dehydrogenation of i -butene into butadiene. kinetics, catalyst coking, and reactor design

8/18/2019 Dehydrogenation of I -Butene Into Butadiene. Kinetics, Catalyst Coking, And Reactor Design

1/11

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.

2, 1976

291


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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


3/11

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,

No.

2, 1976

293


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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


5/11

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.


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.


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.

Eng. Chem., Process

Des. Dev . , Vol. 15, No. 2, 1976

295


6/11

.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

296 Ind. Eng.

Chem.,

Process Des. Dev.,

Vol .

15,

No.

2,1976


7/11

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

Ind. Eng. Chem.,

Process

Des. Dev.,

Vo l . 1 5 ,

No. 2 1976

297


8/11

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

Ind. Eng.

Chem., Process Des. Dev.,

Vol.

15, No. 2,

1976


9/11

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.

Eng.

C h e m . ,

Process Des. Dev.,

Vol.

15, No.

2

1976

299


10/11

\ 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


11/11

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

Literature Cited

Aris,

R.,

Chem.

Eng.

Sci., 6 , 262 (1957).

Bartiett,

M. S.

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Bischoff, K. B ., Chem. Eng. Sci., 22, 525 (1967).

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R.

L., Haller, G. L.. Taylor,

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C., Read,

J.

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De Pacw, R.. Froment, G. F., Chem. Eng. Sci. , 30, 789 (1975).

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F.,

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J.,

Ph.D. Thesis, Rijksuniversiteit Gent, 1975.

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J.,

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Hamill, T. D., lnd. Eng. Chem., Fundam.,

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Mills, G. A,, Adv. Petr. Chem. Ref.,

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J.,

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Sherwood, T., The Properties of Gases and Liquids , McGraw-Hill ,

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Accep ted

October

28 ,1975

Ind. Eng. Chem., Process Des. Dev.,

Vol.

15, No.

2,

1976

301

dehydrogenation of i -butene into butadiene. kinetics, catalyst coking, and reactor design

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