Measurement and modelling of kinetics of hydrogen sorption by LaNi5 and two related pseudobinary...

International Journal of Hydrogen Energy 32 (2007) 576–587www.elsevier.com/locate/ijhydene

Measurement and modelling of kinetics of hydrogen sorption byLaNi5 and two related pseudobinary compounds

H. Dhaoua,∗, F. Askria, M. Ben Salaha, A. Jemnia, S. Ben Nasrallaha, J. Lamloumib

aLaboratoire des Etudes des systèmes Thermiques et Energétiques, ENIM, Route de Kairouan, 5019 Monastir, TunisiabLaboratoire de Mécanique, Matériaux et procédés, ESSTT, 5 Avenue Taha Hussein, 1008 Tunis, Tunisia

Received 6 July 2006; accepted 6 July 2006Available online 14 September 2006

Abstract

The hydriding/dehydriding rates and the pressure–composition isotherms were measured for LaNi5, LaNi4.85Al0.15 and LaNi4.75Fe0.25under quasi-isothermal and variable pressure conditions. Isothermal conditions were obtained by reducing the thermal time constant of theexperimental device. Empirical rate equations to describe the sorption reaction kinetics were derived. These rates are expressed as a functionof temporal composition, saturated composition, temperature, applied pressure and essentially the initial operating conditions which were notconsidered in most of all the previous studies related to the reaction kinetics of metal hydrides. Besides, the rate equations presented in thiswork can be integrated easily in the numerical models that predict dynamic flow and heat and mass transfer within realistic metal–hydrogendevices. This paper also discusses the effects of Fe and Al as substituents for Ni on P–C isotherms and reaction rates of LaNi5 alloy.� 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

Keywords: Hydrogen; Alloys; Hydriding; Dehydriding; LaNi5; LaNi4.85Al0.15; LaNi4.75Fe0.25

1. Introduction

Metal hydrides are formed by reacting hydrogen with met-als or alloys. These metal hydrides find many applications inthe processing of hydrogen isotopes. Most metal hydrides canattain very high densities of hydrogen that can be as high asliquid hydrogen. This permits the storing of large amounts ofhydrogen in small volumes and the generation of high pres-sures when heated. This provides the opportunity of using heatto replace mechanical pumps and compressors. Also the reac-tion enthalpy of the hydriding/dehydriding process can be usedin thermal energy stores and thermodynamic machines.

The optimal design of these installations requires a correctprediction of the main operating properties of these metal hy-drides during the period of operation in real conditions. On theother hand, fast hydriding/dehydriding kinetics are necessaryfor some applications (full cell for example). For these reasonsa great deal of experimental and numerical research have been

∗ Corresponding author.E-mail address: dhaou_2000tn@yahoo.fr (H. Dhaou).

done to understand and to model the mechanisms controllingthe hydrogen absorption and desorption kinetics.

Hydrogen sorption by activated LaNi5 was first investigatedby Boser [1] and by Tanaka et al. [2] by means of pressure vari-ation in a constant volumetric apparatus. Boser performed hiswork in the 273–363 K temperature range, while Tanaka et al.limited their observations at the low temperature of 195 K, toslow down the reaction rate. From their experimental data theydeveloped different arguments to justify the choice of a possiblemechanism, controlling the hydride precipitation. Thus, Boserproposed the phase transformation as a regulating step, whilefor Tanaka et al., mass transfer limitations through crocks withinthe particles or in the channels were advanced, by eliminatingall the chemical processes which were considered to be too fast.

Reaction rates in the hydriding and the dehydriding pro-cesses for alloys such as LaNi5, MmNi5(Mm mischmetall),aluminum-substituted mischmetall nickels, TiMn10.5 andTi0.8Zr0.2Cr0.8 Mn1.2 were studied experimentally by Sudaet al. [3]. Their study shows that the annealed MmNi4.5Al0.5hydride has smaller rate constants than those of the other hy-drides under the same experimental conditions and that each

H. Dhaou et al. / International Journal of Hydrogen Energy 32 (2007) 576–587 577

Thermostatic bath

Thermostat

Sensor of pressure

Hydrogen

Support

D.C. Constant

Data acquisition

Atmosphere

Reservoir

VaccumPump

Reactor

Voltage source

Fig. 1. Synoptic scheme of the installation.

hydriding alloy has temperature bands where the hydriding anddehydriding reactions proceed at much higher speeds.

Suda and Komazaki [4] studied the kinetics of the hydridingand dehydriding reactions in aluminum- and iron-substitutedmischmetal–nickel hydrides and they correlated their experi-mental data as a function of pressure, temperature and hydridecomposition. The authors noted that the extent of the reactiondepended more strongly on the system pressure and tempera-ture than on the hydride composition.

The P–C isotherms and kinetic properties of LaNi5and MmNi4.5Al0.5 hydrides and deuterides (LaNi5D3,MmNi4.5Al0.5D3) were experimentally studied under isother-mal conditions ranging from 30 to 60 ◦C by Suda et al. [5].The authors mentioned that the equilibrium plateau pressuresof the deuterides are much higher than those of the hydridesfor both the hydriding and the dehydriding isotherms. How-ever, the hydrides had much faster hydriding reaction ratesthan those of the deuterides.

The kinetics of well-activated LaNi5 and LaNi4.9Al0.1 alloywere investigated by Miyamoto et al. [6] using a mass flowme-ter under constant pressure. The authors have proposed ananalytical expression of kinetic rate only for LaNi5 and theyconcluded that (i) the effect of hydrogen pressure on the hy-driding reaction rate can be expressed as ln(P/Pe), (ii) themobility can be represented by an Arrhenius law characteriz-ing thermally activated processes, (iii) the rate-controlling stepin the plateau range of LaNi5 is assumed to be the chemicalreaction at the interface between the unreacted core of the par-ticle and the hydride, (iv) LaNi4.9Al0.1 has a lower equilibriumpressure than LaNi5 alloy.

A kinetic study was conducted by Goudy et al. [7] in orderto ascertain whether heat transfer controls the rate of hydrogenevolution from LaNi5H6. Their experimental results show that

the rate of hydrogen evolution from a LaNi5–Al mixture sys-tematically increases when the amount of aluminum increases.Also, the reaction was found to be first order for each mixtureconsidered under isobaric conditions.

Gerard et al. [8] reported thermogravimetric studies in theLaNi5/H2 system. They concluded that in LaNi5/H2 systems,fast exothermic formation exhibits a complex relationship be-tween the reaction rate and the sample mass and they have ob-served a significant decrease in the reaction rate when the massis reduced in the range of 30 to 5 mg and as a result they con-firmed that heat flow cannot be the regulating step for theseconditions.

By applying a thermal ballast technique (manganese) andusing a highly heat conductive copper tube reactor with bal-lasts, Chung and Lee [9] achieved quasi-isothermal conditionsand an empirical rate equations for understanding the intrin-sic hydriding kinetics of FeTi was obtained. Their hydridingrate data, which were obtained by applying thermal ballast inthe copper reactor, show parabolic dependence on the appliedhydrogen pressure at low temperature and high hydrogen con-centration and linear dependence at high temperature and lowhydrogen concentration, indicating a transition of the kineticmechanism with temperature and hydrogen concentration. Be-sides, their results show that the heat effect is more pronouncedduring the dehydriding reaction than the hydriding reaction.

Lamloumi et al. [10] found, in their study of thermodynamic,structural and magnetic properties of LaNi5−xFex hydrides,that the substitution of iron for nickel in LaNi5 induces a slightincrease in the stability of the related hydrides and a reductionof the equilibrium plateau pressure and the amount of hydrogenabsorbed by the substituted compounds.

The hydriding kinetics of LaNi5 and LaNi4.7Al0.3 were in-vestigated at a constant pressure by Han and Lee [11]. In order

578 H. Dhaou et al. / International Journal of Hydrogen Energy 32 (2007) 576–587

Table 1The equilibrium pressure polynomial function coefficients for the three alloys in the absorption case

Alloys a0 a1 a2 a3 a4 a5 a6 a7

LaNi5 −0.34863 10.1059 −14.2442 10.3535 −4.20646 0.962371 −0.115468 0.00563776LaNi4.75Fe0.25 −0.0187494 4.10765 −4.30981 3.47074 −1.79548 0.531538 −0.0807431 0.00485911LaNi4.85Al0.15 −0.0195943 3.57703 −5.27742 4.22546 −1.9593 0.538844 −0.0824377 0.00543319

Table 2The equilibrium pressure polynomial function coefficients for the three alloys in the desorption case

Alloys a0 a1 a2 a3 a4 a5 a6 a7 a8 a9

LaNi5 0.420605 −4.11352 14.1799 −13.1085 4.55729 0.165833 −0.5923 0.178977 −0.023008 0.00112613LaNi4.75Fe0.25 −0.599396 6.02081 −6.04252 3.23537 −1.29716 0.604521 −0.255789 0.0665013 −0.00893603 0.000478102LaNi4.85Al0.15 −0.16516 3.53147 −10.4589 17.7889 −17.1395 9.76262 −3.35238 0.681405 −0.0754789 0.00351154

to avoid the effect of the heat evolved in the hydriding reac-tion and to obtain the intrinsic kinetic data, the authors havemixed the samples with a large amount of Al powder and theyhave used a Cu tube reactor which has a good thermal conduc-tivity. Their result shows that the dissociative chemisorptionof hydrogen molecules on the sample surface is the rate con-trolling step up to F = 0.6–0.8 and 0.4–0.5 (F is the reactedfraction) at the low applied hydrogen pressure for the hydrid-ing reaction of LaNi5 and LaNi4.7Al0.3, respectively. However,at high applied hydrogen pressures, the rate controlling step isthe nucleation and growth of the hydride phase at the site ofthe hydrogen chemisorption. At a later stage of the hydridingreaction, irrespective of the applied hydrogen pressure, hydro-gen diffusion through the hydride phase is the rate controllingstep. In both alloys, the rate controlling step has changed fromthe dissociative chemisorption of hydrogen at the surface orthe nucleation and growth to the hydrogen diffusion throughthe hydride phase. The transition of the rate controlling steptakes place at a much earlier stage in the hydriding reaction ofLaNi4.7Al0.3 than LaNi5. The authors explain this result by theslower diffusion rate of hydrogen atoms through the hydridephase in LaNi4.7 Al0.3 than in LaNi5 particles.

Dantzer and Orgaz [12] have presented a simple kineticmodel in a case of hydrating assuming a non-isothermal regime,for two types of experiments. One is described as an opensystem where constant pressure is imposed (thermogravimet-ric measurements) and the second is realized in a closed sys-tem where a small concentration step is produced (volumetricdevice). The authors have shown that the kinetic experimentsare influenced by a large contribution due to heat transfer andthat if the thermal time constant of the experimental device isreduced, quasi-isothermal conditions can be realized.

Wang and Suda [13] proposed two technical approaches toalleviate the thermal effects on the intrinsic kinetic behaviorby designing a highly sensitive reaction cell acting against thereaction heat and by providing an appropriate experimentaltechnique.

In his study of the dynamic behaviur of heat and masstransfer in metal hydride energy systems, Gambini [14]

by using only some boundary conditions proposed flowrate equations for hydriding/dehydriding reactions. In spiteof the large difference between the absorption and des-orption processes, the same expressions for the mobilityand the driving forces are used by the author for the tworeactions.

The rates of hydriding and dehydriding of LaNi5Hx weremeasured under isothermal and isobaric conditions by Inomataet al. [15]. By analyzing the obtained data, the authors pro-posed a model for hydriding and dehydriding kinetics. In thismodel hydride reaction is assumed as a phase transformationfrom solid solution phase (� phase) to hydride phase (� phase).This model considered that the rate controlling step, in the hy-driding case, is the nucleation and growth process of the hy-dride phase and then changed to hydrogen diffusion throughthe hydride phase at the later stage. On the other hand, forthe desorption of hydrogen, the rate controlling step is onlythe homogeneous chemical. The reaction of the hydride phase.Two rates for the nucleation and growth and for the hydro-gen diffusion are presented by the authors. These rates areexpressed as a function of composition, equilibrium plateaupressure and the applied pressure. For the dehydriding case,Inomata et al. found that the reaction rate depends only on tem-perature and the difference between the temporal and saturatedcomposition.

P–C isotherms of La(28.9)Ni(67.5)Si(3.55) which were fabri-cated by substitution of Ni by Si in LaNi5 have been studiedby Jain and Abu Dakka [16]. The authors found that (i) the ac-tivation of the alloy is sufficiently easy, (ii) the composition atsaturation is about 1.0 at room temperature (293 K), (iii) thevalues of composition at saturation were found to be 0.9, 0.85,0.8 at 313, 323, 333 K, respectively, and equilibrium pressureswere 1.01×105, 1.41×105, 1.71×105, 2.12×105 Pa at thesetemperatures, (iv) the maximum amount of hydrogen releasedby the alloy is in the temperature range 313–343 K, (v) forP –C–T curves the � + � phase decreases, compared to LaNi5alloy, at higher temperatures.

It comes out from this overview of past work which is re-lated to the reaction kinetics of metal hydrides and essentially

0 1 2 3 4 5 6

203040

Absorption LaNi4.75Fe0.25

Absorption LaNi4.85Al0.15

Absorption LaNi5

Desorption LaNi4.75Fe0.25

Desorption LaNi4.85Al0.15

Desorption LaNi5

H/M0 1 2 3 4 5 6

0 1 2 3 4 5 6

Fig. 2. Theoretical fit and experimental evolution of equilibrium pressure as a function of (H/M) and temperature for the three alloys.

the LaNi5 alloys and related compounds that the initialoperating conditions (pressure, temperature, …) are notconsidered in almost all the proposed rate equations for hy-driding/dehydriding kinetics. Also there is no rate equation thatcan be used to describe hydriding/dehydriding processes ofLaNi4.85Al0.15 and LaNi4.75Fe0.25. On the other hand, numer-ical modelling studies of metal hydride beds are of practicalimportance in the optimisation of bed design and performance.Consequentially, several numerical models describing the heat

and mass transfer phenomena in metal hydrogen systems havebeen done [17–26]. However, to extend these numerical modelsto a large group of metals and alloys and to simulate metal hy-drogen systems under large operating conditions (constant pres-sure and/or temperature, variable pressure and/or temperature),general rate equations for kinetics are necessary. So the aim ofthe present work is to develop, basing on experimental data, rateequations for the hydriding/dehydriding reactions of LaNi5,LaNi4.85Al0.15 and LaNi4.75Fe0.25 suitable for engineering

T (°C) P (bar)

0 42 6 8 10 12 140.00

(N-1)[Ln (P/Pe) / (P/Pe)] (1-F)

Fig. 3. Hydriding rates versus (N −1)[ln(P/Pe)/(P/Pe)] (1−F) in the caseof LaNi5 alloy.

applications and design purposes and that can be integratedeasily in the numerical models that simulate metal hydrogensystems working.

3.7E-4 3.8E-4 3.9E-4 4.0E-4 4.1E-4 4.2E-4

1/ (Rg T)

LaNi4.85Al0.15

3.8E-4 3.9E-4 4.0E-4 4.1E-4 4.2E-4

1/ (Rg T)

3.8E-4 3.9E-4 4.0E-4 4.1E-4 4.2E-4

1/ (Rg T)

LaNi4.75Fe0.25

Fig. 4. Arrhenius plot for hydriding reaction.

2. Experimental setup

The experiments were carried out using the device presentedin Fig. 1. The gas used is the hydrogen of the UP type 99.99%.The reactor and the reservoir are submerged in a bath in whichthe temperature is controlled by a thermostat with circulation(Julabo SC-3). The used reactor is cylindrical connected to thereservoir and composed of two parts made of brass: a cylin-drical body and a lid. The pressure in reservoir is measuredby a pressure gauge (type PA-21LC, 0–100 bar). The sensorof pressure is connected to a D.C. constant voltage and toa data acquisition system. The reactor tightness for vacuum(10−3 bar) and for hydrogen pressure of more than 16 bar wastested. It is important to note that a numerical study of the ef-fect of different parameters using the model which was pre-sented in our previous work [25] has been done in order tochoose the suitable dimensions of the reactor (diameter, height,thickness…) and the quantity of alloy introduced in the re-actor that permits to achieve quasi-isothermal conditions inthe bed.

2.1. Equilibrium pressure determination

Initially a primary vacuum is realized in the reactor and inthe reservoir. Then a quantity of hydrogen is introduced in thereservoir under a known pressure. When the reservoir is put

0 50 100 150 200 2500

20 1020 6

Model Experience T(°C) P (bar)

Time (s)

0 50 100 150 200 2500

40 1040 8

Time (s)

0 50 100 150 200 250 3000

30 1030 830 6

Time (s)

Model Experience T(°C) P (bar)

Fig. 5. The calculated and measured hydrogen-to-metal-atomic ratio evolution under different experimental conditions for LaNi5 alloy in the absorption case.

in communication with the reactor, absorption of hydrogen bythe alloy takes place and the pressure in the reservoir decreasesuntil the equilibrium one. This operation is repeated at con-stant temperature using a higher initial reservoir pressure untilsaturation of the hydride bed.

In the case of desorption, the reservoir initially under a pri-mary vacuum is put in communication with the reactor. Thenthe pressure in the reservoir increases until the equilibrium isobtained. The operation is repeated at a constant temperature,until desorption is complete.

The measurement of the reservoir pressure and the knowl-edge of the reservoir volume and of the temperature lead tothe determination of the hydrogen-to-metal atomic ratio H/M

(M = represents alloys or compound metal) from the idealgas law.

Using the van’t Hoff equation form, the equilibrium pressureis expressed by

T− 1

)). (1)

�H is reaction heat function (J), Rg is the gas constant (J/K),T0 is a reference temperature, f (H/M) is equilibrium pressure(bar) at T0.

The equilibrium pressure obtained experimentally at T0 =303 K is fitted in the case of the three samples by a polynomialform of f (H/M). The polynomial coefficients for the absorp-tion and desorption cases are given, respectively, in Tables 1and 2.

Experimental and theoretical equilibrium pressure as a func-tion of H/M for different temperatures and for the three alloysis presented in Fig. 2. These profiles show that the substitu-tion of aluminum causes a reduction of the equilibrium pres-sure and that this effect is not important for iron. Also, it isnoted that the amount of hydrogen that can be stored in theLaNi5 alloy decreases with the substitution of the two metals((H/M)s is of about 5.1 for the aluminium and 5.6 for theiron).

2.2. Kinetics reaction determination

In this paper, the reaction kinetics were determined experi-mentally for LaNi5, LaNi4.85Al0.15 and LaNi4.75Fe0.25. For theabsorption case, the reactor is put in contact with the reservoirfilled with hydrogen. For the desorption case, a desirable pres-sure in the reservoir is imposed using a vacuum pump and an at-mospheric valve. The measure of the pressure time evolution in

0 20 40 60 80 100

Time (s)

Model Experience T (°C) P(bar)

LaNi4.85Al0.15

0 20 40 60 80 100 1200

Time (s)

LaNi4.75Fe0.25

Fig. 6. The calculated and measured hydrogen-to-metal-atomic ratio evo-lution under different experimental conditions for LaNi4.85Al0.15 andLaNi4.75Fe0.25 alloys in the absorption case.

the reservoir leads to the determination of the metal–hydrogenatomic ratio evolution.

The kinetics of a gas–solid reaction can be written as

dt= k g1(p) g2(F ), (2)

where F is the fraction conversion of the solid reactant, g1(p)

is the dependence of the rate on the applied pressure, g2(F ) isthe dependence of the rate on the fractional conversion of thesolid and k is the reaction rate constant [26].

Table 3Reaction rate constants k of hydrogen absorption

LaNi5 LaNi4.75Fe0.25 LaNi4.85Al0.15

ln(k) 6.39449 − 26386.9

RgT3.122888 − 14475.4

RgT0.467959 − 8064.6

270 275 280 285 290 295

LaNi4.85Al0.15

LaNi4.75Fe0.25

290 300 310 320 330 340 350 360

LaNi4.85Al0.15

LaNi4.75Fe0.25

Fig. 7. Comparison of the reaction rate constants of the three alloys for thehydriding reaction.

2.3. Absorption

To formulate reaction kinetics we have first tested differ-ent forms for the functions g1(p) and g2(F ) and different

reaction rates which have been proposed in the literature. Asa result, we have noted that the experimental data obtained inthis work cannot be expressed by these models. This result can

[P0 (Pe-P)/ (P.Pe)]F0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0E+0

5.0E-3

1.0E-2

1.5E-2

2.0E-2

2.5E-2

T (˚C) P (bar)

40 0.5

30 0.5

Fig. 8. Hydriding rates versus [P0(Pe − P)/(P · Pe)]F 0.5 in the case ofLaNi5 alloy.

3.6E-4 3.7E-4 3.8E-4 3.9E-4 4.0E-41/ (Rg T)

3.6E-4 3.7E-4 3.8E-4 3.9E-4 4.0E-4

1/ (Rg T)

LaNi4.75Fe0.25

3.6E-4 3.7E-4 3.8E-4 3.9E-4 4.0E-41/ (Rg T)

LaNi4.85Al0.15

Fig. 9. Arrhenius plot for dehydriding reaction.

be explained by the fact that some models are determined usingexperimental data obtained under constant hydrogen pressure.For the other models, the initial conditions of temperature andpressure have not been taken in consideration.

In this work, a precise analysis of the LaNi5 experimentaldata permitted us to propose the following forms of the func-tions g1(p) and g2(F ):

g1(p) = (N − 1)ln(P/Pe)

(P/Pe), (3)

g2(F ) = (1 − F), (4)

where F = (H/M)/(H/M)s, (H/M)s is the saturationhydrogen-to-metal-atomic ratio, P is the hydrogen pressure ata given time, Pe is the equilibrium pressure and N is the ini-tial applied pressure P0 to the mid-plateau pressure P m

e ratio(N = P0/P

Combining Eqs. (3) and (4), we obtain

dt= k(N − 1)

ln(P/Pe)

(P/Pe)(1 − F). (5)

Fig. 3 shows the reaction rate versus g1(p)g2(F ) under differ-ent conditions of temperature and pressure. Straight lines areobtained and the reaction rate constants are calculated fromtheir slopes. The Arrhenius plot of the reaction rate constant ispresented in Fig. 4a. The equation of this straight line is shownin Table 4.

Table 4Reaction rate constants k of hydrogen desorption

LaNi5 LaNi4.75Fe0.25 LaNi4.85Al0.15

ln(k) 11.5016 − 39790.4

RgT4.95603 − 23805.7

RgT8.07169 − 30945.9

The comparison between the experimental data for the LaNi5alloy and the theoretical results, obtained by Eq. (5), shows thatthe proposed chemical reaction control model is appropriate(Fig. 5).

To evaluate the effect of the substitution of the aluminum andthe iron on the reaction kinetics, the rate data on LaNi4.85Al0.15and LaNi4.75Fe0.25were measured using the same apparatus.The chemical reaction model derived in this work was also usedto analyze these data.

Figs. 4b and c show the Arrhenius plot of the reaction rateconstants k of the two alloys. Straight lines were obtained inthese figures. The equations of these straight lines are shownin Table 4.

The curves presented in Fig. 6 show that there is a goodagreement between the experimental data and the theoretical

Model Experience T (°C) P (bar)

0 40 80 120 160 2000

40 150 1

0 40 80 120 160 2000

40 1.550 1.5

0 40 80 120 160 2000

30 0.5

40 0.5

50 0.5

Time (s)Time (s)

Time (s)

Fig. 10. The calculated and measured hydrogen-to-metal-atomic ratio evolution under different experimental conditions for LaNi5 alloy in the desorption case.

results in the case of the hydrogen absorption by LaNi4.85Al0.15and LaNi4.75Fe 0.25 alloys.

Using the expressions given in Table 3, the evolu-tions of the reaction rate constants k, of the three sam-ples of alloy, versus temperature are presented in Fig. 7.These curves show that the hydriding rate constants in therange temperature of 273–293 K were in the following ra-tio: LaNi4.85Al0.15 > LaNi4.75Fe0.25 > LaNi5. However, inthe range temperature of 293–353 K, the hydriding rateconstants of the three alloys were in the following ratio:LaNi4.75Fe0.25 > LaNi4.85Al0.15 > LaNi5. This result can beattributed to the stability of the alloys.

2.4. Desorption

For the desorption case, we have assumed the followingforms of the functions g1(p) and g2(F ):

g1(p) = −P0(Pe − P)

P · Pe, (6)

g2(F ) = F 0.5 (7)

where F = (H/M)/(H/M)0, (H/M)0 is the initial hydrogen-to-metal-atomic ratio, P0 is the initial pressure, P is the

0 25 50 75 100 125 150 175 200 225 2500

Time (s)

30 0.5

40 0.5

50 1.5

LaNi4.75Fe0.25

0 50 100 150 200 250 3001

Time (s)

0 50 100 150 200 250 3001

30 0.5

40 0.5

50 0.5

Model Experience T (°C) P(bar) Model Experience T (°C) P(bar)

Model Experience T (°C) P(bar)

Time (s) LaNi4.85Al0.15

Fig. 11. The calculated and measured hydrogen-to-metal-atomic ratio evolution under different experimental conditions for LaNi4.85Al0.15 and LaNi4.75Fe0.25alloys in the desorption case.

hydrogen pressure at a given time and Pe is the equilibriumpressure.

Substituting Eqs. (6) and (7) in Eq. (2), we obtain

P0(Pe − P)

P · PeF 0.5. (8)

Plots of (−dF/dt) versus P0(Pe−P)P ·Pe

F 0.5, in the case of LaNi5alloy, for different conditions of temperature and pressure areshown in Fig. 8. The plots yield good straight lines and thereforeEq. (8) is considered to be appropriate for hydrogen desorptionby the LaNi5 alloy. The reaction rate constants are obtainedfrom the slope of the obtained straight lines.

Fig. 9a shows an Arrhenius plot of the rate constant for hy-drogen desorption by LaNi5 alloys. The equation of the ob-tained straight line is given in Table 4.

Compared to the experimental results, the hydrogen-to-metal-atomic ratio calculated using Eq. (8) shows a goodagreement (Fig. 10).

The reaction rate given by Eq. (8) was also used to analyzethe experimental data obtained in the case of the hydrogen des-orption by LaNi4.85Al0.15 and LaNi4.75Fe0.25 alloys. Arrheniusplot of the rate constants for hydrogen desorption by these al-

loys is shown in Figs. 9b and c. The equations of the obtainedstraight lines are given in Table 4.

Fig. 11 shows that, in the case of the LaNi4.85Al0.15 andLaNi4.75Fe0.25 alloys, the dehydriding rate equation proposedin this paper predicts correctly the dependence of the reactionrate on the hydrogen pressure and the hydrogen concentration.

Using the expressions given in Table 4, the evolutions of thereaction rate constants k, of the three samples of alloy, versustemperature are presented in Fig. 12. It can be noted that above303 K, the LaNi4.75Fe0.25 alloy has the lowest reaction rateconstant.

3. Conclusion

The kinetics of the hydrogen hydriding/dehydriding by thealloys LaNi5, LaNi4.85Al0.15, and LaNi4.75Fe0.25 under dif-ferent conditions have been experimentally investigated. Theresults show a strong dependence on the pressure and tem-perature. Based on the experimental data, analytic expressionsof the reaction kinetics have been obtained and give a goodagreement with experimental data under different conditions.It is important to note that these analytic expressions comparedto the other kinetics models can be integrated easily in the

320 340 360 380

0.00E+0

1.00E-1

2.00E-1

3.00E-1

LaNi4.85Al0.15

LaNi4.75Fe0.25

275 280 285 290 295

2.00E-3

4.00E-3

6.00E-3

8.00E-3

1.00E-2

LaNi4.85Al0.15

LaNi4.75Fe0.25

294 296 298 300 302 304

6.00E-3

8.00E-3

1.00E-2

1.20E-2

1.40E-2

1.60E-2

LaNi4.85Al0.15

LaNi4.75Fe0.25

Fig. 12. Comparison of the reaction rate constants of the three alloys for the dehydriding reaction.

numerical approaches that predict dynamic behavior of realisticmetal–hydrogen reactor.

In addition, in this paper the effect of Fe and Al as sub-stituents for Ni on P–C isotherm and reaction rates of LaNi5alloy has been experimentally studied.

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Measurement and modelling of kinetics of hydrogen sorption by LaNi5 and two related pseudobinary...

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