Jou nal P e-p oo
Modelling calcium looping a indus ial scale o ene gy s o age in concen a ing sola
powe plan s
Manuel Baile a, Sa a Pascual, Pila Lisbona, Luis M. Romeo
PII: S0360-5442(21)00555-7
DOI: h ps://doi.o g/10.1016/j.ene gy.2021.120306
Re e ence: EGY 120306
To appea in: Ene gy
Recei ed Da e: 6 Oc obe 2020
Re ised Da e: 28 Janua y 2021
Accep ed Da e: 4 Ma ch 2021
Please ci e his a icle as: Baile a M, Pascual S, Lisbona P, Romeo LM, Modelling calcium looping a
indus ial scale o ene gy s o age in concen a ing sola powe plan s, Ene gy, h ps://doi.o g/10.1016/
j.ene gy.2021.120306.
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Manuel Baile a: Concep ualiza ion, Me hodology, So wa e, Valida ion, Fo mal analysis,
W i ing – O iginal D a , W i ing – Re iew & Edi ing, Visualiza ion. Sa a Pascual:
Concep ualiza ion, Me hodology, So wa e, Fo mal analysis, W i ing – O iginal D a , W i ing –
Re iew & Edi ing, Visualiza ion. Pila Lisbona: Concep ualiza ion, Me hodology, W i ing –
O iginal D a , W i ing – Re iew & Edi ing. Luis M Romeo: Concep ualiza ion, W i ing – O iginal
D a , W i ing – Re iew & Edi ing, Funding acquisi ion.
Jou nal P e-p oo
1
Modelling calcium looping a indus ial scale o ene gy
s o age in concen a ing sola powe plan s
Manuel Baile a
a
, Sa a Pascual
a
, Pila Lisbona
b
and Luis M. Romeo
a
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 :
Ca-Looping ep esen s one o he mos p omising echnologies o he mochemical ene gy s o age. This
p ocess based on he ca bona ion-calcina ion cycle o CaO o e s a high po en ial o be coupled wi h sola
powe plan s o i s long- e m s o age capaci y and high empe a u es. P e ious s udies analyzed di e en
con igu a ions o CaL in eg a ed in o powe cycles aiming o imp o e e iciency. Howe e , mos o hese
assessmen s based on lumped models did no accoun o scale e ec in he mos c i ical eac o . In his
wo k, a de ailed 1D-model o a la ge-scale ca bona o is included in he comp ehensi e model o he
in eg a ed acili y. The esul s ob ained se ed o assess he a ailable hea , he minimum echnical pa load
o his equipmen , he equi ed size o he s o age anks and he o e all e iciency o he plan . The main
issue in he ope a ion o la ge-size ca bona o is he hea emo al, hus a mul i- ube in e nally cooled eac o
is p oposed. The designed ca bona o p o ides 80 MW h a nominal ope a ion and 40 MW h a minimum
pa load ope a ion. The sizing o s o age anks depends on he ope a ion managemen , anging be ween
5,700-11,400 m
3
o 15 hou s. Di e en e iciencies o he sys em we e de ined and p esen ed h ough
ope a ing maps, as a unc ion o he eac o loads.
Keywo ds:
Ene gy s o age, Calcium looping, Concen a ed sola powe , CO2, The mochemical ene gy s o age
1. In oduc ion
Deploying enewable ene gy sou ces (RES) con ibu es o he deca bonisa ion o ene gy sys ems
[1]. Howe e , cu ailmen s a e necessa y when RES ep esen abo e 10% o he annual elec ici y
gene a ion [2], since ope a o s only con ol 5–10% o wind and sola dispa ch [3]. To ace his
si ua ion, he Eu opean Commission p oposed ene gy s o age as solu ion [4] since 10–20% a iable
RES sha es a e es ima ed o abou 50 egions in he wo ld by 2023 [5].
In his s udy, we ocus on concen a ing sola powe (CSP) plan s. Dispa ch o CSP has a peak
a ound noon and signi ican a ia ions o e minu es o hou s due o cloud co e age. To manage
elec ici y p oduc ion, hal o he CSP plan s wo ldwide use he mal ene gy s o age (TES) [6]. TES
sys ems e ain he mal ene gy wi hin speci ic ma e ials and elease i when needed. Acco ding o
he physical phenomena occu ing while abso bing/ eleasing he ene gy, he mal ene gy s o age is
classi ied in sensible TES, la en TES and he mochemical ene gy s o age (TCES).
Sensible TES use ma e ials wi h high speci ic hea (131–4187 J/kg·K) o s o e/ elease he ene gy by
hea ing/cooling hei mass. These sys ems a e simple, eliable and cheap, bu he ene gy s o age
densi y is low (1001–4453 kJ/m
3
·K) [7]. Mos o sensible TES used in comme cial CSP plan s a e
based on mol en sal s [8], combining wo anks (packed beds) o high and low empe a u e o
sho - and long- e m s o age [9].
La en TES use ma e ials wi h high la en hea (112–260 kJ/kg), o s o e/ elease he ene gy du ing
phase ansi ions a cons an empe a u e, wha educes luc ua ions in elec ici y p oduc ion [7].
Phase change akes place be ween liquid and solid, in o de o ha e small a ia ions in olume
(<10%) [10] and high ene gy s o age densi ies (50 o 150 kWh/ ). Howe e , he low he mal
conduc i i y o hese ma e ials (< 0.5 W/m·K) p olongs he ime o cha ging and discha ging
ene gy [7]. To ob ain la ge hea exchange su aces in la en TES, shell and ubes con igu a ions a e
commonly used [11][12].
Jou nal P e-p oo
2
The mochemical ene gy s o age sys ems a e based upon e e sible chemical eac ions (endo he mic
in one di ec ion and exo he mic in he o he ) o s o e/ elease ene gy h ough a cyclic p ocess. As
TCES wo ks a e y high empe a u es (450–1300 ºC), i is he mos p omising candida e o
he mal ene gy s o age in new gene a ion CSP plan s wo king abo e 800 ºC [7][13]. Mo eo e ,
TCES p o ides seasonal s o age wi h no hea losses ( he ene gy is s o ed in he chemical bound o
he compounds) wi h highe ene gy densi ies han sensible and la en TES (abou 240-1090 kWh/ )
[14]. Among many ma e ials o TCES (hyd ides, me al oxides and ca bona e sal s), he calcium
looping eac ion (CaL), CaO
3
↔CaO+CO
2
, s ands ou because he ma e ial is cheap and ea h-
abundan , p oduc s a e non- oxic, and ene gy s o age densi y eaches 390 kWh/ [14][15].
The u iliza ion o CaL o TCES was p oposed by Ba ke in 1974 [16], and he scien i ic
communi y in ensi ied i s esea ch du ing he las decade. Recen ly, se e al pape s deal wi h he
in eg a ion o CaL TCES wi h di e en powe cycles [17][18], e iciency op imiza ion
[19][20][21], and managemen o he s o age sys em [22]. O iz e al. [17] and Tesio e al. [18]
assessed di e en powe plan op ions o ind he echnology ha leads o be e pe o mance when
in eg a ed wi h calcium looping TCES. Bo h o hem concluded ha bes esul s a e achie ed wi h
CO
2
powe cycles (CO
2
closed B ay on cycle acco ding o O iz, and supe c i ical CO
2
powe block
acco ding o Tesio). A e iden i ying he mos sui able echnology, hey op imized he e iciency o
he concep by s udying di e en plan layou s. They ound o e all e iciencies (ne elec ic
p oduc ion o ne sola he mal inpu ) in he ange 32-44% o he CO
2
closed B ay on cycle
[19][20], and 40.4% o he supe c i ical CO
2
cycle [21]. Rega ding managemen , B a o e al. used
a mul i-objec i e op imiza ion amewo k o de e mine he bes ope a ional s a egy. Howe e ,
au ho s s a e ha u he esea ch on his issue is necessa y o each au ho i a i e conclusions, as
economic aspec s we e no included in he op imiza ion [22].
So a , he eac o s design has no been aken in o accoun in he exis ing s udies which a e mainly
based on lumped models o he p ocess. Howe e , he ex ension o he chemical eac ions in he
ca bona o and calcine clea ly a ec s he mass lows, he managemen o s o ages and he o e all
e iciency o he plan [14]. The main eason is ha expe imen s on calcium looping applied o
TCES a e sca ce making di icul he alida ion o de ailed models o he eac o s [23]. Sola
calcina ion (CaO
3
→CaO+CO
2
, endo he mic) has been es ed by he Paul Sche e Ins i u e in a
cyclone gas-pa icle sepa a o wi h a window-less ape u e. Sola he mal inpu o he p o o ype was
54 kW, eaching 85% limes one con e sion wi h 88% ene gy e iciency [24]. Ca bona ion
(CaO+CO
2
→ CaO
3
, exo he mic), wi hin he amewo k o sola CaL, is es ed in he SOCRATCES
p ojec . They use an en ained low eac o o 10 kW he mal ou pu , cooled by ex e nal cooling
coils. The cooling luid is ai , which is la e used in a S i ling engine o p oduce powe [25].
A indus ial scale, he compu a ional luid dynamics simula ions o he Paul Sche e Ins i u e
show ha sola calcina ion may ope a e e ec i ely a 55 MW he mal inpu s by using a alling
pa icle ecei e . In his ype o eac o s, a cu ain o alling CaCO
3
pa icles abso b he sola
adia ion ha en e s h ough he ape u e o he ecei e [24]. Rega ding ca bona ion, Baile a e al.
showed ha ene gy could no be p ope ly eco e ed in en ained low eac o s when scaled-up o
indus ial scale, i hey a e cooled by ex e nal coils. Since he eac o hea s up, he eac ion eaches
he equilib ium empe a u e and i p og esses limi ed by he a e a which hea is e acua ed. This
leads o un easible dimensions o eac o s (7 m diame e and 52 m leng h o ca bona o s o 100
MW sola inpu ) [26]. The e o e, o he po en ial con igu a ions mus be e alua ed o imp o e he
hea emo al in indus ial ca bona o s o CaL TCES.
In his wo k, we ocus on he wo main gaps ound in li e a u e when assessing he u iliza ion o
calcium looping as he mochemical ene gy s o age in concen a ing sola powe plan s: (i) he
design o a sui able eac o o ca bona ion a indus ial scale and (ii) he analysis o he concep
aken in o accoun he eac o design and i s beha io a pa load ope a ion. Thus, he no el y o
his wo k consis in quan i ying a ealis ic e iciency o CaL TCES a indus ial scale. Fi s , he
pape in oduces he concep o calcium looping TCES in CSP, es ablishing he case unde s udy.
Then, he me hodology p esen s he ca bona o modelling and he design c i e ia om ew kW o
Jou nal P e-p oo
3
100 MW scale. Resul s show how pa load ope a ions in ca bona o modi y mass lows and he
s o age managemen (CaO, CaCO
3
and CO
2
). Finally, we quan i y he o e all pe o mance o he
plan .
2. Calcium looping o ene gy s o age in CSP plan s
The ene gy s o age sys em based on calcium looping p ocess consis s o wo eac o s, namely
calcine and ca bona o . In he calcine , solids all om he op, and sola adia ion p o ides he mal
ene gy o calcina ion (Eq. (1)). In ou s udy, we conside 100 MW o sola powe inpu as nominal
ope a ion. I he a ailabili y o sola ene gy is less han he nominal powe , he calcine will ope a e
a pa ial load. The calcine load is de ined as he a io be ween he a ailable sola powe inpu and
he nominal sola powe inpu (100 MW). The solids mass low is a mix u e o limes one and lime
(197.7 kg/s), and i s inle empe a u e is se a 850 ºC h ough he hea exchange HE-ER
CaCO3+CaO
(Fig. 1). The ope a ing empe a u e inside he calcine is kep below 950 ºC, o limi deg ada ion o
he solid pa icles [19].
CaCO

↔CaO+CO

∆H

=180kJ/mol, (1)
Lime and CO
2
a e ob ained a e calcina ion o limes one. These p oduc s a e con eyed o he
second eac o , whe e ca bona ion akes place and he s o ed chemical ene gy is eco e ed ( e e se
o Eq. (1)). The hea eleased is ans e ed o he powe block h ough a cooling luid. The inle
empe a u e o he ca bona o is se a 850 ºC [20], o which eason he hea exchange s HE-ER
CaO
and HE-ER
CO2
a e used. Finally, he solids lea ing he ca bona o a e con eyed again o he
calcine , hus closing he loop.
Fig. 1. The mochemical s o age sys em based on Ca-looping p ocess o a la ge scale CSP plan :
nominal ope a ion mode.
Full calcina ion can be assumed a he ou le o he calcine . Howe e , he mass composi ion a e
ca bona ion depends on he a e age so p ion ac i i y o he solid popula ion, as only pa o he
CaO pa icle will eac wi h he CO
2
[27]. An a e age maximum con e sion o 13.54% is assumed
o he selec ed limes one [26][28][29] and he mola a io CaO:CO
2
a he ca bona o inle is se a
6.8:1 [28][29][30].
Addi ionally, a small ac ion o lime is pu ged om he sys em (
p
=1%) and he co esponding
amoun o esh limes one is added o compensa e he emo al o calcium. The addi ion o esh
limes one o he sys em inc eases he a e age so p ion ac i i y o lime popula ion gi en he decay
o so p ion capaci y o indi idual lime pa icles wi h he numbe o cycles. In his layou , lime is
pu ged a e calcina ion, while limes one is added a he inle o calcine . I mus be no ed ha he e
is a ne inpu o ca bon and oxygen in o he sys em, because he ca bon dioxide eleased om esh
limes one calcina ion is accumula ed. The e o e, a small amoun o CO
2
has o be emo ed om he
Jou nal P e-p oo

4
loop o close he ca bon mass balance. Ac ually, he only CO
2
exi ing he ca bona o is his ne mass
inpu coming om he di e ence be ween he esh CaCO
3
and he pu ged CaO, as he mola a io
in he ca bona o was se o consume he es o CO
2
du ing eac ion.
This mode o ope a ion co esponds o he nominal poin used o ca bon cap u e applica ions in
which nei he s o age no discha ge o ene gy ake place. The ene gy en e ing he calcine is
eco e ed in he ca bona o wi hou delaying powe p oduc ion. This mode o ope a ion is no
use ul o ene gy s o age applica ions bu i s p ope desc ip ion is signi ican o unde s and he
pe o mance o he calcium looping. In he ollowing subsec ions, he layou o he sys em unde
s o age and discha ge ope a ion modes is desc ibed.
2.1. Ene gy s o age ope a ion mode
When he elec ici y demand om he sys em decays o he selling p ice o elec ici y does no
co e he ope a ing cos , pa o he sola ene gy handled in he CSP is s o ed. Unde ene gy s o age
ope a ion, a ac ion o he lime (
s ,CaO
) and CO
2
(
s ,CO2
) ob ained h ough calcina ion a e s o ed
ins ead o con eyed o he ca bona o (Fig. 2). Thus, he he mal powe eleased in he ca bona o is
educed, and he s o ed p oduc s allow p oducing he mal ene gy in a la e pe iod. Addi ionally, o
keep cons an he mass low en e ing he calcine , solids mus be added o he loop h ough he
discha ge om a limes one and lime ese oi . The discha ge low o his ank is de ined as a
ac ion o he nominal solid low lea ing he ca bona o ou le (
dch,CaCO3
).
Fig. 2. The mochemical s o age sys em based on Ca-looping p ocess o a la ge scale CSP plan :
pa ial ene gy s o age ope a ion mode.
I he ac ion o CaO and CO
2
sen o s o age anks inc eases, he load o he ca bona o may be
educed below i s minimum pa ial load, equi ing o shu -down he eac o ( he pa load in he
ca bona o is de ined as he a io be ween he inpu mas low and he nominal inpu mass low).
Unde his si ua ion, he plan s a s ope a ing only in s o age mode, no p oducing he mal powe in
he ca bona o (Fig. 3). The discha ge ac ion om he limes one ese oi
dch,CaCO3
will depend on
he amoun o sola ene gy en e ing he ecei e .
Jou nal P e-p oo
5
Fig. 3. The mochemical s o age sys em based on Ca-looping p ocess o a la ge scale CSP plan :
ene gy s o age ope a ion mode.
In his s udy, he p ope ies o s o ed CO
2
a e 100 ºC and 73 ba [20], h ough a comp ession s age
including wo cooling s eps o 50 °C (HE-EE
CO2
) and 100 ºC (HE-EE
CO2,C
). Solids s o age
empe a u e and p essu e a e 200 °C (HE-EE
CaO
) and 1 ba [19].
2.2. Ene gy elease ope a ion mode
Whene e sola ene gy is no enough o keep ca bona o wo king a a speci ic load, he plan can
un unde ene gy elease mode. In his case, pa o he p e iously s o ed lime and CO
2
a e now
discha ged om hei ese oi s o en e in he ca bona o and p oduce he desi ed he mal powe
(Fig. 4). The CO
2
and CaO lea ing he s o age anks a e de ined as a ac ion o he nominal low o
CO
2
(
dch,CO2
) and CaO (
dch,CaO
) a calcine ou le . Addi ionally, as he e is no enough a ailable
sola ene gy o comple ely calcine he mass low exi ing he ca bona o , pa o his is di e ed o
s o age (
s ,CaCO3
) be o e closing he loop.
Fig. 4. The mochemical s o age sys em based on Ca-looping p ocess o a la ge scale CSP plan :
pa ial ene gy discha ge ope a ion mode.
When sola powe is no a ailable, he ope a ion is limi ed o elease s o ed ene gy (Fig. 5). The
mass lows discha ged om he ese oi s depend on he demanded he mal powe o be p oduced.
In ou s udy, whe he we s o e o elease ene gy, he ac ions o CaO and CO
2
en e ing and exi ing
Jou nal P e-p oo
6
he anks will be he same in o de o keep cons an he CaO:CO
2
mola a io in he ca bona o (i.e.,
s ,CaO
=
s ,CO2
and
dch,CO2
=
dch,CaO
). Hea losses o hea exchange s a e assumed as 2% o he o al
eleased ene gy.
Fig. 5. The mochemical s o age sys em based on Ca-looping p ocess o a la ge scale CSP plan :
ene gy discha ge ope a ion mode.
3. Me hodology
Me hodology co e s ca bona o modelling, design c i e ia and assessmen o he s o age anks
equi ed o he co ec managemen o he plan .
3.1. Ca bona o modelling
The ene gy emo ed om he ca bona o ep esen s he main sou ce o hea sen o he powe cycle.
Howe e , he ope a ing load in he ca bona o ema kably a ies h oughou he day due o cloud
co e age, he sola adia ion pa e n and he demand o elec ici y. The e o e, i s design mus be
assessed o quan i y he e ec s o pa ial load ope a ion in he o e all e iciency o he sys em. In
his sense, a de ailed model o a la ge scale ca bona o eac o has been de eloped. Besides, he
minimum echnical load in he ca bona o ha e an e ec on he size o s o age anks, and will
de e mine he minimum amoun o hea a ailable o he powe cycle.
The ca bona o is an en ained low eac o in which eac an s en ance is loca ed a he op. This is
a complex sys em whe e he e ogeneous exo he mic chemical eac ions ake place oge he wi h hea
anspo phenomena. The model conside s ca bona ion kine ics, hea ans e mechanisms and he
speci ic geome y o he eac o , in o de o compu e axial p o iles o con e sion, empe a u e and
esidence ime unde di e en ope a ing loads. The eac o was disc e ized in 100 slices o cons an
leng h, o which he equa ions p esen ed in he ollowing subsec ions we e compu ed. In he case
o hose equa ions ha comp ise an in eg a ion, some o he a iables a e assumed cons an along
he slice o pe o m he in eg a ion (whene e he case, i is men ioned in he ex ). The model is
sol ed in s eady-s a e h ough a nume ical mesh wi h 100 disc e e 1-D elemen s.
The Fig. 6 illus a es he lowcha o he ca bona o model o one slice o he disc e ized eac o .
The e a e ou main blocks ha simula e he solid phase, he gas phase, he kine ics and he hea
ans e . The ‘gas phase’ module p o ides in o ma ion o he ‘solid phase’ module in o de o
compu e he downwa d eloci y o he solids alling h ough he eac o . Then, he ‘solid phase’
module p o ides he esidence ime o he solids o he ‘kine ics’ module o calcula e he
con e sion. Also, bo h he ‘gas phase’ and he ‘solid phase’ modules ans e he mole lows da a o
he ‘hea ans e ’ module in o de o calcula e he inal empe a u e inside he eac o . A his
poin , he compu ed alues o con e sion and empe a u e mus be e-in oduced in he di e en
Jou nal P e-p oo
7
modules (i e a i e p ocess) un il hey con e ge. Once con e gence is achie ed, he da a on
esidence imes, con e sion and empe a u e a e p o ided o he nex disc e ized slice. The o me
allows compu ing he o al esidence ime, while con e sion and empe a u e a e used as ini ial
alues in he i e a i e loops o he nex slice.
Fig. 6. Ca bona o modelling lowcha o he disc e ized slice o index i, and i s in e ac ions wi h
he p e ious (i-1) and nex (i+1) slice.
I mus be no ed ha each slice does no only depends on he p e ious one, bu also in he ollowing
one because o he hea ans e model. Since he eac o uses a coun e -cu en cooling
con igu a ion, he ini ial empe a u e o he cooling luid is p o ided by he ollowing slice, which
is no ye sol ed. The bounda y condi ion ha ixed he inle empe a u e o he cooling luid, in he
Jou nal P e-p oo
14
¬




.
b6
0
=
3
.
66
+
.
0
.
049
+
0
.
020
4
⁄
0
·
·¸
B
.
B
1
+
0
.
065
·
·¸

.
Ú


(51)
To compu e he local Nussel numbe a an axial posi ion 

, Eq. (42) is used, ob aining he
ollowing exp ession (Eq. (52)):
¬

.
b6
0
=
3
.
66
+
·¸

B
.
B
·
.
1
.
8473
·
·¸


.
Ú
·
4

+
0
.
754
·
·¸


.
Ú
−
5
.
88
·
4

−
2
.
4
0
10

·
4

·
3
1
+
0
.
065
·
·¸


.
Ú
8


(52)
Whe e he G ae z and P and l numbe s a e calcula ed wi h Eq. (37) and Eq. (40).
Wi h his me hodology, he empe a u e along he ca bona o can be calcula ed by knowing he
ini ial empe a u e o eac an s and cooling luid.
3.2. Design c i e ia a di e en scales
The scale o he sys em is cha ac e ized by he sola powe a ailable in he calcine , 
!
( om 10
kW o 100 MW). The co esponding inpu lows o CaO and CO
2
en e ing he ca bona o (a
nominal load) a e compu ed h ough he ene gy balance in he calcine (Eq. (53)).

!
=
h
!"#
.
Ü°
!
0
·

!"#
,

,

+
h
!#

.
Ü°
!
0
·

!#

,

,

+
h
!"#
.
Ü°
!
0
·

!"#
,
m
−
h
!"!#

.
d°
!
0
·

!"!#

,

,

−
h
!"#
.
d°
!
0
·

!"#
,

,

−
h
!"!#

.
°
!
0
·

!"!#

,
7
(53)
whe e h
zY
is he speci ic en halpy o he componen } a empe a u e 2, 
z,,
is he mole low o
componen } en e ing he ca bona o (which a e ou le lows in he calcine ), 
z,,
is he mole
low o componen } exi ing he ca bona o (which a e inle lows in he calcine ), 
!"#,m
is he lime
pu ged a e exi ing he calcine , and 
!"!#,7
is he esh limes one in oduced in he calcine o
eplace he pu ge. All hese mole lows can be w i en as a unc ion o 
!"#,,
(Eq. (54) o Eq. (57))
by ixing he con e sion achie ed in he ca bona o (assumed as /
Ý
=0.1354) and he CaO:CO
2
mola a io (R=6.8776).

!#

,

,

=

!"#
,

,

R
(54)

!"!#

,

,

=

!"#
,

,

·
/
Ý
(55)

!"#
,

,

=

!"#
,

,

·
.
1
−
/
Ý
0
(56)

!"#
,
m
=

!"!#

,
7
=

!"#
,

,

·
R
1
R
−
/
Ý
V
(57)
Ope a ing in Eq. (53) and using en halpy da a om Aspen Plus da abase, i is ound Eq. (58) and
Eq. (59) o he calcula ion o he nominal inpu lows o CaO and CO
2
in he ca bona o as a
unc ion o he sola powe en e ing he calcine .

!"#
,

,

=

!
32
,
162
.
19

ß
Hà
H±
á










§








)
!"#
,

,

=

!
573
.
53
ß
Hà
H,
á

(58)

!#

,

,

=

!
221
,
198
.
68

ß
Hà
H±
á








§








)
!#

,

,

=

!
5
,
027
.
24
ß
Hà
H,
á

(59)
In addi ion o he inpu low calcula ion, some design c i e ia ha e been ollowed o keep simila
con e sion and empe a u e p o iles along he eac o a di e en scales. Fi s , a single ube eac o
wi h inne cooling has been modelled, looking o p ope hea emo al a small scale (10 kW). This
eac o is made o wo concen ic ubes o small diame e . The eac an s low om op o bo om
h ough he ou e ube, while cooling luid lows in coun e -cu en h oughou he inne ube (Fig.
7). The aim is o eco e ew kW a his s age. The equi ed inpu lows o 10 kW a e 0.0174 kg/s
o CaO and 0.0020 kg/s o CO
2
.
Once p ope dimensions a e ixed o single- ube, a mul i- ube con igu a ion is s ablished. This
mul i- ube eac o encloses 150 – 200 cooling ubes, be ween which he eac an s low om op o
Jou nal P e-p oo

15
bo om. In p inciple, he cooling pipes a e o he same diame e and leng h ha he one used in
single- ube con igu a ion ( he enclosu e is also o he same leng h han he cooling pipes). The
cooling ubes a e se in iangula con igu a ion and he dis ance among hem is ixed in o de o
keep he c oss-sec ional a ea in p opo ion o he inc emen o eac an s olume. In o he wo ds, he
c oss-sec ional a ea h ough which he eac an s low is ¬ imes he a ea o he single ube
con igu a ion, being ¬ he numbe o cooling ubes inside he enclosu e o he mul i- ube. This
con igu a ion is aimed o each he MW scale (abou 
!
=2 MW), by keeping simila empe a u e
p o iles along he eac o .
Fig. 7. Ca bona o con igu a ions o small and la ge scale.
Las ly, he la ge-scale mul i- ube con igu a ion is designed by keeping cons an he a io be ween
he leng h o he eac o and he eloci y o he gas-solid mix u e lowing downwa d (/&), and he
a io be ween he leng h o he eac o and he diame e o he enclosu e (/l) [38]. Besides, he
numbe o cooling ubes is inc eased, ins ead o inc easing hei diame e . The aims o his
con igu a ion is o achie e he 100 MW h scale and o quan i y he beha io a pa ial load. Again,
we look o conse ing empe a u e p o iles, and ou le empe a u es o bo h p oduc s and cooling
luids, since powe p oduc ion is he main objec i e o his eac o .
3.3. Ope a ion modes and e iciency de ini ions
The wo ope a ions conside ed in his s udy a e ene gy s o age ope a ion mode (ESOM) and ene gy
elease ope a ion mode (EROM). Unde hese modes, a la ge numbe o ope a ion poin s leads o
di e en pai s o calcine -ca bona o powe s and di e en alues o s o age powe . The ope a ion
poin s a e ela ed o he mass low a es s o ed o eleased om he anks.
3.3.1. Ene gy s o age ope a ion mode
Two pa ame e s a e used o desc ibe he ope a ion poin s o ESOM: he ac ion o he lime
p oduced in he calcine ha is sen o s o age, and he ac ion o limes one in he ank ha is
discha ged.
The s o age ac ion o lime, 
',!"#
in Eq. (60), is he a io be ween he mass low a e di e ed o
he CaO s o age ank and he maximum mass low a e ha could lea e he calcine ope a ing a ull
capaci y (100 MW).

',!"#
=
 ¡â¢,ZF
 ¡â¢,ãâä
(60)
Jou nal P e-p oo
16
The discha ge ac ion o limes one, 
g°,!"!#
in Eq. (61), is he a io be ween he mass low a e
discha ged om he limes one ank and he maximum mass low a e ha could lea e he ca bona o
ope a ing a ull capaci y.

g°,!"!#
=
 ¡â¡¢¶¡â¢,åÖæ
 ¡â¡¢¶¡â¢,ãâä
(61)
All he po en ial pai s o hese wo pa ame e s co e he ope a ion poin s encompassed du ing
ESOM.
The speci ic s o age consump ion (SSC) exp essed in Eq. (62) p o ides he amoun o o al ene gy
( he mal and elec ical) equi ed o s o e a mass uni o lime. This alue is use ul o unde s and
whe he he s o age p ocess is p o i able o no in e ms o ene gy unde speci ic ope a ion poin s. I
mus be kep in mind he quali a i e in e es o he pa ame e bu i s limi a ion as quan i a i e
measu e gi en he mix o ene gy ypes in i s de ini ion. The ene gy consumed in he p ocess
includes he ac ion o hea used o p oduce he lime sen o he s o age ank (
! ,'
), he
p ehea ing o he limes one discha ged om he s o age ank which is la e s o ed in he o m o
lime (
Xçç½!"!#,'
) and he elec ic powe demanded in he comp ession o he s o ed ca bon
dioxide (è
m|6''|
).
55==
é ¡p,ZFCé êNNë¡â¡¢¶,ZFCì ÖÐãhÒTZZÐÒ
 ¡â¢,ZF
(62)
A s o age e iciency, η
s
, is de ined by Eq. (63) o compa e he amoun o s o ed ene gy and he ne
ene gy consumed du ing he s o age p ocess. The s o ed ene gy comp ises he sensible hea o he
s o ed subs ances (lime and ca bon dioxide, =5
!#C!"#,'
) and he chemical ene gy po en ially
s o ed in he lime which will be la e ca bona ed, ∆
½
∙
!"!#,!½
. This pa ame e p o ides an idea
o he po ion o ene gy ha is s o ed and he po ion ha is los du ing he s o age p ocess.
î
'
=
é ZF,¡â¢
é ¡p,ZFCé êNNë¡â¡¢¶,ZFCì ÖÐãhÒTZZÐÒ
=
!W¡¢O¡â¢,ZFC∆XëG∙~ ¡â¡¢¶,¡ë
é ¡p,ZFCé êNNë¡â¡¢¶,ZFCì ÖÐãhÒTZZÐÒ
 (63)
Ano he signi ican alue o he ope a ion is he e iciency o he ca bona o in e e ence o he
ene gy p o ided by his equipmen , η
CR
, Eq. (64). I compa es he amoun o powe eleased in he
ca bona o and he ene gy in es ed. The la e includes he hea o calcina ion equi ed o p oduce
he lime ed in o he ca bona o , 
! ,!½
, and he p ehea o his limes one p io he calcine ,

Xçç½!"!#,!½
.
î
!½
=
é ¡ë
é ¡p,¡ëCé êNNë¡â¡¢¶,¡ë
(64)
Finally, an e iciency ela ed o he a ailable he mal ene gy is de ined by Eq. (25) and Eq. (65),
wi h he o me including he sensible hea o he s o ed subs ances. This e iciency compa es he
a ailable hea o he ene gy in es ed. The a ailable hea accoun s o he he mal powe eleased in
he ca bona o , and he he mal powe p o ided by he di e en hea exchange s (EE hea
exchange s always p o ide he mal powe , while ER hea exchange s only p o ide he mal powe
unde ESOM).
î
"q,B
=
é ¡ëC∑é êNNNCé êNNë¡¢OCé êNNë¡â¢
é ¡pCé êNNë¡â¡¢¶C!W¡â¡¢¶¡â¢,åÖæ
(25)
î
"q.çW#ï0
=
é ¡ëC∑é êNNNCé êNNë¡¢OCé êNNë¡â¢
é ¡pCé êNNë¡â¡¢¶
(65)
3.3.2. Ene gy elease ope a ion mode
Analogously, he s o age ac ion o he limes one p oduced in he ca bona o , Eq. (66), and he
discha ge ac ion o lime om he s o age anks, Eq. (67), desc ibe he se o ope a ion poin s ha
con o m he ene gy elease ope a ion mode.
Jou nal P e-p oo
17

',!"!#
=
 ¡â¡¢¶¡â¢,ZF
 ¡â¡¢¶¡â¢,ãâä
(66)

g°,!"#
=
 ¡â¢,åÖæ
 ¡â¢,ãâä
(67)
The s o age ac ion o limes one, 
',!"!#
, ep esen s he a io be ween he mass low a e di e ed
o he s o age ank om he ou le s eam o he ca bona o and he maximum mass low a e which
could lea e he ca bona o ope a ing a ull capaci y. The discha ge ac ion o lime, 
g°,!"#
, is he
ela ion be ween he mass low a e discha ged om he CaO ank and he maximum mass low a e
o CaO lea ing he calcine a ull load.
The ene gy e iciency in he ca bona o , η
CR
, unde EROM is calcula ed h ough Eq. (68). The
ene gy in es ed in his p ocess includes (i) all he hea o calcina ion demanded in he calcine , 
!
,
(since no calcined ma e ial is di e ed o s o age anks unde EROM) (ii) he s o age consump ion
o he mass low a e o lime discha ged om he anks, (iii) he p ehea ing o his limes one be o e
in oduced in o he calcine , 
Xçç½!"!#
and (i ) he p ehea ing o he mass low a es o lime and
ca bon dioxide, 
Xçç½!#
and 
Xçç½!"#
(i needed).
î
!½
=
é ¡ë
é ¡pCWW!∙ ¡â¢,åÖæCé êNNë¡â¡¢¶Cé êNNë¡¢OCé êNNë¡â¢
(68)
Unde EROM, he he mal e iciency o he sys em is de ined bo h conside ing, Eq. (30), and no
conside ing, by Eq. (69), he sensible hea o he s o ed subs ances. In his case, he a ailable hea
only includes he he mal powe om he ca bona o and EE hea exchange s.
î
"q,B
=
é ¡ëC∑é êNNN
é ¡pCé êNNë¡â¡¢¶C!W¡â¢,åÖæC!W¡¢O,åÖæCWW!∙ ¡â¢,åÖæCé êNNë¡¢OCé êNNë¡â¢
(30)
î
"q.ç½#ï0
=
é ¡ëC∑é êNNN
é ¡pCé êNNë¡â¡¢¶CWW!∙ ¡â¢,åÖæCé êNNë¡¢OCé êNNë¡â¢
(69)
3.4. Sizing o s o age anks
The sizing o s o age anks accoun s o he ope a ing mode and he in oduced/ex ac ed mass
low a es o CO
2
, CaO and CaCO
3
. The ope a ing mode dic a es he numbe o hou s and he
s o age/discha ge ac ions. S o age and discha ge ac ions di ec ly de ine he inle and ou le
low a es, while he numbe o hou s p o ides he ime in e al o in eg a e. The s o age olume o
he anks is calcula ed h ough Eq. (70).
w
'

.+0=oL
 µM ÐÑF
Ql+

G
+w
',

(70)
The maximum s o age low a e o CO
2
and CaO akes place when sola calcine ope a es a
nominal load and ca bona o ope a es a minimum load.
4. Resul s
In his sec ion, he model alida ion and he esul s o he small- and la ge-scale ca bona o s a e
p esen ed. Besides, i is assessed he pa ial load ope a ion o he la ge-scale ca bona o . Las ly, a
model o he coupled CaL TCES and CSP sys ems is un a h eshold ope a ion condi ions o
p o ide he sizing o s o age anks.
4.1. Model alida ion
The i s impo an issue o be alida ed is he independency o esul s wi h espec o he numbe o
disc e ized elemen s (i.e., wi h he leng h o each disc e ized slice). As case o s udy, i has been
Jou nal P e-p oo
18
chosen he single- ube con igu a ion ope a ing a 50% pa ial load ( he pa load in he ca bona o is
de ined as he a io be ween he inpu mass low and he nominal inpu mass low). The Fig. 8
p esen s he ela i e e o ha exis s in he mos impo an compu ed a iables e sus he numbe o
disc e iza ion elemen s, wi h espec o 300 disc e iza ion elemen s (in a 4-me e eac o , he la e
means slices o 1.3 cm). I can be seen ha he ela i e e o emains below 1% in all cases
whene e he numbe o disc e iza ion elemen s is abo e 15. The e o e, we selec 100 disc e iza ion
elemen s o he simula ions p esen ed in Sec ion 4.2.
Fig. 8. Rela i e e o in he mos ele an compu ed a iables s. he numbe o disc e iza ion
elemen s (wi h espec o 300 disc e iza ion elemen s).
These small a ia ions in he compu ed a iables come om assuming cons an olume low in Eq.
(8) when in eg a ing o e he leng h o each disc e ized elemen . This can be clea ly seen in Fig. 9
when compa ing he empe a u e and con e sion p o iles o a simula ion wi h 100 disc e iza ion
elemen s (depic ed wi h symbols) wi h a simula ion wi h 300 disc e iza ion elemen s (depic ed wi h
lines). In hose egions in which he a ia ion o olume low occu s as e (i.e., wi h highe
eac ion a es), he e o becomes no iceable. I mus be no ed ha , since he case chosen as
example is ope a ing a 50% pa ial load, he eac ion occu s in a sho e leng h, wha accen ua es
he ela i e e o . I he eac o ope a es a ull load, he a ia ion in olume is less s eep, and he
e o less signi ican .
Fu he mo e, he selec ed ope a ing condi ions in ou simula ions make CO
2
o eac almos
comple ely, so any a ia ion in olume low is ema kable compa ed o he o al olume low in he
eac o . This makes he ela i e e o o be mo e signi ican . S ill, ou simula ion keeps ela i e
e o s below 1% in he a iables o in e es . In he case o analysing a eac o se up wi h highe
a io o CO
2
:CaO, he e o would be e en lowe .
Jou nal P e-p oo
19
Fig. 9. Compa ison be ween 100 (symbols) and 300 (lines) disc e iza ion elemen s, o he esul s
on CaO con e sion and empe a u e p o iles ( eac o and cooling sides) s. leng h ( om op o
bo om), in a single- ube ca bona o ope a ing a 50% pa ial load.
The second impo an issue o be alida ed is he ep oducibili y o expe imen al esul s. In his
aspec , he model is alida ed using expe imen al esul s o an en ained low ca bona o om Plou
e al. [39]. 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 owa ds he
wall). The eac o is kep 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 /
H
(i.e., con e sion a he end o he eac ion con olled phase) and +

(i.e., he ime aken o each a
/
H
/2 con e sion) han he ma e ial assumed in he simula ions o his s udy. Lime #1 has /
H
=
0.10 and +

abou 2 seconds, while he ma e ial used in ou simula ions has /
H
=0.1354 and
+

=1.515 seconds. These a e ypical con e sions o highly deac i a ed ma e ials.
The Fig. 10 shows he CO
2
cap u e e iciency, which is de ined as he CO
2
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
M
kg/s). The gas is composed o 10% CO
2
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 .
Fig. 10. CO
2
cap u e e iciency achie ed in he en ained low eac o o Plou e al. [39] 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 measu ed
esidence ime is 1.8 seconds, while he simula ed esidence ime 1.78 seconds o he gas and 1.77
seconds o he solids.
4.2. Ca bona o assessmen
The echnical da a ega ding he h ee ca bona o s unde s udy a e p esen ed in Table 2 (single- ube
a lab scale, 7.6 kW, mul i- ube a pilo scale, 1.4 MW, and he la ge-scale mul i- ube, 79.9 MW).
The eac an s en e a 850 ºC and 2 ba , and he cooling luid is CO
2
en e ing a 100 ºC and 50 ba .
The mass o he cooling luid is calcula ed o se i s exi empe a u e a 650 ºC.
Table 2. Technical da a o he s udied ca bona o s.
Single- ube Mul i- ube La ge-scale mul i- ube
Ca bona o
Leng h (m) 4.0 5.0 15.0 Design c i e ia (Sec ion 3.2)
Enclosu e inne diame e (m) 0.074 0.970 3.3 Design c i e ia (Sec ion 3.2)
CaO mass inle (kg/s)
0.01740 3.2533 178.6 Eq. (58)
Jou nal P e-p oo

20
CO
2
mass inle (kg/s)
0.00198 0.3712 20.8 Eq. (59)
Final CaO con e sion (%)
13.53 13.54 13.54 Ou pu o he model
Gas esidence ime (s) 7.1 10.0 7.55 Ou pu o he model
Solid esidence ime (s) 4.8 6.6 6.51 Ou pu o he model
Inle T (ºC) 850.0 850.0 850.0 Bounda y condi ion
Ou le T (ºC) 850.7 844.8 841.1 Ou pu o he model
A e age T (ºC) 850.8 871.5 850.6 Ou pu o he model
P essu e (ba ) 2.0 2.0 2.0 Fixed
Reynolds (-)
34 – 493 0.4 – 5.5 1.5 – 21.3 Ou pu o he model
Cooling ubes
Leng h (m) 4.0 5.0 15.0 Design c i e ia (Sec ion 3.2)
Inne diame e (m) 0.02 0.02 0.02 Design c i e ia (Sec ion 3.2)
Numbe o ubes (-) 1 187 2,705 Design c i e ia (Sec ion 3.2)
CO
2
mass inle ( o al) (kg/s)
0.0121 2.32 127.4 Ou pu o he model ( ixed
2
7
,

)
Reco e ed hea (MW) 0.0076 1.45 79.9 Ou pu o he model
Inle T (ºC)
100.0 100.0 100.0 Bounda y condi ion
Ou le T (ºC)
650.0 650.0 650.0 Fixed
P essu e (ba ) 50.0 50.0 42.8 – 50.0 Ou pu o he model
Reynolds (-) 9,862 – 19,995 10,098 – 20,476 38,411 – 77,804 Ou pu o he model
The CaO con e sion and empe a u e p o iles along he eac o a e p ese ed a he di e en scales
(Fig. 11). A pilo scale (mul i- ube eac o ), he con ec i e coe icien diminishes one o de o
magni ude in he eac an s side; i.e. shell side. The e o e, he eac o has o be ex ended 1 me e in
leng h ( om 4 m in single ube o 5 me e in mul i- ube) in o de o b ing he p oduc s again o 850
ºC and hus eco e hei sensible hea . O he wise, pa o he exo he mal hea om ca bona ion
would no be eco e ed in he eac o .
Besides, when ollowing he c i e ia o cons an /& and /l a ios o pass om mid o la ge scale,
he mass o cooling luid pe ube has o be inc eased o main ain i s exi empe a u e a 650 ºC.
Doing so, he leng h o he eac o can be sho ened o 15 m (ins ead o he 19 m ha would esul
om he /l es ic ion). The inal con igu a ion is sui able o a la ge-scale ca bona ion, in e ms
o ope a ing empe a u e (a e age 850.6 ºC, compu ed as ∑2

B
ÇB
100
⁄), esidence ime (6.5 – 7.5
s) and dimensions (15 m leng h and 3.3 m diame e ).
Jou nal P e-p oo
21
Jou nal P e-p oo
22
Fig. 11. CaO con e sion and empe a u e p o iles ( eac o and cooling sides) s. leng h ( om op
o bo om) o he single- ube, mul i- ube and la ge-scale mul i- ube con igu a ions. P o iles a e
kep simila a he di e en scales (a ows depic he di ec ion o he low).
Once he eac o a la ge-scale is de ined, pa ial load ope a ion is assessed ( he pa load in he
ca bona o is de ined as he a io be ween he inpu mass low and he nominal inpu mass low).
Reducing he load in he ca bona o means ha he inle mass low a es o eac an s a e
p opo ionally educed, so he a ailable exo he mal hea om ca bona ion will diminish. The e o e,
he amoun o cooling luid ha can be hea ed diminishes (always keeping i s exi empe a u e a
650 ºC). The de ini ion o minimum pa ial load o he eac o co esponds wi h he poin in which
he cooling mass low a e is educed o he hal o i s nominal alue; i.e. he minimum low a e o
cooling luid will be 63.7 kg/s o CO
2
a 650 ºC (below his mass low we assumed ha he
coupling wi h he powe block canno longe ake place) [40]. This poin co esponds o a pa ial
load o 23.9% in he ca bona o (Fig. 12) (only he 23.9% o he nominal inpu low o CO
2
and
CaO is en e ing he ca bona o ).
Jou nal P e-p oo
23
Fig. 12. Cooling mass low and eco e ed hea s. ope a ing load ( a io be ween he inpu mass
low in he ca bona o and i s nominal inpu mass low) o he la ge-scale mul i- ube. Ou le
empe a u e o cooling luid is kep a 650 ºC.
When load is educed, he olume o eac an s is lowe ed and so does hei eloci y h oughou he
eac o . The eac ion ends ea lie , and he cooling luid s a s eco e ing sensible hea om he
p oduc s. Fig. 13 illus a es his ac o a 50% pa ial load. Thus, he o al eco e ed hea does no
diminish linea ly wi h pa load (see Fig. 12), and ollows Eq. (71) when i ed o a polynomial
exp ession by he leas squa es me hod.

$
=3.27+184.5·load−137.8·load

+30.0·load

(71)
Fig. 13. CaO con e sion and empe a u e p o iles s. leng h ( om op o bo om) o he la ge-
scale mul i- ube a 50% pa ial load (a ows depic he di ec ion o he low).
4.3. Plan managemen and size o s o ages
Jou nal P e-p oo
30
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Jou nal P e-p oo
• Calcium looping he mochemical ene gy s o age has been modelled a la ge scale.
• The minimum ope a ing load o ca bona o is 23.9% due o echnical limi a ions.
• The a ailable ene gy e iciency o he o e all sys em is in he ange 55 – 97%.
• The equi e size o s o e CaO and CaCO
3
solids du ing 15 h is 5,700 – 11,400 m
3
.
Jou nal P e-p oo
Decla a ion o in e es s
☒
The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal ela ionships
ha could ha e appea ed o in luence he wo k epo ed in his pape .
☐The au ho s decla e he ollowing inancial in e es s/pe sonal ela ionships which may be conside ed
as po en ial compe ing in e es s:
Jou nal P e-p oo