INTERNATIONAL STANDARD ISO 18466 First edition 2016-12-15 Stationary source emissions — Determination of the biogenic fraction in CO in stack gas using the balance method Émission des sources fixes — Détermination de la fraction biogénique de CO2 dans les gaz de cheminées en utilisant la méthode des bilans Reference number ISO 18466:2016(E) I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n © ISO 2016 ISO 18466:2016(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 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ISO 18466:2016(E) Page Contents Foreword iv Introduction v Scope Normative references Terms and definitions Symbols and abbreviated terms Requirements Sampling Test methods 5.1 5.2 Input stream parameters Output stream parameters 6.1 6.2 Sampling of input streams Sampling of output streams 7.1 7.2 General Process input 7.2.1 Amount of fuel that is combusted 7.2.2 Amount of combustion air 7.2.3 Auxiliary fuel or oxygen enrichment Process output 7.3.1 Stack emissions 7.3.2 Energy production 7.3.3 Solid outputs 7.3 10 Balance calculation 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 General Mass balance Ash balance Carbon balance Energy balance O consumption balance Difference between O consumption and CO production Water balance 10 Composition of the organic matter 10 Operating data o f the Waste for Energy (WfE) plant and plausibility checks 11 Mathematical solution with data reconciliation 12 Calculation model 13 9.1 9.2 Installation routines 20 Ongoing operation calculation routines 21 Operating the model 20 Uncertainty budget methodology and interpretation 21 (informative) Annex A Reference chemical compositions of moisture and ash free biogenic and fossil organic matter 22 Annex B (informative) Reference chemical compositions for the auxiliary fuels 23 Bibliography 24 © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n iii ISO 18466:2016(E) Foreword I SO (the I nternational O rganiz ation for Standardiz ation) is a worldwide federation of national s tandards 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 b een es tablished has the right to b e represented on that committee I nternational organi zation s , governmental and non- governmental, in liaison with I SO, al so take p ar t in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters o f elec trotechnical s tandardi z ation T he procedures used to develop this cument and those intended for its fur ther maintenance are describ ed in the I SO/I E C D irec tives , Par t I n p ar ticu lar 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 ru les of the I SO/I E C D irec tives , Par t (see www iso org/direc tives) 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 I SO l is t of p atent declarations received (s ee www iso org/p atents) Any trade name used in this document is in formation given for the convenience o f users and does not cons titute an endorsement For an explanation on the meaning o f ISO specific terms and expressions related to formity assessment, as well as information about I SO ’s adherence to the World Trade O rganization ( WTO) principles in the Technical B arriers to Trade (TB T ) see the following URL: www iso.org/iso/foreword html T he committee res p ons ible for this document is I SO/ TC 146 , Air quality, Sub committee S C , Station ary source emissions iv I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ISO 18466:2016(E) Introduction During the combustion of solid fuels, O2 is consumed and CO2 and fo s s i l i s s i mu ltane ou sly pro duce d B io gen ic organ ic matter no t on ly s how s d i fference s rega rd i ng O consumption and CO2 pro duc tion, but a l s o d i fference s i n thei r re s p e c tive c a lori fic va lue and c arb on content a re ob s er vable T he b a lance me tho d c an b e u s e d when the elementar y comp o s ition o f moi s tu re a nd a sh fre e biomas s and fossil matter present in the fuel used is known and online stack gas composition measurements (O2 and CO2 f f 14 C) determined biomass fuel ratio The results obtained using this fraction in stack gas from plants with unknown fuel composition is determined using the 14 C method If the chemical composition of pure biogenic and fossil matter (contents of C, H, N, S, O referred of moisture f f f biogenic CO2 f ff f f f f balances ) are avai lable at h igh acc u rac y I t wi l l enable on l i ne mo del l i ng o bioma s s o s s i l ratio’s i n s tack ga s givi ng the u s er the opp or tu nity to control or rep or t that ratio T he generate d mo del data c an b e veri fie d us i ng the rad io c arb on ( c u ment wi l l b e complementar y to the re s u lts ob tai ne d with I S O 3 I n I S O 3 , the bio gen ic and a sh re e biomas s a nd o s s i l organ ic matter, re s p e c tively) pre s ent i n the rac tion c a n b e c a lc u late d uti l i z i ng d i erent op erati ng d ata o uel u s e d i s known, the the Was te or E nerg y ( W E ) plant When the ch lori ne content i s s u ficiently h igh, it ca n b e add itiona l ly u s e d to op ti m i z e the mas s © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n v I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n INTERNATIONAL STANDARD ISO 18466:2016(E) Stationary source emissions — Determination of the biogenic fraction in CO in stack gas using the balance method Scope This document enables the determination of the biogenic fraction in CO2 in stack gas using the balance method The balance method uses a mathematical model that is based on different operating data of the f f f composition of biogenic and fossil matter present in the fuel used Wa s te or E nerg y ( W E ) pl ant (i nclud i ng s tack ga s comp o s ition) and i n ormation ab out the elementar y NO TE T he Us e o n l y m i xe d fuel s when u s i ng the c a lc u l ation me tho d Normative references fol lowi ng c u ments are re ferre d to i n the tex t i n s uch a way th at 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 cite d appl ie s For u ndate d re ference s , the late s t e d ition o f the re ference d c ument (i nclud i ng a ny amend ments) appl ie s ISO 12039, Stationary source emissions — Determination of carbon monoxide, carbon dioxide and oxygen — Performance characteristics and calibration of automated measuring systems EN 14181, Quality assurance of automated measuring systems EN 15259, Air quality — Measurement of stationary source emissions — Requirements for measurement sections and sites and for the measurement objective, plan and report EN 15267-3, Air quality — Certification of automated measuring systems — Part 3: Performance criteria and test procedures for automated measuring systems for monitoring emissions from stationary sources Terms and definitions For the pu r p o s e s o f th i s c u ment, the fol lowi ng term s and defi n ition 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 https://www.iso.org/obp/ 3.1 biogenic pro duce d i n natu l pro ce s s e s by l ivi ng organ i s m s but no t fo s s i l i ze d or derive d from fo s s i l re s ou rce s 3.2 biomass material of biological origin excluding material embedded in geological formation or transformed to fossil 3.3 radiocarbon radioactive isotope of the element carbon, 14 C, having neutrons, protons, and electrons 3.4 sample quantity o f materia l, repre s entative o f a larger qua ntity © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n for wh ich the prop er ty i s to b e de term i ne d ISO 18466:2016(E) 3.5 sample preparation a l l the ac tion s ta ken to ob ta i n repre s entative ana lys e s , samples (3 4) or test portions (3 6) from the original s ample 3.6 test portion qua ntity o f materi a l d rawn from the te s t s a mple (or from the l ab orator y s ample i f b o th are the s ame) and on wh ich the te s t or ob s er vation i s ac tua l ly c arrie d out 3.7 balance method numerical pro cedure to calculate the frac tion of biogenic (3 ) matter i n wa s te conti nuou sly by s olvi ng a s et of equations Symbols and abbreviated terms C (f) organic carb on content of the was te fuel derived from op erating data (kg C/ kg was te fuel) ne t enth a lpy o f s te a m c ycle o f the Wa s te ΔH Jx for E nerg y ( WfE ) plant (M J/ kg) Jacobia n matri x o f range 6xN , with N repre s enti ng the nu mb er o f the me a s ure d variables Jy Jacobia n matri x o f range 6xK, with K repre s enti ng the nu mb er o f the un known variables Lvap evap oration he at (M J/ kg) wB , wF, w H O , wI iner t matter ( kg/ kg was te fuel) M M M M M M mas s frac tions of mois ture and ash free biogenic and fos s i l matter, water and C relative molecular mas s of carb on (1 ,010 g/mol) H relative mole c u l ar ma s s o f hyd ro gen (1 , 0 g/mol) O relative mole c u l ar ma s s o f ox ygen (1 ,9 9 g/mol) N relative molecular mas s of nitrogen (14, 0 g/mol) S relative molecular mas s of s u l fur (3 ,0 65 g/mol) ga s mole c u la r weight o f au xi l i ar y gas MH 2O (g/mol) molecu lar weight of water (g/mol) ox ygen s ump tion o f the wa s te O (f) fuel fuel derive d from op erati ng data (mol O / kg was te fuel) ; p vap our pres s ure of the in let combus tion air (Pa) ; v q LHVw q LHV fe e d with i n a defi ne d p erio d Δ t (M J/ kg) elemental lower heating value of the combus tible frac tions k q LHVgas average lower he ati ng va lue o f the was te I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ( k i s ca rb on, hyd ro gen, ox ygen, n itro gen a nd s u l fu r) average lower he ati ng va lue o f the au xi l i ar y gas fuel (M J/ kg) (M J/m ,1 K, , b a r) ISO 18466:2016(E) average lower he ati ng va lue o f the au xi l ia r y oi l q LHV Ras * s p e ci fic gas s tant Svap for (M J/ kg) the d r y r [2 7, 5 14 J/( kg K ) ] s te a m pro duc tion o f the Wa s te ( kg/Δ Δ fuel oil t ) t for E nerg y ( WfE ) pla nt with i n a defi ne d p erio d defi ne d ti me p erio d (a rbitrar y ti me u n it, e g d ays) temperature of the inlet combustion air (°C); volume of the inlet combustion air (m3 Tair Vair Vfg ); K, b a r d r y flue ga s volu me o f the Wa s te (m3 Vgas ,1 K, , au xi l i ar y ga s fuel b a r/Δ ) t for E nerg y ( WfE ) pla nt with i n a defi ne d p erio d volu me i nto the Was te for E nerg y ( WfE ) pl ant with i n a defi ne d period (m3 t) molar volume of ideal gas under standard temperature and pressure (22,414 dm3 /mol) ,1 K, , b a r/Δ Vm ,1 K, , b a r m oil ma s s o f au xi l i ar y oi l fuel a defi ne d p erio d ( kg/Δ m tot ma s s o f wa s te fe e d ) i nto the Was te t i nto the Was te for ) vapour mass in the combustion air p erio d ( kg/Δ Wv Ws t for E nerg y ( WfE ) pla nt with i n E nerg y ( WfE ) pla nt with i n a defi ne d s u m o f s ol id re s idue s (d r y s ub s tance) o f the Was te Σ for E nerg y ( WfE ) pla nt with i n ) elemental concentration of the combustible fractions of the biogenic matter (ash and moisture free; k f elemental concentration of the combustible fractions of the fossil organic matter (ash and moisture free; k f a defi ne d p erio d ( kg/Δ c Bk t i s c a rb on, hyd ro gen, ox ygen, n itro gen and s u l u r) ( kg/ kg) c Fk i s c a rb on, hyd ro gen, ox ygen, n itro gen and s u l u r) ( kg/ kg) elementa l concentration o f the au xi l i ar y ga s k c gas nitrogen and sulfur) (kg/kg) k c oil nitrogen and sulfur) (kg/kg) average O2 and CO2 elementa l concentration o f the au xi l i ar y oi l , x O ,fg x CO ,fg 2 , x O ,air x CO ,air xH O xs fuel fuel ( ( k i s c a rb on, hyd ro gen, ox ygen, i s c arb on, hyd ro gen, ox ygen, content i n the d r y flue ga s o f the Wa s te pl ant with i n a defi ne d p erio d Δ average O2 and CO2 t (vol %) for content o f d r y combu s tion a i r o f the Wa s te pl ant with i n a defi ne d p erio d Δ t (vol %) average water content i n the flue gas o f the Was te for E nerg y ( WfE ) for E nerg y ( WfE ) E nerg y ( WfE ) pla nt with i n (vol %) vector of N estimated values of the measured variables a defi ne d p erio d Δ t ys ve c tor o f the K u n known vari able s η energ y e fficienc y o f the s te am b oi ler o f the Was te © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n k for E nerg y ( WfE ) pl ant ISO 18466:2016(E) ε vap ou r mole c u lar weight/d r y r mole c u lar weight (0 , 62 8) σ Bk weighted standard deviation for the k-th content of the moisture and ash free biogenic matter present in the waste feed (k = C, O, N, H, S) σ Fk weighted standard deviation for the k-th content of the moisture and ash free fossil matter present in the waste feed (k = C, O, N, H, S) σwk s tandard devi ation a s s o ci ate d to the ma s s flow o f the k-th typ e o f wa s te SRF solid recovered fuel WfE wa s te 5.1 for energ y p lant Requirements Input stream parameters For the application of the balance method, the following input parameters are required: — ma s s o f wa s te — ma s s/volu me o f au xi l ia r y — fe e d (with i n a defi ne d p erio d, Δ fuel s s uch a s elementa l comp o s ition o f the au xi l i ar y nitrogen and sulfur); — fuel t); oi l or gas (with i n a defi ne d p erio d, Δ fuel s t); (fuel oi l or ga s) u s e d (for c a rb on, hyd ro gen, ox ygen, to ta l mas s a nd elementar y comp o s ition o f fuel s th at are either comp o s e d o f bio gen ic matter or fo s s i l matter on ly (e g s ewage sludge, wo o d was te) ; — elemental composition (probable range) of moisture and ash free biogenic and fossil organic m atter (wi th re s p e c t to the co ntent o f c a rb o n , hyd ro gen , o x ygen , n i tro gen a nd s u l fu r) p re s ent i n the waste feed; — ratio o f d i fferent was te typ e s pre s ent i n the wa s te fe e d s uch a s mun icip a l s ol id wa s te ( M S W ) or ho s pita l was te (i n c a s e that the was te typ e s a re charac teri z e d b y d i fferent elementa l comp o s ition of biogenic and fossil organic matter); — energ y e ffic ienc y o f the b oi ler; — average temp erature o f — amou nt o f a i r u s e d 5.2 for fe e d water for the b oi ler (with i n defi ne d p erio d, Δ t); t the combu s tion (with i n defi ne d p erio d, Δ ) , no t compu l s or y Output stream parameters For the application of the balance method, the following output stream parameters are required: — CO — O2 concentration i n d r y flue ga s (with i n defi ne d p erio d, Δ concentration i n d r y flue ga s (with i n defi ne d p erio d, Δ t); t); t (s tanda rd i ze d — flue ga s flow volu me with i n defi ne d p erio d, Δ to K a nd 101 , kPa) ; — moi s tu re content with i n defi ne d p erio d, Δ — temp eratu re i n s tack at me a s urement p oi nt o f flue ga s flow, with i n defi ne d p erio d , Δ t; t (in order to conver t flue ga s flow to s ta nda rd temp eratu re o f K) , no t compu l s or y; — pres s u re i n s tack at me a s u rement p oi nt o f flue ga s flow, with i n defi ne d p erio d, Δ conver t flue ga s flow to s ta nda rd pre s s u re o f 101 , kPa) , no t compu l s or y; I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n t (in order to ISO 18466:2016(E) The operating data accuracy is important, but even where uncertainties are taken into account, gross errors due to sensor failure can occur so secondary checks need to be made to veri fy the data A suggested approach is to veri fy i f the oxygen consumption and organic carbon contents corresponding to the operating data recorded is in the range o f theoretical values when only biogenic matter or only fossil matter is attributed to the waste mixture, both evaluated in correspondence of the theoretical (f) lower heating value q LHV , calculated as shown in Formula (16): q LHV (f) S vap = DH η m tot q LHV gas − Vgas + q LHV m oil oil (16) m tot The corresponding organic carbon contents and oxygen consumption are evaluated as shown in Formula (17): 10 C (f) = 10 Vfg x CO ,fg M gas Vm = M gas Vm − x C O ,air MC 100 Vm − C c gas Vgas c oCi l m oil + (17) m tot C c gas x CO ,fg 100 − x O ,fg 10 Vfg x O ,air 100 − x O ,air (f) 10 x CO air 100 − x O ,air − m tot and Formula (18): O − 100 − x O ,fg MC H c gas + + MH − x CO ,fg x CO ,air − x O ,fumi 100 V m m tot N c gas MN m tot − Vgas − 10 C c oi l + MC H c oil MH − O c oil + MO N c oil MN + S c oil MS m oil (18) m tot − The evaluation of the theoretical range is performed starting from the consideration that the combustion o f g o f carbon corresponds to a total amount o f energy evaluated by the energy balance, between 33,25 kJ and 44 kJ, and similarly to mol o f consumed oxygen corresponds an amount o f energy between 360 kJ and 400 kJ There fore, evaluated the theoretical lower heating value from Formula (16), the corresponding carbon content evaluated from Formula (17) shall be in the range: f C ( ) = 250 + 50 q LHV ( f) − f 10 / and C ( ) max = 260 + 90 q LHV ( f) − / 4 (19) while the oxygen consumed evaluated from Formula (18) shall be in the range: f O ( ) = 25 + 15 q LHV ( f) − f 10 / , and O ( ) max = 30 + , q LHV ( f) − 11 (20) 8.11 Mathematical solution with data reconciliation Because the set of formulae applied in the balance method is over determined (i.e number of ormulae > number o f unknowns), data reconciliation has to be per formed to improve the accuracy o f f 12 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ISO 18466:2016(E) the measurements (chemical compositions and operating data) accounting for the corresponding uncertainties, currently with the exception o f chemical composition and operating data o f auxiliary uel, having no uncertainties Subsequently, the improved values are used to calculate the unknown quantities (wI , wB , wF, w H O ) including their uncertainties The quantities of wI , wB , wF, w H O including their uncertainties are subsequently used by inserting into the respective balance formula to compute the ratio of biogenic or fossil CO2 (using the carbon balance) or the ratio of energy from biogenic sources (using the energy balance) All these final results o f the balance method are characterized by a mean value and a statistically derived uncertainty f The mathematical solution o f the equation system shall take into account that the formula o f di fference between O2 consumption and CO2 production can also be considered as the linear combination of the carbon balance and the oxygen consumption formulae, so one o f them shall be omitted in the numerical equation system Furthermore, the water balance formula is not essential for the system solution, but it can be added to the numerical equation system i f the required data are available in order to improve accuracy 8.12 Calculation model The balance method combines the standard data of the chemical composition of biogenic and fossil organic matter with routinely measured operating data o f the incineration plant The method is based on six mass balances and one energy balance, whereby the result o f each balance describes a certain waste characteristic (e.g content of organic carbon, heating value, ash content, etc.) Each balance formula encompasses a theoretically derived term that has to be reconciled with measured data o f the plant In order to set-up the theoretical formulae, the di fferent materials comprised in the waste are virtually divided into four “groups”: inert (wI ), biogenic and fossil organic material (wB , wF ) and water ( w H O ) that are the unknown variables Inert materials include all incombustible matter from bio wastes and plastics (e.g kaolin in paper) Biogenic and fossil organic material groups re fer only to the moisture and ash free organic matter Due to the fact that the qualitative composition o f organic materials in waste is well known [e.g biogenic matter encompasses paper, wood, kitchen waste, etc and fossil organic matter includes polypropylene (PP), polyethylene (PE), polyethylene terephthalate (PET), polyvinyl chloride (PVC), etc.], typical ranges for the content o f carbon (C) hydrogen (H), oxygen (O), nitrogen (N) and sul fur (S) biogenic and fossil organic materials can be taken from literature The balance formulae considered, as detailed in 8.2 to 8.8, are summarized in Figure 1, accounting for the fact that the O2 -CO2 balance is not an independent formula being the linear combination of carbon balance and oxygen balance, so only two o f these three formulae can be considered simultaneously Each balance formula encompasses at least one of the mass fractions (wI , wB , wF, w H O ), that represent therein the four unknowns of the nonlinear set of formulae, that can be solved using a data reconciliation algorithm being the system over determined (six formulae with four unknowns) It is also important to clari fy the variable classification o f data reconciliation technique, for which measured variables are classified as redundant and non-redundant, whereas unmeasured variables are classified as observable and non-observable, being: — a redundant variable is a measured variable that can be estimated by other measured variables via process models, in addition to its measurement; — a non-redundant variable is a measured variable that cannot be estimated other than by its own measurement; — an observable variable is an unmeasured variable that can be estimated from measured variables through physical models; — a non-observable variable is a variable for which no information is available © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n 13 ISO 18466:2016(E) M ore pre ci s ely, the c a lc u lation mo del re fers to a cond ition o f s te ady- s tate non l i ne a r mo del i nclud i ng re du ndant me as u re d va riable s a nd ob s er vable e s ti mate d by the data re conc i l i ation a lgorith m 14 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n un me a s ure d variable s , s i nce thei r va lue s c an be ISO 18466:2016(E) Figure — Formulae used for the balance method for determining the biogenic fraction in CO in stack gas © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n 15 ISO 18466:2016(E) T he non l i ne a r data re conci l i ation problem i s e s s enti a l ly a weighte d le as t s quare s op ti m i z ation prob lem: Min ( x m − x) T S − ( xm − x ) (2 1) with the as so ciated cons traint conditions: f (x, y, z) = (2 ) x b eing is the vec tor of ( c B , c F , m tot , Vfg , x O , CO , air , x O , CO , fg , Σ Ws , S vap , η , ∆ H ) , x k k m values , and y is N I, B, variables is the vec tor of corres p onding N meas ured w w w wH 2O the ve c tor o f K un me a s ure d va riable s ( meas ured F, ), z is the vec tor of M cons tant values Σ is the NxN covariance matri x of the meas ured variables Si nce the s trai nts are p ar tly non l i ne a r, iteratively, p er form i ng the l i ne ari z ation o f the data re conci l iation s l l b e ne ce s s ari ly c a rrie d out formu lae and p er form i ng a s e quence o f s e c utive l i ne ar reconci l iations unti l a convergence condition is achieved T he idea is that the non linear cons traints f (x, y, z) ca n b e l i ne a ri z e d u s i ng a fi rs t order Taylor ’s arou nd an e s ti mation o f the va riable s: f (x, y, z) where xs is = Jy ( y − ys) Jx (x − xs) + + Jy = the vec tor of N es timated values of the meas ured variables , values of the unmeas ured variables , and f (xs , ys , z) Jx (2 ) ys i s the ve c tor o f the K e s ti mate d i s the Jacobi an matri x o f range 6xN o f the me a s u re d vari able s i s the Jacobi an matri x o f nge 6xK o f the u n me a s u re d va ri able s T he e quation s ys tem c an then b e written in the matri x form: J y J x f (y − y ) s s (x − x ) = (2 4) b eing ¶f1 ¶y ¶f2 J = ¶y y ¶f1 ¶y ¶f2 ¶y ¶f6 ¶y1 ¶f6 ¶y ¶f1 ¶x ¶f2 J = ¶x x ¶f1 ¶x ¶f2 ¶x ¶f6 ¶x ¶f6 ¶x ¶f1 ¶y K ¶f2 ¶y K (2 ) ¶f6 ¶y K and 16 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ¶f1 ¶x N ¶f2 ¶x N ¶f6 ¶x N (2 6) ISO 18466:2016(E) The weighted least squares relationship in Formula (20), together with the constraints of Formula (21), as shown in Formula (22), allow to rewrite the data reconciliation problem as: Min ( xm − x) S T −1 ( xm − (27) x ) J x+ J y = b x y The matrices Jx and Jy are the incidence matrices in Jacobian form of the balance formulae, the first one related to the vector of measured variables and the second one related to the vector of the unmeasured variables The right side term b can be evaluated as: b = J x x ( n −1 ) + s J y y ( n −1 ) s − ( n −1 ) f xs , y (n −1 ) s (28) , z where xs(n−1) and ys(n−1) are the estimated values of measured variables at the iteration (n −1)-th of the iterative cycle, with the Jacobian matrices Jx [ Formula (26) ] and Jy [ Formula (25) ] also evaluated using the estimated values xs(n−1) and ys(n−1) ; the measured values xm are used as estimated values xs(n−1) at the first iteration, while to the unmeasured variables ys (n −1) , arbitrary guess values are assigned More precisely, for each n -th step o f the iterative cycle, the first task is the evaluation o f the new values of the measured variables xs(n) through Formula (26) and considering the corresponding constraint condition Being F [xs(n) , ys(n) ], the function for which the minimum condition shall be searched, Formula (26) can be written as: F x J x x (n ) s (n ) s , y + (n ) = xm − s J y y (n ) s = x (n ) s T ∑ −1 xm − x (n ) s (29) b The data reconciliation problem can be solved by first eliminating the unmeasured variables ys from the constraint formulae multiplying both sides by a projection matrix P such that: PJy =0 (30) Then, the data reconciliation problem becomes: F x (n ) s = xm − (n ) ( PJ y ) x s = x (n ) s T ∑ −1 xm − x (31) (n ) s Pb The solution of this optimization problem can be performed using the Lagrange multipliers technique This approach allows to reduce the stationary points o f a function F (x), defined by a set o f I variables associated to J boundary constraints f (x) = 0, to the stationary points o f a further not constrained function Λ(x, λ) having I+ J variables, named “Lagrangian function”, where λ is the multiplier vector: L ( x , y ) = F ( x ) + »f ( x ) = F ( x ) + ∑ Jj =1 λ j fj ( x ) (32) Applying this technique to Formula (30), the corresponding Lagrangian function will be: © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n 17 ISO 18466:2016(E) (n) F ( x) = x − x m s T ∑ −1 xm − x (n ) s (n ) λ T ( PJ x ) s s − ∂x ∂F = −2 = ∂λ −1 ∑ ( PJ x ) x xm − (n ) s − x (n ) − s Pb = ( PJ x ) T λ = xm − x (n ) + s ∑ ( PJ x ) + fu nc tion are: (34) T λ = Pb + PJ ∑ ( PJ x ) T Σ in Formula (33) yield s: (35) a nd mu ltiplyi ng agai n b o th the term s b y ( PJ x ) x m (33) Mu ltiplyi ng e ach term b y the covari ance matri x Pb T he ne ce s s a r y cond ition s to ob tai n the m i n i mum o f th i s ∂F − λ = PJx , Formula (34) becomes: (36) being the term (PJx) xs (n) is equal to - Pb from Formula (33) Rearranging Formula (35), the vector of Lagrange multiplier λ is evaluated: λ = − PJ x ( ) ∑ ( PJ x ) T −1 ( PJ x ) x m − (37) Pb Substituting the λ values in Formula (34), the vector of the estimated measured variables xs (n) at the n -th iteration can be evaluated: x (n ) s = x m − ∑ ( PJ x ) T ( PJ x ) ∑ ( PJ x ) T −1 ( PJ x ) x m − (38) PJ P There are more methods to obtain a matrix Formula (29) I n th i s mo del , the proj e c tion matri x P i s eva luate d b y the QR factorization technique applied to the matrix Jy Being Jy, a 6xK matri x h avi ng l i ne a rly i ndep endent Now it i s ne ce s s ar y to eva luate the proj e c tion matri x s ati s fyi ng the re qu i rements o f colum n s s o its ran k i s e qua l to the nu mb er K o f u n known s , it c an b e proven that it c an b e Q (6x6) s ati s fyi ng 18 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n Formula (39): fou nd a matri x ISO 18466:2016(E) = QR Jy (39) and s ati s fyi ng a l s o the or tho gona l ity cond ition: =I T Q Q (40) whereas R is characterized as: R R = (41) being R1 I matrices Q Q1 Q2 so Formula (38) becomes: , an upp er tri angu lar a nd non- s i ngu la r matri x with d i men s ion (K xK ) , the nu l l matri x o f d i men s ion (2 xK ) and = [ J y the identity matri x ] , where T he matri x Q can then be partitioned into two other Q2 is a matrix of dimension (6x2), i s a matri x o f d i men s ion (6xK ) wh i le (42) R = Q Q 2 Mu ltiplyi ng b o th the s ide s b y Q Q Q T: (43) R T T J = Q Q Q y 2 and being Q an orthogonal matrix, the matrix Q2 Q R T Q Q 2 R = 0 1 = a s s ume s the fol lowi ng prop er ty: (44) that is: Q T J y (45) =0 Therefore, the Q2 T P so starting from Formula (37), it is possible to evaluate the vector of the estimated values for the measured variables xs(n) at the n -th iteration knowing the measured values xm matri x i s the s e arche d proj e c tion matri x x (n ) = s x m − ∑( T Q J x T T Q2 J x ) ( )∑( T Q J x ) T −1 T ( Q2 J x ) xm − T Q b (46) whereas the solution for the unmeasured variables can be obtained from Formula (28) rewritten as (n ) J y y s = (47) (n ) b− J x x s where the terms at the right side can be evaluated from Formula (45) and Formula (27), so the vector of estimated unmeasured variables at the n -th iteration can be evaluated as: y (n ) s = T ( Jy Jy ) −1 T J b− y T ( Jy Jy ) −1 J (48) (n ) T J x y x s After the evaluation of the estimated variables, the iteration loop continues with the (n +1)-th iteration starting from the calculation of the matrices Jx and J and of the known term b using the estimated y © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n 19 ISO 18466:2016(E) xs (n) values ys (n) , and evaluating a new set of es timated values of meas ured variables ys unmeas ured variables n ( +1) xs (n +1) and n is the current iteration step, the calculation cycle continues until the − ys If relationship s: (n ) xs (n −1 ) xs − < ε (n ) ys and ( n −1 ) < ε (49) satisfied, where ε is the value of the as s igned convergence criterion Now it is p os s ible to evaluate the covariance matri x of the reconci liated data rewriting Formu la (45 ) as x (n ) s = I − ∑( T ∑ ( Q2 where W J Q T J x T ) ( T x Q T ) ( Q2 J x T J x )∑( T ) ∑ ( Q2 J Q x T J x ) T T ) −1 ( Q T J x x m + ) −1 (5 0) T Q b I is the identity matrix Assuming that = I − H = ∑( ∑( T T Q2 J x T Q A x T Q2 J x ) ( T T Q2 A x ) ( )∑( )∑( T Q2 J x T Q A x ) T ) T −1 ( T Q2 J x ) (51) −1 T Q b then, Formu la (49) b ecomes x n ( ) s = W x m + Hx T herefore, b eing the n ( ) s = W x m + H (52 ) H matri x a cons tant matri x, the covariance matri x of the meas ured variables can b e given as cov ( x ) = Wcov ( x m ) W T = W∑ W T (5 ) and for the unmeas ured variables cov ( y ) 9.1 = T ( Jy Jy ) −1 J T J cov ( x ) y x T ( Jy Jy ) −1 J T J y x (5 4) Operating the model Installation routines When installing the method at a given facility, great care shall be taken to ensure that the measurements used not contain systematic errors and the facility specific constants shall be collected Furthermore, documentation o f measurements, constants and uncertainties shall be collected and stored for easy access during any validation Validating the installation o f the model is required as it will provide certainty that errors not exist with the model at a given facility 20 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ISO 18466:2016(E) 9.2 Ongoing operation calculation routines When this document is used to report the fossil CO2 emission by the year, the calculations and input data quality have to be monitored continuously throughout the year (minimum monthly evaluations) to ensure countermeasures are put into force i f/when measurements become untrustworthy There fore, the method shall be used running continuously or at least on a monthly basis Furthermore, the following shall be available to allow the user to interpret results find mistakes and act accordingly: — the so ftware shall produce warnings and error messages based on the plausibility testing; — user interface shall contain results for all plant lines (numeric and graphical representation) for comparison and the warnings and error messages; — the user shall be able to see both results and inputs (ideally both be fore and a fter the reconciliation routine); — the user shall be able to extract the results to a database program 10 Uncertainty budget methodology and interpretation The input for the uncertainty calculation is the actual uncertainty on the measurement including both systematic and random uncertainty I f this is not measured and meters are well maintained and calibrated (hence without systematic uncertainty), the meter nameplate uncertainty could be used The procedures applicable in the area where the measurement is performed shall be followed The procedures followed shall be documented together with the results For example, in the EU the QAL1 measurement, uncertainty is to be used according to EN 14181 for CEMS measurements and systematic uncertainty can be neglected i f QAL2 calibrations are per formed for, as minimum, O2 , CO2 The procedure for flow and moisture is described in EN 14181 When per forming calibrations and using calibration factors identified (di fference between re ference method and plant method), it has to be tested if the results are still equal and within theoretical limits For mixed waste, the CO2 measurement corrected to % H O and % O2 shall always be between 16 % and 19 % When feeding two lines from a common waste storage, the corrected CO2 (0 % H O and % O2 ) shall be very similar (i f not identical) © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n 21 ISO 18466:2016(E) Annex A (informative) Reference chemical compositions of moisture and ash free biogenic and fossil organic matter Biogenic matter Content Unit C H O N kg/kg moisture and ash free matter S Symbol Fossil organic matter Mean Standarddeviation Symbol Mean Standarddeviation C CB 0,483 0,004 C CF 0,777 0,016 C HB 0,065 0,001 C HF 0,112 0,006 C OB 0,443 0,007 C OF 0,061 0,013 C NB 0,007 0,002 C NF 0,014 0,005 C SB 0,001 0,000 C SF 0,003 0,001 Source: United Nations Clan Development Mechanism Large Scale Consolidated Methodology ACM0022: Alternative Waste Treatment Processes Version 02.0 Sectorial scope: 01 and 13 – CDMEB81-A13 (2013) Page 76 22 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ISO 18466:2016(E) Annex B (informative) Reference chemical compositions for the auxiliary fuels Fuel Low sulfur oil High sulfur oil H e av y oi l Standard oil Natural methan Pure methan C N O (g/kg) S (g/kg) (g/kg) q LHV q LHV (g/kg) 864 (g/kg) 127 1 41,87 — 856 857 862 745,9 750 117 105 123 250,3 250 0 4 0 20 29 0 41,03 40,49 41,85 — — — — — 34,54 35,838 © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n H ( M J/ kg) ( M J/Nm 3) 23 ISO 18466:2016(E) Bibliography [1] ISO 625, Solid mineral fuels — Determination o f carbon and hydrogen — Liebig method [2] ISO 925, Solid mineral fuels — Determination of carbonate carbon content — Gravimetric method [3] ISO 1171, Solid mineral fuels — Determination of ash [4] ISO 7934, Stationary source emissions — Determination o f the mass concentration of sulfur [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] dioxide — Hydrogen peroxide/barium perchlorate/Thorin method ISO 10396, Stationary source emissions — Sampling for the automated determination of gas emission concentrations for permanently-installed monitoring systems ISO 10780, Stationary source emissions — Measurement of velocity and volume flowrate of gas streams in ducts ISO 13833, Stationary source emissions — Determination of the ratio of biomass (biogenic) and fossil-derived carbon dioxide — Radiocarbon sampling and determination ASTM D6866, Standard Test Methods for Determining the Bio-based Content of Solid, Liquid, and Gaseous samples Using Radiocarbon Analysis ASTM D7459, Standard Practice for Collection of Integrated Samples for the Speciation of Biomass (Biogenic) and Fossil-Derived Carbon Dioxide Emitted from Stationary Emissions Sources EN 14775, Solid Biofuels — Determination of ash content EN 14778, Solid Biofuels — Sampling EN 14789, Stationary source emissions — Determination of volume concentration of oxygen (O2) — Reference method — Paramagnetism EN 14918, Solid Biofuels — Determination of calorific value EN 15103, Solid Bio fuels — Determination o f bulk density EN 15104, Solid Biofuels — Determination of total content of carbon, hydrogen and nitrogen — instrumental methods EN 15400, Solid recovered fuels — Determination of calorific value EN 15403: Solid recovered fuels — Determination of ash content EN 15407, Solid recovered fuels — Methods for the determination of carbon (C), hydrogen (H) and nitrogen (N) content EN 15440, Solid recovered fuels — Methods for the determination of biomass content EN 15442, Solid recovered fuels — Methods for sampling C iceri G , C ipri ano D , S c acchi C , B i anchilli B , C atanz ani G 2009 Quantification o f Biomass Content in Municipal Solid Waste and Solid Recovered Fuels by Means o f the Measuring o f C 14 at the Plant E m is s ion P roceedings of SE E P2 0 rd I nternational C on ference on Sus tainable Energy & Environmental Protection Dublin 12-15 August 2009 [22] F ellner J., C encic O , R echberger H A new method to determine the ratio o f electricity production from fossil and biogenic sources in waste-to-energy plants Environ Sci Technol 07, 41 (7 ) pp 579 –2 24 I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n ISO 18466:2016(E) [23] [24] [25] [26] [27] [28] [29] H Abundance of 14 C in biomass fractions of wastes and solid recovered fuels Waste Manag 2009, 29 pp 1495–1503 F uglsang K., P ederson N.H., L arsen A.W., A strup T 2011 Measurement method for determination of the ratio of biogenic and fossil-derived CO2 in stack gas 10th Int conference on emissions monitoring 5-7 October 2011, Prague G uandalini R 2010 Determination of the biomass content of waste: the optimized mass F ellner J., & R echberger balance method IEA – Bioenergy Task 36 Meeting, 17-19 November 2010, Roma, Italy M ohn J., S zidat S., F ellner J., R echberger H., Quartier R., B uchm ann B Determination of biogenic and fossil CO2 emitted by waste incineration based on 14 CO2 and mass balances Bioresour Technol 2008, 99 pp 6471–6479 O bermoser M., F ellner J., R echberger H Determination of reliable CO emission factors for waste-to-energy plants Waste Manag Res 2009, 27 pp 907–913 S taber W., F l amme S., F ellner J Methods for determining the biomass content o f waste Waste Manag Res 2008, 26 pp 78–87 United Nations Clan Development Mechanism Large Scale Consolidated Methodology ACM0022: Alternative Waste Treatment Processes Version 02.0 Sectorial scope: 01 and 13 – CDM-EB81-A13 (2013) p 76 © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n 25 ISO 18466:2016(E) ICS 13.040.40 Price based on 25 pages © ISO 2016 – All rights reserved I n tern ati o n al Org an i z ati o n fo r S tan d ard i z ati o n