ISO 6145-2:2014

INTERNATIONAL ISO
STANDARD 6145-2
Second edition
2014-08-15
Gas analysis — Preparation of
calibration gas mixtures using
dynamic methods —
Part 2:
Piston pumps
Analyse des gaz — Préparation des mélanges de gaz pour étalonnage
à l’aide de méthodes volumétriques dynamiques —
Partie 2: Pompes à piston
Reference number
©
ISO 2014
© ISO 2014
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Published in Switzerland
ii © ISO 2014 – All rights reserved

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols . 2
5 Principle and equipment . 3
5.1 Principle . 3
5.2 Equipment . 3
6 Calibration gas mixture preparation . 5
6.1 Safety issues . 5
6.2 Mixture feasibility . 6
6.3 Preparation system and setting-up of mixture composition . 7
6.4 Input pressure control . 7
6.5 Temperature control . 7
6.6 Homogenization . 7
6.7 Stability . 8
6.8 Output pressure and flow pulsation . 8
6.9 Composition of the parent gases . 8
7 Calculation of volume fractions and associated uncertainty evaluation .9
7.1 Calculation method A . 9
7.2 Calculation method B .10
8 Gas mixture composition verification .12
Annex A (normative) Amount-of-substance fractions .13
Annex B (informative) Uncertainty evaluation of the gas mixture composition .15
Annex C (informative) Gas mixture verification .21
Annex D (informative) Numerical example .25
Bibliography
.............................................................................................................................................................................................................................30
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. 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. 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 WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 158, Analysis of gases.
This second edition cancels and replaces the first edition (ISO 6145-2:2001), which has been technically
revised. The main objective of this revision is to extend the first edition for calculating the composition
in volume and amount–of–substance fractions from the displacement volumes of piston pumps.
Appropriate measurement functions and guidance on uncertainty evaluation are given for the mixing of
real gases at unequal operational conditions of the piston pumps.
ISO 6145 consists of the following parts, under the general title Gas analysis — Preparation of calibration
gas mixtures using dynamic methods:
— Part 1: Methods of calibration
— Part 2: Volumetric pumps
— Part 4: Continuous syringe injection method
— Part 5: Capillary calibration devices
— Part 6: Critical orifices
— Part 7: Thermal mass-flow controllers
— Part 8: Diffusion method
— Part 9: Saturation method
— Part 10: Permeation method
— Part 11: Electrochemical generation
ISO 6145-3, entitled Periodic injections into a flowing gas stream, has been withdrawn.
iv © ISO 2014 – All rights reserved

INTERNATIONAL STANDARD ISO 6145-2:2014(E)
Gas analysis — Preparation of calibration gas mixtures
using dynamic methods —
Part 2:
Piston pumps
1 Scope
ISO 6145 comprises a series of International Standards dealing with various dynamic methods used for
the preparation of calibration gas mixtures. This part of ISO 6145 describes a method and preparation
system using piston pumps. The mixture composition and its associated uncertainty are based on
calibration of the piston pumps by dimensional measurements.
The calibration gas mixtures prepared using this method consist of two or more components, prepared
from pure gases or other gas mixtures using gas-mixing pumps. Such gas-mixing pumps contain at
least two piston pumps, each driven with a defined ratio of strokes, and appropriate accessories for gas
feeding and mixture homogenization.
This part of ISO 6145 is applicable only to mixtures of gaseous or totally vaporized components including
corrosive gases, as long as these components neither react with each other nor with the wetted surfaces
of the mixing pump. The use of gas mixtures as parent gases is covered as well. Multi-component gas
mixtures and multi-step dilution procedures are included in this International Standard as they are
considered to be special cases of the preparation of two-component mixtures.
This part of ISO 6145 describes a method of preparing calibration gas mixtures whose composition
is expressed in volume fractions. The necessary equations and associated uncertainty evaluation to
express the gas composition in amount–of–substance fractions are given in Annex A.
With this method, provided that sufficient quality assurance and control measures are taken, calibration
gas mixtures can be prepared with a relative expanded uncertainty of 0,5 % (coverage factor k = 2) in
the volume fraction. Numerical examples showing that under specified conditions smaller uncertainties
are attainable are given in Annexes B through D.
Using this method, dilution ratios of 1:10 000 can be achieved in discrete increments. Lower fractions
−8
(down to 1 × 10 ) can be achieved by multi-stage dilution or by the use of gas mixtures as input gases.
Final mixture flow rates of 5 l/h to 500 l/h can be realized depending on the equipment used.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 7504, Gas analysis — Vocabulary
ISO 14912, Gas analysis — Conversion of gas mixture composition data
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, terms and definitions given in ISO/IEC Guide 99, ISO/IEC Guide 98-3,
ISO 14912, ISO 7504, and the following apply.
3.1
operational conditions
pressure and temperature in the piston pumps at which the gas mixture is prepared
3.2
parent gas
pure gas or gas mixture used for preparation of a gas mixture
3.3
piston pump
gas forwarding system comprising cylinder, piston, steering plate, and eccentric driving disk mounted
on a common plate
3.4
reduction gear ratio
quotient of the number of strokes and the maximum number of strokes of the piston pump that can be
set in distinct steps by the switch gear
3.5
reference conditions
pressure and temperature to which volume fractions refer
3.6
stroke volume
forwarding geometric displacement volume per stroke of a piston pump
4 Symbols
Symbol Quantity Unit
−1
B’ second virial coefficient (virial equation–of–state in pressure) Pa
i index of a component
k,l index of a piston pump; index of a parent gas
L gear ratio
N number of strokes (in a given period of time)
N maximum number of strokes (in a given period of time)
max
n amount–of–substance mol
n total amount–of–substance of a mixture mol
mix
p pressure Pa
−1 −1
R ideal gas constant J mol K
T temperature K
u standard uncertainty
V gas volume m
2 © ISO 2014 – All rights reserved

Symbol Quantity Unit
V stroke volume m
geo
x amount–of–substance fraction (of a component in a parent gas) 1
y amount–of–substance fraction (of a component in the prepared gas mixture) 1
Z compressibility 1
ϕ volume fraction (of a component in the prepared gas mixture) 1
φ volume fraction (of a component in a parent gas) 1
5 Principle and equipment
5.1 Principle
The principle of the dynamic preparation method described in this part of ISO 6145 is based on the
displacement volume of piston pumps forwarding defined gas portions that are continuously merged and
homogenized for obtaining the required gas mixture. For pure gases, the volume fraction of component
i in the prepared gas mixture is approximately equal to the volume of component i divided by total
volume of all components, as given by Formula (1):
NV⋅
igeo,i
ϕ (1)
≈
i
NV⋅
∑ kgeo,k
k
where ϕ denotes the volume fraction of component i at the operational conditions of the piston pumps.
i
These conditions may differ from the conditions at which the calibration gas mixture thus prepared is
going to be used.
The calculation of volume fractions is described in Clause 7, in two variants. Method A requires the
prepared gas mixture to be used at the operational conditions (7.1), whereas method B covers the
expression of the volume fractions at reference conditions (7.2). Depending on the situation, one of these
methods shall be used in applications where volume fractions are needed.
In applications, where amount–of–substance fractions are needed, these shall be calculated directly
from the displacement volumes. The necessary expressions and associated uncertainty evaluation are
given in Annex A.
5.2 Equipment
Calibration gas mixtures with defined composition are prepared using gas-mixing pumps containing
two or more piston pumps, pneumatically separated from each other. A common motor drives the piston
pumps via separate gear trains and individual switch gears. The number of strokes of the individual
piston pumps is defined by preset reduction gear ratios. The gas portions forwarded by each of the
piston pumps are quantified by the stroke volume V and by their individual number of strokes N
geo,k k
(see Figure 1).
Key
d diameter of cylinder
h height of piston stroke
Figure 1 — Principle of a piston pump
To achieve the required calibration gas mixture, separately forwarded gas portions are merged and
homogenized. Since the stroke volume V is constant, different gas compositions are prepared only
geo,k
by variation of the number of strokes N . The use of both quantities is sufficient for the calculation of
k
mixture composition when using pure gases.
The stroke volume of piston pump k is calculated from the diameter of its cylinder and the height of its
piston stroke
π
Vd=⋅ ⋅h (2)
geok, kk
The forwarded gas volume is usually given as a whole number times the stroke volume. The number of
strokes can be chosen in order to achieve the desired mixing ratio. The gear ratio L relates the stroke
k
number to the maximum number of strokes
NL=⋅N (3)
kk max
An example of realization of the described method is shown in Figure 2 for a gas-mixing pump comprising
two piston pumps 1 and 2 of the same size. Both piston pumps are driven by a common electrical motor,
key 8, via defined gear trains with switch gears key 2 and key 4, respectively. Gases 1 and 2 are fed to
the piston pumps via gas inlets figure footnotes a and b, respectively. Bubbling vessels (key 5) at the
gas inlets are used to control the input pressure to the piston pumps and to adjust a small excess gas
flow which is vented at ambient pressure. The temperature of each piston pump can be measured with
temperature sensors T and T that shall be integrated into the body of the piston pumps. The gases
1 2
forwarded by the piston pumps are merged and homogenized in mixing vessel (key 6). The final gas
mixture is provided at gas outlet (key 7) to the intended application. Details of the implementation
of temperature control of piston pumps and parent gases attaining reduced uncertainties is given in
Annex B.
4 © ISO 2014 – All rights reserved

Gas 1
+ Gas 2
2 4
1 2
1 3 6
T T
1 2
p p
5 1 5
a Gas 1 b
Gas 2
Key
p pressure, piston pump 1 4 switch gears 2
p pressure, piston pump 2 5 bubbling vessel
T temperature sensor, piston pump 1 6 mixing vessel
T temperature sensor, piston pump 2 7 gas outlet for gas mixture
1 piston pump 1 8 drive motor
a
2 switch gears 1 Gas inlet for gas 1.
b
3 piston pump 2 Gas inlet for gas 2.
NOTE Piston pumps 1 and 2 as shown in Figure 1.
Figure 2 — Example of realization for the dynamic preparation of two-component calibration
gas mixtures
6 Calibration gas mixture preparation
6.1 Safety issues
The possibility of dangerous reactions, such as explosions (e.g. mixtures containing flammable gases
and oxygen) or strongly exothermic polymerisations (e.g. hydrogen cyanide) and decompositions (e.g.
acetylene), shall be excluded for safety reasons. If there is the possibility of formation of hazardous
gas mixtures, all appropriate safety precautions shall be applied. Information on dangerous reactions
and dangerous combinations that shall be excluded for safety reasons is provided in dangerous goods
[1]
regulations and in gas supplier handbooks.
Safe discharge of toxic or flammable gases and gas mixtures shall be ensured. Contact with ignition
sources shall be avoided, if merging of the parent gases can form flammable mixtures. Short–term
concentration peaks can occur when the composition is changed.
Precautions shall be taken during feeding the parent gases to the piston pumps, handling the
intermediate gas mixtures and final mixtures. The compliance with applicable safety instructions of
the mixing pumps, pressurization pumps, and filling reservoirs shall be confirmed before beginning the
preparation.
6.2 Mixture feasibility
The choice of appropriate set-up and suitable procedure for dynamic preparation of gas mixtures can be
a complex procedure. At first, all requirements concerning the intended application of the prepared gas
mixture shall be defined. Then, the properties of available gases and gas mixtures, possible reactions
between gas components and the wetted material of the pumps and peripherals, and the purity and
impurities of the mixed gases shall be considered. Further, the characteristics of the applied gas-mixing
pumps and the blending method shall be considered.
The following phenomena shall be taken into account when considering the feasibility of preparing the
required gas mixture:
a) reactions between mixture components;
b) reactions with piston pump, pressurization pump, and container material;
c) reactions with elastomers and greases (e.g. in the piston pumps, the pressurization pump, the valve
seat and seals).
Reactions with elastomers and greases should be prevented by using only materials that are inert to
all components of the mixture. If this is not possible, measures should be taken to minimize corrosive
attack on the materials with which the gases will make contact such that there is no significant effect on
mixture composition and no danger in storage and use.
When choosing a suitable preparation procedure, a number of considerations should be made to ensure
that the most appropriate method is used. The following parameters should be considered:
a) number of components in the final mixture;
b) range of fractions of each component of the final mixture;
c) flow rate of the final mixture;
d) flow rate of the parent gases;
e) established composition of each parent gas mixture used;
f) blending method: parallel method — serial method — multiple dilution;
g) mechanical characteristics of the piston pumps to be used;
h) performance characteristics of the mixing pump to be used;
i) pressure to which the final gas mixture has to be delivered;
j) characteristics of the pressurization pump (if necessary);
k) possibility of condensation;
l) requirements on the preparation tolerance.
Using Formula (1), the target composition can be calculated and a preparation procedure selected.
The final mixture composition is calculated using the expressions given in Clause 7 for volume fractions
and Annex A for amount–of–substance fractions.
In principle, it is recommended to use gas mixing pumps at those operating conditions where the
influence of the sources listed in Table B.1 can be considered not significant. If this is not possible, the
6 © ISO 2014 – All rights reserved

corresponding influences have to be considered by an appropriate uncertainty contribution. Table B.1
and further information about potential sources of uncertainty are listed in Annex B. An example for a
set-up with reduced contribution of uncertainty of temperature is given in B.4.
6.3 Preparation system and setting-up of mixture composition
Examples for the setup of a complete system for the dynamic preparation of calibration gas mixtures
according to the volumetric method described in this part of ISO 6145 are shown schematically in
Figure 2, and in B.4 for high-end applications (i.e. applications with reduced uncertainty).
Gas containing the component(s) of interest and matrix gases shall be fed to piston pumps with slight
excess gas flow at a pressure slightly above ambient pressure and at constant temperature (preferably
at ambient temperature). The requirement of gas intake at the desired pressure can be met by use of
bubblers in a by-pass flow at the gas inlets. This excess gas flow also inhibits the leakage of air into the
pump.
Before starting preparation of calibration gas mixtures, the entire flow system external to the mixing
pump itself shall be checked for leak tightness and contaminations of gas conduits.
Gas portions forwarded by piston pumps are preset by positioning the reduction gear ratio in a way that
the target composition of the calibration gas mixture is obtained as described in Clause 7.
NOTE Expressions for the calibration gas mixture in terms of amount–of–substance fractions are given in
Annex A.
6.4 Input pressure control
Elimination of differences between input pressures of piston pumps is highly relevant for the performance
of the method. Pressures at the inputs of the gas-mixing pump shall be maintained as close as possible
to the same values for all pistons. For this purpose, the level of sealing liquid in the bubblers shall be the
same.
The pressure of gases taken from gas cylinders shall be reduced to the appropriate pressure using 1- or
2-stage pressure reducers. The use of precisely adjustable needle valves or diaphragm pressure reducing
valves is recommended to reduce the gas consumption. The regulators shall be directly connected to
the gas inputs of the gas-mixing pump. A slight excess of gas is conducted to ambient pressure via a by-
pass that is equipped with a bubbling vessel. The use of appropriate bubbling vessels allows reducing
pressure difference in the pumps to 10 Pa or less between the gas inlets.
6.5 Temperature control
Elimination of temperature differences between the piston pumps is highly relevant for the performance
of the method. The exposure of the mixing pump to all kinds of radiation and air flow shall be avoided.
The Joule-Thomson effect of expanding gases due to pressure reduction or evaporation in case of liquids
shall be minimized. If large gas volumes from compressed gas-cylinders are used, reheating of the gases
can be necessary.
For optimal performance, it is recommended to measure the temperatures using calibrated temperature
sensors using calibrated temperature sensors that are introduced into the sockets integrated into each
piston pump and to take temperature differences into account as necessary.
NOTE The operation of the piston pumps and the gas feed at a constant temperature reduces the uncertainty
associated with the composition, an example of its realization is given in B.4.
6.6 Homogenization
The gases forwarded by the piston pumps shall be merged and homogenized in a flow process. For this
purpose, the gas mixture is continuously conducted through one or more appropriate mixing vessels.
The design and volume of the mixing vessels shall be adapted to the stroke volume of the piston pumps,
their capacities being preferably 10 to 15 times the stroke volume of the largest piston pump.
NOTE An improvement of gas mixture homogeneity is attained by cascading two or three mixing vessels of
the same capacity rather than using only one mixing vessel with increased capacity.
The efficiency of the homogenization equipment, e.g. the mixing vessels, shall be verified by appropriate
methods for different gas mixtures and intended applications.
6.7 Stability
Calibration gas mixtures prepared according to this part of ISO 6145 are intended for direct use. If the
safety and mixture feasibility conditions are met, no degradation of the mixture composition occurs.
The reproducibility of a gas mixture generated by the preparation system is ensured under the condition
that the influencing factors, in particular temperature and pressure, are kept constant.
6.8 Output pressure and flow pulsation
After homogenization, the gas mixtures are available at the gas outlet at approximately ambient
pressure. Diameter and length of connecting tubes shall be of appropriate dimensions to avoid an
unacceptably high back pressure caused by flow resistance. Tubes with sufficiently wide inner diameter
are preferably used. Possible flow restrictions of connected analysers or other devices and apparatus
shall be minimized to the extent possible. If so necessary, an outlet pressure above ambient shall be
generated separately using suitable compression pumps with appropriate accessories.
Owing to the forwarding principle of piston pumps, the gas flow at the outlet is subject to pulsations in
flow. The influence of these pulsations can be minimized by technical means, e.g. appropriate diameter
of conduits, reduced flow resistance inside connected units, inserted buffers, or by-pass installations.
6.9 Composition of the parent gases
If pure gases are used, then the volume or amount–of–substance fraction of the main component shall be
corrected for the presence of impurities. In case of composition data in terms of amount–of–substance
fractions, the amount–of–substance fraction of the main component can be calculated using Formula
(4):
J
xx=−1 (4)
1 ∑ j
j=2
The standard uncertainty associated with the amount–of–substance fraction of the main component
(x ) is calculated using Formula (5)
J
2 2
ux()= ux() (5)
1 ∑ j
j=2
If the gas composition data are expressed as volume fractions, the volume fraction of the main component
is calculated using Formula (6)
J
φφ=−1 (6)
1 ∑ j
j=2
It is important to verify that the conditions (p and T) at which the volume fractions are given match
those at which the gases are mixed and used, respectively. Otherwise, the volume fraction shall be
converted from the stated conditions to the required conditions, using, e.g. the method of ISO 14912.
More guidance in converting volume fractions is given in 7.2.
8 © ISO 2014 – All rights reserved

The standard uncertainty associated with the volume fraction of the main component (φ ) is calculated
using Formula (7)
J
2 2
uu()φφ= () (7)
1 ∑ j
j=2
When using gas mixtures as parent gases, the composition (expressed in volume or amount–of–
substance fractions) can be used as such, provided that for volume fractions the conditions at which
the composition is stated match the operational and reference conditions. If these conditions differ,
appropriate correction(s) shall be applied in accordance with ISO 14912.
7 Calculation of volume fractions and associated uncertainty evaluation
7.1 Calculation method A
This calculation method can be used when the calibration gas mixture is used at the same conditions (p
and T) as those of the piston pumps. If this is not the case, the method of 7.2 shall be used instead.
The volume fraction of a component i in the calibration gas mixture is computed using Formula (8):
V φ
kki
∑
k
ϕ = (8)
i
V
∑ k
k
or, equivalently, using Formula (1),
NV⋅ φ
∑ kgeo,kki
k
ϕ = (9)
i
NV⋅
∑ kgeo,k
k
where φ denotes the volume fraction of component i in parent gas k. If the gas composition of the
ki
mixture to be diluted is given in amount–of–substance fractions, ISO 14912 shall be applied to convert
the amount–of–substance fractions into volume fractions.
If the stroke volumes and the maximum number of strokes of all piston pumps are the same, then the
volume fraction can also be computed using the gear ratios in Formula (10):
L φ
∑ kki
k
ϕ = (10)
i
L
∑ k
k
The standard uncertainty associated with ϕ is computed using Formula (11)
i
 
 
 
V L
22 2 2
1 k
uu()ϕϕ= + u ()φ (11)
 
 
ii ∑ ki
V L
 2  ∑ l 
k
 
 l 
where
2 2
 
V 2uV()+−()VV
2 1 21
u = (12)
 
V
V
 2 
where V and V denote the geometric volumes of the piston pumps P and P .
1 2 1 2
NOTE 1 The expression in Formula (12) accounts for the assumption that the stroke volumes of any two pistons
are the same. The formula is also applicable if the nominal volumes are the same, but V ≠ V . If both volumes are
1 2
exactly equal, Formula (12) reduces to the common expression for the squared standard uncertainty of a ratio of
two independent variables, as the second term in the nominator is zero.
NOTE 2 In case of multiple pumps with the same nominal volume, the difference in Formula (12), ()VV− is
to be replaced by s (V), where s denotes the standard deviation of the volumes of the pumps.
If not given as volume, the stroke volume shall be computed using Formula (2). The standard uncertainty
associated with the stroke volume can be computed using Formula (13)
2 2
2 2
V  V 
1  1 
geok, geok,
2 22 2 2 2
uV()= ππhd ud()+ du ()h + up()+ uT() (13)
   
geok,     k k
   
2 4 p T
   
k k
   
In B.3, examples are given for this calculation method, including an uncertainty statement for a gas
mixture with 4 components prepared with a gas-mixing pump with 4 piston pumps having different
geometric stroke volumes with a ratio of 100: 10: 1 giving a maximum dilution ratio of 1: 1 000.
An example with this calculation method, performing the calibration of a gas analyser for NO
1)
measurement in the environmental field with a measuring range 0 ppm to 100 ppm volume fraction is
given in Annex D.
7.2 Calculation method B
7.2.1 Calculation of volume fraction
The volume fraction of component i at p and T is given by Formula (14):
ref ref
−−11
Vp TZ Z φ
∑ kk kref ,kk ki
k
ϕ = (14)
i
−−11
Vp TZ Z
∑ kk kref .kk
k
1) ppm = parts per million
10 © ISO 2014 – All rights reserved

7.2.2 Calculation of compressibility and associated standard uncertainty
The expression for the volume fraction Formula (14) requires the calculation of the compressibility
twice: once at the conditions of mixing (p and T ) and a second time at conditions p and T . The
k k ref ref
evaluation of the compressibility can be carried out in different ways, including the use of equations–
[5] [5]
of–state. Alternatives to the use of equations–of–state include the use of tabulated data. ISO 14912
provides a calculation method based on the virial equation–of–state given by Formula (15):
Zp(,TB)'=+1 ()Tp (15)
Values for B’(T) are given, among others, in ISO 14912. The calculation of the gas compressibility is
described in detail in ISO 14912, including the evaluation of associated measurement uncertainty.
7.2.3 Uncertainty evaluation of the volume fraction
The basis for the uncertainty evaluation is Formula (17). The standard uncertainty associated with the
volume fraction of component i can be computed using
2 2 2 2
       
∂ϕ ∂ϕϕ∂ ∂ϕ
2 i 2 i 2 i 2 i 2
uu()ϕ = ()φ + uT()+ up()+ uV()+
       
i ∑∑ki k ∑∑k k
∂φ ∂T ∂p ∂V
 ki   k   kk   k 
k k k k
(16)
 
 
∂ϕ ∂ϕ
2 2
i i
u (ZZ )(+   uZ )
 
∑ k ∑ refk,
 
∂Z ∂Z
 k  refk,
k k  
The expressions for the sensitivity coefficients in Formula (16) read as follows
pV Z
∂ϕ 1
kk refk,
i
=
*
∂φ TZ
W
ki kk
pV ZVφϕ+ pZ
∂ϕ
kk refk,,ki ik kref k
i
=−
2 *
∂T
TZ W
k
kk
VZ φϕ− VZ
∂ϕ
kref ,,kkii kref k
i
=
*
∂p
TZ W
k
kk
pZ φϕ− pZ
∂ϕ
kref ,,kkii kref k
i
=
*
∂V
TZ W
k
kk
pV ZVφϕ+ pZ
∂ϕ
kk refk,,ki ik kref k
i
=
2 *
∂Z
ZT W
k
kk
∂ϕφpV −ϕ pV
i kk ki ik k
=
*
∂Z
TZ W
refk,
kk
where
* −−11
WV= pT ZZ
∑ kk k refk, k
k
The evaluation of the standard uncertainty associated with the pressure, temperature and volume is
exemplified in Annex B. Variations in gas temperature and pressure shall be duly incorporated in the
values for the respective standard uncertainties.
8 Gas mixture composition verification
Verification of the calculated gas mixture composition prepared by gas-mixing pumps shall be done
using one of the following methods:
a) comparison measurements with gas mixtures whose composition is established independently (e.g.
using ISO 6143);
b) determination of the gas density with gas density measuring systems (e.g. sink body gauges); this
method is only appropriate for binary gas mixtures if used as exclusive verification method; the
required minimum difference of density of the respective gases is a further limitation.
c) verification by gas mixtures pair–wise prepared using the gas-mixing pump to be verified
comprising the symmetry check performing comparison of two gas mixtures with x = 0,5 or ϕ = 0,5,
and verification of linearity performing comparison of two gas mixtures prepared with reduction
gear ratios L = 0,5; L = 0,2 and with L = 1,0; L = 0,4.
1 2 1 2
NOTE More information about these methods is given in Annex C.
The availability of reference gas mixtures with appropriate uncertainty levels for the amount–of–
substance fractions shall be established. A recommended scope of a validation procedure is given in
Annex D.
If there is no appropriate validation available for the intended range of application with respect to
the kind of gases of interest, the mixing ratios, and the forwarded gas volumes, it is necessary to do
verification with comparison measurements with 5 (better 7) reference gas mixtures. A recommended
scope of validation procedure is given in Annex D.
12 © ISO 2014 – All rights reserved

Annex A
(normative)
Amount-of-substance fractions
A.1 Calibration gas mixture composition
The number of moles (amount–of–substance) forwarded by piston pump k is given by Formula (A.1):
pV
kk
n = (A.1)
k
RT Z
kk
and shall be directly calculated from the forwarding displacement volumes [see Formula (1)].
Formula (A.1) is based on the equation–of–state for real gases.
For a gas mixture, the expression for the amount–of–substance fraction of component i is given by
Formula (A.2):
nx
∑ kki
k
y = (A.2)
i
n
∑ k
k
Apart from n , which can be computed using Formula (A.1), the amount–of–substance fractions of the
k
components of the parent gases are required. When mixing a gravimetrically prepared gas mixture with
a pure gas, usually the composition is available in amount–of–substance fractions. If other quantities are
used, the procedures of ISO 14912 shall be used to convert the gas composition data into amount–of–
substance fractions.
When purity data are available, these shall be processed as detailed in 6.9.
A.2 Uncertainty evaluation
The uncertainty evaluation can be carried out as follows. Applying the law of propagation of uncertainty
to Formula (A.2) leads to Formula (A.3)
2 2
   
∂y ∂y
2 2 2
i i
uy()= un()+ ux() (A.3)
   
i ∑∑k ki
∂n ∂x
 k   ki 
k k
The expressions for the sensitivity coefficients read as
∂y x y
i ki i
=−
∂n n n
k mix mix
and
∂y n
i k
=
∂x n
ki mix
where
nn=
mixk∑
k
The standard uncertainty associated with n is calculated using Formula (A.4):
k
2 2 2 2
n  n  n  n 
2 k 2 k 2 k 2 k 2
un()= up()+ uT()+ uV( )(+ uZ ) (A.4)
       
k k k kk k
p T V Z
 k   k   k   k 
NOTE Formula (A.4) is obtained by applying the law of propagation of uncertainty to Formula (A.1).
The evaluation of the standard uncertainty associated with p , T , V , and Z is analogous to that in 7.2.3
k k k k
and exemplified in Annex B.
14 © ISO 2014 – All rights reserved

Annex B
(informative)
Uncertainty evaluation of the gas mixture composition
B.1 Potential sources of uncertainty
All quantities having the potential of influencing the output quantities (i.e. volume or amount–of–
substance fractions) should be evaluated as uncertainty components. The list of all potential sources of
uncertainty is given in Table B.1. The sources of uncertainty are arranged in three groups, assigned to
the piston pumps, the gas components, and the gas mixture, respectively.
Table B.1 — Sources of uncertainty
Category of N° Source of uncertainty Notes
source
Sources 1 Uncertainty of the cylinder diameter *
assigned to
2 Uncertainty of the height of stroke *
the piston
3 Uncertainty of the number of strokes (stroke ratio) negligible
pumps
4 Influence of the expansion of cylinder diameter negligible
5 Influence of the expansion of the eccentric disk (height of stroke) negligible
Sources 6 Uncertainty of the compressibility *
assigned to
7 Uncertainty of the gas constant R negligible
the gas
components 8 Uncertainty of the operational pressure *
9 Uncertainty of the operational temperature *
10 Uncertainty of the parent gas composition *
11 Influence of the flow rate on the flow resistance at the *
cylinder inlet and outlet
12 Influence of density and viscosity on the flow resistance at the *
cylinder inlet and outlet
13 Adsorption and desorption of gases inside the piston-pump *
Sources 14 Influence of incomplete gas-mixture homogenization *
assigned to (inhomogeneity)
the gas
15 Influence of the dynamic pressure at the homogenization unit outlet *
mixture
16 Loss of gas components due to piston-pump leakage *
17 Permeation of air components into the system *
18 Influence of intrusion of gas components due to diffusion / leakage *
19 Influence of adsorption and desorption of gases inside the *
homogenization unit and gas ducts
* Uncertainty source to be considered in an uncertainty evaluation of the composition of a calibration gas mixture.
NOTE 1 The number of strokes (line 3) is a count and therefore assumed to have zero uncertainty.
NOTE 2 The expansion of the cylinder and eccentric disk (lines 4 and 5) are by far exceeded by the influence of temperature
and pressure on the forwarded gas volume. Hence, these factors can be regarded as negligible.
NOTE 3 The uncertainty associated with the ideal gas constant (line 7) is much smaller than that of other model variables
and cancels out in the combination and propagation of uncertainties.
According to the intended application and the required level of uncertainty, the identified sources should
be individually assessed and their contribution to the combined uncertainty of composition should be
quantified using the numerical procedure for uncertainty calculation given in Clause 7 and Annex A. The
individual assessment of the indicated sources of uncertainty is described in B.2.
The uncertainty of input quantities with significant contribution to the combined uncertainty of
composition is preferably evaluated as type A, i.e. by statistical analysis of series of measurements on
the input quantities. Type B evaluations of uncertainty are acceptable as well.
During the validation for each application the complete system should be assessed for the uncertainty
sources listed in Table B.1 marked with an “*” whether these cause a significant influence to the
combined uncertainty of the composition of the calibration gas mixture. If possible, this influence should
be minimized. In those cases where this is not possible, the remaining contribution should be included in
the evaluation of the overall uncertainty.
B.2 Assessment of potential sources and quantification of significant sources of
uncertainty
B.2.1 General
All sources of uncertainty listed in Table B.1 should be evaluated, except for those indicated as “negligible”.
The expressions for propagating the uncertainties are given in Clause 7 and Annex A.
B.2.2 Major sources of uncertainty
The uncertainty sources n° 1 and n° 2 as well as the influencing quantities n° 8 and n° 9 are assessed
as major and can be quantified by statistical analysis of different series of measurement (type A
analysis) as standard deviation. The measurement values are achieved by using calibrated gauges and
measuring instruments. The contribution of these sources of uncertainty to the combined uncertainty
of the quantities of composition volume fraction ϕ and amount–of–substance fraction y are calculated
separately according to the numerical method given in Clause 7 and Annex A.
Examples of quantity values for u(E) are given in Table B.2. These examples are based on measurements
using the commercially available gas-mixing pumps. The examined pumps comprise piston pumps of
−2 −2
the same size as mentioned in Clause 6 for calibration gases with fractions of 10 × 10 to 90 × 10 as
−2
well as piston pumps of different size with stroke-volume ratios of 100: 10 for fractions of 1 × 10 to
−2
10 × 10 .
Table B.2 — Uncertainty contributions expressed in volume fraction
Contribution of uncertainty u(ϕ)
Uncertainty
N° Source of uncertainty E
ϕ = (1,0– ϕ = (10–
u(E)
−2 −2
10) × 10 90) × 10
−5 −5
1 Uncertainty of the cylinder diameter 0,001 4 mm 1,0 × 10 3,6 × 10
−5 −5
2 Uncertainty of the height of stroke 0,002 mm 0,7 × 10 2,7 × 10
−5 −5
8 Uncertainty of the mixture pressure 10 Pa
...