science and technology - · pdf filedr olga p. molchanova, faculty of economics, lomonosov...

Science and Technology

published byPipeline Transport Institute

Technical Productions (London) LtdISSN 2514-541X

Vol. 2, No. 1, March 2018

Areas of activities:

Pipeline Transport Institute 47a, Sevastopolskiy prospekt St.,Moscow, 117186Tel.: (495) 950-8295, Records Management: (499) 799-8285, fax: (495) 950-8297www.niitnn.transneft.ru, e-mail: [email protected]

• carryingoutofresearch-and-development,design-and-experimental,andtechnologicaloperations,aswellasdevelopmentoftechnicalsolutions,ensuringsafeandreliableoperationofmainandtechnologicalpipelines,buildings, and structures (facilities) of Transneft, PJSC, and Transneft system organizations (TSO);

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Pipeline Transport Institute is a research and development center of the Transneft, PJSC, for carrying out of research-and-development and design-and-experimental operations, as well as development of new technologies, equipment, materials, and regulatory documen-tation in the field of design, construction, operation, and repair of the pipelines for transportation of oil and petroleum products.

Founder, Pipeline Science and Technology

Ya. M. Fridlyand, General Director, Pipeline Transport Institute, Moscow, Russian Federation

Chairman of the Editorial Board and Editor-in-ChiefDr Anatoly E. Soschenko, Head, Department of Innovation Development and R&D,

Transneft, Moscow, Russian Federation

Deputy Chairman of the Editorial BoardDr Yu. V. Lisin, Moscow, Russian Federation

Editorial Board Members

Dr Samer M. Adeeb, Southwest Petroleum University China, Chengdu, ChinaDr Samuel Ariaratnam, Ira A. Fulton Schools of Engineering, Arizona State University, Tucson, AZ, USA

Dr Anatoly N. Dmitrievsky, Oil and Gas Research Institute, Moscow, Russian FederationNikolay N. Gorban, Caspian Pipeline Consortium JSC, Moscow, Russian Federation

Erik Green, Total E&P Russie, FranceDr Mohammed Hadj-Meliani, Hassiba Benbouali Unibersity, Chlef, Algeria

Dr Galina Ilieva, Shipbuilding Faculty, Technical University-Varna, Varna, BulgariaCliff Jonhson, PRCI, Falls Church, VA, USA

Dr Saravanan Karuppanan, Mechanical Engineering Department, Petronas Universiti Teknologi, Malaysia

Dr Anatoly M. Korolyonok, Pipeline Network Design, Construction and Operation Faculty, Gubkin Russian State University of Oil and Gas, Moscow, Russian Federation

Dr Jyant Kumar, Indian Institute of Science, Bangalore, IndiaDr Yuanhua Lin, School of Materials Science and Engineering, Southwest Petroleum University,

Chengdu, ChinaDr Nikolay A. Makhutov, Center for Steel and Welding, Strength Analysis, Pipeline Transport Institute,

Moscow, Russian FederationDr Yerbol S. Makhmotov, KazTransOil JSC, Astana, Kazakhstan

Dr Yury G. Matvienko, Department of Strength, Survivability and Safety of Machines, Mechanical Engineering Research Institute, RAS, Moscow, Russian Federation

Dr Atef Mohany, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Ontario, Canada

Dr Olga P. Molchanova, Faculty of Economics, Lomonosov Moscow State University, Moscow, Russian Federation

Dr Georgy V. Nesyn, Service for Efficiency Assessment of Hydraulic Resistance Methods, Pipeline Transport Institute, Moscow, Russian FederationDr Fabrizio Paolacci, University of Rome III, Rome, Italy

Dr Dimitrios G. Pavlou, University of Stavanger, Sravanger, NorwayDr Guy Pluvinage, Polytechnic University of Tirana (Albania), Metz, France

Dr Pathmanathan Rajeev, Swinburne University of Technology, Melbourne, Vic., AustraliaBerik K. Sayahov, KazTransOil JSC, Astana, Kazakhstan

Pavel Y. Serikov, Department of Economics, Transneft, Moscow, Russian FederationDr Sergei S. Sherbakov, Belarus State University, Minsk, Belarus

Dr Vladimir B. Sigitov, Institute of Polymeric Materials and Technologies, Almaty, KazakhstanDr Leonid A. Sosnovskiy, Tribofatigue Ltd, Gomel, Belarus

Dr Lakhdar Taleb, Department of Mechanics, INSA, Rouen, FranceJohn Tiratsoo, Technical Productions (London) Ltd, Eastleigh, UK

Dr Moran Wang, Multiscale Interfacial Transport, Tsinghua University, Beijing, ChinaDr Shugen Xu, College of Chemical Engineering, China University of Petroleum, Qingdao, China

Dr Jie Zhang, School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, ChinaDr Vladimir V. Zholobov, Department of Mathematical Modelling of Oil Trunk Pipeline Operation,

Pipeline Transport Institute, Moscow, Russian Federation

Vol.2, No.1, March 2018

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Pipeline Science and Technology

Volume 2, No 1, March 2018

Contents

Developing design schemes for underground pipelines with out-of-spec axial curvature using ILI data ...........3 Dmitry A. Neganov, Victor M. Varshitsky, Eldar N. Figarov, and Sergey V. Ermish

Event announcements ............................................................................................................................. 18, 54, 66

An analysis of methods and approaches to evaluating reliability when predicting equipment failures ..........19 Oleg V. Aralov and Ivan V. Buyanov

Technical and methodological support of leak-detection systems at Transneft’s facilities .............................. 33 R.Z. Sunagatullin, S.A. Korshunov, and Yu. V. Datsov

Mechanical behaviour of a pipe impacted by an object, based on numerical simulation ............................. 45 Jie Zhang and Han Zhang

Seismic vulnerability analysis of storage tanks for oil and gas industry .......................................................... 55 H.N.Phan, F.Paolacci, D.Corritore, and S.Alessandri

Undamped vibration of fibre-reinforced polymer overwrapped pipes under fluid-hammer conditions ...... 67 Kristen Rege


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1. Disclaimer: While every effort is made to check the accuracy of the contributions published in Pipeline Science and Technology, the publishers do not accept responsibility for the views expressed which, although made in good faith, are those of the authors alone.

2. Copyright and photocopying: © 2017 Pipeline Transport Institute, Moscow, Russian Federation, and Technical Productions (London) Ltd, Beaconsfield, UK. All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means without the prior permission in writing from the copyright holder. Authorization to photocopy items for internal and personal use is granted by the copyright holder for libraries and other users registered with their local reproduction rights organization. This consent does not extend to other kinds of copying such as copying for general distribution, for advertising and promotional purposes, for creating new collective works, or for resale. Special requests should be addressed to Pipeline Transport Institute, Moscow, Russian Federation, or to the editor.

3. Publisher: Pipeline Science and Technology is published by Pipeline Transport Institute, Moscow, Russian Federation, in association with Technical Productions (London) Ltd, Eastleigh, UK:

Pipeline Transport Institute (PTI, LLC) , 47 A Sevastopolskiy prospekt, Moscow 117186, Russian Federationtel: +7 (495) 950-82-95 ext.2234

Technical Productions (London) Ltd, PO Box 660, Eastleigh SO50 0NT, UKtel: +44 1494 675139

Editor in chief (Russian Federation): Anatoly E. Soschenko ([email protected])Managing editor (Russian Federation): Valentin Komaritsa ([email protected])Leading editorial manager (Russian Federation): Victoria Malinina ([email protected])Production editor (UK): John Tiratsoo ([email protected])

4. ISSN 2514-541X


Administrative information


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Developing design schemes for underground pipelines with out-of-spec axial curvature using ILI data

by Dmitry A. Neganov1, Victor M. Varshitsky*1, Eldar N. Figarov1, and Sergey V. Ermish2

1 Pipeline Transport Institute, LLC, Moscow, Russian Federation2 Transneft Diascan JSC, Lukhovitsy, Moscow Region, Russian Federation

WHEN CONDUCTING IN-LINE INSPECTIONS (ILIs) of trunk pipelines, pipe sections may be found with curvature exceeding the values required by specifications. An out-of-spec bend in pipe sections leads to the pipeline operating in conditions of

increased stress-strain state, which does not comply with regulatory requirements. Where sections with out-of-spec curvature are found, repair works are carried out in order to return them to a state which complies with specifications. The priority shall be given to a method which does not involve cutting into the pipeline. In order to develop the project of the pipeline repair and to predict the stress-strain state during repairs and in subsequent operation, it is necessary to create design schemes which take into account the actual operating conditions of the pipeline, data from ILI, and the reasons why out-of-spec curvature formed at the section.

In this article, an algorithm is proposed for the development of design schemes which describe the actual curvature of pipeline sections before repair, while repair works are carried out, and after they are finished.

The methodology is based on a set of design scheme parameters, which allow a combination to be obtained, including both the design curvature and the actual pipeline section curvature according to ILI data. Design schemes for various situations where an out-of-spec curvature has formed were developed using actual data from ILI.

Key words: strength, stress, design scheme, ILI, repair, axis curvature, axial bend radius

Corresponding author’s contact details:

e-mail: [email protected]

Introduction

Repair works which are carried out in a timely manner play an important role in ensuring the safe operation of trunk pipelines [1]. At the same time, for the intended using and planning these works, it is necessary to give an accurate estimate of the current and predicted stress-strain state (SSS) of the pipeline wall.

One of the instruments for determining the initial data for evaluating the pipeline’s SSS is in-line inspection (ILI). Modern inspection facilities, such as ILI

devices with navigational systems, allow curvature to be determined for each pipe section. Analysis of the ILI results shows that in an operational pipeline sections can be found with axial curvature that does not correspond to the design: the bending stresses which arise here are significantly higher than those allowed by specifications.

These sections form for a variety of reasons, such as the pipeline laying on a non-profiled foundation; tie-ins; mismatch between angle tips of prefabricated bent branches and the trench bottom; and


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pipeline subsidence. It is possible to evaluate the SSS of sections with out-of-spec curvature at the moment when the ILI device is launched using design formulae, given in regulatory documents at the planning stage. However, in order to predict changes to the curvature and elevation of the pipeline during and after repair works, it is necessary to develop design schemes which correspond to the real conditions of the pipeline’s construction and which reflect the actual curvature distribution in the section.

Design schemes are examined in Russian technical literature for various conditions of pipelines construction. In particular, in Refs 2 and 3, design schemes are given for cross-over beams of pipelines, and Ref. 4 includes standard design schemes for laying pipelines in complex conditions and with crossings over artificial and natural obstacles. Research paper [5] examines cases of bending both in straight pipelines and pipelines with initial curvature. It is worth noting that the design schemes in the works indicated were developed for cases where a straight pipeline was laid, or for pipelines with known curvature, and did not take into account the actual position of the pipeline or inspection data. Both Russian and foreign engineers have carried out a great deal of research into the SSS of pipelines under loads from the surrounding environment [6-9]. However, these works also fail to take into account inspection data and the results of observation of the actual pipeline position.

Russian engineers have conducted research into evaluating the SSS for pipeline sections on the basis of measuring the horizontal location and elevation [10]. However, calculations for a pipeline section based on measurements of the elevation at discrete points may not reflect the actual stress state and the actual curvature. Modern methods of ILI which are used at Transneft PJSC allow the actual curvature to be calculated for each pipe section of the pipeline [11]. Taking into account the considerable uncertainty

of data regarding the actual conditions of laying pipelines, it is advisable when developing design schemes not to us values for elevation, but the curvature of the pipe sections as measured by the results of ILI.

Method of analysing data from ILI and choosing design schemes

Analysis of data from ILI has shown that the majority of pipe sections with out-of-spec curvature, detected during the launch of ILI devices, have bend direction in the vertical plane. Out-of-spec curvature has been detected both in places with assumed design elastic bending of the pipeline axis, and at straight linear sections of the route, as well as at sections adjoining prefabricated bent branches.

ILI data were analysed to identify the most appropriate design scheme. A history of changes to the bend radius was formed; curvature distribution at the given section was plotted; the presence of designed bend radiuses was analysed, as well as the presence of short pipe sections, prefabricated bent branches, and the nature of the local terrain. Based on data from ILI, the diagrams were plotted which characterize the position of the pipeline and the bending of the axis at pipe sections. Using data from ILI, the projections of the curvature onto the vertical (OY) and horizontal (OX) planes can be calculated in the following way:

ρ γ

ρ γ

OY

OX

R

R

=

=

1

1

cos( )

sin( )

where:

R = the bend radius at the pipe section, in m

γ = the angle of the bending direction at the pipe section, in degrees.

In the case of a bend radius being found at the first launch of ILI device, before the pipeline is put into operation (during


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its testing), it can be concluded that the bend radiuses have originated at the stage of construction and installation works. The key reasons why out-of-spec bends may occur are:

• a non-profiled trench bottom with a convex section;

• a non-profiled trench bottom with a concave section;

• pipeline displacement, and laying straight pipe sections adjoining prefabricated bent branches into a trench, which has a bend in the route;

• the use of tie-ins at sections of the pipeline.

As a consequence of the reasons indicated here, sections with convex and concave lengths of pipe may arise during pipeline construction. A separate design scheme should be developed for each of the cases listed.

When laying a pipeline at a section with a convex trench bottom, as a rule, the maximum bend is reached at one or two lengths of pipe, and the curvature of the section increases in the area of the examined lengths of pipe and decreases at the adjacent sections.

The design scheme developed for these cases should model pipeline laying on unprofiled earth foundations. The irregularity of the trench bottom is modelled with a so-called soil prism which has length, height, and stiffness.If the pipeline is laid at a section with a concave trench bottom, then the maximum bend is usually reached at the length of pipe located in the middle of the section. In this case, the design scheme should model laying the pipeline at a section with a hollow.

Where the pipeline is laid at a section with a turn in the route, the curvature increases sharply, as a rule in one or (more rarely) in two lengths of pipe. Most typical is the bending of lengths of pipe placed between prefabricated bent branches. In this case the pipeline axis bending may occur when laying straight lengths of

pipe at the bottom of trenches which are profiled for a turn to a certain angle and designed for laying prefabricated bent branches.

Taking into account the significant non-uniformity and high uncertainty regarding the actual properties of soil and geometry of trench foundations, when calculating soil properties, benches heights, hollows, the turning angles are selected in such a way that the designed curvature coincides with the curvature of examined sections according to ILI data, and reflects the character of changes to the curvature at adjacent sections.

One more of the possible reasons why out-of-spec curvatures may arise during construction and installation works is the application of loads to the pipeline in order to ensure its alignment at tie-ins of separate pipeline sections. These sections are distinguished by the presence of installation joints, short pipe sections, and prefabricated bent branches in direct proximity to the examined lengths of pipe. The curvature of the section is characterized by several decaying half-waves, found at sections adjacent to the lengths of pipe with the maximum curvature. The design schemes for these cases shall model the displacement of the pipeline due to artificially applied loads to it.

Where out-of-spec curvature is detected close to prefabricated bent branches, the most probable reasons for that are the angle of the pipe bend not corresponding to the turn angle of the trench bottom, or mismatch between angle tips of branches and the trench bottom during construction and installation works.

Developing a design scheme for cases of tie-ins and mismatches between the pipe bend and trench angles requires thorough analysis and is a promising area of current research. The present article examines design schemes when laying pipeline into a trench with unprofiled bottom and bending of the length of pipe installed between two branches.


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Additional requirements are applied to the design schemes being developed, regarding their possible use for assessing changes in the curvature of the section during repair works without cutting the pipeline, and to determine the optimum length of the section to be excavated.

Developing a design scheme and performing calculations for convex lengths of pipe

ILI data

The radius and bend direction of each length of pipe can be determined by processing data from profilometers. A demo example is the section of 1067-mm x 14-mm pipeline. The parameters of the length of pipe and the distribution of the curvature at the pipeline section are presented in Table 1. As can be seen from the table, the bending radius was detected from the first launch of the ILI device and, consequently, it must have formed during construction and installation works. Figure 1 presents a diagram of changes to the curvature at the section based on data from the final launch of the pig.

Developing a design scheme

Design scheme No.1 for a section of pipeline at a convex section of trench can be presented as a beam which is placed on a soil prism with height H, and is modelled

by an elastic foundation with stiffness C1 (section L

1). It has sags (sections L

2) and

lies on a soil foundation with stiffness C2 (Fig.2). Given that it is symmetrical, only half of the section is examined.

At the section 2L1 < x < 0, the pipeline

is laid on a soil prism; at the section 0 < x <L

2 it sags, while at the section x > L

2

it contacts the trench bottom. A system of differential equations for pipeline sections 1, 2, and 3 can be expressed as follows:

EJy Ny c y

EJy Ny q

EJy Ny c y

1 1 1 1

2 2

3 3 2 3

0

0

IV

IV

IV

+ ′′ + =

+ ′′ =

+ ′′ + =

where:

E = the modulus of elasticity, in PaJ = the inertia moment, in m4

N = the longitudinal force, in Nс

1 = the stiffness of the soil prism,

in Paс

2 = the stiffness of the soil

foundation, in Paq = the lateral load, in N/m.

The general solutions to the equations for the right half from the axis of symmetry have the form of Equns 1 and 2 (below).

C1, C2, C3, C4, C5, C6, C7, C8, C9, and C10 are unknown constants, which are calculated from boundary conditions.

y x C x C x x C x C1 1 1 1 1 11 2 3 4= − + + +exp( )( sin( ) cos( )) exp( )( sin( )α β β α β ccos( ))β1x H+

y C kx C kxq

EJkx C x C2 2

25 62

7 8= + + + +sin( ) cos( ))

y x C x C x3 2 2 29 10= − +exp( )( sin( )) cos( ))α β β

α β11

11

4 4 4 4= − = +

c

EJ

N

EJ

c

EJ

N

EJ;

Equations 1:

α β22

22

4 4 4 4= − = + =

c

EJ

N

EJ

c

EJ

N

EJk

N

EJ; ;

Equations 2:


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The boundary conditions for the given system of coordinates are the following:

when x L y y= − ′ = ′′′=1 1 10 0: ;

when x y y y y

y y y y

= = ′ = ′′′ = ′′ ′′′= ′′′

0 1 2 1 2

1 2 1 2

: ; ;

; ;

when x L y y y y

y y y y

= = = ′ = ′′′ = ′′ ′′′ = ′′′

2 2 3 2 3

2 3 2 3

0: ; ;

;

The solution to the non-linear system of algebraic equations can be found using computation methods (the authors used Mathcad software).

Calculating the curvature from the developed design scheme

Calculations are made for the section of 1067-mm x 14-mm pipeline, shown in Fig.1. The calculated curvature describes the character of the curvature distribution according to ILI data for the examined section given the following initial data:

external diameter: D = 1.067 mwall thickness: d = 0.014 minternal pressure p = 5.5 MPatemperature drop: Dt = 35°Cdepth of backfill: h = 1.5 m

Relative pipe lengthnumber

Distance from the

start of the section

Bend direction, in degrees

Bend radius

(first pig launch, m

Bend radius (last pig

launch), m

Curvature projection on the OY axis,

1/m

Internal pressure,

MPa

Temp.drop, oC

Wall thickness,

mm

1 0 16 839 990 0.000971

5.5 35 14

2 13.7 14 672 788 0.001231

3 27.6 9 869 882 0.00112

4 41.6 163 2258 2211 –0.00043

5 55.5 152 1317 1241 –0.00071

6 69.6 179 892 925 –0.00108

7 83.6 11 613 497 0.001975

8 97.7 8 467 458 0.002162

9 111.7 177 680 891 –0.00112

10 125.6 176 636 891 –0.00112

11 139.6 15 2120 2625 0.000368

12 153.8 149 2625 2625 –0.00033

13 167.5 168 2625 1225 –0.0008

14 181.2 168 891 1225 –0.0008

Table 1. Curvature distribution at the

examined section of the pipeline, and parameters

according to ILI data.

Fig.1. Curvature and elevation markers for

a section of pipeline based on ILI data.

Curvature distribution, based on in-line

inspection data

Curvature, 1/m Elevation markers, m

Curvature based on ILI dataElevationmarkers, m


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Fig.2. Design scheme for a pipeline at a convex section of the trench:

2L1 is the distance at which the pipeline contacts the soil prism;

L2 is the distance at which the pipeline has a sag.

Fig.3. Results of calculations for a pipeline section (top-bottom):

a) elastic axis line, in mb) axis turn angle, in radc) bending moment, in Nmd) shear force, in N.

Pipeline axis

Elastic axis line, m

Axis turn angle, rad

Bending moment

Shear force

Distance, m

Distance, m

Distance, m

Distance, m


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Relative pipe length number

Distance from the

start of the section

Bend direction, degrees

Bend radius

(first pig launch),

m

Bend radius (last pig launch),

m


1/m

Internal pressure,

MPa

Temp. drop,

oC

Wall thickness,

mm

1 0 51 3050 2511 0.000251

5.5 35 24

2 11.5 69 2410 2179 0.000164

3 23 71 2450 2195 0.000148

4 34.5 7 2258 3000 0.000331

5 46.2 348 2289 3000 0.000326

6 57.7 203 2171 3000 -0.00031

7 69.3 337 1491 1972 0.000467

8 81.0 353 1693 1144 0.000868

9 92.4 356 2964 1248 0.000799

10 104.1 164 1164 655 -0.00147

11 115.7 183 829 437 -0.00229

12 127.3 183 828 435 -0.0023

13 139.0 196 2225 722 -0.00133

14 150.7 357 1893 774 0.00129

15 161.9 353 1176 725 0.001369

16 173.2 358 812 799 0.001251

17 184.7 8 980 934 0.00106

18 191.0 344 3050 3000 0.00032

19 203.0 9 3050 948 0.00104

20 214.5 282 3050 1655 0.00013

21 225.8 324 3050 824 0.000982

Table 2. Curvature distribution at the

examined section of the pipeline and the

parameters according to ILI data.

Fig.4. Distribution of actual and design

curvature at a convex section of pipelin:

Blue: Curvature based on ILI data;

Red: Design curvature with soil load;

Green: Design curvature without soil load;

Orange: Design curvature with neither

soil load nor oil.

density of backfill soil: r = 1800 kg/m3

width of prism: L1 = 10 m

height of soil prism H = 0.35mstiffness of soil prism c

1 = 1.3 MPa

stiffness of soil foundation c2 = 0.1

MPa

Plots of the pipeline deflections, turn angle, shear force and bending moment, obtained from calculations, are presented in Fig.3. The actual bend radius, recorded at pipe section No.8, was R

act = 458 m, while the design bend radius was R

des = 457 m.


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The results of calculations for curvature at the pipeline section are presented in Fig.4 (the red line). As can be seen from the figure, the design scheme describes the curvature of the pipeline section with the necessary accuracy, which confirms that the scheme can be used in pipeline operating conditions.

An additional calculation was performed to model the removal of backfill soil during repair works. The results of the calculation showed that the curvature of the examined pipe length No. 8 is decreasing significantly. The bend radius when the soil load is removed was R

rep1 = 753 m in the case of the soil

being removed from the section with a length of 64 m, while when the pipeline

is drained, Rrep2

= 1086 m. The curvature distribution at the section when the soil load is removed (the green line) and when the pipeline is drained (the orange line) are presented in Fig.4.

Results

The authors have developed a design scheme which models a pipeline section laid on a convex, unprofiled soil foundation. It has been demonstrated that it would be possible to use the developed design scheme when planning repair works. Predictive calculations were presented for the change in the curvature of the section during and after repair works are carried out. The limits of the repaired section were defined.

Fig 5. Curvature and elevation markers for a concave pipeline section, based on ILI data.

Fig.6. Design scheme of a pipeline for a concave length of pipe.

Curvature distribution, based on ILI dataCurvature, 1/m Elevation markers, m

Curvature based on ILI dataElevationmarkers, m

Pipeline axis


11

Developing a design scheme and performing calculations for a concave pipe section

ILI data

A concave section with out-of-spec curvature was examined. The parameters of a length of pipe and curvature distribution are presented in Table 2 for the 1067-mm x 24-mm pipeline section. The bend radius was detected during the first launch of an ILI device. Figure 5 presents a plot showing changes to the curvature at the section according to data from the final launch of an ILI device.


Design scheme No.2 for a pipeline at a concave section of trench can be presented as an elastic beam on an elastic foundation, laid in a hollow (Fig.6).

At the section 0 < х < L the pipeline sags, and at the edges of the section it rests on the elastic foundation. The balance differential equations of sections 1 and 2 of the pipeline have the following form:

EJy Ny cy

EJy Ny q

1 1 1

2 1

0IV

IV

+ ′′ + =

+ ′′ =

In this system of equations, the notation is the same as in the system of Equns 1.

Given the symmetry, only half of the section is examined. The general solutions to the equations are as follows:

y x C x

C x1 1 1

2

= −+

exp( )( sin( )

cos( ))

α ββ

y C kx C kx

q

EJkx C x C

2

22

3 4

25 6

= +

+ + +

sin( ) cos( )

C1, C2, C3, C4, C5, and C6 are unknown constants which can be calculated from the boundary conditions.

The boundary conditions for the given system of coordinates (in the case of

examining half of the section) can be written as:

when x y y y y

y y y y

= = ′ = ′′′ = ′′ ′′′= ′′′

0 1 2 1 2

1 2 1 2

: ; ;

; ;

when x L y y= ′ = ′′′ =: ;2 20 0

The solution to the non-linear system of algebraic equations can be found using computation methods (the authors used Mathcad software).

Calculating curvature from the developed design scheme

Calculation was performed for the section of 1067-mm x 24-mm pipeline, shown in Fig 1. The calculated curvature describes the character of curvature distribution based on ILI data for the examined section given the following initial data:

external diameter: D = 1.067 mwall thickness: d = 0.024 minternal pressure: p = 5.5 MPatemperature drop: Dt = 35°Cdepth of backfill: h = 1.45 mdensity of backfill soil: r = 1800 kg/m3

stiffness of soil foundation: c = 1.2 MPa.

Plots of pipeline deflections, turn angle, shear force and bending moment, obtained from calculations, are shown in Fig. 7.

The actual bend radius recorded at pipe section No. 11 was R

act = 435 m, while the

design bend radius for this section was R

des = 436.2 m.

As in the previous case, a range of calculations were performed for the pipeline section for operational conditions and for repair works. The results of the calculations of the curvature of the pipeline section are presented in Fig.8. When the results of the calculations are compared with the actual values of the bend radiuses, it can be concluded that the design scheme describes the lengths of pipe with least possible curvature quite accurately.


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Modelling repair works showed that the curvature of the examined pipe length No.11 is significantly decreasing. The bend radius with soil load removed was

Rrep1 = 1370 m, where soil was removed

from a section with length 29.8 m, and when the pipeline was drained, it was R

rep2 = 2910 m.

Fig.7. The results of calculations for a concave section of the pipeline (for half the section - top-bottom):

a) elastic axis line, in mb) axis turn angle, in radc) bending moment, in Nmd) shear force, in N.


13

Results

The authors have developed a design scheme which models a pipeline section laid on a concave, unprofiled soil foundation. It has been demonstrated that it would be possible to use the

developed design scheme when planning repair works. Predictive calculations were presented for the change in the curvature of the section during and after repair works are carried out. The limits of the repaired section are defined.

Fig.8. Distribution of actual and design curvature at a concave section of pipeline.

Fig.9. Curvature and elevation markers for a

pipeline section in the vicinity of pipe bends,

based on ILI data.

Actual and design curvature distributionCurvature, 1/m

Curvature based on ILI data


Design curvature with soil load

Design curvaturewithout soil load

Design curvature with neither soil load nor oil


Elevationmarkers, m


14

Developing a design scheme and performing calculations when an out-of-spec curvature is found near a pipe-bend

This section examines lengths of pipe where out-of-spec curvature has been found in the vicinity of prefabricated bent branches.

ILI data

Table 3 presents the distribution of bend radiuses and curvatures for convex pipeline section 1067-mm x 21-mm, located between the prefabricated bent branches. Because they are in an unstressed condition, their curvature is taken to be equal


Design scheme No.3 for a pipeline is presented in Fig.10, for a symmetrical case of bending of convex lengths of pipe when laid in a trench, which turns by the

angle ϕ.

At the section L1 < х < 0 the pipeline rests

on the elastic foundation, which has a turn; at the section 0 < х < L

2 a pipeline

bend is formed and there is separation from the soil; at the section х > L

2 the

pipeline rests on the elastic foundation. The balance equation for the pipeline section has the following form:

EJy Ny c y

EJy Ny q

EJy Ny c y

1 1 1 1

2 2

3 3 2 3

0

0

IV

IV

IV

+ ′′ + =

+ ′′ =

+ ′′ + =

(3)

where:

c1 = the stiffness of the foundation at

the turn section, in MPa c

2 = the stiffness of the foundation at a

straight section, in MPa.

Equations of the pipeline axis for the system of differential Equns 3 are similar to the equations described for design

q

X

Y

0

î ñü òðóáî ï ðî âî äà

N

N

1 2 3

L L1 2Fig.10. Design scheme for a pipeline at a convex section.

Relative pipe length number

Distance from the start of the

section

Bend direction, degrees

Bend radius (first pig

launch), m

Bend radius (final pig

launch), m


1/m

Internal pressure,

MPa

Temp.drop, oC

Wall thickness,

mm

1 0 22 46.2 46.2 0

5.1 32 21

2 11.6 82 64.6 64.6 0

3 23.1 6 194 215 0.004626

4 34.7 351 224 228 0.00433

5 46.3 86 68.2 68.2 0

6 57.9 7 42.5 42.5 0

Table 3. The curvature distribution at a convex pipeline section, located between the prefabricated bent branches.

Pipeline axis


15

Fig.11. Results of calculations for a convex

pipeline section (for the half-section - top-

bottom):

a) elastic axis line, in mb) axis turn angle, in rad

c) bending moment, Nmd) shear force, N.


16

scheme No.1 (Equn 2).

The boundary conditions for the given system of coordinates can be written in the following form:

when x L y

y

= − ′ =′′′=

1 1

1

2

0

: ;

;

ϕ

when x y y y y

y y y y

= = ′ = ′′′ = ′′ ′′′= ′′′

0 1 2 1 2

1 2 1 2

: ; ;

;

when x L y y

y y y y y y

= = =′ = ′ ′′ = ′′ ′′′ = ′′′

2 2 3

2 3 2 3 2 3

0: ;

; ;

Calculating curvature from the developed design scheme

In order to evaluate the chosen design scheme, the calculation can be performed for 1067-mm x 21-mm pipeline section (Fig.10).The initial data for the calculation are as follows:

external diameter: D = 1.067 mwall thickness: d = 0.021 minternal pressure: p = 5.1 MPatemperature drop: Dt = 32°Cdepth of backfill: h = 1.5 mdensity of backfill soil: r = 1500 kg/

m3

stiffness of soil foundation: c

1 = c

2 = 1.3 MPа

turn angle: ϕ = 5°.

Plots of the pipeline axis, turn angle and curves of the shear force and bending moment for the half-section, obtained from calculations, are presented in Fig.11. The actual bend radius, recorded at pipe section No.3, was R

act = 215 m, while the design bend radius for this section was R

des = 211 m.

A range of calculations were performed for the pipeline section for operational conditions and for repair works. The results of curvature calculations for the pipeline section are presented in Fig.12.

When modelling repair works, the calculated curvature of the examined lengths of pipe decreases. The bend radius with soil load removed was R

rep1 = 220 m, where soil was removed from a section with length 40 m, and R

rep2 = 225 m when the pipeline was drained.

The calculation results show that in the case of pipe lengths being placed at a turn in the route, the removal of soil load barely affects the curvature values. In this case, carrying out works without cutting the pipeline may be inadvisable.

Fig.12. Distribution of actual and design curvature at a concave section of pipeline.


Design curvature with soil load

Design curvaturewithout soil load

Design curvature with neither soil load nor oil


17

Results

The authors have developed a design scheme, which models laying lengths of pipe at a section where the route turns. Having performed calculations, it was demonstrated that calculation results correspond to actual ILI data. It has been shown that where the soil load is removed, the change to the curvature of the section is insignificant and it is advisable to carry out repair works by installing a prefabricated bent branch.

Conclusions

A methodology has been presented for developing design schemes using ILI data.

Examples have been given to show how design schemes were developed for sections with out-of-spec curvature using data from ILI devices with navigational systems.

Calculations have been performed which predict the curvature of sections during and after repairs are carried out. The results obtained may be used to calculate the strength of sections during and upon completing repair works.

References

1. Ya. M. Fridlyand, A. M. Korolyonok, Yu. V. Kolotilov, 2016. Monitoring repair costs in safe operating conditions for trunk

pipelines, Science and Technologies: Oil and Oil Products Pipeline Transportation, 4, pp 38-41.

2. B. Ainbinder, Strength and resistance calculations for trunk and field pipelines. M. : Nedra, 1991, p 288.

3. P. P. Borodavkin, Underground trunk pipelines. M.: Nedra, 1982, p 384.

L. A. Babin, L. I. Bykov, V. Ya. Volokhov, Standard calculations for constructing pipelines. M.: Nedra, 1979, p 174

4. E. M. Yasin, V. I. Chernikin, The stability of underground pipelines. M.: Nedra, 1967, p 120.

5. P. V. Burkov, M. A. Filimonenko, S. P. Burkova, 2016. Stress-strain state of pipeline depending on complicated environment. IOP Conference Series: Earth and Environmental Science, 43, 1.

6. Altaee, B. H. Fellenius, Finite element modelling of lateral pipeline-soil interaction: proceeding of 14th International conference on Offshore Mechanics and Arctic Engineering (OMAE 96), 1996, Florence, Italy.

7. R. Popescu, A. Nobahar, 3D Finite element analysis of pipe-soil interaction – Effects of groundwater. Final Report C-CORE. St. John, 2003. 34 p.

8. T. Tanaka, M. Ariyosh, Y. Mohri, Displacement, stress and strain of flexible buried pipe taking into account the construction process. Numerical methods in geotechnical engineering. Collection of scientific papers. SPb., 2012; 282–288.


18

Independent energy and commodity price reporting agency Argus invites you to participate in the

Argus Oil Pipeline Systems 2018: Focus on Sustainability international conference,

which will take place in Prague, Czech Republicon 17-18 May, 2018.

The event’s general partner is the International Association of Oil Transporters (IAOT).

The conference will bring together international experts, scientists and academics to discuss the trends and prospects for pipeline transportation and its role in securing sustainable oil supplies. Participants will also focus on technical solutions and innovation for the oil pipeline industry.

The programme provides a unique opportunity to visit Mero’s Central Crude Oil Tank Farm at Nelahozeves, one of the biggest such facilities in central Europe, and Unipetrol’s Kralupy refinery. Key topics of discussion:

• Logistics of crude supplies to Europe: pipeline projects• Quality control in pipeline transportation of variable quality crude • Energy efficiency in oil pipeline transportation • Applying innovative solutions in construction of oil pipelines, including in challenging climates• Operating pipeline infrastructure: current challenges and future technologies• Technologies for detecting leaks and defects in oil pipeline systems

For more details, please, visit IAOT web-site www.iaot.eu/iaotconference 2018

or contact Argus Media Marketing department ([email protected], tel. +7 495 933 75 71 ext. 437)

or the IAOT Secretariate ([email protected], tel. +420 601 358 491).


19

An analysis of methods and approaches to evaluating reliability when predicting equipment failures

by Oleg V. Aralov and Ivan V. Buyanov*Pipeline Transport Institute, LLC, Moscow, Russian Federation

THE QUALITY OF EQUIPMENT plays an important role in ensuring its reliability. The production of poor-quality goods at manufacturing facilities can be avoided when the manufacturer observes the requirements of state standards, construction regulations

and rules, technical specifications. etc. However, checking that the manufacturer is complying with these requirements is rather complicated.

The authors of this article have analysed approaches to creating a mathematical tool capable of making a quantitative and qualitative prediction of equipment failures, evaluating current operational readiness, and determining the optimum degree of load to ensure principles of maximum reliability and conservability.

Approaches to quantitative predicting equipment failures, developed and described using the research results, could be introduced into the current system of conformity assessment, given that there is a sufficient amount of statistical data regarding equipment functioning. These data have been collected by Transneft PJSC, over the last decade.

Keywords: conformity assessment, reliability, product quality, equipment failure prediction, mathematical tool, oil pump

Corresponding author’s contavt details:


Introduction

The system of trunk pipeline transportation for hydrocarbons includes a large quantity of equipment designed for various technological operations. The variety and number of types of equipment depends on the types of production facilities at which it is used. For example, various shut-off, control, and safety valves, pipeline systems, cathodic, ground, and drainage protection systems etc. are used at linear facilities. Crude oil quality control systems (CQCS), tank farms with service equipment, mechanical and power equipment for pumping hydrocarbons (main-line pumps and electric motors) are used at site facilities. In this article, an oil-pumping units (OPUs) will be examined

as an integrated facility consisting of a multitude of structural modules.

An OPU is a multi-component equipment, and has a complex design. It includes a power-driven mechanism, pumping-power equipment, variable-frequency pump rotation mechanisms, as well as cooling systems with various modifications. In particular, at the present time, five different types of electric motor are in use (each of which includes several models), and five basic mechanisms for variable-frequency rotation of the pump rotor (means the mechanisms installed in OPU, which allow the variable RPM; bypassing and choking are not considered in this case). Pumping-power equipment also includes a large number of operating


20

models: today, around 20 basic models of main-line pumps are in use. This increases the variety of assemblies of different versions (up to approximately 500 options).

Considering the variety of OPU options, a general diagram is presented here in simplified form for ease of analysis (Fig.1).

An OPU as a multi-component equipment has a large number of failure types, which can be divided into two basic groups: latent factory, and operational. As a result of analysis, it has been established that in the period from 2013 to 2015, 64% of irreparable OPU failures affected main-line pumps, and only 36% affected electric motors. This indicates that main-line pumps are by far the least reliable element of OPU. The division of the specific quantity of failures into the separate types most characteristic for OPU is shown in Fig.2.

In accordance with the database for the products quality assessment (QA DB), which is being developed by the leading scientific research institute at Transneft PJSC, all types of OPU failures were sorted into specific groups for the period from 2013 to 2015. The groups were based on similarities in the reasons why the failures occurred. The basic types of OPU failure are shown in Fig.3, where the blue boxes mark types of failures related to the electric drives, and the black boxes mark those related to the main-line pumps. As

can be seen, the reasons for these failures may have either factory or operational character.

The specific number of operational failures out of the total number of failures at main-line pumps was determined through detailed analysis, which involved identification of the basic reasons for the failures to occur. They include:

• imperfections in the construction of the frame at the manufacturing plant;

• the presence of defects in the main line pump case castings;

• insufficient reliability of attachment fixtures for the bearings and pump shafts;

• axial shift of the pump shafts;• poor quality repair and

maintenance works;• rapid changes to the operating

parameters of main-line pumps.

During analysis it was established that the specific number of operational failures was 47%, while the remaining 53% belonged to the category of latent factory failures.

A conformity assessment system has been created at Transneft PJSC aimed at preventing the appearance of failures and worsening equipment characteristics during operation. This assessment is carried out in order to establish the conformity of manufactured articles to

Motor Pump

Explosion-proof synchronous electric motors;

•General-purpose industrial synchronous electric motors;

•Electric motors with voltage of 6(10) kV, for main line and

booster OPUs;•Horizontal explosion-proof

induction electric motors;•Vertical explosion-proof induction electric motors;

Oil and oil-product centrifugal

main line pumps and

electric pump units on their

basis

Fig.1. Oil-pumping unit layout.


21

the technical regulations of EurAsEC (the EU Customs Union and the Russian Federation), to national standards, construction rules and regulations, the high-level budget estimates, as well as to general and special technical specifications (GTS and STS respectively), where they do not contradict federal regulations. GTS and STS are developed on the basis of integrated scientific studies and set the requirements for the most significant types of equipment and materials with the aim of ensuring the greatest safety of hydrocarbon transportation.

Given the imperfect nature of equipment and technological process, an accumulation of latent fatigue stresses can be observed fairly often at various stages of product manufacture. These stresses are impossible to detect during the outgoing inspection, carried out by the manufacturer, of the given product type when it is released to the customer.

In turn, it is also difficult to assess the presence of latent factory defects during the incoming inspection when the equipment is delivered.

Latent defects become apparent after the acquired product has run many operating cycles. This significantly complicates assessing the nature of the occurrence of the given defect at its non-steady state. Given these conditions, it seems hard to prove the natural or accidental reason of the defect’s occurrence without statistical processing of a large sample group of defects in this type of products, which have the same sorts of failures during operation.

Where a defect which has arisen during operation of some type of product is naturally-occurring (i.e. is occurs due to the development of a latent defect), then there are grounds for increasing the requirements for the equipment

Fig.2. Specific quantity of the most characteristic failures for OPU, %:

1 - axial shift of the pump shaft2 - insufficient frame stiffness

3 - mechanical defects in the form of through-thickness cracks, pores etc.4 - defects in the seal membranes

5 - defects in the pump case casting6 - axial shift of the shaft

7 – leakage of mechanical seals8 - increased vibration of the bearing units

9 – short-circuit in the stator winding10 - failure of the vacuum circuit-breaker

11 - defects in the stator winding insulation12 - rotor disbalance

13 - loose anchoring for foundation14 - emergency temperatures of the stator winding.


22

in use and toughening the system for assessing it. It should be noted here that the development of company in-house requirements for product quality is grounded in the necessity of ensuring maximum safety and the operating conditions specific to that company. The quality requirements for manufacturing the basic product types in operation at Transneft PJSC have a scientific basis in the R&D results for creating various methods to establish the reasons for defects arising, identifying optimal operating modes for equipment, etc.

Methodology

The delivery of high-quality equipment by manufacturers guarantees its reliability during operation. However, in practice cases of manufactured defective goods can be found. Moreover, manufactured defective goods may include both obvious defects and latent defects, which may lead to failure in certain operational conditions. Manufactured defective goods can also be understood as products

released with sufficient deviation (both in design features, and materials used) from the actual operating conditions that, in the future, will also lead to the incidence of failure. The occurrence of poor-quality (defective) products at manufacturing facilities can be avoided if the manufacturer complies with the requirements of state standards, construction rules and regulations, technical specifications, etc. However, it is extremely challenging to check whether a manufacturer is complying with these requirements. The solution can be found in the organization of multi-level procedures for incoming goods inspections from manufacturers, which should be based on the internal requirements of the customer. This method has been implemented effectively by Transneft PJSC where a register of basic types of goods is being formed and updated.

A current priority is creating a separate methodological tool, which would allow qualitative and quantitative predictions of failures to be made, and the equipment’s current operational readiness to be

Motor

Electrical

Pump

Mechanical

1. Defect in the insulation of the electric motor case;2. Defect in the insulation on the stator winding;3. Failure of the vacuum circuit-breaker;4. Short-circuit in the rotor winding;5. Failure of the protective thermal resistor;6. Loose anchoring for foundation;7. Emergency temperatures of the stator winding.

1. Defects in the welded joints;2. Defects in the impeller casting;3 Insufficient frame stiffness;4. Defects in the seal membranes;5. Defects in the pump case casting;6. Other mechanical defects in the form of through-thickness cracks, pores etc.;7. Damage to the bearings;8. Axial shift of the shaft;9. Leakage of mechanical seals;10 Increased vibration and noise of the bearing units;

11. Rotor disbalance;

12. Emergency temperatures of the stator winding.

Fig.3. Types of OPU failures, which occurred during operation, in the period from 2013 to 2015.


23

assessed. It would also enable the optimum utilization rate to be identified, in order to ensure maximum reliability and conservability (here the equipment characteristic is implied, which is described by the indicator ‘average period of conservability’).

At present there are methods in Russian and international practice which allow the technical condition of equipment during operation to be determined, and prediction of its behaviour after a certain number of operating cycles. However, none of the methods analysed in this article allows for a solution to identifying the original reason for a defect to arise, which casts doubt on their practical use. It is therefore a relevant and promising direction of research to develop a methodological tool which would allow companies in the oil and gas industry to make qualitative and quantitative predictions of equipment failure.

As a result of this analysis, it has been established that the following methods are the most relevant in terms of applied mathematical approaches and possibilities of evaluating the system’s technical condition:

• integrated condition monitoring of the dynamic objects and systems;

• point estimation of the probability of failure-free work in a technical system, based on a complete sample group (‘failure-free’ is understood as the equipment characteristic, which is illustrated by such indicators as the probability of failure-free operation, the mean time between failures (MTBF), the mean time to failure (MTTF), the failure rate);

• calculating the probability of detecting defects, initial and residual defectiveness using results from non-destructive inspection;

• constructing probability models of reliability based on sample groups of current conditions;

• computational-experimental method of evaluating reliability

indicators for the system as a whole, based on results of separate tests for the reliability of its components.

It should be noted that the method of point estimation of the probability of failure-free work in a technical system, based on a complete sample group, involves computational technology. It may be used when analysing and making an exact estimation of the information for reliability indicators for a technical system. It enables to develop a tool capable of automating the point estimation of the probability of failure-free work in a technical system based on a complete sample group. The functional of the tool is attained by using a specific number of computational blocks with specially organized links between them, which enable to implement the method of point estimation of the probability of failure-free work in a technical system, based on a complete sample group. This method can be expressed mathematically with the formula:

P t p P t t pd t t

NN N

∧= + − −

* ( ) ( ) ' ( )

( ) '' ''0 1 1

where:

t = the length of operating time, in hours

ˆ * ( )P t is the probability of a work failure arising during the operating time

P0(t) = is the a priori value of the

probability of failure-free work during the operating time

d(t) = the number of failures observed in the interval of time between 0 and t

N = the number of experiments for which the operating time of the technical system was calculated

pN = the relativity factor, which

characterises the share of a priori information impact on the probability estimation for failure-free work, calculated according to the formula:

p

NN =β


24

where:

β is the number of events which involved receiving reliable information about the probability estimation for failure-free work.

The method described here allows a point estimation to be made for the probability of failure-free work in the system, i.e. to assess its discrete value. In practice, however, a continuous estimate of the system’s technical condition is needed. This can lead to the distortion of received results and severely delayed responses in the system when applying this method to the non-discrete inspection types.

The method of calculating the probability of detecting defects, initial and residual defectiveness using the results of non-destructive inspection is distinguished by the fact that for a specific product or group m of the products of same type, the critical dimensions ccs of the defects in operational mode can be calculated, together with the dimensions [c]po.

of defects which are permissible in operation, and the dimensions [c]pm

of defects which are permissible in manufacturing. The results of the inspection are presented in the form of a bar graph in coordinates (Ndd, c), where Ndd

is the number of defects found during the inspection, and c is the typical size of a defect. The required bar graph can be approximated with the equation:

N

A exp

dd

n

χ

χ η α χ χ η

( )=– – – – – ( ) [ ( )] – 1 1 0

N

A exp n expdd χ

χ η χ χ η( )=

– – – – – –( ) ( ) [ ( )] 1 1 1 0

where:A, n, α, η are constants which are

calculated based on approximating as much as possible the Equn Ndd(c) to the results of the inspection, presented in the form of a bar graph;

c 0 is the minimum defect size which may be detected.

The initial defectiveness Nres can be

calculated using the formula:

N A or N A exp nidn

id, ––= = ( )χ χ

The probability of detecting a defect Ppdd is calculated using the formula:

P exppdd – – – – –[ ( )]= ( )1 1 0η α χ χ η In turn, the residual defectiveness N

res is

calculated as the difference between Ndd and Nres.

The method of calculating the probability of detecting defects, both initial and residual, using the results of non-destructive inspection largely depends on the input parameters of the inspection, and specifically on the values of permissible and critical defect sizes during operation and manufacture. It is practically impossible to acquire this information for all types of defect from companies in the oil and gas industry due to the large quantity of the latter. Moreover, the estimation of defect sizes in equipment which is necessary for calculations significantly complicates the process of this probabilistic method implementation.

The method of integrated condition monitoring of the dynamic objects and systems involves establishing the interval boundaries for permissible parameter values, which are entered into a base for managing monitoring methods directly before analysis is carried out. The type of analysis is also determined, as well as guidelines for presenting the results. Remote and contact methods are then used to determine values for the groups of the inspected parameters and to compare them with permissible values; then the degree of conformity to the interval of permissible values can then be calculated. As a result, a graphic image can be formed in the polar coordinate system, which allows the condition of the dynamic system to be interpreted graphically. After this, the converted information is transferred to a processing and control centre, where graphic and textual solutions are compared to simultaneously present the


25

results of assessing the condition of the dynamic system.

The method examined here allows the condition of the technical system during operation to be determined fairly accurately, but at the same time it entirely fails to fulfil the requirement for finding a reason for failure to occur. Therefore, using the mathematical process described for this method of assessing the condition of dynamic objects and systems may be effective for solving the task formulated here, but under the condition of reorganizing the process of statistical and probabilistic evaluation. Theoretically, this reorganization can be carried out by combining the method of integrated condition monitoring of the dynamic objects with the methods described above: the method of point estimation of the probability of failure-free work in a technical system based on a complete sample group, and the method of calculating the probability of detecting defects, initial and residual defectiveness using the results of non-destructive inspection (both taken separately and in combination).

The combination of the methods listed above allows the moment when a defect is formed to be identified, as well as the degree of its development, and the probability of a similar defect occurrence, as well as the reason of it occurrence can be approximately determined. However, it is still very difficult to identify precisely whether the defect’s appearance has a natural or accident-related nature. Taking into account the fact that the initial parameters characterizing the defect during analysis should not be used when forming a methodology for evaluating the product’s technical condition due to increase of mathematical error in the model obtained, it may be concluded that using a combined approach to establish the technical condition of the equipment is not advisable.

In contrast to the methods of determining the technical condition of equipment outlined above, a method of forming a probability model for reliability based on

sample groups of the current conditions, and a computational-experimental method of evaluating indicators for the reliability of the technological complex based on the results of separate tests of the reliability of its components, seems to be more independent and universal for their approbation in real equipment operating conditions at oil and gas industry enterprises.

The method of building probability models of reliability based on samples groups of current conditions involves designing the probability model of failures based on the results of equipment reliability tests. In the case of the accident-free operation, there exists the observation ordered from the right; while if the device failed, it means that the failure occurred before the moment of testing, and the observation is ordered from the left. The obtained sample group of the observations ordered from the left and from the right (without full observations) is called the sample group of current states, after which it becomes possible to calculate the relationship of the Fisher information quantity regarding parameters in the sample group of current states to the Fisher information in the full sample group. As a result of maximizing the Fisher information quantity, the optimal moments for testing the products can be established (from the standpoint of highest likelihood evaluation accuracy).

This method allows the duration of testing products to be fully evaluated in order to detect the maximum quantity of embryonic defects in the equipment. However, its use to determine the technical condition of the equipment without excluding the latter from technological processes does not seem to be possible.

The computational-experimental method of evaluating reliability indicators for a technological complex, based on the results of separate tests, is a system of mathematical models. These models allow to convert input parameters, which are presented in the form of results from equipment reliability tests, into output


26

parameters, which allow the equipment’s current condition to be determined using the values of reliability indicators. As the method described previously, this method is not appropriate for most of equipment at oil and gas industry enterprises (this is especially true for process equipment units, which do not have technical back-up), because it is impossible to carry out

inspections without excluding equipment from the technological process.

Evidently, there is an insufficient quantity - both in Russian and international practice - of methods which enable equipment failure to be predicted using statistical probability (and which satisfy the relevant technical specifications). It can thus be

Ope

ratin

g tim

e of

the

equi

pmen

t, m

onth

s

Failure rate, 1/month

Average at Transneft PJSC

An individual unit of equipment

Fig.4. A comparison of the equipment failure rates versus operating time for pumps from an arbitrary series between the following values:

Failu

re in

tens

ity, 1

/tim

e; n

umbe

r of

failu

res

Operating time

Fig.5. The calculated curve for predicting the number of equipment failures over time.


27

concluded that creating a mathematical process which is capable of making a quantitate and qualitative prediction of equipment failure, evaluating its current operational readiness, and determining the optimum capacity utilization rate to ensure the principles of maximum reliability and conservability, is a topical and promising area for R&D studies.

Results

The proposed mathematical model will be based on the Weibull distribution, the key variables of which will be failure rate and the equipment operating time. The failure rate is the apparent density of equipment failures, calculated for the moment in time under examination or for the operating time, given the condition that before this moment no failure had occurred. It is worth noting here that the Weibull distribution used in this case may have a much more informative character. The established values of average failure rates for separate types of equipment may also be used to make a quantitative prediction of failures, in particular the quantity of failures in separate batches of a given type of equipment.

Correlations are outlined below which enable the number of equipment failures to be predicted based on specific intervals of operating time with reference to the average values for equipment failure rate, calculated for all units of technological equipment in operation at Transneft PJSC.

The basis for the proposed functions is the assumption that all similar modifications and types of equipment have analogous quantitate and qualitative characteristics regarding failures. In other words, if on average at Transneft PJSC pumps from an arbitrary series (for example single-section pumps of the NM series) have the curve of failure rate versus operating time, shown in Fig.4 by the blue curve, then individual pumps of the same series will have analogous characteristics for failure rate versus operating time, as shown by the red curve.

This assumption means that when using the characteristic for failures of all units of individual process equipment in operation at Transneft, PJSC over a specific interval of time, values can be calculated for certain intervals of the operating time. These values will be fair both for individual units of equipment of the given type in the time range under examination, and for equipment issued or brought into operation during a period not corresponding to the original time interval.Assigning the task of predicting the number of equipment failures at certain stages of the operating time can be formulated in the following way. This assumes known average values of failure intensity at the necessary stages, determined for equipment of this type on average at Transneft PJSC.

Assume that for a certain type of equipment, the relationship between failure intensity and the total operating time has been established (Fig.5). Then the individual units of the equipment of this type, as was mentioned above, will have analogous characteristics. That is, at separate time intervals the number of failures may not coincide with the average arbitrary value, calculated for the whole codification series; however, the function will be in a form comparable to the general function.

Supposing that for a certain modification of an arbitrary type of equipment, statistics were collected regarding failures over a set period of time. Figure 5 shows the failure rate for a given equipment versus the operating time (blue curve), as well as the change in the specific number of failures which occurred at a certain interval of time versus the total operating life of the equipment (green curve). If these curves are divided at certain time intervals, then each interval will be characterized by its own value for failure rate for equipment λ and by the number of equipment failures r. That is, the time interval examined Dt

i

will have its own corresponding values λi

and ri.

As has been established above, the


28

relationship of the failure rate, calculated for all units of equipment of a specific type, will be the basic function, i.e. the values for failure rate, established for individual units of technological equipment, will tend towards the given function by their absolute value. Thus, for the interval ∆ti i i: λ λ1 → where λi

1 is the failure rate, calculated for an individual unit of the process equipment.

This assertion can be confirmed by the fact that the equation for failure rate alters in proportion to the ratio r t

Nav

∆( ) .

This is because it is functionally dependent on only two dynamic parameters: the number of failures in the specific interval of operating time and the average quantity of equipment properly functioning in a specific interval of operating time. This also accounts for the fact that in order to describe the failure rate curve for equipment of a certain type as a whole at Transneft PJSC, the proportional relationship r t

N

i

i

( )∆∑∑ av

is

used, which is an additive ratio of the separate elements r t

Nav

∆( ) .

These elements characterise the functional interrelation of the failure quantity for equipment for a certain interval of operating time and the average quantity of operational equipment at a given time interval. That is, coefficients obtained for the given correlations will co-ordinate: at corresponding stages it is highly likely that the dynamics of change in the failure quantity (either on the positive or the negative side) in comparison with the former stage will be identical. This serves as the basis for the possible use of failure rate values for a certain type of equipment established at Transneft PJSC for predicting the number of failures for

separate units of process equipment in the future.

Number of failures for one unit (several units, or batch) of equipment should be calculated at stages of its lifetime cycle. For this common failure rate values for equipment at separate time intervals are established, as well as the initial value for the number of failed equipment. For example, for the time interval r(Dt)

i–1 (denoted by the solid blue and solid

black curves in Fig.5) a curve is shown for equipment failures, which should be obtained. The crosshatched area in Fig.5 depicts the first interval of time at which it is necessary to predict the number of equipment failures, the interval of time is marked out (by the green area) which is characterized by a specific number of equipment failures (as initial data for calculation).

Having denoted the target value for the number of equipment failures in the predictable time interval r(Dt)’, this value can be expressed through the general equation for failure rate:

r t N t

r tN t N t r t

t

av∆ ∆

∆∆

∆

( ) =

=+ −

'

( ) ' ( ) [ ( ) ( ) ']

,

λ

λ 0 0

2 (1)

where N0(t) is the quantity of properly

functioning equipment at the moment equipment started operating from the specified interval of time.

Equn 1 describes only the first in order time interval for equipment operation. Having expressed it in a general form for possible implementation across the whole range of operating time, Equn 1a is obtained - see below.

r tN r t N r t r t

t

r t

ii i i

( ) '( ) ( ) ( ) '

( )

∆∆ ∆ ∆

∆

∆

=− + − −( )

∑ ∑− −λ

0 1 0 1

2

''( ) ( ) '

ii iN r t r t

t=− −( )∑ −λ

2 2

2

0 1∆ ∆

∆

(1a)


29

In the relationships presented above, the value of the equipment failure rate is included in the equations without index because the given parameters at specific intervals of the operating time will be differentiated in Equns 2 and 3 (see below).

After several conversions of Equn 1, the final results can be obtained: as shown in Equns 2 and 3 in which:

λi = the general failure intensity for a certain type of equipment, established as a whole at Transneft PJSC in the predicted interval of time;r t i( )∆ −∑ 1

= the total number of equipment failures in the intervals of time preceding the predicted interval;

λi–1

= the general failure intensity for a specific type of equipment, established as a whole at Transneft PJSC at an interval of time preceding the predicted one;

Dt = the value of the interval of operating time used to analyse the predicted failures number.

The values r(Dt)’ obtained at specific intervals should be reduced to the general trend for the value of general failure rate. The equation used for this is usually applied for discounting cash flow:

PP

En

t=

+( )1

where:

Pn = the value of the probability

of failure-free work, observed

over some time of equipment operation;

P = the value of the probability of failure-free work, characteristic for the initial period of equipment operation;

E = the value of the discount rate;t = the year of equipment operation.

Discussion

Applying the method of mathematical discounting allows for the correction of the number of equipment failures, which was originally obtained at the first stage of prediction using Equn 3 for the probability of failure-free work. It also makes it possible to average the given value for the examined interval of operating time to the general trend of values for failure rate, calculated for all technological units of equipment of a specific type. These conversions allow for better calculating accuracy.

The proposed relationship is in a general form:

r t r t Pi i itav( ) ( ) ' ( )∆ ∆= ⋅ + ⋅1 0λ

(4)

If Equn 3 is substituted into Equn 4, the target relationship in Equn 4a (see below) can be obtained, in which:

t0 is the operating time of the equipment, corresponding to the end of the running-in stage, which is calculated using the formula in Equn 4b (see overleaf).

r tt

N r t tii

i i i( ) ' ( ) ,∆∆

∆ ∆12 0 1 1+

= −

− −∑λ

λ λ

r tN r t t

ti

i i i

i( ) '

( )∆

∆ ∆

∆=

−

+

− −∑λ λ

λ0 1 1

12

(2)

(3)

(4a)r tN r t t

tPi

i i i

ii

tav( )[ ( ) ]

( )( )∆

∆ ∆∆

=−

++

− − ⋅∑λ λλ

λ0 1 1

12

1 0


30

The basis for using values ti, N

i–1, λ

0, r(Dt)

i

is presented in Ref.1.

The adequacy of this model can be proved using the example of the following example.

It is known that one type of equipment was in operation at Transneft PJSC, totalling 180 units, from 2006 to 2010. In this period, numbers of failures were established at certain intervals of operating time, and the following reliability indicators were determined: probability of failure-free work, failure rate. The results of this analysis are presented in Table 1.

Number of failures should be determined for a certain batch of equipment of the same type, 120 units of which were brought into operation in 2011. It is known that during the 0-100 operating days, ten equipment failures occurred (the number of failures in the following intervals of operating time is also presented in the table as rint with values Navint and λint corresponding to them, aiming to make it possible to compare results in the future).

The calculation will be performed for up to 700 days of the operating time of the equipment. The average value of equipment failure rate corresponds

t tr t

N tr t t

N tt r t

ii

i ii i

i ii

0

1

0

1

2

= +−

−

⋅

−

−

−( )( )

( )∆

∆

∆

λ

ii

i iiN r t

r t

2

2

2

1

2

− +− ( )( )

∆∆

(4b)

Indicator

Operating time, in days

0–100 100–200 200–300 300–400 400–500 500–600 600–700 700–800800–900

2 3 4 5 6 7 8 9 10 11

r(Dt) 12 8 6 4 3 8 9 10 13

r(t) 12 20 26 30 33 41 50 60 73

Nav

174 164 169 172 174.5 173 167.5 166 163.5

P 0.93 0.88888 0.8555 0.8333 0.8166 0.7722 0.7222 0.6666 0.5944

λ 0.01 0.00049 0.0004 0.0002 0.0002 0.0005 0.0005 0.0006 0.0008

IndicatorOperating time, in days

0–100 100–200 200–300 300–400 400–500 500–600 600–700

2 3 4 5 6 7 8 9

rint10 7 5 4 3 8 11

Nav

int 115 106.5 100.5 96 92.5 87 77.5

λint 0.00087 0.000657 0.000498 0.000417 0.000324 0.00092 0.001419

r(Dt)’ 10 5.041051 3.850539 2.583146 1.953224 5.373318 5.918806

r(Dt) 10.58811 5.628682 4.522089 3.187314 2.530042 7.236001 8.231729

Table 1. Reliability indicators for a certain group of equipment of arbitrary type in the Transneft system.

Table 2. Results of analysis predicting the number of failures for a certain group of equipment of an arbitrary type.


31

to this operating time. The results of the calculation are presented in Table 2. Figure 6 compares the dynamics of predicted failures with target data at stages of operating time.

Under the conditions of this example, the total number of failures for equipment of this type in the operating time period from 0 to 700 hours was 48. As a result of primary analysis, the value equal to 34.72 was calculated. The corrected value, based on the probability of failure and on the average level of failure rate, was equal to 41.924. Thus, the proposed mathematical model enables evaluating the number of failures for specific technological unites of equipment and individual batches with maximum error of up to 15% (with an average error in the model of 4.5%). It is also worth noting that refining Equn 3 makes it possible to increase the calculation accuracy by approximately 20%.

Conclusions

At present, there is a considerable number of latent factory failures of equipment at production facilities of the oil and gas industry (based on the authors’ estimate,

the proportion of failures due to latent factory defects comprises around 32.5% of the total quantity of failures for equipment operating in the Transneft system). Correspondingly, measures aimed at creating and subsequently using industry-wide systems to assess product conformity to established requirements are fundamental measures for managing the reliability of the equipment. It should be noted that Transneft PJSC is one of the foremost organizations in this sector, and the corporate system of conformity assessment is implemented at all production facilities within organizations in the Transneft system. Due to the established tendency for optimizing the resources used in production (including during equipment inspection), the basis of the corporate system of conformity assessment is made up of various methods and methodologies for probability prediction of the condition of equipment. However, the probabilistic-statistical approach is an essentially new step in resolving this issue in Russian and international practice, therefore R&D studies in this area are particularly important and relevant at the moment.

The approaches developed and described in this article to making a quantitative

Indicator

Operating time, in days

0–100 100–200 200–300 300–400 400–500 500–600 600–700 700–800800–900

2 3 4 5 6 7 8 9 10 11

r(Dt) 12 8 6 4 3 8 9 10 13

r(t) 12 20 26 30 33 41 50 60 73

Nav

174 164 169 172 174.5 173 167.5 166 163.5

P 0.93 0.88888 0.8555 0.8333 0.8166 0.7722 0.7222 0.6666 0.5944

λ 0.01 0.00049 0.0004 0.0002 0.0002 0.0005 0.0005 0.0006 0.0008

IndicatorOperating time, in days

0–100 100–200 200–300 300–400 400–500 500–600 600–700

2 3 4 5 6 7 8 9

rint10 7 5 4 3 8 11

Nav

int 115 106.5 100.5 96 92.5 87 77.5

λint 0.00087 0.000657 0.000498 0.000417 0.000324 0.00092 0.001419

r(Dt)’ 10 5.041051 3.850539 2.583146 1.953224 5.373318 5.918806

r(Dt) 10.58811 5.628682 4.522089 3.187314 2.530042 7.236001 8.231729

Operating time of the equipment, in hours

Num

ber

of e

quip

men

t fai

lure

s

Target number of failures

Predicted number of failures

Fig.6. Comparison of the dynamics of predicted failures

with target values.


32

prediction of equipment failures may be introduced into the current system of conformity assessment, given that over the past decade a sufficient quantity of statistical data has been collected about the equipment functioning at Transneft PJSC. Using probability-based methods of prediction makes it possible to improve the current systems of equipment inspection and, consequently, to increase its failure-free operation, conservability, and general operational readiness (by ‘general operational readiness’ the authors understand the characteristic of the equipment, which is described by basic integrated reliability indicators: the coefficient of readiness and the utilization rate).

References

1. O.V.Aralov, Yu.V.Lisin, and B.N.Mastobaev, 2017. Methodological principles for managing product quality using conformity assessment mechanisms in trunk pipeline transportation. Monograph. St Petersburg: Nedra, p 350.

2. O.V.Aralov, 1999. A methodology for optimising the planning of research and engineering work in technical means, communication systems, and automization, when using programmed planning. Dissertation for Cand. Sci. (Eng.) St Petersburg: MAC, p 285.

3. O.V.Aralov and A.V.Babkin, 1997. Problems in optimising the planning of research and engineering works in communications technology: deposited manuscript. M. : CMRI MoD RF.

4. O.V.Aralov snd A.V.Babkin, 1997. The basis for the optimization task in planning research and engineering works in communications technology. St Petersburg, p 20.

5. O.V.Aralov and A.V.Babkin, 1997. An analysis of methods and the current condition of solving the optimization task in planning research and engineering works in communications technology. St Petersburg, p 28.

6. O.V.Aralov, I.V.Buyanov, B.N.Mastobaev, N.V.Berezhansky, and D.V.Bylinkin, 2016. The main statements of optimization methodology of life-cycle parameters of process equipment. Science & Technologies: Oil and Oil Products Pipeline Transportation, 16 (6) pp23–29.

7. O.V.Aralov, D.V.Bylinkin, and N.V.Berezhansky, 2016. Developing a methodological apparatus for calculating the probability of a defect appearing in equipment during its manufacture on the basis of the linear-dynamic programming method. Pipeline transportation. Material XI, International Scientific Research and Practice Conference, Ufa: USOTU publishers, 2016. pp 12-14.

8. O.V.Aralov et al., 2016. Determining the optimal time for qualification testing of pumping-power equipment. Pipeline Transportation: Material XII, International Scientific Research and Practice Conference, Ufa: USOTU publishers, 2017. pp 126-129.

9. E.Y.Barzilovich., Y.K.Belyaev, V.A.Kashtanov, I.N.Kovalenko, A.D.Solovyev, and I.A.Ushakov, 1983. Aspects of Mathematical Theory of Reliability. B.V.Gnedenko, editor. Moscow (M): Radio i Svyaz, p 376.

10. R.E.Barlow aaand F.Proschan, 1960. Mathematical theory of reliability. Moscow: Soviet Radio, p 488.

11. M.G.Kendall and A.Stuart, 1976. Multivariate statistical analysis and time series. Moscow (M): Nauka; p 736.

12. A.I.Kobzar, 2006. Applied mathematical statistics for engineers and scientists. Moscow (M): Fizmatlit, p 816.

13. Y.V.Lisin, O.V.Aralov, B.N.Mastobaev, N.V.Berezhansky, and D.V.Bylinkin, 2016. Development of a mathematical model for evaluating financial feasibility of the R&D plan for creation of complex technical systems. Transport and storage of oil products and hydrocarbons (3) pp17–23.

14. Y.V.Lisin, O.V.Aralov, B.N.Mastobaev, N.V.Berezhansky, and D.V.Bylinkin, 2016. Development of mathematical model for parameters optimization of R&D plan at homogeneous groups of technological equipment. Transport and storage of oil products and hydrocarbons, (4) pp 5–10.


33

Technical and methodological support of leak-detection systems at Transneft’s facilities

by R.Z. Sunagatullin, S.A. Korshunov*, and Yu.V. DatsovPipeline Transport Institute, LLC, Moscow, Russian Federation

THIS ARTICLE ANALYSES the current situation in the global market for leak-detection systems (LDS). The main operational problems for existing parametric LDSs are identified based on a comparative analysis of statistical data on leaks in European and

American trunk pipeline operators, and the proportion of leaks detected by LDSs. Reasons are formulated for these problems, which lead to deterioration in LDS characteristics. The study includes a brief classification and description of the most commonly used leak detection methods. Based on comparison of regulatory documentation in the field of LDSs in Russia and abroad, provisions are identified describing the requirements and important processes within the design and operation of LDSs, which are missing in the domestic regulatory framework and are recommended for inclusion. A comprehensive approach is proposed for the task of improving and introducing parametric LDS, as used by the Pipeline Transport Institute.

Key words: leak-detection systems, parametric methods, leak detection statistics, trunk pipelines

Corresponding author’s contact details:


Introduction

Oil and oil product leakage is a serious problem for pipeline transportation not only in Russia, but also elsewhere. Leaks carry a serious threat to environmental safety, and cause significant economic damage in the form of costs for pipeline repair work, oil-spill response, and punitive damages. They also affect the efficiency of oil transportation and negatively impact on the image of oil transportation companies.

The main causes of leaks [1] can be classified as related to natural wearing of pipes over time; natural phenomena; operator errors; damage inflicted during maintenance and repair works; and illegal tapping, which, according to official data [1-3], is becoming an increasingly significant problem.

Comparative analysis of leak occurrence and detection statistics: problems in the operation of existing LDSs

One pertinent question is whether it is possible at present to ascertain a noticeable reduction in the trend of the average number of leaks in trunk pipelines (TP) over recent years. Judging by statistical data for oil pipeline operation in Russia, the United States, and Europe, the answer to this question is no.

According to Rostekhnadzor – Russia’s Federal Environmental, Industrial and Nuclear Supervision Service - dozens of accidents involving fossil fuel leakages occur at the linear part of trunk pipelines every year in the Russian Federation. Similar statistics can be observed for Europe [1] according to the


34

European Association of Oil Companies (Conservation of Clean Air and Water in Europe - CONCAWE). The average number of leaks is not decreasing (Fig.1).

At the same time, this fact does not imply there has been no improvement in the quality of designing and operating trunk oil pipelines. These statistics are largely due to the ageing of the transport systems in operation, as well as the increased complexity and length of the pipelines, which naturally entails an increase in the likelihood of oil leaks.Furthermore, a significant factor contributing to the total number of oil leaks on trunk pipelines (henceforward TPs) is the theft of fossil fuels through illegal pipeline tapping. For example, a sharp increase in recorded oil leaks for the period from 2010 to 2014 (Fig.1) was precisely caused by thefts. This is also illustrated by statistics for attempts at such crimes at European pipelines, as shown in Fig.2. Thus, the statistics for leaks from TPs mean it can today be stated with confidence that the organizations operating oil- and product pipelines have a serious demand for effective pipeline leak-tightness control systems. Moreover, given the present situation of complex infrastructure involving long and inaccessible TPs, automated leak-detection systems (LDSs)

are of particular importance in terms of safely and efficiently operating pipeline facilities.

According to current forecasts [4], there will be steady growth in the market for leak identification systems in the near future. The positive trends forecast for the development of the global LDS market are influenced by a number of factors, such as the general prediction of increasing global oil consumption and oil production (Fig.3), the expectation of high energy consumption in Asia and in developing countries and, as a result, infrastructure development and expanding pipeline systems. Thus, given the current demand for leak-detection systems among oil transportation companies, and predicted pipeline system development, the efficiency of existing LDSs is an urgent issue.

A comparative analysis of historical data on the occurrence of leaks and their detection by LDSs demonstrates significant problems in the pipeline tightness control systems currently in use in Russia as well as elsewhere.

According to data from the Office of Pipeline Safety under the Pipeline and Hazardous Materials Safety Administration of the USA (OPS

Num

ber

of le

aks

Fig.1. Statistics for oil / oil products leaks from transportation pipelines (source - CONCAWE).

Value for one year

Current average


35

Num

ber

of a

ttem

pted

ille

gal t

appi

ng in

cide

nts

Value for one yearCumulative total

Fig.2. Statistics for attempted thefts

from transportation pipelines (source -

CONCAWE).

Oil production Oil consumption

Fig.3. Predicted global oil consumption

and oil production, million barrels per

day (Source - BP Statistical Review of World Energy, 2015).

Fig.4. Leak detection (total 960) in oil

pipelines from 2002 to 2012 (source -

PHMSA).

Detected by company employees at the leak locationDetected by LDS

Detected by LDSDetected by third parties

Detected by third partiesDetected by inspectors at pipeline management centres

Detected by inspectors at pipeline management centres

Other

Other

Detected by company employees at the leak location

Fig.5. Detection of “serious” leaks (total

71) in oil pipelines from 2002 to 2012 (source -

PHMSA)


36

PHMSA), it can be ascertained that despite the assurances of LDS manufacturers and LDS suppliers, the systems in use are currently capable of identifying only a small proportion of leaks [5]. Thus, Fig.4 shows general statistics for leak detection based on the analysis of American trunk pipeline operation. The number of leaks identified by LDSs was about 5% of the total number [6].

Furthermore, as shown in Fig.5, such a small percentage of detected leaks cannot be unequivocally attributed to the low intensity of most leaks. Low-intensity leaks are genuinely difficult to identify due to their insignificant impact on the technological parameters of pumping [6]. According to these statistics, from 2002 to 2012 the LDSs installed in American TPs were able to detect only 20% of so-called ‘serious’ leaks. These leaks resulted in losses of more than 1000 barrels of oil, which is a small fraction of the total number of such leaks.

The ‘effectiveness’ issues surrounding existing LDSs are also confirmed by statistical data [1] from operating European TPs (Fig.6). Despite the slight upwards trend in the average number of leaks detected over the past 40 years, largely attributable to growth in the length of TPs, great volatility can be seen in the proportion of leaks detected by LDS; while the annual values for the proportion

of detected leaks are consistently less than 50%.

LDS classification Work has long been ongoing aiming to build LDSs to solve the issue of reliable and prompt leak detection on trunk pipelines. During this time, many leak detection methods have been suggested as a basis for LDS, and many corresponding classifications proposed [7-12].

For the convenience of the following account, one of these classifications will be used, based on dividing LDSs into ‘external’ and ‘internal’. This takes into account the principles on which their functioning is based (Fig.7). This type of classification is given in regulatory document API 1130 [13], which is one of the most authoritative standards regarding tightness control systems on TPs.

Over the past 10 years, ‘external’ LDSs mainly based on remote, fibre-optic, and acoustic leak-detection methods have developed significantly.

Despite the objectiveness of the leak detection principle used in remote methods [14], such methods rely on periodic monitoring and have a number of significant limitations related to the inaccessibility of TP routes and weather conditions, which suggests it is expedient

Value per year

Current average

Length, in thousands of km

Fig.6. Leak-detection statistics (source - CONCAWE).

% o

f lea

ks d

etec

ted


37

to use them only as supplementary LDSs.The clear advantage of fibre-optic methods [14] is their potential ability to detect leaks with very low rate, and their high accuracy in determining the coordinates of such leaks along the TP route, thanks to the physical nature of such systems. The leak signal is formed on the basis of the interaction of the leaking oil or oil product with the sensitive distributed element of the system directly at the point of leakage. However, along with acoustic systems, these systems have serious disadvantages, which means they can be considered only as auxiliary monitoring systems. This is the very high cost of equipping trunk pipelines with a correctly operating system, and the high level of false alarms.

‘Internal’ LDSs deserve the most attention and, in particular, parametric methods of leak detection. These are currently

Fig.7. Classification of LDSs.the most widely used in the world, and

look to continue this trend in the future, according to current forecasts [4]. The wide distribution of parametric LDSs was achieved thanks to their ability to function using the telemetry equipment already installed on a TP, as well as their ability to work in any geoclimatic conditions along trunk pipeline routes.

The so-called RTTM-method (real-time transient modelling) and its variations should be singled out here [14]. This method is based on modelling non-stationary real-time TP operating modes. They are becoming an increasingly integral part of parametric LDSs, because of their ability to function independently of the operating mode at the process section.It should be taken into account that such methods require knowledge of a number of pipeline parameters (diameter, wall thickness, topology, location of

“Internal” LDS “External” LDS

Based on sensor readings for measuring parameters of the fluids

pumped inside TP (parametric)

Based on the results of ILI

Method of comparing local pressure

drops at a section

Method of monitoring the linear balance at a

section

Method of comparing the speed of change in flow rate at a section

Negative pressure wave method

Statistical methods

Methods based on real-time transient processes (RTTM method and its

variations)

Ultrasonic inspection devices

Magnetic inspection devices

Remote leak- detection methods

Methods based on aerial satellite imagery

Radar sensing methodsInfrared method

Laser gas-analysis method

Based on readings from measurement sensors located outside the TP

Fibre-optic methods(vibroacoustic, thermal

and other)

Acoustic methods


38

equipment) and oil properties (bulk modulus, viscosity, density), which may introduce additional errors. Causes of operating problems for LDSs

Improvements to LDSs aimed at solving the problems listed in the first part of this article are not possible without understanding the root causes of these problems.

In the authors’ opinion, the main reason leaks are missed on trunk pipelines as a result of incorrect LDS operation is the insufficient level of understanding of how the performance characteristics of these LDSs (such as location accuracy and leak rate, system response time, false alarms) depend on a large set of parameters for the process of oil pumping. Numerical estimates must be known for the impact on the LDS ability to detect the presence of a leak, and to determine the location and the volume of such parameters as the time of development and existence of a leak, the errors in measuring instruments and data-transmission channels, the discreteness of data acquisition, the threshold for data transmission, as well as many parameters of the current operating mode of the TP process section. Correct entire estimating these relationships for LDSs is not possible without understanding how these relationships are arranged for each parametric method separately.

The reason mentioned above indicates the insufficient degree of detailing the existing regulatory framework for designing and operating LDS. Due to the uncertainty of requirements for choosing leak-detection methods and telemetry characteristics, this in turn adversely affects the efficiency of LDS operation, which ultimately results in missed leaks.

A brief analysis of regulatory documentation for leak-detection systems in Russia and abroad

In order to unify the approach to developing and operating LDSs, as well

as to define and specify the requirements indicated in the previous section, it is necessary to make a comparative analysis of the regulatory documents in the field of LDSs used in Russia and elsewhere.

Major international organizations currently support several key regulatory documents defining requirements and recommendations for the design, implementation and operation of LDS: API 1130, API 1149, API 1175 (USA), CSA-Z662 (Canada), TRFL (Germany).

In Russia, the requirements for LDSs are determined by the regulatory documents of Transneft PJSC, which are divided by methods of leak detection in the following systems:

• parametric systems – OTT-13.320.00-KTN-051-12 (General Specifications);

• fibre-optic systems – RD-35.240.00-KTN-076-12 (Guiding document);

• combined systems (a combination of parametric LDS and LDS based on monitoring the passage of pressure waves caused by a leak) – RD-13.320.00-KTN -223-09 (Guiding document).

At present, one of the most credible organizations outside Russia in the field of safety regulations for the oil and gas industry is the American Petroleum Institute, which has an extensive regulatory framework of standards covering many issues of LDS design and operation.

In contrast to Russian regulatory documents, the standards of the USA, Canada, and Europe do not contain requirements for LDS characteristics such as sensitivity to the minimum detectable leakage, accuracy in determining leak coordinates, or detection time. Nevertheless, they determine the need for the existence and specific character of the use of methods which make it possible to obtain the characteristics listed with better indicators. The regulatory documents of the API details the methodology for


39

implementing LDS, taking into account measurement errors and the technological features of pipeline oil transportation. API also issues guidelines for constructing an interface in order to minimise the number of false alarms, operator actions in emergency situations, and training personnel to improve the efficiency of leak detection. Presented in this way, the material is a step-by-step guide to build the parametric LDS on the basis of data for the pumped fluids, taking into account the accumulated experience and most known factors affecting the required characteristics.

A comparative analysis of regulatory systems in Russia and elsewhere shows that some of the existing requirements and descriptions of technological processes presented in domestic regulatory documentation can be supplemented by the provisions of API standards, in order to improve LDSs:

• recommendations for using parametric methods for detecting leaks, taking into account the tasks to be solved and the level of TP instrumentation;

• recommendations for equipping trunk pipelines with measuring instruments for correct LDS operation;

• provisions regarding the dependence of the possibility of leak detection on the size and complexity of a TP, and the reliability and errors of the measuring instruments installed at the TP;

• recommendations for developing a methodology for the algorithmic control of various parametric methods of leak detection in the LDS framework.

Methods of solving problems: the integrated approach taken by the Pipeline Transport Institute to the task of improving LDS

Among the many important tasks at present in the field of mathematically

modelling the processes of pumping oil and oil products, developing specialized software and computer systems, as well as performing thermal and hydraulic calculations, the Pipeline Transport Institute has been assigned with one more task: to establish the Pipeline Transport Institute as the main developer and supplier of parametric LDSs for the needs of pipeline transportation for Transneft PJSC. The Institute’s goal is to develop, upgrade, and implement an efficient LDS to the organizations of the Transneft system, which meets the highest requirements of sensitivity, reliability, accuracy, and sustainability.

Solving this task involves a combination of research, methodological, technical, and organizational measures, which are already being put into practice at the Pipeline Transport Institute. The procedure for implementing measures in order to achieve the above-mentioned goal is presented below.

1. In the first place, it involves research and development (R&D) work aimed at identifying existing problems, understanding the principles of how LDS characteristics depend on a whole range of process parameters, as well as studying and identifying opportunities to improve the accuracy and reliability of leak-detection methods.

Within the framework of the R&D projects underway at present, the Institute is studying the fundamental principles of the impact on characteristics of leak-detection parametric methods of factors such as the operating mode of the TP process sections, the presence of gravity-flowing sections, the presence of several leaks at the TP process section, the degree of completeness, discreteness, reliability of the measuring instrument readings, and other parameters. Numerical estimates are being made for the maximum attainable capabilities


40

of parametric methods; and algorithmic approaches to combining methods are being investigated, with the aim of developing an approach to improving parametric LDSs.

In addition to the R&D activity within the framework of the task of improving LDS, the Institute is developing specialized software to facilitate a comprehensive approach to solving technological problems in oil pipeline transportation. At the moment, the Pipeline Transport Institute has created and is already introducing the software and computer package ‘Automated workstation for the process engineer’ (AWPE) into industry standards. An ‘Automated system for monitoring trunk pipeline process parameters’ (PC flow-monitoring system) is currently at the development stage.

The AWPE software (Fig.8) is a software tool unified for the Transneft system that provides process engineers in system organisations with essential functional possibilities:

• input and storage of process data:• construction of process section

diagrams• identification of equipment

characteristics

• conducting hydraulic calculations• work planning and analysis of the

actual operation of the process section

The PC flow-monitoring system (Fig.9) is a specialized software package for monitoring the operating parameters of a trunk pipeline, including:

• calculating process parameters for pipeline operation in real-time mode on the basis of the mathematical model developed;

• monitoring and identifying possible reasons for the technological parameters to deviate from the calculated and planned values;

• identifying the process operating modes for the TP;

• tracking pipeline runs of cleaning and inspection

devices

A module for monitoring pipeline leak-tightness with determining detected leak parameters is also provided within the framework of the PC flow-monitoring system, based on the hydrodynamic model of oil flow through a process section taking into account a number of process factors. At the present time, the Institute is working on the development and future improvement of this

Fig.8. An example of the AWST PC interface.


41

module, taking into consideration parallel studies of mechanisms and numerical estimates of the maximum attainable characteristics of parametric methods for leak detection. A unified information field is thus created for the integrated solution of pipeline transport technological problems.

2. The next step is expansion, refinement, and specification of the existing regulatory documentation requirements at Transneft PJSC in the field of LDSs. This should be based on R&D, comparative analysis of regulatory frameworks in Russia and elsewhere, as well as on upgrading programs and methodologies for testing LDSs. Improving the regulatory framework makes it possible:

• to clarify requirements for accuracy and leak-detection

time for various cases where LDS characteristics deteriorate, caused by the process features of the pumping mode;

• to clarify the requirements for determining the occurrence of a leak, taking into account that the leak must be confirmed by various algorithms;

• to harmonize the solutions for the procedure and number of LDS tests at the process

section of the TP.

3. The final step, which is interconnected with the previous one, is a detailed analysis of the operational characteristics of the measuring instruments and data-transmission channels installed in a process section of a TP, given that the correct operation of parametric LDS is not possible without the use of telemetry of the appropriate quality. This work should include:

Fig.9. An example of the PC flow-monitoring

system interface.


42

• a primary evaluation of retrospective SCADA data using statistical analysis applied at LDS telemetry facilities, in order to draft a list of out-of-spec deviations and propose recommendations for their elimination;

• developing criteria for evaluating the characteristics of measuring instruments based on dependencies which determine the sensitivity of parametric LDSs on the frequency of data acquisition and amplitude fluctuations caused by errors in measuring instruments and vibrations in the transported fluids;

• analysis of SCADA data for LDS telemetry facilities in accordance with the criteria developed, with the aim of determining the maximum attainable LDS characteristics for leak-detection accuracy at the TP process sections under

consideration.

Conclusion

Analysis of the current situation in the field of oil and oil products transportation points to the conclusion that automated leak and illegal tapping detection systems are in great demand. These systems are based on the parameters of the pumped fluids. The integrated approach, implemented within the framework of work at the Pipeline Transport Institute, makes it possible to create an LDS with improved characteristics, and has potential for its further development. It also allows important requirements for the characteristics of measuring instruments to be defined and relevant changes to existing regulatory documentation to be introduced.

References

1. Conservation of Clean Air and Water in Europe (CONCAWE). Performance

of European cross-country oil pipelines. Statistical summary of reported spillages in 2014 and since 1971. Report no. 7/16.

2. N. Tokarev, 2015. The Eastern tendency in oil export will remain a premium for a long time. Russian news Agency TASS. Access date 25.05.2015. http://tass.ru/opinions/interviews/1993172.

3. Illegal tapping in the Transneft oil pipeline system came to 2 billion roubles in 2014. Gazeta.ru Access date 06.02.2015. h t t p : / / w w w. g a z e t a . r u / b u s i n e s s /news/2015/02/06/n_6898309.shtml.

4. Pipeline leak detection expected to see muted growth through 2020. Pipeline & Gas Journal, November 2016, 243, 11, pp 68-70.

5. US Department of Transportation, Pipeline and Hazardous Materials Safety Administration. Final Report 12-173 Leak Detection Study – DT PH56-11-D-000001.

6. Li.Song, 2012. Few oil pipeline spills detected by much-touted technology. Inside Climate News, 19 Sept. https://insideclimatenews.org/news/20120919/few-oil-pipeline-spills-detected-much-touted-technology.

7. M.V.Lurye and P.S.Makarov, 1998. Hydraulic location of oil product leaks at a pipeline section. Transportation and Storage of Oil Product, 12 pp 65–69.

8. S.M.Vaynshtok et al., 2004. Oil pipeline transportation. M: LLC Nedra-Business centre, 2, p 621.

9. T.E.Mamonova, 2013. Leak detection method based on the time difference of pressure. Bulletin of the Tomsk Polytechnic University, 323, 1, pp 216–219.

10. R .A.Shestakov, 2014. On the issue of methods for leak detection and illegal tapping at trunk pipelines. Proc. Gubkin Russian State University of Oil and Gas, 3, pp 85–94.

11. F.S.Zverev, 2010. Improving technologies for oil leak detection: Thesis: Ph D in Technical Science. M., pp 173.

12. A.A. Golyanov, 2004. Leak detection at trunk oil product pipelines by means of scanning pressure pulses. Thesis: PhD in Technical Science, Ufa, p 196

13. API 1130 (Computational Pipeline Monitoring for Liquids), 2012. API Recommended Practice 1130, First Edition, September 2007 (Reaffirmation Notice, April 2012).

14. J.Zhang, A.Hoffman, K.Murphy, J.Lewis, and M.Twomey, 2013. Review of pipeline leak detection technologies. ATMOS International Conference, Report PSIG 2013.


43


44


45

Mechanical behaviour of a pipe impacted by an object, based on numerical simulation

by Jie Zhang* and Han ZhangSchool of Mechatronic Engineering, Southwest Petroleum University, Chengdu, Sichuan, China

DAMAGE TO A PIPE squeezed by other object are one of the key damages for oil and gas pipelines. Mechanical behaviour of a pipeline section in a deformed state was investigated by numerical simulation. Effects of initial dent depth and pipe

diameter / wall thickness ratio on the mechanical behaviour of the dented pipe were studied. The results show that the squeezing force, high stress area, and the maximum stress increase in the loading process. In the unloading process, there is a high probability for recovery of the pipeline section elastic strain to initial values. Cross-section of the middle plane is flatted. The deformation of the pipe in the vertical plane is V-shaped. In the first stage, the maximum equivalent plastic strain appears in the centre part of the pipe. There are two maximum equivalent plastic strain areas with the increasing of the squeezing object’s displacement. In the unloading process, the equivalent plastic strain increases. With the increasing of the initial indentation depth, the resilient rate of the pipe dent decreases, but the maximum equivalent plastic strain increases. With the increasing of pipe diameter / wall thickness ratio, the resilient rate increases but the maximum equivalent plastic strain decreases.

Keywords: numerical simulation, plastic deformation, mechanical stress, resilient rate.

*Corresponding author’s contact details:


Introduction

According to the latest estimates, within the next 20 years the level of energy consumption in the world will significantly increase, as will the demand for hydrocarbons. The main way oil and gas are transported is by trunk pipelines. One of the most common reasons they fail is mechanical damage, namely dents, ruptures, buckling, etc. [1]. This damage can lead to the transported product leaking and, as a consequence, to accidents, fires, and explosions. One of the most common causes of damage to above-ground pipelines is the pipe being squeezed by other objects. Therefore, it is extremely important to study the mechanical behaviour of pipeline sections which are deformed in this way.

In 1980, O.Furnes and J.Amdahl investigated the behaviour of deformed sections (dents) of pipe elements on the basis of the rigid-plastic approach, and developed the equation which was used in API RP 2A-WSD standard [2]. C.P.Ellinas derived the reaction equation for bending under a load of a deformed pipe, based on the semi-empirical method [3]. Using the rigid-plastic method, T.Wierzbicki studied the deformation of constantly supported pipes under a longitudinal force and squeezing-in load [4]. K.Chen conducted 226 impact tests on low-carbon steel pipes and examined the effects of the pipe geometry, point of impact, and internal pressure on the critical value of the initial impact energy [5]. K.Ruggeri studied the structural properties of a pipe with a dent under a transverse load using experimental and numerical


46

methods [6]. G.Lu presented a simple empirical formula, which was obtained after tests on capped and uncapped pipes under the pressure of indenters located on opposite sides in the middle section

[7]. S.E.Firouzsalari determined the deformation and mechanical behaviour of pre-compressed steel pipes based on experiments and modelling using the finite-element method. However, the

External object

Pipe

External objectLoad

Pipe

(a) Schematic

(b) Finite-element model

(a) Schematic

Time

Dis

plac

ing

load

Fig. 1. Model of calculations for a pipe squeezed by a foreign object.

Fig.2. The displacing load-time curve.


47

resulting equations are not suitable for all conditions. The mechanical behaviour of pipes is largely related to the shape and the size of the object [8].

In this paper, stresses and deformations of a pipe squeezed by another object were calculated on the basis of numerical simulation. The impact of the initial indentation depth and the ratio of the thickness and diameter of the pipe was studied to check the mechanical behaviour of the deformed section of the pipeline.

Pipe dents

The pipe squeezing leads to the formation of a dent, which is a residual equivalent plastic deformation of a circular cross-section. This is a significant distortion to the transverse cross-section of the pipe. The depth of the dent is calculated at the point of maximum reduction of the pipe diameter. The dent can be either a local indentation or any deviation from the nominal circular cross-section. Different types of pipe dents include [9]:

• smooth dents: dents that form a smooth change of the pipe walls’ curvature;

• curved dents: dents that form a

sudden change of the pipe walls’ curvature (the curvature radius of the sharpest part of the dent is at least five times less than the wall thickness);

• simple dents: smooth dents that do not reduce the wall thickness (for example, recesses or cracks) or other defects or inhomogeneities (for example, girth welds);

• free dents: dents capable of elastic recovery (straightening) after the squeezing load is removed, and capable of returning to a round shape when the internal pressure changes;

• non-free dents: dents incapable of both elastic recovery and returning to a round shape, as the squeezing load is not removed (e.g. a dent made by a stone);

• recesses: surface damage caused by contact with a foreign object, due to which the pipe has lost part of its material (the recess depth is equal to the total depth of the defect of metal loss and any crack in the base of the recess).

The finite-element model

A design scheme showing the impact of an external object on the pipe is

Maximum displacement (m)

Forc

e (k

N)

Fig.3. The force-displacement curve

for a pipe during the compression process.


48

presented in Fig.1a. The squeezing object has a triangular prism shape. The contact area of the object with the pipe is arc-shaped with a radius of 100 mm. The length of the squeezing object is greater than the diameter of the pipe. In this case there is no internal pressure in the pipe. Numerical simulation of pipe behaviour during deformation was performed using the ABAQUS software package.

Figure 1b shows the finite-element model of the pipe and its squeezing object. With regard to the general symmetry of the structure and the load applied to it, one quarter of the pipe is taken as the simulation model. The diameter of the pipe examined here is 508 mm, and its length is taken to be six times its diameter. The initial wall thickness of the pipe is 8 mm. Four-node elements of the shell with curtailed integration are used to model the cylindrical pipe. The squeezing object is modelled by eight-node elements with curtailed integration. The finite element grid is concentrated in the contact zone. The plasticity model with isotropic strengthening is used to simulate the material of the steel which the pipe is

made of. Numerical results were obtained for X65 grade steel; this steel grade is usually used for manufacturing oil and gas pipelines. The yield strength of this steel is equal to 488 MPa; the Young’s modulus is 210 GPa; the Poisson’s ratio is 0.3; and the density of the steel is 7800 kg/m3. In the process of calculations, a displacement load is applied to the external object. The corresponding boundary conditions are applied within the planes of symmetry. Calculations are carried out for two steps of loading: squeezing loading and unloading. The displacement load-time curve is shown in Fig.2. The initial maximum displacement of the object is equal to 160 mm.

Modelling results

Figure 3 shows the force-displacement curve for a pipe compressed by an object in the shape of a triangular pyramid. As the depth of the pipe deformation increases, the compression force increases, but the degree of displacement gradually decreases. After the maximum deformation depth reaches its limit value, the unloading process begins,

Fig.4. Von Mises stresses for the pipe at different stages.


49

during which elastic strain is recovered. According to this study, the whole process can be divided into ten stages. Figure 4 shows the von Mises stresses for a pipe when it is deformed by a foreign object. In the initial stage, the dent depth is very small, and high mechanical stresses are concentrated only in the upper part of the pipe. Stress distribution is oval-shaped. The pipe wall experiences only equivalent plastic deformations. As the depth of the dent increases, the zone of high mechanical stresses expands, and their values increase. In the third stage, the high-stress zone expands along the pipe in axial and circular directions. The stress distribution is mountain-shaped. The maximum stress is found in the contact zone between the pipe and the squeezing object. The stresses at the bottom of the pipe also increase. From the third to the seventh stages, the maximum stresses do not change, but the area with high stresses increases. In the seventh stage, the depth of the dent reaches its limit value of 160 mm.

In the process of loading, the stresses on the upper surface of the pipe are higher than on the lower one. The dent appears on the upper surface, and its depth is equal to the load displacement. In the eighth stage, there is a significant change

in the stress distribution during the unloading process, and the elastic strain recovers. Maximum stresses remain only on the two edges of the dent. Stresses in other areas are reduced when the load is displaced. In the ninth stage, the shape of stress distribution along the pipe becomes more stable. High stresses remain only on the two edges, but not in the central part of the pipe wall. After the seventh stage, the squeezing object no longer has contact with the pipe, so the size and distribution of the stresses do not change. Figure 5 shows the displacement of the upper line of the pipe wall. Under compressive stress, the deformation first occurs in the contact area between the squeezing object and the pipe. Elastic strain is further formed in the adjacent area. As the load increases, the equivalent plastic strain increases and the overall

Fig.5. Plot of length (m) vs displacement (m) for

the upper line of the pipe wall.

Fig.6. Shape of the pipe cross-section

during the compression process.


50

deformation of the pipe becomes more substantial. The pipe deformation in a vertical projection is V-shaped. After the seventh stage, the elastic strain recovers during unloading. Ultimately, the constant equivalent plastic strain persists after the compressing object is no longer in contact with the pipe.

Figure 6 shows the shape of the cross-section of the pipe in the middle plane. If the displacement of the squeezing object is small, the pipe cross-section becomes oval-shaped. As the displacement increases, local collapse appears. It occurs only in the top part of the pipe. Since the length of the squeezing object is larger than the diameter of the pipe, its upper surface is flattened under the impact of compression. During loading, the curvature radius of the bottom part of the pipe increases. During unloading, the elastic strain recovers, but the upper part of the pipe remains flat. The distribution of equivalent plastic strain at different stages is shown in Fig.7. At the first and second stages, the maximum equivalent plastic strain occurs in the central part of the pipe. As the displacement of the squeezing object increases, two areas of maximum equivalent plastic strain appear at the top of the pipe. During the loading process, the equivalent plastic strain increases gradually. However, in the process of unloading it also enhances, to 0.224.

In order to describe the change in the equivalent plastic strain of the pipe more accurately, points A and B (Fig.8) may be considered. Point A is in the centre of the middle plane, and point B is the maximum equivalent plastic strain. Figure 8 shows the equivalent plastic strain curve in two points with maximum displacement. At point A, the equivalent plastic strain increases at a significant rate until the displacement reaches 0.05 m; then it increases insignificantly, at point B, there is no equivalent plastic strain at the initial stage, but during the middle stages it increases very quickly. There is only one inflection point for each of the two curves, and it marks the transition point from the loading process to the unloading process. During the unloading process, the equivalent plastic strain enhances at both points, but the rate of change at point B is greater than at point A.

The impact of sensitivity parameters

The resilient rate k is used to describe the recovery of elastic strain in the pipe wall:

ku u

uf= max

max

-

where:

Fig.7. The distribution of equivalent plastic strain in the pipe.


51

umax

= the maximum depth of the dentu

f = the initial depth of the dent.

The resilient rate at a different initial dent depth (the limit displacing load) is shown in Fig.9. As the initial depth of the dent increases, coefficient k decreases nonlinearly. This is due to the fact that the local bend is greater than the initial depth of the dent, resulting in a decrease in indicators for elastic strain recovery.

Displacement of point A (m)

Equ

ival

ent p

last

ic s

trai

n

Breaking point

Initial dent depth (m)

Res

ilien

t rat

e (1

00%

)

Figure 10 shows the maximum equivalent plastic strain of the pipe section given different initial depth of the dent. The greater the initial depth of the dent, the higher the maximum equivalent plastic strain. However, the degree of the strain enhancement gradually decreases with the increase in the depth of the dent. The pipe diameter / wall thickness ratio has a significant impact on the mechanical

Fig.8. The equivalent plastic strain curve for

two points.

Fig.9. The resilient rate for the pipe dent given

different initial dent depth.


52

properties of the deforming section of pipeline. Figure 11 shows the resiliance rate and the maximum equivalent plastic strain given different pipe diameter / wall thickness ratios and initial dent depth of 160 mm. The resilient rate grows non-linearly as the pipe diameter / wall thickness ratio increases. This is due to the fact that higher pipe diameter / wall thickness ratio can reduce its stiffness. The maximum equivalent plastic strain of the pipe decreases with the increase in the pipe diameter / wall thickness ratio. If the pipe diameter / wall thickness ratio is less than 35, then the rate of change of the maximum equivalent plastic strain is higher. If the ratio of these parameters is higher than 35, the rate of deformation change gradually decreases. Conclusion

Using the numerical simulation method, the study of the mechanical behaviour of a deformed pipe section squeezed by a foreign object enabled the following conclusions to be drawn:

• The compressive force, the area of high stresses, and the maximum stresses increase during the loading

process. During the unloading process, there is a significant change in the stress distribution, and the elastic strain recovers.

• Under the influence of the squeezing object, local collapse appears on the upper surface of the pipe. The cross-section of the middle surface is flat. The pipe deformation in the vertical projection is V-shaped. The maximum equivalent plastic strain appears in the central part of the pipe. When the displacement of the squeezing object increases, two areas of maximum equivalent plastic strain appear. In the unloading process, the equivalent plastic strain increases.

• As the initial depth of the dent increases, the resilient rate of the pipe decreases, but the maximum equivalent plastic strains increase. As pipe diameter / wall thickness ratio increases, the resilient rate increases and the maximum equivalent plastic strain decreases.

Acknowledgements

This research work was conducted with the support of the Key Laboratory for the

Initial dent depth (m)

Equ

ival

ent p

last

ic s

trai

n

Fig.11. Resilient rate and maximum equivalent plastic strain of the pipe given different pipe diameter / wall thickness ratios.


53

Study of Accident and Safety Mechanisms in the Energy Sector (Sichuan University) (No. EES201604) and the Ministry of Education of China.

References

1. Z.Jie, L.Zheng, H.Chuanjun eti al., 2015. Buckling behaviour analysis of a buried steel pipeline in rock stratum impacted by a rockfall. Engineering Failure Analysis, 58, pp 281–294.

2. O.Furnes and J.Amdahl, 1980. Ship collision with offshore platforms. Intermaritec 80.

3. C.P.Ellinas and A.C.Walker, 1983. Damage on offshore tubular bracing members. Proc Int Assoc Bridge Struct Eng.

4. T.Wierzbicki and M.S.Suh, 1983. Indentation of tubes under combined loading. Int J Mech Sci, 30 pp229–248.

5. K.Chen and W.Q.Shen, 1998. Further experimental study on the failure of fully

Pipe diameter / wall thickness ratio

Equ

ival

ent p

last

ic s

trai

n

Res

ilien

t rat

e (1

00%

)

Equivalent plastic strain

Resilient rate

clamped steel pipes. Int J Impact Eng 28 (3) pp177–202.

6. C.Ruggieri and J.A.Ferrari Jr, 2004. Structural behaviour of dented tubular members under lateral loads. J Offshore Mech Arct Eng, p 126.

7. G.Lu, 1993. A study of the crushing of tubes by two indenters. Int J Mech Sci, 35 pp267–278.

8. S.E.Firouzsalari and H.Showkati, 2013. Thorough investigation of continuously supported pipelines under combined pre-compression and denting loads. International Journal of Pressure Vessels and Piping, 4 pp83–95.

9. A. Cosham and P.Hopkins, 2004. The effect of dents in pipelines-guidance in the pipeline defect assessment manual. International Journal of Pressure Vessels and Piping, 81 pp 127–139.

10. J.Zhang, Z.Liang, and C.Han, 2014. Buckling behaviour analysis of buried gas pipeline under strike-slip fault displacement. Journal of Natural Gas Science and Engineering, 21 pp 921–928.

Fig. 11. Resilient rate and maximum

equivalent plastic strain of the pipe given different pipe diameter / wall thickness ratios.


54

The 18th International Conference on New Trends in Fatigue and Fracture (NT2F18)

will be held in Lisbon, Portugal, from July 17 to 20, 2018.

The purpose of NT2F18 is to provide the opportunity for scientists and engineers to meet and to discuss current research, new concepts and ideas

and establish opportunities for future collaborations.

It is our pleasure to invite you, your co-workers and students to present your research work at the NT2F18 conference. Abstract submission is now

open.

Please visit the conference webpage http://nt2f.tecnico.ulisboa.pt/ for further information regarding registration, instructions for authors,

submission procedure and other issues, and for up-to-date information.

Looking forward to see you in Lisbon for next NT2F18 conference.

Yours sincerely, The Conference Chairmen

Luis Reis, Manuel Freitas, Moussa Nait Abdelaziz

v v v


55

Seismic vulnerability analysis of storage tanks for oil and gas industry

by H.N.Phan, F.Paolacci*, D.Corritore, and S.AlessandriDepartment of Engineering, Roma Tre University, Rome, Italy

OIL AND GAS TRANSPORTATION LINE components are particularly vulnerable to natural hazard events. Steel tanks are recognized as the most vulnerable equipment to seismic action, whose damage may result in the release of materials and thus the

increase of overall damage to nearby areas. The seismic vulnerability of tanks is commonly expressed by fragility curves, which are conditional probability statements of potential levels of damage over a range of earthquake intensities. This paper aims to present an appropriate procedure for analytically deriving fragility curves of tanks with the treatment of uncertainties. At first, the analysis of critical damage states of steel storage tanks observed during past earthquakes is presented. Possible numerical models of tanks subjected to earthquakes are then discussed. An overview of seismic fragility methodologies for tanks is next presented. Attention is paid to an analytical method, i.e. cloud method, which is conducted by using a probabilistic seismic demand model and non-linear time-history analyses. A broad tank, which is located in a refinery in Italy, is considered for the fragility evaluation. Resulting fragility curves for critical damage states of the tank, such as the plastic rotation of the shell-to-bottom plate joint, the buckling of the bottom shell course, and the material yielding of the shell plate, show a high seismic vulnerability of the tank.

Keywords: steel storage tank, damage identification, seismic vulnerability analysis, numerical model

Introduction

Oil and gas transportation lines components can be considered particularly vulnerable to natural-hazard events, in particular earthquakes. Due to the interaction between the natural events and the industrial risk, several effects take place in the plant, and in particular the storage site, causing damage to pipelines and equipment like storage tanks, and consequently, the release of hazardous materials. Since a large amount of flammable materials is often handled by storage equipment, e.g., piping, vessels, and tanks, the consequences of failures can affect wide surrounding areas.

There are different types of natural event triggering industrial accidents, e.g., landslides, hurricanes, high winds, tsunamis, floods, earthquakes, etc. Several industrial accidents occurring in the last

decades demonstrated that earthquakes might cause severe damage to storage equipment items, resulting in losses of contents, and in multiple and extended releases of hazardous substances.

Earthquake damage in recent decades (e.g. 1995 Hyogoken-Nanbu Japan, 1999 İzmit Turkey, 2003 Tokachi-oki Japan, 2008 Wenchuan China, 2011 Great East Japan, 2012 Emilia Italy, etc.) has revealed that storage tanks are one of the most vulnerable components in industrial plants. Damage to tanks can cause significant disruption to the facility operation. Seriously, the extensive seismic-induced uncontrolled fires, when flammable materials or hazardous chemicals leak, naturally increase the overall damage to nearby areas.

Prediction and prevention of possible accidental scenarios depends upon

*Corresponding author’s contact details:

e-mail:[email protected]


56

the reliability of available tools for the structural design and assessment. Unfortunately, despite the continuous evolution of the knowledge on this matter, there is a lack of standard and established procedures to evaluate the effects of the seismic action on equipment. An emerging tool, i.e. seismic fragility curves, provides valuable support for seismic risk assessment of equipment used in industrial installations. These curves are conditional probability statements of potential levels of damage over a range of earthquake intensities and can be used as initial fragility-based damage scenarios in the seismic risk assessment procedure [1]. The availability of reliable fragility curves would allow for assessment of the effects of various failure conditions, which are associated with the loss of contents, on the performance of equipment. Such curves are essential tools for decision-support frameworks such as performance-based and cost-benefit analyses.

This paper aims to provide an enhanced understanding of the impact of natural disasters, especially earthquakes, on the performance of steel storage tanks in oil and gas industry. A primary objective is to introduce a reliable procedure for vulnerability assessment of steel storage tanks in seismic-prone areas. This procedure is then applied to a case study of the oil storage tank. The vulnerability

of the tank is represented by resulting fragility curves for different damage states.

Seismic damage to storage tanks in the oil and gas industry

The storage of material received form oil and gas transportation lines can be considered a particularly critical facility in seismic-prone areas, because cylindrical steel storage tanks, usually adopted to storage raw and refined material, have been recognized as highly vulnerable components. They are characterized by aspect ratios ranging between 0.2 and 2, as shown in Figs 1a and 1b. The roof can be welded to the shell (i.e. a fixed conic roof) or floating over the contained liquid. The operating volume varies from some tens to 200,000 m3. The typical damage states associated to these structures are related to buckling phenomena of the wall such as elephant’s foot buckling or elastic-plastic buckling (Fig.2) and diamond-shaped buckling or elastic buckling (Fig.3).

Another damage to tanks is related to excessive sloshing motion, especially in the presence of floating roofs, which can cause liquid overtopping and fire due to the crash between the roof itself and the wall. For example, during the 1999 Izmit and 2003 Tokachi-Oki earthquakes, most of the tanks were destroyed due to the

Fig.1. Typical tanks in an oil and gas industrial storage facilities (l-r): (a) broad tank, (b) slender tank, and (c) spherical LNG tank.


57

excessive sloshing motion (Fig.4). Damage involving the rupture of the pipes attached to the tank is also rather common. This is due to the excessive relative displacement between the pipe and the tank wall, which is caused by the uplift, sliding, or shell buckling (Fig.5).

Another important category of tanks for the oil and gas industry is represented by spherical storage vessels, which are essentially used to store pressure-liquefied gases. They are generally elevated with respect to the ground, using steel columns placed along the circumference and welded to the shell at the equatorial level and normally linked each other by diagonal braces, as shown in Fig.1c. Vertical large storage vessels for cryogenic liquefied gases are also common in gas industry; their configuration is similar to that of the large atmospheric storage vessels for liquids, but their walls are formed of a double shell, in the inner-space of which an efficient thermal insulation is located, and their bases are anchored to a concrete plates, supported by short reinforced concrete columns. This equipment is used to heat or vapourize large amounts of liquid products. For these tanks, collapse is mainly due to the soft-story

Fig.2. Shell elephant’s foot buckling or elastic-plastic bucking.

Fig.3. Shell diamond-shaped buckling or elastic buckling.

Fig.4. Floating-roof damage. Fig.5. Detachment of the pipe due to sliding and shell buckling.

phenomenon caused by the shear failure of the columns [2].

The above framework offers an easy guideline to individuate the typical seismic damage conditions in storage tanks for oil and gas industry. This is particularly useful to identify the criticality concerning the loss of containment (LOC) and damage propagation effects. It is important to note that the occurrence of these damage states can result in LOC events with different degrees of severity. This is necessary in order to perform a reliable quantification of the risk of storage plants in seismic prone areas [1].

Main issues in seismic vulnerability analysis of storage tanks

Seismic vulnerability of structures and equipment is traditionally expressed in the form of fragility curves. A lognormal cumulative distribution function is often used to define a fragility function:

P D LS IMIM

EDP > =( )

Φ

ln / µβ

(1)


58

where:

P[DEDP

> LS|IM] is the probability that a ground motion with intensity measure IM will cause a demand D

EDP exceeding a selected

structural limit state LSΦ(.) is the standard normal cumulative

distribution functionµ is the median of the fragility

function, and β is the standard deviation of ln(IM).

Seismic fragility curves are commonly generated using a non-linear time-history analysis approach. Although this type of approach tends to be the most computationally expensive, it is also one of the most reliable methodologies available. The general procedure of this approach is the following:

• The first step is to obtain a suite of ground motions that is appropriate and representative of the target geographic area, and captures the uncertainty inherent in ground motions. The characteristics of ground motions are usually based on the magnitude, the source-to-site distance, and the site condition.

• Next, based on a reliable numerical model of tanks, the peak structural responses are obtained from non-linear time-history analyses, which are performed using a set of selected ground-motion records, to generate a probabilistic seismic demand model (PSDM).

• The capacity or limit state of each component is determined using expert-based, experimental, and/or analytical methods.

• Finally, the seismic demand and the structural capacity models are combined assuming a log-normal distribution, as shown in Equn 1.

The above procedure clearly shows five distinct aspects in developing fragility curves:

• definition of reliable numerical models of storage tanks;

• definition of seismic hazard-consistent input signals and selection of proper seismic intensity measures (IMs);

• selection of a set of representative engineering demand parameters (EDPs) and EDP-consistent damage states along with the corresponding limit states; and

• selection of proper fragility analysis and fitting methods.

In what follows, all these aspects are critically examined.

Numerical modelling of storage tanks

The seismic response of above-ground storage tanks subjected to earthquakes has been widely studied in the past [3]. The analysis procedure has been commonly based on three possible models:

• the simplified spring-mass model in which the impulsive and convective components are modelled as SDOF systems;

• the added-mass model in which the impulsive and convective forces are converted to equivalent masses along the height of the shell and bottom plate; and

• the full non-linear finite-element model in which the real interaction between fluid and structure is considered.

The simplified approach has been widely used thanks to its efficiency in reducing the computational effort, especially in a probabilistic manner. The basic idea is based mainly on the spring-mounted masses analogy proposed by Housner (1963) [4]. The liquid mass is ideally subdivided into two parts: an impulsive component, which accounts for the base motion and the deformability of the tank wall, and a convective component, whose oscillations cause superficial waves of different frequency frequencies. While the impulsive mass moves rigidly with the tank wall, the convective mass oscillates in different modes. As mentioned in


59

literature, it is enough to consider only the first convective mode to reproduce correctly the sloshing effect of the liquid [5]. The possible numerical model of the anchored tank represented by two viscoelastic oscillators is shown in Fig.6. In particular, the impulsive and convective masses (m

i and m

c, respectively) are

connected to the tank wall by equivalent one-dimensional spring-dashpot systems at heights h

i (or h’

i) and h

c (or h’

c). The

calculations of mass, height and natural period for each system can be obtained by the method presented by Malhotra et al. (2000) [6]. This procedure has been adopted by Eurocode 8 (EN 1998-4 2006) [7].

In the case of unanchored tanks, the partial uplift of the bottom plate occurs when the tanks are subjected to strong seismic excitations. The uplift mechanism of the tanks can be simulated by a rotation spring that represents the rocking resistance of the base, as shown in Fig.7. The behaviour of the resistance spring can be obtained using either the simplified approach presented by Malhotra and Veletsos (1994) [8] or the more refined approach presented by Phan et al. (2018) [9].

Selection of seismic-hazard-consistent input signals

The selection of seismic-hazard-consistent input signals to perform linear and non-linear analyses of tanks is an important issue which the scientific community is still discussing. For the construction of fragility curves, it is often necessary to use non-linear analysis, which requires seismic motion records. If a scalar IM is used, such as PGA, the correlation with the response is generally very low. As an alternative, accelerograms whose spectrum individually matches the target seismic-response spectrum could be used. These records can be artificially built or obtained by modifying the frequency content of records. The first approach has been completely abandoned while the second one still represents an interesting alternative.

To reduce the dispersion of the response without modifying the spectral content of the records, Shome et al. (1998) [10] proposed to use the response spectrum at the most significant vibration period of the structure as an IM. This criterion works properly only if the structural response depends mainly on one

Fig.6. Lumped mass model of above-ground anchored tanks.

Fig.7. Lumped mass model of above-ground unanchored tanks.


60

vibration mode and behaves elastically. To overcome this approximation, Baker (2011) [11] proposed to use the conditional mean spectrum (CMS), which is obtained by taking into account the correlation between the spectral ordinates at different periods. The accelerograms are then selected so that the average of their spectra approximates the CMS and their dispersion is contained within the CMS 1 standard deviation.

Oil and gas transportation lines and storage components are often characterized by a variegate frequency content. Therefore, the above record-selection criteria could fail. For example, storage tanks, which are among the most vulnerable components, exhibit at least two significantly different natural periods, due to impulsive and convective motions. This clearly complicates the problem of the accelerograms selection. In civil engineering, where complex structures exhibit similar problems, vector-valued IMs have been defined. However, in many applications, this approach shows a limited effectiveness, whereas a much more complicated procedure is required by including the necessity of performing a vector probabilistic seismic hazard analysis (Bazzurro and Cornell 2002) [12].

Selection of EDPs and EDP-consistent damage states

The definition of proper EDPs and EDP-consistent damage states represents another delicate aspect of the fragility

analysis; however, a limited number of contributions has been offered in the literature. For example, an interesting contribution by Vathi et al. (2015) [13] provided the performance criteria for the design of storage tanks and piping systems, which identify the most critical failure modes for each structural category. The definition of damage states and the calculation of limit-state capacities are also presented in the current seismic design guidelines, e.g. Eurocode 8 (EN 1998-4) [7], API 650 (API 650 2007) [14], NZSEE (NZSEE 2009) [15]. The critical EDPs and EDP-consistent damage states for steel storage tanks are summarized in Table 1.

Fragility analysis methods

As mentioned in literature, different analytical methods to build fragility curves have been proposed either considering or not the randomness of structural characteristics. The most common use is the cloud analysis (CA). This method implements non-linear dynamic analyses through (linear) regression-based probabilistic model (Shome et al. 1998) [10]. A second common approach is the incremental dynamic analysis (IDA), where a suite of ground motions are repeatedly scaled to find the IM level at which each ground motion causes the exceeding of a certain limit state (Vamvatsikos and Cornell 2002) [16]. For the same computational effort, the CA method provides a good estimate of the first two PSDM moments across the range

EDP Damage state

1 Maximum sloshing wave height Sloshing damage of the roof and fracture of the shell-to-roof joint

2 Hoop hydrodynamic stress Material yielding of the shell and bottom plate

3 Compressive meridional stress Elastic and elastic-plastic buckling of the shell plate

4 Plastic rotation of the shell-to-bottom joint

Fracture and fatigue of the shell-to-bottom joint

5 Overturning moment Uplift

6 Total base shear Sliding

Table 1. Critical EDPs and EDP-consistent damage states for steel storage tanks.


61

of intensities considered in the suite of ground motions. IDA provides the same information; however, it is subjected to scaling issues and requires more computational effort. With a prudent selection of ground motions, both CA and IDA provide robust estimates of the median and dispersion across a range of ground motion intensities. A detailed discussion about the two approaches for the fragility analysis of steel storage tanks can be found in Phan et al. (2016, 2017) [2, 17, 18], where the priority of the CA method was demonstrated.

Fragility analysis example of an existing fuel storage tank

Description of case study

An existing tank ideally installed in a refinery in Sicily (Italy), which well represents a broad geometry, is selected for this study. The tank is a 54.8-m diameter cylindrical steel tank and unanchored with respect to the foundation. The tank height is 15.6 m, and the capacity of the tank is 37,044 m3. The tank is provided with a floating roof; however, the effect of the floating roof is neglected in this study. The shell thickness has been designed varying from 8 mm at the top shell course to 33 mm at the bottom one. The bottom

plate has a uniform thickness of 8 mm. The tank is filled with crude oil at a filling level of 14 m (i.e. 90% of the tank height). Both shell and bottom plate are structured in S235 carbon structural steel having a yield strength of 235 MPa. A detail of nominal material and geometry properties is illustrated Table 2.

Numerical modelling

The hydrodynamic pressures caused by the liquid motion can be expressed by sum of two components:

(i) an impulsive component which represents the effect of the part of the liquid that moves unison with the shell plate; and

(ii) a convective component which represents the effect of the part of liquid undergoing a sloshing motion.

The sloshing effects are characterized by long period oscillations, whereas the impulsive ones are dominated by oscillations of a shorter period. The contribution of the convective component to the response is small and can be neglected. Therefore, the tank-liquid system may be considered to respond as a single degree-of-freedom (SDOF) system, as shown in Fig.8.

Property Design value

Tank Density (kg/m3) 7850

Young’s modulus (MPa) 200,000

Poisson’s ratio 0.3

Yield strength (MPa) 235

Radius of tank (m) 27.432

Height of tank (m) 15.6

Bottom plate thickness (mm)

33, 29.5, 25.5, 21.5, 17.5, 14, 10, 8, 8, 10

Shell plate thickness (mm) 8

Liquid Density (kg/m3) 900

Liquid level (m) 14

Table 2. Nominal material and

geometry properties of the tank.


62

The uplift resistance is represented by the M-ψ curve. This curve is obtained from the static analysis of the above refined finite element model and implemented in OpenSees using an elastic multilinear material. In fact, cyclic analyses demonstrated that a limited hysteresis is present and thus its effect has been here neglected, preserving only the geometrical non-linearity. The horizontal spring for the sliding resistance is a pure friction element with a constant friction coefficient, µ= 0.4.

Calculation of limit-state capacities

The commonly observed failure modes of unanchored steel liquid storage tanks during past earthquakes involved elephant’s foot buckling of the bottom shell course and plastic rotation of the shell-to-bottom plate joint (Malhotra and Veletsos 1994) [8]. These failure modes have occasionally resulted in the loss of contents due to the weld or piping fracture (Alessandri et al. 2017) [1]. The elephant’s foot buckling is caused by the concentration and high magnitude of the compressive stress developed in the shell when the tank base is uplifted from the ground support. The maximum compressive meridional stress in the shell (s

z) is calculated using the formulas

provided in Malhotra and Veletsos (1994) [8]. The critical buckling stress is calculated using the formula developed by Rotter (1985) [19]. It is noticed that the buckling stress limit is in terms of the maximum pressure response of the seismic analysis. Thus it is conditioned on

the IM. The median estimate of the EFB limit can also be predicted by the power function.

The second common failure mode developed at the joint of the shell and bottom plate is due to the plastic rotation of the joint caused by the base uplift. The rotation demand of the shell-to-bottom plate joint (θ) associated with an uplift at the edge and a base separation is given in Eurocode 8 (EN 1998-4) [14], which should be less than the estimated rotation capacity of 0.2 radians.

The third common failure mode is the material yielding of the shell plate due to the excessive hoop hydrodynamic stress (σ

h). As described in API 650 (2007) [14],

the maximum allowable hoop tension membrane stress is the lesser of the basic allowable membrane for the shell plate material increased by 33% or 0.9 σ

y,

where σy is the yielding strength of the

steel.

Selection of ground motions

A total of 120 accelerograms has been selected based on six target uniform hazard spectra (UHS), which were obtained from the seismic hazard analysis of the selected site. The selection procedure is conducted with the following parameters: moment magnitude: 4.5-7.5, source-to-site distance: 3-80 km, soil type: B, and period interval: 0.001-4 s. The records of each set are selected so that the mean response spectrum and its 84% fractile have the best fit to those of the target UHS. An

Fig.8. Spring-mass model of

the tank.


63

Fig.9. Example of ground motion selection.

Fig.10. Linear regression analysis results (top-bottom):

(a) joint rotation demand;(b) shell meridional stress; and (c) shell hoop stress.


64

example of the selected ground motions for a UHS with a return period of 75 years is shown in Fig.9.

Fragility analysis

The seismic demand placed on each component is assessed against its capacity, or limit state, which is modelled by a lognormal distribution. The regression analysis results for the two demands are shown in Fig.10. The spectra acceleration at the impulsive period S

a(T

i) is selected

as IM of the regression analysis, which is based on the suggestion by Phan and Paolacci (2016) [18]. The fragility curve for each failure mode is then generated. The plot of fragility curves is shown in Fig.11.

It is observed that the failure of the shell-to-bottom plate joint in the examined unanchored tank is more frequent, with a failure probability of 50% at S

a(T

i) = 1.0 g.

The results show a high seismic demand of the shell-to-bottom plate joint rotation when the uplift occurs. The probability of exceeding the design buckling stress in the bottom shell course is also significant. A high seismic demand ( 50%) related to the shell buckling failure mode can be recognised when S

a(T

i) > 2.0 g. The

occurrence of the material yielding of the shell plate is instead limited. A probability under 5% is recognized at a IM level S

a(T

i)

= 2 g.

Conclusions

The main objective of this study was to develop an appropriate methodology for the treatment of uncertainties for the fragility curve evaluation of steel tanks for oil and gas storage facilities. From an overview of past earthquake damage to steel liquid-storage tanks, critical failure modes of the tanks have been analysed. The most critical damage was classified as elastic and elastic-plastic buckling of the shell wall, sloshing damage of the roof, failure of the attached piping system, etc. The comprehensive analysis procedure of the fragility evaluation was then presented with the attention paid to four aspects: the numerical modelling, the selection of seismic hazard-consistent input signals, the selection of EDPs and EDP-consistent damage states, and the selection of proper fragility analysis and fitting methods. Finally, an application of the procedure to an unanchored oil storage tank in a refinery in Italy was presented. The fragility curves of three critical damage states of the tank - the plastic rotation of the shell-to-bottom plate joint, the buckling of the bottom shell course, and the material yielding of the shell plate - were obtained. The curves show a high vulnerability of the tank in terms of the failure of the joint and the buckling of the bottom shell course.

Fig.11. Fragility curves of the

tank.


65

Acknowledgment

This work has been partially funded by the European project INDUSE-2-SAFETY (Grant No. RFS-PR13056) and the project MSMART by the National Institute for Insurance against Accidents at Work (INAIL) (Grant No. F82F16001460005).

References

1. S.Alessandri, A.C.Caputo, D.Corritore, G.Renato, F.Paolacci, and H.Phan, 2017. On the use of proper fragility models for quantitative seismic risk assessment of process plants in seismic prone areas. ASME Pressure Vessels and Piping Conference, 8, No. V008T08A022.

2. H.N.Phan, F.Paolacci, O.S.Bursi, and N.Tondini, 2017. Seismic fragility analysis of elevated steel storage tanks supported by reinforced concrete columns. Journal of Loss Prevention in the Process Industries, 47, pp 57-65.

3. F.Paolacci, 2015. On the effectiveness of two isolation systems for the seismic protection of elevated tanks. Journal of Pressure Vessels and Technology, 137, 3, pp 031801-031801-8.

4. G.W.Housner, 1963. The dynamic behaviour of water tanks. Bulletin of the Seismological Society of America, 53, pp 381-387.

5. M.De Angelis, R.Giannini, and F.Paolacci, 2010. Experimental investigation on the seismic response of a steel liquid storage tank equipped with floating roof by shaking table tests. Earthquake Engineering & Structural Dynamics, 39, pp 377-396.

6. P.K.Malhotra, T.Wenk, and M.Wieland, 2000. Simple procedure for seismic analysis of liquid storage tanks. Structural Engineering International, 3/2000.

7. EN 1998-4, 2006. Eurocode 8: Design of structures for earthquake resistance - Part 4: Silos, tanks and pipeline, Brussels, Belgium.

8. P.K.Malhotra and A.S.Veletsos, 1994c. Uplifting response of unanchored liquid-storage tanks. Journal of Structural Engineering, 120, 12, pp 3524-3546.

9. H.N.Phan, F.Paolacci, and S.Alessandri, 2018. Enhanced seismic fragility analysis of unanchored steel storage tanks accounting for aleatoric and epistemic uncertainties. Journal of Pressure Vessels and Technology.

10. N.Shome, C.A.Cornell, P. Bazzurro, and J.E.Carballo, 1998. Earthquakes, records, and non-linear responses. Earthquake Spectra, 14 (3) pp 469-500.

11. J.W.Baker, 2011. Conditional mean spectrum: tool for ground-motion selection. Journal of Structural Engineering, 137 (3) pp 322-331.

12. P.Bazzurro and C.A.Cornell, 2002. Vector-valued probabilistic seismic hazard analysis (VPSHA). Proceedings of the 7th U.S. National Conference on Earthquake Engineering, Boston, Massachusetts, USA.

13. M.Vathi, S.A.Karamanos, I.A.Kapogiannis, and K.V.Spiliopoulos, 2015. Performance criteria for liquid storage tanks and piping systems subjected to seismic loading. Proc. of ASME 2015 Conference on Pressure Vessels and Piping PVP2015, Paper # PVP2015-45700, July 19-23, Boston, MA, USA.

14. API 650, 2007. Seismic design of storage tanks - Appendix E: Welded steel tanks for oil storage. 11th Edition, Washington, DC.

15. NZSEE, 2009. Seismic design of storage tanks. Wellington: New Zealand National Society for Earthquake Engineering.

16. D.Vamvatsikos and C.A.Cornell, 2002. Incremental dynamic analysis. Earthquake Engineering & Structural Dynamics, 31, 3, pp 491-514.

17. H.N.Phan, F.Paolacci, and S.Alessandri, 2016. Fragility analysis methods for steel storage tanks in seismic prone areas. ASME Pressure Vessels and Piping Conference, 8, No. V008T08A023.

18. H.N.Phan and F.Paolacci, 2016. Efficient intensity measures for probabilistic seismic response analysis of anchored above-ground liquid steel storage tanks. ASME Pressure Vessels and Piping Conference, 5, No. V005T09A010.

19. J.M.Rotter, 1985. Local inelastic collapse of pressurised thin cylindrical steel shells under axial compression. Research Report, School of Civil and Mining Engineering, University of Sydney.


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Author’s contact details:email address:

[email protected]

Undamped vibration of fibre-reinforced polymer overwrapped pipes under fluid-hammer conditions

by Kristen RegeDepartment of Mechanical and Structural Engineering and Materials Science, University of Stavanger, Stavanger, Norway

AN APPROXIMATE DYNAMIC MODEL describing the undamped radial vibration of thin-walled steel pipes with an overwrap of laminated fibre-reinforced polymer (FRP), due to fluid-hammer conditions, is derived. The derived model is an uncoupled model,

in which the elastic properties of the pipe and fluid are used to estimate the properties of the fluid-hammer-induced pressure wave. This pressure wave is used as the exciting load in a dynamic analysis of the pipe wall. The derived governing equation is solved analytically by utilizing the properties of Fourier series. The model is implemented on a representative example. It is observed that increasing the number of FRP laminae may lead to larger radial deflections, because the natural frequency of the pipe is significantly altered.

Key words: fluid hammer, shell theory, laminate theory, pipe vibration, overwrapped pipelines

Introduction

The main material for pipeline manufacturing today is still carbon steel [1]. During the service life, the carbon steel pipelines are subjected to various deterioration mechanisms, like corrosion and erosion. If unattended to, these mechanisms may lead to reduced pipe thickness and surface cracks or, in the worst case, complete failure. However, pipeline monitoring and assessment are in widespread use, which often makes repair or replacement prior to failure possible [2]. The use of fibre-reinforced polymer (FRP) composites to repair and strengthen such pipelines is increasing. Some advantages of using FRP for repairing the pipes are the possibility of repair without pipeline shutdown, and the elimination of the explosion risk due to welding [3]. These attributes make the repair process simpler. Additionally, FRP is also made viable by its high-tensile strength, lightness of weight, and non-corroding attributes [4].

Stress and strain analyses of FRP overwrapped pipes under static pressure

have been examined [3, 5], but according to the author’s knowledge, there has not been any theoretical analysis of how a FRP overwrapped pipe behaves under fluid-hammer conditions. Fluid hammer is a phenomenon which is generated by abrupt changes to steady flow conditions, such as the rapid closing of a valve in the end of a pipeline [6]. This causes a pressure wave in the fluid, which travels up and down the pipe, alternating between higher and lower values than the static pressure. This pressure wave will lead to increased deformations and stresses in the pipe, which may result in catastrophic consequences to the pipeline integrity [1] if not taken into account in the design phase. Several theoretical models of varying degree of sophistication exist for pipes made of isotropic materials [6, 7], and some are also available for multi-layered FRP pipes [1].

In this study, a model for the radial displacement of a laminated FRP overwrapped metallic pipe is derived. As the purpose is to derive a simple and approximate tool for estimating this displacement, an uncoupled model [6]


68

neglecting the effects of material damping and friction between fluid and pipe will be used. The model takes into account the Korteweg model for the magnitude and velocity of the pressure wave [7], the equations of motion for a thin-walled shell element, the relationships between its displacements and the corresponding strains and curvatures, and the laminate stiffness matrix. The resulting fourth-order differential equation governing the radial motion of the pipe wall is solved by utilizing Fourier series.

Formulation of the equation of motion for the pipe wall

The equations of motion for a thin cylindrical shell element

The internal pressure is assumed to act axisymmetrically on the pipe wall. In addition, the layout of the filament wound material is assumed to be symmetric and balanced, so that the circumferential displacement and all its derivatives are equal to zero. The equations of motions for a thin-walled, axisymmetric cylinder may then be found to be [1]:

∂∂

=∂∂

N

xh

u

tx

mρ2

2 (1)

N

R

V

xh

w

tp x ty x

m−∂∂

+∂∂

= ( )ρ2

2, (2)

∂∂

=M

xVx

x (3)

Here, x and y are the axial and circumferential axes of the cylinder, rm is the average density of the composite pipe, h is the total pipe wall thickness, R is the mean radius of the composite pipe, p(x,t) is the internal pressure, Ni, Vi and Mi are tensile force, shear force and bending moment per unit length acting in the corresponding axes, and u and w are the axial and radial displacements, respectively.

In theoretical fluid-hammer analyses, three different axial support conditions are standard [6]. The one adopted in this work is that the pipe is anchored throughout against axial motion, causing u and all its derivatives to be equal to zero. For less-

Fig.1. Definition of coordinate system for the composite cylinder.


69

restrained systems, fluid-structure interaction may become of importance [6], which is beyond the scope of the current work. By adopting this support condition, and combining Equns 2 and 3, the following expressions can be obtained:

N constx = . (4)

N

R

M

xh

w

tp x ty x

m−∂∂

+∂∂

= ( )2

2

2

2ρ ,

(5)

Relationships between internal forces, moments and radial displacement

The relationship between internal forces, bending moments, middle surface strains, and curvatures for a laminate plate under plane stress conditions is known [8]:

N

N

N

M

M

M

A A A B B B

Ax

y

xy

x

y

xy

=

11 12 16 11 12 16

12 AA A B B B

A A A B B B

B B B D D D

B B

22 26 12 22 26

16 26 66 16 26 66

11 12 16 11 12 16

12 22 BB D D D

B B B D D D

x

y

26 12 22 26

16 26 66 16 26 66

0

0

ε

ε

γ xxy

x

y

xy

k

k

k

0

0

0

0

(6)

The 6x6 matrix is the laminate-stiffness matrix, and its components are given as:

A Q z zij ijk k kk

N

= −( )−=∑ 1

1

(7)

B Q z zij ijk k kk

N

= −( )−=∑1

22

12

1

(8)

D Q z zij ijk k kk

N

= −( )−=∑1

33

13

1

(9)

Qijk are the transformed reduced stiffnesses for layer k, and are given in the appendix for fibre-reinforced laminae; zk is the distance from the mean radius of the pipe to the top of layer k, which means that z h0 2= − and z hN = 2 , as shown in Fig.1.

It is assumed that the metallic pipe is free from stress when it is wrapped in laminated FRP, and that the metallic pipe therefore acts just like any other lamina in the laminate, but with different material properties. Metals like steel are isotropic, in which case the stiffnesses under plane-stress conditions are given as [9]:

Q QE

I II

I11 22 21

, ,= =−ν (10)

Q

EI

I I

I12 21

, =−νν

(11)

Q G

EI I

I

I66 2 1, = =

+( )ν (12)

In these equations, EI is the modulus of elasticity, GI is the shear modulus and νI is Poisson’s ratio for the isotropic material. The metallic pipe is as such considered to be


70

the first layer in the composite pipe, extending from z0 to z1 in Fig.1.

In order to take the variation of hoop strain between the different layers into account, Flügge’s shell theory is adapted, as has been done for composite cylinders in other works [1, 10]. The corresponding expressions for strains and curvatures for the middle surface are given as [10]:

ε x xu

xk

w

x0 0

2

2=∂∂

= −∂∂

, (13) ε y y

w

Rk

w

R0 0

2= = −, (14)

γ xy xyv

xk

R

v

x0 0 2=∂∂

= −∂∂

, (15)

As previously noted, u, ν, and their derivatives are equal to zero, causing ε x0

, γ xy0

, and kxy

0 to be equal to zero. With the aid of Eqns 13-15, the three equations required from the set of Equns 6 may now be written as:

N Aw

RB

w

xB

w

Rx = −

∂∂

−12 11

2

2 12 2 (16)

N Aw

RB

w

xB

w

Ry = −

∂∂

−22 12

2

2 22 2 (17)

M B

w

RD

w

xD

w

Rx = −

∂∂

−12 11

2

2 12 2 (18)

Equation 16 may be used to estimate the axial stress resultant in the pipe.

The governing equation of motion

The combination of Equns 17 and 18 with Equn 5 yields the governing equation of motion for a FRP overwrapped isotropic pipe:

λ λ λ ρ1

4

4 2

2

2 3

2

2

∂∂

+∂∂

+ +∂∂

= ( )w

x

w

xw h

w

tp x tm , (19)

where:

λ1 11= D (20)

(21)

λ3

222

223

= −A

R

B

R (22)

The term representing the inertia of the pipe wall contains the average density of the pipe wall, rm. Because the pipe consists of two different materials, this average density needs to be defined. Let IR be the inner radius of the isotropic pipe, MR is the outer radius of the isotropic pipe, and OR is the outer radius of the FRP overwrap. Furthermore, let hI be the thickness of the isotropic pipe, and hla is the thickness of each FRP lamina. The relationships between the different radii are found from the following expressions:

IR MR hI= − (23)

λ2122

122= −D

R

B

R


71

OR MR Nhla= + (24)

ROR IR

=+2

(25)

Using these quantities, the average density of the pipe wall may be expressed as: ρ

ρ ρm

I FRPMR IR OR MR

OR IR=

−( ) + −( )−

2 2 2 2

2 2 (26)

where rI is the density of the isotropic pipe, while rFRP is the density of the FRP overwrap.

Mathematical formulation of the pressure wave

The magnitude of the pressure change due to a sudden stop in a fluid flow has been derived by Joukowsky [6]:

∆ =p Vfρ α (27)

where rf is the density of the fluid, α is the velocity of sound through the fluid in the pipe, and V is the steady-state fluid velocity.

When the fluid flow is suddenly stopped, for example by the rapid closure of a valve, the fluid pressure directly upstream the valve will rise by the magnitude Dp. As time goes by, the part of the pipe being subjected to the pressure increase Dp will grow, until an instant when the full length of the pipe is subjected to this pressure increase [11]. The velocity of the pressure wave is equal to the velocity of sound through the fluid. The total pressure in the pipe will later also decrease by Dp, which may cause cavitation [6], but this is beyond the scope of this work.

The velocity of sound through the fluid may be estimated by applying the Korteweg approximation, in which the inertia and bending stiffness of the pipe wall are neglected [7]. The pipe is then considered as a series of massless rings expanding and contracting in accordance with the internal pressure [6]. In this case, N Ay y= 22ε , and the expression for the velocity of sound is the same as for an axially restricted laminated FRP pipe, which has been derived by Pavlou [1]:

αρ ρ

=+

12

22

f f

K

R

A

(28)

The pressure increase due to fluid hammer, as described above, may be expressed by the Heaviside step function [12]. The total internal pressure in the pipe may therefore be expressed as:

p x t p p H x ttot ,( ) = + ∆ − −( ) 0 1 α (29)

where p0 is the static pressure and H •( ) is the Heaviside step function. This expression

is applicable from the flow is suddenly stopped, until the pressure wave has reached the end of the pipe, i.e. for 0≤ t ≤ T

0. The time required for the pressure wave to reach the

end of the pipe is given by:

TL

0 = α (30)


72

where L is the length of the pipe. In this study, only the structural response due to the dynamic term will be studied:

p x t p H x t,( ) = ∆ − −( ) 1 α (31)

The structural response of the pipe due to a static pressure may be found by its static governing differential equation, and superposed to the dynamic response.

Analytical solution of the governing equation of motion

By implementing Equn 31 into Equn 19, the governing equation of motion may be expressed as: λ λ λ ρ α1

4

4 2

2

2 3

2

21

∂∂

+∂∂

+ +∂∂

= ∆ − −( ) w

x

w

xw h

w

tp H x tm (32)

The ends of the pipe are assumed to be simply supported along their perimeters, yielding the following boundary conditions to the differential equation:

w t w L t0 0, ,( ) = ( ) = (33)

∂ ( )∂

=∂ ( )∂

== =

2

20

2

20

w x t

x

w x t

xx x L

, , (34)

As the pipe is not deformed at t = 0, the following initial conditions may be applied:

w x andw x t

tt

,,

0 0 00

( ) =∂ ( )∂

==

(35)

Equation 32 is a partial differential equation with two variables. It may be transformed to an ordinary differential equation with respect to time, by applying a Fourier series solution. The boundary conditions 33-34 are automatically satisfied by a Fourier sine series given as:

w x tL

W tn x

Lnn

, sin( ) = ( )=

∞

∑2

1

π (36)

The coefficient is defined as:

W t w x tn x

Ldxn

L( ) = ( )∫ , sin

π0

(37)

The derivatives may be found to be:

∂∂

= − ( )=

∞

∑2

2

2 2

21

2w

x LW t

n

L

n x

Lnn

π πsin (38)

∂∂

= ( )=

∞

∑4

4

4 4

41

2w

x LW t

n

L

n x

Lnn

π πsin (39)

A Fourier sine series for the dynamic pressure may be found to be:

∆ − −( ) = ∆ −

=

∞

∑p H x tL

L

np

n t

L

n x

Ln

12

11

απ

πα πcos sin (40)

With expressions 36-40 implemented, Equn 32 may be rewritten as:

ρ λπ

λπ

λπm n n n nhW t W t

n

LW t

n

LW t

L

np

n ( ) + ( ) − ( ) + ( ) = ∆ −1

4 4

4 2

2 2

2 3 1 cosππαt

L

(41)


73

The following coefficients are introduced:

ωπ

nn

L2

2 2

2= (42)

Ωn

mn nh

2 41

22 3

1= − +( )ρ

ω λ ω λ λ (43)

ωπα

=L

(44)

p

p

h

L

nnm

∗ =∆ρ π (45)

Taking these coefficients into account, Equn 41 may be expressed as:

W t W t p n tn n n n( ) + ( ) = −( )∗Ω2 1 cos ω (46)

Equation 46 is an ordinary differential equation, which may easily be solved. The particular solution is found to be:

W t pn

n tn p nn n

, cos( ) = −−

∗ 1 12 2 2 2Ω Ω ω

ω (47)

The general solution may be found from its characteristic equation:

a n2 2 0+ =Ω (48)

The roots of the characteristic equation are:

a in= ±Ω (49)

These roots yield the following general solution of the differential Equn 46:

W t C t D tn h n n, cos sin( ) = +Ω Ω (50)

C and D are constants, which are found from the initial conditions (35). The solution of the ordinary differential Equn 46 is the sum of the general and the particular solution:

W t pn

t n t tn nn

nn

n( ) =−

−( ) + −( )

∗ 1 11

2 2 2 2ΩΩ

ΩΩ

ωωcos cos cos

(51)

With the implementation of Equn 51 into Equn 36, an analytical solution for the radial displacement has been found:

w x tL

pt n t

n

t nn

n

n

n

n

,cos cos cos

sin( ) = −−

+−

∗2 12 2 2 2

ΩΩ

ΩΩ

ωω

π xx

Ln=

∞

∑1

(52)

The radial displacements found from this solution may be inserted into Equns13 and 14 to obtain the strains and curvatures, which then may be used to find the resulting stresses in each layer, using the procedure found in [8], together with Hooke’s law for the isotropic pipe. The resulting stresses may then be evaluated against failure criteria for isotropic and anisotropic materials. It should be noted that the Fourier series in Equn 52 does not rapidly converge, due to


74

the denominator Ωn n2 2 2− ω , which may approach zero for some values of n. The series should therefore not be terminated before it has converged. The number of terms which should be included must be decided on a case-to-case basis. However, if there exist some n for which Ωn n2 2 2 0− ≤ω , the absolute minimum number of terms required may be found by setting the denominator equal to zero:

Ωnm

nh

n

L

n

L

n

L2 2 2

4 4

4 1

2 2

2 2 3

2 2 2

2

10− = − +

− =ω

ρπ

λπ

λ λπ α

(53)This equation may be solved with respect to its largest value for n:

N

L h hm m

min =+ + +( ) −

π

λ α ρ λ α ρ λ λ

λ

22

22 2

1 3

1

4

2

(54)

The series should then be terminated after including sufficiently more terms than Nmin

, for example 10 % more.

Implementation of the model

A calculated example will now be shown. Consider a steel pipe with length L = 50 m, outer radius MR = 0.2 m, and effective load-carrying thickness h

I = 3.5 mm. The steel

pipe has density rI = 8000 kg/m3, elastic modulus E

I = 210 GPa, and Poisson’s ratio ν

I

= 0.3. This pipe has been repaired by a overwrap composed by twenty E-Glass/Epoxy laminae with fibre orientation θ = ± 45o, thickness h

la = 0.15 mm, and density r

FRP =

1000 kg/m3. The mechanical properties of the E-Glass/Epoxy laminae [1] are E1 = 39

GPa, E2 = 8.6 GPa, G

12 = 3.8 GPa, and ν

12 = 0.28. The above pipe is conveying water

with density rf = 1000 kg/m3 and bulk modulus of elasticity K = 2.9 x 107 N/m2, at a

flow speed of V = 3 m/s. The initial pressure is neglected. A sudden stop of the flow happens, and fluid-hammer conditions occur.

Using the Appendix, together with Equns 7-12, the following components of the stiffness matrix are calculated:

A12

= 2.7091 x 108

A22

= 8.5910 x 108

B11

= - 1.1216 x 106

B12

= - 3.1341 x 105

B22

= - 1.1216 x 106

D11

= 2.8378 x 103

D12

= 901.6

The coefficients of the governing differential equation then take the values λ1 = 2837.8,

λ2 = 3.1606 x 106, and λ

3 = 2.1672 x 1010 by using Equns 20-22. The velocity of the

pressure wave may be found from Equn 28 to be α = 1041.6 m/s, while the pressure rise is found from Equn 27 to be Dp = 3.1249 MPa. N

min from Equn 54 is multiplied by

1.10 to find the number of terms of the series to be used; NF = 1940. The corresponding

dynamic displacement may now be found by applying Equns 42-45 and 52.

The resulting dynamic displacement is difficult to properly visualize with figures, because it is heavily oscillating with respect to time. An attempt is made here with figures generated with MATLAB, but the best option is to use a software package to


75

generate animated plots of the radial displacement with respect to position along the pipe. Figure 2 shows the radial displacement when the pressure wave is midway through the pipe; t = T

0/2.

The static displacement wst due to a static

pressure pst may be approximated as:

w

pst

st≈λ3

(55)

In this case, this corresponds to 0.144 mm. Hence, the radial displacement due to the pressure wave is observed to oscillate heavily about this static displacement. At the current instant, the maximum radial deflection is 2.2 times higher than this static displacement. This factor is called the dynamic load factor DLF [12]. Figure 2 also indicates a small precursor vibration in front of the pressure wave, as earlier also calculated for steel pipes [12].

In Fig.3, the pressure wave front has been zoomed in, in order to better visualize how the displacement is oscillating along the length of the pipe. It is observed that over a length of 125 mm, the displacement goes from its maximum to its minimum value.

The variation of the radial displacement versus time at x = L/2 is shown in figure 4, where the low amplitude precursor vibration is clearly visible. It is observed that the radial displacement, and therefore also the hoop stress, is oscillating with a

very high frequency. This indicates that the possibility of fatigue damages needs to be taken into account when designing the FRP overwrap for fluid-hammer conditions.

The effect of the number of FRP laminae applied

When a FRP overwrap is designed, the influence of the number of laminae on the dynamic response of the pipe will be of interest. Therefore, the average static and maximum dynamic displacement has been calculated for every second new lamina from 0 to 40 laminae. When more than 40 laminae are applied, one reaches the limit of the thin-walled shell theory on which this work is based. Equation 55 has been used to calculate the static displacement. The maximum dynamic displacement has been estimated by calculating the radial displacement at every 10 mm along the pipe for every 20 µs numerically, for then to find the maximum. All the maximum displacements were found to occur for t > 40 ms. Therefore, the displacements in the interval 40 ms ≤ t ≤ T

0 were calculated

once more with a time step of 10 µs, to increase the probability of hitting the maximum values. Better estimates may be found by using smaller length or time steps, at the cost of increased computation time, but the difference when doing so has been found to be small. The results are shown in Fig.5.

Fig.2. Radial deflection of a FRP overwrapped 16-in steel pipe.


76

As expected, the average static displacement is steadily decreasing when the number of FRP laminae is increased. The maximum dynamic displacement, on the other hand, does not follow a monotonic trend. Instead, it decreases for the first ten laminae, before it starts to increase. When 40 laminae are applied, the maximum dynamic displacement is 6 % higher than when no laminae are applied.

The reason for the increasing dynamic displacements is assumed to be that the natural frequency of the pipe changes. E-Glass is approximately eight times lighter than steel, which makes the average pipe wall density decrease when more laminae are applied. Because of

this, the stiffness of the pipe increases faster than its inertia, causing its natural frequency to change. This means that a FRP-overwrapped steel pipe may be closer to a state of resonance than the steel pipe itself, leading to increased amplitudes of its oscillation due to fluid hammer. The occurrence of resonance in a pipeline due to fluid hammer has earlier been described by Leishear [12], and also mentioned by Shepherd et al. [7]. Using the same procedure as Leishear has used for isotropic pipes, the critical velocity for which resonance occurs, for an axially restricted composite pipe, may be expressed as:

αλ λ λρcr

mh=

−2 1 3 2 (56)

Fig.3. Detail of the wave front

in Fig.2.

Fig.4. Mid-pipe radial

displacement as function of time.


77

where the symbols from Equn 19 are used. If the velocity of the fluid hammer from Equn 28 approaches this critical velocity, the maximum radial displacement will increase significantly [12]. It will therefore be in the overwrap designer’s interest to make sure a sufficient margin exists between α and α

cr, which both depend on

the stiffness of the pipe.

In Fig.6, the model has been applied to a steel pipe with outer diameter 1.2 m and thickness 10 mm. The rest of the configuration is equal to the previous example. As the pipe diameter is larger, the thin-walled shell theory may be used for a thicker pipe. As the figure shows, the maximum dynamic radial deformation is reduced for the first 60 laminae. However, when 130 laminae are applied, this

deformation has increased, being 8.5% higher than when no laminae are applied. Thus, the increasing deformation is experienced for pipes of both small and large diameters.

Conclusions

An analytic uncoupled model, giving an approximate estimation of the dynamic radial deflection of a laminated fibre-reinforced polymer (FRP) overwrapped isotropic pipe, subjected to fluid-hammer conditions, has been derived.

The model takes the elastic properties of the conducted fluid and the two piping materials into account, in order to estimate the pressure rise and wave speed.

Fig.5. Influence of the number of overwrap FRP laminae on a 16-in steel pipe.

Fig.6. Influence of the number of overwrap FRP laminae on a 1.2-m steel pipe.


78

The dynamic response of the pipe, caused by the pressure wave described by these two properties, has been derived using thin-walled shell theory and the laminate-stiffness matrix. The resulting partial differential equation has been solved by utilizing Fourier sine series.

The model has been implemented for a representative example. The radial deformation was found to oscillate, both along the pipe at any given instant, and for each point with respect to time. As the frequency is very high, there is a risk for fatigue damage to occur.

Calculations have been performed in order to investigate how the number of FRP laminae influences the dynamic response of the pipe. The maximum radial displacement during the first fluid-hammer pressure wave is decreased when the first laminae are applied. When even more laminae are added, the oscillation amplitude and the maximum displacement increases, due to the change of the natural frequency of the pipe, compared to the fluid-hammer wave speed.

The model presented in this work is only applicable up to the moment when the whole length of the pipe is subjected to increased pressure, i.e. for 0 ≤ t ≤ T

0. For

T0 ≤ t ≤ 2T

0, the differential equation has

to be solved for the reflected pressure wave, which cancels the original pressure rise. The initial conditions for this new differential equation will be the solution of equation (52) when t = T

0.

The model could be enhanced by taking fluid friction and pipe material damping into account. In order to obtain a more realistic model, for a pipe which is not axially restricted throughout, a fluid-structure interaction model should be developed, taking Poisson coupling into account [6].

Acknowledgement

The author is grateful to Dimitrios G Pavlou, for suggesting research of the

topic which is discussed in this article, and for proof reading the article.

References

1. D.G.Pavlou, 2015. Undamped vibration of laminated fiber-reinforced polymer pipes in water hammer conditions. ASME J. Offshore Mech. Arct. Eng. 137 (6) pp 061701. DOI: 10.1115/1.4031669.

2. M.Geraghty, A.Pridmore, and J.Sanchez, 2011. Transitioning from leak detection to leak prevention: proactive repair of steel pipelines using fiber reinforced polymer (FRP) composites. Pipelines 2011: A sound conduit for sharing solutions, ASCE, Reston, VA, USA, 2011, pp. 100-107. DOI: 10.1061/41187(420)10.

3. N.Saeed, 20-15. Composite overwrap repair system for pipelines – onshore and offshore application. PhD dissertation, The University of Queensland, Queensland, Australia.

4. M.Ehsani, 2015. Repair of corroded/damaged metallic pipelines using fiber-reinforced polymer composites. In: Rehabilitation of pipelines using fiber-reinforced polymer (FRP) composites, V.M.Karbhari, Ed., Woodhead Publishing, pp 39-59. DOI: 10.1016/B978-0-85709-684-5.00003-5.

5. H.Toutanji and S.Dempsey, 2001. Stress modeling of pipelines strengthened with advanced composites materials. Thin-Walled Structures 39 (2) pp 153-165. DOI: 10.1016/S0263-8231(00)00049-5.

6. A.S.Tijsseling, 1996. Fluid-structure interaction in liquid-filled pipe systems: a review. J. Fluids Struct. 10 (2) pp 109-146. DOI: 10.1006/jfls.1996.0009.

7. J. Shepherd and K.Inaba, 2010. Shock loading and failure of fluid-filled tubular structures. In: Dynamic failure of materials and structures, A.Shukla, G.Ravichandran, Y.D.S.Rajapakse, Eds, Springer, New York, pp 153-190. DOI: 10.1007/978-1-4419-0446-1_6.

8. D.G.Pavlou, 2013. Composite materials in piping applications. Destech Publications Lancaster, CA.

9. A.P.Boresi and R.J.Schmidt, 2003. Advanced mechanics of materials, Sixth Edition John Wiley & Sons, Inc., New York, p 87.

10. L.P.Kollár and G.S.Springer, 2003. Mechanics of composite structures. Cambridge University Press, West Nyack, NY, p 371.

11. E.B.Wylie and V.L.Streeter, 1983. Fluid transients, FEB Press, Ann Arbor,


79

Michigan, p 7.12. R.A.Leishear, 2007. Derivations for hoop

stresses due to shock waves in a tube. In:

ASME 2007 Pressure Vessels and Piping Conference, Volume 3: Design and Analysis, San Antonio, Texas, USA, pp 185-194. DOI: 10.1115/PVP2007-26722.

Appendix

The transformed reduced stiffnesses Qijk for each FRP lamina k are required in Equns 7-9. They are given by the following expressions [8]:

Q Q m Q Q n m Q nk11 114

12 662 2

2242 2= + +( ) + (A.1)

Q Q Q Q n m Q n mk12 11 22 66

2 212

4 44= + −( ) + +( ) (A.2)

Q Q Q Q nm Q Q Q n mk16 11 12 663

12 22 6632 2= − −( ) + − +( ) (A.3)

Q Q n Q Q n m Q mk22 114

12 662 2

2242 2= + +( ) + (A.4)

Q Q Q Q n m Q Q Q nmk26 11 12 663

12 22 6632 2= − −( ) + − +( ) (A.5)

Q Q Q Q Q n m Q n mk66 11 22 12 662 2

664 42 2= + − −( ) + +( ) (A.6)

m n= =cos , sinθ θ (A.7)

QE

QE

111

12 2112

12 2

12 211 1=

−=

−ν ννν ν

, (A.8)

QE

Q G222

12 2166 121

=−

=ν ν

, (A.9) ν ν21

2

112=

E

E (A.10)

E1 and E

2 are the moduli of elasticity, ν

12 and ν

21 are the Poisson’s ratios, and G

12 is the

shear modulus in the principal directions 1, 2 of the FRP material. θ is the orientation of the fibres; the fibres run along the pipe if θ = 0o, and they run circumferentially if θ = 90o.

Nomenclature

Aij ,

Bij , D

ij members of the laminate stiffness matrix

EI modulus of elasticity for the isotropic pipe material

GI shear modulus for the isotropic pipe material

H •( ) the Heaviside step functionh total thickness of the pipe wall, both the metallic and FRP

laminae


80

hI thickness of isotropic pipe wall

hla thickness of one FRP lamina

IR inner radius of the metallic/isotropic pipeK modulus of elasticity of the fluidk layer numberk k kx y xy

0 0 0, , curvatures for the middle surfaceL length of the pipeM

i bending moment per unit length with respect to the i axis

MR outer radius of the metallic/isotropic pipeN total number of layers in the composite pipeN

F number of terms which are included in the Fourier series solution

Ni tensile force per unit length with respect to the i axis

Nmin

absolute minimum number of terms which must be included in the Fourier series solutionn number of term in the Fourier seriesOR outer radius of the FRP overwrapp(x,t) dynamic internal pressurep*

n coefficient in the n’th term of the Fourier sine series

ptot

(x,t) total internal pressurep

0 static internal pressure

Qijk transformed reduced stiffnesses for layer k

R mean radius of the composite pipeT

0 time required for the pressure wave to reach the end of the pipe

t timeu, v, w axial, circumferential, and radial displacements, respectivelyV initial steady-state fluid velocityV

i shear force per unit length with respect to the i axis

Wn(t) coefficient in term n of the Fourier sine solution of w(x,t)

w(x,t) dynamic radial displacement of the pipe wallx, y,r axial, circumferential and radial cylindrical coordinates, respectivelyz

k distance from the mean radius of the pipe to the top of layer k

α speed of sound and fluid hammer through the liquidα

cr critical velocity of fluid hammer, causing resonance

Dp pressure change due to fluid hammerε ε γx y xy

0 0 0, , strains in the middle surface of the overwrapped pipeλ

i coefficients in the governing differential equation

νI Poisson’s ratio for the isotropic pipe material

rf density of the fluid

rFRP

density of the FRP materialr

I density of the isotropic pipe material

rm average density of the pipe

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Founder, Pipeline Science and Technology

Ya. M. Fridlyand, General Director, Pipeline Transport Institute, Moscow, Russian Federation

Chairman of the Editorial Board and Editor-in-ChiefDr Anatoly E. Soschenko, Head, Department of Innovation Development and R&D,

Transneft, Moscow, Russian Federation

Deputy Chairman of the Editorial BoardDr Yu. V. Lisin, Moscow, Russian Federation

Editorial Board Members

Dr Samer M. Adeeb, Southwest Petroleum University China, Chengdu, ChinaDr Samuel Ariaratnam, Ira A. Fulton Schools of Engineering, Arizona State University, Tucson, AZ, USA

Dr Anatoly N. Dmitrievsky, Oil and Gas Research Institute, Moscow, Russian FederationNikolay N. Gorban, Caspian Pipeline Consortium JSC, Moscow, Russian Federation

Erik Green, Total E&P Russie, FranceDr Mohammed Hadj-Meliani, Hassiba Benbouali Unibersity, Chlef, Algeria

Dr Galina Ilieva, Shipbuilding Faculty, Technical University-Varna, Varna, BulgariaCliff Jonhson, PRCI, Falls Church, VA, USA

Dr Saravanan Karuppanan, Mechanical Engineering Department, Petronas Universiti Teknologi, Malaysia

Dr Anatoly M. Korolyonok, Pipeline Network Design, Construction and Operation Faculty, Gubkin Russian State University of Oil and Gas, Moscow, Russian Federation

Dr Jyant Kumar, Indian Institute of Science, Bangalore, IndiaDr Yuanhua Lin, School of Materials Science and Engineering, Southwest Petroleum University,

Chengdu, ChinaDr Nikolay A. Makhutov, Center for Steel and Welding, Strength Analysis, Pipeline Transport Institute,

Moscow, Russian FederationDr Yerbol S. Makhmotov, KazTransOil JSC, Astana, Kazakhstan

Dr Yury G. Matvienko, Department of Strength, Survivability and Safety of Machines, Mechanical Engineering Research Institute, RAS, Moscow, Russian Federation

Dr Atef Mohany, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Ontario, Canada

Dr Olga P. Molchanova, Faculty of Economics, Lomonosov Moscow State University, Moscow, Russian Federation

Dr Georgy V. Nesyn, Service for Efficiency Assessment of Hydraulic Resistance Methods, Pipeline Transport Institute, Moscow, Russian FederationDr Fabrizio Paolacci, University of Rome III, Rome, Italy

Dr Dimitrios G. Pavlou, University of Stavanger, Sravanger, NorwayDr Guy Pluvinage, Polytechnic University of Tirana (Albania), Metz, France

Dr Pathmanathan Rajeev, Swinburne University of Technology, Melbourne, Vic., AustraliaBerik K. Sayahov, KazTransOil JSC, Astana, Kazakhstan

Pavel Y. Serikov, Department of Economics, Transneft, Moscow, Russian FederationDr Sergei S. Sherbakov, Belarus State University, Minsk, Belarus

Dr Vladimir B. Sigitov, Institute of Polymeric Materials and Technologies, Almaty, KazakhstanDr Leonid A. Sosnovskiy, Tribofatigue Ltd, Gomel, Belarus

Dr Lakhdar Taleb, Department of Mechanics, INSA, Rouen, FranceJohn Tiratsoo, Technical Productions (London) Ltd, Eastleigh, UK

Dr Moran Wang, Multiscale Interfacial Transport, Tsinghua University, Beijing, ChinaDr Shugen Xu, College of Chemical Engineering, China University of Petroleum, Qingdao, China

Dr Jie Zhang, School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, ChinaDr Vladimir V. Zholobov, Department of Mathematical Modelling of Oil Trunk Pipeline Operation,

Pipeline Transport Institute, Moscow, Russian Federation

Science and Technology

published byPipeline Transport Institute

Technical Productions (London) LtdISSN 2514-541X

Vol. 2, No. 1, March 2018

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