SIST EN ISO 21013-3:2016

Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination (ISO 21013-3:2016)

ISO 21013-3:2016 provides separate calculation methods for determining the required mass flow to be relieved for each of the following specified conditions:
-      vacuum-insulated vessels with insulation system (outer jacket + insulating material) intact under normal vacuum, outer jacket at ambient temperature, inner vessel at temperature of the contents at the specified relieving pressure;
-      vacuum-insulated vessels with insulation system (outer jacket + insulating material) intact under normal vacuum, outer jacket at ambient temperature, inner vessel at temperature of the contents at the specified relieving pressure, pressure regulator of the pressure build-up system functioning at full potential;
-      vacuum or non-vacuum-insulated vessels with insulation system remaining in place, but with loss of vacuum in the case of vacuum-insulated vessels, outer jacket at ambient temperature, inner vessel at temperature of the contents at the specified relieving pressure or vacuum or non-vacuum-insulated vessels with insulation system remaining fully or partially in place, but with loss of vacuum in the case of vacuum-insulated vessels, fire engulfment, inner vessel at temperature of the contents at the specified relieving pressure;
-      vacuum-insulated vessels containing fluids with saturation temperature below 75 K at 1 bar with insulation system remaining in place, but with loss of vacuum with air or nitrogen in the vacuum space;
-      vacuum insulated vessels containing fluids with saturation temperature below 75 K at 1 bar with insulation system remaining in place, but with loss of vacuum with air or nitrogen in the vacuum space with fire engulfment;
-      vessels with insulation system totally lost and fire engulfment.
Good engineering practice based on well-established theoretical physical science needs to be adopted to determine the required mass flow where an appropriate calculation method is not provided for an applicable condition.
Recommendations for pressure relief devices for cryostats are given in Annex A.

Kryo-Behälter - Druckentlastungseinrichtungen für den Kryo-Betrieb - Teil 3: Bestimmung von Größe und Durchfluss (ISO 21013-3:2016)

Récipients cryogéniques - Dispositifs de sécurité pour le service cryogénique - Partie 3: Détermination de la taille et du volume (ISO 21013-3:2016)

ISO 21013-3:2016 établit des méthodes de calcul distinctes permettant de déterminer le débit massique à décharger pour chacune des conditions spécifiées suivantes:
-      récipients isolés sous vide comportant un système d'isolation (enveloppe extérieure + matériau isolant) intact sous vide normal, enveloppe extérieure à température ambiante, récipient intérieur à la température du contenu à la pression de décharge spécifiée;
-      récipients isolés sous vide comportant un système d'isolation (enveloppe extérieure + matériau isolant) intact sous vide normal, enveloppe extérieure à température ambiante, récipient intérieur à la température du contenu à la pression de décharge spécifiée, régulateur de pression du système de mise en pression fonctionnant à pleine charge;
-      récipients isolés sous vide ou non, comportant un système d'isolation restant en place mais avec perte de vide en cas de récipients isolés sous vide, enveloppe extérieure à température ambiante, récipient intérieur à la température du contenu à la pression de décharge spécifiée, ou récipients isolés sous vide ou non, comportant un système d'isolation restant totalement ou partiellement en place, mais avec perte de vide dans le cas des récipients isolés sous vide, feu environnant, récipient intérieur à la température du contenu à la pression de décharge spécifiée;
-      récipients isolés sous vide contenant des fluides avec une température de saturation inférieure à 75 K à 1 bar avec un système d'isolation restant en place, mais avec perte de vide avec de l'air ou de l'azote dans l'espace sous vide;
-      récipients isolés sous vide contenant des fluides avec une température de saturation inférieure à 75 K à 1 bar avec un système d'isolation restant en place, mais avec perte de vide avec de l'air ou de l'azote dans l'espace sous vide avec feu environnant;
-      récipients avec perte totale du système d'isolation et feu environnant.
Il est nécessaire qu'une bonne pratique d'ingénierie reposant sur des données de physique théorique bien établies soit adoptée afin de déterminer le débit massique requis lorsqu'aucune méthode de calcul appropriée n'est fournie pour une condition donnée.
Des Recommandations concernant les dispositifs de décharge de pression pour cryostats sont données dans l'Annexe A.

Kriogene posode - Oprema za razbremenitev tlaka za kriogene namene - 3. del: Določanje velikosti in pretoka (ISO 21013-3:2016)

Ta standard določa ločeno računsko metodo za določanje prispevka masnega pretoka, ki se sprosti kot posledica vsakega od naslednjih določenih pogojev: – vakuumsko izolirane posode z izolacijskim sistemom (zunanja obloga + izolacijski material), ki je nepoškodovan pri normalnem tlaku. Zunanja obloga pri temperaturi v prostoru. Notranja posoda pri temperaturi vsebine pri tlaku za razbremenitev; – vakuumsko izolirane posode z izolacijskim sistemom, ki ostanejo na mestu, a izgubijo vakuum, ali nevakuumsko izolirane posode z nepoškodovanim izolacijskim sistemom. Zunanja obloga pri temperaturi v prostoru. Notranja posoda pri temperaturi vsebine pri tlaku za razbremenitev; – vakuumsko ali nevakuumsko izolirane posode z izolacijskim sistemom, ki delno ali v celoti ostanejo na mestu, a izgubijo vakuum v primeru vakuumsko izoliranih posod in v primeru izpostavljenosti ognju. Notranja posoda pri temperaturi vsebine pri tlaku za razbremenitev; – posode s povsem izgubljenim izolacijskim sistemom in v primeru izpostavljenosti ognju. Za določanje prispevka masnega pretoka, če ločena računska metoda ni na voljo za zadevno stanje, je treba uporabiti dobro inženirsko prakso.

General Information

• Status: Published
• Public Enquiry End Date: 11-Jan-2015
• Publication Date: 11-Oct-2016
• ICS: 13.240 - Protection against excessive pressure
• ICS: 23.020.40 - Cryogenic vessels
• Technical Committee: TLP - Pressure vessels
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 26-Sep-2016
• Due Date: 01-Dec-2016
• Completion Date: 12-Oct-2016
• Directive: 2008/68/EC - Directve 2008/68/EC of the European Parliament and of the council of 24 September 2008 on the inland transport of the dangerous goods
• Directive: 2014/68/EU - Directive 2014/68/EU of the European Parliament and of the Council of 15 May 2014 on the harmonisation of the laws of the Member States relating to the making available on the market of pressure equipment
• Directive: 97/23/EC - Directive 97/23/EC of the European Parliament and of the Council of 29 May 1997 on the approximation of the laws of the Member States concerning pressure equipment
• Mandate: M/071 - Mandate to CEN for standardization in the field of Pressure equipment
• Mandate: M/086 - Mandate to CEN for standardization in the field of transport of dangerous goods
• Ref Project: EN ISO 21013-3:2016 - Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination (ISO 21013-3:2016)

Relations

• Replaces: SIST EN 13648-3:2003 - Cryogenic vessels - Safety devices for protection against excessive pressure - Part 3: Determination of required discharge - Capacity and sizing
• Effective Date: 01-Nov-2016
• Revised: oSIST prEN ISO 21013-3:2025 - Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination (ISO/DIS 21013-3:2025)
• Effective Date: 01-Apr-2025

Overview

EN ISO 21013-3:2016 - "Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination" provides standardized calculation methods for determining the required mass flow to be relieved from cryogenic vessels under a range of operating and upset conditions. The standard is the CEN-endorsed version of ISO 21013-3:2016 and supersedes EN 13648-3:2002. It also includes informative recommendations for cryostats (Annex A) and supports conformity with the EU Pressure Equipment Directive (2014/68/EU).

Key topics and requirements

• Specified relief scenarios - Separate calculation methods are provided for:
  • Vacuum‑insulated vessels with intact insulation under normal vacuum (outer jacket at ambient, inner vessel at liquid temperature).
  • Same as above with a pressure‑build up regulator functioning at full potential.
  • Vacuum or non‑vacuum insulated vessels with loss of vacuum (insulation remaining) and fire engulfment scenarios.
  • Vessels containing fluids with saturation temperature below 75 K at 1 bar with loss of vacuum involving air or nitrogen, with and without fire.
  • Vessels with insulation system totally lost under fire engulfment.
• Heat transfer calculations - Procedures to compute total heat transfer per unit time from outer jacket to inner vessel for normal, loss‑of‑vacuum and fire conditions.
• Mass flow determination - Methods to convert heat input to the mass flow that pressure‑relief devices must handle.
• Relief device sizing - Guidance for sizing pressure relief valves and bursting discs, including:
  • Determination of critical vs. subcritical flow regimes.
  • Discharge capacity calculations.
  • Consideration of piping pressure drops, back pressure, and heat transfer in relief lines.
• Supporting content - Symbols, worked examples, calculation steps and normative references to support engineering application.
• Good engineering practice - Where the standard does not cover a specific condition, established physical science and engineering judgment are required.

Practical applications and users

EN ISO 21013-3:2016 is intended for professionals involved with cryogenic systems safety and compliance:

• Design engineers sizing pressure‑relief accessories for liquid oxygen, nitrogen, hydrogen, LNG and other cryogenic storage vessels.
• Safety and loss‑prevention engineers evaluating relief capacity for fire, vacuum loss or regulator failure scenarios.
• Manufacturers and suppliers of pressure relief valves, bursting discs and cryostats who need to demonstrate device capacity.
• Inspectors and notified bodies assessing conformity with safety regulations, including the Pressure Equipment Directive.
• Facility operators preparing safety cases and emergency relief system documentation.

Related standards and compliance

• Supersedes EN 13648-3:2002.
• Supports conformity with EU Directive 2014/68/EU (Pressure Equipment Directive) - see Annex ZA.
• Part of the ISO 21013 family (other parts address different aspects of cryogenic vessel safety and accessories).

Keywords: EN ISO 21013-3:2016, cryogenic vessels, pressure‑relief accessories, sizing, capacity determination, pressure relief valve, bursting disc, loss of vacuum, fire engulfment, cryostats.

Standards Content (Sample)

SLOVENSKI STANDARD
01-november-2016
1DGRPHãþD
SIST EN 13648-3:2003
.ULRJHQHSRVRGH2SUHPD]DUD]EUHPHQLWHYWODND]DNULRJHQHQDPHQHGHO
'RORþDQMHYHOLNRVWLLQSUHWRND,62
Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and
capacity determination (ISO 21013-3:2016)
Kryo-Behälter - Druckentlastungseinrichtungen für den Kryo-Betrieb - Teil 3: Bestimmung
von Größe und Durchfluss (ISO 21013-3:2016)
Récipients cryogéniques - Dispositifs de sécurité pour le service cryogénique - Partie 3:
Détermination de la taille et du volume (ISO 21013-3:2016)
Ta slovenski standard je istoveten z: EN ISO 21013-3:2016
ICS:
13.240 Varstvo pred previsokim Protection against excessive
tlakom pressure
23.020.40 Proti mrazu odporne posode Cryogenic vessels
(kriogenske posode)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 21013-3
EUROPEAN STANDARD
NORME EUROPÉENNE
June 2016
EUROPÄISCHE NORM
ICS 23.020.40 Supersedes EN 13648-3:2002
English Version
Cryogenic vessels - Pressure-relief accessories for
cryogenic service - Part 3: Sizing and capacity
determination (ISO 21013-3:2016)
Récipients cryogéniques - Dispositifs de sécurité pour Kryo-Behälter - Druckentlastungseinrichtungen für
le service cryogénique - Partie 3: Détermination de la den Kryo-Betrieb - Teil 3: Bestimmung von Größe und
taille et du volume (ISO 21013-3:2016) Durchfluss (ISO 21013-3:2016)
This European Standard was approved by CEN on 15 April 2016.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2016 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 21013-3:2016 E
worldwide for CEN national Members.

Contents
European foreword . 3
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of EU Directive (2014/68/UE — Pressure Equipment Directive) . 4
European foreword
This document (EN ISO 21013-3:2016) has been prepared by Technical Committee ISO/TC 220
“Cryogenic vessels” in collaboration with Technical Committee CEN/TC 268 “Cryogenic vessels and
specific hydrogen technologies applications” the secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by December 2016, and conflicting national standards
shall be withdrawn at the latest by December 2016.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent
rights.
This document supersedes EN 13648-3:2002.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of EU Directive.
For relationship with EU Directive, see informative Annex ZA, which is an integral part of this
document.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Endorsement notice
The text of ISO 21013-3:2016 has been approved by CEN as EN ISO 21013-3:2016 without any
modification.
Annex ZA
(informative)
Relationship between this European Standard and the Essential
Requirements of EU Directive (2014/68/UE — Pressure Equipment
Directive)
This European Standard has been prepared under a mandate given to CEN by the European
Commission to provide a means of conforming to Essential Requirements of the New Approach
Directive (2014/68/UE – Pressure Equipment Directive)
Once this standard is cited in the Official Journal of the European Union under that Directive and has
been implemented as a national standard in at least one Member State, compliance with the clauses of
this standard given in Table ZA.1 confers, within the limits of the scope of this standard, a presumption
of conformity with the corresponding Essential Requirements of that Directive and associated EFTA
regulations.
Table ZA.1 — Correspondence between this European Standard and Directive (2014/68/UE –
Pressure Equipment Directive)
Clause(s)/subclause(s) of this EN Essential Requirements (ERs) of Qualifying remarks/Notes
Directive …
4, 5 Protection against exceeding the Annex I, 2.10
allowable limits of pressure
equipment
6, 7 Safety accessories Annex I, 2.11
4.3 External fire Annex I, 2.12
WARNING — Other requirements and other EU Directives may be applicable to the product(s) falling
within the scope of this standard.

INTERNATIONAL ISO
STANDARD 21013-3
Second edition
2016-05-01
Cryogenic vessels — Pressure-relief
accessories for cryogenic service —
Part 3:
Sizing and capacity determination
Récipients cryogéniques — Dispositifs de sécurité pour le service
cryogénique —
Partie 3: Détermination de la taille et du volume
Reference number
ISO 21013-3:2016(E)
©
ISO 2016
ISO 21013-3:2016(E)
© ISO 2016, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 1
3 Symbols . 2
4 Calculation of the total quantity of heat transferred per unit time from the hot wall
(outer jacket) to the cold wall (inner vessel) . 6
4.1 General . 6
4.2 Under conditions other than fire . 6
4.2.1 Vacuum-insulated vessels under normal vacuum . 6
4.2.2 Pressure build-up device . 7
4.2.3 Vacuum-insulated vessels in the case of loss of vacuum and non-vacuum
insulated vessels . 7
4.2.4 Supports and piping . 9
4.3 Under fire conditions . 9
4.3.1 Insulation system remains fully or partially in place during fire conditions . 9
4.3.2 Insulation system does not remain in place during fire conditions .10
4.4 Air or Nitrogen condensation . .10
4.4.1 General.10
4.4.2 Loss of vacuum with air and nitrogen .10
4.4.3 Fire with loss of vacuum with air or nitrogen .11
4.5 Heat transfer per unit time (watts) .12
4.5.1 General.12
4.5.2 Normal operation .12
4.5.3 Pressure build up regulator fully open .12
4.5.4 Loss of vacuum condition .12
4.5.5 Fire condition with loss of vacuum, vacuum jacket, and insulation fully or
partially in place .13
4.5.6 Fire condition with loss of vacuum, insulation not in place .13
4.5.7 Total heat transfer rate .13
5 Calculation of the mass flow to be relieved by pressure relief devices .13
5.1 Relieving pressure, P, less than the critical pressure .13
5.2 Relieving pressure, P, equal to or greater than the critical pressure .14
5.3 Example .
............................................................................................................................................................................................................................14
6 Piping for pressure relief devices .15
6.1 Pressure drop .15
6.1.1 General.15
6.1.2 Relief valves .15
6.1.3 Bursting discs .15
6.2 Back pressure consideration .16
6.3 Heat transfer .16
7 Sizing of pressure relief devices .17
7.1 General .17
7.2 Sizing of pressure relief valves .17
7.2.1 Discharge capacity.17
7.2.2 Determination of critical vs. subcritical flow for gases .18
7.2.3 Critical flow .18
7.2.4 Subcritical flow .19
7.2.5 Recommended analysis method .20
7.2.6 Example .22
7.3 Sizing of bursting discs .26
7.3.1 Discharge capacity.26
ISO 21013-3:2016(E)
7.3.2 Determination of critical vs. subcritical flow for gases .27
7.3.3 Critical flow .27
7.3.4 Subcritical flow .27
7.3.5 Recommended analysis method .28
7.3.6 Example .31
Annex A (informative) Cryostats .34
Bibliography .35
iv © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 220, Cryogenic vessels.
This second edition cancels and replaces the first edition (ISO 21013-3:2006), which has been
technically revised.
ISO 21013 consists of the following parts, under the general title Cryogenic vessels — Pressure-relief
accessories for cryogenic service:
— Part 1: Reclosable pressure-relief valves
— Part 2: Non-reclosable pressure-relief devices
— Part 3: Sizing and capacity determination
— Part 4: Pressure-relief accessories for cryogenic service
INTERNATIONAL STANDARD ISO 21013-3:2016(E)
Cryogenic vessels — Pressure-relief accessories for
cryogenic service —
Part 3:
Sizing and capacity determination
1 Scope
This part of ISO 21013 provides separate calculation methods for determining the required mass flow
to be relieved for each of the following specified conditions:
— vacuum-insulated vessels with insulation system (outer jacket + insulating material) intact under
normal vacuum, outer jacket at ambient temperature, inner vessel at temperature of the contents at
the specified relieving pressure;
— vacuum-insulated vessels with insulation system (outer jacket + insulating material) intact under
normal vacuum, outer jacket at ambient temperature, inner vessel at temperature of the contents at
the specified relieving pressure, pressure regulator of the pressure build-up system functioning at
full potential;
— vacuum or non-vacuum-insulated vessels with insulation system remaining in place, but with loss of
vacuum in the case of vacuum-insulated vessels, outer jacket at ambient temperature, inner vessel at
temperature of the contents at the specified relieving pressure or vacuum or non-vacuum-insulated
vessels with insulation system remaining fully or partially in place, but with loss of vacuum in the
case of vacuum-insulated vessels, fire engulfment, inner vessel at temperature of the contents at the
specified relieving pressure;
— vacuum-insulated vessels containing fluids with saturation temperature below 75 K at 1 bar
with insulation system remaining in place, but with loss of vacuum with air or nitrogen in the
vacuum space;
— vacuum insulated vessels containing fluids with saturation temperature below 75 K at 1 bar with
insulation system remaining in place, but with loss of vacuum with air or nitrogen in the vacuum
space with fire engulfment;
— vessels with insulation system totally lost and fire engulfment.
Good engineering practice based on well-established theoretical physical science needs to be adopted
to determine the required mass flow where an appropriate calculation method is not provided for an
applicable condition.
Recommendations for pressure relief devices for cryostats are given in Annex A.
2 Normative references
There are no normative references in this document.
ISO 21013-3:2016(E)
3 Symbols
A arithmetic mean of inner and outer surface areas of vessel insulating material m
A actual flow area of a pipe element m
B
A total outer surface area of pipe network between the outer jacket and location xm
e
A minimum flow area (reference area) in a pipe network m
F
A minimum flow area (reference area) in the pipe network, downstream of m
Fd
relief valve
A minimum flow area (reference area) in the pipe network, upstream of relief valvem
Fu
A total outside surface area of inner vessel m
i
A total outer surface area of pipe network between the inner and outer jackets m
j
(interspace)
A larger flow area of a pipe element containing two different flow area sizes m
L
A cross-sectional area, support, or pipe material m
n
A area ratio, A /A —
R S L
A smaller flow area of a pipe element containing two different flow area sizes m
S
A actual flow (orifice) area of a pressure relief valve mm
V
A actual flow (orifice) area of pressure relief valve selected for final analysis mm
Va
A minimum required relief valve flow (orifice) area mm
V1
A external heat transfer surface area of ambient air vaporizer m
c constant pressure specific heat capacity at the average of T and T kJ/(kg·K)
p n e
C experimentally determined flow rate through a pipe element or device gal/min/psi
V
e nominal insulating material thickness, normal vacuum, non-fire condition m
e minimum insulating material thickness, considering loss of vacuum, non-fire m
condition
e insulating material thickness remaining in place during fire conditions m
f pipe flow friction coefficient —
T
h enthalpy of fluid at conditions of ν kJ/kg
h specific enthalpy at relief valve inlet and outlet kJ/kg
r
K flow resistance coefficient of a pipe element in terms of A —
A F
K flow resistance coefficient of a pipe element in terms of A —
B B
K subcritical flow coefficient —
b
K derated coefficient of discharge —
dr
2 © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
K derated coefficient of discharge of next largest available valve orifice area —
dr,a
greater than A
V1
K derated coefficient of discharge of initially analyzed valve —
dr,1
k mean thermal conductivity of an individual support or pipe, between T and T W/(m·K)
n a
K flow resistance coefficient of complete pipe network in terms of reference —
R
area, A
F
K flow resistance coefficient at the transition between critical and subcritical flow—
RC
K overall flow resistance coefficient of pipe network, downstream of pressure —
Rd
relief valve
K overall flow resistance coefficient of pipe network, upstream of pressure —
Ru
relief valve
K total flow resistance coefficient of a series or parallel pipe network —
SUM
K experimentally determined flow rate through a pipe element or device m /h/bar
V
k mean thermal conductivity of insulating material, normal vacuum, non-fire W/(m·K)
condition
k mean thermal conductivity of insulating material with air or gaseous lading, W/(m·K)
non-fire condition
L latent heat of vaporization of cryogenic liquid at relieving conditions kJ/kg
l length, pipe element m
L latent heat of vaporization of cryogenic liquid at a pressure of 1,013 bar kJ/kg
a
l length of support or pipe in vacuum interspace m
n
L’ enthalpy-to-volume expansion ratio for critical or all-gas fluid flow conditions kJ/kg
M molar mass kg/mol
m maximum mass capacity of vessel kg
max
N normal evaporation rate (NER) %/day
P relieving pressure, inner vessel bar
P pressure, safety relief valve outlet bar
b
P pressure at relief valve outlet for a downstream built-up backpressure of 10 % bar
b10
P pressure at pipe network exit bar
exit
P pressure, safety relief valve inlet bar
i
P pressure relief valve set pressure bar
S
Q mass flow rate kg/h
m
Q mass flow rate of a relief valve within a given pipe network kg/h
ma
Q mass flow rate due to the normal evaporation rate kg/h
mNER
ISO 21013-3:2016(E)
R universal gas constant J/(mol·K)
r pipe elbow transition radius m
T relieving temperature, inner vessel K
T maximum external ambient temperature, non-fire condition K
a
T temperature at relief valve outlet K
b,Pb
T temperature at relief valve outlet for a downstream built-up backpressure K
b10
of 10 %
T external temperature for a given condition K
e
T temperature at pipe network exit K
exit,Pb
T external temperature, fire condition K
f
T temperature, safety relief valve inlet K
i
T temperature of fluid at a given flow start location along the pipe network K
n
T saturation temperature of fluid at a pressure of 1 bar K
sat
T temperature of fluid at a given location x along the pipe network K
x
U overall heat transfer coefficient of a pipe network for given temperature W/ (m ·K)
p
conditions
U heat transfer coefficient of insulating material, normal vacuum, non-fire W/ (m ·K)
condition
U overall convective heat transfer coefficient of ambient air vaporizer W/ (m ·K)
U heat transfer coefficient of insulating material with air or gaseous lading, non- W/ (m ·K)
fire condition
U heat transfer coefficient, air or nitrogen condensation, loss of vacuum, non-fire W/m
3a
condition
U heat transfer coefficient of insulating material with air or gaseous lading, fire W/ (m ·K)
condition
U heat transfer coefficient, air or nitrogen condensation, loss of vacuum, fire W/m
5a
condition
w heat leak from an individual support or pipe W/K
n
W total heat transfer rate for specified conditions Watt [W]
T
W total heat transfer rate under normal operation Watt [W]
T1
W total NER heat transfer rate under normal operation Watt [W]
T1NER
W total heat transfer rate under normal operation, including pressure build-up Watt [W]
T2
device
W total NER heat transfer rate under normal operation, including pressure build- Watt [W]
T2NER
up device
4 © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
W total heat transfer rate, loss of vacuum, insulation in place, non-fire condition, Watt [W]
T3
T ˃ 75 K
sat
W total heat transfer rate, loss of vacuum, insulation in place, non-fire condition, Watt [W]
T3a
T ≤ 75 K
sat
W total heat transfer rate, loss of vacuum, insulation in place, fire condition, Watt [W]
T5
T ˃ 75 K
sat
W total heat transfer rate, loss of vacuum, insulation in place, fire condition, Watt [W]
T5a
T ≤ 75 K
sat
W total heat transfer rate, loss of vacuum, insulation not in place, fire condition Watt [W]
T6
W heat transfer rate through insulation system, normal vacuum, non-fire conditionWatt [W]
W heat transfer rate through pressure build-up device, fully open regulator Watt [W]
W heat transfer rate through insulation system, loss of vacuum, non-fire conditionWatt [W]
W heat transfer rate through air or nitrogen condensation, loss of vacuum, non- Watt [W]
3a
fire condition
W heat transfer rate through interspace supports and piping Watt [W]
W heat transfer rate through vessel walls, insulation in place, fire condition Watt [W]
W heat transfer rate through air or nitrogen condensation, loss of vacuum, fire Watt [W]
5a
condition
W heat transfer rate through vessel walls, insulation not in place, fire condition Watt [W]
x lengthwise location along a pipe network m
X number of insulation layers —
Y heat transfer rate U or U —
3a 5a
Z compressibility factor at pressure, P , and temperature, T —
i i i
φ pressure ratio P /P —
exit
κ isentropic exponent —
λ subcritical flow coefficient —
λ subcritical flow coefficient —
ν specific volume of critical or all-gas fluid at a given temperature at pressure, P m /kg
ν specific volume at relief valve outlet for a downstream built-up backpres- m /kg
b10
sure of 10 %
ν specific volume at pressure relief valve outlet, evaluated at h and a trial m /kg
b,Pb r
value of P
b
ν maximum average downstream specific volume, as per desired backpres- m /kg
dmax
sure limit
ν average downstream specific volume, for a downstream built-up backpres- m /kg
d10
sure of 10 %
ISO 21013-3:2016(E)
ν specific volume at pipe network exit, evaluated at P and T m /kg
exit,Pb exit exit,Pb
ν specific volume at pipe network exit for a downstream built-up backpres- m /kg
exit10
sure of 10 %
ν specific volume of saturated gas at relieving pressure, P m /kg
g
ν specific volume of saturated gas at a pressure of 1,013 bar m /kg
ga
ν specific volume, safety relief valve inlet m /kg
i
ν specific volume of saturated liquid at relieving pressure, P m /kg
l
ν specific volume of saturated liquid at a pressure of 1,013 bar m /kg
la
ν average specific volume of flowing fluid upstream of pressure relief valve inlet m /kg
u
3/2 1/2
ψ expression for determining Q and T for critical or gas-full-vessel fluid flow m ·kg /kJ
m
conditions
4 Calculation of the total quantity of heat transferred per unit time from the hot
wall (outer jacket) to the cold wall (inner vessel)
4.1 General
P (in bar abs) is the actual relieving pressure inside the vessel which is used for calculating the required
mass flow through pressure relief devices.
T (in K) is the maximum ambient temperature for conditions other than fire (as specified, for example,
a
by a regulation or standard).
T (in K) is the external environment temperature under fire conditions which is taken to be 922 K in
f
this part of ISO 21013.
T (in K) is the relieving temperature in the vessel to be taken into account.
a) For subcritical fluids, T is the saturation temperature of the liquid at pressure, P.
b) For critical or supercritical fluids, T is calculated from 5.2.
4.2 Under conditions other than fire
4.2.1 Vacuum-insulated vessels under normal vacuum
W is the quantity of heat transferred per unit time (in watts) by heat leak through the insulation system.
WU=⋅AT −T (1)
()()
11 a
where
6 © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
U is the overall heat transfer coefficient of the insulating material under normal vacuum,
in W/(m ⋅K);
k
U = ;
e
k is the mean thermal conductivity of the insulating material under normal vacuum, between
T and T , in W/(m⋅K);
a
e is the nominal insulating material thickness, in metres;
A is the arithmetic mean of the inner and outer surface areas of the vessel insulating material,
in m .
4.2.2 Pressure build-up device
W is the quantity of heat transferred per unit time (in watts) by the pressure build-up device circuit
with the regulator fully open. W is determined from the type (ambient air, water or steam, electrical,
etc.) and design of the pressure build-up device circuit. For example, in the case of an ambient air
vaporizer.
WU=⋅AT −T (2)
()()
22 2 a
where
U is the overall convective heat transfer coefficient of the ambient air vaporizer, in W/(m ⋅K);
A is the external heat transfer surface area of the vaporizer, in m .
As a first approximation, the following may be used:
UT −TT=≤19000W/mfor 75K (3)
()
2 a
UT −TT=>2850W/mfor 75K (4)
()
2 a
4.2.3 Vacuum-insulated vessels in the case of loss of vacuum and non-vacuum insulated vessels
W is the quantity of heat transferred per unit time (in watts) by heat leak through the insulating
material.
WU=⋅AT −T (5)
()()
33 a
where
If the insulation is fully effective for conduction, convection, and radiation heat transfer at 328 K,
U may be calculated using Formula (6).
ISO 21013-3:2016(E)
k
U = (6)
e
U is the overall heat transfer coefficient of the insulating material when saturated with
gaseous lading or air at atmospheric pressure, whichever is greater, in W/(m ·K);
k is the mean thermal conductivity of the insulating material saturated with gaseous lading
or air at atmospheric pressure, whichever provides the greater coefficient, between
T and T , in W/(m·K). Values of k for gases are listed in Table 1;
a 3
e is the minimum insulating material thickness taking into account the manufacturing
tolerances or effects of sudden loss of vacuum, in metres.
NOTE This formula might not be applicable at temperatures below 75 K with a small thickness of insulating
material as the maximum heat transfer coefficient would be given by air condensation.
Vacuum space, gas space, or space occupied by the deteriorated insulation shall not be included in the
thickness of the insulation. The effectiveness of these spaces or deteriorated insulation in reducing
conduction, convection, or radiation heat transfer may be evaluated separately and included in
the overall heat transfer coefficient, U , using methods found in published heat transfer literature.
Deterioration of the insulation can be caused by the following:
— moisture condensation;
— air condensation;
— increase in the density of the insulation due to a sudden loss of vacuum.
Table 1 — Thermal conductivity for refrigerated (cryogenic) fluids at the mean temperature
between saturation and 328 K (k ) and 922 K (k ) at 1 bar
3 5
Fluid k [W/(m·K)] k [W/(m·K)]
3 5
Air 0,019 0,043
Argon 0,013 0,027
Carbon dioxide 0,017 0,039
Carbon monoxide 0,020 0,039
Helium 0,104 0,211
Hydrogen 0,116 0,217
Methane 0,024 0,074
Neon 0,034 0,067
Nitrogen 0,019 0,040
Oxygen 0,019 0,043
Krypton 0,007 0,015
Xenon 0,005 0,009
Ethane 0,016 0,064
Trifluoromethane 0,012 0,027
Ethylene (ethene) 0,015 0,056
Nitrous oxide 0,014 0,038
8 © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
4.2.4 Supports and piping
W is the quantity of heat transferred per unit time (in watts) by supports and piping located in the
interspace.
Ww=+ww++…+wT −T (7)
()()
41 23 na
where
w is the heat leak per degree K contributed by one of the supports or the pipes, in W/K.
n
 
A
n
wk= (8)
 
nn
l
 n 
k is the mean thermal conductivity of the support or pipe material between T and T , in
n a
W/(m⋅K);
A is the support or pipe section area, in m ;
n
l is the support or pipe length in the vacuum interspace, in metres.
n
4.3 Under fire conditions
4.3.1 Insulation system remains fully or partially in place during fire conditions
W is the quantity of heat transferred per unit time (in watts) by heat leak through the vessel walls.
08, 2
WT=⋅26, 922− ⋅⋅UA (9)
()
where
If the insulation is fully effective for conduction, convection, and radiation heat transfer for an
external temperature of 922 K, U may be calculated using Formula (10).
k
U = (10)
e
U is the overall heat transfer coefficient of the container-insulating material when saturated
with gaseous lading or air at atmospheric pressure, whichever is greater, in W/(m ·K);
k is the mean thermal conductivity of the insulating material saturated with gaseous lading
or air at atmospheric pressure, whichever provides the greater coefficient, between T and
922 K, in W/(m·K). Values of k for gases are listed in Table 1;
e is the thickness of the insulating material remaining in place during fire conditions, in metres;
A is the arithmetic mean of the inner and outer surface areas of the insulating material
remaining in place during fire conditions, in m .
Vacuum space, gas space, or space occupied by the deteriorated insulation shall not be included in the
thickness of the insulation. The effectiveness of these spaces or deteriorated insulation in reducing
conduction, convection, or radiation heat transfer may be evaluated separately and included in
the overall heat transfer coefficient, U , using methods found in published heat transfer literature.
Deterioration of the insulation can be caused by the following:
— moisture condensation;
— air condensation;
ISO 21013-3:2016(E)
— increase in the density of the insulation due to a sudden loss of vacuum;
— degradation due to heat.
If the outer jacket remains in place during fire conditions, but the insulating material is entirely
destroyed, U is equal to the overall heat transfer coefficient with gaseous lading or air at atmospheric
pressure in the space between the outer jacket and the inner vessel, whichever provides the greater
coefficient, between T and 922 K. A is equal to the mean surface area of the interspace.
4.3.2 Insulation system does not remain in place during fire conditions
W is the quantity of heat transferred per unit time (in watts) by heat leak through the vessel walls.
40,82
WA=⋅71, 10 ⋅ (11)
6 i
where
A is the total outside surface area of the inner vessel, in m .
i
The heat transferred by supports and piping located in the interspace can be neglected in this case.
4.4 Air or Nitrogen condensation
4.4.1 General
The air or nitrogen condensation case for the loss of vacuum condition shall be considered for fluids
with a saturation temperature below 75 K at 1 bar.
Air condensation, for the case of loss of vacuum to the atmosphere on a vacuum insulated container, is
highly dependent on the type of insulation and how the insulation is designed. Since air condensation
occurs primarily below 75 K, and fluids with saturation temperatures below 75 K are generally stored
and transported in containers insulated with multi-layer insulation, this part of ISO 21013 covers air
condensation on multi-layer insulated containers only. In the absence of pertinent reliable data on
perlite insulated vessels, 4.2.3, 4.3.1, and 4.3.2 shall be used with thermal conductivity values shown in
Table 1 increased by a factor of two in Formula (6) for k and Formula (10) for k , respectively.
3 5
Condensation of air on a multi-layer insulated surface below 75 K will depend on the rate of air access
to the insulated surface. On a multi-layer insulated container, the air condensation rate can vary
depending on the number of layers and the air access allowed by the design of the insulation.
Figure 1 provides heat transfer rates from air condensation to the stored fluid as a function of
the number of layers of insulation. The fire engulfment curve is an extrapolation for 922 K ambient
temperature. Unless heat transfer rates under the loss of vacuum condition from air condensation can
be determined for the same type and design of multi-layer insulation from prototype tests or actual
incidents, heat transfer rates from Figure 1 shall be used.
4.4.2 Loss of vacuum with air and nitrogen
W is the quantity of heat transferred per unit time (in watts) through air or nitrogen condensation for
3a
vacuum-insulated vessels in the case of a loss of vacuum with air or nitrogen.
WU=⋅A (12)
33aa i
where
U is the heat transfer through air or nitrogen condensation, in watts per square metre of the
3a
inner vessel outer surface area, from Figure 1.
10 © ISO 2016 – All rights reserved

ISO 21013-3:2016(E)
4.4.3 Fire with loss of vacuum with air or nitrogen
W is the quantity of heat transferred per unit time (in watts) through air or nitrogen condensation for
5a
vacuum-insulated vessels in the case of a fire and loss of vacuum with air or nitrogen.
08, 2
WU=⋅19, 5 ⋅A (13)
55aa i
where
U is the heat transfer through air or nitrogen condensation during fire conditions, in watts per
5a
square metre of the inner vessel surface area, from Figure 1.
Key
X number of insulation layers
Y heat transfer [W/m ]
07, 3
38400+⋅420 X
1 UY==
3a
07, 3
09, 6+X
07, 3
92160+⋅1000 X
2 UY==
5a
07, 3
09, 6+X
Figure 1 — Heat transfer rate for air or nitrogen condensation
ISO 21013-3:2016(E)
4.5 Heat transfer per unit time (watts)
4.5.1 General
The required mass flow rate, Q , to be relieved can be calculated from the heat transfer, W , for the
m T
following specified conditions, where W is the total heat transfer applicable to the specified condition.
T
4.5.2 Normal operation
WW=+W (14)
T1 14
Alternatively, the heat transfer rate, W , can be determined from the normal evaporation rate (NER).
T1NER
 
v
QL⋅ 
ga
mNER a
W =   (15)
TN1 ER  
 
36, v −v
 
ga la
 
where
Q is the mass flow rate due to the normal evaporation rate, in kg/h;
mNER
L is the latent heat of vaporization of the cryogenic liquid at a pressure of 1,013 bar, in kJ/kg;
a
ν is the specific volume of saturated gas at a saturation pressure of 1,013 bar, in m /kg;
ga
ν is the specific volume of saturated liquid at a saturation pressure of 1,013 bar, in m /kg;
la
W is the total heat leak cal
...