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Op imized syn hesis/design o he ca bona o side o di ec in eg a ion o
he mochemical ene gy s o age in small size Concen a ed Sola Powe
U. Tesio
a,⁎
, E. Guelpa
a
, C. O iz
b
, R. Chaca egui
c
, V. Ve da
a
a
Ene gy Depa men , Poli ecnico di To ino, Tu in, I aly
b
Facul ad de Física, Uni e sidad de Se illa, A enida Reina Me cedes s/n, 41012 Se illa, Spain
c
Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa, Camino de los descub imien os s/n, 41092 Se illa, Spain
ARTICLE INFO
Keywo ds:
Concen a ed Sola Powe
Calcium-Looping
HEATSEP
B ay on cycle
Long e m ene gy s o age
ABSTRACT
Two o he mos a ac i e cha ac e is ics o Concen a ed Sola Powe a e he high-quali y hea exploi able and
i s capaci y o he mal ene gy s o age, which enhance he ene gy dispa chabili y in compa ison wi h o he
enewable sou ces such as pho o ol aics o wind. Consis en e o s a e he e o e di ec o he esea ch o sui-
able he modynamic cycles and ene gy s o age sys ems wi h low he mal losses and high ope a ing empe a-
u es. Howe e , in he mos de eloped echnologies, based on sensible and la en hea s o age, high he mal
losses a e he di ec consequence o high ope a ing empe a u es. As al e na i e, The mochemical Ene gy
S o age sys ems a e gaining a en ion in he las yea s.
The p esen wo k in es iga es he adop ion o a no el Calcium-Looping sys em o The mochemical Ene gy
S o age, ocusing on he in eg a ion on ca bona o side. This key in eg a ion is di ec ly linked o he ene gy
deli e y om he ene gy s o age sys em and he e o e powe gene a ion capaci y o he plan . An op imiza ion
o he ca bona o side plan is pe o med o a di ec in eg a ion layou , whe e ca bon dioxide om he ca -
bona o e ol es h ough he powe block. This analysis aims o maximize he sys em e iciency ac ing bo h on
he p ocess componen s ope a ion and on he he mal ans e be ween he in ol ed s eams. The op imiza ion
elies on a no el me hod based on a gene ic algo i hm. The pinch analysis is adop ed o his s udy and p ope
cons ain s a e p o ided o ob ain a con igu a ion exploi ing only he enewable ene gy sou ce. A mul i-ob-
jec i e op imiza ion is pe o med o ind ou he hea exchange ne wo k opology changes ha occu o di -
e en ope a ing condi ions and de i ed om his analysis sugges ion o sys ems in eg a ion a e p o ided.
1. In oduc ion
The numbe o Concen a ed Sola Powe (CSP) plan s unde -de-
elopmen [1], he o al capaci y o ecas s o he nex ew yea s and
he expec ed alling cos s (wi h a consequen Le elized Cos O Elec-
ici y dec ease) [2] show he g ea in e es and po en ial o Con-
cen a ed Sola Powe plan s. The possibili y o exploi high empe a-
u es and, he e o e, he a ailabili y o high-quali y hea , is one o he
cha ac e is ics o his echnology. Dispa chabili y in enewable ene gy
plan s is a majo issue o be imp o e in nex yea s o o e come he
inhe en in e mi ency o he sou ces [3]. Mo eo e , he mal ene gy
s o age is undamen al o main ain a cons an elec ical p oduc ion, o
a oid a plan o e sizing and o keep he ope a ing condi ions as close as
possible o he nominal con igu a ion. Among he di e en ene gy
s o age echnologies in CSP plan s [4], The mochemical Ene gy S o age
(TCES) based on Calcium Looping, is one o he mos p omising
al e na i es [5,6] due o a high ene gy s o age densi y and a po en ially
highe maximum empe a u e in he powe cycle because o he high
eac ions empe a u e [7]. O he consis en ad an ages ela ed o Cal-
cium-Looping (CaL) TCES a e: i) a low cos ma e ial in ol ed by he
p ocess (< 10 €/ on [8]); ii) educed cos o he TCES i sel as i is
based on well-known equipmen a indus ial scale (excep ing he sola
pa icle ecei e ) [9]; iii) negligible he mal losses du ing he s o age
pe iod ( essels a e kep a ambien empe a u e) and he e o e he
possibili y o long e m ene gy s o age [10]. All hese conside a ions
con ibu ed o s a up he Eu opean p ojec SOCRATCES [11], whose
aim is o demons a e (bo h heo e ically and on a p o o ype scale) he
easibili y o a Calcium-Looping in eg a ion in a CSP plan .
Sui able powe blocks o he ene gy p oduc ion in he CSP ield a e
p oposed in [12–14]; he mos common al e na i es a e Rankine cycles,
in eg a ed wi h mol en sal s s o age, and CO
2
B ay on cycles, wi h
hea ing di ec ly pe o med a he ecei e . In his wo k a speci ic
h ps://doi.o g/10.1016/j.ecmx.2019.100025
Recei ed 26 July 2019; Recei ed in e ised o m 12 Oc obe 2019; Accep ed 14 Oc obe 2019
⁎
Co esponding au ho .
E-mail add ess: [email p o ec ed] (U. Tesio).
Ene gy Con e sion and Managemen : X 4 (2019) 100025
A ailable online 21 Oc obe 2019
2590-1745/ © 2019 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/BY-NC-ND/4.0/).
T
analysis o he in eg a ion o he CaL p ocess is pe o med ocused on
he in eg a ion o he ca bona o , he eac o whe e he s o age ene gy
is elease o he powe cycle. Fig. 1 shows a concep ual scheme o he
CSP-CaL in eg a ion; e y b ie ly, he s o ed CaCO
3
is p ehea ed and
sen o he calcine , whe e, abso bing he sola adia ion (φ
sol
), is
con e ed in o CaO and CO
2
, which a e cooled down and sen o hei
s o ages. Being s o ed a high p essu e, he CO
2
is comp essed and
again cooled. Fo he discha ge phase i is hea ed up, expanded and
mixed wi h a eci cula ed s eam; hen, bo h he CaO and he CO
2
a e
p ehea ed and en e he ca bona o . The solid s eam exi ing he eac o
is b ough o he s o age condi ions, while he gaseous low is ex-
panded, cooled down and comp essed in o de o be eci cula ed.
The e a e wo di e en ways o design he ca bona o -powe cycle
in eg a ion: i) by using he CO
2
s eam exi ing he ca bona o as
wo king luid o powe p oduc ion o ii) h ough an indi ec in eg a-
ion based on a sepa a e he modynamic cycle ed by a he mal e-
co e y pe o med on he ca bona ion p oduc s. A deep in es iga ion
abou he o me al e na i e is conduc ed in [15], he expansion o he
CO
2
ex ac ed om he s o age is he mally coupled wi h he
comp ession o he CO
2
eci cula ed om he ca bona o in o de o
maximize he expansion wo k and minimize he comp ession abso p-
ion espec i ely. In [16] is p oposed a di ec CaL in eg a ion wi h an
ai /CO
2
open cycle showing high pe o mances and a simple layou bu
whose ope a ion de e mines he elease o he a mosphe e o an e -
luen gas no CO
2
- ee; he impo ance o he hea eco e y bo h o he
cha ging and discha ging phase o his con igu a ion is demons a ed in
[17]. A de ailed s udy pe o med in [18] compa es he pe o mances o
bo h di ec in eg a ion wi h closed CO2 cycle and he indi ec in-
eg a ion o some sui able powe blocks (Rankine cycle, SCO2 B ay on
cycle and combined cycle). An al e na i e CaL layou is in es iga ed in
[19], whe e he ene gy s o age occu s a high empe a u e o simpli y
he p ocess in eg a ion scheme. Simila o his las con igu a ion, bu
wi h a mo e complex design, in [20] is analyzed he choice o a di ec
(closed CO
2
loop) o indi ec (Rankine cycle) in eg a ion in se ies wi h
an O ganic Rankine Cycle (ORC) o he low- empe a u e hea e-
co e y. Fu he mo e, a s udy o he adop ion o a CaL di ec in eg a-
ion o he s o age o ene gy p oduced by pho o ol aic (PV) is pe -
o med in [21], demons a ing a signi ican ly lowe plan in es men
Nomencla u e
CaCO
3
Calcium ca bona e
CaO Calcium oxide
CO
2
Ca bon dioxide
EI Excess index
h Speci ic en halpy, kJ/kg
m
Mass low a e, kg/s
M Mixe
MC Main comp esso
MT Main u bine
n
Numbe o moles
P P essu e, ba
ST S o age u bine
T Tempe a u e, K
U Global hea ans e coe icien , kW/(m
2
*K)
X CaO con e sion
W
Powe lux, kW
Abb e ia ions
CaL Calcium-Looping
CCS Ca bon Cap u e and S o age
CIP Comp esso inle p essu e, ba
CIT Comp esso inle empe a u e, K
COP Comp esso ou le p essu e, ba
COT Comp esso ou le empe a u e, K
CSP Concen a ed Sola Powe
HEN Hea Exchange s Ne wo k
HEX Hea exchange
LCOE Le elized Cos O Elec ici y
ORC O ganic Rankine Cycle
TIP Tu bine inle p essu e, ba
TIT Tu bine inle empe a u e, K
TOP Tu bine ou le p essu e, ba
TOT Tu bine ou le empe a u e, K
G eek le e s
Δ Del a
β P essu e a io
ηCa bona o side e iciency
φ The mal lux, kW
Subsc ip s and supe sc ip s
0 s anda d condi ions
amb ambien
ca b ca bona o
s oic el
in inle
lm loga i hmic mean
mix mixed
ou ou le
pp pinch poin
eac ion
ec eci cula ed
s oic s oichiome ic
s o s o age
un un eac ed
Fig. 1. CaL di ec in eg a ion essen ial schema ic.
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
2
cos when compa ed o ba e ies. Mos o hese wo ks a e summed up in
[8], whe e he di e en layou s a e compa ed bo h in e ms o e i-
ciency and cha ac e is ics.
Howe e , in he analysis pe o med in hese wo ks a e p esen some
d awbacks: in some cases he CaL in eg a ion is no op imized, he CO
2
comp ession/expansion s ages become pa icula ly complex (up o 8
in e coolings/ ehea ings), he use o hea e s does no allow o ope a e
wi h a comple ely enewable ene gy sou ce o a poo numbe o a i-
ables is assumed in he op imiza ion p ocess. The aim o his wo k is o
in es iga e he p omising applica ion o he CaL di ec in eg a ion in a
cen al owe CSP plan based on an inno a i e me hod which applies
he pinch analysis [22] o he syn hesis o an op imized design in
which he men ioned issues a e sol ed. In his no el me hodology, plan
e iciency maximiza ion is a ained h ough he simul aneous op imi-
za ion o bo h he hea exchange and componen s pe o mance. Main
no el ies and con ibu ions o his pape a e: 1) a ull op imiza ion
amewo k, he HEATSEP [23] (desc ibed in Sec ion 3), which is ap-
plied o he i s ime o he syn hesis/design o he discha ge sec ion
o he CaL-CSP plan , allowing o pe o m an op imiza ion o all he
independen a iables o he p ocess; 2) unlike he adi ional in-
es iga ions pe o med wi h he HEATSEP me hod, whe e he analysis
ends wi h he calcula ion o he he mal in eg a ion cu es and he Hea
Exchange Ne wo k (HEN) emains he e o e unknown, in he p esen
wo k he HEN is designed o he op imized con igu a ion and he
conside a ions made o his layou a e exploi ed in he un o a second
op imiza ion, p o iding a u he imp o ed design; 3) a mul i-objec i e
op imiza ion is pe o med in o de o in es iga e he possible ade-o
be ween he plan pe o mances and i s hea eco e y sys em com-
plexi y and size, p oposing a no el app oach o he adi ional
HEATSEP me hod, in which he HEN s i ness is no aken in o accoun ;
and 4) a 100% enewable ex e nal hea ing equi emen is imposed in
he analysis hus ob aining con igu a ions which ully exploi he sola
esou ce.
The pape is s uc u ed as ollows:
•Sec ion 2: he mos impo an aspec s and cha ac e is ics ela ed o
he CaL di ec in eg a ion a e discussed;
•Sec ion 3: he plan simula ion and op imiza ion a e explained;
•Sec ion 4: he ene gy op imiza ion esul s a e epo ed and com-
men ed;
•Sec ion 5: he mul i-objec i e op imiza ion is pe o med in;
•Sec ion 6: some sugges ions o he plan layou imp o emen a e
p o ided;
•Sec ion 7: some conside a ions wi h a mo e gene al ex en a e ex-
posed;
•Sec ion 8: pa ag aph dedica ed o he analysis conclusions.
2. Case s udy
As p esen ed in [18], he di ec in eg a ion is one o he mos in-
e es ing al e na i es o CSP powe p oduc ion be ween he CaL in-
eg a ion al e na i es: i shows an excellen pe o mance, he bes be-
ween he o he in es iga ed cycles, and i s layou is ela i ely simple i
compa ed o he indi ec in eg a ions, in ol ing a educed numbe o
componen s, mos o hem well-known a indus ial scale. In he cal-
cine side, a e a p ehea ing p ocess, he solid s eam made o bo h
CaCO
3
and un eac ed CaO en e s he calcine eac o . Unde pu e CO
2
a mosphe e, calcina ion empe a u e has o be a ound
930–950 °C o
ensu e comple e calcina ion in sho esidence imes [24]. Lowe cal-
cina ion empe a u es a e needed by pe o ming he calcina ion unde
He o s eam [25–27], al hough in his case he ene gy penal y could be
highe due he sepa a ion p ocess ene gy consump ion. A e calcina-
ion, CO
2
and CaO a e cooled down and sen o hei s o age essels. To
manage he s o age anks size, CO
2
is comp essed up o i s design
p essu e o 75 ba [18,19] and [28] and, in o de o minimize he
comp ession wo k equi ed, one o mo e in e cooling s eps should be
included. Anyway, as explained u he on, he ca bon dioxide will be
e-expanded and pa o he ene gy p e iously consumed is eco e ed,
educing conside ably he ene ge ic penal y b ough by i s comp ession
[15]. Due he s o age s ep, he calcine and ca bona o sides wo k in-
dependen ly and he e o e he layou can be op imized sepa a ely.
In he CaL discha ge p ocess, CO
2
is ex ac ed om he s o age ank,
hea ed and expanded up o he ca bona o ope a ing p essu e. E en in
his case, in o de o maximize he expansion wo k, can be added one o
mo e ehea ing s eps. The o he eac an , he CaO, is p ehea ed and sen
o he eac o o p oduce calcium ca bona e acco ding he exo he mal
ca bona ion eac ion. A e ca bona ion, solids a e sepa a ed om he
gaseous s eam and he CO
2
is expanded in he main u bine; hen,
sensible hea is eco e ed om bo h CO
2
and solids s eams. Finally, he
ca bon dioxide is comp essed and eci cula ed inside he p ocess, while
he CaCO
3
and he un eac ed CaO a e sen o s o age essels.
Bo h in he calcine and ca bona o side is equi ed o mo e he
solid s eams a high empe a u e en e ing o exi ing he chemical e-
ac o s. This can be done by sc ew con eyo s as p oposed by [28] and
demons a ed in p ac ice by he Ca ina Eu opean P ojec [29] and [30];
u he mo e, he same echnology bu wi h a e ical con igu a ion can
be exploi ed as solid ele a o [31].
Two o he main pa ame e s ha ha e a pa icula in luence on he
en i e CaL p ocess a e he CaO con e sion (X) and he CO
2
excess index
(EI). CaO con e sion (also e e ed as CaO ac i i y o eac i i y) is
de ined as he mass a io be ween he calcium oxide ha pa icipa es
ac i ely o he ca bona ion eac ion and he o al amoun en e ing he
eac o ; his e m is de ined because, in eal ope a ion condi ions, CaL
p ocess is no comple ely e e sible [32]. A e a ew cycles, mul icyclic
CaO deac i a ion decays up o each a esidual alue, which is highly
dependen on he eac o condi ions, he pa icle size and he CaO
p ecu so s used [8]. CO
2
excess index exp esses he su plus o ca bon
dioxide ha is sen o he ca bona o in o de o con ol he ope a ing
empe a u e. I is de ined as he a io be ween he o al amoun o CO
2
p o ided o he s oichiome ic alue.
=Xn
n
CaO eac ed
CaOp o ided
(1)
=EI m
m
CO p o ided
CO s oich
2
2
(2)
Fo he pu poses o his wo k, a small/medium size plan is ana-
lyzed, so, he ne powe ou pu in co espondence o he main sha
(main u bine, main comp esso and gene a o ) is se o 1MWe.
The e o e, wi h his powe plan size, a educed complexi y layou is
conside ed, wi h di e ences om some wo ks ound in li e a u e o
la ge plan s [18,33], whe e mul iple s ages o in e cooling and e-
hea ing o espec i ely he main comp esso and he s o age u bine
a e sugges ed. In he p esen wo k, he p ocesses o comp ession and
expansion a e pe o med in a single s ep, allowing o ob ain a mo e
essen ial layou . The minimum achie able p essu e a he main u bine
ou le is se o 1 ba ; in ac , acco ding o [15] and [19], a oiding op-
e a ion unde acuum condi ions leads he plan o ope a e unde no
pa icula ly demanding condi ions and bo h he pipelines and u bo-
machine y dimensions a e no excessi ely penalized. This assump ion
b ings o ano he bene i , since any e en ual ai in il a ion (due o non-
ideal sealings) is consequen ly elimina ed.
The objec i e unc ion assumed o he op imiza ion p ocess is he
ca bona o side e iciency, which is de ined as ollows
= =
W
Q
W
m X h· ·
ca b
ne el
ca b
ne el
CaO
, ,
0
(3)
whe e
mCaO
is he CaO mass low a e en e ing he ca bona o , X is he
CaO con e sion and he ne elec ic powe p oduc ion (
W
ne el,
) includes
he con ibu ion o main u bine, main comp esso , s o age u bine and
auxilia ies ( o hea ejec ion and solid con eying). This analysis does
no include o he aspec s ela ed o he comple e CaL in eg a ion such
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
3
as he calcine side e iciency and he elec ici y consumed o he
comp ession o he ca bon dioxide up o he s o age condi ions. So,
being e e ed o only a plan po ion, o he aims o his s udy he
ca bona o side e iciency is su icien o pe o m a cohe en compa -
ison o he TCES discha ge p ocess, di e en ly om [15,18] and [33],
whe e he en i e p ocess is simula ed and he e iciency mus be
he e o e de ined di e en ly.
The choice o he op imiza ion s uc u e is made in acco dance wi h
he objec i e o ob aining a con igu a ion wi h he highes achie able
e iciency o he case in which he sola adia ion is he only ex e nal
hea sou ce. In o de o op imize he plan ope a ing condi ions is e-
qui ed a layou composed by p ocess componen s ( u bines, com-
p esso s and chemical eac o s) and by a sui able hea eco e y sys em
o he eac an s p ehea ing and he cooling equi ed o each he s o-
age condi ions. To ensu e he op imum ca bona o side con igu a ion
is no possible jus analysing a speci ic HEN om a pinch analysis bu
also adop ing an op imiza ion s age able o maximize simul aneously
he p ocess ope a ion and he hea exchange s ne wo k.
3. Model desc ip ion/me hodology
Acco ding o he op imiza ion c i e ia p e iously exposed, he
me hodology ha seems o be he mos sui able o he p esen wo k is
he HEATSEP me hod, which is exhaus i ely explained and applied o
ene gy p oblems (powe cycles, combined hea and powe , indus ial
p ocesses, hea eco e y, e c.) in [34–36]. Ve y b ie ly, his me hod
ackles sepa a ely he he mal powe exchange and he o he p ocesses
in which he plan s eams a e in ol ed; his is made possible wi h he
( i ual) subs i u ion o all he hea exchange s wi h a single “black
box” in which any luid is ee o ans e he mal powe wi h he o he
ones. The simula ion o his ic i ious elemen is based on he pinch
analysis. In his way i is possible o pe o m he ene gy plan op imi-
za ion wi hou p o iding a speci ic HEN o he en i e execu ion o he
p ocess and lea ing he hea exchange s de ini ion o he pos p oces-
sing phase.
The e o e, a e he subs i u ion o any componen in ol ed in he
hea exchange wi h a co esponding “ he mal cu ”, a con igu a ion only
cons i u ed by p ocess componen s and he black box is ob ained, as
showed in Fig. 2 (whe e MT is he Main Tu bine, ST is he S o age
Tu bine, MC is he Main Comp esso and M is he Mixe ); he ope a ion
o his layou is op imized keeping he HEN unde ined up o he las
s age.
This ini ial s ep equi es o ake a i s decision: in co espondence
o he s eams en e ing and exi ing he mixe , he he mal cu s inse ion
can be execu ed in h ee di e en ways (shown in Fig. 3, whe e he
dashed lines ep esen s he inse ion o a he mal cu and he e o e a
hea exchange s ep). The i s al e na i e con ains he smalle numbe
o he mal cu s and he e o e in oduces he smalle numbe o hea
exchange p ocesses, in acco dance wi h he pu poses o simpli ying as
much as possible he plan layou .
Fu he mo e, in addi ion o he ype o analysis execu ed in he
wo ks ound in li e a u e abou he HEATSEP, an a emp o syn hesize
he op imum HEN is pe o med in he p esen pape .
All he da a assump ions o he componen s and he in ol ed
p ocesses a e summed up in Table 1; in addi ion, he mixed s eams o
CO
2
a e imposed o ha e he same p essu e and bo h he mixe and he
sepa a o p essu e losses a e neglec ed. The alues o hese pa ame e s
a e es ablished in acco dance o [18,19] and [37].
Rega ding he he mophysical p ope ies, he co ela ions in [38],
he SysCAD da abase [37] and he COOLPROP lib a y [39]a e used o
CaO, CaCO
3
and CO
2
espec i ely. Conce ning he componen s simu-
la ion, u bomachine y pe o mance is calcula ed h ough he isen-
opic e iciency, while he chemical eac o is simula ed wi h ene gy
balances adop ed in [18] and [37], in which he ac ion o calcium
oxide ha eac s wi h he ca bon dioxide is imposed. The s udy pe -
o med is he e o e 0-D (ze o-dimensional, i.e. componen ’s geome y is
no in es iga ed) and he eac o ype is no de ined since he analysis
o he eac ion kine ics is no one o he pu poses o he p esen wo k.
The successi e s ep es ablishes how he di e en plan pa ame e s
(p essu es, empe a u es and low a es) ha e o be handled wi hin he
op imiza ion p ocess, so, o i s he s o age physical condi ions a e
assumed as cons an . Then, a e a ca e ul e alua ion o all he pa a-
me e s in ol ed in he analyzed p ocess, a selec ion o es ablish he
op imiza ion e ms is made (i.e. he independen a iables o he p o-
blem) in o de o ob ain he maximum plan e iciency. They a e: CaO
ac i i y (X), ca bona o empe a u e (T
ca b
), ca bona o p essu e (P
ca b
),
main u bine p essu e a io (β
MT
), CO
2
empe a u e a he ca bona o
inle (T
CO2,in
), CaO empe a u e a he ca bona o inle (T
CaO,in
), main
comp esso inle empe a u e (CIT
MC
) and s o age u bine inle em-
pe a u e (TIT
ST
). Fu he mo e, some o hese layou pa ame e s mus
sa is y design, he mal o echnical cons ain s, such as he plan a ed
powe , he absence o an ex e nal hea ing need and he minimum
empe a u e achie able wi h he ex e nal cooling (see Table 2). A his
poin , s a ing om hese cons an e ms, independen a iables and
cons ain s, any o he physical quan i y can be calcula ed pe o ming
he componen s simula ion.
The a ia ion anges ( epo ed in Table 3) p o ided o he in-
dependen a iables ha e o be bo h physically and echnically easible,
so hey a e again se in acco dance o [18,19] and [37]. Rega ding he
ca bona o ope a ing empe a u e and p essu e, i is e i ied ha he
alues assumed (ma ked in g een in Fig. 4) a e espec ul o he lim-
i a ions de e mined by he equilib ium condi ions.
Once he p ocess componen s simula ion is comple ed and all he
p essu es, empe a u es and low a es a e calcula ed, i is possible o
execu e he pinch analysis on he s eams ha go ac oss he black box.
These lows in ol ed in hea ans e and hei ela i e da a a e e-
po ed in Table 4. The i h s eam, al hough lis ed be ween he cold
luids, is ac ually ee o become a ho o cold low, since no cons ain s
a e speci ied abou ha . This is es ablished in o de o a oid any lim-
i a ion on he pa ame e s space in which he op imal con igu a ion is
analyzed.
Taking in o accoun he a iables numbe , he p oblem cons ain s
and he expec ed i ness unc ion complexi y, he gene ic algo i hm is
chosen as op imiza ion me hod and i s execu ion is pe o med on
MATLAB so wa e. Fig. 5 shows wi h a low cha he s uc u e o he
comple e op imiza ion p ocess, which can be syn he ically desc ibed as
a pinch analysis nes ed in he e olu iona y algo i hm. The di e ence
be ween he me hod used in he p esen wo k and he simple pinch
Fig. 2. Ca bona o side layou o he op imiza ion based on he HEATSEP
me hod.
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
4
analysis (which is only able o op imize he he mal exchange) is ha
he physical condi ions o he s eams in ol ed in he hea ans e a e
con inuously changed du ing he p ocess, as a consequence o he u -
bomachine y ope a ion op imiza ion. The double le el a he whom he
op imiza ion is execu ed allows o ob ain a layou in which he powe
p oduc ion maximiza ion is eached in a comple e way.
Finally, in o de o p o e he e ec i eness o he me hod, andom
simula ions a e pe o med o obse e he pe o mance o a casual
con igu a ion, whose ope a ing condi ions a e no op imized; Fig. 6
shows ha mos o he simula ions ha e an e iciency be ween 3% and
13%, which is much below he op imized esul epo ed in he ol-
lowing sec ion.
Fig. 3. The mal cu s inse ion al e na i es in co espondence o he mixe .
Table 1
Da a assump ion o he main pa ame e s in ol ed in he p ocess.
Pa ame e Componen /s eam Value
The mal losses Ca bona o 1% o eac ion hea
S o age empe a u e (T
AMB
) CaO, CO
2
, CaCO
3
20 °C
S o age p essu e CO
2
s o age 75 ba
P essu e losses S oichiome ic CO
2
1%
Reci cula ed CO
2
4%
Mixed CO
2
6%
Isen opic e iciency MT 0.9
MC 0.87
ST 0.75
Mechanical and elec ical e iciency (MT + MC), ST 0.97
Solid con eying elec ical consump ion CaO, CaCO
3
s eams 10 kJ/(kg*100 m)
S o ages-ca bona o dis ance CaO, CaCO
3
s eams 100 m
Hea ejec ion elec ical consump ion Coole s 0.8% o hea
ejec ed
Minimum ΔT a pinch poin Hea exchange s 15 °C
Table 2
Op imiza ion p oblem’s cons ain s.
Pa ame e Componen /s eam Value
Ne powe p oduc ion MT + MC 1 MW
Ex e nal hea ing need Hea e s 0 MW
P
MIN
CO
2
CO
2
s eams 1 ba
T
MIN
cooling Coole s T
AMB
+ ΔT
pp
(T
CaO,in
)
MAX
CaO s eam T
CARB
− ΔT
pp
(T
CaCO3,in
)
MAX
CaCO
3
s eam T
CARB
− ΔT
pp
Table 3
Op imiza ion p oblem’s independen a iables wi h hei co esponding a ia-
ion ange.
Independen a iable Lowe bound Uppe bound
X 0.2 0.5
T
ca b
775 °C 875 °C
P
ca b
1.5 15
β
MT
1.2 14
TIT
ST
250 °C 650 °C
CIT
MC
T
AMB
+ ΔT
pp
300 °C
T
CaO,in
310 °C (T
CARB
)
MAX
− ΔT
pp
T
CO2,in
T
AMB
+ ΔT
pp
(T
CARB
)
MAX
− ΔT
pp
Fig. 4. Equilib ium condi ions as a unc ion o CO
2
pa ial p essu e and em-
pe a u e. The a ea in g een ep esen s he ca bona o ope a ing condi ions in-
es iga ed. (Fo in e p e a ion o he e e ences o colou in his igu e legend,
he eade is e e ed o he web e sion o his a icle.)
Table 4
P ocess lows condi ions p o ided o he pinch analysis.
S eam ype Flow a e T
IN
T
OUT
Ho CO
2
eci cula ed TOT
MT
CIT
MC
CaCO
3
+ CaO un eac ed T
ca b
T
s o age
Cold CO
2
s oichiome ic T
s o age
TIT
ST
CaO T
s o age
T
CaO,in
CO
2
mixed T
MIX,ou
T
CO2,in
Fig. 5. Op imiza ion s uc u e summed up in o m o low cha : op imiza ion
o p ocess componen s ope a ion in blue, hea ans e op imiza ion in ed. (Fo
in e p e a ion o he e e ences o colou in his igu e legend, he eade is
e e ed o he web e sion o his a icle.)
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
5

4. Resul s
In e ms o ene gy pe o mance, he ca bona o side op imal ope -
a ing condi ions show a well-de ined dependence on some o he
pa ame e s assumed as independen a iables o he p ocess. Fig. 7
shows he e ec o calcium oxide ac i i y. E iden bene i s a e en-
coun e ed wi h he educ ion o he ine ma e pa icipa ing o he
p ocess, so, o he es o his s udy, he case o X = 0.5 is e e ed as
e e ence case; his beha io is encoun e ed in any layou in which he
hea eco e y is p ope ly op imized, such as [15,18] and [19]. Re-
ma kably, he CaO ac i i y in a eal plan is highly dependen on he
p ocess condi ions, he pa icle size and he CaO p ecu so s [8]. Any
o he esul o he he mophysical pa ame e s and machine y powe s
a e gi en in Appendix A.
A cons an end is ound o he ca bona o ope a ing empe a u e
and o he main comp esso inle empe a u e: in he i s case he
maximum alue is always eached ( o maximize he main u bine
p oduc ion, as obse ed in [18;33]), while in he second case appea s o
be con enien o minimize his pa ame e in o de o educe he com-
p ession powe .
The op imal ca bona o p essu e eaches alues nea o 2.8 ba ,
which is no a pa icula ly demanding ope a ing condi ion and is si-
mila o he alue o 3.2 ba ob ained in [15] and [19]; a he same
ime, he main u bine p essu e a io ollows closely he P
ca b
end wi h
he aim o keep he main comp esso inle p essu e a ound he
minimum accep able alue o 1 ba . Excep o he s eam composi ion,
he main u bine ope a ion is no e y di e en wi h espec o he case
in which ope a es he u bogas indus y, which has by now eached an
ad anced s a e o de elopmen , so, implemen a ion o sui able CO
2
u bomachine y unde hese ope a ion condi ions seems easible.
Conce ning he s o age u bine, al hough eaching highe inle
empe a u e de e mines a highe powe p oduc ion, om he op imi-
za ion esul s i is obse ed ha his a iable con e ges o ela i ely
low alues and his phenomenon can be explained as ollowing: i s , as
i is well known om he exe gy analysis ield, i is always be e o mix
wo lows wi h equal (o simila ) empe a u es, so, he s o age u bine
(ST in Fig. 2) ou le empe a u e ends o each he main comp esso
ou le empe a u e. Second, hea ing up consis en ly he s oichiome ic
CO
2
inc eases he hea equi ed om he eac ion p oduc s, bu , being
his low a e ela i ely small, he bene i encoun e ed in he powe
p oduc ion does no jus i y his subs an ial hea ans e . The elec ici y
gene a ion is he e o e p e e ed o ake place on he main u bine.
Fig. 8a summa ize he p ocess componen s powe p oduc ion/abso p-
ion, while in Fig. 8b is epo ed he powe subdi ision ha akes place
in he plan ( he e m “O he losses” includes he ca bona o and
elec ic gene a o s losses); bo h a e o he e e ence case.
The powe consump ions ela ed o auxilia y cooling p ocess a e
nea ly negligible while he e m o he solid con eying is mo e con-
sis en (abou one o de o magni ude highe ) and shows a close de-
pendence on he calcium oxide ac i i y. The lowe is he CaO ac i i y,
he highe is he solids con eying powe consump ion because o he
con eying o ine . In addi ion, he main comp esso size a ises o be
abou one hal o he main u bine. Op imiza ion esul s show ha he
CO2 mass low a e en e ing he ca bona o is well in excess ega ding
he sc echiome ic amoun (EI
20, an in e media e alue wi h espec
o he esul s in [15;19]) as can be seen in he esul s shown in
Appendix A.
Conce ning he pinch analysis, he op imiza ion ou comes clea ly
demons a e he impo ance o an op imal hea eco e y.
As shown in Fig. 9b, pinch poin s a e ound a 725.5 °C and 123.5 °C.
I is wo h o no ice ha he pinch poin s a e loca ed in co espondence
o he inle empe a u e o wo s eams: he eci cula ed CO
2
and he
mixed CO
2
. This happens because he pa icipa ion o he he mal
ans e o hese lows de e mines a ema kable change in he cu es
slope, while hei dis ance be ween he pinch poin s is g an ed by he
pa ial p esence o he s oichiome ic ca bon dioxide, which allows he
di e gence abo e he lowe pinch poin and he con e gence below he
uppe one. Ano he ema kable aspec is ha , being he esul ing u -
bomachine y p essu e a io and inle /ou le empe a u es e y simila
o he di e en alues o CaO ac i i y, he pinch poin s occu s p ac-
ically a he same empe a u es and, wi h he excep ion o he egion
abo e he high- empe a u e pinch poin , he g and composi e cu es
a e nea ly o e lapped. No e ha he g and composi e cu e ze oing a
he highes empe a u e (875 °C) means only ha he ex e nal hea ing
equi emen is null. Fo he e e ence case a hea exchange ne wo k is
designed in Fig. 10: ho luids a e in ed, cold luids in blue, pinch
poin s a e highligh ed wi h dashed yellow lines, coole s a e in ligh blue
and he s eam spli s a e named wi h le e s o m A o E; s eams a e
abb e ia ed wi h CaCO
3
+ CaO
un
(solids exi ing he ca bona o , CO
2REC
(CO
2
exi ing he eac o ), CaO (CaO eac o inle ), CO
2MIX
(CO
2
eac o
inle ), CO
2STOIC
(CO
2
s oichiome ic).
Fig. 6. Pe o mance dis ibu ion o andom simula ions.
Fig. 7. Ca bona o side e iciency and he mal ans e esul ing om he op-
imiza ion p ocess.
Fig. 8. a) Con ibu es o he elec ic powe gen-
e a ion and abso p ion; b) Ca bona o side balance
o plan .
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
6
The HEN layou is de eloped ying o ollow wo echnical e-
commenda ions [33]: i s , i is p e e ed o a oid solid s eams spli
since hey a e mo e di icul o be execu ed i compa ed o luid s eams
spli ; and second, i should be be e o a oid he mal ans e be ween
solids s eams because i is based on a non- ully de eloped echnology,
so gas–gas and gas–solid hea exchange a e a o i e. Unluckily he
con igu a ion o he whom he gene ic algo i hm con e ges does no
allow o sa is y his second ecommenda ion because he only ho
s eam p esen abo e he high- empe a u e pinch poin is he solids
s eam (CaCO
3
and un eac ed CaO); anyway, a sugges ion o a oid his
issue is p o ided a he end o he p esen wo k.
Finally, i mus be aken in o accoun he possibili y o elimina e he
solid s eam coole below he low- empe a u e pinch poin (colo ed
wi h s iped ligh blue in Fig. 10) and di ec ly send he low o i s
s o age; a li le imp o emen is ob ained in his way because bo h he
use o a hea exchange and he pa asi ic elec ic consump ion o hea
ejec ion a e a oided and his shouldn’ cons i u e a c i ical issue o he
CaCO
3
s o age since he s eam is a ela i ely low empe a u e.
5. Mul i-objec i e op imiza ion
As obse ed om he pinch analysis esul s and HEN (Figs. 7 and 8),
he op imiza ion p ocess seems o con e ge o con igu a ions ha en-
hance he hea exchange s age, making he ho and cold composi e
cu es o app oach each o he as much as possible. Anyway, despi e
his phenomenon b ings bene i s o he plan e iciency, he esul ing
HEN may show some c i icali ies bo h in e ms o complexi y and di-
mensions (hea ans e a ea). As an a emp o o e come his issue i is
in oduced a new pa ame e which should ac as an indica o o he
hea eco e y sys em s i ness: he
UAeq
(equi alen p oduc be ween
he global hea ans e coe icien and he exchange a ea) calcula ed on
he disc e ized ho and cold composi e cu es (Eq. (4)) wi hou aking
in o accoun he ex e nal cooling s ep, since his p ocess doesn’ con-
s i u e a c i icali y o he hea exchange ne wo k. Assuming he
equi alen p oduc be ween U and A ins ead o only he equi alen A
allows o a oid aking in o accoun he di e en e ec i eness cha -
ac e izing he hea exchange in case o gas–gas, gas–solid o solid–solid
he mal ans e and he e o e makes unnecessa y o add ess a cohe en
alue o U o any s eam coupling. The o al UA o he eal HEN will be
highe han he alue ound wi h his indica o since i ’s ob ained
p e ending ha all he ho and cold luids a e mixed oge he and only
he wo esul ing lows pa icipa e o he hea ans e , which is an ideal
condi ion. Anyway, as al eady explained, his pa ame e p o ides only
a quali a i e and no quan i a i e in o ma ion o he pu poses o his
analysis. The e can be wo causes o an inc ease o he equi alen UA:
one consis s in an inc ease o he powe ans e ed be ween he
s eams, while he o he is ep esen ed by he app oach o he wo
composi e cu es; bo h o hem de e mine a g ow h o he HEN size, bu
he las one may b ing o an addi ional issue, which is he o ma ion o
pinch poin s. This ac , acco ding o he pinch analysis heo y, leads o
he concep ual sepa a ion o he hea eco e y p ocess in o wo (o
mo e) subsys ems which a e ene gy independen be ween hem and
don’ sha e any hea exchange ; as a consequence, he numbe o uni s
used o he he mal ans e becomes highe and he HEN complexi y
ends o inc ease.
=UA T
eq
i
i
lm i,
(4)
Fig. 9. a) Composi e cu es and b) g and composi e cu e o he op imized ope a ing condi ions o e e ence case.
Fig. 10. Hea exchange ne wo k o he op imized ope a ing condi ion o e e ence case.
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
7
whe e
i
is he he mal lux and
T
lm i,
s ands o he loga i hmic mean
empe a u e di e ence, bo h de ined o he i-in e al.
Finally, in addi ion o he aspec s al eady explained, he use o UA
eq
as second objec i e unc ion ins ead o he plan cos (which would
allow o pe o m an economic analysis) is due o he ac ha some o
he main componen s in ol ed in he p ocess a e s ill in an ea ly s age
o de elopmen , so ep esen a i e da a a e no a ailable ye .
A his poin is possible o se up a double- a ge op imiza ion whose
objec i e unc ions a e he ca bona o side e iciency (
ca b
) and he
UAeq
; he en i e plan simula ion emains unchanged wi h espec o he
in es iga ion p e iously pe o med. Resul s show clea ly he e ec s o
an op imal he mal ans e p ocess on he plan pe o mance: he mo e
e ec i e is he hea ans e be ween eac an s and p oduc s, he highe
a e bo h he e iciency and he equi alen UA. As expec ed, o he same
ca bona o side e iciency alue, lowe alues o calcium oxide e-
ac i i y de e mine an inc ease in he HEN dimensions because o he
highe amoun o ine ma e ha akes pa o he p ocess.
In Fig. 11a a e epo ed he pa e o cu es o he mul i-objec i e
op imiza ion, while 11b shows he alues eached by he independen
a iables no malized by hei co esponding a ia ion ange o he
e e ence case; he main comp esso inle empe a u e is he only e m
o p esen a cons an beha io since i s ays p ac ically always a i s
lowe bound, while he o he pa ame e s ha e di e en ends. In
pa icula , he ca bona o p essu e and he main u bine p essu e a io
a e e y s ic ly bonded be ween hem, con i ming he con enience o
each a main u bine ou le p essu e close o 1 ba (se as he minimum
achie able alue); highe alues o bo h con ibu e o simpli y he
he mal ans e sys em. The same e ec is ob ained wi h lowe ca -
bona o empe a u es and lowe eac o inle empe a u es. This is due
o he ac ha all hese ends de e mine a dec ease o he empe a-
u es o bo h he eac an s ha mus be hea ed up and he p oduc s ha
needs o be cooled down; as a consequence, accep ing an e iciency
educ ion (which can be no pa icula ly disad an ageous, especially
when i s alue is high) i is possible o consis en ly educe he HEN size
and pe haps e en i s complexi y (al hough his mus be demons a ed).
F om he p e ious analysis and wi h he aim o obse e he possible
HEN opology changes, se e al hea exchange s ne wo ks a e p oposed
o di e en alues o he equi alen UA. The cases conside ed a e
chosen in e e ence o he con igu a ion ha p o ides he highe
UAeq
alue (which coincides wi h he single objec i e op imiza ion esul )
wi h a CaO ac i i y se o he e e ence alue. Fig. 12 shows he e-
sul ing g and composi e cu es o hese selec ed con igu a ions.
As expec ed, he he mal lux exchanged be ween he luids de-
c eases wi h he educ ion o he equi alen UA; he ho and cold
composi e cu es end any way o app oach each o he , bu wi h a
lowe ing e ec i eness. This e ec is shown in Fig. 8: he wo pinch
poin s p esen in he i s con igu a ion g adually disappea when he
UAeq
becomes smalle , while he cooling need inc eases as a
consequence o he e iciency educ ion. This means ha he he mal
ans e is no execu ed in he bes way since he same hea exchange
could be pe o med wi h a highe alue o he minimum empe a u e
di e ence achie able (in pa icula , 22 °C o he case o 40%UA
max
and
58 °C o 10% UA
max
); howe e , his does no ep esen a p oblem be-
cause a oiding hese pinch poin s is exac ly one o he pu poses o his
in es iga ion.
The layou s epo ed in Appendix B a e designed wi h he same
c i e ia explained in he p e ious op imiza ion. F om hese layou s i is
possible o obse e ha he hea exchange a angemen does no un-
de go adical changes, since he s eam spli s di e only in he pe -
cen age amoun s bu no in hei posi ion o numbe . Fu he mo e,
ega ding hei size and complexi y, pe o ming a wo s hea eco e y
allows o educe he hea exchange s dimensions and, in some cases,
hei numbe , ob aining he e o e a simple ne wo k. Finally, i should
no be o go en ha he solid s eam cooling (CaCO
3
and un eac ed
CaO) can be heo e ically a oided sending i di ec ly o i s s o age, so i
is possible o imagine one o he wo coole s as absen .
6. Sys em op imiza ion imp o emen
In o de o e ine om a echnological pe spec i e he esul s
achie ed om he ene gy op imiza ion, as a oiding he solid–solid hea
exchange, a single-objec i e op imiza ion wi h an addi ional cons ain
(Eq. (5)) is pe o med. This equa ion imposes an uppe limi o he
empe a u e o he CaO en e ing he ca bona o (
T
CaO in,
); in his way
his cold s eam does no appea abo e he high- empe a u e pinch
poin whe e he only ho low is he solid s eam exi ing he ca bona o .
T TOT T
CaO in MT pp,
(5)
Fig. 11. a) Pa e o cu es om he mul i-objec i e op imiza ion and b) a iables no malized end along he pa e o o e e ence case.
Fig. 12. G and composi e cu e o he in es iga ed cases (X = 0.5).
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
8
Fig. 13 shows he designed HEN conside ing he p e ious cons ain
o he e e ence case. As consequence o his new design, he plan is
no only i ’s managed o o e come he p oblem o solid–solid he mal
ans e , bu he numbe o hea exchange s is dec eased by one. An-
o he posi i e aspec is ha he ca bona o side e iciency dec ease is
p ac ically negligible since in ela i e e ms is equal o 0.16%. Fu -
he mo e, he o he elemen s disposi ion emains equal o he o iginal
case and he o al UA unde goes only a li le dec ease (3.4% in ela i e
e ms). These las aspec s demons a e he high complexi y and lex-
ibili y o he objec i e unc ion, since e en much di e en alues as-
sumed by he independen a iables can b ing o esul s e y close o
he op imum.
As shown in Fig. 14, he op imum ca bona o side consis o eigh
HEXs, o which: wo a e gas–gas hea exchange s, i e a e gas–solid
hea exchange s and one is a coole .
As demons a ed by he esul s ob ained om he ene gy op imi-
za ions pe o med up o his poin , he o ma ion o a high- empe a u e
pinch poin occu s whene e he o al CO
2
en e ing he ca bona o has
a empe a u e highe han he main u bine ou le empe a u e. So,
looking a he ad an ages ob ained om he las analysis, ano he
a emp o ind a simple design o he he mal eco e y p ocess is
pe o med wi h he addi ion o ano he cons ain (Eq. (6)) simila o
p e ious one, bu applied o he o he ca bona o inle s eam: he
mixed ca bon dioxide.
T TOT T
CO in MT pp,
2
(6)
Howe e , as shown in Fig. 15, he e ec s encoun e ed wi h his
addi ional limi a ion a e mo e complex han he p e ious ones. In ac ,
despi e bo h he pinch poin s disappea and he numbe o hea ex-
change s dec eases o i e, he ca bona o side e iciency educ ion
(6.8% in ela i e e ms) and he o al UA inc ease (9.8% in ela i e
e ms) cons i u e wo conside able d awbacks. The eason o ha is due
o he ac ha he mixed CO
2
is one o he mos impo an con ibu o s
o he hea eco e y and a es ic ion on his pa ame e will gene a e a
much mo e consis en penal y wi h espec o he one applied on he
CaCO
3
s eam.
The con enience o his layou should be he e o e e alua ed o
wha his con igu a ion ac ually ep esen s: a comp omise be ween
good pe o mances and a simple HEN s uc u e, ob ained a he p ice o
a consis en size o he hea eco e y sys em.
Fig. 13. Hea exchange ne wo k o he op imal ope a ing condi ions (in e e ence case), which a oid solid–solid ans e .
Fig. 14. P ocess in eg a ion scheme om he HEN analysis shown in Fig. 9.
U. Tesio, e al. Ene gy Con e sion and Managemen : X 4 (2019) 100025
9