Modelling calcium looping at industrial scale for energy storage in concentrating solar power plants

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. This is a PDF ile o an a icle ha has unde gone enhancemen s a e accep ance, such as he addi ion o a co e page and me ada a, and o ma ing o eadabili y, bu i is no ye he de ini i e e sion o eco d. This e sion will unde go addi ional copyedi ing, ypese ing and e iew be o e i is published in i s inal o m, bu we a e p o iding his e sion o gi e ea ly isibili y o he a icle. Please no e ha , du ing he p oduc ion p ocess, e o s may be disco e ed which could a ec he con en , and all legal disclaime s ha apply o he jou nal pe ain. © 2021 Else ie L d. All igh s ese ed. 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 [10] Le che TM. S o ing Ene gy: Wi h Special Re e ence o Renewable Ene gy Sou ces. Else ie Inc.; 2016. doi:10.1515/ci-2016-0627. [11] Almend os-Ibáñez JA, Fe nández-To ijos M, Díaz-He as M, Belmon e JF, Sob ino C. A e iew o sola he mal ene gy s o age in beds o pa icles: Packed and luidized beds. Sol Ene gy 2019;192:193–237. doi:10.1016/j.solene .2018.05.047. [12] P ie o C, Cabeza LF. The mal ene gy s o age (TES) wi h phase change ma e ials (PCM) in sola powe plan s (CSP). Concep and plan pe o mance. 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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