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Ind. Eng. Chem. Res. 2003, 42, 5482-5488
Kinetic Modeling of the Heterogeneously Catalyzed Oxidation of Propene to Acrolein in a Catalytic Wall Reactor Hubert Redlingsho1 fer,*,† Achim Fischer,† Christoph Weckbecker,† Klaus Huthmacher,† and Gerhard Emig‡ Feed Additives Division, Degussa AG, Rodenbacher Chaussee 4, 63457 Hanau, Germany, and Lehrstuhl fu¨ r Technische Chemie I, University of Erlangen-Nuremberg, Egerlandstrasse 3, 91058 Erlangen, Germany
Using data from isothermal investigations in a catalytic wall reactor (Redlingsho¨fer, H.; Kro¨cher, O.; Bo¨ck, W.; Huthmacher, K.; Emig, G. Ind. Eng. Chem. Res. 2002, 41, 1445), the kinetics of the highly exothermic vapor-phase oxidation of propene was determined by statistical parameter estimation. It was shown that the oxidation of propene to acrolein follows a redox mechanism, with a change in the rate-determining step that depends on temperature. Two kinetic equations for the reduction and reoxidation regimes were necessary for a good fit to the experimental values. About a 3-fold higher activation energy for the reoxidation step and different propene and oxygen concentration dependencies of the rate equations in the two regimes were observed. An increasing water content improves catalyst reoxidation. This special catalytic effect was modeled by including an activity function. The kinetics of the byproducts acrylic acid, carbon oxides, formaldehyde, acetaldehyde, and acetic acid were considered with a reaction scheme consisting of 10 reactions. The model describes the experimental data very well. It includes 31 significant kinetic parameters. 1. Introduction Because of the exponential dependence of the reaction rate on temperature according to the Arrhenius law, a precise description of the thermal behavior of laboratory reactors is essential for kinetic investigations. Otherwise, small deviations in temperature profiles lead to errors in kinetic parameters. One possibility for ensuring isothermal conditions during highly exothermic reactions is the use of the catalytic wall reactor (CWR) where the catalyst is directly coated on the wall, thus allowing the temperature of the catalyst to be easily controlled. Because of its isothermal behavior under extreme conditions, the catalytic wall reactor has already been used for kinetic investigations in highly exothermic reactions.2-7 The kinetics of the oxidation of propene to acrolein on bismuth molybdates has already been investigated several times.8-19 The results show major differences in the rate equations and kinetic parameters, which probably can be attributed to deviations in catalyst composition and structure. Many models are either valid only over a narrow range of reaction conditions or include kinetic parameters that vary with test conditions. Most models include only the main reaction and occasionally a few byproducts. Furthermore, they do not consider the special role of water vapor. Additionally, the kinetics only sometimes corresponds to the redox mechanism of the main reaction, which is understood quite well.20 On the basis of our extensive experimental isothermal data on the oxidation of propene1,21 gained in a laboratory CWR without the influence of heat- and mass* To whom correspondence should be addressed. Fax: + 49 6181 5973659. E-mail:
[email protected]. † Degussa AG. ‡ University of Erlangen-Nuremberg.
transport limitations, the aim of the present study was to develop a detailed kinetic model. The model should fit all experimental values including the reaction behavior of the important byproducts with high accuracy. Furthermore, it should reflect the influence of temperature, residence time, and the contents of propene, oxygen, and water over a wide range of test conditions with one set of kinetic parameters. 2. Modeling 2.1. Reactor Model. The conservation equations for mass, energy, and momentum are the basis for reactor modeling.22 Because the laboratory CWR1,21 guarantees isothermal conditions and the pressure drop inside is negligible, only the mass balance must be solved. The absence of external and internal diffusion limitations allows the use of a pseudo-homogeneous model. Bodenstein numbers always much greater than 100 allow the axial dispersion to be neglected. After an induction period, the catalyst did not deactivate during the kinetic measurements,1,21 whereby the reactor model describes the relevant stationary state. The resulting mass balance of the ideal plug-flow tubular reactor for a volumestable reaction must be solved for each component i
0 ) -u
dci
∑j υijrj
+F
dz
(1)
Using the ideal gas law and considering the linear gas velocity u inside the reactor as well as the modified residence time τmod
u)
n˘ totRT ptotAR
10.1021/ie030191p CCC: $25.00 © 2003 American Chemical Society Published on Web 10/03/2003
(2)
Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5483
τmod )
mcat n˘ tot
(3)
eq 1 can be transformed as follows
dxi dτmod
)
∑j υijrj
(4)
2.2. Influence of Temperature on the Main Reaction. As the formation of acrolein was especially influenced by reaction temperature during the measurements,1 for a first approximation, only the main reaction was considered for each temperature separately. Therefore, the power-law expression
rAC ) kACpPRnPRpO2nO2
Figure 1. Influence of temperature on the reaction rate of acrolein formation (xPR ) 0.045, xO2 ) 0.10).
(5)
including the partial pressures of propene (pPR) and oxygen (pO2), was used to calculate the reaction rate rAC. For determination of the model parameters, eq 4 was integrated with gPROMS, and the simulated molar fractions were fitted to the measured molar fractions for each temperature separately. The results are shown in Figure 1 and Table 1, respectively. Figure 1 indicates that, for a given gas composition, the influence of temperature on the reaction rate can be described correctly only by using two power-law expressions with different activation energies. This finding is in accordance with the stronger influence of the reaction temperature on the conversion of propene below 633 K, which was already expected from the experimental studies in the isothermal CWR.1 At temperatures below 633 K, the order in propene is zero, and only oxygen shows an influence on the reaction rate (Table 1). At higher temperatures, the order in oxygen is zero, and that in propene is 1.0. This result corresponds with the experimentally determined role of oxygen in accelerating acrolein formation only at low temperatures.1 Consequently, a sudden change in the rate-determining step (RDS) is observed between 623 and 643 K. Below 633 K, the reoxidation of the oxide catalyst with oxygen from the gas phase is ratedetermining, with about a 3-fold higher activation energy compared to the reduction by propene, which is the slowest step at higher temperatures. These observations are in close agreement with the redox mechanism for selective propene oxidation.20 Similar changes of the RDS have already been described in the literature.14-18 2.3. Reaction Scheme and Kinetic Equations. A selective oxidation consists of a reaction network with many parallel and consecutive reactions. A quantitative description of all real reactions is almost impossible because the number of kinetic parameters that have to be determined increases significantly with the number of reactions. Therefore, in this work, the number of reactions in the model was restricted to a degree at which the experimental data of all components were described satisfactorily. Apart from propene (PR), acrolein (AC), oxygen, and water, the reaction behaviors of the byproducts acrylic acid (acrA), CO2, CO, acetaldehyde (AA), formaldehyde (FA), and acetic acid (aceA) were investigated in the kinetic measurements.1,21 These 10 species and the elements (C, H, O) result in a rank of 3 in the elementsspecies matrix. Thus, on the basis of the stoichiometry,
Figure 2. Reaction scheme. Table 1. Reaction Orders of the Main Reaction for Different Temperatures T (K)
nPR
nO2
603 623 633 643 663 683 703
0 0 0.96 0.92 1.03 1.06 1.00
0.86 0.93 0.49 0 0 0 0
seven key components and seven key reactions exist, which are the fewest necessary for modeling without lumping. The reaction scheme that fits the data best and is in close agreement with the experimental observations is shown in Figure 2. It includes 10 reactions, with more than one side reaction leading to carbon oxides. As the experimental investigations in the CWR indicated, in this scheme, acrylic acid, acetaldehyde, and acetic acid are further oxidized particularly at higher temperatures.1,21 This was also described by Boreskov et al.11 and Gorshkov et al.23 Leaving out these subsequent total oxidation reactions led to a poor fit of the hydrocarbon byproducts. The initial slopes of the yield-time curves of the byproducts1,21 indicate that acrylic acid is exclusively formed in a consecutive reaction step from acrolein and that both carbon oxides, as well as acetaldehyde, result at least from parallel reactions. Because of the experimental results, which show a widely varying ratio between carbon monoxide and carbon dioxide over the range of measurements, the two species were considered separately. To restrict the number of reactions, only the formation of carbon dioxide was modeled for the oxidations of acetaldehyde, acrylic acid, and acetic acid. Applying the concept of the RDS, the rate expressions in eqs 6-17 gave the best fit of the experimental data. According to the observed change of the RDS (section 2.2), two power-law expressions with constant reaction orders and activation energies were formulated to model
5484 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003
the main reaction. Thus, in the reactor simulation program, the switch between the two rate expressions had to be incorporated by calculating both reaction rates from which the lower one was used. The partial pressure of propene determines the rate of the reduction step (eq 6). The rate of catalyst reoxidation is influenced by oxygen and water (eq 7). The experimental results show that water increases the activity of the catalyst only at low temperature, i.e., when reoxidation is rate-determining.1,21 As water probably does not act as directly an oxidizing agent for the reduced catalyst, the special role of water is taken into consideration using the empirical activity function aH2O (which influences the rate in the opposite direction compared to catalyst deactivation) instead of a powerlaw expression (eq 8). The exponential activity function includes the experimentally observed saturation effect at high water contents.
rAC,red ) kAC,redpPR
(6)
rAC,ox ) kAC,oxpO2n1aH2O
(7)
aH2O ) 1 + [1 - exp(-RH2OpH2O)]
(8)
Additionally, most of the side reactions were described using power-law expressions. As water suppresses the formation of both carbon oxides and leads to higher yields of acrolein and acrylic acid,1,21 eqs 13-15 consider water in the adsorption term of the hyperbolic rate expressions. The same temperature-independent adsorption constant of water, KH2O, is used in the rate expressions for the formation of both carbon oxides from propene (eqs 13 and 14). Many of the side reactions can be described best if the rate equations include the partial pressure of oxygen. This finding is in accordance with the kinetic investigations of Haber and Turek,19 who attribute this fact to unselective electrophilic oxidation pathways. The similarity in the reaction behaviors of acetaldehyde and acetic acid is reflected in the equivalent rate expressions for their formation (eqs 11 and 12) and for their consecutive oxidation (eqs 16 and 17).
racrA ) kacrApACn2pO2n3
(9)
rFA ) kFApACn4pO2n5
(10)
rAA ) kAApO2
(11)
raceA ) kaceApO2
rCO )
1 + KH2OpH2O kPR-CO2pPR 1 + KH2OpH2O
(12)
(13)
(14)
kacrA-CO2pO2
(15)
1 + KH2O,acrApH2O
rAA-CO2 ) kAA-CO2pAA
(16)
raceA-CO2 ) kaceA-CO2paceA
(17)
For modeling, the chemical equations (Figure 2) have to be formulated under consideration of oxygen and water and with stoichiometric coefficients. The mass balances of the ideal plug-flow tubular reactor (eq 4) must be solved for all components simultaneously using the above rate equations. Integration of the coupled differential equations and fitting of the kinetic parameters to the experimental data using the log-likelihood principle24 was done with the software tool gPROMS. The temperature dependence of the reaction rate constants, kj, was described according to the Arrhenius law (eq 18). To avoid correlations between the collision factors, kj,0, and the activation energies, EA,j, during parameter estimation, the following transformation was applied for each reaction j
[
( )
kj ) kj,0 exp
(
)]
-EA,j Tref / -1 ) exp k/j - EA,j RT T
(18)
EA,j RTref
(19)
/ EA,j )
/ ) kj,0 ) exp(k/j + EA,j
Tref )
Tmin + Tmax 2
(20) (21)
For the starting values of the parameters and during parameter estimation, the transformed parameters k/j / and EA,j were used. By applying eqs 19-21, the true collision factors, kj,0, and the true activation energies, EA,j, were then calculated. 2.4. Other Models. In addition to the model that describes the experimental data best (section 2.3), many different reaction schemes and rate equations for the main reaction and the side reactions were examined. No changes of the rate-determining steps were observed for the side reactions. Of our modeling studies, only a selection is shown by varying the rate expression of the important main reaction. Instead of two power-law expressions for the main reaction, a Mars-van Krevelen rate expression was used that also contains two steps for catalyst reduction and reoxidation.
rAC ) n6
kCOpO2
rPR-CO2 )
racrA-CO2 )
kAC,redpPRkAC,oxpO2n1aH2O kAC,redpPR + kAC,oxpO2n1aH2O
(22)
A Langmuir-Hinshelwood approach for the selective oxidation of propene to acrolein is presented in eq 23. However, it does not include a change of the RDS. The addition of the products acrolein or water to the adsorption term did not improve the fit.
rAC )
kACpPRnPRpO2n1aH2O (1 + KPRpPR + KO2pO2)2
(23)
Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5485 Table 2. Results of Parameter Estimation for the Best Model no.
parameter, units
estimated value
standard confidence deviation interval (95%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
kAC,ox,0, mol/(kg s barn1) kAC,red,0, mol/(kg s bar) EA,AC,ox, kJ/mol EA,AC,red, kJ/mol n1 RH2O, bar-1 kPR-CO2,0, mol/(kg s bar) kPR-CO,0, mol/(kg s bar) EA,PR-CO2, kJ/mol EA,PR-CO, kJ/mol KH2O, bar-1 EA,acrA, kJ/mol kacrA,0, mol/(kg s bar(n2+n3)) n2 n3 kFA,0, mol/(kg s bar(n4+n5)) EA,FA, kJ/mol kAA,0, mol/(kg s bar) EA,AA, kJ/mol n4 n5 kaceA,0, mol/(kg s barn6) EA,aceA, kJ/mol kaceA-CO2,0, mol/(kg s bar) EA,aceA-CO2, kJ/mol n6 kAA-CO2,0, mol/(kg s bar) EA,AA-CO2, kJ/mol kacrA-CO2,0, mol/(kg s bar) EA,acrA-CO2, kJ/mol KH2O,acrA, bar-1
1.60 × 107 62.8 114.0 39.6 0.75 8.2 0.34 36.3 38.1 60.9 1.9 72.5 2.32 × 103 0.86 0.30 2.03 × 103 78.8 15.0 52.4 0.58 0.80 1.47 × 103 86.7 4.75 × 1012 178.7 0.73 0.38 14.9 1.38 × 103 82.9 55.1
4.0 × 105 0.3 1.1 0.5 0.01 0.8 0.02 0.3 4.1 0.3 0.1 0.9 1.4 × 102 0.02 0.01 6.0 × 101 0.4 0.1 0.5 0.01 0.01 2.0 × 101 0.7 1.1 × 1011 2.2 0.01 0.01 2.3 1.1 × 102 4.4 12.1
9.0 × 105 0.6 2.1 1.0 0.02 1.5 0.04 0.6 8.0 0.7 0.2 1.8 2.6 × 102 0.04 0.03 1.2 × 102 0.8 0.2 1.1 0.02 0.02 5.0 × 101 1.4 2.7 × 1011 4.3 0.02 0.02 4.6 2.0 × 102 8.7 23.7
3. Results and Discussion On the basis of 160 steady-state measurements in the CWR,1,21 including the results for all byproducts under a wide range of conditions (T ) 603-703 K, xPR ) 0.050.15, xO2 ) 0.07-0.33, xH2O ) 0-0.30), the kinetic parameters were fitted to the experimental values. The estimated kinetic constants of the above model (section 2.3) that are valid over the whole range of measurements are listed in Table 2. All parameters can be considered significant because each standard deviation amounts to less than half of the parameter’s value. The narrow confidence intervals verify the precise determination of the parameters and the reliability of the experimental data. Furthermore, the correlation matrix showed no strong correlations among the parameters.21 All reaction orders (values of 0-2.0) and activation energies (with one exception between 35 and 200 kJ/ mol) are within the normal range of values for heterogeneously catalyzed reactions. The reaction order of 1.0 for propene in the reduction step is in accordance with the assumed rate-determining step, i.e., the first Habstraction from propene and the subsequent adsorption of the symmetric allylic species.20 The reaction order in oxygen for catalyst reoxidation (n1 ) 0.75) does not reveal whether the adsorption of molecular oxygen (n ) 1.0) or the incorporation (or diffusion) of oxygen in the lattice (n ) 0.5) is rate-determining in this regime.25,26 The activation energy for reoxidation (114.0 kJ/mol) is about 3 times higher than that for the reduction step (39.6 kJ/mol), which is slower at high temperatures. Accordingly, for the incorporation of oxygen into the lattice, a higher energy barrier than for the H-abstraction from propene exists. Furthermore, the resulting kinetics reflects the redox mechanism of acrolein formation with the participation of lattice oxygen.
Figure 3. Parity plots of the main components: (a) propene, (b) acrolein.
The activation energy of the consecutive reaction leading to acrylic acid (parameter 12) is higher than that for the formation of acrolein. This result was already expected because the formation of acrylic acid increases with increasing temperature.1 The high activation energy for the total oxidation of acetic acid (parameter 25) means that acetic acid is quite stable and its oxidation is relevant at high temperatures only. Figure 3 shows the parity plots of the calculated and experimental outlet molar fractions of propene and acrolein (main components). There is no tendency toward positive or negative deviations between the experimental and calculated data. With the exception of a few points, the deviations are within 10%, and for most data, they are significantly smaller. The model also describes the experimental data for oxygen and water with the same accuracy (within 10%, parity plots not shown). Leaving out the activity factor (i.e., setting aH2O ) 1) leads to a poor fit of the experimental data. Then, especially propene and acrolein are described with systematic deviations of 10-20%. One explanation for the improved catalyst reoxidation by the addition of water might be the hydrolysis of the catalyst surface. Thus, water might facilitate the incorporation of oxygen
5486 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003
Figure 4. Parity plots of the byproducts: (a) acrylic acid, (b) acetic acid, (c) carbon dioxide, (d) carbon monoxide, (e) formaldehyde, (f) acetaldehyde.
into the lattice or create additional sites for the reoxidation step. These explanations are in accordance with the increased conversion of oxygen upon addition of water at low temperatures. The parity plots for the byproducts are presented in Figure 4. Because the concentrations of the byproducts
in the reaction mixture are very low (xi < 0.01) compared to those of the main components, the relative deviations are larger. However, for the most part, the deviations are within 20%, and in the cases of acrylic acid, formaldehyde, and both carbon oxides, they are clearly less than 20%. Even acetaldehyde (xAA < 0.003)
Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003 5487 Table 3. Comparison of Different Rate Expressions for the Main Reaction
rate expression two power laws Mars-van Krevelen LangmuirHinshelwood
objective function value -4540 -4311 -1413
EA,AC,red, kJ/mol
EA,AC,ox, kJ/mol
n1
39.6 ( 1.0 114.0 ( 2.1 0.75 ( 0.02 13.6 ( 2.2 157.3 ( 4.2 0.68 ( 0.03 64.2 ( 0.5 0.75 ( 0.02
and acetic acid (xaceA < 0.0001) are described well by the model. For all components, there is statistical scattering of the deviations. Altogether, the detailed kinetic model of propene oxidation including all important byproducts shows an outstanding accuracy over the entire range of measurements. Varying the rate equation of the main reaction and repeating the estimation of all kinetic parameters led to a poorer fit of the experimental data by the model (Table 3). The value of the objective function is smallest (the smaller the value, the better the fit for the same variance-model) for two separate power-law expressions for catalyst reduction and reoxidation (section 2.3). Applying the Langmuir-Hinshelwood rate expression (eq 23), the reaction order of oxygen stays unchanged, and the activation energy of this rate equation is between the two values for reduction and oxidation (Table 3). However, this expression leads to a very poor fit with a high value of the objective function. The experimental data for propene and acrolein are described with particularly large deviations for high and low temperatures. This result can be attributed to the absence of a change of the RDS in the model. As all rate expressions that are not able to describe the two different regimes gave a poor fit, the change of the RDS must be included in the model. The Mars-van Krevelen rate equation for the main reaction (eq 22) also led to a good description of the experimental data. The value of the objective function is slightly higher, and the fit correspondingly poorer, compared to the two-power-law expression (Table 3). Again, the reaction order of oxygen stays almost unchanged. Compared to the power-law model, the activation energy of the reoxidation step was shifted to a higher value, whereas that of catalyst reduction was clearly smaller. The value of 13.6 kJ/mol is below the normal range of activation energies for heterogeneously catalyzed reactions. Moreover, the influence of internal and external mass-transport limitations and therefore the miscalculation of the activation energy at high temperatures were excluded theoretically by a priori criteria and experimentally by varying the pellet diameter and the gas velocity.21 Using the equation of Mars-van Krevelen the whole temperature range from 603 to 703 K is described as a transition region between the reduction and the reoxidation regimes (Figure 5). Therefore, the activation energies according to Mars-van Krevelen can be seen only outside the investigated range of temperatures. Consequently, for the Mars-van Krevelen expression, the activation energy of catalyst reduction was shifted to an unrealistic low value. However, inside the range of measurements, the Mars-van Krevelen model and the two-power-law model give almost identical fits (Figure 5). The two-power-law expression enables the description of the abrupt change in the RDS. This corresponds much better to the marked change of the reaction behavior between 623 and 643 K observed for the investigated
Figure 5. Comparison of the influence of temperature on the reaction rate of acrolein formation for the Mars-van Krevelen model and the model using two separate power-law expressions (xPR ) 0.045, xO2 ) 0.10, xH2O ) 0.05).
industrial catalyst.1 Therefore, we prefer the expression using two separate power laws compared to the equation of Mars-van Krevelen. A change in the RDS was not observed for the byproducts, which suggests that their formation is not limited by lattice oxygen. 4. Summary and Conclusions The stationary kinetics of the highly exothermic oxidation of propene on an industrial multicomponent oxide catalyst based on bismuth and molybdenum was determined by parameter estimation using experimental data from isothermal investigations in a CWR. It was shown that a change in the RDS of the main reaction depending on temperature occurs. This change could be modeled best using two separate power-law expressions for catalyst reduction and reoxidation, which are the major steps in the mechanism of selective acrolein formation. Applying the Mars-van Krevelen rate equation for the main reaction leads to erroneous kinetic parameters because the range of temperatures is then described as an intermediate region with no abrupt change in the RDS. In the reduction regime, i.e., at high temperatures, the reaction rate is first order in propene and independent of the other components. At lower temperatures, catalyst reoxidation is the slowest step, with oxygen and water accelerating acrolein formation. Compared to catalyst reduction, about a 3-fold higher activation energy for the reoxidation step was observed. The special role of water, with increasing water content improving catalyst reoxidation, was modeled using an activity function in the rate equation for the reoxidation step. The other role of water in suppressing the formation of carbon oxides was described by considering water in the adsorption terms of these side reactions. To consider all important byproducts, a reaction scheme consisting of consecutive and parallel reactions was derived from initial slopes of yield-time curves and from modeling studies. Including the byproducts acrylic acid, both carbon oxides, formaldehyde, acetaldehyde, and acetic acid, a model consisting of 10 reactions and 31 kinetic parameters was developed. This model describes the experimental data over the entire range of measurements very well, and all parameters that were determined were found to be significant.
5488 Ind. Eng. Chem. Res., Vol. 42, No. 22, 2003
With respect to these results, the CWR represents a very useful tool for isothermal investigations of highly exothermic reactions, especially when the reaction behavior is closely linked to temperature. Acknowledgment This research was carried out with financial support of Degussa AG, Hanau, Germany. Nomenclature aH2O ) activity function for water AR ) cross-sectional area of reactor tube, m2 ci ) concentration of species i, mol/m3 CWR ) catalytic wall reactor EA ) activation energy, J/mol E/A ) transformed activation energy K ) adsorption constant, bar-1 k ) reaction rate constant, variable units k* ) transformed reaction rate constant, variable units k0 ) collision factor, variable units m ) mass, kg n, n1, ..., n6 ) reaction orders n˘ tot ) total molar flux, mol/s pi ) partial pressure of species i, bar ptot ) total pressure, bar R ) ideal gas law constant, (J mol)/K RDS ) rate-determining step r ) reaction rate, mol/(kg s) T ) temperature, K Tref ) reference temperature, K u ) gas linear velocity, m/s x ) molar fraction z ) axial reactor coordinate, m Greek Letters RH2O ) activity parameter for water νij ) stoichiometric coefficient of species i in reaction j F ) apparent density of the catalyst in the reactor, kg/m3 τmod ) modified residence time, (kg s)/mol Subscripts AA ) acetaldehyde AC ) acrolein aceA ) acetic acid acrA ) acrylic acid cat ) catalyst Exp ) experiment FA ) formaldehyde i ) species i j ) reaction j mod ) model ox ) oxidation step PR ) propene red ) reduction step
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Received for review February 27, 2003 Revised manuscript received August 8, 2003 Accepted August 25, 2003 IE030191P
