INTERNATIONAL STANDARD ISO 6976 Third edition 2016-08-15 Natural gas — Calculation of calorific values, density, relative density and Wobbe indices from composition Gaz naturel — Calcul des pouvoirs calorifiques, de la masse volumique, de la densité relative et des indices de Wobbe partir de la composition Reference number ISO 6976:2016(E) © ISO 2016 ISO 6976: 01 6(E) COPYRIGHT PROTECTED DOCUMENT © ISO 2016, Published in Switzerland All rights reserved Unless otherwise specified, no part o f this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission Permission can be requested from either ISO at the address below or ISO’s member body in the country o f the requester ISO copyright o ffice Ch de Blandonnet • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel +41 22 749 01 11 Fax +41 22 749 09 47 copyright@iso.org www.iso.org ii © ISO 2016 – All rights reserved ISO 6976:2016(E) Contents Page Foreword v Introduction vi Scope Normative references Terms and de finitions Symbols and units 5 Principles 6 4.1 4.2 4.3 Quantities Subscripts Superscript Behaviour of ideal and real gases 6.1 6.2 Enthalpy o f combustion Calculation of compression factor Calculation of calori fic value on a molar basis 8 Calculation of calori fic value on a mass basis 9 10 7.1 7.2 Gross calorific value Net calorific value 8.1 8.2 Gross calorific value Net calorific value 10 9.1 9.2 9.3 9.4 Ideal-gas gross calorific value 10 Ideal-gas net calorific value 10 Real-gas gross calorific value 11 Real-gas net calorific value 11 10.1 10.2 Ideal-gas relative density 11 Ideal-gas density 12 Calculation of calori fic value on a volume basis 10 Calculation of associated properties 11 10.3 Ideal-gas gross Wobbe index 12 10.4 Ideal-gas net Wobbe index 12 10.5 Real-gas relative density 13 10.6 Real-gas density 13 10.7 Real-gas gross Wobbe index 13 10.8 Real-gas net Wobbe index 14 11 12 Uncertainty of calculation 14 11.1 Principles 14 11.2 Formulae for the analytical method 15 11.3 Inputs for the analytical method 15 11.3.1 Composition and compositional uncertainties 15 11.3.2 Non-compositional inputs 16 11.4 Expanded uncertainty 17 11.5 Expression of results 17 11.5.1 General 17 11.5.2 Analytical method 17 11.5.3 Generic method 17 11.5.4 Contingency method 17 11.6 Application o f uncertainty 18 Tables of data 19 Annex A (normative) Values of auxiliary constants 25 © ISO 2016 – All rights reserved iii ISO 6976:2016(E) Annex B (normative) Formulae for uncertainty calculations 27 Annex C (informative) Conversion factors 32 Annex D (informative) Example calculations 34 Bibliography 57 iv © ISO 2016 – All rights reserved ISO 6976:2016(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work o f 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 o f electrotechnical standardization The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part In particular the different approval criteria needed for the di fferent types o f ISO documents should be noted This document was dra fted in accordance with the editorial rules of the ISO/IEC Directives, Part (see www.iso.org/directives) Attention is drawn to the possibility that some o f the elements o f this document may be the subject o f patent rights ISO shall not be held responsible for identi fying any or all such patent rights Details o f any patent rights identified during the development o f the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents) Any trade name used in this document is in formation given for the convenience o f users and does not constitute an endorsement For an explanation on the meaning o f ISO specific terms and expressions related to formity assessment, as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following URL: www.iso.org/iso/foreword.html The committee responsible for this document is ISO/TC 193, Natural gas, Subcommittee SC 1, Analysis of natural gas This third edition cancels and replaces the second edition (ISO 6976:1995), which has been technically revised © ISO 2016 – All rights reserved v ISO 6976:2016(E) Introduction B o th i nternationa l and i ntra-nationa l c u s to dy tra n s fer of natu l gas u s ua l ly re qui re pre ci s e de term i nation o f b o th the qua ntity and the qua l ity o f the gas to b e trade d T h i s c u ment s p e ci fie s me tho d s va lue, for the c a lc u lation o f key prop er tie s that de s c rib e ga s qua l ity, namely gro s s a nd ne t c a lori fic den s ity, relative den s ity, and gro s s a nd ne t Wob b e o f c a lc u lati ng the s e prop er tie s and thei r uncer ta i ntie s s i m i l ar combu s tible gas e ou s fuel for i ndex T he me tho d s provide the me an s any natura l ga s , natura l ga s s ub s titute or o f known comp o s ition at com mon ly u s e d re ference cond ition s Values of the various properties calculated in accordance with this document will, in general, differ f f this context, it is recognized that: a) adoption of the revisions detailed in this document will not be without cost, since instrumental software will need updating; on ly b y ver y s ma l l a mounts b) c) rom tho s e c a lc u late d u s i ng the s e cond (19 ) e d ition o th i s c u ment I n re corde d energ y content a nd hence bi l le d energ y wi l l, i n s e quence o f the s e revi s ion s , cha nge b y small amounts; u n i ntende d i mp ac ts cou ld o cc ur i f the revi s ion s are i mplemente d u ncritic a l ly; for i n s ta nce, i f the revi s ion s a re i mplemente d at i nput p oi nts to a pip el i ne s ys tem but no t at exit p oi nts , then a co s tly accou ntanc y i mb a lance may re s u lt; d) com merci a l, contrac tua l, re gu l ator y a nd legi s lative obl igation s wi l l ne e d to b e ta ken i nto accou nt For the s e re a s on s , and dep end i ng up on the u s er ’s appl ic ation, it may b e appropri ate to u nder ta ke an impact assessment in order to determine an agreed timing and procedure for implementation of the provisions of this document vi © ISO 2016 – All rights reserved INTERNATIONAL STANDARD ISO 6976:2016(E) Natural gas — Calculation of calorific values, density, relative density and Wobbe indices from composition Scope This document specifies methods for the calculation o f gross calorific value, net calorific value, density, relative density, gross Wobbe index and net Wobbe index o f natural gases, natural gas substitutes and other combustible gaseous fuels, when the composition o f the gas by mole fraction is known The methods specified provide the means o f calculating the properties o f the gas mixture at commonly used reference conditions Mole fractions by definition sum to unity Guidance on the achievement o f this requirement by chromatographic analysis is available in ISO 6974-1 and ISO 6974-2 The methods o f calculation require values for various physical properties o f the pure components; these values, together with associated uncertainties, are provided in tables and their sources are identified Methods are given for estimating the standard uncertainties of calculated properties The methods of calculation of the values of properties on either a molar, mass or volume basis are applicable to any natural gas, natural gas substitute or other combustible fuel that is normally gaseous, except that for properties on the volume basis the method is restricted to mixtures for which the compression factor at reference conditions is greater than 0,9 Example calculations are given in Annex D for the recommended methods of calculation NOTE The qualifiers “superior”, “higher”, “upper” and “total” are, for the purposes o f this document, synonymous with “gross”; likewise, “in ferior” and “lower” are synonymous with “net” The term “heating value” is synonymous with “calorific value”; “mass density” and “specific density” are synonymous with “density”; “specific gravity” is synonymous with “relative density”; “Wobbe number” is synonymous with “Wobbe index”; “compressibility factor” is synonymous with “compression factor” The dimensionless quantity molecular weight is numerically equal to the molar mass in kg·kmol−1 NOTE There are no explicit limits of composition to which the methods described in this document are applicable However, the restriction of volume-basis calculations to mixtures with a compression factor greater than 0,9 at reference conditions sets implicit limits on composition NOTE Because the mole fraction o f any water present is not normally available from chromatographic analysis, it is common practice to calculate the physical properties on a dry gas basis and to allow for the e ffects of water vapour in a separate procedure However, if the mole fraction of water vapour is known then the property calculations can be carried out completely in accordance with the procedures described herein The e ffects o f water vapour on calorific value, whether the latter is directly measured or calculated, are discussed in ISO/TR 29922 NOTE For aliphatic hydrocarbons o f carbon number or above, any isomer present is included with the normal isomer of the same carbon number NOTE If the user’s requirement includes the replacement of, for example, a C6+ or C7+ grouping of analytically unresolved components by a single pseudo-component, then it is the user’s own task to set the mole fraction composition, and hence properties, o f this pseudo-component so as to be fit for purpose in the particular application Any so-called “spectator water” and “non-combustible hydrogen sulfide” are treated as pseudocomponents by setting the appropriate enthalpy o f combustion values to zero © ISO 2016 – All rights reserved ISO 6976:2016(E) Normative references T he fol lowi ng c u ments are re ferre d to i n the te xt i n s uch a way that s ome or a l l o f thei r content s titute s re qu i rements o f th i s c u ment For date d re ference s , on ly the e d ition c ite d appl ie s For undate d re ference s , the l ate s t e d ition o f the re ference d c u ment (i nclud i ng a ny amend ments) appl ie s ISO 6974-1, Natural gas — Determination of composition and associated uncertainty by gas chromatography — Part 1: General guidelines and calculation of composition ISO 6974-2, Natural gas — Determination of composition and associated uncertainty by gas chromatography — Part 2: Uncertainty calculations ISO 14912:2003, Gas analysis — Conversion of gas mixture composition data Terms and de finitions For the pu rp o s e s o f th i s c ument, the fol lowi ng term s and defi nition s apply ISO and IEC maintain terminological databases for use in standardization at the following addresses: — IEC Electropedia: available at http://www.electropedia.org/ — ISO Online browsing platform: available at http://www.iso.org/obp 3.1 gross calori fic value amou nt o f he at that wou ld b e rele as e d by the comple te combus tion with ox ygen o f a s p e ci fie d quantity p1 , at which the reaction takes place remains constant, and all the t1 , as that of the reactants, all of these products being in the gaseous state except for water, which is condensed to the liquid state at t1 o f gas , i n s uch a way that the pres s u re, pro duc ts o f combu s tion are re turne d to the s ame s p e ci fie d temp erature, N o te to entr y: W here the qu a ntity o f ga s i s s p e c i fie d o n a mo l a r b a s i s , the gro s s c a lo ri fic va lue i s de s ign ate d a s (Hc) G(t1 , p1 gas volume (metering) reference conditions (see Figure 1) Hm) G(t1 , p1 f Hv) G(t1 , p1 ; t2 , p2 ), where t2 and p2 are the ) ; on a m a s s b a s i s , the gro s s c a lor i fic va lue i s de s ign ate d a s ( s p e c i fie d on a volu me b a s i s , the gro s s c a lor i fic va lue i s de s ign ate d a s ( ) W here the qu a ntity o ga s i s 3.2 net calori fic value amou nt o f he at that wou ld b e rele a s e d b y the comple te combu s tion with ox ygen o f a s p e ci fie d qua ntity o f gas , i n s uch a way th at the pre s s u re, p1 , at which the reaction takes place remains constant, and all t1 , as that of the reactants, the pro duc ts o f combu s tion a re re tu rne d to the s ame s p e c i fie d temp eratu re, all of these products being in the gaseous state N o te to entr y: On mol a r, mas s a nd volu me (Hc) N(t1 , p1), (Hm) N(t1 , p1) and (Hv) N(t1 , p1 ; t2 , p2 ) bases, the ne t c a lo r i fic va lue is de s ign ate d re s p e c ti vel y as 3.3 density ma s s o f a ga s s ample d ivide d b y its volume at s p e c i fie d cond ition s o f pre s s u re and temp eratu re 3.4 relative density den s ity o f a gas d ivide d b y the den s ity o f d r y a i r o f re ference conditions of pressure and temperature comp o s ition at the s ame s p e ci fie d N o te to entr y: T he ter m ide a l rel ati ve den s ity app l ie s when b o th ga s a nd a i r a re co n s idere d a s ga s e s th at o b e y the ideal gas law (3.8 (3.9 f ) T he ter m re a l rel ative den s ity app l ie s when b o th ga s a nd a i r a re s idere d a s re a l flu id s ) Fo r the fi xe d re erence comp o s itio n o f d r y a i r, s e e I S O/ T R 9 2 © ISO 2016 – All rights reserved ISO 6976:2016(E) 3.5 gross Wobbe index volume-basis gross calorific value, at specified re ference conditions, divided by the square root o f the relative density at the same specified metering re ference conditions Note to entry: In common usage, and in the absence o f any other qualifier, the term Wobbe index is taken to mean the quantity that is here identified as gross Wobbe index 3.6 net Wobbe index volume-basis net calorific value, at specified re ference conditions, divided by the square root o f the relative density at the same specified metering re ference conditions 3.7 enthalpy of transformation amount of heat release that accompanies the change in condition (transformation) of a substance or system from one (initial) condition to another (final) condition Note to entry: A positive heat release is represented by thermodynamic convention as a numerically equal negative increment o f enthalpy Note to entry: In the context o f this document, the following can be identified: — enthalpy of combustion: the initial condition is that of an unburned stoichiometric mixture of reactants and — standard enthalpy of vaporization: the initial condition is that of a substance in the liquid state at saturation — — the final condition is that o f the products o f combustion at the same pressure and temperature; and the final condition is that o f the same substance in the hypothetical state o f the ideal gas at the same temperature; enthalpy (or enthalpic) difference: the initial condition is that of a gas or gas mixture at temperature T1 and the final condition is that o f the same gas or gas mixture at the same pressure but at a di fferent temperature T2 ; enthalpy (or enthalpic) correction (residual enthalpy): the initial condition is that of a gas or gas mixture in the hypothetical state o f an ideal gas and the final condition is that o f the same gas or gas mixture at the same pressure and temperature in the state of the real gas 3.8 ideal gas gas that obeys the ideal gas law Note to entry: The ideal gas law can be expressed as · =R·T p Vo where p is the absolute pressure; T is the thermodynamic temperature; Vo is the volume occupied by one mole o f ideal gas (ideal molar volume); R is the gas constant in coherent units 3.9 real gas gas that deviates from volumetric ideality Note to entry: No real gas obeys the ideal gas law Deviations from volumetric ideality can be written in terms of the equation of state · = ( , ) ·R·T p V Z pT © ISO 2016 – All rights reserved ISO 6976:2016(E) where V is the volume occupied by one mole o f the real gas (real molar volume); ( , ) is a variable, o ften close to unity, and is known as the compression factor (3.10) Z pT 3.10 compression factor actual (real) volume o f a given amount o f gas at a specified pressure and temperature divided by its volume under the same conditions as calculated from the ideal gas law 3.11 combustion reference conditions specified temperature, t1 , and pressure, p1 , at which the fuel is notionally burned 3.12 metering reference conditions specified temperature, t2 , and pressure, p2 , determined at which the volume o f fuel to be burned is notionally Note to entry: There is no a priori reason for the metering reference conditions to be the same as the combustion reference conditions (see Figure 1) Note to entry: A range o f re ference conditions is in use throughout the world Note to entry: Throughout this document, the use o f 15,55 °C is intended as shorthand for the exact Celsius equivalent o f 60 °F, i.e 15 5/9 or 15,55 (recurring) °C Note to entry: The exact equivalent o f 101,325 kPa in psi can be calculated from (101 325) · (0,304 8/12) / (0,453 592 37) · (9,806 65) = 14, 695 949 … This value is, in practice, normally rounded to 14,696 psi and the rounded value deemed equal to 101,325 kPa Figure — Calori fic value on a volume basis — Metering and combustion reference conditions © ISO 2016 – All rights reserved ISO 6976:2016(E) = 288,706 K T from A.1 from Formula (11) — gas constant = 8,314 462 J·mol K — molar volume = 0,023 632 824 m3 ·mol −1 R · −1 V −1 D.3.5 Calculation of molar-basis gross calori fic value Component methane ethane nitrogen carbon dioxide water sum from Formula (2) xi 0,931 819 0,025 618 0,010 335 0,015 391 0,016 837 1,000 000 o ( Hc ) G i 891,460 1562,060 0,000 0,000 44,408 — mola r-b a s i s gro s s ca lori fic va lue o x i ⋅ ( Hc ) G i 830,679 365 40,016 853 0,000 0,000 0,747 697 871,443 916 ( Hc ) G = 871,443 916 kJ·mol o −1 D.3.6 Calculation of uncertainty in molar-basis gross calori fic value 44 © ISO 2016 – All rights reserved © ISO 2016 – All rights reserved ( , ) r xi xj Component methane ethane nitrogen carbon dioxide water sum Component methane ethane nitrogen carbon dioxide water sum o ( Hc ) G i u ( xi ) 891,460 562,060 0,000 0,000 44,408 0,000 350 0,000 243 0,000 195 0,000 111 0,000 162 0,312 011 00 0,379 580 58 0,000 000 00 0,000 000 00 0,007 194 10 xi x i2 u ( Hc ) G u ( Hc ) G 0,868 286 649 0,000 656 282 0,000 106 812 0,000 236 883 0,000 283 485 0,190 0,510 0,000 0,000 0,004 0,036 10 0,260 10 0,000 00 0,000 00 0,000 02 0,931 819 0,025 618 0,010 335 0,015 391 0,016 837 1,000 000 from Formula (B.4) — o ( Hc ) G ⋅ u x i i o ( Hc ) G ⋅ u x i i ( ) o ( ) 0,097 350 864 0,144 081 417 0,000 000 000 0,000 000 000 0,000 051 755 0,241 484 036 I o CH C H N CO H O CH C H6 N2 CO H2O 0 0 0 0 0 0 0 0 x i2 ⋅ u ( Hc ) G I (( ) ) = 0,241 484 036 + 0,031 515 852 = 0,272 999 888 u ((Hc) G) = 0,522 493 911 kJ·mol U((Hc) G) = 1,0 kJ·mol (using a coverage factor of k o i 0,031 345 148 0,000 170 699 0,000 000 000 0,000 000 000 0,000 000 005 0,031 515 852 u Hc G −1 −1 = a nd e x pre s s i ng the re s u lt to two s ign i fic a nt figu re s) ISO 6976:2016(E) 45 ISO 6976: 01 6(E) D.3.7 Calculation of mass-basis gross calori fic value from D.3.5 — (Hc) G = 871,443 916 kJ·mol from D.3.3 — M = 16,989 170 kg·kmol from Formula (4) −1 −1 — ma s s -b a s i s gro s s c a lori fic va lue ( Hm) G = 51,294 085 MJ·kg −1 D.3.8 Calculation of uncertainty in mass-basis gross calori fic value 46 © ISO 2016 – All rights reserved © ISO 2016 – All rights reserved Component methane ethane nitrogen carbon dioxide water sum Component methane ethane nitrogen carbon dioxide water sum (( ) ) Hc o G ( ) / Hc I 1,022 968 1,792 496 0,000 000 0,000 000 0,050 959 G Mi / M 0,944 275 1,769 894 1,648 897 2,590 444 1,060 397 (( ) ) Hc o G ( ) / Hc I G − M i / M 0,078 693 0,022 601 −1 , 8 −2 , 4 4 −1 , 0 43 8 {column value} · u(xi) 0,000 027 0,000 005 ( ) u xi 0,000 350 0,000 243 0,000 195 0,000 111 0,000 162 {column value}2 × 10 0,075 860 0,003 016 10,338 476 8,267 887 2,674 176 21,359 415 −0,000 321 − 0,0 0 87 − ,0 0 163 NOTE Assuming correlation matrix r(xi, xj) is the same as in D.3.6 xi 0,931 819 0,025 618 0,010 335 0,015 391 0,016 837 1,000 000 0,868 286 649 0,000 656 282 0,000 106 812 0,000 236 883 0,000 283 485 methane 1,000 000 000 000 0,996 804 383 768 0,000 000 000 000 0,755 086 685 092 0,139 700 393 083 ( u Hc ) Go 0,190 0,510 0,000 0,000 0,004 I ethane 0,996 804 383 768 1,000 000 000 000 0,000 000 000 000 0,773 784 772 303 0,107 369 828 180 u Hc ( ) Go 0,036 10 0,260 10 0,000 00 0,000 00 0,000 02 I x i2 ⋅ u Hc ) Go 0,031 345 148 0,000 170 699 0,000 000 000 0,000 000 000 0,000 000 005 0,031 515 852 ( , ) nitrogen 0,000 000 000 000 0,000 000 000 000 1,000 000 000 000 0,000 000 000 000 0,000 000 000 000 r Mi Mj ( I ( x i2 ⋅ u Hc carbon dioxide 0,755 086 685 092 0,773 784 772 303 0,000 000 000 000 1,000 000 000 000 0,543 709 883 997 ) Go / I ( ( Hc ) ) G × 10 4,127 541 0,022 478 0,000 000 0,000 000 0,000 001 4,150 020 water 0,139 700 393 083 0,107 369 828 180 0,000 000 000 000 0,543 709 883 997 1,000 000 000 000 47 ISO 6976:2016(E) methane ethane nitrogen carbon dioxide water x i2 methane ethane nitrogen carbon dioxide water sum xi 0,931 819 0,025 618 0,010 335 0,015 391 0,016 837 1,000 000 ( ) 0,000 423 79 0,000 827 10 0,000 200 00 0,000 500 00 0,000 166 00 xi · u(Mi) u Mi [xi · u(Mi) · r(Mi, Mj) · xj · u(Mj)] / M2 0,000 394 0,000 021 0,000 002 0,000 007 0,000 002 0,061 785 × 10 from Formula (B.5) — u((Hm) G) / (Hm) G] = [21,359 415 + 4,150 020 + 0,061 785] × 10 = 25,571 220 × 10 u ((Hm) G) = [25,571 220 × 10 × (51,294 085) ] 1/2 = 0,025 938 MJ·kg U((Hm) G) = 0,052 MJ·kg (using a coverage factor of k −8 −8 −8 −8 −1 −1 figu re s) = a nd e xp re s s i n g the re s u lt to two s ign i fic a nt ISO 6976:2016(E) 48 Component © ISO 2016 – All rights reserved ISO 6976: 01 6(E) D.3.9 Calculation of real-gas volume-basis gross calori fic value from D.3.5 from D.3.4 from Formula (10) — (Hc) G = 871,443 916 kJ·mol−1 — V = 0,023 632 824 m3 ·mol−1 — (Hv) G = 36,874 304 MJ·m−3 D.3.10 Calculation of uncertainty in volume-basis gross calori fic value © ISO 2016 – All rights reserved 49 methane ethane nitrogen carbon dioxide water sum Component methane ethane nitrogen carbon dioxide water sum o Hc ) ( G I / ( Hc ) G 1,022 968 1,792 496 0,000 000 0,000 000 0,050 959 · si · s / Z o ( Hc ) G / ( Hc ) G + ⋅ s i ⋅ s / Z I ( ) 0,004 386 0,009 054 0,001 670 0,007 404 0,025 167 1,027 354 1,801 551 0,001 670 0,007 404 0,076 126 u xi 0,000 350 0,000 243 0,000 195 0,000 111 0,000 162 o ( Hc ) G / ( Hc ) G + ⋅ s i ⋅ s / Z ⋅ u ( x i ) I 0,000 359 574 0,000 437 777 0,000 000 326 0,000 000 822 0,000 012 333 NOTE Assuming correlation matrix r(xi, xj) is the same as in D.3.6 xi 0,931 819 0,025 618 0,010 335 0,015 391 0,016 837 1,000 000 x i2 0,868 286 649 0,000 656 282 0,000 106 812 0,000 236 883 0,000 283 485 u (( ) ) Hc o G 0,190 0,510 0,000 0,000 0,004 u I (( ) ) Hc o G 0,036 10 0,260 10 0,000 00 0,000 00 0,000 02 i o 2 x i ⋅ u ( Hc ) G I 0,031 345 148 0,000 170 699 0,000 000 000 0,000 000 000 0,000 000 005 0,031 515 852 xi ⋅ u (( ) ) Hc o G {column value}2 × 10 12,929 362 19,164 863 0,000 011 0,000 068 0,015 209 32,109 513 I ( ) G × 10 / Hc 4,127 541 0,022 478 0,000 000 0,000 000 0,000 001 4,150 020 ISO 6976:2016(E) 50 Component © ISO 2016 – All rights reserved © ISO 2016 – All rights reserved Component methane ethane nitrogen carbon dioxide water sum u ( si ) xi 0,931 819 0,025 618 0,010 335 0,015 391 0,016 837 1,000 000 0,000 0,001 0,001 0,002 0,015 x i2 ⋅ u ( s i ) × 10 21,707 166 0,079 410 0,010 681 0,094 753 6,378 403 from A.1 — [u(R) / R] = 0,000 081 × 10 from Formula (B.6) — [u(Hv) G / (Hv) G)] = [32,109 513 + 4,150 020 + 0,276 247 + 0,000 081] × 10 = 36,535 861 × 10 u (Hv) G = [36,535 861 × 10 × (36,874 304) ] 1/2 = 0,022 289 MJ·m U(Hv) G = 0,045 MJ·m (using a coverage factor of k 2 ⋅ s ⋅ xi ⋅ u ( s i ) / Z × 10 0,212 114 0,000 776 0,000 104 0,000 926 0,062 327 0,276 247 −8 −8 −8 −8 −3 −3 = a nd e xpre s s i ng the re s u lt to two s ign i fic a nt figu re s) ISO 6976:2016(E) 51 ISO 6976:2016(E) D.3.11 Conversion to non-SI units The results obtained in D.3.5 to D.3.10 f values (Hc) G, (Hm) G and (Hv) G (Hc) G = (871,4 ± 1,0) kJ·mol (Hm) G = (51,294 ± 0,052) MJ·kg (Hv) G = (36,874 ± 0,045) MJ·m or the molar-b as i s , mas s-b a s i s and volu me -b as i s gro s s c a lori fic , re s p e c tively, may b e s u m mari z e d and prop erly rep or te d a s −1 −1 −3 C onvers ion o f the s e va lue s to non-S I un its i s ach ieve d b y u s e o f — using Table C.1: (Hc) G = (871,4 ± 1,0) kJ·mol Annex C as follows: = [(871,4 ± 1,0) / 0,002 326] BtuIT·lb-mol = (374 635 ± 430) BtuIT·lb-mol −1 −1 −1 — using Table C.2: (Hm) G = (51,294 ± 0,052) MJ·kg = [(51,294 ± 0,052) / 0,002 326] BtuIT·lb = (22 052 ± 22) BtuIT·lb −1 −1 −1 — using Table C.3: (Hv) G = (36,874 ± 0,045) MJ·m = [(36,874 ± 0,045) / 0,037 258 9] BtuIT·ft = (989,7 ± 1,2) BtuIT·ft −3 −3 −3 D.4 Example 3: A more complex mixture of 11 components D.4.1 General I n th i s exa mple, c a lc u lation re s u lts o f i nterme d iate s tep s a re no t rep or te d, but i n s te ad the fi na l re s u lts of calculation of a wider range of properties are provided for a more complete 11-component mixture The properties are calculated in D.4.3 f f f f f f and in D.4.4 f f f f , and me teri ng re erence cond ition s o , or combu s tion re erence cond ition s o 15 ° C and 101 , or combu s tion re erence cond ition s o ° C a nd 101 , kPa, kPa (I S O Sta nda rd Re erence C ond ition s) , ° C a nd 101 , kPa, a nd me teri ng re erence cond ition s o f ° C and 101 , kPa For b o th s e ts o f re ference cond ition s , the c a lc u lation s are made fi rs t b y u s i ng the a s s u mp tion o f an identity matri x rigorous normalization matrix for mole frac tion correlation s , a nd then b y u s i ng the more D.4.2 Compositional analysis T he mole - frac tion ana lys i s rep or t o f a natu l gas s ample provide d the fol lowi ng i n formation normalized composition (rounded to six decimal places) and associated uncertainties: 52 for the © ISO 2016 – All rights reserved ISO 6976:2016(E) ( ) 0,000 348 0,000 247 0,000 149 0,000 018 0,000 027 0,000 007 0,000 009 0,000 004 0,000 008 0,000 195 0,000 112 xi Component methane ethane propane n-butane u xi 0,922 393 0,025 358 0,015 190 0,000 523 0,001 512 0,002 846 0,002 832 0,001 015 0,002 865 0,010 230 0,015 236 1,000 000 -me thylp rop a ne n-pentane -me thylb uta ne , - d i me thylprop a ne n-hexane nitrogen carbon dioxide sum D.4.3 Properties and uncertainties for ISO standard reference conditions D.4.3.1 Results from use of an identity matrix for mole fraction correlations Property Units gro s s c a lor i fic va lue - volu me b a s i s (after rounding according to 11.5.2) ne t c a lo ri fic va lue - volu me b a s i s (after rounding according to 11.5.2) MJ·m −3 MJ·m −3 kg·m den s ity (after rounding according to 11.5.2) Y 39,733 51 39,734 35,868 11 35,868 0,764 62 0,764 0,623 91 0,623 91 50,303 18 50,303 45,409 54 45,410 −3 rel ative den s ity (after rounding according to 11.5.2) gross Wobbe index (after rounding according to 11.5.2) net Wobbe index (after rounding according to 11.5.2) D.4.3.2 MJ·m −3 MJ·m −3 ( ) 0,026 917 u Y 0,024 757 0,000 586 0,000 478 0,021 588 0,020 151 U(Y) 0,053 833 0,054 0,049 515 0,050 0,001 172 0,001 0,000 956 0,000 96 0,043 177 0,043 0,040 302 0,040 Results from use of the normalization matrix for mole fraction correlations Values for the elements r(xi, xj f f f calculated according to ISO 14912:2003, 8.5.2.3, Formula (69) and rounded to six decimal places, ) are given i n the fol lowi ng o the mole rac tion correlation tabu lation Revi s e d e s ti mate s for co e ficient (norma l i z ation) matri x, the variou s prop er ty va lue u ncer tai ntie s ob ta i ne d b y u s e o f th i s comple te correl ation co e ffic ient matri x i n place o f a n identity matri x a re s hown i n the s ub s e quent tabu lation I t i s cle a r that, smaller than those given in D.4.3.1 © ISO 2016 – All rights reserved for th i s typica l example, the s e a re, i n genera l, s ub s tanti a l ly 53 CH 1,000 000 − 0,657 46 C2 H6 C3H8 nC iC − 0,657 46 − , 7 45 − , 41 − 0,056 924 − , 61 − , 0 45 − , 0 4 42 1,000 000 1,000 000 − , 7 45 − , 61 − , 41 − , 0 45 − , 0 4 42 −0,05 924 − 0,01 72 − , 0 810 − 0,0 0 82 − ,0 85 69 −0,03 877 − 0,0 0 592 − 0,063 95 − , 67 − , 0 51 −0,05 908 − 0,02 5 − 0,0 00 372 0,099 228 0,061 961 0,064 295 0,080 202 1,000 000 nC 0,099 228 iC 0,061 961 − 0,01 72 − , 69 − 0,063 95 −0,05 908 − , 0 810 − 0,03 877 − , 67 − 0,00 824 − 0,0 0 592 − , 0 51 1,000 000 0,002 803 0,001 827 0,001 811 0,002 303 0,002 803 1,000 000 0,079 557 0,071 180 0,094 670 0,001 827 0,079 557 1,000 000 0,051 085 0,067 927 neoC nC 0,064 295 0,080 202 N2 CO − , 47 − 0, 65 66 − , 74 61 − 0,03 668 − , 71 − ,02 5 − , 74 − 0,024 94 − 0,02 92 − 0,0 0 372 − , 0 67 − , 0 70 − 0,0 03 373 − , 74 − 0,0 05 392 − , 72 79 − , 14 19 − , 62 − , 45 − 0,0 46 653 − 0,0 08 952 0,001 811 0,071 180 0,051 085 1,000 000 0,060 788 0,002 303 0,094 670 0,067 927 0,060 788 1,000 000 − , 74 61 − , 74 − , 0 67 − , 51 47 −0,03 668 − ,02 9 − , 0 70 − , 74 − , 72 79 − , 62 − 0,0 46 65 − , 45 −0, 65 66 − , 71 − ,02 92 −0,0 03 373 −0,005 392 − , 14 19 − , 45 − 0,0 952 − ,01 57 − , 45 1,000 000 − , 02 69 − ,01 57 − , 02 69 1,000 000 ISO 6976: 01 6(E) 54 ( , ) CH C2 H6 C3H8 nC iC nC iC neoC nC N2 CO r xi x j © ISO 2016 – All rights reserved ISO 6976:2016(E) Property gro s s c a lor i fic va lue - volu me b a s i s (after rounding according to 11.5.2) ne t c a lo r i fic va lue – volu me b a s i s (after rounding according to 11.5.2) den s ity (after rounding according to 11.5.2) Units MJ·m −3 MJ·m −3 kg·m −3 rel ative den s ity (after rounding according to 11.5.2) gross Wobbe index (after rounding according to 11.5.2) net Wobbe index (after rounding according to 11.5.2) MJ·m −3 MJ·m −3 Y 39,733 51 39,734 35,868 11 35,868 0,764 62 0,764 62 0,623 91 0,623 91 50,303 18 50,303 45,409 54 45,410 u ( Y) 0,016 316 0,015 305 0,000 277 0,000 226 0,019 823 0,018 498 U(Y) 0,032 631 0,033 0,030 609 0,031 0,000 554 0,000 55 0,000 453 0,000 45 0,039 646 0,040 0,036 996 0,037 D.4.4 Properties and uncertainties for 25 °C/0 °C reference conditions D.4.4.1 Results from use of an identity matrix for mole fraction correlations Property gro s s c a lor i fic va lue - volu me b a s i s (after rounding according to 11.5.2) ne t c a lo ri fic va lue - volu me b a s i s (after rounding according to 11.5.2) den s ity (after rounding according to 11.5.2) Units MJ·m −3 MJ·m −3 kg·m −3 rel ative den s ity (after rounding according to 11.5.2) gross Wobbe index (after rounding according to 11.5.2) net Wobbe index (after rounding according to 11.5.2) © ISO 2016 – All rights reserved MJ·m −3 MJ·m −3 Y 41,893 60 41,894 37,852 28 37,852 0,807 01 0,807 0,624 11 0,624 11 53,029 30 53,029 47,913 76 47,914 ( ) 0,028 425 u Y 0,026 164 0,000 619 0,000 479 0,022 783 0,021 278 U(Y) 0,056 850 0,057 0,052 327 0,052 0,001 238 0,001 0,000 958 0,000 96 0,045 566 0,046 0,042 557 0,043 55 ISO 6976:2016(E) D.4.4.2 Results from use of the normalization matrix for mole fraction correlations O f cou rs e, the change i n re ference cond ition s e s no t a ffe c t the mole frac tion correlation co e fficient (normalization) matrix, which remains unchanged from that presented in D.4.3.2 So too, as the results show, e s the conclu s ion that u s e o f a n identity matri x i n place o f the norma l i z ation matri x re s u lts i n a “s a fe” (over) e s ti mate o f the u ncer tai nty for Property gro s s c a lor i fic va lue - volu me b a s i s (after rounding according to 11.5.2) ne t c a lor i fic va lue – vo lu me b a s i s (after rounding according to 11.5.2) den s ity (after rounding according to 11.5.2) a l l prop er tie s Units MJ·m −3 MJ·m −3 kg·m −3 rel ative den s ity (after rounding according to 11.5.2) gross Wobbe index (after rounding according to 11.5.2) net Wobbe index (after rounding according to 11.5.2) 56 MJ·m −3 MJ·m −3 Y 41,893 60 41,894 37,852 28 37,852 0,807 01 0,807 01 0,624 11 0,624 11 53,029 30 53,029 47,913 76 47,914 u ( Y) 0,017 241 0,016 181 0,000 293 0,000 227 0,020 914 0,019 528 U(Y) 0,034 483 0,034 0,032 361 0,032 0,000 586 0,000 59 0,000 454 0,000 45 0,041 828 0,042 0,039 057 0,039 © ISO 2016 – All rights reserved ISO 6976:2016(E) Bibliography [1] ISO 20765-2, Natural gas — Calculation [2] [3] ISO 80000-1:2009, Quantities and units — Part 1: General ISO/TR 29922:—1) , Natural gas — Supporting in formation on the calculation ofphysical properties [4] ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated terms (VIM) [5] Evaluation o f measurement data — Guide to the expression o f uncertainty in measurement (GUM 1995 with minor corrections), Joint Committee for Guides in Metrology, JCGM 100:2008 of thermodynamic properties — Part 2: Single-phase properties (gas, liquid, and dense fluid) for extended ranges of application according to ISO 6976 (BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML), 120+viii p [6] H umphre ys A.E Some Thermophysical Properties of Components of Natural Gas and Cognate Fluids Groupe Européen de Recherches Gazières, GERG Technical Monograph TPC/1 1986, 43 p [7] M ohr P.J., Taylor B.N., Ne well D.B CODATA recommended values of the fundamental physical constants: 2010 Rev Mod Phys 2012, 84 (4) pp 1527–1605 [8] Wieser M.E., & B erglund M Atomic weights of the elements 2007 Pure Appl Chem 2009, 81 (11) pp 2131–2156 [9] P ic ard A., Davis R.S., Gl äser M., F ujii K Revised formula for the density o f moist air (CIPM2007) Metrologia 2008, 45 pp 149–155 [10] Kunz O., Klimeck R., Wagner W., J aeschke M The GERG-2004 Wide- Range Equation of State for Natural Gases and Other Mixtures, GERG Technical Monograph TM-15 2007, 535 p [11] Wagner W., & P russ A The IAPWS formulation 1995 for the thermodynamic properties o f ordinary water substance for general and scientific use J Phys Chem Ref Data 2002, 31 pp 387–535 [12] IAPWS (International Association for the Properties o f Water and Steam) Advisory Note No.1 (2003), Uncertainties in Enthalpy for the IAPWS Formulation 1995 for the Properties o f Ordinary Water Substance for General and Scientific Use (IAPWS-95) and the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties o f Water and Steam (IAPWS-IF97) 1) Under preparation Stage at the time of publication: ISO/DTR 29922 © ISO 2016 – All rights reserved 57 ISO 6976: 01 6(E) ICS 75.060 Price based on 57 pages © ISO 2016 – All rights reserved