eni S.p.A.
San Donato Milanese, Italy
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture
Propagation Control (DFPC) Assessment in Steel
Pipeline
Validation Report
Doc. No. P0031384-130 Rev. 1 – March 2024
Rev.
Description
Prepared by
Checked by
Approved by
Date
1
Issue for comments
L. Mancini
M. Di Biagio
A. Fonzo
G. Mannucci
L. Allleva
19/12/2024
0
Issue for comments
L. Mancini
M. Di Biagio
A. Fonzo
G. Mannucci
L. Allleva
21/12/2023
All rights, including translation, reserved. No part of this document may be disclosed to any third party,
for purposes other than the original, without written consent of RINA Consulting S.p.A.
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
TABLE OF CONTENTS
Page
LIST OF TABLES
LIST OF FIGURES
ABBREVIATIONS AND ACRONYMS
1
GENERAL
1.1
INTRODUCTION
1.2
PURPOSE OF THIS DOCUMENT
2
DESCRIPTION OF THE TOOL
2.1
GENERAL INFORMATION
2.2
STRUCTURE OF THE TOOL
3
API 5L EPRG GUIDELINES EQUATION & TABLE SHEET VALIDATION
3.1
PROTOCOL OVERVIEW
3.2
STEP 1 – GENERAL CHECK OF CORRESPONDANCE WITH TABLE
3.3
STEP 2 – GENERAL CHECK OF EQUATIONS
4
API 5L BATTELLE TWO-CURVE METHOD SHEET VALIDATION
4.1
PROTOCOL OVERVIEW
4.2
STEP 1 – GENERAL CHECK OF EQUATIONS
4.3
STEP 2 – VALIDATION BY COMPARISON WITH OTHER TOOLS
5
API 5L BATTELLE SIMPLIFIED EQUATION SHEET VALIDATION
5.1
PROTOCOL OVERVIEW
5.2
STEP 1 – GENERAL CHECK OF EQUATIONS
6
API 5L AISI METHOD SHEET VALIDATION
6.1
PROTOCOL OVERVIEW
6.2
STEP 1 – GENERAL CHECK OF EQUATIONS
7
DNVGL-RP-F104:2021 METHOD SHEET VALIDATION
7.1
PROTOCOL OVERVIEW
7.2
STEP 1 – GENERAL CHECK OF EQUATIONS
7.3
STEP 2 – VALIDATION BY COMPARISON WITH OTHER TOOLS
8
ISO 27913:2016 ANNEX D METHOD SHEET VALIDATION
8.1
PROTOCOL OVERVIEW
8.2
STEP 1 – GENERAL CHECK OF EQUATIONS
8.3
STEP 2 – VALIDATION BY COMPARISON WITH OTHER TOOLS
9
CONCLUSIONS
10 DISCLAIMER
Doc. No. P0031384-130 Rev. 1 – March 2024
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Page 2
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
LIST OF TABLES
Table 2.1:
Table 3.1:
Table 7.1:
Table 8.1:
Key details and features of the spreadsheet
4
Calculated Minimum CVN Absorbed Energy Requirement using tool
7
Full scale test data for COOLTRANS Tests 01, 02, 03, CO2SafeArrest Tests 01 and Test 02
(table 4 and 5 Cosham’s paper)
23
Calculated arrest pressure using tool
26
LIST OF FIGURES
Figure 3-1:
Figure 3-2:
Figure 3-3:
Figure 3-4:
Figure 3-5:
Figure 3-6:
Figure 3-7:
Figure 4-1:
Figure 4-2:
Figure 4-3:
Figure 4-4:
Figure 5-1:
Figure 6-1:
Figure 7-1:
Figure 7-2:
Figure 7-3:
Figure 8-1:
Figure 8-2:
Minimum CVN Absorbed Energy Requirement for a Design Factor of 0.625
Minimum CVN Absorbed Energy Requirement for a Design Factor of 0.72
Minimum CVN Absorbed Energy Requirement for a Design Factor of 0.80
API5L (EPRG Guidelines – Approach 1)
Sheet Sample for Grade ≤ L450 or X65
Sheet Sample for Grade > L450 or X65 but ≤ L485 or X70
Sheet Sample for Grade > L485 or X70 but ≤ L555 or X80
Sheet Sample
Sheet Sample
Example fracture arrest problem (Figure 43 at page 97 of Leis’ report)
Comparison of resistance curves
Sheet Sample
Sheet Sample
Sheet Sample
Example fracture arrest problem (Figure 3a page 9 of Cosham’s paper)
Example fracture arrest problem (Figure 3a page 9 of Cosham’s paper)
Sheet Sample
Example of predicted arrest pressure (Table 2 page 5 of Gruben’s paper)
6
7
7
8
9
10
11
12
14
14
15
16
18
20
22
22
24
26
ABBREVIATIONS AND ACRONYMS
ENI
RINA
Eni S.p.A.
RINA Consulting – Centro Sviluppo Materiali S.p.A.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 3
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
1
GENERAL
1.1
INTRODUCTION
RINA Consulting - Centro Sviluppo Materiali S.p.A. (in the following “RINA”) has been appointed by Eni S.p.A. (in
the following “ENI”) to provide support for the development and validation of a series of pipeline design
spreadsheets.
1.2
PURPOSE OF THIS DOCUMENT
Purpose of this report is to describe the validation protocol developed by RINA for the spreadsheet described in
Section 2 (see Table 2.1 for a summary of the key details) and to document relevant findings and conclusions.
2
DESCRIPTION OF THE TOOL
2.1
GENERAL INFORMATION
The following table summarizes the key details and features of the spreadsheet subject of this validation report.
Table 2.1:
Key details and features of the spreadsheet
Title
Title
Tool ID
MOD.PLI.CAL.030
Version
01
Title
Ductile Fracture Propagation Control (DFPC) Assessment in Steel Pipeline
Developed by
RINA Consulting – Centro Sviluppo Materiali S.p.A.
Purpose and key features
This spreadsheet allows to perform assessment regarding ductile fracture
propagation resistance in natural gas and CO2 dense phase pipelines.
Reference codes and standards
API5L 46th Edition; DNV-GL-RP-F104:2021; ISO 27913:2016
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 4
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
2.2
STRUCTURE OF THE TOOL
The spreadsheet subject of this report consists of the following sheets (tabs):
▪
COVER PAGE
Reports name of the project, codes and title block
▪
REFERENCES
Reports reference codes, standards, notes and assumptions
▪
MANUAL
Gives an overview on how to use the tool and on the structure
▪
▪
API5L-EPRG Guid. Equation & EPRG guideline in tabular approach as reported in API5L Annex G
Tables
approach 1
API5L-Battelle Simplified Eq
Battelle Simplified formula as reported in API 5L Annex G approach 2
▪
API5L-Battelle TwoCurve Method
Battelle Two-Curve method as reported in API 5L Annex G approach 3
▪
API5L-AISI Method
AISI Formula method as reported in API 5L Annex G approach 4
▪
DNV-GL-RP-F104_2021
▪
ISO 27913_2016
▪
COEFF
DNV-GL-RP-F104:2021 approach for the evaluation of ductile fracture
arrestability in CO2 dense phase pipelines
ISO 27913_2016 approach for the evaluation of ductile fracture
arrestability in CO2 dense phase pipelines
Is a sheet of support for macro calculation
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 5
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
3
API 5L EPRG GUIDELINES EQUATION & TABLE SHEET
VALIDATION
3.1
PROTOCOL OVERVIEW
In order to get confidence that the spreadsheet under subject works properly, RINA has implemented a validation
protocol consisting of the following key step:
•
Step 1:
General check that the results of tool supply the same values reported in the tables included in
the API 5L standard.
•
Step 2:
General check of all equations implemented in the spreadsheet to confirm no major mistakes are
present. Such step includes also spot checks of the intermediate results of selected equations by
comparison with hand calculations.
The following sections provide details of the checks performed by RINA.
3.2
STEP 1 – GENERAL CHECK OF CORRESPONDANCE WITH TABLE
Based on the scope of the spreadsheet under subject, three values for each table have been compared with the
result of the spread sheet. The values, object of comparison, are highlighted in the following figures:
Figure 3-1:
Minimum CVN Absorbed Energy Requirement for a Design Factor of 0.625
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 6
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Figure 3-2:
Minimum CVN Absorbed Energy Requirement for a Design Factor of 0.72
Figure 3-3:
Minimum CVN Absorbed Energy Requirement for a Design Factor of 0.80
Table 3.1:
Diameter (in)
36
48
44
Calculated Minimum CVN Absorbed Energy Requirement using tool
Grade
X65
X70
X80
UF 0.625
40
58
82
UF 0.72
46
71
102
UF 0.80
55
84
125
As shown in the above, the results correspond with the values given in the standard tables sheet.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 7
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
STEP 2 – GENERAL CHECK OF EQUATIONS
3.3
Based on the scope of the spreadsheet under subject, a calculation was made for each of the three equations in
the API5L (EPRG Guidelines – Approach 1).
Figure 3-4:
API5L (EPRG Guidelines – Approach 1)
For Grade ≤ L450 or X65
Based on the scope of the spreadsheet under subject, the following checks have been made:
−
Outer Diameter (from “in” to “mm”)
−
Minimum Wall Thickness
−
Design Hoop Stress
−
Full-Size CVN Energy KV:
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 8
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Figure 3-5:
Sheet Sample for Grade ≤ L450 or X65
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 3-5 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 36𝑖𝑛 = 914.4 𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Substituting the data reported in Figure 3-5 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 12.6 𝑚𝑚 − 1.0𝑚𝑚 − 1.00 𝑚𝑚 = 10.6𝑚𝑚
Design Hoop Stress
Design Hoop Stress is calculated using Mariotte formula:
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 ∙ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
2 ∙ 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠
𝑝 ∙ 𝑅 8 𝑀𝑃𝑎 ∙ 914.4 𝑚𝑚
𝜎ℎ =
=
= 345.1 𝑀𝑃𝑎
𝑡
2 ∙ 10.6 𝑚𝑚
𝐷𝑒𝑠𝑖𝑔𝑛 𝐻𝑜𝑜𝑝 𝑆𝑡𝑟𝑒𝑠𝑠 =
Full-Size CVN Energy KV
𝐾𝑉 = 𝐶1 ∙ 𝜎ℎ1.5 ∙ 𝐷0.5
Substituting the data reported in Figure 3-5 in the equation leads to:
𝐾𝑉 = 2.67𝑒 −4 ∙ 345.11.5 ∙ 914.40.5 = 51.74 𝐽
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
For Grade > L450 or X65, but ≤ L485 or X70
Based on the scope of the spreadsheet under subject, the following checks have been made:
−
Outer Diameter (from “in” to “mm”)
−
Minimum Wall Thickness
−
Design Hoop Stress
−
Full-Size CVN Energy KV:
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 9
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Figure 3-6:
Sheet Sample for Grade > L450 or X65 but ≤ L485 or X70
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 3-6 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 42𝑖𝑛 = 1066.8 𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Substituting the data reported in Figure 3-6 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 15 𝑚𝑚 − 1.0𝑚𝑚 − 0.5 𝑚𝑚 = 13.5 𝑚𝑚
Design Hoop Stress
Design Hoop Stress is calculated using Mariotte formula:
𝐷𝑒𝑠𝑖𝑔𝑛 𝐻𝑜𝑜𝑝 𝑆𝑡𝑟𝑒𝑠𝑠 =
𝜎ℎ =
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 ∙ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
2 ∙ 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠
𝑝 ∙ 𝑅 8 𝑀𝑃𝑎 ∙ 1066.8 𝑚𝑚
=
= 316.1 𝑀𝑃𝑎
𝑡
2 ∙ 13.5 𝑚𝑚
Full-Size CVN Energy KV
𝐾𝑉 = 𝐶2 ∙ 𝜎ℎ1.5 ∙ 𝐷0.5
Substituting the data reported in Figure 3-6 in the equation leads to:
𝐾𝑉 = 3.21𝑒 −4 ∙ 316.11.5 ∙ 1066.80.5 = 58.91 𝐽
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
For Grade > L485 or X70, but ≤ L555 or X80
Based on the scope of the spreadsheet under subject, the following checks have been made:
−
Outer Diameter (from “in” to “mm”)
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 10
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
−
Minimum Wall Thickness
−
Design Hoop Stress
−
Full-Size CVN Energy KV:
Figure 3-7:
Sheet Sample for Grade > L485 or X70 but ≤ L555 or X80
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 3-7 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 48𝑖𝑛 = 1219.2 𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Substituting the data reported in Figure 3-7 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 15 𝑚𝑚 − 1.0𝑚𝑚 − 1.0 𝑚𝑚 = 13 𝑚𝑚
Design Hoop Stress
Design Hoop Stress is calculated using Mariotte formula:
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 ∙ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
2 ∙ 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠
𝑝 ∙ 𝑅 8 𝑀𝑃𝑎 ∙ 1219.2 𝑚𝑚
𝜎ℎ =
=
= 375.1 𝑀𝑃𝑎
𝑡
2 ∙ 14 𝑚𝑚
𝐷𝑒𝑠𝑖𝑔𝑛 𝐻𝑜𝑜𝑝 𝑆𝑡𝑟𝑒𝑠𝑠 =
Full-Size CVN Energy KV
𝐾𝑉 = 𝐶3 ∙ 𝜎ℎ2 ∙ (
𝐷 ∙ 𝑡 1/3
)
2
Substituting the data reported in Figure 3-7 in the equation leads to:
1
𝐾𝑉 = 3.57𝑒 −5 ∙ 375.12 ∙ (
1219.2 ∙ 14 3
) = 100.1 𝐽
2
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 11
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
4
API 5L BATTELLE TWO-CURVE METHOD SHEET VALIDATION
4.1
PROTOCOL OVERVIEW
In order to get confidence that the spreadsheet under subject works properly, RINA has implemented a validation
protocol consisting of the following key steps:
•
Step 1:
General check of all equations implemented in the spreadsheet to confirm no major mistakes are
present. Such step includes also spot checks of the intermediate results of selected equations by
comparison with hand calculations.
•
Step 2:
Validation of the spreadsheet through comparison with results obtained with another applicable
tool, such as an in-house spreadsheet, a commercial software or another tool, depending on the
features subject to validation.
The following sections provide details of the checks performed by RINA.
STEP 1 – GENERAL CHECK OF EQUATIONS
4.2
Based on the scope of the spreadsheet under subject, the following checks have been made:
−
Outer Diameter (from “in” to “mm”)
−
Minimum Wall Thickness
−
Specific toughness energy (CV spec):
−
Arrest Pressure
−
Fracture Velocity.
Figure 4-1:
Sheet Sample
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 4-1 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 18𝑖𝑛 = 457.2𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 12
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Substituting the data reported in Figure 4-1 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 9.1𝑚𝑚 − 1.0𝑚𝑚 − 0.5𝑚𝑚 = 7.6𝑚𝑚
Sigma flow
Sigma Flow is calculated as follows:
𝑆𝑖𝑔𝑚𝑎 𝑓𝑙𝑜𝑤 = 𝑆𝑀𝑌𝑆 + 68.9 𝑀𝑃𝑎
Substituting the data reported in Figure 4-1 in the equation leads to:
𝑆𝑖𝑔𝑚𝑎 𝑓𝑙𝑜𝑤 = 450𝑀𝑃𝑎 + 68.9𝑀𝑃𝑎 = 518.9 𝑀𝑃𝑎
Specific toughness energy (CV spec):
Specific toughness energy (CV spec) is calculated as follows considering the standard full size Charpy energy
specimen with fracture surface (A) of 80mm2:
𝐶𝑉 𝑠𝑝𝑒𝑐 =
𝐶𝑉(1: 1)
𝐴
Substituting the data reported in Figure 4-1 in the equation leads to:
𝐶𝑉 𝑠𝑝𝑒𝑐 =
25.3 𝐽
𝐽
= 0.316
80 𝑚𝑚2
𝑚𝑚 2
Arrest Pressure
Arrest pressure (Pa) is calculated as follows:
2𝑡𝜎̅
𝑃𝑎 =
arccos (𝑒
3.33𝜋𝑟
−
𝜋𝑅𝐸
𝐷
24𝜎
̅ 2√𝑡
[
2 ])
Substituting the data reported in Figure 4-1 in the equation leads to:
2 ∙ 7.6 ∙ 518.9
𝑃𝑎 =
arccos (𝑒
457.2
3.33 ∙ 𝜋 ∙ ( 2 )
𝑃𝑎 =
−
1000 ∙ 𝜋 ∙ 0.316 ∙ 208000
457.2
2√
[ 24∙(518.9) 7.6 ∙ 2 ] )
206490602
7887.28
arccos (𝑒 −[24 ∙ 268531.24 ∙41.682] )
2390.29
𝑃𝑎 = 3.3 ∙ arccos (𝑒 −0.768 )
𝑃𝑎 = 3.3 ∙ arccos(0.4639) = 3.3 ∙ 1.0883 = 3.59 𝑀𝑃𝑎
Fracture Velocity
Fracture velocity is calculated as follows:
𝑉𝑓 = 𝐶
𝜎̅
1⁄
6
𝑃𝑑
[ − 1]
𝑃𝑎
√𝐶𝑉𝑁
𝐴
Substituting the data reported in Figure 4-1 in the equation leads to:
Doc. No. P0031384-130 Rev. 1 – March 2024
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Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
518.9
1⁄
6
15
𝑉𝑓 = 0.275 ∙
[
− 1]
3.59
√0.316
= 307.8 𝑚/𝑠
Comparing with data reported in Figure 4-2 for the first line (P=15.0 MPa)
Figure 4-2:
Sheet Sample
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
4.3
STEP 2 – VALIDATION BY COMPARISON WITH OTHER TOOLS
In order to validate the spreadsheet under subject, RINA has compared the resistance curve outcomes with the
results found in the following report:
B. N. Leis and R. J. Eiber Report “Fracture Control Technology For Transmission Pipelines” PRCI Materials
Committee - Pipeline Research Council International Contract No. PR-003-00108 and PR-003-084506
This check is aimed at demonstrating that, starting with the same input data, the resistance curve obtained from
both tools is overlapped.
In the Figure 4-3 is reported the application of the Battelle Two-Curve Model for a specific condition and with three
different levels of toughness:
Figure 4-3:
Example fracture arrest problem (Figure 43 at page 97 of Leis’ report)
Input data:
•
Diameter: 36in
Doc. No. P0031384-130 Rev. 1 – March 2024
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Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
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•
•
•
•
•
Wall thickness: 9.1mm
Material grade: X65
Initial pressure: 6.449 MPa
Backfill: soil
Toughness: 41J, 55J and 68J
Starting from the input data above, it is possible to plot the resistance curves for the three different levels of
toughness. Using the Leis’ report chart as background for the comparison chart it is possible to check that the
curves of the two charts are exactly overlapped.
Figure 4-4:
Comparison of resistance curves
As shown in Figure 4-4, the results are pretty the same for both tools; slightly differences are due to the rounding
of decimals.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 15
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
5
API 5L BATTELLE SIMPLIFIED EQUATION SHEET VALIDATION
5.1
PROTOCOL OVERVIEW
In order to get confidence that the spreadsheet under subject works properly, RINA has implemented a validation
protocol consisting of the following key step:
•
Step 1:
General check of all equations implemented in the spreadsheet to confirm no major mistakes are
present. Such step includes also spot checks of the intermediate results of selected equations by
comparison with hand calculations.
The following sections provide details of the checks performed by RINA.
5.2
STEP 1 – GENERAL CHECK OF EQUATIONS
Based on the scope of the spreadsheet under subject, the following checks have been made:
•
•
•
•
•
Outer Diameter (from in to mm)
Minimum Wall Thickness
Design hoop stress
Design factor
Full-Size CVN Energy (KV).
Figure 5-1:
Sheet Sample
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 5-1 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 20𝑖𝑛 = 508.0 𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Substituting the data reported in Figure 5-1 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 8.0𝑚𝑚 − 1.0𝑚𝑚 − 0.5𝑚𝑚 = 6.5 𝑚𝑚
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 16
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Design hoop stress
Design hoop stress is calculated as follows:
ℎ𝑜𝑜𝑝 𝑠𝑡𝑟𝑒𝑠𝑠 =
𝑃∙𝐷
2∙𝑡
Substituting the data reported in Figure 5-1 in the equation leads to:
ℎ𝑜𝑜𝑝 𝑠𝑡𝑟𝑒𝑠𝑠 =
6 ∙ 508
= 234.5 𝑀𝑃𝑎
2 ∙ 6.5
Design factor
Design hoop stress is calculated as follows:
𝑑𝑒𝑠𝑖𝑔𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 =
ℎ𝑜𝑜𝑝 𝑠𝑡𝑟𝑒𝑠𝑠
𝑆𝑌𝑀𝑆
Substituting the data reported in Figure 5-1 in the equation leads to:
𝑑𝑒𝑠𝑖𝑔𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 =
234.5
= 0.52
450
Full-Size CVN Energy (KV):
Full-Size CVN Energy (KV) is calculated as follows:
𝐾𝑉 = 𝐶3 ∙ 𝜎ℎ2 ∙ (
𝐷𝑡 1⁄3
)
2
Substituting the data reported in Figure 5-1 in the equation leads to:
𝐾𝑉 = 3.57 ∙ 10−5 ∙ 234.52 ∙ (
508 ∙ 6.5 1⁄3
)
= 23.2 𝐽
2
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 17
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
6
API 5L AISI METHOD SHEET VALIDATION
6.1
PROTOCOL OVERVIEW
In order to get confidence that the spreadsheet under subject works properly, RINA has implemented a validation
protocol consisting of the following key step:
•
Step 1:
General check of all equations implemented in the spreadsheet to confirm no major mistakes are
present. Such step includes also spot checks of the intermediate results of selected equations by
comparison with hand calculations.
The following sections provide details of the checks performed by RINA.
6.2
STEP 1 – GENERAL CHECK OF EQUATIONS
Based on the scope of the spreadsheet under subject, the following checks have been made:
•
•
•
•
•
Outer Diameter (from in to mm)
Minimum Wall Thickness
Design hoop stress
Design factor
Full-Size CVN Energy (KV).
Figure 6-1:
Sheet Sample
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 6-1 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 20𝑖𝑛 = 508.0 𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Substituting the data reported in Figure 6-1 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 8.0𝑚𝑚 − 1.0𝑚𝑚 − 0.5𝑚𝑚 = 6.5 𝑚𝑚
Design hoop stress
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 18
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Design hoop stress is calculated as follows:
ℎ𝑜𝑜𝑝 𝑠𝑡𝑟𝑒𝑠𝑠 =
𝑃∙𝐷
2∙𝑡
Substituting the data reported in Figure 6-1 in the equation leads to:
ℎ𝑜𝑜𝑝 𝑠𝑡𝑟𝑒𝑠𝑠 =
6 ∙ 508
= 234.5 𝑀𝑃𝑎
2 ∙ 6.5
Design factor
Design hoop stress is calculated as follows:
𝑑𝑒𝑠𝑖𝑔𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 =
ℎ𝑜𝑜𝑝 𝑠𝑡𝑟𝑒𝑠𝑠
𝑆𝑌𝑀𝑆
Substituting the data reported in Figure 6-1 in the equation leads to:
𝑑𝑒𝑠𝑖𝑔𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 =
234.5
= 0.52
450
Full-Size CVN Energy (KV):
Full-Size CVN Energy (KV) is calculated as follows:
𝐾𝑉 = 𝐶4 ∙ 𝜎ℎ1.5 ∙ 𝐷1⁄2
Substituting the data reported in Figure 6-1 in the equation leads to:
𝐾𝑉 = 3.57 ∙ 10−4 ∙ 234.51.5 ∙ (508)1⁄2 = 28.9 𝐽
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 19
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
7
DNVGL-RP-F104:2021 METHOD SHEET VALIDATION
7.1
PROTOCOL OVERVIEW
In order to get confidence that the spreadsheet under subject works properly, RINA has implemented a validation
protocol consisting of the following key steps:
•
Step 1:
General check of all equations implemented in the spreadsheet to confirm no major mistakes are
present. Such step includes also spot checks of the intermediate results of selected equations by
comparison with hand calculations.
•
Step 2:
Validation of the spreadsheet through comparison with results obtained with another applicable
tool, such as an in-house spreadsheet, a commercial software or another tool, depending on the
features subject to validation.
The following sections provide details of the checks performed by RINA.
7.2
STEP 1 – GENERAL CHECK OF EQUATIONS
Based on the scope of the spreadsheet under subject, the following checks have been made:
•
•
•
•
•
Outer Diameter (from in to mm)
Minimum Wall Thickness
Specific toughness energy (CV spec):
Arrest Pressure
Fracture Velocity.
Figure 7-1:
Sheet Sample
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 7-1 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 24𝑖𝑛 = 609.6𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 20
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Substituting the data reported in Figure 7-1 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 22.0𝑚𝑚 − 1.0𝑚𝑚 − 1.0𝑚𝑚 = 20.0𝑚𝑚
Flow stress
Flow stress is calculated as follows:
𝑓𝑙𝑜𝑤 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑆𝑀𝑌𝑆 + 69
Substituting the data reported in Figure 7-1 in the equation leads to:
𝑓𝑙𝑜𝑤 𝑠𝑡𝑟𝑒𝑠𝑠 = 415𝑀𝑃𝑎 + 69𝑀𝑝𝑎 = 484𝑀𝑃𝑎
Characteristic CNV energy:
Characteristic CNV energy is calculated as follows considering the Charpy energy samples with fracture surface
(A) of 80mm2:
𝐶𝑉 𝑠𝑝𝑒𝑐 =
𝐶𝑉(1: 1)
𝐴
Substituting the data reported in Figure 7-1 in the equation leads to:
𝐶𝑉 𝑠𝑝𝑒𝑐 =
250 𝐽
𝐽
= 3.13
80 𝑚𝑚2
𝑚𝑚 2
X value:
X value is calculated as follows:
𝑋=
1000 ∙ 𝑅𝐶𝑉𝑁 ∙ 𝐸
𝜎𝑓2 ∙ √𝑅 ∙ 𝑡
Substituting the data reported in Figure 7-1 in the equation leads to:
𝑋=
1000 ∙ 3.13 ∙ 208000
609.6
4842 ∙ √ 2 ∙ 20
= 35.59
Y value:
Y value is calculated as follows:
𝑌=
𝑃∙𝐷
2 ∙ 𝑡 ∙ 𝜎𝑓
Substituting the data reported in Figure 7-1 in the equation leads to:
𝑌=
7.0 ∙ 609.6
= 0.22
2 ∙ 20 ∙ 484
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
Doc. No. P0031384-130 Rev. 1 – March 2024
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Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
7.3
STEP 2 – VALIDATION BY COMPARISON WITH OTHER TOOLS
In order to validate the spreadsheet under subject, RINA has compared the position of some full scale test points
with those reported in the following paper:
A.Cosham et al. “The Decompressed Stress Level in Dense Phase Carbon Dioxide Full-Scale Fracture
Propagation Tests” IPC2022-86855, Proceedings of the 2022 14th International Pipeline Conference IPC2022
September 26-30, 2022, Calgary, Alberta, Canada
This check was aimed at demonstrating that starting the same input data the points position in DNV chart obtained
are overlapped.
In the Figure 7-2 is reported a plot of the normalised decompressed stress level (= Y) versus the normalised
toughness (=X) for the full-scale tests conducted with carbon dioxide.
Figure 7-2:
Example fracture arrest problem (Figure 3a page 9 of Cosham’s paper)
Input data as from table 4 and table 5 of Cosham’s paper. All these tests have been used for the evaluation of X
and Y values with the validating tool (X and Y values are reported in Table 7.1).
Plotting the calculated X and Y values on Figure 7-2 and making a zoom in interest area, it is possible to observe
the overlapping of points calculated by Cosham in his paper and the values calculated using the validating tool.
Figure 7-3:
Example fracture arrest problem (Figure 3a page 9 of Cosham’s paper)
Doc. No. P0031384-130 Rev. 1 – March 2024
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Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Table 7.1:
Full scale test data for COOLTRANS Tests 01, 02, 03, CO2SafeArrest Tests 01 and Test
02 (table 4 and 5 Cosham’s paper)
Test
Designation Pipe No. diameter,
wall
average
average
average CVN Crack tip
thickness,
yield
tensile
impact energy, pressure,
strength,
CoolTrans #1
3W
CoolTrans #1
2W
CoolTrans #1
1W
CoolTrans #1
initiation
CoolTrans #1
1E
CoolTrans #1
2E
CoolTrans #1
3E
CoolTrans #1
4E
CoolTrans #2
CoolTrans #2
3W
2W
CoolTrans #2
1W
CoolTrans #2
initiation
CoolTrans #2
1E
CoolTrans #2
2E
CoolTrans #2
3E
CoolTrans #3
CoolTrans #3
2W
1W
CoolTrans #3
initiation
CoolTrans #3
1E
CoolTrans #3
2E
CO2SafeArrest #1 3W
CO2SafeArrest #1 2W
CO2SafeArrest #1 1W
CO2SafeArrest #1 1E
CO2SafeArrest #1 2E
CO2SafeArrest #1 3E
CO2SafeArrest #2 4W
CO2SafeArrest #2 3W
CO2SafeArrest #2 2W
CO2SafeArrest #2 1W
CO2SafeArrest #2 1E
CO2SafeArrest #2 2E
CO2SafeArrest #2 3E
CO2SafeArrest #2 4E
strength, [2 mm] [8mm]
barg
Arrest
or
Propagate
mm
914
914
914
914
914
914
914
914
914
914
914
914
914
914
914
mm
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
N.mm
507
485
510
483
505
499
511
523
497
512
495
499
456
477
476
N.mm
596
582
628
606
616
617
633
639
613
622
613
614
582
598
577
J
331
302
273
259
226
201
183
186
213
202
207
224
273
267
292
X
Y
-
75,7
75,8
71,0
76,7
70,8
73,8
73,8
73,4
73,4
73,4
73,9
71,2
72,5
74,1
71,4
A
P
P
P
P
P
P
P
P
P
P
P
P
P
A
24,0
23,8
19,6
20,4
16,6
15,1
13,1
12,8
16,1
14,4
15,7
16,7
23,9
21,6
23,8
0,24
0,25
0,22
0,25
0,22
0,23
0,23
0,22
0,23
0,23
0,24
0,23
0,25
0,24
0,24
13N
44996N
44996S
62S
62N
34N
34S
61N
61S
43S
43N
14S
914
914
914
914
914
914
914
914
914
914
914
914
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
25,4
445
497
496
492
499
499
495
501
503
506
518
481
538
588
627
612
612
619
614
619
618
628
617
558
388
227
230
212
179
179
187
191
203
217
246
356
-
62,0
62,0
62,0
62,0
60,8
60,8
60,8
60,8
62,0
62,0
62,0
62,0
A
P
P
P
P
P
P
P
P
P
P
A
35,4
17,2
17,4
16,3
13,4
13,4
14,2
14,2
15,0
15,8
17,2
28,4
0,22
0,20
0,20
0,20
0,19
0,19
0,19
0,19
0,20
0,19
0,19
0,20
65N
78N
78S
2A
2B
81S
81N
66N
610
610
610
610
610
610
610
610
19,6
19,1
19,1
19,4
19,3
19,2
19,2
19,5
522
477
473
462
478
494
487
528
597
591
586
582
572
607
592
608
342
152
152
97
106
172
174
328
-
85,5
83,2
80,6
80,6
83,2
83,2
82,9
82,7
A
P
P
P
P
P
P
A
32,9
17,4
17,7
11,6
12,1
18,4
19,1
31,1
0,23
0,24
0,24
0,24
0,24
0,23
0,24
0,22
N
S
N
S
S
N
S
N
S
N
S
610
610
610
610
610
610
610
610
610
610
610
13,7
13,6
13,5
13,6
13,4
13,4
13,4
13,5
13,6
13,6
13,6
503
459
517
493
438
463
449
457
475
505
509
612
584
631
612
606
619
620
602
611
616
619
302
302
143
176
107
91
110
114
215
215
247
436
438
218
268
130
110
112
116
422
199
419
67,8
65,0
64,8
65,5
63,9
63,9
62,1
62,1
65,0
66,1
64,5
A
P
P
P
P
P
P
P
P
P
A
37,1
43,7
16,9
22,5
16,9
13,0
16,7
16,7
29,3
26,3
29,8
0,26
0,28
0,25
0,26
0,29
0,27
0,27
0,27
0,27
0,26
0,25
N
S
S
N
N
S
N
S
S
N
S
N
N
S
N
610
610
610
610
610
610
610
610
610
610
610
610
610
610
610
15
15
15
15
14,7
14,7
14,7
14,7
14,7
14,6
14,7
14,7
14,7
14,7
15
502
465
508
507
492
463
458
445
457
450
463
494
492
501
478
603
579
616
615
599
589
611
604
616
601
576
599
606
611
580
312
308
238
222
262
242
99
122
110
135
265
266
252
277
315
445
439
340
338
331
266
117
122
110
135
254
357
330
378
441
79,0
78,5
74,0
74,7
74,6
74,4
76,0
76,0
75,0
75,0
75,6
76,3
77,1
75,8
76,4
A
P
P
P
P
P
P
P
P
P
P
P
P
P
A
36,8
41,5
27,5
25,7
32,3
33,2
13,8
17,9
15,4
19,5
36,4
32,6
31,1
33,2
40,4
0,28
0,30
0,26
0,26
0,28
0,29
0,30
0,31
0,30
0,30
0,29
0,28
0,29
0,28
0,28
26N
26S
47N
47S
44N
44S
32S
32N
41S
41N
42S
42N
48S
48N
25S
-2
-2
J
As shown in the Figure 7-2, Figure 7-3 and Table 7.1, the results are pretty the same for both tools; slightly
differences are due to the rounding of decimals.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 23
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
8
ISO 27913:2016 ANNEX D METHOD SHEET VALIDATION
8.1
PROTOCOL OVERVIEW
In order to get confidence that the spreadsheet under subject works properly, RINA has implemented a validation
protocol consisting of the following key steps:
•
Step 1:
General check of all equations implemented in the spreadsheet to confirm no major mistakes are
present. Such step includes also spot checks of the intermediate results of selected equations by
comparison with hand calculations.
•
Step 2:
Validation of the spreadsheet through comparison with results obtained with another applicable
tool, such as an in-house spreadsheet, a commercial software or another tool, depending on the
features subject to validation.
The following sections provide details of the checks performed by RINA.
8.2
STEP 1 – GENERAL CHECK OF EQUATIONS
Based on the scope of the spreadsheet under subject, the following checks have been made:
•
•
•
•
•
Outer Diameter (from in to mm)
Minimum Wall Thickness
Specific toughness energy (CV spec):
Arrest Pressure
Fracture Velocity.
Figure 8-1:
Sheet Sample
Outer Diameter (from in to mm)
Diameter conversion from in to mm is calculated as follows:
𝐷𝑚𝑚 = 25.4 ∙ 𝐷𝑖𝑛
Substituting the data reported in Figure 8-1 in the equation leads to:
𝐷𝑚𝑚 = 25.4 ∙ 20𝑖𝑛 = 508.0 𝑚𝑚
Minimum Wall Thickness
Minimum wall thickness is calculated as follows:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 − 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 − 𝑀𝑖𝑙𝑙 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 24
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
Substituting the data reported in Figure 8-1 in the equation leads to:
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑊𝑎𝑙𝑙 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 17.4𝑚𝑚 − 1.0𝑚𝑚 − 1.0𝑚𝑚 = 15.4 𝑚𝑚
Sigma flow
Sigma Flow is calculated as follows:
𝑆𝑖𝑔𝑚𝑎 𝑓𝑙𝑜𝑤 = 𝑆𝑀𝑌𝑆 + 68.9
Substituting the data reported in Figure 8-1 in the equation leads to:
𝑆𝑖𝑔𝑚𝑎 𝑓𝑙𝑜𝑤 = 450𝑀𝑃𝑎 + 68.9𝑀𝑝𝑎 = 518.9 𝑀𝑃𝑎
Sigma arrest
Sigma arrest is calculated as follows:
𝜎𝑎 =
𝑃𝑠 ∙ 𝑂𝐷
2∙𝑡
Substituting the data reported in Figure 8-1 in the equation leads to:
𝜎𝑎 =
7.5 𝑀𝑃𝑎 ∙ 508.0 𝑚𝑚
= 123.7 𝑀𝑃𝑎
2 ∙ 15.4 𝑚𝑚
Energy toughness requirement
Energy toughness requirement (Full size CVN energy KV) is calculated as follows:
1000
𝐶𝑉 ∙ 𝐸
𝐴𝐶 ∙
𝜎𝑓2
∙ √𝑅 ∙ 𝑡
=
24
𝜋 𝑐𝑓 ∙ 3.33 ∙ 𝜎𝑎
∙ ln (𝑠𝑒𝑐 ( ∙
))
𝜋
2
𝜎𝑓
Substituting the data reported in Figure 8-1 in the equation leads to:
𝐶𝑉 =
𝐶𝑉 =
𝐴𝐶 ∙ 𝜎𝑓2 ∙ √𝑅 ∙ 𝑡 24
𝜋 𝑐𝑓 ∙ 3.33 ∙ 𝜎𝑎
∙
∙ ln (𝑠𝑒𝑐 ( ∙
))
1000 ∙ 𝐸
𝜋
2
𝜎𝑓
80 ∙ 518.92 ∙ √245.3 ∙ 15.4 24
𝜋 1.2 ∙ 3.33 ∙ 123.7
∙
∙ ln (𝑠𝑒𝑐 ( ∙
)) = 126.5 𝐽
1000 ∙ 207000
𝜋
2
518.9
As shown in the above, the results are pretty the same, slightly differences are due to the rounding of decimals.
8.3
STEP 2 – VALIDATION BY COMPARISON WITH OTHER TOOLS
In order to validate the spreadsheet under subject, RINA has compared the resistance curve outcomes with the
results found in the following paper:
Gaute Gruben et al. "Pipeline Fracture Control Concepts for Norwegian Offshore Carbon Capture and
Storage" Proceedings of the 2020 13th International Pipeline Conference IPC2020 September 28-30, 2020,
Virtual, Online
This check was aimed at demonstrating that, starting with the same input data, the resistance curve obtained from
both tools are overlapped.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 25
Tool ID MOD.PLI.CAL.030_00 – Ductile Fracture Propagation Control (DFPC)
Assessment in Steel Pipeline
Validation Report
In the Figure 8-2 is reported the application of ISO27913:2016 for a specific condition and with three different level
of toughness:
Figure 8-2:
Example of predicted arrest pressure (Table 2 page 5 of Gruben’s paper)
Input data (source page 3):
•
•
•
•
•
Diameter: 323.9 mm
Wall thickness: 15.9 mm
Material grade: X65
Young's modulus: 207 GPa
Sigma flow: 492.5 MPa (source page 5)
Starting from input data above, it is possible to calculate the same values of arrest pressure in the given conditions.
Table 8.1:
Calculated arrest pressure using tool
Case
Cv = 100J
Cv = 125J
Cv = 200J
No Correction
139.7 Barg
142.5 Barg
144.9 Barg
ISO 27913
116.4 Barg
118.7 Barg
120.7 Barg
As shown in the Table 8.1, and considering the conversion between barg and bar, the results are pretty the same
for both tools; slightly differences are due to the rounding of decimals.
9
CONCLUSIONS
Based on the findings of the checks performed by RINA, as described in the previous sections of this document,
the spreadsheets under subject, in the current version indicated in Table 2.1, can be considered validated.
10
DISCLAIMER
This is a formal notice to the Users of the spreadsheet under subject.
The spreadsheet shall be used by Users having appropriate technical background and engineering knowledge. The
User shall use his/her own engineering judgement before using the outcomes of this spreadsheet in the engineering
design process.
Use of the spreadsheet subject of this document will be sole responsibility of the User and RINA denies any and all
liability for any damages arising out of using the spreadsheet as well as denies any implied warrant.
Doc. No. P0031384-130 Rev. 1 – March 2024
Page 26
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