ISHPC2024 In e na ional So p ion Hea Pump Con e ence
S eady-s a e Model o Closed-So p ion The mochemical Hea
S o age Sys ems
Do ian Hö ne (a), Elisabe h Thiele(a), Robe Kno e(a), Thomas Meye (a)
(a) Technical Uni e si y Be lin, Ins i u e o Ene gy Enginee ing
Ma chs aße 18, 10587 Be lin, Ge many
do ia[email p o ec ed]
ABSTRACT
In he ield o ene gy s o age, he classi ica ion and e alua ion o he mochemical s o age sys ems
pose signi ican challenges. Unlike o adi ional he mal s o age sys ems, capaci y, powe , and o he
key pe o mance indica o s (KPIs) canno be desc ibed easily, because hey s ongly depend on
di e se and in e dependen bounda y condi ions. The lack o a s aigh o wa d me hodology o
assessing hese sys ems hinde s he unde s anding o hei applica ion po en ials and hence i s
deploymen . This pape in oduces a modeling app oach aimed a simpli ying he assessmen o
abso p ion based he mo-chemical s o age sys ems, pa icula ly assessing he he modynamic s eady-
s a e condi ions. Me hodically, he p oposed model applies he NTU-e ec i eness me hod o he
desc ip ion o he coupled hea and mass ans e and wo ks as a modeling amewo k. While no
speci ic hea o mass ans e co ela ions a e implemen ed, he model allows o he inco po a ion o
such, making i a e sa ile modeling ool. The p ac ical u ili y o he p oposed model is demons a ed
h ough i s applica ion o a speci ic so p ion s o age sys em using sodium hyd oxide (NaOH) ha
could i in o a basemen o a single- amily dwelling. Wi h a comple e sys em se up consuming
app oxima ely 8.5m3, simula ions p edic ed an o e all capaci y o 473.3 kWh. The sys em s o age
densi y esul s in 55.7 kWh/m3. The ene gy densi y based on he s o age ma e ial alone was es ima ed
o 126.2 kWh/m3. Al hough he cu en s a e o he model does no include dynamic sys em beha io ,
i s alue as a con ol planning ool and design heu is ic could be shown. Fu he mo e, he model's
applicabili y a an ene gy sys em le el o e s po en ial h ough which he applica ion o he mo-
chemical s o age sys ems can be e alua ed, and hence con ibu es o he b oade unde s anding and
op imiza ion o ene gy s o age solu ions.
Keywo ds: abso p ion, he mal s o age, he mochemical s o age, he modynamics, hea and mass
ans e , model, simula ion
1. INTRODUCTION
The mo-chemical ene gy s o age (TCES) sys ems a e gaining signi ican a en ion due o hei
po en ially high ene gy s o age densi y and hei long- e m s o age capaci y. This documen
in oduces a simple nume ical model designed o p edic he modynamic s eady-s a e wo king
condi ions in a TCES sys em u ilizing he physiso p ion mechanism. The de eloped model aims o
ill a gap in exis ing li e a u e, whe e a comp ehensi e sys em-le el model o es ima e key
pe o mance indica o s (KPIs) has been lacking.
While sys em-based models o abso p ion he mal s o age a e sca ce in he li e a u e, alling ilm
eac o s ha e been analyzed and modeled by nume ous scien is s, ocusing on i ing expe imen al
da a o hea and mass ans e co ela ions. Fo example, [1] conduc ed expe imen s o a e ical
alling ilm eac o o LiB and Wa e by o mula ing Nu- and Sh-co ela ions o hea and mass
ans e . [2] conduc ed an expe imen al s udy on e ical alling ilm eac o s ocusing on luid low
and hea ans e . Speci ic mass low co ela ions o pu e wa e we e desc ibed by [3] and [4], who
de e mined e apo a ion and condensa ion coe icien s. Falling ilm hea ans e was in es iga ed and
ISHPC2024 In e na ional So p ion Hea Pump Con e ence
modeled by [5] and [6] o wa e . [7] de eloped a gene al app oach aiming o desc ibe hea ans e
o alling ilms o di e se luids and pipe diame e s.
In summa y, al hough abso p ion chille s and so p ion hea pumps ha e been p e iously in eg a ed
in o sys em simula ions using TRNSYS o simila p og ams [8] [9] [10], speci ic simula ions o
abso p ion-based TCES sys ems ha e been mo e limi ed. Fo ins ance, [11] conduc ed simula ions o
compa e di e en wo king luids, while [12] modeled he dynamic in eg a ion o sola he mal ene gy
wi h he LiB -wa e wo king pai , e alua ing TCES as a seasonal ene gy s o age solu ion. Howe e ,
[12] add esses he po en ial c ys alliza ion o he sal solu ion, p esen ing ope a ional challenges, and
[11] omi s a solu ion hea exchange , c ucial o sys em e iciency. Addi ionally, bo h s udies lack
de ailed in o ma ion on empe a u e condi ions in he hea ing and cooling ci cui s, which is essen ial
o sys em in eg a ion.
2. SYSTEM DESCRIPTION
The sys em unde conside a ion is a he mochemical s o age based on a closed abso p ion cycle,
whe e wa e is abso bed by a highly concen a ed sodium hyd oxide (NaOH) b ine. This app oach
le e ages he hyg oscopy o NaOH - and he esul ing apo p essu e dep ession e ec - o s o e and
elease he mal ene gy.
Figu e 1: Simpli ied illus a ion o he he mochemical s o age sys em modeled in his s udy.
Du ing he cha ging (deso p ion) phase, ex e nal hea , ypically sou ced om sola he mal ene gy,
is applied o he sys em's high- empe a u e side. This p ocess in ol es anspo ing dilu ed NaOH o
he Abso be -Deso be (AD) uni , whe e i is dispe sed o e a ho izon ally o ien ed alling ilm
eac o . The applied hea induces he e apo a ion o wa e , e ec i ely concen a ing he NaOH
solu ion, which is subsequen ly di ec ed o a s o age ank. Concu en ly, he wa e apo gene a ed is
condensed in he E apo a o -Condense (EC) uni , ans e ing hea o a low- empe a u e sink, such
as he ambien ai . This p ocess con inues un il he dilu ed solu ion ank is comple ely emp ied,
signi ying he sys em's ully cha ged s a e.
Con e sely, he discha ging (abso p ion) phase is ini ia ed when he e is a demand o hea . In his
phase, wa e is e apo a ed a low p essu es and empe a u es wi hin he EC uni , u ilizing hea sou ces
like ambien ai o low empe a u e geo he mal ene gy. The apo is hen abso bed by he high-
concen a ed NaOH solu ion as i lows o e he alling ilm eac o in he AD uni . This exo he mal
ISHPC2024 In e na ional So p ion Hea Pump Con e ence
abso p ion p ocess eleases he hea o condensa ion and mixing, making i a ailable o hea ing
applica ions a he high empe a u e hea sink. The sys em con inues o discha ge un il he
concen a ed NaOH solu ion ank is comple ely emp ied.
3. MODEL
The p ima y objec i e o his model is o p edic he s eady-s a e condi ions be ween he
E apo a o /Condense (EC) uni and he Abso be /Deso be (AD) uni , ocusing on hei coupled
he modynamic s a es conside ing he low and high empe a u e hea sink and sou ce, espec i ely.
The scope o his model includes p o iding a s uc u ed app oach o s eady-s a e modeling o closed-
anspo ed so p ion he mal ene gy s o age sys ems as desc ibed by [13] and illus a ed in Figu e 2.
While he model does no aim o de ail speci ic hea o mass ans e phenomena, i s s uc u e is
designed o accommoda e he u u e inco po a ion o such de ails.
The model uses all inpu pa ame e s and gene al sys em pa ame e s om he in lowing s eams o
calcula e s eady-s a e condi ions. This is illus a ed in Figu e 2, whe e inpu a iables a e depic ed in
black and he ou pu a iables in g ay. This igu e is applicable o bo h he cha ging and discha ging
p ocesses, p o iding a comp ehensi e o e iew o he model's capabili ies.
Figu e 2: Inpu and ou pu pa ame e s o he p oposed model. Legend: p - p essu e, A - a ea, U - hea ans e
coe icien , d - hickness, 𝝀 - hea conduc i i y, x - b ine mass ac ion, T/ - empe a u e, 𝒎
- mass low,
𝜻 - ic ion coe icien o pipe low
The model is buil on he ounda ion o hea and mass balances, u ilizing NTU-e ec i eness (ε-NTU)
me hods o desc ibe hea and mass ans e p ocesses wi hin he EC and AD uni s. A dis inc i e
ea u e o ou app oach is he coupling o ε-NTU o hea and ε-NTU o mass ans e h ough
subs ance p ope ies, as illus a ed exempla y in Figu e 3.
This coupling me hod was inspi ed by [14] and allows o he p edic ion o he ilm su ace
empe a u e. Addi ionally, he model inco po a es one-dimensional, s eady-s a e, and linea modeling
o hea conduc ion h ough he ilm and ubes in he AD uni , whe e he ilm bulk empe a u e is
assumed o be he a i hme ic mean be ween he liquid su ace and he ube wall. As men ioned abo e,
he model inhe en ly en ails he possibili y o inco po a ing mo e de ailed hea and mass ans e
coe icien s in u u e e sions.
ISHPC2024 In e na ional So p ion Hea Pump Con e ence
Figu e 3: Illus a ion o he p ocess condi ion ε-NTU model o he hea and mass exchange s. 𝑻𝑨𝑫,𝒔𝒂𝒕 and 𝒙𝑨𝑫,𝒔𝒂𝒕
ep esen he solu ion ilm su ace condi ions. The depic ed g aphs show he discha ging p ocess.
4. RESULTS
Wi h he p oposed model, a calcula ion o he mean ilm su ace empe a u e and concen a ion
in ela ion o ce ain bounda y condi ions and design ea u es o a speci ic sys em is achie ed. This
mean su ace condi ion, in u n, can hen be used o calcula e he mean hea and mass ans e a es
and help p edic ing he sys em beha io . Figu e 4 illus a es he wo king condi ions o an exempla y
sys em o ypical condi ions. As isible, he subs ance sa u a ion condi ions a e di e en om he
ilm su ace condi ions as hea and mass ans e limi a ions a e imposed. This is shown in Figu e 4
(le ).
Figu e 4: Illus a ion o he ilm su ace condi ions calcula ed by he model. On he le side, a single ope a ion
poin is shown. On he igh side, he solu ion mass low was a ied.
Using he model, we can heo e ically analyze how he pe o mance (KPIs) o he s o age sys em
a ies wi h a single inpu a iable, while keeping o he pa ame e s cons an , such as hea and mass
ans e coe icien s and ilm hickness. Fo ins ance, by adjus ing he solu ion mass low, we
iden i ied a empe a u e maximum (Figu e 4, igh ) and powe maximum (Figu e 5, le ). The
posi ions o hese maxima depend on he ope a ional bounda y condi ions, o example he size o he
solu ion hea exchange (SHX) as illus a ed in Figu e 5. Speci ically, when he solu ion en e s he
ISHPC2024 In e na ional So p ion Hea Pump Con e ence
abso be a a lowe empe a u e, he necessa y p ehea ing educes he powe ou pu and shi s he
powe maximum downwa d and o he le .
Figu e 5: E ec o he a ia ion o solu ion mass low and solu ion hea exchange (SHX) hea ans e a ea.
5. CASE STUDY
This chap e demons a es he p ac ical applica ion o he he mochemical abso p ion s o age model
in oduced ea lie . By u ilizing he model, key pe o mance indica o s (KPIs) o he s o age sys em
a e calcula ed and analyzed, highligh ing he sys em's po en ial e ec i eness and a eas o
imp o emen . KPIs such as e iciency, ene gy densi y, and ope a ional imes a e c ucial o
e alua ing he pe o mance and iabili y o he mal s o age sys ems.
The simula ed case s udy was buil a ound a seasonal s o age sys em designed o i in o a basemen
o a single- amily dwelling. Speci ically, he s o age ank o he high concen a ed solu ion is 3.0 m3,
esul ing in a solu ion mass o 4584 kg. Assuming a concen a ion change o 10%, he low
concen a ed solu ion ank would need o be 3.7 m3. In a combined ank se up using mo able
memb anes, we assume a o al space consump ion o 5.0 m3. The sepa a e wa e ank would equi e
an addi ional 1.5 m3 o space. The e apo a o /condense (EC) and he abso be /deso be (AD) uni s
a e designed as ho izon ally s agge ed ube alling ilm eac o s. The hea ans e a ea o he EC-
uni is 1.0 m², while he AD-uni a ea is 3.0 m². The solu ion hea exchange a ea is con igu ed as a
pla e hea exchange wi h a hea ans e a ea o 2.0 m².
Hea and mass ans e assump ions we e collec ed om he li e a u e. The U- alue o he
e apo a o /condense (E/C) uni was assumed o be 1600 W/m²K, based on li e a u e alues anging
om 700 o 4000 W/m²K o alling ilm wa e e apo a o s [15] [16]. The U- alue o he A/D-uni
was assumed o be 700 W/m²K du ing abso p ion, de i ed om esea ch on ho izon al alling ilm
abso be s wi h alues be ween 300 and 3000 W/m²K [17] [18] [19]. These s udies ocused on coppe
ubes, which ha e signi ican ly be e hea conduc i i y han he s ainless-s eel ubes used in ou case
s udy. Du ing deso p ion, an inc eased hea ans e coe icien o 1000 W/m²K was assumed, due o
s eam o ma ion and he esul ing hea ans e imp o emen epo ed by [16]. The mass ans e
coe icien 𝛽 was es ima ed o be 0.005 kg/m²s. This assump ion was backed by heo e ically
calcula ing 𝛽 = 𝐷
𝛿𝜌 based on he di usion coe icien s 𝐷 o wa e in aqueous sodium hyd oxide [20]
and an es ima ed mean bounda y laye hickness 𝛿 o 0.01 mm. The ilm hickness o he ixed
solu ion mass low was se o 0.2 mm. The hea ans e coe icien o he solu ion hea exchange
was assumed o be 1600 W/m²K.
Bounda y condi ions o he model include a ank empe a u e o 12°C, a geo he mal sou ce
empe a u e o 10°C, and a sola he mal empe a u e o 75°C du ing cha ging imes. To each a
ISHPC2024 In e na ional So p ion Hea Pump Con e ence
sa is ac o y mass ac ion change du ing abso p ion, he solu ion needs o be eci cula ed. The
building e u n empe a u e was se a 36, 35, 34 °C o he i s , second, and hi d pass, espec i ely.
The ex e nal mass lows we e se o eaching a empe a u e li o 2 K. The solu ion mass low was
ixed a 0.02 kg/s, ensu ing good we ing and unc ionali y as p o en by expe imen al wo k. Unde
he speci ied bounda y condi ions, he model p oduces se e al key pe o mance indica o s (KPIs),
which a e displayed in Table 2.
Table 2: Simula ion esul s and basic s o age KPIs. The cha ging and discha ging powe and he cha ged o
discha ged ene gy indica e he powe /ene gy ans e ed be ween he A/D uni and he ho empe a u e
sink/sou ce. Cycle e iciency is de e mined as he a io o discha ged ene gy o cha ged ene gy.
Cha ging (Single Pass)
Discha ging (Th ee Passes)
Cha ging Powe
7.538
kW
Discha ging Powe
2.478
kW
Cha ged Ene gy
478.9
kWh
Discha ging Ene gy
473.3
kWh
Cha ging Time
63.7
h
Discha ging Time
191.0
h
Cycle E iciency*
0.986
Sys em Ene gy Densi y
55.7
kWh/m3
*no hea losses du ing so p ion
o p ehea ing modeled
Ma e ial Ene gy Densi y
126.2
kWh/m3
6. CONCLUSION AND FURTHER RESEARCH
The p esen ed model se es as a cohe en amewo k ha can be in eg a ed wi h a ious hea and
mass ans e co ela ions. I o e s a obus app oach o modeling abso p ion-based s o age sys ems,
accommoda ing all ele an bounda y condi ions. This comp ehensi e model enables o e all
pe o mance assessmen s and suppo s he de elopmen o op imized s o age solu ions con aining all
key design pa ame e s.
Fu u e i e a ions o he model should inco po a e addi ional ea u es o enhance i s accu acy and
applicabili y. These ea u es include accoun ing o he mal losses du ing he p ocess o be e e lec
eal-wo ld condi ions and dynamizing he model o depic ansien beha io s, po en ially h ough
ime cons an s de i ed om u he expe imen al wo k. Addi ionally, conduc ing in-dep h
compa isons wi h o he s o age sys ems using a b oade se o KPIs will p o ide a mo e
comp ehensi e analysis. De ailed expe imen al alida ion will also be c ucial o con i m he model's
eliabili y and accu acy. These enhancemen s will con ibu e o a mo e ho ough unde s anding and
op imiza ion o he mochemical abso p ion s o age sys ems, pa ing he way o hei p ac ical
implemen a ion and in eg a ion in o ene gy sys ems.
ACKNOWLEDGEMENTS
This esea ch was unded by he Eu opean Union’s Ho izon p og am. The unding was g an ed by
he Eu opean Clima e, In as uc u e and En i onmen Execu i e Agency (CINEA) unde he BEST-
S o age p ojec (101096516).
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