EN ISO 6976:2005

SLOVENSKI STANDARD
01-julij-2005
=HPHOMVNLSOLQ±,]UDþXQNDORULþQLKYUHGQRVWLJRVWRWHUHODWLYQHJRVWRWHLQ
:REEHMHYHJDLQGHNVDL]NRPSR]LFLMH,62YNOMXþXMRþ3RSUDYHNLQ
3RSUDYHN
Natural gas - Calculation of calorific values, density, relative density and Wobbe index
from composition (ISO 6976:1995 including Corrigendum 1:1997, Corrigendum 2:1997
and Corrigendum 3:1999)
Erdgas - Berechnung von Brenn- und Heizwert, Dichte, relativer Dichte und Wobbeindex
aus der Zusammensetzung (ISO 6976:1995 + Corrigendum 1:1997 + Corrigendum
2:1997 + Corrigendum 3:1999)
Gaz naturel - Calcul du pouvoir calorifique, de la masse volumique, de la densité relative
et de l'indice de Wobbe a partir de la composition (ISO 6976:1995, Corrigendum 1:1997,
Corrigendum 2:1997 et Corrigendum 3:1999 inclus)
Ta slovenski standard je istoveten z: EN ISO 6976:2005
ICS:
75.060 Zemeljski plin Natural gas
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 6976
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2005
ICS 75.060
English version
Natural gas - Calculation of calorific values, density, relative
density and Wobbe index from composition (ISO 6976:1995
including Corrigendum 1:1997, Corrigendum 2:1997 and
Corrigendum 3:1999)
Gaz naturel - Calcul du pouvoir calorifique, de la masse Erdgas - Berechnung von Brenn- und Heizwert, Dichte,
volumique, de la densité relative et de l'indice de Wobbe à relativer Dichte und Wobbeindex aus der
partir de la composition (ISO 6976:1995, Corrigendum Zusammensetzung (ISO 6976:1995 + Corigendum 1:1997
1:1997, Corrigendum 2:1997 et Corrigendum 3:1999 inclus) + Corigendum 2:1997 + Corigendum 3:1999)
This European Standard was approved by CEN on 17 April 2005.
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 Central Secretariat 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 Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 6976:2005: E
worldwide for CEN national Members.

Foreword
The text of ISO 6976:1995 has been prepared by Technical Committee ISO/TC 193 "Natural
gas” of the International Organization for Standardization (ISO) and has been taken over as EN
ISO 6976:2005 by CMC.
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 November 2005, and conflicting national
standards shall be withdrawn at the latest by November 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,
Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary,
Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

Endorsement notice
The text of ISO 6976:1995 has been approved by CEN as EN ISO 6976:2005 without any
modifications.
INTERNATIONAL
IS0
STANDARD
Second edition
1995-l Z-01
Corrected and reprinted
1996-02-01
Natural gas - Calculation of calorific
values, density, relative density and Wobbe
index from composition
Gaz na turel - Calcul du pouvoir calorifique, de la masse volumique, de la
densit relative et de I’indice de Wobbe P partir de la composition
Reference number
IS0 6976:1995(E)
IS0 6976:1995(E)
Contents
Page
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................................. ............ ......................
2 Definitions . .
...................................... .................. ................. 3
3 Principle .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Behaviour of ideal and real gases
........................ 3
4.1 Enthalpy of combustion .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.2 Calculation of compression factor
. . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Calculation of calorific value on a molar basis
5.1 Ideal gas . . .
........................................... ...................... ................. 4
5.2 Real gas
. . . . . . . . . . . . . . . . . . . . . . . . . . 4
6 Calculation of calorific value on a mass basis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
6.1 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Real gas . . . 5
. . . . . . . . . . . . . . . . . . 5
7 Calculation of calorific value on a volumetric basis
............................. 5
7.1 Ideal gas . .
........................ ................. ......................................... 5
7.2 Real gas
. . . . . . . . 6
8 Calculation of relative density, density and Wobbe index
8.1 Ideal gas - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Real gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Accuracy . . 6
9 .
9.1 Precision . . . 6
9.2 Trueness . . . 8
................................. ............................. 9
9.3 Expression of results
IO Tables of recommended data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IO
0 IS0 1995
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopyrng and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
II
0 IS0
IS0 6976: 1995(E)
Annexes
A Symbols and units . . . . . .*. . . . . . . . . . . . . . . 15
B Values of auxiliary constants, etc. . . 17
B.l Molar gas constant . . .
B.2 Critical constants and acentric factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3 Properties of dry air . . . . 17
B.4 Enthalpy of vaporization of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
C Conversion of volume fractions to mole fractions . . . . . . . . . . . . . . . . 20
D Examples of calculations . .
........ 21
D.l Calorific value on a molar basis (clause 5) . . . . . . . . . . . . . . . . . . . . . . . . . . 21
D.2 Calorific value on a mass basis (clause 6) . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
D.3 Calorific value on a volumetric basis (clause 7) . . . . . . . . . . . . . . . . . . 21
D.4 Relative density, density and Wobbe index (clause 8)
....... 22
D.5 Precision (clause 9) . . 23
E Behaviour of ideal and real gases . . 25
E.l Variation of ideal-gas enthalpy of combustion with
temperature . . . . 25
E.2 Corrections for non-ideality: volumetric effects .
E.3 Corrections for non-ideality: enthalpic effects
..................... 28
F Effects of water vapour on calorific value
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
F.l General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F.2 Excluded volume effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F.3 Latent heat (enthalpic) effect . . 31
F.4 Compression factor effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
G Summary, discussion and selection of the calorific value of
methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
H Derivation of equations relating to precision .
H.l Methane by difference . 36
H.2 Methane by analysis . .
J Approximate conversion factors between reference states
. . 38
K Computer implementation of recommended methods . . . . . . . . . 40
L Calorific values on a molar basis for 60 “F reference
............................ ...........
temperature . . 43
iii
IS0 6976:1995(E) 0 IS0
IV! Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*.
iv
0 IS0
IS0 6976:1995(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work
of preparing International Standards is normally carried out through IS0
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. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard IS0 6976 was prepared by Technical Committee
ISO/TC 193, Natural gas, Subcommittee SC I, Analysis of natural gas.
This second edition cancels and replaces the first edition
(IS0 6976:1983), of which it constitutes a technical revision.
Annexes A and B form an integral part of this International Standard. An-
nexes C, D, E, F, G, H, J, K, L and M are for information only.

This page intentionally left blank

IS0 6976:1995(E)
INTERNATIONAL STANDARD 0 IS0
- Calculation of calorific values, density,
Natural gas
relative density and Wobbe index from composition
synonymous with “calorific value ”; “specific gravity” is
1 Scope
synonymous with “relative density ”; “Wobbe number” is
synonymous with “Wobbe index ”; “compressibility factor”
is synonymous with “compression factor ”.
This International Standard specifies methods for the
3 If the composition of the gas is known by volume frac-
calculation of the superior calorific value, inferior
tions these must be converted to mole fractions (see
calorific value, density, relative density and Wobbe
annex C). Note, however, that the derived mole fractions
index of dry natural gases, natural gas substitutes and
will have uncertainties greater than those of the original
other combustible gaseous fuels, when the compo-
volume fractions.
sition of the gas by mole fraction is known. The
4 For the purposes of this International Standard, the sum
methods provide a means of calculating the proper-
of the mole fractions used must be unity to the nearest
ties of the gas mixture at commonly used metric ref-
0,000 I, and all components with mole fractions greater
erence conditions.
than 0,000 05 must be accounted for.
The methods of calculation require values for various
5 For the calorific value calculated on a volumetric basis,
physical properties of the pure components; these
there are limitations on the amounts of components other
values are provided in tables and their sources are
than methane which may be present. It is impossible to be
definitive on this matter, but the following guidelines may
identified.
be useful:
Methods are given for estimating the precision of
N, should not be present in amounts exceeding 0,3
calculated properties.
mole fraction;
The methods of calculation of the values of properties
CO, and C,H, should each not exceed 0,15 mole frac-
on either a molar or mass basis are applicable to any
tion;
dry natural gas, natural gas substitute or other
combustible fuel which is normally gaseous. For the
no other component should exceed 0,05 mole fraction.
calculation of the values of properties on a volumetric
basis, the methods are restricted to gases consisting
Given these limits, the expected trueness of the calculation
preponderantly of methane (not less than 0,5 mole
is within 0,l %.
fraction).
6 The effects of water vapour on the calorific value, either
directly measured or calculated, are discussed in annex F.
Examples of calculations are given in annex D for the
recommended methods of calculation.
7 For the methods of calculation described to be valid, the
gas must be above its hydrocarbon dew-point at the pre-
NOTES
scribed reference conditions.
1 The symbols used in this International Standard, to-
8 The values of basic physical property data are subject to
gether with their meanings, are given in annex A.
revision as more accurate values become available from
authoritative sources.
2 The qualifiers “higher ”, “upper ”, “total” and “gross”
are, for the purposes of this International Standard, syn-
onymous with “superior ”; likewise, “lower” and “net” are
synonymous with “inferior ”. The term “heating value” is

0 IS0
IS0 6976:1995(E)
On molar, mass and volumetric bases, the inferior
2 Definitions
calorific value is designated respectively as q (tl ,I+),
W,~Pl) and 4Kb P1w(~*~P2)1~
For the purposes of this International Standard, the
following definitions apply.
2.3 density: The mass of a gas sample divided by
its volume at specified conditions of pressure and
2.1 superior calorific value: The amount of heat
temperature.
which would be released by the complete combustion
in air of a specified quantity of gas, in such a way that
2.4 relative density: The density of a gas divided
the pressure p1 at which the reaction takes place re-
by the density of dry air of standard composition (see
mains constant, and all the products of combustion
annex B) at the same specified conditions of pressure
are returned to the same specified temperature t, as
and temperature. The term ideal relative density ap--
that of the reactants, all of these products being in the
plies when both gas and air are considered as fluids
gaseous state except for water formed by com-
which obey the ideal gas law (see 2.7); the term real
bustion, which is condensed to the liquid state at t,.
relative density applies when both gas and air are
considered as real fluids.
Where the quantity of gas is specified on a molar ba-
sis, the calorific value is designated as &(t,,pJ; on a
2.5 Wobbe index: The superior calorific value on a
mass basis the calorific value is designated as
volumetric basis at specified reference conditions,
Hs (4 IPI > - divided by the square root of the relative density at
the same specified metering reference conditions.
Where the quantity of gas is specified on a volumetric
value is designated as
basis, the calorific
2.6 enthalpy of transformation: The enthalpy of
is [t,,p,, V(t2,p2)], where t2 and p2 are the gas volume
transformation of a substance from state A to state
(metering) reference conditions (see figure 1).
B is thermodynamic terminology for the amount of
heat release which accompanies the transformation
2.2 inferior calorific value: The amount of heat between states. A positive heat release is taken by
convention to be a numerically identical negative
which would be released by the complete combustion
enthalpy increment. The quantities enthalpy of com-
in air of a specified quantity of gas, in such a way that
bustion and enthalpy of vaporization therefore have
the pressure p1 at which the reaction takes place re-
meanings which should be contextually self-evident;
mains constant, and all the products of combustion
the term enthalpic correction refers to the (molar)
are returned to the same specified temperature t, as
that of the reactants, all of these products being in the enthalpy of transformation between the ideal and real
states of a gas.
gaseous state.
Water as vapour
lnferio value I?,
rc alorif ic
Air
z1
Metering
/-p--t--
at h PI
I
Gas at
tz, P2
i
Water as liquid
Superi or calorific value &
Combustion
Heat release
= Calorific value ti
Metered volume of gas
- Metering and combustion reference conditions
Figure 1 - Calorific value on a volumetric basis

0 ISQ
IS0 6976:1995(E)
sponding mole fraction, all the terms then being
2.7 ideal gas and real gas: An ideal gas is one
added together to obtain the “mole fraction average”
which obeys the ideal gas law:
of the property for the ideal-gas mixture. Values on a
. . .
= RmT
(1)
P=v,
volumetric basis are then converted to values for the
real-gas state by applying a volumetric correction fac-
where
tor.
is the absolute pressure;
P
NOTE 10 An enthalpic correction factor which is also, in
principle, required in calorific value calculations is deemed
T is the thermodynamic temperature;
to be negligible in all relevant cases.
is the volume per mole of gas;
In clause 10, values are given for the physical
properties of the pure components of natural gas on
R is the molar gas constant, in coherent
molar, mass and volumetric bases for the con- lmonly
units.
used reference conditions . Examples of calcu lations
No real gas obeys this law. For real gases, equation
are given in annex D.
(1) must be rewritten as
= Z(T,p) -RgT . . .
4 Behaviour of idea I and rea I gases
(2)
PT-ll
where Z(T,p) is a variable, often close to unity, and is
4.1 Enthalpy of combustion
known as the compression factor (see 2.8 and E.2).
The most fundamental physical quantities required in
2.8 compression factor: The actual (real) volume
the calculation of calorific values from first principles
of a given mass of gas at a specified pressure and
are the ideal-gas (standard) molar enthalpies of com-
temperature divided by its volume, under the same
bustion for the component gases of the mixture.
conditions, as calculated from the ideal gas law.
These quantities are complex functions of tempera-
ture; thus, the values required depend upon the
2.9 combustion reference conditions: The speci-
combustion reference temperature t,. For practical
fied temperature t, and pressure pl. These are the
reasons, it is not intended that the user himself car-
conditions at which the fuel is notionally burned (see
ries out calculations which give the appropriate values
figure 1).
at any arbitrary combustion reference temperature.
Instead, tabulations are given for the temperatures
2.10 metering reference conditions: The specified
t, = 25 “C, 20 “C, 15 “C and 0 “C. In clause E.l the
temperature + and pressure pz. These are the con-
derivations of the values tabulated are discussed; the
ditions at which the amount of fuel to be burned is
important point is that all four values for any sub-
notionally determined; there is no a priori reason for
stance are mutually consistent in a thermodynamic
these to be the same as the combustion reference
sense.
conditions (see figure I).
For the calorific value (on any of the three possible
NOTE 9 A range of reference conditions is in use
bases), a so-called enthalpic correction is, in principle,
throughout the world; appropriate data for the principal sets
required in order to convert the ideal-gas enthalpy of
of metric reference conditions are given in tables in this
combustion for the gas mixture to a value appropriate
International Standard.
to the real gas. This, however, is generally small
enough to be negligible. A discussion justifying such
2.11 dry natural gas: Gas which does not contain
neglect is given in clause E.3.
water vapour at a mole fraction greater than 0,000 05.
42 . Calculation of compression factor
3 Principle
For the volumetric-basis calorific value, a second real-
Methods are provided for the calculation of the gas correction is required to account for the deviation
calorific values, density, relative density and Wobbe of the gas from volumetric ideality, and this is gener-
index of any dry natural gas, natural gas substitute or ally not negligible. This correction is also required in
the calculation of density, relative density and, by im-
other combustible gaseous fuel from a known com-
plication, Wobbe index. Clause E.2 gives the back-
position. These methods use equations in which, for
ground to the way in which corrections for volumetric
all individual molecular species of the gas mixture, the
values of ideal-gas thermophysical properties (which non-ideality should be applied, discusses the princi-
are given) are weighted in accordance with the corre- ples involved, and justifies the simplifications em-
0 IS0
IS0 6976:1995(E)
have been derived from the 25 “C values in accord-
ployed which enable tractable calculations to be made
ance with the methods described in clause E.I.
without necessitating machine computation.
NOTES
Such corrections for volumetric non-ideality are made
using the compression factor Zmix. The formulation to
II Values of ??y are independent of pressure; conse-
be used for Zmix at the metering reference conditions,
quently the combustion reference pressure JI, is irrelevant
as required for the calculations described in clauses
for the ideal-gas case and is omitted from the nomenclature
5 to 9, is (equation E.17):
adopted.
L
12 The ideal-gas calorific value on a molar basis of a gas
. . .
or gas mixture is defined in this International Standard as a
zr-nix (t*lp*) = I - xj’ hj (3)
s
positive number. The values given in table3 are numerically
j=l
i I
equal to the standard molar enthalpies of combustion,
which are, however, conventionally expressed as negative
where the summation is taken over all N components
quantities (see 2.6).
of the mixture. Values of the so-called summation
factor bj are given in table2 (clause 10) at the
II-
three metering reference conditions of common in- 5.2 Real gas
terest, for all of the components of natural gas and
For the purposes of this International Standard the
substitute natural gas considered in this International
real-gas calorific value on a molar basis is taken as
Standard. Values are also given for all pure component
numerically equal to the corresponding ideal-gas
compression factors (or hypothetical compression
value.
factors) 5, from which the &i ’s have generally been
Zjs Any user re-
derived using the relationship-h, = 1 -
NOTE 13 A rigorous approach to the calculation of the
quiring greater detail should consult clause E.2.
real-gas calorific value on a molar basis from the ideal-gas
value would require the calculation of an enthalpic cor-
rection (see 4.1) for the mixture. In practice, this correction
5 Calculation of calorific value on a
is very small for typical natural gases, and can usually be
neglected with resultant errors not exceeding 50 J*mol- ’
molar basis
(approximately 0,005 %) (see clause E.3).
5.1 Ideal gas
6 Calculation of calorific value on a mass
The ideal-gas calorific value on a molar basis, at a basis
of a mixture of known composition is
temperature t,,
calculated from the equation
6.1 Ideal gas
;E70(tj) = F,Xj’T(tj)
. . .
(4) The ideal-gas calorific value on a mass basis, at a
j=l
temperature t,, of a mixture of known composition is
calculated from the equation
Ho(tl)
=-
. . .
(5)
PO(+) is the ideal molar calorific value of the fiO(t,)
M
mixture (either superior or inferior);
where
HjT(t,) is the ideal molar calorific value of com-
ponent j (either superior or inferior);
M is the molar mass of the mixture, and is
calculated from the equation
is the mole fraction of component j.
-5
N
.
Numerical values of T for t, = 25 “C are given rn
M = XjmMj . . .
(6)
c
table3 (clause 10); the values for (i?& are taken
i=l
from the original literature sources cited in annex M,
and the values for (fl,‘), derived using the accepted
value of the standard enthalpy of vaporization of water being the mole fraction of
xi
at 25 “C (see annex B). component j;
Values for $’ for other temperatures (t, = 20 “C, being the molar mass of com-
Mj
ponent j;
15 “C and 0 “C) are also given in table3; these values
IS0 6976:1995(E)
0 IS0
h ”(t-,) is the ideal calorific value on a mass basis is the molar gas constant
of the mixture (either superior or inferior). (= 8,314 510 J=mol- ‘=K-I,
see clause B.l);
Table 1 (clause IO) lists values of the molar mass for
all components considered in this International Stan- T2( = t2 + 273,15) is the absolute temperature, in
kelvins.
dard.
The use of equation 1 represents the definitive
Use of equations (5) an$ (6) represents the definitive (8)
-0
method for calculating H. An alternative method uses
method for calculating H . An alternative method uses
the equation
the equation
Mj
fi”(tj) = t Xj x -$
. . .
'y('l) (9)
(7)
( 1 =
j=l
J ’
-0
A0 where Hj [tl,V(t2,p2)] is the ideal calorific value on a
wh ere Hi (t,) is the ideal calorific value on a mass ba-
volumetric basis of component j (either superior or
sis of component j (either superior or inferior).
*0
values of Hj for four values
For convenience,
For convenience, values of fiJy for a variety of com-
of tl (25 “C, 20 “C, 15 “C and 0 “C) are given in
bustion and metering reference conditions are given
table4 (clause 1 O), in order that the user may avoid
in table 5 (clause IO), in order that the user may avoid
the necessity of using values of HI? as the starting
the necessity of using values of flJy as the starting
point of a calculation.
point of a calculation.
Numerical values obtained from either method will be
Numerical values obtained from either method will be
concordant to within 0,Ol MJ-kg-l, which is within
concordant to within 0,Ol MJmmB3, which is within
the limits of significance for the current state-of-the-
the limits of significance for the current state-of-the-
art.
art.
7.2 Real gas
6.2 Real gas
The real-gas calorific value on a volumetric basis, for
For the purposes of this International Standard, the
combustion at temperature t, and pressure p1 of a gas
real-gas calorific value on a mass basis is taken as
mixture metered at a temperature t2 and pressure p2
numerically equal to the corresponding ideal-gas
is calculated from the equation
value.
See 5.2 for clarification and justification. ii” [t, f WP*) 1
NOTE 14
. . .
fi[tl J(t2fP*)l = z @* p*)
mix 1
7 Calculation of calorific value on a
volumetric basis
is the real-gas calorific value on a
lumetric basis (either superior
inferior);
7.1 Ideal gas
is the compression factor at the
zmix P*&)
The ideal-gas calorific value on a volumetric basis, for
metering reference conditions.
a combustion temperature t,, of a mixture of known
The compression factor Zmix(t2,p2) is calculated from
composition, metered at a temperature t2 and press-
ec@ion (3), using values of the summation factor
ure p2, is calculated from the equation
bj given for individual pure substances in table 2
(clause IO).
. . .
ii” [ty ,v(t*&) ] = PO(t,) x -$- (8)
l 2
NOTE 15 See 5.2 for clarification and justification of the
practical approach to real-gas calorific values. Since no
enthalpic correction is made to the ideal-gas calorific value
is the ideal calorific value on a
~"[41V(t21P2)1 on a volumetric basis in this calculation, the combustion
of the mixture
volumetric basis is irrelevant and is omitted from the
reference pressure p1
r inferior); nomenclature adopted.
(either sup #erior 0
IS0 6976:1995(E)
8.2 Real gas
8 Calculation of relative density, density
and Wobbe index
The relative density of the real gas is calculated from
the equation
8.1 ideal gas
domzair CtfP)
d(t,p) = . . .
(14)
Zmix Ct,p>
The relative density of the ideal gas is independent
of any reference state, and is calculated from the
where
is the relative density of the real gas;
d(t,p)
N
Mj
do= XjXM . . .
(11>
c z,i,(t,p) is the compression factor of the gas;
air
j=l
is the compression factor of dry air of
‘air W
where
standard composition.
.
do is the relative density of the idea I
gas
The compression factor Zmix(t,p) is calculated from
-. e uation (3), using values of the summation factor
is the molar mass of component
II
Mj
bj given for individual pure substances in table2
IT-
(clause IO). The compression factor z,i,(t,p) is given
is the molar mass of dry air of standard
Mair
composition. in clause B.3 as
Zair(273,15 K, 101,325 kPa) = 0,999 41
Table 1 (clause IO) lists values of molar mass. Clause
B.3 gives the composition of standard air; the derived
Zai,(288,15 K, 101,325 kPa) = 0,999 58
value for Mair is 28,962 6 kgmkmol- I.
Zair(293,15 K, 101,325 kPa) = 0,999 63
The density of the ideal gas depends upon its tem-
perature t and pressure p, and is calculated from
The density of the real gas is calculated from the
equation
. . .
(12)
PO (tfP> = ( & ) F,xj ’Mj
PO kP>
j=l
. . *
( ‘15)
P (LP) =
?-nix bP>
where p(t,p) is the density of the real gas.
is the density of the ideal gas;
PO @IP>
The Wobbe index of the real gas is calculated from
R is the molar constant
gas
the equation
(= 8,314 510 J=mol-I%- ‘,
see clause B.l);
H, PI WbP*H
w[t, ,Vtt2,P*)l =
T (= t + 273,151 is the absolute tempera-
j/G *--u6)
ture, in kelvins.
The Wobbe index of the ideal gas is calculated from
the equation
W is the Wobbe index of the real gas;
N
is calculated as described in 7.2.
ii," PI J%P*) 1
*s
. . .
w” [t1 lv(t21Pdl = (13)
do
J- NOTE 16 Some care in the use of units is required for the
calculations described in this subclause, particularly for cal-
culations of density. With R expressed in joules per mole
kelvin, I, in kilopascals and A.4 in kilograms per kilomole, the
value of p is obtained automatically in kilograms per cubic
is the Wobbe index of the ideal gas;
W0
metre, the preferred SI unit.
-0
is calculated as described in 7.1.
*s
IS0 6976:1995(E)
63 IS0
is the value of the physical property
ri
9 Accuracy
calculated from the ith analysis of the
gas;
9.1 Precision
Y is the arithmetic mean of n values of
Yim
9.1 .I Repeatability and reproducibility
NOTE 17 For definitions of repeatability and
reproducibility, their interpretation in terms of the stan-
The precision of a calculated physical property value,
dard deviation of the population of values as given b
which results solely from random errors in the ana-
equation (17), and for the origin of the factor 2 2
J”
lytical procedures, may be expressed in terms of re-
therein, see for example reference [26] in annex M.
peatability and/or reproducibility, where these are
defined as follows.
By combining, in an appropriate manner, the re-
b)
peatability or reproducibility of the concentration
Repeatability: The value below which the absol-
of each component in the gas analysis; the ap-
ute difference between a pair of successive test
propriate combination formulae are given in 9.1.2
results obtained using the same method, on
and 9.1.3 (for the derivation of these equations,
identical test material, by the same operator, using
see annex H).
the same apparatus, in the same laboratory, within
a short interval of time, may be expected to lie
NOTE 18 The equivalence of a) and b) in practice as op-
with a specified probability. In the absence of
posed to principle is open to discussion. This is because the
other indications, the probability is 95 %. statistical link between the methods assumes that the re-
peatedly measured analytical values are distributed in a
Gaussian (normal) fashion for each component concen-
Reproducibility: The value below which the ab-
tration, and that this is also the case for the set of calculated
solute difference between two single test results
physical property values. Experience has shown that these
obtained using the same method, on identical test
criteria are not usually met, especially for small data sets
material, by different operators, using different
and/or sets containing outliers.
apparatus, in different laboratories, may be ex-
pected to lie with a specified probability. In the
absence of other indications, the probability is
95 %.
9.1.2 Estimation of repeatability
The latter quantity is usually significantly larger than
The repeatability AH, at a 95 % confidence level, of
the former. Each measure of the precision of a calcu-
the calorific value H may be calculated either from
lated physical property depends only upon the pre-
equation (17) (with Y replaced by H), or directly from
cision of the analytical data.
the analytical data, using the appropriate expression,
as follows:
concepts of repeatability and
The general
reproducibility may be applied not only to physical
a) When all components except methane are analy-
properties calculated from compositional analyses,
sed, the methane (i = I) concentration being cal-
but also to each component concentration in the
culated by difference, then
analyses from which the properties are derived. Con-
I/*
sequently, the repeatability or reproducibility of a
physical property value may actually be obtained in
AH~ix = A [AXjm (Hp - HP)] * . . .
(Is>
either of two apparently equivalent ways, viz.
j=2
I
a) By direct application of the above definitions to
where
repeated calculations of the physical property in
question, i.e. from the equation
AHki, is the repeatability of the calculated
l/2
n
ideal-gas calorific value (molar or volu-
metric basis) for the mixture;
r >wY,* i
AY =
AXj is the repeatability of the mole fraction
of component j in the mixture of N
components;
AY is either the repeatability or Hi" is the ideal-gas calorific value of com-
ponent j;
reproducibility of Y, as appropriate;

Q IS0
IS0 6976: 1995(E)
NOTE 19 The contribution of the repeatability AZ of the
of
the ideal-gas calorific value
*,O
calculated compression factor 2 to the overall repeatability
methane.
AH of the calorific value on a volumetric basis is small, and
is therefore ignored in the above formulation; likewise, the
When all components including methane are
b)
contribution of AZ to the overall repeatability Ap of the real-
analysed, then
gas density, Ad of the real-gas relative density and AW of the
real-gas Wobbe index is also ignored.
9.1.3 Estimation of reproducibility
The reproducibilities AH, Ad, Ap and AW of the calorific
where, although Hii, is calculated using the nor-
values, relative density, density and Wobbe index may
malized mole fractions xj, AxjT is the repeatability
be calculated by means of the equations (I 8) to (24)
of the mole fraction of component j in the mixture
inclusive, provided that the AXj and Ax,: in equations
of N components before normalization is carried
(I 8), (I 9), (22) and (23) are now identified as the ap-
out.
propriate reproducibilities of the mole fractions +. The
reproducibilities may also be determined from the
The repeatability Ad of the relative density and
Ap of the density may be calculated from the fol-
calculation of 2 2 times the standard deviation of
lr
lowing equations, respectively:
the population of calculated values of H, d, p or W,
using equation (17), where the analyses of compo-
Ad = -@f-
. . .
(20)
sitions have been carried out in accordance with the
Mair
definition of reproducibility given in 9.1 .I.
AM-P
. . .
(21)
Ap = R.T
9.2 Trueness
where AM is the repeatability of the mean molar
Observations of the precision of analytical data cannot
mass M of the natural gas, given by
be regarded as carrying any implication for the
- for case a):
trueness of those data; it is entirely possible to
achieve excellent precision at the same time as very
bad trueness.
The absolute trueness of a calculated physical
property value of a natural gas mixture may be con-
sidered as resulting from the combination of three in-
- For case b):
dependent sources of systematic error, viz.
a) uncertainties in the basic data given in tables 1 to
5;
(j= 1
b) bias in the method of calculation which uses
where Mj is the molar mass of component j.
these data;
The repeatability AW of the Wobbe index may be
c) uncertainties (as distinct from random impre-
calculated from the equation
cision) in the analytical data used as input to the
method.
(24)
In practice, it is difficult to make calculations of
trueness due to the lack of adequate information; for
example, reference back to original sources of basic
As for the calorific value, the repeatabilities AM, Ad, data often reveals information concerning precision
Ap and AW may also be determined by calculation of
only (see, in this context, the discussion of methane
the standard deviation of a set of calculated property
given in annex G), and the same is often true for
values [i.e., from equation (17) with Y replaced by M,
analytical data. In addition, a rigorous approach would
d, p or W, as appropriate] where the compositional provide an absolute uncertainty, whereas what is of-
analyses have been carried out in accordance with the ten required in practice is an estimate of the uncer-
definition of repeatability given in 9.1 .I. However, the tainty of a physical property value relative to some
provision given in note 18 to 9.1 .I still applies. datum point. For example, calorific values are often

0 IS0
IS0 6976: 1995(E)
referenced to the calorific value of pure methane; and possibly in the future, when the accuracy of
consequently any uncertainty in the assumed calorific natural gas analysis has improved), a more rigorous
approach, based on a), b) and c), may be necessary.
value of methane does not contribute to the relative
uncertainty of the calorific value of a natural gas, or to
the difference between the calorific values of two
9.3 Expression of results
different natural gases.
The number of significant figures which are given for
Experience has shown that the relative uncertainties
the value of each property should reflect the expected
of the physical property values considered herein will
accuracy of calculation of the property in question.
be most strongly influenced by uncertainties in the
Even in the case of a “perfect,, analysis, the results
analytical data, and that contributions from uncer-
of calculations for mixtures should be reported to no
tainties in basic data and bias in the method of calcu-
better than the following levels of significance.
lation will be very small. The contributions from the
Calorific value - molar basis: 0,Ol kJ-mol- ’
basic data are expected to be less than 0,05 % and
from bias in the method of calculation to be less than
- mass basis: 0,Ol MJekg- ’
0,015 %. These contributions may be neglected when
- volumetric basis: 0,Ol MJ=mm3
compared to the uncertainty in the analytical data
Relative density: 0,000 1
from the analysis of a typical natural gas mixture
Density: 0,000 1 kg-mm3
containing 12 to 20 components.
Wobbe index: 0,Ol MJ=mm3
For those cases where the contributions from uncer-
tainties in the basic data and from bias in the method However, attention must be paid to whether the ana-
of calculation are significant when compared with the lytical data do in fact justify quoting to this level of
analytical uncertainty (for example, for the high accu- supposed significance and, if not, the number of sig-
racy analysis of mixtures of only a few components, nificant figures quoted should be reduced accordingly.

IS0 6976:1995(E)
10 Tables of recommended data
Table 1 - Molar mass for components of natural gases
Values
Values
Component Component
kgmkmol- ’
kgmkmol- ’
1 Methane 16,043
39 Methanol 32,042
2 Ethane 30,070
40 Methanethiol 48,109
3 Propane 44,097
41 Hydrogen
2,015 9
4 n-Butane 58,123
42 Water
18,015 3
5 2-Methylpropane 58,123
43 Hydrogen sulfide 34,082
6 n-Pentane 72,150
44 Ammonia
17,030 6
7 2-Methylbutane 72,150
45 Hydrogen cyanide 27,026
8 2,2-Dimethylpropane 72,150
46 Carbon monoxide 28,010
9 n-Hexane 86,177
47 Carbonyl sulfide 60,076
10 2-Methylpentane 86,177
48 Carbon disulfide 76,143
11 3-Methylpentane 86,177
12 2,2-Dimethylbutane 86,177
49 Helium
4,002 6
13 2,3-Dimethylbutane 86,177
50 Neon
20,179 7
14 n-Heptane 100,204
51 Argon 39,948
15 n-Octane 114,231
52 Nitrogen 28,013 5
16 n-Nonane 128,258
53 Oxygen 31,998 8
17 n-Decane 142,285
54 Carbon dioxide 44,010
55 Sulfur dioxide 64,065
18 Ethylene 28,054
56 Dinitrogen monoxide 44,012 9
19 Propylene 42,081
57 Krypton 83,80
20 1 -Butene 56,108
58 Xenon 131,29
21 &-2-B utene 56,108
Air
28,962 6
22 trans-IL-Butene 56,108
23 2-Methylpropene 56,108
NOTE - Values of the molar mass are numerically
24 1 -Pentene 70,134
identical to values of relative molecular
...