CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 28,aNo. 6,a2015

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DOI: 10.3901/CJME.2015.0909.111, available online at www.springerlink.com; www.cjmenet.com; www.cjme.com.cn

Numerical Analysis of Deteriorated Sub-sea Pipelines under Environmental Loads

GÜCÜYEN Engin*

Department of Civil Engineering, Faculty of Engineering, Celal Bayar University, Manisa 45020, Turkey

Received March 27, 2015; revised August 31, 2015; accepted September 9, 2015

Abstract: The significant point is the bidirectional interaction technique in FSI analysis while investigating subsea corrosion effect. By

this way, pipe environment is accurately modelled and fluid effects are also considered. The effect of external corrosion defects on

structural behaviour of a pipeline is studied by creating a nonlinear numerical model based on the finite element method according to

ABAQUS analysis program. Corrosion losses of sections are obtained from experimental results and applied to the model. Numerical

model is formed by a span of sub-sea pipeline that is subjected to environmental loads. Seismic and wind-generated irregular wave loads

are considered as environmental loads. Irregular wave is represented with equivalent eight regular waves via FFT. The pipe is modelled

according to two different types which are non-corroded(intact) and corroded (deteriorated) to demonstrate corrosion effects on it. The

visible type of corrosion in marine environment is named ‘pitting’ corrosion, in which the material loss is locally interpenetrated over

the surface. By considering this situation, the corroded and non-corroded pipes are modelled as 3D solid elements. The main point is

revealing how the subsea corrosion affects the structural behaviour of pipelines on the basis of implementation of experimental results to

a model structure due to changes of stresses and displacement.

Keywords: offshore pipelines, environmental loads, corrosion, numerical analysis

1 Introduction

Submarine pipelines are lifeline systems that support oil, gas, energy industries and water supply plants. Submarine pipelines are the effect of several environmental loads such as wave, current, seismic ones during their service lives. In addition to these mentioned loads, pipelines are subjected to destructive loads due to severe storms, ship anchors, impact loads, fishing trawlers and corrosion etc. Among these loads, corrosion is the dominant one in marine and offshore structures because of the well-known fact that the sea water is an aggressive corrosive environment. Pitting is the most common and extreme type of corrosion in the ocean environment. It is a form of corrosion where the degradation of the material that is localized to small areas rather than the whole surface uniformly. Main reasons of this type corrosion can be classified as inclusions, discontinuities in protective coating and surface defects[1–3].

Similar studies are investigated to determine the starting point of this study. The effect of pitting corrosion on stresses according to both constant inner pressure and increasing axis force values were investigated by RAJABIPOUR, et al[4]. They also compared the results of the previous studies. The pipe is modelled by ABAQUS analysis program and numerical values of the inner and outer environments are transferred to the solid model

* Corresponding author. E-mail: engin.gucuyen@cbu.edu.tr

© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2015

without modelling. XUE, et al[5], studied the symmetric and anti-symmetric buckling modes according to varying external pressure by ABAQUS analysis program. Then, researchers have compared the results with analytical methods. ABDALLA, et al[6], numerically investigated the stress distribution around pits present on a pipe for various depths, several pressure values and three different pipe diameters. KAZEROUNI, et al[7], estimated the amount of pressure capacity reduction of a pipe-containing a semi-elliptical pitting corrosion and the rate of corrosion under external (hydrostatic) and internal pressure by using ABAQUS analysis program again.

Even though pipelines are protected from corrosion by different techniques[8], corrosion effects in even insulated pipes were analytically presented by VEDELD, et al[9], and experimentally by CAINES et al[10], due to the destructive effect of the marine environment.

Because of corrosion effects in the applications of submarine pipelines on lands, similar studies are also investigated in the scope of this paper. In the study of CHEN, et al[11], corrosion defect on failure pressure of X80 type pipeline is studied via non-linear finite element method. Structural behaviour of the corrosion on a single point of the pipe is investigated and compared with test results. CHEN, et al[12], studied the same structural behaviour of the corrosion on single and many points by the same way and compared the results with X90 pipeline type. Similar study was also performed by NETTO, et al[13], for API X65 type gas pipeline ad solution of limit load of

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corrosion defects in gas pipelines is developed by comparing experimental data with the results of ABAQUS analysis. Determination of limit load in X65 type gas pipeline was performed by CHOIA, et al[14], in the way of comparing both experimental and numerical(ABAQUS) studies.

Loads on offshore structures are dominated by environmental loads that are only described by their statistical properties. Due to random changes of the wind velocity and its direction[15], the typical wave heights and periods change randomly by time[16]. Spectral analysis techniques have been extensively used on marine structures, since the time-domain analyses are generally more difficult than some of the frequency-domain techniques[17–18].

As submarine pipelines provide the transfers of materials which have economical and biological importance, damages in these pipelines may cause major problems. The most negative cases shall be taken into consideration in design phase to avoid this situation. For this purpose, seismic forces are also considered on the related structures in addition to dominant wave loads[19–20].

Studies about corrosion effects on pipelines in the literature are presented above. It’s seen that ABAQUS finite elements analysis program is frequently used in the studies to investigate the corrosion effects on steel pipelines. However, only pipeline is modelled in these studies. Force of the fluid which passes inner and outer of pipeline is effected as an external force without modelling. It’s stated that interaction of pipeline and fluid is ignored in corrosion studies. Corrosion effects on submarine pipelines are investigated by using fluid-structure interaction technique (FSI) according to ABAQUS analysis program[21]. Realistic conditions are provided by modelling flow environment with structure due to fluid-structure interaction technique[22]. In this way, corrosion effects on pipelines are determined according to displacements and stresses. Properties of submarine pipelines and effective forces are given in section 2.

2 Analysing Procedure

The model in the literature[4] is evaluated to examine the

corrosion defects on structural behaviour of offshore pipelines by analysing the same model. In the related study, finite elements analysis program is used in accordance with

previous studies. In this paper, structural behaviour of the model under corrosion effect for four different cases is determined under irregular wave and seismic loads. While these loads are effecting the structure, the pipeline is still in service. These four cases according to load and structural situation are given in Table 1.

Table 1. Case explanations

Condition Case 1 Case 2 Case 3 Case 4

Model Intact Intact Deteriorated Deteriorated Load Wave Wave+seismic Wave Wave+seismic

As seen from Table 1, the structure is modelled for two

different types; intact and deteriorated under two different load conditions to compare the corrosion defects on the structure. The results that are obtained from small-scaled specimens are generally considered to be applied to full-scaled structures directly[23]. According to this assumption, submerged intact structure is subjected to lose 10% weight by pitting the wall of members according to Ref. [24] via Ref. [21]. Environmental loads are also modelled while modelling the pipeline. While solid pipe model and seismic force are created by ABAQUS/Explicit, fluid passing through the pipe and marine environment are formed by ABAQUS/CFD.

2.1 Modelling of structures

Properties of the fixed supported pipe having 10 m span length which is used to model submarine pipeline under corrosion effect are seen in Table 2. Specific pittings on pipe are randomly distributed to reach the determined weight loss ratio.

Table 2. Geometric and material properties of solid model

Geometric property Material property

Length/m 10 Yield stress/MPa 240 Outer diameter/m 0.50 Young’s modulus/GPa 210 Inner diameter/m 0.47 Mass density/(kg • m–3) 7850

Non-corroded pipe is also modelled with corroded pipe

to investigate corrosion effect on the structural behaviour of submarine pipeline under environmental loads. Sizes of the semi elliptic pits which are used in corrosion modelling phase and pipe that is applied by these pits are seen in Fig. 1.

Fig. 1. Intact and deteriorated submarine pipes with pit dimensions

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Distribution of 1972 semi-eliptic pits having 1.16´10–5

m3 volume capacity in determined sizes on pipe is seen in the figure above. While height(h) and width(w) of the pits are 0.01 m, length(Lp) of the pits is 0.05 m. 10% weight loss has occurred in the undamaged pipe whose mass is 1794.12 kg with these pits.

The models are divided into seeds in finite elements method to perform analysis of complex models. 10-node modified tetrahedron elements(C3D10M), which are

compatible with contact problems, are utilized to perform analysis in ABAQUS/Explict. While distance between seeds is constant and 0.01 m in corroded and non-corroded pipe, 40 seeds are used in pit mouth due to seed densification. By this way, 232 423 nodes with 465 038 elements for intact model and 247 989 nodes with 497 590 elements for deteriorated model are appeared. Meshed intact and deteriorated models are shown in Fig. 2.

Fig. 2. Mesh structure of pipes and pits

More section and weight losses are observed in corroded

pipe instead of non-corroded one. On the other hand, increase in mesh density is also seen in corroded pipe. Seed densification around ellipses is the main reason of this situation. Mesh structure around pit region is presented in Fig. 2.

2.2 Modelling of loads on structures

In this section, wave and seismic loads effecting the single span of submarine pipeline at 40 m depth(d ) are modelled by analysis program. First of all, wave theories are determined in the depth where pipeline is located.

Afterwards, velocity relations are transferred to ABAQUS/CFD. After this operation, a real seismic acceleration record is applied to the structures which are modelled in Section 2.1 by ABAQUS/Explicit.

2.1.1 Wave loads

As it is known, ocean waves are always irregular. In present study, the irregular wave condition is represented with equivalent regular wave via Power Spectral Density (PSD) of the wave elevation. The adopted irregular wave elevation in the scope of this study is given by Fig. 3[25].

Fig. 3. Irregular sea surface elevations

In spectral methods, multi sinusoidal waves (2n) approach can be charged to represent irregular wave. The Power Spectral Density E(f ) is directly obtained from a continuous time series of the surface elevation η(t) as seen in Fig. 3 with the help of the Fourier analysis. Irregular sea surface elevations can be written as an infinite sum of sinusoids of amplitude (An) and frequency (ωn) as given in the following equations:

( )0

cos( ).t n nn

A t ¥

=

=å (1)

The power spectral density of surface elevation is given

in the equation below:

2

r 0

1( ) ( )exp(2 if( )) .

N

n

E f n t n t tT

=

é ùê ú= ê úê úë ûå (2)

In Eq. (2), f represents frequency, Tr is the record length and t is the sampling interval. The power spectral density of the irregular wave elevation is computed in the signal processing toolbox of the Matlab software[26] via FFT. In this study, irregular wave record is divided into 8 sinus waves by FFT method. Height(H) and period(T) values of each individual regular wave are calculated by Eqs. (3), (4):

1

1/21 ( )( ) 2[2 ] ,fH f E f= (3)

1 11 .T f= / (4)

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Water surface profiles are determined according to height and period values of each wave. Afterwards, multi-sinusoidal wave is obtained by adding these values.

Consistency between irregular wave elevation and multi sinusoidal waves is seen in Fig. 4.

Fig. 4. Sea surface elevations

Consistency of water surface profiles which are matched as seen in Fig. 4, is also controlled by Chi-Square test. According to this test; group number (g=8), degrees of freedom (df=81=7), predetermined alpha level of significance (0.01), are taken in displacement dispersal and test is completed in the end (2

observed=16.39<20.01,7=

18.47). In this way, accuracy of the analysis is confirmed.

Although each of the multi sinus waves have different amplitude and period values which belong to different wave theories, the waves behave like Airy wave according to[27] away from mean water. In prospect of this assumption, parameters of eight waves which are seen in Table 3 are modelled as Airy wave model.

Table 3. Wave heights, periods and lengths

Wave number n 1 2 3 4 5 6 7 8

Wave height H/ m 0.52 0.45 2.19 1.50 1.09 0.66 0.49 0.38

Wave period T/s 16.00 8.00 5.33 4.00 3.20 2.66 2.85 2.00

Wave length Lw/ m 282.81 98.71 44.35 24.99 15.98 12.68 11.05 6.74

While wave loads on corroded and non-corroded pipes

are calculated by ABAQUS/CFD, velocity relations belonging to eight waves is required to be applied as inlet boundary to the analysis program. Velocity profile equation belonging to Airy theory is given below:

8

,

, , ,1

cosh[2 ( ) ] 2 2cos .

2 cosh(2 )w nn n

nw n w n w n nn

y d LH gTu x t

L d L L T=

æ ö+ / ÷ç ÷ç= - ÷ç ÷÷ç/ è øå

(5) The equation above which is used for four cases is

implemented to the ABAQUS/CFD model as external flow inlet boundary condition. The second inlet boundary condition is also implemented for steady pipe flow with velocity of 0.70 m/s. Boundary condition is not defined in the outlet of pipe and sustainability of the pipe is provided. An outlet boundary condition is specified with fluid pressure set to zero in the outlet of external flow. Bottom of external flow is set to wall where all velocity components are zero and the far field velocity is assumed to be equal to inlet velocity at external flow. Application areas of mentioned boundary conditions are seen in the right side of Fig. 5. On the other hand, dimensions of external flow are given in the left side of Fig. 5. The dimensions of the outlet fluid domains which are considered in the analysis are 10.00 m in the direction of pipe(L), 1.5 m perpendicular to pipe direction(b) and 40 m in vertical direction(d). These

values are given in the left side of Fig. 5. Internal flow takes part in the same model with external flow. Contact surfaces of internal flow-pipe and external flow-pipe are defined as FSI surface.

Fig. 5. Meshed and unmeshed with boundary conditioned fluid domains

As it’s seen from the middle part of Fig. 5, FC3D4 (4-node modified tetrahedron) typed members which are proper for FSI problems are used in the analyses for fluid domains. 11 930 nodes and 49 894 elements for fluid domain of intact model and 12 261 nodes and 51148 elements for second model constitute the fluid domains. The fluid properties are chosen to represent salty water at temperature of 20 C with density (ρ) of=1025 kg/m3 and

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dynamic viscosity (μ) of = 0.001 5 N • s/m2. Properties of fresh water passing through the pipe are determined as (ρ) of = 998 kg/m3 and (μ) of = 0.001 0 N • s/m2. Outlet and inlet fluids are modelled as EOS materials with velocity of sound (co) in salty water 1560 m/s, in fresh water 1480 m/s.

2.1.2 Seismic loads A medium intensity earthquake record is used in analysis

to investigate the seismic effect of the model under corrosion effect. Acceleration-time relationship of the earthquake record is presented in Fig. 6. It is applied to non-corroded (Case 2) and corroded (Case 4) models.

Fig. 6. Earthquake record and application region

Earthquake record is effected to ABAQUS/Explicit at x

direction and shown by yellow arrows. Fixed supports with 40 cm lengths that are shown in two ends of pipe are used in all models. Structural behaviour under this earthquake record is given in Results section. 2.2 FSI computation

In FSI technique, behaviour of sub-sea pipeline is modelled by two separate models including solid and fluid ones. Mesh displacements is satisfied on contact surfaces by modelling FSI coupling. By determining the contact surfaces, where the forces transfer from fluid(CFD) to structure and deformations transfer from structure (Explicit) to fluid, is also identified. CFD technique evaluates the equations of motion reduce to incompressible Navier-Stokes equations given between Eqs. (6)(8).

2 2 2

2 2 2x

u u u uu v w

t x y z

P u u ug

x x y z

æ ö¶ ¶ ¶ ¶ ÷ç ÷+ + + =ç ÷ç ÷ç ¶ ¶ ¶ ¶è øæ ö¶ ¶ ¶ ¶ ÷ç ÷ç- + + + + ÷ç ÷÷ç¶ ¶ ¶ ¶è ø

(6)

2 2 2

2 2 2y

v v v vu v w

t x y z

P v v vg

y x y z

æ ö¶ ¶ ¶ ¶ ÷ç ÷+ + + =ç ÷ç ÷ç¶ ¶ ¶ ¶è øæ ö¶ ¶ ¶ ¶ ÷ç ÷ç- + + + + ÷ç ÷÷ç¶ ¶ ¶ ¶è ø

(7)

2 2 2

2 2 2z

w w w wu v w

t x y z

P w w wg

z x y z

æ ö¶ ¶ ¶ ¶ ÷ç ÷+ + + =ç ÷ç ÷ç ¶ ¶ ¶ ¶è øæ ö¶ ¶ ¶ ¶ ÷ç ÷ç- + + + + ÷ç ÷÷ç¶ ¶ ¶ ¶è ø

(8)

While the velocity components at the x, y and z direction

are represented by u, v and w, the gravitational components at the same directions are represented by gx, gy and gz respectively. ρ represents density, μ symbolizes dynamic viscosity and P is pressure in the equations. The pressure loads obtained from CFD solver are adapted to solid

domain through FSI technique. After the equation given below is used to obtain displacement values by Explicit analysis, the values are transferred to fluid by FSI technique:

( )| | .NJ N J J

t tm X P I= - (9) In Eq. (9), mNJ is mass matrix, X represents acceleration,

t is time, PJ symbolizes external applied load vector transferred from CFD, IJ is internal force vector which is occurred by stresses in the elements. The equations of motion for the body are integrated due to equations given below.

( 1) ( )1 1

( ) ( )2 2

,2

i iN N Ni

i i

t tX X X

+

+ -

+= + (10)

( 1) ( ) ( 1) 1( )

2

,N N Ni i i

iX X t X+ +

+= + (11)

where NX and NX are degree of freedom(N) of displacement and velocity components in Eqs. (10)(11), respectively. The nodal accelerations are calculated by using Eq. (12):

1( ) ( ) ( ).N NJ J Ji i iX m P I-= - (12)

Velocity and displacement values can be obtained after

determining accelerations. In this paper, the analyses are completed by 2e5 time increment for 16 seconds and the results are comprehensively presented below.

3 Results

Two analysis outputs have been created after performing analyses. Whereas one represents the ABAQUS/Explicit structural model, the other one is the ABAQUS/CFD model. Displacements and Von-Mises stress values are determined after structural analysis results. Time varying displacement values for four cases are seen in Fig. 7.

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Fig. 7. Time varying displacement values

Effect of seismic forces on displacements is seen in Fig.

7. Earthquake record with 8 sec has caused sudden increases and decreases in displacement values. In intact model, while displacement values of Case 1 which is under the effect of only wave force vary between 3.81 mm and 3.73 mm, these values change between 4.71 mm and 4.12 mm in Case 2 which is also effected by seismic force. In

deteriorated model, displacement values are between 4.11 mm and 4.02 mm in Case 3 that is only effected by wave force. On the other hand, the displacements are between 5.23 and 4.51 mm in Case 4 under wave and seismic forces. Distribution of displacement values on pipes besides time varying displacements are presented in Figs. 8 and 9.

Fig. 8. Displacement distributions of Case 1 and Case 2

Fig. 9. Displacement distributions of Case 3 and Case 4

Von-Mises stress distributions on pipes are presented in

Figs. 10 and 11. While maximum stress value is 138.5 MPa in Case 1, it is reached to 173.2 MPa in Case 2 with the effect of seismic force.

Stress distributions including deteriorated models belonging to Case 3 and Case 4 are given in Fig. 11. Maximum stress value among four Cases is obtained from Case 4 as expected. This value is 197.3 MPa. However, it is

decreased to 152.7 MPa in Case 3. Structural analysis results of FSI technique is presented

between Figs. 711. Fluid results are seen in Fig. 12. Internal-external flow section is seen in the lower left side of the Figure. External flow vectors varying with time from the beginning to the end of the analysis is seen in the right side of Fig. 12. Wave velocity increases from base to water surface and it changes in time. Maximum flow velocity has

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increased to 3.52 m/s at 40 m.

Fig. 10. Stress distributions of Case 1 and Case 2

Fig. 11. Stress distributions of Case 3 and Case 4

Fig. 12. Velocity vectors of internal and external flows

3 Conclusions

(1) Structural effects on submarine pipelines due to corrosion are numerically investigated after analyses. One single span of submarine pipeline at 40 m depth is modelled under wave and seismic forces. Accuracy of the numerical model is confirmed by analytical models in previous studies. Geometrical and material properties of the pipe with water depth have also been used in former studies. FSI technique in the analyses is used with the difference of other studies. In this way, the environment of the pipe is

precisely modelled and fluid effects are taken into consideration. Time varying external flow is determined by Airy Theory while velocity of internal flow is constant. Marine environment is created by using irregular wave in modelling phase.

(2) Semi elliptic pits are randomly distributed on pipe surfaces to cause 10% weight loss for a realistic corrosion model. Displacements in Case 3 which is corroded and under the effect of only wave forces are 7.89% bigger than non-corroded Case 1. Displacements in corroded pipe under wave and seismic forces (Case 4) are 10.63% bigger than non-corroded Case 2 under same forces. In terms of

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stresses, the values have increased 10.30% from Case 1 to Case 3 and have also increased 13.91% from Case 2 to Case 4. These values present negative effects of corrosion.

(3) After analyses, it is also stated that effects of corrosion effects with medium intensity earthquake on design of submarine pipelines shall be considered. While displacement value in non-corroded pipe under wave and seismic forces (Case 2) is 23.68% bigger, stress value is 25.10% bigger than non-corroded pipe under only wave forces (Case 1). On the other hand, displacement and stress values of Case 4 are 26.82% and 29.20% bigger than Case 3 respectively.

(4) FSI technique in modelling phase has both provided a more reliable model and fluid results after analyses. In previous studies, corrosion effect has been modelled by one-two pitting or weight loss per unit area. Flow environment around pipe is effected from outside of the model by calculating forces before modelling phase. However, more reliable model and results are obtained by modelling pipe environment with pits after solutions. The most critical case is the corroded one (Case 4) where both wave and seismic forces are effective. It can be said that, while effect of wave force increases, seismic effect may decrease in different water levels. Besides, corrosion has destructive effects on the structure for each situation. Change in pit sizes on corrosive damages can be investigated in the further studies in the light of performed analyses this paper.

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Biographical note GÜCÜYEN Engin, born in 1983, in Manisa, Turkey, is currently an assistant professor and a doctor at Department of Civil Engineering, Faculty of Engineering Celal Bayar University. He received his bachelor degree from Celal Bayar University, Turkey in 2013. His research interests include computational fluid mechanics(CFD), fluid structure interaction(FSI) and numerical analysis. Tel: +90-236-2412321; E-mail: engin.gucuyen@cbu.edu.tr