saheb del far 2012

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

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Research and Design

journal homepage: www.elsevier .com/ locate /cherd

Kinetic study of propane dehydrogenation and side

reactions over Pt–Sn/Al2O3 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/Al2O3 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 devel-

oped for the main and side reactions were verified by integral and a combination of integral–differential analysis of

reactor data, respectively, andthe kinetic parameters were obtained. Thedeactivation 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 vari-

ety 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):

C3H8 ⇔ C3H6 + H2, H298◦= +129 kJ/mol (1)

The reaction is highly endothermic and equilibrium-

limited; therefore, higher temperatures and lower pressures

are necessary to achieve acceptable conversions. Unfortu-

nately, 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

∗ Corresponding author. Tel.: +98 21 44580100; fax: +98 21 44580505.E-mail addresses: [email protected], [email protected] (M.T. Ravanchi).Received15 April2011;Receivedin revisedform20 October 2011;Accepted4 November 2011

for paraffin dehydrogenation. Platinum exhibits high catalytic

activity in dehydrogenation of paraffins. To achieve high plat-

inum 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)

C3H8 ⇔ C2H4 + 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)

C3H8 +H2 ⇔ C2H6 + CH4, H298◦= −63.4 kJ/mol (3)

In commercial catalysts, Sn is used as promoter to sup-

press hydrogenolysis reaction through reduction of surface

Pt ensemble size by dividing Pt surface to smaller ensembles

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

http://www.sciencedirect.com/science/journal/02638762http://www.elsevier.com/locate/cherdmailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.cherd.2011.11.004http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.cherd.2011.11.004mailto:[email protected]:[email protected]://www.elsevier.com/locate/cherdhttp://www.sciencedirect.com/science/journal/02638762

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chemical engineering researchand design 9 0 ( 2 0 1 2 ) 1090–1097 1091

Nomenclature

a catalyst activity

C concentration (mol/m3)

F feed rate (mol/h)

ki forward rate constant of reaction i

kdi rate constant for catalyst deactivation in reac-tion i (h−1)

Keq concentration equilibrium constant (mol/m3)

ri

rate of reaction i per mass of catalyst

(mol/(kg h))

W weight of catalyst in the reactor (kg)

Xi conversion of key reactant A in reaction i

Xei equilibrium conversion of key reactant A in

reaction i

t 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 volumet-

ric feed flow rate) ((kgh)/m3)

Subscripts

0 reactor inlet

A key reactant, propane

B key product, propylene

H hydrogen

i reaction numberout reactor outlet

(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 reactionsstill occur to a rather apprecia-

ble 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, reac-

tions (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 dehydro-

genation 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 imple-

mentation of paraffin dehydrogenation is rapid catalyst

deactivation due to coke formation (Moulijn et al., 2001). Dur-

ing thecourse 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

studied elsewhere (Moghimpour Bijani and Sahebdelfar, 2008).

Qing et al.(2011) studied the kinetics of propane dehydrogena-

tion, cracking and coke formation over Pt–Sn/Al2O3 catalyst,

assuming same activity for all sites. The distinction of active

sites as differenttypes hasalso been proposed in theliterature

(Kumbilieva et al., 2006).

Compared to the studies on the mechanism of propane

dehydrogenation including coke formation and the efforts toimprove 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 kinet-

ics 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/Al2O3 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 sup-

plied by Roham Gas Co. with purity 99.5wt.%, 99.99 wt.% and

99.99wt.%, respectively. Commercial Pt–Sn/-Al2O3 catalyst

(Pt= 0.58wt.%, 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 sup-

plied by Procatalyse company. Quartz powder with grain size0.1 mm was used as catalyst diluent.

2.2. 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 (SS-

316). A tubular fixed-bedquartz reactor with inner diameter of

15mm was used, the temperature of which was controlled by

a furnace. Space above and below the catalyst bed (1.5g) was

packed with quartz powder (3g) 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 diam-

eter) 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 N ml/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 1h 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 productswere analyzed

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1092 chemical engineering researchand design 9 0 ( 2 0 1 2 ) 1090–1097

Fig. 1 – Schematic diagram of the experimental setup.

using online gas chromatography Agilent 6890N RGA, which

was equipped with a capillary column, HP-Plot Al2O3 /Na2SO4,

50m, 530m, 15.0m 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 iwas calculated as:

Conversion by reactioni

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

mole of propane in

(4)

The test run times were comparable to one catalyst cycle

(5–7 days)in theOleflex process when thecatalyst being sent to

continuous catalyst regeneration (CCR) unit for regeneration.

3. Kinetic and reactor model

3.1. Kinetic expressions

Mostprevious studies have shown that dehydrogenation reac-

tion 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 paraf-

fin concentration, hydrogen-inhibition effect, and chemical

equilibrium limitation, the following expression is assumed

to represent kinetics of the reaction:

−r1 = k1CA − k−1CBCH2 = k1

CA −

CBCH2Keq

(5)

where r

1

is the rate of conversion of propane to propy-

lene (reaction (1)) per catalyst weight, k1 and k−1 are the

rate constants of forward and backward reactions, respec-

tively, Keq is the equilibrium constant at reaction temperature,

C is the concentration, and, A and B, respectively, rep-

resenting the key components, propane and propylene.

Larsson et al. (1996) f ound that among several kinetic mod-

els tested for dehydrogenation of propane on Pt–Sn/Al2O3catalysts, 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 dehydrogena-

tion practice.To account for catalyst deactivation, the reaction rate can

be written in terms of site activity as:

−r1 = k1a1

CA −

CBCH2Keq

(6)

in which the activity of dehydrogenation sites, a1, is defined

as (Scott Fogler, 1999):

a1(t) =−r1(t)

−r1(t = 0) (7)

Considering volume change of reaction, following neces-sary algebraic manipulations, one arrives at the following

expression for reaction rate in terms of propane conversion

(Moghimpour Bijani and Sahebdelfar, 2008):

−r1 =k1a1CA0(Xe1 − X1)(˛+ ˇX1)

(1 + εAX1)2

(8)

in which

˛ =Xe1 + (H + B)+ HB(1 − εA + εAXe1)

(H + Xe1)(B + Xe1) (9)

ˇ =(1 + ε

AX

e1−X

e1)+ ε

AX

e1(

H+

B)+ ε

A

H

B(H +Xe1)(B + Xe1) (10)

where H, B and CA0 are hydrogen/paraffin, olefin/paraffin

molar ratios and propane concentration in the feed, respec-

tively, 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 con-

centrations 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:

−r2 = k2a2CA0(1 −X1)

(1 + εAX1) (11)

−r3 = k3a3C2A0

(1 −X1)(H + X1)

(1 + εAX1)2

(12)

The deactivation rates could be considered as first-order

and independent. Consequently, for reaction i:

−dai

dt = kdiai (13)

where kdi is the respective rate constant of deactivation. Inte-

grating this equation yields a correlation for ai as a function

of time, t:

ln ai = −kdit (14)

3.2. Reactor model

The plug-flow reactor performance equation for reactions in

parallel is:

dW

FA0=

dXi

−ri (15)

As the propane and hydrogen concentration profiles are

largely determined by the main reaction (Eq. (1)), itsextent 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):

ln

ˇ−1

(ˇ − εA˛)

2

ˇ(˛ + ˇXe1) ln

˛ + ˇX1,out˛

−ˇ(1 + εAXe1)

2

(˛ + ˇXe1) ln

Xe1 − X1,out

Xe1

− ε2AX1,out

= −kd1t + ln(k1 ) (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 out-

let value of the parameter. Plots of Eq. (16) should result in

straight lines the slope of which giving kd1 and the intercept

giving k1.

0

10

20

30

40

50

60

70

0 20 40 60 80 100 120

Time-on-stream, h

C o n v e r s

i o n ,

%

Fig. 2 – Overall conversion of propane ( ) and conversion to

propylene ( ), ethylene ( ) and ethane ( ) ( T =620 ◦C,

H2 /HC=0.6mol/mol and WHSV=2.2h−1 ).

The rate of reactions (2) and (3) depends on reaction (1) asimplied by Eqs. (11) and (12). Dividing Eq. (15) f or reactions (2)

and (3) to that for reaction (1), and using Eq. (14) f or deactiva-

tion terms, one obtains respectively;

(Xe1 −X1)(˛ + ˇX1)

(1 − X1)(1 + εAX1)

dX2dX1

=k2k1

exp((kd1 − kd2)t) (17)

(Xe1 −X1)(˛ + ˇX1)

(1 −X1)(H +X1)

dX3dX1

=CA0k3

k1exp((kd1 − kd2)t) (18)

Eqs. (17) and (18) hold for any point along the reactor.

Rearranging, integrating with respect to Xi and then dif-

ferentiating with respect to t, the following correlations are

obtained for cracking and hydrogenolysis reactions, respec-tively:

ln

((1/X2,out)(dX2,out/dt)) − (kd1 − kd2)

(1/X2,out)(dX1,out/dt)(((1− X1,out)(1 + εAX1,out))/((Xe1 − X1,out)(˛ + ˇX1,out)))

= (kd1 − kd2)t + ln

k2k1

(19)

ln

((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)))

= (kd1 − kd3)t + ln

k3CA0

k1

(20)

Interested reader is referred to Appendix f or detailed mathe-

matical derivations.

The derivative terms could be obtained numerically from

time-on-stream conversion data for different reactions. Sim-

ilarly, plots of Eqs. (19) and (20) should result in straight lineswith the slope giving the difference of deactivation rate con-

stants 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.

4. Results and discussion

4.1. Performance test results

Fig. 2 shows the overall conversion and conversion of indi-

vidual reactions versus time-on-stream. The first data points

showing the “initial activity”, characterized by large devi-

ations, are never actually observed due to experimental

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y = 0.063x - 0.2411

R² = 0.9303

y = 0.0439x + 2.4186

R² = 0.9516

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 10 20 30 40

Conversion to propylene, %

C o n v e r s

i o n

t o b y - p r o

d u c

t s ,

%

Fig. 3 – Conversion of propane to ethylene ( ) and ethane

( ) versus conversion to propylene at different

time-on-streams ( T =620 ◦C, H2 /HC=0.6mol/mol and

WHSV=2.2h−1 ).

limitations. After a sharp initial decline in side reactionsaccompanied 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 showsthat 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, espe-

cially in early time-on-streams.

The fact that extrapolation of the line for hydrogenolysis in

Fig. 3 passes close theorigin could be attributed to thefactthat

both dehydrogenation and hydrogenolysis reactions occur on

platinum sites. This is notthe case forcracking reactionwhich

occurs on different sites and also thermally. From Fig. 3 one

concludes thatcracking reaction could proceed even when the

catalystis fully deactivatedand thatmore thanhalf 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.

4.2. Modeling results

Fig. 4 showsa plot of Eq. (16) f or a long-term run using exper-

imental 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 dehydro-

genation reaction, respectively (Table 1).

In this way Eq. (16) provides a method to obtain time-

zero 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

Table 1 – Calculated values of the rate constants( T =620 ◦C).

Reaction no. ki kdi

1 4.7 m3 /(kg h) 0.016 h−1

2 0.40 m3 /(kg h) 0.0027h−1

3 0.023 m6 /(mol kg h) 0.011 h−1

y = -0.0159x - 0.2855

R2 = 0.9543

-2.5

-2

-1.5

-1

-0.5

0

120100806040200

Time-on-stream, h

L H S o

f E q .

1 6

Fig. 4 – Typical plot of Eq. (16) using experimental data

( T =620 ◦C, H2 /HC=0.6mol/mol, WHSV=2.2h−1 ).

more accurate experimental data because of the appear-

ance of time-derivative terms in these equations. To avoid

the fluctuations encountered in numerical differentiation, ithas been proposed to fit the data with an appropriate func-

tion and then differentiate the resulted interpolating function

(Levenspiel, 1999). The trends of time-data propose exponen-

tial 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 conver-

gence 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 thoseof 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 selectiv-

ity 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 deactiva-

tion 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

y = 0.01318x - 2.45327

R² = 0.97686

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

120100806040200

Time-on-stream, h

L H S o

f E q .

1 9

Fig. 5 – Plot of Eq. (19) using experimental data with

kd1 − kd2 =0.0132 ( T =620◦C, H2 /HC=0.6mol/mol and

WHSV=2.2h−1 ).

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y = 0.0049x - 3.3575

R² = 0.8367

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

-2

120100806040200

Time-on-stream, h

L H S o

f E

q .

2 0

Fig. 6 – Plot of Eq. (20) using experimental data with

kd1 − kd3 =0.0049 ( T =620◦C, H2 /HC=0.6mol/mol and

WHSV=2.2h−1 ).

better fits for apparentdeactivationof 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 partiallydeactivated catalystwill 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, gener-

ally, 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 dehydrogena-

tion reaction in propane consumption) is not applied to have

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 reac-

tions, 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 calculatedfrom these data and reported in Table 1 have a reasonable

accuracy.

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 anddifferential analysesthe accuracy of which is lim-

ited 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 differ-

entiate 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 decreaseof conversions within the specifiedstep-size time

interval becomes smaller than that of experimental accuracy

and/or system disturbances. Therefore, using direct numeri-

cal differentiation formulas, these errors largely maskthe 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. Conse-

quently, 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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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 reac-

tant (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

catalystdeactivation(Qing et al., 2011). The independent deac-

tivation 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 reac-

tions due to rather low reaction temperature compared to the

melting point of Pt do not favor deactivation by sintering dur-

ing 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 ethy-

lene to ethane ratio in the product is much higher thanthe equilibrium ratio implying that there is thermodynamic

driving force for hydrogenation of ethylene to ethane. How-

ever, 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 con-

tribute an importantrole in selectivity to ethaneand ethylene.

Consequently, ethane and ethylene production rates can be

adequately considered as measuresfor the rateof hydrogenol-

ysis 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 selectiv-ity 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

andhydrogen within thereactor. Therefore, the kinetic param-

eters obtained should be accurate to at least one significant

figure.

Higher selectivities are not uncommon both on lab or com-

mercial 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/Al2O3 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 magni-

tude larger than those of cracking and hydrogenolysis side

reactions. On the other hand, the rate constant of the deac-

tivation 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)

(1 − X1)(1 + εAX1)

dX2dX1

= k exp( At) (A1)

where

k =k2k1

(A2)

A = kd1 − kd2 (A3)

Rearranging Eq. (A1), one obtains:

dX2 = k exp( At) (1 − X1)(1 + εAX1)

(Xe1 −X1)(˛ + ˇX1)dX1 (A4)

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

X2,out = k exp( At)

X1,out0

(1 − X1)(1 + εAX1)

(Xe1 −X1)(˛ + ˇX1)dX1 (A5)

Differentiating this equation with respect to t, gives:

dX2,outdt

= kA exp( At)

X1,out0

(1 −X1)(1 + εAX1)

(Xe1 − X1)(˛ + ˇX1)dX1

+k exp( At) ∂

∂t

X1,out0

(1 − X1)(1 + εAX1)

(Xe1 −X1)(˛ + ˇX1)dX1

(A6)

inwhich,thefirsttermontherighthandsideis AX2,out

(accord-

ing 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

F(x, t) =

b(t)a(t)

f (x, t)dx (A7)

the time derivative is:

dF

dt =

ba

∂f

∂t dx + f (b, t)

db

dt − f (a, t)

da

dt (A8)

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

k exp( At)

X1,out0

∂

∂t

( 1−X1)(1 + εAX1)

(Xe1 −X1)(˛ + ˇX1)

×dX1 +(1 − X1,out)(1 + εAX1,out)

(Xe1 −X1,out)(˛+ ˇX1,out)

dX1,outdt

(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:

dX2,outdt

= AX2,out + k exp( At) ( 1−X1,out)(1 + εAX1,out)

(Xe1 − X1,out)(˛ + ˇX1,out)

dX1,outdt

(A10)

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By rearranging Eq. (A10), one obtains:

ln

((1/X2,out)(dX2,out/dt))− A

(1/X2,out)(dX1,out/dt)(((1− X1,out)(1 + εAX1,out))/((Xe1 −X1,out)(˛+ ˇX1,out)))

= At + ln(k) (A11)

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

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