Kinetics of sodium borohydride hydrolysis reaction for
hydrogen generation
Ai-Jen Hung
a, Shing-Fen Tsai
b, Ya-Yi Hsu
b, Jie-Ren Ku
b, Yih-Hang Chen
c,
Cheng-Ching Yu
a,*
a
Department of Chemical Engineering, National Taiwan University, Taipei 106-17, Taiwan
bEnergy and Environment Research Laboratories (EEL), Industrial Technology Research Institute (ITRI), Hsinchu 310, Taiwan
cDepartment of Process Engineering, CTCI Corporation, Taipei 106, Taiwan
a r t i c l e
i n f o
Article history:
Received 13 March 2008 Received in revised form 29 July 2008
Accepted 29 July 2008
Available online 11 September 2008
Keywords: Kinetics Sodium borohydride Hydrolysis reaction Hydrogen generation
a b s t r a c t
In this work, a ruthenium catalyst was prepared for hydrogen generation from the hydrolysis reaction of an alkaline sodium borohydride solution. The reactions were carried
out in a batch reactor at temperatures of 10, 30, 40 and 60C for at least 70% conversion or
500 min, whichever came first. The experimental data was fitted to the following three kinetic models: zero-order, first-order, and Langmuir–Hinshelwood. The results indicate that the Langmuir–Hinshelwood model gives a reasonable description of the hydrogen generation rate over the entire temperature range studied as well as the time spans of the experiments. The zero-order model gives good behavior description only at relatively low
temperature, i.e. 10C. The first-order model works fairly well for a temperature range up
to 30C.
ª2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights
reserved.
1.
Introduction
Hydrogen has become one of the most promising future energy resources due to concerns about global warming and the depletion of fossil fuels. Hydrogen generation from the hydrolysis reaction of an alkaline sodium borohydride solution
(NaBH4) has drawn much attention due to its theoretically high
hydrogen storage capacity (10.8 wt%). In addition, it is favored as the hydrogen supplier for proton exchange membrane (PEM) fuel cells due to the high purity of the hydrogen.
A hydrolysis reaction takes place only when an alkaline
NaBH4solution is in contact with certain catalysts. Different
catalysts such as ruthenium (Ru) [1–7], platinum (Pt) [8,9],
palladium (Pd)[10], nickel (Ni)[11,12], cobalt (Co)[11,13,14],
Co–B[15,16], Ni–B[17], Ni–Co–B[18], carbon nanotubes (CNT)
[19]have been extensively studied.
For the design of reactors, it is essential to determine a reliable kinetic model for the hydrogen generation.
Hydrogen generation from an alkaline NaBH4 solution has
been extensively investigated and three kinetic models have
been proposed [1–7,10–13,15–19]. They are zero-order,
first-order and Langmuir–Hinshelwood.
Several authors have used a zero-order model. Amendola
et al.[1]used Ru on IRA-400 as the catalyst to study the effect
of different temperatures on the kinetics of the hydrolysis
reaction. Factors including the concentration of NaBH4, the
concentration of sodium hydroxide (NaOH) and the reaction temperature (which could affect the hydrogen generation rates) were investigated using the catalyst Ru on different
supports in[2,3]. The catalysts Co[11,13], Ni[11], Co–B[15,16],
Ni–B[17]and Ni–Co–B[18]were implemented for the
hydro-lysis reaction.
* Corresponding author. Fax: þ886 2 2362 3040.
E-mail address:[email protected](C.-C. Yu).
A v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / h e
0360-3199/$ – see front matter ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2008.07.109
Other authors have used a first-order model. Ozkar and
Zahmakiran[4,5]used a water-dispersible Ru(0) nanocluster
catalyst to increase activity. Shang and Chen[6]explored the
effect of a concentrated NaBH4solution on hydrogen
genera-tion rates. The performance and reliability of carbon nano-tubes (CNT) as the catalyst for the hydrolysis reaction were
investigated in Ref.[19]. The synthesis and characterization of
a water-dispersible Ni(0) nanocluster catalyst was explored in
Ref.[12]and the activity of Pd on the hydrolysis reaction was
investigated in Ref.[10].
Finally, at least one author has used a
Langmuir–Hin-shelwood model. Zhang et al. [7] used the commercial
catalyst Ru to analyze the effects of different substrates, the catalyst sizes, the stirring speed and the reaction
temperature on the hydrogen generation rate. Table 1
summarizes published investigations of the kinetics of the Nomenclature
C concentration, mol L1
CNaBH4;0 initial concentration of NaBH4based on maximum
hydrogen generation rate, mol L1
FH2 filtered data for hydrogen generation rate,
ml min1
FH2;raw raw data for hydrogen generation rate, ml min
1
Ka adsorption constant, L mol1
k reaction rate constant based on the solution
volume for zero-order, mol L1min1; for
first-order, min1; for Langmuir–Hinshelwood,
mol L1min1
k0 reaction rate constant based on the catalyst weight
for zero-order, mol g cat1min1; for first-order,
L g cat1min1; for Langmuir–Hinshelwood,
mol g cat1min1
MNaBH4 molecular weight of NaBH4, 37.8 g mol1
MH2O molecular weight of H2O, 18 g mol1
MNaBO2 molecular weight of NaBO2, 65.8 g mol
1
MH2 molecular weight of H2, 2 g mol1
N number of moles, mol
r rate of reaction, mol L1min1
R gas constant, 8.314 103kJ mol1K1
R2 correlation coefficient
T reaction temperature, K
t time, min
V solution volume, L
wcat catalyst weight, g
z discrete variable
Greek letters
DHrxn heat of reaction, kJ mol1
rNaBH4 density of NaBH4, 1070 g L
1
rH2O density of H2O, 1000 g L
1
rNaBO2 density of NaBH4, 2460 g L1
rH2 density of H2, 8.988 105g ml1
Table 1 – Kinetic models for different catalysts, initial concentration of NaBH4(aq), temperature ranges, activation energy
and time spans
Catalyst/support Initial concentration
of NaBH4(aq) Kinetic model Temp. range (oC) Activation energy (kJ/mol) Time span (min) Reference
Ru(5 wt%)/IRA-400 20 wt% NaBH4þ10 wt% NaOH Zero-order 25–55 47.0 27 Amendola et al.[1]
Ru(5 wt%)/IRA-400 7.5 wt% NaBH4þ1 wt% NaOH Zero-order 0–40 56.0 42 Amendola et al.[2]
Ru(1 wt%)/IR-120 5 wt% NaBH4þ1 wt% NaOH Zero-order 5–55 49.7 60 Hsueh et al.[3]
Ni 0.9 wt% NaBH4þ10 wt% NaOH Zero-order 10–50 62.7 150 Liu et al.[11]
Co Zero-order 10–50 41.9 30
Raney Ni Zero-order 10–30 50.7 50
Raney Co Zero-order 10–30 53.7 50
Raney Ni50Co50 Zero-order 10–30 52.5 30
Co–B 20 wt% NaBH4þ5 wt% NaOH Zero-order 10–30 64.9 40 Jeong et al.[15]
Co–B 0.7wt% NaBH4þ4 wt% NaOH Zero-order 25–40 57.8 14 Zhao et al.[16]
Co/g-Al2O3 5 wt% NaBH4þ5 wt% NaOH Zero-order 30–50 32.6 80 Ye et al.[13]
NixB 1.5 wt% NaBH4þ10 wt% NaOH Zero-order 20–60 56.0 35 Dong et al.[17]
Ni–Co–B 4.7 wt% NaBH4þ15 wt% NaOH Zero-order 8–27 62.0 50 Ingersoll et al.[18]
Ru(0) nanoclusters 0.5 wt% NaBH4 First-order 30–45 28.5 5 Ozkar and Zahmakiran[4]
Ru(0) nanoclusters 0.5 wt% NaBH4þ10 wt% NaOH First-order 25–55 41.0 6 Zahmakiran and Ozkar[5]
Ru/C 5 wt% NaBH4þ5 wt% NaOH First-order 42–60 37.3 35 Shang and Chen[6]
Carbon nanotubes (CNT) 1 wt% NaBH4 First-order 29–59 19.0 120 Pena-Alonso et al.[19]
Ni(0) nanoclusters 0.5 wt% NaBH4 First-order 25–45 54.0 100 Metin and Ozkar[12]
Pd/C 0.5 wt% NaBH4 First-order 10–55 28.0 20 Patel et al.[10]
Ru/C 0.8 wt% NaBH4þ3 wt% NaOH Langmuir–
Hinshelwood
25–85 67.0 14 Zhang et al.[7]
Ru/g-Al2O3 12 wt% NaBH4þ1 wt% NaOH Zero-order 10–60 54.9 500 This work
Ru/g-Al2O3 12 wt% NaBH4þ1 wt% NaOH First-order 10–60 55.7 500 This work
Ru/g-Al2O3 12 wt% NaBH4þ1 wt% NaOH Langmuir–
Hinshelwood
hydrolysis of NaBH4, including the kinetic models for different catalysts, initial concentration of the alkaline
NaBH4solution, temperature ranges, activation energy and
time spans. As shown in Table 1, the models are mostly
zero-order or first-order with the exception of the work of
Ref. [7]. Furthermore, the time spans of the experiments
range from 5 to 150 min. Because we are interested in
utilizing the kinetic model to design a hydrogen generation device, a model capable of describing the hydrogen gener-ation rate over the entire batch reactor opergener-ation is preferred. The objective of this work is to determine an appropriate kinetic model of this hydrolysis reaction in a batch reactor based on experiments at four different temperatures.
PC for recording data
Flow meter
Steam trap
H2
NaBH4(aq)+NaOH(aq)
Coolant out
Coolant in Thermocouple
Water flow Water
bath Water surge tank
Cooling water out
Circulation Pump
Cooling water makeup TT Tsp (Reactor) Tsp (Water bath) TC TT TC LC LT Stir Plate magnet
Fig. 1 – Experimental setup for hydrogen generation from the hydrolysis reaction of an alkaline NaBH4solution.
0 20 40 60 80 100 120 140 160 0 1 2 3 4 5 6 7 8 time (min) Hydrogen generated (L) 1 wt% NaBH4 12 wt% NaBH4 13 wt% NaBH4 31 wt% NaBH4
Fig. 2 – Hydrogen generation volume with respect to time
at the concentration of NaBH4of 1, 12, 13 and 31 wt% at
30 8C with the concentration of NaOH at a constant 1 wt%.
0 20 40 60 80 100 120 140 160 0 1 2 3 4 5 6 7 8 time (min) Hydrogen generated (L) 1 wt% NaOH 5 wt% NaOH 10 wt% NaOH
Fig. 3 – Hydrogen generation volume with respect to time at the concentration of NaOH of 1, 5 and 10 wt% at 30 8C
2.
Experimental
2.1. Hydrolysis reaction
A NaBH4 solution with an alkaline stabilizer, NaOH, reacts
with water to generate hydrogen and sodium metaborate
(NaBO2) in the presence of a catalyst. The catalytic hydrolysis
reaction for hydrogen generation is irreversible, heteroge-neous, and highly exothermic, with the heat of reaction of
210 kJ/mol[20]:
NaBH4ðaqÞþ2H2OðlÞ! catalyst
4H2ðgÞþNaBO2ðaqÞ DHrxn
¼ 210 kJ=mol (1)
This reaction system also has several advantages, including,
hydrogen can be produced even when the temperature is 0C,
the hydrogen generation rate can be easily controlled, and an
alkaline NaBH4solution is nonflammable and stable.
2.2. Preparation of Ru/g-Al2O3catalyst
The metal Ru was selected as a catalyst for hydrogen generation
due to high hydrogen production[21,22]and gamma-alumina
(g-Al2O3) was used as the support. The catalyst Ru/g-Al2O3
was prepared by the impregnation–reduction method. The synthesis procedure is summarized as follows:
1. Ten grams of g-Al2O3pellets (Alfa Aesar) were dehydrated
at 600C.
2. The g-Al2O3 pellets were placed in 10 ml of 0.24 M
RuCl3$3H2O (Sigma–Aldrich) for 24 h.
3. They were then dried for 2 h at 120C in nitrogen and then
calcined for 3 h at 550C in nitrogen.
4. Finally, they were reduced for 6 h at 700C in hydrogen,
producing the catalyst Ru/g-Al2O3.
2.3. Experimental setup
The experiments for the hydrolysis reaction were performed at the Industrial Technology Research Institute/Energy and Environment Research Laboratories (ITRI/EEL) facility in
Hsinchu. Fig. 1shows the experimental setup for hydrogen
generation from the hydrolysis reaction of an alkaline NaBH4
solution. The reaction took place in a round-bottomed glass-ware flask with three necks. A thermocouple in the first neck was used to monitor the solution temperature which was kept constant, via a thermostatic circulation water bath, to within
0.1C of the temperature set point. The second neck was
connected to a funnel, which contained an alkaline NaBH4
solution. The reaction was initiated when 30 ml of 12 wt%
NaBH4solution, including 1 wt% NaOH solution as an alkaline
stabilizer, was added to the flask to come into contact with
0.5 g of the catalyst Ru/g-Al2O3. The catalyst was pre-soaked in
16 ml of de-ionized water. This level of solution concentration was used because it was found to produce the highest level of
hydrogen generation, as shown inFigs. 2 and 3. As can be seen
inFig. 2, the hydrogen generation decreases with an increase
in NaBH4concentration from 12 to 31 wt%. Similarly, as can be
0 100 200 300 400 500 0 3 6 9 time (min) Hydrogen generated (L) Trxn=10°C Trxn=30°C Trxn=40°C Trxn=60°C
Fig. 4 – Hydrogen generation volume with respect to time at temperatures of 10, 30, 40, and 60 8C with the
concentrations of NaBH4and NaOH at 12 and 1 wt%,
respectively. 0 100 200 300 400 500 0 0.5 1 1.5 2 2.5 3 3.5 time (min) 0 100 200 300 400 500 time (min) CNaBH4 (mol/L) 0 20 40 60 80 100
B
A
XNaBH4 (%) t = 33.86 min t = 107.50 min t = 265.86 min Trxn=10°C Trxn=30°C Trxn=40°C Trxn=60°C Trxn=10°C Trxn=30°C Trxn=40°C Trxn=60°CFig. 5 – (A) Concentration of NaBH4with respect to time, (B)
conversion of NaBH4with respect to time for four
seen inFig. 3, the hydrogen generation decreases when the NaOH concentration is increased. The reagent solution was stirred by a magnet to maintain a uniform temperature. The hydrogen that was generated exited through the third neck into a coil condenser and then passed through a steam trap in order to remove the water vapor. During the experiments, the hydrogen generation rates were measured by a flow meter at
the following temperatures: 10, 30, 40, and 60C. The
sampling times for the temperature and flow measurements are 1.06 s.
3.
Results and discussions
3.1. Kinetics
3.1.1. Data treatment
Because of the noise associated with measurements, it is desirable to use an exponential filter to smooth the raw data for hydrogen generation rates. Raw data was smoothed with a filter with a time constant of 0.42 min. The relatively small time constant will not alter the dynamic behavior of the reaction because the process time constant is much large, at
least 40 min. TheAppendixshows the hydrogen generation
rate before and after the filtering at 30 and 60C. The
accu-mulative volumetric hydrogen generation with respect to
time is shown in Fig. 4at temperatures of 10, 30, 40, and
60C.
For kinetic analysis, it is preferable to convert the hydrogen generation rate into the reactant (sodium borohydride) concentration – both as functions of time. From the reaction
stoichiometry, the number of moles of NaBH4remaining in
the batch reactor with respect to time can be expressed as:
NNaBH4ðzÞ ¼ NNaBH4ðz 1Þ NH2ðz 1Þ=4 (2)
where N is the number of moles and z is the discrete variable.
The number of moles of H2O remaining in the batch reactor
with respect to time is:
NH2O z¼NH2O z 1NH2 z 12 (3)
The number of moles of NaBO2 remaining in the batch
reactor with respect to time is:
NNaBO2ðzÞ ¼ NNaBO2ðz 1Þ þ NH2ðz 1Þ=4 (4)
The solution volume with respect to time can then be evaluated as follows: VðzÞ ¼ NNaBH4ðzÞ$MNaBH4 rNaBH4 þNH2OðzÞ$MH2O rH2O þNNaBO2ðzÞ$MNaBO2 rNaBO2 (5)
where V is the solution volume, r denotes the density, M stands for the molecular weight. Consequently, the
concen-tration of NaBH4as a function of time can be obtained from
CNaBH4¼NNaBH4/V as shown inFig. 5(A). The corresponding
conversion of NaBH4can be calculated as shown inFig. 5(B). In
10°C
A
B
C
D
30°C 40°C 60°C 0 100 200 300 400 500 0 0.2 0.4 0.6 0.8time (min) 0 100 200time (min)300 400 500
0 50 100 150 200 250
time (min) 0 20 40time (min)60 80 100
(CNaBH4,0 -CNaBH4 ) (mol/L) R2 = 0.9991 (CNaBH4,0-CNaBH4) =0.001455•t+0.06476 R2 = 0.9947 (CNaBH4,0-CNaBH4) =0.006153•t R2 = 0.9987 (CNaBH4,0-CNaBH4) =0.01486•t R2 = 0.9999 (CNaBH4,0-CNaBH4) =0.04628•t 0 0.5 1 1.5 2 2.5 3 3.5 (CNaBH4,0 -CNaBH4 ) (mol/L) 0 1 2 3 4 (CNaBH4,0 -CNaBH4 ) (mol/L) 0 1 2 3 4 5 (CNaBH4,0 -CNaBH4 ) (mol/L)
this work, the following three kinetic models were used to describe the behavior of the hydrolysis reaction for hydrogen generation using an integral method.
3.1.2. Zero-order
If the rate of consumption of NaBH4(CNaBH4) with respect to
time is equal to a reaction rate constant, the reaction has zero-order kinetics (independent of any concentration).
dCNaBH4
dt ¼ rNaBH4¼ kðTÞ (6)
where C is the concentration, r is the rate of reaction, k is the reaction rate constant based on the solution volume.
Integrating the differential Eq.(6)it then becomes:
CNaBH4;0CNaBH4
¼kt (7)
A plot of ðCNaBH4;0CNaBH4Þshould be a linear function of time,
where the slope is simply the reaction rate constant. Here, the maximum hydrogen generation rate was used as an initial condition. In theory, the maximum rate occurs while the concentration of the reactants is at its highest. Since the time delay to evolve the maximum amount of hydrogen caused by the pore diffusion resistance was only about 6 s, it is reason-able to assume that it can be applied as an initial condition.
Fig. 6 shows plots of ðCNaBH4CNaBH4Þ versus time for four
temperature settings. As can be seen in Fig. 6(A), data
collected before the time of 50 min was excluded at the
temperature of 10C for the linear regression due to the low
reaction rate. The data at 10C could be linearly regressed in
the range of 50–500 min with the correlation coefficient of
0.9991. The data at temperatures of 30, 40, and 60C could be
linearly regressed only within the cut-off time, where the
conversion of NaBH4is 50%, as shown inFig. 6(B–D). As can be
seen from Fig. 5(A), the concentration of NaBH4 at 10C is
always higher than 2.5 (mol/L) within the whole reaction
time whereas the variations in the concentration of NaBH4
at 30, 40, and 60C are greater. Therefore it is appropriate
to apply the zero-order model while the concentration of
NaBH4 remains high. Table 2 summarizes the following
Table 2 – Products of reaction rate constant and catalyst weight, correlation coefficients of regression and correlation coefficients for the entire range for zero-order, first-order, Langmuir–Hinshelwood at 10, 30, 40, and 60 8C
Temp. (C) Time span
for regression (min)
k (mol/L/min) Correlation
coefficient (R2)
of regression
Correlation
coefficient (R2)
for the entire
rangea
Zero-order 10 50–500 0.001455 0.9991 0.9957
30 0–265.86 0.006153 0.9947 0.8965
40 0–107.50 0.01486 0.9987 0.9424
60 0–33.86 0.04628 0.9999 0.8969
Temp. (C) Time span
for regression (min)
k (1/min) Correlation
coefficient (R2)
of regression
Correlation
coefficient (R2)
for the entire
rangea
First-order 10 50–500 0.0004909 0.9999 0.9989
30 0–500 0.002356 0.9967 0.9967
40 0–107.50 0.005347 0.9929 0.6446
60 0–33.86 0.01663 0.9859 0.2663
Temp. (C) Time span
for regression (min)
k (mol/L/min) Correlation
coefficient (R2)
of regression
Correlation
coefficient (R2)
for the entire
rangea
Langmuir–Hinshelwood 10 50–500 0.001705 0.9993 0.9963
30 0–265.86 0.007287 0.9971 0.9835
40 0–250 0.01729 0.9990 0.9990
60 0–100 0.05659 0.9997 0.9997
a Full time span range: 0–500 min for 10 and 30C, 0–250 min for 40C, and 0–100 min for 60C.
3 3.1 3.2 3.3 3.4 3.5 3.6 x 10-3 -7 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 1/T (1/K) ln (k) R2 = 0.9971 6599.7 ln (k) = T = 16.765
regression data for zero-order: The reaction rate constants, which are signified by the slopes of the linear regression; the correlation coefficients for regression; and the correlation coefficients for the full time span. According to the Arrhe-nius equation, the plot of ln(k) versus 1/T for four
tempera-ture settings as shown inFig. 7gave a good linear regression
with the correlation coefficient of 0.9971. Therefore, the activation energy of 54.90 kJ/mol (the slope of the linear
regression) and the pre-exponential factor of 1.91 107mol/
L/min (the intercept of the linear regression) could both be
determined, as shown in Table 3. Because of the gradual
deterioration of the NaBH4concentration at higher
temper-atures toward the end of the time frame, e.g., 30, 40, and
60C, the first-order model is employed to compensate for
this deterioration.
3.1.3. First-order
Considering the case when the reaction rate is first-order in
the concentration of NaBH4, we have:
dCNaBH4
dt ¼ rNaBH4¼ kCNaBH4 (8)
Integrating the differential Eq.(8)it then becomes:
ln C NaBH4;0 CNaBH4 ¼kt (9)
A plot of lnðCNaBH4;0=CNaBH4Þas a function of time should give
a straight line, the slope of which is the reaction rate constant.
Fig. 8(A) and (B) shows that plots of lnðCNaBH4;0=CNaBH4Þversus
time at temperatures of 10 and 30C produce good linear
regression with correlation coefficients of 0.9999 and 0.9967.
Nevertheless, the data at 40 and 60C could be regressed
linearly only over the full cut-off time. The reason for this is that higher temperatures bring about higher reaction rates, thus this significantly increases the effect of the adsorption of
NaBH4 on the catalyst. Table 2 summarizes the following
regression data for a first-order model: the reaction rate constants, the correlation coefficients from the linear regres-sion and the correlation coefficients for the entire range. The Arrhenius plot, which is ln(k) versus 1/T, for first-order is
shown inFig. 9. The activation energy and the pre-exponential
factor can then be obtained from the slope and intercept of the
regression line, being 55.70 kJ/mol and 9.53 1061/min as
shown inTable 3. The regression results indicate that neither
zero-order nor first-order can describe the hydrogen genera-tion rate over the entire experimental duragenera-tion at higher
temperatures (40 and 60C). The Langmuir–Hinshelwood
model is considered next.
3.1.4. Langmuir–Hinshelwood
The Langmuir–Hinshelwood model[7,23]is commonly used to
describe reaction kinetics for catalytic reactions. Consider the following rate expression:
dCNaBH4
dt ¼ rNaBH4¼ k
KaCNaBH4
1 þ KaCNaBH4
(10)
where Kais the adsorption constant which is assumed to be
a constant. Integrating Eq.(10), one obtains:
1 Ka ln C NaBH4;0 CNaBH4 þCNaBH4;0CNaBH4 ¼kt (11) Table 3 – Pre-exp onentia l factors an d activa tion energ y fo r zero-o rder, first-o rde r and La ngmu ir–Hinsh elwo od mode ls Kinet ics Ra te expre ssion Kinet ic parame ter Comm ents Zero-order d CNaBH 4 d t ¼ kk mol Lmin ! ¼ 1 :91 10 7exp 54 :90 RT ðK Þ ! This model is recommended for low temperature, e.g., 10 C, or for the case of low NaBH 4 conversion, e.g., x < 50%. k 0 mol g cat min ! ¼ 1 :15 10 6exp 54 :90 RT ðK Þ ! * First-order d CNaBH 4 d t ¼ kC NaBH 4 k 1 min ! ¼ 9 :53 10 6exp 55 :70 RT ðK Þ ! This model is recommended for the reactor temperature up to 30 C. k 0 L g cat min ! ¼ 5 :72 10 5exp 55 :70 RT ðK Þ ! a Langmuir–Hinshelwood d CNaBH 4 d t ¼ k Ka CNaBH 4 1 þ Ka CNaBH 4 k mol Lmin ! ¼ 2 :82 10 7exp 55 :40 RT ðK Þ ! This model is recommended for the reactor temperature up to 60 C. k 0 mol g cat min ! ¼ 3 :59 10 6exp 55 :40 RT ðK Þ ! a and Ka L mol ! ¼ 1 :96 a k 0¼ k V wcat ¼ k 0 :03 L 0 :5 g cat .
A plot of ð1=KaÞlnðCNaBH4;0=CNaBH4Þ þ ðCNaBH4;0CNaBH4Þas a func-tion of time should give a straight line, the slope of which is the reaction rate constant. The objective function can be minimized by varying the adsorption constant using the data
at 40 and 60C. Therefore, it can be formulated as follows:
min Ka f ðKaÞ ¼1 R240C þ1 R2 60C (12)
where R2is the correlation coefficient.Fig. 10shows that the
optimal adsorption constant (Ka,opt) was obtained by
minimizing Eq.(12)at temperatures of 40 and 60C. In order to
determine the reaction rate constant for Langmuir–Hinshel-wood, the optimal adsorption constant was input into the data
at temperatures of 10 and 30C, as shown inFig. 11(A) and (B).
As can be seen inFig. 11(C) and (D), the data at 40 and 60C
could be linearly regressed within the whole time span.Table
2 also shows the reaction rate constants, the correlation
0 100 200 300 400 500 0 0.05 0.1 0.15 0.2 0.25 0.3 time (min) 0 100 200 300 400 500 time (min)
time (min) time (min)
ln(C NaBH4,0 /C NaBH4 ) ln(C NaBH4,0 /C NaBH4 ) ln(C NaBH4,0 /C NaBH4 ) ln(C NaBH4,0 /C NaBH4 ) R2 = 0.9999 CNaBH4,0 ln = 0.0004909•t+0.01263 CNaBH4 ⎛ ⎜⎜ ⎝ ⎛ ⎜ ⎜ ⎝ R2 = 0.9967 CNaBH4,0 ln = 0.002356•t CNaBH4 ⎛ ⎜⎜ ⎝ ⎛ ⎜ ⎜ ⎝ R2 = 0.9859 CNaBH4,0 ln = 0.01663•t CNaBH4 ⎛ ⎜⎜ ⎝ ⎛ ⎜ ⎜ ⎝ R2 = 0.9967 CNaBH4,0 ln = 0.005347•t CNaBH4 ⎛ ⎜⎜ ⎝ ⎛ ⎜ ⎜ ⎝ 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 250 0 0.5 1 1.5 2 2.5 0 20 40 60 80 100 0 0.5 1 1.5 2 2.5 3 3.5 4 10°C
A
B
C
D
30°C 40°C 60°CFig. 8 – Linear regression based on first-order while the temperature is (A) 10 8C (B) 30 8C (C) 40 8C (D) 60 8C.
3 3.1 3.2 3.3 3.4 3.5 3.6 x 10-3 -8.5 -8 -7.5 -7 -6.5 -6 -5.5 -5 -4.5 -4 1/T (1/K) ln (k) R2 = 0.9980 6700.4 ln (k) = -T + 16.07
Fig. 9 – Arrhenius plot for first-order.
1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6x 10 -3 Ka (L/mol) (1-R 2 40°C )+(1-R 2 60°C ) Ka,opt=1. 96
Fig. 10 – Optimization of the adsorption constant for Langmuir–Hinshelwood using the data at 40 and 60 8C.
coefficients of both regression and the entire range for Lang-muir–Hinshelwood. Therefore from the Arrhenius plot of ln(k)
versus 1/T as shown inFig. 12, the activation energy and the
pre-exponential factor could be determined to be 55.40 kJ/mol
and 2.82 107mol/L/min. The reaction rate constants based
on the solution volume and the catalyst weight for zero-order, first-order, and Langmuir–Hinshelwood are summarized in
Table 3.
3.2. Batch reactor model
With the kinetic models available, a constant-pressure batch reactor model can be constructed. From the mole balance and 10°C 0 100 200 300 400 500 0 0.2 0.4 0.6 0.8 1 time (min) 1/K a
*
ln(C NaBH4,0 /CNaBH4 ) +(C NaBH4,0 -CNaBH4 ) 30°C 0 100 200 300 400 500 0 1 2 3 4 time (min) 1/K a*
ln(C NaBH4,0 /CNaBH4 ) +(C NaBH4,0 -CNaBH4 ) 40°C 0 50 100 150 200 250 0 1 2 3 4 5 time (min) 1/K a*
ln(C NaBH4,0 /CNaBH4 ) +(C NaBH4,0 -CNaBH4 ) 60°C 0 20 40 60 80 100 0 1 2 3 4 5 6 time (min) 1/K a*
ln(C NaBH4,0 /CNaBH4 ) +(C NaBH4,0-CNaBH4 ) CNaBH4,0 1 ln (CNaBH4,0 - CNaBH4) 1.96 CNaBH4 = 0.001705•t + 0.07120 R2 = 0.9993 ⎛ ⎜⎜ ⎝ ⎛ +⎜⎝ 1 CNaBH4,0 ln (C NaBH4,0 - CNaBH4) 1.96 CNaBH4 = 0.007287•t R2 = 0.9971 ⎛ ⎜⎜ ⎝ ⎛ +⎜⎝ CNaBH4,0 1 ln (CNaBH4,0 - CNaBH4) 1.96 CNaBH4 = 0.05659•t R2 = 0.9997 ⎛ ⎜⎜ ⎝ ⎛ +⎜⎝ CNaBH4,0 1 ln (CNaBH4,0 - CNaBH4) 1.96 CNaBH4 = 0.01729•t R2 = 0.9990 ⎛ ⎜⎜ ⎝ ⎛ +⎜⎝A
B
C
D
Fig. 11 – Linear regression based on Langmuir–Hinshelwood with the temperature set at (A) 10 8C (B) 30 8C (C) 40 8C (D) 60 8C.
3 3.1 3.2 3.3 3.4 3.5 3.6 x 10-3 -7 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 1/T (1/K) ln (k) R2 = 0.9979 6667.3 ln (k) = -T + 17.155
Fig. 12 – Arrhenius plot for Langmuir–Hinshelwood.
0 20 40 60 80 100 0 3 6 9 time (min) Hydrogen generated (L) Exp. data (Trxn = 60°C) Zero-order First-order Langmuir-Hinshelwood
Fig. 13 – Model predictions for zero-order, first-order, and Langmuir–Hinshelwood with the experimental data at 60 8C.
the stoichiometric relationship the variation of the number of
moles of NaBH4with respect to time is the product of the rate
of reaction and the solution volume, which can be expressed as follows:
dðVCNaBH4Þ
dt ¼ ðrNaBH4ÞV (13)
The variation of the number of moles of H2O with respect to
time is:
dVCH2O
dt ¼2ðrNaBH4ÞV (14)
The variation of the number of moles of NaBO2with respect
to time is:
dVCNaBO2
dt ¼rNaBH4V (15)
The solution volume can be calculated in Eq. (5) and the
concentration profiles of NaBH4, H2O, and NaBO2can then be
obtained. The hydrogen generation rate can be computed as follows:
FH2 ¼4ðrNaBH4VÞ
MH2
rH2
(16)
where FH2 is the hydrogen generation rate. Because of the
constant reaction temperature, the energy balance
equa-tions are negligible in this system. Eqs. (13)–(15) can be
solved by using the Euler method, the code is programmed in FORTRAN.
3.3. Validation of the kinetic model
The hydrogen generated from the hydrolysis reaction of an
alkaline NaBH4solution can be used for PEM fuel cell
appli-cations due to its high purity. The operating fuel cell
temperature is normally set at 60C for optimal performance.
For this reason, the experimental data at 60C was used to
validate the kinetic models, which are zero-order, first-order,
and Langmuir–Hinshelwood. As can be seen in Fig. 13, the
Langmuir–Hineshelwood model gave the best prediction among the three models.
4.
Conclusions
In this study, the catalyst Ru/g-Al2O3was prepared by the
impregnation–reduction method for the hydrogen generation
from the hydrolysis reaction of an alkaline NaBH4solution.
Next, the reaction was carried out in a batch reactor at 10, 30,
40 and 60C, respectively, until at least 70% conversion was
achieved, except for the case of 10C when the reaction was
terminated at 500 min. The results indicate that the zero-order model can only be applied for low conversion, e.g.,
x < 50%, and/or low temperature, e.g., 10C. The first-order
model shows somewhat better applicability and gives a reasonably good concentration trajectory for temperatures
up to 30C. The Langmuir–Hinshelwood model gives
reason-able behavior description for the entire temperature range of
interest, 10–60C. Therefore, the Langmuir–Hinshelwood
model is recommended for the hydrogen generation device modeling and design.
Acknowledgement
This work is supported in part by the National Science Council of Taiwan.
Appendix
The raw data is filtered by an exponential filter with a time
constant of 0.42 min, i.e., FH2¼FH2=ð0:42s þ 1Þ.Fig. A1shows
the hydrogen generation rate before (in blue) and after (in red)
filtering at 30C (Fig. A1(A)) and 60C (Fig. A1(B)). (For
inter-pretation of the references to color in this figure, the reader is referred to the web version of this article.)
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