Parametric studies on a metal-hydride cooling system

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 2

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Parametric studies on a metal-hydride cooling system

S. Melloulia,*, F. Askria, H. Dhaoua, A. Jemnia, S. Ben Nasrallaha,b

aLaboratoire des Etudes des systemes Thermiques et Energetiques (LESTE), ENIM, Route de Kairouan, 5019 Monastir, TunisiabCentre de recherche en Science et Technologies de l’Energie, Technopole de Borj, Cedria-Tunisie 1000, Tunisia

a r t i c l e i n f o

Article history:

Received 16 May 2008

Received in revised form

14 December 2008

Accepted 7 March 2009

Available online 29 March 2009

Keywords:

Metal hydride

Cooling system

Operating parameters

* Corresponding author. Tel.: þ216 97 644 09E-mail address: mellouli_sofiene@yahoo.

0360-3199/$ – see front matter ª 2009 Interndoi:10.1016/j.ijhydene.2009.03.010

a b s t r a c t

A mathematical model and software set for computer simulation of operational metal-

hydride cooling system are developed. The numerical model is able to take into account the

coupled heat- and mass-transfer equations of the two reactors. Thus the model allows us

to know and to foresee the effects of operational and design parameters on the perfor-

mance of the metal-hydride cooling system. The model was validated by being compared

to experimental data obtained by other authors and good agreements were obtained. Using

this model, the effects of operating parameters are presented and discussed.

ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights

reserved.

1. Introduction and a relatively large irreversible heat loss during the

Metal hydrides have been explored for diverse applications

such as hydrogen storage, energy conversion, heat storage,

hydrogen compression, hydrogen separation, etc. Of these,

energy conversion, heat transformation, heat pumping and

refrigeration are important applications because hydrogen

and hydriding alloys are environment-friendly and can be

operated on low potential energy sources such as solar heat or

wasted heat.

Metal-hydride heating and cooling systems offer many

advantages over conventional systems. They are compact,

environmentally safe, utilize low-grade energy sources and

offer wide operating temperature ranges. Studies have been

carried out on various aspects of hydride cooling and heating

systems such as: heat- and mass-transfer aspects [1–5],

system simulation [6–8], hydride properties [9–11] etc. A few

hydride cooling and heating systems have also been built and

tested [11–14].

The main obstacles for the practical use of metal-hydride

systems are a low-heat transport rate of the metal hydride

0.fr (S. Mellouli).ational Association for H

hydriding and dehydriding processes. Extensive investiga-

tions are required to overcome these obstacles, which are

both time-consuming and costly. In order to save both time

and cost, computer simulation can be introduced in the

development of such metal-hydride systems. In particular,

simulation can provide useful technical knowledge for

improving the system by optimum reactor construction and

identification of optimum operational parameters. This

requires optimization of design parameters and operating

conditions based on heat- and mass-transfer characteristics

of the coupled reactors.

In this paper, the design aspects and performance of

a system working with a MmNi4.5Al0.4/MmNi4.2Al0.1Fe0.7 pair

are predicted by solving the coupled heat- and mass-transfer

equations for the two reactors. Effects of operating parame-

ters such as heat-source temperature and refrigeration

temperature and reactor parameters such as efficiency of heat

exchangers are studied. Results show that the specific output,

and hence the COP of the system, depends significantly on

these parameters.

ydrogen Energy. Published by Elsevier Ltd. All rights reserved.

Nomenclature

C Thermal capacity, kJ K�1

COP Coefficient of performance

cp, cv Specific heat of hydrogen at constant pressure,

volume, kJ kg�l K�1

E Activation energy, kJ kg�1

G Flow rate of heat-transfer fluid, kg s�1

DH Reaction enthalpy, kJ kg�1

h Heat-transfer coefficient, W m�2 K�1

K Overall heat-transfer coefficient, W m�2 K�1

k Coefficient

M Molecular weight of alloy, kg of alloy_m Flow rate, kg s�1 (1 Nl H2 min�1¼ 1.5� 10�6 kg s�1)

N Number of metal atoms per mole of alloy

n Number of moles

NTU Number of transfer units

p Pressure, Pa

Q Energy transferred, J

q Specific output, W kg�1 of alloy B

R Universal gas constant, J mol�1 K�l

DS Reaction entropy, J mol�1 k�1

S Heat-transfer surface, m2

T Temperature, K

t Time, s

w Hydride and container mass, kg

X Hydrogen concentration (atoms of H2/atoms of

alloy)

Subscripts

A High-temperature hydride/reactor

a, d Absorption, desorption

B Low-temperature hydride/reactor

b Bed

eq Equilibrium

f Heat-transfer fluid

g Gas

h High temperature

l Low temperature

m Intermediate, metal

0 At t¼ 0

r Reactor, hydride container

t Total

i Initial

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 23946

2. Physical model

The physical model of a dual-bed metal-hydride cooling

system is shown in Fig. 1. It consists of two metal-hydride

reactors connected in such a way that hydrogen can flow

freely between them. Each reactor consists of a metal-hydride

bed which is separated from the heat-transfer fluids by two

spiral heat exchangers. The gas spaces of the two reactors are

connected by a short pipe with a connecting valve.

Initially, the metal-hydride in reactor A (the high-temper-

ature reactor) is in a hydrided form and the hydride in reactor

B (the low-temperature reactor) is in an unhydrided form.

Fig. 1 – Schematic diagram of metal-hydride cooling

system.

Fig. 2 shows the operating cycle on a Clausius–Clapeyron

chart. As shown, the cycle consists of the following four

processes:

2.1. Process 1

Initially, the valve between the reactors is kept closed, and

reactors A and B are sensibly heated to high temperature Th,

and intermediate temperature Tm respectively.

2.2. Process 2

During this process, the system is set into operation by

opening the connecting valve and supplying the heat-transfer

fluid through the reactors at the required temperatures. Since

hydride A is at higher temperature and pressure, hydrogen gas

flows from reactor A to reactor B until a pressure equilibrium

is reached. As a result of the new pressure in the gas space, the

Fig. 2 – Operating cycle of metal-hydride cooling system.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 2 3947

equilibrium between hydride beds and hydrogen gas is

disturbed.

Hence, reactor A starts desorbing hydrogen by taking heat

from the bed and the heat-transfer fluid, and reactor B starts

absorbing hydrogen gas, rejecting the heat of absorption to the

bed and to the fluid flowing outside the bed. This process is

continued until the required amount of hydrogen transfer

takes place.

2.3. Process 3

During this process the valve is closed. Hydride A should be

cooled to the intermediate temperature Tm, and hydride B is

sensibly cooled to the low temperature Tl.

2.4. Process 4

When hydride A and hydride B attain temperatures Tm and Tl,

respectively; the valve between the two reactors is opened.

Due to the difference in P–C–T characteristics of the hydrides,

hydride B starts desorbing hydrogen by extracting heat from

the heat-transfer fluid, yielding a refrigeration effect. Hydride

A absorbs this hydrogen, rejecting the resultant heat to the

heat-transfer fluid and the bed. Thus, the refrigerating effect

is obtained at the low temperature Tl while heat rejection

takes place at the intermediate temperature Tm. This process

is continued until a required amount of hydrogen transfer (the

same as process 2) takes place.

3. Mathematical model

The present mathematical model is based on the following

assumptions:

1. The whole bulk material of the reaction bed is continuous

and in solid phase, i.e. heat transfer through the bed is by

conduction only. The convection heat transfer between the

gas and the hydride particles is neglected. This is justified

because of the very high volumetric heat-transfer coeffi-

cient between hydrogen gas and the solid particles inside

the bed. Studies show that the importance of the convec-

tive heat-transfer term increases with the reaction rate, bed

thickness and operating pressure. Moreover, convection is

noticeable only at the beginning of the process, when the

reaction rate is high [4]. Hence the assumption may be

justified, as thin beds are used in the analysis, the operating

pressures during process 4 are large, and the time taken for

process 2 is large.

2. The thermal properties of the hydride beds are constant.

This assumption is made to simplify the problem formu-

lation even though it is well known that the effective

thermal conductivity varies with hydrogen pressure and

concentration. This assumption leads to a slight underes-

timation of the actual performance of the system [16].

3. Pressure drops through the beds are neglected. This is

justified because for thin beds and low hydrogen flow rates

the pressure drop is not a rate-limiting factor [5].

4. The temperature and pressure of hydrogen gas in the

combined gas space are uniform throughout: they vary

with time only.

5. The reactors are assumed to be well insulated: that is, heat

transfer between hydride reactors and the surrounding

atmosphere is neglected.

6. At any given instant the average temperature of the reactor

material (other than the alloy and heat-transfer fluid) is

equal to the average temperature of the hydride bed [5].

The process starts with hydrogen in the gas space in

equilibrium with the hydride bed. Hence, gas pressure before

the valve is opened is equal to the equilibrium pressure at that

temperature and is given by Vant Hoff’s equation:

LnPeq ¼DHRT� DS

R(1)

Since pressure equilibrium is reached as soon as the valve is

opened, the pressure of the hydrogen gas in the combined gas

space immediately after the valve opening is given by:

Pi ¼Peq;A þ Peq;B

2(2)

Since it has been assumed that the rate of absorption is equal

to the rate of desorption, and also that the hydrogen

temperature in the combined gas space is equal to the average

temperature, the temperature of hydrogen leaving the gas

space at any time during the H2 transfer is given by:

Tdi ¼2 _mcP � hS2 _mcP þ hS

Taj þ2hS

2 _mcP þ hSTN (3)

i, j¼ 1, 2: respectively of MH1 and MH2

As stated in the physical model, the operating cycle

consists of two sensible heat-transfer processes (process 1

and process 3) and two hydrogen transfer processes (process 2

and process 4). The heat- and mass-transfer rates during

processes 2 and 4, and the heat-transfer rates during

processes 1 and 3 are obtained by simultaneously solving the

coupled energy and mass balance equations in both reactors.

From this, the performance of the system is computed.

The governing equations for the pair hydride beds

considered here are given below.

3.1. Process 1

During this process only sensible heat transfer between the

heat-transfer fluid and the bed takes place and there is no

hydrogen transfer. Hence the governing equation for reactor A

is given by:

Ct1dT1

dt¼ dQ1

dt(4)

where Ct1 is the total heat capacity of the reactor.

Initially beds A and B are at uniform temperature and

concentration. Hence,

T1 ¼ T0;1 ¼ Tf;i T2 ¼ T0;2 ¼ Tm at t ¼ 0 (5)

X1 ¼ Xs X2 ¼ 0 at t ¼ 0 (6)

The boundary conditions are the temperatures of the heating–

cooling fluids at inlets of the heat exchangers.

Table 1 – Input data of the numerical application.

MH1 MH2

Properties of hydride

Molecular weight

of alloy

M 418.3 429.0

Reaction enthalpy

(kJ kg�1)

DH 15090 13690

Reaction entropy (J mol�1 k�1) DS 106.0 100.15

Number of metal

atoms per mole

of alloy

N 6 6

Coefficient ka 1.52� 104 3.58� 101

kd 1.42� 106 1.32� 103

Activation energy

(kJ kg�1)

Ea 13890 8430

Ed 20330 12400

Thermal capacity

(kJ K�1)

C 1.00 1.00

Hydride and container

mass (kg)

w 2.0 2.0

Heat exchanger characteristics

Specific heat

of transfer fluid

CPf 1.5 4.19

Number of transfer units NTU 0.4 0.4

Specific heat

of reactor (kJ kg�l K�1)

cr 0.5 0.5

Overall heat-transfer

coefficient (W m�2 K�1)

K 500 500

Heat-transfer surface (m2) S 0.40 0.40

Properties of hydrogen gas

Specific heat

of hydrogen at constant

pressure, volume

(kJ kg�l K�1)

cp 14.4

cv 10.28

Universal gas constant (J mol�1 K�l) R 8.314

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 23948

3.2. Process 2

During this process, hydrogen is transferred from reactor A to

reactor B. The governing energy and mass balance equations

for this process are as follows:

� Reactor A (desorption)

Assuming a homogeneous metal-hydride bed (no spatial

distribution of temperature and hydrogen concentration) and

taking into account that the variation of Ct in the time is due

only to the hydrogen desorption mass m1 (specific heat

constant), the previous equation is written as:

dT1

dt¼ 1

Ct1

�d _m1

dt

�DHr1 þ cpTg � cvT1

�� dQ1

dt

�(7)

where the total heat capacity of the system is given by:

Ct1 ¼ wMH1cMH1 þwr1cr1 þm1cv (8)

The heat flow rate is expressed both by the thermal balance

of the cooling fluid and by the overall heat-transfer coefficient:

dQ1

dt¼ Gf1cpf1

�T1 � Tf1

��1� e�NTU1

�(9)

The mass-transfer equation may be written as:

d _m1

dt¼ aX1

dX1

dt(10)

where dX1/dt is the kinetic of hydrogen desorption:

dX1

dt¼ kde

�Ed=RTd ln

�Peq

P

X1 (11)

The hydrogen concentration is related to the moles of

hydrogen in the hydride by:

X1 ¼2nMMH1

NmMH1(12)

and the constant aX1 is:

aX1 ¼NmMH1MH2

2MMH1(13)

Here the equilibrium pressure at that temperature is

obtained from Vant Hoff’s relation given by Eq. (1).

� Reactor B (absorption)

The previous equation describes the heat transfer during

the desorption process. The analogous equation referring

to the absorption process may be developed by taking into

account that the direction of heat and mass transfer is oppo-

site with respect to the desorption process. Then, for the

hydrogen absorption, equations (7), (9) and (11) become

respectively:

dT2

dt¼ 1

Ct2

��d _m2

dt

�DHr2 þ cpTg � cvT2

��� dQ2

dt

(14)

dQ2

dt¼ Gf;2cp;f2

�Tf;2 � T2

��1� e�NTU2

�(15)

dX2

dt¼ kae�Ea=RTa ln

�P

Peq

ðXS � X2Þ (16)

The initial conditions stated above are valid for the first cycle.

For subsequent cycles, the initial conditions are obtained from

the final conditions of process 1.

3.3. Process 3

During this process, only sensible heat transfer between the

heat-transfer fluids and the beds takes place and there is no

hydrogen transfer. Hence the governing equations for reactors

A and B are given by:

Ct1dT1

dt¼ dQ1

dt(17)

Ct2dT2

dt¼ dQ2

dt(18)

The initial conditions for process 3 are obtained from the final

conditions of process 2.

3.4. Process 4

During this process, hydrogen is transferred from reactor B to

reactor A. The governing equations for this process are similar

Fig. 3 – Hydride temperatures vs time. Fig. 5 – Transferred hydrogen.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 2 3949

to those of process 2. However, the reaction rate equations (11)

and (16) for this process become respectively:

dX1

dt¼ kae

�Ea=RTa ln

�P

Peq

ðXS � X1Þ (19)

dX2

dt¼ kde

�Ed=RTd ln

�Peq

P

X2 (20)

The initial conditions are the final conditions of process 3.

For the system, the coefficient of performance (COP) is

defined as:

COP ¼ Ql

Qh

(21)

where

Fig. 4 – Transferred hydrogen flow rate.

Ql ¼ QB;4 � QB;3 (22)

Ql is the refrigerating effect obtained at low temperature Tl;

QB;3 and QB;4 are the energy transferred between the heat-

transfer fluid and the hydride bed B during processes 3 and 4

respectively.

The energy input at high temperature Th is given by

Qh ¼ QA;2 þ QA;1 (23)

here, QA;1 and QA;2 are the energy supplied to the hydride bed A

during processes 2 and 1 respectively.

The specific output q defined as the cooling capacity for

1 kg of alloy B, is given by

q ¼ Q1

MBtc(24)

Fig. 6 – Variation of average bed temperatures over a cycle.

Fig. 8 – Variation of equilibrium pressure over a cycle.Fig. 7 – Variation of average bed concentrations over

a cycle.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 23950

where MB is the mass of alloy B and tc is the time taken for one

complete cycle.

Fig. 9 – Effect of efficiency of the heat exchanger on specific

alloy output.

4. Model validation and results

The system of equations that is presented in the previous

section is solved numerically by a FORTRAN program.

In order to validate the developed model, we have

compared numerical and experimental results reported by

Bjustrom et al. [15]. The pair of metal hydrides used in the

calculations is MmNi4.5Al0.5 (the high-pressure hydride) and

MmNi4.2Al0.1Fe0.7 (the low-pressure hydride).

In Table 1, the input data used to develop this calculation

has been summarized [8–15].

Figs. 3–5 show the average bed temperatures, transferred

hydrogen flow rate and transferred hydrogen respectively for

the pair of metal hydrides. From these profiles we note

that the mathematical model predicts correctly the evolution

of the considered parameters.

Figs. 6–8 show the average bed temperatures, bed concen-

trations and equilibrium pressure. It can be seen that the time

taken for process 4 (low-temperature desorption) is much

larger than that of process 2 (high-temperature desorption).

The times taken for the sensible heat-transfer processes 1 and 3

are negligible in comparison with the heat- and mass-transfer

processes 2 and 4. As shown in Fig. 6, owing to the poor heat-

transfer characteristicsof thebed, initially thebed temperature

decreases during desorption and increases during absorption.

It is observed that the bed pressure is pulled towards the

equilibrium pressure of the faster reactor, as shown in Fig. 8.

Fig. 9 shows the effect of efficiency of the heat exchanger

on specific alloy output of the cooling system. It can be seen

that a very low efficiency of the heat exchanger reduces the

specific alloy output significantly. Hence some form of heat-

transfer enhancement technique has to be adopted to

improve the efficiency of the heat exchanger. It can be

observed that for a given flow of heat-transfer fluid there

exists a value of efficiency of the heat exchanger, above which

its effect on system performance is negligible. This is because,

up to the optimum flow of heat-transfer fluid value, the heat

transfer through the hydride beds controls the whole process,

and above this value either the overall heat-transfer coeffi-

cient or the reaction kinetics assumes importance.

Figs. 10 and 11 show the effects of heat rejection and

refrigeration temperatures on specific alloy output and COP

respectively. The refrigeration temperature has a significant

effect on specific alloy output, as the desorption during

refrigeration process 4 controls the cycle time. Hence

increasing the refrigeration temperature increases the alloy

output. The time taken for processes 3 and 4 increases as the

Fig. 12 – Effects of refrigeration and heat-source

temperatures on specific alloy output.

Fig. 10 – Effects of refrigeration and heat rejection

temperatures on specific alloy output.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 2 3951

heat rejection temperature increases. Consequently, the

specific alloy output decreases with increasing heat rejection

temperatures. For a given reactor thermal capacity, the COP

increases as refrigeration temperature increases and the heat

rejection temperature decreases. This is due to the variation

in sensible heat loads during processes 1 and 3 with temper-

ature levels. Similarly, the availability of the output decreases,

and that of the input increases as the heat rejection temper-

ature decreases.

It can be observed that the COP and the specific alloy

output increase as the refrigeration temperature increases.

Hence an optimum value of refrigeration temperature has to

Fig. 11 – Effects of refrigeration and heat rejection

temperatures on COP.

be selected so that sufficiently high values of specific alloy

output and COP can be obtained.

Figs. 12 and 13 show the effect of heat-source temperature

on specific alloy output and the COP at different refrigeration

temperatures.

For a given heat rejection temperature, as the heat-source

temperature increases the pressure difference between reac-

tors A and B during process 2 increases. Therefore, the cycle

time decreases and the specific alloy output increases.

However, the effect of heat-source temperature is not signif-

icant when the refrigeration temperature is low. This is

because, when refrigeration temperature is low, the low-

temperature desorption during process 4 controls the cycle

time, and the time taken for process 2 is small compared with

Fig. 13 – Effects of refrigeration and heat-source

temperatures on COP.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 3 9 4 5 – 3 9 5 23952

that of process 4. However, at higher refrigeration tempera-

tures the times taken for process 2 and 4 are comparable, and

hence heat-source temperature also assumes importance.

COP decreases with heat-source temperature as the heat

input during the sensible heating process 1 increases.

Since the specific alloy output increases and COP as the

heat-source temperature increases, an optimum value of this

parameter has to be selected.

5. Conclusion

From the different simulations presented in this study, we

concluded that the performance of the cooling system can be

controlled by optimizing the refrigeration, heat rejection and

heat-source temperatures. However, since these three

temperatures depend upon the cooling requirement, ambient

temperature and available heat sources, additional heat

exchangers are required to recover the heat. The design

optimization should be based mainly on the optimum value of

these parameters. Using the system, an average COP of 0.45–

0.50 is obtained. The low value of COP is due to the low

enthalpy of formation of the low-temperature alloy

MmNi4.2Al0.1Fe0.7. However, this COP is still comparable with

that of the conventional adsorption systems such as zeolite–

water and zeolite–methanol.

Acknowledgements

The authors would like to express their deep gratitude to Mr. Ali

AMRI and his company ‘‘The English Polisher’’ for the minute,

painstaking proofreading of the present paper’s full text and of

the overall comments over of the article’s structure.

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