ProductsFoundry | Thriller | Warrior Baek Dong Soo 20.Bölüm 39901

TiO2 catalyst

TiO2 catalyst

Applied Catalysis A: General 242 (2003) 297–309 Kinetics of oxidative dehydrogenation of propane over V2 O5/TiO2 catalyst Ryszard Grabowski a,∗ , Jer...

287KB Sizes 0 Downloads 60 Views

Applied Catalysis A: General 242 (2003) 297–309

Kinetics of oxidative dehydrogenation of propane over V2 O5/TiO2 catalyst Ryszard Grabowski a,∗ , Jerzy Słoczyñski a , Narcyz Mirosław Grzesik b a

Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, 30-239 Kraków, Poland b Institute of Chemical Engineering, Polish Academy of Sciences, 44-100 Gliwice, Poland

Received 4 February 2002; received in revised form 17 September 2002; accepted 17 September 2002

Abstract Application of the pseudo-homogenous and steady-state adsorption model (SSAM) was analyzed for the description of the oxidative dehydrogenation (ODH) of propane over vanadia-titania catalyst, using an extensive set of the experimental data. It has been shown that the SSAM model adequately describes the kinetics of the studied reaction for a broad range of feed mixture, propane conversion and temperature. The pseudo-homogenous models must be consider as a rough approximation of the experimental results. It is possible to solve analytically the set of differential equations describing the SSAM model and to present the selectivities to propene and to the products of total oxidation (CO, CO2 ) as a function of the propane conversion and the temperature. Numerical methods (the Runge–Kutta method combined with the Levenberg–Marquardt method) were applied to solve the systems of differential equations which describe the kinetic of the ODH of propane as a function of contact time and to fit the solutions to the experimental data. The calculations allowed us to determine the rate constants (activation energies and pre-exponential factors) for all reaction steps considered. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Propane oxidative dehydrogenation; Vanadia-titania catalyst; Reaction kinetics

1. Introduction Oxidation upgrading of light paraffins to the corresponding olefins, diolefins and/or oxygenated products is a topic of a current commercial interest [1]. Olefins produced in this manner can be used as alkylation or etherification feedstocks to enhance the octane number pool of refinery streams, while oxygenates can be added directly to reformulated gasoline to increase both its oxygen content and octane number. Kinetic studies of the oxidative dehydrogenation (ODH) of alkanes is one of the ways to elucidate the reaction mechanism and to facilitate selection of the appropriate catalyst for this type of the reactions. ∗

Corresponding author.

Previous studies have not explained entirely the mechanism of the ODH of propane and some controversies in determination of macroscopic steps of the reaction still exist. Though it is well known that the kinetic studies are not able to determine molecular mechanism of the reaction, but they allow to exclude some of the possible paths and to determine the reaction network. Nevertheless, kinetic studies were often used in the past (and still are) to provide useful information about the studied reaction and the catalyst operation. On the basis of these studies one can define intermediate products, the nature and quantitative participation of particular reaction routes (parallel and consecutive reaction paths, branching of the reactions, etc.) which decide about the selectivity of the process, and one can also identify the rate determining step in the

0926-860X/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 6 - 8 6 0 X ( 0 2 ) 0 0 5 2 0 - 3

298

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

sequence of consecutive reactions. The macrokinetic model obtained in this way is usually a starting point for the description of a molecular mechanism. The kinetic of the ODH of propane in stationary conditions was analysed for different systems contained vanadium, like V-Mg-O [2], vanadium oxide supported on AlPO4 [3], VTiO [4]and Mg-V-Sb-O [5]. In [2], the kinetics of ODH of propane was investigated by a non-linear regression analysis using both simple power law and mechanistic models. In the papers [3–6], the kinetic studies were less extensive and only the relative reaction rates or the qualitative information about the kinetic of this reaction are given. Andersson and co-workers [2] undertook an attempt to compare different models of the ODH reaction on V-Mg-O catalyst, i.e. the redox model (Mars van Krevelen, M-K), the adsorptive model (Langmuir–Hinselwood, L–H) and the simple pseudo-homogenous power law model (PM). Probably due to limited experimental basis confined to low propane conversions, it was impossible to discriminate between the models. In the paper [7], the parallel-consecutive scheme of the ODH of propane over V2 O5 /TiO2 and V2 O5 + Rb/TiO2 was applied. It was assumed that the rate of the reaction is proportional to the concentration of propane and independent of the oxygen concentration (the first-zero order model—FZO). Kinetic studies of the ODH of propane on the V-contained catalysts by the transient method in non-stationary conditions [8–10], have led to the conclusion that propane reacts directly from the gaseous phase with the catalyst oxygen and that the desorption of the products from the surface of the catalyst is rapid, i.e. this step of the reaction occurs according to the Eley–Rideal (E–R) mechanism. On the other hand, the redox studies have shown that reoxidation of the VOx /TiO2 catalyst at the surface layer is much more rapid than the reduction of the catalyst by propane [11]. At the stationary conditions, a small degree of the catalyst reduction is observed. This shows that the reduction and the reoxidation of the catalyst occurs only at the surface layer, which in turn suggests application of the steady-state adsorption model (SSAM) model as an adequate way of describing the reaction under study. This model was successfully used for the kinetic description of oxidation of aromatic hydrocarbons over the vanadia catalyst [12,13]. In this paper, simple pseudo-homogenous models (FZO and PM) were compared with the SSAM model

which is based on the assumption of the steady-state of the surface oxygen. Within the framework of the SSAM model, the analysis of the catalytic results has been carried out both on the basis of analytical and numerical solutions of equations describing this model. Ample set of data on propane conversion and selectivities to oxidation products as a function of the reagent mixture composition, temperature and contact time was used for the verification of the above-mentioned models.

2. Experimental 2.1. Catalyst The catalyst used in the studies is denoted further in the text as 1VTi. This catalyst contained one monolayer (mnl) of vanadia phase deposited on TiO2 anatase (commercial support, product of Tioxide Ltd., 48 m2 /g). One monolayer of the VOx phase, calculated from crystallographic data of V2 O5 as 10 V/nm2 , corresponded to 6.7% V2 O5 for a given specific surface area of TiO2 . The catalyst was prepared by impregnation of ammonium methavanadate from aqueous solution at pH = 6, followed by solvent evaporation, drying for 18 h at 393 K and calcination in a stream of air at 723 K for 5 h. The specific surface area of a sample after the calcination was 44.4 m2 /g. The detailed characteristic of the preparation has been given in [14]. 2.2. Catalytic activity measurements The steady-state activity of the catalyst in the oxidative dehydrogenation of propane was measured in a fixed bed flow apparatus. A stainless steel reactor (120 mm long, i.d. 13 mm) was coupled directly to a series of gas chromatographs. Propene, carbon monoxide and carbon dioxide were found to be the main reaction products. The details of the experimental set-up can be found in [15]. The flow rate of the reaction mixture was controlled with a mass flow controller type ERG-1MKZ. 0.4–0.5 g samples of a catalyst of the grain size of 0.6–1 mm, diluted with glass beads, were used. It has been checked in the preliminary experiments, in which the mass and the grain size of a catalyst sample were varied, that under these conditions the transport phenomena do not limit the

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

reaction rate. The reaction mixture contained propane, oxygen and helium as a balance gas. The kinetic measurements were performed by measuring conversion of propane (X) and selectivities (Sj ) to propene and CO at three temperatures (498, 523 and 558 K) as a function of contact time and composition of the reaction mixture. X = (ci –cf )/ci , Sj = cj / cj , where ci and cf are the concentration of the respective alkane at the entrance and the exit of the reactor, respectively, and cj is the concentration of product j in the exit gas. For each temperature, four different compositions of the reaction mixture—with ratio propane/O2 2/1, 2/3, 1/1 and 1/3—were used. The contact time τ was varied between 0.2 and 1.5 s by changing the flow rate of the reaction mixture. The complete set of the experimental data is listed in Table 1.

299

changes of propane—the conversion and the selectivity to propene and COx (CO + CO2 )—as a function of the contact time τ . Considerable decrease in the selectivity to propene, S␲ and at the same time increase in the selectivity to COx , SCOx (combustion products), with an increase in the contact time shows that propene is an intermediate product and the ODH of propane has a consecutive character. It is also evident from Fig. 1 that the extrapolation to τ = 0, which is equivalent to X = 0, gives the initial se0 lectivity S␲0 < 100% and SCO > 0. This implies that x part of the combustion products is formed in the parallel reaction directly from propane. Such course of changes of the selectivities with the contact time implies a parallel-consecutive network of the reaction.

3. Determination of the reaction network and physicochemical base for the SSAM model Selective reaction of the ODH of propane leading to the formation of propene is accompanied by the total oxidation of hydrocarbons, which leads to the formation of CO and CO2 . Fig. 1 exemplifies typical

(1)

Fig. 1. Changes of propane conversion and selectivities to propene and to COx (CO + CO2 ) as a function of contact time. Propane/oxygen ratio equal 0.66, temperature 523 K.

300

Table 1 Experimental data and results of calculation for SSAM model Temperature (◦ C)

Propane/O2 ratio

Experimental conversion of propane

Calculated conversion of propane

Experimental selectivity to propene

Calculated selectivity to propene

Experimental selectivity to CO

Calculated selectivity to CO

0.250 0.500 1.000 1.200 1.500

225 225 225 225 225

1/1 1/1 1/1 1/1 1/1

0.029 0.048 0.077 0.093 0.109

0.029 0.046 0.077 0.089 0.106

0.464 0.350 0.226 0.188 0.154

0.464 0.342 0.230 0.204 0.173

0.404 0.471 0.542 0.561 0.579

0.404 0.478 0.543 0.558 0.575

0.300 0.500 1.000 1.200 1.500

225 225 225 225 225

2/1 2/1 2/1 2/1 2/1

0.026 0.037 0.057 0.063 0.068

0.026 0.340 0.053 0.060 0.070

0.527 0.448 0.324 0.294 0.263

0.527 0.436 0.317 0.288 0.254

0.352 0.398 0.469 0.489 0.512

0.352 0.411 0.485 0.503 0.523

0.250 0.500 1.000 1.200 1.500

225 225 225 225 225

1/3 1/3 1/3 1/3 1/3

0.039 0.063 0.099 0.112 0.125

0.039 0.062 0.106 0.123 0.148

0.356 0.261 0.166 0.142 0.121

0.356 0.265 0.171 0.148 0.122

0.509 0.558 0.600 0.612 0.621

0.509 0.548 0.592 0.602 0.615

0.300 0.500 1.000 1.200 1.500

225 225 225 225 225

2/3 2/3 2/3 2/3 2/3

0.030 0.045 0.066 0.074 0.082

0.030 0.043 0.072 0.083 0.099

0.463 0.370 0.263 0.234 0.205

0.463 0.366 0.246 0.217 0.184

0.412 0.473 0.530 0.547 0.561

0.412 0.468 0.537 0.552 0.571

0.250 0.500 1.000 1.200 1.500

250 250 250 250 250

1/1 1/1 1/1 1/1 1/1

0.061 0.104 0.168 0.187 0.212

0.061 0.090 0.142 0.161 0.188

0.300 0.194 0.111 0.093 0.075

0.300 0.197 0.118 0.101 0.085

0.505 0.565 0.601 0.612 0.622

0.505 0.557 0.598 0.606 0.614

0.300 0.500 1.000 1.200

250 250 250 250

2/1 2/1 2/1 2/1

0.052 0.068 0.106 0.116

0.052 0.065 0.095 0.105

0.389 0.318 0.205 0.183

0.389 0.298 0.192 0.171

0.435 0.471 0.538 0.547

0.435 0.486 0.546 0.558

0.250 0.500 1.000 1.200 1.500

250 250 250 250 250

1/3 1/3 1/3 1/3 1/3

0.069 0.120 0.196 0.226 0.263

0.069 0.109 0.186 0.215 0.256

0.264 0.158 0.083 0.067 0.052

0.264 0.159 0.086 0.071 0.057

0.549 0.602 0.635 0.642 0.646

0.549 0.593 0.623 0.629 0.636

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

Contact time (s)

250 250 250 250 250

2/3 2/3 2/3 2/3 2/3

0.061 0.088 0.148 0.161 0.181

0.061 0.083 0.134 0.154 0.182

0.317 0.235 0.130 0.114 0.094

0.317 0.223 0.127 0.108 0.088

0.506 0.548 0.606 0.611 0.614

0.506 0.551 0.597 0.606 0.616

0.250 0.500 1.000

285 285 285

1/1 1/1 1/1

0.129 0.205 0.235

0.129 0.181 0.255

0.175 0.095 0.065

0.175 0.085 0.050

0.595 0.635 0.644

0.595 0.626 0.636

0.300 0.500

285 285

2/1 2/1

0.106 0.127

0.106 0.125

0.226 0.176

0.226 0.157

0.545 0.570

0.545 0.574

0.250 0.500 1.000 1.200 1.500

285 285 285 285 285

1/3 1/3 1/3 1/3 1/3

0.148 0.257 0.381 0.426 0.473

0.148 0.225 0.364 0.412 0.479

0.146 0.070 0.033 0.025 0.019

0.146 0.061 0.030 0.024 0.018

0.623 0.663 0.664 0.666 0.660

0.623 0.645 0.649 0.650 0.651

0.300 0.500 1.000 1.200 1.500

285 285 285 285 285

2/3 2/3 2/3 2/3 2/3

0.128 0.185 0.281 0.302 0.319

0.128 0.171 0.268 0.301 0.342

0.164 0.101 0.048 0.039 0.034

0.164 0.091 0.046 0.039 0.032

0.598 0.631 0.648 0.658 0.655

0.598 0.623 0.636 0.638 0.640

2 ; propane conversion, 0.94; selectivity to propene, 0.47; selectivity to CO, 0.05; F 2 2 Approximate lack of fit test: response, Slf2 /Spe (42,33,0.95) = 1.76; slf /spe —ratio of mean square due to lack of fit plus pure error to estimate of pure error variance, degrees of freedom for each response: νpe = 33, νlf = 42, νtotal = 75.

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

0.300 0.500 1.000 1.200 1.500

301

302

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

(3b)

is proportional to the oxygen concentration CO2 ; and (b) the oxygen dissociation is slow and then the rate is proportional to CO0.52 . This alternative will be verified further. In Eq. (5), the opposite reaction, e.g. the desorption of oxygen is not taken into consideration, because it is evident from our earlier experiments [16] that this process is not occurring in the temperature range of the catalytic reaction. Taking into account the above conclusion, one can calculate the steady-state oxygen coverage of the catalyst surface

(4a)

dΘs = kos COn 2 (1 − θs ) − (3k21 + 4.5k22 )C␲ θs dt − (k1 + 3.5k31 + 5k32 )Cp θs = 0

Let us assume that the ODH of propane proceeds through the following individual steps. Formation of propene: k1

C3 H8(g) + O(s) → C3 H6(g) + H2 O(g) + Vo

(2)

consecutive combustion of propene k21

C3 H6(g) + 6O(s) → 3CO(g) + 3H2 O(g) + 6Vo k22

C3 H6(g) + 9O(s) → 3CO2(g) + 3H2 O(g) + 9Vo

(3a)

parallel combustion of propane k31

C3 H8(g) + 7O(s) → 3CO(g) + 4H2 O(g) + 7Vo

where CO2 , Cp and C␲ are concentrations of oxygen, propane and propene, respectively, and

k32

C3 H8(g) + 10O(s) → 3CO2(g) + 4H2 O(g) + 10Vo (4b) reoxidation of the surface of the catalyst by gaseous oxygen kos

2Vo + O2(g) → 2O(s)

(6)

(5)

where Vo and Os denote oxygen vacancy and surface oxygen species on the surface of the catalyst, respectively. It is obvious, that none of the above reactions is an elementary reaction. Therefore, one must assume the appropriate reaction orders on the experimental basis. As it was mentioned in Section 1, the transient experiments indicate that the steps described by Eqs. (2)–(4) proceed through the E–R mechanism. According to this mechanism, the hydrocarbon reacts directly from the gaseous phase with the surface oxygen of the catalyst, the reaction products desorb quickly and the surface in not blocked. This assumption is reflected in Eqs. (2)–(4). At the same time, the E–R mechanism implies that reactions (2), (4a) and (4b), and reactions (3a) and (3b) should be of the first order with respect to propane and propene concentrations, respectively. Because there is no experimental evidence as to the reaction order in relation to the surface oxygen, we have taken as a first approximation—as it is usually done— that the reaction rate is proportional to the oxygen surface coverage θ s of the catalyst. In case of reaction (5), two possibilities can be considered: (a) the adsorption of the gaseous oxygen on the vacancies is slow compared to its dissociation and therefore the reaction rate

θs =

kos COn 2 +(k1

kos CnO2 + 3.5k31 +5k32 )Cp +(3k21 +4.5k22 )Cπ

(7)

where n = 1 or 0.5. The coefficients at the constants of the reaction rates reflect the reaction stoichiometry after recalculation of O(s) to O2 . At the steady-state the equations for the rates of the individual steps of the ODH of propane can be expressed as: rate of propane consumption rp = −

kos (1 + κ3 )Cp COn 2 dCp dX = Cp0 = dτ dτ M

(8)

where M = κos COn 2 + (1 + 3.5κ31 + 5κ32 )Cp + (3κ21 + 4.5κ22 )Cπ kij kos , κij = , k1 k1 κ3 = κ31 + κ32 κos =

(8a) κ2 = κ21 + κ22 , (8b)

rate of propene formation r␲ =

kos (Cp − κ2 C␲ )COn 2 dC␲ = dτ M

(9)

rate of CO and CO2 formation 3kos (κ31 Cp + κ21 C␲ )COn 2 dCCO = dτ M

(10)

3kos (κ32 Cp + κ22 C␲ )COn 2 dCCO2 = = dτ M

(11)

rCO = rCO2

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

In Eqs. (8)–(11) the same term kos CnO2 /M is present. It can be eliminated by dividing both sides of the corresponding equations by each other. Taking Cp as an independent variable and dividing Eq. (9) by (8), we obtain expression −

C p − κ 2 C␲ dC␲ = dC p (1 + κ3 )Cp

or κ2 1 dC␲ − C␲ = − dCp (1 + κ3 )Cp 1 + κ3

(12)

(13) Taking into account definitions of the conversion and selectivity, one can express Eq. (13) in its equivalent form in which S␲ is the function of the propane conversion X. 1 1−X 1 + κ3 − κ2 X × [(1 − X)(κ2 −κ3 −1)/(1+κ3 ) − 1]

(14)

Likewise we can calculate selectivity to CO.   1 κ21 κ31 − SCO = 1 + κ3 1 + κ 3 − κ2 +

κ21 1 − (1 − X)κ2 /(1+κ3 ) κ2 (1 + κ3 − κ2 ) X

(15)

Selectivity to CO2 is calculated as 1 − S␲ − SCO . It follows from (14) and (15) that for X → 0 S␲0 =

1 , 1 + κ3

0 SCO =

κ31 1 + κ3

to stress that the direct analytical solution of Eqs. (9) and (10) to find the C␲ (τ ) and CCO (τ ) functions is impossible. The same goes for Eq. (8), the integration of which gives the dependence of the propane conversion on the contact time. Finally, we can derive the expression for the yield of propene 1 1 + κ 3 − κ2 × (1 − X)[(1 − X)(κ2 −κ3 −1)/(1+κ3 ) − 1]

Y␲ = XS␲ =

Such linear differential equation can be solved analytically. Taking into consideration the initial condition C␲ = 0 for Cp = Cp0 we can express C␲ as    (1+κ3 −κ2 )/(1+κ3 ) Cp0 Cp  C␲ = − 1 1 + κ 3 − κ2 Cp

S␲ =

303

(16)

As it follows from (14) and (15), the expression describing dependence of the selectivity on the conversion has a universal character, e.g. in the stationary-state it does not depend on the initial concentration of the substrates nor on the detailed form of the expression for θ s , because these variables were eliminated when solving the equations. It is necessary

(17)

It easy to show that this function attains a maximum for conversion  (1+κ3 )/(1+κ3 −κ2 ) κ2 Xmax = 1 − (18) 1 + κ3 and the maximum yield of propene is given by  κ2 /(1+κ3 −κ2 ) κ2 1 Y␲ max = (19) 1 + κ3 1 + κ3 4. Results and discussion To verify the SSAM model, 12 sets of data described in Section 2 were used (selectivities to propene and CO as well as conversion of propene as a function of contact time at three different temperatures). To determine the relative rate constants, κ ij , Eqs. (14) and (15) were used in which the Arrhenius relation was included to introduce temperature as a second variable.   Eij κij = κij0 exp (20) RT The pre-exponential coefficient and the activation energies were determined by the non-linear leastsquare method (the Levenberg–Marquardt gradient method). Figs. 2 and 3 show the computer simulations of the selectivity to propene and CO as a function of the temperature and the conversion of propane. Relative rate constants κ ij , calculated as described, were used for simulation of the catalytic results. It is evident from Figs. 2 and 3 that all experimental points cluster along three lines. Their positions depend on the temperature but they are independent of the initial concentrations of the substrates. The curves

304

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

Fig. 2. Selectivity to propene as a function of propane conversion and temperature, surface-simulated by SSAM model, points-experimental data. Selectivity and conversion is given as a fraction; (䊉) −498 K, (䉱) −523 K, (䊏) −558 K.

show the dependence of selectivities S␲ and SCO on the propane conversion at the constant temperature. In accordance with Eqs. (14) and (15), they show that the selectivities are independent on the composition of the reaction mixture. It is an important experimental confirmation of the predictions of the model described above. The rate constants κ 2 and κ 3 —which are determined from the fitting of the selectivities to CO and to propene—are mutually consistent within the limit of error. The highest difference is observed for κ 3 due to a high error in estimation associated with the participation of the parallel reaction, which is small in comparison with the propene combustion in the successive reaction. This is the reason why the selectivities S␲ and SCO are sensitive only to a small

extent to changes of κ 3 . This in turn causes a high error when this constant rate is estimated. The reasonable limit values for the selectivity of propene—74, 71 and 67.5% at 498, 523 and 558 K, respectively— were calculated from the first of Eq. (16). Estima0 on the basis of the rate constants values tion of SCO (Eq. (16)) which are determined by the fitting of CO, gives too high values, due to a significant fitting error at low conversions. It should be stressed that the procedure of solving Eqs. (9) and (10) described above, allows one to determine only the relative rate constants κ ij . To determine their absolute values kij , a numerical solution of the Eqs. (8)–(11) is required. Basing on scheme (1) and the assumptions of the SSAM model and using

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

305

Fig. 3. Selectivity to CO as a function of propane conversion and temperature, surface-simulated by SSAM model, points-experimental data. Selectivity and conversion is given as a fraction. Notation as in Fig. 2.

kos (κ31 Cp + κ21 C␲ )CO0.52 SCO (dX/dτ ) dSCO − = 0 dτ X MCp X

the dependencies Cp = Cp0 (1 − X), 1 3 CCO

C␲ = Cp0 XS␲ ,

(23)

= Cp0 XSCO ,

CO2 = CO0 2 − 0.5Cp X(10 − 3SCO − 9S␲ ) the steady-state model of the propane ODH can be written as a next set of linear differential equations kos (1 + κ3 )Cp CO0.52 dX = dτ MC0p

(21)

kos (Cp − κ2 C␲ )CO0.52 dSπ S␲ (dX/dτ ) − = 0 dπ X MCp X

(22)

The above Eqs. (21)–(23) allow us to determine rate constant kos and all remaining relative rate constants κ ij . On the basis of these values, it is possible, using Eq. (8b) to determine all absolute rate constants (k1 , k21 , k22 , k31 , k32 ) which are present in the kinetic network (1). The fitted kinetic parameters are listed in Table 2 and the comparison between experimental and calculated values is presented in Table 1. The calculated values reproduce the experimental data with a comparatively small fitting error (matching mean error 4.9%). In Table 1 results of approximate lack of fit tests described by Draper and Smith [17] are shown.

306

Model

Rate constants k1

k21

First-zero order model (FZO) Power model (PM)

−1.73a (11.1)b

7.89 (39.0)

8.06 (36.9)

8.64 (37.6)

11.56 (61.9)

3.06 (72.0)

12.65 (65.0)



2.96 (27.4)

8.34 (42.0)

9.24 (42.0)

9.58 (42.0)

13.75 (68.6)

14.76 (77.4)

14.60 (70.9)



6.3 (35.5 ± 3.6)e

9.05 (34.5)

14.04 (54.5)

9.21 (48.4)

6.52 (43.9)

Steady-state adsorption model (SSAM)

k22

k2 = k21 + k22 , k3 = k31 + k32 . a Natural logarithm of ki0 . b Activation energy (kJ/mol) in parenthesis. c Fixed exponents. d Estimated exponents. e Activation energies estimates—region of confidence.

k2

12.49 (44.9 ± 4.2)

k31

k32

k3

9.16 (47.6 ± 7.1)

kos

14.81 (69.7 ± 16.5)

Exponents α β α β γ δ –

= γ = 1c , =δ =0 = γ = 0.8d , = 0.5, = 0.8, = 0.5

Fitting error (%) 11.5 7.6

4.9

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

Table 2 Kinetic constants for studied models

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

307

Fig. 4. Parity plots for the conversion of propane and for the selectivities to propene and CO.

2 ) with the Comparison of the value of the ratio (slf2 /spe appropriate tabulated F value revealed no lack of fit. Fig. 4 shows the parity plots for the conversion of propane and for the selectivities to propene and CO. It is evident from this figure and from the F-test that estimated values of the rate constants are not charged with the model error, i.e. SSAM model adequately describes the kinetics of the ODH of propane on the studied catalyst. In the case when the catalyst oxygen is replenished by gaseous oxygen without a dissociation (CO1 2 ) the fitting error is considerably higher (∼13%). The power models have been used in the literature for an approximate description of the kinetics of the complex chemical reactions. Assuming that the rate of the reaction is proportional to the concentration of

the substrates in the appropriate powers, both the exponents and the rate constants, can be obtained by fitting the model to the experimental data. Though the models of this type frequently describe well the studied reactions, they do not have any physical interpretation, which is their serious disadvantage. In the case of the PM model, Eqs. (21)–(23) can be replaced by β

(k1 + k3 )Cpα CO2 dX = dτ Cp0 α

β

(24) γ

δ

dS␲ (k1 Cp CO2 −(k21 +k22 )C␲ CO2 −Cp S␲ (dX/dτ )) = dτ Cp0 X 0

(25)

308

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

dSCO dτ γ β (k1 k31 Cpα CO2 + k21 C␲ COδ 2 − Cp0 SCO (dX/dτ )) = Cp0 X (26) where α and γ are the orders of the reaction with respect to propane and propene, respectively (reactions (2) and (3)), β is the order with respect to oxygen in the reaction of the selective formation of propene (reaction (2)) and δ is the order with respect to oxygen in the combustion reactions of propane and propene (reactions (3) and (4)). Results of fitting the exponents and the rate constants from the scheme (1) are given in Table 2. As it can be seen from this table the matching error is about 1.5 higher in the case of the PM model than for the SSAM model. Thus, the kinetics of ODH of propane on vanadia-titania catalyst is poorly described by the PM model. Moreover, lack of physical meaning does not allow to draw conclusions regarding the mechanism of the reaction. The first-zero order model is both particular and extreme case of the PM model. It is obtained by taking α = γ = 1 and β = δ = 0, i.e. it is assumed that the rate of the reaction does not depend in all steps on oxygen partial pressure and is proportional to the hydrocarbon concentration. Results given in Table 2 show that matching the error exceeds 11% and is the highest, which qualify the FZO model as a rough approximation of the kinetics of the studied reaction. As one can see from Table 2, the activation energy for CO and CO2 formation on the consecutive path is small in comparison with their activation energies for the parallel path. This suggests that at the higher temperatures the parallel route will play a more significant role as a source of carbon oxides. In spite of quantitative differences between the PM and SSAM models, both lead to the same qualitative results. Similar studies were done by Andersson and co-workers for the V-Mg-O catalyst [2]. The authors tried three different models of the ODH of propane reaction (the power model and the models of Langmuir–Hinselwood, L–H; and Mars van Krevelen, M-K). However, the fitting errors for all these models are practically the same (e.g. 7.5%), and it is difficult to distinguish which is the best one. In our opinion, there are two reasons for such results. The first is a

small range of the propane conversions and the second is a simplified (only consecutive) kinetic network, used by the authors in their calculations. Our models are based on the parallel-consecutive kinetic network (1) and the kinetic data cover broader range of the propane conversions and selectivities to propene, CO and CO2 . The difference in the kinetic networks becomes important especially for high conversions of propane, which is justified by a relatively high activation energy of the parallel path. For this reason a quantitative comparison of the activation energies and the rate constants determined in this paper with the data obtained by Andersson and co-workers [2] is impossible. Moreover, catalytic activity of V-Mg-O is considerably lower in comparison with V2 O5 /TiO2 — i.e. for the V-Mg-O catalyst the same catalytic activity is attained at the temperature about 200 K higher. On the basis of the estimated kinetic results we can evaluate the stationary coverage of oxygen. Values of the exponents calculated in the PM model, as well as values applied in the FZO model show that both the rate of propane ODH reaction and the rate of total oxidation of hydrocarbon depend to a small extent on the oxygen concentration. It means that the oxygen coverage during the reaction is practically constant and close to the saturation. This conclusion corresponds with our data on the reduction of the V2 O5 /TiO2 catalyst with propane and its reoxidation with gaseous oxygen [11], which indicates that the rate of the surface reoxidation is considerably higher than that of the reduction. It seems then justified to assume that a degree of the catalyst reduction is small in the present measurements. This was confirmed by the determination of the V4+ content in the catalyst after the reaction. The same conclusion came Andersson applied the PM model. Kinetic studies were also carried out for the ODH of propane on the other catalysts like V-Mg-Sb-O [5], nickel cobalt molybdate [6] and vanadia/AlPO4 [3]. In the case of the V-Mg-Sb-O catalyst the published results, like our own data indicate that CO, CO2 are produced largely by the sequential oxidation of the in situ produced intermediate propene, and to a lesser extent by a parallel route of the direct deep oxidation of propane. Unfortunately the authors do not give any quantitative results. The primary reaction path of the propane ODH on nickel cobalt molybdate [6] is to propene as the

R. Grabowski et al. / Applied Catalysis A: General 242 (2003) 297–309

exclusive primary product. Propene formed oxidizes subsequently primarily to acrolein which oxidizes further to waste products, CO and CO2 . Our computational results obtained for the ODH of propane qualitatively agree with results obtained by the authors in the part which concerns formation of propene and CO, CO2 . Lack of activation energies for particular steps in the ODH of propane reaction makes impossible a more detailed comparison of the results. Similar calculations for the ODH reaction were done in [3] for the ODH of propane over vanadia supported on amorphous ALPO4 catalyst but the applied kinetic model is very simplified and based on a few experimental data (only one contact time and one mixture composition). The authors suggest that the adopted Eley–Rideal model is more appropriate to describe the experimental data than the LH model but neither the activation energies nor the pre-exponential coefficients related to the different steps of the reaction are given.

309

Eley–Rideal mechanism, i.e. without participation of the adsorbed species of the hydrocarbons; • a steady-state of the oxygen coverage is established on the catalyst surface; • oxygen adsorption has a dissociative character; • propene formation and hydrocarbon combustion require only one type of the surface oxygen. 5. The analysis of the reaction network indicates that propene is the only useful product primary produced, and that CO and CO2 are produced largely by the sequential oxidation of the in situ produced propene, and to a lesser extent by a parallel route of the direct deep oxidation of propane. 6. Both the PM and SSAM models imply that the vanadia-titania catalyst is nearly saturated with oxygen or completely oxidized at the reaction conditions, which is confirmed by the close to zero degree of the reduction of the catalyst after the reaction. References

5. Conclusions 1. Various kinetic models have been tested using data on the propane oxidative dehydrogenation on the V2 O5 /TiO2 catalyst. The steady-state model, in which the surface oxygen plays an important role, provided the best description of the experimental results. 2. The equations describing the SSAM model for the ODH of propane were solved analytically. The selectivities to propene, CO and CO2 are functions of two variables, e.g. temperature and propane conversion. The solutions also imply that the selectivities are independent of the feed mixture composition, which has been confirmed by the experimental results. 3. The kinetics of the ODH of propane can be described in a rough approximation by the PM and FZO models. 4. The assumptions of the SSAM model have been confirmed by a good agreement between the experimental data and results of the calculations, e.g. • the reaction of the hydrocarbons (propane, propene) on the catalyst proceeds through the

[1] F. Cavani, F. Trifiro, Catal. Today 24 (1995) 307. [2] D.B. Creaser, B. Andersson, Appl. Catal. A: Gen. 141 (1966) 131. [3] S.L.T. Andersson, Appl. Catal. A: Gen. 112 (1966) 209. [4] N. Boisdron, A. Monnier, L. Jalowiecki-Duhamel, Y. Barbaux, J. Chem. Soc., Faraday Trans. 91 (1995) 2899. [5] J.N. Michaels, D.L. Stern, R. Grasselli, Catal. Lett. 42 (1996) 139. [6] D.L. Stern, R. Grasselli, J. Catal. 167 (1997) 560. [7] J. Słoczy´nski, R. Grabowski, K. Wcisło, B. Grzybowska– ´ Swierkosz, Polish J. Chem. 71 (1997) 1585. [8] R. Grabowski, S. Pietrzyk, J. Słoczy´nski, F. Genser, K. ´ Wcislo, B. Grzybowska-Swierkosz, Appl. Catal. A: Gen. 232 (2002) 277. [9] A. Holtzwarth, P. Denton, H. Zanthoff, C. Mirodatos, Catal. Today 67 (2001) 309. [10] H.W. Zanthoff, J.C. Jalibert, Y. Schuurman, P. Slama, J.M. Herrmann, C. Mirodatos, Stud. Surf. Sci. Catal. A 130 (2000) 761. [11] J. Słoczy´nski, Appl. Catal. A: Gen. 146 (1996) 401. [12] J.A. Jussola, R.F. Mann, J. Downie, J. Catal. 17 (1970) 106. [13] J.F. Boag, D.W. Bacon, J. Downie, J. Catal. 38 (1975) 375. [14] R. Grabowski, B. Grzybowska, K. Samson, J. Słoczy´nski, J. Stoch, K. Wcislo, Appl. Catal. A: Gen. 125 (1995) 129. [15] R. Grabowski, B. Grzybowska, K. Wcislo, Polish J. Chem. 68 (1994) 1803. [16] J. Słoczy´nski, A. Kozłowska, unpublished data. [17] N.R. Draper, H. Smith, Applied Regression Analysis, Wiley, New York, 1966.