Chemical and Catalytic Reactor Modeling - American Chemical Society

17 Safe Design of Cooled Tubular Reactors for Exothermic Multiple First Order Reactions K. R. WESTERTERP, K. J. PTASINSKY, and R. R. M. OVERTOOM

Downloaded by TUFTS UNIV on November 19, 2016 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch017

Chemical Reaction Engineering Laboratories, Department of Chemical Engineering, P.O. Box 217, Twente University of Technology, 7500 AE Enschede, The Netherlands

Available c r i t e r i a for the prevention of runaway have been derived for single reactions only. In this paper results are presented for multiple reactions. For mul tiple reactions not only runaway has to be prevented, but also selectivity or y i e l d have to be maintained. By carefully separating dimensionless groups descri bing the properties of the reaction system from those describing the operating or design conditions, crite ria could be developed to maintain the selectivity or the y i e l d of the cooled, tubular reactor. These cri teria require more s t r i c t operating conditions than the prevention of runaway and always lead to safely operating reactors.

At

designing

reactions ratures in and

the

a

with past

on

ν

design

and

cooling or

the

a

concentration

tubular

reactor

has

C

of

one

of

meter

in

the

c r i t i c a l

operate

at

a

"run A l l

c

,

the

the

reactor

to

the

be

after

temperature

of

inlet

in

the

a

small the

design

c r i t e r i a

are

relevant

diameter

d

t

temperature reactor change

of

reactor

the 0

the

to

the

a

starts

, T

feed,

sensitive

suddenly

level,

end

safe

parametric

the

tube

extremely

reactor

of

tempe

To t h i s

the

A l l these

values as

reactant

parameters: region

the

such

the

proven

much h i g h e r

c r i t e r i a that

operate

outside

Moreover,

of

for

phenomenon

exothermic

reactor

para

to tempera

away".

ception

reaction

these

T

of

A o

been

value

tures

range

the

for

runaway.

c r i t e r i a

reactors.

on

parameters,

medium t e m p e r a t u r e

excessive

developed

and

certain

operating

reactor

avoid

temperature

tubular

reactions n

*

authors

tubular to

reactor

cooled

single

5225ίϊίΥί:§ ·

required

to

several of

(catalytic)

is

respect

operation

based

cooled

much c a r e

the

this of

developed

up

should

avoided

the

region

available

taking

place

be

to

now

have

and

been

that

the

of

high

parametric

c r i t e r i a

have

been

and

on

a

specified

based

based

on

reactor

the

con

should

sensitivity. on

a

single

maximum a l l o w a b l e

0097-6156/84/0237-0323$06.00/0 © 1984 American Chemical Society

Dudukovi and Mills; Chemical and Catalytic Reactor Modeling ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

tempe-

324

CHEMICAL AND CATALYTIC REACTOR MODELING

rature up

T

m

, which

a

to

now

are

which

the

reactor

regions cess

of

low

can

be

available i f

that

really

the

the

tive.

arbitrary,


industrial wable

temperature

catalyst

discuss

reactor

aspects. reactor

that

selectivity ourselves

or

to

pseudo-homogeneous,

Literature

Bilous of

and

Amundson

for

and

diagrams

order

With order plot

the

Q

van

not

the

in

itself

can

on

small

scale

a

is

m

a

based

does

give

scale-up

or

and

strong

for

limit w i l l or

derive

will

are

not

tubular

to.

Here for

we

i f

a l l o such

we

w i l l

and

maintaining

will

the

We w i l l in

for

e.g.

runaway

later

reactions

laboratory

construction

to

occur,

adhered

order

of

c r i t e r i a

and

ac

rather

A maximum

limits.

ourselves

yield

be

reasons

strength

explosion

construc

indications

problems.

various

mat

higher

T

the

used

for

but

a

demon

desired restrict

a

one

describe

the

dimensional

reactor.

and

by

[7] c o n s i d e r e d the

selectivities Multiple

also

reaction

states

a

less in

same

parameter and

in

the

required

same

or

vice

for

points

in

f i r s t the

trajectories,

A

tubular

reactor.

conservative

a

method

a

temperature

as

criterion.

for

Barkelew

design of

d^/dp.

account;

the

runaway

X

the

second

presented

single conversion

[5].

presented

i n

in

devised

order,

t

inflexion

para

design

He

the

conversion

Stern

the

d

avoid

[3] d i d

the

isoclines and

f i r s t

place.

to

phenomenon This

develop

diameter

reaction

reactions into

tube

derived

and

achieved

steady

the

the

which take

Froment

recently

the

in

relative

of

reactors.

[2] t o

derived

used

diameters

multiple

secondary

also

[6] d i d

particle

the

be

and

Oroskar

reactors

including

catalyst

on

Barkelew

reactions

they

[4]

based

to

tubular

reactors

Τ versus

Potter

catalytic

by

certain

course

and Varma

f i r s t

cooled

can

c

they

trajectories

proposed

the

in

Welsenaere

the

reactions

runaway,

the

remains

i t

tubular

temperature

Agnew

high;

Firstly

does

the

f i r s t

and T

C^

describe

as

neous

of

reactions,

Morbidelli

very

i t

catalyst

inhibited

from which

these

place,

provided

[1] w e r e

cooled

Later

reactor which

imperfections.

takes

pro

the

c r i t e r i a

was

product-

combination versa.

prevented.

be,

runaway

sensitivity

sensitivity

criteria order

that

survey

parametric

metric

so

selectivity,

cooled

the

the

is

runaway

at

of

can

We f i r s t

yield

boundary

and

selectivity

exothermic

the

enough

runaway

temperature

at

developed

conditions

sensitivity,

some

specified

multiple_reactions

required

strate

be

is

a

c r i t e r i a process

reactor

course,

despite

m

gets

specifying

temperature

selectivity a

the

strong

of

The the

that

exhibit

temperature

can

l i f e ,

such

reaction

usually

which,

reactors

materials,

one

because

T

parametric

shorter

although

experiments,

specified

c r i t e r i a

remain

Secondly

surpassed.

determining

chosen

only

reactor

materials

be

on

the

and

temperature

as

for

high

The

tion

not

based

conditions

because ter

must

then

the

for

diagrams ratio

of

Burghardt and also

took

however,

the

they

heteroge to

prevent

the

tube

to

Warmuzinski heat

did

effect

not

study

reactor.

catalyst

particles

have

been


stu-

of


17.

WESTERTERP ET AL.

Safe Design of Cooled Tubular Reactors

325

died by McGreavy and Adderley [ 8 ] and by Rajadhyaksha, Vasudeva and Doraiswamy [ 9 ] and they presented c r i t e r i a to avoid t h i s mult i p l i c i t y . However, i t has been shown [ 1 0 , 1 1 ] t h a t m u l t i p l i c i t y a r i s i n g from i n t e r p a r t i c l e gradients are not very l i k e l y under i n d u s t r i a l operating c o n d i t i o n s . Other c r i t e r i a t o avoid runaway were developed by Dente and C o l l i n a [ 1 2 ] and Hlavâcek, Marek and John [ 1 3 ] . Emig, Hofmann, Hoffmann and Fiand [ 1 4 ] proved experimentally that the c r i t e r i a o f Barkelew, of Agnew and P o t t e r and of McGreavy and Adderley a l l p r e d i c t runaway remarkedly w e l l f o r a s i n g l e f i r s t order r e a c t i o n i n a cooled c a t a l y t i c t u b u l a r r e a c t o r . Only Westerterp [ 1 5 ] up t o now a l s o took the r e q u i r e d s e l e c t i v i t y i n t o account i n a r e a c t o r s t a b i l i t y study, but only f o r tank r e a c t o r s . We w i l l use h i s study as a s t a r t i n g p o i n t and extend i t to m u l t i p l e r e a c t i o n s i n a cooled tubular r e a c t o r . Recently Westert e r p , Ptasinsky [ 1 6 , 1 7 ] and Overtoom [ 1 8 , 1 9 ] published s t u d i e s on m u l t i p l e r e a c t i o n s i n t h i s r e a c t o r type. Existing c r i t e r i a for s i n g l e reactions i n tubular

reactors

For the prevention of runaway the maximum allowable temperature ma known. For a f i r s t order r e a c t i o n w i t h k = A exp(-E/RT) Barkelew [ 2 ] d e r i v e d the c o n d i t i o n t h a t :

T

m

u

s

t

Ε RT

Τ

ma

-Τ

c

< 1

(D

Further he d e r i v e d e m p i r i c a l l y by c a l c u l a t i o n the border l i n e between the regions w i t h and without runaway i n a p l o t of the c o o l i n g c a p a c i t y of the r e a c t o r as a f u n c t i o n of the a d i a b a t i c temperature r i s e of the r e a c t i o n . Van Welsenaere and Froment [ 3 ] proved that the l e s s s t r i c t c o n d i t i o n Τ

ma

-Τ

c

RT

(2)

< 1

a l s o g i v e s s a t i s f a c t o r y r e s u l t s . Moreover, e m p i r i c a l l y they found for f i r s t order r e a c t i o n s a mathematical expression f o r the border l i n e between the regions with and without runaway: ΔΤ

4U pc d k P t . ÏÏ3 i n which k = A exp (-E/RT ). To compare t h e i r r e s u l t s with those of Barkelew and by suï s t i t u t i o n of E/RT * < m a - c c and i n t r o d u c i n g N = 4U/pCpd k and S = Ε kT^/RT^, i n which A exp (-E/RT ) we can r e w r i t e Eq.(3) i n t o : Τ

ad -Τ ma c

1 + /Ν + N

with

c

c

t

(3)

Ν

T

T

)/T

c

C


=

1


326

i n which e = 2.718. We see t h a t N /S reaches a l i m i t e f o r very high values of the a d i a b a t i c temperature r i s e . The r e s u l t s of van Welsenaere and Froment enable us to c a l c u l a t e a minimum coolant temperature T w i t h equation 2 and then a maximum r e a c t a n t concen t r a t i o n i n the r e a c t o r feed ( A T = (-^H )C /pCp) with Equation 3 f o r a c e r t a i n value o f Ν or f o r a f i x e d value o f feed concentra t i o n a minimum value of N. From Equation 3 i t f o l l o w s t h a t no run away occurs, provided: c

c

a d

u

T

T

< ma- > c


t

R

1

(-*V

Ao

1 -1

Ao

T h i s equation can l a t e r on be compared with the c r i t e r i a d e r i v e d by us. The mathematical model f o r the plug flow r e a c t o r with m u l t i p l e reactions Several authors a p p l i e d i n v a i n the same method of Barkelew and others to m u l t i p l e r e a c t i o n s without f i n d i n g c r i t e r i a f o r safe design o f t u b u l a r r e a c t o r s . We t h i n k t h i s i s mainly caused by the f a c t that the dimensionless groups used by them i n s t r i n s i c a l l y are s t r o n g l y dependent on the o p e r a t i n g c o n d i t i o n s . S p e c i a l l y N i s s t r o n g l y a f f e c t e d by the coolant temperature t o be chosen ( k = A exp (-E/RT )). We t h e r e f o r e should look f o r dimensionless groups which are e i t h e r e x c l u s i v e l y r e p r e s e n t a t i v e f o r the reac t i o n system or f o r the design and operating parameters. We t h e r e f o r e followed a d i f f e r e n t approach. We consider a t u b u l a r r e a c t o r i n which two p a r a l l e l or consecutive r e a c t i o n s occur: c

c

C

Ρ

/ A

or

A

Ρ

X

(6)

Ν χ In these r e a c t i o n s A i s the r e a c t a n t , Ρ i s the d e s i r e d and X the undesired product. Both r e a c t i o n s are i r r e v e r s i b l e , exothermic and of the f i r s t order and conversion r a t e s are given by: R R

wP

= k C Ρ A

wX

= k C X A

or

R , = k C - k C wP Ρ A Χ Ρ

(7)

R

(8)

wX

= k C Χ Ρ

Here R i s expressed as kmoles converted per u n i t of time and per u n i t of mass of c a t a l y s t . The pseudo-homogeneous one-dimensional model o f the cooled, t u b u l a r r e a c t o r used by us i s based on the f o l l o w i n g assumptions: - the c o n c e n t r a t i o n and temperature g r a d i e n t s only occur i n the axial direction; - the only t r a n s p o r t mechanism o p e r a t i n g i n the a x i a l d i r e c t i o n i s the o v e r a l l flow i t s e l f , which i s supposed to be the p l u g flow; w


17.

WESTERTERP ET AL.

327

Safe Design of Cooled Tubular Reactors

- the p h y s i c a l and chemical data ρ , ρ , C , Δ Η and U are assumed to be independent of temperature? - the temperature o f the c o o l i n g medium T i s constant. The mass and heat balances f o r t h i s r e a c t o r model are e.g. f o r consecutive r e a c t i o n s : β

p

c

dC u ~~~ = R ρ dz wA'B dC u ~r"-~ dz

=

R

dT

ψ= dz


u

-

(9)

(10)

ρ wX^B (ΔΗ

R + A wA

ΔΗ

R ) X wX

—

v

4U do C t g ρ

-

ρ C g P

(τ-τ c)

(11)

In order to compare the two competing r e a c t i o n s we use the r e f e rence temperature T introduced by Westerterp [15]. T h i s i s the temperature a t which the r e a c t i o n v e l o c i t y constants k and k are equal and have the value o f k as shown i n F i g u r e 1. From this condition follows: R

p

x

R

-Ε k

Ξ k , P|T

Q

R

= k , l r> X

= A

T

e

n

R T

-E

Ρ

R = A

P

e

v

R T

X

R

(12)

X

R R We now can d e r i v e the value o f the r e f e r e n c e temperature a l s o a reference r e a c t i o n v e l o c i t y constant k :

T

R

and

D

T

R

=

P

R ll

( S

ipC

1+H(S

}

ip iDa

P

l,2

>

K

P

ma l 2,3 f

i n which:

_

ma

c

c

ρ

_

m _tri^P""

ri

) *

m

a

c

l

C -κ Τ -Τ -[ hs ~~"hs 'ma ~c 3 ~ T. -T AT κ hs c ad ma i n which T, f o l l o w s f o r chosen hs Τ from: ρ

+

J

m

H

^

·

,

,

2

„

„

,

ad

< s

n

'p

Cooling medium temperature should be Τ > T > ( T ) . , where ma c c mm Ύ (T ) . = c min

2

(ijt V min }

1

Ύ

Ρ -

L N C

5Γ75Γ:

and i n which Da /Da . c min

=

Ύ Ρ ln(Da /Da )+γ /T c mm ρ ma

]

=3-5



332 conditions design ty

or

or

than

yield The

tion

of

tions

a

the

e.g. in

cooled


the

the to

should

for

reactions method

with

w i l l

of

To

this

cooled, tion

of

o

u

l d

changes

method of

has

c

can or

be

been

reac

designed

and

Moreover,

constant

or u

o

now

chosen

yield

different

opera

multiple been

kept A

starts.

safe

anymore.

be

i n

temperature selectivity

the

has

changed n

runaway the

i f

selectivi

at

values

[17,19]

constant.

developed order

for

and

f i r s t

especially

Eley-Rideal

kinetics

work.

c r i t e r i a

article

to

two

tubular

scheme

C

industrial

processes

examples

of

application

ethylene

oxide

of

the

on

the

c r i t e

Table

III. give

we

large

(

OT

H

"

2

1

0

kmole

on

is

a

based

silver

excess

of

direct

catalyst

ethylene

in

the

reac

)

/

2

reactions

the

is

has

have for

°2

= 11.3

S

This

would

vity

requirement

give

one-dimensional

results

applied

made

a

N

Q

the

tube asks

diameters

the on

longer

c r i t e r i a of

d

tube

pseudo-homogeneous

this

proves

tube

diameters

that

to

the

m

t

of

tube

becomes;

and

conditions

-

0.14

model

the

to

1"

selectivity.

Welsenaere

diameter

de in

grounds.

reaction

= 534 =

from

desired

reactor

A

given

van

main a

are

runaway

maintaining

than

the

economic

diameter

m,

0.14

tube

lead

T

smaller

oxygen.

with and

for

a

in

results

the

for

order

some

for

= 20.6

2

[17],

determination

expression

and

i n

reactors

be

0 )

MJ/kmole

pseudo-first

diameter, to

the

rate

find

are

given

that

tube

choice

[3]

(- 473

H 0

+

2

We s e e

kinetic

=

For a

phase

to:

satisfactory

would

Froment

much

gas

simplified

2 4°

^C0

larger

the

be

elaboration

final

If

reactors.

can

which both

The

of the

H

tailed

2.5"

in

2 4 N

in

production

ethylene

C

t

s

the and

order,

Langmuir-Hinshelwood or

the

industrial

oxidation

d

be

words,

follow.

The

a

like

reactions

not

Application

f i r s t

reactor

-

that

for

then

for

other

strict,the

design

the

(Tma !^ )/^Fad

reactor

warn

the

cannot

conditions the

for

Once

required coolant

reactions;

conclude

II.

Or i n

less

much e a r l i e r

diameter U*

runaway. chosen

reactor

Table

tube

keep

the

ria

tubular

in

of are

procedure

requirement

for

We

variables

deteriorate

operating

order

order

w i l l

given

installed,

varying

prevention

recommended

is

with

the

operating

Κ and m,

Chemical and Catalytic Reactor Modeling - American Chemical Society

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