Repositorio Institucional

Report

Bilateral Comparison EUROMET 919 Natural gas

Rob M. Wessel1, Adriaan M.H. van der Veen1, Paul R. Ziel1, Celia Puglisi2

1NMi Van Swinden Laboratorium B.V. (NMi VSL), Thijsseweg 11, 2629 JA Delft, the Netherlands 2Instituto Nacional de Tecnologia Industrial (INTI), Parque Tecnológico Miguelete Colectora Av. Gral. Paz 5445, B1650KNA, C.C. 157 B1650WAB San Martin, Buenos Aires Argentinië

Field

Amount of substance

Subject

Comparison in the field of natural gas analysis

Table of contents

Field .................................................................................................................................................... 1 Subject ................................................................................................................................................ 1 Table of contents................................................................................................................................. 1 Introduction......................................................................................................................................... 1 Participants.......................................................................................................................................... 2 Measurement standards....................................................................................................................... 2 Measurement protocol ........................................................................................................................ 2 Measurement equation ........................................................................................................................ 2 Measurement methods ........................................................................................................................ 4 Degrees of equivalence ....................................................................................................................... 4 Results................................................................................................................................................. 5 Discussion of results ........................................................................................................................... 8 Conclusions......................................................................................................................................... 8 References........................................................................................................................................... 8 Coordinator ......................................................................................................................................... 9 Project reference ................................................................................................................................. 9 Completion date .................................................................................................................................. 9 Annex A: Measurement Reports....................................................................................................... 10 Measurement Report from INTI ....................................................................................................... 10 Measurement Report from NMi VSL ............................................................................................... 13

Introduction

The measurement of composition of natural gas mixtures is commonly used for the calculation of its calorific value. Natural gas is a fossil fuel and its economic value per unit of volume or mass is mainly determined by its calorific value. Other aspects that might influence the economic value of natural gas, such as its sulphur content, have not been addressed in this EUROMET consultation. In most cases, the calorific value and other thermodynamical properties are calculated from composition data.

At the highest metrological level, natural gas standards are commonly prepared gravimetrically as PSMs (Primary Standard Mixtures). This comparison is using the same design as international key comparison CCQM-K23b [1]. The mixture concerned contains nitrogen, carbon dioxide and the alkanes up to butane.

1



Participants

As in CCQM-K23b, NMi-VSL was the coordinating laboratory. The natural gas PSM was prepared by NMi-VSL and subsequently checked against other PSMs for consistency. After analysis the mixture was shipped to INTI for measurement.



Measurement standards

Table 1 shows the nominal composition of the mixtures used (expressed as amount of substance fractions).



Table 1: Nominal composition of the mixtures



Component

Nitrogen Carbon dioxide Ethane Propane n-Butane iso-Butane Methane



Amount fractions x (10-2 mol mol-1) 4 1 3 1 0.2 0.2 Balance



The mixture is prepared gravimetrically and subsequently verified.

The preparation of the mixture has been carried out using the normal procedure for the preparation of gas mixtures [6]. The following gases were used: methane (5.5), ethane (5.0), n-butane (3.5) and isobutane (3.5) from Scott Specialty Gases, Nitrogen (6.0) from Air Products, Carbon dioxide (5.2) from AGA, and propane (3.5) from Air Liquide. All gases were directly introduced in the final mixture. The final mixture had a pressure of approximately 7 MPa.

After preparation, the mixture was verified by comparing the mixture with PSMs from the standards maintenance programme. The mixtures have been verified using GC/TCD (nitrogen, carbon dioxide, methane, and ethane) and GC/FID (propane, iso-butane, and n-butane).



Measurement protocol

The laboratories were requested to use their normal procedure for the measurement of the composition of the gas mixtures. For participation in this bilateral comparison, it had been requested that participants determine all components in the mixture, and not just a subset.

The participants were also requested to describe their methods of measurement, and the models used for evaluating the measurement uncertainty.



Measurement equation

The reference values used in this consultation are based on gravimetry, and the purity verification of the parent gases/liquids. In the preparation, the following four groups of uncertainty components have been considered: 1. gravimetric preparation (weighing process) (xi,grav) 2. purity of the parent gases (Δxi,purity) 3. stability of the gas mixture (Δxi,stab) 4. correction due to partial recovery of a component (Δxi,nr)



2



The amount of substance fraction xi,prep of a particular component in mixture i, as it appears during use of the cylinder, can now be expressed as



xi, prep = xi,grav Δ + xi, purity + Δxi,stab + Δxi,nr ,



(1)



The value obtained from equation (1) is sometimes referred to as “gravimetric value”. Assuming independence of the terms in equation (1), the expression for the combined standard uncertainty becomes



u2 i, prep



=



u2 i , grav



+ u2 i, purity



+



u2 i ,stab



+



u2 i ,nr



.



(2)



For the mixtures used in this consultation, the following statements hold (for all components involved). First of all, the preparation method has been designed in such a way that



Δxi,nr = 0,



(3)



and its standard uncertainty as well. Furthermore, long-term stability study data has shown that



Δxi,stab = 0,



(4)



and its standard uncertainty as well. In practice, this means that the scattering of the results over time in the long-term stability study can be explained solely from the analytical uncertainty (e.g. calibration, repeatability of measurement). On this basis, using the theory of analysis of variance [8,9] the conclusion can be drawn that the uncertainty due to long-term stability can be set to zero.



Summarising, the model reduces to



xi, prep = xi,grav + Δxi, purity ,



(5)



and for the associated standard uncertainty, the following expression is obtained



u = u + u 2 i, prep



2 i , grav



2 i, purity



.



(6)



The validity of the mixtures has been demonstrated by verifying the composition as calculated from the preparation data with that obtained from (analytical chemical) measurement. In order to have a positive demonstration of the preparation data (including uncertainty, the following condition should be met [7]



xi, prep − xi,ver ≤ 2



u2 i, prep



+



u2 i ,ver



.



(7)



The factor 2 is a coverage factor (normal distribution, 95% level of confidence). The assumption must be made that both preparation and verification are unbiased. Such bias has never been observed. The uncertainty associated with the verification highly depends on the experimental design followed. In this particular consultation, an approach has been chosen which is consistent with CCQM-K3 [10] and takes advantage of the work done in the gravimetry study CCQM-P23 [11].

The reference value of mixture i in a consultation1 can be defined as



xi,ref = xi,ref + δxi,ref ,



(8)



where



xi,ref = xi, prep + Δxi,ver .



(9)



1 This definition of a reference value is consistent with the definition of a key comparison reference value, as stated in the mutual recognition arrangement (MRA) [4].

3



Since the amount of substance fraction from preparation is used as the basis, the expectation of the correction <Δxi,ver> due to verification can be taken as zero, which is consistent with the assumption made earlier that both preparation and verification are unbiased. Thus, (9) can be expressed as



xi,ref = xi, prep + δxi, prep + δΔxi,ver .



(10)



This expression forms the basis for the evaluation of degrees of equivalence in this consultation. For all mixtures, it has been required that



Δxi,ver = 0,



(11)



that is, there is no correction from the verification. The verification experiments have demonstrated that within the uncertainty of these measurements, the gravimetric values of the consultation mixture agreed with older measurement standards.

The expression for the standard uncertainty of a reference value becomes thus



u2 i ,ref



=



u2 i, prep



+



u2 i ,ver



.



(12)



The values for ui,ref are given in the tables containing the results of this consultation.



Measurement methods

The measurement methods used by the participants are described in annex A of this report. A summary of the calibration methods, dates of measurement and reporting, and the way in which metrological traceability is established is given in table 2.



Table 2: Summary of calibration methods and metrological traceability



Laboratory INTI

NMi VSL



Measurements Calibration

2007-01-09 2-points 2007-05-09 2007-21-09 2006-08-18 OLS



Traceability NPL

Own standards



Degrees of equivalence

A unilateral degree of equivalence in comparisons is defined as [4]



Δxi = Di = xi − xRV ,



(13)



and the uncertainty of the difference Di at 95% level of confidence. Here xRV denotes the reference value, and xi the result of laboratory i. 2 Appreciating the special conditions in gas analysis, it can be expressed as



Δxi = Di = xi − xi,ref .



(14)



The standard uncertainty of Di can be expressed as



( ) u2 Δxi



=



+ui2,lab



+



u2 i, prep



+



u2 i ,ver



,



(15)



assuming that the aggregated error terms are uncorrelated. As discussed, the combined standard uncertainty of the reference value comprises that from preparation and that from verification for the mixture involved. A bilateral degree of equivalence is defined as [4]



2 Each laboratory receives one cylinder, so that the same index can be used for both a laboratory and a cylinder. 4



Dij = Di − D j ,



(16)



and the uncertainty of this difference at 95% level of confidence. Under the assumption of independ-



ence of Di and Dj, the standard uncertainty of Dij can be expressed as



( ) u2 Dij



=



+ui2,lab



+ ui2, prep



+



u2 i ,ver



+



u



2 j ,lab



+



u



2 j,



prep



+



u



2 j ,ver



.



(17)



The assumption of independence is not satisfied by the preparation and verification procedures. It is well known that the use of pre-mixtures leads to correlations in the final mixtures. The standard uncertainty from verification is based on the residuals of a straight line through the data points (response versus composition), and these residuals are correlated too. However, the uncertainty of a degree of equivalence is still dominated by the uncertainty of the laboratory, so that these correlations, which certainly influence Dij and its uncertainty, will have little practical impact.

In the figure 1, the degrees of equivalence are given relative to the gravimetric value. The uncertainties are, as required by the MRA [4], given as 95% confidence intervals. For the evaluation of uncertainty of the degrees of equivalence, the normal distribution has been assumed, and a coverage factor k = 2 was used. For obtaining the standard uncertainty of the laboratory results, the expanded uncertainty (stated at a confidence level of 95%) from the laboratory was divided by the reported coverage factor.



relative deviation (%) N2 CO2 C2H6 C3H8 i-C4H10 n-C4H10 CH4 N2 CO2 C2H6 C3H8 i-C4H10 n-C4H10 CH4



1.50 0.50 -0.50 -1.50 -2.50 -3.50



Euromet 919 natural gas



components



INTI



NMi



Figure 1: Degrees of equivalence



Results

In this section, the results of this consultation are summarised. In the tables, the following data is presented xprep amount of substance fraction, from preparation (10-2 mol/mol) uprep uncertainty of xprep (10-2 mol/mol)

5



uver uncertainty from verification (10-2 mol/mol) uref uncertainty of reference value (10-2 mol/mol) xlab result of laboratory (10-2 mol/mol) Ulab stated uncertainty of laboratory, at 95% level of confidence (10-2 mol/mol) klab stated coverage factor Δx difference between laboratory result and reference value (10-2 mol/mol) U(Δx) Expanded uncertainty of difference Δx, at 95% level of confidence3 (10-2 mol/mol)

3 As defined in the MRA [4], a degree of equivalence is given by Δx and U(Δx). 6



Table 3: Results (expressed in 10-2 mol/mol)



N2 CO2 C2H6 C3H8 i-C4H10 n-C4H10 CH4 N2 CO2 C2H6 C3H8 i-C4H10 n-C4H10 CH4



xprep

INTI



uref



xlab



4.1266 0.0051



klab

4.12



INTI



1.0129 0.0013 1.000



INTI



2.9270 0.0036 2.918



INTI



0.9993 0.0013 0.998



INTI



0.2061 0.0003 0.207



INTI



0.2036 0.0002 0.204



INTI



90.5240 0.0720



89.4



NMi



4.1266 0.0051 4.118



NMi



1.0129 0.0013 1.0119



NMi



2.9270 0.0036 2.925



NMi



0.9993 0.0013 0.9992



NMi



0.2061 0.0003 0.2059



NMi



0.2036 0.0002 0.2034



NMi



90.5240 0.0720 90.505



Ulab

2



Δx

0.39



2 0.015



2 0.032



2 0.019



2 0.003



2 0.003



2



1.7



2 0.008



2 0.0022



2 0.007



2 0.0026



2 0.0005



2 0.0007



2



0.1



U(Δx)

-0.0066 0.390 -0.0129 0.015 -0.0090 0.032 -0.0013 0.019 0.0009 0.003 0.0004 0.003 -1.1240 1.702 -0.0086 0.009 -0.0010 0.003 -0.0020 0.008 -0.0001 0.003 -0.0002 0.001 -0.0002 0.001 -0.0190 0.123



7



Discussion of results

In all cases, the departure from the reference value is smaller than the associated expanded uncertainty. For nitrogen, the reported uncertainty for INTI is very large. The laboratory reported that this is caused by the effect that the nitrogen content in Argentine natural gas differs appreciably from the content in this mixture and that the reference gas standards were rather far away from the nominal value.

Conclusions

The agreement of the results in bilateral comparison is acceptable. For all parameters, the results agree within 1.5% (or better) with the reference value.

References

[1] Van der Veen A.M.H., Ziel P.R., De Leer E.W.B., Smeulders D., Besley L., Smarçao da Cunha V., Zhou Z., Qiao H., Heine H.-J., Tichy J., Lopez Esteban T., Mace T., Nagyné Szilágyi Z., , Kim J.S., Perez Castorena A., Perez Urquiza M., Rangel Murillo F., Serrano Caballero V.M., Carbajal Alarcón C.E., Ramírez Nambo C., Avila Salas M., Rakowska A., Dias F., Konopelko L.A., Popova T.A., Pankratov V.V., Kovrizhnih M.A., Meshkov A.V., Efremova O.V., Kustikov Y.A., Musil S., Milton M.J.T., “Final Report International Comparison CCQM K23ac – Natural gas types I and III”, April 2006

[2] Alink A., “The first key comparison on Primary Standard gas Mixtures”, Metrologia 37 (2000), pp. 35-49

[3] BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, “Guide to the expression of uncertainty in measurement”, first edition, ISO Geneva, 1995

[4] CIPM, “Mutual recognition of national measurement standards and of calibration and measurement certificates issued by national metrology institutes”, Sèvres (F), October 1999

[5] BIPM, Annex B to the MRA, http://kcdb.bipm.fr/BIPM-KCDB//AppendixB/

[6] Alink A., Van der Veen A.M.H., “Uncertainty calculations for the preparation of primary gas mixtures. 1. Gravimetry”, Metrologia 37 (2000), pp 641-650

[7] International Organization for Standardization, ISO 6142:2001 Gas analysis - Preparation of calibration gas mixtures - Gravimetric methods, 2nd edition

[8] Van der Veen A.M.H., Pauwels J., “Uncertainty calculations in the certification of reference materials. 1. Principles of analysis of variance”, Accreditation and Quality Assurance 5 (2000), pp. 464-469

[9] Van der Veen A.M.H., Linsinger T.P.J., Lamberty A., Pauwels J., “Uncertainty calculations in the certification of reference materials. 3. Stability study”, Accreditation and Quality Assurance 6 (2001), pp. 257-263

[10] Van der Veen A.M.H, De Leer E.W.B., Perrochet J.-F., Wang Lin Zhen, Heine H.-J., Knopf D., Richter W., Barbe J., Marschal A., Vargha G., Deák E., Takahashi C., Kim J.S., Kim Y.D., Kim B.M., Kustikov Y.A., Khatskevitch E.A., Pankratov V.V., Popova T.A., Konopelko L., Musil S., Holland P., Milton M.J.T., Miller W.R., Guenther F.R., International Comparison CCQM-K3, Final Report, 2000

[11] Van der Veen A.M.H., Van Wijk J.I.T., “CCQM P23 – Gravimetry”, Protocol, NMi VSL, Delft (NL), October 2000

8



Coordinator

NMi Van Swinden Laboratorium B.V. Department of Chemistry Rob M. Wessel Thijsseweg 11 2629 JA Delft the Netherlands Phone +31 15 2691 733 Fax +31 15 261 29 71 E-mail avdveen@nmi.nl

Project reference

EUROMET 919

Completion date

June 2007

9



Annex A: Measurement Reports



Measurement Report from INTI



Laboratory Cylinder number



: INTI (Instituto Nacional de Tecnología Industrial) : D751971



Measurement #1



Component



Date (dd/mm/yy)



Nitrogen



09/01/07



Carbon dioxide



09/01/07



Ethane



09/01/07



Propane



09/01/07



iso-Butane



09/01/07



n-Butane



09/01/07



Methane



09/01/07



Result (%-mol/mol)

4,1040 1,001 2,9076 0,9972 0,2070 0,2032 89,482



Measurement #2



Component



Date (dd/mm/yy)



Nitrogen



09/05/07



Carbon dioxide



09/05/07



Ethane



09/05/07



Propane



09/05/07



iso-Butane



09/05/07



n-Butane



09/05/07



Methane



09/05/07



Result (%-mol/mol)

4,1133 0,999 2,9236 0,9959 0,2066 0,2031 89,604



Standard deviation (% relative)

1,0 0,3 0,4 0,4 0,5 0,5 0,3

Standard deviation (% relative)

1,4 0,3 0,3 0,2 0,6 0,4 0,3



number of replicates

5 5 5 5 5 5 5

number of replicates

5 5 5 5 5 5 5



Measurement #3



Component



Date (dd/mm/yy)



Nitrogen



21/05/07



Carbon dioxide



21/05/07



Ethane



21/05/07



Propane



21/05/07



iso-Butane



21/05/07



n-Butane



21/05/07



Result (%-mol/mol)

4,1456 0,999 2,9227 1,001 0,2062 0,2043



Standard deviation (% relative)

0,3 0,5 0,3 0,3 0,4 0,4



number of replicates

7 7 7 7 7 7



10



Methane



21/05/07



89,220



0,3



7



Results

Component

Nitrogen Carbon dioxide Ethane Propane iso-Butane n-Butane Methane



Result (%mol/mol)

4,12 1,000 2,918 0,998 0,207 0,204 89,4



Expanded Uncertainty (%mol/mol)

0,39 0,015 0,032 0,019 0,003 0,003

1,7



Coverage factor4

2 2 2 2 2 2 2



Reference Method: Method: Gas chromatography Instrument: HP 6890 Columns: HP – PLOT Q 19095P-Q04

HP – PLOT mol Sieve 5A19095P- MSO serial installation Sample injection: 6 port injection valve, loop 0.5 ml Detector CO2, methane and N2: TCD Detector other components: FID Carrier: He 5.0

Calibration Standards: Primary Reference Gas Mixtures prepared by NPL (Cylinder number A 348, NG 80 and NG 120).

Instrument Calibration: The instrument was calibrated using one point comparison between reference and sample gas.

For each component the reference gas with the most similar concentration to the sample was chosen.

The measurement sequence used was: standard – sample – standard.

The Nitrogen composition in the sample is very different from the typical values found in our country for natural gas. For this reason the composition of our gas standards are not very close to the sample.

Nevertheless, we used the closer standard we have to make the measurement and to check the results we also measured N2 using a calibration curve made with the three standards already mentioned.

Sample Handling: The sample was termostatized at room temperature and homogenized by rotation. Sample injection: Manual, 6 port injection valve



4 The coverage factor shall be based on approximately 95% confidence. 11



Uncertainty: The uncertainties of each component in measurements number 1, 2 and 3 were estimated using the following model:

One point calibration Cx = C1 * Ax / A1 Where Cx = concentration of x component in the sample

C1 = concentration of x component in the calibration gas Ax = response obtained for x component in the sample A1 = response obtained for x component in the calibration gas As both the sample and the calibration gas were analyzed in the same conditions: (UCx / Cx)2 = (UC1/ C1 )2 + (UAx/ Ax )2 + (UA1/ A1)2 Where UC1 = absolute uncertainty of x component in the calibration gas UCx = absolute uncertainty of x component in the sample UAx = Standard deviation of the response obtained for x component in the sample UA1 = Standard deviation of the response obtained for x component in the calibration gas. The uncertainties of each component in each measurement were combined to obtain the final uncertainty: (U final)2 = (U measurement 1)2 + (U measurement 2)2 + (U measurement 3)2

12



Measurement Report from NMi VSL



Reference Method:



One GC (specifically set up for natural gas analysis) was used in the analyses.



1.



Natural Gas Analyser (NGA):



GC:



HP6890 N (ISO 6974 configuration, Molsieve chanel not used)



Column: Porapak R , 3 m, 1/8 in od, 80/100 mesh.



Detectors:



1 Thermal Conductivity Detector (μ-TCD) and a Flame Ionisation



Deterctor (FID) placed at the exhaust of the TCD.



Valves:



1 sampling valve with 0,25 ml sampleloop



Sample introduction: Multi position gas sampling valves, injection at ambient pressure.



Oven Temperature: temperature program: 40 °C for 12 minutes, ramp 10 °C/min



to 150 °C, hold for 8 minutes.



Carrier:



He



Data Collection:



HP Chemstation software



The temperature program of the Porapak R column results in base-line separation of all the constituents of the samples. The TCD signal is used for nitrogen, carbon dioxide, methane, and ethane. Propane, iso-butane, and n-butane are analysed using the FID signal.



Calibration Standards: All standards have been prepared by the gravimetric method, according to ISO 6142. Several multi component calibration standards were used, all having methane as balance gas. Depending on the concentrations of the components, standards are prepared directly from pure gases or from so called preliminary mixtures that are prepared from the pure gases. After preparation the standards were verified against existing standards. A detailed composition of the standards is given below.

All pure gases were analysed before use by GC-FID and GC-TCD, except for methane and nitrogen. For nitrogen and methane purity analyses are only performed on selected cylinders using FT-IR and GC-DID in order to check the specifications given by the producer. The results of these purity analyses are expected to be representative for the cylinders that are not tested. The result of these analyses are combined in so called purity tables, that are used to calculate the composition and uncertainties of the gas mixtures that are prepared in the laboratory. The calculated mole fractions of the different components in a mixture therefore are not only based on the purity of the pure substances, but are also based on the presence of this component as an impurity in the other pure gases.

Instrument Calibration: The set of standards used for a measurement and the mixtures to be analysed are connected to the gas chromatograph as described in the paragraph “sample handling” . A measurement of a cylinder consist of 5 injections that are averaged and corrected for pressure using the following equation.

Y'=Y ⋅ P P0

Where Y’ is the corrected response, Y is the average response of the 5 injections, P is the average of the pressures measured when injecting the sample and P0 is the standard pressure.

The models used for the different curves are in all cases second order and unweighted regression is used.



Sample Handling: The cylinders were let to acclimatise to laboratory conditions before analysis was started. Each cylinder was equipped with a pressure-reducing unit set to approximately 2 bar. These pressure reducers were flushed at least 8 times before the first measurement. These flushings were distributed over a 24 hours time period. After the first measurement the connected reducers remained connected to the cylinder, until all measurements were performed. Before following measurements of the sample the pressure-reducing unit was

13



flushed only once. Afterwards the cylinders were connected by Teflon tubing to an electronic multiple stream selection valve. Stainless steel tubing to the sample inlet port/ sample loop of the GC connected the outlet valve of this valve. Before starting the automated analysis the Teflon tubings were flushed for 3 minutes and before injection the whole system was (pulsated) flushed for 3 minutes. Just before injection a valve positioned directly behind the stream selection valve is closed and the gas in the sample loop is allowed to reach ambient pressure after which the sample is injected.

Uncertainty:

Gravimetric preparation and impurities The uncertainty of the gravimetric preparation of the standards used was evaluated according to Alink and Van der Veen5. The uncertainty in the impurities present in all pure components and mixtures, that are used to prepare the standards are stored in purity tables. When a mixture is prepared, the uncertainty of the components is automatically calculated from the uncertainty of the gravimetric preparation and the uncertainties of the components present in the mother mixtures.

Stability, non-recovery and leakages All new prepared standards are verified for their composition against existing (gravimetrically prepared) standards. This verification is a check of the gravimetric preparation process, which includes determination of errors due to leakage of air into the cylinder, leakage of gas from the cylinder valve during filling, escape of gas from the cylinder, absorption of components on the internal surface of the cylinder. Only when no significant difference between the analysed and the gravimetric composition is found, the cylinder is approved as a new standard. Several selected cylinders covering the concentration ranges of all constituents in the natural gas standards are used for long term stability testing. During these tests no instability has been detected for any of the components. Because it is difficult or impossible to discern between these different uncertainty contributions, the standard deviation of the results of the stability measurements for a cylinder having a similar mole fraction was chosen to cover these uncertainties.

Calibration curve and repeatability The calibration curves where constructed using software based on ISO 6143. As indicated, second order curves where used. Together with the uncertainty of the gravimetrical concentrations of the calibration mixtures and the repeatability of the analyses of the calibration mixtures and the sample mixture, the concentration and its accompanied uncertainty where calculated for each constituent.



Model used for evaluating measurement uncertainty:

The uncertainty of the analyses is the combined uncertainty of two uncertainty sources: • Uncertainty of the component mole fraction in the standards, which is the combined uncertainty for the gravimetrical preparation, impurities, the stability, non recovery and leakages (XPSM). • Uncertainty of the calibration process, which is uncertainty contribution coming from the appropriateness of the calibration curve (model and its residuals) and the repeatability of the analysis (Δxanalysis)



Typical evaluation of the measurement uncertainty for nitrogen:



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.07034 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.05

0.04



Sensitivity coefficient

ci

1 1



Contribution ui(y)

% relative

0.05 0.08



Total:



xanalysis



0.07034



0.10



5 A. Alink and A.M.H. van der Veen, Uncertainty Calculations for the preparation of primary gas mixtures, Metrologia, 37 (2000) , pp. 641-650.

14



Typical evaluation of the measurement uncertainty for carbon dioxide:



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.02994 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.06

0.05



Total: xanalysis



0.02994



Typical evaluation of the measurement uncertainty for ethane:



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.09415 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.09

0.07



Total: xanalysis



0.09415



Typical evaluation of the measurement uncertainty for propane:



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.03394 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.12

0.02



Total: xanalysis



0.03394



Typical evaluation of the measurement uncertainty for iso-butane:



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.007967 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.07

0.03



Total: xanalysis



0.007967



Typical evaluation of the measurement uncertainty for n-butane:



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.009960 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.14

0.04



Total:



xanalysis



0.009960



Typical evaluation of the measurement uncertainty for methane:



Sensitivity coefficient

ci

1 1

Sensitivity coefficient

ci

1 1

Sensitivity coefficient

ci

1 1

Sensitivity coefficient

ci

1 1

Sensitivity coefficient

ci

1 1



Contribution ui(y)

% relative

0.06 0.09

0.11

Contribution ui(y)

% relative

0.09 0.07

0.12

Contribution ui(y)

% relative

0.12 0.04

0.13

Contribution ui(y)

% relative

0.10 0.06

0.12

Contribution ui(y)

% relative

0.14 0.08

0.17



15



Quantity Xi

xpsm Δxanalysis



Estimate xi

mol/mol

0.7537 0



Evaluation type (A or B)



Distribution



B



Normal



A



Normal



Standard uncertainty

u(xi) % relative

0.04

0.03



Total: xanalysis



0.7537



Standards and their mole fractions per measured component.



N2



Cylinder code Gravimetric Mole fraction



VSL205178



0.006132



VSL307429



0.007994



VSL209604



0.011914



VSL202608



0.024950



VSL203657



0.060075



Sensitivity coefficient

ci

1 1



Contribution ui(y)

% relative

0.04 0.03

0.05



CO2



Cylinder code Gravimetric Mole fraction



VSL209423



0.003985



VSL205178



0.006135



VSL307429



0.007998



VSL209604



0.011941



VSL203657



0.025174



VSL209546



0.060065



VSL507425



0.12021



C2H6



Cylinder code Gravimetric Mole fraction



VSL209423



0.009977



VSL205178



0.014957



VSL202608



0.020020



VSL307429



0.030115



VSL507425



0.045161



VSL209546



0.065695



VSL203657



0.079880



VSL209604



0.110020



16



C3H8



Cylinder code Gravimetric Mole fraction



VSL209423



0.0010126



VSL209545



0.001996



VSL202608



0.004005



VSL209604



0.005937



VSL205178



0.007924



VSL507425



0.010020



i-C4H10



Cylinder code Gravimetric Mole fraction



VSL307429



0.0003027



VSL209423



0.0004963



VSL209545



0.0006967



VSL202608



0.0010037



VSL205178



0.0014751



VSL209546



0.0019668



VSL209604



0.0029989



VSL309424



0.0049685



n-C4H10



Cylinder code Gravimetric Mole fraction



VSL307429



0.0003018



VSL209423



0.0004959



VSL209545



0.0007027



VSL202608



0.0009978



VSL205178



0.0014822



VSL209604



0.0029997



VSL309424



0.0049843



CH4



Cylinder code Gravimetric Mole fraction



VSL209546



0.64776



VSL507425



0.69674



VSL202608



0.74311



VSL203657



0.79689



VSL209604



0.84811



VSL307429



0.89865



VSL223555



0.93855



VSL205178



0.96189



VSL209423



0.98003



VSL209545



0.99210



17