p ocesses
A icle
No el S udy o Ene gy Reco e y om he
Cooling–Solidi ica ion S age o Syn he ic Slag
Manu ac u ing: Es ima ion o he Po en ial
Ene gy Reco e y
F ancisco M. Baena-Mo eno * , Mónica Rod íguez-Galán, Beni o Na a e e and Luis F. Vilches
Chemical and En i onmen al Enginee ing Depa men , Technical School o Enginee ing, Uni e si y o Se ille,
C/Camino de los Descub imien os s/n, 41092 Se illa, Spain; [email p o ec ed] (M.R.-G.);
[email p o ec ed] (B.N.); [email p o ec ed] (L.F.V.)
*Co espondence: [email p o ec ed]
Recei ed: 6 No embe 2020; Accep ed: 25 No embe 2020; Published: 2 Decembe 2020


Abs ac :
He ein, a no el me hod o ene gy eco e y om mol en syn he ic slags is analyzed. In his
wo k, he po en ial ene gy ha could be eco e ed om he p oduc ion o syn he ic slag is es ima ed
by means o an in eg a ed expe imen al– heo e ical s udy. The ene gy o be eco e ed comes om he
cooling–solidi ica ion s age o he syn he ic slag manu ac u ing. T adi ionally, he solidi ica ion s age
has been ca ied ou h ough quick cooling wi h wa e , which does no allow he ene gy eco e y.
In his pape , a no el cooling me hod based on me al sphe es is p esen ed, which allows he ene gy
eco e y om he mol en slags. Two poin s p esen no el y in his wo k: (1) he me hod o measu ing
he me al sphe es empe a u e (2) and he es ima ion o he ene gy ha could be eco e ed om hese
sys ems in slag manu ac u ing. The esul s o ecas ed ha he empe a u e achie ed by he me al
sphe es was in he ange o 295–410
◦
C in he cen e and 302–482
◦
C on he su ace. Fu he mo e,
we es ima ed ha 325–550 kJ/kg o mol en ma e ial could be eco e ed, o which 15% o he ene gy
consump ion is in he syn he ic slag manu ac u ing p ocess. O e all, he esul s ob ained con i med
he po en ial o ou p oposal o ene gy eco e y om he cooling–solidi ica ion s age o syn he ic
slag manu ac u ing.
Keywo ds:
sus ainable syn he ic slag p oduc ion; ene gy eco e y; me al sphe es; ixed bed egene a o ;
was e and ene gy nexus
1. In oduc ion
1.1. Backg ound
The u u e challenges ela ed o he known ci cula economy policy need o in ensi y he esea ch
o mo e en i onmen al p ocesses and less ene gy-in ensi e indus ial p ocesses [
1
,
2
]. In his sense,
one o he key poin s is he de elopmen o new p oduc manu ac u ing h ough he eco e y o
was e/by-p oduc s in applica ions wi h high added alue and easy echnology ans e o he indus ial
sec o [
3
,
4
]. The use o was e o o m new i eous ma e ials o e a po en ial possibili y o was e
alo iza ion. E en hough he idea o alo izing was e as cons i uen s o cemen s is documen ed in
he li e a u e h ough pa en s and esea ch wo ks [
5
–
10
], no el ies can be s udied in di e en ways
such as (1) explo ing new ma e ials and seeking simila p ope ies o hose p esen ed by blas u nace
slags; (2) he ob aining o syn he ic slags exclusi ely om was e mix u es ha could be managed in
non-haza dous was e land ills; and (3) he ene gy-e icien p oduc ion o syn he ic slag manu ac u ing.
P ocesses 2020,8, 1590; doi:10.3390/p 8121590 www.mdpi.com/jou nal/p ocesses
P ocesses 2020,8, 1590 2 o 20
The i s and second op ions poin ed ou abo e seek o p o ide alue-added p oduc s om
was e based on compliance wi h egula o y equi emen s. Ne e heless, he hi d one is conside ed
associa ed o he iabili y o he manu ac u ing p ocess o hese new ma e ials om an ene gy
pe spec i e. The e o e, he ene gy-e iciency s udy o he p oduc ion p ocess is conside ed one o
he keys o ob ain i s echnical–economic iabili y, oge he wi h he minimiza ion o was e anspo
cos s. In a p e ious wo k o his esea ch g oup, cemen subs i u i e wi h p ope ies simila o blas
u nace slags (syn he ic slags) was ob ained. The ypical composi ion o blas u nace slag can be seen
in Table 1. In his p ocess, a mix o was e was p oposed o ob ain he syn he ic slag ma e ial [
11
].
As announced in p e ious wo k, a deep ene gy eco e y s udy is needed o es ima e he iabili y o
his no el p oduc ion me hod.
Table 1. Typical composi ion anges o blas u nace slags. Own elabo a ion based on [12–14].
Composi ion Range SiO2CaO Al2O3MgO Fe2O3SO3Na2O K2O
27–40 30–50 5–15 1–15
0.2–2.5
1–2.5 0.1–3 0.1–3
In acco dance wi h EN 15167-1 [
15
], g anula ed blas u nace slag is a i i ied ma e ial p oduced
by apid cooling o a mol en slag o sui able composi ion. This kind o slag is ob ained by mel ing
i on o e in a blas u nace, con aining a leas wo- hi ds o c ys alline slag mass and ha ing hyd aulic
p ope ies when ac i a ed p ope ly. The pa ame e s ha in luence he hyd aulic beha io o he inal
slag a e he i eous phase con en , he chemical composi ion, he ineness, he addi i es, and he
me hods and/o subs ances o he ac i a ion s age, p esen ing wha is called la en o po en ial
hyd aulic capaci y [
16
]. The chemical composi ion o he blas u nace slags is one o he p ope ies
ha ma ks i s hyd aulic po en ial, since he g ea e he basici y o he slags, he be e he hyd aulic
beha io . Howe e , he main cha ac e is ic ela ed o hyd aulic beha io is he p opo ion o he
i eous phase o he slag, which mus exceed 70% o gua an ee he hyd aulic beha io [17].
The e icien p oduc ion o he manu ac u e o syn he ic slags needs a s udy o he ene gy eco e y
in i s manu ac u ing p ocess. These s udies ha e been conduc ed in dep h by nume ous au ho s [
18
–
22
],
ocusing especially on he ene gy ha can be eco e ed in he cooling s age o he mol en ma e ial.
Slag cooling sys ems can be classi ied acco ding o he cooling luid o ma e ial used o hei impac
on he ene gy e iciency o he p ocess (ene gy eco e y in he o m o s eam and/o wa m gases). Thus,
basically, all cooling sys ems consis o a hea exchange be ween he mol en ma e ial and he selec ed
luid (wa e and/o ai ) o solid ma e ial (me allic ma e ial). In any case, he echnologies applicable
o he de elopmen o he cooling sys ems mus pe o m a quick cooling, as well as being capable
o ha nessing he po en ial ene gy con ained in mol en ma e ial du ing he cooling p ocess. Below,
some me hods o ene gy eco e y om he mol en ma e ial a e explained, which a e mainly based on
we sys ems (wa e as cooling luid) o d y sys ems (whe e he cooling luid used is ai /gases).
Cooling wi h wa e achie es he objec i es ega ding he i eous p ope ies o he ma e ial.
Howe e , he disad an ages o wa e -based sys ems a e ela ed o hei low ene gy e iciency and
con amina ion wi h pa icles and o he pollu an s, gene a ing a highly co osi e apo due o he
p esence o acid gases ha inc ease ea men , equipmen main enance, and ene gy eco e y cos s.
In he d y cooling sys em, a ansmission occu s o hea om he mol en ma e ial o a s eam o ai ,
which is in con ac wi h eco e y boile s. In many o he ai -cooling echniques, a p io a omiza ion
o he mol en solid could be pe o med. Subsequen ly, a con ac ing s age wi h a s eam o ai in a
luidized o non- luidized bed is ca ied ou , which abso bs he hea , achie ing solidi ica ion o he
mel . O he g anula ion op ions a ise when he mol en ma e ial is agmen ed by o a ing de ices [
23
].
Ano he possibili y o cooling could be by con ac o he mol en ma e ial wi h solid ma e ials such as
sphe ical bodies. This op ion equi es ha he solid ma e ial ha no eac chemically wi h he mol en
slag (i.e., me al sphe es [
24
] o cooling on o a ing me al d ums [
25
–
27
]). Wi h hese example sys ems,
he ene gy eco e y om he mol en slag is possible. In addi ion, combining he ene gy e iciency o
P ocesses 2020,8, 1590 3 o 20
hese ene gy eco e y sys ems wi h he imp o emen o slag p ope ies, he o e all ene gy eco e y
e iciency o cooling p ocesses can be inc eased [28].
This pape s udies he po en ial ene gy eco e y o he cooling p ocess o syn he ic slags p oduc ion
by means o a mass cooling sys em wi h me al sphe es. Concep ually, he mass cooling sys em by
means o he mal egene a ion wi h me al sphe es achie es apid cooling o he mol en ma e ial as a
consequence o he ans e o ene gy om he mol en ma e ial o he me al sphe es. Subsequen ly,
he e is he possibili y o a eco e y o he ene gy con ained in he sphe es by means o an ai cu en .
In addi ion, he cha ac e is ics associa ed wi h he p ope ies o he solid elemen s and he solidi ied
ma e ial, gene ally o low he mal esis ance, allow hea o dissipa e apidly. Once he me al sphe es
and he ma e ial ha e been cooled by he ai low in he egene a o and a pos e io sepa a ion s age o
he solidi ied ma e ial om he balls, he me al sphe es would come back in o con ac wi h he syn he ic
slags in a con inuous cycle. The concep ual scheme o he ene gy eco e y sys em is p esen ed in
Figu e 1. In his sys em, he slag is sepa a ed om he me al sphe es a e cooling h ough sc eening
by he size o he sphe es and solidi ied slags. This sepa a ion is possible as he slag a e no adhe ed o
he su ace o he me al sphe es.
P ocesses2020,8,xFORPEERREVIEW3o 21
Thispape s udies hepo en ialene gy eco e yo  hecoolingp ocesso syn he icslags
p oduc ionbymeanso amasscoolingsys emwi hme alsphe es.Concep ually, hemasscooling
sys embymeanso  he mal egene a ionwi hme alsphe esachie es apidcoolingo  hemol en
ma e ialasaconsequenceo  he ans e o ene gy om hemol enma e ial o heme alsphe es.
Subsequen ly, he eis hepossibili yo a eco e yo  heene gycon ainedin hesphe esbymeans
o anai cu en .Inaddi ion, hecha ac e is icsassocia edwi h hep ope ieso  hesolidelemen s
and hesolidi iedma e ial,gene allyo low he mal esis ance,allowhea  odissipa e apidly.Once
heme alsphe esand hema e ialha ebeencooledby heai  lowin he egene a o andapos e io 
sepa a ions ageo  hesolidi iedma e ial om heballs, heme alsphe eswouldcomebackin o
con ac wi h hesyn he icslagsinacon inuouscycle.Theconcep ualschemeo  heene gy eco e y
sys emisp esen edinFigu e1.In hissys em, heslagissepa a ed om heme alsphe esa e 
cooling h oughsc eeningby hesizeo  hesphe esandsolidi iedslags.Thissepa a ionispossible
as heslaga eno adhe ed o hesu aceo  heme alsphe es.

Figu e1.Concep ualschemeo  heene gy eco e yp ocessp oposedin hiswo k.
1.2.GoalandScope
Basedon heno elconcep o de elopingsyn he icslags omwas e,asexplainedinou 
p e iouswo k[11], hemainobjec i eo  hiss udyis oe alua e hep ope ieso syn he icslags
and heene gy eco e ycapaci yo  hea o emen ionedcoolingsys emdesc ibedinFigu e1.
Likewise, heene gy eco e edin hecoolingai s eamwases ima edin ela ion o heene gy
possessedby hemol enma e ialino de  oanalyze hepossibleene gysa ings ha would esul 
in hemanu ac u eo slags.Twomainpoin sp esen no el yin hiswo k.The i s oneis heme hod
o measu ing he empe a u es ha  heme alsphe esachie e.To heknowledgeo  heau ho s, his
is he i s  ime ha bo h heme hodologyand he eal empe a u eda aa epublished.Thesecond
no el yo  hiswo kis ha knowing he eal empe a u eachie edin heme alsphe es,i was
possible oes ima e heene gy ha couldbe eco e edby hesesys emsinslagmanu ac u ing.
Thees ima iono ene gy eco e y om hemol enma e ialconsis edinse e als eps,which
a eindica edbelow:
‐ Jus i ica iono  he empe a u e eachedby heme alsphe esa  a iousmol enmass(m
m
)/me al
sphe es(m
s
)mass a io.
Figu e 1. Concep ual scheme o he ene gy eco e y p ocess p oposed in his wo k.
1.2. Goal and Scope
Based on he no el concep o de eloping syn he ic slags om was e, as explained in ou p e ious
wo k [
11
], he main objec i e o his s udy is o e alua e he p ope ies o syn he ic slags and he ene gy
eco e y capaci y o he a o emen ioned cooling sys em desc ibed in Figu e 1. Likewise, he ene gy
eco e ed in he cooling ai s eam was es ima ed in ela ion o he ene gy possessed by he mol en
ma e ial in o de o analyze he possible ene gy sa ings ha would esul in he manu ac u e o
slags. Two main poin s p esen no el y in his wo k. The i s one is he me hod o measu ing he
empe a u es ha he me al sphe es achie e. To he knowledge o he au ho s, his is he i s ime ha
bo h he me hodology and he eal empe a u e da a a e published. The second no el y o his wo k is
ha knowing he eal empe a u e achie ed in he me al sphe es, i was possible o es ima e he ene gy
ha could be eco e ed by hese sys ems in slag manu ac u ing.
The es ima ion o ene gy eco e y om he mol en ma e ial consis ed in se e al s eps, which a e
indica ed below:
P ocesses 2020,8, 1590 4 o 20
-
Jus i ica ion o he empe a u e eached by he me al sphe es a a ious mol en mass (m
m
)/me al
sphe es (ms) mass a io.
-
Co obo a ion o he indus ial easibili y o he p oposed sys em in Figu e 1by means o ixed
bed (o egene a o ) heigh calcula ion. Fo his pu pose, he calcula ion o he con ec i e hea
ans e coe icien by solid–ai con ec ion is needed. The de ini ion o his s ep is c ucial o
checking ha he p ocess p oposed is o indus ial in e es .
- Es ima ion o he po en ial ene gy eco e ed pe kg o mol en ma e ial.
To mee his end, his wo k is o ganized as ollows. Fi s , expe imen s o measu ing he maximum
empe a u e ha could be eached by he me al sphe es we e pe o med. Inasmuch han he s udy
aims o be use ul o indus ial pu poses, he expe imen s we e pe o med a di e en m
m
/m
s
a ios
o ep oduce eal indus ial scena ios. Subsequen ly, he mol en ma e ial ha was pou ed o e
he me al sphe es was analyzed by means o X- ay di ac ion (XRD) o e i y he o ma ion o he
cha ac e is ic i eous phase. A e wa ds, be o e es ima ing he po en ial ene gy eco e y, he echnical
easibili y o he p oposed cooling p ocess was cha ac e ized. To his end, he ixed bed heigh was
calcula ed ollowing he me hodology explained in Sec ion 2.2.4. Fo i s es ima ion, he p e ious
de e mina ion o he con ec i e hea ans e coe icien (h) was necessa y. The me hodology employed
o h es ima ion can be seen in Appendix A. Two expe imen s we e pe o med o es ima e he me al
sphe es—ai low empe a u e p o iles in a eal ixed bed. The expe imen s allowed he es ima ion
o h ollowing he assump ions explained in Sec ion 2.2.4. Once he indus ial ixed bed heigh was
ob ained and analyzed as easible, he ene gy eco e y pe kg o mol en ma e ial was es ima ed.
To es ima e he app oxima e pe cen age o he ene gy eco e y in he o e all slag manu ac u ing
p ocess, a compa ison o he i eous–mine al phases be ween ou mol en ma e ial and adi ional
clinke was done. This compa ison allowed ensu ing ha no signi ican di e ences a e ound and
hence ha he o al ene gy consump ion o ou mol en ma e ial can be app oxima e o he one o
clinke p oduc ion.
2. Ma e ials and Me hods
In o de o s udy he ene gy eco e y e iciency o he cooling and solidi ica ion sys em o he
mol en syn he ic slags, a h ee-s age labo a o y expe imen was p oposed:
(1)
Mel he was e mix u e in an o en in app op ia e p opo ions o achie e a composi ion simila o
blas u nace slags. This s age was add essed in dep h in ou p e ious wo k [11].
(2)
Ob ain he empe a u e eached by he me al sphe es when he mol en ma e ial is pou ed wi h
di e en mel ing/me al mass a ios. De e mina ion o he cha ac e is ics o he i eous phase
ob ained in o de o ensu e he i eous p ope ies o he ma e ial solidi ied.
(3)
E alua e he ene gy ha can be ex ac ed om a ixed bed o me al sphe es a he empe a u e
eached in he p e ious phase by exchanging ene gy wi h an ai cu en .
Below, he ma e ials and me hods employed o ul ill his scheme a e explained in dep h.
2.1. Ma e ials
The mix o was e o manu ac u ing syn he ic slags was de ined in a p e ious wo k o ou
g oup [
11
]. Th ee di e en was es we e selec ed as aw ma e ials, which we e cons uc ion and
demoli ion was e, he solid was e s eam gene a ed in an aluminum eco e y plan , and mussel shell
was e om he aquicul u e indus y. Fo mo e in o ma ion, please see [11].
2.2. Expe imen al Se up
2.2.1. Mel ing Fu nace
The mix o was e was mel ed by employing he mel ing u nace (4 kW powe ) schemed in Figu e 2,
which was he same one employed in ou p e ious wo k [
11
]. In b ie , he mel ing u nace consis s
P ocesses 2020,8, 1590 5 o 20
o six elec ical esis ances loca ed inside a hexagonal usion chambe . The discha ge o he mol en
ma e ial is ca ied ou om he bo om o he u nace.
P ocesses2020,8,xFORPEERREVIEW5o 21

Figu e2.Mel ing u nacescheme.
2.2.2.Me alSphe es:Coolingo  heMol enMa e ial
Thecoolings age oene gy eco e y om hemol enma e ialwasbasedonme alsphe es.The
i s s agewas hes udyo  he empe a u ee olu ioninsideasingleme alsphe e.To hisend, he
sys emshowninFigu e3wasdesigned.In hissys em,asingleme alsphe ewelded oapla ewas
buil .Thesphe ewasdesignedwi h wope o a ionsin helowe pa inwhich wo he mocouples
we einse ed ha allowmeasu ing he empe a u eda ain hecen e andon hesu aceo  he
sphe e.All he mocoupleswe econnec ed o heco espondingda aacquisi ionsys em.Fo sakeo 
sa e y, hesphe ewasassemblediname alcon aine andinsula edbya e ac o yma e ial,ascan
beseeninFigu e3.Thesys emwasplacedunde  hemel ing u nace,and hemol enma e ialwas
pou eddi ec ly om he u naceon o hesphe e.Ino de  o ep oduceanindus ialen i onmen 
close o ealcases, wosizeso sphe eso 40and50mmdiame e we eused.Figu e3shows he
cha ac e is icdimensionso  he50mmdiame e me alsphe eand heduc sinwhich he
he mocoupleswe einse ed.Fu he mo e,pho oso  hepla esa o emen ionedwi h hesphe es
coupledcanbeseen.Ade ailedexplana iono p ope iesandcomposi iono  hesphe escanbe
oundin e e ence[29].
Figu e 2. Mel ing u nace scheme.
2.2.2. Me al Sphe es: Cooling o he Mol en Ma e ial
The cooling s age o ene gy eco e y om he mol en ma e ial was based on me al sphe es.
The i s s age was he s udy o he empe a u e e olu ion inside a single me al sphe e. To his end,
he sys em shown in Figu e 3was designed. In his sys em, a single me al sphe e welded o a pla e was
buil . The sphe e was designed wi h wo pe o a ions in he lowe pa in which wo he mocouples
we e inse ed ha allow measu ing he empe a u e da a in he cen e and on he su ace o he sphe e.
All he mocouples we e connec ed o he co esponding da a acquisi ion sys em. Fo sake o sa e y,
he sphe e was assembled in a me al con aine and insula ed by a e ac o y ma e ial, as can be seen
in Figu e 3. The sys em was placed unde he mel ing u nace, and he mol en ma e ial was pou ed
di ec ly om he u nace on o he sphe e. In o de o ep oduce an indus ial en i onmen close o eal
cases, wo sizes o sphe es o 40 and 50 mm diame e we e used. Figu e 3shows he cha ac e is ic
dimensions o he 50 mm diame e me al sphe e and he duc s in which he he mocouples we e
inse ed. Fu he mo e, pho os o he pla es a o emen ioned wi h he sphe es coupled can be seen.
A de ailed explana ion o p ope ies and composi ion o he sphe es can be ound in e e ence [29].
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Figu e2.Mel ing u nacescheme.
2.2.2.Me alSphe es:Coolingo  heMol enMa e ial
Thecoolings age oene gy eco e y om hemol enma e ialwasbasedonme alsphe es.The
i s s agewas hes udyo  he empe a u ee olu ioninsideasingleme alsphe e.To hisend, he
sys emshowninFigu e3wasdesigned.In hissys em,asingleme alsphe ewelded oapla ewas
buil .Thesphe ewasdesignedwi h wope o a ionsin helowe pa inwhich wo he mocouples
we einse ed ha allowmeasu ing he empe a u eda ain hecen e andon hesu aceo  he
sphe e.All he mocoupleswe econnec ed o heco espondingda aacquisi ionsys em.Fo sakeo 
sa e y, hesphe ewasassemblediname alcon aine andinsula edbya e ac o yma e ial,ascan
beseeninFigu e3.Thesys emwasplacedunde  hemel ing u nace,and hemol enma e ialwas
pou eddi ec ly om he u naceon o hesphe e.Ino de  o ep oduceanindus ialen i onmen 
close o ealcases, wosizeso sphe eso 40and50mmdiame e we eused.Figu e3shows he
cha ac e is icdimensionso  he50mmdiame e me alsphe eand heduc sinwhich he
he mocoupleswe einse ed.Fu he mo e,pho oso  hepla esa o emen ionedwi h hesphe es
coupledcanbeseen.Ade ailedexplana iono p ope iesandcomposi iono  hesphe escanbe
oundin e e ence[29].
Figu e 3. Con .

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Figu e3.Schemeo  hede ice o coolingmol enma e ialwi hme alsphe esand iewso  he
con ainmen  essel.
Figu e4showsa ealpho oinwhich hecouplingbe ween hemel ing u naceou le and he
coolingde icewi h heme alsphe ecanbeobse ed.

Figu e4.Couplingo  hemel ing u naceou le and hecoolingde ice.
2.2.3.Me alSphe esPackingDe ice o Ene gyReco e y
Toes ima e hepo en ialene gy eco e y om heme alsphe eswi hai ,a ixedbedcomposed
by wobaske s illedwi hme alsphe eswasdesigned.Thebaske sa emadeo s ainlesss eeland
ha eamesh ha allows hegas opass h ough hebed.Theneeded he mocouples( o  empe a u e
measu emen s)we econnec ed o heda aacquisi ionsys em.Figu e5showsanimageo  he ixed
bedandme alsphe ebaske s.
Figu e 3.
Scheme o he de ice o cooling mol en ma e ial wi h me al sphe es and iews o he
con ainmen essel.
Figu e 4shows a eal pho o in which he coupling be ween he mel ing u nace ou le and he
cooling de ice wi h he me al sphe e can be obse ed.
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Figu e3.Schemeo  hede ice o coolingmol enma e ialwi hme alsphe esand iewso  he
con ainmen  essel.
Figu e4showsa ealpho oinwhich hecouplingbe ween hemel ing u naceou le and he
coolingde icewi h heme alsphe ecanbeobse ed.

Figu e4.Couplingo  hemel ing u naceou le and hecoolingde ice.
2.2.3.Me alSphe esPackingDe ice o Ene gyReco e y
Toes ima e hepo en ialene gy eco e y om heme alsphe eswi hai ,a ixedbedcomposed
by wobaske s illedwi hme alsphe eswasdesigned.Thebaske sa emadeo s ainlesss eeland
ha eamesh ha allows hegas opass h ough hebed.Theneeded he mocouples( o  empe a u e
measu emen s)we econnec ed o heda aacquisi ionsys em.Figu e5showsanimageo  he ixed
bedandme alsphe ebaske s.
Figu e 4. Coupling o he mel ing u nace ou le and he cooling de ice.
2.2.3. Me al Sphe es Packing De ice o Ene gy Reco e y
To es ima e he po en ial ene gy eco e y om he me al sphe es wi h ai , a ixed bed composed
by wo baske s illed wi h me al sphe es was designed. The baske s a e made o s ainless s eel and
ha e a mesh ha allows he gas o pass h ough he bed. The needed he mocouples ( o empe a u e
measu emen s) we e connec ed o he da a acquisi ion sys em. Figu e 5shows an image o he ixed
bed and me al sphe e baske s.
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Figu e5.Me alsphe espackingde ice.
Theme alsphe epacking,a e beinghea edinano en o hedesi ed empe a u e,was
deposi edina he mallyinsula ed essel ha canbeseeninFigu e6.

Figu e6.The mallyinsula ed essel(dimensionsinmm).
Mo eo e , hedesignedde iceinco po a esanai p ehea e bymeanso elec ical esis ance,
whichallowedpe o ming es sa di e en ini ialai  empe a u es.All heelemen sdesc ibedin his
sec iona ein eg a edin he inalexpe imen alse upshowninFigu e7.
Figu e 5. Me al sphe es packing de ice.
The me al sphe e packing, a e being hea ed in an o en o he desi ed empe a u e, was deposi ed
in a he mally insula ed essel ha can be seen in Figu e 6.
P ocesses2020,8,xFORPEERREVIEW7o 21
Figu e5.Me alsphe espackingde ice.
Theme alsphe epacking,a e beinghea edinano en o hedesi ed empe a u e,was
deposi edina he mallyinsula ed essel ha canbeseeninFigu e6.

Figu e6.The mallyinsula ed essel(dimensionsinmm).
Mo eo e , hedesignedde iceinco po a esanai p ehea e bymeanso elec ical esis ance,
whichallowedpe o ming es sa di e en ini ialai  empe a u es.All heelemen sdesc ibedin his
sec iona ein eg a edin he inalexpe imen alse upshowninFigu e7.
Figu e 6. The mally insula ed essel (dimensions in mm).
Mo eo e , he designed de ice inco po a es an ai p ehea e by means o elec ical esis ance,
which allowed pe o ming es s a di e en ini ial ai empe a u es. All he elemen s desc ibed in his
sec ion a e in eg a ed in he inal expe imen al se up shown in Figu e 7.
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Figu e7.Comple eme alsphe espackingde ice o ene gy eco e y.
2.2.4.FixedBedHeigh Es ima ion
Theconcep ualidea o  he ixedbedo me alsphe eshe einappliedconsis so  he ollowing
s eps.Fi s , hemol enma e ialispou edon heme alsphe es.A e  ha , hesphe es oge he wi h
he i i iedma e iala eloca edina ixedbedinwhich hesphe esmo ebyg a i yslowly
( ollowingaplug luxmodel).Thus, hesphe esgo om heuppe pa o  he ixedbed o hebo om,
coolingwi hcoun e cu en ai  om400°C o oom empe a u e.AswillbeexplainedinSec ion3.1,
a empe a u eo 400°Ccanbe eachedin hesphe es, o examplewi hanm
m
/m
s
 a ioo 0.4and
wi hasphe ediame e o 50mm.
Thees ima iono  hepo en ialene gy eco e y om hep oposedp ocessneeds hep e ious
calcula ionso somepa ame e s.The e o e, hepu poseo  hissec ionwas oes ima e he esidence
imeo  hesphe es op oducea empe a u edec ease om400°C o oom empe a u e,aswellas
henecessa yai  lowand he empe a u e ha wouldbe eachedin heai .Thep oposedme hod
oob ain hese esul sisasemi‐empi icalmodel a ia iono  he empe a u eo  hesphe esin he
bed.PleaseseeAppendixA o mo ein o ma ion.Thisallowedes ima ingh’,whichisa a ia iono 
heo iginalhunde  heassump ionsimposed,whicha eexplainedinAppendixA.
Onceh’wasknown,i waspossible oes ima e hedimensionso  heequipmen .To hisend,a
s eady‐s a ebalancewaspe o medin he ixedbed egene a o showninFigu e8.Equa ions(1)
and(2)collec  hecomponen so  hesebalanceequa ions.The esidence imenecessa y o achie ing
adec easein heme alsphe es empe a u e om400 o40°Cwascalcula edalsobymeanso  hese
balanceequa ions.Thiscalcula ionallowedob aining he empe a u ep o ilealong he ixedbed
egene a o (Figu e8).
Figu e 7. Comple e me al sphe es packing de ice o ene gy eco e y.
2.2.4. Fixed Bed Heigh Es ima ion
The concep ual idea o he ixed bed o me al sphe es he ein applied consis s o he ollowing
s eps. Fi s , he mol en ma e ial is pou ed on he me al sphe es. A e ha , he sphe es oge he
wi h he i i ied ma e ial a e loca ed in a ixed bed in which he sphe es mo e by g a i y slowly
( ollowing a plug lux model). Thus, he sphe es go om he uppe pa o he ixed bed o he bo om,
cooling wi h coun e cu en ai om 400
◦
C o oom empe a u e. As will be explained in Sec ion 3.1,
a empe a u e o 400
◦
C can be eached in he sphe es, o example wi h an m
m
/m
s
a io o 0.4 and
wi h a sphe e diame e o 50 mm.
The es ima ion o he po en ial ene gy eco e y om he p oposed p ocess needs he p e ious
calcula ions o some pa ame e s. The e o e, he pu pose o his sec ion was o es ima e he esidence
ime o he sphe es o p oduce a empe a u e dec ease om 400
◦
C o oom empe a u e, as well as
he necessa y ai low and he empe a u e ha would be eached in he ai . The p oposed me hod o
ob ain hese esul s is a semi-empi ical model a ia ion o he empe a u e o he sphe es in he bed.
Please see Appendix A o mo e in o ma ion. This allowed es ima ing h
0
, which is a a ia ion o he
o iginal h unde he assump ions imposed, which a e explained in Appendix A.
Once h
0
was known, i was possible o es ima e he dimensions o he equipmen . To his end,
a s eady-s a e balance was pe o med in he ixed bed egene a o shown in Figu e 8. Equa ions (1)
and (2) collec he componen s o hese balance equa ions. The esidence ime necessa y o achie ing
a dec ease in he me al sphe es empe a u e om 400 o 40
◦
C was calcula ed also by means o hese
balance equa ions. This calcula ion allowed ob aining he empe a u e p o ile along he ixed bed
egene a o (Figu e 8).
ms· kg
h!·cs kJ
kg·K!·(Ts(x−∆x)−Ts(x))(K)=ma kg
h!·ca kJ
kg·K!·(Ta(x−∆x)−Ta(x))(K)(1)
h0(x)kJ
h·m2·K·A(∆x)(m2)·Ts(x−∆x)+Ts(x)
2−
Ta(x−∆x)+Ta(x)
2(K)=makg
h·cakJ
kg·K·(Ta(x−∆x)−Ta(x))(K)(2)
P ocesses 2020,8, 1590 9 o 20
P ocesses2020,8,xFORPEERREVIEW9o 21

Figu e8.Fixedbed egene a o scheme.
m

·kg
h·c
s
kJ
kg·K·󰇛T

(x−∆x)−T

(x)󰇜󰇛K󰇜=m

kg
h·c
a
kJ
kg·K·󰇛T
a
(x−∆x)−T
a
(x)󰇜󰇛K󰇜
(1)
hʹ󰇛x󰇜kJ
hm
2
·K·A󰇛∆x󰇜m
2
·󰇧T

󰇛x−∆x󰇜+T

󰇛x󰇜
2-
T
a
󰇛x−∆x󰇜+T
a
󰇛x󰇜
2󰇨󰇛K󰇜=m

kg
h·c
a
kJ
kg·K·󰇛T
a
󰇛x-∆x󰇜−T
a
(x)󰇜󰇛K󰇜
(2)
Theequa ionswe esol ed ollowingas andalonepa h.Imposing ha Ts(x),Ts(x–“∆”x),and
Ta(x−“∆”x)a eknown,i ispossible oob ainTa(x) omEqua ion(1),aswellas“∆”x om
Equa ion(2).
2.3.PhysicochemicalCha ac e iza ion
Thephysicochemicalcha ac e iza ionwasca iedou bymeansXRDanalysis,modelAXIOS
omPanaly ical.The2θanglewasinc easedby0.05°,wi ha450 imepe s epo e a angeo 10–
90°.Then,di ac ionpa e nswe e eco deda 40mAand45kVin hecasesinwhichi was
necessa y,usingCuKα adia ion(λ=0.154nm).
2.4.Expe imen alPlan
To ul ill hescopeo  hewo kp e iouslyde ined, he ollowingexpe imen alplanwas
designed.Thewholeexpe imen al es swe edi idedin o womaing oupso expe imen s,
co esponding o hesamep e iousdi isionbe ween hejus i ica iono  he empe a u e ha me al
sphe escanachie eand hemeasu emen o  heai  empe a u ein he ixedbedpacking o 
es ima ing hepo en ialene gy eco e y.Table2shows he es spe o medinbo hs ages.The
objec i eo  he i s s agewas oco e all hepossibili ies ega dingme alsphe esdiame e sand
mol enquan i y.Howe e , hedesigno  heseconds agewasaimed oacqui eda a o ene gy
eco e yes ima ion.All heexpe imen sincludedinTable2we econduc ed wice,ensu ing ha  he
esul sa e ep oduciblewi hano e allexpe imen ale o o ±2%.
Figu e 8. Fixed bed egene a o scheme.
The equa ions we e sol ed ollowing a s andalone pa h. Imposing ha Ts(x), Ts(x – “
∆
” x), and Ta
(x
−
“
∆
” x) a e known, i is possible o ob ain Ta(x) om Equa ion (1), as well as “
∆
” x om Equa ion (2).
2.3. Physicochemical Cha ac e iza ion
The physicochemical cha ac e iza ion was ca ied ou by means XRD analysis, model AXIOS
om Panaly ical. The 2
θ
angle was inc eased by 0.05
◦
, wi h a 450 ime pe s ep o e a ange o 10–90
◦
.
Then, di ac ion pa e ns we e eco ded a 40 mA and 45 kV in he cases in which i was necessa y,
using Cu Kα adia ion (λ=0.154 nm).
2.4. Expe imen al Plan
To ul ill he scope o he wo k p e iously de ined, he ollowing expe imen al plan was designed.
The whole expe imen al es s we e di ided in o wo main g oups o expe imen s, co esponding o he
same p e ious di ision be ween he jus i ica ion o he empe a u e ha me al sphe es can achie e and
he measu emen o he ai empe a u e in he ixed bed packing o es ima ing he po en ial ene gy
eco e y. Table 2shows he es s pe o med in bo h s ages. The objec i e o he i s s age was o
co e all he possibili ies ega ding me al sphe es diame e s and mol en quan i y. Howe e , he design
o he second s age was aimed o acqui e da a o ene gy eco e y es ima ion. All he expe imen s
included in Table 2we e conduc ed wice, ensu ing ha he esul s a e ep oducible wi h an o e all
expe imen al e o o ±2%.
P ocesses 2020,8, 1590 16 o 20
3.4. Po en ial Use o he Ene gy Reco e ed in he Regene a o in he Manu ac u e o Syn he ic Slags
A possible i eous ma e ial p oduc ion scheme could co espond o a ypical clinke manu ac u ing
p ocess [
31
], in which, a e he o a y kiln, an o en is included whe e he comple e usion o he
ma e ial occu s. The p ocess would consis o a p ehea e , in which pa o he calcina ion eac ions
would occu ; a o a y kiln, in which he deca bona ion o he ma e ial would be inished and ha
would ake he ma e ial o 1300
◦
C; and inally, a mel ing o e e be a ing u nace, whe e he ma e ial
ha a i es om he o a y kiln would be mol en and hea up o 1500
◦
C o gua an ee i s luidi y.
A e mel ing, he ma e ial would be cooled quickly in he ixed bed o me al sphe es o achie e he
desi ed i eous p ope ies.
To con i m he p oposed p oduc ion p ocess, an XRD analysis o he mixed ma e ial was pe o med
in he p opo ions indica ed in Sec ion 2.1 and hea ed o empe a u es p io o he mel ing poin
(1250–1280
◦
C). As shown in Figu e 16 in which he XRD esul s a e p esen ed, a hose empe a u es,
c ys alline phases appea simila o hose ha occu in he clinke iza ion p ocess (C2S—Dicalcium
Silica e, C3S—T icalcium Alumina e, C3A—T icalcium Silica e, CAF—Te acalcium Alumino e i e).
P ocesses2020,8,xFORPEERREVIEW17o 21
poin (1250–1280°C).AsshowninFigu e16inwhich heXRD esul sa ep esen ed,a  hose
empe a u es,c ys allinephasesappea simila  o hose ha occu in heclinke iza ionp ocess
(C2S—DicalciumSilica e,C3S—T icalciumAlumina e,C3A—T icalciumSilica e,CAF—
Te acalciumAlumino e i e).

Figu e16.Di ac og amwi hc ys allinephaseso  hewas emix u e(1250–1280°C).
The e o e,i canbeconcluded ha syn he icslagsha echa ac e is icsandmine alphases ha 
a e ypically oundin he awma e ialsusedin hemanu ac u eo  heclinke .Fu he mo e,i can
bea i med ha  heene gyconsump ion o i smanu ac u ewillbeo  hesameo de as ha 
consumedin hemanu ac u eo clinke .In hiscon ex , heene gy eco e edin he ixedbed
egene a o p esen edin hiswo kcouldbeusedasai a abou 350–400°C.Fo example,sa ingsin
uelconsump ioncouldoccu i  he egene a o ai s eamwasusedas hecombus ionai inle 
s eam.B oadly,i 10%highe  han heene gyconsump iono clinke p oduc ion(abou 3800kJ/kg
clinke [32])is akenasa e e ence o  heene gyconsump iono syn he icslags, he egene a o ’s
ai  lowcould esul inene gysa ingsin hemanu ac u eo syn he icslags ha couldbea ound
15%o  heene gyneeded o i sp oduc ion.
4.Conclusions
In hiswo k,ano elme hod o ene gy eco e y om hecooling–solidi ica ions ageo a
syn he icslagmanu ac u ingp ocesswassa is ac o ys udied.Thes udywase alua edbymeanso 
anexpe imen als udy ha wascomplemen edby heo e icalcalcula ions oclose heo e all
pe o mance.
Theexpe imen als agewasdi idedin o wodi e en ia edg oupo  es s.The i s g oupaimed
oob ain he empe a u e alueo  heme alsphe eswhen hemol enma e ialwaspou edo e 
hem.Thesecondexpe imen alwasca iedou  oe alua e heme alsphe es–ai  low empe a u e
p o ilesina eal ixedbed.Du ing heexpe imen al es s, hescopewas oanalyze he empe a u es
ob ainedin hecen e andon hesu aceo  heme alsphe es.Thanks o hisexpe imen als udy,i 
waspossible omeasu ea empe a u ein he angeo 295–410°Cin hecen e o  hesphe eand302–
482°Co e  hesu ace.Thus,i allowedse ingupa empe a u e alue o  hesecondexpe imen al
s age,whichconsequen lyallowed he heo e icalcalcula iono  heene gy eco e ype kgo mol en
slag.Mo eo e , hemol enma e ial ha waspou edo e  heme alsphe eswasanalyzedbymeans
o XRD,and he o ma iono  hecha ac e is ic i eousphasewas e i ied.
Themainpu poseo  he heo e icalapp oachwas oachie ea ixedbed egene a o heigh ,
whichp o ed ha  hep ocessis iableindus ially.Tomee  hisend,hwasp e iouslyes ima ed
wi h hehelpo  he aluesob ainedin hesecondexpe imen als age.The ixedbedheigh calcula ed
p o ed obeindus iallyachie able.Once hepo en ialindus ial ixedbedheigh wasob ainedand
Figu e 16. Di ac og am wi h c ys alline phases o he was e mix u e (1250–1280 ◦C).
The e o e, i can be concluded ha syn he ic slags ha e cha ac e is ics and mine al phases ha
a e ypically ound in he aw ma e ials used in he manu ac u e o he clinke . Fu he mo e, i can be
a i med ha he ene gy consump ion o i s manu ac u e will be o he same o de as ha consumed in
he manu ac u e o clinke . In his con ex , he ene gy eco e ed in he ixed bed egene a o p esen ed
in his wo k could be used as ai a abou 350–400
◦
C. Fo example, sa ings in uel consump ion could
occu i he egene a o ai s eam was used as he combus ion ai inle s eam. B oadly, i 10% highe
han he ene gy consump ion o clinke p oduc ion (abou 3800 kJ/kg clinke [
32
]) is aken as a e e ence
o he ene gy consump ion o syn he ic slags, he egene a o ’s ai low could esul in ene gy sa ings
in he manu ac u e o syn he ic slags ha could be a ound 15% o he ene gy needed o i s p oduc ion.
4. Conclusions
In his wo k, a no el me hod o ene gy eco e y om he cooling–solidi ica ion s age o a
syn he ic slag manu ac u ing p ocess was sa is ac o y s udied. The s udy was e alua ed by means o an
expe imen al s udy ha was complemen ed by heo e ical calcula ions o close he o e all pe o mance.
The expe imen al s age was di ided in o wo di e en ia ed g oup o es s. The i s g oup aimed
o ob ain he empe a u e alue o he me al sphe es when he mol en ma e ial was pou ed o e
hem. The second expe imen al was ca ied ou o e alua e he me al sphe es–ai low empe a u e
p o iles in a eal ixed bed. Du ing he expe imen al es s, he scope was o analyze he empe a u es
ob ained in he cen e and on he su ace o he me al sphe es. Thanks o his expe imen al s udy, i was

P ocesses 2020,8, 1590 17 o 20
possible o measu e a empe a u e in he ange o 295–410
◦
C in he cen e o he sphe e and
302–482 ◦C
o e he su ace. Thus, i allowed se ing up a empe a u e alue o he second expe imen al s age,
which consequen ly allowed he heo e ical calcula ion o he ene gy eco e y pe kg o mol en slag.
Mo eo e , he mol en ma e ial ha was pou ed o e he me al sphe es was analyzed by means o XRD,
and he o ma ion o he cha ac e is ic i eous phase was e i ied.
The main pu pose o he heo e ical app oach was o achie e a ixed bed egene a o heigh ,
which p o ed ha he p ocess is iable indus ially. To mee his end, h was p e iously es ima ed
wi h he help o he alues ob ained in he second expe imen al s age. The ixed bed heigh calcula ed
p o ed o be indus ially achie able. Once he po en ial indus ial ixed bed heigh was ob ained and
analyzed as easible, he ene gy eco e y pe kg o mol en ma e ial was es ima ed. We es ima ed
ha be ween 325 and 550 kJ/kg o mol en ma e ial could be eco e ed, which is 15% o he ene gy
consump ion in syn he ic slag manu ac u ing p ocess.
O e all, he esul s ob ained con i med he po en ial o ou p oposal o ene gy eco e y om he
cooling–solidi ica ion s age o syn he ic slag manu ac u ing. Ou wo k he ein s udied p o ed o be o
g ea in e es o he indus ial scale. The ene gy eco e y o high-ene gy consump ions indus ies is
one o he key poin s o achie e a mo e sus ainable indus ial model.
Au ho Con ibu ions:
Concep ualiza ion, L.F.V., B.N. and M.R.-G.; me hodology, M.R.-G., F.M.B.-M.; so wa e,
M.R.-G., F.M.B.-M.; alida ion, M.R.-G., F.M.B.-M.; o mal analysis, F.M.B.-M.; in es iga ion, L.F.V., B.N., M.R.-G.,
F.M.B.-M.; esou ces, L.F.V., B.N.; da a cu a ion, M.R.-G.; w i ing—o iginal d a p epa a ion, L.F.V., F.M.B.-M.;
w i ing— e iew and edi ing, L.F.V., M.R.-G., F.M.B.-M.; isualiza ion, M.R.-G., F.M.B.-M., X.X.; supe ision, L.F.V.,
F.M.B.-M.; p ojec adminis a ion, L.F.V., B.N.; unding acquisi ion, L.F.V., B.N. All au ho s ha e ead and ag eed
o he published e sion o he manusc ip .
Funding:
This wo k was suppo ed by Uni e si y o Se ille h ough V PPIT-US. Financial suppo o his wo k
was also p o ided by MAVIT p ojec (FEDER-INNTERCONECTA).
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Abb e ia ions
mmmol en mass
mssphe es mass
Tsi sphe es empe a u e inle
Tso sphe es empe a u e ou le
Tai ai empe a u e inle
Tao ai empe a u e ou le
Ts sphe es empe a u e
Ta ai empe a u e
H ixed bed egene a o heigh
D ixed bed egene a o diame e
h con ec i e hea ans e coe icien
h0con ec i e hea ans e coe icien a ia ion
Cs sphe es calo i ic alue
Ca ai calo i ic alue
A(“∆” x) ans e a ea me al sphe es–ai
Appendix A
Exis ing models o he mal egene a o s equi e a e y igo ous adjus men o a ious pa ame e s such
as speed, Reynolds numbe , P and l numbe , o he cha ac e is ic diame e o he sphe es. In addi ion, when
conside ing he balance equa ions ha allow de e mining he beha io o he equipmen , i is necessa y o
sol e a nonlinea equa ion sys em ha equi es app oxima e nume ical echniques o i s esolu ion. Howe e ,
semi-empi ical bed models a e usually esol ed unde he conside a ion ha he sphe e in e nal esis ance is
negligible o hea conduc ion [
33
]. This hypo hesis allows easily es ima ing he cooling empe a u e along he
ixed bed wi h an exponen ially unc ion as ollows (Equa ion (A1)):
T( ) = T∞+ (Ti−T∞)·e
−h
ρs·cs·Dp· (A1)
P ocesses 2020,8, 1590 18 o 20
whe e T( ) is he sphe e empe a u e a ime (
◦
C); T is he ambien empe a u e ha su ounds he sphe e (
◦
C); T
i
is he sphe e empe a u e in =0 (
◦
C);
ρs
is he sphe e densi y (kg/m
3
); c
s
is he speci ic hea o he sphe e (J/kg
·
K);
h is he con ec i e hea ans e coe icien by solid–ai con ec ion (W/m
2·
K); and D
p
is he sphe e diame e (m).
A a cons an descen a e o he sphe es along he ixed bed and in a s eady s a e, Equa ion (1) can be
exp essed as ollows (Equa ion (A2)):
T(x) = A(x) + B(x)·eC(x). (A2)
Thus, o a coo dina e x in he bed, T(x) is he empe a u e o he sphe es; A(x) is he empe a u e o he
ai su ounding he sphe es inside he bed; B(x) is a cons an unc ion o A(x); and C(x) has he exp ession he
ollowing exp ession (Equa ion (A3)):
C(x)=h0(x)
ρs·cs·Dp(A3)
whe e h
0
(x) is he con ec i e hea ans e coe icien a coo dina e x. Since
ρs
, c
s
, and D
p
a e cons an , i can
be a i med ha C(x) only depends on h
0
(x). This allows inding exp essions ha explain he a ia ion o h
0
(x)
knowing he empe a u es o he sphe e and he su ounding ai . Fu he mo e, h
0
(x) depends on bo h ai
p ope ies– low condi ions and he geome y o he me al sphe es o he bed.
S ic ly, he h coe icien should be calcula ed unde a comple e expe imen al design in a s eady s a e o
he empe a u es o he sphe es and a ying he ollowing pa ame e s: Reynolds numbe (Re), P and l numbe
(P ), and sphe e diame e o bed diame e a io. Ne e heless, due o he es ima i e pu poses o his wo k, he
calcula ion o h
0
(x) was done wi h a ixed bed o me al sphe es simila o he one shown in Figu e A1. In his
sys em, he ollowing pa ame e s we e measu ed: he empe a u e o he sphe es (T
s
) and he ai empe a u es a
he inle and ou le o he bed (Tai and Tao, espec i ely), as well as he mass ai low.
P ocesses 2020, 8, x FOR PEER REVIEW 19 o 21
T󰇛x󰇜=A(x)+B(x)·eC(x). (A2)
Thus, o a coo dina e x in he bed, T(x) is he empe a u e o he sphe es; A(x) is he empe a u e
o he ai su ounding he sphe es inside he bed; B(x) is a cons an unc ion o A(x); and C(x) has he
exp ession he ollowing exp ession (Equa ion (A3)):
C󰇛x󰇜=h’(x)
ρs·cs·Dp (A3)
whe e h’(x) is he con ec i e hea ans e coe icien a coo dina e x. Since ρs, cs, and Dp a e cons an ,
i can be a i med ha C(x) only depends on h’(x). This allows inding exp essions ha explain he
a ia ion o h’(x) knowing he empe a u es o he sphe e and he su ounding ai . Fu he mo e, h’(x)
depends on bo h ai p ope ies– low condi ions and he geome y o he me al sphe es o he bed.
S ic ly, he h coe icien should be calcula ed unde a comple e expe imen al design in a s eady
s a e o he empe a u es o he sphe es and a ying he ollowing pa ame e s: Reynolds numbe
(Re), P and l numbe (P ), and sphe e diame e o bed diame e a io. Ne e heless, due o he
es ima i e pu poses o his wo k, he calcula ion o h’(x) was done wi h a ixed bed o me al sphe es
simila o he one shown in Figu e A1. In his sys em, he ollowing pa ame e s we e measu ed: he
empe a u e o he sphe es (Ts) and he ai empe a u es a he inle and ou le o he bed (Tai and Tao,
espec i ely), as well as he mass ai low.
Figu e A1. Scheme o he expe imen al sys em used o es ima e h’(x).
Wi h his sys em, he ene gy ans e balance o a ime o expe imen a ion app oxima es he
exp ession indica ed by Equa ion (A4):
h’·A·󰇛T

S-T

a󰇜=m·cg·󰇛T

ai-T

ao󰇜. (A4)
whe e h’ is he con ec i e hea ans e coe icien (W/m2·K); A is he ans e a ea (m2); T
s is he
a e age sphe es empe a u e in he expe imen a ion ime (°C); T
a is he a e age empe a u e
be ween he inle ai and ou le ai in he expe imen a ion ime (°C); T
ao is he a e age ou le ai
empe a u e in he expe imen a ion ime (°C); T
ai is he a e age inle ai empe a u e in he
expe imen a ion ime (°C); ma is he inle ai mass low (kg/s); and Cg is he ai -speci ic hea
(J/kg·K).
Re e ences
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empe a u e PCM-based he mal ene gy s o age o indus ial u naces ins alled in ene gy-in ensi e
indus ies. Ene gy 2019, 173, 1030–1040, doi:10.1016/j.ene gy.2019.02.118.
2. Baena-Mo eno, F.M.; Rod íguez-Galán, M.; Vega, F.; Reina, T.R.; Vilches, L.F.; Na a e e, B. Regene a ion
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ca bona e: An expe imen al in luence s udy o eac ion pa ame e s. P ocesses 2018, 6, 205,
doi:10.3390/p 6110205.
Figu e A1. Scheme o he expe imen al sys em used o es ima e h0(x).
Wi h his sys em, he ene gy ans e balance o a ime o expe imen a ion app oxima es he exp ession
indica ed by Equa ion (A4):
h0·A·TS−Ta=ma·cg·Tai −Tao(A4)
whe e h
0
is he con ec i e hea ans e coe icien (W/m
2·
K); A is he ans e a ea (m
2
);
Ts
is he a e age sphe es
empe a u e in he expe imen a ion ime (
◦
C);
Ta
is he a e age empe a u e be ween he inle ai and ou le ai
in he expe imen a ion ime (
◦
C);
Tao
is he a e age ou le ai empe a u e in he expe imen a ion ime (
◦
C);
Tai
is he a e age inle ai empe a u e in he expe imen a ion ime (
◦
C);
ma
is he inle ai mass low (kg/s); and C
g
is he ai -speci ic hea (J/kg·K).
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