EN ISO 21013-3:2026

• Abstract:

  This document specifies calculation methods for determining the required mass flow to be relieved for each specified conditions described in Table 1.; Recommendations for pressure relief devices for cryostats are given in Annex A.

• Status: Published
• Publication Date: 20-Oct-2026
• ICS: 23.020.40 - Cryogenic vessels
• Technical Committee: CEN/TC 268 - Cryogenic vessels
• Drafting Committee: CEN/TC 268 - Cryogenic vessels
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 21-Oct-2026
• Completion Date: 21-Oct-2026
• Directive: 2008/68/EC - Directive 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
• Mandate: M/071 - Mandate to CEN for standardization in the field of Pressure equipment
• Mandate: M/601 - COMMISSION IMPLEMENTING DECISION of 1.3.2024 on a standardisation request to the European Committee for Standardization and the European Committee for Electrotechnical Standardization as regards pressure equipment and assemblies in support of Directive 2014/68/EU of the European Parliament and of the Council
• Mandate: M/TDG - Standards for referencing in the RID-ADR
• Ref Project: SIST EN ISO 21013-3:2026 - Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination (ISO 21013-3:2026)

• Replaces: EN ISO 21013-3:2016 - Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination (ISO 21013-3:2016)
• Effective Date: 18-Jan-2023
• Referred By: EN 13648-2:2002 - Cryogenic vessels - Safety devices for protection against excessive pressure - Part 2: Bursting disc safety devices for cryogenic service
• Effective Date: 28-Oct-2026
• Referred By: EN 13458-2:2002 - Cryogenic vessels - Static vacuum insulated vessels - Part 2: Design, fabrication, inspection and testing
• Effective Date: 28-Oct-2026
• Referred By: EN 14398-1:2003 - Cryogenic vessels - Large transportable non-vacuum insulated vessels - Part 1: Fundamental requirements
• Effective Date: 28-Oct-2026
• Referred By: EN 14398-2:2003+A2:2008 - Cryogenic vessels - Large transportable non-vacuum insulated vessels - Part 2: Design, fabrication, inspection and testing
• Effective Date: 28-Oct-2026
• Consolidated By: ISO 21013-3:2026 - Cryogenic vessels — Pressure-relief accessories for cryogenic service — Part 3: Sizing and capacity determination
• Effective Date: 12-Feb-2026

EN ISO 21013-3:2026 is a CEN standard for cryogenic vessels that covers pressure-relief accessories for cryogenic service. It specifies calculation methods for the mass flow that must be relieved under defined conditions, so designers can size pressure relief valves and bursting discs and check the effect of piping, heat leak, loss of vacuum, and fire cases.

What does EN ISO 21013-3:2026 specify?

EN ISO 21013-3:2026 specifies separate calculation methods for determining the required mass flow to be relieved for the conditions listed in the standard’s condition table. It also gives recommendations for pressure relief devices for cryostats in Annex A.

The document is organized into:

• Clause 1 Scope
• Clause 2 Normative references
• Clause 3 Symbols
• Clause 4 Heat transfer calculations
• Clause 5 Mass flow to be relieved
• Clause 6 Piping for pressure relief devices
• Clause 7 Sizing of pressure relief devices
• Annex A on cryostats
• Annex ZA on the relationship with the Pressure Equipment Directive
• Bibliography

Annex	What it covers
Annex A	Cryostats and design recommendations for their pressure relief devices
Annex ZA	Relationship between this European Standard and Directive 2014/68/EU

In practice, the standard is about turning operating and upset conditions into a required discharge capacity, then using that requirement to size the relief system.

What are the key requirements of EN ISO 21013-3:2026?

EN ISO 21013-3:2026 builds the sizing method in three steps: estimate heat input, convert that heat input into required mass flow, then verify that the complete relief path can pass that flow. The clause structure matters because it separates vessel heat loads, piping effects, and the final device sizing.

Heat transfer cases in Clause 4

Clause 4 covers the heat transferred from the warm side to the cold side of the vessel in the main service cases. EN ISO 21013-3:2026 distinguishes normal operation, pressure build-up device operation, loss of vacuum, fire exposure, and air or nitrogen condensation.

In practice, this means you do not size a relief device from one generic heat load. You choose the case that matches the vessel construction and upset condition, because different insulation states and different ambient conditions can change the required relieving capacity.

Fire and pressure build-up conditions

Clause 4 treats fire as a separate case, using an external fire temperature of 922 K, and it also requires pressure build-up device conditions to be considered. The text notes that fire may not be the worst case, so fire and PBU conditions both have to be checked.

In practice, a vessel that is safe for normal service can still need a larger relief system for fire exposure or for a pressure build-up circuit. If the PBU arrangement changes later in the field, the sizing needs to be reviewed again.

Loss of vacuum and low-temperature condensation

Clause 4 also covers loss of vacuum and, for fluids with a saturation temperature below 75 K at 1 bar, air or nitrogen condensation. The document applies this to multi-layer insulated containers and gives guidance for handling other insulation types.

In practice, this matters for very cold fluids such as liquid hydrogen. The relief load may be governed by condensation and insulation performance rather than by the vessel contents alone.

Converting heat load to mass flow in Clause 5

Clause 5 turns total heat transfer into the mass flow to be relieved. For pressures below the critical pressure, the method is based on heat input or on normal evaporation rate. For pressures at or above the critical pressure, it uses the relieving temperature approach with thermophysical properties.

In practice, the relieving pressure determines which calculation route to use. That choice affects the discharge rate that must be met by the relief device.

Piping effects in Clause 6

Clause 6 requires pressure drop, back pressure, and heat transfer in the piping to be taken into account. The text also says that if piping between the outer jacket and the safety relief device is longer than 0.6 m, heat transfer to the flowing fluid must be included.

In practice, the relief valve or bursting disc cannot be sized in isolation. The upstream and downstream piping can reduce capacity, increase back pressure, and change the fluid temperature before discharge.

Final sizing in Clause 7

Clause 7 gives separate sizing methods for pressure relief valves and bursting discs. It distinguishes critical and subcritical gas flow, requires the selected device capacity to meet or exceed the required mass flow, and explains how to combine multiple devices when they discharge together.

In practice, the selected orifice or net flow area must match the actual system conditions, including inlet pressure drops and outlet back pressure. For bursting discs, the flow resistance of the complete pipe network is part of the sizing check.

Cryostat-specific guidance in Annex A

Annex A adds cryostat-specific recommendations. It says to include heat generated by upset process conditions, and it gives design advice on gas space volume, set pressure, outlet pressure, and certified flow area after rupture for bursting discs.

In practice, cryostats can need extra attention because process upsets can add heat load and create mixed flow in the relief piping.

What terms does EN ISO 21013-3:2026 define?

• NER - Normal evaporation rate, the fraction of vessel mass that evaporates per day and can be used as an alternate basis for heat leak.
• PBU - Pressure build-up, the condition where a pressure build-up device adds heat input to the system.
• Relieving pressure, P - The absolute inner-vessel pressure used to calculate required relief capacity.
• Critical flow - A gas or vapour flow regime where lowering outlet pressure no longer increases discharge capacity.
• Subcritical flow - A gas flow regime where outlet pressure still influences the discharge capacity.
• Built-up back pressure - The pressure rise at the relief outlet caused by flow through the downstream piping and fittings.
• Coefficient of discharge, Kd - The discharge coefficient used in valve capacity calculations, with a derated form used in the sizing equations.

Who uses EN ISO 21013-3:2026?

EN ISO 21013-3:2026 is used by engineers who design cryogenic vessels, pressure-relief systems, and the piping connected to them. It is also used by manufacturers and suppliers of pressure relief valves and bursting discs when they need to rate device capacity for a specific cryogenic application.

Quality managers, buyers, and certifiers use it to check that a proposed relief system has been sized against the correct vessel condition and that piping effects have been considered. It is particularly relevant in cryogenic industries such as liquid hydrogen, helium, nitrogen, oxygen, and other low-temperature storage and transport applications. Cryostat designers use Annex A when the vessel protects low-temperature test or operating equipment such as superconducting devices.

What changed in EN ISO 21013-3:2026 from the previous edition?

EN ISO 21013-3:2026 is the third edition and it cancels and replaces ISO 21013-3:2016. The foreword says the document was technically revised.

The changes stated in the document are:

• precision added on the total outer surface area of the pipe network containing flow of fluid
• inclusion of the coefficient of discharge symbol
• precision added on the overall convective heat transfer coefficient of the ambient air vaporizer
• additional information added on the fire case and PBU conditions
• correction of the molar mass in kg/kmol and modification of formulas 32 and 43
• supplementary information added on cryostats

Which standards are used with EN ISO 21013-3:2026?

The document lists no normative references. Its bibliography names these related pressure-relief standards:

• ISO 4126-1 - safety valves for protection against excessive pressure
• ISO 4126-6 - application, selection, and installation of bursting disc safety devices
• ISO 4126-10 - sizing of safety valves and bursting discs for gas/liquid two-phase flow

These references help readers place EN ISO 21013-3:2026 in the wider pressure-relief family, especially when comparing valve sizing, disc selection, and two-phase flow practice.

What does the EN ISO 21013-3:2026 document contain?

EN ISO 21013-3:2026 contains the calculation framework, symbols, thermophysical-property tables, and worked methods needed to size relief devices for cryogenic vessels. It includes tables for fluid properties, pipe friction and transition resistance, and flow coefficients used in the sizing equations.

The document also contains a figure for air or nitrogen condensation, examples for relief valve sizing and bursting disc sizing, and detailed pipe-network analysis steps. Annex A adds cryostat-specific design guidance, while Annex ZA maps the European standard to Directive 2014/68/EU for pressure equipment.

SLOVENSKI STANDARD
01-december-2026
Nadomešča:
SIST EN ISO 21013-3:2016
Kriogene posode - Oprema za razbremenitev tlaka za kriogeno območje - 3. del:
Določanje velikosti in pretoka (ISO 21013-3:2026)
Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and
capacity determination (ISO 21013-3:2026)
Kryo-Behälter - Druckentlastungseinrichtungen für den Kryo-Betrieb - Teil 3:
Bestimmung von Größe und Durchfluss (ISO 21013-3:2026)
Récipients cryogéniques - Dispositifs de sécurité pour le service cryogénique - Partie 3:
Détermination de la taille et du volume (ISO 21013-3:2026)
Ta slovenski standard je istoveten z: EN ISO 21013-3:2026
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
October 2026
EUROPÄISCHE NORM
ICS 23.020.40 Supersedes EN ISO 21013-3:2016
English Version
Cryogenic vessels - Pressure-relief accessories for
cryogenic service - Part 3: Sizing and capacity
determination (ISO 21013-3:2026)
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 21013-3:2026) Durchfluss (ISO 21013-3:2026)
This European Standard was approved by CEN on 26 September 2026.

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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2026 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 21013-3:2026 E
worldwide for CEN national Members.

Contents Page
European foreword . 3
Annex ZA (informative) Relationship between this European Standard and the essential
requirements of Directive 2014/68/EU aimed to be covered . 4

European foreword
This document (EN ISO 21013-3:2026) 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 April 2027, and conflicting national standards
shall be withdrawn at the latest by April 2027.
Attention is drawn to the possibility that some of the elements of this document may be the subject
of patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 21013-3:2016.
This document has been prepared under a standardization request addressed to CEN by the
European Commission. The Standing Committee of the EFTA States subsequently approves these
requests for its Member States.
For the relationship with EU Legislation, see informative Annex ZA, which is an integral part of this
document.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
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, France, Germany, Greece, Hungary,
Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Türkiye and the United Kingdom.
Endorsement notice
The text of ISO 21013-3:2026 has been approved by CEN as EN ISO 21013-3:2026 without any
modification.
Annex ZA
(informative)
Relationship between this European Standard and the essential
requirements of Directive 2014/68/EU aimed to be covered
This European Standard has been prepared under a Commission’s standardization request M/601
to provide one voluntary means of conforming to essential requirements of Directive 2014/68/EU
on the harmonization of the laws of the Member States relating to the making available on the
market of pressure equipment.
Once this standard is cited in the Official Journal of the European Union under that Directive,
compliance with the normative 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 Annex I of Directive
2014/68/EU
Essential Requirements of Clause(s)/sub- Remarks/Notes
Directive 2014/68/EU clause(s) of this EN
(Pressure Equipment
Directive)
2.10 4, 5 Protection against exceeding the
allowable limits of pressure
equipment for safety accessories
(2.10 b) e.g. alarms and
indicators are excluded)
2.11.2 6, 7 Pressure limiting devices
2.12 4.3 External fire only for suitable
accessories and not for pressure
equipment design
WARNING 1 Presumption of conformity stays valid only as long as a reference to this European
Standard is maintained in the list published in the Official Journal of the European Union. Users of
this standard should consult frequently the latest list published in the Official Journal of the
European Union.
WARNING 2 Other Union legislation may be applicable to the product(s) falling within the
scope of this standard.
International
Standard
ISO 21013-3
Third edition
Cryogenic vessels — Pressure-relief
2026-09
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 21013-3:2026(en) © ISO 2026

ISO 21013-3:2026(en)
© ISO 2026
All rights reserved. Unless otherwise specified, or required in the context of its implementation, 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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
ISO 21013-3:2026(en)
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 2
3 Terms, definitions and symbols . 2
3.1 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 .7
4.2.1 Vacuum-insulated vessels under normal vacuum .7
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 . .8
4.2.4 Supports and piping.9
4.3 Under fire conditions .10
4.3.1 Insulation system remains fully or partially in place during fire conditions .10
4.3.2 Insulation system does not remain in place during fire conditions .10
4.4 Air or nitrogen condensation . .11
4.4.1 General .11
4.4.2 Loss of vacuum with air and nitrogen .11
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 . 13
4.5.4 Loss of vacuum condition . 13
4.5.5 Fire condition with loss of vacuum, vacuum jacket, and insulation fully or
partially in place .14
4.5.6 Fire condition with loss of vacuum, insulation not in place .14
4.5.7 Total heat transfer rate .14
5 Calculation of the mass flow to be relieved by pressure relief devices . 14
5.1 Relieving pressure, P, less than the critical pressure .14
5.2 Relieving pressure, P, equal to or greater than the critical pressure . 15
5.3 Example . 15
6 Piping for pressure relief devices .16
6.1 Pressure drop .16
6.1.1 General .16
6.1.2 Relief valves .16
6.1.3 Bursting discs .16
6.2 Back pressure consideration . .17
6.3 Heat transfer .17
7 Sizing of pressure relief devices .18
7.1 General .18
7.2 Sizing of pressure relief valves.18
7.2.1 Discharge capacity .18
7.2.2 Determination of critical vs. subcritical flow for gases .19
7.2.3 Critical flow .19
7.2.4 Subcritical flow .19
7.2.5 Recommended analysis method . 20
7.2.6 Example . 22
7.3 Sizing of bursting discs .27
7.3.1 Discharge capacity .27
7.3.2 Determination of critical vs. subcritical flow for gases . 28

iii
ISO 21013-3:2026(en)
7.3.3 Critical flow . 28
7.3.4 Subcritical flow . 28
7.3.5 Recommended analysis method . 29
7.3.6 Example .32
Annex A (informative) Cryostats .36
Bibliography .37

iv
ISO 21013-3:2026(en)
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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 220, Cryogenic vessels, in collaboration with
the European Committee for Standardization (CEN) Technical Committee CEN/TC 268, Cryogenic vessels
and specific hydrogen technologies applications, in accordance with the Agreement on technical cooperation
between ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 21013-3:2016), which has been technically
revised.
The main changes are as follows:
— precision added on the total outer surface area of the pipe network containing flow of fluid;
— inclusion of the symbol of coefficient of discharge;
— precision added on the overall convective heat transfer coefficient of the ambient air vaporizer,
— additional information added on the fire case and PBU conditions;
— correction of the molar mass in kg/kmol and modification of Formulae (32) and (43);
— supplementary information added on cryostats.
A list of all parts in the ISO 21013 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

v
International Standard ISO 21013-3:2026(en)
Cryogenic vessels — Pressure-relief accessories for cryogenic
service —
Part 3:
Sizing and capacity determination
1 Scope
This document specifies calculation methods for determining the required mass flow to be relieved for each
specified conditions described in Table 1.
a
Table 1 — Subclause required for calculating mass flow rate based on specified condition
Insulation
Type of system (outer Pressure
Use clauses
insu- Vacuum Inner vessel jacket + Ambient buildup
Condition including any
lation status temperature insulating conditions system
subclauses
system material) condition
condition
normal
(ambient 4.2.3,4.2.4, 4.5.1,
1 intact
tempera- 4.5.2, 4.5.7, 5, 6, 7
non-
ture)
N/A
vacuum
normal
fully or
condition 4.3.1, 4.5.1, 4.5.7, 5,
2 partially in fire (922 K)
6, 7
tempera- place
ture of the
4.2.1, 4.2.4, 4.5.1,
contents at
4.5.2, 4.5.7, 5, 6, 7
the specified
normal
normal
4.2.1, 4.2.2, 4.2.4,
relieving
(ambient
4 intact full open 4.5.1, 4.5.3, 4.5.7, 5,
pressure
tempera-
6, 7
ture)
4.2.3, 4.2.4, 4.5.1,
4.5.4, 4.5.7 ,5, 6, 7
loss of
fully or
vacuum vacuum
4.3.1, 4.4.3, 4.5.1,
6 partially in fire (922 K)
4.5.5, 4.5.7, 5, 6, 7
place
normal
(ambient 4.4.2, 4.5.1, 4.5.4,
7 normal
loss of
tempera- 4.5.7, 5, 6 ,7
condition
intact
vacuum
ture)
contents with
with air or
relieving 4.4.3, 4.5.1, 4.5.5,
8 nitrogen
temperature 4.5.7, 5, 6, 7
in the
below 75 K
Vacuum
vacuum
fire (922 K)
and 4.5.1, 4.5.6, 4.5.7, 5,
space
9 totally lost
non- 6, 7
vacuum
When no appropriate calculation method is provided for a condition, the required mass flow is determined using good engineering
practice based on well-established theoretical physical science.
Recommendations for pressure relief devices for cryostats are given in Annex A.

ISO 21013-3:2026(en)
2 Normative references
There are no normative references in this document.
3 Terms, definitions and symbols
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1 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 the pipe network containing flow of fluid, from the outer m
e
jacket up to the flow temperature location x under consideration; applicable only
when l > 0,6 m (See 6.1.1)
A minimum flow area (reference area) in a pipe network m
F
A minimum flow area (reference area) in the pipe network, downstream of relief valve m
Fd
A minimum flow area (reference area) in the pipe network, upstream of relief valve m
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 experimentally determined flow rate through a pipe element or device m /h
V
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 coefficient of discharge —
d
ISO 21013-3:2026(en)
K derated coefficient of discharge —
dr
K derated coefficient of discharge of next largest available valve orifice area greater —
dr,a
than A
V1
K derated coefficient of discharge of initially analysed valve —
dr,1
K flow resistance coefficient of complete pipe network in terms of reference area, A —
R 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 relief —
Rd
valve
K overall flow resistance coefficient of pipe network, upstream of pressure relief valve —
Ru
K total flow resistance coefficient of a series or parallel pipe network —
SUM
3 1)
K experimentally determined flow rate through a pipe element or device m /h/bar
V
L latent heat of vaporization of cryogenic liquid at relieving conditions kJ/kg
1)
L latent heat of vaporization of cryogenic liquid at a pressure of 1,013 bar kJ/kg
a
L’ enthalpy-to-volume expansion ratio for critical or all-gas fluid flow conditions kJ/kg
M molar mass kg/kmol
N normal evaporation rate (NER) %/day
P relieving pressure, inner vessel in absolute pressure bar
P pressure, safety relief valve outlet in absolute pressure bar
b
P pressure at relief valve outlet for a downstream built-up backpressure of 10 % bar
b10
P pressure at pipe network exit in absolute pressure bar
exit
P pressure, safety relief valve inlet in absolute pressure bar
i
P pressure relief valve set pressure in absolute 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
R universal gas constant J/(mol·K)
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 of 10 % K
b10
T external temperature for a given condition K
e
5 2
1) bar = 0,1 MPa = 10 Pa; 1 MPa = 1 N/mm .

ISO 21013-3:2026(en)
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 heat transfer coefficient of insulating material, normal vacuum, non-fire condition W/ (m ·K)
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-fire W/ (m ·K)
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 condition W/m
5a
U overall heat transfer coefficient of a pipe network for given temperature conditions W/ (m ·K)
p
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 device Watt [W]
T2
W total NER heat transfer rate under normal operation, including pressure build-up Watt [W]
T2NER
device
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, T ˃ 75 K Watt [W]
T5 sat
W total heat transfer rate, loss of vacuum, insulation in place, fire condition, T ≤ 75 K Watt [W]
T5a 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 condition Watt [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 condition Watt [W]
W heat transfer rate through air or nitrogen condensation, loss of vacuum, Watt [W]
3a
non-fire condition
W heat transfer rate through interspace supports and piping Watt [W]
ISO 21013-3:2026(en)
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, Watt [W]
5a
fire condition
W heat transfer rate through vessel walls, insulation not in place, fire condition Watt [W]
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
a
c constant pressure specific heat capacity at the average of T and T kJ/(kg·K)
p n e
e nominal insulating material thickness, in 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 mean thermal conductivity of insulating material, normal vacuum, W/(m·K)
non-fire condition
k mean thermal conductivity of insulating material with air or gaseous lading, W/(m·K)
non-fire condition
k mean thermal conductivity of an individual support or pipe, between T and T W/(m·K)
n a
l length, pipe element m
l length of support or pipe in vacuum interspace m
n
m maximum mass capacity of vessel kg
max
r pipe elbow transition radius m
x lengthwise location along a pipe network m
φ —
PP P
exit exit
pressure ratio 1
P P
κ isentropic exponent —
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 backpressure of 10 % m /kg
b10
ν specific volume at pressure relief valve outlet, evaluated at h and a trial value of P m /kg
b,Pb r b
ISO 21013-3:2026(en)
ν average downstream specific volume, for a downstream built-up backpressure m /kg
d10
of 10 %
ν maximum average downstream specific volume, as per desired backpressure limit m /kg
dmax
ν specific volume at pipe network exit for a downstream built-up backpressure of 10 % m /kg
exit10
ν specific volume at pipe network exit, evaluated at P and T m /kg
exit,Pb exit exit,Pb
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 /
m
conditions kJ
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 absolute) 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, by a
a
regulation or standard).
T (in K) is the external environment temperature under fire conditions which is taken to be 922 K in this
f
document.
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.

ISO 21013-3:2026(en)
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, as
per Formula (1).
WUAT T (1)

11 a
where
U is the overall heat transfer coefficient of the insulating material under normal vacuum, in W/
k
(m ⋅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 m;
A is the arithmetic mean of the inner and outer surface areas of the vessel insulating material, in
m ;
T is the relieving temperature, inner vessel;
T is the maximum external ambient temperature, non-fire condition.
a
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, W is
calculated using Formula (2):
WUAT 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 ;
T is the relieving temperature, inner vessel;
T is the maximum external ambient temperature, non-fire condition.
a
As a first approximation, Formula (3) or Formula (4) may be used:
UT TT19 000 W/mfor 75K (3)

2 a
UT TT2 850 W/mfor 75K (4)

2 a
U shall not be lower than the values proposed but manufacturers can use greater values if their design
requires.
ISO 21013-3:2026(en)
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. It
is calculated using Formula (5):
WUAT T (5)

33 a
where
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);
T is the relieving temperature, inner vessel;
T is the maximum external ambient temperature, non-fire condition;
a
A is the arithmetic mean of inner and outer surface areas of vessel insulating material.
If the insulation is fully effective for conduction, convection, and radiation heat transfer at 328 K, U may be
calculated using Formula (6):
k
U = (6)
e
where
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 2);
a 3
e is the minimum insulating material thickness taking into account the manufacturing
tolerances or effects of sudden loss of vacuum, in m.
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.

ISO 21013-3:2026(en)
Table 2 — 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
k k
3 5
Fluid
[W/(m·K)] [W/(m·K)]
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
Values are for reference only. Use fluid properties given in current databases, such as from NIST.
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, given by Formula (7):
WwwwwT 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, given by
n
Formula (8):
 A 
n
wk (8)
 
nn
 
l
 
n
where
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 m.
n
ISO 21013-3:2026(en)
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, given by
Formula (9):
08, 2
WT26, 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
where
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 2);
e is the thickness of the insulating material remaining in place during fire conditions, in m;
A is the arithmetic mean of the inner and outer surface areas of the insulating material
remaining in place during fire conditions, in m ;
T is the relieving temperature, inner vessel.
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;
— 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,
calculated using Formula (11):
40,82
WA71, 10  (11)
6 i
where A is the total outside surface area of the inner vessel, in m .
i
ISO 21013-3:2026(en)
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
...