Reac Kinet Mech Cat DOI 10.1007/s11144-017-1308-6
Theoretical investigation of non-uniform bifunctional catalyst for the aromatization of methyl cyclopentane T. F. Boukezoula1 • L. Bencheikh1
Received: 4 September 2017 / Accepted: 10 November 2017 Ó Akade´miai Kiado´, Budapest, Hungary 2017
Abstract In this work, a mathematical model is considered to investigate the influence of the concentration and the non-uniform distribution of the catalytic sites on the performances of an isothermal fixed bed reactor with axial dispersion and mass transfer resistance under steady state conditions. This model is applied to the methyl cyclopentane aromatization network. The simulation of the model for a particular chemical reaction network showed that the catalyst activity depends on the balance between the number, per unit volume, of the active sites and the way they are distributed throughout the pellet. The model involves the use of two types of catalytic functions (bi-functional) and can be applied to any chemical reaction network related to catalytic reforming. Keywords Bifunctional catalyst Non-uniform distribution Activity Catalytic reforming Abbreviation Ai, Aj CsI CsII Bio ci ci;s
Active species Average concentration of the acid sites (site/cm3) Average concentration of the metallic sites (site/cm3) Biot number Concentration of species Ai inside the pellet (mol/cm3) Concentration of species Ai at the surface of pellet (mol/cm3)
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11144017-1308-6) contains supplementary material, which is available to authorized users. & T. F. Boukezoula
[email protected] 1
Laboratoire de Ge´nie des Proce´de´s Chimiques, De´partement de Ge´nie des Proce´de´s, Faculte´ de Technologie, Universite´ Ferhat Abbas Se´tif 1, 19000 Se´tif, Algeria
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Concentration of species Ai in the fluid phase (mol/cm3) Concentration of species Ai just before the entrance of the reactor (mol/cm3) ui ð 0Þ Concentration of species Ai at the entrance of the reactor (mol/ cm3) Ui Dimensionless concentration of Ai species in the fluid phase Xc ðnÞ ¼ 1 U1 ðnÞ Conversion Wi Dimensionless concentration of Ai species in the solid phase q Dimensionless radial position in the catalytic particle n Dimensionless axial coordinate of the reactor KL Dimensionless mass transfer coefficient Dimensionless distribution function of the active sites U‘ D Effective diffusion coefficient (cm2/s) Dea Effective axial dispersion coefficient (cm2/s) a Indicates the half thickness of the catalytic pellet (cm) rij Kinetic rate (mol/cm3 s) kij Kinetic constant (cm3 / site s) S Number of species x Position in relation with the particle center (cm) e Porosity of the catalytic bed l Parameter denoting the type of the distribution Pe Peclet number L Reactor length ss Residence time in the fluid phase (s) sD Diffusion time in the catalytic pellet (s) ui ui0
Introduction It is well established that the presence of poisoning and deactivation phenomena by coke deposit on the external lateral surface of the catalytic pellet reduces activity and selectivity and stability of the bi-functional catalytic pellet. The performance of this latter is conditioned by the way the catalytic sites are distributed inside the pellet. It has long been known [1–9] that a uniform distribution is not always the best choice for an optimal functioning. This is particularly important when using noble and costly materials as catalysts. An optimal use of these materials is thus necessary.
Literature review The non-uniform distribution of the metal sites on the catalytic pellet has been largely studied in literature (Becker and Wei [1, 2]; Dario and others [3, 4]; Morbidelli and others [5–7]; Gavriilidis and Varma [8, 9]; Baratti and others
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[10, 11]; Drewsen and others [12]; Brunovska and al [13–17]; Pavlou and Vayenas [18–20]; Letkova` and Markos [21]; Cominos and others [22]; Hwang and others [23]; Lawrence and others [24]; Dietrich and others [25]; Khanaev and others [26]). It is well known that the active site deposition in a non-uniform way results in catalytic performance improvement in terms of activity, selectivity and stability. For a fixed total amount of catalyst, Wei and Becker [1] have reported that « eggyolk » catalysts have a better activity for CO oxidation on Pt for low values of the Thiele modulus and isothermal conditions. Then, Becker and Wei [2] showed numerically, for a solid–gas reaction with Langmuir kinetics, that a distribution of the egg-yolk catalyst, when the reaction is kinetically controlled (small Thiele modulus), leads to an optimal performance. While for a high Thiele modulus, it is the egg-white and egg-shell distribution that gives better results. Dario and others [3, 4] studied theoretically the influence of the distribution profiles of the active sites on both the activity and selectivity of a bi-functional non-uniformly distributed catalyst in a catalytic cylindrical particle and in a fixed bed reactor without axial dispersion. They established that the catalytic activity and selectivity of the different species were largely influenced by the active site concentration and distribution when searching optimal performances of the catalyst. Morbidelli and others [5–7], showed analytically that for a given amount of active metal, the Dirac distribution, in which the catalyst was concentrated at a specified position, leads to an optimal efficiency. Gavriilidis and Varma [9] analyzed numerically the problem of practically positioning the active material. The active sites were distributed in a narrow zone (thin layer) around the optimal position, with a thickness less than 5% of the catalytic particle diameter. This optimal position, which depends on the Thiele modulus, corresponds to a maximum reaction rate. The optimal position moves towards the surface of the pellet when increasing the Thiele modulus and inversely. R. Baratti and others [10, 11], considered the case of two exothermal parallel reactions: one with a first order kinetics and low activation energy and the other with Langmuir kinetics and high activation energy. They observed that the yield is maximal for the first order reaction when the catalyst is concentrated near the surface of the pellet while this yield is maximal for the Langmuir kinetics when the catalyst is concentrated in the center of the pellet. It is worth mentioning that besides the theoretical work carried in this field, experimental works have also been carried out. We can, for example, mention Gavriilidis and Varma [8], who investigated the optimal distribution concept of the active sites, for an ethylene epoxidation reaction network on a catalytic type particle Ag=a Al2 O3 . For a fixed amount of Ag, they studied the influence of both the position and width of the catalytically active layer on ethylene conversion. They also investigated the selectivity and the yield in ethylene oxide, in oxygen rich conditions, in a temperature range between 210 and 270 °C. The results showed that the silvered metal must be placed in a thin layer near the surface of the pellet in order to get a high selectivity in ethylene oxide. To the best of our knowledge, apart from Dario and others [3, 4] and some unpublished work carried out in our laboratory, very few works exist involving the non-uniform distribution effect of the active sites applied to catalytic reforming.
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Site II
Fig. 1 Catalytic aromatization of methyl cyclopentane [4]
A1
A4
A2
A5
A3
Site I
Mathematical formulation of the problem Kinetic model Let us consider a complex reaction scheme involving ‘‘S‘‘ species which can be represented by R reaction series. kij
Ai ! Aj ði; j ¼ 1; 2; . . .SÞ i 6¼ j
ð1Þ
In the case of a bifunctional catalytic particle, with two types of active sites (site I and site II) existing simultaneously, the reaction rate is supposed to be written as follows: rij ¼ kij U‘ ð xÞ ci
ð2Þ
Here ‘ ¼ I if the reaction is taking place on site I and ‘ ¼ II if the reaction is taking place on site II. The active site distribution is represented by the function U‘ ð xÞ. It should be noted that it is assumed that a given reaction can only take place on one type of sites, either I or II. Mass Balance in the catalytic particle A mass balance, under steady state conditions, leads to the following equations: X S S X 1 d p dci Di p x rij rji ð3Þ ¼ x dx dx j¼1 j¼1 j6¼i
j6¼i
Here p ¼ 0; 1 or 2 for a catalytic slab, cylindrical or spherical particle with the following boundary conditions:
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8 dci > > < ¼ 0 dx x¼0 : > > Di dci ¼ KC ui ci;s : dx x¼a
ð4Þ
Mass balance in the fluid phase Similarly, a mass balance, under steady state conditions, in the fluid phase gives the following equations: Dea
d 2 ui dui ð p þ 1Þ KC ui ci;s ¼ 0 ð1 eÞ v 2 a dz dz
The boundary conditions are as follows: 8 dui > > < Dea ¼ vðui ui0 Þ dz z¼0 du > i > : ¼ 0 dz z¼L
ui0 6¼ 0 for i ¼ 1 ui0 ¼ 0 for i ¼ 6 1
ð5Þ
ð6Þ
Dimensionless equations Before solving these equations, they are converted into a dimensionless form. Let us introduce the following dimensionless variables: x z ci ui q ¼ ; n ¼ ; Wi ¼ ; Ui ¼ a L u10 u10 Equations 3 and 4 then become: S X d2 Wi p dWi s þ b W ¼ s bji Wj D i i D q dq dq2 j¼1
for i ¼ 1; . . .; S
ð7Þ
j6¼i
8 dWi > > > < dq ¼ 0 q¼0 dWi > > > ¼ Bio Ui Wi;s : dq q¼1
ð8Þ
Here: bi ¼
X
kij Csl Ul ðqÞ; bji ¼ kji Csl Ul ðqÞ
ð9Þ
j¼1 j6¼i
Similarly, Eqs. 5 and 6 give:
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1 d2 Ui dUi KL Ui Wi;s ¼ 0 2 Pe dn dn 8 > > > < > > > :
ð10Þ
dUi ¼0 dn n¼1 1 dUi Ui ð0Þ 1 for i ¼ 1 ¼ U i ð 0Þ for i 6¼ 1 Pe dn n¼0
ð11Þ
2
Here Pe ¼ Dv eaL ; Bio ¼ KDc a KL ¼ ð1 eÞðp þ 1ÞBio ssDs , sD ¼ aD ; ss ¼ Lv : We have assumed that all the species have roughly the same size which enables us to consider that all the Di are independent of the species and are denote hereafter D. Moreover, D and Dea are assumed to be constant.KL is a dimensionless transfer coefficient (fluid–solid). Solution of the differential equations Equations 7 and 10 cannot be solved analytically. Resort to a numerical method is necessary. Attempts to solve these equations with an explicit finite difference method, a fourth order Runge–Kutta scheme, a fourth order Runge–Kutta-Gill scheme and an implicit Gear method led to a problem of convergence. An implicit finite difference scheme turned out to be more successful. Choice of the distribution function The distribution functions used for the two catalytic functions must satisfy the following normalization condition: 1 Vp
ZZZ
U‘ ðqÞdVp ¼ ðp þ 1Þ Vp
Z1
U‘ ðqÞqp dq ¼ Cs
ð12Þ
0
The mathematical expressions of the different distribution functions used are summarized in Table 1. Application In order to simulate our mathematical model, it was tested on a reaction scheme involving the catalytic aromatization of methylcyclopentane (see Fig. 1). Two kinds of reactions appear in this reaction network: – –
The reactions taking place on acid sites are represented horizontally (Site I). The reactions taking place on metallic sites are represented vertically (Site II).
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Reac Kinet Mech Cat Table 1 Continuous distribution functions [4]
Nature of UðqÞ
l
Mathematical expression
Variation
Parabolic
-2
U‘ ðqÞ ¼ 6ð1 qÞ2
Decreasing
?2
U‘ ðqÞ ¼ 2q2
Increasing
-1
U‘ ðqÞ ¼ 3ð1 qÞ
Decreasing
?1
U‘ ðqÞ ¼ 1:5q
Increasing
0
U‘ ðqÞ ¼ 1
Constant
Linear The l parameter here is used to identify the nature of the distribution profile
Uniform
Results and discussions The numerical results presented here are the concentration profiles of the five species in the fluid phase. The influence of the following parameters:Bio number, Pe number, residence time ss , the average concentration CsII of the metallic sites and the nature of their distribution lII on the concentration profiles is investigated. In what follows, the parameter lI and the average concentration CsI , corresponding to the acid sites, are supposed to be equal to 0 and 1 site=cm3 .The parameter values of the reaction network are chosen as shown in Table 2. Effect of CsII on the concentration profile of all species along the catalytic reactor Fig. 2 shows that the concentration profiles of the five species, in the fluid phase, are strongly affected by CsII . It should be noted that the concentration of species A1 Table 2 Physicochemical parameters of the reaction network [4] Rate constants
k12
k21
k23
k32
k24
k42
k45
k54
cm3 =site: s
1.0
0.1
0.5
0.1
0.5
0.2
1.0
0.01
(a)
1,0
Ui
0,9
U1
0,9
0,8
U2
0,8
0,7
U3
0,7
0,6
U4
0,6
0,5
U5
Ui
0,4
0,3
0,3
0,2
0,2
0,1
0,1 0,2
0,4
ξ
0,6
0,8
1,0
U2 U2 U3 U4 U5
0,5
0,4
0,0 0,0
(b)
1,0
0,0 0,0
0,2
0,4
0,6
0,8
1,0
ξ
Fig. 2 Effect of CsII on the concentration profile of the five species in the fluid phase a CsII = 0.1 b CsII = 1 with the following conditions: p = 1, pe = 1000, Bio = 100, ss ¼ 25s, sD ¼ 50s, lI ¼ 0, lII ¼ þ 2, CsI = 1
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Reac Kinet Mech Cat 0,25
1,0
2 1 0 -2 -1
0,8 0,7 0,6
U1
μII
μII
0,9
0,5
2 1 0 -2 -1
0,20
0,15
U2
0,4
0,10
0,3 0,05
0,2 0,1 0,0 0,0
0,2
0,4
0,6
0,8
0,00 0,0
1,0
0,2
0,4
ξ 0,40 0,35 0,30 0,25
U3
0,6
0,8
1,0
ξ 0,10
μII
2 1 0 -2 -1
0,08
0,06
μII 2 1 0 -2 -1
U4
0,20
0,04
0,15 0,10
0,02
0,05 0,00 0,0
0,2
0,4
0,6
0,8
0,00 0,0
1,0
0,2
0,4
0,6
0,8
1,0
ξ
ξ 0,6
μII
2 1 0 -2 -1
0,5
0,4
U5
0,3
0,2
0,1
0,0 0,0
0,2
0,4
ξ
0,6
0,8
1,0
Fig. 3 Effect of the metallic site distribution on the concentration profiles of the five species in the fluid phase with following conditions: p = 1, pe = 1000, Bio = 100, ss ¼ 25s, sD ¼ 50s, lI ¼ 0, lII ¼ þ 2, CsI = 1
decreases rapidly with higher values of CsII . This is probably due to the fact that most active metallic sites are concentrated at the inner peripheral surface of the particle (lII ¼ þ2Þ. The concentration of the desired species A5 also seems to increase with higher values of CsII .
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Reac Kinet Mech Cat 0,40
0,9
0,35
0,8 0,7
0,30
0,6
0,25
U3
U5
0,20
τs 10s 25s 50s 100s
0,15 0,10 0,05 0,00 0,0
0,2
0,4
0,6
τs 10s 25s 50s 100s
0,5 0,4 0,3 0,2 0,1
0,8
1,0
0,0 0,0
0,2
ξ
0,4
0,6
0,8
1,0
ξ
Fig. 4 Effect of the residence time on the concentration, in the fluid phase, of the final products A3 and A5 with following conditions: p = 1, pe = 1000, Bio = 100, ss ¼ 25s, sD ¼ 50s, lI ¼ 0, lII ¼ þ 2, CsI = 1
Effect of the metallic site distribution on the concentration profiles of the five species in the fluid phase Fig. 3 illustrates the concentration profiles of the all species along the catalytic reactor. It can be seen that higher values CsII and increasing distributions of metallic sites seem to favor the production of species A3 and A5 while decreasing distributions of metallic sites seem to favor the production of A4 . Effect of the residence time on the concentration, in the fluid phase, of the final products A3 and A5 Fig. 4 represents the concentration profiles, in the fluid phase, of the final products for different residence times. It should be noted, here, that the desired product is A5 . It can be seen that higher values of the residence time, ss leads to higher values for the concentrations of the final products. The highest exit value, 90%, of the concentration of the final product A5 corresponds to the highest value of CsII , i.e. 1; the exit value of the concentration of the final product A3 is 10%.
Conclusion In order to improve the catalytic performances in terms of efficiency and selectivity with respect to the desired species A5 , a mathematical model, based on the assumption of an isothermal fixed bed reactor with axial dispersion and under steady state conditions, was proposed and simulated. The results obtained for the concentration profiles of the active species led to the following conclusions: the concentrations of the active sites and their distributions have an influence on the selectivity of the desired product. In order to obtain a high conversion rate, the site II
metallic sites involved in the first reaction, i.e. (A1 ! A2 ) must be concentrated at the inner peripheral surface of the catalytic particles.
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It was shown in this work that the mathematical model considered can be applied to any chemical reaction network and an appropriate choice of the different parameters of the problem can lead to better results.
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