Al2O3 catalyst

chemical engineering research and design 9 0 ( 2 0 1 2 ) 1090–1097

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Kinetic study of propane dehydrogenation and side reactions over Pt–Sn/Al2 O3 catalyst Saeed Sahebdelfar, Maryam Takht Ravanchi ∗ , Farnaz Tahriri Zangeneh, Shokoufeh Mehrazma, Soheila Rajabi Catalyst Research Group, Petrochemical Research and Technology Company, National Petrochemical Company, No. 27, Sarv Alley, Shirazi-south, Mollasadra, P.O. Box 14358-84711, Tehran, Iran

a b s t r a c t The kinetics of reactions involved in dehydrogenation of propane to propylene over Pt–Sn/Al2 O3 catalyst was studied. The simultaneous deactivation of individual dehydrogenation, hydrogenolysis and cracking sites was also studied. A model was developed to obtain the transient conversion of propane, product selectivity and catalytic site activity. The dehydrogenation reaction was considered as the main reaction governing propane and hydrogen concentrations along the reactor. Catalytic test runs were performed in a fixed-bed quartz reactor. The kinetic expressions developed for the main and side reactions were verified by integral and a combination of integral–differential analysis of reactor data, respectively, and the kinetic parameters were obtained. The deactivation of the active sites for the three reactions was found to follow a first-order independent decay law. The rate constants of deactivation were found to decrease in the order of dehydrogenation, hydrogenolysis and cracking. Noncatalytic thermal cracking was found to be comparable to the catalytic route resulting in a very low apparent deactivation rate constant for cracking reaction. © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Propane dehydrogenation; Pt–Sn catalysts; Cracking; Hydrogenolysis; Catalyst deactivation; Kinetics

1.

Introduction

Propylene is an important feedstock for producing a variety of petrochemicals such as polypropylene, acrolein and acrylic acid. Due to ever-increasing demand and insufficient supply by crackers, alternative production methods such as propane dehydrogenation (PDH) has received attention (Heinritz-Adrian et al., 2008): C3 H8 ⇔ C3 H6 + H2 ,

H298 ◦ = +129 kJ/mol

(1)

The reaction is highly endothermic and equilibriumlimited; therefore, higher temperatures and lower pressures are necessary to achieve acceptable conversions. Unfortunately, these conditions favor side reactions and accelerate catalyst deactivation as well. In commercial practice both chromia (Arora, 2004; Miracca and Piovesan, 1999; Weckhuysen and Schoonheydt, 1999) and platinum (Bricker et al., 1990; Heinritz-Adrin et al., 2003; Pujado and Vora, 1990) based catalysts have been employed

∗

for paraffin dehydrogenation. Platinum exhibits high catalytic activity in dehydrogenation of paraffins. To achieve high platinum dispersions, high-surface area supports are commonly used. Acidic sites on the support promote cracking (reaction (2)) and coke formation reactions. These sites are effectively neutralized by application of alkaline promoters (Bai et al., 2009; Bhasin et al., 2001; Padmavathi et al., 2005; Sanfilippo and Miracca, 2006; Yu et al., 2006; Zhang et al., 2006a) C3 H8 ⇔ C2 H4 + CH4 ,

H298 ◦ = +79.4 kJ/mol

(2)

Dehydrogenation virtually occurs on all platinum sites, while hydrogenolysis (reaction (3)) occurs on low coordination sites (steps and kinks) (Resasco, 2003) C3 H8 + H2 ⇔ C2 H6 + CH4 ,

H298 ◦ = −63.4 kJ/mol

(3)

In commercial catalysts, Sn is used as promoter to suppress hydrogenolysis reaction through reduction of surface Pt ensemble size by dividing Pt surface to smaller ensembles

Corresponding author. Tel.: +98 21 44580100; fax: +98 21 44580505. E-mail addresses: [email protected], [email protected] (M.T. Ravanchi). Received 15 April 2011; Received in revised form 20 October 2011; Accepted 4 November 2011 0263-8762/$ – see front matter © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2011.11.004

chemical engineering research and design 9 0 ( 2 0 1 2 ) 1090–1097

Nomenclature a C F ki kdi Keq ri W Xi Xei t

catalyst activity concentration (mol/m3 ) feed rate (mol/h) forward rate constant of reaction i rate constant for catalyst deactivation in reaction i (h−1 ) concentration equilibrium constant (mol/m3 ) rate of reaction i per mass of catalyst (mol/(kg h)) weight of catalyst in the reactor (kg) conversion of key reactant A in reaction i equilibrium conversion of key reactant A in reaction i time-on-stream (h)

Greek symbols ˛ parameter defined by Eq. (9) ˇ parameter defined by Eq. (10) ε expansion factor, fraction change in volume resulting from change in total number of moles ratio of number of moles of species initially  entering to that of paraffin  a capacity factor (catalyst weight per volumetric feed flow rate) ((kg h)/m3 ) Subscripts 0 reactor inlet A key reactant, propane B key product, propylene hydrogen H i reaction number reactor outlet out

studied elsewhere (Moghimpour Bijani and Sahebdelfar, 2008). Qing et al. (2011) studied the kinetics of propane dehydrogenation, cracking and coke formation over Pt–Sn/Al2 O3 catalyst, assuming same activity for all sites. The distinction of active sites as different types has also been proposed in the literature (Kumbilieva et al., 2006). Compared to the studies on the mechanism of propane dehydrogenation including coke formation and the efforts to improve the activity and stability of the catalyst, relatively few efforts have been made to establish a complete and reliable kinetic model of engineering significance, including kinetics of dehydrogenation, hydrogenolysis and cracking as well as deactivation of the corresponding sites. These models are essential for optimization of the reactor performance through increasing propylene yield and catalyst lifetime. In the present work, reaction kinetics and deactivation of different catalytic sites of a commercial Pt–Sn/Al2 O3 catalyst in dehydrogenation of propane to propylene are studied. A model is developed to obtain the kinetics of the reactions involved and the deactivation of the corresponding sites and to obtain the related kinetic parameters.

2.

Experimental

2.1.

Materials

The propane, hydrogen and nitrogen feed gases were supplied by Roham Gas Co. with purity 99.5 wt.%, 99.99 wt.% and 99.99 wt.%, respectively. Commercial Pt–Sn/␥-Al2 O3 catalyst (Pt = 0.58 wt.%, Sn = 0.8 wt.% and surface area = 187 m2 /g) with trade name DP-803, the characteristics of which is reported elsewhere (Sahebdelfar and Tahriri Zangeneh, 2010), was supplied by Procatalyse company. Quartz powder with grain size 0.1 mm was used as catalyst diluent.

2.2. (Barbier et al., 1980; Carvalho et al., 2001; Larese et al., 2000; Takehira et al., 2004; Waku et al., 2003; Yu et al., 2007; Zhang et al., 2006c, 2007). Nevertheless, side reactions still occur to a rather appreciable extent on the catalysts, so that the selectivity of the UOP Oleflex process in dehydrogenation of propane and isobutane is 90% and 92%, respectively (Bhasin et al., 2001). Both cracking and hydrogenolysis reactions may occur by single or multiple C–C bond rupture according to the catalyst formulation and operating conditions. However, a recent study (Sahebdelfar and Tahriri Zangeneh, 2010) has shown that over the catalyst and under reaction conditions employed in this work, the former path is predominant. Consequently, reactions (2) and (3) can represent the side reactions. It has been shown that side reactions result in significant influence on the performance of commercial-sized dehydrogenation reactors (Sahebdelfar et al., 2011). Unfortunately, it is difficult to study individual reactions independent of other reactions. Hydrogenolysis occurs virtually on the same sites as dehydrogenation. Cracking can occur separately, but under conditions different from that of dehydrogenation reaction. Another important difficulty in commercial scale implementation of paraffin dehydrogenation is rapid catalyst deactivation due to coke formation (Moulijn et al., 2001). During the course of reaction, different sites deactivate at different rates resulting in a change in activity and selectivity with time-on-stream. The overall deactivation kinetics has been

1091

Set-up

The experimental setup, a schematic diagram of which is depicted in Fig. 1, was a fully automated system. All lines and fittings of the setup were made of stainless steel 316 (SS316). A tubular fixed-bed quartz reactor with inner diameter of 15 mm was used, the temperature of which was controlled by a furnace. Space above and below the catalyst bed (1.5 g) was packed with quartz powder (3 g) to ensure proper distribution of fluid flow. A thermocouple was inserted into the center of the catalyst bed to indicate bed temperature. The channeling and heat transfer effects in the reactor could be neglected as the radial aspect ratio (bed diameter to catalyst particle diameter) was >15. The axial aspect ratio i.e. the ratio of catalyst bed length to catalyst particle diameter was >30 and hence the dispersion effects can be also neglected (Anderson and Pratt, 1985). In all runs, except for the initial data points, the carbon and hydrogen balance was within ±1.5%.

2.3.

Experimental procedure

The reactor was first heated under hydrogen flow of 18.3 Nml/min at about 5 ◦ C/min to 530 ◦ C to desorb the adsorbed moisture, if any, and then the catalyst was reduced in hydrogen flow at 530 ◦ C for 1 h in the reactor. The kinetic experiments were carried out at 620 ◦ C with molar ratio of hydrogen to hydrocarbon equal to 0.6 and weight hourly space velocity (WHSV) 2.2 h−1 . The gas products were analyzed

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Fig. 1 – Schematic diagram of the experimental setup. using online gas chromatography Agilent 6890N RGA, which was equipped with a capillary column, HP-Plot Al2 O3 /Na2 SO4 , 50 m, 530 ␮m, 15.0 ␮m and FID detector. The concentration of propane, propylene and lower hydrocarbons was measured in the product stream to calculate conversion, selectivity and yield of the reactions. The product selectivities were calculated based on moles of carbon converted. The conversion of propane by reaction i was calculated as: Conversion by reaction i =

moles of propane in − moles of propane converted by reaction i mole of propane in

Larsson et al. (1996) found that among several kinetic models tested for dehydrogenation of propane on Pt–Sn/Al2 O3 catalysts, simple power-law model of this type resulted in the best fit. In fact most mechanistic kinetic models, e.g. Longmuir–Hinshelwood–Hougen–Watson (LHHW) based model of Padmavathi et al. (2005) with surface reaction as rate-limiting step, approach to power law expressions at the high-temperature, low-partial pressure (low surface coverage (Scott Fogler, 1999)) prevalent in lower-paraffin dehydrogenation practice. To account for catalyst deactivation, the reaction rate can be written in terms of site activity as:

(4)

 −r 1 = k1 a1

The test run times were comparable to one catalyst cycle (5–7 days) in the Oleflex process when the catalyst being sent to continuous catalyst regeneration (CCR) unit for regeneration.

3.

Kinetic and reactor model

3.1.

Kinetic expressions

 −r 1 = k1 CA − k−1 CB CH2 = k1

CB CH2 CA − Keq

 (5)

where r1 is the rate of conversion of propane to propylene (reaction (1)) per catalyst weight, k1 and k−1 are the rate constants of forward and backward reactions, respectively, Keq is the equilibrium constant at reaction temperature, C is the concentration, and, A and B, respectively, representing the key components, propane and propylene.

CB CH2 Keq

 (6)

in which the activity of dehydrogenation sites, a1 , is defined as (Scott Fogler, 1999): a1 (t) =

Most previous studies have shown that dehydrogenation reaction is first-order in paraffin concentration and negative half to zeroth-order in hydrogen concentration (Resasco, 2003). Therefore to incorporate the first-order dependence on paraffin concentration, hydrogen-inhibition effect, and chemical equilibrium limitation, the following expression is assumed to represent kinetics of the reaction:

CA −

−r 1 (t) −r 1 (t = 0)

(7)

Considering volume change of reaction, following necessary algebraic manipulations, one arrives at the following expression for reaction rate in terms of propane conversion (Moghimpour Bijani and Sahebdelfar, 2008): −r 1 =

k1 a1 CA0 (Xe1 − X1 )(˛ + ˇX1 ) (1 + εA X1 )

2

(8)

in which ˛=

Xe1 + (H + B ) + H B (1 − εA + εA Xe1 ) (H + Xe1 )(B + Xe1 )

ˇ=

(1 + εA Xe1 − Xe1 ) + εA Xe1 (H + B ) + εA H B (H + Xe1 )(B + Xe1 )

(9)

(10)

where H , B and CA0 are hydrogen/paraffin, olefin/paraffin molar ratios and propane concentration in the feed, respectively, X1 is propane conversion to propylene, Xe1 is the

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equilibrium conversion under reaction conditions and εA is the volume expansion factor. Similarly, assuming reaction (1) as the main propane consuming reaction governing propane and hydrogen concentrations along the reactor and noting that side reactions are far from equilibrium under dehydrogenation conditions (Waku et al., 2004), one may use the following power-law rate expressions for cracking (Lobera et al., 2008; Qing et al., 2011) and hydrogenolysis (Chin et al., 2011) reactions, respectively: −r 2 = k2 a2 CA0

−r 3 = k3 a3 C2A0

(1 − X1 ) (1 + εA X1 )

(1 + εA X1 )

2

where kdi is the respective rate constant of deactivation. Integrating this equation yields a correlation for ai as a function of time, t: ln ai = −kdi t

(14)

Reactor model

The plug-flow reactor performance equation for reactions in parallel is: dW dXi = FA0 −r i

(15)

 ln

ln ˇ

 −1

2

(ˇ − εA ˛) ln ˇ(˛ + ˇXe1 ) 2

ˇ(1 + εA Xe1 ) − ln (˛ + ˇXe1 )

20

40

 ˛ + ˇX

1,out



˛

Xe1

 − ε2A X1,out

60

80

100

120

Conversion, %

Time-on-stream, h

Fig. 2 – Overall conversion of propane () and conversion to propylene (), ethylene (䊉) and ethane () (T = 620 ◦ C, H2 /HC = 0.6 mol/mol and WHSV = 2.2 h−1 ).

The rate of reactions (2) and (3) depends on reaction (1) as implied by Eqs. (11) and (12). Dividing Eq. (15) for reactions (2) and (3) to that for reaction (1), and using Eq. (14) for deactivation terms, one obtains respectively; (Xe1 − X1 )(˛ + ˇX1 ) dX2 k2 = exp((kd1 − kd2 )t) k1 (1 − X1 )(1 + εA X1 ) dX1

(17)

(Xe1 − X1 )(˛ + ˇX1 ) dX3 CA0 k3 = exp((kd1 − kd2 )t) k1 (1 − X1 )(H + X1 ) dX1

(18)

Eqs. (17) and (18) hold for any point along the reactor. Rearranging, integrating with respect to Xi and then differentiating with respect to t, the following correlations are obtained for cracking and hydrogenolysis reactions, respectively:

((1/X3,out )(dX3,out /dt)) − (kd1 − kd3 ) (1/X3,out )(dX1,out /dt)(((1−X1,out )(H + X1,out ))/((Xe1 −X1,out )(˛ + ˇX1,out )))

X − X  e1 1,out

= −kd1 t + ln(k1   )

20

((1/X2,out )(dX2,out /dt)) − (kd1 − kd2 ) (1/X2,out )(dX1,out /dt)(((1 − X1,out )(1 + εA X1,out ))/((Xe1 − X1,out )(˛ + ˇX1,out )))

As the propane and hydrogen concentration profiles are largely determined by the main reaction (Eq. (1)), its extent can be obtained independent of other reactions. Consequently, the integral analysis of the conversion data for reaction (1) along the reactor results in (Moghimpour Bijani and Sahebdelfar, 2008):



30

10

(12)

(13)



40

0

(1 − X1 )(H + X1 )

ln

50

0

dai = kdi ai dt

3.2.

60

(11)

The deactivation rates could be considered as first-order and independent. Consequently, for reaction i: −

70

 = (kd1 − kd2 )t + ln

 = (kd1 − kd3 )t + ln

k  2

k1

k C  3 A0 k1

(19)

(20)

Interested reader is referred to Appendix for detailed mathematical derivations. The derivative terms could be obtained numerically from time-on-stream conversion data for different reactions. Similarly, plots of Eqs. (19) and (20) should result in straight lines with the slope giving the difference of deactivation rate constants and the intercept giving the ratio of rate constants. Since the parameters kd1 − kd2 and kd1 − kd3 appear on both sides of Eqs. (19) and (20), respectively, an iterative procedure is necessary for their determination. Because of low deactivation rate compared to chemical conversion rates, the pseudo-steady condition was assumed to be valid in the above derivations.

(16)

where W is the catalyst weight, FA0 is the molar flow rate of the feed to reactor and   , the ratio of catalyst weight per volumetric feed flow rate, is a capacity factor known as the weight-time. The subscript out refers to reactor outlet value of the parameter. Plots of Eq. (16) should result in straight lines the slope of which giving kd1 and the intercept giving k1 .

4.

Results and discussion

4.1.

Performance test results

Fig. 2 shows the overall conversion and conversion of individual reactions versus time-on-stream. The first data points showing the “initial activity”, characterized by large deviations, are never actually observed due to experimental

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chemical engineering research and design 9 0 ( 2 0 1 2 ) 1090–1097

Time-on-stream, h

y = 0.0439x + 2.4186 R² = 0.9516

4 3.5

0

3

2 1.5

y = 0.063x - 0.2411 R² = 0.9303

1 0.5

60

80

100

120

y = -0.0159x - 0.2855 R2 = 0.9543

-1 -1.5 -2

0

10

20

30

40

-2.5

Conversion to propylene, %

limitations. After a sharp initial decline in side reactions accompanied by an increase in dehydrogenation selectivity, a gradual decline of the conversions is observed which is due to deactivation of the active sites involved. The initial period is due to the presence of too many active side-reaction sites which deactivate quickly leaving moderate sites for longer times-on-stream. Fig. 3 shows that plot of conversions to ethylene and ethane versus that to propylene results in reasonably straight lines. This, along with Fig. 2, shows that the contribution of side reactions in overall consumption of propane is small, especially in early time-on-streams. The fact that extrapolation of the line for hydrogenolysis in Fig. 3 passes close the origin could be attributed to the fact that both dehydrogenation and hydrogenolysis reactions occur on platinum sites. This is not the case for cracking reaction which occurs on different sites and also thermally. From Fig. 3 one concludes that cracking reaction could proceed even when the catalyst is fully deactivated and that more than half of cracking reaction originates from noncatalytic thermal cracking route. Cracking reaction occurs mainly on acidic sites of the carrier (Zhang et al., 2006b) and also proceeds thermally.

Modeling results

Fig. 4 shows a plot of Eq. (16) for a long-term run using experimental data with LHS showing the left-hand-side of that equation. A favorable fit is observed. The slope and intercept give the deactivation and reaction rate constants for dehydrogenation reaction, respectively (Table 1). In this way Eq. (16) provides a method to obtain timezero conversion to propylene i.e. an estimate of conversion in the absence of deactivation effects which is useful for kinetic study of the main reaction. Unlike the integral method of analysis used in Fig. 4, the plots of Eqs. (19) and (20) require a higher number and

ki 3

4.7 m /(kg h) 0.40 m3 /(kg h) 0.023 m6 /(mol kg h)

more accurate experimental data because of the appearance of time-derivative terms in these equations. To avoid the fluctuations encountered in numerical differentiation, it has been proposed to fit the data with an appropriate function and then differentiate the resulted interpolating function (Levenspiel, 1999). The trends of time-data propose exponential functions as good candidates (Fig. 2) which in fact result in fair fits. Figs. 5 and 6, respectively, show plots of Eqs. (19) and (20) obtained by this approach after achieving convergence of deactivation rate constant difference terms by the iterative procedure explained above, with LHS showing the left-hand-side of these equations. Favorable fits are observed. The resulted rate constants for side reactions are also given in Table 1. Table 1 reveals that the rate constants of side reactions are more than one order of magnitude smaller than those of the main reaction as required by a selective catalyst. Also, the dehydrogenation sites deactivate more rapidly than those of side reactions. This explains the observed drop of selectivity to propylene with time-on-stream. The seemingly smaller deactivation rate constant in the case of cracking reaction can be attributed to the simultaneous occurrence of non-catalytic thermal cracking. The numerical values of rate and deactivation constants are also consistent with the experimental data trends observed in Figs. 2 and 3. The existence of a noncatalytic component in cracking activity implies that higher orders of deactivation could give Time-on-stream, h 0

20

40

60

80

100

0 -0.5 -1 -1.5 -2 -2.5

y = 0.01318x - 2.45327 R² = 0.97686

-3

Table 1 – Calculated values of the rate constants (T = 620 ◦ C). Reaction no.

Fig. 4 – Typical plot of Eq. (16) using experimental data (T = 620 ◦ C, H2 /HC = 0.6 mol/mol, WHSV = 2.2 h−1 ).

LHS of Eq. 19

Fig. 3 – Conversion of propane to ethylene () and ethane () versus conversion to propylene at different time-on-streams (T = 620 ◦ C, H2 /HC = 0.6 mol/mol and WHSV = 2.2 h−1 ).

1 2 3

40

-0.5

2.5

0

4.2.

20

0

LHS of Eq. 16

Conversion to by-products, %

4.5

-3.5

kdi −1

0.016 h 0.0027 h−1 0.011 h−1

-4

Fig. 5 – Plot of Eq. (19) using experimental data with kd1 − kd2 = 0.0132 (T = 620 ◦ C, H2 /HC = 0.6 mol/mol and WHSV = 2.2 h−1 ).

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chemical engineering research and design 9 0 ( 2 0 1 2 ) 1090–1097

Time-on-stream, h -2

0

20

40

60

80

100

120

-2.5 LHS of Eq. 20

-3 -3.5 -4

y = 0.0049x - 3.3575 R² = 0.8367

-4.5

1095

a better insight of the capability of the modeling. The best results are observed for the total conversion and conversion to propylene. In case of side reactions, however, the approach of experimental and calculated results occurs at shorter and longer time-on-streams for cracking and hydrogenolysis reactions, respectively. As in Fig. 7a, which is for total conversion of propane to products, there is a good correlation between experimental and model results, the rate constants calculated from these data and reported in Table 1 have a reasonable accuracy.

-5 -5.5 -6

Fig. 6 – Plot of Eq. (20) using experimental data with kd1 − kd3 = 0.0049 (T = 620 ◦ C, H2 /HC = 0.6 mol/mol and WHSV = 2.2 h−1 ).

better fits for apparent deactivation of cracking sites for longer times-on-stream. This could complicate the corresponding formulations. However, too much long times-on-stream are not of practical interest as partially deactivated catalyst will be sent to regeneration unit before complete deactivation could occur. In Fig. 7 parity plots for total conversion of propane (Fig. 7a) and propane conversion to species (Figs. 7b–d) are presented. These plots compare the calculated conversions versus experimental conversions. As it can be seen, generally, the difference between experimental results and model estimation is within 20% which confirms the accuracy of the results. It is noteworthy that in constructing these plots, the main assumption of modeling (i.e. predominance of dehydrogenation reaction in propane consumption) is not applied to have

4.3.

Issues on validity and accuracy

While the method of data analysis of the main reaction is purely integral, that of side reactions is a combination of integral and differential analyses the accuracy of which is limited by the latter (that is, by time derivatives of conversions data). As mentioned above, an approach is to fit experimental conversion data with an appropriate function and then differentiate the resulted fitting function. The use of this approach for evaluation of the derivatives is inevitable in analysis of long-term deactivation data, as after certain time-on-stream the decrease of conversions within the specified step-size time interval becomes smaller than that of experimental accuracy and/or system disturbances. Therefore, using direct numerical differentiation formulas, these errors largely mask the true value of the derivatives. The function should be checked by the eye to give both close fit to data and relevant slopes. The exponential function is the simplest one to satisfy both these requirements fairly. However, no simple function can fit both data points and their derivatives over a long range. Consequently, a small downward curvature is observed in plots of Eqs. (19) and (20) with the exponential functions employed for fitting (see Figs. 5 and 6). Alternatively, direct numerical differentiation of data using up to fourth-order formulas did

Fig. 7 – Correlation between experimental data and model predictions for total propane conversion and propane conversions to species in operating conditions used.

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chemical engineering research and design 9 0 ( 2 0 1 2 ) 1090–1097

not result in satisfactory values when applied to the whole of time-on-stream domain, due to considerable fluctuations in calculated derivatives. The apparent concentration-independent deactivation in decay laws implies that deactivation might be caused both by reactant and products (Levenspiel, 1999). In fact, both the reactant (e.g. through pyrolysis reaction) and products (through oligomerization–aromatization of the olefinic products e.g. of reactions (1) and (2)) can bring about coke formation and catalyst deactivation (Qing et al., 2011). The independent deactivation is also a characteristic of catalyst decay by thermal sintering (Levenspiel, 1999). However, the observed low orders of deactivation and negligible Pt crystal growth during reactions due to rather low reaction temperature compared to the melting point of Pt do not favor deactivation by sintering during reaction. Finally, ethylene/ethane hydrogenation/dehydrogenation could occur as additional side reactions. The rate of these reactions should be very small due to the low concentration of C2 products within the reactor. Furthermore, the ethylene to ethane ratio in the product is much higher than the equilibrium ratio implying that there is thermodynamic driving force for hydrogenation of ethylene to ethane. However, in an earlier work no appreciable decrease in ethylene to ethane ratio observed upon decreasing the space-velocity (Sahebdelfar and Tahriri Zangeneh, 2010). This illustrates that hydrogenation reaction rate is not sufficiently high to contribute an important role in selectivity to ethane and ethylene. Consequently, ethane and ethylene production rates can be adequately considered as measures for the rate of hydrogenolysis and cracking reactions, respectively. The applicability of the simple yet practical approach employed in this work depends on the selectivity to the main product, propylene, becoming more accurate as the selectivity approaches to unity. The propylene selectivities in the data series employed in this work were mostly within the range 80–85%. This range is still sufficiently large such that the main reaction determines the concentrations of propylene and hydrogen within the reactor. Therefore, the kinetic parameters obtained should be accurate to at least one significant figure. Higher selectivities are not uncommon both on lab or commercial scale runs (Barias et al., 1996; Kogan and Herskowitz, 2001). This indicates that the proposed model could be used in most of the cases of practical interest.

5.

Conclusions

The activity and deactivation kinetics of dehydrogenation, hydrogenolysis and cracking sites in dehydrogenation of propane over Pt–Sn/Al2 O3 catalyst were obtained when the reactions occur simultaneously. Power law expressions and first order independent decay laws fitted the kinetic data of the reactions favorably. The rate constant of the main reaction was found to be more than one order of magnitude larger than those of cracking and hydrogenolysis side reactions. On the other hand, the rate constant of the deactivation of dehydrogenation reaction was found to be larger than those side reactions which explain the loss of selectivity to propylene with time-on-stream. The findings of this work could be applicable in modeling of commercial size reactors where side reactions and catalyst deactivation play important roles.

Appendix. Eq. (17) can be written as below: (Xe1 − X1 )(˛ + ˇX1 ) dX2 = k exp(At) (1 − X1 )(1 + εA X1 ) dX1

(A1)

where k=

k2 k1

(A2)

A = kd1 − kd2

(A3)

Rearranging Eq. (A1), one obtains: dX2 = k exp(At)

(1 − X1 )(1 + εA X1 ) dX1 (Xe1 − X1 )(˛ + ˇX1 )

(A4)

Integrating this equation, gives X2,out as a function of X1,out as:



X1,out

X2,out = k exp(At) 0

(1 − X1 )(1 + εA X1 ) dX1 (Xe1 − X1 )(˛ + ˇX1 )

(A5)

Differentiating this equation with respect to t, gives: dX2,out = kA exp(At) dt ∂ + k exp(At) ∂t





X1,out

0

X1,out

0

(1 − X1 )(1 + εA X1 ) dX1 (Xe1 − X1 )(˛ + ˇX1 )

(1 − X1 )(1 + εA X1 ) dX1 (Xe1 − X1 )(˛ + ˇX1 )



(A6)

in which, the first term on the right hand side is AX2,out (according to Eq. (A5)). In the second term, as differentiation is with respect to t and the integral limits are functions of time, the Leibniz’s rule (Bird et al., 2002) must be applied. According to this rule, for function F(x, t), where



b(t)

F(x, t) =

f (x, t)dx

(A7)

a(t)

the time derivative is: dF = dt



b

a

∂f db da dx + f (b, t) − f (a, t) ∂t dt dt

(A8)

Hence, the second term of the right hand side of Eq. (A6) is

 k exp(At) 0

× dX1 +

X1,out

∂ ∂t



(1 − X1 )(1 + εA X1 ) (Xe1 − X1 )(˛ + ˇX1 )

(1 − X1,out )(1 + εA X1,out ) dX1,out (Xe1 − X1,out )(˛ + ˇX1,out ) dt



(A9)

As the catalyst lifetime is much larger than the residence time within the reactor, a pseudo-steady state condition can be assumed within the reactor by which the first term of Eq. (A6) is negligible. Consequently, Eq. (A6) is simplified to the below equation: (1 − X1,out )(1 + εA X1,out ) dX1,out dX2,out = AX2,out + k exp(At) dt (Xe1 − X1,out )(˛ + ˇX1,out ) dt (A10)

chemical engineering research and design 9 0 ( 2 0 1 2 ) 1090–1097

1097

By rearranging Eq. (A10), one obtains:

 ln

((1/X2,out )(dX2,out /dt)) − A (1/X2,out )(dX1,out /dt)(((1 − X1,out )(1 + εA X1,out ))/((Xe1 − X1,out )(˛ + ˇX1,out )))

Similar approach can be used to obtain Eq. (20).

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 = At + ln(k)

(A11)

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