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)

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/DIS 21013-3:2025)

Récipients cryogéniques - Dispositifs de sécurité pour le service cryogénique - Partie 3: Détermination de la taille et du volume (ISO/DIS 21013-3:2025)

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 kriogeno območje - 3. del: Določanje velikosti in pretoka (ISO/DIS 21013-3:2025)

General Information

• Status: Not Published
• Public Enquiry End Date: 02-May-2025
• ICS: 13.240 - Protection against excessive pressure
• ICS: 23.020.40 - Cryogenic vessels
• Technical Committee: TLP - Pressure vessels
• Current Stage: 4020 - Public enquire (PE) (Adopted Project)
• Start Date: 20-Feb-2025
• Due Date: 10-Jul-2025
• Completion Date: 30-Apr-2025
• 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
• 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: prEN ISO 21013-3 - Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and capacity determination (ISO/DIS 21013-3:2025)

Relations

• Revises: SIST 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: 01-Apr-2025

Overview

prEN ISO 21013-3 (ISO/DIS 21013-3:2025) specifies methods for sizing and capacity determination of pressure‑relief accessories for cryogenic vessels. This draft international standard updates ISO 21013-3:2016 and provides calculation procedures to determine the required mass flow to be relieved under a range of realistic operating and fault conditions, including normal operation, loss of vacuum, pressure‑build‑up systems, and fire engulfment. Annex A gives recommendations specific to cryostats.

Key topics and requirements

• Calculation of heat transfer from outer jacket (hot wall) to inner vessel (cold wall) under multiple scenarios, including:
  • Vacuum‑insulated vessels with intact insulation under normal vacuum
  • Vacuum‑insulated vessels with active pressure‑build‑up (PBU) devices
  • Loss of vacuum or non‑vacuum‑insulated vessels, with and without fire
  • Special cases for fluids with saturation temperature below 75 K and air/nitrogen condensation
• Mass‑flow determination methods that convert heat input to vaporization mass flow to size relief devices
• Piping considerations for relief devices: pressure drop, back‑pressure effects, and heat transfer in pipe networks
• Sizing rules for pressure relief valves and bursting discs, including:
  • Determination of critical vs. subcritical flow regimes
  • Recommended analysis methods and worked examples
• Informative guidance: annex on cryostat relief devices and a relationship to the Pressure Equipment Directive (Annex ZA)
• Good engineering practice requirement where a specific calculation is not provided

Practical applications

• Designing and verifying pressure relief systems for LNG, liquid oxygen, liquid nitrogen, liquid helium and other cryogenic storage and transfer vessels
• Selecting and sizing relief valves, bursting discs, and piping to safely manage boil‑off and emergency venting loads
• Assessing safety for scenarios such as loss of vacuum, air ingress, nitrogen condensation, and fire engulfment
• Supporting compliance with regulatory frameworks (e.g., PED) and plant safety case documentation

Who should use this standard

• Cryogenic vessel designers and manufacturers
• Process, mechanical and safety engineers involved in LNG, industrial gas, and research cryogenics
• Stationary storage operators, tank farm and cryogenic piping engineers
• Certification bodies, notified bodies and regulators assessing pressure‑relief compliance

Related standards

• Other parts of the ISO 21013 series (see ISO website for full listing)
• Pressure equipment and safety standards referenced in Annex ZA (e.g., Pressure Equipment Directive guidance)

Keywords: cryogenic vessels, pressure-relief, sizing, capacity determination, vacuum-insulated, loss of vacuum, fire conditions, relief valves, bursting discs, cryostats, ISO 21013-3:2025.

Standards Content (Sample)

SLOVENSKI STANDARD
01-april-2025
Kriogene posode - Oprema za razbremenitev tlaka za kriogeno območje - 3. del:
Določanje velikosti in pretoka (ISO/DIS 21013-3:2025)
Cryogenic vessels - Pressure-relief accessories for cryogenic service - Part 3: Sizing and
capacity determination (ISO/DIS 21013-3:2025)
Kryo-Behälter - Druckentlastungseinrichtungen für den Kryo-Betrieb - Teil 3:
Bestimmung von Größe und Durchfluss (ISO/DIS 21013-3:2025)
Récipients cryogéniques - Dispositifs de sécurité pour le service cryogénique - Partie 3:
Détermination de la taille et du volume (ISO/DIS 21013-3:2025)
Ta slovenski standard je istoveten z: prEN ISO 21013-3
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.

DRAFT
International
Standard
ISO/DIS 21013-3
ISO/TC 220
Cryogenic vessels — Pressure-relief
Secretariat: AFNOR
accessories for cryogenic service —
Voting begins on:
Part 3: 2025-02-14
Sizing and capacity determination
Voting terminates on:
2025-05-09
Récipients cryogéniques — Dispositifs de sécurité pour le service
cryogénique —
Partie 3: Détermination de la taille et du volume
ICS: 23.020.40
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
AND MAY NOT BE REFERRED TO AS AN
INTERNATIONAL STANDARD UNTIL
PUBLISHED AS SUCH.
This document is circulated as received from the committee secretariat.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
ISO/CEN PARALLEL PROCESSING
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS.
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
PROVIDE SUPPORTING DOCUMENTATION.
Reference number
ISO/DIS 21013-3:2025(en)
DRAFT
ISO/DIS 21013-3:2025(en)
International
Standard
ISO/DIS 21013-3
ISO/TC 220
Cryogenic vessels — Pressure-relief
Secretariat: AFNOR
accessories for cryogenic service —
Voting begins on:
Part 3:
Sizing and capacity determination
Voting terminates on:
Récipients cryogéniques — Dispositifs de sécurité pour le service
cryogénique —
Partie 3: Détermination de la taille et du volume
ICS: 23.020.40
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
AND MAY NOT BE REFERRED TO AS AN
INTERNATIONAL STANDARD UNTIL
PUBLISHED AS SUCH.
This document is circulated as received from the committee secretariat.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
© ISO 2025
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
STANDARDS MAY ON OCCASION HAVE TO
ISO/CEN PARALLEL PROCESSING
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
BE CONSIDERED IN THE LIGHT OF THEIR
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POTENTIAL TO BECOME STANDARDS TO
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or ISO’s member body in the country of the requester.
NATIONAL REGULATIONS.
ISO copyright office
RECIPIENTS OF THIS DRAFT ARE INVITED
CP 401 • Ch. de Blandonnet 8
TO SUBMIT, WITH THEIR COMMENTS,
CH-1214 Vernier, Geneva
NOTIFICATION OF ANY RELEVANT PATENT
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Email: [e-mail]
Website: www.iso.org
Published in Switzerland Reference number
ISO/DIS 21013-3:2025(en)
ii
ISO/DIS 21013-3:2025(en)
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 2
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.8
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 .9
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 .10
4.5 Heat transfer per unit time (watts) .11
4.5.1 General .11
4.5.2 Normal operation.11
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 . 12
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 . . 15
6.3 Heat transfer . 15
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 .17
7.2.3 Critical flow .17
7.2.4 Subcritical flow .19
7.2.5 Recommended analysis method .19
7.2.6 Example .21
7.3 Sizing of bursting discs . 26
7.3.1 Discharge capacity . 26
7.3.2 Determination of critical vs. subcritical flow for gases . 26
7.3.3 Critical flow .27

iii
ISO/DIS 21013-3:2025(en)
7.3.4 Subcritical flow .27
7.3.5 Recommended analysis method .27
7.3.6 Example . 30
Annex A (informative) Cryostats .34
Annex ZA (informative) Relationship between this European Standard and the essential
requirements of Directive 2014/68/UE (Pressure Equipment Directive) aimed to be
covered .35
Bibliography .36

iv
ISO/DIS 21013-3:2025(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.
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 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 mentioned in this standard.
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
DRAFT International Standard ISO/DIS 21013-3:2025(en)
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 specified conditions described in the following table:
Insulation
system
Pressure
Type of Inner ves- (outer
Vacuum Ambient buildup Use clauses including
Condition insulation sel temper- jacket +
status: conditions: system con- any sub-clauses
system: ature: insulating
dition:
material)
condition:
normal
(ambient 4.2.3/4.2.4/4.5.1/4.5.2/4.5.
1 intact
tempera- 7/5/6/7
non-vacu-
ture)
N/A
um
normal con-
fully or
dition
2 partially in fire (922 K) 4.3.1/4.5.1/4.5.7/5/6/7
temperature
place
of the con-
4.2.1/4.2.4/4.5.1/4.5.2/4.5.
tents at the
7/5/6/7
specified
normal
normal
relieving
(ambient 4.2.1/4.2.2/4.2.4/4.5.1/4.5.
4 intact full open
pressure
tempera- 3/4.5.7/5/6/7
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
4.3.1/4.4.3/4.5.1/4.5.5/4.5.
6 partially in fire (922 K)
7/5/6/7
place
normal
(ambient normal con-
7 4.4.2/4.5.1/4.5.4/4.5.7/5/6/7
loss of
tempera- dition
intact
contents
vacuum
ture)
with reliev-
with air or
8 ing temper- 4.4.3/4.5.1/4.5.5/4.5.7/5/6/7
nitrogen in
ature below
vacu-
the vacu-
75 K
fire (922 K)
um and
um space
9 totally lost 4.5.1/4.5.6/4.5.7/5/6/7
non-vacu-
um
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.

ISO/DIS 21013-3:2025(en)
2 Normative references
There are no normative references in this document.
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 is the total outer surface area of the pipe network containing flow of fluid, from the m
e
outer jacket up to the flow temperature location x under consideration, in m ; Appli-
cable only when length > than 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 (inter- m
j
space)
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 condi- m
tion
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
ISO/DIS 21013-3:2025(en)
K subcritical flow coefficient —
b
Kd coefficient of discharge —
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 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 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
K experimentally determined flow rate through a pipe element or device m /h/bar
V
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
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/kmol
m maximum mass capacity of vessel kg
max
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
ISO/DIS 21013-3:2025(en)
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)
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 of 10 % K
b10
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 conditions W/ (m ·K)
p
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 condi- W/m
3a
tion
U heat transfer coefficient of insulating material with air or gaseous lading, fire condi- W/ (m ·K)
tion
U heat transfer coefficient, air or nitrogen condensation, loss of vacuum, fire condition W/m
5a
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 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
ISO/DIS 21013-3:2025(en)
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]
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 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 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
ν maximum average downstream specific volume, as per desired backpressure limit m /kg
dmax
ν average downstream specific volume, for a downstream built-up backpressure m /kg
d10
of 10 %
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 backpressure of 10 % m /kg
exit10
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
ISO/DIS 21013-3:2025(en)
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 condi- m ·kg /
m
tions 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 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, 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
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
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 .
ISO/DIS 21013-3:2025(en)
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
U shall not be lower than the values proposed but manufacturers can use greater values if their design
requires.
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).
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;
ISO/DIS 21013-3:2025(en)
— 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
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
ISO/DIS 21013-3:2025(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.
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;
— 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.

ISO/DIS 21013-3:2025(en)
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.
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.

ISO/DIS 21013-3:2025(en)
Key
X number of insulation layers
Y heat transfer [W/m ]
07, 3
38400+⋅420 X
UY==
3a
07, 3
09, 6+X
07, 3
92160+⋅1000 X
UY==
5a
07, 3
09, 6+X
Figure 1 — Heat transfer rate for air or nitrogen condensation
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 following
m T
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
 
ISO/DIS 21013-3:2025(en)
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 calculated from the experimentally determined normal evaporation
T1NER
rate, in watts.
4.5.3 Pressure build up regulator fully open
WW=+W (16)
TT21 2
Or for the NER method:
WW=+W (17)
TN21ER TNER 2
4.5.4 Loss of vacuum condition
The heat transfer rate is to be the larger of W or W .
T3 T3a
WW=+W (18)
T3 34
WW=+W (19)
Ta33a 4
where
W is the total heat transfer rate if the saturation temperature of the fluid is greater than or equal to
T3
75 K at 1 bar;
W is the total heat transfer rate if the saturation temperature of the fluid is less than 75 K at 1 bar.
T3a
Alternatively, W may be calculated using Formula (20)
T3
WW=+W (20)
TT31 3
or approximately, using Formula (21)
WW=+W (21)
TT31NER 3
W may be calculated using Formula (22)
T3a
WW=+W (22)
Ta31Ta3
or approximately, using Formula (23)
WW=+W (23)
Ta31TNER 3a
4.5.5 Fire condition with loss of vacuum, vacuum jacket, and insulation fully or partially in place
The heat transfer rate is to be the larger of W or W .
T5 T5a
ISO/DIS 21013-3:2025(en)
where
W is equal to the heat transfer rate, W , if the saturation temperature of the fluid is greater than or
T5 5
equal to 75 K at 1 bar
W is equal to the heat transfer rate, W , if the saturation temperature of the fluid is less than 75 K
T5a 5a
at 1 bar
4.5.6 Fire condition with loss of vacuum, insulation not in place
The heat transfer rate is to be the larger of W = W or W = W , where W is calculated with U for the
T6 6 T5 5a 5a 5a
bare surface condition from Figure 1.
4.5.7 Total heat transfer rate
W is the total heat transfer rate and is equal to W , W , W , W , W , W , W , W , or W , as
T T1 T1NER T2 T2NER T3 T3a T5 T5a T6
applicable.
The fire case may not be the worst case, so fire and PBU conditions shall both be checked. If PBU is changed
later in the field, the sizing and capacity of pressure relief devices shall be verified according to new PBU
capacity.
5 Calculation of the mass flow to be relieved by pressure relief devices
5.1 Relieving pressure, P, less than the critical pressure
For a relieving pressure,
...