ISO/TS 29041:2008

Gas mixtures — Gravimetric preparation — Mastering correlations in composition

In ISO/TS 29041:2008, the gravimetric mixture preparation as given in ISO 6142 is investigated for existing a priori influences, as well as correlations introduced by data processing. All calculations refer to an example which consists in the preparation of a synthetic natural gas of a target composition as follows: 1,4 mol % N2, 1,8 mol % CO2, 9,4 mol % ethane, 3,4 mol % propane, 1 mol % n-butane, and 83 mol % methane. All considerations given for this example concerning mixture feasibility, choice of preparation procedure, and weighing steps and sequences are the same as given in ISO 6142. This also applies to all estimates for basic uncertainty sources and the purity tables of the gases used for preparation.

Mélanges de gaz — Préparation gravimétrique — Maîtrise des corrélations en composition

General Information

• Status: Published
• Publication Date: 23-Jan-2008
• ICS: 71.040.40 - Chemical analysis
• Technical Committee: ISO/TC 158 - Analysis of gases
• Drafting Committee: ISO/TC 158/WG 3 - Gravimetric methods
• Current Stage: 9060 - Close of review
• Start Date: 02-Sep-2026

Standards Content (Sample)

TECHNICAL ISO/TS
SPECIFICATION 29041
First edition
2008-02-01

Gas mixtures — Gravimetric
preparation — Mastering correlations in
composition
Mélanges de gaz — Préparation gravimétrique — Maîtrise des
corrélations en composition



Reference number
ISO/TS 29041:2008(E)
©
ISO 2008

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ISO/TS 29041:2008(E)
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ISO/TS 29041:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Symbols and abbreviated terms . 1
4 Mixture preparation by gravimetry. 2
5 Unit conversion. 5
6 Inclusion of purity data . 5
7 Gas property calculation. 8
8 Summary and recommendations. 10
Annex A (normative) Generic approach to uncertainty calculation . 11
Bibliography . 14

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ISO/TS 29041:2008(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
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International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. 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.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of document:
⎯ an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
⎯ an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
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.
ISO/TS 29041 was prepared by Technical Committee ISO/TC 158, Analysis of gases.
This document is not to be regarded as an “International Standard”. It is proposed for provisional application
so that information and experience of its use in practice may be gathered. Comments on the content of this
document should be sent to the ISO Central Secretariat.

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ISO/TS 29041:2008(E)
Introduction
ISO/TC 158 decided at its meeting in Prague (October 2002) to investigate the influence of possible
correlations (both extrinsic and intrinsic) on the uncertainty calculation(s) for mixture composition and gas
mixture property data. Methods should be developed for taking all existing correlations into account, and
exemplified appropriately.
This Technical Specification describes the tools needed for full accounting of correlations, and exemplifies
how these tools should be applied to practical examples. Some recommendations are given which are
intended to provide support to the decision on whether or not, and in which situations, the full calculatory
scheme as described herein should be applied in practice, and in which situations simplified approaches as
given in ISO 6142 are considered sufficient for the intended purpose.


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TECHNICAL SPECIFICATION ISO/TS 29041:2008(E)

Gas mixtures — Gravimetric preparation — Mastering
correlations in composition
1 Scope
In this Technical Specification, the gravimetric mixture preparation as given in ISO 6142 is investigated for
influences of a priori existing, as well as correlations introduced by data processing.
All calculations refer to an example which consists in the preparation of a synthetic natural gas of a target
composition as follows: 1,4 mol % N , 1,8 mol % CO , 9,4 mol % ethane, 3,4 mol % propane, 1 mol % n-
2 2
butane, and 83 mol % methane.
All considerations given for this example concerning mixture feasibility, choice of preparation procedure, and
weighing steps and sequences are the same as given in ISO 6142. This also applies to all estimates for basic
uncertainty sources and the purity tables of the gases used for preparation.
All calculations follow the principles, and use the tools and algorithms laid down in Annex A. For the sake of
simplicity, procedural steps such as matrix transformation, inversion or matrix calculus are not detailed each
time they are used in the calculations.
2 Normative references
The following referenced documents are indispensable for the application 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 6142, Gas analysis — Preparation of calibration gas mixtures — Gravimetric method
3 Symbols and abbreviated terms
CV calorific value of gas component i, i = 1, …, n
i
CV calorific value of the gas mixture
G system of model equations describing the measurand
J Jacobian
m mass
m mass of the gas component in the mixture cylinder, as determined by gravimetry
g
m mass difference, as determined, between mixture and reference cylinder after the corresponding
m
filling step
m mass difference corrected between mixture and reference cylinder after the corresponding filling
x
step
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ISO/TS 29041:2008(E)
M molar mass of gas component i, i = 1, …, n
i
M molar mass of the gas mixture
Q transfer matrix
U(x) expanded uncertainty of a value x
u(x) standard uncertainty of a value x
2
u (p , p) variance (for i = j) of a value p , or covariance (for i ≠ j) of two values p and p
i j i i j
u buoyancy correction (see Note)
B
u correction accounting for cylinder expansion
exp
u uncertainty of balance indication (cumulated estimate)
m
u correction for residual gas in the cylinder after evacuation
R
V variance/covariance matrix for a set of results or parameters
w mass fraction of a component as determined by gravimetry
g
x mole fraction of gas component i in the final mixture, i = 1, ., n
i
pur
x mole fraction of gas component k in pure gas i used for gravimetric preparation
ik,
NOTE ISO 6142 uses symbols with lower-case letter “u” (e.g. u ) for variables other than uncertainties, namely for
B
corrections made for influential factors in the gravimetric mixture production process, e.g. buoyancy. This symbol
assignment to variables is also retained for the purposes of this document. The reader should be careful not to confound
values and value uncertainties. The uncertainty of, say, u is u(u ).
B B
4 Mixture preparation by gravimetry
For the weighing steps and sequence as described in the example, the values for the m and their
x
corresponding uncertainties (as given in Table 1) can be obtained from the raw data and uncertainty source
estimates.
Estimates for the corrections and their uncertainties are the same as in the CO in N example in ISO 6142.
2
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ISO/TS 29041:2008(E)
Table 1 — Component weighing data and their uncertainties for the gas mixture
Masses and Component
their
Vacuum n-Butane Propane Ethane CO N Methane
2 2
uncertainties
m [g] 50,000 21 37,999 302 7,999 707 50,000 21 65,999 937 73,999 78 345,998 422
m
u [g] −0,011 0,157 −0,731 −0,299 0,052 0,065 0,13
m
u [g] 0,007 45 0,005 66 0,001 19 0,007 45 0,009 84 0,001 1 0,051 58
B
u [g]   0,001 49 0,015 9
exp
u [g]    0,003 3
R
u(m ) [mg] 0,015 0,019 3 0,010 8 0,015 0,020 2 0,015 1 0,06
m
u(u ) [mg] 2,3 2,3 2,3 2,3 2,3 2,3 2,3
m
u(u ) [mg] 0,019 0,014 0,003 0,019 0,025 0,028 0,13
B
u(u ) [mg]   0,86 9,16
exp
u(u ) [mg]    1,9
R
m [g] 49,996 660 38,161 962 7,269 897 49,708 660 66,063 267 74,065 880 346,199 202
x
u(m ) [mg] 2,300 128 2,300 124 2,300 027 2,300 127 2,455 735 2,300 220 9,634 630
x
The following reasoning applies to possible correlations: it is assumed that u is a random variable governed
m
by a common distribution, and each realisation is a drawing from the distribution. Under this assumption, there
is no reason for making allowances for correlation(s) since the realisations are independent. The uncertainty
sources for the u estimates are the same, namely pressure, temperature, and humidity. This causes
B
correlation, but the common sources are not quantified in ISO 6142. There is no reason for assuming
correlations for the u estimate, and u occurs only once for methane. For m , a clear correlation exists
exp R m
since the same mass pieces are used, but their combinations are unknown (except for some cases). Usually,
these correlations are small and may be neglected in practice. Here, for demonstrating the principle of the
method they are included where obvious. The corresponding variance-covariance matrix for the data table is
given in Table 2.
Table 2 — Variance-covariance matrix for the weighing data in Table 1
V(m ) Vacuum n-Butane Propane Ethane CO N Methane
x 2 2
Vacuum 5,290 586 0 0 0,000 225 0,000 225 0,000 225 0
n-Butane 0 5,290 568 49 0 0 0 0 0
Propane 0 0 5,290 125 64 0 0 0 0
Ethane 0,000 225 0 0 5,290 586 0,000 225 0,000 225 0
CO 0,000 225 0 0 0,000 225 6,030 633 04 0,000 225 0
2
N 0,000 225 0 0 0,000 225 0,000 225 5,291 012 01 0
2
Methane 0 0 0 0 0 0 92,826 1
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ISO/TS 29041:2008(E)
Values in Table 1 are exemplified for the N column: The uncertainty of the m value for N is combined from
2 x 2
the contributing sources of uncertainty according to the usual uncertainty propagation rule. It holds
22 2 2
um()=+um( ) u(u )+u(u) (1)
x mm B
2
delivering a value of 2,300 3 mg. The corresponding variance is 5,291 012 01 mg and contained in the sixth
row of the N column. The m values for the N and the methane filling step are quite different, it was
2 m 2
assumed that different mass pieces were used. Other common sources of uncertainty are the corrections u
m
and u for which either an absence of correlation is assumed, or the correlations are negligible or unknown.
B
Thus, the covariance term is set to zero (seventh row of the N column). The same reasoning holds for the n-
2
butane/N and the propane/N pairs (second and third row of the N column).
2 2 2
The m values for the initial weighing (vacuum) and the ethane and CO filling step are quite similar or at least
m 2
in the region of 50 g, so it can be assumed that the same mass pieces were used. For simplicity, the
2
covariance arising from this instance was estimated as the variance u (m ) of the initial weighing of the
m
2 2
mixture cylinder containing only vacuum [u(m ) = 0,015 mg, u (m ) = 0,000 225 mg ]. It is the same for all
m m
three pairs (first, fourth and fifth row of the N column). Note that the values which appear in rows 1 to 7 in the
2
N column are repeated in columns 1 to 7 of the N row since variance-covariance matrices are symmetric.
2 2
From the set of equations:
m (butane) − m + m = 0
g vac butane
m (propane) − m + m = 0
g butane propane
m (ethane) − m − m = 0
g propane ethane
m (CO ) − m + m = 0
g 2 CO2 ethane
m (N ) − m + m = 0
g 2 N2 CO2
m (methane) − m + m = 0
g methane N2
the transfer matrix Q is formed according to the recipes given in Annex A, and the gas masses and the
variance-covariance matrix of the mixture composition are calculated from the m data of Table 1 and the
x
variance-covariance matrix in Table 2. This yields the values given in Table 3.
Table 3 — Gas masses in the mixture, their uncertainties and the variance-covariance matrix
n-Butane Propane Ethane CO N Methane
2 2
m [g] 11,834 698 30,892 065 56,978 557 16,354 607 8,002 613 272,133 322
g
u(m ) [mg] 3,252 869 3,252 798 3,252 801 3,364 635 3,364 698 9,905 408
g

V n-Butane Propane Ethane CO N Methane
2 2
n-Butane 10,581 154 −5,290 568 5 0,000 225 0 0 −0,000 225
Propane −5,290 568 5 10,580 694 −5,290 125 6 0 0 0
Ethane 0,000 225 −5,290 125 6 10,580 712 −5,290 361 0 −0,000 225
CO 0 0 −5,290 361 11,320 769 −6,030 408 0
2
N 0 0 0 −6,030 408 11,321 195 −5,290 787 01
2
Methane −0,000 225 0 −0,000 225 0 −5,290 787 98,117 112
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ISO/TS 29041:2008(E)
5 Unit conversion
The above composition is given as gas masses in grams (uncertainties in milligrams) and should now be
converted to mol/mol. This will also enable the inclusion of purity data which are given in the tables in mol/mol.
[1]
Calculations are carried out using CONVERT and yield the mole fraction
...