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Modeling and analysis of energetic and exergetic efficiencies of a LiBr/H20 absorption heat storage system for solar space heating in buildings

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Abstract

The development of efficient long-term heat storage systems could significantly increase the use of solar thermal energy for building heating. Among the different heat storage technologies, the absorption heat storage system seems promising for this application. To analyze the potential of this technology, a numerical model based on mass, species, energy, and exergy balances has been developed. The evolution over time of the storage imposes a transient approach. Simulations were performed considering temperature conditions close to those of a storage system used for space heating coupled to solar thermal collectors (as the heat source), with ground source heat exchangers (as the cold source). The transient behavior of the system was analyzed in both the charging and discharging phases. This analysis highlights the lowering of energetic and exergetic performance during both phases, and these phenomena are discussed. The thermal efficiency and the energy storage density of the system were determined, equal to 48.4 % and 263 MJ/m3, respectively. The exergetic efficiency is equal to 15.0 %, and the exergy destruction rate is 85.8 %. The key elements in terms of exergy destruction are the solution storage tank, the generator, and the absorber. The impact of using a solution heat exchanger (SHX) was studied. The risk of the solution crystallizing in the SHX was taken into account. With a SHX, the thermal efficiency of the system can reach 75 %, its storage density was 331 MJ/m3, and its exergetic efficiency and exergy destruction rate was 23.2 and 77.3 %, respectively.

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Abbreviations

Ex :

exergy (J)

Ėx :

exergy flux (W)

ex :

specific exergy (J/kg)

h :

specific enthalpy (J/kg)

m :

mass (kg)

:

mass flow rate (kg/s)

P :

pressure (Pa)

Q :

heat (J)

\( \dot{Q} \) :

thermal power (W)

s:

specific entropy (J/(kg.K))

t :

time (s)

T :

temperature (K)

U :

internal energy (J)

u :

specific internal energy (J/kg)

V :

volume (m3)

v :

specific volume (m3/kg)

W :

mechanical work (J)

:

mechanical power (W)

x :

mass fraction of lithium bromide (x = m LiBr /m sol ) (kgLiBr/kgsol)

ε :

heat exchanger effectiveness

μ:

chemical potential (J/kg)

η:

efficiency (−)

ρ :

volumetric energy storage density (J/m3)

τ:

exergy destruction ratio (−)

a :

absorber

c:

condenser

d :

destruction

e:

evaporator

ex:

exergetic

ext :

external

g :

generator

gr :

ground

h :

high

hs :

heat source

hx :

heat exchanger

i :

inlet

int :

internal

ints :

intermediate Heat Source

l :

low

LiBr :

lithium bromide

max :

maximum

min :

minimum

nf :

non-flow

o :

outlet

p :

pump

pinch :

temperature pinch

ref :

reference state

s/i :

interface between a heat source and a system component

sol :

water–lithium bromide solution

syst:

system

tank :

solution or water tank

th :

thermal

v :

vapor

w :

water

‘:

during the discharging phase

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Acknowledgments

We thank the ANR (French National Research Agency) for its financial support under the research projects PROSSIS2 ANR-11-SEED-0011-01.

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Correspondence to Nolwenn Le Pierres.

Appendix A: Detailed mass, species, power, and exergy balances for the components of the system

Appendix A: Detailed mass, species, power, and exergy balances for the components of the system

A.1 Charging phase

Based on the hypothesis described in section “Main equations and hypothesis of the model”, the mass, species, energy, and exergy balances for the system components can be expressed as following for the charging phase.

Generator:

$$ 0={\dot{m}}_{sol\kern0.2em i\kern0.2em g}\kern0.5em -{\dot{m}}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_w $$
(A-1)
$$ 0={\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;{x}_{sol\kern0.2em i\kern0.2em g}-{\dot{m}}_{sol\kern0.2em o\kern0.2em g}\;{x}_{sol\kern0.2em o\kern0.2em g} $$
(A-2)
$$ 0={\dot{Q}}_g+{\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;{h}_{sol\kern0.2em i\kern0.2em g}-{\dot{m}}_{sol\kern0.2em o\kern0.2em g}\;{h}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_w\;{h}_{w\kern0.2em o\kern0.2em g} $$
(A-3)
$$ 0=\dot{E}{x}_{hs}^{th}+{\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;e{x}_{sol\kern0.2em i\kern0.2em g}-{\dot{m}}_{sol\kern0.2em o\kern0.2em g}\;e{x}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_w\;e{x}_{w\kern0.2em o\kern0.2em g}+\dot{E}{x}_{pinch\kern0.2em g}^d+\dot{E}{x}_g^d $$
(A-4)

Condenser:

$$ 0={\dot{Q}}_c+{\dot{m}}_w\left({h}_{w\kern0.2em o\kern0.2em g}-{h}_{w\kern0.2em o\kern0.2em c}\right) $$
(A-5)
$$ 0={\dot{m}}_w\left(e{x}_{w\kern0.2em o\kern0.2em g}-e{x}_{w\kern0.2em o\kern0.2em c}\right)+\dot{E}{x}_{pinch\kern0.5em c}^d+\dot{E}{x}_c^d $$
(A-6)

Solution tank:

$$ \frac{d{m}_{tank\kern0.2em \mathrm{sol}}}{dt}={\dot{m}}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_{sol\kern0.2em i\kern0.2em g} $$
(A-7)
$$ \frac{d{m}_{LiBr\kern0.2em tank\kern0.2em sol}}{dt}={\dot{m}}_{sol\kern0.2em o\kern0.2em g}\;{x}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;{x}_{sol\kern0.2em i\kern0.2em g} $$
(A-8)
$$ \frac{d{m}_{LiBr\kern0.3em tank\kern0.3em sol}{u}_{tank\kern0.3em sol}}{dt}={\dot{Q}}_{tank\kern0.3em sol}+{\dot{m}}_{sol\kern0.2em o\kern0.2em g}\;{h}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;{h}_{sol\kern0.2em i\kern0.2em g} $$
(A-9)
$$ \frac{dE{x}_{{}_{tank\kern0.2em sol}}^{nf}}{dt}={\dot{m}}_{sol\kern0.2em o\kern0.2em g}\;e{x}_{sol\kern0.2em o\kern0.2em g}-{\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;e{x}_{sol\kern0.2em i\kern0.2em g}+\dot{E}{x}_{tank\kern0.2em sol}^d $$
(A-10)

Water tank:

$$ \frac{d{m}_{tank\kern0.2em w}}{dt}={\dot{m}}_w $$
(A-11)
$$ {u}_{tank\kern0.3em w}\frac{d{m}_{tank\kern0.3em w}}{dt}={\dot{Q}}_{tank\kern0.3em w}+{\dot{m}}_w\;{h}_{w\kern0.2em o\kern0.2em c} $$
(A-12)
$$ \frac{dE{x}_{tank\kern0.3em w}^{nf}}{dt}={\dot{m}}_w\;e{x}_{w\kern0.2em o\kern0.2em c}+\dot{E}{x}_{tank\kern0.3em w}^d $$
(A-13)

Solution pump:

$$ 0={\dot{W}}_p+{\dot{m}}_{sol\kern0.2em i\kern0.2em g}\;\left({h}_{\mathrm{sol}\kern0.2em o\kern0.3em tank\kern0.3em sol}\kern0.5em -{h}_{sol\kern0.2em i\kern0.2em g}\right) $$
(A-14)

A.2 Discharging phase

Based on the same hypothesis described in section “Main equations and hypothesis of the model”, the balances for the system components can be expressed as following for the discharging phase.

Absorber:

$$ 0={\dot{m}}_{sol\kern0.2em i\kern0.2em a}\kern0.5em -{\dot{m}}_{sol\kern0.2em o\kern0.2em a}+{\dot{m}}_w $$
(A-15)
$$ 0={\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;{x}_{sol\kern0.2em i\kern0.2em a}-{\dot{m}}_{sol\kern0.2em o\kern0.2em a}\;{x}_{sol\kern0.2em o\kern0.2em a} $$
(A-16)
$$ 0={\dot{Q}}_a+{\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;{h}_{sol\kern0.2em i\kern0.2em a}-{\dot{m}}_{sol\kern0.2em o\kern0.2em a}\;{h}_{sol\kern0.2em o\kern0.2em a}+{\dot{m}}_w\;{h}_{w\kern0.2em o\kern0.2em e} $$
(A-17)
$$ 0=\dot{E}{x}_{ints}^{th}+{\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;e{x}_{sol\kern0.2em i\kern0.2em a}-{\dot{m}}_{sol\kern0.2em o\kern0.2em a}\;e{x}_{sol\kern0.2em o\kern0.2em a}+{\dot{m}}_w\;e{x}_{w\kern0.2em o\kern0.2em e}+\dot{E}{x}_{pinch\kern0.2em a}^d+\dot{E}{x}_a^d $$
(A-18)

Evaporator:

$$ 0={\dot{Q}}_e+{\dot{m}}_w\left({h}_{w\kern0.2em o\kern0.3em tank\kern0.3em w}-{h}_{w\kern0.2em o\kern0.2em e}\right) $$
(A-19)
$$ 0={\dot{m}}_w\left(e{x}_{w\kern0.2em o\kern0.3em tank\kern0.3em w}-e{x}_{w\kern0.2em o\kern0.2em e}\right)+\dot{E}{x}_{pinch\kern0.2em e}^d+\dot{E}{x}_e^d $$
(A-20)

Solution tank:

$$ \frac{d{m}_{tank\kern0.3em sol}}{dt}={\dot{m}}_{sol\kern0.2em o\kern0.2em a}-{\dot{m}}_{sol\kern0.2em i\kern0.2em a} $$
(A-21)
$$ \frac{d{m}_{LiBr\kern0.3em tank\kern0.3em sol}}{dt}={\dot{m}}_{sol\kern0.2em o\kern0.2em a}\;{x}_{sol\kern0.2em o\kern0.2em a}-{\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;{x}_{sol\kern0.2em i\kern0.2em a} $$
(A-22)
$$ \frac{d{m}_{LiBr\kern0.2em tank\kern0.2em sol}{u}_{tank\kern0.2em sol}}{dt}={\dot{Q}}_{tank\kern0.2em sol}+{\dot{m}}_{sol\kern0.2em o\kern0.2em a}\;{h}_{sol\kern0.2em o\kern0.2em a}-{\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;{h}_{sol\kern0.2em i\kern0.2em a} $$
(A-23)
$$ \frac{dE{x}_{{}_{tank\kern0.2em sol}}^{nf}}{dt}={\dot{m}}_{sol\kern0.2em o\kern0.2em a}\;e{x}_{sol\kern0.2em o\kern0.2em a}-{\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;e{x}_{sol\kern0.2em i\kern0.2em a}+\dot{E}{x}_{tank\kern0.2em sol}^d $$
(A-24)

Water tank:

$$ \frac{d{m}_{tank\kern0.2em w}}{dt}=-{\dot{m}}_w $$
(A-25)
$$ {u}_{tank\kern0.3em w}\frac{d{m}_{tank\kern0.2em w}}{dt}=-{\dot{m}}_w\;{h}_{w\kern0.2em o\kern0.2em tank\kern0.2em w} $$
(A-26)
$$ \frac{dE{x}_{tank\kern0.3em w}^{nf}}{dt}=-{\dot{m}}_w\;e{x}_{w\kern0.2em o\kern0.2em tank\kern0.2em w}+\dot{E}{x}_{tank\kern0.2em w}^d $$
(A-27)

Solution pump:

$$ 0={\dot{W}}_p+{\dot{m}}_{sol\kern0.2em i\kern0.2em a}\;\left({h}_{sol\kern0.2em o\kern0.2em tank\kern0.2em sol}\kern0.5em -{h}_{sol\kern0.2em i\kern0.2em a}\right) $$
(A-28)

A.3 Values over the whole charging or discharging phase

Heat (Q) and the associated exergy (Ex th), work (W), and exergy destruction (Ex d) are obtained for the whole phases by the integration, over time, of the respective exchange rates.

$$ Q={\displaystyle \int \dot{Q}}.dt $$
(A-29)
$$ W={\displaystyle \int \dot{W}}.dt $$
(A-30)
$$ E{x}^{th}={\displaystyle \int \dot{E}{x}^{th}}.dt $$
(A-31)
$$ E{x}^d={\displaystyle \int \dot{E}{x}^d}.dt $$
(A-32)

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Perier-Muzet, M., Le Pierres, N. Modeling and analysis of energetic and exergetic efficiencies of a LiBr/H20 absorption heat storage system for solar space heating in buildings. Energy Efficiency 9, 281–299 (2016). https://doi.org/10.1007/s12053-015-9362-2

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