Product distribution analysis of the hydrogen peroxide direct synthesis in an isothermal batch reactor

Article abstract of DOI:10.1016/j.cattod.2014.03.020

The direct synthesis of hydrogen peroxide from molecular hydrogen and oxygen on a supported palladium catalyst was studied at 258-297 K in a laboratory-scale batch reactor. The catalyst was in the form of finely dispersed slurry in methanol/CO₂ to suppress the internal and external mass transfer resistances. Experiments carried out under kinetic control revealed that hydrogen peroxide was successfully formed on the catalyst surface, but it was hydrogenated as the reaction time was prolonged. The mass balances of the components were considered in detail and a reaction mechanism was proposed, based on the competitive adsorption of hydrogen and oxygen on the palladium surface. The surface reactions leading to the formation of hydrogen peroxide and water were assumed to be rate determining, and the rate equations describing direct synthesis, water formation as well as peroxide hydrogenation and decomposition were derived. A special kind of product distribution analysis was used to interpret the kinetic phenomena and to make the estimation of the kinetic parameters very robust. The parameters were estimated by nonlinear regression analysis and the model gave a good fit to the experimental data. The usefulness of the product distribution analysis was clearly demonstrated.

Full text of DOI:10.1016/j.cattod.2014.03.020

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Contents lists available at ScienceDirect
Catalysis Today
journal homepage: www.elsevier.com/locate/cattod
Product distribution analysis of the hydrogen peroxide direct
synthesis in an isothermal batch reactor
Tapio Salmia,∗, Nicola Gemoa,b,∗∗, Pierdomenico Biasia, Juan Garcia Sernac
a Åbo Akademi, Department of Chemical Engineering, FI-20500 Turku/Åbo, Finland
b Università di Padova, Dipartimento di Ingegneria Industriale, IT-35131 Padova, Italy
c Universidad de Valladolid, Chemical Engineering and Environmental Technology Department, EII-Mergelina, ES-47014 Valladolid, Spain
a r t i c l e i n f o
a b s t r a c t
Article history:
The direct synthesis of hydrogen peroxide from molecular hydrogen and oxygen on a supported palla-
dium catalyst was studied at 258–297 K in a laboratory-scale batch reactor. The catalyst was in the form
of finely dispersed slurry in methanol/CO2 to suppress the internal and external mass transfer resis-
tances. Experiments carried out under kinetic control revealed that hydrogen peroxide was successfully
formed on the catalyst surface, but it was hydrogenated as the reaction time was prolonged. The mass
balances of the components were considered in detail and a reaction mechanism was proposed, based
on the competitive adsorption of hydrogen and oxygen on the palladium surface. The surface reactions
leading to the formation of hydrogen peroxide and water were assumed to be rate determining, and
the rate equations describing direct synthesis, water formation as well as peroxide hydrogenation and
decomposition were derived. A special kind of product distribution analysis was used to interpret the
kinetic phenomena and to make the estimation of the kinetic parameters very robust. The parameters
were estimated by nonlinear regression analysis and the model gave a good fit to the experimental data.
The usefulness of the product distribution analysis was clearly demonstrated.
Received 12 November 2013
Received in revised form 10 March 2014
Accepted 16 March 2014
Available online xxx
Keywords:
Hydrogen peroxide
Direct synthesis
Palladium catalyst
Kinetics
Product distribution analysis
Batch reactor modelling
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
It has been a long time the dream of chemists and chemical
engineers to develop a new process, based on the direct synthe-
The currently applied industrial process for the production of
hydrogen peroxide, the anthraquinone process, is based on succes-
sive hydrogenation and oxidation of quinonic components. Despite
the high yield of hydrogen peroxide per cycle, the process major
disadvantages are the side reactions, requiring regeneration of both
the working solution and the hydrogenation catalyst, and the sev-
eral steps necessary for the purification and concentration of the
peroxide [1]. For both these reasons, the cost of the hydrogen per-
oxide is nowadays relatively high, limiting the industrial large scale
use of H2O2. Moreover, the current process has high capital and
operation costs, and is suitable for real large-scale operation only.
In future, the interest towards on-site production of chemicals in a
smaller scale is predicted to increase. This would require a simpler
process for the synthesis of hydrogen peroxide.
sis of hydrogen peroxide from its primary molecular constituents,
molecular hydrogen and oxygen. The pioneering work was carried
out by Pospelova et al. [2] in early 1960s. A lot of catalyst devel-
opment work has taken place during the recent decade, the most
promising heterogeneous catalysts for the direct synthesis being
Pd and Pd–Au catalysts [3].
Catalyst development alone does not bring us to a success in the
development of a hydrogen peroxide process based on the direct
synthesis. Early attempts to apply direct synthesis failed because of
low reaction rates and selectivities – the catalyst enhances water
formation and hydrogen peroxide decomposition, too. Thus, the
study of direct synthesis should also be combined to studies of
the optimal reaction conditions. For instance, very recently our
research group has carried out an optimization study to maximize
H2O2 productivity in a trickle bed reactor [4]. The introduction of
methanol as solvent and the presence of carbon dioxide in the reac-
tion environment have implied real breakthroughs in the process
development. In this way, the solubilities of the reacting gases can
be essentially improved and the reaction rate is enhanced.
In spite of the huge interest on the direct synthesis, only
few detailed kinetic studies are available in open literature [5,6].
∗
Corresponding author. Tel.: +358 2 2154427; fax: +358 2 2154479.
Corresponding author at: Åbo Akademi, Department of Chemical Engineering,
∗∗
FI-20500 Turku/Åbo, Finland. Tel.: +358 2 2154431.
E-mail addresses: Tapio.Salmi@abo.fi (T. Salmi), Nicola.Gemo@abo.fi,
nicola.gemo@gmail.com (N. Gemo).
http://dx.doi.org/10.1016/j.cattod.2014.03.020
0920-5861/© 2014 Elsevier B.V. All rights reserved.
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batch reactor, Catal. Today (2014), http://dx.doi.org/10.1016/j.cattod.2014.03.020

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hydrogen was fed as a limiting reactant (total pressure in the
Notation
range 14–20 bar, depending on temperature). The stirring rate was
adjusted to 1000 rpm to ensure the operation in the kinetic regime.
Samples were withdrawn from the liquid phase; the water and
hydrogen peroxide concentrations in the samples were determined
by Karl Fischer and iodometric titrations, respectively. Isothermal
experiments were carried out at 258, 268, 273, 283 and 297 K. Note
that, though the presence of CO2 can theoretically lead to an acidic
environment, it is assumed acid-free in the actual experimental
condition, where methanol was used as solvent and the measured
concentration of H2O was always very low. The details of the exper-
imental equipment and procedures are described in the previous
publications of our group [9,10].
A
interfacial area
frequency factor
concentration
concentration of a surface species
denominator in rate expression
activation energy
equilibrium constant
reaction rate constant
Aꢀ
c
c*
D
Ea
K
k
kꢀ
merged rate constant, product of rate constant,
adsorption equilibrium constant and total concen-
tration of active sites
N
n
flux
3. Reaction mechanism and rate equations
amount of substance
number of experimental data (Eqs. (44) and (48))
gas constant
reaction rate
component (i) generation rate
temperature
nexp
R
The following overall reactions, confirmed by Biasi et al. [11] and
Gemo et al. [8], are considered in connection of hydrogen perox-
ide formation and decomposition: the reactions between hydrogen
and oxygen yielding hydrogen peroxide and water as well as spon-
taneous decomposition and hydrogenation of hydrogen peroxide.
The overall reactions are summarized below:
r
ri
T
t
time
volume
V
˛
ˇ
ꢀ
gas-to-liquid volume ratio
parameter in product distribution analysis
stoichiometric number
parameter in product distribution analysis
H2 + O2 = H2O2 (DS)
H2 + (1/2)O2 = H2O (WF)
H2O2 + H2 = 2H2O (H)
H2O2 = H2O + (1/2)O2 (DE)
ω
Subscripts and superscripts
G
i, j
L
gas
component indices
liquid
P
TOT
0
reaction route
total amount
initial property
All these reactions are highly exothermic and thermodynamically
favourable, as discussed for instance by Biasi et al. [12] and Gemo
et al. [8]. The experiments of Gemo et al. [8], carried out in a
laboratory-scale batch reactor, revealed that the hydrogenation
reaction (H) clearly dominates over the decomposition reaction
(DE) in the conditions studied.
The rate equations for reactions (DS to DE) should in princi-
ple be based on the knowledge of the true reaction mechanism: if
the mechanism is precisely known, the appropriate rate equations
can be derived based on the elementary steps on the solid catalyst
surface.
Abbreviations
H
O
P
hydrogen
oxygen
hydrogen peroxide
water
W
Deguchi et al. [7] were the only one taking into account the
adsorption of the promoters in the kinetic study. Therefore, we
constructed a special batch reactor system to determine the very
precise kinetics of hydrogen peroxide synthesis and decomposi-
tion. The reaction rates and product distribution were measured at
different temperatures and partial pressures of hydrogen and oxy-
gen to reveal the kinetic phenomena [8]. The goal of this work is to
improve our previous kinetic analysis [8] and obtain a more rapid
and reliable estimation of the kinetic parameters, neglecting mass
transfer limitations and negligible reactions. The time dependence
of the concentrations was also eliminated with the aid of product
distribution analysis. In particular, the product distribution analy-
sis was applied in order to improve the reliability of the parameter
estimation in this multicomponent system of composite reactions.
Several surface mechanisms on palladium can give the
overall process described by equations (DS to DE). Voloshin
et al. [5] screened some mechanisms to describe kinetic data
obtained from microstructured reactors and concluded that a
Langmuir–Hinshelwood-type mechanism with the surface reac-
tion steps as rate determining ones gave the best agreement with
experimental data. Some mechanistic studies have given informa-
tion about the reaction mechanism. For instance, Dissanyake and
Lunsford [13] proposed that the O O bond does not dissociate
during the H2O2 synthesis process and Sivadinarayana et al. [14]
confirmed the species HO2 on a gold catalyst surface. However,
it is clear that water formation requires the rupture of the O
O
bond on the catalyst surface. Oxygen is known to adsorb both dis-
sociatively and non-dissociatively on Pd surfaces. Concerning the
state of the active site on the Pd surface, no general agreement
exists. Both Pd0 and PdO have been proposed as active oxidations
states for the direct synthesis [15–18]. Very many support mate-
rials, such as carbon, alumina, silica, ceria and titania have been
screened, and the catalyst performances have been compared [11].
In a recent study, Rossi et al. [19] have shown that Pd single crystals
exhibit a considerable activity in the direct synthesis of H2O2. The
recent development is summarized, for instance, by Samanta [20]
and Centi et al. [3].
2. Experimental
The batch reactor was a 600 ml unbaffled autoclave (Büchi)
equipped with a self-sucking six-blade impeller. Typically, 0.15 of
a commercial 5 wt% Pd/C catalyst was loaded in the reactor ves-
sel. Methanol expanded with carbon dioxide was used as solvent
in all experiments. Carbon dioxide and oxygen were introduced
to the vessel, after which 400 ml of methanol was injected and
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Table 2
3
Table 1
Reaction steps, reaction routes and stoichiometric numbers.
Simplified reaction mechanism.
Routes (DS to DE)
Step #
H2 + 2* = 2H*
O2 + * = O2*
I
II
III
Step #
ꢀDS
ꢀWF
ꢀH
ꢀDE
H2 + 2* = 2H*
O2 + * = O2*
I
II
1
1
0
1
1
1
0
0
0
0
0
1
0
1/2
0
0
0
1
1
1
1
0
0
0
0
0
0
O
2 + 2* = 2O*
O2* + 2H* = HOOH* + 2*
HOOH* = H2O2 + *
O* + 2H* = HOH* + 2*
HOH* = H2O + *
HOOH* + 2H* =2HOH* + *
HOOH* + * = HOH* + O*
IV and V
VI
VII and VIII (combined step)
IX
VIII and XI (combined step)
X
O
2 + 2* = 2O*
III
IV
V
VI
VII
VIII
IX
X
−1/2
O2 * + H* = OOH* + *
OOH* + H* = HOOH* + *
HOOH* = H2O2 + *
O* + H* = OH* + *
OH* + H* = HOH* + *
HOH* = H2O + *
0
0
−1
−1
0
0
1
2
0
1
0
1
1
0
HOOH* + * = HOH* + O*
HOOH* + H* = OH* + HOH*
0
0
steps of the process. Nonetheless, the quasi-equilibrium assump-
tion has already proven to give reliable results using the same Pd
catalyst [8]. An investigation on the adsorption/desorption steps
is certainly desirable, and our research group is at the moment
investigating this possibility. However, this investigation goes well
beyond the scope of this work, mainly focused on a rapid and reli-
able estimation of the kinetic constants. Once a more accurate
reaction mechanism has been proven, the same technique pre-
sented in this work could be used to estimate the new reaction
parameters. The rate-limiting steps are assumed to be irreversible,
because the equilibria of the overall reactions (DS to DE) are
strongly shifted to the side of the products.
XI
Some essential features can, however, be extracted from the pre-
vious studies. Hydrogen and oxygen are known to adsorb on Pd
surfaces. Oxygen co-exists on Pd surfaces in molecularly adsorbed
and atomic forms; the first one might being active in the direct syn-
thesis and second one in the water formation. We cannot exclude
that the uppermost atomic layers of the solid catalyst surface
change during the reaction, since oxygen is typically present in
excess compared to hydrogen in the reaction system. This could
be confirmed by XPS analysis of fresh and used Pd catalysts.
Still, we are in the situation that a water-proof evidence on
the true mechanism on the catalyst surface does not exist, but the
derivation of plausible rate equations has to be based on reasonable
hypotheses about the adsorption, surface reaction and desorp-
tion processes. Several basic assumptions are introduced here to
describe the rate equations for the overall reactions (DS) to (DE) in
as simple as possible manner. Hydrogen is assumed to adsorb disso-
ciatively on the metal surface, while oxygen co-exists in molecular
and dissociated form on the surface. Surface hydroxyl groups are
formed and they play a key role in the formation of both hydro-
gen peroxide and water; hydrogen peroxide and water adsorb on
the metal surface. The decomposition of hydrogen peroxide in the
absence of the catalyst was neglected, since it did not play any
role under the current experimental conditions. Based on these
assumptions, the reaction mechanism – the adsorption, desorption
and surface reaction steps along with the stoichiometric numbers
(ꢀ) – are summarized in Table 1. By combining each reaction step
with the corresponding stoichiometric number along the reaction
routes, the four overall reactions are obtained (DS to DE).
The rates of the rate-limiting steps can now be written as
r1 = k1cO c2
(step IV–V)
(1)
(2)
(3)
(4)
∗
2
H∗
r2 = k2cO∗cH2∗ (steps VII–VIII)
r3 = k3cHOOH∗cH2∗ (steps VIII–IX)
r4 = k4cHOOH∗
c
(step X)
∗
The further development of the equations is a standard procedure.
Application of the quasi-equilibrium hypothesis for the adsorption
and desorption steps yields
c
= K c c j = O2, H2O, H2O2
(5)
∗
∗j
j j
for non-dissociative adsorption steps, and
(6)
c
= (Kkck)1/2
c
k = O, H
∗
∗k
dissociative adsorption steps. The total concentration of surface
species is
cTOT = c + cH∗ + cO∗ + cO ∗ + cHOH∗ + cHOOH∗
(7)
∗
2
The addition of the reaction steps gives the overall reactions
described above (DS to DE).
After inserting the expressions (5) and (6) in Eq. (7) and solving the
concentration of vacant sites (c*), we obtain
The table illustrates the complexity of the reaction mechanism:
11 steps are needed in total to explain the processes on the catalyst
surface. Note that in principle also other steps are possible to give
the same intermediate. However, though not explicitly given, they
can be obtained by combinations of the reactions in Table 1. For
instance, the breaking of the O O bond in the OOH* intermediate
is obtained by combination of step V and X: OOH* + H* = HOOH* + *,
HOOH* + * = HOH* + O*. The complete mechanism is difficult to
apply in practice, because it comprises so many adsorption and
kinetic parameters, which cannot be determined separately. There-
fore, a further step is taken and some of the reaction steps are
merged to obtain a simplified mechanism, which is displayed in
Table 2. Specifically, the hydrogenation steps were assumed to be
very fast, because they are known to be very favourable over het-
erogeneous Pd catalysts. Hence, they were assumed to occur in a
single step.
−1
c
∗
1/2
1/2
= (1 + (KHcH
)
+ (KOcO
)
+ KO cO + KH O cH + KH 2 cH
)
O
2 2
= D−1
O
O
2
2
2
2
2
2
cTOT
(8)
Eq. (8) is inserted into Eqs. (5) and (6) which are inserted in rate
equations (1)-(4). The final forms of the rate equations become
k1ꢀ cH cO
2
2
r1
=
(9)
D3
k2ꢀ cH cO
1/2
2
2
r2
r3
r4
=
=
=
(10)
(11)
(12)
D3
kꢀ cH cH
O
3
2
2
2
D3
k4ꢀ cH
O
2
2
The adsorption and desorption steps are assumed to be rapid
enough to reach quasi-equilibria, while the surface reaction steps
are presumed to be slow steps, which limit the rates. It is in princi-
ple possible that the adsorption and/or desorption are the limiting
D2
The merged rate parameters (kꢀ) are explained in Notation. It should
be noticed that slightly different forms of the rate equations are
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obtained, depending on the form of the adsorption/desorption
steps. However, the only difference would be the definition of the
parameter D (Eq. (8)) and its power in the rate equations (9)–(12),
making the analytical procedure very flexible towards any varia-
tion in the reaction network. For instance, if molecularly adsorbed
hydrogen is presumed to active in the reaction mechanism, the
hydrogen adsorption step is written in the form H2 + * = H2* and,
consequently, the surface reactions for direct synthesis and water
formation become H2* + O2* = HOOH* + * and H2* + O* = H2O* + *.
Following a similar procedure as described above, it can be eas-
ily shown that the only difference in the rate equations (9)–(11) is
the power of D (becoming 2 instead of 3), whereas the rate equation
(12) remains unchanged.
For rapid interfacial mass transfer, gas–liquid equilibrium can
be assumed throughout the entire reaction volume,
cGi = KicLi
(26)
where Ki is the equilibrium ratio, which depends on the com-
position, total pressure and temperature. The values of Ki were
estimated according to our previous study on vapour–liquid equi-
librium in this system [10]. Values of Ki for the key components
O2 and H2 were in the range 3.5–4.5 and 6.1–16, respectively. The
validity of the hypothesis of rapid gas–liquid mass transfer was
confirmed in a previous paper of Gemo et al. [8]. The gas and liq-
uid volumes can be assumed constant in the present case, since the
liquid volume is in fact determined by the solvent, methanol. After
inserting the relations (24)–(26) in the balance equation (23) and
carrying out the differentiation, an explicit differential equation is
obtained for the liquid-phase concentrations:
The generation rates of the components are obtained from the
rate equations and the stoichiometry:
rH = −r1 − r2 − r3
(13)
(14)
2
dcLi
ꢀ ꢁ
ꢀ ꢁ
= (˛i + 1)−1ꢁBri
(27)
1
2
1
2
dt
rO = −r1
−
r2
+
r4
2
where ˛i is given by
rP = r1 − r3 − r4
(15)
(16)
KiVG
˛i =
(28)
rW = r2 + 2r3 + r4
VL
The balance equation can be alternatively expressed with the
gas-phase concentrations as well:
4. Mass balances and product distribution analysis in batch
reactor
ꢀ
ꢁ−1
dcGi
dt
˛
i
= Ki
+ 1
Ki
ꢁBri
(29)
The product distribution analysis were carried out assuming
D = 1 in the rate equations (9)–(11), because of the low concen-
trations of reagents and products. The decomposition of hydrogen
peroxide (Eq. (12)) was neglected, since its significance was very
minor compared to that of hydrogen peroxide hydrogenation under
the actual experimental conditions. Consequently, the generation
rates of the components were calculated from a simplified set of
equations,
For the products, water and hydrogen peroxide, Ki = 0 because of
their low volatilities in the low experimental temperatures. Appli-
cation of Eq. (27) to hydrogen, oxygen, hydrogen peroxide and
water in liquid phase gives
dcH
= (˛H + 1)−1ꢁB(−r1 − r2 − r3)
(30)
(31)
(32)
(33)
2
2
dt
ꢀ
ꢀ ꢁ
ꢁ
dcO
dt
1
2
= (˛O + 1)−1ꢁB −r1
−
r2
rH = −r1 − r2 − r3
(17)
(18)
2
2
2
ꢀ ꢁ
1
2
rO = −r1
−
r2
dcH
2
O
2
2
= ꢁB(r1 − r3)
= ꢁB(r2 + 2r3)
dt
dcH
rP = r1 − r3
(19)
(20)
O
2
rW = r2 + 2r3
dt
By regarding at the above equations, some interesting stoichio-
metric relationships are immediately noticed, such as
The component mass balances in the vigorously stirred batch
reactor can be written in the following way for the gas and liquid
phases:
(1 + ˛H )dcH2
dcH
dcH
O
2
O
2
2
2
+
+
= 0
(34)
dt
dt
dt
dnGi
0 = NiA +
(21)
(22)
dt
which gives upon integration (no products were present in the
initial solution):
dnLi
dt
ꢁBriVL + NiA =
cH
+ cH = (1 + ˛H2)(c0H − cH
)
2
(35)
O
O
2
2
2
2
where ꢁB is the lumped catalyst concentration (moles of Pd/VL) and
the mass transfer from gas to liquid phase is taken as the positive
direction. The symbols are defined in the Notation. The interfacial
fluxes (N) are equal and can be eliminated by addition of the gas-
and liquid-phase balance equations (21) and (22) giving
where c0H is the initial concentration of dissolved hydrogen.
Another reaction invariant can be found by considering the bal-
ances of hydrogen, oxygen and hydrogen peroxide:
2(1 + ˛O )dcO
dcH
(1 + ˛H )dcH
O
2
2
2
2
2
2
+
=
(36)
dt
dt
dt
dnGi
dt
dnLi
dt
ꢁBriVL
=
+
(23)
Integration of Eq. (36) and rearrangement gives
This expression can be elaborated further, provided that the interfa-
cial mass transfer is rapid compared to the chemical reaction rates.
The amounts of substance are defined by
2(1 + ˛O )(c0O − cO ) − cH = (1 + ˛H )(c0H − cH
)
2
(37)
O
2
2
2
2
2
2
2
where c0O represents the initial concentration of dissolved oxy-
gen. A comparison of Eqs. (35) and (37) reveals that the hydrogen
concentration can be easily eliminated:
nGi = cGiVG
nLi = cLiVL
(24)
(25)
2(1 + ˛O )(c0O − cO ) = 2cH
+ cH
(38)
O
O
2
2
2
2
2
2
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5
Eq. (38) demonstrates that the oxygen concentration – which was
not measured experimentally – is related to the product concen-
trations.
The product distribution analysis is progressed further by divid-
ing the balance equations of peroxide and water. The result
becomes
dcH
r1 − r3
O
2
2
=
(39)
dcH
r2 + 2r3
O
2
Inserting, the rate expressions in the above equation implies that
the denominator (D in Eqs. (9)–(11) is eliminated and an expres-
sion which is independent of the detailed reaction mechanism is
obtained:
dcH
k1ꢀ cO − k3ꢀ cH
O
O
2
2
2
2
2
=
(40)
2
k2ꢀ cO1/2 + 2k3ꢀ cH
dcH
O
O
2
2
2
Eq. (40) also suggests that the momentaneous product distribu-
tion is independent of the hydrogen concentration, provided that
the changes in the state of the catalyst surface are negligible. This
is actually a direct consequence of the assumed reaction mecha-
nism: all the reactions have the same dependence on cH2 , so that
the ratio between the variation of H2O2 and H2O is independent
of the hydrogen concentration. If a different reaction mechanism
is assumed, the momentaneous product distribution may become
dependent of cH2 . The stoichiometric relationship (38) gives the
concentration of dissolved oxygen:
ꢀ
ꢁ
cH
+ cH
O
O
2
−1
)
2
2
2
cO = c0O − (1 + ˛O
(41)
2
2
2
For hydrogen concentration, Eq. (39) gives
cH = c0H − (1 + ˛H
)
−1(cH
+ cH
)
O
2
(42)
O
2
2
2
2
2
Two merged parameters, ˇ and ω, are introduced, ˇ = k1ꢀ /k2ꢀ and
ω = k3ꢀ /k2ꢀ . Eq. (40) becomes now
dcH
ˇcO − ωcH
O
O
2
2
2
2
2
=
(43)
2
cO1/2 + 2ωcH
dcH
O
O
2
2
2
The estimation of the kinetic parameters k1ꢀ , k2ꢀ and k3ꢀ requires the
simultaneous solution of Eqs. (32), (33), (41)–(43). Note that the
product distribution analysis (Eq. (43)) is a function of water con-
centration, whereas the mass balances (32) and (33) are functions
of time. Hence, the regression was necessarily carried out in two
subsequent steps: the parameters ˇ and ω were determined first
(step 1), and their values were subsequently used to determine the
parameter k2ꢀ (step 2). Specifically, the parameters ˇ and ω were
estimated solving the low index algebraic-differential equations
system given by Eqs. (41) and (43) (step 1). The hydrogen peroxide
concentration was determined as a function of water concentra-
tion by non-linear regression analysis using the experimental data
available from the batch reactor. The following error function was
used for each experiment (i.e. any given temperature) to fit the
experimental data:
ꢂ
exp |cHexp − cH
|
ꢃ
n
P
2
O ,i
2 2
i=1
(1/neHxp
O
,i
exp
2
2
err =
(44)
ꢃ
n
P
)
2
cHexp
O ,i
2 2
O
i=1
2
Note that the error between experimental and calculated concen-
trations has been rescaled.
Then, the rate equations (9)–(11) were rewritten as a function
of the parameters ˇ and ω:
r1 = ˇk2ꢀ cH cO
(45)
(46)
Fig. 1. Product distribution and simulated hydrogen and oxygen concentrations at
258 K (a), 268 K (b), 273 K (c), 283 K (d) and 297 K (e). The initial H2 partial pres-
sure was 1.66 (a), 1.72 (b), 1.75 (c), 1.82 (d) and 1.91 atm (e). More details on the
experimental data and procedures are described in our previous work [9].
2
2
r2 = kꢀ cH2 cO1/2
2
2
Please cite this article in press as: T. Salmi, et al., Product distribution analysis of the hydrogen peroxide direct synthesis in an isothermal
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CATTOD-8967; No. of Pages7
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T. Salmi et al. / Catalysis Today xxx (2014) xxx–xxx
Fig. 2. Arrhenius plots of the rate constants (data from Fig. 1).
r3 = ωkꢀ cH cH
(47)
indicates that neglecting the decomposition reaction (DE) is rather
justified under the actual circumstances.
O
2
2
2
2
Note that the denominator D was neglected, as previously men-
tioned. Eqs. (45)–(47) were introduced in the mass balances (32)
and (33), that were solved with the Eqs. (41) and (42) simul-
taneously (step 2). Eqs. (32), (33), (41) and (42) lead to an
algebraic-differential equations system, whose solution yield the
evolution in time of the concentration of the reactants (i.e. H2 and
O2) and the products (i.e. H2O2 and H2O). Note that in this system
only the parameter k2ꢀ has to be determined, since the parameters
ˇ and ω were calculated in step 1. Hence, the value of k2ꢀ was esti-
mated in each experiment fitting the experimental data with the
following error function:
The Arrhenius plots of the rate parameters for direct synthe-
sis, water formation and peroxide hydrogenation are displayed in
Fig. 2a, b, and c, respectively. The plots, the logarithm of the rate
constant versus the reciprocal absolute temperature, gave the acti-
vation energies as follows: 22 kJ/mol (direct synthesis), 42 kJ/mol
(water formation), and 43 kJ/mol (peroxide hydrogenation). These
values are logical and in good agreement with previous results [8].
The activation energies reveal that the direct synthesis of hydrogen
peroxide is favoured by low temperatures, whereas the increase of
the reaction temperature shifts the product distribution towards
water.
ꢂ
ꢂ
exp |cHexp − cH
|
exp |cHexp − cH
|
ꢃ
ꢃ
n
n
P
P
2
2
6. Conclusions
O
,i
O,i
2
i=1
(1/neHxp
O
,i
exp
2
2
i=1
(1/neHxp
O,i
2
2
2
err =
+
exp
ꢃ
ꢃ
n
n
cHexp
)
O
cHexp
O,i
2
P
P
Reaction mechanisms and rate equations were considered for
hydrogen peroxide direct synthesis, water formation and peroxide
hydrogenation on a supported palladium catalyst. A new approach
for the product distribution analysis was proposed and applied
to experimental data which had been recorded from a vigor-
ously stirred and isothermal batch reactor. The work demonstrated
clearly that the proposed concept works very well, improving the
robustness of the parameter estimation procedure and leading to
reasonable values of the rate constants and activation energies.
)
O
i=1
O
,i
i=1
2
2
2
2
2
(48)
Once again, the errors between experimental and calculated con-
centrations have been rescaled. Finally, the rate parameters k1ꢀ
=
ˇk2ꢀ and k3ꢀ = ωk2ꢀ are calculated. All the integrations were effi-
ciently carried out using the ode15s ADEs solver in Matlab, also
suitable for stiff equations, being based on a multistep variable
order method based on the numerical differentiation formulae.
The regressions were independently carried out with the exper-
imental data [9] collected at 258, 268, 273, 283 and 297 K, so that
the temperature dependence of the parameters was checked with
Arrhenius plots.
Acknowledgements
This work is a part of activities at the Åbo Akademi Process
Chemistry Centre (PCC), a centre of excellence financed by Åbo
Akademi. Financial support from Academy of Finland is gratefully
acknowledged. Financial support to Nicola Gemo from Foundation
of Åbo Akademi is gratefully acknowledged (Johan Gadolin Schol-
arship).
5. Estimation results and discussion
The parameter estimation was carried out successfully by
applying the methodology which was described above. All the
experimental data are taken from our previous work [9]. The errors
of the parameters were relatively small and the overall degree of
explanation was high (exceeding 95% in all cases).
The parameter estimation results are presented in Fig. 1a–e,
along with simulated concentrations of hydrogen and oxygen in the
liquid phase. As the figure reveals, the proposed model very truly
describes the experimentally observed concentrations of hydrogen
peroxide, water and hydrogen in the liquid phase. The simulated
liquid-phase concentrations of dissolved hydrogen and oxygen
show a declining trend; this is expected, since the experiments
were done batchwise. The product distribution (hydrogen perox-
ide versus water) is predicted very correctly in most cases, which
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