pressure presented between analytical and numerical models 478
for small curvatures. 479
Compared with analytical methods, numerical modeling seems to be a 480
better option for its ability describing the curvature effect during riser col-481
lapse. A 3D full finite element model which considered all the cross-sectional 482
details of interlocked carcass and pressure armor was constructed by Gay 483
Neto et al. [97]. This time-consuming model was built with a length ade-484
quate to isolate the influence of the boundary conditions. Two case studies 485
were performed on that 3D model to investigate the curvature effect on wet 486
and dry collapse of flexible pipes. Based on the numerical results, a prelim-487
inary conclusion was drawn by Gay Neto that the curvature could cause a 488
significant reduction of the critical pressure in wet collapse while that reduc-489
tion was negligible in dry collapse. This full model was later simplified by 490
the authors themselves due to its impracticality in flexible pipe anti-collapse 491
design [31]. With the aid of displacement coupling and appropriate kinematic 492
constraints at the cutting edges, the length of the original model was reduced 493
to two pitches. This simplified model was employed to study the curvature 494
effect on dry collapse further. The investigation results of curvature effect on 495
dry collapse of flexible pipes presented in this study was in accordance with 496
the previous conclusion drawn by the authors. 497
Another simplified 3D solid model comprising the carcass, the inner sheath 498
and the pressure armor was made by Lu et al. [56] to investigate the curved 499
wet collapse. Interlocked layers in this model were modeled as helical strips 500
(like a spring ring) while the inner sheath was simulated by a continuous 501
cylindrical wall. To simulate the bent collapse of a 6-inch flexible pipe, this 502
model was first bent to a given bend radius (3.6 meter) and then subjected 503
to external pressure. According to the numerical results, a clear onset of col-504
lapse was captured from the pressure vs. displacement curve and the critical 505
pressure was 5% lower than that of a straight pipe approximately. However, 506
as the authors stated, this simplified model required sufficient test data to 507
calibrate and its prediction accuracy needed further inspection. 508
5. Conclusion and discussion 509
As oil and gas exploitation moves towards ultra-deep water fields, many 510
challenges related to anti-collapse capabilities of flexible riser occur. Ultra-511
deep water collapse study of flexible risers is a complicated task but of great 512
importance to the oil and gas industry. The main purpose of this review is 513
to provide researchers in this field a set of relevant references required for 514
their research and highlight the barriers in the prediction of critical pressure. 515
These barriers can be concluded as: 516
i) The lack of an effective equivalent layer method; 517
Determining the real bending stiffness of the carcass is the essence of 518
constructing an effective equivalent layer method since the pipe collapse is 519
a bending-dominated issue. Up till now, the methods that proposed based 520
on bending stiffness equivalence, however, could not give an accurate calcu-521
lation of the bending stiffness of the cross section of the carcass, generally. 522
Although possible factors, e.g. the minimum moment of inertia and super-523
position factor, of the carcass profile were considered in that calculation, the 524
bending stiffness were still overestimated [47]. One possible reason for that 525
phenomenon might be the self-contact between the carcass strips which may 526
lead to a stiffness reduction during the pipe collapse. 527
In addition, many methods are developed based on only one certain struc-528
tural property equivalence, which is inadequate for an equivalent model to 529
perform a similar collapse behavior of the carcass. 530
ii) Geometric and material imperfections generated from manufacture pro-531
cess; 532
Up to date, imperfection studies of flexible risers mostly concentrate on 533
the geometric imperfections. The studies on material stress hardening and 534
residual stress are relatively few. For the most part, such kind of inves-535
tigations are limited to finite element analysis, lacking the verification from 536
experimental data. Additionally, there is always a need for developing analyt-537
ical models for sensitivity analyses instead of re-valuating through repeated 538
numerical model adjustments. 539
iii) Complex collapse behavior under combined external and bending loads. 540
Curved collapse of flexible risers is a difficult issue as the bending state 541
changes several parameters (e.g. pitch, layer gap and void fraction of inter-542
locked layers). The numerical models used for curvature study often require 543
adequate axial lengths to eliminate boundary effects, making the curved col-544
lapse analyses an onerous task. Although some simplified curved collapse 545
models have been proposed, sufficient test data are required to enable them 546
to be a reliable tool in reality. 547
As recent offshore projects have become larger and deeper, the flexible 548
pipes are being demanded to withstand high external pressure and large 549
bending curvature. For the increasing water depth faced by the riser opera-550
tors, an accurate and reliable collapse prediction technique would provide a 551
well-determined operation limit for their products, helping to save costs and 552
increase their confidence. 553
Acknowledgments 554
This work was supported by the China Scholarship Council [grant number 555
201606950011]. 556
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