international journal of hydrogen energy 34 (2009) 3945–3952
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Parametric studies on a metal-hydride cooling system S. Melloulia,*, F. Askria, H. Dhaoua, A. Jemnia, S. Ben Nasrallaha,b a
Laboratoire des Etudes des syste`mes Thermiques et Energe´tiques (LESTE), ENIM, Route de Kairouan, 5019 Monastir, Tunisia Centre de recherche en Science et Technologies de l’Energie, Technopole de Borj, Ce´dria-Tunisie 1000, Tunisia
b
article info
abstract
Article history:
A mathematical model and software set for computer simulation of operational metal-
Received 16 May 2008
hydride cooling system are developed. The numerical model is able to take into account the
Received in revised form
coupled heat- and mass-transfer equations of the two reactors. Thus the model allows us
14 December 2008
to know and to foresee the effects of operational and design parameters on the perfor-
Accepted 7 March 2009
mance of the metal-hydride cooling system. The model was validated by being compared
Available online 29 March 2009
to experimental data obtained by other authors and good agreements were obtained. Using this model, the effects of operating parameters are presented and discussed.
Keywords:
ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights
Metal hydride
reserved.
Cooling system Operating parameters
1.
Introduction
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
and a relatively large irreversible heat loss during the hydriding and dehydriding processes. Extensive investigations 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 parameters 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.
* Corresponding author. Tel.: þ216 97 644 090. E-mail address:
[email protected] (S. Mellouli). 0360-3199/$ – see front matter ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.03.010
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international journal of hydrogen energy 34 (2009) 3945–3952
Nomenclature C COP cp, cv E G DH h K k M _ m N n NTU p Q q R DS
2.
Thermal capacity, kJ K1 Coefficient of performance Specific heat of hydrogen at constant pressure, volume, kJ kgl K1 Activation energy, kJ kg1 Flow rate of heat-transfer fluid, kg s1 Reaction enthalpy, kJ kg1 Heat-transfer coefficient, W m2 K1 Overall heat-transfer coefficient, W m2 K1 Coefficient Molecular weight of alloy, kg of alloy Flow rate, kg s1 (1 Nl H2 min1 ¼ 1.5 106 kg s1) Number of metal atoms per mole of alloy Number of moles Number of transfer units Pressure, Pa Energy transferred, J Specific output, W kg1 of alloy B Universal gas constant, J mol1 Kl Reaction entropy, J mol1 k1
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-temperature reactor) is in a hydrided form and the hydride in reactor B (the low-temperature reactor) is in an unhydrided form.
S T t w X
Heat-transfer surface, m2 Temperature, K Time, s Hydride and container mass, kg 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 t ¼ 0 r Reactor, hydride container t Total i Initial
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. 1 – Schematic diagram of metal-hydride cooling system.
Fig. 2 – Operating cycle of metal-hydride cooling system.
international journal of hydrogen energy 34 (2009) 3945–3952
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.
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 ¼
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 coefficient between hydrogen gas and the solid particles inside the bed. Studies show that the importance of the convective 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 formulation even though it is well known that the effective thermal conductivity varies with hydrogen pressure and concentration. This assumption leads to a slight underestimation 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].
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DH DS RT 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 ¼
Peq;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 ¼
_ P hS 2mc 2hS T þ T _ P þ hS aj 2mc _ P þ hS N 2mc
(3)
i, j ¼ 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: Ct1
dT1 dQ1 ¼ dt 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 X1 ¼ Xs
T2 ¼ T0;2 ¼ Tm
X2 ¼ 0 at t ¼ 0
at t ¼ 0
(5) (6)
The boundary conditions are the temperatures of the heating– cooling fluids at inlets of the heat exchangers.
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3.2.
international journal of hydrogen energy 34 (2009) 3945–3952
dX2 P ðXS X2 Þ ¼ ka eEa =RTa ln dt Peq
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)
(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
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:
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:
dQ1 _1 dT1 1 dm ¼ DHr1 þ cp Tg cv T1 dt dt Ct1 dt
Ct1
dT1 dQ1 ¼ dt dt
(17)
Ct2
dT2 dQ2 ¼ dt dt
(18)
(7)
where the total heat capacity of the system is given by: Ct1 ¼ wMH1 cMH1 þ wr1 cr1 þ m1 cv
(8)
The heat flow rate is expressed both by the thermal balance of the cooling fluid and by the overall heat-transfer coefficient:
The initial conditions for process 3 are obtained from the final conditions of process 2.
3.4. dQ1 ¼ Gf1 cpf1 T1 Tf1 1 eNTU1 dt
(9)
The mass-transfer equation may be written as: _1 dm dX1 ¼ aX1 dt dt
Process 4
During this process, hydrogen is transferred from reactor B to reactor A. The governing equations for this process are similar
(10) Table 1 – Input data of the numerical application.
where dX1/dt is the kinetic of hydrogen desorption: dX1 Peq ¼ kd eEd =RTd ln X1 dt P
(11)
The hydrogen concentration is related to the moles of hydrogen in the hydride by: X1 ¼
2nMMH1 NmMH1
(12)
and the constant aX1 is: aX1 ¼
NmMH1 MH2 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 opposite with respect to the desorption process. Then, for the hydrogen absorption, equations (7), (9) and (11) become respectively: dT2 1 ¼ dt Ct2
_2 dm dQ2 DHr2 þ cp Tg cv T2 dt dt
dQ2 ¼ Gf;2 cp;f2 Tf;2 T2 1 eNTU2 dt
(14)
(15)
Properties of hydride Molecular weight of alloy Reaction enthalpy (kJ kg1) Reaction entropy (J mol1 k1) Number of metal atoms per mole of alloy Coefficient Activation energy (kJ kg1) Thermal capacity (kJ K1) Hydride and container mass (kg) Heat exchanger characteristics Specific heat of transfer fluid Number of transfer units Specific heat of reactor (kJ kgl K1) Overall heat-transfer coefficient (W m2 K1) Heat-transfer surface (m2) Properties of hydrogen gas Specific heat of hydrogen at constant pressure, volume (kJ kgl K1) Universal gas constant (J mol1 Kl)
MH1
MH2
M
418.3
429.0
DH
15090
13690
DS N
106.0 6
100.15 6
ka kd Ea Ed C
1.52 104 1.42 106 13890 20330 1.00
3.58 101 1.32 103 8430 12400 1.00
w
2.0
2.0
CPf
1.5
4.19
NTU cr
0.4 0.5
0.4 0.5
K
500
500
S
0.40
0.40
cp cv
14.4 10.28
R
8.314
international journal of hydrogen energy 34 (2009) 3945–3952
Fig. 5 – Transferred hydrogen.
Fig. 3 – Hydride temperatures vs time.
to those of process 2. However, the reaction rate equations (11) and (16) for this process become respectively: dX1 P ðXS X1 Þ ¼ ka eEa =RTa ln dt Peq
(19)
dX2 Peq ¼ kd eEd =RTd ln X2 dt P
(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
Ql ¼ QB;4 QB;3
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 q¼
Fig. 4 – Transferred hydrogen flow rate.
(22)
Ql is the refrigerating effect obtained at low temperature Tl; QB;3 and QB;4 are the energy transferred between the heattransfer fluid and the hydride bed B during processes 3 and 4 respectively. The energy input at high temperature Th is given by (23) Qh ¼ QA;2 þ QA;1
(21)
where
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Q1 MB tc
(24)
Fig. 6 – Variation of average bed temperatures over a cycle.
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Fig. 7 – Variation of average bed concentrations over a cycle.
where MB is the mass of alloy B and tc is the time taken for one complete cycle.
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 concentrations 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 heattransfer characteristics of the bed, initially the bed 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 heattransfer enhancement technique has to be adopted to improve the efficiency of the heat exchanger. It can be
Fig. 8 – Variation of equilibrium pressure over a cycle.
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 coefficient 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. 9 – Effect of efficiency of the heat exchanger on specific alloy output.
international journal of hydrogen energy 34 (2009) 3945–3952
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Fig. 10 – Effects of refrigeration and heat rejection temperatures on specific alloy output.
Fig. 12 – Effects of refrigeration and heat-source temperatures on specific alloy output.
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 temperature levels. Similarly, the availability of the output decreases, and that of the input increases as the heat rejection temperature 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
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 reactors 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 significant when the refrigeration temperature is low. This is because, when refrigeration temperature is low, the lowtemperature desorption during process 4 controls the cycle time, and the time taken for process 2 is small compared with
Fig. 11 – Effects of refrigeration and heat rejection temperatures on COP.
Fig. 13 – Effects of refrigeration and heat-source temperatures on COP.
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international journal of hydrogen energy 34 (2009) 3945–3952
that of process 4. However, at higher refrigeration temperatures 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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