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Deactivation behavior of the catalyst in solid acid catalyzed alkylation: effect of pore mouth plugging
Chemical Engineering Science 57 (2002) 3611 – 3620
www.elsevier.com/locate/ces
Deactivation behavior of the catalyst in solid acid catalyzed alkylation: e'ect of pore mouth plugging S. Sahebdelfara , M. Kazemeinia; ∗ , F. Khorasheha , A. Badakhshanb a Department
of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Avenue 11365-9465 Tehran, Iran and Petroleum Engineering Department, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
b Chemical
Received 11 September 2001; received in revised form 4 May 2002; accepted 18 May 2002
Abstract The deactivation of solid acid catalysts in liquid-phase alkylation of isobutane with butenes was investigated. The role of pore mouth plugging, in particular, was studied and it was found that it had a signi7cant e'ect on the deactivation behavior. Simple explicit correlations were developed for catalyst lifetime in a CSTR, both in terms of time-on-stream and butene turnover per catalyst weight. The correlations were tested using available experimental data from the literature and a reasonable agreement was observed. It was shown that for a zeolitic catalyst the butene turnover per catalyst weight was proportional to the square root of catalyst loading, while it was inversely proportional to both the ole7n feed concentration and the square root of feed :ow rate. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Isobutane alkylation; Deactivation; Catalyst lifetime; Kinetics; Di'usion; Modeling
1. Introduction Alkylation is a re7nery process by which the C4 cut is converted to heavier, highly branched para
their studies, for the most part, were qualitative in nature and only the e'ect of individual parameters on catalyst lifetime were identi7ed. Quantitative studies (de Jong, Mesters, Peferoen, van Brugge, & de Groot, 1996; Simpson, Wei, & Sundaresan, 1996; Taylor & Sherwood, 1997) focused on the solution of the governing equations for the deactivating catalyst in various reactor systems. However, no attempts were made to develop an explicit equation describing the catalyst lifetime in terms of operating parameters. This is the main objective of the present work. In this paper modeling of catalyst deactivation has been considered in terms of individual site poisoning and pore mouth plugging. The latter phenomenon, generally not considered in the previous studies, was found to have a pronounced e'ect on shortening of the catalyst life.
2. Theoretical background Isobutane alkylation involves the reaction of isobutane with light ole7ns to produce heavier, highly branched isopara
0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 2 ) 0 0 2 4 6 - 4
(1)
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
O + O → D;
(2)
where D represents a dimer. Other reactions include isobutane self-alkylation, disproportionation, and cracking. Cracking is an important side reaction originally, when the very high-strength acid sites are not deactivated, or under high temperature conditions. The detailed chemistry and mechanism have been described elsewhere (Corma & Martinez, 1993; Cardona, Gnep, Guisnet, Szabo, & Nascimento, 1995). Like other hydrocarbon reactions on acidic catalysts, the presence of ole7ns in the feed and=or products results in deposition of carbonaceous compounds or “coke” on the catalyst surface eventually leading to its deactivation. In isobutane alkylation the oligomerization reactions are the main route for production of heavier carbocations which become nondesorbable after some threshold molecular weight, thereby poisoning the active sites. The cations adsorbed on the poisoned sites lacking alkylation activity, can grow further by addition of ole7ns, resulting in too large cations and pore clogging. Both individual site poisoning (Loenders, Jacobs, & Martens, 1998; Pater et al., 1999) and pore mouth plugging (Querini & Roa, 1997) have been proposed as possible mechanisms for deactivation of solid acid catalysts in isobutane alkylation. The desired reaction (1) is of “7rst order”, while the undesired reaction (2) is of “second order” with respect to ole7n concentration. Therefore, a high I=O ratio in the reaction zone enhances both the alkylate selectivity and catalyst lifetime (de Jong et al., 1996; Taylor & Sherwood, 1997). This may be achieved by using a high I=O ratio in the feed, using back-mixed mode of operation, or operating under high ole7n conversions. Solid acid catalysts exhibit a high initial activity and selectivity, but rapidly lose them with time-on-stream (TOS). In a typical conversion and selectivity versus TOS diagram (Fig. 1), four distinct stages may be identi7ed (Taylor & Sherwood, 1997): (i) the stage of initial activity, which is not observable due to experimental limitations; (ii) the useful catalyst lifetime, characterized by high ole7n conversions, alkylate yields and slow deactivation; (iii) the rapid loss of activity, characterized by a sharp decline in ole7n conversion coupled with a shift of selectivity towards oligomeric products; and (iv) the last stage, characterized by low catalyst activity and a rather slow deactivation. In this 7nal stage, when the high-strength acid sites disappear, the products are mainly C9+ oligomeric hydrocarbons. The unsatisfactory TOS behavior, shown in Fig. 1, is typical of all solid acid catalysts and has caused a delay in their
1.2 Butene conversion, %
where I , O, and A stand for isobutane, ole7n, and alkylates, respectively. In the presence of acidic catalysts, the reaction proceeds through a chain mechanism via carbocation intermediates (Corma & Martinez, 1993). Reaction (1) is not the only reaction occurring. Numerous side reactions occur simultaneously. The most important undesired competing reaction is the ole7n oligomerization:
1 0.8
Useful Catalyst Lifetime
0.6 Rapid Deactivation
0.4
Oligomerization
0.2 0 0
0.5
1
1.5
2
TOS/ Lifetime
(a)
1.2 Alkylates
1 TMP's/ C8's
3612
0.8 0.6 0.4
Oligomerization
0.2 0 0 (b)
0.5
1
1.5
2
TOS/ Lifetime
Fig. 1. Typical TOS behavior of solid acid catalysts in liquid-phase alkylation: (a) Conversion; (b) Trimethylpentanes (TMPs) in C8 products (T = 338 K, CB0 = 0:18 kgmol=m3 , = 0:97 h, in a CSTR with USHY zeolite). Modi7ed after Taylor and Sherwood (1997) and, Weitkamp and Traa (1999).
successful commercial utilization (Weitkamp & Traa, 1999). 3. Modeling The simpli7ed chemistry presented above, may now be used in the development of mathematical models to describe the deactivation behavior in liquid-phase alkylation. The elimination of other reactions from the models and its consequences will also be discussed. The alkylation reaction is considered under a back-mixed mode of operation which is not only simpler to treat but also it is the preferred mode of operation (de Jong et al., 1996; Taylor & Sherwood, 1997). When the concentration of isopara
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
In the 7rst case, butene di'usivity is constant throughout the pore and equals to that in clean zone, i.e., DB0 . When the velocity of the di'using component is high with respect to the velocity of poisoning front, the steady-state concentration pro7les for the reactants can be established. This pseudo-steady condition is normally the case for gas–solid systems and is also applicable here, for the liquid phase, due to the very low butene concentrations. In the poisoned portion of the pore there is only straight di'usion, the rate of which is given by
C
CBS
CBX
Coke
DP
Fresh
DB0
L-X
x
X
L
− rB = Fig. 2. Schematic representation of a single pore in the shell progressive model.
reactions, respectively: − rB = kA CB ; −
d = kP CB2 ; dt
3613
(3) (4)
where −rB is the rate of ole7n (i.e., butene) consumption per catalyst volume, kA and kP are the pseudo-rate constants of alkylation and poisoning reactions; and CB are the point activity and local butene concentration within the catalyst, respectively. Eq. (4) implies that the rate of the poisoning reaction is proportional to that of dimerization reaction. In other words, ole7nic dimers are the precursors of heavier hydrocarbons causing permanent loss of active sites. The above rate expressions are consistent with the mechanistic model of Simpson et al. (1996) and the model proposed by de Jong et al. (1996). The strong pore di'usion limitation in liquid-phase solid acid catalyzed alkylation (Simpson et al., 1996) strongly a'ects the overall kinetics of the process. This complicates the kinetic analysis requiring implementation of mathematical models with increasing complexities as outlined below. 3.1. Shell progressive approximation Khang and Levenspiel (1973) showed that the simple phenomenological power law rate is applicable to deactivating catalyst pellet when parallel 7rst-order poisoning occurs along with a 7rst-order gas-phase reaction in the regime of strong pore di'usion limitation. The shell progressive mechanism (SPM) (Butt & Petersen, 1988, Chap. 10) can be used to obtain the power law expression for pellet deactivation. The SPM approach can be extended to a parallel second-order poisoning reaction along with a 7rst-order main reaction as is the case in the present study. Under high di'usion limitations, the catalyst pellet can be approximated by a semi-in7nite slab (Khang & Levenspiel, 1973). Accordingly, a single pore can be sketched as shown in Fig. 2. Depending on the extent of pore mouth plugging, the following two cases can be distinguished.
DB0 (CBS − CBX ); L(L − X )
(5)
where L, X , CBS and CBX are the total pore length, length of the clean portion, butene concentrations at the pore entrance (pellet surface) and poisoned front, respectively. For the reaction step, the rate is − rB = kA
X X CBX ; L
(6)
where X is the e'ectiveness factor based on the clean pore length. The rate of growth of the poisoned zone may be obtained from the overall rate of site poisoning in the active zone, that is X dX d(L − X ) =− = kP CB2 (x) d x; (7) dt dt 0 where CB (x) is the concentration pro7le in the clean zone. The above equality is valid under the conditions of severe di'usion limitations (approaching the SPM requirements) where the concentration gradient in the clean zone is very sharp with concentration approaching zero close to the poisoning front. Thus poisoning occurs almost exclusively at the front. Equating Eqs. (5) and (6) would eliminate CBX , thereby, giving the reaction rate in terms of the bulk concentration and position of deactivation front as − rB =
kA XDB0 X =L CBS : DB0 + kA X (L − X )X
(8)
Noting the high di'usion limitation and utilizing de7nition of the pellet activity, a (Levenspiel, 1972, Chaps. 14, 15), one obtains the following equations, respectively: DB0 LL = XX = (9) kA a= =
−rB DB0 XX =LL = −rB0 DB0 + kA (L − X )XX 1 1 + (L − X )
kA DB0
;
(10)
where L is the e'ectiveness factor based on the total pore length. Integrating Eq. (7) using the steady concentration pro7le for a 7rst-order reaction for CB (x) (Levenspiel, 1972)
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S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
would give: dX kP C 2 − = BX : dt 2 kA =DB0
(11)
Eliminating X and CBX from the above equations results in da kP 2 4 − = C a dt 2 BS
(12)
Eq. (12) shows that the apparent deactivation kinetics becomes second order in external ole7n concentration and fourth order in the overall activity. In the second case, the butene di'usivity in the poisoned zone, DP , is considered to be di'erent from that in the clean zone due to pore mouth plugging e'ects, that is DP ¡ DB0 . This alters the form of Eq. (5), in which DB0 is replaced by DP . Using the same procedure one obtains: −
da DB0 2 4 kP CBS a = dt 2DP
(13)
indicating that the fourth order deactivation kinetics is still retained. The initial rate of decrease in activity is more rapid as DB0 =DP is greater than unity. However, the sharp decrease in activity levels out since the last term becomes dominant because of its fourth power. Eqs. (12) and (13) may be tested through numerical solution presented in the following section. 3.2. Numerical approach Consider a spherical pellet placed in a :uid of bulk concentration of CBS . Mass balance for a spherical shell of radius r yields: 1 @ @CB @CB 2 r + rB = ; (14) D B 2 r @r @r @t where DB is the e'ective di'usivity of butene in the pellet. When the pseudo-steady approximation prevails Eq. (14) becomes: 1 @ @CB 2 r − kA CB = 0: D (15) B r 2 @r @r Bischo' (1963) showed that for a gas–solid system the pseudo-steady approximation (@CB =@t ≈ 0) is valid virtually for the entire range of r. In liquid–solid systems errors inherent in such an approximation is signi7cant (Carberry, 1976, Chap. 7). However, as mentioned earlier, the pseudo-steady assumption is valid in the case of very low butene concentrations. Since the external mass transfer resistance is negligible compared with other resistances in liquid-phase alkylation (Simpson et al., 1996), the boundary and initial conditions of Eqs. (4) and (15) become: CB = CBS
at
r = r0
t ¿ 0;
(16)
@CB =0 @r CB = 0
=1
at at
at
r=0 t=0
t=0
t ¿ 0;
(17)
0 6 r 6 r0 ;
(18)
0 6 r 6 r0 ;
(19)
where r0 is the pellet radius. The local e'ective di'usivity of butene is assumed to be time and space dependent. This dependence may be represented as DB = DB0 f;
(20)
where DB0 is the e'ective di'usivity in clean pores and f is a reduction function. For a given catalyst of uniform cylindrical pores, f is only a function of local activity, i.e., f = f( ). A simple functionality for f may be obtained by additional assumptions that the amount of poison deposition is proportional to (1− ); i.e. the so called linear functionality of activity and the amount of poison or foulant (Butt & Petersen, 1988), and that DB is proportional to the available di'usion area (i.e., neglecting the Knudson di'usivity for liquid phase). Accordingly: DP f=1− 1− (1 − ); (21) DB0 where DP is the e'ective di'usivity in completely poisoned region. For a catalyst with bimodal pore structure, such as zeolites, the functionality would be much more complicated. However, since the SPM prevails, the speci7c functionality of f is not expected to be of importance. Eqs. (4) and (15) and Eqs. (16) – (19) were solved by the 7nite di'erence method using variable step size to obtain the intraparticle concentration and activity pro7les, from which the pellet activity can be calculated (Khang & Levenspiel, 1973): r0 3 a= 3 CB r 2 dr (22) r0 CBS 0 In the case of a :uid bathing of uniform and constant concentration, the power law for pellet activity becomes: −
da 2 d a = −kd CBS dt
(23)
or
da 2 − ln − = ln(kd CBS ) + d ln(a); dt
(24)
where kd and d are deactivation rate constant and deactivation order, respectively. A plot of ln(−da=dt) versus ln(a) should result in a straight line of slope d. Fig. 3 shows such plots for DP =DB0 = 1 (i.e., no pore mouth plugging) and DP =DB0 = 0:01 for a Theile modulus, , of 200, representing strong pore di'usion limitations (Levenspiel, 1972). It is seen that, except for the early phase of deactivation, the results con7rm the SPM predictions for a slope of 4. The
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620 1 3.815
y = 0.4602x 2 R = 0.9972
-da/dθ
0.1
0.01
0.001
0.0001 0.1
(a)
1 Pellet activity, a
1.E+01 1.E+00
y = 22.77x
3.7175
2
R = 0.9817
-da/dθ
1.E-01 1.E-02 1.E-03 1.E-04
3615
respectively. Furthermore, APellet represents the external surface of the pellets, F is the volumetric :ow rate of the feed and V is the reactor free volume. Eqs. (25) and (26) together with the intrinsic reaction rates given by Eqs. (3) and (4) and subject to appropriate initial and boundary conditions can be solved to give the intrapellet point activity and concentration, as well as, the bulk-:uid butene concentration and conversion. To simplify the analysis, one may assume that the right hand sides of both Eqs. (25) and (26) are negligible compared with other terms. The logic behind the former assumption was given previously. The latter assumption (i.e., for Eq. (26)) is valid when deactivation is slow enough (Levenspiel, 1972). Applying the results of the previous sections, the governing equations simplify to: CB0 − CBb = ; −rB
(27)
− rB = ka CB a;
(28)
1.E-05 1.E-06 0.01
(b)
0.1
1
Pellet activity, a
Fig. 3. Deactivation rate versus pellet activity: (a) DP =DB0 = 1, or no pore mouth plugging; (b) DP =DB0 = 0:01. Solid line: results of numerical solution; dashed line: least-squares 7t of numerical results. = 200, and 2 is the dimensionless time. = t kp CBS
initial deviation may be attributed to the fact that the characteristic S-shaped pro7le of has not yet been established (Khang & Levenspiel, 1973; Simpson, 1996). A comparison of Figs. 3a and b reveals that pore mouth plugging results in considerable deviation from the SPM prediction, and a lower average d is obtained. 3.3. Reactor modeling The above analysis simulates the behavior of a pellet placed in a large body of reactants in a batch or mixed reactor, or a plug :ow reactor with extremely short contact time. This method may be extended to a mixed reactor to obtain a correlation for the catalyst lifetime in terms of operating parameters. The material balance equations for a single pellet and for a CSTR are given by Eqs. (25) and (26), respectively: 1 @ @CB 2 @CB DB r + r B = P ; (25) r2 @ @r @t @CB dCBb F(CBb − CB0 ) + APellet DB ; (26) = −V @r r=0 dt where p is the pellet porosity, CB , CB0 , and CBb are the intraparticle, inlet :ow, and bulk butene concentrations;
−
da = kd CB2 ad ; dt
(29)
where is the ratio of catalyst weight per volumetric feed :ow rate (weight-time), −rB is the rate of butene consumption per catalyst weight, ka = kA =#p is the apparent rate constants for alkylation, and #p is pellet density. This set of equations subject to the initial condition of a = 1 may be solved to give CBb and, thereby the catalyst lifetime, tc . The catalyst lifetime is regarded as the time required to drop the conversion below a certain limit, often below 90% (i.e., XB = 0:9). However, from Fig. 1, one may note that the lifetime is nearly the same as the in:ection point of the conversion versus TOS curve, by virtue of the fact that the change of XB is very sharp at the end of catalyst lifetime. The advantage of the latter de7nition is that the solution of Eqs. (27) – (29) is overridden, and that one is concerned with an exact mathematical de7nition, since the former de7nition is somewhat arbitrary. From Eq. (27), the following is obtained: 1 − XB =
1 ; 1 + ma
(30)
where m = ka is a type of DamkRohler number (Da). Applying de7nition of in:ection point (d 2 XB =dt 2 = 0) to Eq. (30), one obtains: a (1 + ma) = 2ma2 ;
(31)
where a and a are the 7rst and second time derivatives of a. Eq. (31) holds only for the in:ection point. Combination of Eqs. (29) and (30) results in the following equation: a =
2 d CB0 a da = −kd : dt (1 + ma)2
(32)
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
Eq. (32) implies again that the pseudo-steady assumption for the reactor is valid when CB0 is su
(33)
Next, combining Eqs. (31) and (33) one obtains the activity at the in:ection point as d : m(4 − d)
(34)
−
4−d d
d−1
m2 2 = −kd CB0 tc : 3−d
md−1 −
1 2m − 1−d 2−d (35)
Since m was assumed to be very large, depending on the value of d either the 7rst or last term of the left-hand side of Eq. (35) will dominate. When d ¡ 3, the last term dominates, otherwise, the 7rst term overwhelms. Therefore, Eq. (35) may be approximated as 2 kd CB0 tc = c(ka )n :
0.8 0.6 0.4 0.2
(36)
where c and n are constants. The exponent n is expected 2 to be close to 2. Therefore, a plot of ln(CB0 tc ) versus ln should result in a straight line of an approximate slope of 2. More realistic results may be obtained through simultaneous solution of Eqs. (4), (15), (22) and (27) subject to appropriate initial and boundary conditions, using numerical methods. Fig. 4 shows typical plots of conversion versus TOS, drawn for DP =DB0 = 1 and 0.01, using = 200. It is evident that the introduction of pore mouth plugging into the model leads to a deactivation behavior typical of solid acid catalysts. The greater the pore mouth plugging e'ects, the sharper and greater is the conversion drop at the end of catalyst lifetime. It is also noted that if pore mouth plugging was absent, a highly desirable deactivation versus TOS would be resulted, that is, the conversion would decrease smoothly and no marked active–deactive transition is observed. Fig. 5 illustrates plots of Eq. (36) for various degrees of pore mouth plugging, from numerical solutions. The ka values are selected such that the initial conversions lie in range of time-zero conversions of practical experiences (i.e., XB0 ¿ 0:9). A series of nearly straight lines are obtained, con7rming Eq. (36). In the case of no pore mouth plugging, as noted above, it is di
0
500
(a)
1000 1500 2000 Dimensionless TOS
2500
1.2 Conversion or activity
1 + 3−d
1
0
Upon integration of Eq. (32) (from 0 to tc ) one obtains: d−1 d−1 1 4−d 4−d 2 + 1−d d 2−d d
1 0.8 0.6 0.4 0.2 0 0
500
1000
1500
Dimensionless TOS
(b)
Fig. 4. Conversion and activity versus TOS from numerical solution of the model for ka = 20 and = 200: (a) No pore mouth plugging; (b) DP =DB0 = 0:01. Solid line: conversion; dashed line: activity. 1000000 100000
y = 2.3347x2.0372
10000 2 tc.kP.CB0
ac =
1.2 Conversion or activity
3616
1.9019
y = 2.056x
1000
y = 2.0817x1.8871
100 10 1 1
10
100 η.kA.τ'/ρp
1000
Fig. 5. Plots of Eq. (36), using numerical results for = 200 and various DP =DB0 values: (•) DP =DB0 = 1; (+) DP =DB0 = 10−2 ; ( ) DP =DB0 = 10−4 .
Eq. (35). This may be explained by the great time-averaged deviation of d in Fig. 3b. 4. Results and discussion From some published experimental data, the extent of pore mouth plugging may be evaluated. Noting that the main and poisoning reactions occur mainly within a thin outer
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
3 Butene turnover, kg/kg
tc.CB02, h(kgmol/m3)2
10 1.7602
y = 0.0001x 1
y = 0.0011x1.2674 R2 = 0.9613 0.1 10
100
τ', kg.h/m
1000 3
y = 0.0044x1.3819 2 R = 0.9931
1
0.1 10
2 1.5 1 0.5 0
0
20
40
60 3
80
100
2 1/2
τ' /CB0, (kg.m .h/kgmol )
100
10
y = 0.028x 2 R = 0.8579
2.5
1/2
Fig. 6. A plot of Eq. (36) versus experimental data for USHY zeolite: (•) T = 367 K, CB0 = 0:17–0:27 kgmol=m3 , = 60–240 kg h=m3 ; (4) T = 339 K, CB0 = 0:18 kgmol=m3 , = 143; 277 kg h=m3 . Experimental data from Taylor and Sherwood (1997).
tc.CB02, h.(kgmol/m3)2
3617
100
1000
τ', kg.h/m
3
Fig. 7. A plot of Eq. (36) versus experimental data (T = 363 K, CB0 = 0:27–0:54 kgmol=m3 , = 40–350 kg h=m3 , zeolite beta). Experimental data from de Jong et al. (1996).
shell of the pellet, and taking into account the approximate density of the “coke” and the density and void fraction of the zeolites, a value of 7 wt% internal coke (Cardona et al., 1995) suggests that the surface pores are practically blocked. Alternatively, the same result may be deduced from a comparison of deactivation trends in Fig. 4 with Fig. 1a. While pore mouth plugging has pronounced e'ect on the TOS behavior of the catalyst, its e'ect on the form of lifetime correlation (Eq. (36)) is not as great as one might expect. The general form of the correlation remains unchanged, although n decreases asymptotically with increasing severity of pore plugging. Similarly, the value of (when su
Fig. 8. A plot of Eq. (38) versus experimental data (T = 367 K, CB0 = 0:17–0:54 kgmol=m3 , = 60–240 kg h=m3 ; USHY zeolite). Experimental data from Taylor and Sherwood (1997).
were in the range of 1.27–1.76 depending on the reaction temperature. The upper limit of the slopes corresponding to the optimum operating temperature is very close to the asymptotic value of 1.89 for severe pore mouth plugging as indicated in Fig. 5. This close agreement is due to the fact that under optimum (or lower) temperatures reactions (1) and (2) are dominant. At higher temperatures other side reactions, not included in the model, such as cracking become increasingly signi7cant, resulting in some deviation from model predictions. Eq. (36) may be transformed into a more useful form in terms of the butene turnover per catalyst weight as a measure of catalyst lifetime. Using an average experimental value of 1.5 for n, Eq. (36) may be rearranged to tc CB0 tc CB0 F k 1:5 0:5 = =c a ; Wc =F Wc kd CB0
(37)
where Wc is the catalyst weight. Since the active phase is characterized by nearly complete butene conversion (see Fig. 1) one obtains: 1:5 1=2 SNB
k = c a ; (38) Wc kd CB0 where SNB is the moles of butene reacted (i.e., turnovered) during the active phase. Fig. 8 shows a plot of turnover per catalyst weight versus
12 =CB0 , based on data of Taylor and Sherwood (1997). Interestingly, in spite of the rather wide range of experimental data, a reasonable 7t is observed. Eq. (38) and its plot provide a further support to Eq. (36) (with n=1:5), because the former equation involves an entirely new dependent variable and a di'erent combination of independent variables. A comparison of Eqs. (36) and (38) reveals that the catalyst lifetime in terms of TOS is more sensitive to operating parameters than when expressed in terms of butene turnover per catalyst weight.
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S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
300
1/(1-XB0)
250
y = 1.0016x 2 R = 0.9764
200 150 100 50 0 0
100
200
300
τ', kg.h/m
3
Fig. 9. Test for goodness of pseudo-steady condition assumption for data of Fig. 6 at 367 K, using Eq. (39).
Eq. (38) implies that butene turnover per catalyst weight increases slowly with increasing . This is, however, in contrast to a recent work of Nivarthy et al. (1998). Using constant feed :ow rate slurry reactor and varying the amount of H-BEA zeolite, they arrived at the conclusion that the amount of butene turnover was proportional to available active sites (or catalyst weight). In other words, the number of turnover per site was independent of the number of available sites. This result, surprising to the authors themselves, may be, in part, due to the limited range of and of number of experimental points employed in that study. Using time-zero conversions, XB0 , one can obtain ka from Eq. (30): ka =
1 : (1 − XB0 )
(39)
A plot of 1=(1 − XB0 ) versus would result in a straight line through the origin with a slope of ka . Fig. 9 shows such a plot for the data set of Fig. 6 at 367 K, con7rming the validity of assumptions made in the derivation of Eq. (30) and the subsequent equations. Some limitations of the present analysis should be addressed. Inherent through most of this paper was the pseudo-steady state assumptions, both for the catalyst pellets and reactor. These assumptions are valid when the residence time is short compared with the catalyst lifetime or, when the time-zero conversion approaches unity. Such conditions in a CSTR can be attained using a rather high I=O ratio in the feed, or a large weight-time. Ideally, the model is applicable to systems in which only reactions (1) and (2) are occurring. This is, at the same time, the goal of practical operations. However, other secondary reactions occur to some extent. High reaction temperatures and low I=O ratios enhances oligomerization-cracking reactions, while a high I=O ratio enhances self-alkylation. Oligomerization-cracking reactions participate both in butene consumption and catalyst deactivation. The inclusion of such reactions into the model is mathematically
cumbersome. During the useful catalyst life, the concentration of the intermediate oligomerates (i.e., ole7ns) is much lower than that of cracked products (i.e., C5 –C7 isoalkanes). Therefore, the net e'ect of the oligomerization-cracking reactions is to produce “lower alkylates” and to slow down the growth rate of adsorbed cations on the poisoned sites. They might be view as a parallel path to the main reaction, though with a much lower extent. From examination of experimental data (Figs. 6 and 7) , one might observe that the e'ect of these reactions is to lower the exponent n in Eq. (36), the extent of which would depend on the reaction temperature. Under the conditions of high I=O ratio employed in the model, self-alkylation reaction is enhanced relative to direct alkylation. Self-alkylation leads to the consumption of butene but do not contribute to catalyst deactivation. In the present treatment, self-alkylation and oligomerization-cracking reactions are lumped with the dominant reaction (direct alkylation) into a pseudo-7rst order reaction for butene consumption, the validity of which is illustrated by Fig. 9. Therefore, under “normal” alkylation conditions which favor direct alkylation over other reactions, the assumptions of the model are satis7ed and it adequately describes the catalyst lifetime. The proposed intrinsic kinetics for the main and poisoning reactions are applicable to situations in which the protonation of the ole7n is the chain-initiating step. This is the case, for example, for zeolite-catalyzed alkylation under normal conditions. In the case of superacid catalysts, however, the isopara
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
concentration or feed :ow rate, or increasing catalyst loading enhanced catalyst lifetime both in terms of TOS or turnover per catalyst weight. Amongst these variables, feed concentration was found to have more pronounced e'ect. Furthermore, it was shown that, the catalyst lifetime, when expressed in terms of TOS is more strongly dependent on operating variables than when described in terms of butene turnover per catalyst weight.
Notation a A C d D D Da F I ka kA kd kP m NB O −rB −rB r0 t tc Wc XB
catalyst activity alkylate concentration, kg mol=m3 deactivation order di'usivity, m2 =s dimer DamkRohler number feed :ow rate, m3 =h isopara
Greek letters
#
point activity porosity e'ectiveness factor dimensionless time density, kg=m3 weight-time, Wc =F, kg s=m3 or kg h=m3 Theile modulus
Subscripts b B d
bulk of butene deactivation
p P S 0
3619
pellet poisoning surface entering or initial condition
References Bischo', K. B. (1963). Accuracy of the pseudo-steady state approximation for moving boundary di'usion problems. Chemical Engineering Science, 18, 711. Butt, J. B., & Petersen, E. E. (1988). Activation, deactivation, and poisoning of catalysts. San Diego: Academic Press. Carberry, J. J. (1976). Chemical and catalytic reaction engineering. New York McGraw-Hill. Cardona, F., Gnep, N. S., Guisnet, M., Szabo, G., & Nascimento, P. (1995). Reactions involved in the alkylation of isobutane with 2-butene and with propene on a USHY zeolite. Applied Catalysis A: General, 128(2), 243–257. Corma, A., Gomez, V., & Martinez, A. (1994a). Zeolite beta as a catalyst for alkylation of isobutane with 2-butene. In:uence of synthesis conditions and process variables. Applied Catalysis A: General, 119(1), 83–96. Corma, A., & Martinez, A. (1993). Chemistry, catalysts, and processes for isopara
3620
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
Taylor, R. J., & Sherwood Jr., D. E. (1997). E'ects of process parameters on isobutane=2-butene alkylation using a solid acid catalyst. Applied Catalysis A: General, 155(2), 195–215. Weitkamp, J., & Traa, Y. (1999). Isobutane=butene alkylation on solid catalysts. Where do we stand? Catalysis Today, 49(1–3), 193–199.
Xiao, X., Tierney, J. W., & Wender, I. (1999). Alkylation of isobutane with 2-butene over anion-modi7ed zirconium oxide catalysts. Applied Catalysis A: General, 183(1), 209–219.
www.elsevier.com/locate/ces
Deactivation behavior of the catalyst in solid acid catalyzed alkylation: e'ect of pore mouth plugging S. Sahebdelfara , M. Kazemeinia; ∗ , F. Khorasheha , A. Badakhshanb a Department
of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Avenue 11365-9465 Tehran, Iran and Petroleum Engineering Department, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
b Chemical
Received 11 September 2001; received in revised form 4 May 2002; accepted 18 May 2002
Abstract The deactivation of solid acid catalysts in liquid-phase alkylation of isobutane with butenes was investigated. The role of pore mouth plugging, in particular, was studied and it was found that it had a signi7cant e'ect on the deactivation behavior. Simple explicit correlations were developed for catalyst lifetime in a CSTR, both in terms of time-on-stream and butene turnover per catalyst weight. The correlations were tested using available experimental data from the literature and a reasonable agreement was observed. It was shown that for a zeolitic catalyst the butene turnover per catalyst weight was proportional to the square root of catalyst loading, while it was inversely proportional to both the ole7n feed concentration and the square root of feed :ow rate. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Isobutane alkylation; Deactivation; Catalyst lifetime; Kinetics; Di'usion; Modeling
1. Introduction Alkylation is a re7nery process by which the C4 cut is converted to heavier, highly branched para
their studies, for the most part, were qualitative in nature and only the e'ect of individual parameters on catalyst lifetime were identi7ed. Quantitative studies (de Jong, Mesters, Peferoen, van Brugge, & de Groot, 1996; Simpson, Wei, & Sundaresan, 1996; Taylor & Sherwood, 1997) focused on the solution of the governing equations for the deactivating catalyst in various reactor systems. However, no attempts were made to develop an explicit equation describing the catalyst lifetime in terms of operating parameters. This is the main objective of the present work. In this paper modeling of catalyst deactivation has been considered in terms of individual site poisoning and pore mouth plugging. The latter phenomenon, generally not considered in the previous studies, was found to have a pronounced e'ect on shortening of the catalyst life.
2. Theoretical background Isobutane alkylation involves the reaction of isobutane with light ole7ns to produce heavier, highly branched isopara
0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 2 ) 0 0 2 4 6 - 4
(1)
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
O + O → D;
(2)
where D represents a dimer. Other reactions include isobutane self-alkylation, disproportionation, and cracking. Cracking is an important side reaction originally, when the very high-strength acid sites are not deactivated, or under high temperature conditions. The detailed chemistry and mechanism have been described elsewhere (Corma & Martinez, 1993; Cardona, Gnep, Guisnet, Szabo, & Nascimento, 1995). Like other hydrocarbon reactions on acidic catalysts, the presence of ole7ns in the feed and=or products results in deposition of carbonaceous compounds or “coke” on the catalyst surface eventually leading to its deactivation. In isobutane alkylation the oligomerization reactions are the main route for production of heavier carbocations which become nondesorbable after some threshold molecular weight, thereby poisoning the active sites. The cations adsorbed on the poisoned sites lacking alkylation activity, can grow further by addition of ole7ns, resulting in too large cations and pore clogging. Both individual site poisoning (Loenders, Jacobs, & Martens, 1998; Pater et al., 1999) and pore mouth plugging (Querini & Roa, 1997) have been proposed as possible mechanisms for deactivation of solid acid catalysts in isobutane alkylation. The desired reaction (1) is of “7rst order”, while the undesired reaction (2) is of “second order” with respect to ole7n concentration. Therefore, a high I=O ratio in the reaction zone enhances both the alkylate selectivity and catalyst lifetime (de Jong et al., 1996; Taylor & Sherwood, 1997). This may be achieved by using a high I=O ratio in the feed, using back-mixed mode of operation, or operating under high ole7n conversions. Solid acid catalysts exhibit a high initial activity and selectivity, but rapidly lose them with time-on-stream (TOS). In a typical conversion and selectivity versus TOS diagram (Fig. 1), four distinct stages may be identi7ed (Taylor & Sherwood, 1997): (i) the stage of initial activity, which is not observable due to experimental limitations; (ii) the useful catalyst lifetime, characterized by high ole7n conversions, alkylate yields and slow deactivation; (iii) the rapid loss of activity, characterized by a sharp decline in ole7n conversion coupled with a shift of selectivity towards oligomeric products; and (iv) the last stage, characterized by low catalyst activity and a rather slow deactivation. In this 7nal stage, when the high-strength acid sites disappear, the products are mainly C9+ oligomeric hydrocarbons. The unsatisfactory TOS behavior, shown in Fig. 1, is typical of all solid acid catalysts and has caused a delay in their
1.2 Butene conversion, %
where I , O, and A stand for isobutane, ole7n, and alkylates, respectively. In the presence of acidic catalysts, the reaction proceeds through a chain mechanism via carbocation intermediates (Corma & Martinez, 1993). Reaction (1) is not the only reaction occurring. Numerous side reactions occur simultaneously. The most important undesired competing reaction is the ole7n oligomerization:
1 0.8
Useful Catalyst Lifetime
0.6 Rapid Deactivation
0.4
Oligomerization
0.2 0 0
0.5
1
1.5
2
TOS/ Lifetime
(a)
1.2 Alkylates
1 TMP's/ C8's
3612
0.8 0.6 0.4
Oligomerization
0.2 0 0 (b)
0.5
1
1.5
2
TOS/ Lifetime
Fig. 1. Typical TOS behavior of solid acid catalysts in liquid-phase alkylation: (a) Conversion; (b) Trimethylpentanes (TMPs) in C8 products (T = 338 K, CB0 = 0:18 kgmol=m3 , = 0:97 h, in a CSTR with USHY zeolite). Modi7ed after Taylor and Sherwood (1997) and, Weitkamp and Traa (1999).
successful commercial utilization (Weitkamp & Traa, 1999). 3. Modeling The simpli7ed chemistry presented above, may now be used in the development of mathematical models to describe the deactivation behavior in liquid-phase alkylation. The elimination of other reactions from the models and its consequences will also be discussed. The alkylation reaction is considered under a back-mixed mode of operation which is not only simpler to treat but also it is the preferred mode of operation (de Jong et al., 1996; Taylor & Sherwood, 1997). When the concentration of isopara
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
In the 7rst case, butene di'usivity is constant throughout the pore and equals to that in clean zone, i.e., DB0 . When the velocity of the di'using component is high with respect to the velocity of poisoning front, the steady-state concentration pro7les for the reactants can be established. This pseudo-steady condition is normally the case for gas–solid systems and is also applicable here, for the liquid phase, due to the very low butene concentrations. In the poisoned portion of the pore there is only straight di'usion, the rate of which is given by
C
CBS
CBX
Coke
DP
Fresh
DB0
L-X
x
X
L
− rB = Fig. 2. Schematic representation of a single pore in the shell progressive model.
reactions, respectively: − rB = kA CB ; −
d = kP CB2 ; dt
3613
(3) (4)
where −rB is the rate of ole7n (i.e., butene) consumption per catalyst volume, kA and kP are the pseudo-rate constants of alkylation and poisoning reactions; and CB are the point activity and local butene concentration within the catalyst, respectively. Eq. (4) implies that the rate of the poisoning reaction is proportional to that of dimerization reaction. In other words, ole7nic dimers are the precursors of heavier hydrocarbons causing permanent loss of active sites. The above rate expressions are consistent with the mechanistic model of Simpson et al. (1996) and the model proposed by de Jong et al. (1996). The strong pore di'usion limitation in liquid-phase solid acid catalyzed alkylation (Simpson et al., 1996) strongly a'ects the overall kinetics of the process. This complicates the kinetic analysis requiring implementation of mathematical models with increasing complexities as outlined below. 3.1. Shell progressive approximation Khang and Levenspiel (1973) showed that the simple phenomenological power law rate is applicable to deactivating catalyst pellet when parallel 7rst-order poisoning occurs along with a 7rst-order gas-phase reaction in the regime of strong pore di'usion limitation. The shell progressive mechanism (SPM) (Butt & Petersen, 1988, Chap. 10) can be used to obtain the power law expression for pellet deactivation. The SPM approach can be extended to a parallel second-order poisoning reaction along with a 7rst-order main reaction as is the case in the present study. Under high di'usion limitations, the catalyst pellet can be approximated by a semi-in7nite slab (Khang & Levenspiel, 1973). Accordingly, a single pore can be sketched as shown in Fig. 2. Depending on the extent of pore mouth plugging, the following two cases can be distinguished.
DB0 (CBS − CBX ); L(L − X )
(5)
where L, X , CBS and CBX are the total pore length, length of the clean portion, butene concentrations at the pore entrance (pellet surface) and poisoned front, respectively. For the reaction step, the rate is − rB = kA
X X CBX ; L
(6)
where X is the e'ectiveness factor based on the clean pore length. The rate of growth of the poisoned zone may be obtained from the overall rate of site poisoning in the active zone, that is X dX d(L − X ) =− = kP CB2 (x) d x; (7) dt dt 0 where CB (x) is the concentration pro7le in the clean zone. The above equality is valid under the conditions of severe di'usion limitations (approaching the SPM requirements) where the concentration gradient in the clean zone is very sharp with concentration approaching zero close to the poisoning front. Thus poisoning occurs almost exclusively at the front. Equating Eqs. (5) and (6) would eliminate CBX , thereby, giving the reaction rate in terms of the bulk concentration and position of deactivation front as − rB =
kA XDB0 X =L CBS : DB0 + kA X (L − X )X
(8)
Noting the high di'usion limitation and utilizing de7nition of the pellet activity, a (Levenspiel, 1972, Chaps. 14, 15), one obtains the following equations, respectively: DB0 LL = XX = (9) kA a= =
−rB DB0 XX =LL = −rB0 DB0 + kA (L − X )XX 1 1 + (L − X )
kA DB0
;
(10)
where L is the e'ectiveness factor based on the total pore length. Integrating Eq. (7) using the steady concentration pro7le for a 7rst-order reaction for CB (x) (Levenspiel, 1972)
3614
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
would give: dX kP C 2 − = BX : dt 2 kA =DB0
(11)
Eliminating X and CBX from the above equations results in da kP 2 4 − = C a dt 2 BS
(12)
Eq. (12) shows that the apparent deactivation kinetics becomes second order in external ole7n concentration and fourth order in the overall activity. In the second case, the butene di'usivity in the poisoned zone, DP , is considered to be di'erent from that in the clean zone due to pore mouth plugging e'ects, that is DP ¡ DB0 . This alters the form of Eq. (5), in which DB0 is replaced by DP . Using the same procedure one obtains: −
da DB0 2 4 kP CBS a = dt 2DP
(13)
indicating that the fourth order deactivation kinetics is still retained. The initial rate of decrease in activity is more rapid as DB0 =DP is greater than unity. However, the sharp decrease in activity levels out since the last term becomes dominant because of its fourth power. Eqs. (12) and (13) may be tested through numerical solution presented in the following section. 3.2. Numerical approach Consider a spherical pellet placed in a :uid of bulk concentration of CBS . Mass balance for a spherical shell of radius r yields: 1 @ @CB @CB 2 r + rB = ; (14) D B 2 r @r @r @t where DB is the e'ective di'usivity of butene in the pellet. When the pseudo-steady approximation prevails Eq. (14) becomes: 1 @ @CB 2 r − kA CB = 0: D (15) B r 2 @r @r Bischo' (1963) showed that for a gas–solid system the pseudo-steady approximation (@CB =@t ≈ 0) is valid virtually for the entire range of r. In liquid–solid systems errors inherent in such an approximation is signi7cant (Carberry, 1976, Chap. 7). However, as mentioned earlier, the pseudo-steady assumption is valid in the case of very low butene concentrations. Since the external mass transfer resistance is negligible compared with other resistances in liquid-phase alkylation (Simpson et al., 1996), the boundary and initial conditions of Eqs. (4) and (15) become: CB = CBS
at
r = r0
t ¿ 0;
(16)
@CB =0 @r CB = 0
=1
at at
at
r=0 t=0
t=0
t ¿ 0;
(17)
0 6 r 6 r0 ;
(18)
0 6 r 6 r0 ;
(19)
where r0 is the pellet radius. The local e'ective di'usivity of butene is assumed to be time and space dependent. This dependence may be represented as DB = DB0 f;
(20)
where DB0 is the e'ective di'usivity in clean pores and f is a reduction function. For a given catalyst of uniform cylindrical pores, f is only a function of local activity, i.e., f = f( ). A simple functionality for f may be obtained by additional assumptions that the amount of poison deposition is proportional to (1− ); i.e. the so called linear functionality of activity and the amount of poison or foulant (Butt & Petersen, 1988), and that DB is proportional to the available di'usion area (i.e., neglecting the Knudson di'usivity for liquid phase). Accordingly: DP f=1− 1− (1 − ); (21) DB0 where DP is the e'ective di'usivity in completely poisoned region. For a catalyst with bimodal pore structure, such as zeolites, the functionality would be much more complicated. However, since the SPM prevails, the speci7c functionality of f is not expected to be of importance. Eqs. (4) and (15) and Eqs. (16) – (19) were solved by the 7nite di'erence method using variable step size to obtain the intraparticle concentration and activity pro7les, from which the pellet activity can be calculated (Khang & Levenspiel, 1973): r0 3 a= 3 CB r 2 dr (22) r0 CBS 0 In the case of a :uid bathing of uniform and constant concentration, the power law for pellet activity becomes: −
da 2 d a = −kd CBS dt
(23)
or
da 2 − ln − = ln(kd CBS ) + d ln(a); dt
(24)
where kd and d are deactivation rate constant and deactivation order, respectively. A plot of ln(−da=dt) versus ln(a) should result in a straight line of slope d. Fig. 3 shows such plots for DP =DB0 = 1 (i.e., no pore mouth plugging) and DP =DB0 = 0:01 for a Theile modulus, , of 200, representing strong pore di'usion limitations (Levenspiel, 1972). It is seen that, except for the early phase of deactivation, the results con7rm the SPM predictions for a slope of 4. The
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620 1 3.815
y = 0.4602x 2 R = 0.9972
-da/dθ
0.1
0.01
0.001
0.0001 0.1
(a)
1 Pellet activity, a
1.E+01 1.E+00
y = 22.77x
3.7175
2
R = 0.9817
-da/dθ
1.E-01 1.E-02 1.E-03 1.E-04
3615
respectively. Furthermore, APellet represents the external surface of the pellets, F is the volumetric :ow rate of the feed and V is the reactor free volume. Eqs. (25) and (26) together with the intrinsic reaction rates given by Eqs. (3) and (4) and subject to appropriate initial and boundary conditions can be solved to give the intrapellet point activity and concentration, as well as, the bulk-:uid butene concentration and conversion. To simplify the analysis, one may assume that the right hand sides of both Eqs. (25) and (26) are negligible compared with other terms. The logic behind the former assumption was given previously. The latter assumption (i.e., for Eq. (26)) is valid when deactivation is slow enough (Levenspiel, 1972). Applying the results of the previous sections, the governing equations simplify to: CB0 − CBb = ; −rB
(27)
− rB = ka CB a;
(28)
1.E-05 1.E-06 0.01
(b)
0.1
1
Pellet activity, a
Fig. 3. Deactivation rate versus pellet activity: (a) DP =DB0 = 1, or no pore mouth plugging; (b) DP =DB0 = 0:01. Solid line: results of numerical solution; dashed line: least-squares 7t of numerical results. = 200, and 2 is the dimensionless time. = t kp CBS
initial deviation may be attributed to the fact that the characteristic S-shaped pro7le of has not yet been established (Khang & Levenspiel, 1973; Simpson, 1996). A comparison of Figs. 3a and b reveals that pore mouth plugging results in considerable deviation from the SPM prediction, and a lower average d is obtained. 3.3. Reactor modeling The above analysis simulates the behavior of a pellet placed in a large body of reactants in a batch or mixed reactor, or a plug :ow reactor with extremely short contact time. This method may be extended to a mixed reactor to obtain a correlation for the catalyst lifetime in terms of operating parameters. The material balance equations for a single pellet and for a CSTR are given by Eqs. (25) and (26), respectively: 1 @ @CB 2 @CB DB r + r B = P ; (25) r2 @ @r @t @CB dCBb F(CBb − CB0 ) + APellet DB ; (26) = −V @r r=0 dt where p is the pellet porosity, CB , CB0 , and CBb are the intraparticle, inlet :ow, and bulk butene concentrations;
−
da = kd CB2 ad ; dt
(29)
where is the ratio of catalyst weight per volumetric feed :ow rate (weight-time), −rB is the rate of butene consumption per catalyst weight, ka = kA =#p is the apparent rate constants for alkylation, and #p is pellet density. This set of equations subject to the initial condition of a = 1 may be solved to give CBb and, thereby the catalyst lifetime, tc . The catalyst lifetime is regarded as the time required to drop the conversion below a certain limit, often below 90% (i.e., XB = 0:9). However, from Fig. 1, one may note that the lifetime is nearly the same as the in:ection point of the conversion versus TOS curve, by virtue of the fact that the change of XB is very sharp at the end of catalyst lifetime. The advantage of the latter de7nition is that the solution of Eqs. (27) – (29) is overridden, and that one is concerned with an exact mathematical de7nition, since the former de7nition is somewhat arbitrary. From Eq. (27), the following is obtained: 1 − XB =
1 ; 1 + ma
(30)
where m = ka is a type of DamkRohler number (Da). Applying de7nition of in:ection point (d 2 XB =dt 2 = 0) to Eq. (30), one obtains: a (1 + ma) = 2ma2 ;
(31)
where a and a are the 7rst and second time derivatives of a. Eq. (31) holds only for the in:ection point. Combination of Eqs. (29) and (30) results in the following equation: a =
2 d CB0 a da = −kd : dt (1 + ma)2
(32)
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
Eq. (32) implies again that the pseudo-steady assumption for the reactor is valid when CB0 is su
(33)
Next, combining Eqs. (31) and (33) one obtains the activity at the in:ection point as d : m(4 − d)
(34)
−
4−d d
d−1
m2 2 = −kd CB0 tc : 3−d
md−1 −
1 2m − 1−d 2−d (35)
Since m was assumed to be very large, depending on the value of d either the 7rst or last term of the left-hand side of Eq. (35) will dominate. When d ¡ 3, the last term dominates, otherwise, the 7rst term overwhelms. Therefore, Eq. (35) may be approximated as 2 kd CB0 tc = c(ka )n :
0.8 0.6 0.4 0.2
(36)
where c and n are constants. The exponent n is expected 2 to be close to 2. Therefore, a plot of ln(CB0 tc ) versus ln should result in a straight line of an approximate slope of 2. More realistic results may be obtained through simultaneous solution of Eqs. (4), (15), (22) and (27) subject to appropriate initial and boundary conditions, using numerical methods. Fig. 4 shows typical plots of conversion versus TOS, drawn for DP =DB0 = 1 and 0.01, using = 200. It is evident that the introduction of pore mouth plugging into the model leads to a deactivation behavior typical of solid acid catalysts. The greater the pore mouth plugging e'ects, the sharper and greater is the conversion drop at the end of catalyst lifetime. It is also noted that if pore mouth plugging was absent, a highly desirable deactivation versus TOS would be resulted, that is, the conversion would decrease smoothly and no marked active–deactive transition is observed. Fig. 5 illustrates plots of Eq. (36) for various degrees of pore mouth plugging, from numerical solutions. The ka values are selected such that the initial conversions lie in range of time-zero conversions of practical experiences (i.e., XB0 ¿ 0:9). A series of nearly straight lines are obtained, con7rming Eq. (36). In the case of no pore mouth plugging, as noted above, it is di
0
500
(a)
1000 1500 2000 Dimensionless TOS
2500
1.2 Conversion or activity
1 + 3−d
1
0
Upon integration of Eq. (32) (from 0 to tc ) one obtains: d−1 d−1 1 4−d 4−d 2 + 1−d d 2−d d
1 0.8 0.6 0.4 0.2 0 0
500
1000
1500
Dimensionless TOS
(b)
Fig. 4. Conversion and activity versus TOS from numerical solution of the model for ka = 20 and = 200: (a) No pore mouth plugging; (b) DP =DB0 = 0:01. Solid line: conversion; dashed line: activity. 1000000 100000
y = 2.3347x2.0372
10000 2 tc.kP.CB0
ac =
1.2 Conversion or activity
3616
1.9019
y = 2.056x
1000
y = 2.0817x1.8871
100 10 1 1
10
100 η.kA.τ'/ρp
1000
Fig. 5. Plots of Eq. (36), using numerical results for = 200 and various DP =DB0 values: (•) DP =DB0 = 1; (+) DP =DB0 = 10−2 ; ( ) DP =DB0 = 10−4 .
Eq. (35). This may be explained by the great time-averaged deviation of d in Fig. 3b. 4. Results and discussion From some published experimental data, the extent of pore mouth plugging may be evaluated. Noting that the main and poisoning reactions occur mainly within a thin outer
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
3 Butene turnover, kg/kg
tc.CB02, h(kgmol/m3)2
10 1.7602
y = 0.0001x 1
y = 0.0011x1.2674 R2 = 0.9613 0.1 10
100
τ', kg.h/m
1000 3
y = 0.0044x1.3819 2 R = 0.9931
1
0.1 10
2 1.5 1 0.5 0
0
20
40
60 3
80
100
2 1/2
τ' /CB0, (kg.m .h/kgmol )
100
10
y = 0.028x 2 R = 0.8579
2.5
1/2
Fig. 6. A plot of Eq. (36) versus experimental data for USHY zeolite: (•) T = 367 K, CB0 = 0:17–0:27 kgmol=m3 , = 60–240 kg h=m3 ; (4) T = 339 K, CB0 = 0:18 kgmol=m3 , = 143; 277 kg h=m3 . Experimental data from Taylor and Sherwood (1997).
tc.CB02, h.(kgmol/m3)2
3617
100
1000
τ', kg.h/m
3
Fig. 7. A plot of Eq. (36) versus experimental data (T = 363 K, CB0 = 0:27–0:54 kgmol=m3 , = 40–350 kg h=m3 , zeolite beta). Experimental data from de Jong et al. (1996).
shell of the pellet, and taking into account the approximate density of the “coke” and the density and void fraction of the zeolites, a value of 7 wt% internal coke (Cardona et al., 1995) suggests that the surface pores are practically blocked. Alternatively, the same result may be deduced from a comparison of deactivation trends in Fig. 4 with Fig. 1a. While pore mouth plugging has pronounced e'ect on the TOS behavior of the catalyst, its e'ect on the form of lifetime correlation (Eq. (36)) is not as great as one might expect. The general form of the correlation remains unchanged, although n decreases asymptotically with increasing severity of pore plugging. Similarly, the value of (when su
Fig. 8. A plot of Eq. (38) versus experimental data (T = 367 K, CB0 = 0:17–0:54 kgmol=m3 , = 60–240 kg h=m3 ; USHY zeolite). Experimental data from Taylor and Sherwood (1997).
were in the range of 1.27–1.76 depending on the reaction temperature. The upper limit of the slopes corresponding to the optimum operating temperature is very close to the asymptotic value of 1.89 for severe pore mouth plugging as indicated in Fig. 5. This close agreement is due to the fact that under optimum (or lower) temperatures reactions (1) and (2) are dominant. At higher temperatures other side reactions, not included in the model, such as cracking become increasingly signi7cant, resulting in some deviation from model predictions. Eq. (36) may be transformed into a more useful form in terms of the butene turnover per catalyst weight as a measure of catalyst lifetime. Using an average experimental value of 1.5 for n, Eq. (36) may be rearranged to tc CB0 tc CB0 F k 1:5 0:5 = =c a ; Wc =F Wc kd CB0
(37)
where Wc is the catalyst weight. Since the active phase is characterized by nearly complete butene conversion (see Fig. 1) one obtains: 1:5 1=2 SNB
k = c a ; (38) Wc kd CB0 where SNB is the moles of butene reacted (i.e., turnovered) during the active phase. Fig. 8 shows a plot of turnover per catalyst weight versus
12 =CB0 , based on data of Taylor and Sherwood (1997). Interestingly, in spite of the rather wide range of experimental data, a reasonable 7t is observed. Eq. (38) and its plot provide a further support to Eq. (36) (with n=1:5), because the former equation involves an entirely new dependent variable and a di'erent combination of independent variables. A comparison of Eqs. (36) and (38) reveals that the catalyst lifetime in terms of TOS is more sensitive to operating parameters than when expressed in terms of butene turnover per catalyst weight.
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300
1/(1-XB0)
250
y = 1.0016x 2 R = 0.9764
200 150 100 50 0 0
100
200
300
τ', kg.h/m
3
Fig. 9. Test for goodness of pseudo-steady condition assumption for data of Fig. 6 at 367 K, using Eq. (39).
Eq. (38) implies that butene turnover per catalyst weight increases slowly with increasing . This is, however, in contrast to a recent work of Nivarthy et al. (1998). Using constant feed :ow rate slurry reactor and varying the amount of H-BEA zeolite, they arrived at the conclusion that the amount of butene turnover was proportional to available active sites (or catalyst weight). In other words, the number of turnover per site was independent of the number of available sites. This result, surprising to the authors themselves, may be, in part, due to the limited range of and of number of experimental points employed in that study. Using time-zero conversions, XB0 , one can obtain ka from Eq. (30): ka =
1 : (1 − XB0 )
(39)
A plot of 1=(1 − XB0 ) versus would result in a straight line through the origin with a slope of ka . Fig. 9 shows such a plot for the data set of Fig. 6 at 367 K, con7rming the validity of assumptions made in the derivation of Eq. (30) and the subsequent equations. Some limitations of the present analysis should be addressed. Inherent through most of this paper was the pseudo-steady state assumptions, both for the catalyst pellets and reactor. These assumptions are valid when the residence time is short compared with the catalyst lifetime or, when the time-zero conversion approaches unity. Such conditions in a CSTR can be attained using a rather high I=O ratio in the feed, or a large weight-time. Ideally, the model is applicable to systems in which only reactions (1) and (2) are occurring. This is, at the same time, the goal of practical operations. However, other secondary reactions occur to some extent. High reaction temperatures and low I=O ratios enhances oligomerization-cracking reactions, while a high I=O ratio enhances self-alkylation. Oligomerization-cracking reactions participate both in butene consumption and catalyst deactivation. The inclusion of such reactions into the model is mathematically
cumbersome. During the useful catalyst life, the concentration of the intermediate oligomerates (i.e., ole7ns) is much lower than that of cracked products (i.e., C5 –C7 isoalkanes). Therefore, the net e'ect of the oligomerization-cracking reactions is to produce “lower alkylates” and to slow down the growth rate of adsorbed cations on the poisoned sites. They might be view as a parallel path to the main reaction, though with a much lower extent. From examination of experimental data (Figs. 6 and 7) , one might observe that the e'ect of these reactions is to lower the exponent n in Eq. (36), the extent of which would depend on the reaction temperature. Under the conditions of high I=O ratio employed in the model, self-alkylation reaction is enhanced relative to direct alkylation. Self-alkylation leads to the consumption of butene but do not contribute to catalyst deactivation. In the present treatment, self-alkylation and oligomerization-cracking reactions are lumped with the dominant reaction (direct alkylation) into a pseudo-7rst order reaction for butene consumption, the validity of which is illustrated by Fig. 9. Therefore, under “normal” alkylation conditions which favor direct alkylation over other reactions, the assumptions of the model are satis7ed and it adequately describes the catalyst lifetime. The proposed intrinsic kinetics for the main and poisoning reactions are applicable to situations in which the protonation of the ole7n is the chain-initiating step. This is the case, for example, for zeolite-catalyzed alkylation under normal conditions. In the case of superacid catalysts, however, the isopara
S. Sahebdelfar et al. / Chemical Engineering Science 57 (2002) 3611–3620
concentration or feed :ow rate, or increasing catalyst loading enhanced catalyst lifetime both in terms of TOS or turnover per catalyst weight. Amongst these variables, feed concentration was found to have more pronounced e'ect. Furthermore, it was shown that, the catalyst lifetime, when expressed in terms of TOS is more strongly dependent on operating variables than when described in terms of butene turnover per catalyst weight.
Notation a A C d D D Da F I ka kA kd kP m NB O −rB −rB r0 t tc Wc XB
catalyst activity alkylate concentration, kg mol=m3 deactivation order di'usivity, m2 =s dimer DamkRohler number feed :ow rate, m3 =h isopara
Greek letters
#
point activity porosity e'ectiveness factor dimensionless time density, kg=m3 weight-time, Wc =F, kg s=m3 or kg h=m3 Theile modulus
Subscripts b B d
bulk of butene deactivation
p P S 0
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pellet poisoning surface entering or initial condition
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