Quan i ying ine ini e ca bon in biocha
Hamed Sanei
a,*
, Małgo za a Woj aszek-Kalai zidi
b
, Niels Hemmingsen Scho sbo
c
,
Rasmus S enshøj
a,c
, Zhiheng Zhou
a
, Hans-Pe e Schmid
d
, Nikolas Hagemann
d
,
Da id Chia amon i
e
, T y onas Kiai sis
a
, A ka Rud a
a
, Anna J. Lehne
, Robe W. B own
g,h
,
Sophie Gill
g
, E ica Do
i
, S a os Kalai zidis
j
, Fa ibo z Gooda zi
k
, Hen ik Inge mann Pe e sen
c
a
Li hosphe ic O ganic Ca bon (LOC), Depa men o Geoscience, Aa hus Uni e si y, Denma k
b
Ins y u Technologii Paliw i Ene gii (ITPE), Poland
c
Geological Su ey o Denma k and G eenland (GEUS), Denma k
d
I haka Ins i u e o Ca bon In elligence, Swi ze land
e
Poli ecnico di To ino and RE-CORD, I aly
Ca bon u u e GmbH, Ge many
g
Isome ic, London, Uni ed Kingdom
h
School o En i onmen al and Na u al Science, Bango Uni e si y, Wales, Uni ed Kingdom
i
Rainbow, Pa is, F ance
j
Depa men o Geology, Uni e si y o Pa as, G eece
k
FG & Pa ne L d, Resea ch G oup, Calga y, Albe a, Canada
ARTICLE INFO
Keywo ds:
Biocha pe manence
Ine ini e benchma king
Random e lec ance (R
o
)
Ca bon dioxide emo al (CDR)
Sampling equency
ABSTRACT
The ca bon dioxide emo al (CDR) po en ial o biocha is de e mined by he long- e m s abili y o i s biogenic
ca bon, de i ed om a mosphe ic CO₂ ixed by pho osyn hesis and s abilized in solid o m. This s abili y (ca bon
pe manence) is commonly assessed using decay models o e alua e esis ance o e-emission as g eenhouse gases.
Howe e , hese models a e limi ed, as hey ocus p ima ily on sho - e m deg ada ion o labile ca bon ac ions
and a e no sui ed o p ojec he beha io o he highly ecalci an componen o biocha o e ex ended
imescales.
Ine ini e ep esen s highly a oma ized and condensed ca bon s uc u es ha a e geochemically s able o e
millennia. This pape builds upon he Ine ini e Benchma king (IBR
o
2) me hodology, di ec ly quan i ying he
s able ca bon ac ion in biocha a he han elying on modeling. The me hod combines he mochemical
analysis and inciden -ligh mic oscopy o measu e he eac i e (labile) componen and solid ca bonized mac-
e als, espec i ely. Random e lec ance analysis (R
o
) p o ides a ep esen a i e dis ibu ion o ca boniza ion
s a es, wi h R
o
alues >2.0 % de ining he ine ini e ac ion a e discoun ing eac i e o ganic ca bon. The R
o
dis ibu ion is p ocessed using ke nel densi y es ima ion (KDE) and nume ical in eg a ion o classi y ine ini e
ca bon wi h p ecision and s a is ical obus ness.
As CDR c edi ing can be linked o measu ed ine ini e con en , s a is ical alidi y is essen ial. A Mon e Ca lo
simula ion model e alua es unce ain ies om sampling equency and p oduc ion a iabili y. Resul s show ha
inc eased sampling educes unce ain y and lowe s he conse a i e sa e y ma gin needed o po en ial e o s.
This amewo k suppo s a jus i ied sa e y ma gin applied o epo ed ine ini e ca bon and co esponding CDR
alues, enabling conse a i e and obus c edi ing.
By combining di ec quan i ica ion o ine ini e ca bon wi h p obabilis ic modeling o unce ain y, he IBR
o
2
me hod o e s a anspa en and igo ous amewo k o assessing biocha pe manence, aligned wi h eme ging
in e na ional ce i ica ion and na ional in en o y me hodologies.
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (H. Sanei).
Con en s lis s a ailable a ScienceDi ec
In e na ional Jou nal o Coal Geology
jou nal homepage: www.else ie .com/loca e/coal
h ps://doi.o g/10.1016/j.coal.2025.104886
Recei ed 7 Augus 2025; Recei ed in e ised o m 24 Sep embe 2025; Accep ed 2 Oc obe 2025
In e na ional Jou nal o Coal Geology 310 (2025) 104886
A ailable online 3 Oc obe 2025
0166-5162/© 2025 Published by Else ie B.V.
1. In oduc ion
The e ec i eness o biocha as a means o ca bon dioxide emo al
(CDR) depends on he pe manence o i s s o ed ca bon. Fo soil-applied
biocha , common assessmen me hods ely on closed-sys em labo a o y
incuba ions o e sho ime ames (o en one o h ee yea s) (Budai
e al., 2016; Dha makee hi e al., 2015; Fang e al., 2014; He a h e al.,
2015; Kuzyako e al., 2014; Majo e al., 2010; Singh e al., 2012; Wu
e al., 2016; Zimme man, 2010; Zimme man and Gao, 2013). While
hese expe imen s p ima ily cap u e he sho - e m decay o labile
o ganic ma e , he highly ca bonized, s able ac ion emains la gely
un eac i e (G oss e al., 2024; Sanei e al., 2025). As a esul , de i ed
decay models e lec only ini ial deg ada ion p ocesses and o e no
di ec empi ical insigh in o he long- e m a e (>100 yea s) o he
s able ca bon ac ion, making ex apola ions highly unce ain (Azzi
e al., 2024; Sanei e al., 2025).
A complemen a y app oach add esses his limi a ion by di ec ly
quan i ying he ac ion o s able ca bon expec ed o pe sis o e en i-
onmen ally ele an imescales (>1000 yea s). This me hod d aws on
geological p inciples, ecognizing ha highly ca bonized o ganic ma e
ans o ms in o ine ini e mace als, condensed and a oma ized s uc-
u es known o hei esis ance o deg ada ion and long- e m p ese -
a ion in sedimen a y ocks (Ascough e al., 2011; Ascough e al., 2010;
Azzi e al., 2024; Hudspi h e al., 2015; Pe e sen e al., 2023; Sanei e al.,
2024).
Mos ine ini e mace als ep esen e minal ans o ma ion s a e o
o ganic ma e wi hin he sedimen a y ca bon cycle, analogous wi h he
endpoin o ino ganic ca bon becoming ca bona e ock. F om a
geological pe spec i e, ine ini e mace als and ca bona e mine als
ep esen wo complemen a y pa hways o he Ea h’s na u al long- e m
ca bon seques a ion sys em. Bo h se e as mechanisms by which a -
mosphe ic o biosphe ic CO
2
is ans o med in o ock- o ming compo-
nen s. These ans o ma ions ha e o e geological imescales
con ibu ed o he egula ion o he Ea h’s clima e, ac ing as na u al
he mos a s du ing pe iods o ele a ed a mosphe ic CO
2
. The ca bon-
iza ion o plan -de i ed o ganic ma e in o ine ini e mace als, in
pa icula , is a well-documen ed and geochemically alida ed mecha-
nism by which he e es ial biosphe e has con ibu ed o geological-
scale ca bon s o age h oughou Ea h’s his o y (K oege e al., 2011;
Mo ga, 2011; Sanei e al., 2024; Tisso and Wel e, 2013).
The Ine ini e Benchma king me hodology (IBR
o
2) builds on his
p inciple by p oposing di ec measu emen o ine ini e ca bon con en
(C
Ine
) in biocha , which ep esen s he po ion o o ganic ca bon ha
can be assumed o emain s able o e millennial imescales. The
ecogni ion and quan i ica ion o he ine ini e ac ion wi hin o ganic
ma e is well es ablished in he ield o o ganic pe ology (Diessel,
1983; In e na ional Commi ee o Coal and O ganic Pe ology (ICCP),
2001; Sco and Glasspool, 2007; Mo ga, 2011; Pe e sen e al., 2023;
Sanei e al., 2024; Mas ale z e al., 2023, 2025). This me hodology, as
applied o biocha , was desc ibed by Sanei e al. (2024) and u he
de eloped in subsequen s udies (Mas ale z e al., 2025; Pe e sen e al.,
2025; Pe e sen and Sanei, 2025; Rud a e al., 2024). The me hod was
also es ed in he longes - unning biocha ield ial in he Eu opean
Union, loca ed a La B accesca, I aly, whe e Chia amon i e al. (2024)
e alua ed he ine ini e ac ion in opsoil a e 15 yea s. These ha e
con ibu ed o he e inemen and s eamlining o he me hodology,
enabling i s b oade applica ion in ca bon c edi ing amewo ks and i s
in eg a ion in o s anda ds used by ca bon egis ies and moni o ing,
epo ing, and e i ica ion (MRV) sys ems.
While u he undamen al wo k is needed o econcile he mace al
composi ion wi h he indings om wo decades o esea ch on ca bon
specia ion in biocha s in o a cohe en pic u e o u he ad ance he
opic o biocha pe sis ence. Howe e , he aim o his pape is o
consolida e hese de elopmen s and o mally es ablish a s anda dized
me hodology o ine ini e quan i ica ion in biocha . Building on p io
esea ch and p ac ical applica ion, he p oposed me hod is p esen ed as
a bes -p ac ice app oach o assessing he long- e m ca bon pe manence
o biocha in he con ex o CDR ce i ica ion. The IBR
o
2 me hod enables
ce i ica ion schemes and hei ce i ica ion bodies o mo e o an
ad anced analysis me hod ha allows a mo e nuanced and i - o -
pu pose cha ac e iza ion o indi idual biocha s ega ding hei pe sis-
ence in soil.
2. Ine ini e Benchma king (IBR
o
2)
The IBR
o
2 me hod in eg a es wo complemen a y analy ical ap-
p oaches, (i) he mochemical analysis and (ii) inciden ligh mic oscopy,
o quan i y he eac i e o ganic ca bon (C
Reac
) con en o biocha
(Fig. 1). This is because o ganic ma e in biocha is p esen in wo
p ima y o ms:
(i) Reac i e o ganic ma e includes mo e labile compounds, con-
sis ing o seconda y-gene a ed o adso bed ma e ial du ing py-
olysis such as condensa es, semi-liquid a s o bi uminous
subs ances, and small ca bonaceous compounds a he inges o
used a oma ic mac omolecules as well as esidual non-
ca bonized ma e ial. These a e mo e p one o deg ada ion bu
a e no obse able unde inciden ligh mic oscopy and canno be
quan i ied by ligh mic oscopy as in oduced in he ollowing
pa ag aph. Howe e , hey a e he mally eac i e and can be
ola ilized h ough con olled e-py olysis. Reac i e o ganic
ca bon con en (C
Reac
) can be quan i ied using he mochemical
me hods such as Rock-E al 6 py olysis, he mal g a ime ic
me hods, o o he simmila analysis (see Sec ion 3).
(ii) Mace als a e emaining solid and semi-solid, pa icula e o ganic
ma e amenable o iden i ica ion and quan i ica ion using inci-
den ligh mic oscopy ( isible ligh ), whe e andom e lec ance
(R
o
) can be measu ed. Because R
o
measu emen s equi e me-
chanical polishing o he sample, only mace als wi h hei solid
and semi-solid na u e a e obse able and quan i iable unde he
mic oscope (see Sec ion 4).
To accu a ely de e mine he C
Ine
, bo h ca bon ac ions mus be
quan i ied using sepa a e bu in eg a ed me hods ((Pe e sen e al., 2025;
Pe e sen and Sanei, 2025; Sanei e al., 2024); see Sec ion 2.3). The
biocha sample is he e o e di ided in o wo ep esen a i e subsamples;
subsample A is subjec ed o he mochemical analysis o quan i y he
C
Reac
(d y w %), and subsample B unde goes inciden -ligh mic oscopy
o de e mine he R
o
dis ibu ion o he ca bonized mace als (Fig. 1).
I is c i ical ha he sample accu a ely ep esen s he en i e p o-
duc ion ba ch o ensu e analy ical accu acy and p ecision. De ailed
guidance on app op ia e sampling p ocedu es is p o ided in he
guidelines o he Eu opean Biocha Ce i ica e (Schmid e al., 2024).
The use o g ab samples alone can in oduce high a iabili y (Bucheli
e al., 2014), which inc eases he isk o ele a ed sa e y ma gin de-
duc ions du ing c edi issuance (see Sec ion 5).
The p ocedu e ollows hese s eps (Fig. 1):
2.1. Quan i y eac i e o ganic ca bon ac ion
Using subsample A, he C
Reac
can be measu ed he mochemically
(see Sec ion 3). This alue, exp essed as a ac ion o o ganic ca bon
(C
O g
, ob ained om elemen al analysis, c . EBC 2025 (Schmid e al.,
2024) p esen in biocha , is de ined as:
FReac =CReac
CO g
(1)
Whe e C
Reac
and C
O g
a e bo h exp essed as weigh pe cen ages on a
d y basis (d y w %) and FReac is exp essed as a ac ion o eac i e
o ganic ca bon (i.e., alues be ween 0 and 1).
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
2
2.2. Calcula e ine ini e ac ion
In subsample B, e lec ance can be measu ed a 500 poin s ac oss he
polished su ace (see Sec ion 3). The ela i e p opo ion o measu e-
men s wi h R
o
>2.0 % is deno ed as FRo>2, ep esen ing he ac ion o
da a poin s exceeding his h eshold (Mas ale z e al., 2023, 2025;
Pe e sen e al., 2023; Sanei e al., 2024).
FIne =FRo>2×(1−FReac )(2)
Whe e FIne and FRo>2 a e bo h exp essed as ac ions (i.e., nondi-
mensional alues be ween 0 and 1).
CIne on a d y weigh basis is hen calcula ed by, based on assump-
ions de ailed in Sec ion 2.3:
CIne (d y w %) = FIne ×CO g(d y w %)(3)
To quan i y he CDR, he CIne is con e ed o i s CO
2
-equi alen s
using he mola mass a io o CO
2
/C (44.01/12.01):
CDR (w %) = CIne (d y w %)×44.01
12.01 (4)
This in eg a ed me hodology p o ides a di ec , empi ical measu e o
he mass ac ion o C
O g
in biocha ha has ans o med in o an
ine ini e-like s uc u e. By isola ing and quan i ying his ac ion, he
IBR
o
2 me hod o e s a scien i ically obus amewo k o assessing long-
e m biocha pe manence in CDR applica ions.
2.3. Combining he mochemical and R
o
me hods o es ima e ine ini e
ca bon
To quan i y CIne (d y w %) using FReac and FRo>2 equi es ha mo-
nizing di e ences in he uni s. The FReac is es ima ed as he mass a io o
ca bon eleased du ing he mal decomposi ion, no malized o he C
o g
.
In con as , he measu ed FRo>2, de i ed om he olume ic dis ibu-
ion o R
o
alues, is based on he well-es ablished poin -coun ing me hod
in o ganic pe ology and ep esen s an equally p obable sampling o
mace als p esen h oughou he sample (In e na ional O ganiza ion o
S anda diza ion (ISO), 2009b; Go don e al., 2021; Sanei e al., 2024;
Zhou and Sanei, 2025). The e o e, he esul ing equency his og am o
R
o
alues p o ides a s a is ically ep esen a i e app oxima ion o he
olume ac ion o biocha a di e en R
o
classes: (i) poo ly ca bonized:
FRo≤1.2; (ii) semi-ine ini e: F1.2<Ro≤2, and (iii) ine ini e: FRo>2 (Sanei
e al. (2024); see Sec ion 4).
Combining he da ase s epo ed in di e en uni s equi es con e -
sion o R
o
-based olume ac ions in o weigh pe cen ages. Because
di ec measu emen s o mace al g ain densi ies a e no p ac ical, he
analysis assumes ha all h ee ca boniza ion classes (poo ly ca bonized,
semi-ine ini e, and ine ini e) ha e iden ical densi ies. Wi h his
assump ion, olume ac ions a e ea ed as equi alen o weigh ac-
ions, allowing o di ec compa ison wi hou he need o densi y
co ec ion. In bo h o ma s, he o al emains no malized o 100 %.
In eali y, ine ini e mace als ha e a highe densi y han o he
ca bonaceous componen s due o hei ele a ed ca bon con en , which
esul s om inc eased a oma ici y and lowe ola ile ma e (Wang
e al., 2024; Wang e al., 2023). Consequen ly, he common assump ion
o equal densi y ac oss all mace al ypes leads o an unde es ima ion o
he ine ini e con ibu ion. Fo example, i he a e age g ain densi ies
o poo ly ca bonized, semi-ine ini e, and ine ini e componen s a e
app oxima ely 1.30, 1.40, and 1.50 g cm
−3
(Wang e al., 2023, 2024),
espec i ely, and each class occupies one hi d o he o al olume, he
esul ing weigh dis ibu ion would be 30.9 %, 33.4 %, and 35.7 %.
Thus, he ac ual ine ini e weigh ac ion exceeds he es ima e based on
equal-densi y assump ions by abou 2.4 pe cen age poin s. This
Fig. 1. Schema ic p o ocol o quan i ying he ine ini e ac ion o o ganic ca bon in biocha using he ine ini e benchma king me hod (IBR
o
2). The d y biocha
sample is di ided in o wo subsamples: (A) analyzed he mochemically o quan i y he eac i e o ganic ca bon ac ion (F
Reac
) ac ion, and (B) analyzed pe o-
g aphically ia e lec ed ligh mic oscopy o ob ain andom e lec ance (R
o
) alues. Based on R
o
h esholds, ca bonized pa icles a e classi ied as poo ly ca bonized
(R
o
≤1.2 %), semi-ine ini e (1.2 % <R
o
≤2 %), and ine ini e (R
o
>2 %). The ine ini e ac ion o o ganic ca bon in biocha (F
Ine
) is calcula ed as he p opo ion
o mace als wi h R
o
>2 % (F
Ro>2
) mul iplied by he non- eac i e o ganic ca bon ac ion (1 – F
Reac
).
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
3
simpli ica ion in oduces a conse a i e bias in o he ca bon accoun ing
amewo k, educing he isk o o e es ima ing he s able ca bon
ac ion.
3. The mochemical measu emen o eac i e o ganic ca bon
The quan i ica ion o C
Reac
con en in biocha can be achie ed by
using he mochemical analysis such as Rock-E al 6, he mal g a ime ic
me hods, o o he simila analysis (Bo dena e e al., 1993; Buss and
Maˇ
sek, 2014; La a gue e al., 1998; Pe e sen e al., 2023). These
me hods aim o e-py olyze he biocha sample unde con olled con-
di ions o ola ilize labile ca bon bonds. The mass o chemical signa u e
o hese ola ile componen s is hen used o es ima e he ac ion o
eac i e o ganic ma e suscep ible o he mal decomposi ion below a
unc ionally de ined empe a u e.
In he mal g a ime ic me hods, he eac i e o ganic ma e ac ion
(o ola ime ma e ) is es ima ed g a ime ically by moni o ing he
sample’s weigh loss du ing py olysis. In con as , Rock-E al analysis
di ec ly measu es he e ol ed hyd oca bons and oxygen-con aining
compounds using lame ioniza ion de ec ion (FID) and in a ed (IR)
spec oscopy, espec i ely. Since app oxima ely 95 % o he o ganic
molecules in biocha a e composed o ca bon, hyd ogen, and oxygen,
he sum o measu ed hyd oca bons, CO, and CO₂ eleased du ing py-
olysis accoun s o he majo i y o he eac i e o ganic ma e in he
biocha sample. F om hese e ol ed gases, he C
Reac
con en can be
s oichiome ically es ima ed.
These me hods di e in hei po en ial biases. Rock-E al me hod
may unde es ima e C
Reac
, as i does no accoun o mino con ibu ions
om he e oa oms such as sul u , ni ogen, phospho us, and ace ele-
men s. In con as , he mal g a ime ic me hods may o e es ima e he
eac i e ac ion, since he g a ime ic signal can include weigh loss
om he mally uns able mine al phases, such as side i e, ha decom-
pose wi hin he py olysis empe a u e ange. Fu he mo e, ac o s such
as he hea ing a e, maximum empe a u e, and esidence ime a he
maximum empe a u e can also in luence he measu ed esul s.
Rock-E al 6 me hodology is calib a ed agains Ins i u F ançais du
P´
e ole (IFP) s anda ds and alida ed o eco e he o al o ganic ca bon
(C
O g
) con en . The py olysis s age in ol es hea ing he sample
iso he mally a 300 ◦C o 3 min, ollowed by a linea empe a u e amp
a 25 ◦C pe minu e up o 650 ◦C. This s ep acili a es he he mal
deg ada ion o labile ca bon s uc u es, eleasing ola ile p oduc s
de i ed om C
–
H and C
–
O bonds. The e ol ed hyd oca bons, CO, and
CO
2
a e hen quan i ied, and hei s oichiome ic ca bon equi alen s a e
used o calcula e he C
Reac
con en , epo ed as a weigh pe cen age on a
d y basis (d y w %) (La a gue e al., 1998).
Following py olysis, he emaining sample is subjec ed o an oxida-
ion phase. I is ans e ed o a combus ion u nace, pu ged wi h ai ,
and hea ed om 150 ◦C o 850 ◦C a a a e o 25 ◦C pe minu e. Du ing
his phase, he emaining o ganic ma e is oxidized, and he esul ing
CO and CO
2
a e measu ed in eal ime. Thei s oichiome ic ca bon
con ibu ions de ine he esidual o ganic ca bon, a ac ion analogous o
ixed ca bon (La a gue e al., 1998; Sanei e al., 2024). The sum o
eac i e and esidual o ganic ca bon yields he o al C
O g
con en o he
biocha sample (d y w %). Howe e , he C
O g
should s ill be de e mined
by elemen al analysis acco ding o In e na ional O ganiza ion o
S anda diza ion (ISO), 2010, ollowed by he a i hme ic deduc ion o
ino ganic ca bon (Bachmann e al., 2016; Schmid e al., 2024).
4. Random e lec ance analysis o biocha
4.1. Sampling and sample p epa a ion
The biocha sample is i s d ied a 40 ◦C, hen c ushed o a pa icle
size below 0.2 mm, allowing in e nal c oss sec ions o he pa icles o be
exposed o op ical measu emen . A e p epa a ion, he esul ing ag-
men s a e embedded in a 2.54-cm diame e cold-se ing epoxy esin
pelle (o simila cold-cu ing esin). The embedding p ocess is ca ied
ou in wo s ages. In he i s s age, a minimal amoun o esin is mixed
ho oughly wi h he biocha o concen a e he agmen s a he base o
he pelle . This is essen ial because biocha ends o loa wi hin he esin
due o i s ela i ely low densi y, and i is he base o he pelle ha will
la e be g ound and polished o mic oscopic analysis. Once he ini ial
laye cu es, a second laye o esin is pou ed o inc ease he pelle heigh
o easie handling. A e comple e cu ing, he base o he pelle is
g ound and polished ollowing s anda d p ocedu es ou lined in In e -
na ional O ganiza ion o S anda diza ion (ISO) (2009a) o ob ain a
sc a ch- ee, elie - ee, highly polished su ace. This ensu es op imal
exposu e o biocha agmen s in andom o ien a ion on he polished
c oss-sec ion o e lec ance measu emen s.
4.2. Re lec ance measu emen p ocedu e
Re lec ance measu emen s a e pe o med using inciden -, whi e-
ligh mic oscopy. An enhanced-con as , oil imme sion 50×objec i e
lens is ecommended, and he use o a came a-based pho ome ic sys em
is ad ised due o i s long- e m calib a ion s abili y and p ecision.
The mic oscope should be calib a ed wi h e lec ance s anda ds nea
he sample’s expec ed R
o
ange, p e e ably using s anda ds wi h highe
alues. A p elimina y es ima e o he sample’s expec ed R
o
can be ob-
ained om i s epo ed py olysis empe a u e using published empi -
ical ela ionships be ween ca boniza ion empe a u e and R
o
(see Fig. 15
in Sanei e al., 2024).
Re lec ance measu emen s should be ca ied ou acco ding o In-
e na ional O ganiza ion o S anda diza ion (ISO), 2009b, using he
smalles a ailable ligh -p obe diame e o minimize he e ec o su ace
impe ec ions such as sc a ches and mic o- elie , bu also o a oid
excluding pa icles wi h a na u ally mo e delica e, ine s uc u e. The
size o he ligh p obe mus no exceed he a ea in ended o measu e-
men , in o de o a oid unin en ional bias om su ounding ma e ial
such as sc a ches, deb is, o adjacen phases, and o ensu e ha only he
a ge su ace is analyzed. Only ca bonized o ganic ma e is a ge ed o
measu emen ; e lec ance alues a e he e o e inhe en ly on an ash- ee
basis. P ope polishing is essen ial o ensu e he accu acy o R
o
eadings
and elimina e su ace a e ac s.
4.3. Measu emen s a egy and s a is ical equi emen s
Each polished pelle should be sys ema ically examined o ob ain R
o
measu emen s om a s a is ically ep esen a i e popula ion o ca bon-
ized o ganic agmen s o he biocha sample. I is ecommended o
collec up o h ee poin measu emen s on h ee dis inc agmen s
wi hin each mic oscope ield o iew du ing scanning. Using he cen al
c osshai as a guide, selec ions should be made om di e en quad an s
o he ield o maximize spa ial andomness and a oid bias. Following
he me hodology ou lined by Sanei e al. (2024), a o al o 500 indi-
idual poin measu emen s pe sample is ad ised o ensu e bo h s a is-
ical eliabili y and ep oducibili y (Fig. 2). Gi en a maximum o h ee
poin s pe ame, his co esponds o app oxima ely 170 mic oscopic
ields pe sample. These ields should be e enly dis ibu ed ac oss he
en i e polished su ace o ensu e ep esen a i e co e age o he sample’s
in e nal he e ogenei y (Fig. 2).
The mean R
o
can be ypically es ima ed wi h as ew as 100 mea-
su emen s acco ding o In e na ional O ganiza ion o S anda diza ion
(ISO), 2009b. This es ima e is based on he ypical s anda d de ia ion
(
σ
) obse ed in R
o
da ase s and a 5 % cons ain on he unce ain y o he
mean alue. Applying he s anda d o mula o he S anda d E o o he
Mean (SE), whe e SE ep esen s he unce ain y in he mean es ima e,
he ollowing ela ionship is used: SE =1.96
σ
/
(N)
√=0.05. Sol ing
his equa ion p o ides a ough es ima e o he minimum numbe o R
o
measu emen s (N) equi ed o achie e a 5 % unce ain y on he mean,
assuming a no mal dis ibu ion and a con idence le el o app oxima ely
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
4
95 % (Al man and Bland, 2005; Ecampus On a io, 2022).
Howe e , eliable quan i ica ion o FRo>2 equi es a ep esen a i e
equency dis ibu ion o R
o
alues. This dis ibu ion mus e lec he
olume ic abundance o biocha pa icles ac oss di e en
ca boniza ion le els and is essen ial o de e mining he ac ion o
highly ca bonized ma e ial (FRo>2) (Sanei e al., 2024).
Recen wo k by Mas ale z e al. (2025) sugges s ha o low-ash,
labo a o y-p oduced lignocellulosic biocha s, he numbe o R
o
Fig. 2. Schema ic illus a ion o he ecommended p o ocol o measu ing andom e lec ance (R
o
) in a biocha sample. The igu e shows sys ema ic scanning o he
esin-embedded pelle using a 50×oil imme sion objec i e ( o al magni ica ion 500×). Up o h ee R
o
measu emen s a e ecommended o be aken pe mic oscopic
ield o iew ( ames), each on a dis inc mace al loca ed in a di e en quad an o he ame. Scanning con inues un il a leas 500 indi idual measu emen s a e
ob ained, ypically equi ing app oxima ely 170 ames.
Fig. 3. Example o a bimodal dis ibu ion o andom e lec ance (R
o
) in a biocha sample, showing he classi ica ion o ca boniza ion s ages based on R
o
h esholds.
The g ay ba s show he his og am o R
o
measu emen s, while he ed cu e ep esen s he ke nel densi y es ima e (KDE) o he R
o
dis ibu ion. Colo -shaded egions
indica e he h ee ca boniza ion classes: poo ly ca bonized ma e ial (R
o
≤1.2 %) in ligh blue, semi-ine ini e (1.2 % <R
o
≤2.0 %) in ligh g een, and ine ini e (R
o
>2.0 %) in ligh ed. The g een e ical line indica es he ine ini e benchma k a 2.0 % R
o
(as de ined in he IBR
o
2 me hod). The dashed blue line shows he mean R
o
alue (in his case mean R
o
=3.28 %). P opo ions o each class a e labeled wi hin he shaded zones (F
Ro≤1.2
=6.4 %, F
1.2<Ro≤2
=12.6 %, and F
Ro>2
=81.0 %),
based on he in eg a ed a ea unde he KDE cu e. The bimodal shape e lec s he e ogeneous he mal condi ions du ing py olysis, wi h a dominan mode in he
ine ini e ange and a seconda y mode in he lowe e lec ance egion. (Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he
web e sion o his a icle.)
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
5
measu emen s equi ed o de e mine FRo>2 may in mos cases be
educed o 200 wi hou signi ican loss o p ecision. Howe e , indus ial
biocha s ypically exhibi highe ash con en and mo e complex, o en
mul imodal, R
o
dis ibu ions. Fo such ma e ials, no consensus has ye
been eached on a educed measu emen coun . A global ound- obin
s udy cu en ly unde way unde he auspices o he In e na ional
Commi ee o Coal and O ganic Pe ology (ICCP) is expec ed o p o ide
u he guidance. Un il mo e de ini i e e idence becomes a ailable, he
500-poin measu emen p o ocol emains a conse a i e and s a is i-
cally obus s anda d o ep oducible quan i ica ion o FRo>2, pa icu-
la ly in he e ogeneous indus ial biocha s, p o iding he esolu ion
necessa y o ba ch-le el c edi ing and he consis ency equi ed o
ce i ica ion pu poses (Sanei e al., 2024).
Re lec ance alues a e plo ed as equency dis ibu ions o illus a e
he spa ial a iabili y o ca boniza ion wi hin a biocha sample (Fig. 3).
The a i hme ic mean R
o
p o ides a single alue p oxy o he o e all
deg ee o ca boniza ion; howe e , i s in e p e i e alue depends
s ongly on he cha ac e is ics o he unde lying dis ibu ion. In cases
whe e he dis ibu ion is bimodal o polymodal, e lec ing he e oge-
neous ca boniza ion and/o he e ogenei y o blending o eeds ock
ma e ials, he mean R
o
does no adequa ely ep esen he a iabili y
wi hin he sample (Pe e sen and Sanei, 2025) (see he example in Fig. 3).
4.4. Random e lec ance (R
o
) p o iling in biocha
The spa ial dis ibu ion o ca boniza ion le els wi hin a biocha
sample is analyzed using he equency dis ibu ion o R
o
alues. The R
o
da a a e compiled in o a equency his og am wi h bin wid hs dynami-
cally de e mined o ensu e s a is ically meaning ul esolu ion (Fig. 3).
This dis ibu ion p o ides a quan i a i e basis o assessing he ex en
and uni o mi y o ca boniza ion, which is c i ical o e alua ing biocha
ca bon s abili y and measu ing he ine ini e ac ion (Sanei e al.,
2024).
Fo ins ance, a c i ical use o he R
o
dis ibu ion is he de e mina ion
o he FRo>2 alue. This can be done di ec ly using equency coun ing.
Howe e , his app oach can in oduce ep oducibili y issues in samples
wi h complex (bi- o mul imodal) R
o
dis ibu ions due o in e -ope a o
measu emen a iabili y. Ope a o s may unin en ionally selec di e en
popula ions o mace als and may be d awn o pa icles wi h di e ing
e lec i i y, in oducing sligh biases (e.g., a o ing lowe - o highe -
e lec ing pa icles). This leads o no iceable di e ences in he esul -
ing equency dis ibu ions and, consequen ly, signi ican di e ences in
he calcula ed p opo ions o FRo>2. Such a iabili y p oduces ep o-
ducibili y issues o non-au oma ed measu emen s ha in ol e human
ope a o s, each wi h inhe en di e ences in wo king s yle and judg-
men . To minimize he ep oducibili y impac ela ed o R
o
dis ibu ion
analysis, applying ke nel densi y es ima ion (KDE) is c i ical. KDE
smoo hs sligh in e -ope a o a iabili ies, ensu ing ep oducibili y and
eliabili y o ac ion es ima es.
4.4.1. Ke nel densi y es ima ion (KDE) o R
o
dis ibu ion
To ob ain a con inuous app oxima ion o he dis ibu ion o R
o
alues, a KDE me hod is applied using a uni a ia e Gaussian ke nel. A
Gaussian ke nel is conside ed sui able o modeling he R
o
dis ibu ion,
as each componen wi hin a biocha sample is expec ed o ollow a
no mal dis ibu ion when measu ed indi idually. In homogeneous
samples, his yields a unimodal dis ibu ion, while he e ogeneous sam-
ples p oduce a polymodal dis ibu ion app oxima ed as a sum o
NGaussians, whe e N ep esen s dis inc componen s. Ra he han
es ima ing N be o ehand, he KDE me hod cap u es he composi e dis-
ibu ion di ec ly.
KDE is a nonpa ame ic echnique ha es ima es he unde lying
p obabili y densi y unc ion (x)o a andom a iable based on a ini e
se o obse a ions, wi hou assuming any p ede ined dis ibu ion shape
(Chen, 2017; Pa zen, 1962). Gi en a se o measu ed R
o
alues {x
1
,x
2
, …,
x
n
}, he KDE is compu ed as:
(x) = 1
nh∑n
i=1K(x−xi)
h(5)
Whe e:
• (x)is he es ima ed p obabili y densi y unc ion a poin x,
•n is he numbe o R
o
measu emen s (i.e., he sample size),
•x
i
a e he indi idual measu ed R
o
alues,
•h is he bandwid h, a smoo hing pa ame e ha de e mines he wid h
o he ke nel and con ols he balance be ween bias and a iance in
he es ima e,
•K(u) is he Gaussian ke nel unc ion, whe e he a iable u is de ined
as he s anda dized dis ance u=x−xi
h, and K(u) is gi en by he
s anda d no mal dis ibu ion: K(u) = 1
2
π
√exp(−u2
2).
The bandwid h h plays a c ucial ole in he shape o he esul ing
densi y es ima e. A small h may lead o o e i ing (a noisy es ima e),
while a la ge h may o e smoo h he dis ibu ion and obscu e impo an
ea u es. In his s udy, he bandwid h is selec ed using Sil e man’s ule
o humb, which p o ides a da a-d i en, closed- o m solu ion o
op imal smoo hing unde he assump ion o no mally dis ibu ed da a.
Sil e man’s ule is exp essed as Sil e man (2018):
h=0.9min(
σ
,IQR
1.34)n−1/5(6)
Whe e:
•
σ
is he s anda d de ia ion o he R
o
alues,
•IQR is he in e qua ile ange o he da ase ,
•n is he numbe o obse a ions.
This o mula ion adap i ely scales he bandwid h o e lec he
dispe sion o he da a while minimizing es ima ion e o in mos p ac-
ical cases.
To ensu e su icien esolu ion ac oss he R
o
ange, he domain x
ε
[x
min
,x
max
] is disc e ized in o 500 equally spaced in e als. The esul ing
KDE cu e is hen o e laid on he empi ical equency his og am,
p o iding a smoo h and con inuous ep esen a ion o he R
o
dis ibu ion
(Fig. 3). This app oach enhances isual in e p e a ion o he ca bon-
iza ion p o ile and allows be e de ec ion o mul imodali y o sub le
shi s in he dis ibu ion ha may no be e iden in he binned his og am
alone.
4.4.2. Nume ical in eg a ion o he KDE cu e
To quan i y he dis ibu ion o R
o
alues ac oss di e en ca boniza-
ion ca ego ies, he ou pu o he KDE is nume ically in eg a ed using
Simpson’s ule (Tal ila and Wie sma, 2012). This highe -o de in e-
g a ion me hod app oxima es he a ea unde he KDE cu e by i ing a
second-o de polynomial o each pai o adjacen in e als, p o iding a
mo e accu a e es ima e han simple me hods such as he apezoidal
ule.
A o al =∫∞
0 (x)dx
≈Δx
3[ (x0)+4∑
odd j (xj)+2+∑
e en j j∕=0,n (xj)+ (xn)](7)
In his exp ession:
•A
o al
is he o al a ea unde he KDE cu e, ep esen ing he in eg al
o he es ima ed p obabili y densi y unc ion o e he en i e e lec-
ance domain,
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
6
• (xj)a e he KDE-es ima ed densi y alues a he disc e ized poin s
x
j
,
•Δx is he spacing be ween consecu i e x- alues (uni o m ac oss he
in e al),
•The summa ions a e aken o e odd and e en indices j (excluding he
endpoin s o e en j),
•x
0
and x
n
a e he lowe and uppe bounds o he disc e ized domain,
espec i ely.
The o al a ea is hen subdi ided in o h ee ca boniza ion ca ego ies
based on R
o
h esholds (Fig. 3): poo ly ca bonized (R
o
≤1.2 %), semi-
ine ini e (1.2 % < R
o
≤2.0 %), and ine ini e (R
o
>2.0 %). The clas-
si ica ion h esholds ollow Sanei e al. (2024), Mas ale z e al. (2023),
Mas ale z e al. (2025), Pe e sen and Sanei (2025), Pe e sen e al. (2023)
and Pe e sen e al. (2025), wi h ine ini e ep esen ing he mos
a oma ized and condensed ac ion, essen ial o long- e m ca bon
pe manence in CDR applica ions. Each ca ego y’s pa ial a ea is calcu-
la ed as:
ARo≤1.2=∫1.2
0 (x)dx,A1.2<Ro<≤2.0=∫2.0
1.2 (x)dx,ARo>2=∫∞
2.0 (x)dx
(8)
Whe e ARo≤1.2, A1.2<Ro≤2, and ARo>2 a e he in eg a ed a eas co e-
sponding o each R
o
ange ac ion.
The ela i e p opo ions o each ca boniza ion ca ego y a e hen
compu ed by no malizing hese pa ial a eas by he o al a ea unde he
KDE cu e (Fig. 3):
FRo≤1.2=ARo≤1.2
A o al
;F1.2<Ro≤2=A1.2<Ro≤2
A o al
;FRo>2=ARo>2
A o al
(9)
Whe e FRo≤1.2, F1.2<Ro≤2, and FRo>2 ep esen he ac ion o each
ca boniza ion class.
No maliza ion ensu es he sum o hese p opo ions sums o 1 (100
%), accoun ing o ounding e o s and nume ical app oxima ions
inhe en in he disc e iza ion and in eg a ion p ocess.
This me hodology p o ides a obus and ep oducible amewo k o
quan i ying ca boniza ion dis ibu ions in biocha . KDE smoo hing and
Simpson- ule in eg a ion enable accu a e es ima ion o ine ini e ac-
ion wi hin each sample. This compu a ional wo k low suppo s s an-
da diza ion and ce i ica ion by enabling anspa en epo ing o
biocha mace al composi ion in acco dance wi h he IBR
o
2 p o ocol.
4.4.3. Example o biocha ’s R
o
p o iling
A case s udy p esen ed he e demons a es he applicabili y o he
KDE me hod h ough compa ing wo app oaches o quan i ying
ca boniza ion class ac ions in a biocha sample wi h a bimodal R
o
dis ibu ion (Table 1). Two ope a o s independen ly measu ed 500 R
o
poin s on he same polished specimen using inciden ligh mic oscopy.
Ca boniza ion classes we e de ined based on es ablished e lec ance
h esholds: Ro≤1.2 % (poo ly ca bonized), 1.2% <Ro≤2.0 % (semi-
ine ini e), and Ro>2.0 % (ine ini e). The pu pose was o assess how
consis en he esul s a e when de i ed using wo di e en da a p o-
cessing me hods.
The ac ions we e calcula ed using wo app oaches: (1) di ec e-
quency coun ing, whe e he numbe o R
o
poin s alling wi hin each
de ined h eshold ange was coun ed and hen no malized o he o al
numbe o measu emen s (500 poin s), and (2) ke nel densi y es ima ion
(KDE), in which a con inuous p obabili y densi y unc ion was gene -
a ed om he same da ase , and he p opo ion o each class was
calcula ed by in eg a ing he a ea unde he KDE cu e wi hin he co -
esponding h esholds (Table 1).
The esul s show ha ca boniza ion ac ions de i ed di ec ly om
he equency dis ibu ion exhibi conside able a iabili y be ween he
wo ope a o s. This is pa icula ly e iden in he in e media e class
(semi-ine ini e), whe e ela i e di e ences be ween ope a o s eached
up o 30 % (Table 1). These disc epancies likely a ise om he disc e e
na u e o he da ase and he sensi i i y o di ec coun ing o small shi s
in he dis ibu ion nea classi ica ion bounda ies. In con as , he KDE-
de i ed alues show much close ag eemen be ween he wo ope a-
o s, wi h ela i e di e ences consis en ly wi hin <10 % o all
ca boniza ion ac ions and <1.5 % o he ine ini e ac ion (Table 1).
This highligh s he ad an age o KDE in smoo hing ou mino local
a ia ions in he da ase , he eby educing ope a o -dependen a i-
abili y and enhancing ep oducibili y. O e all, he KDE app oach p o-
ides a mo e eliable and consis en me hod o de e mining
ca boniza ion ac ions in biocha using e lec ance da a.
4.5. Iden i ica ion and signi icance o ine ini e
Unde inciden whi e ligh , ca bonized mace als in biocha a e easily
ecognized by hei g ay ones ( a ying wi h e lec i i y), hei opo-
g aphic elie compa ed o su ounding esin o mine al ma e , and a
dis inc i e black im su ounding he polished su ace (Pe e sen e al.,
2023, 2025; Sanei e al., 2024). This im is he po ion o he ca bonized
ma e ial ha emains unpolished and lies benea h he exposed c oss
sec ion, s ill embedded wi hin he esin ma ix.
Ine ini e ep esen s a chemically ine mace al g oup composed o
highly used, polya oma ic ca bon s uc u es. I is cha ac e ized by high
e lec i i y, non- luo escen beha io , and dis inc mo phological ea-
u es such as acuoles, which esul om de ola iliza ion du ing he -
mochemical con e sions and om ana omical s uc u es inhe i ed om
he o iginal plan issue (Diessel, 1983; In e na ional Commi ee o Coal
and O ganic Pe ology (ICCP), 2001; Mo ga, 2011). The p edominan
ine ini e mace al is usini e, ypically de i ed om lignocellulosic
biomass, al hough o he o ms may o igina e om lip ini ic ma e
(Howe e al., 2009).
In he con ex o biocha , ine ini e cons i u es he mos chemically
s able ac ion o he o ganic ma e . Re lec ance measu emen s (R
o
)
exceeding 2.0 % ma k he beginning o he ine ini e domain in he
e lec ance dis ibu ion his og am (Mas ale z e al., 2025; Sanei e al.,
2024). These ele a ed R
o
alues indica e ex ensi e ca bon condensa ion
and a e associa ed wi h high esis ance o mic obial deg ada ion and
abio ic oxida ion (Pe e sen e al., 2025; Sanei e al., 2024). Quan i ying
he p opo ion o biocha agmen s wi h R
o
>2.0 % is he e o e c i ical
o e alua ing long- e m ca bon s abili y and pe manence.
4.6. Ine ini e R
o
h eshold
As discussed in he p eceding sec ions, R
o
alues g ea e han 2.0 %
ha e been p oposed as he ine ini e benchma k o biocha (Sanei e al.,
2024). A common misconcep ion is o in e p e his h eshold as e e -
ing o he mean R
o
alue. Howe e , he R
o
>2.0 % benchma k deno es
he lowe bounda y o he ine ini e R
o
ange, no i s mean (see Fig. 3).
In o he wo ds, he ine ini e benchma k is de ined by he onse o he
Table 1
Compa ison o ca boniza ion ac ions in a biocha sample, independen ly
measu ed by wo ope a o s using wo me hods: (1) di ec equency coun ing
based on ixed R
o
h esholds (His o) and (2) ke nel densi y es ima ion (KDE).
Each ope a o analyzed 500 R
o
measu emen s on he same polished specimen.
Ca boniza ion classes we e de ined as R
o
≤1.2 % (poo ly ca bonized), 1.2 % <
R
o
≤2.0 % (semi-ine ini e), and R
o
>2.0 % (ine ini e). Resul s om di ec
equency coun ing show highe in e -ope a o a iabili y, while KDE-de i ed
alues exhibi imp o ed ag eemen , demons a ing he enhanced ep oduc-
ibili y o KDE.
F ac ions Me hod Ope a o 1 Ope a o 2 Rela i e Di e ence
F
Ro≤1.2
His o: 5.6 % 6.6 % 17 %
KDE: 5.7 % 5.6 % 1.8 %
F
1.2<Ro≤2
His o: 15 % 11 % 30 %
KDE: 13 % 12 % 10 %
F
Ro>2
His o: 79 % 82 % 3.8 %
KDE: 81 % 82 % 1.5 %
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
7
e lec ance dis ibu ion, no i s cen al endency.
This means ha a sample wi h a mean R
o
jus abo e 2.0 % (e.g., 2.1
%) would s ill con ain a subs an ial po ion o e lec ance alues below
he 2.0 % h eshold. Assuming a pe ec ly Gaussian (no mal) dis ibu-
ion o R
o
alues, nea ly hal o he popula ion could all below he
ine ini e h eshold. Consequen ly, he mean R
o
alone is insu icien o
classi ying a sample as ine ini e- ich biocha .
Achie ing a e lec ance dis ibu ion en i ely abo e he 2.0 %
h eshold unde no mal dis ibu ion assump ions equi es a mean R
o
g ea e han app oxima ely 2.5 %. This dis ibu ional app oach is
consis en wi h he e lec ance cha ac e is ics o ine ini e- ich mace als
obse ed in coal. Pe e sen e al. (2025) demons a ed ha geological
usini e consis en ly exhibi s mean R
o
alues exceeding 2.5 %, wi h
s uc u al and chemical cha ac e is ics compa able o hose o highly
ca bonized biocha s.
4.7. Ad an ages o e lec ance o e bulk chemical p oxies
Unlike bulk chemical indices such as he mola H/C and O/C a ios,
which can be in luenced by sample he e ogenei y and mine al
con amina ion, he R
o
me hod speci ically a ge s ca bonized o ganic
ma e in a spa ially esol ed manne . Because R
o
alues a e measu ed
di ec ly on indi idual o ganic agmen s, he esul s a e no a ec ed by
he p esence o ash o ex aneous ino ganic ma e ial, making he
me hod pa icula ly obus o high-ash biocha s (Ende s e al., 2012;
Pe e sen and Sanei, 2025; Sanei e al., 2024).
In addi ion, e lec ance analysis cap u es he inhe en a iabili y in
ca boniza ion ac oss he biocha sample by p o iding a dis ibu ion o
esul s a he han a bulk a e age, p o iding a spa ially esol ed ep-
esen a ion o he deg ee o ca boniza ion wi hin a sample. The esul ing
e lec ance his og am e lec s he ull dis ibu ion o low-, in e media e-,
and highly-ca bonized componen s, enabling a mo e accu a e and
nuanced assessmen o he sample’s ca boniza ion. This is especially
impo an o he e ogeneous biocha s, whe e ca boniza ion may a y
widely.
5. Unce ain y in ine ini e quan i ica ion and i s impac on CDR
This sec ion p esen s a Mon e Ca lo simula ion model de eloped o
quan i y how sampling equency and a iance in measu ed CIne a ec
he unce ain y in es ima ing CDR om biocha . Based on he measu ed
a iance, he model subsequen ly de i es a s a is ically jus i ied sa e y
ma gin wi h ega d o CIne quan i ica ion o be applied o epo ed
alues, ensu ing conse a i e and eliable c edi ing.
In he IBR
o
2 me hod, he amoun o CDR ha can be c edi ed is
di ec ly de e mined by he measu ed con en o CIne in he biocha .
Howe e , he epo ed CIne alue can a y due o wo main sou ces:
measu emen unce ain y ( om analy ical a iabili y) and sampling
a iabili y (di e ences be ween indi idual samples). Sampling a i-
abili y is pa icula ly impo an , as biocha o en shows conside able
he e ogenei y wi hin a single p oduc ion ba ch (Bucheli e al., 2014),
such as he annual ou pu o a con inuously ope a ed py olysis acili y,
o be ween ba ches p oduced unde he same condi ions in discon inu-
ously ope a ed sys ems.
P epa ing composi e sampling, whe e mul iple subsamples a e
combined in o one mixed sample, can educe he e ec o small-scale
a ia ions and gi e a mo e ep esen a i e sample. Howe e , i also has
a d awback in smoo hing ou o hiding impo an di e ences be ween
p oduc ion uns. These di e ences may e lec eal changes in ca bon
s abili y and, i no p ope ly accoun ed o , could lead o inaccu a e CDR
es ima es.
To quan i y his unce ain y, i is c ucial o es ablish he coe icien o
a ia ion (CV) om independen ly collec ed samples o he same p o-
duc ion ba ch. I is ecommended o collec a leas h ee indi idual
samples ep esen ing ei he an en i e ba ch o sepa a e uns o a
discon inuous py olysis uni (when assessing a iabili y wi hin a p o-
duc ion p ocess). The mean and s anda d de ia ion (
σ
) o CIne (d y w %)
om hese samples a e hen used o calcula e he CV, a key inpu
pa ame e o he Mon e Ca lo simula ion. This allows s a is ical un-
ce ain y o be embedded in o c edi issuance ules, consis en wi h
quali y c i e ia se o h by amewo ks such as In e na ional O gani-
za ion o S anda diza ion (ISO), 2019, he EU CRCF egula ion
(Eu opean Union, 2024), UNFCCC guidance (Uni ed Na ions F amewo k
Con en ion on Clima e Change (UNFCCC), 2024), o he ICVCM
assessmen amewo k (In eg i y Council o he Volun a y Ca bon
Ma ke (ICVCM), 2024).
This amewo k makes a clea dis inc ion be ween wo sou ces o
a iabili y: (1) na u al a iabili y wi hin a single p oduc ion sys em o
ba ch, including analy ical and sampling unce ain y; and (2) delibe a e
changes made by he p oduce o op imize o modi y he p oduc ion
p ocess. The p ima y pu pose is o assess and ce i y he le el o a i-
abili y wi hin a de ined p oduc ion ba ch. I a iabili y inc eases
signi ican ly, he amewo k helps de e mine whe he his is due o
andom luc ua ions o a modi ica ion o he p oduc ion pa ame e s. In
he la e case, p oduce s a e expec ed o egis e a new ba ch and
submi new baseline samples o analysis. Ce i ica ion bodies can use
he submi ed da a o moni o such changes. The amewo k allows
p oduce s o manage he homogenei y o hei p oduc ion and o clea ly
de ine p oduc ion ba ches. I a iabili y ises unexpec edly, a new ba ch
should be s a ed, o he sys em will au oma ically inc ease he sa e y
ma gin applied o CDR c edi s. This sa e y ma gin can only be adjus ed
downwa d once addi ional da a con i m a mo e consis en ou pu .
I is also impo an o cla i y wha his me hod does and does no
p o ide. The p esen ed s a is ical app oach does no inhe en ly ensu e
he ep esen a i eness o indi idual samples ac oss an ex ended p o-
duc ion pe iod o la ge p oduc ion olumes. The model is alid when
suppo ed by adhe ence o ep esen a i e sampling a he p oduc ion
p emises (see Schmid e al. (2024)). Sampling p o ocols mus be spe-
ci ically designed o he ype o p oduc ion, and implemen ed consis-
en ly using a alida ed p ocedu e, whe he samples a e collec ed c oss
low o om s o age piles. I o e s, howe e , a anspa en , ep oduc-
ible, and ope a o -independen means o quan i y sampling-induced
unce ain y a any gi en poin in ime o p oduc ion in e al. P o-
duce s and ce i ica ion bodies should he e o e in e p e he esul ing
sa e y ma gins and CDR isk es ima es as ools guiding ope a ional
decision-making and biocha ca bon ce i ica ion.
5.1. Va iance es ima ion o ine ini e ca bon in biocha samples
Le
ψ
iwi h i=1,2,3... deno e he epo ed CIne (d y w %) o i-
submi ed biocha samples om a p oduc ion si e, hen he CV can be
calcula ed using a i hme ic mean (
ψ
)and s anda d de ia ion (
σ
) om
he sample:
CV =
σ
ψ
=
(1
N−1∑N
i=1(
ψ
i−
ψ
)2)
√
√
√
√1
N∑N
i=1
ψ
i
(10)
The CV p o ides a no malized measu e o dispe sion ha is inde-
penden o he magni ude o he mean and is used as a key inpu o isk
modeling.
Fo a biocha p oduc ion si e, he o al amoun o ine ini e ca bon
p oduced annually is es ima ed by mul iplying he annual p oduc ion
( onnes pe yea ), by he mean CIne (d y w %). The mass o ine ini e
ca bon is hen con e ed o i s equi alen mass o emo ed CO
2
using he
molecula mass a io o ca bon dioxide (44.01 g/mol) o elemen al
ca bon (12.01 g/mol). This yields he baseline es ima e o CDR in onnes
pe yea :
CDRi=Pi×(Cmean
Ine ,i
100 )×44.01
12.01 (11)
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
8
Whe e P
i
is he p oduc ion olume ( onnes pe yea ; o onnes o a
biocha ba ch) and Cmean
Ine ,i is he measu ed CIne (d y w %). Howe e , in
p ac ical applica ions, he epo ed mean CIne is subjec o analy ical
and spa ial a iabili y, pa icula ly when he sample equency is low.
To model his unce ain y, he simula ion assumes ha he measu ed
CIne ollows a no mal dis ibu ion wi h a s anda d de ia ion (
σ
) de i ed
om he coe icien o a ia ion:
σ
i=(CVi
100)×Cmean
ine ,i(12)
5.2. P edic ing CDR a iabili y h ough Mon e Ca lo simula ion
A Mon e Ca lo simula ion is hen used o gene a e syn he ic sample
means o di e en sampling equencies. Fo each sampling equency n
(e.g., weekly, mon hly), he model gene a es 1000 andom sample se s.
Each se consis s o n indi idual samples d awn om he speci ied
no mal dis ibu ion. The mean o each sample se is hen con e ed in o
an annual CDR es ima e, yielding a dis ibu ion o 1000 possible ou -
comes o ha sampling equency:
CDR(n)
j=Xj
n×44.01
12.01 ×Pi
100 (13)
F om his dis ibu ion, he model calcula es he expec ed (mean)
annual CDR and he 5 h pe cen iles o he simula ed alues.
5.2.1. Quan i ying CDR isk and es ima ing sa e y ma gins
The lowe 5 h pe cen ile is in e p e ed as he conse a i e bound on
c edi able CDR, ep esen ing he minimum quan i y o CO
2
emo al ha
can be claimed wi h 95 % con idence gi en he sampling a iabili y. The
di e ence be ween he expec ed CDR and his lowe bound de ines he
CDR isk:
Risk(n)
CDR =
μ
(n)
CDR −CI(n)
5% (14)
Whe e
μ
(n)
CDR is he mean CDR alue based on n independen samples,
and CI(n)
5% is he 5 h pe cen ile o he co esponding con idence in e al
o he same sample size.
The ela i e isk (%), which is also ega ded as he pe cen age sa e y
ma gin, is compu ed as:
Rela i e Risk(n)
CDR =(Risk(n)
CDR
μ
(n)
CDR )×100% (15)
Whe e Rela i e Risk(n)
CDR exp esses he magni ude o he isk as a pe -
cen age o he expec ed CDR alue. This o mula ion allows o quan-
i ying he sa e y ma gin by cap u ing he ex en o which low equency
sampling inc eases unce ain y in epo ed CDR and de e mining he
pe cen age ha mus be deduc ed om he epo ed mean o ensu e
conse a i e and s a is ically obus c edi ing.
The ma ix cha shown in Fig. 4 is de i ed om he Mon e Ca lo
simula ion model and displays expec ed sa e y ma gin pe cen ages
ac oss a ange o CV alues and sampling equencies. I enables p o-
duce s and ce i ie s o de e mine deduc ion le els app op ia e o he
deg ee o a iabili y in measu ed CIne wi hin a gi en p oduc ion sys-
em. To apply he ma ix, he CV mus i s be calcula ed om CIne
alues measu ed in a leas h ee independen samples submi ed o
ce i ica ion (see Sec ions 5 and 5.1). Once he CV is es ablished, he
ma ix p o ides he co esponding sa e y ma gin o he in ended sam-
pling equency (e.g., weekly, mon hly, o annually).
Al e na i ely, when egula o y equi emen s do no demand exac
decimal p ecision bu only a eliable quick es ima e, he epo ing sa e y
ma gin can be ob ained om a simple closed- o m o mula a he han
unning ull Mon e Ca lo simula ions. In his o mula ion, he sa e y
ma gin is closely ep oduced by a linea ela ionship be ween CV and
he in e se squa e oo o he sampling equency:
Sa ey ma gin (%) ≈ kCV(%)
n
√(16)
whe e n is he numbe o samples pe yea and k is a scaling cons an .
Ac oss a wide ange o simula ions, he bes i was consis en ly ob ained
o k≈1.65, which co esponds o he one-sided 95 % con idence limi .
Fig. 5a-c compa e Mon e Ca lo simula ions wi h he abo e closed- o m
equa ion using k=1.65, shown as dashed linea i s ac oss h ee ep e-
sen a i e mean CIne alues o 10, 40, and 80 w %. Wi h his choice o k,
Fig. 4. Ma ix illus a ing he epo ing sa e y ma gin (%) equi ed o accoun o sampling unce ain y in measu ed ine ini e ca bon con en (C
Ine
) ac oss a ange o
coe icien o a ia ion (CV) alues and sampling equencies. Sampling equencies a e exp essed as numbe o samples pe yea : 96 ( wice pe week), 48 (weekly),
24 (biweekly), 12 (mon hly), 4 (qua e ly), 2 (semi-annually), and 1 (annually). Highe CV alues lead o inc eased le els o sa e y ma gin (%) deduc ions om he
ca bon dioxide emo al (CDR) c edi issuance due o g ea e sampling a iabili y. Con e sely, inc easing he numbe o samples pe yea educes unce ain y,
he eby lowe ing he equi ed sa e y ma gin and imp o ing he accu acy, c edibili y, and ma ke abili y o issued CDR c edi s o biocha acili ies.
H. Sanei e al.
In e na ional Jou nal o Coal Geology 310 (2025) 104886
9
