TECHNICAL SPECIFICATION I-ET-0000.00-0000-274-P9U-001€¦ · FPU Floating Production Unit Hs Wave...

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TECHNICAL SPECIFICATION Nº: I-ET-0000.00-0000-274-P9U-001 CLIENT: GENERAL SHEET: 1 of 49 JOB: GENERAL CC: AREA: GENERAL PROJECT: DP&T TITLE: SLWR DETAILED STRUCTURAL DESIGN REQUIREMENTS EISE / EDR INDEX OF REVISIONS REV. DESCRIPTION AND/OR REVISED SHEETS 0 A B ORIGINAL (THIS DOCUMENT SUPERSEDES THE DOCUMENT I-ET-0000.00-6500-274-P9U-001) Itens 4.4 and 6.4.3 Soil embedment (itens 6 l, 7.1 k, 7.2.1 m); Table 6 (ALS3A and B); Reference [13] REV. 0 REV. A REV. B REV. C REV. D REV. E REV. F REV. G REV. H DATE 28/DEZ/2017 16/FEV/2018 13/MAR/2018 PROJECT EISE/EDR EISE/EDR EISE/EDR EXECUTION BXT4 BXT4 BXT4 CHECK TS8H TS8H TS8H APPROVAL CLZ2 CLZ2 CLZ2 THE INFORMATION CONTAINED IN THIS DOCUMENT IS PETROBRAS PROPERTY AND MAY NOT BE USED FOR PURPOSES OTHER THAN THOSE SPECIFICALLY INDICATED HEREIN. THIS FORM IS PART OF PETROBRAS N-381 REV. L

Transcript of TECHNICAL SPECIFICATION I-ET-0000.00-0000-274-P9U-001€¦ · FPU Floating Production Unit Hs Wave...

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TECHNICAL SPECIFICATION Nº:

I-ET-0000.00-0000-274-P9U-001

CLIENT: GENERAL

SHEET: 1 of 49

JOB: GENERAL CC:

AREA: GENERAL PROJECT:

DP&T

TITLE:

SLWR DETAILED STRUCTURAL DESIGN REQUIREMENTS

EISE / EDR

I N D E X O F R E V I S I O N S

R E V . D E S C R I P T I O N A N D / O R R E V I S E D S H E E T S

0 A B

ORIGINAL (THIS DOCUMENT SUPERSEDES THE DOCUMENT I-ET-0000.00-6500-274-P9U-001)

Itens 4.4 and 6.4.3 Soil embedment (itens 6 – l, 7.1 – k, 7.2.1 – m); Table 6 (ALS3A and B); Reference [13]

REV. 0 REV. A REV. B REV. C REV. D REV. E REV. F REV. G REV. H

DATE 28/DEZ/2017 16/FEV/2018 13/MAR/2018

PROJECT EISE/EDR EISE/EDR EISE/EDR

EXECUTION BXT4 BXT4 BXT4

CHECK TS8H TS8H TS8H

APPROVAL CLZ2 CLZ2 CLZ2

THE INFORMATION CONTAINED IN THIS DOCUMENT IS PETROBRAS PROPERTY AND MAY NOT BE USED FOR PURPOSES OTHER THAN THOSE

SPECIFICALLY INDICATED HEREIN. THIS FORM IS PART OF PETROBRAS N-381 REV. L

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TABLE OF CONTENTS

1 INTRODUCTION ........................................................................................................... 6

1.1 OBJECTIVE ............................................................................................................................................. 6

1.2 SCOPE OF WORK .................................................................................................................................. 6

1.3 TYPICAL SLWR CONFIGURATION ....................................................................................................... 7

2 DESIGN ANALYSIS REQUIREMENTS ....................................................................... 8

3 DESIGN DATA DEFINITION ........................................................................................ 9

4 STRUCTURAL GLOBAL MODEL DEFINITION ........................................................ 13

4.1 FINITE ELEMENT MODEL ................................................................................................................... 13

4.2 WALL THICKNESS REDUCTION ......................................................................................................... 13

4.3 FLEXIBLE-JOINT MODELING .............................................................................................................. 13

4.4 SOIL MODEL ......................................................................................................................................... 14

4.5 MORISON COEFFICIENTS .................................................................................................................. 14

4.6 CLAD AND LINED PIPES ..................................................................................................................... 15

4.7 ANALYSIS SOFTWARE ........................................................................................................................ 15

5 WALL THICKNESS SIZING VERIFICATION ............................................................. 17

5.1 BURSTING ............................................................................................................................................ 17

5.2 COLLAPSE (HOOP BUCKLING) .......................................................................................................... 17

6 EXTREME COMBINED LOAD EFFECT ANALYSIS ................................................. 18

6.1 LOAD COMBINATIONS FOR ULS AND ALS ....................................................................................... 19

6.2 LOAD CASES ........................................................................................................................................ 21

6.3 WAVE SCREENING .............................................................................................................................. 21

6.4 SIMULATION OF IMPOSED MOTIONS AND WAVES ........................................................................ 25 6.4.1 EQUIVALENT HARMONIC MOTION PROCEDURE (EHMP) ......................................................... 25 6.4.2 DESIGN WAVE PROCEDURE (DWP) ............................................................................................ 26 6.4.3 IRREGULAR WAVE PROCEDURE (IWP) ....................................................................................... 26

6.5 SENSITIVITY ANALYSES ..................................................................................................................... 27

7 FATIGUE ANALYSIS ................................................................................................. 28

7.1 WAVE AND MOTION FATIGUE ANALYSIS ......................................................................................... 29 7.1.1 METHODOLOGY REQUIREMENTS ............................................................................................... 29 7.1.2 LOAD CASES ................................................................................................................................... 30 7.1.3 SENSITIVITY ANALYSIS ................................................................................................................. 31

7.2 VIV FATIGUE ANALYSIS ...................................................................................................................... 32 7.2.1 CURRENT VIV FATIGUE ANALYSIS .............................................................................................. 32 7.2.2 HEAVE INDUCED VIV FATIGUE ANALYSIS .................................................................................. 34 7.2.3 SENSITIVITY ANALYSIS ................................................................................................................. 34

7.3 SLUGGING EFFECT ANALYSIS .......................................................................................................... 35

8 TOP LOADS FOR RISER SUPORT STRUCTURE EVALUATION ............................ 36

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8.1 TOP LOADS BY EXTREME LOADING ANALYSIS .............................................................................. 36

8.2 TOP LOADS BY WAVE AND MOTION ANALYSIS .............................................................................. 37

9 INTERFERENCE ANALYSIS ..................................................................................... 38

10 INSTALLATION ANALYSIS ....................................................................................... 38

11 DELIVERABLES ........................................................................................................ 38

11.1 GENERAL DELIVERABLES ................................................................................................................. 39 11.1.1 DESIGN PREMISE AND METHODOLOGY .................................................................................... 39 11.1.2 RISER DESIGN SUMMARY ............................................................................................................ 39

11.2 SPECIFIC TOPIC DELIVERABLES ...................................................................................................... 39 11.2.1 WALL THICKNESS SIZING VERIFICATION REPORT ................................................................... 39 11.2.2 EXTREME COMBINED LOAD EFFECT ANALYSIS REPORT ....................................................... 39 11.2.3 WAVE AND MOTION FATIGUE ANALYSIS REPORT ................................................................... 41 11.2.4 CURRENT VIV FATIGUE ANALYSIS REPORT .............................................................................. 42 11.2.5 HEAVE-INDUCED VIV FATIGUE ANALYSIS REPORT ................................................................. 43 11.2.6 SLUGGING EFFECT ANALYSIS REPORT ..................................................................................... 43 11.2.7 FATIGUE ANALYSIS SUMMARY REPORT .................................................................................... 43 11.2.8 TOP INTERFACE LOADS ................................................................................................................ 44

12 REFERENCES ............................................................................................................ 45

APPENDIX A .................................................................................................................... 46

FJ STIFFNESS AS A FUNCTION OF THE ALTERNATING ANGLE .............................. 46

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DEFINITIONS

The following definitions are used for the purpose of this technical specification:

ALS Accidental Limit State

API American Petroleum Institute

CD Phase Conceptual Design Phase

CFD

C-Mn

Computer Fluid Dynamics

Carbon Manganese Steel

CONTRACTOR The company responsible for the design of the risers and related equipment.

CRA Corrosion Resistant Alloy

CRA Pipes When referred herein, means clad pipes or lined pipes

Critical Sections

The critical riser sections will be the sections that present a total fatigue life value below a minimum value defined by PETROBRAS in Table 1.

DNV

DNV UF

Det Norske Veritas

DNV Usage Factor

DOF Degree of Freedom

ECA Engineering Critical Assessment

EHMP Equivalent Harmonic Motion Procedure

FD Frequency Domain

FEA Finite Element Analysis

FEED Front End Engineering Design

FEM Finite Element Method

FXJ Flexible Joint

FPSO Floating, Production, Storage and Offloading Unit

FPU Floating Production Unit

Hs Wave Significant Height

LRFD Load and Resistance Factor Design

May Verbal form used to indicate a course of action permissible within the limits of the standard.

Metocean

movX, movY, movZ, movRX, movRY,movRY

NRP

PETROBRAS

PLET

Project

Meteorological & Oceanographic

FPU motions (translational and rotational) imposed at riser top connection, at FPU local reference system (see Figure 5).

Non Return Point

PETROBRAS - Petróleo Brasileiro S.A.

Pipeline End Terminal

Scope of activities performed by the CONTRACTOR to design, construct and install the riser system for a specific field and host FPU

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RAO Response Amplitude Operator

RMS Root Mean Square

SCF Stress Concentration Factor

SCR Steel Catenary Riser

Shall Mandatory requirement. Indicates requirements strictly to be followed in order to conform to this Technical Specification and from which no deviation is permitted.

Should

SLWR

SMYS

Indicates that among several possibilities, one is recommended as particularly suitable, without mentioning or excluding others, or that a certain course of action is preferred but not necessarily required. Other possibilities may be applied subject to agreement.

Steel Lazy Wave Riser

Specified Minimum Yield Stress

SN curve

SWL

Stress range versus number of cycles design curve

Still Water Level

TD Time Domain

TDP Touch Down Point – Point on which the riser touches the soil

TDZ

Tp

ULS

Touch Down Zone – Zone of variation of TDP

Wave Peak Period

Ultimate Limit State

TRF Riser/Flowline Transition – Point considered as the transition between riser and flowline

VIM Vortex Induced Motion

VIV Vortex Induced Vibration

WAMIT Wave Interaction Program from Massachusetts Institute of Technology – for floating body motion analysis.

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1 INTRODUCTION

1.1 OBJECTIVE

The purposes of this Technical Specification are:

To define the requirements for the analysis procedure to be employed;

To establish the acceptance criteria to be employed in the Structural Detailed Design of the SLWRs

configuration;

To define the deliverables minimum content.

1.2 SCOPE OF WORK

CONTRACTOR shall proceed to the complete structural verification of SLWR configurations. This work

shall include all aspects related in this Specification and others that may be added as a function of the

Codes or other recommendation, in order to guarantee that the riser is structurally safe for the intended

service life under the operational, accidental, temporary and installation conditions. A complete set of

risers to be installed shall be analyzed and the results documented.

The reference [2] will specify if the Detailed Structural verification shall be carried out in one or two

cycles.

The Detailed Design shall incorporate the real characteristics of the purchased equipment related to the

riser construction, such as:

Riser configuration definition;

Buoyancy modules characteristics (material, dimensions, etc);

Clad or lined pipe length and wall thickness;

C-Mn pipe length and wall thickness;

FJ capacity in terms of angular deflection and tension;

VIV suppressors characteristics (type, length, pitch, dimensions, etc).

For riser construction and installation, the following results shall be included:

Interface loads with FPU and with the riser anchor point;

Stress histograms for the critical and for the non-critical sections;

Installation procedure limitations and requirements.

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1.3 TYPICAL SLWR CONFIGURATION

SLWR - Compliant riser configuration with intermediate buoyancy sections designed in order to

absorb most of UEP vertical motion, improving the riser response in the TDZ and avoiding critical

stresses oscillations.

Figure 1 – SLWR Configuration

Flexible Joint

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2 DESIGN ANALYSIS REQUIREMENTS

A document designated “Design Basis Report" will be generated at the beginning of this Detailed

Structural Design, according to reference [1].

The report “Design Premise and Methodology" shall detail and describe the methodologies and/or

design requirements, applied codes, design criteria and any additional engineering assumption that are

not clearly defined and established in this technical specification. The computer programs or finite

element package to be used shall be named and described. Any methodology criteria or design

parameter that is not mentioned in this Technical Specification or in the “Design Premise and

Methodology" but is considered necessary to the design shall be submitted to PETROBRAS for

approval.

The analyses methodology described in next sections may solely be modified with PETROBRAS

consent. CONTRACTOR may include additional items considered essential to improve the reliability of

the design, and this shall be submitted to PETROBRAS for approval.

The main verification tasks are:

Establishment of a representative structural global analysis model;

Wall Thickness Sizing Verification;

Extreme Combined Load Effect Analysis

Wave and Motion Fatigue Analysis

Current VIV Fatigue Analysis

Heave-Induced VIV Fatigue Analysis

Interference Analysis

Installation Analysis

Slugging Effect Analysis

Riser-Soil Interaction Analysis

The basic Code is the DNVGL-ST-F201 [3]. Other codes may be referenced or used in any specific

aspect if subjected to PETROBRAS for approval.

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3 DESIGN DATA DEFINITION

Table 1 considers the totality of data that will be the input for the detailed verification of the riser.

Table 1 Analysis Data

Seq. Data Data Source

1 FPU Data

1.1 Calibrated RAOs (for all operational drafts) See reference [2]

1.2 Operating time frequency of RAO drafts See reference [2]

1.3 Extreme Offsets in terms of water depth percentage (%)

See reference [2]

1.4 Offsets for Wave Fatigue Load Cases See reference [2]

1.5 Time traces of Low Frequency Motions for Wave Fatigue Load Cases

See reference [2]

1.6 Time traces of Full dynamic response (1st and 2nd order random motions from coupled model) under wave load for Fatigue Conditions

See reference [2]

Can alternatively be used representing offsets, first and second order motions

1.7 The angle magnitudes and directions to be considered in the platform hull damaged - accidental condition

See reference [2]

1.8 Vortex Induced Motions (VIM): time traces or pairs of amplitude-period corresponding to load cases

To be provided by PETROBRAS in reference [2], if PETROBRAS considers applicable.

Not applicable for FPSOs

1.9 FPU Heading See reference [2]

1.10 Drawings showing the riser connection points, the riser function sequence and riser azimuths

See reference [2]

1.11 Data of the fairleads locations and anchor lines configuration to be used in the interference verification between riser and anchor lines

See reference [2]

1.12 FPU drafts See reference [2]

All operational drafts provided will be used

1.13 The relative angle between turret type FPU and waves to be considered in the Extreme Combined Load Effect Analyses

To be provided by PETROBRAS in reference [2], if applicable.

Not applicable for spread moored FPSO

2 Metocean Data

2.1 Wave fatigue load cases with correlated bi-modal waves, current profiles and winds

See reference [2]

2.2 Extreme waves (Metocean Data Report) See reference [2]

2.3 Extreme currents (Metocean Data Report) See reference [2]

2.4 Fatigue Current Profiles (Metocean Data Report) See reference [2]

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3 Geotechnical Data

3.1 Soil Vertical and Lateral Stiffness for different pipe embedments, depending on the analysis type (see section 4.4)

See reference [2]

3.2 Equivalent lateral and axial friction coefficients for different pipe embedments, depending on the analysis type (see section 4.4)

See reference [2]

3.3 Seabed slope in the riser direction on the TDZ See reference [2]

4 Top Connection

4.1 Connection type See reference [2]

4.2 FJ stiffness data related to the dynamic angle variation magnitudes

To be provided by CONTRACTOR, according with the manufacturer information, when FJ is the connection type - See reference [2]

4.3 Length and geometry of the Top Connection joint Extension

See reference [2]

Initial values will be suggested by PETROBRAS together with riser configurations description

4.4 Receptacle angle See reference [2]

4.5 Receptacle limit loads See reference [2]

5 Riser Data

5.1 Internal diameter See reference [2]

5.2 Wall thickness (unique along the riser or the set of values and positions along the riser, if there is variation)

To be defined by CONTRACTOR

5.3 Steel grade See reference [2]

5.4 Top angle To be defined by CONTRACTOR, in acordance with Receptacle angle (4.4) and submitted for PETROBRAS approval.

5.5 Connection points coordinates See reference [2]

5.6 Azimuth See reference [2]

5.7 Riser PLET location See reference [2]

Defined by PETROBRAS at the subsea layout

5.8 Corrosion allowance See reference [2]

5.9 Minimum length of clad pipe See reference [2]

5.10 Thickness for thermal insulation coating To be calculated by CONTRACTOR based on the requirements defined by PETROBRAS - See reference [2]

5.11 Service Life See reference [2]

5.12 S-N curves to be used in the damage evaluation on the internal and external fibers of the riser cross section for the clad pipes, lined pipes and C-Mn pipes, considering critical and non-critical sections

See reference [2]

Any change coming from the welding qualification program shall be incorporated

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5.13 Penalty factor to be used for the S-N curve for C-Mn pipes, as a function of the corrosion-fatigue effect of aggressive internal contents

See reference [2]

5.14 Internal misalignment (hi-lo) value to be used in the SCF calculation

See reference [2]

5.15 Initial ovalization (fabrication and reeling, if applicable)

To be defined by CONTRACTOR

5.16 Fabrication tolerances with relation to wall thickness Clad pipes, lined pipes and C-Mn pipes: to be defined by CONTRACTOR, based on Manufacturer information and PETROBRAS requirements [9][10][11][12]

5.17 Weights (dry and wet) to be considered to represent the J-LAY collars or sleeves, when applicable.

Dimensions shall be proposed by CONTRACTOR

5.18 Maximum structural damping 0.3%

5.19 Safety Factor for Wave&Motion and Slug fatigue analyses

10

5.20 Safety Factor for VIV and Heave induced fatigue analyses

20

5.21 Minimum fatigue life to be achieved by non critical C-Mn riser sections

See reference [2]

6 Operational Conditions

6.1 Riser Function See reference [2]

6.2 Minimum Operating Pressure and corresponding elevation

See reference [2]

6.3 Design Pressure and corresponding elevation See reference [2]

6.4 Incidental Pressure and corresponding elevation See reference [2]

6.5 Hydrostatic Test Pressure and corresponding elevation

See reference [2]

6.6 Internal fluid specific weight data along the length of the riser. Profiles corresponding to different times in the production life of a well will be employed. All internal fluid data provided shall be considered, including hibernation.

See reference [2]

6.7 Definition if the riser can be empty or with zero pressure during its operational life

See reference [2]

6.8 Operational minimum temperature See reference [2]

6.9 Operational maximum temperature See reference [2]

6.10 Slugging data See reference [2], when applicable

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7 Positioning Errors

7.1 Floating Production Unit positioning error See reference [2]

7.2 Subsea equipment (anchor system or fixed point) positioning error

See reference [2]

8 VIV Suppressor

8.1 Suppressor type to be considered See reference [2]

9 Buoyancy Modules

9.1 Buoyancy modules characteristics (for lazy-wave configuration application).

Provided at the preliminary configurations

10 Data for interference Analysis

10.1 Configuration data of neighbor risers for interference calculation

See reference [2]

10.2 FPU geometrical characteristics near riser support See reference [2]

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4 STRUCTURAL GLOBAL MODEL DEFINITION

4.1 FINITE ELEMENT MODEL

The finite element model to be used shall include the steel riser coating (anti-corrosion and thermal

insulation), buoyancy modules, VIV suppressors and FJ including the extension detailed geometry.

The finite element mesh shall be proven adequate through a sensitivity study that shall be presented

and submitted to PETROBRAS for approval. The lengths of the finite element used shall be chosen

according to the criticality of each section under analysis:

Near the top region, the changing in wall thickness of the tapper section shall be represented,

requiring smaller elements. The FJ tapper section and stiffness characteristics shall be preliminary

defined by Manufacturer.

For the TDZ the elements shall be shortened in order to adequately capture the riser-soil interaction.

Also in the buoyancy modules region (the convex and concave regions) smaller elements shall be

used.

The buoyancy modules section shall not be represented by an equivalent continuous section in the

numerical model. However, a sensitivity study can be performed in order to show for which type of

analyses the equivalent continuous section can be used. The results shall be submitted to PETROBRAS

approval before using this in the simulations.

4.2 WALL THICKNESS REDUCTION

Minimum wall thickness for design checks shall be considered as described in DNVGL-ST-F201 [3].

The corrosion allowance, for C-Mn pipes, shall be considered as a corrosion occurring around the entire

circumference of the specific section being verified.

Fabrication tolerances shall be considered as described in the design code and PETROBRAS

requirements [9], [10], [11] and [12], according to the specifications of each pipe used.

The riser shall be simulated with the nominal characteristics and the forces calculated as if no corrosion

or thickness reduction is present. The reduced section shall be considered for stress calculation.

4.3 FLEXIBLE-JOINT MODELING

The FJ stiffness’s in the flexional directions and in the torsional directions shall be considered. A nominal

stiffness may be applied for the static analyses. For the dynamic analyses, the stiffness shall be

increased as a function of the magnitude of the FJ rotations. The stiffening factors shall be obtained

based on the manufacturer stiffness curve and used in a conservative way. See Appendix A.

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The temperature and pressure effects on FJ stiffness shall also be considered, when CONTRACTOR

is defining stiffness values to be employed in the analyses.

The FJ extension shall be modeled, including the representation of the tapered section in the finite

element model.

4.4 SOIL MODEL

The seabed slope in the TDZ shall be considered.

The riser-soil interaction shall be considered and described in the Design Premise and Methodology to

be submitted to PETROBRAS for approval.

For operational conditions, CONTRACTOR shall evaluate, according to the soil-interaction analysis,

which embedment is more probably to occur in order to determine the soil stiffness and the equivalent

friction coefficients to be used in the analysis, and submit to PETROBRAS approval.

For extreme conditions, CONTRACTOR shall evaluate, according to the soil-interaction analysis, which

embedment will result in a more conservative approach for the riser integrity. This embedment shall be

used to determine the soil stiffness and the equivalent friction coefficients for the analysis, and submit

to PETROBRAS approval.

The mean values of vertical and lateral stiffness, axial and lateral friction coefficients shall be calculated

for different riser embedment levels, according to Table 1 . These mean values shall be used as base

case, but the minimum and maximum values shall be used in the sensitivities analyses for each type of

verification: extreme, fatigue, interference, etc. The minimum value represents the lowest nominal value

obtained from LE, BE and UE soil properties. Similarly, the maximum value represents the highest

nominal value obtained from LE, BE and UE soil properties.

4.5 MORISON COEFFICIENTS

The normal drag coefficients to be adopted for bare pipe and buoyancy sections, in the storm and fatigue

simulations, shall be 1.2 and 0.7 respectively. In the buoyancy sections, longitudinal drag coefficient

shall be adopted according to reference [7].

The bare pipe and buoyancy sections inertia coefficient shall be 2.0.

Riser lengths with VIV suppressors shall be properly considered and the adopted values for the drag

and the inertia coefficients shall be justified.

Different values shall be justified in the Design Premise and Methodology and presented in the

Design Basis Report.

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4.6 CLAD AND LINED PIPES

For Extreme Load verification, clad and liner CRA layer shall be considered as contributing for riser

weight and structural stiffness. However, the clad and liner CRA layer shall be neglected for the riser

strength calculation. Thus for the forces and bending moments evaluation, the clad and liner CRA layer

contribution shall be considered.On the other hand, the CRA layer thickness shall be subtracted from

the pipe wall thickness and considered as a corrosion allowance for riser resistance evaluation.

When applying the above proposition, if in some situation the pipe does not meet the DNV code

requirement [3], CONTRACTOR may propose an alternative procedure including clad/liner contribution

to the total pipe resistance [8], [9] and [10]. This procedure shall be approved by PETROBRAS.

Lined pipes minimum curvature radius (RCmin) obtained in the Extreme Loads simulation shall be verified

according to following equation:

𝑅𝐶𝑚𝑖𝑛 =𝑂𝐷. (𝑂𝐷 − 2𝑡2)

𝑡𝑙𝑖𝑛𝑒𝑟. 𝑆𝐹

Where:

OD – pipe outer diameter

t2 – backing steel wall thickness

tliner – liner thickness

SF – Safety Factor = 2

For Fatigue verification, the clad and liner can be considered as contributing for the weight, structural

stiffness and strength, since the resultant stress on CRA layer do not surpass its SMYS.

4.7 ANALYSIS SOFTWARE

Only a few commercially available software packages are accepted to be employed for the analyses.

The adopted software shall consider the LRFD approach of DNVGL-ST-F201 [3].

Table 2 presents the names of the packages and the type of analyses for which they are applicable. In

case of CONTRACTOR intend to use different softwares from the ones listed in Table 2, the requirement

shall be submitted to PETROBRAS approval.

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Table 2 Analysis Software

Type of Analysis Software

Fatigue / Extreme / Installation Fatigue/ Interference

FLEXCOM, from MCS,

RIFLEX, from Marintek or

DEEPLINES, from Principia/IFP

ORCAFLEX

VIV SHEAR7 from MIT

Installation FLEXCOM, from MCS,

RIFLEX, from Marintek or

DEEPLINES, from Principia/IFP and

ORCAFLEX from Orcina

PIPELAY from MCS

General ABAQUS, ANSYS

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5 WALL THICKNESS SIZING VERIFICATION

The wall thickness shall be verified considering all possible extreme situations that can be faced by the

riser during the installation, pressure test and in-service phases. The assumptions shall be made in the

conservative side for parameters such as bending radius and tension, wall thickness tolerances and

corrosion in the pipe wall, and temperature de-rating.

From the three recommended verifications below, the buckle propagation criterion is not mandatory. It

is evaluated only for reference.

See section 4.6 for clad and lined pipe segments.

5.1 BURSTING

Wall thickness shall be designed for net internal overpressure based on DNVGL-ST-F101 [4].

5.2 COLLAPSE (HOOP BUCKLING)

Wall thickness shall be designed for external overpressure based on DNVGL-ST-F101 [4].

CONTRACTOR shall consider that all riser functions can be empty during service life.

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6 EXTREME COMBINED LOAD EFFECT ANALYSIS

The objectives are:

To demonstrate that the riser is designed to resist the potential modes of failure, when submitted to

operational situations and severe environmental conditions, as defined in the DNV-OS-F201 by

using the LRFD method;

To generate the pairs tension x angular deflections at the riser top (including at least Maximum

tension with associate angle and Maximum angle with associate tension) for the specification of the

top interface device such as flexible-joint or stress-joint. The maximum flexible-joint/ stress-joint

rotation shall include the vessel compartment flooded condition;

To demonstrate that the limits of the compressive axial loads to happen at the riser top are not

violated, in order to preserve the interface device integrity, according to Manufacturer’s information;

To generate maximum top loads to be used in the verification of the platform receptacle and support

structure;

To generate riser footprint that corresponds to the envelope of TDP positions during operational life;

To generate loads for the design of the riser anchoring system.

The general methodology requirements are listed below:

a) The dynamic analysis shall consider the effects of wave, currents and wind acting on the platform,

and the effects of currents and waves acting directly along the steel riser;

b) FPU motions should be derived from RAO data unless for cases for which PETROBRAS gives the

time traces;

c) Static platform offsets, considered in the riser analyses, will correspond to the values provided by

PETROBRAS plus the positioning errors, according to sections 7.1 and 7.2 of Table 1. The errors

shall be added to the specified offset always in the most conservative way;

d) The relative phase angle between motions and waves direct action over the riser shall be considered

in the analyses. It is possible that PETROBRAS decides to provide time traces from a coupled

model;

e) All operational drafts shall be considered according to section 1.12 of Table 1;

f) All internal fluid characteristics provided shall be considered according to section 6.6 of Table 1;

g) Negative effective tension values (compression) along the riser can be accepted if DNVGL-ST-F201

[3] recommendations are accomplished;

h) Negative effective tension values (compression) at the riser top shall be limited to the value

prescribed by the Manufacturer of the interface device;

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i) The maximum top loads shall be lower than the limits informed by PETROBRAS in document [2];

j) For lined and clad pipes verification, CONTRACTOR shall refer to section 4.6;

k) Temperature de-rating, according to reference [4], shall be considered;

l) The soil stiffness and friction values adopted shall correspond to the medium values associated to

an appropriate riser embedment;

m) For each dynamic loading case simulated, a FJ alternating angle shall be identified and the stiffening

factor shall be adopted in the analysis. This factor multiplies the basic reference stiffness value

adopted in the static analyses, as a function of the FJ alternating angle. If the resultant standard

deviation of the alternating angle corresponds to a stiffening factor which is higher than the stiffening

factor used in the simulation, then the simulation should be performed again with the higher

stiffening factor which will give higher reactive bending moments. See Appendix A.

6.1 LOAD COMBINATIONS FOR ULS AND ALS

The load combinations to be simulated shall follow DNVGL-ST-F201 [3]. A minimum set is described

inTable 3. PETROBRAS will provide corresponding FPU offsets as indicated in section 1.2 of Table 1.

The internal fluid density varies significantly along the operational life. Therefore, it is anticipated that

CONTRACTOR shall consider in the design the complete set of load combinations for all internal fluid

characteristics specified in [2].

The complete set of RAO tables corresponding to operational FPU drafts shall be considered in the

design. In the following sections, there is a description how CONTRACTOR can proceed in order to

take all of them into account, without having to process a very large number of loading cases.

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Table 3 Load Combinations for the Steel Riser Design

Load Combination

Mode of Operation

Wind Return Period (years)

Wave Return Period (years)

Current Return Period (years)

Pressure/ Internal Fluid

density profile

Obs.

ULS1 Temporary 1 1 1 Hydrotest Pressure

(section 6.5 in Table 1)

Hydrotest: Full of water

ULS2 (1) Operating 100 100 10 (sections 6.2, 6.3, 6.6 and

6.7 in Table 1)

ULS3 (1) Operating 10 10 100 (sections 6.2, 6.3, 6.6 and

6.7 in Table 1)

ALS1 (1) 100 100 10 (sections 6.2, 6.3, 6.6 and

6.7 in Table 1)

One mooring line broken

ALS2 (1) 10 10 100 (sections 6.2, 6.3, 6.6 and

6.7 in Table 1)

One mooring line broken

ALS3A (-) and ALS3B (+) (1)

1 1 1 (sections 6.2, 6.3, 6.6 and

6.7 in Table 1)

Platform with one compartment flooded. Value and inclination direction given by PETROBRAS, according to section 1.7 in Table 1

ALS4 (1) 1 1 1 Incidental Pressure (pinc) (section 6.4, 6.6, 6.7 in Table 1)

ALS5 (2) 100 100 10 (see table 5) Loss of buoyancy modules

ALS6 (2) 10 10 100 (see table 5) Loss of buoyancy modules

(1) All conditions defined in reference [2] for the combination pressure/internal fluid per riser function shall be simulated;

(2) Follow Table 4 to consider the quantity of loss buoyancy modules, located at the top of the HOG and at the beginning of floated segment (from riser top to the segment with buoyancy modules);

Table 4 Number of lost buoyancy modules

Qty of buoyancy modules Qty of lost buoyancy

modules

Less than 15 1

15 to 39 2

40 to 60 3

More than 60 4 or 4%, whichever is higher

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6.2 LOAD CASES

Wave and current data are given in 22,5° intervals between 0° and 360° [2], giving a total of 16 (sixteen)

directions. They shall be defined as N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W,

WNW, NW and NNW, according to Figure 2. So, for each load combination listed onTable 3, 16 (sixteen)

environmental load directions shall be considered, regardless the global reference system (XG, YG), in

order to cover all possible critical situations that can be faced by the riser. Moreover, for each

environmental load direction, a complete set of pairs Hs x Tp shall be considered, as mentioned in

section 6.3.

Figure 2 – Global Environmental Load Directions

In this approach, waves, currents (surface and mid-depth profiles) and FPU offsets shall be assumed

as aligned.

6.3 WAVE SCREENING

In the Metocean, for each recurrence period (1-year, 10-year and 100-year) and direction, there is a set

of Hs-Tp pairs (contour curves). When selecting waves to perform the dynamic analyses, one option is

to process the entire number of existent pairs, but this procedure will result in a high number of dynamic

analyses.

An alternative approach, considered acceptable by PETROBRAS, is the previous calculation of the FPU

short-term responses at each riser connection points, based on each FPU draft RAOs, for each

recurrence period (depending on the loading combination). For storage units, all provided drafts shall

be considered.

S

G XG

H

Y G

H H H

Y G

E

N

Xf

Yf

YG

X X W

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This calculation shall be performed for the entire set of pairs Hs x Tp for the 16 directions. The results

of this preliminary motion study shall be the estimated maximum amplitudes, velocities and

accelerations at the riser connection points for all degrees of freedom.

Based on the results obtained, CONTRACTOR shall select, for each direction, at least four load cases

(waves/drafts) according to the following parameters:

Maximum vertical motion acceleration;

Maximum vertical motion velocity;

Maximum amplitude between surge and sway;

Maximum amplitude between roll and pitch.

Figure 3 presents a flowchart of the alternative motion analysis procedure proposed above.

Figure 3 – Proposed motion analysis procedure

For the riser analysis, all selected loading cases of all 16 environmental load directions from wave

screening (with corresponding FPU draft) shall be simulated, for each corresponding load combination

from Table 3, and for each combination internal fluid density/pressure from reference [2], with two types

of current profiles (surface and mid-depth). From Table 3, some load combinations admit a reduced

Each 16 wave directions

All pairs Hs x Tp per direction

1y, 10y, 100y wave periods

Each FPU Draft

Each Conection Point

Wave

Screening

Selected load cases according to:

1. Maximum vertical motion acceleration AND

2. Maximum vertical motion velocity AND

3. Maximum amplitude between surge and sway AND

4. Maximum amplitude between roll and pitch.

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number of loading cases, based on critical loading selected from other load combinations, as described

in Table 5.

Table 5 Reduced Load Cases for some Load Combinations

Reduced

Load

Cases

Based on

Critical

cases from

Criteria

ALS1 ULS2 Highest DNV UF at TDP and sagbend

Highest DNV UF at SAG & HOG

Highest DNV UF at Top

Maximum and Minimum FX, FY, FZ, MX, MY,

MZ (see Figure 5)

ALS2 ULS3

ALS5 ULS2 Highest DNV UF at TDP and sagbend

Highest DNV UF at SAG & HOG

Highest DNV UF at Top

Maximum and Minimum FX, FY, FZ, MX, MY,

MZ (see Figure 5)

ALS6 ULS3

(*) The reduced load cases may be applied just if the offset difference between intact and damaged condition

is up to 0.5% of SWL.

Additionaly, a non-colinear approach (waves, currents and FPU offsets) shall be verified:

For the worst DNV UF cases (3 different regions: TDP, SAG&HOG and Top) with surface

current profiles aligned cases, combine two more current profiles (±22.5°) from the original

aligned direction. Moreover, combine with original static offset and zero offset.

For the worst DNV UF cases (3 different regions: TDP, SAG&HOG and Top) with mid-depth

current profiles from aligned cases, combine mid-depth current profiles in all direction from

Metocean. Moreover, combine with original static offset and zero offset.

The procedure used by CONTRACTOR in the selection of critical waves shall be presented in the

Design Premise and Methodology and submitted to PETROBRAS for approval.

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Table 6 Number of Load Cases for simulation

Load

Combinations

Waves Directions Current

Profiles

Offset Total

Colin

ea

r C

on

ditio

ns

ULS1 4 16 2 1 128

ULS2 4 16 2 1 128

ULS3 4 16 2 1 128

ALS1 4 16 2 1 128

ALS2 4 16 2 1 128

ALS3 A and B 4 + 4 16 2 1 128 +128

ALS4 4 16 2 1 128

ALS5 4 16 2 1 128

ALS6 4 16 2 1 128

Non-c

linear

Co

nditio

ns

Worst DNV UF at

TDP

1 1 2 2 4

Worst DNV UF at

SAG&HOG

1 1 2 2 4

Worst DNV UF at

TOP

1 1 2 2 4

Worst DNV UF at

TDP

1 1 16 2 32

Worst DNV UF at

SAG&HOG

1 1 16 2 32

Worst DNV UF at

TOP

1 1 16 2 32

Total number of load cases per fluid/pressure and per connection point 1388

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6.4 SIMULATION OF IMPOSED MOTIONS AND WAVES

The motion and wave modeling procedures shall encompass hybrid approaches represented by

equivalent harmonic excitation and complemented by random approach, both in time domain based

on spectral wave description, in order to capture the nonlinearities that are present in the riser dynamic

response under extreme loads.

The hybrid approach can be either the Equivalent Harmonic Motion Procedure (EHMP) or the Design

Wave Procedure (DWP), to be selected by CONTRACTOR.

Critical load cases identified in the hybrid approach analyses shall be checked using the Irregular Wave

Procedure (IWP) analysis to verify if it is possible to capture a more restrictive situation than the one

identified by the use of the hybrid methodology. For the random approach analyses, it is possible that

PETROBRAS decides to provide time traces from coupled model time domain simulations.

As critical load cases CONTRACTOR shall select from Table 6 the ones that give:

The highest value of DNV UF at TDZ and sagbend;

The highest value of DNV UF at buoyancy modules region (hog and sag regions);

The highest value of DNV UF in the top region;

Maximum and Minimum FX, FY, FZ, MX, MY, MZ (see Figure 5).

The mentioned methods are described in the next sections. The EHMP and DWP methodologies require

the definition of a single reference DOF for each analysis. For these procedures, vertical imposed

motion, movZ, shall be always the reference DOF, which affects severely the SAG, HOG and touch

down area. For the riser top region design, other degrees of freedom may be critical, so they may be

adopted also as reference DOF, between movX and movY, and between movRX and movRY,

depending on analyst judgment if additional loading cases should be performed in order to obtain the

most conservative for the riser.

6.4.1 Equivalent Harmonic Motion Procedure (EHMP)

The following steps shall be followed:

a) Transfer the RAO from the FPU center of motion to the riser top connection point;

b) Obtain the response spectrum for the motions at the top connection by crossing the wave

spectrum with the RAO transferred to the riser top connection;

c) Determine, considering the Rayleigh statistical distribution, the most probable maximum value

of displacement (dmax) and acceleration (amax) for the connection points;

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d) Determine for each DOF the dynamic motion period (T) at riser top connection, using the most

probable maximum value of displacement (dmax) and acceleration (amax),as determined in item

c) above, considering the following formula:

MAX

MAX

a

dT 2

e) Assume harmonic motions for the riser top connection, corresponding to the maxima

amplitude values calculated for each DOF as per item c) above (dmax) and a single period

evaluated for the reference DOF according to paragraph d) above (T );

f) Assume, for the regular motions at the top riser connection, the same phase values of the

transferred RAO in paragraph a), taken for the corresponding period of paragraph d).

Note: The above approach does not consider the direct wave action on the riser.

6.4.2 Design Wave Procedure (DWP)

The following steps shall be followed:

a) Transfer the RAO from the FPU center of motion to the riser top connection point;

b) Obtain the response spectrum for the motions of the top connection by crossing the wave

spectrum with the RAO transferred to the riser top connection;

c) Determine, considering the Rayleigh statistical distribution, the most probable maximum value

of displacement (dmax) and acceleration (amax) for the connection points;

d) Determine the most probable maxima wave height (Hdesign) assuming a Rayleigh distribution

for the wave heights; Hdesign can be taken as 1.86 times Hs (significant wave height) as used

to describe wave spectrum in item b);

e) Evaluate periods (Tdesign1 and Tdesign2) which associated with Hdesign, will provide,

respectively, the maximum harmonic displacement and maximum harmonic acceleration, both

calculated as per item (c). Among the possible T design values, chose the closest value to the

wave peak period (Tp).This procedure shall be carried out, at least, 3 times, as described in

section 6.4.

Note: The above approach considers the direct wave action on the riser.

6.4.3 Irregular Wave Procedure (IWP)

This procedure shall be considered as a validation check of the results from the above-mentioned

procedures. Therefore, only the critical load cases, selected according to section 6.4, shall be

analyzed according to this method.

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a) The minimum simulation time shall be 10800s;

b) The minimum number of harmonic components to describe wave spectra shall be 300;

c) The peak values obtained from riser analysis in time domain shall be used to adjust an

extreme distribution to determine the most probable maximum/minimum values;

d) The complete methodology to be adopted, including number of realizations, time duration of

each simulation and determination of extreme values, shall be described at the Design

Premise and Methodology, and submitted to PETROBRAS for approval.

6.5 SENSITIVITY ANALYSES

Sensitivity analyses are intended to provide information about the changes in the riser behaviour,

corresponding to the variation in the input parameters used in the analyses performed. The change can

be reflected in one or more parameters being determined by the Extreme Combined Load Effect

Analyses. The riser model used in the analyses shall be based on the nominal characteristics but the

effect of variations needs to be investigated. The loading cases used in the study shall be the most

critical ones.

As a result from the sensitivity analyses, CONTRACTOR can suggest further investigation or limitations

to the riser construction in order to mitigate undesirable effects.

The minimum set of parameters that needs to be investigated shall include:

Riser installation top angle (± 0.5°);

Riser installation azimuth and/or riser support construction errors;

Internal fluid variation in terms of densities and pressures, including conditions for maximum temperature;

Lower and upper bound hydrodynamic coefficients;

FJ parameters;

Pipe fabrication tolerances;

Error in the buoyancy modules positioning along the riser;

Variations in the efficiency of the buoyancy modules (± 5%);

Soil parameters (upper bound and lower bound parameters);

Influence of soil trench profile;

Marine Growth Profile;

Add 1.5% SWL by offset error to ULS and ALS, for more critical load cases from DNV Utilisation

Factor at the top, sag&hog and sagbend&tdp.

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7 FATIGUE ANALYSIS

The objectives are:

To demonstrate that the riser is designed according to the DNVGL-RP-C203 [5];

To evaluate the fatigue damage along the riser, and especially in the critical riser sections, coming

from:

FPU motion and direct wave action on the riser;

Current VIV;

Heave-induced VIV motion;

Slugging.

To define the length and location of critical riser sections;

To define the length of clad pipes segments, when applicable, to cover the critical lengths of the riser

based on the criterion of item 5.9 of Table 1;

To generate top load and angular deflections to be used for the specification of the top interface

device such as FJ;

To generate top loads to be used in the design of the platform receptacle and support structure;

To generate stress histograms to be used in the ECA study to be performed for the critical riser

sections and other joints along the riser, separately for each source of fatigue damage and together

for all sources of resultant fatigue damage.

The general methodology requirements are listed below:

a) Fatigue life shall be calculated in sixteen (16) points around each welded joint and parent material

cross-sections chosen along the riser. Eight points around pipe internal wall and eight points around

the external wall (seeFigure 4);

Figure 4 – Points around riser section for fatigue evaluation

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b) Convenient SCF shall be considered and evaluated for fatigue damage calculation of steel riser

critical regions such as the riser girth welds, J-Lay collar, etc. The SCF shall be calculated according

to the methodology described in reference [5]. The hi-lo referred to in these references shall be

assumed as described in Table 1, item 5.14;

c) The pipe parent material shall be verified. Depending on the geometrical profile obtained after pipe

ends machining (if applicable), a stress concentration may result and shall be considered;

d) The S-N curves to be adopted will be defined as mentioned in item 5.12 of Table 1;

e) For aggressive corrosion service, the penalty factors to be applied to S-N curves in C-Mn sections

shall be considered, according to the data defined in Table 1, item 5.13;

f) For J-lay collars specific SCF and S-N curve shall be used in the fatigue verification as for the welds

and parent material;

g) The definition of the clad segments length shall be carried out considering not only the wave and

motion induced fatigue damage but all contributions for the fatigue damage that are described within

this report;

h) For production and gas injection risers the internal fluid density may vary significantly along the

operational life. The base case shall consider the internal fluid with the longest duration. The other

fluids shall be considered for the critical cases obtained in the base case, in order to evaluate their

effect to the fadigue damage. CONTRACTOR shall propose a procedure to take into account all the

fluid results obtained to the final combined result;

i) Stress histograms shall be generated for sections that present the minimum fatigue lives at the riser

top region, buoyancy modules region (hog and sag regions) and at the TDZ, and at all the transition

points between clad and lined pipe segments (as defined in the previous item (g)).

7.1 WAVE AND MOTION FATIGUE ANALYSIS

7.1.1 Methodology Requirements

a) The following effects shall be considered in the analysis: the static offset, the wave first and

second order platform motions; and the effect of waves and currents acting directly on the

riser. First order motions shall be considered at six DOF’s, second order motions (or low

frequency motions) shall be considered as a time series acting simultaneously with the first

order motion, at least in surge and sway DOF’s;

b) The relative phase angle between motions and waves direct action over the riser shall be

considered in the analyses;

c) The base case shall consider two most frequent RAO drafts.

d) CONTRACTOR shall consider the medium fluid density, and shall propose a procedure to

take into account the other fluid densities;

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e) The time domain random fatigue analysis approach shall be used;

f) The total integration time for each analysis shall be 3-hours, but CONTRACTOR may propose

a shorter simulation based on previous study with significative loading cases, showing that

the time series shall present a statistical stability (mean and standard deviation values). The

minimum accepted integration time is 1-hour;

g) A realistic frequency range shall be considered, containing at least 300 frequency intervals

for the wave spectrum discretization. Other value may be proposed by CONTRACTOR after

some sensitivity analysis results that shall be submitted to PETROBRAS for approval;

h) In order to identify the stress ranges and corresponding number of cycles contained in the

predicted stresses time series, the Rainflow method shall be employed;

i) For the FJ modeling, CONTRACTOR shall consider the FJ stiffness at 0.01 deg alternating

angle for all loading cases.This is the most conservative approach. Less conservative and

more realistic approach is to update the FJ stiffness as a function of the alternating angle

obtained at the first stage, for the most critical loading cases. The determination of the

alternating angle shall be carefully obtained according to the procedure described in the

Appendix A;

j) The fatigue performance for the risers must satisfy the service life and incorporate a safety

factor defined in item 5.19 from Table 1 on the wave and motion fatigue damage. If

CONTRACTOR intends to reduce the safety factor (item ”Enhanced risk based safety factors

– steel risers” from DNVGL-RP-F204 [6]), the validation study shall be presented to

PETROBRAS approval;

k) The soil stiffness and friction values adopted shall correspond to the medium values

associated to an appropriate riser embedment;

l) Temperature de-rating shall be considered;

m) For lined and clad pipes verification, CONTRACTOR shall refer to section 4.6.

7.1.2 Load Cases

PETROBRAS will provide the complete set of correlated wave, wind and current, and

CONTRACTOR shall assure that a good representation of the typical operational year of the riser

will be chosen. CONTRACTOR shall analyse all set of data from item 2.1 of Table 1, with

correlated waves, current profiles and winds. Storm situations shall also be added.

For Fatigue analysis, bi-modal waves shall be employed, according to reference [2].

PETROBRAS will provide the mean offsets and second order motions time traces or the full

motion time traces according to PETROBRAS choice for the specific design.

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Some storm conditions shall be added to the operational conditions as explained below. The most

critical extreme waves for each category shall be used:

The most damaging direction for 1-year return seastate with a percentage of occurrence that

corresponds to one occurrence of this storm condition for each one year of operational life,

(each occurrence with 3-hours duration);

The most damaging direction for 10-years return seastate with a percentage of occurrence

that corresponds to one occurrence of this storm condition for each ten years of operational

life, (each occurrence with 3-hours duration);

The most damaging direction for 100-years return seastate with a percentage of occurrence

that corresponds to one occurrence of this storm condition for the operational service life,

(each occurrence with 3-hours duration).

7.1.3 Sensitivity Analysis

Sensitivity analyses are intended to provide information about the changes in the riser behaviour,

corresponding to the variation in the input parameters used within the analyses performed. The

change can be reflected in one or more parameters being determined by the Wave and Motion

Fatigue Analysis. The riser model used in the analyses shall be based on the nominal

characteristics but the effect of variations needs to be investigated. The loading cases used in

the study shall be the most critical ones.

As a result from the sensitivity analyses, CONTRACTOR can suggest further investigation or

limitations to the riser construction in order to mitigate undesirable effects.

The minimum set of parameters that needs to be investigated shall include:

Riser installation top angle (± 0.5°);

Riser installation azimuth and/or riser support construction errors;

Internal fluid variations in terms of densities and pressures;

Lower and upper bound hydrodynamic coefficients;

FJ parameters;

Pipe fabrication tolerances;

Accidental loss of buoyancy modules (see Table 4);

Error in the buoyancy modules positioning along the riser;

Variations in the efficiency of the buoyancy modules (± 5%);

Soil parameters (upper bound and lower bound parameters);

Add 1.5% SWL by offset error.

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7.2 VIV FATIGUE ANALYSIS

The objectives are:

To define the VIV suppressor type, length and positioning along the riser;

To guarantee the adequate level of safety, based on the characteristics of the products being

purchased and qualified for the installation;

To evaluate the fatigue damage along the riser, mainly in the buoyancy region (sag and hog regions),

sag-bend and TDZ, coming from the action of currents that causes vortex induced vibration;

To evaluate the fatigue damage along the riser, mainly in the top region, buoyancy region (sag and

hog regions), sag-bend and TDZ, coming from the action of FPU motion that causes vortex induced

vibration (heave induced fatigue);

To generate the stress histograms to be used in the calculation of total damage with the addition of

the all effects that causes fatigue;

To evaluate the drag amplification factor (DAF) for both rigid and flexible risers due to VIV effect, an

important data for the interference analyses, i.e. the check on the likelihood clashing between risers

with each other, as well as between risers and mooring lines;

The fatigue performance for the risers must satisfy the service life and incorporate a safety factor

defined in item 5.20 of Table1 on the VIV fatigue damage.

General requirements:

The total damage corresponding to the wave and motion fatigue and VIV fatigue shall be obtained

according to the reference [6]. Note that if at the wave and motion fatigue hot spot regions, the VIV

damages at the correspondent region are, at least ten times smaller than the wave and motion

fatigue damage, the damage summation will be accepted;

CONTRACTOR shall consider the medium fluid density, and shall propose a procedure to take into

account the other fluid densities.

7.2.1 Current VIV Fatigue Analysis

a) Sheared-flow effects shall be considered;

b) The program SHEAR7 from MIT (Massachusetts Institute of Technology) shall be used. If

considered by CONTRACTOR the use of other computer codes, it shall be submitted to

PETROBRAS for approval;

c) The SHEAR7 steering parameters such as Strouhal number, CL tables, cut-off, reduced

velocity bandwidth, structural damping and others, shall be listed in the Design Basis Report

and submitted to PETROBRAS for approval;

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d) The VIV analyses shall consider the riser mode shapes and curvatures in the riser static

neutral configuration, including the representation of each buoyancy module individually and

the proper soil stiffness at the TDZ;

e) In the analyses, all current profiles shall be considered as aligned along the water depth. It

means that the individual direction associated to each depth level, which is reported in the

provided Metocean Data Report, shall not be considered. The current profiles shall be

considered as unidirectional for VIV analysis purpose. All single current profile shall be

considered as acting in two different directions: in-plane and out-of-plane (without performing

any velocity projection). This means that each current profile shall be aligned with the riser

plane or be considered perpendicular to the riser plane;

f) The VIV analysis of the riser shall be performed for two types of loads, namely: short-term

VIV analysis (extreme) and long-term VIV analysis. The short-term (extreme) events fatigue

damage shall be added to the long-term event fatigue damage;

g) The whole set of currents (including all Reference Level Profiles) with return period of less

than 1-year shall be used in the analyses. These current profiles correspond to the so called

long-term conditions;

h) The short-term VIV analysis will determine the damage induced by the extreme currents of

all directions of the Metocean Data. The damage, for the most critical direction, for each type

of event, will be added to the long-term fatigue damage, assuming the duration described in

reference [2];

i) The short-term response analyses shall be performed considering two types of events: 10-

years return period events and 100-years return period events. These events are composed

of 1-year, 10-years and 100-years return period current profiles. For each of these events,

data from all directions shall be analyzed. Reference [2] will describe how to combine 100-

years and 10-years events for fatigue damage;

j) The fatigue performance for the risers must satisfy the required service life (5.11 of Table 1)

and incorporate a safety factor for the VIV fatigue damage (5.19 and 5.20 of Table 1);

k) Fatigue damage values coming from the complete set of current profiles are usually added

considering the TDP on the same position. This procedure leads to over-conservative results

for free-hanging configurations. For SLWR configuration it is anticipated that this procedure

is a good approach. If CONTRACTOR has another proposal, this can be submitted to

PETROBRAS for approval;

l) CONTRACTOR shall calculate VIV damage at external and internal fibers of the riser

sections;

m) The soil stiffness and friction values adopted shall correspond to the medium values

associated to an appropriate riser embedment.

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7.2.2 Heave Induced VIV Fatigue Analysis

a) The effect of heave induced VIV shall be investigated, with respect to the damage in the top

region, buoyancy modules region (sag and hog regions), sag-bend and TDZ;

b) The criterion for choosing load cases that will be used to evaluate the heave induced VIV,

shall be stated as a function of Keulenger Carpenter (KC) number magnitudes and submitted

to PETROBRAS for approval;

c) In principle, all wave fatigue load cases and all extreme wave analyses shall generate normal

velocity significant value (2*RMS), that will be used to compose a current profile to be applied

in the SHEAR7 analyses. However, some of them can be discharged as a function of the KC

numbers values;

d) Time domain analysis shall be used for the evaluation of the equivalent current profiles;

e) The duration of the extreme events shall be the same assumed for the wave fatigue

calculations as mentioned in section 7.1.2;

f) CONTRACTOR may propose alternative approaches or changes in the herein stated

methodology in order to evaluate the damage contribution from the heave induced VIV that

shall be submitted to PETROBRAS for approval;

g) The fatigue performance for the risers must satisfy the service life and incorporate a safety

factor defined in item 5.20 of Table1 on the VIV fatigue damage.

7.2.3 Sensitivity Analysis

Sensitivity analyses are intended to provide information about the amount of changes in the riser

behaviour, corresponding to the variation in the input parameters used within the analyses

performed. The change can be reflected in one or more parameters being determined by the VIV

Fatigue Analyses. The riser model used in the analyses shall be based on the nominal

characteristics but the effect of variations needs to be investigated. The current profiles used in

the study shall be the most critical ones.

One important feature of the sensitivity analyses is the alternative calculation by means of a

software different from SHEAR7. The selected software has to be able to provide in-line vibration

effects.

As a result from the sensitivity analyses, CONTRACTOR can suggest further investigation or

limitations to the riser construction in order to mitigate undesirable effects.

The minimum set of parameters that needs to be investigated shall include:

Riser installation top angle (± 0.5°);

Lift and added mass coefficient;

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Suppressors coverage (length and positions);

SHEAR7 steering parameters;

Soil parameters;

Variations in the efficiency of the buoyancy modules (± 5%);

Error in the buoyancy modules positioning along the riser;

Internal fluid variations in terms of densities and pressures.

7.3 SLUGGING EFFECT ANALYSIS

A structural evaluation of the effect of slugging on the production risers for Fatigue Analyses results

shall be performed.

Fluid slugging characteristics will be provided by PETROBRAS as described in Table 1, item 6.10.

The fatigue damage shall be properly added to the other contributions and the parameters and

techniques regarding fatigue calculations shall be in accordance with section7.

The stress-block for ECA regarding slugging effect shall be clearly presented in this report for future

analyses.

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8 TOP LOADS FOR RISER SUPORT STRUCTURE EVALUATION

The top force reactions at the FPSO connections for receptacle and support structural verification will

be provided by CONTRACTOR, based on the final SLWR configurations to be constructed and installed.

These forces shall be compared with the limits requirements provided by PETROBRAS for all degrees

of freedom, in order to guarantee that the design of the riser balcony at the FPSO will be in accordance

with the riser final design.

The main analyses to be performed are:

Extreme Loading Analysis

Wave and Motion Fatigue Analysis

The structural global model shall be the same used in the Extreme Combined Load Effect analysis,

according to section 4. Special attention shall be taken with the reference system for riser top support

loads calculation. A fixed reference system at the support shall be adopted and will be called Support

Reference System, supposing to follow motions from the platform and is independent from the riser

motions. This difference is especially important when a FJ type of connection is used. It shall have the

X-axis in the axial direction (Fx, Mx) when the riser is in the neutral position, coincident with support

inclination in the riser direction, which is usually coincident to the riser top angle. The other axes shall

coincide respectively with the riser in-plane (Fz, Mz) and out-of-plane (Fy, My) directions. See Figure 5

below for the fixed axes definition.

Figure 5 – Definition of the Fixed Support Reference System, (a) Top view, (b) Lateral view with conical receptacle and (c) Lateral view with hang-off adaptor

8.1 TOP LOADS BY EXTREME LOADING ANALYSIS

CONTRACTOR shall present the top loads corresponding to all load combinations from Table 3, except

ALS4. For each analysis, maximum and minimum forces and moments of each component (Fx, Fy, Fz,

Mx, My and Mz) shall be presented, all of them with riser empty and full of water. Those values shall be

identified considering their algebraic values, bringing the signals. Morover, CONTRACTOR shall

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present the Functional loads (Loads that occur as a consequence of the physical existence of the

system) and Static loads (with Functional loads, offsets and current profiles).

For the critical load cases, according to item 6, CONTRACTOR shall generate the pairs Tension x FJ

Angle for each time step, in order to construct plots that will allow the visualization of the most critical

Tension x FJ Angle pairs. The methodology accepted to generate the Tension x FJ Angle pairs is

Irregular Wave Procedure (IWP) in time domain.

Figure 6 shows an example of the plot that needs to be generated.

Figure 6 – Plot example of Tension x FJ angle

CONTRACTOR shall consider for the analysis of the Support System the coherent and consistent

combination of the maximum and minimum reaction values identified in the Top Reaction Tables in

order to preserve the conservatism of the design. The plots Tension x FJ Angles shall also be used.

The approach to be used for combining and/or disregarding top reactions shall be justified in the Report.

The choices for simulating loading cases and not simulating other loading cases considered less severe

shall also be explained in the Report. CONTRACTOR can always simulate additional time domain

irregular sea states.

8.2 TOP LOADS BY WAVE AND MOTION ANALYSIS

The riser top loads to perform fatigue verification of platform hull, receptacle and support structure are

calculated based on riser top forces and moments time-series obtained in the wave fatigue analysis,

according to item 7.2. For each loading case simulated, it is necessary to generate time-series of each

component (Fx, Fy, Fz, Mx, My and Mz) on each riser top connection point, and present the statistical

values of each component.

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9 INTERFERENCE ANALYSIS

The methodology and requirements to perform Interference Analyses will be described in document

[13].

10 INSTALLATION ANALYSIS

The methodology and requirements to perform Installation Analyses will be described in document [14].

11 DELIVERABLES

The CONTRACTOR shall issue a number of design reports related with specific events described below,

and following a presentation format and time scheduled in agreement with PETROBRAS

representatives, before the beginning of the work specified herein.

These reports shall be presented in magnetic media (CD-ROM) for PETROBRAS comments. The

CONTRACTOR shall use the following documentation software (IBM-PC compatible): Microsoft®: Word

for Windows as word processor; Excel for Windows as spreadsheet; and Project for Windows as time

schedule software. Drawings shall be presented in: MicroStation® for Windows from Bentley Systems

native format files (DGN) or Adobe® Portable Document Format (PDF).

Every event will be associated with a report issued by the CONTRACTOR. The main reports are:

Design Basis Report

Design Premise and Methodology

Riser Design Summary Report

Wall Thickness Sizing Verification Report

Extreme Combined Load Effect Analysis Report

Wave and Motion Fatigue Analysis Report

VIV Fatigue Analysis Report

o Current VIV Fatigue Analysis Report

o Heave-Induced VIV Fatigue Analysis Report

Slugging Effect Analysis Report

Fatigue Analysis Summary Report

Top Interface Loads

Interference Analysis Report

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Installation Analysis Report

The reports shall contain at least the information described in following items.

11.1 GENERAL DELIVERABLES

The reports considered as general deliverables are:

Design Basis Report [1]

Design Premise and Methodology

Riser Design Summary Report

Appendix F of DNV-OS-F201 may be used as a guide for Design Premise and Methodology.

The final design report shall contain all interim reports and design conclusions issued in their final

revision.

11.1.1 Design Premise and Methodology

This report shall detail and describe the methodologies, procedures and applied computer

programs used in steel riser analyses; the acceptance criteria to be used; all applicable load

cases, limit states and safety classes for all temporary, operating and accidental design

conditions. The Design Premise and Methodology shall be agreed with PETROBRAS

representatives.

11.1.2 Riser Design Summary

This report shall contain the full description of the steel riser configuration and the consolidation

of all results obtained. A summary of each topic and an overall diagnostic of the riser design shall

be provided.

11.2 SPECIFIC TOPIC DELIVERABLES

The delivered specific topic reports are described in detail in following items.

11.2.1 Wall Thickness Sizing Verification Report

This report shall contain all the data and the source and justification of the assumed parameters

and data used in the calculations, as well as the results. The input data and output data from

spreadsheets shall be presented. A Summary item shall bring comments on the evaluation.

11.2.2 Extreme Combined Load Effect Analysis Report

This report shall include at least the following information described below:

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a) The complete data used in the analyses containing all the details of the riser model and the

load data as well, including safety class;

b) Full traceability of the calculations performed;

c) Full description of statistical treatment adopted for EHMP, DWP and IWP;

d) Tabulated results from functional static load cases, with current static analyses and dynamic

analyses. The results shall be given to the riser top connection, buoyancy modules region

(sag and hog), TDZ and sagbend sections of the riser configuration;

e) The tabulated results shall include at least: the load case, the riser imposed top motions and

rotations, FJ rotations, anchoring and top reactions, axial forces, effective tensions, hoop,

bending moments, DNV UF and maximum von Mises stresses along the riser for all critical

sections. Static parcel of results shall be presented separately;

f) For the random time domain analysis, all statistical parameters (mean value, standard

deviation, skewness and kurtosis), extrapolated and historical extreme values of the

parameters shall be tabulated. The complete set of results can be put in the report Appendix

section, but the most critical results shall be highlighted in the main text body;

g) For the steel riser receptacle verification, the loads shall be provided in a fixed reference

system as described in Figure 5. A tabulated result for each load case shall be provided;

h) Graphical results shall be presented as listed below:

Mean or neutral static configuration;

Effective tension along the riser in the mean or neutral position;

Bending moment along the riser for the mean or neutral position;

Envelopes of effective tension along the riser for the most critical cases;

Envelopes of bending moment along the riser for the most critical cases;

Envelopes of maximum von Mises stresses along the riser for the most critical cases;

Envelopes of maximum DNV UF along the riser for the most critical cases;

Time traces for the critical node in the top connection, buoyancy modules region (sag

and hog), TDZ and sagbend for: DNV UF, maximum stresses and minimum effective

tension, for the critical load cases;

Static parcel of results shall be presented in the graphics.

i) Results from sensitivity analyses;

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j) Results from soil-riser interaction study;

k) Time traces, statistical parameters and peak values of the imposed motions and riser response

found in the irregular wave analyses;

l) The riser TDP footprint calculated. The results shall be presented graphically and also by

indicating precisely the distances values.

m) For some results, a model of graphics presentation shall be followed and will be provided by

PETROBRAS.

11.2.3 Wave and Motion Fatigue Analysis Report

This report shall encompass at least the information described below, for welded sections and

parent material, considering at the cross-section for each of those sixteen points as per section

7:

a) The description of the adopted approach, either random analysis performed through the time-

domain approach (random time-domain dynamic non-linear analysis), and the computer

programs used;

b) The set of load cases used with the discrimination of wave, wind and current characteristics,

with the corresponding occurrence;

c) The spectrum discretization adopted;

d) The FJ flexural stiffness used for each simulated load case;

e) The stresses concentration factors adopted for welded joints and their calculation procedure;

f) The description of the adjustments and correction factors used for the time domain non-linear

analyses;

g) For the time-domain approach, the results of the stress time-histories stability study and the

influence of the number of realizations shall be clearly described and justified. Graphics shall

be presented in order to show mean and RMS (Root Mean Square) stability and response in

terms of fatigue damage for different realizations. The calculation of the correction factor

associated with the stability study and number of realizations shall also be presented;

h) Tabulated results of the worst fatigue life case along the riser, coming from the combination

of all load cases. The load case that produce the highest fatigue damage, and the critical

point around the section with this highest damage shall be included in this table;

i) For each critical point (see item h), the list of the load cases according to the damage

contribution regarding the total damage;

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j) For time-domain analysis, the “range of stress amplitudes versus number of cycles”

histograms for the complete set of load cases shall be included;

k) Graphical results of the worst lifetime in some joints of the riser top region, in buoyancy

modules region (sag and hog), TDZ and sagbend and in all the other critical sections of the

riser configuration, showing the contribution to the fatigue damage from each load case;

l) Filenames shall have the same root names of the fatigue load cases table, in order to facilitate

the record tracking procedure;

m) The sensitivity analysis results;

n) Results from soil-riser interaction study;

o) Stress Histograms to be used in the ECA study with the contributions from Wave and Motion

Fatigue;

p) The combination of all sources of fatigue to the resultant damage and in the stress histograms

for the ECA study;

q) The definition of length and locations of the critical riser sections, considering all sources of

fatigue damage.

For some results, a model of graphics presentation shall be followed and will be provided by

PETROBRAS.

11.2.4 Current VIV Fatigue Analysis Report

This report shall encompass the information described below:

a) Computer program used and load cases considered;

b) Mode shapes and curvatures used in the analysis together with the description of the

methodology;

c) The fatigue life, amplitude-diameter ratios (A/D) and stresses along the riser for each current

profile considered in the analyses;

d) The fatigue life final combination of all load cases along the riser shall also be presented. The

damage, corresponding to each current profile considered, shall be provided;

e) Short term VIV results shall be presented separated from the long term VIV results;

f) Magnetic input files for the computer code used, with mode shapes and curvatures and all

input data files related with the VIV analysis;

g) VIV suppressor assumed characteristics;

h) The evaluation of the proposed VIV suppressor system and the possible alternatives, if any

improvement is needed.

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i) Stress Histograms to be used in the ECA study. The stress histograms shall be presented in

a separate way: the contributions from Current VIV and the contribution from Heave Induced

VIV;

j) The sensitivity analysis results and their consequences for the installation and operational life

of the riser;

k) The ranking of the current profiles by the order of damage to the critical sections.

11.2.5 Heave-Induced VIV Fatigue Analysis Report

This report shall encompass all data used, procedures, intermediate results and final results. The

considered equivalent current profiles used shall be provided. The identification of the most

damaging events shall also be reported.

11.2.6 Slugging Effect Analysis Report

This report shall provide:

a) Computer program used and load cases considered;

b) The description of the procedure and the results obtained;

c) Results from dynamic analyses;

d) Results from fatigue damage distribution along the riser;

e) The graphical distribution of fatigue life along the risers studied due to slugging;

f) Stress Histograms to be used in the ECA study;

g) Maximum stresses caused by slugging.

11.2.7 Fatigue Analysis Summary Report

This report shall encompass the information described below, considering the contribution to

fatigue damage due to Wave and Motion, VIM (if applicable), current VIV, heave induced VIV,

Slug and Installation:

a) The combination of all sources of fatigue to the resultant damage;

b) Stress histograms to be used in the ECA study considering the combination of all sources of

fatigue and also in a separate way: the contributions from Wave and Motion, the contributions

from VIM, the contributions from current VIV, the contributions from Heave induced VIV, the

contributions from Slugging effect, the contributions from Installation;

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c) The definition of length and locations of the critical riser sections, considering all sources of

fatigue damage (Wave and Motion, VIM, current VIV, heave induced VIV, Slugging effect,

Installation)

d) The sensitivity analysis results and their consequences for the installation and operational life

of the riser.

11.2.8 Top Interface Loads

The results report shall include at least the following information described bellow:

a) The complete data used in the analyses containing all the details of the riser model and the

loading data as well;

b) The tabulated results shall include at least: the loading case, the platform top motions and

rotations, and the top reactions. If a random time domain analysis is performed, the mean

and standard deviations and maximum values of the parameters shall be tabulated. The

complete set of results can be put in the report Appendix section, but the most critical results

shall be highlighted in the main text body.

c) The tabulated results mentioned in item b), shall also be provided in an ASCII or Excel

spreadsheet file;

d) The forces and moments shall be provided in a fixed reference system as described in 8. A

tabulated result for each loading condition shall be provided;

e) Time traces, statistical parameters and peak values of the top riser reactions (forces and

moments) found in the Irregular Wave Analyses;

f) The description of the adjustments and correction factors used for the time domain non-linear

analyses;

g) The spectrum discretization adopted;

h) Filenamnes shall have the same root names of the load cases table, in order ro facilitate the

record tracking procedure.

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12 REFERENCES

[1] Project Technical Specification for Detailed Design, Procurement, Construction and Installation

[2] Project Design Basis for BID

[3] DNVGL-ST-F201 – “Dynamic Risers”– Det Norske Veritas (Latest Edition)

[4] DNVGL-ST-F101 – “Submarine Pipeline Systems”– Det Norske Veritas (Latest Edition)

[5] DNVGL-RP-C203 – “Fatigue Design of Offshore Steel Structures”, (Latest Edition).

[6] DNVGL-RP-F204 – “Riser Fatigue”, (Latest Edition)

[7] DNVGL-RP-C205 – “Environmental Conditions and Environmental Loads”, (Latest Edition)

[8] DNV Guidelines for Design and Construction of Lined and Clad Pipelines - JIP Lined and Clad Pipelines, Phase 3 – Revision 2 – 20/08/2013

[9] I-ET-0000.00-0000-219-P9U-001 – Mechanically Lined Pipe (MLP) Requirements – (Latest Revision)

[10] I-ET-0000.00-0000-219-P9U-002 – CRA Clad Pipe Requirements – (Latest Revision)

[11] I-ET-0000.00-0000-211-P9U-001 – SAWL Pipes Requirements – (Latest Revision)

[12] I-ET-0000.00-0000-211-P9U-002 – Seamless (SMLS) Pipes Requirements – (Latest Revision)

[13] I-ET-3010.00-1519-274-PPC-001 – Riser Interference Analysis – Revision 0

[14] I-ET-0000.00-0000-966-P9U-001 – Installation Analyses - (Latest Revision)

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APPENDIX A

FJ STIFFNESS AS A FUNCTION OF THE ALTERNATING ANGLE

The FJ bending stiffness curve provided by the manufacturer presents the dynamic bending stiffness

as a function of the angular variation values, which are highly dependent on the type of the applied

loads:

Constant bending stiffness is assumed for static rotations;

Variable bending stiffness for dynamic loads, depending on the amplitude of the alternating

angle.

When the dynamic stiffness are divided by the static stiffness value, it can be obtained a stiffening

factor, which is different for each dynamic loading case. This factor can be assumed as constant along

the dynamic analysis.

This appendix present an alternative approach to determine a less conservative FJ angular variation,

instead of using the value 0.01 deg, constant for all loading cases.

Initially is assumed the stiffest value of the manufacturer curve (in general corresponding to 0.01 deg of

alternating angle) for all loading cases, in order to obtain the level of the alternating angle for each

loading case. In a second analysis cycle, new dynamic stiffness is used for each case.

The angular variation (α) ocurrs around a mean deflection (θm), as presented in Figure 7.

Figure 7 – Eccentric angular variation

x

y

z

qm

a

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The calculation of the curve of total angular variation can be done based on the curves of angular

variation on X-Y and X-Z planes. The proposed procedure preservs the signal of the relative angle, by

projecting the riser in each one of the planes as presented in Figure 8.

Figure 8 – Angular variation in X-Y plane

Figure 9 shows an example of angular variation curves on each plane.

Figure 9 – Angular variation curves on X-Y and X-Z planes

The value employed to determine the FJ dynamic stiffness is obtained by the variation around the mean

position, as presented in Figure 10.

x

y

z

qxy

x

y

z

-qxy

Negative Positive

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500 600

An

gle

(d

eg)

t (s)

Ang_xy Ang_xz

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Figure 10 – Rotation vector path on Y-Z plane.

Figure 11 present only the variation, removing the mean value. Besides, this variation can be calculated

in any direction, i.e., any plane that comprises the x-axis of the fixed FJ support reference system. Two

different approaches to determine these directions are presented below:

Main Direction: linear adjustment for the points that represent the angular variation;

Maximum Amplitude Direction: direction that provide the maximum amplitude of angular

variation

Figure 11 – Directions for angular variation calculation.

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

qxy

qxz

Mean position: (0.70, -0.43)

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

qxy

qxz

Rot. on Planes

Max. Amp. Dir.

Linear (Rot. on Planes)

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The best approach will depend on the aplicability of the analysis. If the most conservative for the analysis

is to use a low stiffness, it is recommended to use Maximum Amplitude Curve. On the other hand, if the

most conservative is a high stiffness, it is recommended to use the Main Direction Curve.

After determining the direction, the angular variation curve is calculated projecting each point in this

direction. Figure 12 presents, as an example, the curves obtained by the point of Figure 11.

Figure 12 – Angular variation curves

The standard deviation of the angular variation curve can be considered as a representative FJ

angular variation, which will correspond to the appropriate stiffness on the manufacturer curve, for each

loading case.

The angular variation representative value depends on the complete signal of the riser top relative

rotations. For this reason, to use a FJ stiffness varying along the dynamic analysis, CONTRACTOR

shall guarantee that the rotation history is considered up to each time step, using the procedure

described above.

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 100 200 300 400 500 600

An

gula

r V

aria

tio

n (

de

g)

Time (s)Total Deflection Main Direction Maximum Amplitude