Simulation of Thermal Cracking Furnaces

22 Simulation of Thermal Cracking Furnaces H. A .

J.

VERCAMMEN

and

G.

F.

FROMENT

Downloaded by UNIV OF ARIZONA on March 8, 2017 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch022

L a b o r a t o r i u m voor Petroehemische T e c h n i e k Rijksuniversiteit, K r i j g s l a a n 271, G e n t , B e l g i u m

Until now the simulation of a thermal cracking coil has g e n e r a l l y been uncoupled from t h a t of the f i r e box by i m p o s i n g either a tube w a l l temperature profile or a heat f l u x profile. I t i s then checked a p o s t e riori whether or not the fire box p e r m i t s such p r o files to be attained. The fire box calculations gene rally proceed a l o n g the Lobo & Evans approach ( 1 ) , a l t h o u g h more recently zone methods have been applied, thus p e r m i t t i n g a temperature distribution in the fire box to be calculated ( 2 , 3, 4, 5 ) . In the work r e p o r t e d here the coil and the fire box were s i m u l a t e d s i m u l t a n e o u s l y by means of an o p t i m i z e d computer package in which the d e s i g n of the r a d i a n t s e c t i o n of the furnace i s an e x t e n s i o n and r e f i n e m e n t of Hottel's zone method ( 3 ) . In this paper the approach i s a p p l i e d to the s i m u l a t i o n of an i n d u s trial ethane c r a c k i n g f u r n a c e . The o n l y a d a p t a b l e parameter left i n the s i m u l a t i o n model is a burner d e s i g n factor, namely the fraction of the heat gene r a t e d i n the burner t h a t i s t r a n s f e r r e d to the burner cup. The parameter i s determined by matching the e x i t

conversion. 1. C r a c k i n g c o i l d e s i g n

equations

The c o n t i n u i t y - , e n e r g y - and p r e s s u r e drop equa t i o n s f o r the t u b u l a r c r a c k i n g r e a c t o r are w e l l known : L dz

(1.1) 1=1

© 0-8412-0401-2/78/47-065-271$05.00/0

Weekman and Luss; Chemical Reaction Engineering—Houston ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

272

1 IF. c

dt dz

k

dp

P

P


at

t

k

]_ dv_ V dz 1

t

dz

with

ïïd Q(z)-

inlet

+

L Ω Σ 1=1

REACTION

r

l

A

H

ENGINEERING—HOUSTOÎ

(1.2)

l

J_ d t ζ t dz Ω β GA +

t "

(1.3)

T=T

F.=(F,) k k o

conditions

o

and P = ( P ) t

t

z=o F

In

(1.1)

r

i

=

k

(

i

T

a 2

2

}

Table I r e a c t i o n scheme a n d k i n e t i c

Molecular

parameters

A s e t o f r e a c t i o n s h a s t o be c o n s i d e r e d d i c t t h e p r o d u c t d i s t r i b u t i o n . The f o l l o w i n g m o l e c u l a r r e a c t i o n s was a d o p t e d : Order

C

2 6^ 2 4

C

2

H

C

H

6 ^ Î

H

C

H

2

+

H

4

+

C H

2

H

2

4

o

C

H

H

2

H

+ H

' 3 6 2 •C H CH

3 8 2C H ^C 2 C

2

2

SV C

2 +

2

2 4-

> C

2

4 +

Frequency Factor

4

4

(Kcal/Kmol).10 82

8. i o

1 2

67

7 .i o

1 3

76

1 .i o

1 3

104.6

5 .i o

1 3

1

-3

63 .3

3. 2 . 1 0

1 3

63

3 .2 . 1 0

1 1

45

4. i o

4

to pre s e t of

6

8 .i o

2

•C H H 2 4" C H + 2 H , 0 >2C0+3H 2 ( H 0)

C

0

60

1 3

S i n c e t h e f e e d c o n t a i n e d some p r o p a n e t h e a b o v e scheme a l s o c o n t a i n s d e c o m p o s i t i o n r e a c t i o n s f o r t h i s com ponent . In (1.3) t h e symbol ζ stands f o r 0.0227R, +0.0847d . (1.4) 0.092 _R -0.2 + . D t t

A

e

R;

In (1.4) t h e a d d i t i o n a l bends of t h e h o r i z o n t a l ed f o r .

p r e s s u r e drop i n t h e r e t u r n c r a c k i n g c o i l a r e a l s o account


22.


2.

V E R C A M M E N AND

Fire

Thermal Cracking Furnace Simuhtion

FROMENT

box heat

273

transfer

2.1 Non r a d i a t i v e h e a t f l u x e s . The f u r n a c e c o n s i d e r e d i n t h i s work, s c h e m a t i c a l l y r e p r e s e n t e d i n F i g . 1, i s f i r e d by 60 r a d i a n t b u r n e r s , p l a c e d i n t h e s i d e w a l l s . A s m a l l f r a c t i o n only of t h e heat o f combustion i s t r a n s f e r r e d t o t h e r a d i a n t b u r n e r c u p i t s e l f . The major f r a c t i o n of t h e r e l e a s e d heat e n t e r s t h e f i r e box w i t h t h e c o m b u s t i o n gases t h r o u g h r a d i a t i o n and c o n v e c t i o n . The e x a c t v a l u e o f t h i s s p l i t , r e p r e s e n t e d by y , i s n o t g i v e n i n t h e t e c h n i c a l l i t e r a t u r e , however. I t w i l l , t h e r e f o r e , be t h e o n l y a d a p t a b l e p a r a m e t e r l e f t i n t h e d e s i g n model o u t l i n e d here. The s i m u l a t i o n m o d e l i s l i m i t e d t o t h e r a d i a n t s e c t i o n . The c o n v e c t i v e h e a t t r a n s f e r t o t h e t u b e s a n d to t h e r e f r a c t o r y w a l l s i n t h a t s e c t i o n was c a l c u l a t e d by means o f t h e u s u a l c o r r e l a t i o n s ( 6 , 7, 8 ) . H e a t l o s s by c o n d u c t i o n t h r o u g h t h e r e f r a c t o r y w a l l s a n d b y n a t u r a l convection a t the outside of the furnace w a l l s was a l s o a c c o u n t e d f o r . 2.2 R a d i a t i v e h e a t t r a n s f e r . To o b t a i n a r e p r e s e n t a t i v e temperature d i s t r i b u t i o n i n the r a d i a n t sec t i o n o f t h e f u r n a c e t h e f i r e box and t h e o u t s i d e w a l l o f t h e c o i l w e r e d i v i d e d i n t o a number o f i s o t h e r m a l z o n e s a s shown i n F i g . 2. The s e t o f h e a t b a l a n c e s o n t h e z o n e s c a n be w r i t t e n c o n c i s e l y i n m a t r i x n o t a t i o n a s shown i n ( 2 . 1 ) . I n e a c h z o n e Z. ( v o l u m e o r s u r f a c e ) t h e n e t r a d i a t i o n captured i s equated to the n e t n o n - r a d i a t i v e f l u x l e a v i n g t h e z o n e Q!. The r a d i a t i v e f l u x f r o m Z. t o Z. i s g i v e n by. Ζ. Ζ . Ε . I w h e r e E.= 0 T . a n d w h e r e Z.i. i s t h e t o t a l excàaneâ a r e a b e t w e e n i . a n d Ζ., i n er . i ι . w o r d s t h e f r a c t i o n o f t h e h e a t r a d i a t i o n e m i t t e d b y Z. t h a t i s a b s o r b e d by Ζ. : ^ 1 .Ζ,Ζ z,z . . i -Σ z . z , 1 1 η 1 z z - Σ τ 7 .Ζ Ζη 2 1 ι 2' (2.1) z

z

2

¥. V l

2

Z

Ε

2

Z

n 2

2

Ζ Ζ -Σ η η i

Ζ .Ζ ι η

Ε

Ε η

The s o l u t i o n o f t h i s s e t o f e q u a t i o n s y i e l d s t h e t e m p e r a t u r e s i n t h e volume and s u r f a c e z o n e s . S i n c e t h e s e t i s n o n l i n e a r i t h a s t o be s o l v e d by i t e r a t i o n . A N e w t o n - R a p h s o n p r o c e d u r e was f o u n d t o be v e r y e f f i c i e n t for this. The t o t a l e x c h a n g e a r e a s a r e o b t a i n e d i n s e v e r a l



274

CHEMICAL

REACTION

ENGINEERING—HOUST(

Figure 1. Representation of thermal cracking furnace



22.

V E R C A M M E N AND

Thermal Cracking Furnace Simulation

FROMENT

275

s t e p s . The f i r s t s t e p i s t h e c a l c u l a t i o n o f t h e v i e w f a c t o r s i . e . t h e f r a c t i o n o f t h e r a d i a t i o n l e a v i n g an e m i t t o r t h a t i s e m i t t e d i n the d i r e c t i o n of a r e c e p t o r The m u l t i p l e i n t e g r a l s i n v o l v e d i n t h i s w e r e o b t a i n e d by M o n t e - C a r l o s i m u l a t i o n , b a s e d u p o n a s a m p l e o f 2 0 0 0 0 e m i t t e d beams. To p e r m i t t h e c a l c u l a t i o n o f v i e v f a c t o r s using other viewfactors obtained i n d i f f e r e n t M o n t e C a r l o i n t e g r a t i o n s and s t i l l a s c e r t a i n t h a t t h e sum o f t h e v i e w f a c t o r s f o r e a c h e m i t t o r e q u a l s o n e , Vercammen & F r o m e n t (9^) d e v e l o p e d a r e g r e s s i o n t e c h n i q u e e l i m i n a t i n g the i n h e r e n t s t a t i s tical errors. The v i e w f a c t o r s f ^ o b t a i n e d i n t h i s way are v a l i d f o r a d i a t h e r m i c medium o n l y . The v i e w f a c t o r f b e t w e e n s u r f a c e z o n e s i n a r e a l , a b s o r b i n g medium f o l l o w s from : f = f X (2.2) J

* where by :

χ

.

d

.

.

i s t h e mean t r a n s m i s s i o n

.

.

coefficient,

given

S Γ

X

= j

max (2.3) X(S)

DDF(y)

dS

I n (2.3) τ(S) mm i s t h e t r a n s m i s s i o n f o r a beam h a v i n g a l e n g h t S and D D F ( y ) i s t h e d i m e n s i o n l e s s beam l e n g h t d i s t r i b u t i o n f u n c t i o n , w i t h y =(S-S . ) (S -S . )· mm max mm Vercammen and F r o m e n t (SO p r o p o s e d t h e f o l l o w i n g f o r m f o r DDF(y) : DDF (y ) = V y ( l - \ / y ) ( - l n y ) (a+by + c y + . . . )/n ! ( 2 . 4 ) T h i s f o r m has b e e n f o u n d t o be q u i t e c o n v e n i e n t f o r w i d e l y v a r y i n g c o n f i g u r a t i o n s of the s u r f a c e z o n e s . The t e m p e r a t u r e d e p e n d e n t t r a n s m i s s i o n c o e f f i c i e n t X (S) i s r e l a t e d t o t h e a b s o r p t i o n f a c t o r k* by : 9

n

z

(

-kS

2

·

5

)

R b

X(S) = e A c c o r d i n g t o E c h i g o e . a . (J_0) t h e mean a b s o r p t i o n t o r k* i s c a l c u l a t e d f r o m : -kS C_Au)(l-e

) =

r /

fac

- k ( ω )S (1-e

)d(0

(2.6)

When t h e v i e w f a c t o r i s m u l t i p l i e d by t h e s u r f a c e of the e m i t t o r the s o - c a l l e d d i r e c t exchange a r e a i s o b t a i n e d . The d i r e c t e x c h a n g e a r e a s b e t w e e n s u r f a c e z o n e s and v o l u m e z o n e s a r e c a l c u l a t e d f r o m t h o s e r e l a ted to a l l the s u r f a c e zones b o u d i n g the volume z o n e s , f i c t i t i o u s zones i n c l u d e d .


CHEMICAL

276

REACTION

ENGINEERING—HOUSTON


The t o t a l e x c h a n g e a r e a t a k e s i n t o a c c o u n t t h e d i r e c t r a d i a t i o n , t h e a b s o r b e d r a d i a t i o n and i n a d d i t i o n m u l t i p l e r e f l e c t i o n on t h e s u r f a c e z o n e s ; M a t r i c e s o f t o t a l e x c h a n g e a r e a s w e r e s e t up f o r CO^ and H«0 a b s o r p t i o n b a n d s and a n o t h e r one f o r t h e d o m a i n i n t h e a b s o r p t i o n s p e c t r u m i n w h i c h no r a d i a t i o n was a b s o r b e d . The m a t r i c e s w e r e w e i g h t e d w i t h r e s p e c t t o the e m i t t e d energy a s s o c i a t e d w i t h the domain of the f r e q u e n c y s p e c t r u m b e i n g c o n s i d e r e d and summed up, y i e l d i n g t h e t o t a l e x c h a n g e a r e a m a t r i x shown i n ( 2 . 1 ) . 3.

Simulation

procedure

The s i m u l a t i o n d i s c u s s e d h e r e i s l i m i t e d t o t h e r a d i a n t s e c t i o n of the f u r n a c e , where the r e a c t i o n i s t a k i n g p l a c e . The s i m u l a t i o n o f t h e c o n v e c t i o n z o n e o f the f u r n a c e i s s t r a i g h t f o r w a r d . The s u b d i v i s i o n shown i n F i g . 2 y i e l d e d 110 i n d e p e n d e n t non z e r o v i e w f a c t o r s . F i f t y f o u r r e a l s u r f a c e zones were c o n s i d e r e d , t o g e t h e r w i t h 3 f i c t i t i o u s , h o r i z o n t a l s u r f a c e z o n e s and 4 v o l u m e z o n e s . O p p o s i t e p a r t s o f t h e s i d e w a l l s ( e . g . A. and C j ) a r e considérée t o be one z o n e o n l y . S e c t i o n s o r t h e two p a r a l l e l c o i l s l o c a t e d a t an e q u a l d i s t a n c e o f t h e i n l e t ( R j e.g.) are a l s o l u m p e d i n t o one z o n e . F i n a l l y , a 5 8 x 5 8 m a t r i x f o r t h e c a l c u l a t i o n o f t h e t o t a l e x c h a n g e a r e a s was ob tained . I t s h o u l d be a d d e d t h a t f o r t h e h e a t t r a n s f e r a s p e c t s t h e c o i l s w e r e s t r a i g h t e n e d t o i n c l u d e on e a c h s i d e h a l f o f t h e b e n d . The f u r n a c e l e n g h t was c o r r e s pondingly adapted. To i l l u s t r a t e t h e c a l c u l a t i o n p r o c e d u r e t h e com p l e t e m a t h e m a t i c a l m o d e l i s s u m m a r i z e d as f o l l o w s : φ

(

η *>

- Q =

φ γ

η

ν

(T

(3-D

n

Q

m ,h*,t±) = Q η' η' η ^n dF

ip(t,F,Q)

= If

Simulation of Thermal Cracking Furnaces

Recommend Documents