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Energy 37 (2012) 346e358

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Energy

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Numerical dynamic simulation and analysis of a lithium bromide/water long-termsolar heat storage system

K. Edem N’Tsoukpoe, Nolwenn Le Pierrès, Lingai Luo*

LOCIE, CNRS UMR 5271-Université de Savoie, Polytech Annecy-Chambery Campus Scientifique, Savoie Technolac, 73376 Le Bourget-Du-Lac Cedex, France

a r t i c l e i n f o

Article history:Received 3 May 2011Received in revised form5 October 2011Accepted 10 November 2011Available online 16 December 2011

Keywords:Solar energyLong-term thermal storageLithium bromide/waterAbsorption systemsEnergy efficiencyDynamic simulation

* Corresponding author. Tel.: þ33 4 79 75 81 93; faE-mail address: lingai.luo@univ-savoie.fr (L. Luo).

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.11.020

a b s t r a c t

With a view towards better efficiency in renewable energy utilisation, particularly solar energy, theauthors study a long-term solar thermal energy storage based on water absorption by a lithium bromideaqueous solution. After a description of the process, the system dynamic simulation model is detailedand used to investigate the influence of certain parameters (heat exchanger size, solution flow rate,absorption percentage) and operating conditions (heat supply temperature to the building, crystal-lisation ratio, heat need) on the system performance (storage density, thermal efficiency, etc.). Theanalysis of simulations made for a low-consumption building in Chambéry shows that the solution flowrate is a critical parameter in the process performance. It also appears that crystallisation in the solutionstorage tank increases the storage density more than three times. The simulation results are used in thedesign of a prototype that is under experimentation for validation of the model.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Energy storage is very important for improving the efficiency ofrenewable energy systems and their large-scale utilisation. In thepast decade, long-term solar sorption and thermochemical heatstorage have generated a lot of interest, especially for solar appli-cations in buildings.

Sorption and thermochemical systems for long-term energystorage use a reversible physicochemical phenomenon [1]:

ABþHeat5Aþ B (1)

These systems operate in the charging mode during sunnyperiods and in the discharging mode during periods of heatingneed (Fig. 1). Solar energy is captured by solar thermal collectors,which provide heat to the compound AB in equation (1). AB is thusdissociated into compounds A and B: this is the charging phase. Aand B are then stored separately in different tanks. In winter,bringing together A and B turns their chemical potential into heat:this is the discharging phase.

This type of storage for buildings is presented by N’Tsoukpoeand colleagues [1], who point out the selection criteria, the

x: þ33 4 79 75 81 44.

All rights reserved.

materials currently studied and recent demonstrative projects.Even though considerable breakthroughs have been made, thereis still no mature long-term sorption heat storage technology.Most of the storage media studied are in the solid form and oftenhave to face a low heat transfer rate during the discharging phase[2e5]. The use of liquid media, such as a salt solution, is a way ofovercoming this limitation [6,7]. However, only a few solutionshave been considered for these applications: NaOH/H2O [8,9],CaCl2/H2O [10] and LiCl/H2O [11]. The last one [11] is commer-cialised for short-term heat storage. A numerical modelling ofthis process was developed to evaluate the system’s heat transferrates. Recently, exergy analyses have also been reported [12,13].They suggest that thermochemical thermal energy storage (TES)may be as efficient as, and more compact than, other types ofTES.

Based on certain selection criteria [1], especially thermody-namic, technical, and ecological ones, the LiBr/H2O pair waschosen as a good compromise in the framework of this researchproject. This well-known couple in absorption refrigerationprocesses offers acceptable thermodynamic equilibrium condi-tions (temperature levels) for the heat storage process [14,15]. Inthis paper, the operating principle of the process is presented anda dynamic model is detailed. Then, a preliminary investigation ofthe system performance is made based on several annual dynamicsimulations.

Fig. 1. Process operating principle.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358 347

2. System components and operating principle

2.1. System description

The principle of the absorption heat storage system is similar tothe absorption heat pump cycle. However, a heat storage system isa discontinuous process that needs at least two storage tanks, forboth the absorbent and the absorbate [1]. Because of this alterna-tion in the storage process, the four classic exchange units(absorber, desorber, condenser and evaporator) are not necessary.Indeed, the desorber may be designed so that it can be operatedalso as an absorber. Similarly, the condenser may be operated as anevaporator.

Fig. 2 shows the main components of the storage system, and anexample of an annual cycle on a Dühring chart is presented in Fig. 3.The process consists of four main components: a generator that canoperate as a desorber or an absorber, a condenser that can also

W1

Solar

supply

Heat to the

building

W2

T2i

T1o

T1i

T2o

T2v

Tgi

Tgo

T1

Generator

Solution tank

T2

LiB

rso

luti

on

Fig. 2. Schematics of the system and paramet

operate as an evaporator, a solution (LiBr aqueous solution) tankand an absorbate (water) storage tank.

At the beginning of the charging period, in summer, the solu-tion, which has a low LiBr mass fraction, is at the storage tankstemperature Ttank (point 1a, Fig. 3). This diluted solution is pumpedfrom the solution tank to the generator (desorber) by pump W1(Fig. 2). It receives the thermal energy supplied by the solarcollectors and increases in pressure until the liquid/vapour pressureequilibrium is reached (point 2a) in the condenser. As the heatsupply continues and its temperature level is sufficient, the solutionreleases water vapour and becomes concentrated (point 2b) whenthe water vapour flows and condenses in the condenser (point 3a):this is the effective phase of desorption. The liquid water leaves thecondenser and is collected in the water tank (point 4). Meanwhile,the concentrated solution (with high LiBr mass fraction) whichexits the generator flows back to the solution tank (point 1b) whereit cools down because the tank is not insulated.

W4

Exchanged heat

with

environment

W3

T3v

T4o

T3o

T4i

Tco

Tci

Water tankT4

T3

Condenser/Evaporator

Liqu

id w

ater

Water vapour

T3i

V

ers/variables of the dynamic simulation.

Fig. 3. Dühring chart of lithium bromide/water cycle in annual absorption heat storage process.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358348

As the charging phase continues, the mass of the solution in thesolution tank decreases progressively. The mass of the water in thewater tank and the concentration of the solution in the solutiontank increase. When stopping the mass transfer between thesolution tank and the other components by closing valve V (Fig. 2),this heat is stored as a chemical potential with little loss.

In heating periods, especially in winter, valve V is opened andthe concentrated solution is transferred to the generator (absorber)by W1 while the water is pumped by W4 from its tank to theevaporator (point 3b). The water vapour produced is absorbed bythe solution until the pressure equilibrium is reached in thegenerator and the evaporator (point 2c). Then, absorption takesplace at a constant pressure (2c/2d) and the useful heat producedis evacuated by the heating loop fluid. The diluted solution ob-tained (point 2d) returns to the solution tank (point 1a).

The above-mentioned cycle description is theoretical and pre-sented for explanatory purposes. In particular, state 2c is a non-equilibrium liquid stage, therefore its pressure and concentrationcan be indicated on the chart but not its temperature. Besides, thetemperature, concentration and pressure levels change throughoutthe year.

During the year, there may be many cycles of repeated chargingand discharging phases, according to the solar heat availability andthe heating needs of the building.

Fig. 4. Desorption heat contribution: comparison between a typical LiBr absorption m

The condenser exchanges heat with the environment througha heat sink (charging phase) and the evaporator with a heat source(discharging phase). A cooling tower and a geothermal source canbe used for the charging and discharging periods, respectively.

2.2. Introductory considerations - terminology

2.2.1. Circulation heat lossThe heat supplied to the desorber is used for two contributions

(Fig. 3):

- a sensible heat that represents the energy required to raise thegenerator inlet solution to the desorption temperature (stage1a/2a in Fig. 3).

- the heat of vaporisation of pure water and the heat of mixing ofthe aqueous solution [16]: this corresponds to the effectivephase of desorption (stage 2a/2b in Fig. 3).

In the typical design of LiBr absorption chillers, the sensible heatis about 13%e15% of the total heat requirement (Fig. 4) with the useof a solution heat exchanger (SHX). Without this SHX, the sensibleheat represents 30% of the energy need. In a storage process withthe same concentrations (generator inlet and outlet) and desorp-tion temperature, this sensible heat share is even larger (40%)

achine and an absorption heat storage process in the same operating conditions.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358 349

because the solution temperature at the generator inlet is lower(about 5 �Ce10 �C when it is usually at least 30 �C (absorber outlet)for typical absorption chillers [17]). This energy, which is releasedto the surroundings when the hot solution returns to the solutiontank, is called “circulation heat loss” in this paper.

2.2.2. Storage densityThe storage density of the process can refer to the amount of

energy accumulated per unit mass of anhydrous LiBr. It could alsobe understood as the amount of energy accumulated per unitvolume of LiBr aqueous solution at the surrounding temperature ofthe solution tank. The higher the amount of water available forabsorption, the greater the amount of sorption heat that can berecovered. To reach this goal, the largest difference between thesolution concentration limits should be reached [15]:

- the minimum concentration (the diluted solution concentra-tion,when thewater tank is empty) shouldbe as lowaspossible.It corresponds to point 1a (Fig. 3) and is fixed by the desiredabsorption temperature (Ta) and evaporator temperature (Te).

- the maximum concentration (the concentrated solutionconcentration, when the water tank is full) is limited by theLiBr solubility (saturation concentration) at the storage tanktemperature.

The storage density of the LiBr aqueous solution in this paper isrelative to the diluted solution [1].

2.2.3. Crystallisation ratio and solution concentrationTo increase the storage density, the solution can be concentrated

beyond the saturationpoint at the tank temperature and storedwithcrystals. Indeed, if themaximumconcentration of the cycle is higherthan the solubility of the LiBr solution, crystals appear. In this case,the tank content in LiBr is the total mass of anhydrous LiBr (LiBr inthe crystal þ LiBr in the solution) divided by the total mass of thetwo-phase mixture (slush ¼ solid þ liquid) in the tank. It will bedesignated as the global concentration of the solution in this paper.

The crystallisation ratio r is the solid mass fraction in the solu-tion tank. It is an indicator of the crystallisation level in the solutiontank. A tank without crystals leads to r ¼ 0. rmax ¼ 80% means thatthe maximum mass fraction of solid in the solution tank duringa complete cycle is 80%. The lower the water contained in thecrystal form (hydrate), the higher the maximum global concen-tration of the solution that can be reached, and thus the higher thestorage density. At the temperature of the storage tank surrounding(5e10 �C), the LiBr crystal is dihydrated and contains 29 m% ofwater (Fig. 3).

When crystallisation is permitted, the technical complexity ofthe process increases, in particular the solution pumping. Forexample, to avoid clogging of the outlet tube of the solution storagetank, the solution has to be pumped near its surface. At the end ofa charging day, the solution is also circulated for a few minutesbetween the tank and the desorber without heat supply to ensurethe solution in the tubes is as diluted as possible.

2.2.4. EfficiencyIn this paper, storage thermal efficiency is defined as the useful

heat provided to the building by the absorber divided by the energysupplied to the generator by the solar collectors :

hstorage ¼

ZQbZQsc

3. System modelling and dynamic simulation

In order to evaluate the system performance (storage density,efficiency, required collector area, etc.) and identify the parametersthat influence significantly the performance, a model was devel-oped for dynamic simulations. This model considers the transientcharacteristics of the system, inherent in the operating conditionsof the process that change year-round: daily variations of the solarradiation, the environment (heat sink or source) and the buildingheating need, variation of solution concentration in the storagetank, crystal formation, etc. Thermal loss to the environment,thermal inertia of the walls, heat and mass transfer limitations invarious components and the energy consumption by auxiliaryequipment (especially the pumps) are also considered. Fig. 5 showsthe computational procedure of the model. Its main originalitycompared to previous absorption machine models [15e19] is that ittakes into account the two distinct storage phases with crystal-lisation of the solution in the storage tank. It can thus quantify theinfluence of crystallisation on the system behaviour andperformance.

3.1. System modelling

The model is based on the energy and mass balance equationsand the properties of the LiBr/H2O pair [18,19]. The main inputs ofthe model are the incident solar radiation and the solar collectorarea, the ambient temperature and the heating demand, the flowrates of the solution and water and the overall heat transfer coef-ficients UA of the heat exchangers. The model calculates the systemvariables such as the component pressures and temperatures, thesolution concentration in the generator and the solution tank, themass of water in the water tank, the mass of solution and of crystalin the solution storage tank, the pump consumption, heat loss tothe environment, etc.

3.1.1. Solar collectorsA simplified model of a flat-plate solar collector in which the

collector thermal inertia is neglected is adopted [20,21]. The usefulheat Qsc delivered by the collector with area Asc to the heat transferfluid is:

Qsc ¼ I$Asc$hsc ¼ mg$Cppw$ðTsco � TsciÞ (2)

The collector efficiency hsc is given by [20]:

hsc ¼ ho � a1$Tm � Text

I� a2$

ðTm � TextÞ2I

(3)

where Tm ¼ Tsco þ Tsci2

(4)

The chosen thermal collector efficiency parameters (Table 1) arethose which are suggested for simulation studies within the IEA-SHC Task 32 [22].

3.1.2. GeneratorThe internal temperature T2 in the generator is assumed to be

uniform (Fig. 2) even if it varies along the heat exchanger due to thevariation in the concentration of the solution [23]. As in moststudies on absorption systems and supported by various experi-ments, the generator model is based on heat transfer [16,24]. Thepower exchanged by the generator’s internal (solution) andexternal flows is evaluated by using the logarithmic meantemperature difference approach. The modelling rests on theassumption that the value of the overall heat transfer coefficient ofthe generator heat exchanger (UA)2 is constant. In fact, the value of

Start

Parameters

Initial conditions

Thermal collectors simulation

Properties of aqueous LiBr

Heating need

Weather data

Simulation of the 4 components, pumps, etc.

No

Store the results

t = t + dt

Variables initialisation

t = last time

Stop

Yes

Fig. 5. Basic flow chart of the computer model for the of the solar absorption heat storage system for building heating.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358350

UA vary somewhat with the temperature as well as with the massflows, but this variation is relatively small inmost cases [23,25]. Theexchanged heat in the generator is therefore:

Q2 ¼ ðUAÞ2$Tgi � Tgo

ln�Tgi � T2Tgo � T2

� ¼ mg$Cppw$�Tgi � Tgo

�(5)

Equations (6) and (7) are solved to estimate the generator heatloss to the environment, assuming that the generator shell isisothermal. Equation (6) expresses the generator shell internalenergy variation, which is the difference between the internal heatreceived by convection and the external one.

ðMCpÞ2sh$dT2shdt

¼ ðUAÞ2shint$ðT2�T2shÞ�ðUAÞ2shext$�T2sh�Tref

�

(6)

Q2loss ¼ ðUAÞ2shint$ðT2 � T2shÞ (7)

In order to take into account the fact that the solution leavingthe generator is not in equilibrium conditions [16], a mass transfereffectiveness a [26], also called absorption percentage [23,27] orabsorption equilibrium factor [28], is introduced in Eq. (11). Theabsorption percentage is the ratio of the actual change in concen-tration of the solution to the maximum possible change that couldbe obtained with an infinitely long plate. The maximum possiblechange is the difference between the generator inlet concentrationand the equilibrium concentration.

Table 1Parameters and inputs for the simulations.

h0 0.8 UA2, UA3 400 W �C�1 dt 60 sa1 3.5 W m�2$�C�1 UA1/2, UA2/1 10 W �C�1 a 1a2 0.015 W m�2$�C�2 UA2/3, UA3/2 0 W �C�1 hisW1, hisW2 0.8v1o 3$10�6 m3 s�1 UA3/4, UA4/3 10 W �C�1 Ttank 5 �Cv1o*a 6$10�6 m3 s�1 UA2shint, UA3shint 4000 W �C�1 Tref 15 �Cv4o 3$10�6 m3 s�1 UA2shext, UA3shext 0.4 W �C�1 Tgmin 40 �Cvg, vc 2$10�4 m3 s�1 MCp2, MCp3 9000 J �C�1 Tint 16/20 �C

a The solution flow rate during desorption v1o* is the double of that in absorptionv1o.

Mass and energy balances in the generator yield equations.(8e17):

m2i ¼ m1o ¼ v1o$rsol

�T1;x1liq

�masscontinuity equation (8)

m2i ¼ m2o þm2v global mass balance (9)

m2i$x2i ¼ m2o$x2o LiBr mass balance (10)

x2i � x2o ¼ a$�x2i � x2oeq

�(11)

m2i$h2iþQ2 ¼m2o$h2oþm2v$h2vþQ2loss energybalance (12)

P2 ¼ P2v ¼ P3v ¼ P3 (13)

P2 ¼ PsolðT2; x2oÞ state equation (14)

T2 ¼ T2o ¼ T2v ¼ T3v (15)

m1o$h1oþw1 ¼m2i$h2iþQ1/2loss energybalanceontube1/2(16)

h2o ¼ hsolðT2; x2oÞ state equation (17)

3.1.3. Condenser/evaporatorThe modelling of the condenser heat exchanger is similar to that

of the generator. It is added to the previous assumptions that theamount of water vapour desorbed in the generator is completelycondensed in the condenser. Conversely, all the water vapourproduced in the evaporator is absorbed by the solution in theabsorber.

m3i ¼ m4o ¼ v4o$rwliqðT4Þ

m3i þm3v ¼ m3o global mass balance (18)

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358 351

m3i$h3iþm3v$h3v ¼m3o$h3oþQ3lossþQ3 energybalance (19)

P3 ¼ PwðT3Þ (20)

T3 ¼ T3o (21)

m4o$h4oþw4 ¼m3i$h3iþQ4/3loss energybalanceontube4/3(22)

h3o ¼ hwliqðT3Þ state equationðsaturationÞ (23)

h3v ¼ hwvðT2; P2Þ state equation (24)

3.1.4. Solution tankThe tank is modelled based on global mass and energy balances.

The solution tank is then assumed to be well mixed (temperatureand concentration) and the solution mass accumulated in the othercomponents of the process is disregarded in comparison to thesolution mass in the storage tank. Crystals are considered to be inequilibrium with the saturated solution when they appear. Thefollowing equations apply:

M1 ¼ M01 þ ðm1i �m1oÞ$dt global mass balance (25)

M1$x1 ¼ M1liq$x1liqþMcr$k ¼ MLiBr LiBrmassbalance (26)

M1liq$h1liq þMcr$hcr ¼ M01liq$h

01liq þM0

cr$h0cr þ ðm1i$h1i � Q1loss

�m1o$h1oÞ$dt energy balance (27)

Q1loss ¼ UA1$ðT1 � TtankÞ heat loss to the ambient (28)

h1o ¼ h1liq ¼ hsol�T1; x1liq

�state equation (29)

P1 ¼ Psol�T1; x1liq

�state equation (30)

m1i$h1i þ Q2/1loss ¼ m2o$h2o energy balance on tube 2/1(31)

hcr ¼ h1liq þ Dhcr Dhcrz64:5 kJ kg�1½29� (32)

3.1.5. Water tankAssumptions in the water tank modelling are the same as in the

case of the solution tank except that there is no crystal formation:

M4 ¼ M04 þ ðm4i �m4oÞ$dt global mass balance (33)

M4$h4 ¼ M04$h

04 þ ðm4i$h4i � Q4loss

�m4o$h4oÞ$dt energy balance (34)

Q4loss ¼ UA4$ðT4 � TtankÞ heat loss to the ambient (35)

h4o ¼ h4 ¼ hwliqðT4Þ state equationðsaturationÞ (36)

P4 ¼ PwðT4Þ state equationðsaturationÞ (37)

m4i$h4i þ Q3/4loss ¼ m3o$h3o energy balance on tube 3/4

(38)

3.1.6. Interconnecting tubesEvaluation of the heat loss of tubes that connect the process

components is made granted that the specific heat of the fluid inthe tube is constant along the tube. Equations (39) and (40), forexample, give the heat loss to the environment for the connectiontube between the generator and the solution tank.

T1i ¼ Tref þ�T2o � Tref

�$exp

��ðUAÞ2/1m1i$Cpsol

�(39)

Q2/1loss ¼ m2o$ðh2o � h1iÞ (40)

Equation (39) results from the local energy balance on the tube:

�m1i$Cpsol$dT ¼ dðUAÞ$�T � Tref

�(41)

3.1.7. PumpsThe energy transferred to the solution and to the water by the

pumps (W1 and W2) is estimated by considering an isentropicefficiency his for each pump. The density of the liquid is assumedconstant between the tank outlet and the heat exchanger inlet.Thus, equation (42) gives the work w1 provided by W1 to thesolution.

w1 ¼ v1o$ðP2 � P1ÞhisW1

(42)

A value of 0.8, which is relatively low, is used for the isentropicefficiency of the pumps, as its influence on the system performanceis low.

3.1.8. Environment: heat sink/low-temperature heat sourceSimplified models for the condenser heat sink (charging period)

and the evaporator low-temperature heat source (dischargingperiod) are introduced. The temperature of the cooling fluid at theentrance of condenser Tci is set to 3 �C below the outdoor airtemperature when the latter is higher than 10 �C; otherwise, Tci isset to 5 �C. The heat transfer fluid temperature entering the evap-orator is constant and equals 10 �C.

3.2. Inputs and assumptions of the simulations

The main input data of the model are the meteorological dataand building heating need. Solar radiation and outdoor airtemperatures measured during 2005 in Chambéry, in the alpineregion of France, are used (the data record interval is 5 min). Toevaluate the heating need, a simplified method is applied since theaim of this work is not an accurate modelling of a building, but thatof the storage process. The heating need, equation (43), is estimatedby an overall heat loss coefficient for the building and a basetemperature Text of 10 �C (the outside temperature above whicha building needs no heating).

Qb ¼ ðUAÞb$ðTint � TextÞ (43)

The comfort temperature Tint is set to 20 �C at daytime and 16 �Cat night-time.

Unless otherwise specified, the parameters are those presentedin Table 1. The simulations were performed for a single familyhouse of 120 m2 that meets Passive House standards [30] in orderto achieve 100% solar fraction. Its annual heating need is about1800 kWh, with a peak heat load of 1.2 kW.

Fig. 6. Masses and concentration change in the storage tanks.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358352

The generator and condenser external loops are charged with35 m% propylene glycol [31]. The generator inlet temperature islimited to 90 �C in order to curb the crystallisation risk in thegenerator. Storage tanks are presumed to be buried underground orput in a basement where the ambient temperature Ttank is assumedconstant. As for the condenser and the generator, they are in a non-heated space in which temperature Tref is also considered to beconstant.

3.3. Dynamic evolution of the system

Fig. 6 describes the masses and concentration changes in thestorage tanks for a system that is designed to reach a maximumcrystallisation ratio rmax ¼ 67%. This means that the crystal massis double that of the liquid solution at the end of the chargingperiod. On the abscissa, the first date is March 11, when thesolution mass is at its maximum. Progressively, this massdecreases while water is desorbed to the water tank. The solutionmass reaches its minimum in September, when the chargingprocess stops because the fixed maximum global concentration isreached (66.5 m%). Crystals first appear by mid-June as the

0

10

20

30

40

50

60

70

80

90

100

00.0800.97Dat

Tem

pera

ture

[°C

]

Generator

Generator

Outdoor te

Exchanged

29-05-2005 30-05-2005

Fig. 7. Temperatures and power exchanged at the gen

solution concentration exceeds the LiBr solubility at about 5 �C(58.1 m%). In November, when heating needs appear, absorptiontakes place and the stored water is consumed until the beginningof a new charging period.

The temperatures and power exchanged at the generator overthree days in charging and in discharging periods are shown inFigs. 7 and 8, respectively. The depicted power is the powerexchanged at the generator with the fluid of the solar loop(charging period) or the heating loop (discharging period). Thus, ithas positive values in charging and negative values in dischargingperiods, respectively. In charging periods, actuating of the solutionpump W1 occurs when the temperature of the heating fluid fromthe solar collectors reaches Tgmin ¼ 40 �C. During a very sunny daylike onMay 29 (Fig. 7), the generator inlet fluid temperature cannotexceed 90 �C. On the contrary, during May 30, which was not verysunny, desorption was not significant (Q2 < 1 kW) because, most ofthe day, the solar loop fluid temperature did not reach Tgmin. Whenthe system is at rest, the temperature of the generator decreases asits wall cools down.

In Fig. 8, the absorber temperature is around 35 �C. It rises whenthe building need is low, during night-time for example, when the

00.2800.18e

Pow

er [

kW]

temperature

inlet water temperature

mperature

power in the generator

31-05-2005 01-06-2005

erator during three days in the charging period.

-10

0

10

20

30

40

50

Date

Tem

pera

ture

[°C

]

-2

-1.5

-1

-0.5

0

0.5

1

Pow

er [

kW]

Generator temperature

Generator oulet water temperature

Outdoor temperature

Exchanged power in the generator

21-12-2005 22-12-2005 23-12-2005 24-12-2005

Fig. 8. Temperatures and power exchanged at the generator during three days in the discharging period.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358 353

comfort temperature is low. In the winter period, there are alsosome sunny days, like on December 23, when desorption can occur(the generator then receives heat from the collectors, Q2 > 0). Thisphenomenon substantially contributes to increasing the storagedensity.

4. Parametric simulations and discussion

The process performances are strongly influenced by the oper-ating conditions but also depend on the design characteristics. Asthe system is complex and the number of independent variables islarge, the numerical model is used to identify the parameters thatmight have major effects on the key performance indicators of thesystem: storage density and thermal efficiency.

4.1. Effects of the design parameters

4.1.1. Heat exchanger sizeThe generator and condenser overall heat transfer coefficients

UA were varied from 0.2 to 0.8 kW �C�1 and results are reported in

200

300

400

4.02.0UAc [

Stor

age

dens

ity

of a

nhyd

rous

LiB

r [k

Wh/

t]

UAg =

UAg =

UAg =

UAg =

14 m²

61 m²

20 m²

15 m²

22 m²

13 m²

11 m²

11 m²

Fig. 9. Effect of heat exchangers transfer coefficients on the

Fig. 9. This UA range is chosen based on the power (<2 kW)necessary to cover the passive house needs. The storage density canbe improved by about 60% when increasing the heat exchangerperformance within the considered UA range. This is due to a lowerminimum concentration of the cycle. Indeed, the smaller temper-ature difference between the heat exchangers sides for high UAvalues for a given power has two consequences on the cycle. One isthat the evaporator temperature increases. The other is that therequired absorber temperature is lower.

The required solar thermal collector area also decreases whenthe UA value increases (Fig. 9) because desorption is more efficient.This is due to a higher generator temperature and lower condensertemperature on average. For very low UA values (for bothUAg ¼ UAc ¼ 0.2 kW �C�1 in the present case), the system perfor-mance drops sharply.

Further simulations with a solution heat exchanger (SHX)between the solution tank and the generator (Fig. 10) show that itstrongly improves the process thermal efficiency and its storagedensity. However, this SHX could lead to technical issues (crystalformation and tube clogging), and thus is not considered further.

8.06.0kW/°C]

0.2 kW/°C

0.4 kW/°C

0.6 kW/°C

0.8 kW/°C

11 m²

10 m²

11 m²

18 m²

18 m²

11 m²

11 m²

10 m²

storage density and the required solar collector area.

Fig. 10. Interpolation of a solution heat exchanger between the solution tank and thegenerator.

10

20

30

40

50

60

70

80

90

Tem

pera

ture

[°C

]

0

10

20

30

40

3424D

Cum

ulat

ive

of d

esor

bed

wat

er [

kg]

22-04-2005 23-04-2005

Fig. 11. Generator temperature and outlet concentration and mass of desorbed

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358354

4.1.2. Solution flow rate in the charging phaseSolution flow rate optimisation is an important issue for this

process, since its sensible heat losses are higher than in a refriger-ation cycle (Fig. 4). Simulations were performed considering threedays in the charging period (April 22e24, Fig. 11). The solution flowrate was varied between 0.0015 l s�1 and 0.012 l s�1 and thesimulation step duration dt was set to 1 s for these simulations. Thisflow rate range meets the specific flow rate (solution flow ratedivided by the generator power) used classically in absorptionchillers [17,32]. The solution side thermal resistance does notchange significantly with the solution flow rate [25]. Thus, UAvalues were set constant for these simulations. The simulationresults are summarised in Fig. 11.

When the solution flow rate is low, the system operates at highgenerator temperature (simulation n�1, Fig. 11) which leads toa lower solar collector efficiency. When the temperature limitationTgmax is taken into account, less profit is made from the solarresource and, therefore, less water is stored. On the other hand, fora high solution flow rate (simulation n�4, Fig. 11), the generatoroperates at low temperature and circulation heat loss increases.Indeed, the solar heat provided to the solution mainly contributesto its increase in temperature; thus, less heat is actually used forwater desorption: on April 24, for example, there was no gain in the

n°1: v = 0.0015 l/s

n°2: v = 0.003 l/s

n°3: v = 0.006 l/s

n°4: v = 0.012 l/s

5444ate

24-04-2005 25-04-2005

water during three days in charging period at different solution flow rates.

30

32

34

36

38

40

Tem

pera

ture

[°C

]

n°5: v = 0.0015 l/s

n°6: v = 0.003 l/s

n°7: v = 0.006 l/s

n°8: v = 0.012 l/s

1700

1750

1800

1850

1900

1950

772672572472Date

Mas

s of

wat

er in

the

wat

er s

tora

ge t

ank

[kg]

10-12-2005 11-12-2005 12-12-2005 13-12-2005

Fig. 12. Generator temperature and outlet concentration and mass of desorbed water during three days in discharging period at different flow rates.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358 355

water tank. Furthermore, as the flow rate increases, the requiredpumping power generally increases.

An optimum flow rate thus needs to be found. The flow rate of0.006 l s�1 in the charging period was retained for the followingsimulations in order to have a reasonable electricity consumption.

4.1.3. Solution flow rate in the discharging phaseSince absorption and desorption do not occur at the same time

in the storage process, the solution flow rate during charging anddischarging periods can easily be chosen differently.

The three considered days in the discharging phase areDecember 10e12 (Fig. 12). During this period, the solution tankcontained saturated solution. Thus, the generator entrance condi-tions were constant over the three days. The building heatingdemand was 51 kWh for the considered period.

Table 2Main simulation parameters and results for various absorption percentages.

simulation n� 9Absorption percentage a 0.75Solution minimum concentration in the storage tank (m%) 52.7Surface area of flat solar collectors (m2) 16Storage density of anhydrous LiBr salt (kWh$t�1) 269Storage density of LiBr aqueous solution (kWh$m�3) 226

When the solution flow rate increases (simulation 7 and 8 inFig. 12), the concentration change in the absorber decreases. Then,the average absorption temperature increases. This leads to highercirculation heat loss because the generator outlet solution flow rateand temperature are higher. Consequently, storage density isaffected negatively.

Moreover, the absorption temperature drops for very high flowrate values (simulation n�8, Fig. 12). This is due to the evaporatortemperature decrease because of the large amount of water thathas to be evaporated (bottom of Fig. 12). In this case, the evaporatorbecomes the limiting exchanger.

Finally, a low solution flow rate that is sufficient to supply therequired power at the desired temperature level and towet thewallof the absorber is advisable. The flow rate of 0.003 l s�1 wasselected for the following simulations.

10 11 12 13 140.80 0.85 0.90 0.95 1.00

52.1 51.7 51.1 50.7 50.415 15 13 13 13

281 292 300 312 321233 239 241 247 252

0

100

200

300

400

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%Maximum crystallisation ratio

Stor

age

dens

ity

of a

nhyd

rous

LiB

r [k

Wh/

t]

Stor

age

dens

ity

of L

iBr

solu

tion

[kW

h/m

3]

Tga = 30°C - mass density

Tga = 33°C - mass density

Tga = 30°C - volume density

Tga = 33°C - volume density

Fig. 13. Effect of the maximum crystallisation ratio and the average heat supply temperature to the building on the storage density.

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358356

4.1.4. Absorption percentageThe effect of the absorption percentage on the storage density is

studied through annual simulations. The requirements to reacha mean heat supply temperature of 30 �C and a maximum crys-tallisation ratio of 67% are summarised in Table 2. The storagedensity decreases with a low absorption percentage. Indeed, thesolution temperature in the absorber is lower than the equilibriumtemperature. Thus, a higher minimum concentration of the cycle isneeded. Similarly, during desorption, with low absorptionpercentage, the generator outlet bulk concentration is lower thanthe interface concentration so that the actual amount of generatedwater is lower than in equilibrium conditions. There are thengreater sensible heat losses and greater heat needs for desorption,which results in a larger solar collector area.

Special attention should thus be paid to the choice of generatorheat exchanger because the absorption percentage depends on theexchanger design and the solution flow rate [23,27].

4.2. Effects of the operating conditions

4.2.1. Maximum crystallisation ratioFig. 13 shows the storage density as a function of the maximum

crystallisation ratio at average heat supply temperatures of 30 �Cand 33 �C. A crystallisation ratio of r ¼ 99% is almost impossible,

Table 3Overview of the system dimensions for two buildings with different annual energyconsumption.

Simulation n� 14 17Maximum heat consumption for heating

purpose (kWh$m�2$year�1)a15 45

Maximum crystallisation ratio (%)a 67 67Mean heat supply temperature to the building (�C)a 30 30Solution flow rate in the generator for absorption (l s�1)a 0.003 0.009Generator and condenser heat exchanger

heat transfer coefficient (kW �C�1)a0.4 1.2

Total heat delivered to the building alongthe year (kWh)

1812 5431

Area of flat solar collector (m2) 13 39Storage density of anhydrous LiBr salt (kWh$t�1) 321 326Storage density of LiBr aqueous solution (kWh$m�3) 252 256Storage efficiency (%) 37.3 37.9

a Design data.

because of the solution circulation difficulties that would arise, butsimulations are made to weight the potential performances. Crys-tallisation can increase the storage density more than three times.However, above a maximum crystallisation ratio of 70%, savingsbecome less and less significant while the technical complexity ofthe process increases. The maximum crystallisation ratio for thefollowing simulations is thus set to 67%.

4.2.2. Average heat supply temperatureFig. 13 also shows the enhancement of the storage density when

reducing the building heating temperature. The lower the desiredabsorption temperature, the lower the required minimumconcentration of the solution. Correspondingly, the storage densityincreases. Such a process is thus quite suitable for energy-efficientbuildings with heating floor system. A medium temperature of30 �C is sufficient to provide comfort conditions in an efficientbuilding as suggested by others [33,34]; thus, this value will beconsidered for the following simulations.

4.2.3. Heat demandFinally, simulations were made for a house three times more

energy-consuming than the previous one, i.e. using45 kWh$m�2$year�1. The power demand, the overall heat transfercoefficients of the heat exchangers, the solution and water flowrates were trebled in order to keep the same range of temperaturedifference, making it possible to compare both systems (Table 3).

When the heating need increases, the required size of the maincomponents (solution and water tanks, solar collector area, etc.)increases almost proportionally.

The previous assumptions are open to criticism because whenthe solar collector surface increases (36 m2 for simulation n�17), itslayout could be optimised in order to have a better thermal effi-ciency, which would result in smaller collectors. Furthermore, thesolution flow rate selection may not lead to treble the rate of theinitial one.

5. Conclusion

This paper has presented a long-term solar heat storage systembased on water absorption by a LiBr aqueous solution. A detaileddynamic model of the system is developed for the system

K.E. N’Tsoukpoe et al. / Energy 37 (2012) 346e358 357

simulation in order to evaluate the process performance andoptimise its design. The following conclusions can be drawn fromthis study:

(1) The storage density increases with the heat exchangers sizebecause of a better heat transfer and smaller temperaturedifference between the heat exchangers sides, at the same flowrate. The required solar thermal collector area is significantlyreduced for the same reasons.

(2) The solution flow rate in the charging period is critical for thestorage density.When the solution flow rate is low, less profit ismade from the solar resource and therefore less water isgenerated and stored. On the other hand, when the solutionflow rate is high, the solar heat provided to the solution mainlycontributes to its increase in temperature and not to desorptionitself. A compromise is then needed.

(3) The solution flow rate in the discharging period also greatlyaffects the storage density. It must be as low as possible butsufficient to supply the required power at the desired dis-charging temperature and to wet the walls of the heatexchanger.

(4) The storage density decreases by about 20% when theabsorption percentage decreases from 1 to 0.75. The requiredcollector area for the system charging also increases due toa higher circulation heat loss.

(5) Crystallisation is necessary for the competitiveness of theprocess, since the required mass and volume are large withoutit.

(6) The discharging temperature selected should be as low aspossible in order to improve the storage density. This storageprocess is thus rather suitable for heating floors.

(7) When the heating need increases, the required size of the maincomponents (solution and water storage tanks, solar collectorarea, etc.) increases quite proportionally.

The current study was not designed to evaluate the interactionsbetween the considered parameters. An alternative to crystal-lisation, whose management also remains a challenge, could be theuse of additives that move the crystallisation line and allow a highmaximum concentration to be reached and, therefore, high storagedensity. Attention should also be paid to the system’s auxiliaryenergy consumptions (pumps). The process performance will beoptimised after model validation by experimental data froma prototype that is presently undergoing tests at the LOCIElaboratory.

Acknowledgements

Financial support was provided by the ANR (French NationalResearch Agency) under the research projects PROSSIS ANR-07-Stock-E-08 and ESSI ANR-08-Stock-E-04.

Nomenclature

GeneralA area (m2)a1 first order collector heat loss coefficient (W$m�2$�C�1)a2 second order collector heat loss coefficient (W$m�2$�C�2)Cp specific heat (J$kg�1$�C�1)dt simulation step duration (s)h specific enthalpy (J$kg�1)Dhcr specific enthalpy of solution of LiBr$2H2O (J$kg�1)I incident solar radiation (W$m�2)k mass fraction of anhydrous LiBr in the crystal hydrate

LiBr lithium bromidem mass flow rate (kg$s�1)m% mass percentM mass (kg)MCp heat capacity of heat exchanger tank shell (J$�C�1)MLiBr mass of anhydrous LiBr (kg)P pressure (Pa)Q heat (W)SHX solution heat exchangert time (s)T temperature (�C)Tm mean collector fluid temperature (�C)Ttank ambient temperature around the storage tanks (�C)U heat transfer coefficient (W$m�2$�C�1)v volume flow (m3$s�1)w work (W)x mass fraction of lithium bromide in the solution (m%)

Subscripts/Superscripts1 solution storage2 generator3 condenser or evaporator4 water storage1/2 tube connecting 1 to 20 value from previous time stepb buildingc condenser external loop fluidcr crystaleq equilibrium conditionsext exterior (outside)g generator external loop fluidi inletint interior (building)is isentropicliq liquidloss lossmax maximumo outletp propylene glycolref surroundingsc solar collectorsh tank shellshext external side of the tank shellshint internal side of the tank shellsol solutionv vapour phasew water

Greek symbolsa absorption percentageh efficiencyh0 optical efficiency of the solar collectorr density (kg$m�3)

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