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

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Product distribution analysis of the hydrogen peroxide direct synthesis in an isothermal batch reactor Tapio Salmi a,∗ , Nicola Gemo a,b,∗∗ , Pierdomenico Biasi a , Juan Garcia Serna c a b c

Åbo Akademi, Department of Chemical Engineering, FI-20500 Turku/Åbo, Finland Università di Padova, Dipartimento di Ingegneria Industriale, IT-35131 Padova, Italy 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

Article history: 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

a b s t r a c t 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. © 2014 Elsevier B.V. All rights reserved.

1. Introduction The currently applied industrial process for the production of hydrogen peroxide, the anthraquinone process, is based on successive 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 several steps necessary for the purification and concentration of the peroxide [1]. For both these reasons, the cost of the hydrogen peroxide is nowadays relatively high, limiting the industrial large scale use of H2 O2 . 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.

∗ 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, [email protected] (N. Gemo).

It has been a long time the dream of chemists and chemical engineers to develop a new process, based on the direct synthesis 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 development 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 H2 O2 productivity in a trickle bed reactor [4]. The introduction of methanol as solvent and the presence of carbon dioxide in the reaction 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].

http://dx.doi.org/10.1016/j.cattod.2014.03.020 0920-5861/© 2014 Elsevier B.V. All rights reserved.

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Notation A A c c* D Ea K k k

N n nexp R r ri T t V ˛ ˇ  ω

interfacial area frequency factor concentration concentration of a surface species denominator in rate expression activation energy equilibrium constant reaction rate constant merged rate constant, product of rate constant, adsorption equilibrium constant and total concentration of active sites flux amount of substance number of experimental data (Eqs. (44) and (48)) gas constant reaction rate component (i) generation rate temperature time volume gas-to-liquid volume ratio parameter in product distribution analysis stoichiometric number parameter in product distribution analysis

Subscripts and superscripts G gas i, j component indices liquid L P reaction route total amount TOT 0 initial property Abbreviations H hydrogen O oxygen P 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 decomposition. The reaction rates and product distribution were measured at different temperatures and partial pressures of hydrogen and oxygen 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 analysis was applied in order to improve the reliability of the parameter estimation in this multicomponent system of composite reactions. 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 vessel. 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

hydrogen was fed as a limiting reactant (total pressure in the 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 H2 O was always very low. The details of the experimental equipment and procedures are described in the previous publications of our group [9,10]. 3. Reaction mechanism and rate equations The following overall reactions, confirmed by Biasi et al. [11] and Gemo et al. [8], are considered in connection of hydrogen peroxide formation and decomposition: the reactions between hydrogen and oxygen yielding hydrogen peroxide and water as well as spontaneous decomposition and hydrogenation of hydrogen peroxide. The overall reactions are summarized below: H2 + O2 = H2 O2

(DS)

H2 + (1/2)O2 = H2 O (WF) H2 O2 + H2 = 2H2 O (H) H2 O2 = H2 O + (1/2)O2

(DE)

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 principle 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. 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 reaction steps as rate determining ones gave the best agreement with experimental data. Some mechanistic studies have given information about the reaction mechanism. For instance, Dissanyake and Lunsford [13] proposed that the O O bond does not dissociate during the H2 O2 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 dissociatively 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 materials, 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 H2 O2 . The recent development is summarized, for instance, by Samanta [20] and Centi et al. [3].

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Table 2 Simplified reaction mechanism.

Table 1 Reaction steps, reaction routes and stoichiometric numbers.

Step #

Routes (DS to DE)

H2 + 2* = 2H* O2 + * = O2 * O2 + 2* = 2O* O2 * + H* = OOH* + * OOH* + H* = HOOH* + * HOOH* = H2 O2 + * O* + H* = OH* + * OH* + H* = HOH* + * HOH* = H2 O + * HOOH* + * = HOH* + O* HOOH* + H* = OH* + HOH*

Step #

DS

WF

H

DE

I II III IV V VI VII VIII IX X XI

1 1 0 1 1 1 0 0 0 0 0

1 0 1/2 0 0 0 1 1 1 0 0

1 0 0 0 0 −1 0 1 2 0 1

0 0 −1/2 0 0 −1 0 0 1 1 0

Some essential features can, however, be extracted from the previous 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 synthesis 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 desorption 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 dissociatively 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 hydrogen 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 addition of the reaction steps gives the overall reactions described above (DS to DE). 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. Therefore, 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 heterogeneous Pd catalysts. Hence, they were assumed to occur in a single step. 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 principle possible that the adsorption and/or desorption are the limiting

H2 + 2* = 2H* O2 + * = O2 * O2 + 2* = 2O* O2 * + 2H* = HOOH* + 2* HOOH* = H2 O2 + * O* + 2H* = HOH* + 2* HOH* = H2 O + * HOOH* + 2H* =2HOH* + * HOOH* + * = HOH* + O*

I II III IV and V VI VII and VIII (combined step) IX VIII and XI (combined step) X

steps of the process. Nonetheless, the quasi-equilibrium assumption 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 reliable estimation of the kinetic constants. Once a more accurate reaction mechanism has been proven, the same technique presented 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. The rates of the rate-limiting steps can now be written as 2 r1 = k1 cO2 ∗ cH∗ 2 r2 = k2 cO∗ cH∗

(1)

(step IV–V)

(2)

(steps VII–VIII)

2 r3 = k3 cHOOH∗ cH∗

r4 = k4 cHOOH∗ c∗

(3)

(steps VIII–IX)

(4)

(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∗j = Kj cj c∗

j = O2 , H2 O, H2 O2

(5)

for non-dissociative adsorption steps, and c∗k = (Kk ck )1/2 c∗

k = O, H

(6)

dissociative adsorption steps. The total concentration of surface species is cTOT = c∗ + cH∗ + cO∗ + cO2 ∗ + cHOH∗ + cHOOH∗

(7)

After inserting the expressions (5) and (6) in Eq. (7) and solving the concentration of vacant sites (c* ), we obtain −1 c∗ 1/2 1/2 = (1 + (KH cH2 ) + (KO cO ) + KO2 cO2 + KH2 O cH2 O + KH2 O2 cH2 O2 ) = D−1 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 r1 = r2 = r3 = r4 =

k1 cH2 cO2 D3 k2 cH2 cO2 1/2 D3 k3 cH2 O2 cH2 D3 k4 cH2 O2 D2

(9) (10) (11) (12)

The merged rate parameters (k ) 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 variation 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* = H2 O* + *. Following a similar procedure as described above, it can be easily 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. The generation rates of the components are obtained from the rate equations and the stoichiometry: rH2 = −r1 − r2 − r3 rO2 = −r1 −

1 2

r2 +

(13)

1 2

r4

(14)

rP = r1 − r3 − r4

(15)

rW = r2 + 2r3 + r4

(16)

4. Mass balances and product distribution analysis in batch reactor The product distribution analysis were carried out assuming D = 1 in the rate equations (9)–(11), because of the low concentrations 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, rH2 = −r1 − r2 − r3

(17)

rO2 = −r1 −

(18)

1 2

r2

(19)

rW = r2 + 2r3

(20)

The component mass balances in the vigorously stirred batch reactor can be written in the following way for the gas and liquid phases: dnGi dt

dnLi B ri VL + Ni A = dt

(21) (22)

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 gasand liquid-phase balance equations (21) and (22) giving dnLi dnGi B ri VL = + dt dt

cGi = Ki cLi

dcLi = (˛i + 1)−1 B ri dt

This expression can be elaborated further, provided that the interfacial mass transfer is rapid compared to the chemical reaction rates. The amounts of substance are defined by

(27)

where ˛i is given by ˛i =

Ki VG VL

(28)

The balance equation can be alternatively expressed with the gas-phase concentrations as well:



−1

dcGi ˛i = Ki +1 Ki dt

B ri

(29)

For the products, water and hydrogen peroxide, Ki = 0 because of their low volatilities in the low experimental temperatures. Application of Eq. (27) to hydrogen, oxygen, hydrogen peroxide and water in liquid phase gives dcH2 dt dcO2

= (˛H2 + 1)−1 B (−r1 − r2 − r3 )



= (˛O2 + 1)−1 B −r1 −

dcH2 O2 dt dcH2 O dt

1  2

r2

(30) (31)

= B (r1 − r3 )

(32)

= B (r2 + 2r3 )

(33)

By regarding at the above equations, some interesting stoichiometric relationships are immediately noticed, such as (1 + ˛H2 )dcH2 dt

+

dcH2 O2 dt

+

dcH2 O dt

=0

(34)

which gives upon integration (no products were present in the initial solution): cH2 O2 + cH2 O = (1 + ˛H2 )(c0H2 − cH2 )

(35)

where c0H is the initial concentration of dissolved hydrogen. Another reaction invariant can be found by considering the balances of hydrogen, oxygen and hydrogen peroxide: 2(1 + ˛O2 )dcO2 dt

(23)

(26)

where Ki is the equilibrium ratio, which depends on the composition, total pressure and temperature. The values of Ki were estimated according to our previous study on vapour–liquid equilibrium 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 liquid 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:

dt

rP = r1 − r3

0 = Ni A +

For rapid interfacial mass transfer, gas–liquid equilibrium can be assumed throughout the entire reaction volume,

+

dcH2 O2 dt

=

(1 + ˛H2 )dcH2 dt

(36)

Integration of Eq. (36) and rearrangement gives 2(1 + ˛O2 )(c0O2 − cO2 ) − cH2 O2 = (1 + ˛H2 )(c0H2 − cH2 )

(37)

nGi = cGi VG

(24)

where c0O represents the initial concentration of dissolved oxygen. A comparison of Eqs. (35) and (37) reveals that the hydrogen concentration can be easily eliminated:

nLi = cLi VL

(25)

2(1 + ˛O2 )(c0O2 − cO2 ) = 2cH2 O2 + cH2 O

(38)

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Eq. (38) demonstrates that the oxygen concentration – which was not measured experimentally – is related to the product concentrations. The product distribution analysis is progressed further by dividing the balance equations of peroxide and water. The result becomes dcH2 O2 dcH2 O

=

r1 − r3 r2 + 2r3

(39)

Inserting, the rate expressions in the above equation implies that the denominator (D in Eqs. (9)–(11) is eliminated and an expression which is independent of the detailed reaction mechanism is obtained: dcH2 O2 dcH2 O

=

k1 cO2 − k3 cH2 O2 1/2

k2 cO

2

(40)

+ 2k3 cH2 O2

Eq. (40) also suggests that the momentaneous product distribution 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 mechanism: all the reactions have the same dependence on cH2 , so that the ratio between the variation of H2 O2 and H2 O 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: cO2 = c0O2 − (1 + ˛O2 )−1

c

H2 O2

+ cH2 O



2

(41)

For hydrogen concentration, Eq. (39) gives cH2 = c0H2 − (1 + ˛H2 )−1 (cH2 O2 + cH2 O )

(42)

Two merged parameters, ˇ and ω, are introduced, ˇ = k1 /k2 and ω = k3 /k2 . Eq. (40) becomes now dcH2 O2 dcH2 O

=

ˇcO2 − ωcH2 O2 1/2

cO

2

(43)

+ 2ωcH2 O2

The estimation of the kinetic parameters k1 , k2 and k3 requires the simultaneous solution of Eqs. (32), (33), (41)–(43). Note that the product distribution analysis (Eq. (43)) is a function of water concentration, 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 k2 (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 concentration 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:



err =

nexp P i=1

exp 2 O2 ,i

|cH



exp ) 2 O2

(1/nH

− cH2 O2 ,i |2

exp n P

i=1

(44)

exp 2 O2 ,i

cH

Note that the error between experimental and calculated concentrations has been rescaled. Then, the rate equations (9)–(11) were rewritten as a function of the parameters ˇ and ω: r1 = ˇk2 cH2 cO2 1/2

r2 = k2 cH2 cO

2

(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 pressure 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].

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Fig. 2. Arrhenius plots of the rate constants (data from Fig. 1).

r3 = ωk2 cH2 O2 cH2

(47)

Note that the denominator D was neglected, as previously mentioned. Eqs. (45)–(47) were introduced in the mass balances (32) and (33), that were solved with the Eqs. (41) and (42) simultaneously (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. H2 O2 and H2 O). Note that in this system only the parameter k2 has to be determined, since the parameters ˇ and ω were calculated in step 1. Hence, the value of k2 was estimated in each experiment fitting the experimental data with the following error function:

 err =



nexp P

exp |cH O ,i i=1 2 2



exp ) 2 O2

(1/nH

− cH2 O2 ,i

exp n P

i=1

exp 2 O2 ,i

cH

|2

nexp P i=1

+

exp 2 O,i

|cH



exp ) 2O

(1/nH

6. Conclusions

− cH2 O,i |2

exp n P

i=1

exp 2 O,i

indicates that neglecting the decomposition reaction (DE) is rather justified under the actual circumstances. The Arrhenius plots of the rate parameters for direct synthesis, 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 activation 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.

cH

(48)

Once again, the errors between experimental and calculated concentrations have been rescaled. Finally, the rate parameters k1 = ˇk2 and k3 = ωk2 are calculated. All the integrations were efficiently 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 experimental data [9] collected at 258, 268, 273, 283 and 297 K, so that the temperature dependence of the parameters was checked with Arrhenius plots. 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 peroxide versus water) is predicted very correctly in most cases, which

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 vigorously 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. 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 Scholarship). References [1] J.M. Campos-Martin, G. Blanco-Brieva, J.L.G. Fierro, Angew. Chem. Int. Ed. 45 (2006) 6962. [2] T.A. Pospelova, N.I. Kobozev, E.N. Eremin, Russ. J. Phys. Chem. 35 (1961) 262. [3] G. Centi, S. Perathoner, S. Abate, Modern Heterogeneous Oxidation Catalysis, Wiley-VCH Verlag GmbH & Co. KGaA, 2009, pp. 253. [4] P. Biasi, J. Garcia-Serna, A. Bittante, T. Salmi, Green Chem. 15 (2013) 2502. [5] Y. Voloshin, A. Lawal, Chem. Eng. Sci. 65 (2010) 1028. [6] T. Moreno, J. García-Serna, M.J. Cocero, J. Supercrit. Fluids 57 (2011) 227. [7] T. Deguchi, M. Iwamoto, J. Catal. 280 (2011) 239. [8] N. Gemo, P. Biasi, P. Canu, T.O. Salmi, Chem. Eng. J. 207–208 (2012) 539. [9] P. Biasi, N. Gemo, J.R. Hernández Carucci, K. Eränen, P. Canu, T.O. Salmi, Ind. Eng. Chem. Res. 51 (2012) 8903.

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[10] N. Gemo, P. Biasi, T.O. Salmi, P. Canu, J. Chem. Thermodyn. 54 (2012) 1. [11] P. Biasi, P. Canu, F. Menegazzo, F. Pinna, T.O. Salmi, Ind. Eng. Chem. Res. 51 (2012) 8883. [12] P. Biasi, F. Menegazzo, F. Pinna, K. Eränen, P. Canu, T.O. Salmi, Ind. Eng. Chem. Res. 49 (2010) 10627. [13] D.P. Dissanayake, J.H. Lunsford, J. Catal. 214 (2003) 113. [14] S. Chinta, J.H. Lunsford, J. Catal. 225 (2004) 249. [15] V.R. Choudhary, S.D. Sansare, A.G. Gaikwad, Catal. Lett. 84 (2002) 81.

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[16] G. Blanco-Brieva, E. Cano-Serrano, J. Campos-Martin, J.L.G. Fierro, Chem. Commun. (2004) 1184. [17] S. Melada, R. Rioda, F. Menegazzo, F. Pinna, G. Strukul, J. Catal. 239 (2006) 422. [18] Q. Liu, K. Gath, J. Bauer, R. Schaak, J. Lunsford, Catal. Lett. 132 (2009) 342. [19] U. Rossi, S. Zancanella, L. Artiglia, G. Granozzi, P. Canu, Chem. Eng. J. 207–208 (2012) 845. [20] C. Samanta, Appl. Catal. A: Gen. 350 (2008) 133.

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