SIST EN ISO 6976:2017

SLOVENSKI STANDARD
01-marec-2017
1DGRPHãþD
SIST EN ISO 6976:2005
=HPHOMVNLSOLQ,]UDþXQNDORULþQHYUHGQRVWLJRVWRWHUHODWLYQHJRVWRWHLQ
:REEHMHYHJDLQGHNVDL]VHVWDYH,62
Natural gas - Calculation of calorific values, density, relative density and Wobbe indices
from composition (ISO 6976:2016)
Erdgas - Berechnung von Brenn- und Heizwert, Dichte, relativer Dichte und Wobbeindex
aus der Zusammensetzung (ISO 6976:2016)
Gaz naturel - Calcul des pouvoirs calorifiques, de la masse volumique, de la densité
relative et des indices de Wobbe à partir de la composition (ISO 6976:2016)
Ta slovenski standard je istoveten z: EN ISO 6976:2016
ICS:
75.060 Zemeljski plin Natural gas
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 6976
EUROPEAN STANDARD
NORME EUROPÉENNE
August 2016
EUROPÄISCHE NORM
ICS 75.060 Supersedes EN ISO 6976:2005
English Version
Natural gas - Calculation of calorific values, density,
relative density and Wobbe indices from composition (ISO
6976:2016)
Gaz naturel - Calcul des pouvoirs calorifiques, de la Erdgas - Berechnung von Brenn- und Heizwert, Dichte,
masse volumique, de la densité relative et des indices relativer Dichte und Wobbeindex aus der
de Wobbe à partir de la composition (ISO 6976:2016) Zusammensetzung (ISO 6976:2016)
This European Standard was approved by CEN on 24 August 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 6976:2016 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 6976:2016) has been prepared by Technical Committee ISO/TC 193 “Natural
gas” in collaboration with Technical Committee CEN/TC 278 “Test gases, test pressures, appliance
categories and gas appliance types” 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 February 2017, and conflicting national standards
shall be withdrawn at the latest by February 2017.
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 ISO 6976:2005.
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 6976:2016 has been approved by CEN as EN ISO 6976:2016 without any modification.
INTERNATIONAL ISO
STANDARD 6976
Third edition
2016-08-15
Natural gas — Calculation of calorific
values, density, relative density and
Wobbe indices from composition
Gaz naturel — Calcul des pouvoirs calorifiques, de la masse
volumique, de la densité relative et des indices de Wobbe à partir de la
composition
Reference number
ISO 6976:2016(E)
©
ISO 2016
ISO 6976:2016(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.
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Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2016 – All rights reserved

ISO 6976:2016(E)
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Symbols and units . 5
4.1 Quantities . 5
4.2 Subscripts . 6
4.3 Superscript . 6
5 Principles . 6
6 Behaviour of ideal and real gases . 7
6.1 Enthalpy of combustion . 7
6.2 Calculation of compression factor . 8
7 Calculation of calorific value on a molar basis . 8
7.1 Gross calorific value . 8
7.2 Net calorific value . 9
8 Calculation of calorific value on a mass basis . 9
8.1 Gross calorific value . 9
8.2 Net calorific value .10
9 Calculation of calorific value on a volume basis .10
9.1 Ideal-gas gross calorific value .10
9.2 Ideal-gas net calorific value .10
9.3 Real-gas gross calorific value .11
9.4 Real-gas net calorific value .11
10 Calculation of associated properties .11
10.1 Ideal-gas relative density .11
10.2 Ideal-gas density .12
10.3 Ideal-gas gross Wobbe index .12
10.4 Ideal-gas net Wobbe index .12
10.5 Real-gas relative density .13
10.6 Real-gas density .13
10.7 Real-gas gross Wobbe index .13
10.8 Real-gas net Wobbe index .14
11 Uncertainty of calculation .14
11.1 Principles .14
11.2 Formulae for the analytical method .15
11.3 Inputs for the analytical method .15
11.3.1 Composition and compositional uncertainties .15
11.3.2 Non-compositional inputs .16
11.4 Expanded uncertainty .17
11.5 Expression of results .17
11.5.1 General.17
11.5.2 Analytical method .17
11.5.3 Generic method .17
11.5.4 Contingency method . .17
11.6 Application of uncertainty .18
12 Tables of data .19
Annex A (normative) Values of auxiliary constants .25
ISO 6976:2016(E)
Annex B (normative) Formulae for uncertainty calculations .27
Annex C (informative) Conversion factors .32
Annex D (informative) Example calculations .34
Bibliography .57
iv © ISO 2016 – All rights reserved

ISO 6976:2016(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 World Trade Organization (WTO) principles in the
Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html.
The committee responsible for this document is ISO/TC 193, Natural gas, Subcommittee SC 1, Analysis
of natural gas.
This third edition cancels and replaces the second edition (ISO 6976:1995), which has been technically
revised.
ISO 6976:2016(E)
Introduction
Both international and intra-national custody transfer of natural gas usually require precise
determination of both the quantity and the quality of the gas to be traded. This document specifies
methods for the calculation of key properties that describe gas quality, namely gross and net calorific
value, density, relative density, and gross and net Wobbe index. The methods provide the means
of calculating these properties and their uncertainties for any natural gas, natural gas substitute or
similar combustible gaseous fuel of known composition at commonly used reference conditions.
Values of the various properties calculated in accordance with this document will, in general, differ
only by very small amounts from those calculated using the second (1995) edition of this document. In
this context, it is recognized that:
a) adoption of the revisions detailed in this document will not be without cost, since instrumental
software will need updating;
b) recorded energy content and hence billed energy will, in consequence of these revisions, change by
small amounts;
c) unintended impacts could occur if the revisions are implemented uncritically; for instance, if the
revisions are implemented at input points to a pipeline system but not at exit points, then a costly
accountancy imbalance may result;
d) commercial, contractual, regulatory and legislative obligations will need to be taken into account.
For these reasons, and depending upon the user’s application, it may be appropriate to undertake an
impact assessment in order to determine an agreed timing and procedure for implementation of the
provisions of this document.
vi © ISO 2016 – All rights reserved

INTERNATIONAL STANDARD ISO 6976:2016(E)
Natural gas — Calculation of calorific values, density,
relative density and Wobbe indices from composition
1 Scope
This document specifies methods for the calculation of gross calorific value, net calorific value, density,
relative density, gross Wobbe index and net Wobbe index of natural gases, natural gas substitutes
and other combustible gaseous fuels, when the composition of the gas by mole fraction is known. The
methods specified provide the means of calculating the properties of the gas mixture at commonly
used reference conditions.
Mole fractions by definition sum to unity. Guidance on the achievement of this requirement by
chromatographic analysis is available in ISO 6974-1 and ISO 6974-2.
The methods of calculation require values for various physical properties of the pure components; these
values, together with associated uncertainties, are provided in tables and their sources are identified.
Methods are given for estimating the standard uncertainties of calculated properties.
The methods of calculation of the values of properties on either a molar, mass or volume basis are
applicable to any natural gas, natural gas substitute or other combustible fuel that is normally gaseous,
except that for properties on the volume basis the method is restricted to mixtures for which the
compression factor at reference conditions is greater than 0,9.
Example calculations are given in Annex D for the recommended methods of calculation.
NOTE 1 The qualifiers “superior”, “higher”, “upper” and “total” are, for the purposes of this document,
synonymous with “gross”; likewise, “inferior” and “lower” are synonymous with “net”. The term “heating value”
is synonymous with “calorific value”; “mass density” and “specific density” are synonymous with “density”;
“specific gravity” is synonymous with “relative density”; “Wobbe number” is synonymous with “Wobbe index”;
“compressibility factor” is synonymous with “compression factor”. The dimensionless quantity molecular weight
−1
is numerically equal to the molar mass in kg·kmol .
NOTE 2 There are no explicit limits of composition to which the methods described in this document are
applicable. However, the restriction of volume-basis calculations to mixtures with a compression factor greater
than 0,9 at reference conditions sets implicit limits on composition.
NOTE 3 Because the mole fraction of any water present is not normally available from chromatographic
analysis, it is common practice to calculate the physical properties on a dry gas basis and to allow for the effects
of water vapour in a separate procedure. However, if the mole fraction of water vapour is known then the
property calculations can be carried out completely in accordance with the procedures described herein. The
effects of water vapour on calorific value, whether the latter is directly measured or calculated, are discussed in
ISO/TR 29922.
NOTE 4 For aliphatic hydrocarbons of carbon number 7 or above, any isomer present is included with the
normal isomer of the same carbon number.
NOTE 5 If the user’s requirement includes the replacement of, for example, a C6+ or C7+ grouping of
analytically unresolved components by a single pseudo-component, then it is the user’s own task to set the mole
fraction composition, and hence properties, of this pseudo-component so as to be fit for purpose in the particular
application. Any so-called “spectator water” and “non-combustible hydrogen sulfide” are treated as pseudo-
components by setting the appropriate enthalpy of combustion values to zero.
ISO 6976:2016(E)
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 6974-1, Natural gas — Determination of composition and associated uncertainty by gas
chromatography — Part 1: General guidelines and calculation of composition
ISO 6974-2, Natural gas — Determination of composition and associated uncertainty by gas
chromatography — Part 2: Uncertainty calculations
ISO 14912:2003, Gas analysis — Conversion of gas mixture composition data
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
3.1
gross calorific value
amount of heat that would be released by the complete combustion with oxygen of a specified quantity
of gas, in such a way that the pressure, p , at which the reaction takes place remains constant, and all the
products of combustion are returned to the same specified temperature, t , as that of the reactants, all
of these products being in the gaseous state except for water, which is condensed to the liquid state at t
Note 1 to entry: Where the quantity of gas is specified on a molar basis, the gross calorific value is designated as
(Hc) (t ,p ); on a mass basis, the gross calorific value is designated as (Hm) (t ,p ). Where the quantity of gas is
G 1 1 G 1 1
specified on a volume basis, the gross calorific value is designated as (Hv) (t ,p ;t ,p ), where t and p are the
G 1 1 2 2 2 2
gas volume (metering) reference conditions (see Figure 1).
3.2
net calorific value
amount of heat that would be released by the complete combustion with oxygen of a specified quantity
of gas, in such a way that the pressure, p , at which the reaction takes place remains constant, and all
the products of combustion are returned to the same specified temperature, t , as that of the reactants,
all of these products being in the gaseous state
Note 1 to entry: On molar, mass and volume bases, the net calorific value is designated respectively as
(Hc) (t ,p ), (Hm) (t ,p ) and (Hv) (t ,p ;t ,p ).
N 1 1 N 1 1 N 1 1 2 2
3.3
density
mass of a gas sample divided by its volume at specified conditions of pressure and temperature
3.4
relative density
density of a gas divided by the density of dry air of reference composition at the same specified
conditions of pressure and temperature
Note 1 to entry: The term ideal relative density applies when both gas and air are considered as gases that obey
the ideal gas law (3.8). The term real relative density applies when both gas and air are considered as real fluids
(3.9). For the fixed reference composition of dry air, see ISO/TR 29922.
2 © ISO 2016 – All rights reserved

ISO 6976:2016(E)
3.5
gross Wobbe index
volume-basis gross calorific value, at specified reference conditions, divided by the square root of the
relative density at the same specified metering reference conditions
Note 1 to entry: In common usage, and in the absence of any other qualifier, the term Wobbe index is taken to
mean the quantity that is here identified as gross Wobbe index.
3.6
net Wobbe index
volume-basis net calorific value, at specified reference conditions, divided by the square root of the
relative density at the same specified metering reference conditions
3.7
enthalpy of transformation
amount of heat release that accompanies the change in condition (transformation) of a substance or
system from one (initial) condition to another (final) condition
Note 1 to entry: A positive heat release is represented by thermodynamic convention as a numerically equal
negative increment of enthalpy.
Note 2 to entry: In the context of this document, the following can be identified:
— enthalpy of combustion: the initial condition is that of an unburned stoichiometric mixture of reactants and
the final condition is that of the products of combustion at the same pressure and temperature;
— standard enthalpy of vaporization: the initial condition is that of a substance in the liquid state at saturation
and the final condition is that of the same substance in the hypothetical state of the ideal gas at the same
temperature;
— enthalpy (or enthalpic) difference: the initial condition is that of a gas or gas mixture at temperature T and
the final condition is that of the same gas or gas mixture at the same pressure but at a different temperature T ;
— enthalpy (or enthalpic) correction (residual enthalpy): the initial condition is that of a gas or gas mixture
in the hypothetical state of an ideal gas and the final condition is that of the same gas or gas mixture at the
same pressure and temperature in the state of the real gas.
3.8
ideal gas
gas that obeys the ideal gas law
Note 1 to entry: The ideal gas law can be expressed as
o
p · V = R · T
where
p is the absolute pressure;
T is the thermodynamic temperature;
o
V is the volume occupied by one mole of ideal gas (ideal molar volume);
R is the gas constant in coherent units.
3.9
real gas
gas that deviates from volumetric ideality
Note 1 to entry: No real gas obeys the ideal gas law. Deviations from volumetric ideality can be written in terms
of the equation of state
p · V = Z(p,T) · R · T
ISO 6976:2016(E)
where
V is the volume occupied by one mole of the real gas (real molar volume);
Z(p,T) is a variable, often close to unity, and is known as the compression factor (3.10).
3.10
compression factor
actual (real) volume of a given amount of gas at a specified pressure and temperature divided by its
volume under the same conditions as calculated from the ideal gas law
3.11
combustion reference conditions
specified temperature, t , and pressure, p , at which the fuel is notionally burned
1 1
3.12
metering reference conditions
specified temperature, t , and pressure, p , at which the volume of fuel to be burned is notionally
2 2
determined
Note 1 to entry: There is no a priori reason for the metering reference conditions to be the same as the combustion
reference conditions (see Figure 1).
Note 2 to entry: A range of reference conditions is in use throughout the world.
Note 3 to entry: Throughout this document, the use of 15,55 °C is intended as shorthand for the exact Celsius
5/9
equivalent of 60 °F, i.e. 15 or 15,55 (recurring) °C.
Note 4 to entry: The exact equivalent of 101,325 kPa in psi can be calculated from
(101 325) · (0,304 8/12) / (0,453 592 37) · (9,806 65) = 14, 695 949 ….
This value is, in practice, normally rounded to 14,696 psi and the rounded value deemed equal to 101,325 kPa.
Figure 1 — Calorific value on a volume basis — Metering and combustion reference conditions
4 © ISO 2016 – All rights reserved

ISO 6976:2016(E)
4 Symbols and units
4.1 Quantities
Symbol Meaning Unit
−1
A atomic mass kg·kmol
a atomic index for carbon in the generalized molecular species —
C H N O S
a b c d e
b atomic index for hydrogen in the generalized molecular species —
C H N O S
a b c d e
c atomic index for nitrogen in the generalized molecular species —
C H N O S
a b c d e
−3
D density kg·m
d atomic index for oxygen in the generalized molecular species —
C H N O S
a b c d e
e atomic index for sulfur in the generalized molecular species —
C H N O S
a b c d e
F function that generates property Y —
G relative density —
−1
Hc molar-basis calorific value kJ·mol
−1
Hm mass-basis calorific value MJ·kg
−3
Hv volume-basis calorific value MJ·m
k coverage factor —
−1
L molar enthalpy of vaporization of water kJ·mol
−1
M molar mass kg·kmol
N number of components in a mixture —
n number of determinations in a set of values —
p pressure (absolute) kPa
q exact input quantity for calculation of Y (varies)
−1 −1
R molar gas constant J·mol ·K
r correlation coefficient —
s summation factor —
T thermodynamic (absolute) temperature K
t Celsius temperature °C
U(Y) expanded uncertainty of Y (varies)
ISO 6976:2016(E)
u(Y) standard uncertainty of Y (varies)
3 −1
V molar volume m ·mol
−3
W Wobbe index MJ·m
x mole fraction —
Y general (unspecified) physical property (varies)
y inexact input quantity for calculation of Y (varies)
Z compression factor —
4.2 Subscripts
Symbol Meaning
G gross (calorific value or Wobbe index)
i serial counter
component identifier
j serial counter
component identifier
k serial counter
m serial counter
N net (calorific value or Wobbe index)
n serial counter
air for air
0 reference (base) value (of pressure)
1 combustion reference state
2 metering reference state
4.3 Superscript
Symbol Meaning
o for the ideal gas state
5 Principles
Methods are provided for the calculation of the calorific values (gross and net), density, relative density
and Wobbe indices (gross and net) of any natural gas, natural gas substitute or other combustible
gaseous fuel from a known molar composition.
For calorific values, these methods use formulae in which, for all individual molecular species of the
gas mixture, the tabulated ideal-gas molar-basis gross calorific value is weighted in accordance with its
mole fraction, all terms then being added together to obtain the mole fraction average of this quantity
for the ideal gas mixture on a molar basis. Further formulae are given that convert this quantity into
6 © ISO 2016 – All rights reserved

ISO 6976:2016(E)
the ideal-gas net calorific value, and then into the ideal-gas gross and net calorific values on either a
mass basis or a volume basis.
Likewise, for density and relative density, the methods use formulae in which, for all individual
molecular species of the gas mixture, the tabulated value of molar mass is weighted in accordance
with its mole fraction, all terms then being added together to obtain the mole fraction average of this
quantity. Formulae are given that convert this mole fraction average molar mass into the ideal-gas
density or relative density.
Values of the density and relative density for the real gas are then obtained by the application of a
volumetric correction factor (compression factor), a prescription for the calculation of which is given.
For calorific values, conversion from the ideal-gas state to the real-gas state is in principle slightly less
simple. The application should first be made of a small enthalpic correction (residual enthalpy) to the
calorific value (gross or net) of the ideal gas on the molar basis, so as to obtain the calorific value of the
real gas on the molar basis. For the purposes of this document, however, this enthalpic correction has
been estimated as so small as to be justifiably negligible (see ISO/TR 29922).
In consequence of neglecting the enthalpic correction, the real-gas calorific values on the molar and
mass bases are in effect set as equal to the corresponding ideal-gas values. To obtain the values of the
real-gas calorific values (gross or net) on the volume basis from the corresponding ideal-gas values,
however, the volumetric correction factor (compression factor) mentioned above is applied.
Finally, formulae are given for the calculation of Wobbe indices, for either the ideal gas or real gas, from
the other properties considered herein.
For each of the natural gas properties for which formulae are provided as described above, the methods
[5]
prescribed in GUM have been applied so as to provide further formulae that enable an estimate of
associated uncertainty.
The derivation of each such uncertainty formula is presented fully in ISO/TR 29922. In essence, each
results from the analytical derivation of sensitivity coefficients, by means of partial differentiation of
the relevant mixture-property formula with respect to each of the input quantities (namely the pure-
component physical properties and component mole fractions) with which an uncertainty may be
associated. The derivations also take into account the unavoidable correlations between the component
mole fractions and the likewise unavoidable, but less obvious, correlations between the component
molar masses (see also Clause 11).
For each property, the total variance (squared uncertainty) is obtained by addition of the independent
contributions to the variance from each source of uncertainty and the overall uncertainty result is
taken as the square root of this quantity. The formulae to be used are given in Annex B.
In Clause 12, tabulated values are given for the relevant physical properties and their associated
uncertainties of the pure components of natural gas for each of the commonly used reference conditions.
Auxiliary data, including uncertainties, are given in Annex A. Example calculations are given in Annex D.
6 Behaviour of ideal and real gases
6.1 Enthalpy of combustion
The most fundamental physical quantities required in the calculation of calorific values from first
principles are the ideal-gas (standard) molar enthalpies of combustion (ideal molar-basis calorific
values) for the pure component gases. These quantities are complex functions of temperature; thus, the
values required depend upon the combustion reference temperature t . For practical reasons, it is not
intended that the user should carry out calculations that give the appropriate values at any arbitrary
combustion reference temperature. Instead, tabulations are given for the temperatures t = 25 °C, 20 °C,
15,55 °C (60 °F, see 3.12, Note 3 to entry), 15 °C (59 °F) and 0 °C. The derivations of the values listed in
Table 3 are discussed in ISO/TR 29922; the important point is that all five values for any substance are
mutually consistent from a thermodynamic perspective.
ISO 6976:2016(E)
6.2 Calculation of compression factor
For any volume-basis calorific value, a real-gas correction is required to account for the deviation of the
real gas from volumetric ideality. This correction is not negligible and is also required in the calculation
of density, relative density and Wobbe index. ISO/TR 29922 discusses the background to the way in
which corrections for volumetric non-ideality shall be applied, the principles involved and justifies the
simplifications employed that enable tractable calculations, as detailed in Formula (1), to be made.
This correction for volumetric non-ideality is made through the use of the compression factor Z of the
mixture. The formulation to be used for Z at the metering reference conditions, as required for the
calculations described in Clauses 9 and 10, is (see ISO/TR 29922)
N
 
 
p
 
Zx()tp,  = 1−  ×⋅ st(),p (1)
∑
22 jj 20
 
p  
 0  j=1
 
where p = 101,325 kPa (14,696 psi) and the metering reference pressure p is expressed in the same
0 2
units. The summation is taken over all N components of the mixture and the formula is valid for the
range 90 < p /kPa < 110 (13,05 < p /psi < 15,95). Values of the so-called summation factor s (t ,p )
2 2 j 2 0
are given in Table 2 at the four metering reference temperatures of common interest for all of the
components of natural gas and substitute natural gas considered in this document. The derivations of
these values are detailed in ISO/TR 29922.
NOTE Formula (1) can also be used to calculate values of compression factor of pure components, but this
will not necessarily give the most accurate result possible. In particular, the formula will not provide acceptable
values for the compression factors of hydrogen, helium or neon, for which Z > 1, nor for any components, such as
the higher hydrocarbons, that are not gaseous at the metering reference conditions. The user should consider
the fitness-for-purpose of any such calculation before its use outside of the context of this document. Definitive
values of compression factor for several pure components, namely the so-called permanent gases, are given in
ISO/TR 29922.
7 Calculation of calorific value on a molar basis
7.1 Gross calorific value
The gross calorific value on a molar basis, at a temperature t , of a mixture of known composition shall
be calculated from
N
o o
()Hc ()tH==()ct() [xH⋅ ()ct]( ) (2)
∑
GG11 jG j 1
j=1
where
o
is the ideal-gas gross molar-basis calorific value of the mixture;
()Hc ()t
G 1
is the real-gas gross molar-basis calorific value of the mixture;
()Hc ()t
G 1
o
is the ideal gross molar-basis calorific value of component j;
[(Hc)] ()t
G j 1
x is the mole fraction of component j.
j
o
NOTE 1 Values of [(Hc)] are independent of pressure; consequently, the combustion reference pressure p
G j
is irrelevant and is omitted from the nomenclature adopted.
8 © ISO 2016 – All rights reserved

ISO 6976:2016(E)
NOTE 2 The ideal-gas molar-basis calorific value of a gas or gas mixture is defined in this document
as a positive quantity. The values given in Table 3 are numerically equal to the standard molar enthalpies of
combustion, which are, however, conventionally expressed as negative quantities (see 3.7).
o o
Numerical values of [(Hc)] ()t for t = 25 °C are given in Table 3. These values for [(Hc)] (25) are
G j 1 G j
o
taken from the original literature sources cited in ISO/TR 29922. Values for [(Hc)] ()t for other
G j 1
temperatures (t = 20 °C, 15,55 °C, 15 °C and 0 °C) are also given in Table 3. These values have been
derived from the 25 °C values in accordance with the methods described in ISO/TR 29922.
7.2 Net calorific value
The net calorific value on a molar basis, at a temperature t , of a mixture of known composition shall be
calculated from
N
b
j
o o o
()Hc ()tH==()ct() ()Hc ()tx− (⋅⋅Lt ) (3)
∑
NN11 G 11j
j=1
where
o
is the ideal-gas net molar-basis calorific value of the mixture;
()Hc ()t
N 1
is the real-gas net molar-basis calorific value of the mixture;
()Hc ()t
N 1
o
L (t ) is the standard enthalpy of vaporization of water at t ;
1 1
b is the number of hydrogen atoms present in each molecule of component j (hydrogen
j
atomic index).
o
Values of L (t ) are given in Annex A for 25 °C, 20 °C, 15,55 °C (60 °F), 15 °C and 0 °C. Values of b are
1 j
given in Table 1.
8 Calculation of calorific value on a mass basis
8.1 Gross calorific value
The gross calorific value on a mass basis, at a temperature t , of a mixture of known composition shall
be calculated from
o
()Hc ()t
o G 1
()Hm ()tH()mt() (4)
GG11
M
where
o
is the ideal-gas gross mass-basis calorific value of the mixture;
()Hm ()t
G 1
is the real-gas gross mass-basis calorific value of the mixture;
()Hm ()t
G 1
M is the molar mass of the mixture, which shall be calculated from
N
Mx = ⋅M (5)
∑
jj
j=1
==
ISO 6976:2016(E)
where
M is the molar mass of component j.
j
The value of molar mass for each component considered in this document is given in Table 1.
8.2 Net calorific value
The net calorific value on a mass basis, at a temperature t , of a mixture of known composition shall be
calculated from
o
()Hc ()t
o N 1
()Hm ()tH()mt() (6)
NN11
M
where
o
is the ideal-gas net mass-basis calorific value of the mixture;
()Hm ()t
N 1
is the real-gas net mass-basis calorific value of the mixture.
()Hm ()t
N 1
9 Calculation of calorific value on a volume basis
9.1 Ideal-gas gross calorific value
The gross calorific value on an ideal-gas volume basis, for a combustion temperature t , of a mixture of
known composition, metered at a temperature t and pressure p , shall be calculated from
2 2
o
()Hc ()t
o G 1
()Hv ()tt;,p = (7)
G 12 2
o
V
where
o
is the ideal-gas gross volume-basis calorific value of the mixture;
()Hv ()tt;,p
G 12 2
o
V is the ideal m
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