Fi s e sion o simula ion model o he
he mo-chemical s o age sys em
Deli e able numbe : D3.1
Ve sion 1.0
Views and opinions exp essed a e howe e hose o he au ho (s) only and do no
necessa ily eflec hose o he Eu opean Union o CINEA. Nei he he Eu opean Union
no he g an ing au ho i y can be held esponsible o hem
This page is in en ionally le blank
Basic in o ma ion on deli e able
P ojec Ac onym BEST-STORAGE
P ojec URL h p://www.bes -s o age.eu
Responsible pa ne Do ian Hö ne (TUB)
Deli e able na u e Repo (R)
Dissemina ion le el Public (PU)
Con ac ual Deli e y Da e 30 h o Sep embe 2024
Ac ual Deli e y Da e 30 h o Sep embe 2024
Numbe o pages 25
Keywo ds so p ion he mals o age, model, he mal ene gy s o age, hea ing, cooling, HVAC.
Au ho s Do ian Hö ne (TUB), Hossein Gha aee (TUB), Robe Kno e (TUB)
Re iew Jose L. Co ales Ciganda (Tecnalia), Daniel Ca bonell (OST)
App o al Hugo G asse (SOLINTEL)
Deli e able D3.1
BEST-STORAGE CONSORTIUM
SOLINTEL SOLINTEL M&P SL
TECNALIA FUNDACION TECNALIA RESEARCH & INNOVATION
CERTH ETHNIKO KENTRO EREVNAS KAI TECHNOLOGIKIS
ANAPTYXIS
TUB TECHNISCHE UNIVERSITAT BERLIN
TEKNIKER FUNDACION TEKNIKER
NEWTON NEWTON ENERGY SOLUTIONS BV
EHPA EUROPEAN HEAT PUMP ASSOCIATION
AVAN AVANZARE INNOVACION TECNOLOGICA SL
TREA MITTETULUNDUSUHING TARTU REGIOONI
ENERGIARGENTUUR
GIR GIROA SOCIEDAD ANONIMA
OST OST – OSTSCHWEIZER FACHHOCHSCHULE
SUPSI SCUOLA UNIVERSITARIA PROFESSIONALE DELLA
SVIZZERA ITALIANA
Deli e able D3.1
CONTENTS
1 In oduc ion 1
2 The modynamic Model o So p ion S o age Sys em 3
2.1 S eady-S a eModel ....................................... 3
2.1.1 ModelDefini ion..................................... 3
2.1.2 Simula ionResul s.................................... 8
2.2 DynamicModel.......................................... 12
3 De ailed Model o he Hea and Mass Exchange 13
3.1 ModelDesc ip ion ........................................ 13
3.2 A/D-Submodel .......................................... 15
3.3 Ma hema ical Modeling App oach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 A/D-Submodel...................................... 17
3.3.2 Main Conse a ion Balances in he A/D . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.3 E/C-Model........................................ 20
3.3.4 Main Conse a ion Balances in he E/C . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Conclusion 24
Deli e able D3.1
EXECUTIVE SUMMARY
This deli e able in oduces and desc ibes wo ad anced simula ion amewo ks designed o model so p ion he -
mal s o age sys ems based on Sodium-hyd oxide and wa e . Bo h models a e based on physical equa ions and al-
low insigh s in o he sys ems’ beha io o di e se bounda y condi ions. The fi s model uses an in eg al app oach
o p edic he s eady-s a e wo king condi ions o bo h he Abso be /Deso be -Uni and he E apo a o /Condense
uni . The second ocuses on he de ailed, ime-dependen in e nal condi ions o he Abso be /Deso be uni .
The in eg al model applies heNTU-E ec i enessme hod, sol ingase o equa ions omain ainsys ems abili yby
ulfilling conse a ion laws. This model, he mos ad anced in he p ojec , will gene a e key pe o mance indica o s
o es ima e he pe o mance o a demons a o uni unde ce ain bounda y condi ions. I will be u he enhanced
o accoun o he mal masses and sys em dynamics, al hough his dynamic e sion is s ill unde de elopmen .
Once comple e, i will simula e he eal sys em’s dynamic beha io .
The second model akes a mo e g anula app oach, using di e en ial equa ions based on hea and mass con-
se a ion. I cap u es he dynamic e olu ion o he sys em, esol ing he mal and concen a ion fields in de ail.
This model p o ides deepe insigh s in o he hea and mass ans e p ocess, o e ing a local iew o sys em
beha io .
Bo h models aim o p edic expe imen al ou comes and p o ide insigh s in o he abso p ion p ocess, enabling an
unde s anding o sys em dynamics and pe o mance po en ial. Addi ionally, hey will in o m con ol s a egies
based on inpu /ou pu condi ions and hea ing sys em cha ac e is ics. Toge he , hese models will suppo he
accu a e assessmen and op imiza ion o he upscaled sys em’s pe o mance, each con ibu ing acco ding o
hei specific s eng hs.
Deli e able D3.1
LIST OF ACRONYMS
A/D Abso p ion/Deso p ion Uni
E/C E apo a o /Condense Uni
HX Solu ion Hea Exchange
HMX Hea and Mass Exchange
NTU The Numbe o T ans e Uni s
TCS The mochemical S o age Sys em
LIST OF VARIABLE NAMES
Symbol Explana ion Uni
AA ea m2
˙
CHea Capaci y Flow W
K
cpSpecific Hea Capaci y J
kg K
dDiame e m
diInne Diame e m
doOu e Diame e m
lTube Leng h m
∆hLV Specific En halpy o E apo a ion J
kg
˙
HEn halpy Flow W
mH2O in sol Mass o Wa e P esen in he Solu ion kg
m ap, EC Mass o Wa e Vapo P esen in he EC Vapo Space kg
m ap, AD Mass o Wa e Vapo P esen in he AD Vapo Space kg
˙
mAD A/D Ex e nal Wa e Mass Flow kg
s
˙
mEC E/C Ex e nal Wa e Mass Flow kg
s
˙
m luid Fluid Mass Flow (Rep esen a i e fluid) kg
s
˙
msol, in Solu ion Inle Mass Flow kg
s
˙
msol, ou Solu ion Ou le Mass Flow kg
s
˙
m ap E apo a ed/Condensed Wa e Vapo Mass Flow kg
s
ap, abs Abso bed/Deso bed Wa e Vapo Mass Flow kg
s
Nu Nussel Numbe -
pP essu e Pa
Con inued on nex page
Deli e able D3.1
Symbol Explana ion Uni
pAD A/D P essu e Pa
pAD, sa , in Solu ion Sa u a ion P essu e a he Inle o one Submodel Pa
pAD, sa , ou Solu ion Sa u a ion P essu e a he Ou le o one Submodel Pa
pEC E/C P essu e Pa
P P and l Numbe -
˙
QHea T ans e W
RHea Resis ance K
W
Re Reynolds Numbe -
Sc Schmid Numbe -
Sh She wood Numbe -
AD, in A/D Wa e Inle Tempe a u e K
AD, ou A/D Wa e Ou le Tempe a u e K
EC, in Ex e nal E/C Wa e Inle Tempe a u e K
EC, ou Ex e nal E/C Wa e Ou le Tempe a u e K
TAD, sa In e nal Solu ion Sa u a ion Tempe a u e K
TEC In e nal EC Tempe a u e K
Tsol, in In e nal Solu ion Inpu Sa u a ion Tempe a u e K
Tsol, ou In e nal Solu ion Ou pu Sa u a ion Tempe a u e K
Twall Wall Tempe a u e o he Pipe K
UIn e nal Ene gy J
UHea T ans e Coe ficien W
m2K
xAD, sa In e nal Solu ion Sa u a ion Tempe a u e -
xin Inle F ac ion o NaOH in Solu ion -
xou Ou le F ac ion o NaOH in Solu ion -
G eek Symbols
αHea T ans e Coe ficien W
m2K
βMass T ans e Coe ficien m
s
δFilm Solu ion Film Thickness m
ϵNTU E ec i eness Coe ficien -
ζF ic ion Coe ficien -
λThe mal Conduc i i y Coe ficien W
m K
Con inued on nex page
Deli e able D3.1
Symbol Explana ion Uni
νKinema ic Viscosi y m2
s
ρDensi y kg
m3
ΓSpecific Mass Flow Ra e o he Solu ion kg
ms
Deli e able D3.1
Figu e 2.2: Illus a ion o he c oss sec ion iew o a single pipe wi h he alling film and in oducing some o he
bounda y pa ame e s used in he model.
TAD,su ace =TAD,sa (2.26)
TAD,sa =Teq(pAD,eq,xAD,sa )(2.27)
To calcula e TAD, sa , by applying equa ion Equa ion 2.27 we use he p e iously calcula ed mass ans e coe ficien
(β) which is de e mined using he fluid’s he mophysical p ope ies, he A/D uni p essu e, PAD, eq u ilizing Equa-
ion 2.28, and xAD, sa by applying he NTU-e ec i eness me hod o mass ans e , as ou lined in Equa ion 2.29 o
2.32.
pAD,eq =pEC,eq −ζ1
2
m2
ap,EC
ρ ap A2
pipe
(2.28)
NTUβ=βAAD
˙
msol,in
(2.29)
ϵβ=1−exp(−NTUβ)(2.30)
ϵβ=xin −xou
xin −xAD,sa
(2.31)
TAD,sa =TNaOH(PAD,xAD,sa )(2.32)
Now, ha TAD, sa has been de e mined, we p oceed o analyze he hea ans e phenomenon in he A/D uni . Fi s ,
we calcula e he e ec i eness o he A/D uni using he same app oach applied o he E/C uni . Fo he A/D uni ,
he co esponding equa ions a e Equa ion 2.33 o 2.35. Wi h he alue o TAD, sa , now a ailable, we can calcula e
AD, ou , using Equa ion 2.36.
7Deli e able D3.1
UAD =1
1
α ube,AD +1
α ubewall,AD +1
α ilm,AD
(2.33)
NTUAD =UAD AAD
˙
CAD,ex
(2.34)
ϵAD =1−exp(−NTUAD)(2.35)
ϵAD = AD,ou − AD,in
TAD,sa − AD,in
(2.36)
Fu he mo e, we can calcula e he hea ans e om he A/D uni using Equa ion 2.38 o pe o m an ene gy balance
assessmen o he en i e sys em o o un op imiza ion algo i hms o enhancing key pe o mance indica o s
(KPIs).
˙
QAD =ϵAD ×˙
CAD,ex ×( AD,in −TAD,sa )(2.37)
=˙
CAD,ex ×( AD,in − AD,ou )(2.38)
By pe o ming he modeling, we can ob ain he empe a u e cu es o he E/C and A/D uni s, as well as he solu ion
concen a ion, which a e depic ed in Figu e 2.3.
Figu e 2.3: Illus a ion o he in e nal and ex e nal empe a u e condi ions a he hea exchange s and o he sal
concen a ion condi ions in he solu ion film o he coupled hea and mass ans e NTU-e ec i eness me hod
used in his wo k, depic ed o he discha ging (abso p ion) p ocess.
The isual ep esen a ion o he model employed is ob ained by conside ing a one-dimensional, s a iona y, and lin-
ea app oach o hea conduc ion h ough he film and pipe in he A/D uni , assuming ha he film bulk empe a u e
is he a i hme ic mean be ween he liquid su ace and he ube wall. In he A/D uni , solu ion concen a ion and
empe a u e a e coupled, wi h he concen a ion dec easing owa ds he sa u a ion concen a ion, xAD, sa , while
he flow empe a u e ises owa ds he asymp o ic sa u a ion empe a u e TAD, sa . In he E/C uni , al hough no
solu ion concen a ion is p esen , a simila p inciple applies, whe e he inle empe a u e dec eases owa ds he
asymp o ic empe a u e TEC, sa .
2.1.2 SIMULATION RESULTS
Following he in oduc ion o he s eady-s a e model, he simula ion esul s aim o p o ide a comp ehensi e un-
de s anding o he sys em beha io unde a ious condi ions. By pe o ming pa ame e a ia ions, we explo e he
pe o mance and con ollabili y o he sys em in de ail. These simula ions ocus on key ope a ional pa ame e s
8Deli e able D3.1
and a iables, using a pa ame e se simila he 1 kW es ig o a sodium hyd oxide-based s o age sys em ha is
build a p ojec pa ne OST’s acili ies. By adjus ing hese a iables, we gain insigh in o how he sys em esponds
unde di e en ope a ional se ings.
The ini ial se o simula ions a e conduc ed using he specific geome y o he hea exchange ins alled in OST’s lab,
wi h he pa ame e s desc ibing he es ig de ailed in Table 2.3. Table 2.4 shows he base ope a ional a iables.
In he ollowing simula ions, only a single inpu a iables is a ied a a ime. This app oach allows us o isola e
he impac o indi idual pa ame e s on sys em beha io . By obse ing how he sys em eac s o changes in single
a iables, we can de i e aluable insigh s in o po en ial con ol s a egies o he sys em. I is impo an o no e
ha he simula ion esul s p esen ed should p o ide a gene al unde s anding o he models unc ionali y and a e
no necessa ily pe ec ly aligned wi h expe imen esul s. In ac , he ends and cu e o ms p edic ed by he
model seem o be in line wi h he expe imen al esul s, based on ini ial compa isons. Howe e , he model seems
o sligh ly unde es ima e he abso p ion powe . This issue will be add essed in u he esea ch.
Table 2.3: Geome ic and he mal pa ame e s o he es ig.
Pa ame e Value Uni Desc ip ion
di, ube,EC 0.008 m Inne Diame e o EC- ubes
do, ube,EC 0.01 m Ou e Diame e o EC- ubes
l ube,EC 0.3 m Leng h o EC- ubes
n ow,EC 10 - Numbe o ube ows pe EC-column
ncol,EC 10 - Numbe o EC-columns
λ ube,EC 20 W/mk The mal conduc i i y o EC- ubes
λH2O0.5918 W/mk The mal conduc i i y o wa e
AEC,amb 0 m²A ea o hea exchange wi h ambien (EC)
di, ube,AD 0.008 m Inne Diame e o AD- ubes
do, ube,AD 0.01 m Ou e Diame e o AD- ubes
l ube,AD 0.2 m Leng h o AD- ubes
n ow,AD 6 - Numbe o ube ows pe AD-column
ncol,AD 1 - Numbe o AD-columns
λ ube,AD 45 W/mk The mal conduc i i y o AD- ubes
λNaOH 0.68 W/mk The mal conduc i i y o sodium lye
AAD,amb 0 m²A ea o hea exchange wi h ambien (AD)
Apipe 0.015 m²C oss-sec ion o pipe be ween EC and AD
A ec 0 m²Recupe a o hea exchange a ea
Table 2.4: Ope a ional pa ame e s o he sys em.
Pa ame e Name Value Uni Desc ip ion
mex ,EC 0.0500 kg/s HTF massflow EC
mex ,AD 0.0230 kg/s HTF massflow AD
msol,in 0.0014 kg/s Solu ion mass flow
xin 0.5000 w % Solu ion inle concen a ion
TAD, om ank 26.0000 °C Solu ion inle empe a u e
EC,in 15.0000 °C HTF empe a u e a EC-inle
AD,in 29.0000 °C HTF empe a u e a AD-inle
mhighC, ank 4584.0000 kg Solu ion ank capaci y
Tamb 24.0000 °C Ambien empe a u e
The beha io o he sys em is significan ly influenced by wo key ex e nal inpu s: he empe a u es o he hea
9Deli e able D3.1
ans e fluids (HTFs) and he mass flows o he HTFs hen p oceed o analyze he impac o mass flows.
As shown in Figu e 2.4, he influence o ex e nal inle empe a u es on he sys em’s pe o mance exhibi s a quasi-
linea end, p o ided ha all o he a iables and pa ame e s a e held cons an . This linea beha io can be a -
ibu ed o he p ope ies o sodium hyd oxide (NaOH). Specifically, he e is a quasi-linea ela ionship be ween he
sa u a ion empe a u e o wa e and he sa u a ion empe a u e o he NaOH solu ion. This ela ionship is com-
monly ep esen ed h ough a Düh ing plo , which illus a es he linea co ela ion be ween he sa u a ion p essu es
o di e en solu ions. As he inle empe a u e in he EC uni inc eases, bo h abso be powe and solu ion con-
cen a ion change ise, wi h li le de ia ion om linea i y. Wi h ising e u n empe a u e om he hea ing ci cui
AD,in he end is he opposi e, bu s ill linea . Consequen ly, abso be powe , concen a ion change and s o age
capaci y a e linea ly dependen on he di e ence be ween AD,in and EC,in.
Figu e 2.4: Influence o ex e nal inle empe a u es on solu ion ou le concen a ion and abso be powe . Each
plo ep esen s a single pa ame e a ia ion. All o he pa ame e s emain unchanged as depic ed in Tables 2.3
and 2.4
Nex , we conside he second ex e nal ac o — he mass flows o he hea ans e fluids (HTFs). Unlike he empe -
a u e e ec s, he beha io o he sys em in esponse o a ying mass flows is non-linea . The ou le concen a ion
o he NaOH solu ion ollows an exponen ial sa u a ion unc ion, whe e he sa u a ion poin is de e mined by he
maximum possible dilu ion based on he e u n empe a u e o he hea ing ci cui . Simila ly, he abso be powe
exhibi s an exponen ial sa u a ion unc ion, limi ed by he powe associa ed wi h he maximum possible dilu ion.
The non-linea beha io s ems om he NTU-e ec i eness o he hea exchange , as desc ibed in sec ion 2.1. The
NTU-e ec i eness ela ionship leads o diminishing e u ns in bo h abso be powe and solu ion dilu ion as he
mass flow inc eases, explaining he exponen ial na u e o he cu es shown in Figu e 2.5.
Figu e 2.5: Influence o ex e nal mass flows on solu ion ou le concen a ion and abso be powe .
In addi ion o ex e nal ac o s, he sys em’s beha io is also shaped by in e nal pa ame e s such as he solu ion
mass flow and inle concen a ion. These inpu s significan ly influence he abso be powe and s o age capaci y.
Figu e 2.6 illus a es he impac o a ying solu ion mass flow on abso be powe and s o age capaci y. As he
mass flow inc eases, abso be powe ises asymp o ically, app oaching a sa u a ion poin . Howe e , his inc ease
in powe comes a he expense o s o age capaci y, which s eadily declines. The decline in s o age capaci y can be
a ibu ed o he educed esidence ime o he solu ion in he abso be as he flow a e inc eases, he eby limi ing
he amoun o mass and ene gy ha can be ans e ed pe kg solu ion.
10 Deli e able D3.1
Figu e 2.6: Influence o NaOH solu ion mass flow on abso be powe and s o age capaci y.
Ano he c ucial in e nal ac o is he NaOH solu ion inle concen a ion, as shown in Figu e 2.7. A dec ease in inle
concen a ion leads o a quasi-linea educ ion in abso be powe , s o age capaci y, and ou le concen a ion. This
phenomenon occu s, because lowe inle concen a ions educe he concen a ion di e ence ha can be achie ed
du ing he abso p ion p ocess, which in u n dec eases he d i ing o ce o abso p ion and hea ans e . In u-
i i ely, he hea and mass ans e is dec eased when he solu ion en e s wi h a concen a ion close o sa u a ion
condi ions. This is isible on he igh side o Figu e 2.7 by he dis ance be ween he wo lines.
Figu e 2.7: Influence o NaOH inle concen a ion on abso be powe , s o age capaci y and ou le concen a ion.
In conclusion, he simula ion esul s indica e dis inc beha io s o he sys em in esponse o bo h ex e nal and
in e nal inpu s. The sys em’s pe o mance unde a ying ex e nal empe a u es is ela i ely linea , la gely due o
he p ope ies o sodium hyd oxide and he ela ionship be ween wa e and NaOH sa u a ion empe a u es. In
con as , ex e nal mass flows ha e a non-linea , exponen ial e ec on abso be powe and solu ion concen a ion,
d i en by he physical connec ion be ween hose alues, cap u ed by he NTU-e ec i eness model o he hea
exchange .
In e nally, solu ion mass flow exhibi s an asymp o ic inc ease in abso be powe bu a co esponding decline in
s o age capaci y. Meanwhile, lowe inle solu ion concen a ions lead o a educ ion in bo h abso be powe and
s o age capaci y due o he dec eased d i ing po en ial o abso p ion. These insigh s in o he beha io o he
sys em p o ide aluable in o ma ion o op imizing bo h con ol and design, ensu ing mo e e ficien ope a ion
unde a ious condi ions.
11 Deli e able D3.1
2.2 DYNAMIC MODEL
Al hough he dynamic model has no ye been ully alida ed, he gene al app oach will be in oduced in his sec-
ion. The model equa ions emain la gely unchanged om he s eady-s a e e sion, wi h he p ima y modifica ions
being he addi ion o hea capaci y e ms o he E apo a o /Condense (E/C) and Abso be /Deso be (A/D) uni s.
Fu he mo e, di e en ial e ms o he empe a u es a e included, as desc ibed below.
Fo he dynamic E apo a o /Condense model, he hea ans e is ep esen ed by equa ion 2.39. Ts eel,EC is as-
sumed o be he empe a u e a he midpoin o he essel wall (assumed o ollow a linea empe a u e g adi-
en ).
˙
QEC =˙
m ap∆h (TEC) + ms eel,EC ·cp,s eel,EC
dTs eel,EC
d (2.39)
+mwa e ·cp,wa e
dTEC
d +˙
Qloss,EC
Ts eel,EC =TEC −dwall,EC
2·λs eel,EC
Qloss,EC
Awall,EC
(2.40)
Fo he dynamic Abso be /Deso be model, he hea ans e and he empe a u e a e exp essed simila ly. Addi-
ionally, he solu ion mass is app oxima ed by Equa ion 2.42.
˙
QAD =˙
m ap ·h (TEC) + ˙
msol,in ·hsol,in(xin,TAD,in)(2.41)
−˙
msol,ou ·hsol,ou (xou ,TAD,ou ) + ˙
Qloss,AD
+ms eel,AD ·cp,s eel,AD
dTs eel,AD
d
+msol,AD ·cp,sol(TAD,bulk,xin +xou
2)dTAD,bulk
d
msol,AD =AAD ·d ilm ·ρsol(TAD,bulk,xin +xou
2)(2.42)
Ts eel,AD =TAD −dwall,AD
2·λs eel,AD
Qloss,AD
Awall,AD
(2.43)
These modifica ions enable he model o accoun o he mal ine ia by conside ing he hea capaci ies o he ma-
e ials in ol ed, he eby p o iding a mo e accu a e ep esen a ion o he sys em’s ansien beha io . To make he
model dynamic, se e al s eps a e s ill equi ed. Fi s , changes in he da a s uc u es o he inpu s mus be made
o accommoda e ime-dependen a iables. Second, adjus men s in he sol ing algo i hm a e necessa y, pa ic-
ula ly he inco po a ion o ime s eps and he use o fini e di e ence me hods o app oxima ing he de i a i e
e ms. These enhancemen s will allow he model o simula e ime-dependen p ocesses and cap u e he dynamic
esponse o he sys em unde a ying condi ions.
12 Deli e able D3.1
3 DETAILED MODEL OF THE HEAT AND MASS EXCHANGER
This chap e p esen s a comp ehensi e model o he hea and mass exchange (HMX). The chap e is o ganized
as ollows: sec ion 3.1 Model Desc ip ion p o ides an o e iew o he implemen ed model, de ailing i s s uc u e
o enable he applica ion o a ious inpu signals and he acking o ou pu signals no only ac oss di e en ube
ows o he A/D uni , bu also wi hin specific sec ions o each ube, e e ed o as "submodels". This me hod allows
o a mo e p ecise and de ailed ep esen a ion o he HMX, pa icula ly in he Abso be /Deso be uni , as opposed
o elying solely on gene alized a iables used o he in eg al ep esen a ion o he HMX uni desc ibed in chap e
2.
Following his, sec ion 3.2 A/D-Submodel, del es in o he specifics o he A/D uni , discussing he inpu , ou pu , and
configu a ion o he sys em ha a e essen ial o composing his de ailed model. Finally, Ma hema ical Modeling
App oach, ou lines he s uc u e o he p og am de eloped, o implemen he a o emen ioned modeling app oach
(a he momen MATLAB is used). This sec ion p o ides an gene al o e iew o he mass- and ene gy balances
which we e used o o mula e he model’s equa ions, ollowed by he defini ion o pa ame e s and a calcula ion
me hodology.
3.1 MODEL DESCRIPTION
As p e iously discussed, he objec i e o his chap e is o p esen a no el app oach o he de ailed modeling o
he he mo-chemical s o age sys em, wi h an emphasis on he Abso be /Deso be (A/D) uni . In his app oach, he
HMX o he A/D uni is di ided in o se e al iden ical submodels ha ope a e independen ly ye a e in e connec ed,
eflec ing he s agge ed ubula geome y o he sys em. These submodels o m he co e ope a ional componen s
o ou de ailed model. Figu e 3.1 p o ides a isual ep esen a ion o he o e all A/D uni , e e ed o as he "In eg al
Model" in g een, along wi h i s cons i uen "submodels" in ed.
Figu e 3.1: Gene al o e iew o he A/D submodel configu a ion. The o e all sys em ou lined wi h g een and he
submodel depic ed in ed.
The In eg al Model is designed o calcula e bo h empo al and simple localized a ia ions in empe a u e and
concen a ion wi hin he HMX uni . To achie e his, ime-dependen di e en ial equa ions ailo ed o he ube ge-
ome y a e o mula ed, wi h bounda y condi ions adjus able o mee he equi ed esolu ion o he esul s. The
13 Deli e able D3.1
In eg al Model enables he simula ion o an en i e ube as whole o di ided in o sec ions ( e e ed o as submod-
els), wi h he assump ion ha empe a u e and concen a ion fields emain locally uni o m wi hin he bounda ies
o each submodel. To accu a ely ep esen a ull ube, mul iple submodels a e in e connec ed, allowing o he
exchange o empe a u e and concen a ion in o ma ion be ween adjacen submodels. This in o ma ion exchange
esembles he physical connec ion o he modelled ube sec ions (submodels).
The concep o he submodel and i s in e ac ions wi h neighbo ing submodels a e illus a ed in Figu e 3.1, and
Figu e 3.2. In Figu e 3.1, submodels aligned side by side ( e e ed o as being in pa allel, such as cells [1,1], [1,2], and
[1,3]) ep esen segmen s o a single ube, whe e he inpu s, s a es, and ou pu s a e assumed o emain cons an
along he local ube leng h o he segmen . Submodels s acked e ically ( e e ed o as being in a ow, such as
[1,2], [2,2], [3,2], and [4,2]) simula e he e ec s o he solu ion d ipping down om one sec ion o he ube o he
nex . The e ms "in ow" and "in pa allel" desc ibe he di ec ion o in e nal fluid (solu ion) flow wi hin he sys em.
To add ess local empe a u e a ia ions along he ube and di e ences be ween ubes, i ’s necessa y o define
and in e connec submodels. O he modeling me hods, such as ay columns o pa ial di e en ial equa ions, a e
expec ed o esul in simila ly complex calcula ions. The coun e -c oss flow configu a ion u he complica es
he empe a u e and concen a ion fields, bu he submodel app oach o e s a mo e p ecise solu ion. By linking
he submodels, his me hod e ec i ely handles local a ia ions and he complex flow a angemen , allowing o a
simplified ep esen a ion o he na u ally dis ibu ed pa ame e sys em.
Figu e 3.2: Gene al o e iew o he comple e A/D Model wi h all incoming and ou going signals. Some can ha e
nega i e signs o accound o deso p ion ope a ion mode.
As depic ed in Figu e 3.1, he A/D uni consis s o mul iple iden ical submodels, in e connec ed by anspo delay
cells, which accoun o he physical lengh o each submodel o he dis ance be ween wo ube ows. E e y sub-
model handles h ee dis inc p ocess flows, wi h an inpu and ou pu signal each. Since i is an in eg al modeling
app oach, all signals and s a es a e conside ed cons an o e he local ube segmen , only changing o e ime.
The ou pu s a e de e mined using he go e ning o dina y di e en ial equa ions. A de ailed schema ic illus a ion
o he flows en e ing o lea ing each submodel is p o ided in Figu e 3.2. In he ollowing subsec ion, de ailed
in o ma ion on he inpu u( ), s a e x( ), ou pu y( ), and pa ame e pconfigu a ion o a single A/D submodel
will be gi en.
14 Deli e able D3.1
3.2 A/D-SUBMODEL
To gain a mo e de ailed unde s anding o he submodel concep , his sec ion in oduces he unde lying logic o
ou app oach, by ea ing he submodel as a con ol olume and ou lining he inpu and ou pu s eams. The
go e ning equa ions will be in oduced in he nex sec ion, because he ocus lies on p o iding a mo e ho ough
unde s anding o he signal flows o he model and o p esen i as clea ly as possible o he eade s.
Each submodel includes h ee sepa a e flow pa hs, one o which is he hea ing/cooling flow, known as he ’Ex-
e nal Fluid.’ This flow in ol es wa e en e ing he cu en submodel om he o me submodel (o he backwa d
eed o he hea ing sys em) and exi ing o he la e submodel (o he o wa d eed o he hea ing sys em). The
signals necessa y o he mass and ene gy balance equa ions o his flow a e H2O( ), and ˙
mH2O( ). As shown in
Figu e 3.3, he inpu and ou pu signals o his s eam a e implemen ed in o he go e ning equa ions o he con ol
olume, defining he ep esen a i e flows. Fo modeling pu poses, he wa e empe a u e, H2O( ), is conside ed
as one o he s a e a iables, which is de e mined by sol ing he go e ning equa ion ep esen ed by ˙
x1.
Figu e 3.3: Inpu s o he submodel om he Ex e nal Fluid.
The second flow en e ing he submodel’s con ol olume is he solu ion flow, e e ed o as he ’In e nal Fluid.’ This
flow in ol es solu ion d ople s descending om he uppe ube (o solu ion dis ibu o ) and d opping on he ube
below (o he solu ion pool). Th ee pa ame e s Tsol( ),˙
msol( ), and xH2O( )cha ac e ize he espec i e inpu and
ou pu signals. Simila o he ex e nal wa e flow, he pa ame e Tsol, ou ( ), is he second s a e a iable, deno ed
by ˙
x2. The isual ep esen a ion o his flow is p o ided in Figu e 3.4.
Figu e 3.4: Inpu s o he submodel om he In e nal Fluid.
The final flow s eam conside ed in he A/D uni is he in e nal sys em apo flow depic ed in Figu e 3.5. This signal
p o ides each submodel wi h in o ma ion abou he apo empe a u e and p essu e in he AD. I is assumed, ha
his empe a u e and p essu e a e cons an o he whole A/D uni , such ha each submodel ecei es he same
15 Deli e able D3.1
alues om he E/C. In gene al, he AD p essu e is a unc ion o he EC condi ions as well as he p essu e d op
wi hin he apou ube connec ing E/C and A/D. By using he signals TEC( ), and pAD( )and sol ing he go e ning
equa ions, he abso bed o deso bed wa e in each submodel can be calcula ed based on he inpu condi ions.
Each submodel hen eeds back he amoun o abso bed wa e apo o he E/C, whe e he esul s om each
submodel can hen be summed up o de e mine he o al amoun o wa e abso bed o deso bed in he HMX. The
E/C hen calcula es he new p essu e. The o al mass o wa e p esen in he solu ion ep esen s he final s a e in
he s a e space model, deno ed by ˙
x3.
Figu e 3.5: Inpu s o he submodel om he E/C.
To summa ize his subsec ion, i is impo an o no e ha he en i e A/D uni is modeled using mul iple submodels,
each go e ned by he same se o equa ions. These submodels a e in e connec ed h ough delay cells, which ac-
coun o he anspo delays be ween cells a anged in pa allel o in se ies. The o e all schema ic o a submodel,
illus a ing all known and unknown a iables as inpu s and ou pu s, is shown in Figu e 3.6. By applying he con-
se a ion laws and s a e equa ions ela ed o he wa e , solu ion and apo , we can de e mine he ep esen a i e
alues o ou s a e ec o . Gene alized in eg al balances o show he o e all dependencies o each s a e will be
gi en in he nex sec ion. Fu he mo e, de ails o he solu ion s uc u e, along wi h he inpu and ou pu ec o s
a e p o ided.
Figu e 3.6: Full inpu and ou pu configu a ion o one submodel.
16 Deli e able D3.1
Coming o he las s a e, i is he en halpy o he wa e in he o e all EC uni . I is employed o de e mine how much
ene gy is used o sensible and la en hea . The o e all ene gy balance is defined as:
∂Ux5, EC
∂ =˙
Hin, EC −˙
Hou , EC +˙
QHT −˙
Qe ap .(3.30)
Exchanging he defini ion o he in e nal ene gy o he o e all en halpy and inco po a ing he anspo equa ions,
we find ha he en halpy o he con ol olume is defined by:
∂x5, EC
∂ =˙
mH2O, in
mH2O, in
·cp·(TEC, in −T e )−˙
mH2O, in −˙
me ap
mH2O, in
·cp·(x1, EC ( )−T e )
(3.31)
+αEC ·AEC
mH2O, in
·(( EC, in −TEC, in)−(x2, EC( )−x1, EC( )))
log ( EC, in−TEC, in)
(x2, EC( )−x1, EC( ))−˙
me ap ·∆hLV
mH2O, in
+∂pEC
∂ ·VEC
To conclude he o e all defini ion o he Abso be /Deso be and E apo a o /Condense model, i needs o be em-
phasized, ha he model has no ye being es e . The equa ion o mula ion is finished howe e , such ha he nex
s ep in he de elopmen p ocess is o fix he model pa ame e s in oduced as pand o es he model simula ion.
23 Deli e able D3.1
4 CONCLUSION
In his epo , wo di e en modeling app oaches o he ope a ion o a sodium hyd oxide-based he mo-chemical
s o age sys em we e p esen ed. The fi s model, an in eg al he modynamic model, was de eloped using a coupled
NTU-e ec i eness app oach o accoun o bo h hea and mass ans e limi a ions. This model demons a es a
good abili y o p edic s eady-s a e sys em condi ions, hough u he expe imen al alida ion is equi ed o ully
assess i s accu acy.
The second model, a de ailed ansien model o he hea and mass exchange (HMX), elies on di e en ial equa-
ions and p o ides insigh s in o bo h he in e nal empe a u e dis ibu ion and he sys em’s ansien beha io .
Al hough he models p esen ed we e de eloped o NaOH sys ems, hei me hodologies can be ex ended o o he
wo king pai s, such as LiB -H2O. Fu u e esea ch will ocus on applying hese models o di e en sys em configu-
a ions and employing op imiza ion echniques o in es iga e how geome ic ac o s, pa icula ly he design o he
adso p ion (A/D) and e apo a ion-condensa ion (E/C) hea and mass exchange s, influence sys em pe o mance
and how his can be aken in o accoun in he p oposed models.
In summa y, hese wo modeling app oaches p o ide aluable ools o unde s anding and op imizing he ope a-
ion o he mo-chemical s o age sys ems, and hey o m he ounda ion o u he ad ancemen s in desc ibing,
con olling and designing so p ion he mal s o age sys ems.
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BIBLIOGRAPHY
Do ian Hoe ne (2024). p ope iesnaoh 0.1.8. h ps://pypi.o g/p ojec /p ope iesNaOH/. Accessed: 30.09.2024.
Magnus Holmg en (2024). X s eam, he modynamic p ope ies o wa e and s eam.
h ps://www.ma hwo ks.com/ma labcen al/fileexchange/9817-x-s eam- he modynamic-p ope ies-o -wa e -
and-s eam. MATLAB Cen al File Exchange. Accessed: 30.09.2024.
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au ho i y can be held esponsible o hem.
©BEST-STORAGE PROJECT. All igh s ese ed.
Any duplica ion o use o objec s such as diag ams in o he elec onic o p in ed publica ions is
no pe mi ed wi hou he au ho ’s ag eemen .
