1、 Reference number ISO/TS 29041:2008(E) ISO 2008TECHNICAL SPECIFICATION ISO/TS 29041 First edition 2008-02-01 Gas mixtures Gravimetric preparation Mastering correlations in composition Mlanges de gaz Prparation gravimtrique Matrise des corrlations en composition ISO/TS 29041:2008(E) PDF disclaimer Th
2、is PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept th
3、erein the responsibility of not infringing Adobes licensing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file;
4、the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOC
5、UMENT ISO 2008 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 photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member bod
6、y in the country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2008 All rights reservedISO/TS 29041:2008(E) ISO 2008 All rights reserved iii Contents Page F
7、oreword 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 uncertain
8、ty calculation . 11 Bibliography . 14 ISO/TS 29041:2008(E) iv ISO 2008 All rights reservedForeword 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 ou
9、t 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 co
10、llaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. 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
11、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 m
12、arket 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 % o
13、f 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
14、 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 Intern
15、ational 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, Analys
16、is 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. ISO/TS 29041:
17、2008(E) ISO 2008 All rights reserved v 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
18、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 ar
19、e 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. TECHNICAL SP
20、ECIFICATION ISO/TS 29041:2008(E) ISO 2008 All rights reserved 1 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
21、 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 2 , 1,8 mol % CO 2 , 9,4 mol % ethane, 3,4 mol % propane, 1 mol % n- butane, and 83 mol % methane. All consid
22、erations 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 calculati
23、ons 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 doc
24、uments 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 me
25、thod 3 Symbols and abbreviated terms CV i calorific value of gas component i, i = 1, , n CV calorific value of the gas mixture G system of model equations describing the measurand J Jacobian m mass m g mass of the gas component in the mixture cylinder, as determined by gravimetry m m mass difference
26、, as determined, between mixture and reference cylinder after the corresponding filling step m x mass difference corrected between mixture and reference cylinder after the corresponding filling step ISO/TS 29041:2008(E) 2 ISO 2008 All rights reservedM imolar mass of gas component i, i = 1, , n M mol
27、ar mass of the gas mixture Q transfer matrix U(x) expanded uncertainty of a value x u(x) standard uncertainty of a value x u 2 (p i , p j ) variance (for i = j) of a value p i , or covariance (for i j) of two values p iand p ju B buoyancy correction (see Note) u exp correction accounting for cylinde
28、r expansion u m uncertainty of balance indication (cumulated estimate) u R correction for residual gas in the cylinder after evacuation V variance/covariance matrix for a set of results or parameters w g mass fraction of a component as determined by gravimetry x imole fraction of gas component i in
29、the final mixture, i = 1, ., n pur , ik x mole fraction of gas component k in pure gas i used for gravimetric preparation NOTE ISO 6142 uses symbols with lower-case letter “u” (e.g. u B ) for variables other than uncertainties, namely for corrections made for influential factors in the gravimetric m
30、ixture 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 Bis u(u B ). 4 Mixture preparation by gravimetry For the weighing
31、steps and sequence as described in the example, the values for the m xand their 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 2example in ISO 6
32、142. ISO/TS 29041:2008(E) ISO 2008 All rights reserved 3 Table 1 Component weighing data and their uncertainties for the gas mixture Component Masses and their uncertainties Vacuum n-Butane Propane Ethane CO 2N 2Methane m m g 50,000 21 37,999 302 7,999 707 50,000 21 65,999 937 73,999 78 345,998 422
33、u m g 0,011 0,157 0,731 0,299 0,052 0,065 0,13 u B g 0,007 45 0,005 66 0,001 19 0,007 45 0,009 84 0,001 1 0,051 58 u exp g 0,001 49 0,015 9 u R g 0,003 3 u(m m ) mg 0,015 0,019 3 0,010 8 0,015 0,020 2 0,015 1 0,06 u(u m ) mg 2,3 2,3 2,3 2,3 2,3 2,3 2,3 u(u B ) mg 0,019 0,014 0,003 0,019 0,025 0,028
34、0,13 u(u exp ) mg 0,86 9,16 u(u R ) mg 1 , 9 m x g 49,996 660 38,161 962 7,269 897 49,708 660 66,063 267 74,065 880 346,199 202 u(m x ) mg 2,300 128 2,300 124 2,300 027 2,300 127 2,455 735 2,300 220 9,634 630 The following reasoning applies to possible correlations: it is assumed that u mis a random
35、 variable governed 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 Bestimates are the same, namely pressure,
36、 temperature, and humidity. This causes correlation, but the common sources are not quantified in ISO 6142. There is no reason for assuming correlations for the u expestimate, and u Roccurs only once for methane. For m m , a clear correlation exists since the same mass pieces are used, but their com
37、binations 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 Var
38、iance-covariance matrix for the weighing data in Table 1 V(m x ) Vacuum n-Butane Propane Ethane CO 2N 2Methane 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 20,000 225 0
39、0 0,000 225 6,030 633 04 0,000 225 0 N 20,000 225 0 0 0,000 225 0,000 225 5,291 012 01 0 Methane 0 0 0 0 0 0 92,826 1 ISO/TS 29041:2008(E) 4 ISO 2008 All rights reservedValues in Table 1 are exemplified for the N 2column: The uncertainty of the m xvalue for N 2is combined from the contributing sourc
40、es of uncertainty according to the usual uncertainty propagation rule. It holds 2222 mmB ()()()() x um um uu uu =+ (1) delivering a value of 2,300 3 mg. The corresponding variance is 5,291 012 01 mg 2and contained in the sixth row of the N 2column. The m mvalues for the N 2and the methane filling st
41、ep are quite different, it was assumed that different mass pieces were used. Other common sources of uncertainty are the corrections u mand u Bfor which either an absence of correlation is assumed, or the correlations are negligible or unknown. Thus, the covariance term is set to zero (seventh row o
42、f the N 2column). The same reasoning holds for the n- butane/N 2and the propane/N 2pairs (second and third row of the N 2column). The m mvalues for the initial weighing (vacuum) and the ethane and CO 2filling step are quite similar or at least in the region of 50 g, so it can be assumed that the sam
43、e mass pieces were used. For simplicity, the covariance arising from this instance was estimated as the variance u 2 (m m ) of the initial weighing of the mixture cylinder containing only vacuum u(m m ) = 0,015 mg, u 2 (m m ) = 0,000 225 mg 2 . It is the same for all three pairs (first, fourth and f
44、ifth row of the N 2column). Note that the values which appear in rows 1 to 7 in the N 2column are repeated in columns 1 to 7 of the N 2row since variance-covariance matrices are symmetric. From the set of equations: m g (butane) m vac+ m butane= 0 m g (propane) m butane+ m propane= 0 m g (ethane) m
45、propane m ethane= 0 m g (CO 2 ) m CO2+ m ethane= 0 m g (N 2 ) m N2+ m CO2= 0 m g (methane) m methane+ m N2= 0 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 xdata of
46、 Table 1 and the 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 2N 2Methane m g g 11,834 698 30,892 065 56,978 557 16,354 607 8,002 613 272,133 322 u(
47、m g ) mg 3,252 869 3,252 798 3,252 801 3,364 635 3,364 698 9,905 408 V n-Butane Propane Ethane CO 2N 2Methane 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 20 0 5,290 361 11,32
48、0 769 6,030 408 0 N 20 0 0 6,030 408 11,321 195 5,290 787 01 Methane 0,000 225 0 0,000 225 0 5,290 787 98,117 112 ISO/TS 29041:2008(E) ISO 2008 All rights reserved 5 5 Unit conversion The above composition is given as gas masses in grams (uncertainties in milligrams) and should now be converted to m
49、ol/mol. This will also enable the inclusion of purity data which are given in the tables in mol/mol. Calculations are carried out using CONVERT1and yield the mole fractions and variance-covariance matrix shown in Table 4. See also ISO 149122for more details on the mathematical and computational background. Table 4 Component mass fractions in the mixture, their uncertainties and the variance-covariance matrix n-Butane Propane Ethane CO 2N 2Methan
