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Dehydrogenation
of
Butene into Butadiene. Kinetics Catalyst
Coking and Reactor Design
Francis
J.
Dumez and Gilbert
F.
Froment
Laboratoriurn voor Petrochernische Techni ek. Rijksuniversiteit Gent, Belgium
The kineti cs of 1-butene dehydrogenation over a Cr203-AI203 catalyst between 490 and
600
OC were deter-
mined 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 equa-
tions derived from differential reactor results gave excellent predictions of the performance of an experimental
integral reactor. The effec t of internal transport limitation was investigated. An industrial reactor was simulated
and optimized.
I. Introduction
An impo rtant fraction of the world butadiene production
is obtained by dehydrogenation of n-but ane
or
n-butene.
This reaction is accompanied by side reactions leading to
carbonaceous deposits which rapidly deactivate the cata-
lyst. The coking tendency may be limited up to a certain
extent either by diluting the feed with steam or by operat-
ing under reduced pressure. The second solution has been
favored. The butadiene production using vacuum processes
amounted to 700000 T in 1971 (Hydrocarbon Process.,
1971). With vacuum processes operating with butene as
feed, the on -stre am time is limited to 7-15 min, after which
regeneratio n of t he catalyst by burning off the coke is re-
quire d. With su ch cycle times the h eat given off by the re-
generation compensates for the heat requirements of the
adiabatic dehydrogenation (Hornada y et al., 1961; Thomas,
1970).
Vacuum processes are based upon Crz03-Al203 cat a-
lysts. Fundamen tal prop erties of such catalysts were stud-
ied by Burwell et al. (1969), Poole and MacIver (19671,
Marcilly and Delmon (1972), Masson an d Delmon (1972),
Trayna rd et al. (1971, 1973). These a uthors found tha t th e
catalytic activity was represen ted by surface Cr3+ and
0 -
ions which ar e incompletely coord inat ed; ions of y-CrzO3-
A1203solid solutions were found to be the most active.
Aspects of the kinetics of butene dehydrogenation on
such catalysts were investigated by Forni et al. (1969),
Hap pel e t al. (1966), and Ti moshenko and Buyanov (1972).
Although the surface reaction was generally found to be
rate determining, there is little more agreement between
th e results. Fu rthe r, none of these studie s was carried out
with particle sizes used in industrial operation. S o far, no
quantitative treatment of the deactivation of the catalyst
by coke deposition has been published. Yet, without such
information n o rigorous optimization of industrial opera-
tion is possible.
This pape r reports on a detaile d study of the kinetics of
the dehydrogenation, of the coke deposition, and of th e as-
sociated catalyst decay. The effect of internal transport
limitations is investigated. Industrial operation is simulat-
ed a nd optimized.
11. Kinetics of the Main Reaction
11.1. Experimental Procedure and Range
of
Operat-
ing Variables. Th e catalyst used in th is investigation was
a
Cr203-Al203 catalyst containing 20 wt % C r z 0 3 and hav-
ing
a
surface area of 57 m2/g. Experimen tal checks on the
absence of partial pressure and temperature gradients in
th e film surrounding th e particle a nd of temperatu re gradi-
ent s inside t he particle were performe d. 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 deter-
mined in a quartz tube inserted in an electrical furnace.
The catalyst particles, diluted with quartz particles, were
supported by a stainless steel gauze. Th e tempera ture was
controlled by two thermocouples, one in the center of the
catalyst section and one near the wall.
Th e feed stream was calibrated and dried in the classical
way, The outlet gases were analyzed by gas chromatogra-
phy on a 20% propylene carbonate/chromosorb column.
Experiments were performed at 4 temperatures: 490, 525,
560, an d 600 C. The butene pressure ranged from 0.02 to
0.27 atm , the hydrogen pressure from 0 to 0.10 atm, and th e
butadiene pressure from
0
to 0.10 atm. Although only
1-
buten e was fed, the ou tlet gases always contained a mixt ure
of 1 -buten e, cis-2-bute ne, and trans -2-bu tene close to the
equilibrium composition. Therefore, the dehydrogenation
equilibrium could be referred to butene equilibrium mix-
tures. In all these expe riments, the conversion was kept
below 2% by adjusti ng the a mount of catalyst an d the gas
flow rates. There fore, the reactor was considered to be di f-
ferential.
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 e xtrapolatio n
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 Tabl e 11.
Th e experime ntal program was designed to discriminate
in an optimal way between the rival models. Sequential
procedures for optimal discrimination have been intro-
duced by Box and Hill (1967) and by Hunter and Reiner
(1965). The methods have been applied to experimental
dat a, but only a posteriori, for illustrative purposes (Fro-
ment and Mezaki, 1970). The present work is probably the
first in which the experiment s were actually and exclusive-
ly designed on the basis of a sequential discrimination pro-
Ind. Eng. Chem., Process Des. Dev., Vol. 15,
No.
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Table
I.
Reaction Schemes for Butene Dehydrogenation
(a) Atomic Dehydrogenation; Surface Recombination
of
Hydrogen
1)
B + L = B L (a1
1
z j B L + L - M L + H L (a2)
( 3) M L + L t D L + H L (a3)
( 4 j
D L = D + L
(a4j
5 ) 2HL+ H,L
+
L
(6 ) H,L
+ H,
+
L
(where B
=
n-butene; D
=
butad iene; H,
=
hydrogen;
M
=
an intermediate complex)
( b ) Atomic Dehydrogenation; Gas Phase Recombination of
1)
B + L t BL (bl )
( 2 )
B L + L + M L + H L (b 2)
(3 ) M L + L t M L + H L (b3)
(4 ) D L t D + L (b4)
5 ) 2HL + H,
+
2L
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
Hydrogen
(c) Molecular Dehydrogenation
(e)
Atomic Dehydrogenation; Intermediate Complex with
Short L ifetime; Gas Phase Hydrogen Recombination
1) B + L t B L ( e l )
( 2 )
BL
+
2L+ 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 ex-
periment was carried out, the parameters of the models
were estimated, and th e curre nt sta te of adequacy of the
rival models was tested. With this information the next ex-
periment was designed and
so
on, until th e discrimination
was achieved. Eventually, some further experiments were
carried ou t to improve the significance of the pa ramete rs of
the retained model(s).
Th e sequenti al choice of exper imenta l conditions for op-
timal discrimination between the rival models was based
upon the following design crit erion
m m
D =
lPHLo
- H,q
(1 )
1=1, = 1
I f
where
PH,O
represents the estimated value of the reaction
rat e according to model i and D is th e divergence between
the predicted rates. The double summation ensures that
each model is take n in tu rn as a reference. Given
n -
1 ex-
periments the nth experiment was performed in the differ-
ential reactor a t those values of
p ~ , ~ ,
nd
p~
which max-
imized
D.
A grid is selected for possible combinations of
p ~ , ~ ,nd p~ within t he operability region. From previ-
ous experience on constructed examples the criterion 1)
was shown to lead t o th e same experiments as t he Box-Hill
criterion tha t accounts for the variances.
The state of model adequacy was tested by means of a
criterion proposed by Hosten and Froment (to be pub-
lished). Th e underlying idea is tha t the minimum sum of
squares of residuals divided by the appropriate number of
degrees of freedom is an unbiased estimate of the experi-
mental error variance for the correct mathematical model
only. For all other models th is qua ntity is biased du e to a
lack of fit of the model. The criterion for adequacy there-
fore consists in testing the homogeneity of the estimates of
the experimental error variance obtained from each of the
rival models. This is done by means of Bartlett's
x2
est
(Bartlet t, 1937). Th e details of the procedure, the designed
operating conditions, and the evolution of th e discrimina-
tion will be reported elsewhere (Dumez et al., to be pub-
lished). Suffice it to mention t ha t at 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 - PHO
between these models were smaller
than the experimental error. The models a2, b2, and d2
were eliminated because they contained a t least one pa-
rameter that was not significantly different from zero at
the 95% confidence level. Model c2, corresponding to mo-
lecular dehydrogenation and the surface reaction on dual
sites as rate determining step, led to a fit which was slightly
superior to th at of e2 and was finally retained. Th e same
conclusion was reached a t 490,560, and
600
C.
It 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 ex-
perimental program.
The parameters of model c2 were estimated by minimiz-
ing
for all the data
=
1, . . . ,N a t the four temperature levels.
This involves nonlinear regression. Indeed, the expression
for r ~ 0ccording to model c2 is
in which the adsorption equilibrium constants KB,
KH,
nd
K D
are related t o 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.
Th e r ate coefficient
~ H O
beyed the Arrhenius temperatu re
depend ence
k H o = AH' exp(-EH/RT)
5 )
AH'
=
AH exp(EH/RT,) (6)
with T, the average temperature, facilitated the estima-
tion. The values of the parameters and their standard de-
viations are given in Table 111. Th e Arrhenius plot for
~ H O
is given in Figure
1.
The dots represent the parameter
values obtained from a treatment of the d at a per tempera-
ture.
Reparameterization according to
111.
Kinetics of Coking
Th e 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.
Th e tempera ture 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-
292
Ind.
Eng. Chem. Process Des. Dev ., Vol. 15.No. 2, 1976
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Table 11. Rate Equat ions for Butene Dehydrogenation
'Ha
\
Table 111. Kinetic Coefficients and Adsorption Constants
of
Butene Dehydrogenation
Approx.
Parameter Value std dev
AHO T,
=
815.36 K ) 0.2697 0.0298
E H
2 9236 732
K B
1.727 0.342
KH
3.593
0.641
KD
38.028 6.165
and butadiene, while hydrogen exerted an inhibiting effect.
An example of the coke content of the catalyst as a func-
tion
of
time is given in Figure 2. Since the thermobalance
is
a differential reactor, operating at point values of the par-
tial pressures and the temperatur e, the decrease in the rate
of coking observed with increasing coke content reflects the
deactivating effect of coke. The rate equation for coke for-
mation therefore has to include a deactivation function,
multiplying the rat e in the absence of coke.
(7 )
rco is the initial coking rate, a function of th e partial pres-
sures and temperature which reduces to a constant for a
given experiment in the thermobalance. Several expres-
sions were tried for cpc (Froment and Bischoff, 1961).
dCc
rcO
pc
dt
ual components as well as mixtures of butene and butadi-
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
ene, butene and hydrogen, and butadiene and hydrogen'
Ind. Eng. Chem., Process Des. Dev., Vol. 15,
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+ model
t 2
model e 2
t 2 calc
115 120 1 25 130
Figure 1 . Arrhenius
diagram of k O .
b l
v
0 1 2
Figure 2. C, vs. t measured on the thermobalance.
pc
= exp(-aC,)
p.2 = 1- ac,
p =
1
- aC,)2
47 =
1/ 1
+ CYC)
$0 = 1/ 1+ CYC,)2
Note tha t the deactivation function is expressed in terms of
the carbon conte nt of th e catalyst, not in terms of time as
has been done frequently; indeed, time is not the true vari-
able into eq 7 and integration with respect to time yields
respectively
(9)
a
and rCowere determined by fitting of the experimental
dat a by means of a least- squares criterion.
For the majority of the 50 experiments
pc
= exp(-aC,)
tu rned ou t to give the best fit. This , by the way, agrees with
the results of Depauw and Froment
(1975)
obtained with a
completely different system. An explanation based upon a
pore blocking mechanism has been attemp ted (Dumez and
Froment, to be published). The parameter a was found to
be identical for coking from either butene or butadiene and
independen t of the operating variables, as can be seen from
the partial correlation coefficients between a and T
~ ,
p ~ ,nd
p ~ ,
espectively, shown in Table IV. This table
also contains th e 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 th e 95% probability
level.
The determination of the complete rate equation for
coke deposition required the simultaneous treatment of all
experiments,
so
that
p ~ ,
~ , ~ ,nd
T
were varied. The
exponential deactivation function was substi tuted into th e
rate equation for coking. After integration of the latter the
parameter s were determined by minimization of
Several rate equations, either empirical or based on the
Hougen-Watson concept, were tested. The best global f i t
was obtained with the following equation.
with
k C e o = Aceo
exp(-EcB/RT) ( 12 )
k c Do
=
A o o
xp(-EcD/RT)
and KCH independent of temperature. The integrated
equation used in t he objective function (10)was
Again the frequency factors
Aceo
and
ACD'
were modified
as follows
ACB' = ACB exp(EcB/RTm) (14)
ACD' = ACD
exp(EcD/RT,)
to facilitate the parameter estimation.
The parameter values and their approximate standard
deviation are given in Table V. An example of the fit ob-
tained wi th this equation is shown in Figure 2.
The frequency factors Aceoand
ACDO
are easily calculat-
ed from (14)
Ace0
= 1.559 X lo8
A ~ ~ O5.108 x 105
Since the order with respect to butene, ~ C B , nd to butadi-
ene, ncD, is smaller tha n
1,
t has been attempted to derive
an adequate mathematical model based on the Langmuir-
Hinshelwood or Hougen-Watson concept.
The formation of what is called cokes proceeds over a se-
quence of s teps involving addition and /or dehydrogenation.
Let the rate-determining step in this sequence be repre-
sented by
IlBL +
nBB)L-
hBL
for coking from butene, and by
IlDL +
( n D D ) L-
h D L
for coking from butadiene. Z ~ B L nd Z ~ D L re adsorbed
lower intermediates in equilibrium with butene and buta-
diene 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-
294 Ind. Eng.
Chem., Process
Des.
Dev., Vol.
15, o. ,
1976
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Table IV . Test of Partial Correlation Coefficients between
Y and the Independent Variables
p Value -0.1612 -0.0627
+0.3042 -0.0530
t Value 0.98 0.38 1.92 0.32
Table V . Kinetic Parameters for Coking
Approx.
Parameter Value std dev
45.53
1.08
32800 7
58
0.2917 0.0209
0.743 0.029
1.3168 0.1158
0.853 0.023
1.695 0.076
21042 501
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
(15)
Th e unmeasurable concentration of adsorbed species can
be eliminated by accounting for the equilibria between bu-
tene and butadiene and the lower intermediates, so that
(15)becomes
rc = k c B ' C r l B r , C i n p B ) I ,
-k
k c D ' C I l n L C i n o D ) L
From (16) the concentration of free active sites C I ~ ay be
eliminated in favor of bulk partial pressures by means of a
balance on the total number of active sites. When the con-
centrations of the adsorbed lower intermediates are ne-
glected with respect to the concentrations of adsorbed bu-
tene, butadiene, a nd hydrogen,
C L
is given by
(17)
with CtL the tot al number of active sites and CSL the num-
ber of sites covered by coke. Th e coking rat e becomes
C tL
-
CSL
C L =
1 + KBPB+
K n P H
+ K D P D
(18)
A deactivation function for the coking may now be defined
kCH ' KI i eL PBn B+' f kCD ' KI i D L p D n D t l
1+ K B P R+ K H P H+ I ~ D P D ) ~
by
Th e problem with this function is that
it
contains the inac-
cessible concentration of adsorbed higher intermediate.
The re is no way out, here, except to resort to th e 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 inte-
grated with respect t o time, since the partial pressures and
temperature remain constant in the thermobalance experi-
ment s, to give
where
Table VI Values of the parameters
of
the
Langmuir-Hinshelwood Model
_ _
Approx.
Parameter Value std dev
Y 39.67 1.724
AcB (T,
=
822.8 K ) 0.6049 0.0694
E C B
30873 1300
n C B
o,
0.970 0.051
ACD 148.66
18.77
E C D
18117 7 84
n C D
1.767
0.034
n C B
=
n B + 1
n C D
=
n D +
1
KB,
K H ,
nd K D have already been es timated (section 11.2).
Th e values of
A c B ~ ,
CB,
C B ,
AcDO,
E C D , cD,
and
CY
were
estimated by nonlinear regression and are given in Table
V I
[AcBO and
ACB'
were also modified according
t o (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 ste p
I ~ B L L Z ~ B L H 2 L
The activation energy E C B agrees remarkably well with
that found for dehydrogenation of butene. The rate-deter-
mining step for coking from butadiene would be
I lDL + (0.75g)L-
h D L
i.e. would mainly consist of addition. The value for ECD
seems to sup port this conclusion.
Th e accuracy of the Langmuir-Hinshelwood model (18)
is lower tha n t ha t of model ( l l ) , however. This is believed
to result, partly a t least, from the lower mathematical flexi-
bility of eq 18 as compared to (11). In addition , the Lang-
muir-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 func-
tions of time. T o eliminate the effect of bypassing, the con-
versions were all referred to the one first measured. It was
checked th at t he rat io of the amounts of gas flowing
through a nd around the basket remained constant and was
not affected by the coke deposition: in a regeneration ex-
periment the burning rate, determined from the weight loss
measured by means of the balance, completely agreed with
th at calculated from the am ount of CO and
COS
in the exit
gases, for the whole duration of the experimen t.
Figure 3 shows the relation between r H / r H n = and the
coke con tent, easily derived from the measurements r H / r H o
=
p~
vs. time a nd coke content vs. time. Although there is a
certain spread on the dat a, no systematic tre nd with re-
spect to the temperature or the partial pressures could be
detected. T he temp erature 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 . Th e agreement with the value found for the deactiva-
Ind.
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Des. Dev . , Vol. 15, No. 2, 1976
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.O1
.02 .03
04 .05
.06
Figure 3. Activi ty of t he ca t a lys t for dehydrogenat ion vs. coke
conten t .
tion parameter for the two coking reactions is remarkable.
It may be concluded that the main reaction and the coking
reactions occur on the same sites.
Th e set of rate equations may now be written
eration without prior investigation of th e effect of the par-
ticle size on the rate of th e overall process consi sting of re-
action and internal transport.
The effect of trans port phenomena inside the particle is
generally expressed by means of the effectiveness factor,
which has been related to t he geometry of the catalyst, the
effective diffusivity and the rate paramete rs of the reaction
in a closed form only for single reactions and simple kinet-
ics. 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 t he me th-
od requires the reaction rate to be expressed as a function
of the concentration of one component only. In the case
studied here the amo unts 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 t o be taken into account for
the gaseous components. Th e equations may be written, for
quasi-steady s tat e conditions, negligible external tran sport
resistance and iso thermal particles
(23)
1.826 X loTexp(-29236/RT)
p~ -
xp( 42.12CJ (21)
(2 2 )
K
rH =
1 + 1 8 7 2 7 ~ ~3.593pH + 3 8 . 0 2 8 ~ ~ ) '
1.5588 x
10'
eXp( -32860 /RT)p~O.~~~5.108
X l o 5
e x p ( - 2 1 0 4 2 / R T ) p ~ ~ . ~ ' ~
r c
=
exp(-45.53Cc)
(1
+ 1.6956)
V. Experiments in an In t eg ra l Reac to 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 divid-
ed into five sections, separated by metal gauze, to enable
unloading the catalyst in well defined sections at 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 cata-
lyst. The catalyst particle size was the same as tha t used in
the differential reactor.
The experimental results were compared with those ob-
tained by numerical integration of the continuity equations
for the different species, containing the rate equations
(21)-(22). The tempera ture 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. It is worthwhile no-
ticing that there is hardly any coke profile. There are two
reasons for this: coke is formed from both butene and buta-
diene, and hydrogen, a reaction product, inhibits the coke
formation.
VI. Influence of Catalyst Par t ic l e S ize
Th e rate equations (21)-(22) were determined with cata-
lyst particles small enough to eliminate resistances to inte r-
nal transport. With experiments at low temperatures, the
diameter was 0.7 mm, at higher temperatures 0.4 mm. In-
dustrially the particle size is generally around 4 mm, to
limit the pressure dr op through the bed. Consequently, the
results given above cannot be extrapolated to industrial op-
with boundary conditions
r
=
R e ;
CB,k
=
CB; CH,k
=
CH; CD,k
=
CD (24)
r H
is expressed in kmollkg of ca t. h, rCB and rCD in kg coke/
kg of cat. h. Therefore, the conversion factors CB and $C D
are required. T hey are expressed in kg of coke per kg of bu-
tene or butadiene involved in the coking and thus account
for the loss of hydrogen associated with the coke formation.
DB, DH, and DD are th e effective diffusivities for butene,
hydrogen, and butadiene and are related to the molecular
and the Knudsen diffusivities. For butene , e.g.
The molecular diffusivities were calculated from a weight-
ed average of the binary diffusion resistances. The binary
diffusion coefficients were estimated from the formula of
Fuller e t al. (Reid and Sherwood, 1958).
Th e calculation O DB,k, DH,k, and DD,k requires informa-
tion ab out the pore size. Th e catalyst studied had a bimod-
al 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,
th e maximum length of the micropores with average diam-
eter 70
A
cannot exceed
5 p.
It is easily calculated tha t this
is too short to develop any significant concentration gradi-
ents. Therefore, only the macropores with a pore volume of
0.155 cm3/g and with average pore diameter of 1000 0
A
were considered in the evaluation of the Knudsen diffusivi-
t Y
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d r rp
~~
CalC
03-
.02
01
\
-
-
10
20 30 40
50 I
mm)
Figure 4.Butadiene yield
vs.
time in the integral reactor.
Ct
2 3
4
5 secl lon
Figure 5 . Coke profile in the integral reactor.
Th e effective diffusivities were allowed to vary with the
composition inside the particle. The only unknown param-
eter left in the continuity equations is the tortuosity factor,
T . This factor was determined from a comparison between
the experimental rates at zero coke content, measured in a
differential reactor, and the surface fluxes. The latter were
calcula ted, using Fick's law, and for a given
T
from the con-
cent ratio n profiles obtained by numerical integ ration of eq
23.
A
value of
5
for T led to the best fit of the experimental
data. This is t he generally accepted value for the tortuosity
factor in catalysts of the ty pe used in th is work.
The calculated value for the effectiveness factor for de-
hydrogenation was obtained by dividing the calculated hy-
drogen flux at the particle surface by the true chemical re-
action rate. T abl e VI1 compare s these values with those ob-
tain ed by dividing the experim ental rate corresponding to a
Table VII . Experimental and Calculated Effectiveness
Factors with r = 5
R,,
m m
pe
atm
T,
C (exptl) (calcd) (Bischoff)
77 77
2.3 0.2165
500
0.334 0.346 0.426
2.3 0.2159
550
0.187 0.229
0.282
2.3 0.2181
550
0.199 0.229
0.282
2.3
0.2492 599
0.140 0.135 0.185
0.6 0.2184
580
0.521 0.493 0.610
0.35 0.2038 595
0.808 0.621
0.723
given particle size, by the true chemical rate calculated
from (21). Except for 0.35 mm the agreement is excellent.
The last column of this table contains the values obtained
by means of the generalized modulus defined by Bischoff.
However, to do
so,
the coking reactions had to be neglected
to be able to express the reaction rate a s a function of the
concentration of one component only. The diffusivities
were supposed to remain constant in the whole particle.
Th e generalized mo dulus is calculated by me ans of the fol-
lowing formula
with
L ,
the length of the pores and p the partial pressure
of the component considered. The effectiveness factor is
the n e valuated from th e graph given by Bischoff (1967). As
can be seen from Ta ble VII, the effectiveness factors dete r-
mined 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
overest imated, as pointed out by Aris (1957): the maximum
deviatio n is observed around
rj
= 0.60 and amounts to 0.09.
The values obtained here are also about 10% higher than
th e calculated ones.
The Bischoff approach does not provide the concentra-
tion profiles inside the particles
so
that the coking of the
catalyst cannot be predicted. The advantage of the method
lies in the simplicity of th e calculations as compared to th e
integrati on of the conti nuity equations.
Figure 6 illustrates the partial pressure profiles inside
the particle for zero deactivation a nd th e coke profile after
0.25 h. The full lines correspond to the results obtained by
numerical integ rati on using a Runge-Kutta-Gill routine.
The circles represent the partial pressures calculated by
the collocation method (Villadsen, 1970), applied with con-
st an t effective diffusivities. Values based on th e gas phase
composition were used. The agreement is perfect and all in
favor of the collocation method, which is much faster from
the computa tional standp oint. The coke profile inside the
particle is relatively flat and very similar to th at measured
in the integral reactor (Figure 5). If coke were formed from
butene only a decreasing profile from the surface to the
cen ter of the particle would be observed;
if
coke would orig-
inate from butadien e only, the profile would be ascending
(From ent 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 th e actua l profile. Th e optimization of th e
process, which will be discussed in a later section, required
a large number of numerical integrations of the reactor
model, including the se t of equ ations
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
dras-
tic simplification was required here, aiming a t eliminating
the se t of equations 23) by relating in an algebraic way the
observed reaction rate t o the conditions in the bulk of the
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10
5
1 . 2 5
0 5 F ;
=
25
0
5
rlR,
Figure 6. Dehydrogenation rates, partial pressure, and coke pro-
files inside the catalyst particles.
fluid. To 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 ob-
tained by integration of the set (23). This effective rate was
then plotted vs. the tr ue reaction rate corresponding with
the gas phase conditions selected. A unique curve was
ob-
tained, 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 ef-
fective rate becomes proportional to
6.
hen 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 calcu-
lated in the way outlined above were in complete agree-
ment with those obtained by the rigorous approach de-
scribed in the next section.
VII. Simulation
of
an Industrial Reactor
Industrially the dehydrogenation is carried out around
600
C
in adiabatic reactors and under reduced pressure.
Th e bed is diluted with ine rt particles which provide a heat
reservoir th at reduces to a certain extent the effect of en-
dothermicity 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. T he characteristics of a
typical reactor and the operating conditions are given in
Table VIII.
The continuity and energy equations are as follows.
Fluid phase:
Table VIII. Characteristics of an Industrial Reactor for
Butene Dehydrogenation
Length 0.8 m
Cross section 1 m'
Catalyst and inert diameter
0.0046 m
Catalyst bulk density 400 kg of cat./m3 of diluted
reactor
Inert bulk density 900 kg of cat ./m3 of diluted
reactor
Catalyst geometrical 274 mz /m3
f
diluted
surface area reactor
Inert surface area 411 m*/m3
f
diluted
reactor
Inlet tota l pressure 0.25 ata
Inlet butene pressure 0.25 ata
Molar flowrate
Feed temperature 600
C
Initial bed temperatu re
600
C
1 5 kmol/m* cross section h
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.
Th e product (uSC,) is kept under th e differential in
these equations to account for the important change in
numbe r of moles in the gas phase owing to the dehydroge-
nation and t o a certain extent to the coking. The right-
hand side in (31) expresses the amount of heat exchanged
between the gas an d th e solid particles, catalytic and inert.
Solid phase:
Th e second term in the right-hand side
of
(32) and (33) ex-
presses the a mount of heat exchanged between the catalyst
and the inert particles, by conduction and radiation. Inside
the catalyst particles
- -2--
2CD,k 2aCDk aCD,k- - K (rH - -)rCD
(36)
ar2 r ar DD a t D D ~CCDMD
(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
298
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1976
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r = O
Th e particle e quations 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. The heat transfer coefficients
were calculated from the j H correlation (Handley and
Heggs, 1968). Th e results of one rigorous computatio n are
shown in Figures 7, 8, and 9. In Figure 7 the temperature is
seen to dro p rapidly under the initial value, due to the en-
dothermic n atu re of the reaction. A temperatu re wave trav-
els rapidly through the reactor as the reaction gradually ex-
tends to increasing depths. In the presence of coking no
true steady s tate is reached, however; the temperature pro-
file is slowly translated upward, because of the decrease in
reaction r ate due to the catalyst deactivation. The corre-
sponding coke profiles are shown in Figure
8.
The profile is
decreasing, mainly because of the higher temperature at
the inlet and of the inhibition of the coke formation due to
the hydrogen near the outlet. Figure 9 illustrates the b uta-
diene flow rate at the outlet as a function of time. The
rapid initial decrease corresponds to the initial tempera-
ture drop.
Beyond this initial period, the decrease in production is
much slower. Th e catalyst is deactivated by th e coke depo-
sition, but as the dehydrogenation rate is lowered the bed
temperatu re slowly rises, thu s favoring again the buta diene
production.
VIII.
Process
Optimization
As mentioned already in section VI, the large number of
simulations involved in the optimization of the process ne-
cessitated the simplification of the system of equations
28-37 into th e se t (28-33), (3 7), 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.
Furt her , to permit the simulation of nonisobaric situations
arising with high flow rates, the Leva pressure dro p equa-
tion was added to th e model (Leva, 1959).
Various aspect s of th e process were optimized: the con-
version 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.
Th e adiabatic reactor considered here has a bed d ept h of
0.80
m, a cross-sectional area of
1
m2, and contains
800
kg
of catalyst, undiluted. Th e 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. It follows from
Figure 7 , however, that the temperature profile is com-
pletely translated through the bed after
5
min
so
that the
following calculations and results are believed to be suffi-
ciently representative, certainly for the longer dehydroge-
nation periods of the order of 45 min. The butadiene yield,
averaged over one complete cycle (including dehydrogena-
tion, purge, regeneration and evacuation) is given by the
following formula
8 70
860.
~
~
850-
840-
I
830
0
-
~
O
040
060 zlm)
Figure 7.
Temperature
profiles
in the reactor.
t f + t ,
The yield, I , is maximized by the optima l choice of the on
stream time t f . 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 ap-
proximation 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 at
600 C, with in let press ure of 0.30 ata an d inl et flowrate of
20.4 kmol/m* h butene. I has a maximum for
t , =
1.1 h.
Th e corresponding average coke content of the cata lyst
amounts to 3.7%. This is much more than the content re-
quired to reheat the catalyst bed to the inlet gas tempera-
ture.
T o avoid excessive tempera tures in the reactor after re-
generation, the inlet temperature of the regeneration gas
would probably have to be monitored, for instance by ad-
mixing cold gas to the preheated s tream. In industrial oper-
ation th e dehydrogenation period
is
interrupted when the
am ount of coke deposited is sufficient to provide, during
the regeneration, the heat compensating the heat lost dur-
ing the on stream period (Hydrocarbon Process., 1971;
Hornaday et al., 1961; Thomas, 1970); 1.5 to
2%
coke suffi-
ces 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.
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\ 1.015
t (hr)
1:OIO
0.01 -
1.005
t :
.025
0.2
0.4 0.6 0.8 Z m )
Figure 8. Coke profiles in the reactor.
Figure 9. Outlet butadiene flowrate
as
a function of time.
‘
I
2 tC
Figure
10.
Optimal cycle time.
300
Ind.
Eng.
Chem.,
Process
Des.
Dev.,
Vol. 15, No.
2,
1976
0.1 h of dehydrogenation, th e 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.
Acknowledgment
F.
Dumez is grateful to the Belgian “Nationaal Fonds
voor Wetenschappelijk Onderzoek” for a gran t over the pe-
riod 1972-1974. Thi s paper was presented a t the Sixty-
eighth Annual Meeting of the American Instit ute of Chem-
ical Engineers held in
Los
Angeles, Calif., Nov 16-20, 1975.
Nomenclature
ai =
exte rnal surface of inert material, m2/m3
U k
= external surface of catalyst , m2/m3
U ; k
= contact surface between inert and catalyst, m*/m3
c i = specific hea t of inert material, kcal/kg
O
ck = specific hea t of catalyst, kcal/kg “ C
cpg = specific hea t of gas, kcal/kmol “C
hi = heat transfer coefficient
of
gas-inert, kcal/m* “C h
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h k =
hea t transfer coefficient of gas-catalyst, kcal/m2 c
h,k =
hea t transfer coefficient inert-catalyst, kcal/m2
C
kcBo = initial rate constant for coking from component B,
~ H O initial rate constant for dehydrogenation, kmol/kg
PB
=
partial pressure of component B, atm
r H o =
initial reaction rate for dehydrogenation, kmol/kg
r H = reaction ra te for dehydrogenat ion, kmol/kg of cat. h
r c o
=
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 dehy drogenation, kmol/kg of cat.
Ac0 = frequency factor coking, kg/kg of cat. h
CB
=
concentration of component in the gas phase, kmol/
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.
C L
=
concentra tion of free active sites, kmol/kg of cat.
CBL = concentration of sites covered with B, kmol/kg of
CSL
=
concentrat ion of deact ivated sites, kmol/kg of cat.
D B = effective diffusitivity of B, m2/h
D B , ~ molar diffusivity of B, m2/h
D g k
=
Knuds en 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)
= hea t of reaction, kcal/kmol
=
objective function, butadiene production averaged
K
=
equilibrium constant for dehydrogenation, atm
K , = equilibrium constant for reaction ste p i
L ,
=
lengt h of pores, m
M I =
molecular weight of component
I,
kg/kmol
R = gas const ant, kcal/kmol K
Re
=
equivalent radius of catalyst particle, m
h
h
kg/kg of cat. h
of cat. h
-
f cat. h
h atm
m3
cat.
over cycle time , kmol/h
SH =
mol of butadiene produced per mol of butene con-
verted, averaged over on-st ream time
T =
gas temperature, C
T k
=
temperature catalyst particle, C
i
=
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.
=
void fraction in reactor
7
=
effectiveness f actor
p k =
specific weight of catalyst, kg/m3
pi
= specific weight of inert materia l, kg/m3
'T
=
tortuosity factor on th e pores
(PH
= deactivation function for dehydrogenation
(pc
=
deactivation function for coking
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301