The use of modelling to understand the mechanism of hydrogen peroxide direct synthesis from batch, semibatch and continuous reactor points of view

Abstract

Hydrogen peroxide direct synthesis was experimentally studied in three different reactors, namely the batch, semibatch and trickle bed reactors (TBR), using a new promising catalyst based on Pd/K2621. Excellent results were obtained from the experimental point of view, achieving high H₂O₂ selectivities, around 90% for a short contact time in the batch reactor, 60% in the semibatch reactor and 70% in the TBR. The simplest rate equations compatible with the acknowledged reaction network have been included in a reactor model, which accounts for mass transfer resistances between the gas and the liquid in the liquid–catalyst surface. The corresponding Arrhenius parameters were estimated from direct synthesis experiments for all the reactions and reactors. The models show how the reaction rates change among the batch, semibatch and trickle bed (TBR) reactors. The results suggest how to improve the reactor set-up and reaction performance in continuous operations and how to compare the results between the different reactors and conditions. The sensitivity analysis on the reaction allowed to gain new insights into the reaction rates. The TBR showed how the mass transfer limitations can help to direct the reaction towards the H₂O₂ synthesis. Remarkably, these results were achieved in the absence of any acids or halide ions, i.e. no known selectivity promoters for direct H₂O₂ synthesis were applied, thus the kinetics are not affected by the presence of promoters.

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Introduction

The H₂O₂ direct synthesis (DS) is a simple but challenging reaction extensively studied in the past 20 years.^1–4 The simplicity of the DS comes from the fact that the H₂ and O₂ dissolved in a reactant medium (e.g. methanol or water) react over a metallic supported catalyst to form H₂O₂ and the only by-product is water. In principle, the DS aims to partially substitute the well-established industrial autoxidation process (AO). The AO process counts some drawbacks such as the need for wastewater treatment, initial CAPEX, big industrial plants, etc. The DS may solve these drawbacks but to be commercialized, a high selectivity of H₂O₂ should be obtained. Indeed, the H₂O₂ produced in the DS is just an intermediate, and can be decomposed or hydrogenated to water by the same catalyst active for the DS³ (Scheme 1).

Scheme 1 Reactions involved in the direct synthesis of H₂O₂.

The need to have an alternative to the AO process is strong enough to attract a lot of attention both from academia^4–7 and industry. The new century industry needs, in most of the cases, to reduce investment costs, to delocalize the production and to have flexible solutions with low waste management. Due to its potential, the DS is a process that will help to develop a new industry concept. Unfortunately, due to the lack of maturity in this research field, the real breakthrough has not happened yet and the commercialization of the process still lags behind.⁴

The reasons discussed above are the driving forces that still make the DS a hot topic in the scientific community. Up to now, the research in the direct synthesis has been very much focused on the catalyst development,^7–22 and only in recent years the investigation on the entire process gained attention and importance.^3,23–29 The publications that cover the catalyst development topic range from the study of the catalyst support, catalyst active metal, metal precursor and promoters in the reaction medium. Only recently, publications have demonstrated the beneficial effect of studying the reaction from a chemical reaction engineering point of view.^{3,5,6,30–32} Indeed, it has been demonstrated that playing with the reaction conditions and reactor set-up can enhance the performance of the catalyst. Despite the latest results, there are only some hypotheses on why the reaction conditions can ameliorate the DS. However, attention should not be placed only on catalyst development or chemical reaction engineering, but the two approaches should be well-integrated in a multidisciplinary research with a holistic approach.³³ Moreover, due to the extensive number of publications on the catalyst development, the comparison of the results obtained is nowadays difficult due to the different systems (reactors and reaction conditions) used to test the catalysts. This problem is not trivial and up to now there is no solution on how to compare the different data. In this regard an appropriate comparison is missing and the real state of the art can appear a little bit chaotic. These problems indicate the importance of an appropriate and fruitful connection between the chemistry and chemical engineering communities, filling the gap between them.³³

With this in mind, it was decided to study a novel promising catalyst³⁴ using three different reactors: a batch reactor, a continuous stirring tank reactor (CSTR) and a trickle bed reactor (TBR).³ The choice of using a new catalyst comes from the fact that we have already demonstrated that by playing with the reaction conditions, using a commercial catalyst, the DS reaction can be enhanced. The new catalyst was tailor-made for the DS and it was developed, as the best practice for multiphase systems recommends, in a batch reactor, at a fixed pressure, temperature and gas composition, to understand its performance.³⁴ After the first promising results, the catalyst was studied under different conditions in the different reactors to clarify its performance, taking into consideration mass transfer, kinetics and to what extent the catalyst performance is affected by the different reactors. The choice to use the batch reactor, the CSTR (or semibatch) and the TBR to study the kinetics comes from the fact that in our previous works we qualitatively observed some phenomena such as the H₂/Pd ratio profile vs. H₂O₂ productivity, the H₂ mass transfer, the hydrogenation extent, etc.^3,6,9,34,35 In this work the aim is to quantify these phenomena and to relate them to the different reactors used. With this approach the reaction was studied from the chemistry level to the chemical reaction engineering level, answering some of the still open issues in the DS. We also present here a powerful tool to understand how the different data in the open literature can be compared between them. Understanding the reaction path and progress with the three reactors helps identify the strategies to improve the reaction conditions and the catalyst design. Moreover, by understanding properly the reactor operation, the catalytic results can be evaluated with more criticism and the discovery of new insights will be faster.

Experimental

Materials

The catalyst was obtained by supporting palladium nanoparticles (0.5 wt%) on a commercial PS-DVB macroreticular resin (Lewatit K2621), which proved to be an efficient support for the direct synthesis of hydrogen peroxide.^17,36,37 Details on the preparation via an ion-exchange method are reported in our previous studies.^37,38 Pd(NO₃)₂ for the catalyst preparation was purchased from Alfa Aesar. Sodium thiosulfate pentahydrate (99.5%), potassium iodide, starch and concentrated sulfuric acid (all used for the peroxide titration) were purchased from Sigma-Aldrich; HPLC grade methanol (99.99%) from J. T. Baker; and H₂, O₂ and CO₂ (99.999% mol mol⁻¹ purity) from AGA (Linde group). Methanol for the Karl Fischer titration, Hydranal composite 2 and ammonium molybdate tetrahydrate were purchased from Fluka. All materials were used as received. Complete characterization of the catalyst is reported in the ESI.†

Experimental set-ups

Using the same catalyst, the experiments were carried out in three reactors: batch, semibatch and continuous (TBR). CO₂ was used to dilute the gas mixture outside the flammability limits and to achieve a high H₂ solubility.³⁹ H₂O₂ and H₂O concentrations were determined at an increasing time on stream by iodometric and Karl-Fischer titrations, respectively.

Batchwise experiments were performed in a 600 ml unbaffled reactor with standard geometry (Buchi), schematically represented in Fig. 1.

Fig. 1 Schematic of the batch apparatus: 1, reactor; 2, cooling/heating jacket; 3, high pressure pump; 4, sampling valve; MFC, mass flow controller.

The experimental apparatus and procedures are described elsewhere.⁴⁰ Shortly, 0.15 g of the catalyst was loaded in the reactor. Carbon dioxide (20 bar) and oxygen (5 bar) were introduced in the vessel (298 K), followed by the injection of 400 ml of methanol. After the pressure and temperature were stabilized at the desired values, hydrogen was fed as the limiting reagent. The reaction was assumed to start immediately after hydrogen loading. The gas mixture was carefully kept outside the flammability limit. A stirring rate of 1000 rpm was conservatively adopted to ensure good mixing of the liquid phase, as verified in dedicated experiments. The liquid phase was sampled from the batch reactor via a dedicated valve. H₂O₂ selectivity and H₂ conversion were calculated as:

The semibatch experiments were performed in a 300 ml unbaffled reactor with standard geometry (Buchi), as described elsewhere.⁴¹Fig. 2 shows a schematic of the apparatus.

Fig. 2 Schematic of the semibatch apparatus: 1, reactor; 2, cooling/heating jacket; 3, condenser; 4, high pressure pump; 5, sampling valve; 6, catalyst chamber; MFC, mass flow controller; BPC, back pressure controller.

Briefly, methanol (200 ml) was introduced in the vessel first, followed by the gas reagents. Throughout the experiments, the gas (300 Nml min⁻¹) was continuously bubbled into the liquid with a 76–20–4 mol% composition of CO₂–O₂–H₂, respectively. The gas outlet was equipped with a condenser to ensure that no methanol left the reactor with the outgoing gas flow. The catalyst (0.2 g) was introduced via a dedicated chamber, after the vapor–liquid equilibrium was reached at the desired temperature and pressure (20 bar). The reactions were assumed to start as the catalyst was loaded into the reactor. Note that introducing the catalyst last allows a very precise identification of the beginning of the reactions. The liquid phase was sampled via a dedicated valve and the selectivity and conversion were calculated viaeqn (1) and (3), respectively:

The continuous experiments were performed in a concurrent, downflow trickle bed reactor, developed from our previous apparatus.²⁸ A schematic of the reactor is shown in Fig. 3.

Fig. 3 Schematic of the continuous TBR apparatus: 1, quartz sand; 2, catalytic bed; 3, cooling/heating jacket; 4, gas/liquid separator; 5, condenser; 6, high pressure pump; 7, methanol reservoir; MFC, mass flow controller; BPC, back pressure controller.

The reactor consisted of an AISI 316 stainless steel pipe, 50 cm long, with an internal diameter of 1.5 cm. A mixture of quartz sand/catalyst filling 30 cm of the reactor was introduced first, followed by pure quartz sand (15 cm) to ensure a good vapor–liquid equilibrium. Then methanol was flowed into the reactor (5 ml min⁻¹ for 5 min) to wet the catalyst bed. Afterwards the methanol flow was decreased at the desired rate and a mixture of CO₂ and O₂ was added. When stable pressure (20 bar) and temperature values were reached, H₂ was fed and the reaction was assumed to start. The gas flow was 11 Nml min⁻¹ with a composition of 73–23–4 mol% of CO₂–O₂–H₂, respectively. The liquid phase was sampled at an increasing time on stream. The selectivity and conversion were calculated by using eqn (1) and (4), respectively:

Modelling

Chemical kinetics

Several surface mechanisms on palladium can give the overall process described in Scheme 1. Voloshin et al.³² screened some mechanisms to describe the kinetic data obtained from microstructured reactors and concluded that a Langmuir–Hinshelwood-type mechanism, with the surface reaction steps as the rate determining ones, gave the best agreement with the experimental data. Dissociative adsorption of the reactant species was also proposed by Deguchi et al.⁴² Some mechanistic studies have given information about the reaction mechanism. For instance, Dissanyake and Lunsford⁴³ proposed that the O–O bond does not dissociate during the H₂O₂ synthesis process and Sivadinarayana et al.⁴⁴ confirm the species HO₂⁻ on a gold catalyst surface. Wilson and Flaherty⁴⁵ proposed a detailed mechanism based on a two-site adsorption, where H₂O₂ forms by heterolytic reaction pathways resembling the two-electron oxygen reduction reaction (ORR). However, it is clear that water formation requires the rupture of the O–O bond on the catalyst surface. All these mechanisms include several reaction constants, which are inevitably correlated when regression is attempted. Hence, in order to avoid overparameterization, no adsorption steps were included in the reaction mechanism; this assumption is also justified by the low reagent concentrations. Assuming that the reactions are irreversible, the simplest rate equations included in Scheme 1 are (were ds = direct synthesis, wf = water formation, d = dissociation, h = hydrogenation):with temperature dependent, Arrhenius-type kinetic constants:The pre-exponential factor (A_i) and activation energy (E_ai) of each reaction are determined from our experimental data, as described below. According to Scheme 1, the production rates are obtained as:

r_H2O2 = R_ds − R_d − R_h (10)

r_H2O = R_wf + R_d + 2R_h (11)

r_H2 = − R_ds − R_wf − R_h (12)

r_O2 = − R_ds − 0.5R_wf + 0.5R_h (13)

Mass balances

The mass balances developed for the mathematical models of the batch, semibatch and trickle bed reactors are described below.

Batch reactor

The reactor and operating procedures have been described elsewhere.³¹ Shortly, it is a batch, slurry reactor with a self-inducing stirrer continuously drawing gas from the atmosphere above the liquid. The mass balances of the components have been written for each phase, i.e. gas and liquid. The balances are based on the following assumptions:

a) Both liquid and gas phases are well-mixed.

b) Carbon dioxide and methanol are not involved in any reaction.

c) An increment in the liquid volume due to the accumulation of H₂O₂ and H₂O is neglected, while the change caused by sampling is taken into account.

Accordingly, the mass balances in the gas and liquid phases are:

The liquid phase is assumed to be pseudo-homogeneous, so that the production rates r_i can be expressed as functions of the liquid phase concentrations (C^L_i). At the gas–liquid interface holds the equilibrium condition:

C^L,*_i − C^G_iH_i (16)

The gas–liquid equilibrium parameter constants H_i depend on the total composition, pressure and temperature. The H_i values are only needed for oxygen and hydrogen, due to assumptions (b) and (c), and are estimated from an equation of state tuned on specific experimental data.³⁹ The proposed model is given by a total of six ordinary differential equations, two for the gas phase and four for the liquid phase. Its integration yields the evolution in time of the concentration of the reactants (H₂ and O₂) in the gas and liquid phases and of the products (H₂O₂ and H₂O) in the liquid phase. According to the experimental procedure,⁴⁰ the following six initial conditions are assumed:

Hydrogen (the limiting reagent) was introduced after all the other species, when stable values of pressure and temperature were reached inside the reactor (filled with O₂, CO₂ and methanol). Since the H₂ feeding was fast compared to the reaction time,⁴⁰ hydrogen is assumed not to dissolve in the liquid phase while introduced (conditions (17b) and (17c)). The initial compositions of the gas and liquid phases were evaluated with an equation of state.³⁹ The initial concentration of water in the reaction medium (condition (17e)) was measured prior to the introduction of hydrogen.⁴⁰ The mass balance eqn (14) and (15), together with initial conditions (17), have been efficiently solved using Matlab's “ode15s” solver, also suitable for stiff equations, being based on a multistep, variable order method based on the numerical differentiation formulae.

Semibatch reactor

The semibatch reactor is a slurry reactor, similar to the batch reactor previously described. Here gas reagents were continuously fed via three mass flow controllers. The pressure was kept constant via a back pressure controller. The mass balances are based on the following assumptions:

a) Both liquid and gas phases are well-mixed.

b) Carbon dioxide and methanol are not involved in any reaction.

c) Any increment in the liquid volume due to the accumulation of H₂O₂ and H₂O is neglected, while the change caused by sampling is taken into account.

d) The gas composition at the outlet is assumed equal to the composition inside the reactor (i.e. the gas phase behaves like a continuous stirred tank reactor).

e) The gas mixture is assumed to be ideal, i.e. the density does not depend on the composition.

Accordingly, the mass balances in the gas and liquid phases can be written as:

where the liquid phase is assumed to be pseudo-homogeneous and at the gas–liquid interface equilibrium holds (eqn (16)). Once again, the H_i values³⁹ are only needed for oxygen and hydrogen (assumptions (b) and (c)) and the production rates r_i are functions of the liquid phase composition (C^L_i). Note that the gas density is constant, because of the assumption (e) and constant T and P. The proposed model is given by a total of seven equations: two ordinary differential equations and one algebraic equation for the gas phase and four ordinary differential equations for the liquid phase. The solution yields the evolution in time of the concentration of the reactants (H₂ and O₂) in the gas and liquid phases, of the products (H₂O₂ and H₂O) in the liquid phase and the total molar flow at the reactor outlet. According to the experimental procedure, the following seven initial conditions are assumed:

The catalyst was introduced last, when stable values of pressure and temperature were reached inside the reactor (filled with H₂, O₂, CO₂ and methanol). The initial compositions of the gas and liquid phases were evaluated with an equation of state.³⁹ The initial concentration of water in the reaction medium (condition (21b)) was measured prior to the introduction of the catalyst. The material balance eqn (18)–(20), together with initial conditions (21), give a mixed algebraic–differential equation (ADE) system, which have been efficiently solved using Matlab's “ode15s” ADE solver.

Trickle bed reactor

In the trickle bed reactor, both gas and liquid were continuously fed via three mass flow controllers and a high pressure pump, respectively. The model is based on an advanced approach reported in our previous study on the fluid dynamics of a trickle bed reactor.⁴⁶ The liquid flow is described by a combination in series of an axial dispersion model (ADM) and a stirred tank (ST) model, whereas the gas phase is described by a plug flow model. A schematic representation is given in Fig. 4.

Fig. 4 Schematic representation of the trickle bed reactor model.

The balances are based on the following assumptions:

a) Carbon dioxide and methanol are not involved in any reaction.

b) Any increment in the liquid volume due to the accumulation of H₂O₂ and H₂O is neglected.

c) Steady state conditions.

d) The reactions only occur in the ADM liquid volume.

e) The ST liquid volume is isolated from the gas phase.

f) Constant pressure.

Accordingly, the mass balances in the gas and liquid phases are:

whereThe liquid phase in the ADM is again assumed to be pseudo-homogeneous and equilibrium holds at the gas–liquid interface (eqn (16), only necessary for oxygen and hydrogen). According to assumption (d), the production rates r_i are a function of the concentrations in the ADM (C^L,ADM_i), and hence the catalyst density (ρ^ADM_B) is referred to the ADM liquid volume. Note that the accumulation term in the ST model, eqn (24), was referred to the spatial coordinate in the ADM:

In eqn (22) the axial dispersion coefficient (D) appears. Its value was calculated according to the following correlation,⁴⁶ based on specific residence time distribution measurements:

The volumes of the liquid (V^L,ADM and V^L,ST) and gas phases (V^G) were calculated as follows:

V^G = επR²L − (V^L,ADM + V^L,ST) (30)

where the dimensionless residence times in the ADM and ST model (θ^ADM and θ^ST, respectively) were calculated according to the following correlations:⁴⁶

The model calculates the compositions along the reactor length at steady state (assumption (c)), so that the time dependence is not taken into account. Therefore, eqn (22)–(24) represent a boundary value problem, which requires the following boundary conditions:

Danckwerts conditions were chosen for eqn (22), i.e. continuous flow at the reactor inlet (condition (32a)) and a zero slope condition at the reactor exit (condition (32b)). The gas phase composition at the reactor inlet (condition (32c)) was imposed via the three mass flow controllers. The liquid phase composition of the reagents at the reactor inlet (condition (32d)) was evaluated with an equation of state,³⁹ whereas water was measured in the methanol reservoir.

The proposed model is given by a total of ten equations: four ordinary differential equations and four second order ordinary differential equations for the liquid phase and two ordinary differential equations for the gas phase. Its integration yields the evolution along the reactor length of the concentration of the reactants (H₂ and O₂) in the gas and liquid phases and of the products (H₂O₂ and H₂O) in the liquid phase. The mass balance eqn (22)–(24), together with boundary conditions (32), have been efficiently solved using Matlab's “bvp5c” solver for boundary value problems, a finite difference code that implements the four-stage Lobatto IIIa formula as an implicit Runge–Kutta method.

Kinetic identification

The kinetic models have been formulated above. The values of the activation energy (E_a) and the pre-exponential factor (A) of each reaction involved were determined by isothermal experimental data fitting. The four irreversible reaction rate constants k_ds, k_wf, k_d and k_h were individually regressed at the given temperatures, minimizing the following error function:

Note that the errors between the experimental and calculated concentrations have been rescaled. The E_a and A values were then assessed by fitting k(T) with the Arrhenius equation. A Nelder–Mead simplex algorithm with positive constraints on the parameters (a modification of the Matlab function “fminsearch”) was used to minimize the error by adjusting the parameters of the model.

The results were critically analyzed by preparing sensitivity plots, in which the objective function was plotted as a function of a single parameter at a time, while the other parameter values were kept fixed, which gave the objective function minimum. The correlation between the parameters is visualized by evaluating the contour plot for each pair, that is plotting a couple of parameter values that result in the same value of the error function (eqn (33)), with the other parameters kept constant (ESI,† Fig. S3–S7).

Experimental results

The experiments were carried out in the batch, semibatch and trickle bed reactors at temperatures in the range from −10 to 30 °C. The results are reported below for each of the experimental set-ups investigated.

Batch reactor

The experimental results obtained in the batch reactor are reported in Fig. 5 as H₂O₂ and H₂O concentrations, selectivity and H₂ conversion at different temperature values. All experiments were carried out within the kinetic regime, as demonstrated in our previous studies.^31,40

Fig. 5 H₂O₂ and H₂O concentrations (top left and right, respectively), selectivity (bottom right) and H₂ conversion (bottom left) as a function of the time on stream in the batch reactor: , −10 °C; , 2 °C; , 15 °C; ■, 30 °C. Solid lines represent the model.

The water concentration increased constantly, prevailing over the hydrogen peroxide concentration only at the higher temperatures (15 and 30 °C). The H₂O₂ concentration rapidly increased for a short contact time, reaching a maximum and gradually decreasing afterwards. A complete consumption of H₂ (the limiting reagent) corresponded to the maximum concentration of H₂O₂: after H₂ was no longer present in the liquid phase, the direct synthesis as well as the hydrogenation was suppressed and thus only the decomposition of H₂O₂ took place; this resulted in a drop of the peroxide formation and consequently in a slower water production rate. Interestingly, the H₂O₂ concentration decreased with the temperature, whereas the opposite effect was observed on H₂O. This resulted in a higher selectivity at lower temperatures, with values up to 90% at −10 and 2 °C for a short contact time. Note also that the selectivity decreased with increasing temperature at the same H₂ conversion. Moreover, the H₂O concentration rapidly increased also for a very short contact time. These observations suggest that a) the direct formation of water is immediately competitive with the H₂O₂ direct synthesis reaction and b) the activation energy of the direct synthesis and the dominant H₂O production reactions are very different, the former being lower than the latter.

Semibatch reactor

The experimental results obtained in the semibatch reactor are reported in Fig. 6 in terms of H₂O₂ and H₂O concentrations, selectivity and H₂ conversion at different temperatures. Mass transfer limitations in the reactor were investigated in our previous work,⁴¹ with the conclusion that the experiments were performed within the kinetic regime.

Fig. 6 H₂O₂ and H₂O concentrations (top left and right, respectively), selectivity (bottom right) and H₂ conversion (bottom left) as a function of the time on stream in the semibatch reactor: , −10 °C; , 2 °C; , 15 °C; ■, 30 °C. Solid lines represent the model.

In all experiments, the H₂O₂ concentration leaned towards a steady state value, and at the same time the H₂O concentration steadily increased. This was expected, since H₂O₂ is a reaction intermediate and water is the final product; in a semibatch apparatus the accumulation of peroxide leads to an increase of the hydrogenation and disproportionation rates, so that the H₂O₂ concentration reaches a steady value, whereas the water concentration increases. The selectivity values decreased with the temperature and time on stream, same as for the batch apparatus (Fig. 5), though higher values were achieved in that reactor. Same as for the batch reactor, H₂O₂ decreased with the temperature, whereas H₂O increased. Hence, the selectivity toward the peroxide decreased with H₂ conversion, as expected for an intermediate product (Scheme 1). Interestingly, H₂ conversion increased with the time on stream; moreover, H₂O production was slow at the beginning and increased with the time on stream. These observations suggest that: a) the H₂O₂ direct synthesis is more favored than the H₂O production reaction (in contrast to the batch reactor, where H₂O production was fast also at a short time on stream); b) same as for the batch reactor, the activation energy of the direct synthesis and the dominant H₂O production reactions are very different, the former being likely lower than the latter; c) hydrogenation is the preferred reaction for H₂O production, because of observation a) and the increasing H₂ conversion with the time on stream.

Trickle bed reactor

The experiments in the TBR were carried out using a constant catalyst amount (0.2 g) with two liquid flow rates (LFR) and an increasing temperature. The results are reported in Fig. 7 in terms of the H₂O₂ and H₂O concentrations at steady state.

Fig. 7 H₂O₂ (left) and H₂O (right) concentrations at steady state as a function of the temperature at different LFR: ♦, 1.75 ml min⁻¹; ◊, 3 ml min⁻¹. Catalyst amount = 0.2 g.

As observed in the batch and semibatch experiments, the H₂O₂ concentration decreased with the temperature, whereas H₂O increased. This confirmed the hypothesis that the activation energy of the direct synthesis reactions is lower than that of H₂O₂ production. As a consequence, the selectivity decreased with the H₂ conversion, as shown in Fig. 8. These results were qualitatively independent of the liquid flow rate. However, an increasing methanol flow rate resulted in a lower H₂O₂ and H₂O production (Fig. 7), due to the reduced contact time. The data are actually consistent in terms of selectivity and H₂ conversion, as shown in Fig. 8.

Fig. 8 Selectivity as a function of H₂ conversion at steady state in the trickle bed reactor at LFR of 1.75 ml min⁻¹ (full symbols) and 3 ml min⁻¹ (void symbols): , −10 °C; , 2 °C; , 15 °C; ♦, 30 °C.

The H₂ conversion values obtained in the TBR were between 20 and 98%, a range more limited than those obtained in the other series of experiments (Fig. 5 and 6). In order to get a better comparison with the data obtained in the batch and semibatch apparatus, the data at lower H₂ conversions are desirable. Hence, the experiments were carried out at the lowest temperature (−10 °C) with an increasing catalyst amount (LFR = 3 ml min⁻¹). The results are reported in Fig. 9.

Fig. 9 H₂O₂ (left) and H₂O (right) concentrations at steady state as a function of the catalyst amount. LFR = 3 ml min⁻¹ and −10 °C.

As expected, the H₂O₂ and H₂O concentrations linearly increased with the catalyst amount in the reactor. The selectivity and H₂ conversion (Fig. 8) are consistent with the data measured at different temperatures and the liquid flow rates, with selectivity values up to 71% at 20% H₂ conversion.

Discussion

In order to quantitatively compare the experimental results, the kinetic parameters of the catalyst were regressed using the experimental data in the three reactor set-ups investigated. The calculated activation energies and pre-exponential factors of all reactions involved (Scheme 1) are reported in Table 1.

Table 1 Activation energy and pre-exponential factors regressed in the batch, semibatch and continuous experiments. ds = direct synthesis, wf = direct water formation, d = decomposition and h = hydrogenation

	Batch		Semibatch		TBR
	E a kJ mol^−1	A	E a kJ mol^−1	A	E a kJ mol^−1	A
ds	42.6	1.47 × 10^9	67.0	8.90 × 10^21	6.9	3.18 × 10^17
wf	92.3	4.38 × 10^23	133.8	1.15 × 10^14	8.0	5.52 × 10^15
d	30.1	1.47 × 10^9	58.9	1.09 × 10^20	5.1	4.66 × 10^3
h	53.2	1.38 × 10^19	29.8	7.07 × 10^2	7.3	3.87 × 10^15

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The rate of each reaction was also calculated. The results are shown in Fig. 10 as the ratios between the rate of the undesired reactions (water formation, hydrogenation and disproportionation) and the direct synthesis reaction rate to mark the favoured undesired reaction.

Fig. 10 Ratios between the water formation, hydrogenation, disproportionation reactions rates and the direct synthesis reaction rate in the batch, semibatch and TBR experiments. , −10 °C; , 2 °C; , 15 °C; ■, 30 °C. R_ds, rate of direct synthesis, R_wf, rate of water formation, R_h, rate of hydrogenation of hydrogen peroxide, R_d, rate of decomposition of hydrogen peroxide.

In the batch reactor, all the kinetic parameters were well-identified, as the sensitivity analysis reveals (ESI,† Fig. S3). The contour plots (ESI,† Fig. S4) show some correlation between the parameters, especially between water formation and hydrogenation, but this is expected, given the complex scheme of the reaction. As qualitatively noticed in the previous section, in the batch reactor, water formation competes with the direct synthesis reaction (Fig. 10); however, the ratio R_wf/R_ds is larger than 1 only for the highest temperature, i.e. the water formation reaction prevails over the direct synthesis only at a high temperature; at the same time, also the hydrogenation and decomposition reactions are significant, although both the R_h/R_ds and R_d/R_ds ratios had values lower than 1. The direct synthesis activation energy is confirmed to be lower than that of the water formation (Table 1).

The data collected in the semibatch apparatus were somewhat different. The sensitivity analysis (ESI,† Fig. S5) reveals that the water formation and decomposition reactions had a negligible effect on the objective function; this confirms that the reaction rate of the water formation and disproportionation reactions were negligible compared to the direct synthesis rate, as actually shown in Fig. 10. The contour plot (ESI,† Fig. S6) reveals a slight correlation between the direct synthesis and the hydrogenation reactions. As noticed in the previous section, the most important reaction competing with the direct synthesis was the hydrogenation, although the R_h/R_ds values were always lower than 1 (Fig. 10). The activation energy of the water formation was higher than that of the direct synthesis reaction, as noticed in the batch reactor (Table 1). However, two major differences are apparent when comparing the results in the batch and semibatch reactors: 1) in the batch apparatus all the undesired reactions were competing with the direct synthesis, whereas in the semibatch only hydrogenation had a significant effect (Fig. 10); 2) although the activation energy of the direct synthesis was lower than that of the water formation, the values obtained in the two apparatus were quite far from each other (Table 1). These observations suggest that the reaction conditions affect the catalyst performance. In the batch reactor, the reagents were only fed at the beginning, so they slowly decreased during the course of the reaction; in particular, the concentration of H₂ (the limiting reagent) widely decreased with the time on stream. In the semibatch reactor the reagent concentrations were constant instead. This difference is likely to affect the catalyst morphology; it is known that the oxidation state of a catalyst has an effect on the reaction rates.^{16,34,38,47–50} In the semibatch reactor, the H₂ concentration in the liquid phase was constant and higher than in the batch apparatus (where it decreased with the time on stream), possibly causing the observed differences in the reaction rates (Fig. 10) and activation energies (Table 1).

In the trickle bed reactor, the kinetic parameters were apparently well-identified, as the sensitivity analysis reveals (ESI,† Fig. S7); the hydrogenation reaction had little effect on the objective function (ESI,† Fig. S7), meaning that its rate was much slower compared to the other reactions. This is confirmed by the reaction rate ratios reported in Fig. 10, where the hydrogenation reaction rate is much lower than that of the direct synthesis reaction (R_h/R_ds values much lower than 1). Fig. 10 also reveals that the disproportionation reaction was much slower than the direct synthesis (R_d/R_ds values much lower than 1). As qualitatively noticed in the previous section, the activation energy of the direct synthesis (Table 1) is lower than the water formation activation energy (the main factor responsible for water production, as Fig. 10 shows). However, the activation energy values of all the reactions were very low (<10 kJ mol⁻¹). This means that the temperature had little effect on the reaction rates, suggesting that the experiments were carried out with some mass transfer limitations. Notwithstanding, other considerations on the different activation energies obtained can be derived from the reactors and their features. Indeed, in the TBR the liquid residence time and the gas residence time can be controlled separately while in the batch and semibatch reactors this is not possible. For example, in the TBR the liquid residence time is very low, keeping the conversion low and thus avoiding the consecutive reactions (the catalyst is in contact with the liquid phase for a limited amount of time). In the batch and semibatch reactors the liquid residence time is fixed; only H₂, the limiting reagent, can be fed in different velocities. Thus if the H₂ feeding is fast, the H₂ conversion is low, otherwise the opposite. In the semibatch reactor the liquid phase is saturated with H₂, and H₂ is always present (the value of H₂ in the liquid phase depends on the H₂ conversion). Despite a low H₂ conversion, the H₂O₂ produced is surrounded by a high concentration of H₂, and this can result in a high hydrogenation rate. In any case, the liquid phase has always a fresh H₂ refilling, so hydrogenation (and decomposition) is highly probable (to a different extent) due to the simultaneous presence of H₂ and H₂O₂. In contrast, the TBR and the batch reactor behave differently due to the different reaction conditions (as explained above). Thus mass transfer limitations can be one explanation, but also the residence time and the H₂ presence in the liquid phase play an important role in the reaction pathway. In this way the different parameters obtained can be ascribed to the different reaction conditions that can affect the nanocluster features, as already reported.³⁴ Hence, care must be taken when carrying out experiments in this kind of continuous apparatus. Higher space velocities are needed to operate beyond the mass transfer limitation in continuous reactors. It is important to underline that we saw for the first time that the hydrogenation and decomposition reactions can be avoided if the reactor operates with mass transfer limitations; however, in the conditions studied the direct water formation prevails. In the semibatch reactor, where the concentration of H₂ in the liquid phase is stable, the direct formation is almost avoided. A continuous reactor with multiple H₂ injection points would favor the H₂O₂ production, as we saw here (and previously) that the saturation of H₂ in the liquid phase is beneficial for the reaction. Of course, a deep analysis on where to add the feed injections, how much hydrogen should be added and the catalyst amount to be used, should be a matter of a future study. Despite this, the work on the catalyst design should also focus on how to tailor-make the porosity of the catalyst to balance the mass transfer inside the pores in order to enhance the direct synthesis.

Remarkably, these results were achieved in the absence of any acids or halide ions, i.e. no known selectivity promoters for the direct H₂O₂ synthesis were applied. The kinetics express the real potential of the catalyst, thus the guidelines for the catalyst design can be given avoiding misinterpretations on the catalyst activity.

Proposed mechanism

The possible mechanism that can be speculated from the present results and from previous discoveries^31,34 takes into consideration the following behavior of Pd.

It is interesting to note that the PdO seems detrimental to the H₂O₂ direct synthesis and that there is a competitive adsorption between H₂ and O₂ on the Pd surface.³⁴ H₂ adsorption on the Pd surface is favoured compared to O₂.³⁴ Moreover, the presence of PdO can be found also after the reaction on the catalyst surface.³⁴ The degree of the oxidation kinetics of Pd surfaces was found to be correlated with the temperature and with the crystal type of Pd.^51–58 Pd(111) nucleation is thermodynamically controlled, and therefore, the nucleation rate decreases with the temperature. On Pd(110), nucleation is predominantly kinetically controlled and thus the oxidation rate increases with the temperature.⁵² The PdO species can be thus nucleated,⁵² and what was seen in a previous study was that a higher degree of oxidation favours water formation.³⁴ O₂ can be molecularly bonded to PdO,^51,52 and this molecule can be active in CO oxidation.⁵¹ The PdO₂ species exists on the surface of PdO.⁵² On Pd (100), the O₂ adsorption can lead to a phase transformation and reconstruction.⁵³ The activation energies for CO oxidation (for the Langmuir–Hinshelwood steps) were found to be different with large oxygen coverage and large CO coverage.⁵⁶ Taking into consideration the behavior of O₂ coverage on palladium it can be derived from the previous cited studies that the activation energies can depend on the oxidation degree of the Pd surface as noted in ref. 56. Thus, our different activation energies obtained in the TBR can be ascribed to a different oxidation state of the Pd clusters compared to the batch or semibatch cases. This is highly probable since the catalyst surface in the TBR has a shorter contact time with H₂O₂, the opposite of what happens under batch and semibatch conditions. Despite this, from the present results, it cannot be ruled out which is the form of the Pd oxidation state in the TBR. What can be said about the mechanism is that probably water formation is correlated with the oxidation degree of Pd and that the process passes through an intermediate on the PdO surface. Most likely O₂ can be activated on the PdO surface, rather than hydrogen that has its activation step on the Pd⁰ surface. H₂ reacts with the PdO₂ complex that can be formed,⁵² leading to water formation. O₂ can be molecularly or atomically adsorbed on PdO and Pd⁰, thus the Pd⁰ surface, in principle, can promote both the direct synthesis and direct water formation. It has to be kept into consideration that depending on the Pd crystallography faces the reaction of the direct synthesis can be enhanced or reduced. From our previous study³⁴ it seems that water formation can be suppressed using catalysts with a low amount of Pd (they result in a low PdO oxidation state). Most probably the H₂O₂ direct synthesis mechanism depends on the surface coverage, which is regulated by the temperature, Pd amount and H₂/O₂ ratio in the liquid phase. What is important to take into account is the fact that the hydrogen solubility is the opposite compared to the other gases: the lower the temperature, the higher the H₂ solubility. This fact helps keeping the surface oxidation state as Pd⁰ at low temperatures. This feature of H₂ solubility helps in speculating that the surface of the Pd at low temperatures has a large H₂ coverage while at high temperatures the oxygen coverage on the Pd surface is more favored (e.g. at low temperatures: higher H₂ solubility and lower O₂ solubility coupled with a favored adsorption of H₂ compared to O₂ on the Pd surface). Indeed, our results confirm that H₂O₂ is more favored at low temperatures compared to the relatively high temperatures. The activation energies calculated from our experiments may reflect the different H₂/O₂ ratios in the liquid phase (in the different reactors) and thus the different Pd oxidation states. This analysis coupled with our present and past results leads to the suggestion that the direct water formation can be ascribed to the H₂ combustion on the PdO surface. In contrast, the H₂O₂ hydrogenation reaction is more difficult to understand. It seems that hydrogenation is predominant when the H₂ combustion rate is low, thus it may happen on the Pd⁰ surface. The reaction involves the H₂ and H₂O₂ and adsorption on the Pd surfaces. Here the probability of H₂O₂ adsorption is due to two main factors: 1) competitive adsorption of H₂O₂ with O₂/H₂ and 2) H₂O₂ concentration. In the semibatch reactor, hydrogenation is important, since the concentration of H₂O₂ increases with time. Moreover, as can be seen from the activation energies, the reaction is highly favored. The mechanism for the H₂O₂ direct synthesis can be similar to the one proposed by Wilson and Flaherty⁴⁵ with two-site adsorption, but with more focus on the Pd oxidation state as responsible for the water formation with the complementary role of the nanocluster size, as similarly reported also by Ouyang et al.⁵⁹ The mechanism discussed is in line with our findings (activation energies and pre-exponential factors) in the batch, semibatch and TB reactors. Despite this, it will be important to monitor more deeply the Pd oxidation state evolution during the reaction, under different operative conditions, to make a further step in the direct synthesis. There is another issue that was never discussed in the H₂O₂ direct synthesis: the O₂ sorption on the Pd subsurface.⁵⁶ The bulk and subsurface oxygen can influence the catalytic activity being directly or indirectly involved in the reaction as studied in the CO oxidation.⁵⁶ It is still difficult to claim the role of the O₂ sorption in the direct synthesis, but is something that in the future should be considered. The present work may help individuating particular reaction conditions that can be studied to implement a more detailed model that takes into consideration: 1) the PdO oxidation state and its role on the water formation, 2) competitive adsorption of H₂/O₂, 3) subsurface and bulk O₂ in the palladium clusters, 4) the β-hydrides that can influence the reaction, 5) the use of a model that features different adsorption sites for the reactions involved and 6) a dynamic approach of the nanocluster evolution during the direct synthesis. Although there are still some unclear phenomena that regulate the direct synthesis, new insights are appearing for a complete understanding of the process.

Conclusions

Despite the extensive literature on the direct synthesis of hydrogen peroxide, this is the first time that three different reactors are compared using the same catalyst and similar reaction conditions. The corresponding Arrhenius parameters were estimated from the direct synthesis experiments for all the reactions and reactors. Comparable activation energies were seen for the H₂O₂ synthesis in the batch and semibatch reactors, 42.6 and 67.0 kJ mol⁻¹, respectively, while the one in the TBR was 6.9 kJ mol⁻¹, and thus the direct synthesis rate in the TBR was almost independent of the temperature. The direct water formation activation energies were quite high in the batch and semibatch reactors, showing that the reaction rate becomes very important with the increase of the temperature. In the TBR the activation energy for the water formation was close to the activation energy of the direct synthesis. It was already clear that the hydrogenation and decomposition can be avoided playing with the temperature; here we found that in the batch and semibatch reactors, the temperature plays a big role while in the case of the TBR operated in mass transfer, the temperature does not affect much the decomposition and hydrogenation. This information indicates the importance of the direct water formation in the TBR, while in the batch and semibatch reactors this effect is less pronounced, especially in the semibatch reactor. Hydrogenation and decomposition have little effect in the batch and semibatch reactors and also in the TBR. It is very interesting to see how the direct water formation rate is more pronounced when the reaction is operated under mass transfer regime. Important guidelines are gained to operate continuously and to enhance the H₂O₂ production in the TBR reactor. To avoid the H₂O formation in a continuous reactor, a short contact time is needed coupled probably with a gas–liquid recirculation; this will enhance the H₂O₂ production suppressing the water formation. The environment should be kept always with a high concentration of hydrogen in the liquid phase and thus favoring the H₂O₂ production. Multiple injection points in the continuous reactor will favor the control of the H₂ dosing and keeping a high concentration of hydrogen in the liquid phase avoiding working in the flammability limits. Once-through reactors for commercialization purposes are impossible at the present moment. The catalyst development should not only take into account the Pd (or PdAu) oxidation state and nanocluster size but also the porosity of the support material and the effect of the mass transfer in it. Indeed, as we have seen in the TBR, the mass transfer plays an important role, and tailoring the porosity of the support could be a fundamental aspect to improve the catalyst for a continuous reactor.

The direct synthesis possibly passes through the limitation of the PdO sites that seem responsible for the water formation (direct combustion). The hydrogenation seems more dependent on the H₂O₂ concentration and the dynamics of H₂/O₂ adsorption on the catalyst surface.

Moreover it is important to take into consideration the reactor used to fully understand the environment conditions that can affect the reaction rate (i.e. the dynamics on the nanocluster surface).

These new findings will help to design new catalysts and to perform the reaction in a chemical reaction engineering point of view, maximizing the reactor design and performance. To conclude, the catalyst design should be made according to the features of the reactor and not only looking at the catalyst itself.

Nomenclature

Dimensionless number

Ga	Galilei number, TBR model (dp^3gρL^2/μL^2)
Pe	Peclet number, TBR model (μLdp/D)
ReGp	Reynolds number of the gas and particle, TBR model (ρGuGdp/μG)
ReLp	Reynolds number of the liquid and particle, TBR model (ρLuLdp/μL)

Greek letters

ε	Bed porosity in the trickle bed reactor (0.33, dimensionless)
u G	Gas viscosity (g cm^−1 s^−1)
u L	Liquid viscosity (g cm^−1 s^−1)
ρ B	Catalyst density in the liquid phase (g cm^−3)
ρ G	Gas density (g cm^−3)
ρ L	Liquid density (g cm^−3)
τ	Residence time, eqn (26) (s)
θ	Dimensionless residence time, TBR model

Symbols

A i	Pre-exponential factor of reaction i
C	Concentration (mol cm^−3)
d p	Equivalent diameter of particle, TBR model (cm)
D	Axial dispersion, TBR model (cm^2 s^−1)
err, errT	Error function total and at a given temperature, respectively (dimensionless)
E ai	Activation energy of reaction i
g	Gravitational acceleration (9.066 m s^−1)
H	Henry constant, eqn (16) (dimensionless)
k i a ^LG	Gas–liquid mass transfer coefficient (s^−1)
k	Kinetic constant
L	Length of the trickle bed reactor (cm)
n	Moles (mol)
	Molar flow, semibatch model (mol s^−1)
N	Number of experimental data, eqn (33)
r	Specific production rate (mol s^−1 gcat^−1))
R	Specific reaction rate (mol s^−1 gcat^−1)
S	Selectivity (%)
t	Time coordinate (s)
u G	Superficial gas velocity, TBR model (cm s^−1)
u L	Superficial liquid velocity, TBR model (cm s^−1)
V	Volume (cm^3)
	Volumetric flow, TBR model (cm^3 s^−1)
X H2	H2 conversion (%)
z	Dimensionless space coordinate, TBR model

Subscripts

i, ith	Species
Tot	Total
ds, wf, d, h	Direct synthesis, water formation, disproportionation and hydrogenation reactions, respectively

Superscripts

ADM	Axial dispersion model, TBR model
calc	Calculated
exp	Experimental
G	Gas
IN	Inlet
L	Liquid
OUT	Outlet
ST	Stirred tank model, TBR model
*	Gas–liquid equilibrium

Acknowledgements

This work is a part of the activities of the Johan Gadolin Process Chemistry Centre (PCC), financed by the Åbo Akademi University (ÅA). Stefano Sterchele, Andrea Bernardini and Marco Cingano are gratefully acknowledged for their help during the experimental work.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5re00073d

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