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Mass transfer and kinetics of H2O2 direct synthesis in a batch slurry reactor

Nicola Gemo a, Pierdomenico Biasi b, Paolo Canu a,, Tapio O. Salmi b

a Dipartimento di Ingegneria Industriale, University of Padova, via Marzolo 9, 35131 Padova, Italyb Process Chemistry Centre (PCC), Laboratory of Industrial Chemistry and Reaction Engineering, bo Akademi, Biskopsgatan 8, 20500 Turku, Finland

h i g h l i g h t s

" Modeling of H2O2direct synthesis,

decomposition and hydrogenationexperiments." Gas to liquid and liquid to solid mass

transfer limitation analysis." Estimation of activation energies and

pre-exponential factors.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:Batch reactor modelingHydrogen peroxideDirect synthesisGreen chemistryPalladium

a b s t r a c t

A model of a gas bubbling, batch slurry reactor for H2O2direct synthesis is presented. Experimental mea-surements were carried out in the absence of halides and acids at temperatures between 258 and 297 K(pressures 1420 bar, depending on temperature) with H2 and O2 diluted in CO2 outside flammabilitylimits (gas phase composition of CO2, O2and H2was 77%, 21% and 2%, respectively). Kinetic experimentsperformed on a commercial 5% Pd/C catalyst (0.15 g in 400 ml methanolic solution) have been used toidentify the intrinsic kinetics and assess the influence of mass transfer. The simplest rate equations com-patible with the acknowledged reaction network has been included in a reactor model, which accountsfor mass transfer resistances between gas and liquid and bulk of the liquid-catalyst surface.

The corresponding Arrhenius parameters were estimated from direct synthesis experiments for all thereactions. Comparable temperature dependence was observed for H2O production, hydrogenation anddecomposition (activation energies close to 45 kJ mol1), while H2O2synthesis has a much lower activa-tion energy (close to 24 kJ mol1), suggesting that a higher selectivity is achievable at low temperature.Decomposition had a very limited influence on the overall peroxide production rate, being quite slow (itsrate is approx. 40% the direct synthesis rate at H2full conversion). Hydrogenation was the most rapid sidereaction, depressing H2O2production as H2conversion increased. Independent investigation on the H2O2hydrogenation in the absence of O2highlighted significant difference in the kinetics, apparently due to a

different oxidation state of the catalyst.A sensitivity analysis on the mass transfer coefficients to allow for uncertainties in the correlations

proved that no resistances in the liquid occur, while gasliquid H2transfer rate may be limiting, althoughunlikely, requiring that literature coefficients overestimates the real transfer rate by an order ofmagnitude.

2012 Elsevier B.V. All rights reserved.

1. Introduction

Hydrogen peroxide is the simplest peroxide and is commer-cially available in aqueous solution over a wide concentrationrange. The main uses of hydrogen peroxide are in the preparation

1385-8947/$ - see front matter 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.cej.2012.07.015

Corresponding author.

E-mail address: [email protected](P. Canu).

Chemical Engineering Journal xxx (2012) xxxxxx

Contents lists available atSciVerse ScienceDirect

Chemical Engineering Journal

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c e j

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consuming H2O2, i.e. decomposition (d) and hydrogenation (h). Theunwanted reactions (wf, d and h) could be minimized acting on theoperating conditions, in addition to designing a suitable catalyst,but kinetics and mass transfer limitation must be known. Mostof the research on hydrogen peroxide DS concentrate on the cata-lyst design[38], where different metals or combination of metalsand supports were studied to minimize the unwanted reactions.Results are difficult to compare mainly because of the different cat-alyst and reaction conditions involved. More recently contributionson the kinetics are growing in the Literature[913]. The main ef-forts were spent in rationalizing the effect of different reactionconditions on the catalyst and develop models to study the actualmechanism, for further optimization of selectivity and productionrate. Recently kinetics has been studied with different approaches[13,12,9],Deguchi et al.[10], Moreno et al.[11].

Menegazzo et al. [13] correlated semi-batch reactor results(mono and bi-metallic Pd/Au catalysts over zirconia and ceria),with power law rates for the H2O2 formation, synthesis of waterand reductionof H2O2, taking advantage of constant H2 and O2 con-centration in the reaction environment. Depending on catalyst typeand conditions, estimated kinetic constants were in the range 2.27.9 mol L1 min1, 0.17.6 mol L1 min1 and 0.98.8 min1 fordirect synthesis, water formation and H2O2hydrogenation, respec-tively. Note that the given kinetic parameters incorporate H2 andO2 liquid concentrations, considered constant in the work. Inoueet al. [12] formulated a power law kinetic constant for the DS usingresults from a microreactor with a commercial 5% Pd/C catalyst,calculating rate constants between 53.5 and 61.9 L2 mol1 s1,depending on operating conditions. Voloshin et al. [9], isolatedand described in a microreactor the decomposition[14],reduction[15] (estimating an activation energy of 43.71 kJ mol1) andsynthesis reactions [9] (calculated activation energy was22.34 kJ mol1), also considering a LangmuirHinshelwood mecha-nism (over a Pd/Si catalyst); then the rate equations were coupledand implemented in a reactor model [16]. The isolation of thedecomposition, H2O2reduction and synthesis reactions was possi-

ble operating the microreactor in differential mode, where the con-version of the reactants was limited to 2%. Gasliquid masstransfer parameters were measured studying the hydrogenationreaction over a range of velocities in order to model the reactorin the mass transfer regime. Deguchi et al.[10]tested a Pd/C cata-lyst in a semi-batch reactor and developed a LangmuirHinshel-wood type mechanism taking into account also hydrido-hyroperoxy intermediate MHOOH for H2O2 formation; they alsodetermined that the mass transfer was controlling their DS data.Deguchi et al. [10] was the only one taking into account theadsorption of the promoters in the kinetic study.

Moreno et al.[11]thoroughly discussed the effect of the pro-moters on the activation energy of the decomposition reaction ina semi-batch reactor at high pressure with a commercial Pd/C cat-

alyst, estimating values in the range 1583.87 kJ mol1

, dependingon the operating conditions and presence/absence of promoters.All the authors mentioned used stabilizers and promoters toreduce the effect of the consecutive reactions. The kinetic modelscited above were all successful in describing their experimentaldata, although only a few accounted for mass transfer, suggestinga key role.

In this work we speculate theoretically on the kinetics andtransport limitations using some knowledge developed in our pre-vious works on hydrogen solubility[17]and kinetics experiments[18]performed without using promoters and stabilizers. We triedto understand the controlling factors that limits the hydrogen per-oxide DS. The kinetic study was carried out both on the DS exper-iments and the decomposition and hydrogenation reactions,

carried out in separate experiments. A multiphase reactor modelwas developed including the influence of transport limitations.

2. Experimental

The experiments were performed batchwise in a 600 ml unbaf-fled reactor with standard geometry (Buchi) and equipped with aself-sucking 6 blade impeller. Experimental apparatus and proce-dures are described elsewhere [18]. Shortly, 0.15g ofa 5%Pd/C cat-alyst were loaded in the reactor, that was then flushed four times

with CO2 to remove air and moisture. Carbon dioxide (18.4 bar)and oxygen (6 bar) were introduced in the vessel (298 K), followedby the injection of 400 ml of methanol. After pressure and temper-ature were stable at the desired values, hydrogen was fed as thelimiting reagent. The reaction was assumed to start immediatelyafter hydrogen loading. The gas mixture was carefully kept outsideflammability limits (composition was 77%, 21% and 2% of CO2, O2and H2 respectively). A stirring rate of 1000 rpm was conserva-tively adopted to ensure a good mixing of the liquid phase, as ver-ified in dedicated experiments. Hydrogenation and decompositionexperiments were carried out following the same procedure, withN2replacing O2or H2, respectively. The liquid phase was sampledat different times and water and H2O2 contents were determinedby volumetric Karl Fischer and iodometric titration, respectively.The amount of liquid subtracted for each analysis was 0.7 ml, sothat the total uptake never exceeded 8% of the initial liquid vol-ume. Errors on H2O2and H2O measurements were estimated ana-lyzing a methanol solution with a known water and hydrogenperoxide content (0.8% and 1.6% respectively), sampled from thereactor at experimental conditions. Estimated error on H2O2 was0.8%, whereas on H2O it was 2%.

3. Model

3.1. Chemical kinetics

Several surface mechanisms on palladium can give the overallprocess described inScheme 1. Voloshin et al.[16]screened some

mechanisms to describe kinetic data obtained from microstruc-tured reactors and concluded that a LangmuirHinshelwood-typemechanism, with the surface reaction steps as rate determiningones, gave the best agreement withexperimental data. Dissociativeadsorption of the reactant species was also proposed by Deguchi etal. [10]. Some mechanistic studies have given information aboutthe reaction mechanism. For instance, Dissanayake and Lunsford[19]proposed that the OO bond does not dissociate during theH2O2synthesis process and Sivadinarayana et al.[20]confirm thespecies HO2 on a gold catalyst surface. However, it is clear thatwater formation requires the rupture of the OO bond on the cat-alyst surface.

All the reactions involved in the seriesparallel network(Scheme 1) are exothermic and thermodynamically favored[21]

and Pd is known to promote all of them. Some basic assumptionsare used here to describe the rate equations for the overall reac-tions in as simple as possible manner. The reaction mechanismproposed is summarized inTable 1.

The mechanism is based on the hypotheses that hydrogen andoxygen adsorb simultaneously and dissociatively on the metal cat-alyst surface, and surface hydroxyls are formed leading to the for-mation of hydrogen peroxide and water. The hydrogen peroxidedecomposition and hydrogenation are described with the simplestpossible mechanisms. Homogeneous reactions in the liquid phaseare neglected, as experimentally demonstrated[18]. The adsorp-tion and desorption steps are assumed to be rapid enough to reachquasi-equilibria, while the surface reaction steps IV, V, VI and VIIare assumed to limit the rates.

For hydrogen and oxygen, the quasi-equilibrium hypothesisyields:

N. Gemo et al. / Chemical Engineering Journal xxx (2012) xxxxxx 3


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KH2C

2H2

CSH2

C2 1

KO2C

2O2

C

S

O2C

2 2

from which the concentrations of the adsorbed species areobtained:

CH2 KH2CSH2

1=2C 3

CO2 KO2CSO2

1=2C 4

Application of the quasi-equilibrium hypothesis on the surfacehydroxyls gives

KOHCOHC

COC

H

5

which combined with the quasi-equilibria for adsorbed hydrogenand oxygen gives

COHKOH KH2CSH2

1=2KO2C

SO2

1=2C

6

Analogously, the adsorption equilibria of hydrogen peroxideand water give the corresponding surface concentrations as de-scribed below:

CH2O2 KH2O2CSH2O2

C 7

CH2O

KH2OCSH2OC 8

The total site balance comprises all the adsorbed species (H, O,OH, HOOH, H2O

) and the vacant sites (). After inserting all thequasi-equilibrium expressions into the balance equation, the frac-tion of vacant sites can be solved:

C

Ctot

KH2CSH2 1=2

KO2CSO2 1=2

KOH KH2CSH2 1=2

KO2CSO2

1=2

KH2OCSH2OKH2O2CSH2O2

11

D1 9

where Ctotdenotes the total concentration of surface sites. The ratesof the rate-limiting steps can now be written as:

R4k4 C2OHCH2O2C.j4

10

R5k5 COHCHCH2OC.j5

11

R6k6 CH2O2CCH2OCO.j6

12

R7k7 CH2O2C2H2

C2H2OC.j7

13

The concentrations of the surface species are expressed with thequasi-equilibria and the concentration of vacant sites. After insert-ing all these expressions, the rate equations can be rearranged. Theconstants can be merged, so that just a forward rate constant andan equilibrium constant is used for each step (the merged con-

stants (kandj0

) are products of surface rate and adsorption equi-librium constants):

R4k04 CSO2CS2H2

CSH2O2.j04

D2 14

R5k05 CSH2CS1=2O2

CSH2O.j05

D2 15

R6k06 CSH2O2 CSH2O

CS1=2O2

.j06

D

2 16

R7k07 CSH2O2CSH2

CS2H2O.j07

D

2 17

Assuming that the steps are practically irreversible under theactual conditions and neglecting the adsorption contribution in

the denominator because of low concentrations (D= 1), gives thesimplest rate equations:

R4RdskdsCSO2CS2H2

; kdsk04 18

R5Rwf kwfCSH2CS1=2O2

; kwf k05 19

R6RdkdCSH2O2 ; kdk06 20

R7RhkhCSH2O2CSH2

; khk07 21with temperature dependent, Arrhenius-type kinetic constants:

kiAieEai=RT 22

Pre-exponential factor (Ai) and activation energy (Eai) of eachreaction are determined from our experimental data, as describedbelow. The generation rates are formulated with the aid of therate-limiting steps IVVII. The following expressions are obtained:

rH2O2RdsRdRh 23

rH2ORwfRd2Rh 24

rH2 RdsRwfRh 25

rO2 Rds0:5Rwf 0:5Rd 26

3.2. Mass transfer

Mass transfer resistances are always involved in a multiphasereacting environment, hence, their role should be taken into ac-count in a kinetic study. Here we consider two mass transfer resis-tances, dissolution of gases into the liquid phase and reactanttransport in the liquid to the catalyst surface. For sake of clarity,a schematic representation is given inFig. 1.

The gas phase is assumed well mixed so that the mass transferbetween gas and liquid is controlled by the liquid side resistance(Fig. 1). At the gasliquid interface, equilibrium holds. Vapor pres-sure of H2O and H2O2are neglected (258 < T(K) < 297) so that gra-dients occur only near the solid interface and species cumulate inthe liquid phase.

Species fluxes are described in terms of mass transfer coefficients

times concentration differences. Coefficients are calculated accord-ing to best available correlation for the reactor used, considering

Table 1

Reaction steps, reaction routes and stoichiometric numbers (mP1, . . .,mP4).

Step # mP1 mP2 mP3 mP4

H2+ 2 = 2H I 1 1 0 1

O2+ 2 = 2O II 1 1/2 0

O + H = OH + III 2 1 0 0OH + OH = HOOH + IV 1 0 0 0OH + H = H2O

+ V 0 1 0 0

HOOH + =H2O + O VI 0 0 1 0HOOH + 2H = 2H2O

+ VII 0 0 0 1HOOH = H2O2+

VIII 1 0 1 1H2O

= H2O + IX 0 1 1 2

Route 1 (mP1): direct synthesis (ds) H2+ O2? H2O2.Route 2 (mP2): water formation (wf) H2+ O2?H2O.Route 3 (mP3): decomposition (d) H2O2? H2O + O2.Route 4 (mP4): hydrogenation (h) H2O2+ H2? H2O.Rate limiting steps: IV, V, VI and VII.

4 N. Gemo et al. / Chemical Engineering Journal xxx (2012) xxxxxx

Please cite this article in press as: N. Gemo et al., Mass transfer and kinetics of H 2O2direct synthesis in a batch slurry reactor, Chem. Eng. J. (2012), http://

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that gas is bubbling in the liquid and catalyst is in the form of finepowder, suspended in the liquid.

3.3. Gasliquid mass transfer coefficients

The gasliquid mass transfer coefficient depends on several fac-

tors (fluids considered, apparatus, agitation rate, temperature) anda suitable correlation for their estimation should be carefully cho-sen. The reactor used for the kinetics experiments was equippedwith a self-suction turbine. Stirring causes a negative pressure atthe impeller that indices suction of gas from the atmosphere abovethe liquid, through the hollow shaft, continuously yielding finebubbles in the liquid phase. Therefore, the liquid mass transfercoefficients for O2 and H2 are estimated with a correlation forsparged stirred tank reactors[22]:

KLi aL 2ffiffiffiffi

pp ffiffiffiffiffi}ip nqLlL

14

aL 27

Values of the diffusion coefficients (}i) are calculated with theWilkeChang equation[23] assuming pure methanol, because it

largely dominates the liquid composition. Assuming that energyat gasliquid interface is consumed at the gas bubbles surface,the energy dissipation rate per unit mass (n) can be evaluated withthe correlation proposed by Garcia-Ochoa et al.[24]:

n PqLp=4dh 28

where the power input (P) is calculated as:

P0:783 P20Nd

3

Q0:56

!0:45929

We used the gas flow rate recirculated through the hollow shaftfor Q. The value of Q was 5 cm3 s1, estimated with dedicated

experiments. P0 is the power consumption in an un-aerated sys-tem. Its values depends on the power number,Np, that can be con-sidered constant assuming turbulent regime[24]. According to thedefinition of the dimensionless power number,P0is given by:

Np P0qLN3d5

30

The power number depends on the impeller type and geometryand is estimated using the correlation proposed by Rutherfordet al.[25]:

Np6:405 55:673t=d 31For the correct evaluation of the mass transfer resistance, also

the gasliquid interfacial area (aL) has to be estimated. Assuming

spherical bubbles, aL

can be calculated from the average bubblesize,db, and the gas hold-up,/, by the following correlations[24]:

aL 6/db

32

/

1/0:5Q=pz22=39:81l1=3

qL

qL qG

33

where

l2 r0:4qL

3=5 h=62=5pNd6=5

! qL

qG

0:134

For Newtonian fluids, the estimation of the average bubble size(db) is given by[26]:

db0:7 r0:6

106P=VL 0:4

qL0:2

lL

lG

0:135

The density (q) and the viscosity (l) of liquid and gas phases, aswell as the interfacial tension (r), required in Eqs.(10)(18), areestimated with an equation of state [17] at experimentalconditions.

3.4. Liquidsolid mass transfer coefficients

The catalyst effectiveness factor is initially considered equal toone because of the small particle size (the average diameter is30lm) and slow reaction rate, so that mass transfer limitation in-side the catalyst is likely to be negligible. This assumption will bediscuss later. The external mass transfer coefficients at the catalystsurface are evaluated assuming no relative velocity between the li-quid and the catalyst. This assumption is justified because of thesmall dimension of the catalyst particles. In this condition theSherwood number can be approximated to 2, and the KSi valuesare essentially the diffusion coefficients (}i):

Sh2KSi dcat}i

105 36

The liquidsolid interface area (as) is evaluated from the cata-lyst amount (0.15 g) and its specific surface area, according toBET measurements (Sorptomatic 1900, CarloErbaInstruments) re-sulted in 855 m2 g1, which impliesas =128m2.

3.5. Reactor model

The reactor and operating procedures have been described else-where [18]. Shortly, it is a batch, slurry reactor with a gasentraining stirrer that continuously creates gas bubbles in the bulkof the liquid, drawing gas from the atmosphere above the liquid.

The species mass balances have been written in each phase, i.e.gas and liquid, the solid being assumed non-porous reduce to a fluxbalance at its interface. Balances are based on the followingassumptions:

(a) both liquid and gas phase are well mixed;(b) carbon dioxide and methanol are not involved in any

reaction;(c) any increment of liquid volume due to the accumulation of

H2O2and H2O is neglected, while the change caused by sam-pling is taken into account;

(d) species cannot accumulate on the catalyst surface, nor in theliquid boundary layer surrounding the catalyst particles.

According to these assumptions, the mass balances in the gasand liquid phases can be written as:

G

iC

,*L

iC

L

iC

L SiC

Fig. 1. Qualitative concentration profile of a reagent from the gas phase to thecatalyst surface.



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minimum of 30 samples was collected at each temperature; a totalof 174 data was used for the regression of the eight parameters, i.e.activation energy and pre-exponential factors. Each isothermal runhas been simulated and a set ofks estimated, for each step in themechanism; results are reported inTable 2, along with the coeffi-cients of determinationr2 measuring the agreement of model pre-dictions with both H2O2 and H2O concentration profiles,qualitatively shown inFig. 2.

The model is always in very good agreement with experimentalresults, withr2 values for H2O2very close to 1. Experimental mea-surements of H2O are less precise, due to the different analyticalprocedure, slightly decreasing the goodness of fit.

With the calculated isothermal rate constants the assumptionof unitary effectiveness factor can be checled. The Thiele modulus,/, is estimated as[28]:

/Rcat3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffikdsC

sO2

kwfCsO2 1=2 khCsH2O2

qcat

104DH2

vuut 46whereDH2 (effective diffusivity of H2) is computed asDH2 e

2cat}H2 ,

whereecat= 0.6 is the porosity of the catalyst. The effectiveness fac-tor is calculated as follows:

g1/ coth3/ 1

3/

47

For a typical particle sizeRcat= 15lm and at the highest tem-perature (i.e. highest reaction rates),/ is in the order of 103 andg 1, so that recalculation of the mass transfer coefficients andrate constants is unnecessary.

The kinetic constants calculated at each temperature are col-lected inFig. 3in the form of Arrhenius plots, and the resultingactivation energies and pre-exponential factor are reported inTable 3.

The temperature dependence of water formation, decomposi-tion and hydrogenation are all comparable (activation energiesclose to 45 kJ mol1). However, the kinetics of these reactions isquite different. Table 2shows that k values can differ by ordersof magnitude, but they are not really comparable, because referto different overall reaction orders. The most appropriate compar-ison must inspect the values of the reaction rates during the courseof each experiments, as shown inFig. 4.

Each reaction rate has been related to the one of direct synthe-sis,Rwf/Rds,Rd/Rds and Rh/Rds. Both decomposition and hydrogena-tion rates are null at the beginning, requiring the presence of theperoxide (i.e. they are reactions consecutive to the direct synthe-sis). Their rates increase during the reactions course, at a differentpace. Decomposition reaction is very slow compared to the direct

synthesis and becomes important only at a high H2 conversion,when the direct synthesis reaction slows down. A strong effect ofthe temperature is also observed on this reaction, where lowertemperature is confirmed to stabilize the H2O2produced. The pre-ferred path of H2O2degradation is the hydrogenation reaction: itsrate rapidly increases as H2O2becomes available, limiting the H2O2production. However this reaction is always slower than the directsynthesis (R

h/R

ds< 1) and it can be limited by decreasing the tem-

perature, up toRh/Rds< 0.5 at 258 K. Unfortunately, theRwf/Rds isalways significant because the formation of water really competeswith the direct synthesis, prevailing (Rwf/Rds> 1) at higher temper-ature, whereas lower temperature favors the direct synthesis(Rwf/Rds< 1). This explains the increased selectivity at lower tem-perature reported in the Literature, including our previous work[18]. At a given temperature, the rate of H2O formation remainsvery close to that of the direct synthesis (constant Rwf/Rds) exceptfor a short initial transient favoring the direct synthesis.

Due to the intrinsic nature of the interconnected reaction mech-anism, a correlation between the estimates of reaction rate con-stants has to be expected. A quantitative evaluation is given inFig. 5as contour plots for the parameter estimates, at T= 268 K.A small correlation is indicated by contours approaching circles.

A strong correlation is observed between most reaction con-stants, and remarkably among direct H2O2synthesis and the otherreactions. The lowest correlation occurs between decompositionand water formation, as expected. The same analysis was carriedout for all isothermal data with similar results. In order to improveor double check our estimates and suppress the correlation amongthe parameters, we studied the decomposition and hydrogenationrate constants independently, with dedicated experiments.

4.2. Decomposition experiments

Rate expression (20) was usedto fitthe H2O2 concentration pro-files during decomposition experiments, to isolate this step. Ateach temperature a minimum of 10 samples was collected; a totalof 45 data was used to calculate the two parameters, i.e. activationenergy and pre-exponential factor. Since in these experiments H2was replaced with N2, calculations were carried out neglecting rateexpressions (18) and (19)and hydrogen mass balance (Eq. (25)).Fig. 6shows the results, both as measured and calculated isother-mal data of H2O2concentration as a function of time, and in termsof Arrhenius plot.

Predictions are in good agreement (r2 very close to 1) withexperimental observations at any temperature considered, con-firming that decomposition is a first order reaction with respectto H2O2 concentration. The calculated reaction rate constants are

Fig. 2. H2O2direct synthesis experiments in the batch reactor: h, 258 K; }, 268 K;s, 273; , 283 K; 4, 297 K; solid line, model.



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shown inFig. 6b and the corresponding kinetic parameters are re-ported inTable 4.

A comparison of the Arrhenius constants obtained by fitting all

the rate constant in Eqs.(18)(21)together, using the direct syn-thesis experimental data, shows that the activation energy for kdobtained here for the decomposition reaction (50.43 kJ mol1)compares well with the above value (45.06 kJ mol1, Table 3),being that their confidence intervals overlap substantially. A higherdeviation is observed in the pre-exponential factors. However, thedeviation on the isothermal kinetic constants kd is less than 10%(T< 273 K), confirming the results reported inTable 3.

4.3. Hydrogenation experiments

H2O2hydrogenation experiments were carried out collecting aminimum of 10 samples; a total of 36 data was used to calculatethe two parameters, i.e. activation energy and pre-exponential fac-

tor. The experiments were performed substituting O2 with N2.Hence, direct synthesis and water formation reactions do not

occur. Accordingly, when regressing these data the mass balanceof O2(Eq.(26)) and rates(18) and (19)are ignored. Decompositionrate constants are not regressed this time and the parameters pre-viously obtained (Table 4) are introduced in the model and keptfixed. Only rate expression (21) is considered and isothermalhydrogenation reaction constants regressed. The deviation be-tween experimental H2O2 concentration measured during purehydrogenation and the best fit predictions is rather high, as showninFig. 7a.

Apparently, the kinetic model in this case is not adequate. Thedecay of H2O2 concentration in time is only approximately expo-nential, as clearly perceivable fromFig. 7a. In the first minutes ofreaction, and more clearly at lower temperature, the H2O2concen-tration decreases more slowly than later on. At higher H2 conver-

sion, the decay is very rapid, in a way that a second-order rateequation, linearly proportional to each reagent concentration, can-not fit. Consequently, the model switch from under- to over-esti-mation of the measured H2O2concentration, when approx. 70% ofthe introduced H2O2 is consumed. The effect of temperature, withinthe approximation discussed above, is well described by a linearArrhenius plot, shown inFig. 7b. The calculated activation energyand pre-exponential factor are respectively 17.85 1.00 kJ mol1

and 7.47 0.11 1012 cm6mol1s1mol1Pd . However, thekh valuesare much higher compared to the ones reported inFig. 3, also re-flected in a significantly lower activation energy. We explain bothresults, a 2-steps H2O2 consumption and its higher rate, in termsof differences in the catalyst oxidation state. Synthesis and hydro-genation experiments use a different experimental condition: the

former are carried out in large excess of O2, the latter does not in-clude any O2, but H2is the only reactant present. Accordingly, the

Table 2

Isothermal reaction rate constants and r-square value on H2O2 and H2O.

T(K) kds/107 cm6 mol1 s1 mol1Pd

kwf/10

5 cm9=2 mol1=2 s1 mol1Pd

kd cm3 s1 mol

1Pd

kh/10 cm6 mol

1 s1mol1Pd

8 r2H2O2() r

2H2O ()

297 26.42 48.78 221 35.20 0.9897 0.9777283 17.68 19.84 227 17.39 0.9846 0.9790273 12.17 7.18 48 5.68 0.9929 0.9525268 8.00 6.18 52 4.46 0.9920 0.9738

258 6.67 3.27 17 2.30 0.9913 0.9716

Fig. 3. Arrhenius plots for the kinetic constants of each individual step in the mechanism.

Table 3

Arrhenius constants for the rate Eqs. (1)(4)(direct synthesis experiments).

Pre-exponential factor(see Table 2 for units)

Activation energy (kJ mol1)

Direct synthesis 4.18 0.15 1012 23.84 2.45Water formation 4.27 0.20 1014 45.31 3.61Decomposition 2.61 0.45 1010 45.06 9.60Hydrogenation 5.65 0.22 1017 46.58 3.72



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active metal on the catalyst can be mostly oxidized in excess of O2(synthesis conditions), and reduced in excess of H2 (hydrogenationconditions). The reduced form of the catalyst can be more effectivefor the hydrogenation reaction, enhancing its rate, consistentlywith literature observations[21,12]that the production of hydro-gen peroxide is favoured by the oxidized form of Pd. In addition,the H2O2hydrogenation on reduced Pd may occur with a non-ele-mentary mechanism, involving a complex model also accountingfor competitive adsorption of H2 and O2. According to the discus-sion above, we rely on the kinetic model and values ofTable2 to de-scribe the reaction network at synthesis (i.e. O2 dominated)

conditions. Further, we question the significance of independentlyestimating the H2O2hydrogenation kinetics in case the catalyst is

vulnerable to oxidation/reduction at conditions of the experiments,which is quite common. Also, in case of non-elementary mecha-nism, a competitive adsorption on the catalyst sites between H2and O2is expected in the synthesis experiments, which is not thecase for hydrogenation experiments.

Unfortunately, the kinetic parameters determined here are dif-ficult to compare numerically with other studies in the Literature,because of the different rate laws, catalysts, and assumptions indescribing the reacting environment. Menegazzo et al.[13] studiedthe kinetics on a bimetallic Pd/Au catalyst, in a semi-batch reactor(batch liquid phase and flowing gas), at ambient conditions. Beingthe concentration of H2and O2constant (albeit not specified), theywere included in the kinetic parameters, making a quantitativecomparison with our results quite difficult. In addition, materialbalances differ in the stoichiometry and reaction orders as well.Voloshin et al.[15]measured the kinetics of H2O2 hydrogenationreaction over a Pd/SiO catalyst in a microreactor; they determinedan activation energy of 43.71 kJ mol1, close to our estimate usingsynthesis experiments (46.58 kJ mol1), but not the pure hydroge-

nation ones, as discussed above. In another study [9], the sameAuthors reported the activation energy for the direct synthesis as

Fig. 4. Ratio of each reaction rate to the direct synthesis during the reaction course. 4, 297 K; , 283 K;s, 273 K; }, 268; h, 258 K.

Fig. 5. Contour plots of regressed kinetic parameters (T= 268 K).

Table 4

Arrhenius constants for rate Eq. (3) (decomposition experiments).

Pre-exponential factor (cm3 s1) Activation energy (kJ mol1)

3.11 0.21 1011 50.43 4.28



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well, in a similar apparatus; they found 22.34 kJ mol1, a value thatcompare well to 23.84 kJ mol1 that we calculated here.

5. Parametric sensitivity on mass transfer coefficients

Values ofKLi aL (mass transfer between gas and liquid) for H2

was calculate in the range 9601880 h1, at 258 and 297 K, respec-tively. Similar values were obtain for O2. Our calculations comparewell with 1080 h1 measured by Meyberg et al. [29] for H2 in liquid

alkyne in a similar apparatus. Deguchi et al.[30]observed smallervalues for H2 dissolution in water at 303 K in a 300 ml flaskequipped with a magnetic stirrer (149560 h1 varying the stirringspeed from 1000 to 1350 rpm). Andersson et al.[31]performed H2dissolution experiments in anthraquinones at different tempera-tures in a two liters autoclave with two turbine impeller, reportingaKLi a

L value of 1400 h1 at 298 K. The deviations observed amongthese works are likely due to differences in the geometry of theequipment used, stirring and operative conditions adopted.

The coefficients of mass transfer resistance at the catalyst sur-face,KSi , estimated by Eq.(36), are in the range 1.4 10

23.5 102 cm s1 at 258 K and 297 K, respectively, for all components.

Since we tried to predict the mass transfer rates a priori, usingthe best available correlations, we expect that the chemical kinet-

ics was properly identified, with the results given inTable 3. Wouldthe mass transfer actually control the process, or part of it, we

should expect the chemical kinetics to be inaccurately determined.We actually used this reasoning to evaluate the extent of masstransfer control at our experimental conditions. The values ofKLi a

L andKSi , first calculated by Eqs.(27)(36),have been increasedor decreased by up to one order of magnitude and the kineticparameters (activation energy and pre-exponential factors) re-esti-mated. Different simulations were carried out changing each indi-vidual mass transfer coefficients, one at a time. As expected, noinfluence on the kinetic parameters was observed varying KLi a

L

andKSi values of O2, H2O2and H2O, the only critical species being

hydrogen, the limiting reagent in all the performed experiments.Further, decomposition reaction is not affected by hydrogen con-centration because of its rate law expression, and it is excludedfrom this analysis. The sensitivities of the reaction rate constantskto KLH2 a

L are shown inFig. 8.Decreasing H2 mass transfer coefficients from gas to liquid af-

fects the estimated rate constants of any reaction; the reducedH2 transfer rate to the liquid phase (and hence to the catalyst) mustbe balanced by the increased reaction kinetics. Interestingly, limi-tations in the H2mass transfer rate cause an apparent increase inthe estimated activation energy, as can be observed in Fig. 9, recall-ing the importance of accounting for mass transfer to properlyidentify the kinetics.

However, some mass transfer effect was only evident at tem-peratures above 283 K, by artificially loweringKLH2 aL at least by

Fig. 6. H2O2decomposition experiments in a batch reactor: (a) normalized experimental and calculated H2O2concentration andr-square values:h, 313 K;}, 283;s, 273 K;, 268 K; solid line, model. (b) Arrhenius plot forkd.

Fig. 7. H2O2hydrogenation experiments in batch reactor: (a) normalized experimental and calculated H 2O2 concentration: h, 313 K;}, 283; s, 273 K; solid line, model. (b)Arrhenius plot.



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one order of magnitude (form 1880 h1 to 140 h1). Accordingly,we conclude that limitations due to the dissolution rate of hydro-gen can be excluded at the experimental conditions, even account-ing for uncertainties in the correlations, that could not be as high as1 order of magnitude.

Fig. 10 shows the effect of the mass transfer rate fromthe liquid

to the solid surface (KS

H2 ) on the reaction rate constants of directsynthesis, water formation and hydrogenation.

At the highest temperature (i.e. 297 K), where the effect is ex-pected to be more evident,KSH2were varied from3.01 10

4 cm s1

to 8.61 102 cm s1. As can be seen, predicted values of reactionrate constants do not significantly change, even varying the resis-tance by two orders of magnitude. Accordingly, the activation en-ergy of the three reaction remains constant (Fig. 9). This proves

that any restriction due to the mass transfer limitation to the cata-lyst surface is negligible at the experimental conditions.

Fig. 8. Effect ofKLH2 aL on the reaction rate constantsof direct synthesis, water formationand hydrogenation. The value given by correlation 10 hasbeenmultiplied by: 0.0035

(h), 0.08 (}), 0.15 (s), 0.5 (), 1 (4), 5 (+), 10 (x).

Fig. 9. Effect ofKLH2 aL andKSH2 on the activation energy of direct synthesis, hydrogenation and hydrogenation reactions.



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