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Dynamic study of a new design of a tanks based on metallic hydrides
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Dynamic study of a new design of a tanks based on metallic hydrides Chaker Briki a,*, Sihem Belkhiria a, Mohamed Houcine Dhaou b, Faouzi Askri c, Abdelmajid Jemni a a
Laboratory of Studies of Thermal Systems and Energy, Ibn Eljazzar Road, National Engineering School of Monastir, University of Monastir, 5019 Monastir, Tunisia b Department of Physics, College of Science, Qassim University, Saudi Arabia c Engineering School University of Abha, Saudi Arabia
article info
abstract
Article history:
It is known that the hydrogen has a very high mass energy density, in fact, that it is a
Received 12 August 2017
lightest gas; therefore, its storage is a great problem. The aim of the hydrogen storage
Received in revised form
technologies is thus to reduce the volume that hydrogen occupies in its thermodynami-
19 October 2017
cally stable state under conditions close to ambient salt. Recent work on hydrogen storage
Accepted 13 November 2017
is mainly based on the use of metal hydrides. These metal hydrides have a high capacity
Available online xxx
for the hydrogen storage in the operating conditions. The effecting parameters on the performance of such a metal-hydrogen reactor are its design and configuration. In this
Keywords:
case, there are a number of problems that need to be considered in designing a reactor.
Hydrogen storage
Among these parameters are the reactor configuration, the thermal and the mechanical
Solid state reactions
strength, the kinetics of hydrogen storage and the security. Our study is concentrated on
Kinetics
the problem of the thermal and the mechanical strength while focusing on the nature of
Activation energy
the metal makes the reactor. In this work, the experimental studies of the hydrogen ab-
Metal-hydride
sorption phenomenon in different reactors, based on metal hydrides, were evaluated. The
LaNi5
characteristics of the reaction kinetics in three different reactors using the same measurement conditions were compared. A numerical model describing the reaction kinetic of the H2 absorption by LaNi5 alloy validates the results were obtained. Of these results, it is found that the rate constant varies from one reactor to another. Moreover, the activation energy of the absorption kinetics were identified. Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
Introduction Great number of research study have been launched to use hydrogen as an energy carrier for many exploit renewable energy resources and to develop fuel cell technology. That also preserve environment by reducing discharges of pollutants and the
emission of greenhouse gases caused by the strong growth in demand for energy. If hydrogen were prevailed in the long term as an energy, the researchers and engineers challenge is to know how to produce, distribute, store and use it [1e5]. Hydrogen has several applications in energy area. It has undergone significant interest in order to meet the demand in terms of industrial development [6].
* Corresponding author. E-mail address: [email protected] (C. Briki). https://doi.org/10.1016/j.ijhydene.2017.11.085 0360-3199/Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. Please cite this article in press as: Briki C, et al., Dynamic study of a new design of a tanks based on metallic hydrides, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.11.085
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Nomenclature Cp Ea Eap l P T t R r
Specific heat, J kg1 K1 Activation energy, J mol1 Apparent absorption energy, J mol1 Thermal conductivity, W m1 K1 Pressure, bar Temperature, K time, s Gas constant, J mol1 K1 Density, kg m3
Subscripts [H/M] Hydrogen-to-metal-atomic ratio G Gas E Equilibrium Ss Saturated
We know that the hydrogen has a low energy capacity per volume, but it offers a good energy capacity per mass compared to others fossil fuels. The only way to make the hydrogen more efficient is to store it in high-density metals, which have small volumes and low masses. However, it is necessary to develop new designs and geometries of hydrogen storage reactors based on metal hydride, which exhibit high volumetric capacity and fast sorption kinetics. Many physical, chemical and dynamic challenge need to be considered for hydrogen storage systems. In particular, the properties of hydrogen gas and heat transfer of the hydride bed are the major problems for a high-dynamic tank operation. Hydrogen must be stored in a small, lightweight system due to the size and weight constraints in vehicles. This is particularly challenging because this gas has the lowest energy density of common fuels. Therefore, many researches are focusing on
the performance of storage system such as; high thermal conductivity, favorable equilibrium pressure, high hydrogen absorption capacity, fast reaction kinetics and simple activation process [7,8]. It has been recognized for a long time that the hydrogen storage in the form of hydride has the advantage of safety and easy recovery than the other types of storage. Much larger quantities of hydrogen can be stored per unit volume than in its liquid and in its gas form. Each one of these techniques has its own advantages and disadvantages [9]. Therefore, metal and complex hydrides have attracted attention as hydrogen storage materials. Among these metals, the LaNi5 intermetallic alloys are commonly chosen as the hydrogen storage medium because of their attractive characteristic features. Such as their high storage capacity, their favorable operating temperatures and pressures, their low hysteresis, their easy activation, their low density, their high volumetric density, their highest safety level compared to other metals and fast reaction rates [10,11]. These metals can be used in reversible hydrogen storage. The kinetic reaction of hydrogen sorption by the metal depends on the heat and the mass transfer within the reactor. This explicates that the hydride reactor designs are extremely important for the heat removing from reactor [12,13]. The effects of operating conditions for performance of metal hydrogen storage tanks are complicated and they need detailed investigations for further optimization [14,15]. The geometry and the design of the metal-hydrogen reactors, which have evolved over years of study, are important factors in the heat and the mass transfer in the hydride bed. Several numerical and experimental research works have been devoted to optimize the design parameters of metalhydrogen tanks [16e41]. In parallel, the rate at which hydrogen can be absorbed and desorbed by a particular metal or alloy is an important factor for the hydrogen storage. This reaction rate depends on
Fig. 1 e (a, b): Photograph of the reactor Aluminum and Copper. Please cite this article in press as: Briki C, et al., Dynamic study of a new design of a tanks based on metallic hydrides, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.11.085
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Fig. 2 e Schematic view of experimental installation. several factors. Among them, the activation energy who is a parameter that characterizes the kinetics reaction of hydrogen absorption by metal. It is defined as being the minimum energy required to start a chemical reaction. In fact, many studies have been done to compare and to model the mechanisms of the hydrogen absorption kinetics [20e35]. Miyamoto et al. [20] investigated the absorption kinetic of LaNi5 and LaNi4.9Al0.1 alloys. They proposed an analytical expression of kinetic rate and then found that the activation energy value for absorption Ea is equal to 29.288 kJ/mol-H2. Suda et al. [21] studied experimentally the reaction rate in the processes hydriding and dehydriding for LaNi5, MmNi5, TiMn10.5 and Ti0.8Zr0.2Cr0.8Mn1.2 alloys. The experimental results showed that the annealed MmNi4.5Al0.5 hydride has smaller rate constants than those of the other hydrides under the same experimental conditions and that each hydriding alloy has temperature bands where the hydriding and dehydriding reactions proceed at much higher speeds. The value of activation energy for LaNi5 is 20.7 kJ mol1 [22]. Osairy et al. [23,24] studied the LaNi5eH6 compound and they found that the reaction rate defined as compound of two functions temperature and pressure. Cheng et al. [25] show that the reaction kinetics of the LaNi5 compound depends on the number of cycles absorption of hydrogen and the rate constant K is 0.0161, 0.0191 and 0.0225 for the value of the cycle number 2, 50 and 150, respectively, and takes as value of the activation energy Ea ¼ 21.179 kJ mol1. The numerical simulation of the heat and the mass behavior in a metal-hydrogen reactor requires the knowledge
of the reaction kinetics. That is why many works, which are related to the reaction kinetics of metal hydrides and essentially the LaNi5 alloy, have been done [20e35]. Several models of the reaction kinetics are encountered in the literature. All these models are taking into account the heat and the mass exchange in the hydride bed. From the previous literature review on the hydrogen absorption kinetics by LaNi5 alloy, we note that Ea varies from 20 to 30 kJ mol1. We know that the Ea is an intrinsic property of the metal used; therefore, it must be constant. Improved of hydrogen storing devices can be obtained through design parameters like heat exchangers, filters, geometrical distribution of the alloy inside the container and the nature of the reactor. Since that, the reactor geometry does not have any effect on hydride formation process but it influences the reaction speed [36]. Likewise, reactor configuration and heat exchanger design will elevate the storage capacity and hydrogen storage density and decrease refueling time [37e41,50e60]. The aim of this study is to test metalhydrogen tanks containing LaNi5 powder. Three metalhydrogen reactors are considered: a copper reactor, an aluminum reactor and a steel reactor. In fact, the used materials for manufacturing the reactor were defined as a remarkable index to the kinetics' effect. The experimental results allowed as proposing a numeric model describing the kinetics of hydrogen absorption by LaNi5 alloy and simulating the behavior of the metal-hydrogen tank. This model takes into account the heat and the mass exchange in hydride bed and in the reactor materials. Once we found the value of the
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Fig. 3 e Simulation and experimental evolution of equilibrium pressure as a function of [H/M] and temperature for the alloy LaN5. activation energy for the LaNi5 alloy, the experimental results obtained were measured and are compared with those calculated.
Design of the reactor A schema of the copper and aluminum reactors design's is shown in Fig. 1(a) and (b). They are formed of a cylindrical body (inner diameter: 30 mm; outer diameter: 38 mm; inner height: 40 mm; outer height: 50 mm) and a lid (diameter: 15 mm, thickness: 1 mm). The reactors are filled with 30 g of LaNi5 alloy to about half their volume in order to both reduce internal mechanical tensions due to the material dilatation and to leave some extra free volume for the non-absorbable gaseous contaminants. The lid is equipped with a filter in
Fig. 5 e Bed temperature vs. time during absorption in two types of reactor. fried stainless steel (diameter of the pre equal to 1.4 mm). A joint is placed between the lid and the body to ensure gas tightness. Two tubes are connected on the lid by a tight passage. The first one allows the input-output of hydrogen and the setting vacuum. The second one allows a pressure pick-up relative to measure the gas pressure in the reactor.
Experimental apparatus Fig. 2 shows a schematic diagram of the used experimental device. The Hydrogenation cycles were carried out with hydrogen gas of 99.999% purity. The reactor is fed with hydrogen, from a buffer reservoir, through steel pipe of 6 mm diameter. The connection between the reactor and the reservoir is ensured by using Swagelok valve. The reservoir is loaded with hydrogen at a desired pressure. The whole device is supplied with hydrogen from pressurized cylinder (200 bars). A thermostat bath is used for the cooling or heating fluid flows, in the sealed cylindrical jacket over the reactor, at flow rates ranging from 1 to 13 g/l. A vacuum pump is used to evacuate the gas from the whole installation. The pressure is measured by a pressure sensor (type PH-21LC, 0e100 bars, sensitivity 0.01 bar) which is connected to a data acquisition system (PC73A) installed in the microcomputer.
Measurement procedure
Fig. 4 e Variation in mass hydrogen absorbed as a function of time for three type of reactors.
The volumetric method of measuring the mass of hydrogen absorbed by a metal is based on the use of pressure, volume and temperature data to calculate the amount of hydrogen absorbed or desorbed by the metal [42]. The experimental procedure for the absorption begins by starting the vacuum pump to maintain a low pressure in the reactor (0.01 bar) at high temperature (323 K) for a period of time to ensure in that the sample is emptied of hydrogen (or other gases). The buffer
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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 x x x ( 2 0 1 7 ) 1 e1 1
(a)
(b)
Fig. 6 e (a): Effect of the cooling water temperature on the kinetics of absorption in reactor Copper. (b): Effect of the cooling water temperature on the kinetics of absorption in reactor Aluminum.
reservoir is loaded at the desired pressure. Then the valve between reservoir and reactors opened and hydrogen is allowed to flow into the reactor. The alloy LaNi5 absorbs hydrogen by releasing heat. This heat is evacuated by cooling fluid circulation within the cylindrical jacket over the reactor. The absorption continues until it reaches steady state, there the acquisition is stopped. The experimental procedure for desorption starts at the end point of an absorption test. The reservoir, emptied via the vacuum pump, is connected to the reactor and then starting the acquisition and the hot water flow to the desired temperature until reaching an equilibrium state. At the beginning of each experiment, the efforts are made to have the same initial conditions of the reactor. Before starting the study of the sorption phenomena, the activation of the alloy is executed and the average particle size of the alloy was approximately 50 mm. It consists of the repetition of an absorption/desorption cycles (30 cycles of absorption/
5
(a)
(b)
Fig. 7 e (a): Effect of the initial hydrogen pressure on the absorption kinetic in reactor Copper. (b): Effect of the initial hydrogen pressure on the absorption kinetic in reactor Aluminum.
desorption) until the maximum hydrogen storage capacity (1.4 wt%) of the metal is reached.
Results and discussion Equilibrium pressure determination The equilibrium pressure (Peq) is one of the most important parameters in the reaction kinetics of hydrogen by a metal. We therefore determined, for the simples studied, its evolu H and temperature. The tion as a function of concentration M experimental procedure for determining the equilibrium pressure is detailing in Refs. [43e46]. The authors proposed, to
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Fig. 8 e Bed temperature vs. time for various applied pressure. simulate the evolution of the equilibrium pressure, the following expression: H H DH 1 1 ;T ¼ f exp (1) M M Rg T T0 H : is the reaction heat function (J), Rg : is the gas where M H constant (J/K), T0 : is the reference temperature, and f M Peq
represents the evolution of the equilibrium pressure (bar) H versus M at the reference temperature T0 . To implement a realistic of isotherms PCT correlation a numerical model which can reproduce the experimental measured values very precisely and can be used for a reliable interpolation has to be found. There are many models to describe PCT correlations available in the literature. For example, the following models were found: Dhaou et al. (model) [47]. An example of equilibrium pressure curve (calculated and measured), relating to LaNi5 alloy, is shown in Fig. 3. These profiles show the dependence of Peq on the H temperature and M . In addition, we note that the used analytic expression of Peq is agree with the measurement.
Fig. 9 e (a): Hydriding rates versus (N ¡ 1)[Ln(P/Peq)/(P/ Peq)](1 ¡- F) in the case of LaNi5 alloy for the reactor manufactured in Copper. (b): Hydriding rates versus (N ¡ 1) [Ln(P/Peq)/(P/Peq)](1 ¡ F) in the case of LaNi5 alloy for the reactor Manufactured in Aluminum.
Kinetic reaction A set of measurement was carried out on the three types of reactors Fig. 1(a) and (b) made in copper, steel and aluminum. The obtained results are shown in Fig. 4. These figures show the evolution of the absorption H2 mass by the LaNi5 alloy at the same operating conditions (temperature, pressure). Although it is the same metal used and submitted to the same operating conditions, there is a difference between the kinetics of hydrogen absorption by LaNi5. The mass of hydrogen absorption reaches a saturation value of 5.8, 5.4 and 4.7 at T ¼ 293 K and P ¼ 8 bar. It can be seen that the amount hydrogen absorption content raises remarkably with time at the nature of the metal makes the reactor. Therefore we
observe clearly that the evidence the effect of reactors material on the dynamic of absorption. Fig. 5 shows the time evolution of the temperature in the center of the hydride bed for the both types of reactors. Our results show that the temperature increases and reaches rapidly a maximum. This increase of temperature is explained by the exothermic reaction of the intermetallic and due to the low thermal conductivity of the hydride. After this rapid increase, the temperature decreases gradually down to the cooling temperature and the system returns to its equilibrium state. Fig. 6(a) and (b) show the evolution of the absorbed hydrogen mass when the copper reactor and the aluminum
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(a)
between metal hydride bed within the reactor and cooling fluid. Lowering the cooling temperature helps to accelerate the kinetics of the exothermic absorption reaction. Similarly, the effect of the initial pressure on the time evolution of the amount of hydrogen absorbed by the hydride were also studied. For that, we vary absorption pressure and by setting the coolant temperature at 283 K and fluid flow rate at 13 g/l. Fig. 7(a) and (b) show the effect of the hydrogen applied pressure on the absorption phenomenon. Four values of pressure (4, 6, 8 and 10 bars) are considered; these values are related to the pressure applied to the input of the tank. These figures shows that the total mass absorbed increases with the operating pressure. In this case, the initial pressure of hydrogen applied is responsible for raising the driving force for mass transfer, speeds up the absorption reaction and stores more hydrogen in the sample. In addition, the characteristic reaction time, in order that the sample reach 90% of maximum hydrogen capacity, depends on used materials to manufacturing the reactor. This reaction time is equal to 302 s, 133 s and 74 s for respectively steel, copper and aluminum. Indeed, the used material for manufacturing the reactor effect the kinetic of the absorption reaction by means of the conduction between the cooling fluid and hybrid bed and by the inertia thermal of reactor. Fig. 8 shows the temperature evolution in the hydride bed within the reactor made in copper, for different applied pressures of hydrogen. The figures show a sudden rise of temperatures in the metal bed at the beginning of the reaction, due to the exothermic hydrogen-metal reaction and under the effect of the applied pressure, and then they decrease gradually with the reaction kinetics decay. However, the time to return to a thermal equilibrium is different according to the applied pressure. This is due to the high gradient of temperature for each pressure and to the low thermal conductivity of the hydride bed.
(b)
Modeling of absorption hydrogen by metal powder The steps of this numerical model are to represent the problem and define appropriate assumptions to simplify the equations and them to be solved analytically. The assumptions listed below are often considered in the modeling of the metal-hydrogen systems. The kinetic reaction of solid gas system can be expressed as [47,48]:
Fig. 10 e (a): Arrhenius rate constant for hydriding reaction for the reactor manufactured in Copper. (b): Arrhenius rate constant for hydriding reaction for the reactor manufactured in Aluminum.
dF ¼ Kg1 ðPÞg2 ðFÞ dt
reactor are cooling at different temperatures. The fluid flow rate is constant and equal to 13 g/l. We note that the low cooling fluid temperature induce an improvement of LaNi5 absorption kinetic. Indeed, it increases heat exchange
(2)
where, F is the fraction solid which reacts, t is time, g1 ðPÞ and g2 ðFÞ are two functions that express the effects of applied pressure and the fraction F of the reaction rate and K is a rate constant.
Table 1 e Thermo-physical proprieties of materials. 3
Density, r (kg/m ) Specific heat, CP (J/kg K) Thermal conductivity l (W m1 K1)
LaNi5
Hydrogen
Aluminum
Copper
Steel
8200 419 3.18
0.0838 14890 0.167
2690 921 205
8700 385 401
7850 420 43
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The comparison of different models proposed in the literature with experimental results can be explained by the fact that some models are only applicable where the applied pressure is constant. On the other hand, the models generally do not take into account the initial conditions of temperature and pressure. Dhaou et al. [47] provides an extended model that considers the initial conditions of temperature and pressure. In fact, the analysis of applied pressure effect and the fraction F on the absorption reaction rate of LaNi5 alloys allowed them to propose the following expression of g1 ðPÞ and g2 ðFÞ function: ln PPeq (3) g1 ðPÞ ¼ ðN 1Þ P Peq
g2 ðFÞ ¼ ð1 FÞ where F ¼
½MH , ½MH ss
(4) H M
is the hydrogen-to-metal-atomic ratio, P ss
is the instantaneous hydrogen pressure at a time t, Peq is the equilibrium plateau pressure and N is the initial applied N ¼ PPm0 . pressure P0 to the mid-plateau pressure Pm e ratio e
Table 2 e Reaction rate constants k of hydrogen absorption. Reactor Steel Reactor Copper Reactor Aluminium lnðkÞ
6:4 26386:9 Rg T
8 21017:4 Rg T
The obtained value of the apparent activation energy for the absorption process (Eap) of LaNi5 alloy was varied from 21 to 26 kJ mol1. In observing that the apparent activation energy for our alloy varies from one reactor to another. But the activation energy, intrinsic property of the hydride, must be independent of the reactor materials. The values of the heat capacity and the density for copper, aluminum, and steel in Table 1 are used to find the better fit for the values of the apparent activation energy. We tested several functions giving the evolution of Eap as a function of ðrCp Þ. Fig. 11 shows the Eap evolution as a function of the thermal capacity (product density and specific heat) of the material used to manufacture the reactor. A better fit for this evaluation is given by: Eap ¼ Ea þ a exp b rCp
Substituting Eqs. (3) and (4) in Eq. (2) gives
8:7 23537:5 Rg T
(8) 1
ln PPeq dF ¼ KðN 1Þ ð1 FÞ P dt
(5)
Peq
To determine the expression of the rate constant K as a function of temperature and to estimate the value of activation energy, we plotted the reaction velocity as a function of g1 ðPÞ g2 ðFÞ for different values of temperature and pressure. By applying this on the measurement obtained by three metal-hydrogen reactors (steel, copper and aluminum) of same size and containing the same mass of LaNi5 alloys, we obtain a linear evolution (Fig. 9(a) and (b)) and K values are determined from the slope of this lines. K depends on the temperature and obeys to the Arrhenius law [49e51] according to the following equation: Eap KðTÞ ¼ K0 exp Rg T
where Ea ¼ 19.079 kJ mol is the activation energy of the LaNi5 alloy, ðrCp Þ is the thermal capacity of reactor metal's, a and b are the two constants determined from fitting experimental data (Fig. 11): a ¼ 224:78 and b ¼ 8:7 107 . By incorporating Eq. (6) into Eq. (4), the final equation becomes: P ln Peq Eap dF ¼ K0 exp ðN 1Þ ð1 FÞ P dt Rg T Peq (9) P ln Ea þ a exp b rCp Peq ðN 1Þ ð1 FÞ ¼ K0 exp P Rg T Peq In this equation, the two terms K0 and Eap represent the
(6)
The logarithm of the rate constant, ln(K), versus the inverse temperature, (1/T) is given by: lnðKÞ ¼ lnðK0 Þ
Eap Rg T
(7)
where K0 is a temperature-independent coefficient, Eap is the apparent activation energy, Rg is the gas constant (8.314 J mol1K1) and T is the temperature. In order to plot this evolution, several studies found in the literatures [45e47] consider only three temperatures. In our study, we have then considered three points corresponding to three temperatures. A plot of ln(K) vs
1 Rg T
(Fig. 10(a) and (b)) is
straight line and provides the value of K0 (intercept value) and E
Rapg (slope value). Based on experimental data related to the three considered reactors (copper, aluminum and steel). The variation of ln(K) as a function of the inverse of temperature are reported in Table 2.
Fig. 11 e Evolution of the activation energy as a function of (rCp)eff.
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(a)
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three reactors of the LaNi5 alloy and for temperature ranging from of 293e313 K, depend on the used materials for manufacturing the reactor. This result can be attributed to the thermal inertia of the reactor.
Conclusion
(b)
During this work, we have studied the effect of the used materials to manufacture the metal hydrogen reactor; on the H2 absorption kinetics' by the alloy, LaNi5 has been studied. Different experimental conditions have been investigated. The obtained results showed a strong dependence of the pressure and the temperature based on the experimental data and fastest kinetics are obtained. The studied analytic expressions of the reaction kinetics' provide a satisfactory agreement with experimental data under different conditions. The apparent absorption energy of the hydride alloy of different reactors has been calculated, and it showed that this activation energy depends on the metal characteristic of the reactor. For the three reactors, the obtained absorption energy activation of the LaNi5 alloy is equal to 19.079 kJ mol1.
references
Fig. 12 e (a): The calculated and measured hydrogen-tometal-atomic ratio evolution under different experimental conditions for LaNi5 alloy in the absorption case for the reactor manufactured in aluminum. (b): The calculated and measured hydrogen-to-metal-atomic ratio evolution under different experimental conditions for LaNi5 alloy in the absorption case for the reactor manufactured in Copper.
Arrhenius factor and the apparent activation energy due to the hydride (LaNi5) and the nature of the metal constituting the reactor. Our model is based on these two terms to compare the numerical and the experimental results. The amount of the stored hydrogen during the absorption process is measured experimentally and compared with the amount of the hydrogen obtained from simulation study for the constant pressure of hydrogen (P ¼ 10 bar) and at different temperatures range of 293e313 K (Fig. 12(a) and (b)). These curves show that the maximum error (gap) between the experimental data and the theoretical results is less than 4%. So a satisfactory agreement is observed. By using the expressions given in Table 2, the evolutions of the reaction rate constants K, of the
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[13] Xie JY, Chen NX. Site preference and structural transition of R(Ni, M)5 (R ¼ La, Nd, Gd), (M ¼ Al, Fe, Co, Cu, Mn). J Alloys Compd 2004;1:381. [14] Stucki F, Schlapbach L. Magnetic properties of LaNi5 and FeTi, Mg2Ni and their hydrides. J Less Common Met 1980;74:143e51. [15] Souahlia A, Dhaou H, Mellouli S, Askri F, Jemni A, Ben Nasrallah S. Experimental study of metal hydride-based hydrogen storage tank at constant supply pressure. Int J Hydrogen Energy 2014;39:7365e72. [16] Kaplan Y, Ilbas M, Mat MD, Demiralp M, Veziroglu TN. Investigation of thermal aspects of hydrogen storage in a LaNi5-H2 reactor. Int J Energy Res 2006;30:447e58. [17] Mat MD, Kaplan Y, Aldas K. Investigation of threedimensional heat and mass transfer in a metal hydride reactor. Int J Energy Res 2002;26:973e86. [18] Inomata A, Aoki H, Miura T. Measurement and modelling of hydriding and dehydriding kinetics. J Less Common Met 1998;278:103e9. [19] Huot J, Liang G, Boily S, Neste AV, Schultz R. Structure study and hydrogen sorption kinetics of ball-milled magnesium hydride. J Alloys Compd 1999;293:495e500. [20] Miyamoto M, Yamaji K, Nakata Y. Reaction kinetics of LaNi5. J Less Common Met 1983;89:111e6. [21] Suda S, Kobayashi N, Yoshida K. Reaction kinetics of metal hydrides and their mixtures. J Less Common Met 1980;73:119e26. [22] Pourpoint TL, Velagapudi V, Mudawar I, Zheng Y, Fisher TS. Active cooling of a metal hydride system for hydrogen storage. Int J Heat Mass Transfer 2010;53:1326e32. [23] El-Osairy MA, El-Osairy IA, Metwally AM, Keshik MM. On the optimization of convective hydrogen storage bed model using LaNi5H6 and FeTiH1.6. Int J Hydrogen Energy 1992;17:961e4. [24] El-Osairy MA, El-Osery IA, Metwally AM, Hassan MA. Temperature and composition distribution of FeTiH1.6 and Mg2NiH4 for two-dimensional hydrogen energy conduction bed model. J Alloys Compd 1993;202:125e8. [25] Cheng HH, Chen DM, Yang K. New type property measuring apparatus and applications for hydrogen storage material. Rare Met Mater Eng 2007;36:78e81. [26] Aldas K, Mat D, Kaplan Y. A three-dimensional mathematical model for absorption in a metal hydride bed. Int J Hydrogen Energy 2002;27:1063e9. [27] Jemni A, Ben Nasrallah S, Lamloumi J. Experimental and theoretical study of metal-hydrogen reactor. Int J Hydrogen Energy 1999;24:631e44. [28] Zhang X, Li Q, Chou K-C. Kinetics of hydrogen absorption in the solid solution region for Laves phase Ho1xMmxCo2 (x ¼ 0, 0.2 and 0.4) alloys. Intermetallic 2008;16:1258. [29] An XH, Pan YB, Luo Q, Zhang X, Zhang JY, Li Q. Application of a new kinetic model for the hydriding kinetics of LaNi5xAlx (0 x 1.0) alloys. J Alloys Compd 2010;63:506. [30] Yang T, Zhai T, Yuan Z, Bu W, Xu S, Zhang YH. Hydrogen storage properties of LaMgNi3.6M0.4 (M ¼ Ni, Co, Mn, Cu, Al) alloys. J Alloys Compd 2014;617:29e33. [31] Souahlia A, Dhaou H, Askri F, Mellouli M, Jemni A, Ben Nasrallah S. Experimental and comparative study of metal hydride hydrogen tanks. Int J Hydrogen Energy 2011;36:12918e22. [32] Dhaou H, Askri F, Ben Salah M, Jemni A, Ben Nasrallah S, Lamloumi J. Measurement and modelling of kinetics of hydrogen sorption by LaNi5 and two related pseudo binary compounds. Int J Hydrogen Energy 2007;32:576e87. [33] Johnson WA, Mehl RF. Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Eng 1939;135:416. [34] Singh A, Maiya MP, Murthy SS. Effects of heat exchanger design on the performance of a solid state hydrogen storage device. Int J Hydrogen Energy 2015;40:9733e46.
[35] Mellouli S, Askri F, Dhaoua H, Jemni A, Ben Nasrallah S. A novel design of a heat exchanger for a metal-hydrogen reactor. Int J Hydrogen Energy 2007;32:3504. [36] Souahlia A, Dhaou H, Askri F, Mellouli S, Jemni A, Ben Nasrallah S. Experimental study and characterization of metal hydride containers. Int J Hydrogen Energy 2011;36:4952e7. [37] Garrison SL, Hardy BJ, Gorbounov MB, Tamburello DA, Corgnale C, Van Hassel BA. Optimization of internal heat exchangers for hydrogen storage tanks utilizing metal hydrides. Int J Hydrogen Energy 2012;37:2850e61. [38] Demircan A, Demiralp M, Kaplan Y, Mat MD, Veziroglu TN. Experimental and theoretical analysis of hydrogen absorption in e reactors. Int J Hydrogen Energy 2005;30:1437e46. [39] Patil SD, Ram Gopal M. Analysis of a metal hydride reactor for hydrogen storage. Int J Hydrogen Energy 2013;38:942e51. [40] Shafiee S, McCay MH. Different reactor and heat exchanger configurations for metal hydride hydrogen storage systems e a review. Int J Hydrogen Energy 2016;41:462e9470. [41] Jemni A, Nasrallah SB. Study of two-dimensional heat and mass transfer during absorption in a metal-hydrogen reactor. Int J Hydrogen Energy 1995;20:43e52. [42] Briki C, Belkhiria S, Dhaou MH, de Rango P, Jemni A. Experimental study of the influences substitution from Ni by Co, Al and Mn on the hydrogen storage properties of LaNi3.6Mn0.3Al0.4Co0.7 alloy. Int J Hydrogen Energy 2017;42:10081e8. [43] Askri F, Jemni A, Ben Nasrallah S. Dynamic behavior of metal-hydrogen reactor during hydriding process. Int J Hydrogen Energy 2004;29:635e47. [44] Askri F, Jemni A, Ben Nasrallah S. Prediction of transient heat and mass transfer in a closed metal-hydrogen reactor. Int J Hydrogen Energy 2004;29:195e208. [45] Askri F, Ben Salah M, Jemni A, Ben Nasrallah S. Optimization of hydrogen storage in metal-hydride tanks. Int J Hydrogen Energy 2009;34:897e905. [46] Dhaou H, Askri F, Ben Salah M, Jemni A, Ben Nasrallah S, Lamloumi J. Measurement and modelling of kinetics of hydrogen sorption by LaNi5 and two related pseudo binary compounds. Int J Hydrogen Energy 2007;32:576e87. [47] Mellouli S, Askri F, Dhaou H, Jemni A, Ben Nasrallah S. A study of the thermal behavior of a deformable metal-hydride bed. Int J Hydrogen Energy 2015;41:5e6. [48] Principi G, Agresti F, Maddalena A, Lo Russo S. The problem of solid-state hydrogen storage. J Energy 2009;34:2087e91. [49] Kaabi A, Khaldi C, Lamloumi J. Thermodynamic and kinetic parameters and high rate discharge-ability of the AB5-type metal hydride anode. Int J Hydrogen Energy 2016;41:9914e23. [50] Sharma VK, Kumar EA. Measurement and analysis of reaction kinetics of La-based hydride pairs suitable for metal hydride-based cooling systems. Int J Hydrogen Energy 2014;39:19156e68. [51] Mellouli S, Abhilash E, Askri F, Ben Nasrallah S. Integration of thermal energy storage unit in a metal hydride hydrogen storage tank. Appl Therm Eng 2016;102:1185e96. [52] Dunikov D, Borzenko V, Blinov D, Kazakov A, Lin CY, Wu SY, et al. Biohydrogen purification using metal hydride technologies. Int J Hydrogen Energy 2016;41:21787e94. [53] Meng X, Wu Z, Bao Z, Yang F, Zhang Z. Performance simulation and experimental confirmation of a mini-channel metal hydrides reactor. Int J Hydrogen Energy 2013;38:15242e53. [54] Gkanas EI, Grant DM, Khzouz M, Stuart AD, Manickam K, Walker GS. Efficient hydrogen storage in up-scale metal hydride tanks as possible metal hydride compression agents equipped with aluminum extended surfaces. Int J Hydrogen Energy 2016;41:10795e810.
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[55] Chibani A, Bougriou C. Effect of the tank geometry on the storage and destocking of hydrogen on metal hydride (LaNi5H2). Int J Hydrogen Energy 2017;42:23035e44. [56] Rusman NAA, Dahari M. A review on the current progress of metal hydrides material for solid-state hydrogen storage applications. Int J Hydrogen Energy 2016;41:12108e26. [57] Boukhari A, Bessaı¨h R. Numerical heat and mass transfer investigation of hydrogen absorption in an annulus-disc reactor. Int J Hydrogen Energy 2015;40:3708e13717.
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[58] Freni A, Cipitı` F, Cacciola G. Finite element-based simulation of a metal hydride-based hydrogen storage tank. Int J Hydrogen Energy 2009;34:8574e82. [59] Bu¨rger I, Komogowski, Linder M. Advanced reactor concept for complex hydrides: hydrogen absorption from room temperature. Int J Hydrogen Energy 2014;39:7030e41. [60] Weckerle C, Bu¨rger I, Linder M. Novel reactor design for metal hydride cooling systems. Int J Hydrogen Energy 2017;42:8063e74.
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Available online at www.sciencedirect.com
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Dynamic study of a new design of a tanks based on metallic hydrides Chaker Briki a,*, Sihem Belkhiria a, Mohamed Houcine Dhaou b, Faouzi Askri c, Abdelmajid Jemni a a
Laboratory of Studies of Thermal Systems and Energy, Ibn Eljazzar Road, National Engineering School of Monastir, University of Monastir, 5019 Monastir, Tunisia b Department of Physics, College of Science, Qassim University, Saudi Arabia c Engineering School University of Abha, Saudi Arabia
article info
abstract
Article history:
It is known that the hydrogen has a very high mass energy density, in fact, that it is a
Received 12 August 2017
lightest gas; therefore, its storage is a great problem. The aim of the hydrogen storage
Received in revised form
technologies is thus to reduce the volume that hydrogen occupies in its thermodynami-
19 October 2017
cally stable state under conditions close to ambient salt. Recent work on hydrogen storage
Accepted 13 November 2017
is mainly based on the use of metal hydrides. These metal hydrides have a high capacity
Available online xxx
for the hydrogen storage in the operating conditions. The effecting parameters on the performance of such a metal-hydrogen reactor are its design and configuration. In this
Keywords:
case, there are a number of problems that need to be considered in designing a reactor.
Hydrogen storage
Among these parameters are the reactor configuration, the thermal and the mechanical
Solid state reactions
strength, the kinetics of hydrogen storage and the security. Our study is concentrated on
Kinetics
the problem of the thermal and the mechanical strength while focusing on the nature of
Activation energy
the metal makes the reactor. In this work, the experimental studies of the hydrogen ab-
Metal-hydride
sorption phenomenon in different reactors, based on metal hydrides, were evaluated. The
LaNi5
characteristics of the reaction kinetics in three different reactors using the same measurement conditions were compared. A numerical model describing the reaction kinetic of the H2 absorption by LaNi5 alloy validates the results were obtained. Of these results, it is found that the rate constant varies from one reactor to another. Moreover, the activation energy of the absorption kinetics were identified. Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.
Introduction Great number of research study have been launched to use hydrogen as an energy carrier for many exploit renewable energy resources and to develop fuel cell technology. That also preserve environment by reducing discharges of pollutants and the
emission of greenhouse gases caused by the strong growth in demand for energy. If hydrogen were prevailed in the long term as an energy, the researchers and engineers challenge is to know how to produce, distribute, store and use it [1e5]. Hydrogen has several applications in energy area. It has undergone significant interest in order to meet the demand in terms of industrial development [6].
* Corresponding author. E-mail address: [email protected] (C. Briki). https://doi.org/10.1016/j.ijhydene.2017.11.085 0360-3199/Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC. Please cite this article in press as: Briki C, et al., Dynamic study of a new design of a tanks based on metallic hydrides, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.11.085
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Nomenclature Cp Ea Eap l P T t R r
Specific heat, J kg1 K1 Activation energy, J mol1 Apparent absorption energy, J mol1 Thermal conductivity, W m1 K1 Pressure, bar Temperature, K time, s Gas constant, J mol1 K1 Density, kg m3
Subscripts [H/M] Hydrogen-to-metal-atomic ratio G Gas E Equilibrium Ss Saturated
We know that the hydrogen has a low energy capacity per volume, but it offers a good energy capacity per mass compared to others fossil fuels. The only way to make the hydrogen more efficient is to store it in high-density metals, which have small volumes and low masses. However, it is necessary to develop new designs and geometries of hydrogen storage reactors based on metal hydride, which exhibit high volumetric capacity and fast sorption kinetics. Many physical, chemical and dynamic challenge need to be considered for hydrogen storage systems. In particular, the properties of hydrogen gas and heat transfer of the hydride bed are the major problems for a high-dynamic tank operation. Hydrogen must be stored in a small, lightweight system due to the size and weight constraints in vehicles. This is particularly challenging because this gas has the lowest energy density of common fuels. Therefore, many researches are focusing on
the performance of storage system such as; high thermal conductivity, favorable equilibrium pressure, high hydrogen absorption capacity, fast reaction kinetics and simple activation process [7,8]. It has been recognized for a long time that the hydrogen storage in the form of hydride has the advantage of safety and easy recovery than the other types of storage. Much larger quantities of hydrogen can be stored per unit volume than in its liquid and in its gas form. Each one of these techniques has its own advantages and disadvantages [9]. Therefore, metal and complex hydrides have attracted attention as hydrogen storage materials. Among these metals, the LaNi5 intermetallic alloys are commonly chosen as the hydrogen storage medium because of their attractive characteristic features. Such as their high storage capacity, their favorable operating temperatures and pressures, their low hysteresis, their easy activation, their low density, their high volumetric density, their highest safety level compared to other metals and fast reaction rates [10,11]. These metals can be used in reversible hydrogen storage. The kinetic reaction of hydrogen sorption by the metal depends on the heat and the mass transfer within the reactor. This explicates that the hydride reactor designs are extremely important for the heat removing from reactor [12,13]. The effects of operating conditions for performance of metal hydrogen storage tanks are complicated and they need detailed investigations for further optimization [14,15]. The geometry and the design of the metal-hydrogen reactors, which have evolved over years of study, are important factors in the heat and the mass transfer in the hydride bed. Several numerical and experimental research works have been devoted to optimize the design parameters of metalhydrogen tanks [16e41]. In parallel, the rate at which hydrogen can be absorbed and desorbed by a particular metal or alloy is an important factor for the hydrogen storage. This reaction rate depends on
Fig. 1 e (a, b): Photograph of the reactor Aluminum and Copper. Please cite this article in press as: Briki C, et al., Dynamic study of a new design of a tanks based on metallic hydrides, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.11.085
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Fig. 2 e Schematic view of experimental installation. several factors. Among them, the activation energy who is a parameter that characterizes the kinetics reaction of hydrogen absorption by metal. It is defined as being the minimum energy required to start a chemical reaction. In fact, many studies have been done to compare and to model the mechanisms of the hydrogen absorption kinetics [20e35]. Miyamoto et al. [20] investigated the absorption kinetic of LaNi5 and LaNi4.9Al0.1 alloys. They proposed an analytical expression of kinetic rate and then found that the activation energy value for absorption Ea is equal to 29.288 kJ/mol-H2. Suda et al. [21] studied experimentally the reaction rate in the processes hydriding and dehydriding for LaNi5, MmNi5, TiMn10.5 and Ti0.8Zr0.2Cr0.8Mn1.2 alloys. The experimental results showed that the annealed MmNi4.5Al0.5 hydride has smaller rate constants than those of the other hydrides under the same experimental conditions and that each hydriding alloy has temperature bands where the hydriding and dehydriding reactions proceed at much higher speeds. The value of activation energy for LaNi5 is 20.7 kJ mol1 [22]. Osairy et al. [23,24] studied the LaNi5eH6 compound and they found that the reaction rate defined as compound of two functions temperature and pressure. Cheng et al. [25] show that the reaction kinetics of the LaNi5 compound depends on the number of cycles absorption of hydrogen and the rate constant K is 0.0161, 0.0191 and 0.0225 for the value of the cycle number 2, 50 and 150, respectively, and takes as value of the activation energy Ea ¼ 21.179 kJ mol1. The numerical simulation of the heat and the mass behavior in a metal-hydrogen reactor requires the knowledge
of the reaction kinetics. That is why many works, which are related to the reaction kinetics of metal hydrides and essentially the LaNi5 alloy, have been done [20e35]. Several models of the reaction kinetics are encountered in the literature. All these models are taking into account the heat and the mass exchange in the hydride bed. From the previous literature review on the hydrogen absorption kinetics by LaNi5 alloy, we note that Ea varies from 20 to 30 kJ mol1. We know that the Ea is an intrinsic property of the metal used; therefore, it must be constant. Improved of hydrogen storing devices can be obtained through design parameters like heat exchangers, filters, geometrical distribution of the alloy inside the container and the nature of the reactor. Since that, the reactor geometry does not have any effect on hydride formation process but it influences the reaction speed [36]. Likewise, reactor configuration and heat exchanger design will elevate the storage capacity and hydrogen storage density and decrease refueling time [37e41,50e60]. The aim of this study is to test metalhydrogen tanks containing LaNi5 powder. Three metalhydrogen reactors are considered: a copper reactor, an aluminum reactor and a steel reactor. In fact, the used materials for manufacturing the reactor were defined as a remarkable index to the kinetics' effect. The experimental results allowed as proposing a numeric model describing the kinetics of hydrogen absorption by LaNi5 alloy and simulating the behavior of the metal-hydrogen tank. This model takes into account the heat and the mass exchange in hydride bed and in the reactor materials. Once we found the value of the
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Fig. 3 e Simulation and experimental evolution of equilibrium pressure as a function of [H/M] and temperature for the alloy LaN5. activation energy for the LaNi5 alloy, the experimental results obtained were measured and are compared with those calculated.
Design of the reactor A schema of the copper and aluminum reactors design's is shown in Fig. 1(a) and (b). They are formed of a cylindrical body (inner diameter: 30 mm; outer diameter: 38 mm; inner height: 40 mm; outer height: 50 mm) and a lid (diameter: 15 mm, thickness: 1 mm). The reactors are filled with 30 g of LaNi5 alloy to about half their volume in order to both reduce internal mechanical tensions due to the material dilatation and to leave some extra free volume for the non-absorbable gaseous contaminants. The lid is equipped with a filter in
Fig. 5 e Bed temperature vs. time during absorption in two types of reactor. fried stainless steel (diameter of the pre equal to 1.4 mm). A joint is placed between the lid and the body to ensure gas tightness. Two tubes are connected on the lid by a tight passage. The first one allows the input-output of hydrogen and the setting vacuum. The second one allows a pressure pick-up relative to measure the gas pressure in the reactor.
Experimental apparatus Fig. 2 shows a schematic diagram of the used experimental device. The Hydrogenation cycles were carried out with hydrogen gas of 99.999% purity. The reactor is fed with hydrogen, from a buffer reservoir, through steel pipe of 6 mm diameter. The connection between the reactor and the reservoir is ensured by using Swagelok valve. The reservoir is loaded with hydrogen at a desired pressure. The whole device is supplied with hydrogen from pressurized cylinder (200 bars). A thermostat bath is used for the cooling or heating fluid flows, in the sealed cylindrical jacket over the reactor, at flow rates ranging from 1 to 13 g/l. A vacuum pump is used to evacuate the gas from the whole installation. The pressure is measured by a pressure sensor (type PH-21LC, 0e100 bars, sensitivity 0.01 bar) which is connected to a data acquisition system (PC73A) installed in the microcomputer.
Measurement procedure
Fig. 4 e Variation in mass hydrogen absorbed as a function of time for three type of reactors.
The volumetric method of measuring the mass of hydrogen absorbed by a metal is based on the use of pressure, volume and temperature data to calculate the amount of hydrogen absorbed or desorbed by the metal [42]. The experimental procedure for the absorption begins by starting the vacuum pump to maintain a low pressure in the reactor (0.01 bar) at high temperature (323 K) for a period of time to ensure in that the sample is emptied of hydrogen (or other gases). The buffer
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(a)
(b)
Fig. 6 e (a): Effect of the cooling water temperature on the kinetics of absorption in reactor Copper. (b): Effect of the cooling water temperature on the kinetics of absorption in reactor Aluminum.
reservoir is loaded at the desired pressure. Then the valve between reservoir and reactors opened and hydrogen is allowed to flow into the reactor. The alloy LaNi5 absorbs hydrogen by releasing heat. This heat is evacuated by cooling fluid circulation within the cylindrical jacket over the reactor. The absorption continues until it reaches steady state, there the acquisition is stopped. The experimental procedure for desorption starts at the end point of an absorption test. The reservoir, emptied via the vacuum pump, is connected to the reactor and then starting the acquisition and the hot water flow to the desired temperature until reaching an equilibrium state. At the beginning of each experiment, the efforts are made to have the same initial conditions of the reactor. Before starting the study of the sorption phenomena, the activation of the alloy is executed and the average particle size of the alloy was approximately 50 mm. It consists of the repetition of an absorption/desorption cycles (30 cycles of absorption/
5
(a)
(b)
Fig. 7 e (a): Effect of the initial hydrogen pressure on the absorption kinetic in reactor Copper. (b): Effect of the initial hydrogen pressure on the absorption kinetic in reactor Aluminum.
desorption) until the maximum hydrogen storage capacity (1.4 wt%) of the metal is reached.
Results and discussion Equilibrium pressure determination The equilibrium pressure (Peq) is one of the most important parameters in the reaction kinetics of hydrogen by a metal. We therefore determined, for the simples studied, its evolu H and temperature. The tion as a function of concentration M experimental procedure for determining the equilibrium pressure is detailing in Refs. [43e46]. The authors proposed, to
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Fig. 8 e Bed temperature vs. time for various applied pressure. simulate the evolution of the equilibrium pressure, the following expression: H H DH 1 1 ;T ¼ f exp (1) M M Rg T T0 H : is the reaction heat function (J), Rg : is the gas where M H constant (J/K), T0 : is the reference temperature, and f M Peq
represents the evolution of the equilibrium pressure (bar) H versus M at the reference temperature T0 . To implement a realistic of isotherms PCT correlation a numerical model which can reproduce the experimental measured values very precisely and can be used for a reliable interpolation has to be found. There are many models to describe PCT correlations available in the literature. For example, the following models were found: Dhaou et al. (model) [47]. An example of equilibrium pressure curve (calculated and measured), relating to LaNi5 alloy, is shown in Fig. 3. These profiles show the dependence of Peq on the H temperature and M . In addition, we note that the used analytic expression of Peq is agree with the measurement.
Fig. 9 e (a): Hydriding rates versus (N ¡ 1)[Ln(P/Peq)/(P/ Peq)](1 ¡- F) in the case of LaNi5 alloy for the reactor manufactured in Copper. (b): Hydriding rates versus (N ¡ 1) [Ln(P/Peq)/(P/Peq)](1 ¡ F) in the case of LaNi5 alloy for the reactor Manufactured in Aluminum.
Kinetic reaction A set of measurement was carried out on the three types of reactors Fig. 1(a) and (b) made in copper, steel and aluminum. The obtained results are shown in Fig. 4. These figures show the evolution of the absorption H2 mass by the LaNi5 alloy at the same operating conditions (temperature, pressure). Although it is the same metal used and submitted to the same operating conditions, there is a difference between the kinetics of hydrogen absorption by LaNi5. The mass of hydrogen absorption reaches a saturation value of 5.8, 5.4 and 4.7 at T ¼ 293 K and P ¼ 8 bar. It can be seen that the amount hydrogen absorption content raises remarkably with time at the nature of the metal makes the reactor. Therefore we
observe clearly that the evidence the effect of reactors material on the dynamic of absorption. Fig. 5 shows the time evolution of the temperature in the center of the hydride bed for the both types of reactors. Our results show that the temperature increases and reaches rapidly a maximum. This increase of temperature is explained by the exothermic reaction of the intermetallic and due to the low thermal conductivity of the hydride. After this rapid increase, the temperature decreases gradually down to the cooling temperature and the system returns to its equilibrium state. Fig. 6(a) and (b) show the evolution of the absorbed hydrogen mass when the copper reactor and the aluminum
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(a)
between metal hydride bed within the reactor and cooling fluid. Lowering the cooling temperature helps to accelerate the kinetics of the exothermic absorption reaction. Similarly, the effect of the initial pressure on the time evolution of the amount of hydrogen absorbed by the hydride were also studied. For that, we vary absorption pressure and by setting the coolant temperature at 283 K and fluid flow rate at 13 g/l. Fig. 7(a) and (b) show the effect of the hydrogen applied pressure on the absorption phenomenon. Four values of pressure (4, 6, 8 and 10 bars) are considered; these values are related to the pressure applied to the input of the tank. These figures shows that the total mass absorbed increases with the operating pressure. In this case, the initial pressure of hydrogen applied is responsible for raising the driving force for mass transfer, speeds up the absorption reaction and stores more hydrogen in the sample. In addition, the characteristic reaction time, in order that the sample reach 90% of maximum hydrogen capacity, depends on used materials to manufacturing the reactor. This reaction time is equal to 302 s, 133 s and 74 s for respectively steel, copper and aluminum. Indeed, the used material for manufacturing the reactor effect the kinetic of the absorption reaction by means of the conduction between the cooling fluid and hybrid bed and by the inertia thermal of reactor. Fig. 8 shows the temperature evolution in the hydride bed within the reactor made in copper, for different applied pressures of hydrogen. The figures show a sudden rise of temperatures in the metal bed at the beginning of the reaction, due to the exothermic hydrogen-metal reaction and under the effect of the applied pressure, and then they decrease gradually with the reaction kinetics decay. However, the time to return to a thermal equilibrium is different according to the applied pressure. This is due to the high gradient of temperature for each pressure and to the low thermal conductivity of the hydride bed.
(b)
Modeling of absorption hydrogen by metal powder The steps of this numerical model are to represent the problem and define appropriate assumptions to simplify the equations and them to be solved analytically. The assumptions listed below are often considered in the modeling of the metal-hydrogen systems. The kinetic reaction of solid gas system can be expressed as [47,48]:
Fig. 10 e (a): Arrhenius rate constant for hydriding reaction for the reactor manufactured in Copper. (b): Arrhenius rate constant for hydriding reaction for the reactor manufactured in Aluminum.
dF ¼ Kg1 ðPÞg2 ðFÞ dt
reactor are cooling at different temperatures. The fluid flow rate is constant and equal to 13 g/l. We note that the low cooling fluid temperature induce an improvement of LaNi5 absorption kinetic. Indeed, it increases heat exchange
(2)
where, F is the fraction solid which reacts, t is time, g1 ðPÞ and g2 ðFÞ are two functions that express the effects of applied pressure and the fraction F of the reaction rate and K is a rate constant.
Table 1 e Thermo-physical proprieties of materials. 3
Density, r (kg/m ) Specific heat, CP (J/kg K) Thermal conductivity l (W m1 K1)
LaNi5
Hydrogen
Aluminum
Copper
Steel
8200 419 3.18
0.0838 14890 0.167
2690 921 205
8700 385 401
7850 420 43
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The comparison of different models proposed in the literature with experimental results can be explained by the fact that some models are only applicable where the applied pressure is constant. On the other hand, the models generally do not take into account the initial conditions of temperature and pressure. Dhaou et al. [47] provides an extended model that considers the initial conditions of temperature and pressure. In fact, the analysis of applied pressure effect and the fraction F on the absorption reaction rate of LaNi5 alloys allowed them to propose the following expression of g1 ðPÞ and g2 ðFÞ function: ln PPeq (3) g1 ðPÞ ¼ ðN 1Þ P Peq
g2 ðFÞ ¼ ð1 FÞ where F ¼
½MH , ½MH ss
(4) H M
is the hydrogen-to-metal-atomic ratio, P ss
is the instantaneous hydrogen pressure at a time t, Peq is the equilibrium plateau pressure and N is the initial applied N ¼ PPm0 . pressure P0 to the mid-plateau pressure Pm e ratio e
Table 2 e Reaction rate constants k of hydrogen absorption. Reactor Steel Reactor Copper Reactor Aluminium lnðkÞ
6:4 26386:9 Rg T
8 21017:4 Rg T
The obtained value of the apparent activation energy for the absorption process (Eap) of LaNi5 alloy was varied from 21 to 26 kJ mol1. In observing that the apparent activation energy for our alloy varies from one reactor to another. But the activation energy, intrinsic property of the hydride, must be independent of the reactor materials. The values of the heat capacity and the density for copper, aluminum, and steel in Table 1 are used to find the better fit for the values of the apparent activation energy. We tested several functions giving the evolution of Eap as a function of ðrCp Þ. Fig. 11 shows the Eap evolution as a function of the thermal capacity (product density and specific heat) of the material used to manufacture the reactor. A better fit for this evaluation is given by: Eap ¼ Ea þ a exp b rCp
Substituting Eqs. (3) and (4) in Eq. (2) gives
8:7 23537:5 Rg T
(8) 1
ln PPeq dF ¼ KðN 1Þ ð1 FÞ P dt
(5)
Peq
To determine the expression of the rate constant K as a function of temperature and to estimate the value of activation energy, we plotted the reaction velocity as a function of g1 ðPÞ g2 ðFÞ for different values of temperature and pressure. By applying this on the measurement obtained by three metal-hydrogen reactors (steel, copper and aluminum) of same size and containing the same mass of LaNi5 alloys, we obtain a linear evolution (Fig. 9(a) and (b)) and K values are determined from the slope of this lines. K depends on the temperature and obeys to the Arrhenius law [49e51] according to the following equation: Eap KðTÞ ¼ K0 exp Rg T
where Ea ¼ 19.079 kJ mol is the activation energy of the LaNi5 alloy, ðrCp Þ is the thermal capacity of reactor metal's, a and b are the two constants determined from fitting experimental data (Fig. 11): a ¼ 224:78 and b ¼ 8:7 107 . By incorporating Eq. (6) into Eq. (4), the final equation becomes: P ln Peq Eap dF ¼ K0 exp ðN 1Þ ð1 FÞ P dt Rg T Peq (9) P ln Ea þ a exp b rCp Peq ðN 1Þ ð1 FÞ ¼ K0 exp P Rg T Peq In this equation, the two terms K0 and Eap represent the
(6)
The logarithm of the rate constant, ln(K), versus the inverse temperature, (1/T) is given by: lnðKÞ ¼ lnðK0 Þ
Eap Rg T
(7)
where K0 is a temperature-independent coefficient, Eap is the apparent activation energy, Rg is the gas constant (8.314 J mol1K1) and T is the temperature. In order to plot this evolution, several studies found in the literatures [45e47] consider only three temperatures. In our study, we have then considered three points corresponding to three temperatures. A plot of ln(K) vs
1 Rg T
(Fig. 10(a) and (b)) is
straight line and provides the value of K0 (intercept value) and E
Rapg (slope value). Based on experimental data related to the three considered reactors (copper, aluminum and steel). The variation of ln(K) as a function of the inverse of temperature are reported in Table 2.
Fig. 11 e Evolution of the activation energy as a function of (rCp)eff.
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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 x x x ( 2 0 1 7 ) 1 e1 1
(a)
9
three reactors of the LaNi5 alloy and for temperature ranging from of 293e313 K, depend on the used materials for manufacturing the reactor. This result can be attributed to the thermal inertia of the reactor.
Conclusion
(b)
During this work, we have studied the effect of the used materials to manufacture the metal hydrogen reactor; on the H2 absorption kinetics' by the alloy, LaNi5 has been studied. Different experimental conditions have been investigated. The obtained results showed a strong dependence of the pressure and the temperature based on the experimental data and fastest kinetics are obtained. The studied analytic expressions of the reaction kinetics' provide a satisfactory agreement with experimental data under different conditions. The apparent absorption energy of the hydride alloy of different reactors has been calculated, and it showed that this activation energy depends on the metal characteristic of the reactor. For the three reactors, the obtained absorption energy activation of the LaNi5 alloy is equal to 19.079 kJ mol1.
references
Fig. 12 e (a): The calculated and measured hydrogen-tometal-atomic ratio evolution under different experimental conditions for LaNi5 alloy in the absorption case for the reactor manufactured in aluminum. (b): The calculated and measured hydrogen-to-metal-atomic ratio evolution under different experimental conditions for LaNi5 alloy in the absorption case for the reactor manufactured in Copper.
Arrhenius factor and the apparent activation energy due to the hydride (LaNi5) and the nature of the metal constituting the reactor. Our model is based on these two terms to compare the numerical and the experimental results. The amount of the stored hydrogen during the absorption process is measured experimentally and compared with the amount of the hydrogen obtained from simulation study for the constant pressure of hydrogen (P ¼ 10 bar) and at different temperatures range of 293e313 K (Fig. 12(a) and (b)). These curves show that the maximum error (gap) between the experimental data and the theoretical results is less than 4%. So a satisfactory agreement is observed. By using the expressions given in Table 2, the evolutions of the reaction rate constants K, of the
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