Modeling the Slugging Fluidized Bed Reactor - ACS Symposium

33 Modeling the Slugging Fluidized Bed Reactor J. R A G H U R A M A N

and Ο. E . P O T T E R

Downloaded by UNIV LAVAL on April 23, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch033

Department of Chemical Engineering, Monash University, Clayton 3168, Victoria, Australia

In some industrial, and nearly all pilot-plant, fluidized bed reactors the aspect ratio is such that slugging behaviour can be expected, as Davidson and his co-workers have suggested. Scale-up therefore frequently involves a jump from slugging-bed behaviour to freely bubbling bed behaviour. Slugging behaviour occurs when the bubbles present in the bed have diameters approaching that of the vessel. By 'freely bubbling' is meant that there are many bubbles present, each bubble being of a diameter much less than that of the vessel. Fryer and Potter (1,2,3) have compared the counter-current backmixing model with experimental results and the predictions of other models and have demonstrated that the countercurrent back mixing model is appropriate to the freely bubbling bed and has advantages over other models which have been proposed. Raghuraman and Potter (4) have extended the concepts of the countercurrent backmixing model to the slugging fluidized bed, basing the analysis on the solids m i x i n g model o f Thiel a n d Potter (5,6). C o m p a r i s o n o f the predictions o f the new model w i t h t h e experi m e n t a l d a t a o f Hovmand and D a v i d s o n ( 7 , 8 ) and Hovmand, Freedman and D a v i d s o n ( 9 ) shows better a g r e e m e n t w i t h e x p e r i m e n t t h a n i s exhibited by the t w o - p h a s e model o f Hovmand and D a v i d s o n . In t h i s p a p e r an e x t e n s i o n o f t h e new model i s d e s c r i b e d . T h i s e x t e n s i o n o f t h e model h a s t h e a i m o f f a c i l i t a t i n g a d e t a i l e d d y n a m i c i n v e s t i g a t i o n o f t h e s l u g g i n g f l u i d i z e d bed r e a c t o r whether o f t h e c a t a l y t i c t y p e o r o f t h e t y p e e x h i b i t i n g r e a c t i o n between g a s and s o l i d a s i n m i n e r a l r o a s t i n g and f l u i d i z e d bed combustion. The e x t e n d e d model r e p o r t e d h e r e s e e k s t o d e s c r i b e t h e c y c l i c v a r i a t i o n s w h i c h o c c u r due t o s l u g g i n g i n a s t e a d y s t a t e c a t a l y t i c system. A l t h o u g h t h e s t u d i e s c o m p l e t e d and p r o p o s e d have d i r e c t a p p l i c a t i o n o n l y t o s l u g g i n g f l u i d i z e d bed r e a c t o r s t h e r e w i l l be i n s i g h t s g i v e n i n t o t h e b e h a v i o u r o f f r e e l y b u b b l i n g beds. P o t t e r (10) h a s r e c e n t l y r e v i e w e d t h e m o d e l l i n g o f f l u i d i z e d bed reactors. © 0-8412-0401-2/78/47-065-400$05.00/0

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

33.

RAGHURAMAN

Slugging Fluidized Bed Reactor

AND POTTER

401

Model o f D a v i d s o n and C o - w o r k e r s Hovmand and D a v i d s o n (8_) p r o p o s e d a t w o - p h a s e model a n d compared t h e p r e d i c t i o n s o f t h a t model w i t h t h e e x p e r i m e n t a l d a t a o f Hovmand a n d D a v i d s o n (7_) a n d Hovmand, Freedman and D a v i d s o n (9). The model assumes c o - c u r r e n t p i s t o n - f low o f b u b b l e g a s (U-U ^) a n d d e n s e - p h a s e g a s ( U ^ ) , w i t h t o t a l m i x i n g o c c u r r i n g when s l u g s c o a l e s c e . This latter a s s u m p t i o n has n o t been j u s t i f i e d a s y e t . The new model r e t a i n s t h e a c c o u n t o f g a s - e x c h a n g e g i v e n by Hovmand a n d D a v i d s o n ( 8 ) . Gas e x c h a n g e due t o d i f f u s i o n and b u l k - f l o w a r e a d d i t i v e .


2_ = ±

^mf U

Dm

In e q u a t i o n

1/2

1

+

mf

1

+

£

mf

J

D

is slug-length.

f o r t h e s l u g , g i v e n by : 1/9

L S

S

(1)

I J

(1) m i s a s h a p e - f a c t o r 4V

Λ ]

Γ

π

495

-

°·

I i s surface

,..(2)

+ 0.061

D

integral

tabulated

in Table I .

Table I Value of Surface Integral I L /D s

I

0.3

0.5

1.0

2.0

3.0

4.0

5.0

0.13

0.21

0.39

0.71

0.98

1.24

1.48

The a u t h o r s a l s o g i v e a n e x p r e s s i o n f o r g a s - e x c h a n g e w h i c h t a k e s i n t o a c c o u n t i n t e r a c t i o n between d i f f u s i o n and b u l k - f l o w b u t recommend f o r use t h e g a s - e x c h a n g e r a t e c a l c u l a t e d by e q u a t i o n ( 1 ) . The s l u g - r i s e v e l o c i t y , w i t h r e s p e c t t o s t a t i o n a r y s o l i d s a h e a d , i s g i v e n by Kehoe a n d D a v i d s o n ( 1 1 ) U

=

s

and t h e r i s e v e l o c i t y o f c o n t i n u o u s l y g e n e r a t e d s l u g s U

SA

U-U

f

,.(3)

0.35 ( g D ) '

+ 0.35 ( g D )

i s g i v e n by:

:

(4)

The e x c h a n g e c o e f f i c i e n t , Q/V , i s used by D a v i d s o n a n d c o - w o r k e r s f o r g a s e x c h a n g e between t h e s l u g and t h e r e s t o f t h e b e d , o r dense p h a s e . The New M o d e l , T i m e - A v e r a g e d T h i e l and P o t t e r ( 4 , 6 ) have shown t h a t m i x i n g o f s o l i d s i n r o u n d - n o s e d s l u g g i n g beds c a n be a c c o u n t e d f o r by a s s u m i n g t h a t t h e s l u g i s f o l l o w e d by a wake o f w e l l - m i x e d s o l i d s w h i c h t a k e s up a b o u t t w o - t h i r d s o f t h e i n t e r s l u g m a t e r i a l . The r e m a i n d e r o f t h e i n t e r - s l u g m a t e r i a l i s i n piston-flow. Thus t h e model a d o p t s t h e g a s - e x c h a n g e r a t e a s g i v e n i n e q u a t i o n ( 1 ) b u t c o n s i d e r s i t a p p l i c a b l e t o gas e x c h a n g e between


CHEMICAL REACTION ENGINEERING—HOUSTON

402

wake and s l u g , Q/V~ being r e l a b e l l e d K^. So f a r as gas-exchange between wake and tne p i s t o n - f l o w region i s concerned, t h i s i s considered t o be determined by the s o l i d s movement, allowance being made f o r gas flow U ^ , with respect t o s t a t i o n a r y s o l i d s . The s o l i d s phase flows i n and out of the wake, which i s of vo I urne f V at a volumetric r a t e , U This exchange can be expressed i n terms of an exchange c: o e f f i c i e n t , namely the volume of s o l i d s phase exchanged with the wake per u n i t s l u g volume per u n i t time, (IL πΟ /4)/V^. If there were no flow of gas through the s o l i d s phase, then the gas-exchange r a t e would be (ε U π ϋ / 4 ) / ν . Following Stewart and Davidson (12) the flow out of the s l u g nose and i n a t the base of t h e s l u g w i l l be U ^ -nD /4. So, the net volume of gas exchanged between the p a r t i c u l a t e p i s t o n - f l o w U J πϋ /4. region and the wake per u n i t time w i l l be (U ε mf mf ç

r

2

$

f


z

ζ

c

(U

S

mf 4 V

U )πϋ mf

ζ

χ

,(5)

r

If the f r a c t i o n of the bed-volume occupied by slugs i s ε^, then

...(6) B

V

2

+ TD(wD /4)

s

where Τ i s the r a t i o of mean i n t e r - s l u g spacing t o column diameter. Therefore, equation (5) may be a l t e r n a t i v e l y presented : (1-ε > Β

Κ

CP

TD ε

,(7)

υε ,- U S mf mf ο

Β

#

Figure 1 i l l u s t r a t e s the gas-exchange process. For f i r s t - o r d e r s t e a d y - s t a t e chemical r e a c t i o n , the m a t e r i a l balances on reactant gas, on a time-averaged b a s i s , a r e as f o l lows : dO,

Slug

Β U GB dz

Wa ke

U G

K

BC

K

CP

(C

,(8)

)ε

C " °Β Β

dCç c

dz

( C

C

P

) £

C B

+

K

k

Pi ston-flow reg ion

5

U GP dz

K

( C

C

CP C " P

) e

B "

k

( C

C

BC B " C

f

ε

) £

B ,(9)

C

w Β C 1

ε

- Β

Π +

ν ...(10)

Here the wake f r a c t i o n i s given by : f

2

w

= wUD /4)TD/V S c


...(11)

33. w

RAGHURAMAN

is the

and

of

the

estimated

conditions

U

GB

=

U

GP

=

Ζ

=

material

and Potter

which

to

by Raghuraman

403

i s we I I - m i x e d

be 0 . 7

*

0.2.

and Potter

(4_).

The

...(12)

=

U

U

and

At

inter-slug

by T h i e l

are given

average,

where


POTTER

proportion

has been

boundary

On

AND

+

GB

U

-

U

U

, mf

U

U

m f -

o,

ε

c

+

GC

U

U

GC =

Vmf GB

,f,,(U-U

mf w = c

B

GP

...(13)

,)

mf

...(14)

0

...(15)


and U

-

The

exit

The

New M o d e l ,

at

reacting

The

cycle

slug

slugs

obtain flow

time

Figure

at

of

assumed

that

becomes

piston-flow

when

slug

New s l u g

formation is

distributor moment on.

of

Since

again 0

of

top

the bed a t

from

i n t e r s lug

it 0

one-third.

risen

by o n e - t h i r d

reached

the top of

In

of

we

7

)

from t h e bed from

non-reacting

time.

here

1

follow

region

the top of

with

(

Only

for

the

comparison

model

of

Hovmand a n d

to

rise

a

t h e bed and s l u g s

above

are

cycle

in the top

it

above

is

seen

detach

also

a

1

Figure

at

being

2 this

τ / 3 , slug

0

the

i n t e r s lug

spacing

t h e bed and b u r s t s ,

is

as

necessarily

t

= 0

from

the

an

is

α

a new

to

forming,

α

at

the

2 and s o

integral remains

detaching

fraction

=

section

renumbered

amount

t h e new s l u g

piston is

produce

renumbered

in general,

fractional

when

that

is

It

calculation.

itself

has detached, 1;

to

are not

in the

the bed

and

the top.

bursting

account

in

conditions

a s t h e wake

and a t

i s no s l u g

to

situations

Special

t h e flow

2,

the

cycle

1,

of

through each

the top.

not contain,

the time

At t

of

slug

to

regions,

form

is approached

zero

progressive

to

into

from

the distributor.

mately

at

the f i r s t

= 0

this

bed t o

the two-phase

the

Figure

t h e bed does

number of

t

In

f o r the slug

+

and a t

Form

At the beginning

is just about

detachment

- - ·

fluidized

and slug

taken to

C

data.

there

and t h i s

numbered

C

mf

:

and the p i s t o n - f l o w

bursts

since

in

Referring

U

by

admitted

behind

mixing. phase

...(16)

t h e bottom

during

C

are presented

TD/U^.

shows

C

p

the bed i s

and r i s e

a

G C

Cyclic

version,

a r e formed

U

the steady-state

gas is

2

=

0

the fluidized

Thus

at

t h e bottom

regimes

slug,

+

i s the time

a r e formed

C

the slug,

i.e.

is admitted

renumbered. as

C

GB B

solutions

length

)

= C

c

and the experimental

inter-slug new

of

the time-averaged

Davidson

G B

is given

in which

steady-state

with

U

C

U

=

bursts.

state

and then

final

H

t h e bottom

the slug

initial

C

-

Mechanistic

t h e wake

formation

gas

U

gas concentration

slug,

where

(

= H,

U

each

+

P

Ζ

At

an

C

GP

is all

a n d s Iug 5

illustrated,

at

the

itself

approxi slugs has a

later.


have just

moment

CHEMICAL REACTION ENGINEERING—]

4*i


Β

wTD f

**0

I

i=^-wJTD

Figure 1. Slugging fluidized bed. (A) well-mixed wake region; (B) piston-flow region.

β β β β aβ β a β ft

ft

ft

ft

β β β β β β β β β β β β f.Wr

Figure 2. The mechanistic model portrayed over one time cycle


33.

RAGHURAMAN

405


AND POTTER

The l e n g t h o f t h e w e l l - m i x e d r e g i o n b e h i n d a s l u g i s wTD. T h e r e f o r e a t t i m e W T , f r a c t i o n w o f a new s l u g 0 h a s f o r m e d a n d t h e l e n g t h o f t h e i n t e r - s l u g m a t e r i a l b e h i n d s l u g 1 i s wTD. As the r e s t o f t h e i n t e r - s l u g m a t e r i a l , behind s l u g 1, f a l l s into p l a c e , a p i s t o n - f l o w r e g i o n i s commenced u n t i l a t t = τ the s i t u a t i o n has r e t u r n e d t o t h a t d e p i c t e d f o r t = 0~.


+

Due t o t h e f r a c t i o n o f TD r e m a i n i n g a t t h e t o p o f t h e b e d , t h e t o p s e c t i o n i s o u t o f p h a s e w i t h t h e f o r m a t i o n o f new s l u g s at t h e bottom of the bed. Thus, r e f e r r i n g t o Figure 2, a t time t = τ/3 the top-most slug bursts, l e a v i n g a l e n g t h TD o f p a r t i c u l a t e phase o r i n t e r - s l u g m a t e r i a l , l y i n g above s l u g 4 w h i c h h a s now b e c o m e t h e t o p - m o s t s l u g . As t i m e i n c r e a s e s t o WT, t h e l e n g t h o f t h i s i n t e r - s l u g ( o r s h o u l d we now s a y "above-slug") material decreases. A t WT t h e new w a k e r e g i o n b e h i n d s l u g 1 i s complete. A t τ the p i s t o n - f l o w region behind s l u g 1 i s a I so complete and the s l u g detaches. At the top of the bed, the length o f i n t e r - s l u g m a t e r i a l w i l l have f a l l e n t o o n e - t h i r d o f TD. T h e b e h a v i o u r now r e p e a t s i t s e l f a n d i s t h u s c y c l i c a l . T h e m o d e l b r i e f l y d e s c r i b e d a b o v e i s now c o n s i d e r e d f r o m a chemical reaction point of view. Fresh r e a c t a n t gas i s s u p p l i e d at a steady flow U and of t h i s flows c o n t i n u a l l y through the b e d w h i l e d J - U ^ ^ a c t s g r a d u a l l y t o r a i s e t h e b e d a b o v e t h e new s l u g a n d , i n a s e n s e , o n l y e n t e r s t h e b e d , a s r e a c t a n t i n t h e new s l u g a t t h e moment o f i t s d e t a c h m e n t . The s t e a d y - s t a t e results p r e s e n t e d here have been a p p r o a c h e d from an i n i t i a l s t a t e i n which t h e bed i s c y c l i n g a s above w i t h no r e a c t a n t gas p r e s e n t , t h e p r o c e s s s t a r t i n g when t h e e n t e r i n g g a s i n s t a n t a n e o u s l y h a s i t s reactant concentration adjusted to C . are and

C o n s i d e r a g e n e r a l c e l l , j . C e l ? s , as d e p i c t e d i n F i g u r e 1, counted from t h e bottom upwards, so t h a t (j+1) i s above c e l l ( j - 1 ) below i t . Material

Balances

on general

j

cell

SI ug 0

^

=

Wake

^BcS-Vj dC

m f

+

M f

p

1

•••

(18)

.

•••

^ B C ^ C - V j

V ^ J - ^ e . j + l *

+ k f

(19)

w C C

P i s t o n - F l o w Region o f P a r t i c u l a t e Phase Since piston-flow o b t a i n s , a c c u m u l a t i o n terms c a n , i n t h i s c a s e , be i g n o r e d a l t h o u g h q u a l i f i c a t i o n s w o u l d b e made t o t h i s s t a t e m e n t i f space permitted. However t h e r e remains a d i s t a n c e - v e l o c i t y l a g w h i c h needs t o be t a k e n i n t o a c c o u n t . If ζ i s t h e length dimension and ζ = 0 a t t h e bottom o f the w e l l - m i x e d wake,


CHEMICAL

406

jnf

REACTION ENGINEERING—HOUSTON

dC, P

...(20)

+ kC . =0 P,j,z

Z

'J'

n

dz

and -kz

exp

,(21)


"mf Note t h a t C earlÎ e r .

.

p

i s r e l a t e d t o C , j , 0 a t time

z

[z/(U -U /ε^)]

p

s

mf

M a t e r i a l Balances on Ce I I 1 The slug-balance i s the same as equation (18). The wake and p i s t o n - f l o w regions are no longer of constant dimensions but of dimensions which vary with time. The wake begins t o form immediately and when i t has grown t o f u l l s i z e , the p i s t o n - f l o w region commences t o form. Wake

ε ,f 0 = - E U xw

. f 4r ( t c . j + K ( C _ - C _ ) C " C 1 "ΒΓ W T dt ΧΓ

W

B pV

D

k f U X + (υ ε mf o S mf ο

U JC mf Ρ

w tc

D

e,2

xw

p 1

(22)

CI

P i s t o n - f l o w Region This region commences t o form a t time wx and the region extends from ζ = 0 t o ζ = [(t/x)-w]TD. Equation (21) a p p l i e s with t h i s p r o v i s o . M a t e r i a l Balances on Top-most Region When a slug reaches t h e top of the bed and b u r s t s , i t leaves behind a well-mixed wake region and p i s t o n - f l o w region and i t i s assumed t h a t flow i s p i s t o n - f l o w t h e r e a f t e r . This material f a l l s around the r i s i n g top-most slug and of course disappears e n t i r e l y a t the moment of slug b u r s t i n g , only t o be replaced by the i n t e r - s l u g m a t e r i a l b,elow t h e b u r s t i n g s l u g . Equation (21) a p p l i e s . When 0 < t £ ατ, the top-most region decreases in length from ζ = aTD t o ζ = 0; when ατ 4 t

Modeling the Slugging Fluidized Bed Reactor - ACS Symposium

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