1
Hyd o he mal CO2 Con e sion Using Zinc As Reduc an : Ba ch
Reac ion, Modeling and pa ame ic analysis o he p ocess
D. Roman-Gonzaleza, A. Mo oa, F. Bu goaa, E. Pé ezb , A.Nie o c , A.Ma ín a M.D. Be mejo a*
aHigh P essu e P ocess G oup, Depa men o Chemical Enginee ing and En i onmen al
Technology, Uni e si y o Valladolid (SPAIN),
bTERMOCAL Resea ch G oup, The modynamics and Calib a ion, Uni e si y o Valladolid,
Escuela de Ingenie ías Indus iales, Paseo del Cauce 59, E-47011 Valladolid, Spain
cDepa men o Mechanical Enginee ing, Chemical and Indus ial. ETSIDI-UPM, Mad id
(SPAIN),
*email: mdbe me[email p o ec ed]
KEYWORDS: CO2 educ ion; hyd o he mal; zinc; modeling; o mic acid, ba ch
Abs ac
Hyd o he mal educ ion o CO2 using Zn as educ an o ob ain o mic acid is a selec i e and
e icien p ocess. This p ocess has he ad an age o a oiding he use o gaseous hyd ogen wi h
all i s sa e y and en i onmen al conce ns, and allowing an easie in eg a ion wi h CO2 cap u ing
s eps such as CO2 abso p ion in aqueous NaOH, because he la e solu ions can be di ec ly ed
o he p ocess as NaHCO3. In his wo k, his eac ion was s udied in ba ch eac o s a
empe a u es om 275 o 325ºC. Con e sions up o 75% we e ob ained wi h selec i i y owa ds
o mic acid nea 100%, a esidence imes be ween 10 and 180 min. Reac ions p oceeds as in
he i s s eps o eac ion, and i is slowed down when he oxida ion o Zn is comple ed. The
expe imen al esul s ob ained we e used o s ablish a model ha can explain bo h expe imen al
da a om his wo k and om li e a u e wi h an a e aged e o o 13%. Using bo h he model
and he expe imen al da a he main a iables o he p ocess we e analyzed: empe a u e,
Zn/HCO3- a io, hea ing a e, Zn pa icle size, p essu e eac o ma e ial and use o supe c i ical
condi ions. The op imum eac ion condi ions ound we e 300ºC wi h a apid hea ing, and
pa icle sizes o 0.75-1 mm. Zn excess d ama ically imp o es he yield, bu wo king wi h a
lowe excess can be compensa ed by wo king a p essu es highe han 300 ba .
1. In oduc ion
In he las yea s, CO2 con e sion p ocesses ha e p oduced a lo o in e es , and di e en
echnologies ha e been in es iga ed. In ac , he e a e al eady indus ial CO2 ca aly ic
con e sion p ocesses ha ope a e a high empe a u es and p essu es [1], and Olah e al. [2]
ha e p oposed a “me hanol socie y” pa adigm based on he ca aly ic con e sion o ca bon
dioxide o me hanol and dime hyl e he . Howe e , some esea che s conside ha om a global
pe spec i e he widesp ead use o CO2 as a chemical esou ce can only make sense i cheap o
su plus enewable ene gy is used o i s ans o ma ion. As CO2 and sola ligh a e uni e sal
esou ces, CO2 pho oca aly ic con e sion acco ding o an “a i icial pho osyn hesis” me hod has
been widely in es iga ed since he seminal wo k o Fujishima and Honda, who in 1972
demons a ed he pho oelec ochemical spli ing o wa e [3]. A lo o in es iga ions ha e been
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ca ied ou ha ha e led o impo an ad ances, especially in he de elopmen o imp o ed
ca alys s [4,5]. Howe e , hese echnologies s ill ace impo an limi a ions, especially wi h
espec o he selec i i y and he p oduc i i y o he con e sion eac ion, and new in es iga ions
ega ding p ocess in ensi ica ion and ene gy in eg a ion a e needed o make hese echnologies
echnically and economically easible [6]
Among he di e en ca bon dioxide con e sion echnologies, he hyd o he mal educ ion o
CO2 s ands ou since i has al eady shown he po en ial o selec i ely con e ca bon dioxide
in o aluable p oduc s such as o mic acid, me hane and me hanol, a o ed by he inc eased
eac i i y o CO2 in hyd o he mal condi ions [7-10]. In his p ocess, gaseous CO2, o CO2
cap u ed in a basic aqueous solu ion as bica bona e, is educed using ze o- alen me als [10-12]
o o ganics [11, 13-15] as educ an s, elimina ing in his way he need o using hyd ogen gas
wi h all i s economical and sa e y issues. In many o hese p ocesses wa e ac s no only as a
sol en bu also as a hyd ogen sou ce, and, wha i is mo e, he educ ion pe o med wi h he
hyd ogen so gene a ed is as e han he eac ion using gaseous hyd ogen [11, 16].
Depending on he ope a ional a iables such as empe a u e, esidence ime, and educ an and
ca alys employed, di e en p oduc s can be ob ained, and in some cases, con e sions nea 80%
ha e been epo ed in li e a u e. The mos equen combina ion is he use o Fe as educing
me al and Ni [11] o Cu [12] as ca alys s. O he me als used as educ an s a e Mg, Mn, Al and
Zn, being he las h ee e y e ec i e e en wi hou ca alys s [10-12]. The mos equen p oduc
is o mic acid, bu some au ho s ha e epo ed he o ma ion o phenol [17], me hane [18] and
me hanol [19].
The hi d and maybe mos impo an ad an age o his p ocess is ha CO2 can be cap u ed by
abso p ion in basic solu ions, which is a well-known echnology. By combina ion o abso p ion
and hyd o he mal con e sion, CO2 can be di ec ly con e ed by hyd o he mal educ ion
elimina ing in his way cos o pu i ica ion, comp ession o s o age associa ed o o he
con e sion echnologies. Mo eo e , he con e sion and selec i i y o he p ocess owa ds
o mic acid has p o ed o be highe when he pH is a ound 9, in which CO2 is mos ly as
bica bona e, o e hose ob ained o gaseous CO2 [8] o ca bona e [14]. This has been a ibu ed
o a s abiliza ion o he o ma e, which educes i s decomposi ion in gaseous by-p oduc s [2].
The mos p omising esul s we e ob ained educing bica bona e using Zn as a educing me al. In
his way con e sions o almos 70%, wi h selec i i ies owa ds o mic acid nea 100% we e
ob ained in esidence imes o a ew minu es, ob aining highe con e sions a longe esidence
imes, a empe a u es be ween 250 o 325ºC.
Mos o he wo k done so a was pe o med a labo a o y scale and i is s ill a o i s
applica ion a indus ial le el, wi h he excep ion o he wo k o Takahashi e al [9] in which he
p ocess was es ed in semi-con inuous way. Addi ionally, some ways o educing back he
oxidized me als ha e been p oposed as he educ ion using glyce in [10] o sola ligh [8].
Fo mic acid inds i s applica ions in ex iles, pha maceu icals and ood chemicals, due o i s
s ong acidic na u e and educing p ope ies. In 2013, he global demand o o mic acid was
579 k , and he global ma ke is expec ed o g ow, wi h an a e age annual g ow h a e o 3.8%,
up o 2019 [21]. One o he mos p omising applica ions o o mic acid p oduced unde
hyd o he mal echnology is i s u he con e sion o me hanol [22], as i is a p omising
al e na i e o oil and na u al gas as a g een uel wi h ega d o s o age and anspo . Compa ed
o o mic acid, me hanol is easily sepa a ed om wa e and has been a common chemical aw
ma e ial o impo an chemicals. T adi ionally, me hanol is p oduced om syngas, an ene gy
in ensi e p ocess which equi es coal gasi ica ion and na u al gas e o ming. I is known ha
using hyd o he mal echnologies i is possible o p oduce me hanol om ca bon dioxide in a
wo-s ep p ocess, i s p oducing o mic acid, and hen con e ing i o me hanol unde
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hyd o he mal condi ions o e coppe -based ca alys s [22]. The in eg a ion o bo h s eps migh
be a g een p ocess o educe ca bon dioxide while p oducing bio uels.
The objec i e o his wo k is o de elop a simple kine ic model o desc ibe he p ocess o
bica bona e educ ion o o mic acid using Zn as educ an , and o in eg a e i in a
ma hema hical model able o p edic he beha io o he p ocess unde di e en ope a ional
condicions such as empe a u e, esidence ime, hea ing a e o amoun and size o he Zn
pa icles. In o de o do so, ba ch expe imen s o bica bona e educ ion wi h Zn we e pe o med
a empe a u es be ween 10 and 180 min a empe a u es be ween 250ºC and 325ºC.
2. Expe imen al
2.1 Ma e ials
Zinc (pa icle size <10 µm, pu i y ≥ 98%. CAS: 7440-66-6) was ob ained om Sigma Ald ich
(S . Louise, USA). Sodium bica bona e (NaHCO3 “A”E500 ii) and Sulphu ic acid (DEL HPLC)
(CAS: 7664-93-9) we e ob ained om Co a cas (Bu gos, Spain). Fo HPLC s anda ds he
ollowing eagen s we e used: Glacial ace ic acid (QP), o mic acid 85% o analysis,
o maldehyde 37-38% w/w s abilized o me hanol o analysis, me hanol o analysis and
e hanol absolu e pa ially dena u ed echnical g ade all o hem supplied by PANREAC.
2.2 Expe imen al p ocedu e
A 42 g/L (0.5 M) solu ion o NaHCO3 p epa ed using MilliQ wa e was used o he
expe imen s. The amoun s o sodium bica bona e we e weighed using a Sa o ius Basic balance
(Accu acy 0.1 mg). Ba ch eac o s cons uc ed using me allic ubing we e used. Two di e en
ypes o eac o s we e used: o mos eac ions, s ainless s eel eac o s (½ ‘’) we e used, while
Ni Alloy 625 eac o s (3/8”) we e used o selec ed eac ions, and o he eac ions pe o med
wi h a sequence o 350-400ºC a Ni Alloy 625 eac o s (1/2”) we e used, as s ainless s eel
eac o s canno ope a e a hese empe a u es. The eac o s had an inne olume o
app oxima ely 15 mL. Each eac o was loaded wi h a known amoun o sodium bica bona e
solu ion, illing app ox. 50% o he olume o he eac o . A known weigh o Zn-powde was
hen added (mola a io Zn/NaHCO3 = 5 o mos expe imen s). As zinc easily oxidizes in he
p esence o ai , i was handled unde ine condi ions. Fo his pu pose an ine bag, which could
be illed wi h ni ogen, was used. Inside he bag, he selec ed amoun o Zn was weighed and
pou ed inside he eac o s. A e ha , eac o s we e closed, weigh ed and in oduced in a Gallu
MR-4N o en p ehea ed o he eac ion empe a u e. In some expe imen s, in o de o s udy he
empe a u e p o ile o he p ocess, bo h wi h and wi hou eac ion, a s ainless s eel eac o
equipped wi h a ype K he mocouple was used o eco d he empe a u e o e ime. A e he
desi ed eac ion ime he eac o was ex ac ed om he o en and quenched o oom empe a u e
by imme sion in a e ige a ed ba h (p opylene glycol +wa e ) o s op he eac ion. Then he
eac o was d ied and weigh ed o check ha he e we e no losses o gaseous p oduc s by
leaking. Then, he eac o s we e pa ially opened o elease he gas p oduced in he eac ion.
A e ha , he eac o s we e weighed again, in o de o ha e an app oxima e alue o he
amoun o gas p oduced du ing he eac ion. Finally, he eac ion p oduc s we e eco e ed, he
solid and liquid ac ion sepa a ed and analyzed sepa a ely. All he expe imen s we e duplica ed
in o de o check ep oducibili y.
2.3 Analysis
The olume o he liquid sample was measu ed and eco ded, and a il a ion was done using
0.45 μm il e s. The liquid sample was spli in wo, one o he HPLC analysis and one o he
TOC analysis. Fo he HPLC analysis he samples we e il e ed using Fil e Lab Nylon Sy inge
Fil e s o 0.22 µm. The e was no need o u he dilu ion o samples be o e in oducing hem
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in o he HPLC equipmen . In he HPLC analysis an Aminex HPX-87 column was used, he
mobile phase was 0.005M H2SO4 a a low a e o 0.6 m/min, he empe a u e was 60ºC and an
IR2414 de ec o was used.
Analyses using a TOC Shimadzu TOC V-se ies equipmen we e pe o med o de e mine
o ganic ca bon (TOC), ino ganic ca bon (IC) and To al Ca bon. Fo hese analysis he samples
equi ed il a ion and dilu ion, in a olume a io 1:25. Addi ionally, o he TOC measu emen s
ni ic acid was added o he dilu ed samples be o e he analysis o con e un eac ed sodium
bica bona e in o CO2, ha i is eleased by ul asounds. The IC samples did no equi e u he
p e ea men . Fo he analysis, s anda d solu ions IC 100 ppm and TOC 100 ppm we e used as
calib a ion samples.
The solid samples om he eac ion we e d ied in a he mos a ed o en a acuum o wo days
a 35 ºC, o emo e he emaining wa e in he me allic samples. A e ha XRD es we e
ca ied ou using a BRUKER D8 DISCOVER A25 de ice, Gene a o 3KW, Ce amic cuppe
ube 2.2 kW ype FFF, o de e mina e he di e en s uc u e o Zn and is oxidized o m, ZnO:
The amoun o ZnO was hen de e mined by he Rie eld me hod.
Mal e n Mas e size 2000 Ligh Sca e ing De ice was used o measu e he a e age Zn pa icle
size, be o e he eac ion akes place. The equipmen could measu e pa icles wi h size anging
be ween 0.02 o 2000 µm. To do ha , he de ice coun wi h a dual wa e leng h de ec ion
sys em. The i s wa eleng h is he ed ligh (633 nm), and he second one is he blue ligh (436
nm). The Zn pa icles we e in oduced as an aqueous suspension in o he s i ing uni (Hyd o
SM). Knowing he e ac ion alue o wa e (1.331), and measu ing he e ac ion o he sample,
he a e age size dis ibu ion can be calcula ed, conside ing all he pa icles in he suspension a e
sphe ical.
Yield o o mic acid is calcula ed as shown in eq. 1
100
3
NaHCO,
×=
i
FA
FA
C
C
Y
eq. 1
Whe e CFA is he mola concen a ion o o mic acid ob ained and Ci,NaHCO3 he ini ial mola
concen a ion o bica bona e.
3. Modeling
In o de o de elop a ma hema ical model o he p ocess, eac ions 1 o 5 we e aken in o
accoun : 𝐻𝐻𝐻3−(𝑎𝑎) + 𝑍𝑍(𝑠) → 𝐻𝐻𝐻𝐻−(𝑎𝑎) + 𝑍𝑍𝐻(𝑠) (1)
(2)
𝐻𝐻𝐻3−(𝑎𝑎) + 𝐻2(𝑎𝑎) → 𝐻𝐻𝐻𝐻−(𝑎𝑎) + 𝐻2𝐻(𝑙) (3)
𝐻𝐻𝐻𝐻−(𝑎𝑎)+𝐻2𝐻 (𝑙)→𝐻𝐻𝐻3−(𝑎𝑎) + 𝐻2 (4)
𝐻𝐻𝐻𝐻−(𝑎𝑎)→𝐻𝐻(𝑔)+𝐻𝐻−(𝑎𝑎) (5)
Wi h his se o eac ions, wo main s ages a e conside ed. The i s s ep is one wi h a high
eac ion a e ( eac ions (1) and (2)), p oduced by eac ion o bica bona e wi h me allic Zn,
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which acco ding o he esul s o Jin e al [8] is only p esen du ing he i s minu es o he
eac ion. Reac ion (1) desc ibes he apid educ ion o bica bona e eac ing di ec ly wi h Zn o
gi e ZnO and o ma e. E en hough i is easonable o hink ha his eac ion occu s h ough a
chemical in e media e, as sugges ed by Jin el al [8], he e is no enough e idence o exac ly
de e mine he eac ion mechanism and he in e media e, and he e o e i has been decided o
conside he global eac ion be ween bica bona e and zinc, as indica ed wi h eac ion (1).
Reac ion (2) is he oxida ion o Zn wi h wa e o o m ZnO and hyd ogen. While i was ound
ha in he case o some me als such as Fe his eac ion is no p oduced in he absence o
bica bona e in he media, in he case o he Zn, Mn o Al, Jin e al [10] p o ed ha he educ ion
o wa e o gi e hyd ogen is p oduced wi hou pa icipa ion o bica bona e.
The second s ep is he one ha con ols he eac ion a e a e Zn is comple ely oxidized. I
mainly consis s o eac ion (3), h ough which he emaining HCO3- eac s wi h hyd ogen
dissol ed in he liquid phase.
Mo eo e , a long esidence imes, and especially a he highe empe a u es conside ed in his
wo k (300 and 325ºC), he esul s o Jin e al [8] show ha he yield o o mic acid sligh ly
dec eases. Acco ding o Yu e al [23], his is because o mic acid and o mia e su e s
decomposi ion unde hyd o he mal condi ions a high empe a u es ollowing eac ions (4) and
(5). Ne e heless, con e sion o o ma e due o eac ion 5 is negligible in compa ison o
eac ion 4 and i has no been aken in o accoun . In eac ion 4 i is conside ed ha CO2 o med
is eadily dissol ed in he aqueous phase as bica bona e. No e ha eac ion 3 and 4 a e e e se
eac ions, bu hey a e exp essed as independen eac ions o cla i y in he adsc ip ion o
subindexes in kine ic cons an s. E en hough hey a e opposi e eac ion he chemical
equilib ium is no eached un il he las s eps o he eac ions, and in many o he simula ions
ca ied ou equilib ium is no eached.
The oxida ion o Zn pa icles is conside ed o ollow a sh inking co e eac ion model, and he
con e sion o zinc ,XZn was de ined as in eq. 2
𝑋𝑍𝑍=𝑅03−𝑟3
𝑅03 eq. 2
Whe e is he adius o he non- eac ed co e o he pa icles and R0 is he ini ial adius o he Zn
pa icle. To selec i he con olling mechanism o he sh inking co e model is he eac ion o he
di usion (in e nal o ex e nal) he e olu ion o he con e sion o bica bona e and o he ela ion
be ween he adius o he un eac ed co e adius ( ) di ided by he ini ial adius o he pa icle
(Ro ): /Ro e sus he ela i e eac ion ime ( a io be ween he ime and he ime a which he
whole Zn pa icle is con e ed ( )), calcula ed om expe imen al da a om Jin el al[11], is
p esen ed in igu e 1. I is obse ed ha a low eac ion imes bo h pa ame e s linea ly dec ease
wi h he ela i e eac ion ime, indica ing a con ol o he chemical eac ion. Howe e , a longe
imes his end changes, adop ing he ypical o m o he in e nal di usion con ol a e.
The e o e, i is concluded ha bo h esis ances con ol he p ocess [24]. Thus he eac ion a e o
Zn is exp essed as he a ia ion o he adius o he un eac ed co e as exp essed in eq. 3 [24] as
a unc ion o he di usion h ough he pa icle and o he kine ics o eac ions 1 and 2.
−𝑑𝑟
𝑑𝑑=1
(𝑅𝑜−𝑟)𝑟/𝑅𝑜
𝐷𝑒+1
𝑘1·𝑐𝐻𝐻𝐻3−+𝑘2 eq. 3
Whe e De (m2/s) is di usi i y o he eagen in he ash laye o med in zinc pa icle ha has
been adjus ed o he expe imen al da a.

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Figu e 1. E olu ion o he zinc con e sion and o he ela ion be ween he adius o he
un eac ed co e di ided by he ini ial adius o he pa icle Ro ( /Ro) wi h he ela i e eac ion
ime ( a ion be ween he ime and he ime a which he whole Zn pa icle is con e ed), using
he expe imen al da a o Jin el al [11]
The mass balances o he main species in ol ed in he eac ion a e p esen ed below. In eq. 4 he
balance o he bica bona e is shown aking in o accoun ha i is consumed by educ ion, i s
di ec ly wi h me allic Zn ( eac ion 1) and la e wi h H2 ( eac ion 3), and ha i is p oduced
h ough he decomposi ion o o mic acid o H2 and CO 2 ( eac ion 4), which in basic media is
abso bed in he liquid phase as bica bona e.
𝑑𝑐𝐻𝐻𝐻3−
𝑑𝑑 =−3𝑍𝑍𝑛𝑜𝑟2
𝑅𝑜3𝑉𝐿�1
(𝑅𝑜−𝑟)𝑟/𝑅𝑜
𝐷𝑒+1
𝑘1·𝑐𝐻𝐻𝐻3
−�−𝑘3·𝑐𝐻2·𝑐𝐻𝐻𝐻3−+𝑘4·𝑐𝐻𝐻𝐻𝐻−
𝑍 eq. 4
Whe e: nZno is he ini ial numbe o mol o zinc and VL is he olume o he liquid phase inside
he eac o .
The exponen n in he kine ic equa ion o eac ion 4 was co ela ed using eq. 5 acco ding o he
wo k o Yu e al [23] ], who indica es ha he eac ion does no ollow a i s o de kine ic
equa ion.
𝑍= 1.4671 +25.6595
𝑇+ 0.0007024 · ln 𝑇;𝑇= [𝐾] eq. 5
The balance o o ma e is p esen ed in eq. 6. The o ma e is gene a ed by educ ion o
bica bona e in eac ions 1 and 3 and consumed by decomposi ion o CO2 and H2 by eac ion 4
and o CO and wa e by eac ion 5.
𝑑𝑐𝐻𝐻𝐻𝐻−
𝑑𝑑 =3𝑍𝑍𝑛𝑜𝑟2
𝑅𝑜3𝑉𝐿�1
(𝑅𝑜−𝑟)𝑟/𝑅𝑜
𝐷𝑒+1
𝑘1·𝑐𝐻𝐻𝐻3
−�+𝑘3·𝑐𝐻2·𝑐𝐻𝐻𝐻3−−𝑘4·𝑐𝐻𝐻𝐻𝐻−
𝑍 eq. 6
0
0.2
0.4
0.6
0.8
1
00.2 0.4 0.6 0.8 1
(1-XZn)/ /Ro
/ 100% Zn con e sion
Zn pa icle con e sion Jin e al. (2014) Zn pa icle adio a ia ion Jin e al. (2014)
7
The balance o he hyd ogen is p esen ed in eq. 7
𝑑𝑍𝐻2
𝑑𝑑 =−𝑑𝑍𝑍𝑛
𝑑𝑑 +𝑑𝑍𝐻𝐻𝐻3−
𝑑𝑑 eq. 7
Whe e nH2, nZn and nHCO3- a e he numbe o mol o H2 ( o al, in gas and in liquid phase), Zn and
o bica bona e. The numbe o mol o Zn and o bica bona e a e calcula ed as indica ed in eq. 8
and 9 espec i ely.
𝑑𝑍𝑧𝑛
𝑑𝑑 =3𝑍𝑍𝑛𝑜𝑟2
𝑅𝑜3𝑑𝑟
𝑑𝑑 eq 8
𝑑𝑍𝐻𝐻𝐻3−
𝑑𝑑 =𝑑𝑐𝐻𝐻𝐻3−
𝑑𝑑 ·𝑉𝐿 eq.9
Mos o he hyd ogen gene a ed passes o he gas phase inc easing he p essu e in he eac o ,
and only a pa emains dissol ed in he aqueous phase, acco ding o i s solubili y, and is hus
able o eac wi h bica bona e. The solubili y o hyd ogen in he liquid phase, is calcula ed
using he p edic i e Soa e-Redlich-Kwong equa ion [25], depending o empe a e and o he
hyd ogen p essu e inside he eac o , which is calcula ed as a unc ion o he amoun o
hyd ogen gene a ed wi h equa ion 10.
𝑃𝐻2=𝑅𝑇
𝑉𝑚𝐻2−𝑏−𝑎
𝑉𝑚𝐻2+𝑏·𝑇0.5;𝑤ℎ𝑒𝑟𝑒 𝑎= 0.42748 𝑅2·𝑇𝑐𝐻2
2.5
𝑃𝑐𝐻2 𝑏= 0.08664 ·𝑅·𝑇𝑐𝐻2
𝑃𝑐𝐻2 eq. 10
Whe e PH2 is he pa ial p essu e o H2, VmH2 is he mola olume o hyd ogen, and TcH2 and PcH2
a e he c i ical empe a u e and p essu e o hyd ogen. In his equa ion, he mola olume o
hyd ogen is no cons an due o he a ying eac ion condi ions ( empe a u e, p essu e and
olume a ailable o he gas phase in he eac o ), and i is calcula ed acco ding o equa ion 11:
𝑑𝑉𝑚𝐻2
𝑑𝑑 =𝑉0+𝑑𝑉𝐻2𝐻 𝑒𝑒𝑒𝑒𝑜𝑟𝑒𝑒𝑒𝑑
𝑑𝑒
𝑑𝑛𝐻2𝐺
𝑑𝑒 eq. 11
Whe e V0 is he ini ial ee olume in he eac o . dVH2O is he olume a ia ion associa ed o
he wa e e apo a ion o condensa ion in he eac o and nH2G is he numbe o mol o hyd ogen
in he gas phase.
The alues o kine ic cons an s and o he di usion cons an De we e ob ained by minimizing
he squa ed e o be ween expe imen al and calcula ed o mic acids yields a a cons an
empe a u e o using he empe a u es egis e ed in he expe imen s, minimizing he alue
ob ained in eq. 12
𝑆𝑆𝑆𝑆𝑅𝑆𝐷 𝑆𝑅𝑅𝐻𝑅= (𝑒𝑥𝑝𝑒𝑟𝑝𝑝𝑒𝑍𝑝𝑎𝑙 𝑓𝑜𝑟𝑝𝑝𝑎𝑝𝑒 𝑦𝑝𝑒𝑙𝑦 𝑣𝑎𝑙𝑣𝑒−𝑝𝑟𝑒𝑦𝑝𝑐𝑝𝑒𝑦 𝑓𝑜𝑟𝑝𝑝𝑎𝑝𝑒 𝑦𝑝𝑒𝑙𝑦 𝑣𝑎𝑙𝑣𝑒)2 eq. 12
Mo eo e , in o de o model he e olu ion o empe a u e du ing he eac ion, he ene gy
balance was added o he model, aking in o accoun he en halpy o eac ion and he hea
ans e ough eac ion walls o he o en, acco ding o he ollowing equa ion:
𝑑𝑇𝑒
𝑑𝑑=(−∆𝐻𝑅1 )·𝑟1+(−∆𝐻2)𝑟2+�−∆𝐻𝑅3�·(𝑟3−𝑟4)+𝑈·𝐴𝑟·(𝑇𝐸𝐸𝑒−𝑇𝑒)−𝑑𝑚𝐻2𝐻𝑒𝑒𝑒𝑒𝑜𝑟𝑒𝑒𝑒𝑑
𝑑𝑒 ∆𝐻𝐻𝑎𝐻
(𝑚𝐻2𝐻+𝑚𝐻𝐻𝐻3)·𝑐𝑃𝐻2𝐻+𝑚𝑍𝑛𝑍𝑐𝑃𝑍𝑛 Eq 13
Whe e ∆HRi is he hea o eac ion associa ed o eac ions 1-3, mi is he mass o he species, Tex
is he empe a u e ou side he eac o , T is he empe a u e inside he eac o , bo h in ºC, cpi a e
he hea capaci ies, mi is he mass o he each specie in he eac ion, U is he global hea
ansmission coe icien , A is he ex e nal a ea o he eac o , and i a e he a e o eac ions o
eac ions 1 o 4, as exp essed in eq 14 o 17
8
𝑟1=3𝑍𝑍𝑛𝑜𝑟2
𝑅𝑜3
⎝
⎜
⎛
1
(𝑅𝑜−𝑟)𝑟
𝑅𝑜
𝐷𝑒+1
𝑘1·𝑐𝐻𝐻𝐻3
−
⎠
⎟
⎞
Eq. 14
𝑟2=3𝑍𝑍𝑛𝑜𝑟2
𝑅𝑜3�1
(𝑅𝑜−𝑟)𝑟
𝑅𝑜
𝐷𝑒+1
𝑘2� Eq. 15
𝑟3= 𝑘3·𝑐𝐻2·𝑐𝐻𝐻𝐻3− Eq.16
𝑟4=𝑘4·𝑐𝐻𝐻𝐻𝐻−
𝑍 Eq. 17
A e m conside ing he la en hea co esponding o wa e e apo a ion was included in o de o
ake in o accoun he e apo a ion o condensa ion caused by he wa e liquid- apo equilib ium
inside he eac o . As a simpli ica ion, he hea capaci y o pu e wa e , ob ained om Na ional
Ins i u e o S anda ds and Technology (NIST) [33], was conside ed ins ead o he hea capaci y
o he bica bona e solu ion. In he case o zinc, he hea capaci y was ob ained om he wo k
ca ied ou by G øn old e al. [27]
Fo ob aining he global hea ans e coe icien s, hea ing p o iles wi hou eac ion we e
co ela ed wi h he model by minimizing he p edic ed empe a u e and he expe imen al
empe a u e p o ile in expe imen s wi hou eac ion, de ining he e o as indica ed in eq. 18
𝑆𝑅𝑅𝐻𝑅= (𝑆𝑥𝑝𝑒𝑟𝑝𝑝𝑒𝑍𝑝𝑎𝑙 𝑇𝑒𝑝𝑝𝑒𝑟𝑎𝑝𝑣𝑟𝑒 𝑣𝑎𝑙𝑣𝑒−𝑃𝑟𝑒𝑦𝑝𝑐𝑝𝑒𝑦 𝑇𝑒𝑝𝑝𝑒𝑟𝑎𝑝𝑣𝑟𝑒 𝑣𝑎𝑙𝑣𝑒)2 eq.
18
The esul s ob ained o he global hea ansmission coe icien U a e p esen ed in able 1:
Table 1. Co ela ed global hea ans e coe icien s
U (kW/m2ºC)
Tempe a u e (ºC)
0.7554
275
0.7941
300
0.8756
325
All he coe icien s a e in he expec ed ange o he ypical alues o ansmission coe icien s in
na u al con ec ion o gasses (0.5 – 1 kW/m2ºC).
Finally, i mus be conside ed ha he eac ion s udied in his wo k in ol es di e en ionic
species, which may eac di e en ly. In pa icula , he di e en ions o med by dissocia ion o
ca bonic acid in he aqueous media may ha e a di e en beha io . I is he e o e necessa y o
quan i y he concen a ion o each o hese ions, in o de o e i y ha he p edominan ion in
he mix u e is bica bona e, as assumed in he mechanism p esen ed wi h eac ions 1-5. Fo his
eason, applying he esul s o he model, he ionic equilib ium has been s udied o de e mine
which a e he p edominan species in he condi ions conside ed in his wo k. Fo his pu pose,
he equilib ium condi ions conside ed a e wa e ionic equilib ium (eq. 19), he acid-base
equilib ium o ca bonic acid (eq. 20) and bica bona e ion (eq. 21), and o mic acid and o ma e
ion (eq. 22). 𝐾𝑤=[𝐻3𝐻+][𝐻𝐻−] eq. 19
9
𝐾𝑎 𝑐𝑎𝑟𝑏𝑐𝑍𝑐𝑐 𝑎𝑐𝑐𝑑=[𝐻𝐻𝐻3−][𝐻3𝐻+]
[𝐻2𝐻𝐻3] eq.20
𝐾𝑎 𝑏𝑐𝑐𝑎𝑟𝑏𝑐𝑍𝑎𝑑𝑏=�𝐻𝐻3−2�[𝐻3𝐻+]
[𝐻𝐻𝐻3−] eq. 21
𝐾𝑎 𝑓𝑐𝑟𝑚𝑐𝑐 𝑎𝑐𝑐𝑑=[𝐻𝐻𝐻2−][𝐻3𝐻+]
[𝐻2𝐻𝐻2] eq. 22
The alues o he wa e ion p oduc wa e ionic p oduc we e calcula ed using eq. 23 p oposed
by Ma shall & F anck [28]
log10𝐾𝑤∗=−4.098 +−3245.2
𝑇+2.2362 ·105
𝑇2+−3.984 ·107
𝑇3+�13.957 +−1262.3
𝑇+8.5641 ·105
𝑇2�·log10𝜌𝑤
∗
Eq. 23
The densi y o wa e in eq. 23 depends on he p essu e inside he eac o , which depends on he
amoun s o hyd ogen and wa e in he gas phase. The amoun o hyd ogen was calcula ed as
desc ibed in eq. 11, and he amoun o wa e in gas phase as esul o he liquid- apo
equilib ium was calcula ed using Raoul ’s Law applying An oine’s equa ion [26].
𝑃𝐻2𝐻=𝑃𝐻2𝐻
0𝑥𝐻2𝐻 Eq. 24
The e o e, he o al p essu e was calcula ing using eq. 25, whe e Pai o=1 a m.
𝑃𝑑𝑐𝑑𝑎𝑡=𝑃𝐻2𝐻+𝑃𝐻2+𝑃𝑎𝑐𝑟0 Eq. 25
The alues o he acid cons an s o ca bonic acid, bica bona e ion and o mic acid we e
calcula ed using eq. 25 [29, 30], 26 and 20. Eq. 27 and 28 we e ob ained by simula ion using he
so wa e Aspen Plus® ELECNRTL package me hod.
𝑝𝐾𝑎𝑓𝑐𝑟𝑚𝑐𝑐 𝑎𝑐𝑐𝑑 =−57.528 +2773.9
𝑇+ 9.1232 · ln 𝑇; 𝑇[=]𝐾 Eq. 26
𝑝𝐾𝑎𝑐𝑎𝑟𝑏𝑐𝑍𝑐𝑐 𝑎𝑐𝑐𝑑 =−231.465 +12092.1
𝑇+36.7816 · ln 𝑇; 𝑇[=]𝐾 Eq. 27
𝑝𝐾𝑎𝑏𝑐𝑐𝑎𝑟𝑏𝑐𝑍𝑎𝑑𝑏 =−216.05 +1243137
𝑇+35.4819 · ln 𝑇; 𝑇[=]𝐾 Eq. 28
Thus, he esul ing ionic balance is shown in eq. 29
eq. 29
As p esen ed in Figu e 2 he ionic balance showed a signi ican a ia ion o he equilib ium in
he i s s ages o he eac ion, bu in he middle and in he inal s ages almos cons an
concen a ions we e obse ed. The ca bonic acid/bica bona e equilib ium shows a s ong
displacemen owa ds bica bona e, especially in he la e eac ion s ages, being he amoun o
ca bonic acid lowe a highe empe a u es as shown in pa a) o igu e 2. Mo eo e , because o
he high H2O/CO2 a io, he high p essu e eached in e e y un and he alkaline na u e o he
sample, all he CO2 o med can be assumed o be dissol ed in he ini ial solu ion and being able
o eac wi h bo h Zn and H2 p oduced acco ding o he mechanism p esen ed in eac ions 1-4.
16
Figu e 8. E olu ion o o ma e yield a di e en ope a ion p essu es (a) and di e en Zn/HCO3-
a ios (b)
4.6 In luence o he size o Zn pa icles
In igu e 9 he e olu ion o he o ma e yield calcula ed wi h he model a ying he ini ial adius
o zinc pa icles is p esen ed, conside ing a Zn/HCO3 a io o 5, a empe a u e o 300ºC, a HCO3
ini ial concen a ion o 0.5 M and an ini ial eac o illing o 50 %. I is obse ed ha , in he
ange o pa icle sizes in es iga ed, he eac ion a e inc eases when pa icle size is inc eased. A
possible eason o his esul is ha , using bigge pa icles, he eac ion o oxida ion o zinc
( eac ion 2) is slowed down, allowing he eac ion be ween zinc and bica bona e ( eac ion 1) o
p oceed o a longe ac ion o he eac ion ime.
Figu e 9. E olu ion o o ma e yield a di e en pa icle sizes
0
10
20
30
40
50
020 40 60 80
Fo ma e yield (%)
Time (min)
Model p edic ion ini ial
adius 5 mic om
Model p edic ion ini ial
adius 17.22 mic om
Model p edic ion ini ial
adius 29 mic om
Model p edic ion ini ial
adius 41 mic om
Model p edic ion ini ial
adius 53 mic om
Model p edic ion ini ial
adius 65 mic om
Model p edic ion ini ial
adius 77 mic om
Model p edic ion ini ial
adius 99 mic om
Expe ime al esul s his
wo k

17
4.6 Expe imen s in supe c i ical condi ions
In he las pa o he eac ion he eac ion, when Zn is al eady comple ely oxidized o ZnO, he
eac ion p oceeds be ween HCO3- and H2, bo h dissol ed in liquid phase, and i is limi ed by he
low solubili y o H2 in in he liquid phase. On he o he hand, in supe c i ical condi ions, H2 and
CO2 would be in he same supe c i ical phase, and he solubili y limi a ion would be o e come.
In o de o es i his condi ion could imp o e he eac ion pe o mance, an expe imen was
ca ied ou se ing a subc i ical empe a u e o 350ºC du ing he i s 25 minu es o he eac ion,
when he p edominan mechanism o o ma e o ma ion is he solid liquid eac ion 1, and a
supe c i ical empe a u e o 400ºC du ing he subsequen 55 min, du ing which he p edominan
eac ion is eac ion 3 be ween bica bona e and hyd ogen. A con e sion o bica bona e o 28%
was achie ed wi h a yield o o mic acid o 14%, esul s ha a e much lowe ha he alues
ob ained a lowe empe a u e condi ions in liquid phase, whe e yields o a leas 40% we e
achie ed. This esul can be due o he as e decomposi ion a e o o ma e a highe
empe a u es. I is he e o e concluded ha he ope a ion a supe c i ical empe a u e condi ions
is no a o able o his eac ion.
4.7 In luence o eac o ma e ials
I is well known he capaci y o Ni o ca alyze chemical eac ions, in his case he educ ion o
bica bona e [32]. Fo his eason, in sc eening eac ions many au ho s p e e o use SS-316
eac o s o Te lon lined eac o s o exclude possible ca aly ic e ec s o he wall o he eac o
[8], e en hough he su ace o he eac o wall in con ac wi h he eac ion mix u e is low in
compa ison o he su ace a ea o a common po ous ca alys . I is also well known ha mos
alloys used o s anding high empe a u es such as Ni alloy 600 o 625 con ains high nickel
amoun s, so i would be use ul o know he di e en beha io ha can be expec ed om hese
ma e ials. In his wo k, selec ed expe imen s a di e en empe a u es we e pe o med bo h in
SS316 eac o s and in Ni alloy 625 eac o s in o de o es he in luence o eac o ma e ials on
he eac ion. The yields ob ained o expe imen s pe o med wi h a HCO3- concen a ion o 42
g/L and Zn/NaHCO3 = 5 in eac o s o bo h ma e ials a di e en empe a u es a e compa ed in
igu e 10. I is obse ed ha using Ni alloy o SS eac o s, o ma e yields a e equi alen .
The e o e, he ca aly ic e ec o he wall o he eac o can be disca ded.
Figu e 10. Compa ison o o ma e yields ob ained wi h a HCO3- concen a ion o 42 g/L and
Zn/NaHCO3 = 5 in eac o s o bo h Ni Alloy and SS 316 a di e en empe a u es
Conclusions
In his wo k, he educ ion o CO2 as bica bona e in ba ch eac o s ope a ing a hyd o he mal
condi ions was in es iga ed, using Zn as a educ an and empe a u es be ween 275 and 400ºC.
18
Using he expe imen al da a ob ained in his wo k and li e a u e da a, a kine ic model was
p oposed and inco po a ed o a ma hema ical model, which was able o p edic yields o o ma e
wi h and a e age e o o 12% and a maximum e o o 25%. The model was able o ep oduce
expe imen al da a epo ed in his wo k and li e a u e da a wi h simila accu acies, and i ed
eac ion cons an s ollowed A henius law. This indica es ha he model is eliable wi h high
p edic i e capaci y. The model includes he in luence o pa ame e s such as empe a u e, me al
educ an pa icle size, me al/HCO3- a io, empe a u e, hea ing a e o p essu e.
Using he model and he expe imen al da a, an analysis o he in luence o he main pa ame e s
o he p ocess was pe o med. Selec i i y o o ma e close o 100% and yields up o 75% we e
eached. The op imum wo king empe a u e was 300ºC, and ope a ion a supe c i ical
empe a u e condi ions was de imen al o eac ion yield due o he decomposi ion o o ma e.
The p ocess kine ics we e a o ed by a high Zn excess, o equi alen ly by ope a ion a high
p essu es ha inc ease hyd ogen solubili y in he liquid phase.
Acknowledgemen s
This esea ch has been inanced by he Spanish Minis y o Economy and Compe i i eness
h ough p ojec ENE2014-53459-R. M.D. Be mejo hanks he Spanish Minis y o Economy
and Compe i i eness o a Ramón y Cajal ellowship. D. Roman-Gonzalez Be mejo hanks he
Spanish Minis y o Economy and Compe i i eness o a FPU ellowship.
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