Modeling of adiabatic moving-bed reactor for dehydrogenation of isobutane to isobutene

Applied Catalysis A: General 395 (2011) 107–113

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Modeling of adiabatic moving-bed reactor for dehydrogenation of isobutane to isobutene Saeed Sahebdelfar a,∗ , Parisa Moghimpour Bijani a , Maryam Saeedizad a , Farnaz Tahriri Zangeneh a , Kamran Ganji b a b

Catalyst Research Group, Petrochemical Research and Technology Company, National Petrochemical Company, P.O. Box 1435884711, Tehran, Iran BIPC/Kimia Petrochemical Company, P.O. Box 314, Mahshar, Iran

a r t i c l e

i n f o

Article history: Received 11 October 2010 Received in revised form 20 December 2010 Accepted 17 January 2011 Available online 21 January 2011 Keywords: Isobutane dehydrogenation Pt–Sn catalyst Moving-bed reactor Kinetics Catalyst deactivation

a b s t r a c t The dehydrogenation of isobutane to isobutene in adiabatic radial-flow moving-bed reactors was studied. First order rate expressions were considered for the primary reaction and deactivation kinetics incorporating the reversibility of dehydrogenation reaction. Kinetic data from a fixed-bed lab-scale reactor were used for modeling of the commercial size moving-bed reactor. The model was solved numerically by dividing the reactor into differential isothermal moving-bed reactors. The conversion of isobutane to isobutene was found to be equilibrium limited in commercial-sized reactors. The model predicted the trends of conversion, temperature, and catalyst activity with conversion levels somewhat lower than observed values which was attributed to the side-reactions. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.

1. Introduction Isobutene is used as a feedstock in the production of a variety of chemicals. It has been mainly used in the production of oxygenate gasoline blending stocks such methyl tert-butyl ether (MTBE) and ethyl tert-butyl ether (ETBE) through etherification with methanol and ethanol, respectively. Alkylation with isobutane produces alkylate, which is a valuable gasoline blending stock. Other important products include methacrolein and polyisobutylene. In recent years, objections to the use of MTBE have been raised because of its potential environmental and health impacts through water contamination. However, demand for polyisobutylene and polybutenes in general is continuously growing. Consequently, the need for C4 olefins will probably remain high. Currently C4 olefins are mainly produced from fluidized catalytic cracking (FCC about 50%) and steam cracking (21%) [1]. The conventional processes for production of olefins such as steam crackers or FCC units alone do not satisfy the growing demand to lower olefins. Consequently, efficient catalytic dehy-

drogenation of light alkanes to the corresponding olefins is much sought as a means of converting relatively inert LPG hydrocarbons to reactive chemical feedstocks such as propylene and butenes. i − C4 H10 ⇔ i − C4 H8 + H2

(1)

The reaction is reversible, highly endothermic and accompanied by volume expansion, therefore, higher temperatures and lower pressures favor the formation of isobutene. Despite the simple chemistry, dehydrogenation of paraffins is very complicated due to occurrence of many side reactions such as hydrogenolysis, cracking and coke formation. Because of thermodynamic limitations, dehydrogenation of light alkanes is conducted at temperatures around 600 ◦ C to achieve reasonable commercial yields. Under these conditions, side reactions and catalyst deactivation are enhanced and frequent catalyst regeneration is necessary [2–5]. The use of too high contact times or high temperatures causes cracking as side reaction as isobutane tend to undergo carbon-carbon bond scission yielding methane and propylene rather than dehydrogenation [6] i − C4 H10 ⇔ C3 H6 + CH4

∗ Corresponding author at: Catalyst Research Group, Petrochemical Research and Technology Company, National Petrochemical Company, No. 27, Sarv Alley, Shirazi south, P.O. Box 1435884711, Tehran, Iran. Tel.: +98 21 88043037; fax: +98 21 88064261. E-mail address: [email protected] (S. Sahebdelfar).

0 H298 = 120 kJ/mol

0 H298 = 80.1 kJ/mol

(2)

For dehydrogenation of light paraffins, a number of commercial processes have been developed which differ in catalyst and reactor types and the regeneration systems utilized [2–5]. In UOP Oleflex process dehydrogenation occurs on a modified Pt alumina-supported catalyst in adiabatic moving-bed reactors with

0926-860X/$ – see front matter. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.apcata.2011.01.027

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S. Sahebdelfar et al. / Applied Catalysis A: General 395 (2011) 107–113

Fig. 2. A sector of the ring-shaped differential volume.

zeroth-order in hydrogen concentration [1]. Larsson et al. 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 [9]. Here, the following rate expression is employed;

Fig. 1. Schematic representation of the Oleflex dehydrogenation reactor.



continuous catalyst regeneration (CCR) [2,7]. The reactors operate adiabatically and to achieve near-isothermal conditions, three or four reactors are employed with inter-stage heaters. The catalyst is progressively coked as it moves down the reactors. The catalyst leaving each reactor enters the next one and the total residence time of catalyst typically ranges from 5 to 7 days. The catalyst leaving the last reactor is sent to the CCR unit, where its coke is burnt, Pt re-dispersed and the excessive moister is removed. The regenerated catalyst is sent back to the first reactor. Fig. 1 depicts the schematic of an Oleflex dehydrogenation reactor. The reactor includes two perforated co-axial cylinders, between which the catalyst moves slowly downwards under the action of gravity. The gaseous feed comprising a mixture of the alkane and hydrogen enters from the bottom; crosses the catalyst bed and the products leave the reactor from the outer side. Radial-flow pattern ensures a low pressure drop. In order to optimize process strategies and to outline the most promising experimental approaches to increase the yield of the product, mathematical modeling of the reactor is necessary. The model of radial-flow moving-bed reactor can be solved analytically for a first order reversible kinetic expression for the main reaction and independent n-th order catalyst deactivation under isothermal conditions [8]. However, due to considerable temperature gradients, adiabatic reactor model should approximate the commercial reactor more precisely. In the present work the dehydrogenation of isobutane to isobutene in commercial scale radial-flow moving-bed reactors operating under adiabatic conditions is studied. An appropriate mathematical model will be developed and solved numerically. The accuracy of the model is studied and compared with industrial data and the limitations are identified. 2. Kinetics and mathematical model To begin with, consider the following reversible reaction: A ⇔ B + H2

(3)

where A and B represent the paraffin and olefin, respectively. Most previous studies have shown that dehydrogenation reaction is first-order in paraffin concentration and negative half to

−rA

= k1 a

CA −

CB CH2



(4)

Keq

where rA is the rate of disappearance of paraffin per catalyst weight, k1 is the rate constant of forward reaction; Keq is the equilibrium constant at reaction temperature and Ci is the concentration of the species i. The catalyst activity, a, is defined as: a(t) =

−rA (t)

−rA (t

= 0)

=

−rA

−rA

(5)

0

Upon algebraic manipulations, the rate can be obtained in terms of paraffin conversion XA as [8]: −rA =

k1 aCA0 (XAe − XA )(˛ + ˇXA ) (1 + εA XA )2

(6)

in which ˛=

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

(7)

ˇ=

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

(8)

where H and B are hydrogen/paraffin and olefin/paraffin molar ratios in the feed, respectively, XAe is the equilibrium conversion under reaction conditions and εA is the volume expansion factor. When XAe approaches unity (i.e., to that of irreversible reactions), the parameters ˛ and ˇ approach unity and εA , respectively. From a paraffin mole balance on the ring-shaped element within reactor bed (Fig. 2), one obtains [8], dXA dW = −rA FA0

(9)

where FA0 is the molar flow rate of paraffin, W is the weight of catalyst, and the subscript 0 refers to the inlet conditions to the reactor. Eq. (9) represents mass conservation equation for the moving-bed reactor. Now, assume the following rate law for catalyst deactivation: −

da = kd a dt

(10)

where kd is deactivation rate constant. This form of decay law has been used for dehydrogenation of light paraffin on Pt-based

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109

Table 1 Specification of input/output dehydrogenation reactor streams.a Reactor 1

Temperature (◦ C) Pressure (barg) Mass flow rate (ton/h) H2 /isobutane ratio a

Reactor 2

Input

Output

Input

Output

Input

Output

634 1.4 106 0.5

538 1.3 106 0.74

639 0.9 106 0.74

561 0.8 106 0.96

637 0.4 106 0.96

575 0.34 106 1.15

Outlet H2 /isobutene ratio are estimates based on the conversion.

catalysts by several authors [10,11]. Integral analysis of fixed-bed reactor data has shown that Eqs. (4) and (10) adequately explain the kinetics of the main reaction and catalyst deactivation in dehydrogenation of isobutane [8]. The contact time of the catalyst moving at a mass flow rate Us within the reactor is: t=

W Us

(11)

Differentiating Eq. (11): dt =

dW Us

(12)

and combining with Eq. (10), one obtains: −

Reactor 3

k da = da Us dW

(13)

Neglecting heat transfer by conduction, the energy balance equation on the elemental volume is: rA (HRx ) dT  = dW US Cps + Fi CPi

(14)

where Cps and Cpi are the heat capacity of the solid and fluid components, respectively. This is a reasonable assumption due to the low thermal conductivity of alumina, high porosity of the catalyst pellets and small contact surfaces between the pellets. Further,  the term Us Cps , heat flow by catalyst, is negligible compared to Fi Cpi , heat flow by the fluid, thus the energy equation can be simplified as: rA (HRx ) dT =  dW Fi CPi

(15)

Because of relatively low pressure drops (∼0.1 bar) across the bed, the pressure gradient was assumed to be linear, as confirmed by results in the similar reactors [12]. Consequently, the momentum equation was not considered. The differential Eqs. (9), (13) and (15) can be solved simultaneously by numerical methods to obtain the reactor performance. The boundary conditions for isobutane conversion and temperature are those of the feed entering the bed at the inner wall. The boundary conditions for catalyst activity are a = 1 at z = 0 for the first reactor and the activity of the catalyst leaving the previous reactor at z = 0 for the next two reactors. The algorithm used here was to divide the catalyst bed region of each reactor into elemental rings of the height z and thickness r, which can be considered as differential isothermal moving-bed reactors, as shown in Figs. 1 and 2. The governing equations can be discretized as follows:



Wi,j = Wrz

2R1 + (2i − 1)r

 Xi+1,j = Xi,j + Wi,j

h(R22 − R12 ) −rA FA0



(16)



(17) i,j

 Ti+1,j = Ti,j + Wi,j

ai,j+1 = ai,j −

rA (HRx )



Fi CPi

 (18) i,j

kd ai,j W

(19)

nUs

where R1 and R2 are reactor bed inner and outer radius, respectively, and h is the reactor bed height. The subscripts i and j refer to the element numbers in r and z directions, respectively, and n is the number of axial steps. Within each reactor the differential Eq. (9) was first solved for the uppermost rings in r direction using Euler method. The conversion in radial direction was calculated by considering each ring as an isothermal reactor at the input temperature. The input temperature to the next ring reactor element was estimated from incremental conversion and energy balance Eq. (15). The activity was considered uniform and same as input activity, that is, the boundary condition for activity. Having temperature profile in the first row of rings, the activity profile in the second row (to which catalyst is fed from the upper row) was estimated from Eq. (13) and the procedure repeated for the entire row. Continuing to the lower most row, the conversion and temperature of the reactor outlet was obtained by mass-average of the values of the rings column adjacent to the outer wall of the bed and the average catalyst activity leaving the reactor was similarly obtained by mass-average of the lower most rings. The product composition and activity of catalyst leaving each reactor was considered as the corresponding input condition to the next reactor. The required thermodynamic properties were obtained from the literature [13]. The catalyst loading was considered as 11.2 ton, 12.0 ton, and 13.8 ton, in the first, second and third reactors, respectively. The total feed flow rate (isobutane + hydrogen) to the first reactor was 106 ton/h with H2 /isobutene molar ratio of 0.5. The catalyst mass flow down the reactor was considered as 320 kg/h corresponding to a nearly five-day catalyst cycle. Feed and product specifications of the commercial dehydrogenation reactors are shown in Table 1. Table 2 represents the numerical values of the parameters required for solution of the model. The activation energy, EA , is from ref [14], the activation energy of catalyst deactivation, Ed = 100 kJ/mol, is an estimate based on reported value of Ed = 140 kJ/mol for dehydrogenation of linear C10 –C14 paraffins over Pt-based catalysts [15]. The presumed lower value for catalyst decay in isobutane dehydrogenation compared to that of higher parrafins was based on the fact that the higher paraffins are thermally less stable and more susceptible to side reactions such as dehydrocyclization which bring about coke formation and cataTable 2 Kinetic parameters that are necessary for modeling (rate constants at 575 ◦ C). Parameter

Numerical value

Unit

Ea Ed k01 kd0

63 100 3.61 0.0127

kJ/mol kJ/mol m3 /(kg h) 1/h

S. Sahebdelfar et al. / Applied Catalysis A: General 395 (2011) 107–113

0.7

640

0.6

620

0.5

600

Temperature,°C

Isobutane conversion

110

0.4 0.3 0.2

0.2

0.4

0.6

0.8

500

lyst deactivation [1]. The rate constants are obtained from Ref. [8] (obtained for the commercial catalyst). Matlab codes were used to calculate the necessary thermodynamic functions and to solve the differential equations. 3. Results and discussion 3.1. Modeling results Fig. 3 shows the radial isobutane conversion profile across the top of the first reactor. One observes that reaction conversion and equilibrium conversion approach to each other and become tangent at the outlet, implying that the components leave the reactor under chemical equilibrium. This profile is consistent with those given in the literature for commercial reactors [2]. The successively lower operating pressure of the reactors (Table 1) can now be understood. This makes the use of thermodynamic advantage of lower pressures at higher conversion levels. Fig. 4 illustrates the radial profiles of isobutane conversion at different bed depths in the first reactor. Conversion increases in radial direction while it decreases along axial direction. The conversion at the outer wall is constant in axial direction because it reached the equilibrium conversion (Fig. 3).

0.12

0.9

Catalyst activity

1/3 2/3

0.08

z/h=1

0.06

0.4

0.6

0.8

Fig. 4. Conversion in the first reactor as a function of radial and axial distances.

1

0.8

1

1 2/3 1/3

0.6

0.02

(r-R1)/(R2-R1)

0.6

(r-R1)/(R2-R1)

0.7

0.5

0.4

0.4

0.8

0.04

0.2

0.2

Fig. 5 shows the radial temperature profiles at different bed depths for the first reactor. The temperature profile in radial direction is declining which is normal for endothermic reactions along the direction of flow. The temperature profile at the outer wall is constant along the axial direction, again, because the outlet conversion is constant and at equilibrium. Fig. 6 shows the axial profiles of the catalyst activity at different radial positions for the first reactor. As the activity decline is strongly affected by temperature according to the Arrhenius law, the sharpest gradient is observed in axial direction at the vicinity of the inner wall characterized by the highest temperature; that is, feed temperature. As the distance from the inner wall increases, the gradient along z-axis becomes less sharp. Another sharp gradient is observed in the radial direction at the bottom of the reactor where the difference in deactivation rates of the inner and outer walls is accumulated. The increasing temperature and declining conversion in axial direction can now be attributed to the ever-decreasing activity of the catalyst as it moves downwards. Figs. 7–10 and 11–14 show the same plots for the subsequent reactors 2 and 3, respectively. The same trends as reactor 1 are observed; however, the gradients become less sharp and the output composition tends to depart from equilibrium successively. This 1

0.1

0

Fig. 5. Temperature in the first reactor as a function of radial and axial distances.

0.14

z/h=0 Isobutane conversion

z/h=0

1

Fig. 3. Equilibrium (–x–) and true (–o–) conversion of isobutane along the first reactor at z = 0.

0

1/3

560

520 0

(r-R1)/(R2-R1)

0

2/3

580

540

0.1 0

z/h=1

(r-R1)/(R2-R1)=0

0

0.2

0.4

0.6

0.8

1

z/h Fig. 6. Catalyst activity in the first reactor as a function of radial and axial distances.

S. Sahebdelfar et al. / Applied Catalysis A: General 395 (2011) 107–113

640

0.7 0.6

620

0.5

Temperature, °C

Isobutane conversion

111

0.4 0.3 0.2

z/h=1 2/3

580

1/3 z/h=0

560

540

0.1 0

600

0

0.2

0.4

0.6

0.8

520

1

(r-R1)/(R2-R1) Fig. 7. Equilibrium (–x–) and true (–o–) conversion of isobutane along the second reactor at z = 0.

trend is due to catalyst deactivation along successive reactors. To cope with this problem and to maintain the required gradient; the catalyst loading should increase in successive reactor as mentioned earlier. Finally Fig. 15 shows the adiabatic operating lines for the commercial reactors and those obtained in this work. In general the predicted output temperature, and consequently, the conversions are lower. The slope of adiabatic operating lines based on the model are lower than those corresponding to the commercial plant which might be because of the rather low selectivity of the reaction (ca. 90% [2]) due to side reactions both over the catalyst and in interstage heaters, with the latter is difficult to estimate. Within the reactors, dehydrogenation reaction is limited by thermodynamic equilibrium, while the side reactions are not limited thermodynamically. These factors influence both on heat of the overall reactions and the heat capacity of the reacting mixture, and consequently, slope of the operating lines. The heat of reaction of dehydrogenation is more positive than those of the competing reactions (for example, reaction 2). This result in lower temperature drop in the presence of side reactions compared to dehydrogenation reaction alone under same conversion of isobutane.

0

0.2

0.4

0.6

0.8

(r-R1)/(R2-R1)

Fig. 9. Temperature in the second reactor as a function of radial and axial distances.

The activity of the catalyst leaving reactors 1, 2 and 3 were obtained as 0.77, 0.50 and 0.25, respectively. The activity loss is, in fact, very large; however, the conversion drop is not so large which can be attributed to the predominance of thermodynamic limitation. The large activity loss also explains why the reactor loading is in excess in the first reactor (see Fig. 4). The observed difference in predicted and commercial conversions could not be attributed to the accuracy of thermodynamic functions and calculations as a comparison of the calculated equilibrium conversions with those reported in the literature [16] showed very close numerical values. 3.2. Sensitivity analysis Except for rate constants which were obtained from testing of the same catalyst, the activation energies are those for similar catalysts or estimates. Under the conditions employed in this work, it was found that the main reactor outputs (T, XA and a) are barely effected by the value of activation energies in a relatively wide range (say 0–100 kJ/mol). This can be explained by the fact that the rate constants were evaluated under some “average” reactors’ 0.8

0.12

0.7

1

z/h=0 Catalyst activity

Isobutane conversion

0.1

1/3 2/3

0.08

z/h=1 0.06

0.4

(r-R1)/(R2-R1)=0

0.02

0.2 0.1 0.2

0.4

0.6

(r-R1)/(R2-R1)

0.8

1

Fig. 8. Conversion in the second reactor as a function of radial and axial distances.

1/3

0.5

0.3

0

2/3

0.6

0.04

0

1

0

0.2

0.4

z/h

0.6

0.8

1

Fig. 10. Catalyst activity in the second reactor as a function of radial and axial distances.

112

S. Sahebdelfar et al. / Applied Catalysis A: General 395 (2011) 107–113

0.7

640

0.6 0.5

Temperature,°C

Isobutane conversion

620

0.4 0.3 0.2

z/h=1 600

2/3 1/3

580

z/h=0

560

0.1 0

0

0.2

0.4

0.6

0.8

540

1

(r-R1)/(R2-R1) Fig. 11. Equilibrium (–x–) and true (–o–) conversion of isobutane along the third reactor at z = 0.

0

0.2

0.4

0.6

0.8

(r-R1)/(R2-R1)

1

Fig. 13. Temperature in the third reactor as a function of radial and axial distances.

0.5

3.3. Computational error analysis The solution method employed in this work was the Euler method. The main program was run for different step sizes in radial and longitudinal directions. It was found that below ten steps, the error is appreciable and some oscillation was observed for steps number smaller than five. Twenty-step number and larger numbers results in convergence of the results. The fact that relatively low numbers of steps result in accurate numerical results is due to the magnitude of the kinetic and operating parameters involved which determines the behavior of system and the resulting smooth variation of the parameters of interest. In the present work 20 steps was used in both directions.

0.45 0.4

Catalyst activity

temperature (Table 2 and Ref. [8]) and that the temperature ranges within the reactors are rather limited. Furthermore, the predominant equilibrium limitation masks the kinetic parameters including activation energies to a large extent. Similarly increasing the rate constant to a much larger value results in only 2% increase in overall conversion (mostly in reactor 3).

1

0.35

2/3

0.3

1/3

0.25 0.2

(r-R1)/(R2-R1)=0

0.15 0.1

0

0.2

0.4

z/h

0.6

0.8

1

Fig. 14. Catalyst activity in the third reactor as a function of radial and axial distances.

The local error of the Euler method is second order, while over many steps the global error becomes first order [17]. This can checked here, for example, by plotting the conversion error of the top catalyst layer (independent of longitudinal step size) and activity error at the vicinity of the inner wall (independent of radial step

0.1

0.6

z/h=0 0.06

Isobutane Conversion (%)

Isobutane conversion

0.08

1/3 2/3

0.04

z/h=1

0.02

0

0

0.2

0.4

0.6

(r-R1)/(R2-R1)

0.8

1

Fig. 12. Conversion in the third reactor as a function of radial and axial distances.

Model Commercial

0.5 0.4 0.3 0.2 0.1 0 470

510

550

590

630

670

Temperature (ºC) Fig. 15. The actual versus simulated adiabatic operating lines.

S. Sahebdelfar et al. / Applied Catalysis A: General 395 (2011) 107–113

Ci CP h H Ea Ed F k1 kd Keq r rA

Fig. 16. The influence of step size on error of activity () and conversion () in the first reactor.

size) versus reciprocal of step numbers (proportional to step size). A first order dependence is expected. Fig. 16 shows that this is very closely satisfied. Alternatively, a plot of the value of these parameters versus reciprocal of step numbers should give nearly straight lines, which is again the case. 4. Conclusions The estimates and trends of temperature, catalyst activity and conversion in dehydrogenation of isobutane in a radial-flow moving-bed reactor can be obtained using lab-scale experimental data and appropriate mathematical model. Under industrial operating conditions, reactor output isobutane/isobutene composition is largely chemical equilibrium controlled. This allows substantial activity loss of the catalyst along the reactors before regeneration become necessary. This also accounts for the successively lower operating pressures in commercial practice. The predicted isobutane conversion is lower than the actual value due to the side reactions and rather low selectivity. Side reactions increase isobutane conversions in dual way. Firstly, they consume isobutane feed. Secondly, they result in higher adiabatic reactor temperatures due to their less endothermic nature and also reduce isobutane partial pressures, both of which are advantageous to the equilibrium limited dehydrogenation reaction. The model developed in this work can be further improved by the inclusion of the side reactions. This requires a more detailed kinetic study and re-evaluation of the kinetic parameters, which is subject of our current works. Nomenclature

A a B

alkane (isobutane) catalyst activity olefin (isobutene)

R1 R2 T Us W X z

113

concentration of species i (mol/m3 ) heat capacity (kJ/mol ◦ C) reactor height (m) heat of reaction (kJ/mol) activation energy of main reaction (kJ/mol) activation energy of catalyst decay (kJ/mol) feed rate (mol/h) reaction rate constant (m3 /(kg h)) rate constant for deactivation of catalyst (h−1 ) concentration equilibrium constant (mol/m3 ) radial distance through reactor bed (m) rate of disappearance of A per mass of catalyst (mol/(kg h)) reactor bed inner radius (m) reactor bed outer radius (m) temperature (◦ C) catalyst flow rate (kg/h) weight of catalyst in the reactor (kg) conversion of key component (A) axial distance along reactor bed (m)

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