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Ind. Eng. Chem. Res. 2003, 42, 3886-3892
Development of an Empirical Model for Catalyst Lifetime in Isobutane/Butene Alkylation M. Kazemeini,*,† S. Sahebdelfar,† F. Khorasheh,† and A. Badakhshan‡ Department of Chemical and Petroleum Engineering, Sharif University of Technology, P.O. Box 11365-9465, Tehran, Iran 11365-9465, and Chemical and Petroleum Engineering Department, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
Dimensional analysis of the governing equations in liquid-phase, solid-acid-catalyzed alkylation was used to develop an empirical model for the catalyst lifetime in terms of important operating variables. It was found that the dimensionless catalyst lifetime in a continuous stirred tank reactor was a function of four dimensionless groups, incorporating all important kinetic and operating variables. A power-law correlation was found to be adequate in representing the available experimental data. Because the alkylation reactions are highly diffusion-limited, it was shown that only three of the four exponents in the power-law correlation were independent. As such, the fourth exponent was obtained without a need to fit the correlation with its corresponding experimental data. The lifetime was found to be proportional to the concentration of active sites raised to the power of 0.8. Among the various operating variables, the olefin feed concentration most significantly influenced the catalyst lifetime. Introduction Current legislation for the reduction of the aromatic and olefinic compounds in gasoline, as well as the possible phase-out of methyl tert-butyl ether, would cause degradation in the gasoline pool both quantitatively and qualitatively. Application of alkylates as a blending stock can mitigate these problems. Alkylates possess all of the desirable properties of an ideal gasoline-blending component such as a high octane number, low (Reid) vapor pressure, and virtually no aromatics, olefins, or sulfur compounds. The current alkylation technologies based on a liquid HF or H2SO4 catalyst, though giving adequate yields, have certain important drawbacks. The main one is dealing with large volumes of highly corrosive (and also toxic, in the case of HF) acids imposing considerable operational costs and environmental concerns.2 Nevertheless, despite great efforts in the past 3 decades to discover an environmentally benign solid-acid catalyst substitute, no alternative with sufficient stability has been found. Numerous strong solid acids such as acidic zeolites, heteropolyacids, and sulfated metal oxides have been tested as potential catalysts. However, all of the solid acids tested exhibited short catalyst lifetimes. The unsatisfactory time-on-stream (TOS) behavior, shown in Figure 1, is common to all solid-acid catalysts.2 These catalysts have a high initial activity and selectivity but lose both rapidly.3 Unlike liquid acids, solid acids possess a rather low acid site density per catalyst weight, the strength of which is not uniform. Moreover, many of the sites are located deep within the internal pores and are thus not easily accessible to the reactants. However, commercially available processes, such as the UOP Alkylene4 and the ABB AlkyClean5 processes * To whom correspondence should be addressed. Tel.: +98 21 602 2853. Fax: +98 21 602 2705. E-mail:
[email protected]. † Sharif University of Technology. ‡ The University of Calgary.
Figure 1. Typical butene conversion trend versus TOS (USHY zeolite in a CSTR reactor, from ref 3).
make use of the “optimized” solid catalysts and, for the most part, rely on their elaborate catalyst reactivation methods. The short catalyst life necessitates continuous catalyst regeneration. Although there are models to describe the deactivation phenomenon for solid-acid, liquid-phase alkylation processes,6-8 no attempt has been made to develop an explicit correlation to express the catalyst lifetime in terms of important operating variables. The complex composition of the product mixture, rapid catalyst deactivation, and the prevailing severe intraparticle diffusion limitations make quantitative analyses difficult. The aim of this paper is to use dimensional analysis to develop a correlation for the catalyst lifetime. Such a correlation may be used to determine operating conditions that result in a longer catalyst lifetime and higher alkylate yields. Chemistry of Reaction Alkylation involves a reaction between isobutane and a light olefin (usually butenes) to produce a heavier highly branched isoparaffin (alkylate). The reaction may be represented as follows:
I+BfA
10.1021/ie030250z CCC: $25.00 © 2003 American Chemical Society Published on Web 07/22/2003
(1)
Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 3887
where I, B, and A represent isobutane, olefin (butene), and alkylate, respectively. This is not the only reaction occurring. Numerous secondary reactions including olefin oligomerization, isobutane self-alkylation, and disproportionation occur simultaneously, degrading the alkylate quality and reducing the catalyst lifetime.9 One of the most important side reactions is the oligomerization of the olefin according to the following reaction:
B+BfD
(2)
where D represents a dimer. Reaction (2) may continue to form higher olefins. These olefins are the precursors of carbonaceous deposits or “coke”, which bring about catalyst deactivation through irreversible adsorption and pore plugging. Reactions (1) and (2) may be considered as the main routes for butene consumption and catalyst deactivation, respectively.6 The desired reaction (1) is “first order” while the poisoning reaction (2) is “second order” with respect to the olefin concentration. A higher I/B ratio in the reaction zone would favor reaction (1) over reaction (2) and enhance the catalyst lifetime by reducing side reactions, leading to polymer deposits. This can be achieved by using a high I/B ratio in the feed or using a back-mixed mode of operation under high olefin conversions. Typically, the catalyst lifetime in a continuous stirred tank reactor (CSTR) is several hours, while in a plug-flow reactor, under the same operating conditions, the lifetime is on the order of a few minutes. The following analysis for modeling the deactivation process will be, therefore, based on a back-mixed mode of operation. Development of the Model The usefulness of the dimensional analysis method lies in the fact that a minimum set of dimensionless groups describing the system is obtained through combination of the variables within each dimensionless group. The important variables may be found by inspection of the system and combined using the Buckingham π theorem. They also may be found by dimensional analysis of the governing equations. The advantage of the latter is the fact that the constraints imposed by the model avoid inclusion of extraneous variables or omission of any important ones. The method adopted here for the analysis is that suggested by Churchill.10 Reaction Rates and Balance Equations. Because the alkylation reaction is carried out at high I/B ratios, the concentration of isobutane may be assumed to be constant within the reaction zone. This assumption simplifies the analysis of the problem because the reaction rate expressions become functions of the butene concentration alone. Therefore, the intrinsic rate for the alkylation reaction is given by
rA ) kARCB
(3)
where rA is the rate of alkylate production per catalyst volume, kA is the pseudo-first-order rate constant of the alkylation reaction, R is the catalyst point (i.e., intrinsic) activity, and CB is the local butene concentration within the catalyst. Similarly, according to eq 2, we may propose the following rate expression for site poisoning:
-dR/dt ) kPRCB2
(4)
where kP is the rate constant for poisoning. The above
intrinsic rate expressions are consistent with the mechanistic models of Simpson et al.7 and de Jong et al.6 Although these models were originally developed for zeolite-catalyzed alkylation, they would be applicable to other catalyst systems where Bro¨nsted acid sites are prominent. To obtain the butene conversion, the above equations should be combined with the material balance equations for butene within both the pellets and the reactor. Assuming isothermal conditions, the mass balance for a shell of radius r within a spherical pellet is given by
[
]
∂CB 1 ∂ 2 ∂CB rD + rA ) p 2 ∂r ∂r ∂t r
(5)
where D is the effective diffusivity of butene within the pellet and p is the pellet porosity. In the case of zeolitecatalyzed alkylation, Simpson and co-workers have shown that the reaction is strongly intraparticle-diffusion-limited.7 This is primarily due to the very low diffusivity of butene in the liquid phase. Therefore, it is reasonable to assume that a similar condition prevails for other solid acids of comparable intrinsic activities. In the absence of external mass-transfer limitations, the initial and boundary conditions for eq 5 become
t)0
CB ) 0
R)1
(6)
r)0
∂CB )0 ∂r
(7)
r ) r0
C B ) CS
(8)
where r0 is the pellet radius and CS is the butene concentration at the pellet surface being equal to that in the bulk fluid phase. The material balance equation for the reactor is given by
v(C0 - CS) + Vr
( )
Vc ∂CB dCS +3 D dt r0 ∂r
r)r0
)0
(9)
subject to the following initial condition:
t)0
CS ) 0
(10)
where v is the volumetric feed flow rate, C0 is butene feed concentration, Vr is the total free volume of the reactor, and Vc is the total volume of the catalyst pellets. The simultaneous solution of eqs 3-10 would give the reactor outlet concentration, CS, and thereby the butene conversion, XB. Although the solution to the above set of equations can be obtained by numerical methods, it does not lead to a general correlation for the catalyst lifetime. Such a correlation can be obtained by utilizing dimensional analysis. Dimensional Analysis of the Governing Equations. In the first step, reference quantities are defined for all of the independent and dependent variables, that is,
x ) Xxa
(11)
where x is the original variable, xa is the reference quantity having the same dimensions as x, and X is the dimensionless form of the variable. For the present system, the equations cannot be solved independently; the pellet, for example, cannot be analyzed first and then the reactor. Therefore, the reference quantities are
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ra ) r 0
defined for the whole system as follows:
r ) Rra
(11a)
Ca ) C0
CB ) ψBCa
(11b)
ta ) τ
t ) θta
(11c)
CS ) ψSCa
(11d)
where τ )Vr/v is the space time. Other dimensionless groups are obtained in terms of these quantities, and eqs 18 and 21 reduce to
(
Upon replacing these variables in the above equations and their corresponding initial and boundary conditions, we obtain the following equations for the main reaction within the pellet:
(
)
2
(12)
θ)0
ψB ) 0
(13)
R)0
∂ψ )0 ∂R
(14)
ψB ) ψS
(15)
and for the poisoning reaction
-dR/dθ ) kPtaCBa2ψB2 θ)0
(
ra kAra2 pra2 , ,k t C 2 ψB ) f R,θ,ψS, , r0 D taD P a a
)
(18)
For the reactor, the governing equation becomes
(C0/Ca - ψS) +
Vr Ca dψS + vCa ta dθ WcD Ca ∂ψB 3 Fcr0vCa ra ∂R
( )
θ)0
[( ) ∂ψB ∂R
∂ψB ∂R
Rra)r0
R)1
ψS ) 0
(20)
]
C0 Vr WcD r0 , , ,3 , Rra)r0 Ca vta Fcr0vra ra
(21)
where Wc and Fc are the catalyst weight and density, respectively. It should be noted that, because ∂ψB/∂R is a new function (i.e., different from ψB), instead of ψB, its derivative at the pellet boundary appears in eq 21. Each unique dimensionless group is equated to a constant, preferably unity. This makes the magnitude of the reference quantities proportional or comparable with those characteristic of the system. In the present system, there are three unknowns (reference quantities) and seven algebraic equations. Therefore, in addition to dimensionless variables, four dimensionless parameters appear in the dimensionless form of the model and the system is overdetermined. The solution of the three equations yields the reference quantities, for example,
∂ψB ∂R
R)1
τ′D ,3 Fcr02
]
)
(22) (23)
(
kA p r02 , ,k τC 2 D τ D P 0
)
(24)
and upon substitution into eq 23, the following is obtained:
(
p r02 τ′D ,k τC 2,3 ψS ) h1 θ,r0 , D τ D P 0 Fr2 k 2 A
c 0
)
(25)
The variables appearing within the dimensionless groups may be either kinetic (D, r0, kP, kA) or operational variables (C0, τ′, τ). The dimensionless groups can be rearranged such that each variable of interest occurs only in one dimensionless group, thereby separated for analysis. Because in this work operating variables are of interest, these are separated through a suitable combination of the dimensionless groups as follows:
(
) 0 (19)
( )
) f1 θ,ψS,r02
ψS ) h2 θ,r02
and therefore
ψS ) g θ,
( )
(17)
The functional relationship for the intrapellet concentration, thus, becomes
kA p r02 , , k τC 2 D τ D P 0
in which τ′ ) Wc/v is a capacity factor for the reactor called the weight time. From eq 22, we obtain the derivative term as
(16)
R)1
[
ψS ) g θ,
2
kAra p ra ∂ψB ∂ψB 1 ∂ R2 + RψB ) 2 ∂R ∂R D ta τD ∂θ R
raR ) r0
ψB ) f R,θ,ψS,r02
kA τ D r2 2 0 τ′D , k C , , D p r 2 P P 0 D F r 2 0
c 0
)
(26)
The second term in eq 26 is the square of the Thiele modulus for alkylation, φA, the third term is proportional to the ratio of the characteristic time for the reactor to that for the pellet, and the fourth one is proportional to the square of the Thiele modulus for the poisoning reaction, φP. Noting that the catalyst lifetime, tc, is the time required for the conversion to fall below a certain level (usually 90%), from eq 26, we obtain
(
0.1 ) h2 or
(
tc 2kA τ D r2 2 0 τ′D , k C ,r0 , , τ D p r 2 p P 0 D F r 2 0
c 0
tc kA τ D r2 2 0 τ′D , k C ) h r02 , , τ D p r 2 p P 0 D F r 2 0
c 0
)
)
(27)
(28)
Equation 28 shows that the dimensionless lifetime is a function of four dimensionless groups incorporating all of the important variables. The form of the function h may be postulated and checked using experimental data.
Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 3889 Table 1. Parameters of Equation 30 from Fitting of Experimental Data experimental data source
p
Taylor and de Jong et al.6 a
q
-1.01 -1.08
Sherwood8
1.05 1.39a
n+1 0.293 1.39a
ln c2
tc
-5.73 -4.03
0.00352τ0.29C0-2.0τ′1.1 0.0178C0-2.2τ′1.4
In this case, q and n cannot be obtained independently; therefore, q + (n + 1) is given.
Figure 2. Comparison of eq 30 (solid line) with experimental data for the USHY zeolite at 367 K. τ ) 0.42-1.8 h, C0 ) 0.17-0.54 kmol/m3, τ′ ) 60-240 kg‚h/m3, and r0 ≈ 0.8 mm. Experimental data were from ref 8.
Development of the Correlation. To obtain a correlation among the variables of eq 28, one should first postulate a functional correlation and then check it with experimental data. For this purpose, we assume that the lifetime can be expressed by a power law as follows:
( ) ( )(
tc kA ) c1 r02 τ D
m
τ D p r 2
n
)( )
2 p
r 2 0
pkPC0
D
0
q
τ′D Fcr02
(29)
where c1, m, n, p, and q are dimensionless constants. Because the objective of this study is to develop an empirical correlation for catalyst lifetime in terms of operating variables, the fitting may be performed using the following simplified equation in terms of the operating variables:
tc ) c2τn+1(C02)pτ′q
(30)
in which c2 is a dimensional coefficient characteristic of the particular catalyst incorporating all of the kinetic parameters. The larger the value of c2, the greater is the catalyst lifetime. To obtain the constants, one may linearize eq 30 and utilize a multiple linear regression.11 Table 1 shows the results for two sets of experimental data using two types of zeolites as the catalyst. For the second set, because the catalyst loading has been constant throughout the tests, τ and τ′ could not be adjusted independently; thus, the exponents n and q appear in combination. As may be observed, the exponents obtained for the two sets of data are very close and consistent, indicating that the selected form of the function is suitable. Figures 2 and 3 show a good fit of the experimental data with eq 30 employing the calculated exponents of eq 30. Using the values of the exponents reported in Table 1, eq 29 can be expressed as follows:
( )( ) (
kA tc ) c1 r02 τ D
m
τ D p r 2 0
-0.7
pkPC02
) ( )
r02 D
-1.0
τ′D Fcr02
1.1
(31)
The exponent m for the first dimensionless group appearing in eq 31 (square of the Thiele modulus) can be evaluated as follows. Because the reaction is strongly intraparticle-diffusion-limited,7 reactions occur only
Figure 3. Comparison of eq 30 (solid line) with experimental data for β zeolite at 363 K. C0 ) 0.27-0.54 kgmol/m3, τ′ ) 40-350 kg‚ h/m3, and r0 ≈ 0.075 mm. Experimental data were from ref 6.
within a thin outer shell of the pellets (i.e., the semiinfinite slab approximation). Therefore, catalysts of different sizes but the same total external surface area should exhibit similar behavior. Ultimately, the catalyst external surface area (3Wc/Fcr0) would appear in the correlation for the catalyst lifetime instead of any other combination of the weight, density, and size of the pellets. Consequently, because τ′ ) Wc/v, we obtain the following relationship among the exponents appearing in eq 29:
2m - 2n + 2p - 2q ) -q
(32)
Thus, the degrees of freedom of eq 29 are reduced by 1. Using data of Table 1 and eq 32, one obtains m ) 0.83. Therefore, the exponent of the Thiele modulus in the correlation is obtained without requiring its values to be fitted, and eq 29 becomes
( )( ) (
kA tc ) c1 r02 τ D
0.8
τ D p r 2
) ( )
2 -1.0
r 2 0
-0.7
pkPC0
0
D
τ′D Fcr02
1.1
(33) Based upon the above discussion, in the case of nonspherical catalyst pellets, r0 may be replaced by an equivalent radius, that is, the radius of a sphere having the same external area as the catalyst pellet. Results and Discussion Although in obtaining the exponents of eq 29 we did not use the kinetic parameters, the dependence of the lifetime upon them is obtained intrinsically because they are involved within the dimensionless groups. The effect of the acid site concentration, for example, can be investigated through its effects on rate constants in the following way. The rates of both reactions (1) and (2) may be considered to be proportional to the concentration of the active sites (per catalyst volume). Therefore, from eq 3, the following correlation describes the dependence of the rate constant on the acid site concentration:
kA ) k/A[S0]
(34)
where [S0] is the concentration of sites per catalyst volume and k/A is the rate constant per site. On the
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other hand, because it was assumed that eq 2 is the main route for catalyst deactivation, the rate of loss of active sites may be considered to be proportional to the rate of eq 2. In other words,
-d[S]/dt ) k1kDRCB2
(35)
where kD ) k/D[S0] and k/D is again the rate constant per site. Then, upon replacement in eq 35, we obtain
-
1 d[S] dR )) k1k/DRCB2 dt [S0] dt
(36)
Upon comparison with eq 4, it is concluded that the rate constant of eq 4 is independent of the site concentration. Therefore, upon replacement of the functionality with the rate constants in eq 33, we obtain
(
k/A tc ) c1 r02 [S0] τ D
)( ) ( 0.8
τ D p r 2 0
-0.7
pkPC02
Figure 4. Catalyst lifetime versus acid site concentration of various NaH-BEA samples. T ) 348 K, p ) 30 bar, and WHSV ) 0.2 h-1. Experimental data were from ref 12.
) ( )
r02 D
-1.0
τ′D Fcr02
1.1
(37) Because the TOS behavior of alkylation is characterized by nearly complete butene conversion during its active phase, followed by a rapid decline in conversion at the end of the catalyst’s life (Figure 1), the moles of butene turned over per unit of catalyst weight may be described in the following way:
∆NB tcvC0 VrC0 tc ) ) Wc Wc Wc τ
(38)
Therefore, when all parameters are constant, the catalyst life in terms of both TOS and butene turnover per unit of catalyst weight is proportional to the initial density (per volume or weight of catalyst) of sites raised to the power 0.8. This shows that the higher the density of acidic sites, the higher the catalyst lifetime and the butene turnover per unit of catalyst weight. The validity of these correlations may be tested against independent experimental data. Nivarthy et al.12 used a series of H-BEA zeolites with varying degrees of Na+ exchanged. The catalysts thus modified had various acid site concentrations according to the amount of Na ion incorporated. Other important physicochemical properties of the NaH-BEA catalysts such as the Si/Al ratio, Brunauer-Emmett-Teller surface area, and micropore volumes were nearly identical in all samples. Their acid site strengths were also nearly the same, as indicated by the fact that their temperature-programmed desorption spectra for NH3 had similar shapes and nearly identical peak temperatures. The catalysts were tested in a CSTR. Figures 4 and 5 show plots of the catalyst life versus the acid site densities. As may be observed, the exponent 0.8 for the acid site concentration as predicted by eqs 37 and 38 is confirmed by the experimental data. This gives an important characteristic of a solid acid to be considered in the “design” of a stable solid-acid catalyst for alkylation. In addition to this, one should note that, at the same time, the catalyst should have sufficiently large pores to minimize the effects of pore-mouth plugging shown to have an adverse effect on the TOS behavior of a solidacid catalyst.13 Because the acid site concentration and the pore size vary in opposite directions, when developing (optimizing) the catalyst, one should look for a compromise between these two important factors.
Figure 5. Variation of the butene turnover number prior to deactivation with catalytic sites. P/O ) 10, WHSV ) 0.2 h-1, T ) 348 K, and p ) 30 bar. Experimental data were from ref 12.
Similarly, temperature is an important operating variable, which does not appear explicitly in these correlations. Nevertheless, the effect of temperature may be deduced by applying the functionality of the kinetic and transport constants with temperature. Neglecting the effect of temperature on diffusivity and applying the Arrhenius law for the rate constants of the alkylation and poisoning reactions result in the following expressions:
kA ) kA0 exp(-EA/RgT) kP ) kP0 exp(-EP/RgT) and
(
)
-mEA - pEP tc ) cT exp τ RgT
(39)
Therefore, when other variables are kept constant, the temperature sensitivity of the catalyst lifetime would depend on the magnitudes of the activation energies of the main and poisoning reactions. Because both of the reactions proceed through similar carbocation intermediates, it is expected that the activation energies are comparable and thus the temperature would not have a significant effect in the range of interest. Figure 6 represents a plot of eq 39 using experimental data indicating that this conclusion is satisfied. However, the experimental points do not lie perfectly on a straight line, predicted by eq 39. Equation 39 is valid only for the range of temperature in which reactions (1) and (2) are the only important reactions in butene consumption and deactivation, respectively. This is only the case for lower temperatures. At higher temperatures, however, other secondary
Ind. Eng. Chem. Res., Vol. 42, No. 17, 2003 3891
Figure 6. Dependence of the catalyst lifetime on absolute temperature. C0 ) 0.17 kmol/m3, τ′ ) 140 kg/h‚m3, and τ ) 0.95 h. Experimental data were from ref 8.
reactions such as cracking become increasingly important, thereby further reducing the catalyst lifetime. At lower temperatures, oligomerization reactions are enhanced. Therefore, there is an optimum temperature in which alkylation is the dominant reaction and the lifetime is maximized (Figure 6). Equation 30 is useful for comparison of catalysts tested under different operating conditions and, therefore, for catalyst screening purposes. Accordingly, a comparison of the values of c2 in Table 1 reveals that the catalyst used in the second set of experiments is more desirable in terms of its stability (lifetime). Because both catalysts were tested under nearly identical temperatures, this difference may be attributed largely to the much smaller average particle size in the case of the second catalyst, which provides a higher external area under similar loading. However, comparing the ratio of the c2’s with that of particle radii and noting eqs 29 and 30, we conclude that the first catalyst would be superior if both particle sizes were the same. Equation 29 together with its calculated exponents implies that at a constant temperature, among the operating variables given in that equation, the olefin feed concentration has the greatest influence on the catalyst lifetime. As noted in this work, the application of the dimensional analysis approach to solid-acid-catalyzed alkylation results in an explicit correlation for catalyst life showing the relative importance of different catalyst characteristics and operating variables. Alternative methods, such as neural network simulation or statistical analysis, act as a “black box” that offers no insight into such issues. More importantly, models based on dimensional analysis can predict the effect of variables that remain unchanged during experimentation and are therefore not included in the fitting. An example, mentioned earlier, is the effect of the acid site concentration on catalyst life, whose dependence was well predicted. To this, one might add the use of a minimal set of experimental data as another advantage of the dimensional analysis method. The model developed in this work is applicable to liquid-phase, solid-acid-catalyzed alkyation in a CSTR under isothermal conditions. The most important assumption of the model is high I/B in the reaction zone, which is practical under “normal” operating conditions in a CSTR, that is, rather high I/B in the feed or high butene conversions. The rate expressions proposed for kinetics of reactions are applicable to catalysis by Bro¨nsted acid sites in which the protonation of the olefin is the initiation step of the reactions. The excess isobutane together with the high heat capacity of the liquid phase makes the isothermal assumption logical.
The fact that all solid acids exhibit a deactivation behavior similar to that shown in Figure 1 implies that solid-acid-catalyzed systems are essentially similar chemically and that the catalyst lifetime may be expressed by a single general correlation. This is reflected in the close agreement of the exponents calculated in the previous section and the reasonably straight lines obtained in both cases. However, it should be realized that, for catalysts other than zeolites, slightly different values for the exponents are expected. This is due to the difference in acid strength distribution, pore structure, and extent of pore clogging, features not included in the present model. A similar argument may be made for a given catalyst at two widely different temperatures because of the violation of chemical similarity. Conclusions Using dimensional analysis, it was shown that the dimensionless lifetime in liquid-phase alkylation in a CSTR is a function of four dimensionless variables including all of the important kinetic and operational parameters. The fitting of experimental data showed that a power law has the capability of correlating the lifetime with the parameters for a wide range of operational variables. The constants obtained for different sets of experimental data were very similar, implying that the lifetime can be expressed by a single correlation. In the limiting case of a very large Thiele modulus, which occurs in liquid-phase alkylation, it was shown that all of the exponents are not independent and one can be obtained in terms of the others. Among the various operating variables, the effect of the olefin feed concentration on the catalyst lifetime was found to be the most significant. On the other hand, under normal alkylation conditions, the effect of the operating temperature was modest, although there is an optimal operating temperature in terms of the catalyst lifetime. The solution of the mathematical model based on the pseudo-steady-state assumption yields a power-law form for the catalyst lifetime.3,13 A comparison of the results of the present empirical model with that of the above model shows that the exponents obtained for the feed concentration and Thiele modulus in the correlation for the catalyst lifetime are the same in both models while other exponents are in good agreement. A more detailed discussion may be found elsewhere.13 Symbols Used A ) alkylate C ) concentration (kmol/m3) D ) diffusivity (m2/s) D ) dimer I ) isoparaffin kA ) alkylation pseudo rate constant (s-1) kP ) poisoning pseudo rate constant (kmol2‚m-6‚s-1) m ) exponent n ) exponent p ) exponent q ) exponent R ) dimensionless radial distance Rg ) gas constant (J/kmol‚K) r ) radial distance (m) rA ) reaction rate (kmol/m3‚s) r0 ) pore radius (m) T ) absolute temperature (K) t ) time (h or s)
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tc ) catalyst lifetime (h or s) v ) feed volumetric flow rate (m3/h) V ) volume (m3) Wc ) catalyst loading (kg) X ) olefin conversion, dimensionless variable x ) dimensional variable Greek Letters R ) point activity ) porosity or void volume θ ) dimensionless time F ) catalyst density (kg/m3) τ′ ) weight time (kg‚s/m3 or kg‚h/m3) τ ) space time (h or s) φ ) Thiele modulus ψ ) dimensionless concentration Subscripts a ) reference quantity A ) alkylate B ) butene c ) catalyst P ) poisoning r ) reactor S ) pellet surface 0 ) initial or output
Literature Cited (1) Rao, P.; Vatcha, S. R. Solid-acid Alkylation Process Development is at Crucial Stage. Oil Gas J. 1996, 94, 56. (2) Weitkamp, J.; Traa, Y. Isobutane/butene Alkylation on Solid Catalysts. Where do We Stand? Catal. Today 1999, 49, 193. (3) Sahebdelfar, S.; Kazemeini, M.; Khorasheh, F.; Badakhshan, A. Deactivation Behavior of the Catalyst in Solid AcidCatalyzed Alkylation: Effect of Pore Mouth Plugging. Chem. Eng. Sci. 2002, 57, 3611.
(4) Barger, P. T.; Frey, S. J.; Gosling, C. D.; Sheckler, J. C.; Hammershaimb, H. U. Integration of Experimental Methodology and Modeling in Development of the Alkylene Process, Utilization of Light Ends, Anaheim, CA, Mar 21-25, 1999; ACS Symposium Series; American Chemical Society: Washington, DC, 1999. (5) D’Amico, V. J.; van Broekhoven, E. H.; Nat, P. J.; Nousiainen, E. H.; Jakkula, J. The AlkyClean Process: A New Solid Acid Catalyst Gasoline Alkylation Technology. NPRA Annual refining meeting, San Antonio, TX, Mar 17, 2002. (6) de Jong, K. P.; Mesters, C. M. A. M.; Peferoen, D. G. R.; van Brugge, P. T. M.; de Groot, C. Paraffin Alkylation Using Zeolite Catalysts in a Slurry Reactor: Chemical Engineering Principles to Extend Catalyst Lifetime. Chem. Eng. Sci. 1996, 51, 2053. (7) Simpson, M. F.; Wei, J.; Sundaresan, S. Kinetic Analysis of Isobutane/butene Alkylation over Ultrastable H-Y Zeolite. Ind. Eng. Chem. Res. 1996, 35, 3861. (8) Taylor, R. J.; Sherwood, D. E., Jr. Effects of Process Parameters on Isobutane/2-butene Alkylation Using a Solid Acid Catalyst. Appl. Catal. A 1997, 155, 195. (9) Corma, A.; Martinez, A. Chemistry, Catalysts, and Processes for Isoparaffin-olefin Alkylation: Actual Situation and Future Trends. Catal. Rev., Sci. Eng. 1993, 35, 483. (10) Churchill, S. W. The Interpretation and Use of Rate Data; McGraw-Hill: New York, 1974; Chapters 8-10. (11) Carnahan, B.; Luther, H. A.; Wilkes, J. O. Applied Numerical Methods; Wiley: New York, 1969; Chapter 8. (12) Nivarthy, G. S.; Seshan, K.; Lercher, J. A. The Influence of Acidity on Zeolite H-BEA Catalyzed Isobutane/n-butene Alkylation. Microporous Macroporous Mater. 1998, 22, 379. (13) Sahebdelfar, S. Preparation and Evaluation of a Solid Acid Catalyst for Alkylation of Isobutane with Butenes. Ph.D. Dissertation, Sharif University of Technology, Tehran, Iran, 2002.
Received for review March 18, 2003 Revised manuscript received June 9, 2003 Accepted June 12, 2003 IE030250Z
