Kinetic modeling of pure hydrogen production from decalin

Article abstract of DOI:10.1016/j.jcat.2007.11.012

We investigate the dehydrogenation of decalin for the production of pure hydrogen for fuel cell applications. Supported Pt catalysts can achieve about 98% conversion with > 99.9 % selectivity for the dehydrogenation reaction. Cracking reactions occur only at high temperature. The partially dehydrogenated product, tetralin, was formed with a molar selectivity < 6 %, depending on the operating conditions. We investigated the kinetics of the dehydrogenation of decalin in a fixed-bed tubular reactor at 275-345 °C and atmospheric pressure. A Hougen-Watson-type kinetic model accounted for the dehydrogenation of cis- and trans-decalin as well as the isomerization between the two isomers, the formation of the intermediate tetralin and the final product, naphthalene. The rigorous discrimination between rival models led to parameter values that are statistically significant and satisfied the physicochemical criteria.

Full text of DOI:10.1016/j.jcat.2007.11.012

Journal of Catalysis 253 (2008) 229–238
www.elsevier.com/locate/jcat
Kinetic modeling of pure hydrogen production from decalin
Bo Wang a, D. Wayne Goodman a, Gilbert F. Froment b,∗
a
Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122, USA
b
Department of Chemistry, Texas A&M University, College Station, TX 77842, USA
Received 10 August 2007; revised 12 November 2007; accepted 13 November 2007
Abstract
We investigate the dehydrogenation of decalin for the production of pure hydrogen for fuel cell applications. Supported Pt catalysts can achieve
about 98% conversion with >99.9% selectivity for the dehydrogenation reaction. Cracking reactions occur only at high temperature. The partially
dehydrogenated product, tetralin, was formed with a molar selectivity <6%, depending on the operating conditions. We investigated the kinetics
◦
of the dehydrogenation of decalin in a fixed-bed tubular reactor at 275–345 C and atmospheric pressure. A Hougen–Watson-type kinetic model
accounted for the dehydrogenation of cis- and trans-decalin as well as the isomerization between the two isomers, the formation of the intermediate
tetralin and the final product, naphthalene. The rigorous discrimination between rival models led to parameter values that are statistically significant
and satisfied the physicochemical criteria.
© 2007 Elsevier Inc. All rights reserved.
Keywords: Hydrogen; Fuel cell; Dehydrogenation; Decalin; Kinetics
1. Introduction
hydrogen. Another advantage of using these liquid hydrocar-
bons as hydrogen storage media is that the present infrastruc-
tures, such as gas stations and oil tankers, can be used for their
storage and transportation. The dehydrogenation of cycloalka-
nes is a reversible process. The products (e.g., benzene, toluene,
naphthalene) can be hydrogenated back to cycloalkanes in spe-
cialized gas stations.
A number of supported metal catalysts have been reported
in the literature for the dehydrogenation of cycloalkane. So-
morjai and co-workers studied the dehydrogenation of cyclo-
hexane over single-crystal Sn/Pt(111) and Pt(111)/Sn/K in a
vacuum chamber at 573 K [14]. It was found that the ad-
sorption of tin and potassium on Pt(111) decreased deactiva-
tion of the surface by coke deposition, as well as the turnover
rate of cyclohexane dehydrogenation, due to site coverage.
Ichikawa and co-workers investigated the dehydrogenation of
cyclohexane, methylcyclohexane, and decalin over activated
carbon-supported Ni, Pt and Ni–Pt catalysts using a spray pulse
mode reactor operating at 287–375 ◦C [8,9]. It was assumed
that pulse spray operation could increase the reaction rate by
suppressing the reverse reaction. The conversions amounted to
25–35%, with a >98.8% selectivity for dehydrogenation re-
Fuel cells have the potential to replace the internal combus-
tion engine in vehicles, offering cleaner, more efficient alterna-
tives to the combustion of gasoline and other fossil fuels [1–5].
The distribution and onboard storage of hydrogen are serious
disadvantages for the application of fuel cells. Today, hydrogen
is produced primarily by catalytic steam reforming of natural
gas and other hydrocarbons [6,7]. The reforming of hydrocar-
bons produces CO as a byproduct, and its presence poisons
the Pt-based electrocatalysts used in PEM fuel cells, so that
the hydrogen must be purified. Another promising technology
for storing and transporting hydrogen is the dehydrogenation
of organic hydrocarbons with high hydrogen content. Hydro-
carbons such as cyclohexane, methylcyclohexane, and decalin
have been considered for this purpose [8–12]. Only hydrogen
and dehydrogenated hydrocarbons are formed as the main prod-
ucts in this reaction. The absence of any substantial amount of
carbon oxides eliminates the need for further purification of the
*
Corresponding author.
E-mail address: g.froment@che.tamu.edu (G.F. Froment).
0021-9517/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcat.2007.11.012

230
B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
actions. Saito and co-workers performed dehydrogenation of
decalin at 210 ◦C with carbon-supported Pt based catalysts
in a batch-type reactor with continuous removal of the pro-
duced hydrogen through the condenser [10]. After 2.5 h of
operation, the conversions were in the range of 25.4–35.8%.
Okada et al. also reported their results for alumina-supported
Pt catalysts in methylcyclohexane dehydrogenation in a fixed-
bed reactor [11]. This catalyst could generate hydrogen from
methylcyclohexane with a conversion of 95% and toluene se-
lectivity >99.9% at 320 ◦C. Recently, Huffman and co-workers
used stacked-cone carbon nanotubes (SC-CNTs) as a support
to prepare Pt catalysts for the dehydrogenation of cycloalkanes
[12,13]. The catalysts exhibited 100% selectivity for the dehy-
drogenation reactions at 240 ◦C. It was reported that Pt and Pd
were more highly dispersed on SC-CNT than on the other sup-
ports, such as granular carbon and γ -Al2O3, thus resulting in
higher catalytic activity. The dehydrogenation rate of decalin
into tetralin was slower than the dehydrogenation of tetralin.
In addition, cis-decalin exhibited a higher conversion rate than
trans-decalin because of its flexible geometric structure. The
regeneration of the deactivated carbon supported catalyst is a
problem and limits its application.
glected when
(riρs)obsL2g(Css)
Φ =
ꢀ 1,
ꢀ
Css
2
s,eq De(C)g(C)dC
C
in which g(C) represents the concentration-dependent part of
the rate equation. The diffusivity of decalin in the reaction mix-
tures, De, is calculated to be 0.27 cm2/s. The calculated values
of Φ for the dehydrogenation of TDC and CDC on 0.1-mm
catalyst pellets are 0.01 and 0.04, indicating negligible intra-
particle diffusional limitation. The operating conditions were
also chosen to avoid external mass and heat transfer limitations.
Thus, intrinsic kinetics were derived.
2.3. Fixed-bed reactor setup
The dehydrogenation of decalin was carried out on sup-
ported Pt catalyst in a fixed-bed reactor operating at at-
mospheric pressure (Fig. 1). The gas feeds (H2, N2, and air
for regeneration of the deactivated catalyst) were controlled
by mass flow controllers. The liquid was fed by a reciprocat-
ing pump. The liquid feed was vaporized in the packed mixing
chamber and mixed with other gas streams before flowing to
the reactor. The reactor was a 1.2-cm-i.d. stainless steel tube
heated by a tubular furnace. The reactor axial temperature pro-
file was monitored by a sliding thermocouple. The reaction
products were analyzed by a HP 5890 online gas chromato-
graph equipped with a thermal conductivity detector (TCD) and
a flame ionization detector (FID). HP-5 capillary columns with
an FID were used to analyze the hydrocarbon components. The
13X packed column connected to a TCD was used to detect H2.
Argon was used as the carrier gas, and the flow rate was main-
tained at 30 mL/min. N2 was fed into the feed stream as an
internal standard to calibrate the hydrogen flow. The exit flow
rate of hydrogen was measured by a bubble meter. For accurate
gas chromatography (GC) analysis, the transfer line from the
reactor exit to the gas chromatograph and the sampling valve
were insulated to keep the reactor effluent in the gas state.
The gravimetric hydrogen content is higher in decalin than
in cyclohexane, and the dehydrogenated product, naphthalene,
is environmentally favorable. These advantages make decalin a
good candidate for a hydrogen carrier. The present study inves-
tigated the dehydrogenation of decalin. Catalysts and operating
conditions were optimized, and a rigorous kinetic model was
derived. This is a valuable tool for scaling-up the process and
guiding its operation.
2. Experimental
2.1. Feed mixtures
Decalin, purchased from Aldrich, consisted of 24% cis-
isomers and 76% trans-isomers. The purity of the H2, Ar, and
N2 amounted to 99.99%.
3. Results
2.2. Catalyst preparation
3.1. Definition of conversions and selectivities
Supported Pt catalysts were used in the dehydrogenation of
cycloalkanes. Three different kinds of high-surface area sup-
ports were used: γ -alumina, silica, and activated carbon. The
catalyst was prepared by adding a certain amount of aqueous
H2PtCl6 solution to the support and impregnating it at 80 ◦C
for 2 h. The resulting Pt/support catalyst was dried in air at
130 ◦C, then calcined at 500 ◦C for 3 h. Sn was added to the
supported Pt catalyst through evaporative impregnation of a cer-
tain amount of nitric solution of tin chloride at 80 ◦C for 2 h,
dried at 130 ◦C, and then calcined at 500 ◦C for 3 h. Before the
reaction, the catalyst was activated first by removing water at
500 ◦C for 2 h, followed by reduction at 500 ◦C with hydrogen.
The catalysts were tested for a particle size <0.1 mm. Accord-
ing to the extension of the Weisz and Prater criterion, based on
the generalized modulus [15], diffusional limitations can be ne-
Conversion of trans-decalin (TDC),
(moles of TDC in) − (moles of TDC out)
XTDC
=
× 100.
× 100.
moles of TDC in
Conversion of cis-decalin (CDC),
(moles of CDC in) − (moles of CDC out)
XCDC
=
moles of CDC in
Conversion of decalin into tetralin (TT),
moles of TT out
XTT
=
× 100.
moles of DC in
Conversion of TDC and CDC into naphthalene (NP),
moles of NP out
XNP
=
× 100.
moles of DC in

B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
231
Fig. 1. Fixed-bed experimental setup for the production of H from decalin.
2
than the reverse reaction. The conversions of both decalin iso-
mers increased with temperature. The selectivity for naphtha-
lene was much higher than that of tetralin. With a temperature
increase from 250 to 350 ◦C, the selectivity for naphthalene in-
creased from 93.6 to 99.7%, whereas, the selectivity for tetralin
decreased from 6.4 to 0.3%. Tetralin is the intermediate product
in decalin dehydrogenation. It can be further dehydrogenated at
higher temperature to additional hydrogen.
3.3. Catalyst stability
The stability of 0.8 wt% Pt–0.3 wt% Sn/γ -alumina cata-
lyst in decalin dehydrogenation was tested in both the absence
and the presence of hydrogen at 340 ◦C and a space-time of
80 kgcat h/kmol. As shown in Fig. 3, the conversion decrease
from the original 98.8 to 95.4% after 40 h, but showed no ap-
parent decrease after 30 h when hydrogen was co-fed.
Fig. 2. Effect of temperature on decalin dehydrogenation (the lines corre-
spond to a visual fit of the experimental data). Operating conditions: 0.8 wt%
Pt/γ -alumina, space time = 60 kg h/kmol, H /cyclohexane = 1.
2
cat
moles of product i formed
Selectivity =
× 100,
3.4. Effect of space-time
moles of DC converted
where i refers to TT or NP selectivity for products.
For a fixed temperature and a H2/decalin molar ratio of 1, the
feed rate of decalin was varied to investigate the effect of the
space-time on the conversion. Fig. 4 shows an example of the
conversions of cis- and trans-decalin and the conversions into
tetralin and naphthalene as a function of space-time at 325 ◦C.
(The points represent the experimental data. The curve is dis-
cussed later.) It can be seen that the conversions of cis- and
trans-decalin, and the conversion into naphthalene, increased
with space-time. The conversion into tetralin was <2.0%. Sim-
ilar experiments were carried out at 345, 300, and 275 ◦C.
3.2. Effect of temperature
The decalin feed consisted of 24% cis-isomers and 76%
trans-isomers. The dehydrogenation was performed at at-
mospheric pressure, 250–350 ◦C, a space-time of 60 gcat h/mol,
and a hydrogen-to-decalin molar ratio of 1. Fig. 2 shows that
the conversion of cis-decalin was much higher than that of
the trans-isomer; for example, the conversions of cis-decalin
and trans-decalin at 300 ◦C were 98.0 and 66.8%, respectively.
Two factors may contribute to this: (1) the cis-isomer was more
active in the dehydrogenation reaction, and (2) isomerization
occurred on the acid sites of the γ -alumina, and the rate of iso-
merization of cis-isomer into trans-isomer was much higher
3.5. Effect of the H2/decalin molar ratio
Whereas the co-feed of hydrogen inhibits catalyst deactiva-
tion, it also may decrease the conversion of the dehydrogenation

232
B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
reaction. Holding the space-time and temperature constant, the
H2/decalin molar ratio was varied from 1 to 7 to check the effect
of H2 on the conversion. Fig. 5 shows the conversions as a func-
tion of ratio at 325 ◦C and space-time of 60 gcat h/mol. (Points
represent the experimental data. The curve is discussed later.)
The conversions of cis- and trans-decalin and naphthalene de-
creased with an increasing H2/decalin molar ratio, whereas the
conversion to tetralin increased with an increasing H2/decalin
molar ratio. Tetralin is the intermediate product in decalin de-
hydrogenation. The co-feed of H2 may inhibit the further dehy-
drogenation of tetralin more than its conversion from decalin,
and thus increase the conversion into the intermediate product,
tetralin.
◦
Fig. 3. Stability of the catalyst in decalin dehydrogenation at 340 C and space
time = 80 kg h/kmol (the lines correspond to a visual fit of the experimental
cat
data).
◦
Fig. 4. Comparison of experimental (Q) and calculated (—) conversions as a function of space time at 325 C for retained model, case I-2).
◦
Fig. 5. Comparison of experimental (Q) and calculated (—) conversions as a function of H /decalin molar ratio at 325 C and space time of 40 kg h/kmol for
cat
2
case I-2).

B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
233
Fig. 6. Values of the equilibrium constants of the reactions involved in the dehydrogenation of decalin.
4. Kinetic modeling
4.1. Thermodynamic aspects
Scheme 1. Reaction scheme for the dehydrogenation of decalin.
The equilibrium constant of each possible reaction in the
dehydrogenation of decalin is shown in Fig. 6. Four possible
reactions are involved in the dehydrogenation of decalin. Both
cis- and trans-decalin can be dehydrogenated to form the in-
termediate product tetralin that can be further dehydrogenated
to form the final product, naphthalene. The equilibrium con-
stants at 325 ◦C for the isomerization of cis-decalin to trans-
decalin and the reverse reaction were 7.40 and 0.135, respec-
tively, meaning that the isomerization of cis- into trans- will
be favored over the reverse reaction. The equilibrium constants
at 275 ◦C for the dehydrogenation reactions of cis-decalin into
tetralin, trans-decalin into tetralin, and tetralin into naphthalene
were 77.08, 8.23, and 2.66, respectively. This means that the
reverse reaction could not be neglected. Furthermore, the equi-
librium constants of all of the dehydrogenation reactions in-
creased with temperature, whereas the equilibrium constant of
cis- into trans-isomerization decreased with temperature. Con-
sequently, high temperatures will favor dehydrogenation, and
low temperature will favor the isomerization of cis-decalin to
trans-decalin.
tween the two decalin isomers occurs over the acid active site.
All of these reactions are reversible.
4.3. Rate equations
When the surface reactions of the adsorbed decalins, tetralin,
and naphthalene are the rate-determining steps (RDSs), the de-
hydrogenation rates on the Pt sites can be formulated for case I,
in which three hydrogen molecules are removed simultaneously
in the RDS. Rate equations can be further discriminated be-
tween molecular (case I-1) and dissociative desorption of hy-
drogen in the RDS (case I-2).
Case I-1 (Molecular desorption of hydrogen in the RDS):
DC + σ ꢀ DCσ,
DCσ + 3σ → TTσ + 3H2σ rds,
TTσ ꢀ TT + σ,
4.2. Reaction scheme
3H2σ ꢀ 3H2 + 3σ.
Two kinds of active sites—metal sites and acid sites—are in-
volved in the dehydrogenation of decalin over Pt–Sn/γ -Al2O3.
A possible reaction scheme for the dehydrogenation of decalin
based on the foregoing thermodynamic calculations is shown
in Scheme 1. Both cis-decalin and trans-decalin can be de-
hydrogenated to form tetralin and H2. Tetralin can be further
dehydrogenated to form the final product, naphthalene, thus
generating more H2. At the same time, the isomerization be-
Case I-2 (Dissociative desorption of hydrogen in the RDS):
DC + σ ꢀ DCσ,
DCσ + 6σ → TTσ + 6Hσ rds,
TTσ ꢀ TT + σ,
6Hσ ꢀ 3H2 + 6σ.

234
B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
For molecular desorption of hydrogen, the dehydrogenation
jected to further dehydrogenation to remove the remaining hy-
rates on the Pt active sites can be written as
drogen. As in case I, the dehydrogenation rate on Pt sites can be
considered to occur with molecular or dissociative desorption
of hydrogen in the RDS. For molecular desorption of hydrogen
(case II-1), the dehydrogenation rate on Pt active sites can be
written as
r1 = ksr1KTDCPTDC/Δ4,
r2 = ksr2KCDCPCDC/Δ4,
r3 = ksr3KTTPTT/Δ3.
The reverse (hydrogenation) rates on the Pt sites can be writ-
ten as
(1)
r1 = ksr1KTDCPTDC/Δ2,
r2 = ksr2KCDCPCDC/Δ2,
r3 = ksr3KTTPTT/Δ2,
(4)
r1ꢁ = ksꢁr1KTTKH PTTP3 /Δ4,
2
H2
r2ꢁ = ksꢁr2KTTKH PTTP3 /Δ4,
and the reverse (hydrogenation) rates on Pt sites can be written
as
2
H2
r3ꢁ = ksꢁr3KNPKH PNPP2 /Δ3.
(2)
2
H2
r1ꢁ = ksꢁr1KTTKH PTTP3 /Δ2,
2
H2
The Δ appearing in the denominator of the above reaction
rates is
r2ꢁ = ksꢁr2KTT
K
PTTP3 /Δ2,
H2
H2
r3ꢁ = ksꢁr3KNPKH PNPP2 /Δ2.
(5)
2
H2
1 + KCDCPCDC + KTDCPTDC + KTTPTT + KH PH
2
2
The Δ’s appearing in the denominator in the foregoing reaction
+ KNPPNP
.
(3)
rates are
As the numbers of active sites involved in the RDSs of the
dehydrogenations of TDC, CDC, and TT in the case of mole-
cular desorption of hydrogen are 4, 4, and 3, the exponents
appearing in the denominator of rate equations r1, r2, and r3
are 4, 4, and 3, respectively. Theꢁsame holds true for the reverse
reactions with rates r1ꢁ , r2ꢁ , and r3.
Δ = 1 + KCDCPCDC + KTDCPTDC + KTTPTT + KH PH
2
2
+ KNPPNP + KTTPTTK2 PH2 /KDC1
H2
2
+ KNPPNPKH PH /KTT1
(6)
2
2
for removal of the remaining two hydrogens simultaneously,
and
When hydrogen is dissociatively desorbed in the RDS on
Pt active sites, the dehydrogenation and reverse hydrogenation
rate equations are similar. But the hydrogen term in the denom-
Δ = 1 + KCDCPCDC + KTDCPTDC + KTTPTT + KH PH
2
2
+ KNPPNP + KTTPTTK2 P2 /(KDC1KDC2
)
inator becomes (K P )
H2 H2
1/2. In addition, because the numbers
H2 H2
of active sites involved in the RDSs of the dehydrogenation of
TDC, CDC, and TT in the dissociative desorption of hydro-
gen are 7, 7, and 5, respectively, the exponents appearing in the
denominator of rate equations r1, r2, and r3 are 7, 7, and 5, re-
spectively. The same holds for the reverse reactions with rates
r1ꢁ , r2ꢁ , and r4ꢁ .
+ KTTPTTKH PH /KDC2 + KNPPNPKH PH /KTT1 (7)
2
2
2
2
for removal of the remaining two hydrogens in two steps. But,
given the selection of the RDSs, the partially dehydrogenated
species are present in very low concentrations, so that they can
be neglected in the denominator. The denominator then can be
written as
Case II-1 (Molecular desorption of hydrogen in the RDS):
1 + KCDCPCDC + KTDCPTDC + KTTPTT + KH PH
2
2
DC + σ ꢀ DCσ,
+ KNPPNP
.
(8)
DCσ → DC1σ + H2σ rds,
H2σ ꢀ H2 + σ,
Because the numbers of active sites involved in the RDSs of
the dehydrogenations of TDC, CDC, and TT are 2, 2 and 2, the
exponents appearing in the denominator of rate equations r1,
r2, and r3 should all be 2 for the reverse reactions r1ꢁ , r2ꢁ , and r4ꢁ
as well.
DC1σ + 2σ ꢀ TTσ + 2H2σ,
TTσ ꢀ TT + σ,
2H2σ ꢀ 2H2 + 2σ.
Assuming dissociative desorption of hydrogen in the RDS
on Pt active sites, as in case I, the hydrogen term in the denom-
Case I-2 (Dissociative desorption of hydrogen in the RDS):
inator becomes (KH PH )
1/2. Moreover, the exponents appear-
2
2
DC + σ ꢀ DCσ,
ing in the denominators of the foregoing rate equations should
all be 3, corresponding to three active sites involved in the RDS.
The acid sites of γ -alumina catalyze the isomerization of cis-
and trans-decalin isomers. The rate of the formation of trans-
isomer from cis-decalin is
DCσ + 2σ → DC1σ + 2Hσ rds,
2H2σ ꢀ H2 + 2σ,
DC1σ + 4σ ꢀ TTσ + 4Hσ,
TTσ ꢀ TT + σ,
r4 = ksr4KCꢁ DCPCDC/Ω.
The rate of the reverse reaction is
(9)
4Hσ ꢀ 2H2 + 4σ.
In case II, the removal of the first hydrogen is assumed to
be the RDS. The partially dehydrogenated species are then sub-
r4ꢁ = ksꢁr4KTꢁ DCPTDC/Ω.
(10)

B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
235
The denominator Ω in the foregoing rate equations is
Table 1
Residual sum of squares (RRS) along with the calculated F values for different
models
1 + KTꢁ DCPTDC + KCDCꢁ PCDC
.
(11)
Model
Residual sum of squares
F values
In Scheme 1, the equations defining the net rate of formation
for the various components are
Case 1-1
Case 1-2
Case II-1
Case II-2
0.095
0.085
0.46
2312
2570
444
RTDC = r1 − r1ꢁ − r4 + r4ꢁ ,
0.16
1394
RCDC = r2 − r2ꢁ + r4 − r4ꢁ ,
RTT = r1 − r1ꢁ + r2 − r2ꢁ + r3ꢁ − r3,
requirement for all the parameters to be positive and statisti-
cally significant, and on the residual sum of squares (RRS) as a
test for the fit of the data.
RNP = r3 − r3ꢁ .
(12)
The set of steady-state continuity equations for the reacting
The RRS along with the calculated F values (the ratio of
the regression sum of squares to the residue sum of squares)
for the rival models are listed in Table 1. Apparently, the two
models of case I based on simultaneous removal of three hy-
drogens fit the experimental data better than those of case II. In
case I, there is a slight improvement in the fit of the data for
the model with dissociative desorption of hydrogen in the RDS
with respect to that with molecular desorption in the RDS. Stu-
dent’s t-test shows that all of the parameters in both models of
case I are statistically significant. The discrimination between
the two models of case I also is based on studies showing con-
vincingly that chemisorption of hydrogen is more likely to be
a dissociative process [16–18]. Finally, the model of case I-2,
based on dissociative desorption of hydrogen in the RDS on Pt
sites and on surface reaction as the RDS with the simultaneous
removal of three hydrogen molecules, was retained. The excel-
lent fit is also illustrated by the parity plots of Fig. 7, including
all of the experiments performed over the entire temperature
range.
components in a plug-flow reactor can be written as
dXi
dW/Fi0
= Ri, i = 1, ... , 4,
(13)
where X1 and X2 represent the conversions of TDC and CDC,
and X3 and X4 their conversion into TT and NP. Fi0 represents
the feed rate of TDC when i = 1, of CDC when i = 2, and the
total feed rate of TDC + CDC when i = 3 and 4.
4.4. Parameter estimation
The integral method was used for the kinetic analysis [15].
The foregoing set of differential equations was numerically in-
tegrated by a fourth-order Runge–Kutta method to yield the
reactor effluent composition. Values for the model parameters
were estimated by means of regression methods. When the ex-
perimental errors were normally distributed with mean 0, the
parameters were estimated by minimization of the following
multiresponse objective function:
Table 2 lists the 22 parameter estimates generated by the For-
tran program using the Levenberg–Marquardt algorithm for this
retained model.
According to Everett [19], the standard entropy change for
Langmuir adsorption is given by
m
m
n
ꢁ ꢁ
ꢁ
S =
Wjl
(yij − yˆij )(yil − yˆil),
(14)
j=1 l=1
i=1
where m is the number of responses, n is the number of ex-
periments, and the wjl’s are elements of the inverse of the
covariance matrix of the experimental errors on response y.
These can be estimated from replicated experiments. Because
the equations are nonlinear in the parameters, the parameter
estimates were obtained by minimizing the objective function
by Marquardt’s algorithm for multiple responses. The forego-
ing model has 22 parameters. The parameter estimation was
performed simultaneously on all of the data obtained at all
temperatures by directly substituting the temperature depen-
dence of the parameters into the corresponding rate equa-
tions:
ꢀSa0 = Sa0 − Sg0,
(17)
where Sg0 is the entropy in the gas phase, taken at unit pres-
sure, and Sa0 is the entropy in the adsorbed state on the catalyst
surface. Mears and Boudart [20] and Trimpont et al. [21] for-
mulated two strict rules for Langmuir adsorption that must be
satisfied by ꢀSa0,
−ꢀSa0 > 0
and
(18)
−ꢀSa0 < Sg0,
(19)
for the rate coefficient,
as well as two relations that can be used as guidelines to assess
ki = Ai exp(−Ei/RT );
for the adsorption constant,
Ki = Ai exp(ꢀHi/RT ).
Models based on adsorption or desorption as RDSs were eas-
ily discarded for apparent lack of fit. The discrimination among
rival models with surface reactions as RDSs was based on the
(15)
(16)
the meaningfulness of the values obtained for ꢀSa0 and ꢀHa0,
−ꢀSa0 > 42
(20)
(21)
and
−ꢀSa0 ꢁ 51 − 1.4ꢀHa0.

236
B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
Fig. 7. Parity plots for the various conversions of decalin.
Table 2
Estimates of frequency factors A, activation energies E and enthalpies of adsorption ꢀH for the model of case I-2 using the Levenberg–Marquardt algorithm
Name of
parameter
95%-confidence limits
Estimate
Lower
Upper
t-value
A
1.54906D+00
7.89457D+00
9.33959D+01
2.26323D+00
3.31108D+00
2.21726D+02
4.08540D+01
3.63431D+05
8.27101D+04
3.35724D+03
1.24695D+01
1.28343D+04
4.41280D+03
3.88825D+03
1.07247D+04
6.54869D+03
1.42062D+04
6.89845D+03
2.34547D+04
9.05243D+03
7.06251D+03
2.84393D+04
1.36662D+00
6.72133D+00
8.33666D+01
2.07828D+00
3.03161D+00
1.96869D+02
3.43210D+01
3.30382D+05
7.43813D+04
2.85790D+03
1.04767D+01
1.22783D+04
4.04248D+03
3.54760D+03
1.01217D+04
6.02799D+03
1.27176D+04
6.17407D+03
2.27024D+04
8.17648D+03
6.00993D+03
2.28637D+04
1.73150D+00
9.06782D+00
1.03425D+02
2.44819D+00
3.59054D+00
2.46582D+02
4.73870D+01
3.96480D+05
9.10389D+04
3.85659D+03
1.44624D+01
1.33903D+04
4.78313D+03
4.22890D+03
1.13277D+04
7.06938D+03
1.56947D+04
7.62283D+03
2.42070D+04
9.92838D+03
8.11509D+03
3.40148D+04
1.69813D+01
1.34577D+01
1.86246D+01
2.44732D+01
2.36957D+01
1.78404D+01
1.25070D+01
2.19936D+01
1.98612D+01
1.34466D+01
1.25141D+01
4.61677D+01
2.38323D+01
2.28285D+01
3.55708D+01
2.51536D+01
1.90872D+01
1.90466D+01
6.23572D+01
2.Q6689D+01
1.34194D+01
1.02014D+01
TDC
A
CDC
A
TT
A
MP
A
H
A
A
A
A
A
A
ꢁ
ꢁ
TDC
CDC
TDC_TT
CDC_TT
TT_HP
CDC_TDC
−ꢀH
−ꢀH
−ꢀH
−ꢀH
−ꢀH
−ꢀH
−ꢀH
E
TDC
CDC
TT
HP
H
ꢁ
ꢁ
TDC
CDC
TDC_TT
CDC_TT
TT_HP
E
E
E
CDC_TDC
Note.
ꢂ
ꢂ
ꢂ
m
m
n
W
yˆ yˆ /p
jl
ij il
Regression sum of squares
Residual sum of squares
j=1
l=1
i=1
ꢂ
ꢂ
ꢂ
F =
=
= 2570.
m
j=1
m
l=1
n
W
(y − yˆ )(y − yˆ )/(mn − p)
jl
ij
ij
il
il
i=1

B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
237
Table 3
pare the experimental conversions versus space-time and exper-
imental conversions versus the H2/decalin molar ratio at 325 ◦C
with the values calculated using the retained model.
Standard adsorption entropies for the model of case 1-2
0
−ꢀS (J/(mol K))
a
0
−ꢀS
aTDC
548
539
482
460
121
422
437
5. Conclusion
0
−ꢀS
aCDC
0
−ꢀS
aTT
The work reported here illustrates that decalin can be a se-
rious candidate for use as hydrogen carrier. Its dehydrogena-
tion into naphthalene selectively yields pure hydrogen, and the
catalyst deactivation is slow. A rigorous kinetic model was de-
rived with the purpose of providing a tool for the design and
optimization of the dehydrogenation/hydrogenation process. It
accounted for a relatively complex reaction network involving
isomerization of the decalin isomers on acid sites, followed
by dehydrogenation into naphthalene on Pt active sites and
proceeding over tetralin. All of the reactions were shown to
be reversible. The rate equations were written in terms of the
Hougen-Watson approach, explicitly accounting for the adsorp-
tion of the various components of the reaction mixture. The
model led to a good fit of the experimental data, with all of
the parameters being statistically significant and satisfying the
physicochemical constraints.
0
−ꢀS
aNP
0
−ꢀS
aH
0
−ꢀS
ꢁ
aTDC
0
−ꢀS
ꢁ
aCDC
Acknowledgments
Financial support was provided by the Department of En-
ergy, Office of Basic Energy Sciences, Division of Chemi-
cal Sciences/Geosciences/Biosciences, Catalysis and Chemical
Transformations Program, and the Robert A. Welch Founda-
tion.
Fig. 8. Arrhenius plot of rate coefficients for the model of case I-2.
Appendix A. List of symbols
Primes on the rates refer to reverse reactions
TDC
CDC
TT
trans-decalin
cis-decalin
tetralin
NP
De
Ai
naphthalene
diffusivity, cm2/s
frequency factor for elementary reaction step i,
kmol/(kgcat h)
AC
frequency factor for formation of the deactivating
agent, kmol/(kgcat bar4 h)
molar concentration of component i, kmol/mf3
Ci
CC
dt
deactivating agent content of the catalyst, kgC /kgcat
C
internal tube diameter, mr
particle diameter, mp
Fig. 9. Van’t Hoff plot of adsorption coefficients for the model of case I-2.
dp
W/F0DC space time in terms of decalin feed, kgcat h/kmol
Ei
activation energy for elementary reaction step i,
kJ/kmol
molar feed rate of reactants decalin, kmol/h
molar feed rate of reactant i, kmol/h
total molar feed rate, kmol/h
All of the adsorption enthalpies reported in Table 2 are neg-
ative, as expected. The standard entropies for the model of
case I-2, calculated based on (17), are listed in Table 3. These
meet all four requirements (18)–(21).
Figs. 8 and 9 show Arrhenius and van’t Hoff plots of the rate
and adsorption coefficients in the retained model. The rate co-
efficients increased, but the adsorption coefficients decreased,
with increasing temperature. As an example, Figs. 4 and 5 com-
FD0C
Fi
Ft
−ꢀH heat of reaction, J/mol
−ꢀSa0 standard adsorption entropy, J/(mol K)
Sa0
entropy in the gas phase, J/(mol K)

238
B. Wang et al. / Journal of Catalysis 253 (2008) 229–238
Sg0
ki
entropy in the adsorbed state, J/(mol K)
reaction rate coefficient, kmol/(kgcat h)
adsorption equilibrium constant, bar−1
volume to surface area of the pellet, mp
rate of elementary reaction step i, kmol/(kgcat h)
net rate of formation for the component i, kmol/(kgcat h)
temperature, K or ◦C
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T
Tm
R
mean temperature, K
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X
TDC, XCDC conversion of TDC and CDC, respectively
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