Co esponding au ho : mbaile a@uniza .es
Calcium looping as chemical ene gy s o age in concen a ed sola powe
plan s: Ca bona o modelling and con igu a ion assessmen
Manuel Baile aa*, Pila Lisbonab, Luis M. Romeoa, Luis I. Díeza
a Escuela de Ingenie ía y A qui ec u a. Uni e sidad de Za agoza, Campus Río Eb o, Ma ía de Luna 3,
50018, Za agoza, Spain
b Fundación Agencia A agonesa pa a la In es igación y el Desa ollo (ARAID), Za agoza, Spain
Abs ac
This pape add esses he analysis o di e en con igu a ions o ca bona o o he mochemical ene gy s o age
o concen a ed sola applica ions. The design o his equipmen is di e en om he p e ious expe ience o
calcium looping cycle o ca bon cap u e. The use o luidized beds and la ge pa icles a e no easible o his
no el applica ion o calcium looping. New eac o s and di e en a angemen s o he ca bona ion p ocess
a e necessa y. The design o a ca bona o eac o o a speci ic Calcium Looping-Concen a ed Sola Powe
applica ion has no been add essed ye in de ail in li e a u e. In his wo k, a compa ison o single s age eac o ,
wo pa allel eac o s and wo eac o s in se ies wi h in e cooling a e simula ed o calcula e con e sion a es,
gas empe a u es and low a es, and hea ans e a es o he ex e nal cooling luid. The modelling
encompasses luid dynamics, lime con e sion kine ics and hea ans e , which a e sol ed using a 1-D disc e e
mesh. The hi d a angemen esul s in he mos easonable sizes, and la ge con e sion a es, a oiding he
occu ence o in e nal eac o zones in which he eac ion is inhibi ed. Ene gy balance componen s a e also
quan i ied o each con igu a ion.
Keywo ds
Calcium-looping; The mochemical ene gy s o age; Concen a ed sola powe ; Ca bona ion
1. In oduc ion
Nowadays, global wa ming is unequi ocal and ex ensi ely endo sed by scien i ic communi y. In 2019, he
global land-ocean su ace empe a u e had inc eased 1.18 °C wi h espec o he pe iod 1951-1980 [1][2].
Hea wa es occu mo e o en and las longe , while ex eme p ecipi a ions ha e become mo e in ense and
equen [3]. Acco ding o he IPCC (In e go e nmen al Panel on Clima e Change), his has a ec ed many
2
species ha ha e shi ed hei geog aphic anges, seasonal ac i i ies o mig a ion pa e ns in esponse o
ongoing clima e changes. Mo eo e , hyd ological sys ems a e con inuously al e ed, wha ha ms esh wa e
esou ces and ood p oduc ion [3].
Ca bon dioxide is he la ges single con ibu o o hese pe u ba ions on he ene gy balance o he Ea h, and
human beings a e undoub edly he main sou ce [3]. Cu en a mosphe ic CO2 concen a ion is inc easing a
he as es e e obse ed a e (2.0 ppm/y ), peaking he a e age o May 2019 a 414.8 ppm [4]. A he Uni ed
Na ions Clima e Change Con e ence held in Pa is a he end o 2015, abou 190 coun ies ag eed o educe
emissions o g eenhouse gases (GHG). The aim is o limi global empe a u e inc ease below 2 °C by he yea
2100, ela ed o p e-indus ial le els [5]. Howe e , hose scena ios ha limi wa ming o 2 °C would equi e
CO2 a mosphe ic concen a ions below 450 ppm, which will be ha dly accomplishable [3].
Key measu es o achie e such mi iga ion lie in deca bonizing elec ici y and hea gene a ion sec o , since i
p oduces mo e han wo- i hs o global CO2 emissions [6]. The Eu opean Union Renewable Ene gy Di ec i e
se s a binding a ge o 20% inal ene gy consump ion om enewable sou ces by 2020 [7]. The ole o
enewable ene gy sou ces will be c ucial o he educ ion o Eu opean pollu an emissions while inc easing
he ene gy secu i y h ough he massi e pene a ion o local enewable ene gy sou ces (RES) and he
di e si ica ion o ene gy ec o s. The “EU Re e ence Scena io 2016” es ima es ha he sha e o elec ici y om
enewable ene gy sou ces is expec ed o g ow up o 37.2% by 2020, o 43% by 2030, and o 53% by 2050 [8].
RES p esen a numbe o ba ie s ha limi hei massi e deploymen . One o he mos signi ican ba ie s is
he con ol and managemen o luc ua ions gi en he in e mi en na u e o he wea he -dependen powe
gene a ion sys ems. The secu i y and s abili y o he elec ic g id would be s ongly comp omised i
misma ches be ween supply and elec ical demand could occu . This issue ep esen s a signi ican limi a ion
o he echnical and economic easibili y o RES.
To achie e he ambi ious Eu opean a ge s o RES deploymen and o de elop o an ene gy sys em based on
a mo e di e si ied echnology mix, which allows a pe ec con ol and ma ch o he ene gy p oduc ion and he
ins an aneous demand, he p oposal and de elopmen o inno a i e ene gy s o age solu ions is needed. In
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he sho - e m, he deploymen o e icien and compe i i e echnologies o ene gy s o age ep esen s one
o he mos challenging equi emen s o he ene gy sys em. Renewable ene gy p oduc ion and ene gy
s o age capaci y mus g ow in pa allel in o de o so en he in insic a iabili y o RES p oduc ion h ough
s o age. The di e en echnical cha ac e is ics o he a ailable me hods o s o ing ene gy (e.g., discha ge
ime, s o age pe iod, p ices o ma e ials) de ine how hey a e coupled wi h RES.
Concen a ed sola powe plan s (CSP) can ope a e beyond sunligh hou s only when hey include ene gy
s o age. The mal ene gy s o age sys ems which ope a e a medium (100 °C o 250 °C) o high empe a u e
le el (abo e 250 °C) a e p e e ed in CSP o achie e highe ound- ip e iciencies [9]. The cu en ly mos
ma u e a e he mol en sal sys ems [10] which a e used in comme cial ins alla ions. Ne e heless, al e na i e
s o age ma e ials a e unde s udies such as na u al ocks and ecycled ce amics made om indus ial was es
[11]. The mochemical ene gy s o age (TCES) was p oposed as an inno a i e possibili y o ace he a iabili y
o CSP p oduc ion [12][13][14]. TCES is based in he ans o ma ion and s o age o he mal sola ene gy in o
chemical bounds c ea ed h ough endo he mic chemical eac ions. The densi y o s o age o TCES is la ge
han o he al e na i es and i ep esen s a signi ican ad an age. The e e se exo he mic eac ion will be used
o elease he s o ed he mal ene gy when i is demanded. P ie o e al. compa ed di e en TCES unde
in es iga ion such as hose based in h ee edox eac ions, sul u -based cycles, me al oxide educ ion–
oxida ion cycles, and pe o ski e- ype hyd ogen p oduc ion, and me al oxide non- edox cycles [12]. They
concluded ha all hese cycles a e p omising bu he calcium ca bona e is he one wi h mos expe imen a ion
and po en ial economic easibili y. Thus, he use o CaCO3 in he Ca-looping p ocess is an in e es ing TCES
al e na i e gi en he wide expe ience in he ca bona ion/calcina ion equilib ium eac ion, he wide a ailabili y
o limes one and i s low p ice [15].
The Ca-Looping (CaL) p ocess has been ex ensi ely applied as a compe i i e op ion o CO2 cap u e [16][17][18]
bu also p oposed as TCES in CSP plan s [12][15][19]. As s a ed, CaL p ocess is based upon he e e sible
ca bona ion/calcina ion eac ion in which limes one and lime a e al e na i ely con e ed. Su plus sola ene gy
can be chemically s o ed h ough he di ec endo he mic calcina ion o limes one a high empe a u es
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p oducing pu e s eams o CaO and CO2. The s o ed ene gy will be eleased by means o he e e se eac ion,
exo he mic ca bona ion eac ion, a ela i ely high empe a u es sui able o powe cycles, bo h B ay on and
Rankine cycles, when elec ici y demand aises. Chaca egui e al. and O iz e al. ha e demons a ed an
ou s anding pe o mance unde bo h si ua ions; i.e. o a egene a i e Rankine cycle an e iciency o 35.5%
has been p esen ed, bu i inc eases o nea 39.0% o a combined cycle o 42.0% o a closed B ay on cycle
[15][19]. As highligh ed by Bayon e al., CaL is also sui able o supe c i ical CO2 cycles [20].
The Ca-L p ocess applied as TCES s a s wi h he decomposi ion o CaCO3 in he sola calcina ion eac o
p oducing CaO and CO2. Apa om he hea equi emen s in he calcina ion eac ion, high-ene gy inpu is
needed o inc ease he empe a u e o inle s eams up o he equi ed alue o he calcina ion eac ion o
occu a a su icien ly as a e. This empe a u e is essen ially de e mined by he CO2 equilib ium [21]. Once
he sensible hea o ou le s eams is eco e ed, he CaO and CO2 p oduced a e s o ed a ambien empe a u e
o hei subsequen use. S o age o he p oduc s could be ex ended om weeks o mon hs depending on
s o age condi ions and ene gy demand pa e n [22]. The eac an s will be eci cula ed in o a ca bona o
eac o whe e chemical ene gy is eleased h ough he exo he mic ca bona ion eac ion when ene gy is
demanded.
De ailed e iews o his TCES concep ha e been p e iously published [12][23][24][25][26] and he e is a
gene al ag eemen on he po en ial economic easibili y o ca bona e sys ems as u u e TCES sys em i hei
cyclic s abili y and e e sibili y a e imp o ed. A key a iable on he sys em is he ac i i y o he so ben . Cyclic
limes one calcina ion leads o a s ong deac i a ion o CaO unde speci ic condi ions o CaL CO2 cap u e which
imply high calcina ion empe a u es unde high CO2 pa ial p essu e [18] and his decay o CaO so ben
capaci y is assumed o also limi he e iciency o he CaL p ocess o TCES [27]. Recen he mog a ime ic
analysis s udies con i m ha calcina ion/ca bona ion condi ions ha op imize he e iciency o he CSP-CaL
in eg a ion a e di e en han hose ha op imize CO2 cap u e applica ions [28]. The lowe calcina ion
empe a u e in CSP-CaL applica ions, he mo e limi ed sin e ing in he CaO and he highe e iciency o he CaL
p ocess. A be e hea dis ibu ion in he calcine keeps he empe a u e p o ile along he eac o in he p ope
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ange, hus leading o less sin e ing o lime pa icles, as e eac ions and minimum ene gy consump ion in
his elemen .
Imp o emen s in so ben ac i i y le els do no a ec e iciency bu capi al cos s and educ ions in he equi ed
s o age olume [29]. One o he mos signi ican ad an ages o he CSP–CaL in eg a ion is he use o na u al
limes one as CaO p ecu so . Limes one is an abundan , non- oxic and cheap ma e ial (6-10 €/ ), which
p esen s sui able physical p ope ies in he empe a u e ange o in e es o CSP he mal ene gy s o age. In
spi e o ha , di e en g oups o esea che s looks o so ben imp o emen s analysing he mul icycle ac i i y
o he na u al CaCO3 mine als [30]; doping and modi ying CaCO3 [31][32], p e-p ocessing limes one o enla ge
he long- e m pe o mance o he so ben upon i e a ed cycles [33], and de eloping syn he ic Ca-based
ma e ials o ene gy s o age [34].
Fu he challenges o he CaL echnology a e he low he mal conduc i i y o he so ben s, i s agglome a ion
disposi ion causing he ca bona ion eac ion o slow down and he di icul y in he design o he eac o s o
hei e icien in eg a ion [23]. Chen e al. also men ioned he las wo challenges as main ac o s ha
de e mine he hea s o age pe o mance, ha ing eac o s design an impo an ole in he es ablishmen o a
eliable ene gy cha ging and eleasing ene gy p ocess [24]. Thus, p ope design o he main eac o s,
ca bona o and calcine , mus be p oposed o achie e a o able e iciency alues. The designs will be
ci cumsc ibed o he p ocess and eac o limi a ions ha will in luence on he pe o mance o he o e all
sys em.
Recen ly, Zsembinszki e al. e iewed he eac o designs wi h po en ial use in he mochemical ene gy s o age
in concen a ed sola powe plan s [35]. Thei classi ica ion c i e ia o he eac o s was he limi ing s ep, which
is essen ial o a p ope design p ocess, kine ics o di usion con olled. Gene ally, he mal decomposi ion
occu ed in he calcine is con olled by chemical eac ion, while solid-gas eac ion in he ca bona o is limi ed
by in e nal and ex e nal di usion o gas in he pa icle. The classi ica ion acco ding he eac o ype is di ided
in s ack, luidized and en ained beds. Fixed beds a e ecommended o sola ca aly ic eac ions while luidized
beds and en ained beds a e be e sugges ed o eac ions equi ing good he mal ans e p ope ies.

6
Fluidized and en ained beds minimize he isk o ho spo s and he mal ins abili y and p esen highe hea
ans e coe icien s. In his e iew, only wo designs o ca bona ion eac o o CaL-CSP a e ga he ed among
exis ing expe imen al igs: (i) O iz e al. designed a p essu ized luidized bed [19] and (ii) a ca bona o /calcine
luidized bed buil and un by Nikulshina e al. [36].
The ca bona ion eac o is a key elemen o he p ocess and ep esen s a complex sys em whe e
he e ogeneous exo he mic chemical eac ions ake place oge he wi h hea anspo phenomena o he
p oduc ion o s eam o he Rankine cycle. Thus, luidized o en ained bed a e p e e ed o he design o his
equipmen . Recen in es iga ions o O iz e al. o he kine ics and p ocess in eg a ion o CaL-CSP showed ha
TCES applica ions equi e much lowe limes one pa icle size han he well-known CaL p ocesses o ca bon
cap u e (80-300 mic ons) [37]. Limes one pa icle sizes o ens o mic ons a e equi ed o an adequa e sola
calcina ion [37]. This echnical limi a ion has impo an implica ions in he design o bo h eac o s, which could
equi e en ained low eac o s when pa icles a e classi ied as Gelda C.
Al hough se e al wo ks p oposed in li e a u e show he heo e ical models and simula ion esul s o a
ca bona o eac o o ca bon cap u e applica ions [38][39][40], up o now, he design o a ca bona o eac o
o a speci ic CaL-CSP applica ion has no been add essed in de ail. The main no el y o his s udy is he
assessmen o he concep ual design o a CaL-CSP ca bona o and he in luence o di e en pa ame e s. In
his wo k, he modelling o a u u e comme cial-scale ca bona o is desc ibed, in he ame o a new
concen a ed sola -based plan . Di e en leng hs, diame e s and con igu a ions (one eac o , se e al eac o s
in pa allel o in se ies) o a comme cial ca bona o a e analysed, as well as he co esponding hea eleased.
The diame e o he pa icles in luences he eac o sizing h ough he esidence imes, and he hea ans e
h ough he emissi i y o he cloud o gas and pa icles.
2. Ca bona o design and s udied con igu a ions
Based on he p o ided in o ma ion, he modelled ca bona o p esen s an in e nal co-cu en en ained low
design and i is co e ed wi h ou sec ions o helical coiled hea exchange s (c 1, c 2, c 3 and c 4) in which
p essu ized wa e en e s a 300 ba and 350 °C. The ou le condi ions o each o he cooling luid s eams (c ou )
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a e se o achie e 600 °C and a maximum p essu e loss o 20 ba , o allow in eg a ion wi h supe c i ical s eam
cycles [41] (see Figu e 1 and Figu e 2). Thus, he simula ions will p o ide as esul s he equi ed cooling luid
mass lows. Hea exchange sec ions 1 and 2 p esen a coun e -cu en low, while sec ion 3 and 4 a co-cu en
low wi h espec o he in e nal ca bona o low di ec ion. En ained low con igu a ion wi h ex e nal cooling
is chosen o keep echnical complexi y low, which in u n would help educing cos s. O he cooling op ions
mo e complex a e ou o he scope o his pape (e.g., in e nal helical coils wi h a iable su ace a ea along
he axis o he eac o ).
Figu e 1. Concep ual design o he powe p oduc ion using a ca bona o in a sola powe plan (c s ands o
cooling luid).
Figu e 2. Concep ual design o he modelled ca bona o (c s ands o cooling luid).
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To al CaO and CO2 inle mass low a es a e 73.41 kg/s and 57.62 kg/s, espec i ely, and a e assumed o en e
o he ca bona o a 800 °C. These mass lows co espond o he ou le o a calcine ope a ing a ull-load wi h
a ne he mal powe inpu o 100 MW h, in which 100% calcina ion is achie ed (Figu e 3).
Figu e 3. Concep ual design o he ene gy s o age p ocess using a calcine in a sola powe plan .
The a e age so ben con e sion in he ca bona o is assumed o be 13.3%, which co esponds o a ma e ial
wi h a maximum esidual con e sion o abou 9-12% ha has been cycled 20-30 imes in a e age [37].
Mo eo e , he solids a e assumed o ha e a pa icle diame e o 60 mic ons. Thus, he ou le mass lows will
be 17.31 kg/s o CaCO3, 63.71 kg/s o CaO, and 50.00 kg/s o CO2. The gas is sepa a ed om he solids, cooled
in o de o be eci cula ed o he ca bona o using a blowe , and hea ed again p io en e ing he ca bona o ;
hus, 86.7% o he inle CO2 ci cula es in a closed loop. The solid s eam is cooled and s o ed o be la e used
in he calcine , whe e he 100 MW h sola inpu is in es ed o hea he ma e ial om oom empe a u e and
o calcine he 100% o he CaCO3 p esen in he solids mix u e.
Th ee di e en con igu a ions (Figu e 4) ha e been p oposed and modelled o assess he beha io o he
ca bona ion eac ion, he equi ed size o he ca bona o and he po en ial o he mochemical ene gy s o age.
 Con igu a ion 1 is a single eac o whe e he o al inle mass lows a e in oduced. This se up aims o
simplici y o ope a ion and educ ion o cos s.
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 Con igu a ion 2 consis s o wo ca bona ion eac o s ope a ing in pa allel and inle mass lows a e
equally di e ed among hem. The objec i e is o educe he eleased hea in each ca bona o and he
equi ed sizes o ca bona o s.
 Con igu a ion 3 ope a es wo ca bona o eac o s connec ed in se ies wi h in e media e cooling. The
objec i e is o a oid he inhibi ion o he eac ion along he ca bona o s. The sensible hea is emo ed
h ough exchange s speci ically designed o ha pu pose ins ead o h ough he helical coils a ound
he ca bona o s.
Hea will be e acua ed om h ee main sou ces: (i) he ca bona ion eac o s h ough he ou supe icial
helical coiled hea exchange s, 𝑄󰇗𝑐 , (ii) he solid –solid hea exchange a he ou le o he eac o , 𝑄󰇗𝑠, and (iii)
he gas-gas hea exchange a he ou le o he eac o , 𝑄󰇗𝐶𝑂2.
Figu e 4. Case s udies o he h ee p oposed ca bona o con igu a ions.
3. Me hodology
To analyze he empe a u e, con e sion, esidence imes and hea exchanges o each con igu a ion, a numbe
o simula ions has been pe o med. The ca bona o model conside s he speci ic geome y, hea ans e
mechanisms and calcina ion kine ics; hus, ob aining he empe a u e p o iles along he ca bona o unde
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Since he con ec i e coe icien inside he helical pipe is se e al o de s o magni ude g ea e han inside he
ca bona o , he empe a u e o he ca bona o ou e wall is assumed o be equal o he empe a u e o he
cooling luid inside he helical pipe o each cell. Thus, he ollowing ene gy balance on he cooling luid is
compu ed (30):
𝐶𝑝𝑐𝑓·𝑛󰇗𝑐𝑓·(𝑇𝑜𝑤,𝐿𝑖−1−𝑇𝑜𝑤,𝐿𝑖)=𝑞󰇗𝐿𝑖
′·(𝐿𝑖−𝐿𝑖−1)
(30)
whe e 𝐶𝑝𝑐𝑓 and 𝑛󰇗𝑐𝑓 a e he speci ic hea and he mole low o he cooling luid. I should be no ed ha (30)
is alid o hea exchange s in which he cooling luid lows om bo om o op (coun e -cu en , HEX sec ions
1 and 2), and he e o e i is hea ed om posi ion 𝐿𝑖 o 𝐿𝑖−1, wi h he hea p oduced inside he ca bona o
om posi ion 𝐿𝑖−1 o 𝐿𝑖. In case o e alua ing a co-cu en hea exchange (HEX sec ions 3 and 4), he ene gy
balance is gi en by (31), whe e he cooling luid lows om op o bo om.
𝐶𝑝𝑐𝑓·𝑛󰇗𝑐𝑓·(𝑇𝑜𝑤,𝐿𝑖−𝑇𝑜𝑤,𝐿𝑖−1)=𝑞󰇗𝐿𝑖
′·(𝐿𝑖−𝐿𝑖−1)
(31)
Thus, he empe a u e along he ca bona o can be compu ed by knowing he ini ial empe a u e o he
cooling luid.
4. Resul s and discussion
In his sec ion, he me hodology desc ibed abo e is applied o h ee po en ial ca bona o schemes (Figu e 4).
The s udy assesses he size equi emen s and echnical pe o mance o each con igu a ion. As s a ed, he scale
o he sys em is 100 MW h o use ul he mal powe inside he calcine .
Mo eo e , in subsec ion 4.1 he model is compa ed wi h expe imen al esul s om li e a u e, and in
subsec ion 4.2 he in luence o he pa icle diame e is p esen ed.
4.1. Compa ison o model esul s wi h expe imen al da a om li e a u e
The expe imen al esul s o an en ained low ca bona o om Plou e al. [45] a e used o alida e he model
p esen ed in his a icle. The eac o o Plou e al. is a 24 me e spi al-shaped s ainless s eel ube, wi h an
ex e nal diame e o 3/8” (inne diame e o 7.54 mm). The gas eloci y used du ing he expe imen s a oids
sal a ion condi ions wi hin he en ained low egime (i.e., a oids alling o pa icles). The eac o is kep

17
iso he mal a 650 °C along he whole pa h. Th ee di e en ma e ials we e analysed: wo ypes o high-pu i y
calcined lime and one cemen aw meal. The esul s o he ma e ial agged as “Lime #1” a e used in his s udy
o compa ison as i has a simila alue o 𝑋𝑘 (i.e., con e sion a he end o he eac ion con olled phase) and
𝑡0 (i.e., he ime aken o each a 𝑋𝑘/2 con e sion) han he ma e ial assumed in he simula ions o his s udy.
Lime #1 has 𝑋𝑘=0.10 and 𝑡0 abou 2 seconds, while he ma e ial used in ou simula ions has 𝑋𝑘=0.13 and
𝑡0=1.5 seconds. These a e ypical con e sions o highly deac i a ed ma e ials.
Figu e 5 shows he CO2 cap u e e iciency, which is de ined as he CO2 cap u ed e sus he maximum possible
acco ding o he equilib ium. The expe imen s we e ca ied ou wi h a gas eloci y o 13.5 m/s a 650 °C and
1 ba (abou 2.4·10−4 kg/s). The gas is composed o 10% CO2 and 90% ai . The mass a io be ween he solid
and he gas was a ied be ween 0.125 and 0.400 by modi ying he mass o CaO en e ed in he eac o .
Figu e 5. CO2 cap u e e iciency achie ed in he en ained low eac o o Plou e al. [45] and in he
simula ions o his s udy unde he same se up, as a unc ion o he solid/gas mass a io.
The esul s show a good ag eemen wi h he expe imen s o Plou e al. o Lime #1. The esidence ime hey
measu ed is 1.8 seconds, while he esidence ime calcula ed by he simula ion is 1.78 seconds o he gas and
1.77 seconds o he solids.
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4.2. In luence o he diame e o pa icles in he esidence ime o he solids
One o he main di e ences ha a ise when using calcium looping as he mochemical ene gy s o age ins ead
o using i as ca bon cap u e me hod is he size o pa icles needed. In case o CaL-CSP applica ions, he p ope
diame e o pa icles is o ens o mic ons (~60 μm). This size o pa icles may ema kably modi y he esidence
ime o he solids inside he ca bona o wi h espec o o he applica ions such as CaL o ca bon cap u e
(~300 μm) (Figu e 6). Wi h 60 mic ons as base case scena io, a a ia ion in he diame e o [-42%,+32%] (i.e.,
pa icles be ween 35 μm and 79 μm) could be assumed keeping he a ia ion o he esidence ime o he
solids below ±5%, o a ca bona o diame e o 7 me e s. In he case o ca bona o has a lowe diame e , he
allowable span o a ia ion in he size o he pa icles inc eases, as can be seen in Figu e 6.
Figu e 6. Va ia ion o he esidence ime o he solids s. he diame e o he pa icles.
4.3. Ideal case – Iso he mal eac o
The ideal case o an iso he mal eac o is p esen ed in his sec ion o con ex ualize he eac o unde s udy.
The eac o is kep a 800 °C (inle empe a u e o eac an s). The hea emo al equi ed o ope a e unde his
condi ion is p esen ed in Figu e 7. An ideal hea exchange should accomplish wi h his hea emo al p o ile
along he eac o (Figu e 7, le ). The o al hea emo al is p esen ed in he igh g aph o Figu e 7, which also
co esponds wi h he e olu ion o he eac ion.
19
Figu e 7. Hea emo al p o ile (le ) and o al emo ed he mal powe o iso he mal ope a ion ( igh ) s.
eac o leng h and in e nal adius dimensions.
These g aphs can be used o unde s and how a om a e he solu ion p oposed om he ideal sys em.
4.4. Con igu a ion 1: One single ca bona o
The i s con igu a ion aims a pe o ming he ca bona ion in one single eac o . Howe e , he leng hs equi ed
o achie e high con e sions may be no easonable because o he la ge mass lows o eac an s (Figu e 8).
When diame e s be ween 7 m and 4 m a e conside ed, ca bona o s ha a e be ween 37 m and 56 m in leng h
a e equi ed o each 12% con e sion. Mo eo e , o inc ease his alue up o 13.2% (i.e., he 99% o he
achie able con e sion) i mus be leng hen he eac o abou 15 – 17 m. Thus, o a ca bona o o 7 m in
diame e , a o al leng h o 52 m would be needed.
Figu e 8. Final con e sion s. eac o ’s o al leng h and in e nal adius dimensions (Con igu a ion 1).
20
The main eason o he equi emen o excessi ely long eac o s is he insu icien hea emo al. The
un emo ed he mal powe apidly hea s he mass lows inside he eac o up o he equilib ium empe a u e
(Figu e 9). Hence, a e he i s me e s he con e sion g ow hs slowly and linea ly wi h he hea emo al.
Wi hin his egime, he con e sion only inc eases be ween 0.076 and 0.116 pe cen age poin s pe me e o
eac o depending on i s diame e .
Figu e 9. Tempe a u es and con e sion p o iles s. axial posi ion (L=52m, =3.5m, Con igu a ion 1).
The exo he mal powe p oduced du ing he ca bona ion is linea ly dependen on he eac an s con e sion.
Thus, he majo elease o hea akes place a he beginning o he eac o . In his s udy (sys em scale o 100
MW h o ne sola inpu in he calcine ), he o al eleased he mal powe due o ca bona ion is 28.4 MW
when he con e sion eaches 12%, while i inc eases o 31.1 MW a 13.2% con e sions (Figu e 10). Howe e ,
he emo ed he mal powe only amoun s o he 35.2% – 36.6% o he ci ed alue in eac o s sized o 12%
con e sion (i.e., 10.0 – 10.9 MW). This pe cen age inc eases o abou he 45.0% – 51.8% (i.e., 14.0 – 16.1 MW)
o eac o s long enough o each 13.2% con e sion. The hea emo ed by he cooling sys em con inues
g owing linea ly o g ea e leng hs e en hough he ca bona ion eac ion s ops, since he eac o empe a u e
is educed. This e ec is pa ially no iceable in Figu e 9, a he end o he eac o .
21
Figu e 10. To al exo he mal powe om ca bona ion (le ) and o al emo ed he mal powe by cooling luid
( igh ) s. eac o ’s o al leng h and in e nal adius dimensions (Con igu a ion 1).
In o de o eco e he es o he hea , he mix u e o gas and solids should be cooled a e exi ing he
ca bona o . This could be pe o med by sepa a ing bo h phases in a cyclone and passing hem h ough gas-
gas and gas-solid hea exchange s o hea an ex a amoun o supe c i ical s eam ( om 350 °C o 600 °C), as
depic ed in Figu e 4. In his s udy, he CO2 is cooled down o 800 °C and eci cula ed o he ca bona o inle .
The e o e, he a ailable he mal powe om his gas anges om 7.8 MW o 8.2 MW a eac o s sized o 12%
con e sions (Figu e 11). This ep esen s he 27% – 29% o he exo he mal hea coming om he eac ion.
Besides, he solids a e cooled o 450 ºC, which p o ides an a ailable he mal powe be ween 36.8 MW and
38.3 MW, o eac o s sized o each 12% eac an ’s con e sion (Figu e 11).

22
Figu e 11. A ailable he mal powe om CO2 (le ) and solids ( igh ) s. eac o o al leng h and in e nal
adius dimensions (Con igu a ion 1).
In summa y, he o al eco e ed he mal powe amoun s o 55.5 – 56.5 MW (i.e., 56% o he ne sola inpu
in he calcine ) o eac o s ha achie e 12% con e sion. This alues inc eases o 58.3 – 59.6 MW when
eac o s a e sized o 13.2% con e sion, which is no a signi ican inc ease conside ing he addi ional leng h
equi ed.
4.5. Con igu a ion 2: Two ca bona o s in pa allel
The second p oposed con igu a ion p esen s wo ca bona o eac o s ope a ing in pa allel whe e inle mass
low a es o eac an s a e equally di e ed among hem. The aim is o assess hea ans e mechanisms when
low a es a e educed and he subsequen in luence on he equi ed leng hs and diame e s o achie e
accep able so ben con e sion. Con e sions abo e 12% a e achie ed o ca bona o leng hs be ween 20 m
and 39 m o diame e s be ween 7 m and 3 m. The leng hs equi ed o achie e hese con e sions a e s ill high,
bu become mo e easonable o eac o s o 6 and 7 me e s in diame e (Figu e 12). I he maximum so ben
capaci y o a cycled ma e ial is o be eached, 13.3%, he ca bona o leng h mus be inc eased in abou 10
me e s; i.e. a 7 m diame e ca bona o would equi e a o al ca bona o leng h o 30 m.
Figu e 12. Final con e sion s. eac o o al leng h and in e nal adius dimensions (Con igu a ion 2).
23
As al eady men ioned, he hea eleased du ing he ca bona ion eac ion ollows a linea ela ion wi h he
so ben con e sion. Du ing he i s me e s o he ca bona o , he la ge amoun o hea is eleased since he
eac ion a e is enhanced by high eac an s concen a ions and mode a e empe a u es. The o al hea om
ca bona ion amoun s o 14.1 MW when he so ben con e sion is 12%. This alue is inc eased up o 15.6 MW
i 13.2% con e sion is achie ed (Figu e 13).
Figu e 13. To al exo he mal powe om ca bona ion (le ) and o al emo ed he mal powe by cooling luid
( igh ) s eac o o al leng h and in e nal adius dimensions (Con igu a ion 2).
The eco e ed hea conside ing he design o he cooling sys em and he p o ile o hea eleased by
ca bona ion amoun s o he 36.0% – 38.0% o he ca bona ion hea in eac o s sized o 12% con e sion (i.e.,
5.1 – 5.4 MW). The eco e ed hea is inc eased up o 7.1 – 7.8 MW which co esponds o a 45.8 – 50.4% o
he ca bona ion hea eleased when so ben con e sion in he eac o achie es 13.2%. As men ioned in
sec ion 4.3, he hea eco e ed wi h he cooling luid is inc eased o la ge leng hs o he ca bona o e en
when maximum ca bona ion con e sion has been eached. This is due o he g adual cooling o he ca bona o
in he las me e s. Figu e 13 illus a es his phenomenon and he alue o eco e ed hea as a unc ion o
eac o dimensions.
The amoun o hea which canno be emo ed om he ca bona o apidly hea s he mass lows inside he
eac o up o he equilib ium empe a u e and he ca bona ion eac ion is a ou ed in he h ee ini ial me e s
24
o he ca bona o (Figu e 14). A e his i s s age, he con e sion a e d ama ically diminishes and he
con e sion g ow h becomes slow and linea wi h hea emo al. The speci ic con e sion inc emen du ing his
lineal s age anges be ween 0.122 and 0.220 pe cen age poin s pe me e o eac o . Again, speci ic hea
emo al pe uni leng h is insu icien o inc ease eac ion a e and long eac o s a e equi ed o con ol he
esidence ime and he con e sion o he so ben .
Figu e 14. Tempe a u es and con e sion p o iles s. axial posi ion (L=30m, =3.5m, Con igu a ion 2)
The hea no eco e ed in he ca bona o i sel h ough he cooling sys em lea es he eac o wi h he mix u e
o gas and solids as sensible hea . This ene gy can be eco e ed by means o cooling hese s eams a e exi ing
he ca bona o . Solid and gas a e sepa a ed in wo cyclones and, hen, each s eam is di ec ed o a gas-gas
and a gas-solid hea exchange o inc ease he empe a u e o an ex a amoun o supe c i ical s eam. CO2
s eam is cooled down o 800 °C and he a ailable hea in he gas-gas hea exchange anges om 4.0 MW o
4.1 MW o eac o s wi h 12% inal so ben con e sion (Figu e 15) which ep esen s he 28.1% - 29.0% o he
ca bona ion eac ion. Solids a e cooled down o 450 °C and he a ailable hea in he gas-solid hea exchange
a ies om 17.9 MW o 18.1MW, o eac o s wi h a 12% o solid so ben con e sion (Figu e 15).
25
Figu e 15. A ailable he mal powe om CO2 (le ) and solids ( igh ) s. eac o ’s o al leng h and in e nal
adius dimensions (Con igu a ion 2).
The o e all esul s ob ained o his second con igu a ion (Table 1), e.g. a ailable hea s om ca bona o and
hea exchange s and so ben con e sion, a e nea o hose ob ained o Con igu a ion 1. Also, he dimensions
o he wo eac o s in pa allel a e o he same o de o magni ude when added and compa ed o he single
eac o con igu a ion.
Table 1. Leng h equi ed, and emo ed he mal powe by cooling luid and a ailable he mal powe in he
p oduc s in Con igu a ion 1 and 2 (ca bona o s sized o 12% con e sion).
Con igu a ion 1
Con igu a ion 2 (only 1 eac o )
[m]
𝑋𝑓 [%]
𝐿 [m]
𝑄󰇗𝑜𝑢𝑡[MW]
𝑄󰇗𝐶𝑂2[MW]
𝑄󰇗𝑠 [MW]
𝐿 [m]
𝑄󰇗𝑜𝑢𝑡[MW]
𝑄󰇗𝐶𝑂2[MW]
𝑄󰇗𝑠 [MW]
2.0
0.12
56
10.6
8.0
38.1
32
5.3
4.0
18.0
2.5
0.12
48
10.4
8.1
38.2
27
5.3
4.1
18.1
3.0
0.12
42
10.3
8.2
38.3
23
5.2
4.1
18.1
3.5
0.12
37
10.1
8.2
38.3
20
5.1
4.1
18.1
4.6. Con igu a ion 3: Two ca bona o s in se ies wi h in e media e cooling
The hi d con igu a ion p esen s wo eac o s ope a ing in se ies wi h a cooling s age be ween hem (Figu e
2). The aim is o ca bona e he ma e ial only du ing he apid egime in which eac ion is no ye inhibi ed. To
32
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35
Lis o igu es
Figu e 1: Concep ual design o he powe p oduc ion using a ca bona o in a sola powe plan
(c s ands o cooling luid).
Figu e 2: Concep ual design o he modelled ca bona o (c s ands o cooling luid).
Figu e 3: Concep ual design o he ene gy s o age p ocess using a calcine in a sola powe
plan .
Figu e 4: Case s udies o he h ee p oposed ca bona o con igu a ions.
Figu e 5: CO2 cap u e e iciency achie ed in he en ained low eac o o Plou e al. [45] and in
he simula ions o his s udy unde he same se up, as a unc ion o he solid/gas mass a io.
Figu e 6: Va ia ion o he esidence ime o he solids s. he diame e o he pa icles.
Figu e 7: Hea emo al p o ile (le ) and o al emo ed he mal powe o iso he mal ope a ion
( igh ) s. eac o ’s leng h and in e nal adius dimensions.
Figu e 8: Final con e sion s. eac o ’s o al leng h and in e nal adius dimensions
(Con igu a ion 1).
Figu e 9: Tempe a u es and con e sion p o iles s. axial posi ion (L=52m, =3.5m,
Con igu a ion 1).
Figu e 10: To al exo he mal powe om ca bona ion (le ) and o al emo ed he mal powe
by cooling luid ( igh ) s. eac o ’s o al leng h and in e nal adius dimensions (Con igu a ion
1).
Figu e 11: A ailable he mal powe om CO2 (le ) and solids ( igh ) s. eac o ’s o al leng h
and in e nal adius dimensions (Con igu a ion 1).
Figu e 12: Final con e sion s. eac o ’s o al leng h and in e nal adius dimensions
(Con igu a ion 2).
36
Figu e 13: To al exo he mal powe om ca bona ion (le ) and o al emo ed he mal powe
by cooling luid ( igh ) s eac o ’s o al leng h and in e nal adius dimensions (Con igu a ion
2).
Figu e 14: Tempe a u es and con e sion p o iles s. axial posi ion (L=30m, =3.5m,
Con igu a ion 2)
Figu e 15: A ailable he mal powe om CO2 (le ) and solids ( igh ) s. eac o ’s o al leng h
and in e nal adius dimensions (Con igu a ion 2).
Figu e 16: Tempe a u es and con e sion p o iles ( i s s age: up, second s age: down) s. axial
posi ion ( =1.5 m, Con igu a ion 3)
Lis o ables
Table 1: Leng h equi ed, emo ed he mal powe by cooling luid and a ailable he mal powe
in he p oduc s in Con igu a ion 1 and 2 (ca bona o s sized o 12% con e sion).
Table 2: Sizes o ca bona o s, inal con e sion and he mal hea s o Con igu a ion 3.