Dehydrogenation of I-Butene into Butadiene. Kinetics, Catalyst Coking, and Reactor Design Francis J. Dumez and Gilbert F. Froment' Laboratoriurn voor Petrochernische Techniek. Rijksuniversiteit, Gent, Belgium
The kinetics of 1-butene dehydrogenation over a Cr203-AI203 catalyst between 490 and 600 OC were determined in a differential reactor. The discrimination between rival Langmuir-Hinshelwood models was based on a sequentially designed experimental program. The kinetics of coking from butene and butadiene and the deactivation functions for coking and for the main reaction were determined with a thermobalance. The equations derived from differential reactor results gave excellent predictions of the performance of an experimental integral reactor. The effect of internal transport limitation was investigated. An industrial reactor was simulated and optimized.
I. Introduction An important fraction of the world butadiene production is obtained by dehydrogenation of n-butane or n-butene. This reaction is accompanied by side reactions leading to carbonaceous deposits which rapidly deactivate the catalyst. T h e coking tendency may be limited up to a certain extent either by diluting the feed with steam or by operating under reduced pressure. T h e second solution has been favored. T h e butadiene production using vacuum processes amounted to 700000 T in 1971 (Hydrocarbon Process., 1971). With vacuum processes operating with butene as feed, the on-stream time is limited to 7-15 min, after which regeneration of the catalyst by burning off the coke is required. With such cycle times the heat given off by the regeneration compensates for the heat requirements of the adiabatic dehydrogenation (Hornaday e t al., 1961; Thomas, 1970). Vacuum processes are based upon Crz03-Al203 catalysts. Fundamental properties of such catalysts were studied by Burwell et al. (1969), Poole and MacIver (19671, Marcilly and Delmon (1972), Masson and Delmon (1972), Traynard e t al. (1971, 1973). These authors found that the catalytic activity was represented by surface Cr3+ and 0'ions which are incompletely coordinated; ions of y-CrzO3A1203solid solutions were found to be the most active. Aspects of the kinetics of butene dehydrogenation on such catalysts were investigated by Forni e t al. (1969), Happel e t al. (1966), and Timoshenko and Buyanov (1972). Although the surface reaction was generally found to be rate determining, there is little more agreement between the results. Further, none of these studies was carried out with particle sizes used in industrial operation. So far, no quantitative treatment of the deactivation of the catalyst by coke deposition has been published. Yet, without such information no rigorous optimization of industrial operation is possible. This paper reports on a detailed study of the kinetics of the dehydrogenation, of the coke deposition, and of the associated catalyst decay. The effect of internal transport limitations is investigated. Industrial operation is simulated and optimized. 11. Kinetics of the Main Reaction
11.1. Experimental Procedure and Range of Operating Variables. T h e catalyst used in this investigation was a Cr203-Al203 catalyst containing 20 wt % Crz03 and having a surface area of 57 m2/g. Experimental checks on the
absence of partial pressure and temperature gradients in t h e film surrounding the particle and of temperature gradients inside the particle were performed. Also, preliminary runs were carried out in order to determine the catalyst particle size which permits neglecting internal transport limitation. The kinetics of butene dehydrogenation were determined in a quartz tube inserted in an electrical furnace. The catalyst particles, diluted with quartz particles, were supported by a stainless steel gauze. The temperature was controlled by two thermocouples, one in the center of the catalyst section and one near the wall. T h e feed stream was calibrated and dried in the classical way, The outlet gases were analyzed by gas chromatography on a 20% propylene carbonate/chromosorb column. Experiments were performed a t 4 temperatures: 490, 525, 560, and 600 "C. T h e butene pressure ranged from 0.02 to 0.27 atm, the hydrogen pressure from 0 to 0.10 atm, and the butadiene pressure from 0 to 0.10 atm. Although only 1butene was fed, the outlet gases always contained a mixture of 1-butene, cis-2-butene, and trans-2-butene close to the equilibrium composition. Therefore, the dehydrogenation equilibrium could be referred to butene equilibrium mixtures. In all these experiments, the conversion was kept below 2% by adjusting the amount of catalyst and the gas flow rates. Therefore, the reactor was considered to be differential. Due to coke deposition the dehydrogenation rate was found to decrease with time. T o determine the rate of the main reaction in the absence of coke required extrapolation to zero time. Since the first analysis was taken after 2 min, while a run extended to 30 min, the extrapolation was no problem. 11.2. Kinetic Analysis. Five possible reaction schemes, shown in Table I, were derived for the main reaction. For each of these mechanisms several rate equations may be derived, depending upon the postulated rate-determining step. Fifteen possible rate equations were retained. They are listed in Table 11. The experimental program was designed to discriminate in an optimal way between the rival models. Sequential procedures for optimal discrimination have been introduced by Box and Hill (1967) and by Hunter and Reiner (1965). The methods have been applied to experimental data, but only a posteriori, for illustrative purposes (Froment and Mezaki, 1970). The present work is probably the first in which the experiments were actually and exclusively designed on the basis of a sequential discrimination proInd. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
291
Table I. Reaction Schemes for Butene Dehydrogenation (a) Atomic Dehydrogenation; Surface Recombination of Hydrogen (1) B + L = B L (a11 (zj BL+L-ML+HL (a2) (3) M L + L t D L + H L (a3) (a4j (4j D L = D + L ( 5 ) 2HL+ H,L + L ( 6 ) H,L + H, + L (where B = n-butene; D = butadiene; H, = hydrogen; M = an intermediate complex) ( b ) Atomic Dehydrogenation; Gas Phase Recombination of Hydrogen (1) B + L t BL (bl) (2) B L + L + M L + H L (b2) (3) M L + L t M L + H L (b3) (4) D L t D + L (b4) ( 5 ) 2HL + H, + 2L (c) Molecular Dehydrogenation (1) B + L = B L (cl) ( 2 ) BL + L + DL + H,L (c2) (3) D L + D + L (c3) ( 4 ) H,L + H, + L ( d ) Atomic Dehydrogenation; Intermediate Complex with Short Lifetime Surface Recombination of Hydrogen (1) B + L + B L (dl) ( 2 ) BL + 2L t DL + 2HL (d2) (3) D L + D + L ( 4 ) 2HL= H,L + L ( 5 ) H,L + H, + L (e) Atomic Dehydrogenation; Intermediate Complex with Short Lifetime; Gas Phase Hydrogen Recombination (1) B + L t B L (el) ( 2 ) BL + 2 L + DL + 2HL (e2) (3) D L = D + L ( 4 ) 2HL t H, + 2L cedure. The operating conditions for an experiment were selected on the basis of the design criterion. Then the experiment was carried out, the parameters of the models were estimated, and the current state of adequacy of the rival models was tested. With this information the next experiment was designed and so on, until the discrimination was achieved. Eventually, some further experiments were carried out to improve the significance of the parameters of the retained model(s). The sequential choice of experimental conditions for optimal discrimination between the rival models was based upon the following design criterion m
D
=
m
- PH,q
lPHLo 1=1, = 1
(1)
the experimental error variance obtained from each of the rival models. This is done by means of Bartlett's x2 test (Bartlett, 1937). The details of the procedure, the designed operating conditions, and the evolution of the discrimination will be reported elsewhere (Dumez et al., to be published). Suffice it to mention that a t 525 "C, e.g., a total of 14 experiments, 7 of which were preliminary, i.e., required to start the sequential design, allowed discarding all the models except a2, b2, c2, d2, and e2, all corresponding to surface reaction on dual sites as rate-determining step. The differences PH,O - PH,O between these models were smaller than the experimental error. The models a2, b2, and d2 were eliminated because they contained a t least one parameter that was not significantly different from zero a t the 95% confidence level. Model c2, corresponding to molecular dehydrogenation and the surface reaction on dual sites as rate determining step, led t o a fit which was slightly superior to that of e2 and was finally retained. The same conclusion was reached a t 490,560, and 600 "C. I t should be pointed out here how efficient sequential design procedures for model discrimination are. A classical experimental program, less conscious of the ultimate goal, would no doubt have involved a much more extensive experimental program. The parameters of model c2 were estimated by minimizing
for all the data 1 = 1, . . . , N a t the four temperature levels. This involves nonlinear regression. Indeed, the expression for r ~ according 0 to model c2 is
in which the adsorption equilibrium constants KB,KH,and K D are related to the equilibrium constants of the steps of the reaction in the following way (4) Statistical tests indicated that the adsorption equilibrium constants were not significantly temperature dependent. The rate coefficient ~ H obeyed O the Arrhenius temperature depend en ce kHo
= AH' exp(-EH/RT)
(5)
Reparameterization according to
If'
where PH,O represents the estimated value of the reaction rate according to model i, and D is the divergence between the predicted rates. T h e double summation ensures that each model is taken in turn as a reference. Given n - 1 experiments the n t h experiment was performed in the differential reactor a t those values of p ~p , ~and , p~ which maximized D. A grid is selected for possible combinations of p ~p , ~and , p~ within the operability region. From previous experience on constructed examples the criterion (1) was shown to lead to the same experiments as the Box-Hill criterion that accounts for the variances. T h e state of model adequacy was tested by means of a criterion proposed by Hosten and Froment (to be published). The underlying idea is that the minimum sum of squares of residuals divided by the appropriate number of degrees of freedom is an unbiased estimate of the experimental error variance for the correct mathematical model only. For all other models this quantity is biased due to a lack of fit of the model. The criterion for adequacy therefore consists in testing the homogeneity of the estimates of 292
Ind. Eng. Chem., Process Des. Dev., Vol. 15.No. 2, 1976
AH' = AH" exp(EH/RT,)
(6)
with T, the average temperature, facilitated the estimation. The values of the parameters and their standard deviations are given in Table 111. The Arrhenius plot for ~ H O is given in Figure 1. The dots represent the parameter values obtained from a treatment of the data per temperature. 111. Kinetics of Coking The kinetics of coking and the deactivation functions for coking and for the main reaction were determined by means of a Cahn RH thermobalance. The catalyst was placed in a stainless steel basket suspended a t one balance arm. The temperature was measured in two positions by thermocouples placed just below the basket and between the basket and the quartz tube surrounding it. The temperature in the coking experiments ranged from 480 to 630 "C, the butene pressure from 0.02 to 0.25 atm, and the butadiene pressure from 0.02 to 0.15 atm. Individ-
Table 11. Rate Equations for Butene Dehydrogenation
\
I
'Ha
Table 111. Kinetic Coefficients and Adsorption Constants of Butene Dehydrogenation Parameter
Value
Approx. std dev
AHO(T, = 815.36 K )
0.2697 2 9236 1.727 3.593 38.028
0.0298 732 0.342 0.641 6.165
EH
KB KH KD
ual components as well as mixtures of butene and butadiene, butene and hydrogen, and butadiene and hydrogen' were fed. The hydrogen pressure range was 0-0.15 atm. Coke deposition on the basket itself was always negligible. The deactivation function for coking was determined from the experimental coke vs. time curves as described below. Coke was shown to be deposited from both butene
and butadiene, while hydrogen exerted an inhibiting effect. An example of the coke content of the catalyst as a function of time is given in Figure 2. Since the thermobalance is a differential reactor, operating a t point values of the partial pressures and the temperature, the decrease in the rate of coking observed with increasing coke content reflects the deactivating effect of coke. The rate equation for coke formation therefore has to include a deactivation function, multiplying the rate in the absence of coke. dCc dt
-= rcO pc
(7)
rco is the initial coking rate, a function of the partial pressures and temperature which reduces to a constant for a given experiment in the thermobalance. Several expressions were tried for cpc (Froment and Bischoff, 1961). Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
293
the results of Depauw and Froment (1975) obtained with a completely different system. An explanation based upon a pore blocking mechanism has been attempted (Dumez and Froment, to be published). The parameter a was found to be identical for coking from either butene or butadiene and independent of the operating variables, as can be seen from the partial correlation coefficients between a and T,p ~ , p ~ and , p ~ respectively, , shown in Table IV. This table also contains the calculated t values for the zero hypothesis for the partial correlation coefficients. The t values do not exceed the tabulated value of 2.03 for the 95% probability level. The determination of the complete rate equation for coke deposition required the simultaneous treatment of all experiments, so that p ~ p , ~p , ~and , T were varied. The exponential deactivation function was substituted into the rate equation for coking. After integration of the latter the parameters were determined by minimization of
+ model t 2 o model e 2
t 2 calc
115
120
125
Figure 1. Arrhenius diagram of
130
bl
k"O.
Several rate equations, either empirical or based on the Hougen-Watson concept, were tested. The best global fit was obtained with the following equation.
with
kCeo = Aceo exp(-EcB/RT)
(12)
kcDo = A o o exp(-EcD/RT) and KCH independent of temperature. The integrated equation used in the objective function (10) was
v
c
0
2
1
1
Figure 2. C, vs. t measured on the thermobalance.
Again the frequency factors Aceo and ACD' were modified as follows
ACB' = ACB" exp(EcB/RTm)
pc = exp(-aC,) p.2 = 1 -
ac,
ACD' = ACD" exp(EcD/RT,)
p, = (1- aC,)2 47, = $0,
+
1/(1 CYC,)
+
= 1/(1 CYC,)2
Note that the deactivation function is expressed in terms of the carbon content of the catalyst, not in terms of time as has been done frequently; indeed, time is not the true variable into eq 7 and integration with respect to time yields respectively
(9)
to facilitate the parameter estimation. The parameter values and their approximate standard deviation are given in Table V. An example of the fit obtained with this equation is shown in Figure 2. The frequency factors Aceo and ACDO are easily calculated from (14)
Ace0 = 1.559 X lo8 A
~ = 5.108 ~ O x 105
Since the order with respect to butene, ~ C B and , to butadiene, ncD, is smaller than 1, it has been attempted to derive an adequate mathematical model based on the LangmuirHinshelwood or Hougen-Watson concept. The formation of what is called cokes proceeds over a sequence of steps involving addition and/or dehydrogenation. Let the rate-determining step in this sequence be represented by IlBL
IlDL
a and rCo were determined by fitting of the experimental data by means of a least-squares criterion. For the majority of the 50 experiments pc = exp(-aC,) turned out to give the best fit. This, by the way, agrees with Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 2, 1976
-
+ (nBB)L
for coking from butene, and by
294
(14)
+ (nDD)L
IhBL
ZhDL
for coking from butadiene. Z ~ B Land Z~DLare adsorbed lower intermediates in equilibrium with butene and butadiene and I h B L and I h D L higher intermediates. For pure addition ne and n D would be unity, for pure dehydrogena-
Table IV. Test of Partial Correlation Coefficients between CY and the Independent Variables p Value
t Value
-0.1612 0.98
+0.3042 1.92
-0.0627 0.38
-0.0530 0.32
Table VI Values of the parameters of the Langmuir-Hinshelwood Model
__
Parameter
Value
Approx. std dev
CY
39.67 0.6049 30873 0.970 148.66 18117 1.767
1.724 0.0694 1300 0.051 18.77 7 84 0.034
AcB"(T,
ACD Approx.
Value 45.53 0.2917 32800 0.743 1.3168 21042 0.853 1.695
822.8 K )
n C B o,
Table V. Kinetic Parameters for Coking Parameter
= ECB
std dev
ECD nCD
1.08
0.0209 7 58 0.029
0.1158 501 0.023 0.076
n B
+1
nCD = n D
+1
nCB
=
KB,K H ,and K D have already been estimated (section 11.2). , n C B , AcDO, E C D ,ncD, and CY were The values of A c B ~ ECB, tion zero, whereas if both mechanisms would be involved in the rate-determining step ne and n D would be between zero and one. Neglecting possible reverse reactions the rate of coking may be written
rc = k c B ' C r l B r , C i n p B ) I , -k
kcD'CIlnL CinoD)L
(15)
The unmeasurable concentration of adsorbed species can be eliminated by accounting for the equilibria between butene and butadiene and the lower intermediates, so that (15) becomes
From (16) the concentration of free active sites C I may ~ be eliminated in favor of bulk partial pressures by means of a balance on the total number of active sites. When the concentrations of the adsorbed lower intermediates are neglected with respect to the concentrations of adsorbed butene, butadiene, and hydrogen, CL is given by CL =
C t L - CSL 1 + KBPB+ K n P H
+ KDPD
(17)
with C t L the total number of active sites and CSL the number of sites covered by coke. The coking rate becomes
k C H ' K I i e L PBnB+'
f kCD'KIiDL pDnDtl
(18) (1 + K B P R+ K H P H+ I ~ D P D ) ~
A deactivation function for the coking may now be defined by
T h e problem with this function is that it contains the inaccessible concentration of adsorbed higher intermediate. There is no way out, here, except to resort to the empirical relation between coke and the deactivation derived from the experiments, qc = exp(-pCc). When this expression is substituted into (181, the resulting equation can be integrated with respect to time, since the partial pressures and temperature remain constant in the thermobalance experiments, to give
where
estimated by nonlinear regression and are given in Table VI [AcBO and ACB' were also modified according to (14)]. From the values of n c B and ncD, it can be concluded that the rate-determining step for coking from butene would be dehydrogenation step
+
I~BL L
+
+H 2 L
Z~BL
T h e activation energy E C B agrees remarkably well with that found for dehydrogenation of butene. The rate-determining step for coking from butadiene would be
IlDL
+ (0.75g)L
-
IhDL
i.e. would mainly consist of addition. The value for ECD seems to support this conclusion. The accuracy of the Langmuir-Hinshelwood model (18) is lower than that of model ( l l ) , however. This is believed t o result, partly a t least, from the lower mathematical flexibility of eq 18 as compared to (11). In addition, the Langmuir-Hinshelwood model is probably oversimplified. On the other hand and apart from kinetics, the approach seems to lead to some interesting conclusions as to the mechanisms of coking.
IV. Effect of Coke on the Rate of Dehydrogenation The deactivation function for the dehydrogenation was also determined by means of the thermobalance, in the same way as done by Tackeuchi et al. (1966) and by Ozawa and Bischoff (1968), i.e., by measuring simultaneously the coke content and the composition of the exit gases as functions of time. T o eliminate the effect of bypassing, the conversions were all referred to the one first measured. It was checked that the ratio of the amounts of gas flowing through and around the basket remained constant and was not affected by the coke deposition: in a regeneration experiment the burning rate, determined from the weight loss measured by means of the balance, completely agreed with that calculated from the amount of CO and COS in the exit gases, for the whole duration of the experiment. Figure 3 shows the relation between r H / r H n = and the coke content, easily derived from the measurements r H / r H o = p~ vs. time and coke content vs. time. Although there is a certain spread on the data, no systematic trend with respect to the temperature or the partial pressures could be detected. The temperature ranged from 520 to 616 "C; the butene pressure from 0.036 to 0.16 atm. Again, the best fit was obtained with an exponential function: VH = exp(-nC,). A value of 42.12 was calculated for a. The agreement with the value found for the deactivaInd. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
295
.O1
.02
04
.03
.05
.06
eration without prior investigation of the effect of the particle size on the rate of the overall process consisting of reaction and internal transport. The effect of transport phenomena inside the particle is generally expressed by means of the effectiveness factor, which has been related to the geometry of the catalyst, the effective diffusivity and the rate parameters of the reaction in a closed form only for single reactions and simple kinetics. Bischoff (1967) has proposed the use of a generalized modulus which allows handling any reaction rate equation along the lines developed for simple kinetics, but the method requires the reaction rate to be expressed as a function of the concentration of one component only. In the case studied here the amounts of butene and butadiene involved in coking reactions were too important to be neglected with respect to those involved in the main reaction. Therefore, three continuity equations had to be taken into account for the gaseous components. The equations may be written, for quasi-steady state conditions, negligible external transport resistance and isothermal particles
Figure 3. Activity of t h e catalyst for dehydrogenation vs. coke content.
(23)
tion parameter for the two coking reactions is remarkable. I t may be concluded that the main reaction and the coking reactions occur on the same sites. The set of rate equations may now be written 1.826 X loTexp(-29236/RT)
(
p~ - -
K
+ 1 8 7 2 7 +~ ~3.593pH + 3 8 . 0 2 8 ~ ~ ) ' exp(-42.12CJ 1.5588 x 10' e X p ( - 3 2 8 6 0 / R T ) p ~ O .+~ 5.108 ~ ~ X lo5 e x p ( - 2 1 0 4 2 / R T ) p ~ ~ . ~ ' ~ rc = exp(-45.53Cc) (1 + 1.695 6)' rH
=
(1
V. Experiments in a n I n t e g r a l R e a c t o r The equations derived from experiments in differential reactors were tested by a few experiments carried out in an integral reactor. In this reactor the catalyst bed was divided into five sections, separated by metal gauze, to enable unloading the catalyst in well defined sections a t the end of a run. The temperature was measured in each section by means of thermocouples. The exit gas compositions were measured as a function of time. The temperature varied during an experiment, because of deactivation of the catalyst. The catalyst particle size was the same as that used in the differential reactor. The experimental results were compared with those obtained by numerical integration of the continuity equations for the different species, containing the rate equations (21)-(22). The temperature variations were also accounted for through (21)-(22). Figures 4 and 5 show the results for a typical run (PB = 0.22 atm, T = 595 "C). The agreement between calculated and experimental results is excellent. I t is worthwhile noticing that there is hardly any coke profile. There are two reasons for this: coke is formed from both butene and butadiene, and hydrogen, a reaction product, inhibits the coke formation. VI. Influence of Catalyst P a r t i c l e Size The rate equations (21)-(22) were determined with catalyst particles small enough to eliminate resistances to internal transport. With experiments a t low temperatures, the diameter was 0.7 mm, a t higher temperatures 0.4 mm. Industrially the particle size is generally around 4 mm, to limit the pressure drop through the bed. Consequently, the results given above cannot be extrapolated to industrial op296
Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 2, 1976
(21) (22)
with boundary conditions
r = Re;
CB,k = CB; CH,k = CH; CD,k = CD
(24)
is expressed in kmollkg of cat. h, rCB and rCD in kg coke/ kg of cat. h. Therefore, the conversion factors $CB and $CD are required. They are expressed in kg of coke per kg of butene or butadiene involved in the coking and thus account for the loss of hydrogen associated with the coke formation. DB, DH, and DD are the effective diffusivities for butene, hydrogen, and butadiene and are related to the molecular and the Knudsen diffusivities. For butene, e.g. rH
The molecular diffusivities were calculated from a weighted average of the binary diffusion resistances. The binary diffusion coefficients were estimated from the formula of Fuller et al. (Reid and Sherwood, 1958). The calculation Of DB,k, DH,k, and DD,k requires information about the pore size. The catalyst studied had a bimodal pore size distribution. Further, via electron microscopy, it was found that the catalyst consisted of crystallites of about 5 p separated by voids of about 1 p. Consequently, the maximum length of the micropores with average diameter 70 A cannot exceed 5 p. I t is easily calculated that this is too short to develop any significant concentration gradients. Therefore, only the macropores with a pore volume of 0.155 cm3/g and with average pore diameter of 10000 A were considered in the evaluation of the Knudsen diffusivitY.
Table VII. Experimental and Calculated Effectiveness Factors with r = 5
d
R,, mm
p e , atm
T, "C
77 (exptl)
77 77 (calcd) (Bischoff)
2.3 2.3 2.3 2.3 0.6 0.35
0.2165 0.2159 0.2181 0.2492 0.2184 0.2038
500 550 550 599 580 595
0.334 0.187 0.199 0.140 0.521 0.808
0.346 0.229 0.229 0.135 0.493 0.621
rrp
~~
CalC
\
0.426 0.282 0.282 0.185 0.610 0.723
given particle size, by the true chemical rate calculated from (21). Except for 0.35 mm the agreement is excellent. T h e last column of this table contains the values obtained by means of the generalized modulus defined by Bischoff. However, t o do so, the coking reactions had to be neglected t o be able to express the reaction rate as a function of the concentration of one component only. The diffusivities were supposed t o remain constant in the whole particle. T h e generalized modulus is calculated by means of the following formula
10
20
30
40
50
I (mm)
Figure 4. Butadiene yield vs. time in the integral reactor. Ct
t
03-
.02
-
01 -
1
2
3
4
5
secllon
Figure 5 . Coke profile in the integral reactor. T h e effective diffusivities were allowed to vary with the composition inside the particle. The only unknown parameter left in the continuity equations is the tortuosity factor, T . This factor was determined from a comparison between the experimental rates a t zero coke content, measured in a differential reactor, and the surface fluxes. The latter were calculated, using Fick's law, and for a given T , from the concentration profiles obtained by numerical integration of eq 23. A value of 5 for T led to the best fit of the experimental data. This is the generally accepted value for the tortuosity factor in catalysts of the type used in this work. The calculated value for the effectiveness factor for dehydrogenation was obtained by dividing the calculated hydrogen flux a t the particle surface by the true chemical reaction rate. Table VI1 compares these values with those obtained by dividing the experimental rate corresponding to a
with L , the length of the pores and p the partial pressure of the component considered. The effectiveness factor is then evaluated from the graph given by Bischoff (1967). As can be seen from Table VII, t h e effectiveness factors determined in this way are higher than the values obtained through integration of the continuity equations. However, Bischoff showed the integral to be exact for plates only. When applied to spheres, the effectiveness factor may be overestimated, as pointed out by Aris (1957): the maximum deviation is observed around rj = 0.60 and amounts to 0.09. T h e values obtained here are also about 10% higher than t h e calculated ones. T h e Bischoff approach does not provide the concentration profiles inside the particles so that the coking of the catalyst cannot be predicted. T h e advantage of the method lies in the simplicity of the calculations as compared to the integration of the continuity equations. Figure 6 illustrates the partial pressure profiles inside the particle for zero deactivation and the coke profile after 0.25 h. The full lines correspond to the results obtained by numerical integration using a Runge-Kutta-Gill routine. T h e circles represent the partial pressures calculated by the collocation method (Villadsen, 1970), applied with constant effective diffusivities. Values based on the gas phase composition were used. The agreement is perfect and all in favor of the collocation method, which is much faster from the computational standpoint. The coke profile inside the particle is relatively flat and very similar to that measured in the integral reactor (Figure 5). If coke were formed from butene only a decreasing profile from the surface to the center of the particle would be observed; if coke would originate from butadiene only, the profile would be ascending (Froment and Bischoff, 1961; Masamune and Smith, 1966). The combination of both mechanisms and the inhibiting effect of hydrogen, whose concentration is maximum a t the center, leads to the actual profile. The optimization of the process, which will be discussed in a later section, required a large number of numerical integrations of the reactor model, including the set of equations ( 2 3 ) . The integration of this set in each node of the grid selected for the fluid field equations was the time consuming step in the reactor simulation, even when collocation was resorted to. A drastic simplification was required here, aiming a t eliminating the set of equations (23) by relating in an algebraic way the observed reaction rate to the conditions in the bulk of the Ind. Eng. Chem., Process Des. Dev., Vol. 1 5 , No. 2 , 1976
297
Table VIII. Characteristics of an Industrial Reactor for Butene Dehydrogenation Length Cross section
Catalyst and inert diameter Catalyst bulk density Inert bulk density Catalyst geometrical surface area Inert surface area
.10
I
Inlet total pressure Inlet butene pressure Molar flowrate Feed temperature Initial bed temperature
!5
0.8 m 1 m' 0.0046 m 400 kg of cat./m3 of diluted reactor 900 kg of cat./m3 of diluted reactor 274 mz/m3of diluted reactor 411 m*/m3of diluted reactor 0.25 ata 0.25 ata 1 5 kmol/m* cross section h 600 "C 600 " C
1.25
0
5
F
+ I = ;25
0
0
5
1
rlR,
Figure 6. Dehydrogenation rates, partial pressure, and coke profiles inside the catalyst particles.
fluid. T o do so, the effective reaction rate was calculated, for various temperatures and partial pressures in the bulk gas phase, as the surface flux derived from the profiles obtained by integration of the set (23). This effective rate was then plotted vs. the true reaction rate corresponding with the gas phase conditions selected. A unique curve was obtained, with very little spread (Dumez and Froment, to be published) and which could be expressed as rE = -0.0034
+ dO.O0685(r~+ 0.0067)
(27)
For large values of rH and thus for small values of 7, the effective rate becomes proportional to When both sides of (27) are divided by rH, the resulting equation behaves asymptotically like the relation between 7 and the Thiele modulus 4 for first-order irreversible reactions. Note that this simplification is only possible either in the absence of coke inside the particle or with uniform coke deposition. The butene and butadiene profiles in the reactor calculated in the way outlined above were in complete agreement with those obtained by the rigorous approach described in the next section.
6.
VII. Simulation of an Industrial Reactor Industrially the dehydrogenation is carried out around 600 "C in adiabatic reactors and under reduced pressure. The bed is diluted with inert particles which provide a heat reservoir that reduces to a certain extent the effect of endothermicity of the reactor. Due to catalyst deactivation the run length is generally limited to about 15 min, after which regeneration is necessary. Before the regeneration is started the reactor has to be purged. The heat given off during the regeneration restores the original temperature level in the reactor. After purging the reactor, butene may be fed again and a new cycle starts. The characteristics of a typical reactor and the operating conditions are given in Table VIII. The continuity and energy equations are as follows. Fluid phase: 298
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
where Ct = CB + CH + CD. Nonsteady-state terms were considered here. However, since the interstitial flow velocity is 4 m/sec and the bed length is only 0.8 m the second terms in the left-hand sides of the equations can be neglected. The product (uSC,) is kept under the differential in these equations to account for the important change in number of moles in the gas phase owing to the dehydrogenation and t o a certain extent to the coking. The righthand side in (31) expresses the amount of heat exchanged between the gas and the solid particles, catalytic and inert. Solid phase:
T h e second term in the right-hand side of (32) and (33) expresses the amount of heat exchanged between the catalyst and the inert particles, by conduction and radiation. Inside the catalyst particles
-++-2-a2CD,k 2aCDk t aCD,k - - PK (rH
ar2
r ar
DD at
DD
-
-)rCD ~CCDMD
(36) (37)
Again the nonsteady-state tcrms in (34), (35), and (36) can be neglected. Notice further that no energy equation is written for the catalyst particle, for the reasons already mentioned. The boundary conditions are
8 70
r=O
860. ~
The particle equations were solved by means of collocation, the continuity equations for the fluid phase by means of a Runge-Kutta-Merson routine, and the energy equations in a semianalytical manner. T h e heat transfer coefficients were calculated from the j H correlation (Handley and Heggs, 1968). The results of one rigorous computation are shown in Figures 7, 8, and 9. In Figure 7 the temperature is seen to drop rapidly under the initial value, due to the endothermic nature of the reaction. A temperature wave travels rapidly through the reactor as the reaction gradually extends to increasing depths. In the presence of coking no true steady state is reached, however; the temperature profile is slowly translated upward, because of the decrease in reaction rate due to the catalyst deactivation. The corresponding coke profiles are shown in Figure 8. The profile is decreasing, mainly because of the higher temperature a t the inlet and of the inhibition of the coke formation due to the hydrogen near the outlet. Figure 9 illustrates the butadiene flow rate a t the outlet as a function of time. The rapid initial decrease corresponds t o the initial temperature drop. Beyond this initial period, the decrease in production is much slower. The catalyst is deactivated by the coke deposition, but as the dehydrogenation rate is lowered the bed temperature slowly rises, thus favoring again the butadiene production.
VIII. Process Optimization As mentioned already in section VI, the large number of simulations involved in the optimization of the process necessitated the simplification of the system of equations 28-37 into the set (28-33), (37), and (27). This eliminated the integration of the particle equations in each node of the grid used in the integration of the fluid field equations. Further, to permit the simulation of nonisobaric situations arising with high flow rates, the Leva pressure drop equation was added to the model (Leva, 1959). Various aspects of the process were optimized: the conversion and selectivity, by the choice of reactor bed depth, flow rate and operating pressure; the dilution with inert material and the optimal on stream time (Dumez, 1975). Only the last aspect will be dealt with here. The adiabatic reactor considered here has a bed depth of 0.80 m, a cross-sectional area of 1 m2, and contains 800 kg of catalyst, undiluted. The initial catalyst temperature was taken to be uniform and equal to the inlet temperature. In industrial operation the initial temperature is not entirely uniform after regeneration and evacuation. I t follows from Figure 7, however, that the temperature profile is completely translated through the bed after 5 min so that the following calculations and results are believed to be sufficiently representative, certainly for the longer dehydrogenation periods of the order of 45 min. The butadiene yield, averaged over one complete cycle (including dehydrogenation, purge, regeneration and evacuation) is given by the following formula
~
850-
i I
1 840-
I 830 0
~~
OM
040
-
* 060
zlm)
Figure 7. Temperature profiles in the reactor.
tf
+ t,
The yield, I , is maximized by the optimal choice of the on stream time tf. But t , is a complex function of t f , through the coke content of the catalyst. The following expression was chosen for t ,
t, = t,
+ t , + A@,
(39)
with t , the purge time and t , the evacuation time, both equal to 2 min in industrial operation. The linear relation between the regeneration time and the average coke content of the catalyst is a reasonable approximation of the true relation: the rate of oxidation of coke is proportional to the coke content and decreases as the regeneration proceeds, but this is nearly compensated by the temperature rise of the bed. A value of 0.05 h/% coke was chosen for A. In Figure 10, the yield I and the average coke content are plotted vs. t,, the total cycle time for a reactor operating a t 600 "C, with inlet pressure of 0.30 ata and inlet flowrate of 20.4 kmol/m* h butene. I has a maximum for t , = 1.1 h. The corresponding average coke content of the catalyst amounts to 3.7%. This is much more than the content required to reheat the catalyst bed to the inlet gas temperature. T o avoid excessive temperatures in the reactor after regeneration, the inlet temperature of the regeneration gas would probably have to be monitored, for instance by admixing cold gas to the preheated stream. In industrial operation the dehydrogenation period is interrupted when the amount of coke deposited is sufficient to provide, during the regeneration, the heat compensating the heat lost during the on stream period (Hydrocarbon Process., 1971; Hornaday et al., 1961; Thomas, 1970); 1.5 to 2% coke suffices for this purpose. According to Figure 10 the cycle time is then 0.4 h, which is clearly suboptimal, not only for the butadiene yield, but also for the selectivity. Indeed, after Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
299
! \
1.015
1:OIO
0.01 1.005
t :0.025
* 0.2
0.6
0.4
0.8
Z(m)
Figure 8. Coke profiles in the reactor.
t (hr)
Figure 9. Outlet butadiene flowrate as a function of time.
0.1 h of dehydrogenation, the cumulative selectivity is only 0.776, after 0.3 h it amounts to 0.813, and after 0.9 h (the value of tf corresponding to the optimum) to 0.855.
‘t
Acknowledgment
F. Dumez is grateful to the Belgian “Nationaal Fonds voor Wetenschappelijk Onderzoek” for a grant over the period 1972-1974. This paper was presented a t the Sixtyeighth Annual Meeting of the American Institute of Chemical Engineers held in Los Angeles, Calif., Nov 16-20, 1975. Nomenclature = external surface of inert material, m2/m3 = external surface of catalyst, m2/m3 U ; k = contact surface between inert and catalyst, m*/m3 ci = specific heat of inert material, kcal/kg OC ck = specific heat of catalyst, kcal/kg “C cpg = specific heat of gas, kcal/kmol “C hi = heat transfer coefficient of gas-inert, kcal/m* “C h ai Uk
I 2
) tC
Figure 10. Optimal cycle time. 300
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
h k = heat transfer coefficient of gas-catalyst,
"c
kcal/m2 h h,k = heat transfer coefficient inert-catalyst, kcal/m2 "C h kcBo = initial rate constant for coking from component B, kg/kg of cat. h ~ H O= initial rate constant for dehydrogenation, kmol/kg of cat. h P B = partial pressure of component B, atm r H o = initial reaction rate for dehydrogenation, kmol/kg of cat. h r H = reaction rate for dehydrogenation, kmol/kg of cat. h rco = initial reaction rate for coking, kg/kg of cat. h r c = reaction rate for coking, kg/kg of cat. h T E = effective reaction rate, kmol/kg of cat. h t = time, h t , = evacuation time, h t f = on-stream time, h f'; = purge time, h t , = regeneration time, h t , = cycle time, h u = superficial flow velocity, m/h u = dilution catalyst bed X D = conversion of butene into butadiene z = reactor coordinate, m AHO = frequency factor dehydrogenation, kmol/kg of cat. h atm Ac0 = frequency factor coking, kg/kg of cat. h CB = concentration of component in the gas phase, kmol/ m3 CB,k = concentration in catalyst pores, kmol/m3 C, = coke content of the catalyst, kg of coke/kg of cat. C t ~ = total concentration of active sites, kmol/kg of cat. CL = concentration of free active sites, kmol/kg of cat. CBL = concentration of sites covered with B, kmol/kg of cat. CSL = concentration of deactivated sites, kmol/kg of cat. D B = effective diffusitivity of B, m2/h D B ,= ~ molar diffusivity of B, m2/h D g k = Knudsen diffusivity of B, m2/h E H = activation energy for dehydrogenation, kcal/kmol Ecg = activation energy for coking from B, kcal/kmol F D = outlet butadiene flowrate, kmol/m2 h (-AH) = heat of reaction, kcal/kmol I = objective function, butadiene production averaged over cycle time, kmol/h K = equilibrium constant for dehydrogenation, atm K , = equilibrium constant for reaction step i L , = length of pores, m M I = molecular weight of component I, kg/kmol R = gas constant, kcal/kmol K R e = equivalent radius of catalyst particle, m
SH =
mol of butadiene produced per mol of butene converted, averaged over on-stream time T = gas temperature, "C T k = temperature catalyst particle, "C Ti = temperature inert particle, "C T B = generalized modulus according to Bischoff a = deactivation parameter, kg of cat./kg of coke t k = pore volume of catalyst, m3/kg of cat. t = void fraction in reactor 7 = effectiveness factor p k = specific weight of catalyst, kg/m3 pi = specific weight of inert material, kg/m3 'T = tortuosity factor on the pores (PH = deactivation function for dehydrogenation (pc = deactivation function for coking
Literature Cited Aris, R., Chem. Eng. Sci., 6, 262 (1957). Bartiett, M. S.,J. Roy. Stati. SOC.,Suppl., 4, 137 (1937). Bischoff, K. B., Chem. Eng. Sci., 22, 525 (1967). Box, G. E. P., Hill, W. J., Technometrics, 9, 57 (1967). Burwell, R. L., Haller, G. L.. Taylor, K. C., Read, J. F.. Adv. Catal., 20, 1 (1969). , De Pacw, R.. Froment, G. F., Chem. Eng. Sci., 30, 789 (1975). , Dumez, F. J., Hosten, L. H., Froment, G. F., Chem. Eng. Sci. (1976). Dumez, F. J., Ph.D. Thesis, Rijksuniversiteit Gent, 1975. Forni, L.. Zanderighi, L., Carra, S.,Cavenaghi, C., J. Catai., 15, 153 (1969). Froment, G. F.. Bischoff, K. B.. Chem. Eng. Sci., 16, 189 (1961). Froment, G. F., Mezaki, R.. Chem. Eng. Sci., 25, 293 (1970). Handley, D., Heggs. P., Trans. lnst. Chem. Eng., 46, 251 (1966). Happel, J., Blanck. H., Hamill, T. D., lnd. Eng. Chem., Fundam., 5, 3 (1966). Hornaday, G. F., Ferrell, F. M.. Mills, G. A,, Adv. Petr. Chem. Ref., IV, 10 (1961). Hosten, L. H.. Froment, G. F., Proc. 4th lnt. Symp. Chem. React. Eng. Heidelberg, 1976. Hunter, W. G., Reiner, A. M., Technometrics, 7, 307 (1965). Hydrocarbon Process., 136 (1971). Leva, M.. Chem. Eng., 56, 115 (1959). Marcilly, C., Delmon, B., J. Catai., 24, 336 (1972). Masamune, S.,Smith, J. M., A.l.Ch.E. J., 12, 2 (1966). Masson. J., Delmon. B.. 5th Congr. Cat., (1972). Ozawa, I., Bischoff, K. B., Ind. Eng. Chem., Process Des. Dev., 7, 67 (1968). Poole, C. P., Maclver, D. S., Adv. Catal., 17, 223 (1967). Reid, R., Sherwood, T., "The Properties of Gases and Liquids", McGraw-Hill, New York, N.Y., 1958. Tackeuchi, M., ishige, T., Fukumuro, T., Kubota, H., Shindo, M., Kagoku Kogyo, 4, 38 (1966). Thomas, C. L., "Catalytic Processes and Proven Catalysts", Academic Press, New York, N.Y., 1970. Timoshenko, V., Buyanov, R. A,, lnt. Eng. Chem., 2, 314 (1972). Traynard. P.. Masson, J., Delmon, B.. Bull. SOC.Chim. Fr., 4266 (197 1). Traynard. P.. Masson, J., Delmon, B., Bull. SOC.Chim. Fr., 2652 (1973). Traynard. P., Masson, J., Delmon, B.. Bull. SOC.Chim. Fr., 2892 (1973). Villadsen, J., "Selected Approximation Methods in Chemical Engineering Problems", lnstituttet for Kemiteknik, Danmarks Tekniske H@jskole,1970.
Received for reuiew J u n e 30, 1975 Accepted October 28,1975
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