- Email: [email protected]
Al2O3
Applied Catalysis A: General 273 (2004) 303–307 www.elsevier.com/locate/apcata
Kinetics and modeling of H2/D2 exchange over Ag/Al2O3 Henrik Backman, Jenny Jense´n, Fredrik Klingstedt, Johan Wa¨rna˚, Tapio Salmi, Dmitry Yu. Murzin* Laboratory of Industrial Chemistry, Process Chemistry Centre, A˚bo Akademi, Biskopsgatan 8, FIN-20500 Turku-A˚bo, Finland Received 14 April 2004; received in revised form 25 June 2004; accepted 28 June 2004 Available online 6 August 2004
Abstract An alumina supported silver catalyst was studied with a transient step-response technique for the reduction of NO and N2O with H2. Dissociation of hydrogen and deuterium was observed on the Ag/alumina catalyst and a kinetic model was proposed for the isotopic exchange between H2 and D2. The proposed model describes the observed dissociation and isotope exchange reaction sufficiently well. # 2004 Elsevier B.V. All rights reserved. Keywords: Modeling; Transient response; Kinetics; Parameter identification; Isotopic exchange; Mechanism
1. Introduction Nitrogen oxides in the combustion waste from automobile engines cause environmentally undesired effects, such as formation of acid rains and smog. Most of the vehicles nowadays have catalytic converters, typically a monolith, to remove the pollutants from the exhaust gas. Metal oxides are stable and durable catalysts for reduction of NO and are therefore practically used in three-way converters for automobile use. The converters utilized in gasoline-engine automobiles are effective at or below stoichiometric air/fuel ratio. Since the concentration of CO and hydrocarbons are lower and O2 higher in diesel exhausts three-way catalysts cannot effectively remove NOx from diesel exhausts. Stationary resources typically use a selective catalytic reduction process with ammonia as the reductant, which has turned out to be a successful way to remove NO. This reaction occurs in the presence of oxygen but the process involves environmental and economical concerns and the utilization of other reductants such as CH4, CO and H2 are desirable [1]. By itself, hydrogen does not contribute to the conversion of NOx over Ag/alumina, but there seems * Corresponding author. Tel.: +358 2 215 4985; fax: +358 2 215 4479. E-mail address: [email protected] (D.Yu. Murzin). 0926-860X/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apcata.2004.06.048
to be a synergetic effect between hydrogen and hydrocarbons in the HC-SCR reactions according to laboratory tests done at our laboratory. Transient methods have recently become popular because experiments performed under transient conditions give valuable information that is not obtained under steady-state experiments. Isotope-labeled reactants are frequently used to follow reaction pathways and to determine reaction mechanism. Steady-state isotopic transient kinetic analysis involves replacement of a reactant by its isotopically labelled counterpart in the form of a step or pulse input function [2]. In the present work, deuterium step changes have been utilized to trace the hydrogen reaction pathways over Ag/alumina, as it eventually can help in developing a fundamental understanding of the role of hydrogen in the reduction of NO.
2. Experimental 2.1. Catalyst The Ag/alumina catalyst was prepared by impregnating a commercial alumina support (LaRoche, A-201, BET surface area of 289 m2/g) with a 0.022 M solution of AgNO3. The
304
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
Nomenclature c c* M N P r r* R R R2 t T V V_ x z
concentration vector, gas phase components concentration vector, surface intermediate stoichiometric matrix, surface intermediates stoichiometric matrix, gas phase intermediates total pressure rate vector, gas phase components rate vector, surface components rate vector, elementary steps gas constant degree of explanation time temperature volume volumetric flow rate molar fraction vector dimensionless length coordinate
Greek letters d dimensionless change in the volumetric flow rate e void fraction u fractional coverage vector Q dimensionless time r catalyst bulk density s specific surface area of the catalyst t contact time Ag content (2%) was determined by the direct current plasma technique (Spectraspan IIIA). The dispersion (51.2%) and mean particle diameter (26.2 nm) of the metal were determined by oxygen adsorption at 170 8C, using a Sorptomatic 1900 (Carlo Erba Instruments) at a pressure range 1–200 Torr. The amount of the reversibly adsorbed gases on the catalysts was determined by the back-sorption method. Metal dispersions and mean particle diameters were calculated by the Langmuir method. A stoichiometry of Ag/ O2 = 2 was assumed according to Hoost et al. [3]. After impregnation and calcination at 550 8C for 3 h the surface area dropped to 185 m2/g.
Fig. 1. The experimental set-up for the transient experiments.
Ar. The experiments were carried out at atmospheric pressure in the temperature range 80–400 8C and the total gas flow at 25 8C was 400 cm3/min.
3. Results 3.1. H2/D2 exchange The dynamic of the isotope exchange between hydrogen and deuterium is displayed in Fig. 2. In general, hydrogen dissociates easily over metallic surfaces [4] but reports on non-dissociative adsorption of hydrogen on Ag systems are available in the literature [5,6]. In the present study, hydrogen was initially pre-adsorbed on the surface. Once deuterium is introduced to the reactor and hydrogen taken to the by-pass the isotopic exchange takes place with the hydrogen atoms already adsorbed, and formation of HD is immediately observed. At this point the formation of HD starts to grow until a maximum, after which it decreases in a short period of time. The production of water could be noticed in the first and third step of the experiment, which can be attributed to the reaction of chemisorbed hydrogen with OH-
2.2. Experimental set-up The catalyst was tested in a quartz micro reactor having a length of 300 mm and a diameter of approximately 8 mm, which was inserted into a temperature controlled oven. The experimental set-up for the catalyst testing is illustrated in Fig. 1. Mass flow controllers regulated the gas flows and a split of the product flow was analyzed by a quadrupole mass spectrometer (Balzers Omnistar). The dried catalyst (125– 150 mm particles, 0.25 g) was heated to 400 8C with a rate of 10 8C/min in a flow of 6% O2/Ar and kept at 400 8C for 30 min. After the oxidation the catalyst was cooled down to the desired reaction temperature and the reaction mixture was switched on. The inlet flows were 1% H2/Ar and 1% D2/
Fig. 2. The H2/D2 exchange over oxidized Ag/alumina at 400 8C.
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
groups present in the alumina support and oxide precursor. This can, however, be considered as negligible because the molar fraction value of water is extremely small compared to the values of H2 and D2. Different reaction mechanisms for the H2/D2 exchange have been reported in the literature. Bonhoeffer and Farkas proposed a mechanism involving dissociation of hydrogen on the metal surface and chemisorbed atoms link up randomly in pairs and evaporate as molecules. An alternative mechanism was proposed by Rideal where he stated that interaction takes place between a chemisorbed atom and physisorbed molecules, according to a exchange reaction between H* and D2 to form HD and D* [7]. The fast response of HD obtained in the experimental result evidences that Rideal pathway is probably the one followed. It can be thought that at the beginning of the experiment, when the surface was covered by H*, the exchange reaction was enhanced due to the lack of free active sites for deuterium to dissociate. Once there were more vacant sites, it was possible to form D* to react with the H* atoms. H þ D2 Ð D þ HD
(1)
D þH2 Ð gH þ HD
(2)
H2 þ 2 Ð 2H
(3)
D2 þ 2 Ð 2D
(4)
H þ D ! HD þ 2
(5)
305
where the single steps are expressed as: r1 r2 r3 r4 r5
¼ k 1 c D2 c H ¼ k 2 c H2 c D ¼ k3 cH2 c2 ¼ k4 cD2 c2 ¼ k 5 c H c D
r1 r2 r3 r4
¼ k1 cD cHD ¼ k2 cH cHD ¼ k3 c2H ¼ k4 c2D
In these equations, the reaction rate is denoted by ri, concentrations by ci, the rate constant by ki and adsorbed species by *. The concentration of vacant sites is expressed as c*. The kinetic analysis of a reaction can be performed with the use of model fitting and non-linear regression analysis. This allows testing of alternative reaction mechanisms since commonly the case is that several models could be fitted to the same reaction. A challenge in kinetic analysis is hence to distinguish a unique functional form of the kinetic model. Transient techniques provide in general better mechanism identifiability than static experiments. In the present work the transient step-responses were described quantitatively with a dynamic plug flow model. Adsorption, surface reaction and desorption steps, as well as isotopic exchange steps were included in the model. The gas phase components and surface intermediates were described with separate mass balances. The kinetic parameters were determined with nonlinear regression analysis. (The meaning of the parameters used in the equations in this section is explained in Nomenclature) The isothermal plug flow model for the components in the gas phase is written as:
To clarify the reaction mechanism and to reveal the importance of the steps included in the proposed mechanism parameter estimation and modeling was performed. The proposed reaction mechanism includes adsorption, dissociation, surface reaction and desorption steps. The adsorbed species are denoted by H*, D* and HD. * is an active empty site on the surface.
dc dðcV_Þ ¼ e1 þ srB e1 r (6) dt dV Defining the dimensionless quantities and replacing the concentrations by mole fractions the mass balance can be written in dimensionless form dx dx dd sr tRT0 1 ¼ e d þx NR (7) þ B dQ dz dz eP0
4. Modeling
The rates of the elementary steps are given by vector R and the generation rates of gas-phase (r) and surface components (r*) are calculated from:
The rates of the elementary steps are given by the following equations: Gas phase species
r ¼ NR
(8)
r ¼ MR
(9)
RH2 ¼ r2 þ r2 r3 þ r3 ; RHD ¼ r1 r1 þ r2 r2 þ r5 ;
where N and M denote the stoichiometric matrices for the gas phase and surface components [8]. For the surface intermediates the mass balance can be written as:
RD2 ¼ r1 þ r1 r4 þ r4 Surface species R ¼ 2r3 þ 2r3 2r4 þ 2r4 þ 2r5 ; RD ¼ r1 r1 r2 þ r 2 þ 2r4 2r4 r5 ; RH ¼ r1 þ r1 þ r2 r2 þ 2r3 2r3 r5
dc ¼ MR (10) dt Instead of using surface concentration one can use surface coverage (uj), calculated from c* = ujc0, where c0 is the total concentration of active sites. When dimensionless time
306
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
is inserted the final form of the balance becomes du t ¼ MR dQ c0
(11)
The initial conditions of the gas-phase and surface balance equations are: x ¼ x0 ðzÞ u ¼ u0 ðzÞ;
(12) Q < 0; 0 ¼ z ¼ 1
(13)
The model predictions were obtained by solving the differential equations for all of the components during the parameter estimation. A stiff ODE-solver (BzzOde) was used to solve the system of ODEs, Eq. (7), with the backward difference method. The ODE solver connected to a parameter estimation software, Modest [9], was used in the estimation of the kinetic parameters. The simplex algorithm implemented in the software minimized the residual sum of squares. The most common measure for the goodness of fit is the R2-value, given by the expression: ! jjcexp cest jj2 2 R ¼ 100 1 (14) jjcexp c¯ exp jj2 where the values cest denote the predictions given by the model and c¯ exp the mean value of all the data points. In addition to the proposed model for the H2/D2 exchange (Eqs. (1)–(5)) some variations of the model were also tested, i.e. adsorption of molecular hydrogen (deuterium) on the surface, prior to decomposition and isotopic exchange. Since the surface most probably is covered with pre-adsorbed H atoms coverage of molecularly adsorbed species is very low. This was also visible in the results of the parameter fitting.
Table 1 The estimated parameters for the modeling of H2/D2 exchange over Ag/ alumina Parameter
Estimated values
Relative standard error (%)
k1 k1 k2 k2 k3 k3 k4 k4 k5
0.166 0.0137 (l/mol s) 0.141 8.53103 (l/mol s) 0.249 0.018 (l/mol s) 0.176 0.0111 (l/mol s) 3.88 0.544 (l2/mol2 s) 0.0089 5.8104 (l/mol s) 2.71 0.179 (l2/mol2 s) 0.0121 7.3104 (l/mol s) 0.068 5.08103 (l/mol s)
12.1 16.5 13.9 15.8 7.1 15.5 15.5 16.5 13.4
If molecular adsorption was applied an adequate fit to the experimental data could not be reached, supporting an assumption of fast dissociation of molecular to atomic hydrogen. The kinetic modeling demonstrated that the Rideal mechanism is predominant The parameter statistics for the modeling of the H2/D2 exchange over Ag/Al2O3 is summarized in Table 1 and the comparison between the experimental data and the simulations are presented in Fig. 3. The standard errors of the estimated parameters are within reasonable limits and the fits to the experimental data show a very good agreement (99.7%) with the experimentally collected data. To confirm the significance of the two routes (steps 1–2 and 3–5) for the H2/D2 exchange the routes were separately fitted to the experimental data. However, this resulted in a lower degree of explanation and larger errors for the estimated parameters. In order to have a sufficient degree of explanation, both routes for the isotopic exchange have to be taken into account.
Fig. 3. H2/D2-exchange on Ag/alumina. Comparison between experimental data (symbols) and calculations (curves). The degree of explanation is 99.7%.
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
When a deuterium atom replaces a hydrogen atom, both equilibrium constants and the rate constants are altered. Isotope effects are greatest when there is a large relative change in the masses. The effect is typically large when an ordinary hydrogen atom is replaced by deuterium [10]. The H2 molecule will tend to react more rapidly and its reactions will tend to have a higher equilibrium constant both in the gas phase and in the adsorbed state, as the adsorption enthalpy is relatively small. Considering the reactions D þ H2 ! DH þ H and H þ D2 ! HD þ D the rate constant for the first reaction should be larger than for the second reaction, which could be understood in terms of initial-state zero-point energies that are higher for H2 than for D2 [10]. The values of the estimated parameters are consistent with this kinetic isotope effect theory, as the rate constant derived for D2 dissociation on the surface is lower than the rate constant for the dissociation of H2. The parameter estimation of the rate constants for the kinetic model assumed in this work suggests that the Rideal mechanism is the dominating one. However, all steps included in the model (e.g. Bonhoeffer–Farkas and Rideal mechanisms) are significant for the adequate fit of the model to the experimental data.
5. Conclusions The isotopic exchange between hydrogen and deuterium was studied over a Ag/Al2O3 catalyst by steady state and transient kinetic experiments. Based on the experimental results a mechanism was proposed and a kinetic model describing the isotopic exchange between H2 and D2 was developed. In terms of practical applications the Ag/Al2O3 catalyst becomes more interesting for the selective reduction of NO
307
when hydrogen is used in combination with hydrocarbons. In this work, a reaction mixture consisting of H2 and D2 was used in order to develop a better understanding of the dynamic behavior of hydrogen on a Ag/Al2O3 catalyst. The obtained results, namely the numerical values of the rate constants and adsorption coefficients will further be used in the extended kinetic modeling where all components (H2 and hydrocarbon) needed for the reduction of NO are included.
Acknowledgements This work is part of the activities within the Finnish Centre of Excellence Programme (2000–2005) by the Academy of Finland. H. Backman acknowledges the financial support from Fortum Foundation.
References [1] J. Armor, Appl. Catal. B 1 (1992) 221. [2] K. Tamaru, S. Naito, in: G. Ertl, H. Kno¨ zinger, J. Weitkamp (Eds.), Handbook of Heterogeneous Catalysis, vol. 3, VCH Weinheim, 1997, p. 1005. [3] T.E. Hoost, R.J. Kudla, K.M. Collins, M.S. Chattha, Appl. Catal. B 13 (1997) 59. [4] E. Miyazaki, J. Catal. 65 (1980) 84. [5] F. Healey, R.N. Carter, G. Worthy, A. Hodgson, Chem. Phys. Lett. 243 (1995) 133. [6] R. Dus´, E. Nowicka, Prog. Surf. Sci. 74 (2003) 39. [7] B.M.W. Trapnell, Catalysis: Hydrogenation and Dehydrogenation, Reinhold Publishing Corporation, New York, 1955 (p. 1). [8] T. Salmi, Chem. Eng. Sci. 43 (1988) 503. [9] H. Haario, Modest 6.0—A User’s Guide, ProfMath, Helsinki, 2001. [10] K.J. Laidler, Chemical Kinetics, Harper & Row, New York, 1987 (p. 427).
Kinetics and modeling of H2/D2 exchange over Ag/Al2O3 Henrik Backman, Jenny Jense´n, Fredrik Klingstedt, Johan Wa¨rna˚, Tapio Salmi, Dmitry Yu. Murzin* Laboratory of Industrial Chemistry, Process Chemistry Centre, A˚bo Akademi, Biskopsgatan 8, FIN-20500 Turku-A˚bo, Finland Received 14 April 2004; received in revised form 25 June 2004; accepted 28 June 2004 Available online 6 August 2004
Abstract An alumina supported silver catalyst was studied with a transient step-response technique for the reduction of NO and N2O with H2. Dissociation of hydrogen and deuterium was observed on the Ag/alumina catalyst and a kinetic model was proposed for the isotopic exchange between H2 and D2. The proposed model describes the observed dissociation and isotope exchange reaction sufficiently well. # 2004 Elsevier B.V. All rights reserved. Keywords: Modeling; Transient response; Kinetics; Parameter identification; Isotopic exchange; Mechanism
1. Introduction Nitrogen oxides in the combustion waste from automobile engines cause environmentally undesired effects, such as formation of acid rains and smog. Most of the vehicles nowadays have catalytic converters, typically a monolith, to remove the pollutants from the exhaust gas. Metal oxides are stable and durable catalysts for reduction of NO and are therefore practically used in three-way converters for automobile use. The converters utilized in gasoline-engine automobiles are effective at or below stoichiometric air/fuel ratio. Since the concentration of CO and hydrocarbons are lower and O2 higher in diesel exhausts three-way catalysts cannot effectively remove NOx from diesel exhausts. Stationary resources typically use a selective catalytic reduction process with ammonia as the reductant, which has turned out to be a successful way to remove NO. This reaction occurs in the presence of oxygen but the process involves environmental and economical concerns and the utilization of other reductants such as CH4, CO and H2 are desirable [1]. By itself, hydrogen does not contribute to the conversion of NOx over Ag/alumina, but there seems * Corresponding author. Tel.: +358 2 215 4985; fax: +358 2 215 4479. E-mail address: [email protected] (D.Yu. Murzin). 0926-860X/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apcata.2004.06.048
to be a synergetic effect between hydrogen and hydrocarbons in the HC-SCR reactions according to laboratory tests done at our laboratory. Transient methods have recently become popular because experiments performed under transient conditions give valuable information that is not obtained under steady-state experiments. Isotope-labeled reactants are frequently used to follow reaction pathways and to determine reaction mechanism. Steady-state isotopic transient kinetic analysis involves replacement of a reactant by its isotopically labelled counterpart in the form of a step or pulse input function [2]. In the present work, deuterium step changes have been utilized to trace the hydrogen reaction pathways over Ag/alumina, as it eventually can help in developing a fundamental understanding of the role of hydrogen in the reduction of NO.
2. Experimental 2.1. Catalyst The Ag/alumina catalyst was prepared by impregnating a commercial alumina support (LaRoche, A-201, BET surface area of 289 m2/g) with a 0.022 M solution of AgNO3. The
304
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
Nomenclature c c* M N P r r* R R R2 t T V V_ x z
concentration vector, gas phase components concentration vector, surface intermediate stoichiometric matrix, surface intermediates stoichiometric matrix, gas phase intermediates total pressure rate vector, gas phase components rate vector, surface components rate vector, elementary steps gas constant degree of explanation time temperature volume volumetric flow rate molar fraction vector dimensionless length coordinate
Greek letters d dimensionless change in the volumetric flow rate e void fraction u fractional coverage vector Q dimensionless time r catalyst bulk density s specific surface area of the catalyst t contact time Ag content (2%) was determined by the direct current plasma technique (Spectraspan IIIA). The dispersion (51.2%) and mean particle diameter (26.2 nm) of the metal were determined by oxygen adsorption at 170 8C, using a Sorptomatic 1900 (Carlo Erba Instruments) at a pressure range 1–200 Torr. The amount of the reversibly adsorbed gases on the catalysts was determined by the back-sorption method. Metal dispersions and mean particle diameters were calculated by the Langmuir method. A stoichiometry of Ag/ O2 = 2 was assumed according to Hoost et al. [3]. After impregnation and calcination at 550 8C for 3 h the surface area dropped to 185 m2/g.
Fig. 1. The experimental set-up for the transient experiments.
Ar. The experiments were carried out at atmospheric pressure in the temperature range 80–400 8C and the total gas flow at 25 8C was 400 cm3/min.
3. Results 3.1. H2/D2 exchange The dynamic of the isotope exchange between hydrogen and deuterium is displayed in Fig. 2. In general, hydrogen dissociates easily over metallic surfaces [4] but reports on non-dissociative adsorption of hydrogen on Ag systems are available in the literature [5,6]. In the present study, hydrogen was initially pre-adsorbed on the surface. Once deuterium is introduced to the reactor and hydrogen taken to the by-pass the isotopic exchange takes place with the hydrogen atoms already adsorbed, and formation of HD is immediately observed. At this point the formation of HD starts to grow until a maximum, after which it decreases in a short period of time. The production of water could be noticed in the first and third step of the experiment, which can be attributed to the reaction of chemisorbed hydrogen with OH-
2.2. Experimental set-up The catalyst was tested in a quartz micro reactor having a length of 300 mm and a diameter of approximately 8 mm, which was inserted into a temperature controlled oven. The experimental set-up for the catalyst testing is illustrated in Fig. 1. Mass flow controllers regulated the gas flows and a split of the product flow was analyzed by a quadrupole mass spectrometer (Balzers Omnistar). The dried catalyst (125– 150 mm particles, 0.25 g) was heated to 400 8C with a rate of 10 8C/min in a flow of 6% O2/Ar and kept at 400 8C for 30 min. After the oxidation the catalyst was cooled down to the desired reaction temperature and the reaction mixture was switched on. The inlet flows were 1% H2/Ar and 1% D2/
Fig. 2. The H2/D2 exchange over oxidized Ag/alumina at 400 8C.
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
groups present in the alumina support and oxide precursor. This can, however, be considered as negligible because the molar fraction value of water is extremely small compared to the values of H2 and D2. Different reaction mechanisms for the H2/D2 exchange have been reported in the literature. Bonhoeffer and Farkas proposed a mechanism involving dissociation of hydrogen on the metal surface and chemisorbed atoms link up randomly in pairs and evaporate as molecules. An alternative mechanism was proposed by Rideal where he stated that interaction takes place between a chemisorbed atom and physisorbed molecules, according to a exchange reaction between H* and D2 to form HD and D* [7]. The fast response of HD obtained in the experimental result evidences that Rideal pathway is probably the one followed. It can be thought that at the beginning of the experiment, when the surface was covered by H*, the exchange reaction was enhanced due to the lack of free active sites for deuterium to dissociate. Once there were more vacant sites, it was possible to form D* to react with the H* atoms. H þ D2 Ð D þ HD
(1)
D þH2 Ð gH þ HD
(2)
H2 þ 2 Ð 2H
(3)
D2 þ 2 Ð 2D
(4)
H þ D ! HD þ 2
(5)
305
where the single steps are expressed as: r1 r2 r3 r4 r5
¼ k 1 c D2 c H ¼ k 2 c H2 c D ¼ k3 cH2 c2 ¼ k4 cD2 c2 ¼ k 5 c H c D
r1 r2 r3 r4
¼ k1 cD cHD ¼ k2 cH cHD ¼ k3 c2H ¼ k4 c2D
In these equations, the reaction rate is denoted by ri, concentrations by ci, the rate constant by ki and adsorbed species by *. The concentration of vacant sites is expressed as c*. The kinetic analysis of a reaction can be performed with the use of model fitting and non-linear regression analysis. This allows testing of alternative reaction mechanisms since commonly the case is that several models could be fitted to the same reaction. A challenge in kinetic analysis is hence to distinguish a unique functional form of the kinetic model. Transient techniques provide in general better mechanism identifiability than static experiments. In the present work the transient step-responses were described quantitatively with a dynamic plug flow model. Adsorption, surface reaction and desorption steps, as well as isotopic exchange steps were included in the model. The gas phase components and surface intermediates were described with separate mass balances. The kinetic parameters were determined with nonlinear regression analysis. (The meaning of the parameters used in the equations in this section is explained in Nomenclature) The isothermal plug flow model for the components in the gas phase is written as:
To clarify the reaction mechanism and to reveal the importance of the steps included in the proposed mechanism parameter estimation and modeling was performed. The proposed reaction mechanism includes adsorption, dissociation, surface reaction and desorption steps. The adsorbed species are denoted by H*, D* and HD. * is an active empty site on the surface.
dc dðcV_Þ ¼ e1 þ srB e1 r (6) dt dV Defining the dimensionless quantities and replacing the concentrations by mole fractions the mass balance can be written in dimensionless form dx dx dd sr tRT0 1 ¼ e d þx NR (7) þ B dQ dz dz eP0
4. Modeling
The rates of the elementary steps are given by vector R and the generation rates of gas-phase (r) and surface components (r*) are calculated from:
The rates of the elementary steps are given by the following equations: Gas phase species
r ¼ NR
(8)
r ¼ MR
(9)
RH2 ¼ r2 þ r2 r3 þ r3 ; RHD ¼ r1 r1 þ r2 r2 þ r5 ;
where N and M denote the stoichiometric matrices for the gas phase and surface components [8]. For the surface intermediates the mass balance can be written as:
RD2 ¼ r1 þ r1 r4 þ r4 Surface species R ¼ 2r3 þ 2r3 2r4 þ 2r4 þ 2r5 ; RD ¼ r1 r1 r2 þ r 2 þ 2r4 2r4 r5 ; RH ¼ r1 þ r1 þ r2 r2 þ 2r3 2r3 r5
dc ¼ MR (10) dt Instead of using surface concentration one can use surface coverage (uj), calculated from c* = ujc0, where c0 is the total concentration of active sites. When dimensionless time
306
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
is inserted the final form of the balance becomes du t ¼ MR dQ c0
(11)
The initial conditions of the gas-phase and surface balance equations are: x ¼ x0 ðzÞ u ¼ u0 ðzÞ;
(12) Q < 0; 0 ¼ z ¼ 1
(13)
The model predictions were obtained by solving the differential equations for all of the components during the parameter estimation. A stiff ODE-solver (BzzOde) was used to solve the system of ODEs, Eq. (7), with the backward difference method. The ODE solver connected to a parameter estimation software, Modest [9], was used in the estimation of the kinetic parameters. The simplex algorithm implemented in the software minimized the residual sum of squares. The most common measure for the goodness of fit is the R2-value, given by the expression: ! jjcexp cest jj2 2 R ¼ 100 1 (14) jjcexp c¯ exp jj2 where the values cest denote the predictions given by the model and c¯ exp the mean value of all the data points. In addition to the proposed model for the H2/D2 exchange (Eqs. (1)–(5)) some variations of the model were also tested, i.e. adsorption of molecular hydrogen (deuterium) on the surface, prior to decomposition and isotopic exchange. Since the surface most probably is covered with pre-adsorbed H atoms coverage of molecularly adsorbed species is very low. This was also visible in the results of the parameter fitting.
Table 1 The estimated parameters for the modeling of H2/D2 exchange over Ag/ alumina Parameter
Estimated values
Relative standard error (%)
k1 k1 k2 k2 k3 k3 k4 k4 k5
0.166 0.0137 (l/mol s) 0.141 8.53103 (l/mol s) 0.249 0.018 (l/mol s) 0.176 0.0111 (l/mol s) 3.88 0.544 (l2/mol2 s) 0.0089 5.8104 (l/mol s) 2.71 0.179 (l2/mol2 s) 0.0121 7.3104 (l/mol s) 0.068 5.08103 (l/mol s)
12.1 16.5 13.9 15.8 7.1 15.5 15.5 16.5 13.4
If molecular adsorption was applied an adequate fit to the experimental data could not be reached, supporting an assumption of fast dissociation of molecular to atomic hydrogen. The kinetic modeling demonstrated that the Rideal mechanism is predominant The parameter statistics for the modeling of the H2/D2 exchange over Ag/Al2O3 is summarized in Table 1 and the comparison between the experimental data and the simulations are presented in Fig. 3. The standard errors of the estimated parameters are within reasonable limits and the fits to the experimental data show a very good agreement (99.7%) with the experimentally collected data. To confirm the significance of the two routes (steps 1–2 and 3–5) for the H2/D2 exchange the routes were separately fitted to the experimental data. However, this resulted in a lower degree of explanation and larger errors for the estimated parameters. In order to have a sufficient degree of explanation, both routes for the isotopic exchange have to be taken into account.
Fig. 3. H2/D2-exchange on Ag/alumina. Comparison between experimental data (symbols) and calculations (curves). The degree of explanation is 99.7%.
H. Backman et al. / Applied Catalysis A: General 273 (2004) 303–307
When a deuterium atom replaces a hydrogen atom, both equilibrium constants and the rate constants are altered. Isotope effects are greatest when there is a large relative change in the masses. The effect is typically large when an ordinary hydrogen atom is replaced by deuterium [10]. The H2 molecule will tend to react more rapidly and its reactions will tend to have a higher equilibrium constant both in the gas phase and in the adsorbed state, as the adsorption enthalpy is relatively small. Considering the reactions D þ H2 ! DH þ H and H þ D2 ! HD þ D the rate constant for the first reaction should be larger than for the second reaction, which could be understood in terms of initial-state zero-point energies that are higher for H2 than for D2 [10]. The values of the estimated parameters are consistent with this kinetic isotope effect theory, as the rate constant derived for D2 dissociation on the surface is lower than the rate constant for the dissociation of H2. The parameter estimation of the rate constants for the kinetic model assumed in this work suggests that the Rideal mechanism is the dominating one. However, all steps included in the model (e.g. Bonhoeffer–Farkas and Rideal mechanisms) are significant for the adequate fit of the model to the experimental data.
5. Conclusions The isotopic exchange between hydrogen and deuterium was studied over a Ag/Al2O3 catalyst by steady state and transient kinetic experiments. Based on the experimental results a mechanism was proposed and a kinetic model describing the isotopic exchange between H2 and D2 was developed. In terms of practical applications the Ag/Al2O3 catalyst becomes more interesting for the selective reduction of NO
307
when hydrogen is used in combination with hydrocarbons. In this work, a reaction mixture consisting of H2 and D2 was used in order to develop a better understanding of the dynamic behavior of hydrogen on a Ag/Al2O3 catalyst. The obtained results, namely the numerical values of the rate constants and adsorption coefficients will further be used in the extended kinetic modeling where all components (H2 and hydrocarbon) needed for the reduction of NO are included.
Acknowledgements This work is part of the activities within the Finnish Centre of Excellence Programme (2000–2005) by the Academy of Finland. H. Backman acknowledges the financial support from Fortum Foundation.
References [1] J. Armor, Appl. Catal. B 1 (1992) 221. [2] K. Tamaru, S. Naito, in: G. Ertl, H. Kno¨ zinger, J. Weitkamp (Eds.), Handbook of Heterogeneous Catalysis, vol. 3, VCH Weinheim, 1997, p. 1005. [3] T.E. Hoost, R.J. Kudla, K.M. Collins, M.S. Chattha, Appl. Catal. B 13 (1997) 59. [4] E. Miyazaki, J. Catal. 65 (1980) 84. [5] F. Healey, R.N. Carter, G. Worthy, A. Hodgson, Chem. Phys. Lett. 243 (1995) 133. [6] R. Dus´, E. Nowicka, Prog. Surf. Sci. 74 (2003) 39. [7] B.M.W. Trapnell, Catalysis: Hydrogenation and Dehydrogenation, Reinhold Publishing Corporation, New York, 1955 (p. 1). [8] T. Salmi, Chem. Eng. Sci. 43 (1988) 503. [9] H. Haario, Modest 6.0—A User’s Guide, ProfMath, Helsinki, 2001. [10] K.J. Laidler, Chemical Kinetics, Harper & Row, New York, 1987 (p. 427).