Analysis of hydrogen storage performance of metal hydride reactor with phase change materials

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Analysis of hydrogen storage performance of metal hydride reactor with phase change materials Hafsa El Mghari a, Jacques Huot b, Jinsheng Xiao a,b,* a

Hubei Key Laboratory of Advanced Technology for Automotive Components and Hubei Collaborative Innovation Center for Automotive Components Technology, School of Automotive Engineering, Wuhan University of Technology, Hubei 430070, China b  Trois-Rivieres, QC G9A 5H7, Canada Hydrogen Research Institute, Universit
e Du Qu
ebec a

highlights
A metal hydride (MH) tank equipped with phase change material (PCM) was investigated.
A model was developed and validated for both absorption and desorption processes.
The use of PCM shows an improvement in the energy efficiency of the MH system.
The effect of some properties of PCM on the performance of MH-PCM system was studied.
The latent heat of the PCM affects more on the MH bed than the thermal conductivity.

article info

abstract

Article history:

Using phase change materials (PCM) as thermal energy storage material in metal hydride

Received 3 July 2019

reactor bed is an effective method to store the heat emitted during hydrogen charging and

Received in revised form

retrieving it later during discharging. The present work examines the effect of a PCM on the

23 August 2019

behaviour of the metal hydride in the reactor bed. A two-dimensional model was devel-

Accepted 12 September 2019

oped to describe the mass and heat transfer inside the metal hydride and the PCM as well

Available online xxx

as the interaction between them. The results were compared with other numerical simulation and experimental data. In the simulations, thermal conductivity and the latent

Keywords:

heat were varied in order to evaluate the effect of these parameters on the kinetics of

Hydrogen storage

absorption, desorption and melting of the phase change material.

Metal hydride

© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Phase change material Heat and mass transfer Latent heat Thermal conductivity

Introduction Hydrogen is a promising energy vector owing to its clean, renewable and versatile characteristics [1]. In addition to

the production and the utilization of hydrogen, the storage of hydrogen is another hurdle that has to be overcome for large scale applications of hydrogen [2]. Safe and efficient hydrogen storage is a challenge that is addressed using four main techniques: compression, liquefaction,


du Que
bec a  Trois-Rivie res, QC G9A 5H7, Canada. * Corresponding author. Hydrogen Research Institute, Universite E-mail addresses: [email protected] (H. El Mghari), [email protected] (J. Huot), [email protected] (J. Xiao). https://doi.org/10.1016/j.ijhydene.2019.09.090 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: El Mghari H et al., Analysis of hydrogen storage performance of metal hydride reactor with phase change materials, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.090

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Nomenclature A, B C Cp E f h H H/f.u. Ha K L m _ m Mg ! n P r R Ra S t T u V z

plateau pressure coefficients reaction rate coefficient heat capacity, J kg1 K1 activation Energy, J mol1 liquid fraction sensible volumetric heat, J m3 total volumetric enthalpy, J m3 number of hydrogen per formula unit reactor height, m permeability, m2 latent heat of the PCM, J kg1 mass, kg hydrogen mass per unit time and unit volume, kg m3 s1 molecular weight hydrogen, g mol1 normal vector pressure, MPa radial coordinate, m universal gas constant J mol1 K1 reactor radius, m source term time, s temperature, K component of velocity vector, m s1 volume, m3 axial coordinate, m

Greek letters DH Enthalpy of reaction, kJ mol1 ε porosity l thermal conductivity, W m1 K1 m dynamic viscosity, kg m1 s1 r density, kg m3 Subscripts 0 initial a absorption d desorption eff effective eq equilibrium emp empty sat saturated g gas s solid mel melting sol solidification p phase change material ref reference a ¼ int; ext inner, external Abbreviation LHS Latent heat storage MH metal hydride

adsorption on large specific surface area nanoporous materials and absorption in metal hydrides [3]. Every technique has its own advantages, limitations, and possibly its own niches [4].

Metal Hydrides (MHs) are one amongst the promising candidates for numerous stationary and mobile hydrogen storage applications [5,6]. The main advantages of metal hydrides over the other storage techniques are their high hydrogen volumetric density, comparatively low operating pressure, the possibility of operation at room temperature and relatively low cost [7,8]. As the hydrogenation/dehydrogenation of metal hydrides is highly exothermic/endothermic reactions, thermal management is critical for safe and optimal utilization of a metal hydride tank [9,10]. There is abundant literature on the mass and heat transfer in an MH reactor bed [11e21]. These studies show that the loading time is affected by the heat removal from the MH bed. Therefore, loading time might be reduced by employing a bed design that gives a larger heat exchanger area. Various configurations of MH tanks have an external heat source to generate the heat of desorption and a cooling system to extract the absorption heat. A more elegant solution is to store the heat emitted during the absorption process of hydrogen and to use it in the desorption step where the metal hydride has to be heated. Latent heat thermal storage (LHTS) using the PCM is an attractive way to store the released heat during the hydrogen absorption and to use it later for the dehydrogenation step. In addition, latent heat thermal storage allows high energy density to be stored and emitted in a narrower temperature range throughout the fusion and solidification temperature of the PCM [22e24]. Garrier et al. [25] proposed to store the reaction heat in an MgeZn mixture PCM in an MgeH2 reservoir. They designed a reservoir of 7000 NL of hydrogen and investigated it throughout several experimental conditions. They concluded that the entire volume storage capacity of hydrogen is charged or discharged within 3 h and also the daily storage effectiveness of this reservoir was around 70%. Ph. Marty et al. [9] presented several modelling tools to optimize a large-scale Mg metal hydride hydrogen reactor equipped with a PCM to predict the time evolution of varied physical parameters like the position of hydriding front, the temperature, the volume of absorbed hydrogen and the liquid fraction of the phase change material. It was shown that precise results may be acquired from numerical modelling. Additionally, analytical expressions of the charging time of varied geometries were proposed and showed good agreement with the experiments. Mellouli et al. [26] have designed two configurations of Mg metal hydride hydrogen reactors with PCM including cylindrical and spherical tanks. The results revealed that the spherical tank had the best performance. It was also concluded that the PCM quantity should be carefully optimized to make sure to store all the heat released throughout ^ad H et al. [27] the charging process of hydrogen. Ben Ma developed a transient 2D model to predict the mass and heat transfer inside a metal-hydrogen reactor with a PCM. It was found that, by using a PCM thermal store, the MH reactor discharges up to 80% of the stored hydrogen without an auxiliary heat source. Three-dimensional (3D) models were developed for simulating fluid flow, heat and mass transfer in metal hydride tanks [28e31,52]. Yun Wang et al. [28] expressed that due to the geometrical symmetry, a vertically laid tank can be treated as a two-dimensional (2D) case. To demonstrate the 3D

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capability of their model, they also consider another case with the same geometry but a different arrangement of the tank which is laid down horizontally [28]. Sunghyun Kyoung et al. [29] stated that a 2D simulation is sufficient to analyze the cylindrical vessel design owing to its axisymmetric configuration, but they carried out 3D simulations to determine the 3D computational capability of their model [29]. Threedimensional models may be really necessary for the metal hydride hydrogen storage systems equipped with multitubular heat exchanger [30] or coiled-tube heat exchanger [31]. To reduce computing time, we developed a reduced two dimensional model for metal hydride reactor with coiled-tube heat exchanger. The simulation results of the reduced model generally agree with those of complete three-dimensional model [52]. For simple cylindrical structure without multitubular or coiled-tube heat exchangers inside the tank and with uniform boundary condition outside the tank, it can be assumed as an axisymmetric model (2D model), in which the thermodynamic variables such as pressure and temperature and density do not vary with circumferential location. The metal hydride hydrogen storage reactor equipped with phase change materials was simplified as a two-dimensional axisymmetric model in our previous work [53]. The axisymmetric assumption will also be adopted in this work. In this paper, we report a systematic study of the effect of PCMs on the hydrogen storage behaviour of a metal hydride tank. A two-dimensional model has been developed to predict the mass and heat transfer inside the metal hydride reactor bed, as well as the temperature variation in the PCM domain. The model was built using the COMSOL Multiphysics™ 5.3 platform to discretize the mass and energy balance equations for a cylindrical hydride bed. The simulation results were validated by comparison with experimental and numerical data from other works in the literature. Some numerical computations were then accomplished to evaluate the effect of the variation of both the thermal conductivity and the latent heat of the PCM on the hydrogen absorption and desorption in the metal hydride bed.

(LiNO3e3H2O) was chosen as the heat storage medium (PCM). Its thermal physical properties are listed in Table 3. Hydrogen is inserted in the MH bed from a small slot with a radius R ¼ 0.005 m situated on the inner tube axis. The hydride reactor bed consists of two phases: a gas phase (hydrogen) and a solid phase (LaNi5 powder), so forming a discontinuous porous media. Considering the symmetry of the MH-PCM reactor (Fig. 1), only half of the cross-section of the tank was simulated. Within the MH-PCM system, the macroscopic differential equations were acquired by averaging the microscopic conservation equations of mass, energy and momentum on a representative volume and using simplification assumptions. The subsequent assumptions were made to get a closed set of the equations at the macroscopic scale:
The gas phase behaves as a thermodynamically ideal gas [34].
The media is in local thermal equilibrium [12].
The natural convection [34] and thermal radiation [12] in the hydride powder are negligible.
Heat transfer through the phase change media is by conduction only, due to the weakness of PCM melting front velocity hence the convection is negligible [35].
The solid phase is isotropic and has a uniform porosity [36].
The advection transport term is negligible [34,37].
Thermo-physical properties are constant [34,38,39].
Hydrogen is supplied to the hydride reactor at a known constant pressure [40].
The MH-PCM system is adiabatic [27,36]. Under these assumptions, the equations within the MHPCM system are as follows.

Mathematical model of the metal hydride bed Energy equation The energy equation for an MH bed in 2D cylindrical coordinates (r, z) can be expressed as:   
 vT  1 v vT v2 T ¼ l r þ leff 2 þ m_ DH þ T Cp;g  Cp;s (1) eff eff vt r vr vr vz h i h i 1 1 where Cp;g J kg K1 and Cp;s J kg K1 are the heat capacity of the gaseous phase and solid phase respectively. The 1 DH [kJ mol  is the enthalpy of reaction, where ðrCp Þeff represents the effective heat capacity and leff is the effective thermal conductivity. These two terms are averaged over the MH bed and hydrogen via


Models, method and validation Geometrical model and material properties of the metal hydride reactor Fig. 1 shows a schematic diagram of the MH reactor used in this investigation. The geometrical properties of this MH/PCM system are listed in Table 1. It consists of two concentric cylinders in which the inner tube has a volume of 117.8 cm3 (Hint ¼ 0.06 m, Rint ¼ 0.025 m) and is packed with 0.424 kg of MH powder. The inner tube is surrounded by 0.391 kg of phase change material located in the annular space. The external enclosing walls of the reactor (Hext ¼ 0.07 m, Rext ¼ 0.038 m) are adiabatic. The metal hydride considered in the present work is LaNi5. Its thermophysical properties are presented in Table 2. Choosing an adequate PCM to store or release the heat during the hydrogen absorption/desorption processes is an essential task. The PCM ought to have a suitable temperature of fusion inside the practical range of LaNi5 alloy and have a maximum latent heat of fusion. Therefore, lithium nitrate trihydrate




rCp

rCp

 eff

¼ εb rg Cp;g þ ð1  εb Þrs Cp;s

(2)

leff ¼ εb lg þ ð1  εb Þls

(3) 3

3

1

1

where εb [1], rg [kg m ], rs [kg m ], lg [W m K ] and ls [W m1 K1 ] are respectively the porosity of the MH bed, the density of hydrogen and metal, and the thermal conductivity of hydrogen and metal.

Mass conservation equation The hydrogen mass conservation equation is written as:

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Fig. 1 e Schematic of MH reactor equipped with PCM: (a) cross-sectional view, (b) The 2D axisymmetric computational domain.

εb

vrg ¼  m_ vt

(4)

Hydrogen is assumed to be ideal gas from the thermodynamic viewpoint so it obeys the ideal gas law:

Table 1 e Geometrical parameters of the reactor. Parameters The The The The The The

inner radius, Rint inner height, Hint external radius, Rext external height, Hext volume occupied by hydride, VLaNi5 volume of PCM, VPCM

Values 0.025 m 0.06 m 0.038 m 0.07 m 58.9 cm3 199.7 cm3

rg ¼

Mg Pg RTg

(5) 1

1

where Mg [kg kmol ] and R [J mol K1 ] are respectively the hydrogen molecular weight and the universal gas constant. The equation of mass conservation of the MH bed is given by: ð1  εb Þ

vrs ¼ m_ vt

(6)

_ is the mass of hydrogen absorbed/desorbed per unit where m time and volume.

Kinetic reaction _ is given by Refs. [4,10]: The mass of hydrogen rate m

Table 2 e Thermophysical properties of LaNi5 metal hydride and hydrogen [34,36,41,54]. Parameters Ca Cd Cp;g Cp;s Ea Ed DH K Mg R lg ls εb m rsat remp mLaNi5

Description

Values

Rate coefficient for absorption Rate coefficient for desorption Heat capacity of hydrogen gas Heat capacity of metal hydride Activation Energy for absorption Activation Energy for desorption Enthalpy of reaction Permeability Molecular weight of hydrogen Universal gas constant Thermal conductivity of hydrogen Thermal conductivity of metal Porosity of the metal hydride bed Dynamic viscosity of the hydrogen gas Saturated metal bed density Hydrogen-free metal density Mass of LaNi5

59.187 s1 9.57 s1 14,890 J kg1 K1 419 J kg1 K1 21,179.6 J mol1 16,473 J mol1 30,478 J mol1 108 m2 2.016 kg kmol1 8.314 J mol1 K1 0.1815 W m1 K1 2 W m1 K1 0.5 8:4  106 kg m1 s1 7164 kg m3 7259 kg m3 0.424 kg

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Table 3 e Thermo-physical properties of (LiNO3e3H2O) PCM [48,51]. Parameters Cp;p;l Cp;p;s Lp Tm DTp lp;l lp;s rp;l rp;s m PCM

Description

Values

Liquid Heat capacity of PCM Solid Heat capacity of PCM latent heat of PCM Melting temperature Range of transition temperature Liquid thermal conductivity of PCM Solid thermal conductivity of PCM Liquid density of PCM Solid density of PCM Mass of PCM

2770 J kg1 K1 1730 J kg1 K1 296 kJ kg1 303 K 2K 0.58 W m1 K1 1.32 W m1 K1 1780 kg m3 2140 kg m3 0.391 kg

For absorption case:     Pg Ea ln m_ ¼ Ca exp  ½rsat  rs  RT Pa;eq

(7)

(12) (8)

where Ca ½s1  and Cd ½s1  are respectively the rate coefficients 1 1 for absorption and desorption. Ea [J mol ] and Ed [J mol ] are the absorption and desorption activation energies. The rsat [kg m3 ] and remp [kg m3 ] are respectively the saturated density and the hydrogen-free density of the MH. The values of these coefficients in Eqs. (7) and (8) cited from the literature [34,41] are presented in Table 2. The Pg [MPa] is the pressure of the hydrogen while Pa;eq ½MPa; Pd;eq ½MPa are respectively the absorption and desorption equilibrium pressures. The equilibrium pressures Pa;eq ; Pd;eq are calculated by using the general form of the van’t Hoff relationship whose dependence on temperature is given by Refs. [36,41]: ln

  Pa;eq Ba ¼ Aa  Pref T

  Pd;eq Bd ¼ Ad  ln Pref T

      vPg vuz v 1 v v2 uz vuz vuz ðruz Þ þ 2  rg ur ¼ þm þ uz vr r vr vt vz vz vr vz  Sz

For desorption case:     Pg  Pd;eq  Ed m_ ¼ Cd exp  rs  remp RT Pd;eq

rg

(9)

(10)

The values of the plateau pressure coefficients A and B for absorption and desorption are taken from the Hydride Databases [42]. For a reference pressure of 1 MPa ðPref ¼ 1 MPa), the values of the coefficients are for absorption and desorption: Aa ¼ 10.7, Ba ¼ 3704.6 and Ad ¼ 10.57, Bd ¼ 3704.6 [36,41].

where Sr and Sz represent the pressure drop of the gas due to viscous dissipation. The Si in each direction is obtained from Darcy’s law [43] and calculated by: Si ¼

m K

ui

where m [kg m1 s1 ] is the dynamic viscosity of the gas, and K [ m2 ] is the permeability of the porous bed, their values cited from the literature [41,43] are also represented in Table 2.

Mathematical model of the PCM The thermal energy equation is expressed in the function of total volumetric enthalpy and temperature as follows [44]: vHP ¼ V$ðlP VðTÞÞ vt

The momentum conservation equations for the hydrogen flow along r and z directions are respectively given by:
In r-direction:

     vPg vur v 1 v v2 ur vur vur ðrur Þ þ 2  rg ur ¼ þm þ uz  Sr rg vr r vr vt vr vz vr vz 

(11)

(14)

where HP is the total volumetric enthalpy of the PCM which is expressed as the total of the enthalpy (h, [J m3 ]) and  sensible i h 1 the latent heat of the PCM Lp ; J kg : HðTÞ ¼ hðTÞ þ rp Lp f ðTÞ

(15)

where f is the liquid fraction. And the sensible enthalpy (h) can be written as [45]: ZT rp Cp;p dT

hðTÞ ¼

Momentum equation

(13)

(16)

Tm

h i   1 where rp ½kg m3 ; Cp;p J kg K1 , and lP W m1 K1 are respectively the density, the heat capacity and the thermal conductivity of the PCM. The liquid fraction f can be expressed as follows [46]: 8 1 > > > > < ðT  T Þ Sol f¼ > > ðTmel  TSol Þ > > : 0

if T  Tmel if TSol < T < Tmel

(17)

if T  TSol

where Tmel [K] and TSol [K] are the melting and solidification temperatures.
In z-direction: Please cite this article as: El Mghari H et al., Analysis of hydrogen storage performance of metal hydride reactor with phase change materials, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.090

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Tðr; z; 0Þ ¼ T0 ¼ 313 K

(22)

Pg ðr; z; 0Þ ¼ P0 ¼ 0:1 MPa

(23)

rs ðr; z; 0Þ ¼ r0 ¼ rsat

(24)

The value Pg ¼ 0:8 MPa > Pa;eq (T ¼ 293K) ¼ 0.143 MPa is set for absorption, and Pg ¼ 0.1 MPa < Pd;eq (T ¼ 313 K) ¼ 0.282 MPa for desorption.

Boundary conditions The boundaries of the computational domain are shown in Fig. 1b. The boundary conditions are expressed as follows:
Inlet/outlet boundary conditions:

Pg ðr; z; tÞ ¼ Pint=out at z ¼ Hext ; 0  r  R

(25)


Symmetry boundary condition (Adiabatic wall):

n ¼ VTP ,! n ¼0 VTMH ,!

(26)

Fig. 2 e Computational mesh by software COMSOL.
Inlet boundary condition for hydrogen: From Eqs. (15) and (16), an alternative form of Eq. (14) for the 2D heat storage in PCM media can be expressed as:    vT
1 v vT v2 T vðf Þ ¼ lP r þ lP 2  rp Lp rp Cp;p vt r vr vr vz vt

(18)

Initial and boundary conditions

VT , ! n ¼ 0

(27)


The inter-domain MH bed/PCM boundary condition is:

Initial conditions For both the charging and discharging processes, the MH bed temperature, the hydrogen pressure, and the PCM temperature are assumed to be constant. The initial MH density is taken as a hydrogen-free metal density for hydriding case and fully hydrided density for the dehydriding case. Therefore.

(28)

Numerical method and model validation The above equations for the metal hydride bed and the PCM were discretized and solved numerically using the software COMSOL Multiphysics™ V 5.3. A time-dependent solver was used to evaluate the equations with a time step of 1.5s. The


For hydriding:

Tðr; z; 0Þ ¼ T0 ¼ 293 K

(19)

Pg ðr; z; 0Þ ¼ P0 ¼ 0:8 MPa

(20)

rs ðr; z; 0Þ ¼ r0 ¼ remp

(21)


For dehydriding:

n ¼ lP VTP ,! n lMH VTMH , !

Table 4 e The mesh statistic. Description Number of elements Number of boundary elements Number of vertex elements Minimum element quality Element area ratio Mesh area

Value 555 84 8 0.6847 0.3641 0.00266 m2

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Fig. 3 e Validation of the numerical results compared with Jemni et al. [38] and Chung et al. works [41]: (a) Evolutions over time of the total released hydrogen amount per formula unit and the temperature at r ¼ 1.5 cm, z ¼ 3 cm in absorption process, (b) Evolutions over time of the total released hydrogen amount per formula unit and the temperature at r ¼ 0 cm, z ¼ 3 cm in desorption process.

finite element mesh consists of 555 fine triangular elements as shown in Fig. 2. The mesh statistics is given in Table 4. The validation of our developed model was carried out in two parts. In the first part, the numerical results are given in Fig. 3 were compared with the experimental results of Jemni et al. [38] and the numerical data of Chung et al. [41] in the case of MH reactor without PCM submerged in a water bath at a constant temperature. For the absorption case, the hydrogen charge pressure was 8 bar and the working temperature 293 K. In the case of desorption, the hydrogen pressure was set at 0.1 MPa and working temperature 313 K. Apart from a small deviation, our numerical results are in agreement with the experiments of Jemni et al. [38] and the numerical study of Chung et al. [41]. We have thus established that our model is valid to simulate the operation of a hydrogen storage tank. To validate the usefulness of our model for a tank with PCM, we compared our numerical results with the ones of H ^ ad et al. [40]. Ben Ma ^ ad et al. developed a transient twoBen Ma

Fig. 4 e Verification of the obtained numerical results by comparing the liquid fraction against time with H Ben ^ ad et al. work. Ma

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dimensional mathematical model and solved this model to predict the dynamic behaviour of a cylindrical metalhydrogen tank filled with LaNi5 equipped with a PCM. Fig. 4 plot the liquid fractions versus time for our simulation and ^ ad et al. [40]. We see that both simulations the one by H Ben Ma agree. Therefore, we are confident that our model could also be applied to tanks with PCM.

Results and discussion Absorption process Fig. 5 represents the distribution of the temperature, the absorbed amount of hydrogen and also the liquid fraction of PCM within the MH-PCM reactor at selected times during the

Fig. 5 e Time distributions of the temperature, the absorbed amount of hydrogen per formula unit and also the liquid fraction of PCM in absorption case: at t ¼ (a) 60s (b) 3000s (c) 6000s and (d) 9000s.

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Fig. 6 e Evolution over time during absorption process of: (a) the hydrogen amount per formula unit within the MH-PCM reactor and also the liquid fraction of PCM, (b) the average temperature of the MH bed and the PCM.

absorption process. It is seen from Fig. 5a, that at initial charging times (t < 60s) the MH bed temperature increases progressively due to the exothermic reaction. The PCM at the inter-surface with the hydride bed experiences a phase transformation to the liquid state. As shown by the hydriding timeline of Fig. 5bed, the temperature inside the MH bed decreases gradually until the thermal equilibrium with the PCM domain is reached. Fig. 5 also presents the distributions of the hydrogen amount and the liquid fraction of the PCM in the reactor throughout the hydrogenation process. It is noted that the hydriding fraction increases progressively to the center of the reactor as the hydrogenation proceeds until reaching saturation. Simultaneously, the PCM melting fraction extends to the exterior walls of the tank. For a better understanding of the mass and heat transfer phenomenon inside the MH-PCM reactor, the evolution over time of the hydrogen amount in the reactor, the liquid fractions of the PCM, as well as the average temperature of the MH bed and the PCM throughout the absorption process are presented in Fig. 6. It is seen that there is a good correspondence between the hydrogenation amount and the liquid fraction during hydrogenation. As shown in Fig. 6a, the liquid fraction of the PCM increases progressively with the charging process throughout the first hour. Afterward, the increase in the melted fraction is much slower. This is maybe because of the reduction of the contact surface between the liquid and solid phases of the PCM that is essentially confined to the bottom corner of the reactor as seen in Fig. 5b,c. A small fluctuation appeared in the PCM temperature during the first hour when it increases from the ambient temperature (293 K) to a maximum value of 314 K and then it decreases slowly until it becomes approximately constant at the value of 311 K (Fig. 6b). Furthermore, it can be seen from Fig. 6a that the hydrogen amount in the hydride bed

increases progressively until reaching saturation after about 7600 second. At this time, the PCM temperature reaches the maximum value of 314 K. This means that the temperature of the PCM predicts the behaviour of the reactor. When the reactor reached the saturation state, the MH was fully hydrided while 94% of the PCM was melted. This indicates that there is a sufficient amount of PCM to enable total absorption of all the reaction heat produced by the hydrogenation. Moreover, as seen in Fig. 6b, at the beginning of the charging process the average temperature of the hydride bed increases quickly from ambient temperature to 338 K. This rapid increase is due to the heat created by the exothermic hydrogenation process. The temperature then decreases gradually until equilibrium with the PCM is reached.

Desorption process The distribution of the temperature, the released amount of hydrogen and also the liquid fraction of PCM within the MHPCM reactor at various times during the desorption process are presented in Fig. 7. As can be observed from Fig. 7a at the initial time of the discharging process (t < 60s) the MH temperature decreases progressively due to the endothermic dehydrogenation. The PCM at the interface with the hydride bed experiences a phase transformation to the solid state. As the dehydrogenation reaction progresses, the temperature inside the hydride bed increases while the PCM temperature decreases until the thermal equilibrium is achieved (Fig. 7b,c,d). The dehydrogenation is sustained by the released heat from the PCM that solidified from the inner to the outer walls. Simultaneously, the hydrogen amount decreases progressively to the middle of the reactor as the reaction proceeds until complete dehydrogenation.

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Fig. 7 e Time distributions of the temperature, the released amount of hydrogen per formula unit and also the liquid fraction of PCM in desorption case: at t ¼ 60s (a), 5000s (b), 10000s (c) and 15000s (d).

The time evolution of the hydrogen amount within the MH-PCM reactor, the liquid fraction of the PCM, as well as the average temperature of the MH bed and the PCM throughout the desorption process are presented in Fig. 8. Throughout the dehydriding process, there is a good correspondence between the amount of hydrogen dehydrided and the liquid fraction. It can be seen from Fig. 8a that the liquid fraction of the PCM decreases progressively with the discharging process throughout the first 6000 second. At the

start of dehydrogenation, the average temperature inside the MH bed decreases rapidly from 312 K to 285 K due to the endothermic dehydrogenation reaction. After this initial strong reduction of temperature, the MH bed temperature increases slowly until the thermal equilibrium with the PCM is reached. A small decrease in the average PCM temperature from 312 K to 298 K was observed during the first 10,000 s of the dehydriding process. The small ‘spike’ in the PCM temperature curve is due to the reduction of the

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Fig. 8 e Evolution over Time during desorption process of: (a) the hydrogen amount per formula unit within the MH-PCM and also the liquid fraction of the PCM, (b) the average temperature of the MH bed and the PCM.

surface contact between the solid and liquid phases of the PCM. As seen in Fig. 7b,c the PCM liquid state is progressively reduced only to the bottom corner where the heat exchange with the exterior is reduced.

Based on these results, it can be deduced that the use of PCM can enhance the energy efficiency of the MH hydrogen storage system even without an auxiliary heat source. However, the effect of thermal conductivity and latent heat of PCM

Fig. 9 e Evolution over time of the hydrogen amount per formula unit within the MH-PCM and also the liquid fraction of the PCM for different values of the thermal conductivity (lP ¼ 0.24, 1.32, 2.34 and 16.7 W/m/K) in: (a) absorption case (b) desorption case. Please cite this article as: El Mghari H et al., Analysis of hydrogen storage performance of metal hydride reactor with phase change materials, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.090

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Fig. 10 e Relationship between the charging Time and the thermal conductivity of the PCM.

on the performances of the MH/PCM tank should be investigated. In order to evaluate the impact of the thermal conductivity of the PCM on the hydrogenation and dehydrogenation within the MH-PCM reactor, four different values of thermal conductivity of PCM were considered (lP ¼ 0.24, 1.32, 2.34 and 16.7 W/m/K). These four thermal conductivity values were chosen because they are respectively for RT27 paraffin wax

[47], lithium nitrate trihydrate LiNO3e3H2O, Manganese (II) nitrate hexahydrate Mn (NO3)2$6H2O [48] and Cerrolow 117 [48]. The other thermo-physical properties were kept the same as in the previous calculations. Fig. 9 shows the evolution over time of the hydrogen amount within the MH-PCM reactor and the liquid fraction of the PCM during hydrogenation and dehydrogenation processes for the four different values of thermal conductivity of PCM. It is clear that when the thermal conductivity of PCM increases from 0.24 to 2.34 W/m/K, the loading and unloading times decreases significantly. A further increase of thermal conductivity to 16.7 W/m/K only marginally reduces the loading time. In Fig. 10, the charging time (t) as a function of three different values of the thermal conductivity of the PCM (lP ¼ 0.24, 1.32 and 16.7 W/m/K) is plotted. For the small thermal conductivity, the charging time decreases linearly with increasing the thermal conductivity. For higher conductivity, the decrease is much smaller. This means that thermal conductivity is not the only parameter responsible for the charging time. Fig. 11 represents the evolution over time of the average temperature of the MH bed and the PCM during the absorption and desorption processes for the four different values of PCM thermal conductivity. As seen from this figure, the average temperature of the MH bed is also affected by the PCM thermal conductivity, when the value of lP increases from 0.24 to 16.7 W/m/K, the temperature reaches the thermal equilibrium faster. Furthermore, the equilibrium temperature of the MH bed and the PCM decreases significantly when the thermal

Fig. 11 e Evolution over time of the average temperature of the MH bed and the PCM for different values of the thermal conductivity (lP ¼ 0.24, 1.32, 2.34 and 16.7 W/m/K) in: (a) absorption case (b) desorption case. Please cite this article as: El Mghari H et al., Analysis of hydrogen storage performance of metal hydride reactor with phase change materials, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.090

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Fig. 12 e Evolution over time of the hydrogen amount per formula unit within the MH-PCM and also the liquid fraction of the PCM for three different values of latent heat of fusion of PCM (Lp ¼ 296, 179 and 157 kJ/kg) in: (a) absorption case (b) desorption case.

conductivity increases from 0.24 to 2.34 W/m/K until becoming almost constant. This means that increasing the thermal conductivity of the PCM to a certain value it is not sufficient to improve the heat transfer between the

MH bed and the PCM. Thus, other parameters like the latent heat of the PCM should be studied. In order to examine the impact of the latent heat of the PCM on the MH-PCM reactor, three different values of latent

Fig. 13 e Evolution over time of the average temperature of the MH bed and the PCM for three different values of latent heat of fusion of PCM (Lp ¼ 296, 179 and 157 kJ/kg) in: (a) absorption case (b) desorption case. Please cite this article as: El Mghari H et al., Analysis of hydrogen storage performance of metal hydride reactor with phase change materials, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.09.090

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heat of fusion of PCM were considered (Lp ¼ 296, 179 and 157 kJ/kg). These three latent heat values are respectively for LiNO3e3H2O, RT27 paraffin wax [47] and Rubitherm RT35 PCM [49]. The other thermophysical properties were kept identical as in the previous calculations. Fig. 12 shows the evolution over time of the hydrogen amount within the MH-PCM reactor and also the liquid fraction of the PCM during absorption and desorption processes for different PCM latent heat values. As can be seen from this figure, when the latent heat of fusion of PCM decreases from 296 to 157 kJ/kg, the absorption and desorption kinetics are significantly reduced. The total heat of reaction of the LaNi5 in the tank is 90 kJ which is smaller than the 115.73 kJ total latent heat of fusion of the LiNO3e3H2O PCM but larger than the two other PCMs (70 kJ, and 61.38 kJ respectively). Hence, an important amount of the heat of the reaction is transformed as sensible heat and the mass of the PCM are too small to give a total latent heat of fusion equal or bigger than the total heat of reaction of the metal hydride. Furthermore, it can be observed that a large amount of the reaction heat at the beginning of the hydriding and dehydriding process leads to fast melting and solidification of the PCM. Consequently, it can be seen from Fig. 13 which shows the time evolution of the average temperature of the metal hydride bed and the PCM during absorption and desorption process for the three different values of latent heat of fusion of PCM, that the temperature of the PCM increases during the charging process and decreases during the discharging process which in turn causes the blocking of the absorption and desorption process. These results show that the effect of latent heat of the PCM on the MH bed is more important than the effect of the thermal conductivity. Thus an increase in the latent heat of the PCM leads to an important improvement in the energy efficiency of the MH hydrogen storage system.

Conclusion The absorption and desorption processes of hydrogen for a cylindrical MH reactor equipped with a phase change material (PCM) was numerically investigated. A two-dimensional model was developed to describe the mass and heat transfer inside the metal hydride and the PCM as well as the interaction between them. The effect of thermal conductivity and latent heat of the PCM on the charging and discharging processes were evaluated. The results show that the rates of hydriding and dehydriding and the storage capacity of hydrogen are strongly influenced by the PCM thermal conductivity and latent heat. An increase of the thermal conductivity from 0.24 to 2.34 W/m/ K reduces the charging and discharging times because of a better heat transfer between the MH bed and the PCM. A reduction of the melting enthalpy of the PCM from 296 to 157 kJ/ kg significantly reduces the absorption and desorption kinetics. It was found that the effect of latent heat of the PCM on the MH bed is more important than the effect of thermal conductivity. From this investigation, it can be deduced that an adequate loading and unloading time and hydrogen storage capacity of MH reactor equipped with PCM necessitate a good choice of the melting temperature and the thermal conductivity of the PCM. For optimum performances, the latent heat of

fusion of PCM should be equal or bigger than the total heat of reaction of the metal hydride.

Acknowledgements We wish to thank the financial support from the National Natural Science Foundation of China (Project No. 5147610), the 111 Project of China (No. B17034). Miss Hafsa El Mghari wishes to thank the support from the China Scholarship Council (No.2017GXZ001367).

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