Chemical Reactors - American Chemical Society

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4 Simulation of a Fluidized Bed Reactor for the Production of Maleic Anhydride

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J. L. JAFFRÈS, W. IAN PATTERSON, C. CHAVARIE, and C.

1

LAGUÉRIE

Ecole Polytechnique, Montréal, Canada

The s i m u l a t i o n o f a fluidized bed p r e h e a t e r - f l u i d i zed bed r e a c t o r system f o r the c a t a l y t i c o x i d a t i o n of benzene to maleic anhydride was attempted. The experimental apparatus and r e s u l t s of K i z e r e t a l ( 7 ) together with the k i n e t i c s proposed by Quach e t al ( 8 ) formed the b a s i s f o r the s i m u l a t i o n . I t was determined that the r a t e constants and a c t i v a t i o n energies would not s u c c e s s f u l l y describe the exper i m e n t a l r e s u l t s , and these parameters were estimated using a p o r t i o n o f the r e s u l t s . The r a t e constants and a c t i v a t i o n energies found in this manner were c l o s e to those reported by other workers f o r s i m i l a r c a t a l y s t s . The s i m u l a t i o n using these estimated parameters gave reasonable agreement with the comp l e t e experimental r e s u l t s f o r conversion and selectivity as f u n c t i o n s o f temperature, a i r flow r a t e and bed h e i g h t , except f o r selectivity versus bed h e i g h t . An unsteady-state s i m u l a t i o n agreed q u a l i t a t i v e l y with the l i m i t e d data a v a i l a b l e . The production of maleic anhydride by the c a t a l y t i c o x i d a t i o n of benzene is an e s t a b l i s h e d i n d u s t r i a l process. While hydrocarbons are o f t e n suggested as a feedstock, it has been pointed out r e c e n t l y by De Maio ( 1 ) that they are an a l t e r n a t i v e but not n e c e s s a r i l y a s u b s t i t u t e . " The benzene o x i d a t i o n is done commerc i a l l y in f i x e d bed r e a c t o r s and, because of i t s e x o t h e r m i c i t y , is d i f f i c u l t t o c o n t r o l in any optimal sense. The process is thus a n a t u r a l candidate f o r a fluidized-bed r e a c t o r . The r e a c t i o n has been s t u d i e d in both f i x e d bed ( 2 , 3 ) and fluidized bed ( 4 - 7 ) r e a c t o r s . These s t u d i e s , with the exception o f that of K i z e r e t a l Ç7) do not give s u f f i c i e n t i n f o r m a t i o n f o r s i m u l a t i o n purposes. The a v a i l a b i l i t y of the r e a c t i o n data of K i z e r e t a l and the k i n e t i c s t u d i e s o f Quach e t a l ( 8 ) using a s i m i l a r c a t a l y s t suggested the p o s s i b i l i t y o f s i m u l a t i n g the process. -

1

I n s t i t u t du génie chimique, Toulouse,

France

0097-6156/81/0168-0055$05.00/0 © 1981 American Chemical Society Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

CHEMICAL REACTORS

56

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Reaction

Kinetics

The key to good r e a c t o r s i m u l a t i o n is undoubtedly a knowled­ ge of the r e a c t i o n k i n e t i c s . The k i n e t i c s of the c a t a l y t i c o x i ­ dation of benzene to maleic anhydride has been studied f o r d i f f e ­ rent c a t a l y s t s and conditions by many workers (8-13) however only Quach e t a l (8) examined a c a t a l y s t , FX203, of a type s i m i l i a r to that employed by K i z e r e t a l (FB203-S). Both c a t a l y s t s are f a b r i c a t e d by Halcon C a t a l y s t I n d u s t r i e s , but are of d i f f e r e n t formulation. Quach e t a l studied the c a t a l y s t ( i n the form of O.4 cm gra­ nules) in a Carberry-type r e a c t o r . Reaction conditions were: a temperature range of 280°C to 430°C and a benzene to a i r feed r a t i o v a r i a t i o n of O.45 to 8.23 mol percent. Their results dic­ tated a two-step o x i d a t i o n of the form: C H 6

+ 40

6

C H 0

2

4

2

+ CO + C 0

3

+ 2H 0

2

(1)

2

C.H 0_ + 20 -> 2C0 + 2C0 + H 0 4 2 3 2 2 2 o

o

o

o

Both r e a c t i o n s are exothermic and e s s e n t i a l l y i r r e v e r s i b l e . The maleic anhydride formation occurs only a t the c a t a l y s t surface while i t s degradation takes place in the gas phase ( 8 ) . I t is therefore expected that the s e l e c t i v i t y and the conversion w i l l be e q u a l l y important in the operation of fluidized bed r e a c t o r . Quach e t a l found that the benzene conversion rate was best des­ c r i b e d by the Langmuir-Hinshelwood r e l a t i o n : k

Γ β

=

k

P

1

/

k D 0 0

2

1 / 2

k

5

k

+ 4k_n O ^ B

P

where:

P

B 0 B 0

=

B

=

3

4

5

9

,

0

0

1 e

e

x

p

x

p

(-

2 4 6 0

R T

°/ )

6

(- *300/RT)

(

3

)

P

τ- = r e a c t i o n rate in gmol · g ^ · h D

The form of equation (3) i n d i c a t e s that oxygen d i s s o c i a t i o n occurs before i t s adsorption on the c a t a l y s t . When the r e a c t i o n has a be ne l a r g e excess of a i r ( *gg « χ i %) equation (3) can be r e ­ w r i t t e n as: m

k

Γ

Β = -

o

p

B R =

V~

k

B

P

B

Vo and

f i r s t order k i n e t i c behaviour w i l l be observed. The gas phase degradation of the maleic anhydride is d e s c r i ­ bed by: 1/2 Μ M M ; *Μ (-33400/RT) (5) —3 —1 where r = r e a c t i o n rate in gmol · m «h Γ

=

k

P

=

9

0

0

0

0

e

x

p

M

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

JAFFRES E T AL.

4.

Maleic Anhydride Production

57

P i l o t Reactor The r e a c t o r used by K i z e r and simulated in this workisi l ­ l u s t r a t e d in Figure 1. I t c o n s i s t s of a fluidized bed preheater s e c t i o n feeding d i r e c t l y the fluidized bed r e a c t o r s e c t i o n . Each s e c t i o n was a O.4 m high c y l i n d e r of O.184 m diameter. The pre­ heater contained sand and was heated by an e x t e r n a l e l e c t r i c a l element. The FB203S c a t a l y s t is a powder o f O.173 mm diameter p a r t i c l e s (weight average) and has a minimum fluidization veloci­ t y , U f , of O.021 m · s ~ l a t normal temperature and pressure. The r e a c t o r was cooled by ambient a i r blown through a j a c k e t . The r e a c t o r d i s t r i b u t o r was made from a 50 mm t h i c k f i x e d bed of 5 mm diameter pebbles supported on a p e r f o r a t e d p l a t e with the benzene introduced a t i t s centre. N i c k e l p a r t i c l e s (O.53 mm diameter) to a depth o f 25 mm on top of a second p e r f o r a t e d p l a t e formed a second f i x e d bed and completed the d i s t r i b u t o r . The r e a c t o r was completely i n s u l a t e d with g l a s s wool.

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m

Experimental

Results

The e f f e c t s of the r e a c t i o n temperature, T, the a i r flow rate F (reported a t 20°C and 1 atm), the depth of the c a t a l y s t bed, H ^ , and the molar concentration of benzene, c, on the conversion, s e l e c t i v i t y and production were reported by K i z e r e t a l (14). The experiments were performed according to a f a c t o r i a l p l a n o f 2^ ex­ periments w i t h i n the f o l l o w i n g l i m i t s : a

430°C £ Τ £ 490°C 4 £ F 3 <

a

£ 8 m3 · h "

1

* 7 cm C

O.5 £ c ^ 1.5 mol percent, v

H

6 6

9

air The r e s u l t s f o r conversion, s e l e c t i v i t y and production were ex­ pressed as: Y = 74.79 + O.29(T - 460) - 10.52(c - 1) - 3.91(F - 6) + a

C

Y= g

3.83(11^ - 5)

(6)

51.34 - O.22(T - 460) - 3.48(F

a

- 6) - 3.76 ( H

m f

- 5)

Y = 3 8 . H - 6.40(c - 1) Ρ Reactor Model

(7) (8)

The fluidized bed c h a r a c t e r i s t i c s o f high s o l i d s heat capaci­ t y , l a r g e i n t e r f a c i a l heat t r a n s f e r area, and good s o l i d s mixing allow the assumptions o f thermal e q u i l i b r i u m between the s o l i d s and the gas, uniform bed temperature and n e g l i g i b l e heat c a p a c i ­ tance o f the gas. An a d d i t i o n a l assumption r e q u i r e d to use equa­ t i o n (9) is that the r e a c t i o n s do not change the gas volume. The r e a c t o r and preheater each d i v i d e n a t u r a l l y i n t o three types of thermal zone.

These are:

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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CHEMICAL REACTORS

Figure 1. Experimental apparatus: preheater-reactor system

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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4.

JAFFRÈS E T AL.

Maleic Anhydride Production

59

1) the fluidized beds of sand (preheater) or c a t a l y s t ( r e a c t o r ) , 2) the f i x e d d i s t r i b u t o r beds and 3) the s e p a r a t i o n space above the fluidized beds. Some o f these zones have been d i v i d e d i n t o isothermal regions. This is shown in Figure 2 which shows that the preheater c o n s i s t s simply of the above three zones whereas the r e a c t o r d i s t r i b u t o r and s e p a r a t i o n space have been represented by three and f i v e regions r e s p e c t i v e l y . The reactor was cooled by forced a i r from a fan c o n t r o l l e d in an on-off manner. Heat t r a n s f e r to the c o o l i n g a i r was modelled as e i t h e r forced or n a t u r a l convection depending on whether the fan was on or o f f . The r e a c t o r was simulated f o r both steady and t r a n s i e n t behaviour. The steady-state model is s t r a i g h t f o r w a r d and w i l l not be discussed in d e t a i l . The unsteady-steady s t a t e s i m u l a t i o n took advantage of the f a c t that the r a t e of r e a c t i o n is much f a s t e r than the thermal response r a t e . The concentration t r a n s i e n t r e s ponse can thus be modelled as pseudo-steady s t a t e in the a c t u a l fluidized bed; this pseudo-steady s t a t e then follows the slowly changing temperature p r o f i l e . A mass balance on the s p e c i e s , j , f o r each region (see Figure 2) is w r i t t e n as: 3c. -(~r\"~) Vp = 0 = Σ V V. . r , . + Fc. . - Fc. at R R IJ i j i,m ι D

(9)

i

where:

Reaction

i r e f e r s to the r e a c t i n g species j r e f e r s to the product s p e c i e s . Considerations

The r e a c t i o n k i n e t i c s suggest the s e p a r a t i o n of the r e a c t o r i n t o the fluidized-bed and s e p a r a t i o n space zones. The conver­ s i o n of benzene to maleic anhydride and the degradation of the maleic anhydride both occur w i t h i n the fluidized bed. Only the degradation r e a c t i o n takes place in the space above the bed which has been d i v i d e d i n t o f i v e regions, each of which is t r e a t e d as a p e r f e c t l y mixed, homogeneous gas-phase r e a c t o r . I t has been shown by Chavarie and Grace (15) that the decom­ p o s i t i o n of ozone in a fluidized-bed is best described by K u n i i and Levenspiel's model (16) but that the Orcutt and Davidson mo­ dels (17) gave the next best approximation f o r the o v e r a l l beha­ v i o u r and are e a s i e r to use and were chosen f o r the s i m u l a t i o n . They suppose a uniform bubble s i z e d i s t r i b u t i o n with mass transfer accomplished by p e r c o l a t i o n and d i f f u s i o n . The d i f f e r e n c e between the two models is the presumption o f the type of gas flow in the emulsion phase: p i s t o n flow, PF, f o r one model and a p e r f e c t l y mixed, PM, emulsion phase f o r the other model. The two models give the f o l l o w i n g expressions a t the surface of the fluidized bed f o r f i r s t - o r d e r r e a c t i o n mechanism:

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

CHEMICAL REACTORS

Product outlet

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Seporotion Spoce

1 1

Γ 1

Cotolytic fluidized bed

Nickel

beods

b

0

Perforoted plote] { Pebbles

Benzene inlet

r Separation space

Sand

Nickel

beads

J Air

inlet

Figure 2. Physical model of the preheater-reactor system. Isothermal regions are indicated as: a, fixed beds; b,fluidizedbeds; c, gaseous regions.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

4.

X

PM:

Y„ = l - [ s e - + C

PF:

^ " P*~V 1 + K' - g e "

1

(10) X

t l (m e i ( i - m

Γ 1 • —

Y =1 c

61

Maleic Anhydride Production

JAFFRES ET A L .

2

H U

1

mf, E

r

m

- ) -

v

-m,H,. 2 2 ( l -

H U

i

r

mf] - ) | (11)

where

and 2

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(1 - 3) m H

2

are the roots o f : f

T

- (X + K ) niH + XK = 0

(12)

K i n e t i c s other than f i r s t - o r d e r r e q u i r e the numerical i n t e g r a t i o n of the d i f f e r e n t i a l mass balances and the conversions cannot be expressed in simple equations. The fluidized bed r e a c t o r model requires a d e s c r i p t i o n of the bubble diameter, D^. The r e l a t i o n s h i p of Mori and Wen (18) was chosen using the D^ of a porous p l a t e d i s t r i b u t e r : 0

bm

bo

R

Equation (13) was checked using the expression of Yacono (19) which was obtained from a d i s t r i b u t o r c o n f i g u r a t i o n s i m i l a r to that employed by K i z e r . Values from the two r e l a t i o n s h i p s were compared a t bed mid-height, H/2, f o r t y p i c a l r e a c t i o n c o n d i ­ tions and d i f f e r e d by 3%. Reactor Simulation:

Thermal Aspects

The energy balances on the d i f f e r e n t zones and regions of the preheater-reactor system y i e l d the f o l l o w i n g types o f terms: I. heat introduced by convection from the zone (α - 1) to the zone a, AQ ; c

= F p or a

II.

heat l o s t to the surroundings, AQ^;

AQ^

= haAT

H

III.

1

ΣΗ. c. - F. , . p , ΤΣδ., ^ c , i ία i a j (a-l) (a-l) i ι(α-1) ι(α-1) I

AQ c

K

1 N

1 N

heat introduced by the chemical r e a c t i o n s o f species i pro­ ducing j , AQ ; R

AQ_ = Σ v. .r. .ΔΗ. .ν R i i j 13 i j R X

IV. accumulation;

JQ. JL =

3t

3t

(W C + s s \

i

C

c

i i

) T

a]

which comprise the thermal balance:

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

62

CHEMICAL REACTORS

8q 3t

Δο

c

+

(14)

The s i m p l i f y i n g assumption that the p r o p e r t i e s of the r e a c t i o n mixture are those of a i r is j u s t i f i e d by the maximum benzene con­ c e n t r a t i o n of 1.5 mol percent. I t has a l s o been assumed that the gas volume is unchanged by the r e a c t i o n s . Heat t r a n s f e r to the w a l l s from the d i s t r i b u t e r was evaluated by Froment s expression f o r f i x e d beds (20): O.9 hD. D G = O.813 _J2_ (15) exp(-6D /D_) Ρ

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1

R

while that of Wen and Leva was used f o r the O.4

Vf L \\

hD

Τ

= O.16

D

p P f

U

O.76

c

Ρ

Ρ Ρ P C f

f

O.4

fluidized

bed (21)·

-O.2

kl

O.36 η

W

(16)

The r e l a t i o n s h i p of Pohlhausen was used f o r the heat t r a n s f e r in the s e p a r a t i o n space(22): RePrD Nu =

4H

In n

Pr

2.6 RePrD,. O.5 O.167 S

(17)

J

The r e l a t i o n s h i p of Mac Adams was used to estimate the heat trans­ f e r due to n a t u r a l convection(23): h = 1.42

AT O.25

(18)

A c t i v a t i n g the c o o l i n g blower causes a i r to enter the j a c k e t t a n g e n t i a l l y to the w a l l of the r e a c t o r and is assumed to f o l l o w a h e l i c a l path to the e x i t . The heat t r a n s f e r c o e f f i c i e n t was c a l c u l a t e d from Perry (24): D. 1 + 3.5

(19)

The thermal s i m u l a t i o n was v e r i f i e d by choosing a benzene concen­ t r a t i o n of zero (no r e a c t i o n ) and n a t u r a l convection c o o l i n g only. An ambient temperature of 20°C was assumed and, to minimise c a l c u ­ l a t i o n time, the accumulation terms in the s e p a r a t i o n regions were neglected. For a 1.2 kW power i n p u t , the model p r e d i c t e d a steady-state c a t a l y s t temperature of 473°C which was reached about seven hours a f t e r heating was begun. A temperature l o s s of 42°C between the pebble benzene mixer and the c a t a l y s t was p r e d i c t e d while the d i f f e r e n c e between the c a t a l y s t and the fluidized bed preheater was 57°C. This l o s s was a t t r i b u t e d to the increased

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

4.

JAFFRÈS E T A L .

63

Maleic Anhydride Production

heat t r a n s f e r through the flanges used to a t t a c h the preheater to the r e a c t o r . The s i m u l a t i o n r e s u l t s agreed to w i t h i n 10% with the observed behaviour of the apparatus and are presented in Figure 3.

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Reactor Simulation:

Steady State

The r e s u l t s of the thermal s i m u l a t i o n were s u f f i c i e n t l y encouraging f o r us to proceed to the r e a c t o r s i m u l a t i o n f o r a number of s t e a d y - s t a t e operating c o n d i t i o n s , but n e g l e c t i n g the maleic anhydride degradation in the fluidized bed. Both the s i m p l i f i e d k i n e t i c expression (equation (4)) and the more exact equation (3) were used and the r e s u l t s are shown in Table I as Case 1 and Case 2 r e s p e c t i v e l y . TABLE I PREDICTED CONVERSIONS: ORCUTT-DAVIDSON PM MODEL

Τ (°C) 430 460 490

X

Be-

Conversion given by K i z e r s model

X

1

2.10 1.91 1.73

O.113 O.138 O.165

66% 76% 83%

Operating c o n d i t i o n s :

Case 2

Case 1 K

1

K

Y

Y

f

c

c O.364 O.432 O.506

c = 1%, H - = 5 cm, F

27% 30% 33% = 6 m

O.327 O.398 O.475

25% 29% 32%

h ,

=O.9 cm bo I t is obvious that the s i m u l a t i o n p r e d i c t s conversions f o r below those obtained by K i z e r and this cannot be due s o l e l y to the n e g l e c t of the maleic anhydride degradation. There may be s e v e r a l p o s s i b l e causes f o r the low p r e d i c t e d values: the OrcuttDavidson PM model may not be s u f f i c i e n t l y accurate or the bubble s i z e estimate may be i n c o r r e c t . A l t e r n a t i v e l y , n e i t h e r equation (3) nor (4) c o r r e c t l y describe the r e a c t o r k i n e t i c s . The number of p o s s i b i l i t i e s may be reduced by c o n s i d e r i n g F i g u r e 4 which p l o t s conversion versus the non-dimensional r e a c t i o n rate constant, Κ , with ββ as a parameter. Two p o s s i b l e zones of opera­ t i o n are shown in the f i g u r e , zones A and B. Zone A is bounded by the Orcutt-Davidson PF model and the values of βε~" from Table 1 together with Quach's k i n e t i c s a l l o w i n g f o r a 10% e r r o r in the k i n e t i c parameters. Zone Β is d e l i n e a t e d by the PF model, the maximum value of β θ ~ from Table 1 and the values of conversion obtained by K i z e r . E v i d e n t l y an i n c r e a s e in K is r e q u i r e d to allow the two regions to overlap and furthermore, f o r the range of β ε " reported in Table 1, both k i n e t i c s and bed hydrodynamics (bubble diameter) play a s i g n i f i c a n t r o l e in determining r e a c t o r conversion. I t was a t this p o i n t that the s i m u l a t i o n , per se, was 1

χ

χ

1

Χ

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

CHEMICAL REACTORS

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600

2

4

3

Time hours

Figure 3. Thermal unsteady response of the apparatus during reactor start-up: 1, sandinpreheater; 2, pebble distributer; 3, catalyst

01

10

100

Figure 4. Conversion vs. nondimensional reaction rate constant, K'. The two limiting cases of one phase (Orcutt-Davidson) PM and PF models are the solid lines. Zone A is the limit of operation allowing for a 10% error in the kinetic parameters of Quach et al. Zone Β is the experimental limit of operation.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

4.

JAFFRÈS ET AL.

65

Maleic Anhydride Production

abandoned. The p r e v i o u s l y c i t e d r e s u l t s of other workers gave evidence that the form of the k i n e t i c expression of Quach e t a l was probably adequate to simulate K i z e r s r e a c t o r . Thus, we undertook to f o r c e the conversions obtained from the " s i m u l a t i o n " to c o i n c i d e with those obtained experimentally by K i z e r f o r a number of operating c o n d i t i o n s . The Marquardt (25) algorithm was chosen f o r this n o n - l i n e a r least-squares minimization problem in which the rate constants, a c t i v a t i o n energies and initial bubble diameter were the v a r i a b l e s manipulated to o b t a i n the minimal d e v i a t i o n s f o r three combinations of r e a c t o r regime and k i n e t i c expressions (cases A, Β and C) as shown in Table I I . I t is seen that, f o r a given set of k i n e t i c parameters the value of D^ is almost independent of the gas flow r a t e and the assumption o f f i r s t - o r d e r k i n e t i c s (equation (4)) gives a conversion that is in­ dependent of the benzene c o n c e n t r a t i o n in the feed. This l a t t e r feature s i g n i f i c a n t l y reduced the computation time and was r e t a i n ­ ed f o r the s e l e c t i v i t y and t r a n s i e n t behaviour c a l c u l a t i o n s . This was j u s t i f i e d by the agreement of the conversions over the range of operating c o n d i t i o n s . The s i m u l a t i o n could now be advanced to i n c l u d e the maleic anhydride degradation. T h i s gas phase r e a c t i o n takes place only in the bubble phase, the i n t e r s t i t i a l gas and the s e p a r a t i o n spa­ ce. The i n t e r s t i t i a l gas and the bubbles account f o r about 15% of the t o t a l free volume of the r e a c t o r and t h e r e f o r e cannot be ne­ g l e c t e d . Moreover the degradation k i n e t i c s depend on a f r a c t i o n a l power of the maleic anhydride concentration (equation ( 5 ) ) ; hence the fluidized bed cannot be i n t e g r a t e d a n a l y t i c a l l y to y i e l d a simple r e l a t i o n s h i p . However, it has been shown by Grace (26) that f o r a f a s t r e a c t i o n the major p a r t of conversion occurs in the f i r s t few m i l l i m e t e r s c l o s e to the d i s t r i b u t e r . The maleic anhydride concentration in the bed is thus very n e a r l y constant and can be estimated from the conversion s i n c e the degradation r e a c t i o n is r e l a t i v e l y slow. This permits the fluidized bed to be modelled as a b i p a r t i t e r e a c t o r as shown in Figure 5, and avoids the computer-time consuming s u b d i v i s i o n of the bed i n t o regions. Despite this s i m p l i s t i c treatment the s i m u l a t i o n has become q u i t e complex and y i e l d e d s e l e c t i v i t y and production values that d i f f e r e d s i g n i f i c a n t l y from those obtained by K i z e r . Again, it was apparent that the k i n e t i c parameters f o r equation (5) needed adjustment to r e c o n c i l e the d i f f e r e n c e s . This was done by a simple t r i a l and e r r o r method.

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T

Q

D i s c u s s i o n and Conclusions:

Kinetics

I t was p o s s i b l e to determine a s e t of k i n e t i c r e l a t i o n s which gave the best p o s s i b l e s i m u l a t i o n of the reported r e s u l t s . These r e l a t i o n s are:

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

„.

0

r

Eq. 4

B

β

Κ

Κ

/

Vu

Ρ

B

1

/

Ρ

2

Β 0 Β 0

+

4 k

2

P

B B

.

; k fi

1.75

1.68

1.71 1

80

66

75

k k p p

= k^p

=

1.56

1.49

-

= f

e

1.44

87

2.08

1.32

1.97

Β

81

62

65

-ED/RT

1.89

1.71

77

1.53

75

80

1.13

65

65

1.22

75

O.5 5 6 460

80

1.59

80

1 7 6 460

82

1.79

O.82

65

1 3 6 460

67

1.49

68

1 5 8 460

67

1.71

72

1.53

75

1.22

75

1.5 5 6 460

69

B

fr> =11900 Ε 3 =58100 f0 =2900

bo

B

f =10260 Eg =60000 D =O.420

bo

B

f =37500 E =66800 D =O.043

D

= 0

c

5

n

6 4 3

„ . ™ *°-J £° bo -

Optimized parameters

* These c o n d i t i o n s a r e the c e n t r a l p o i n t of the f a c t o r i a l p l a n and are counted four times f o r the purposes of o p t i m i z a t i o n .

Γ

λ

b

Eq. Y c 3 D (cm)

b

1.25

87

80

67

75

1.53

O.93

1.25

1.18

82

1 5 4 460

83

1.22

b

82

1 5 6 490

83

75

66

1 5 6 430

66

c D (cm)

1 5 6 460

*

75

Y

Eq. Y c 4 D (cm)

Eq. 4

a

mf ι F (m3h-1) T(°C)

H

c(mol %)

Y, % c

Eq. 3

η

OrcuttDavidson PF

OrcuttDavidson PM

Operating conditions

Kinetics:

_.

Case C

Case Β

Case A

1

Kizer s data

TABLE I I RESULTS OF OPTIMIZATION OF MODEL PARAMETERS

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4.

JAFFRÈS E T AL.

Maleic Anhydride Production

!

^

67

Maleic anhydride degradation Iproducts

plus p iu

^

I

Emulsion

Bubble

Homogeneous oxidation of

phase

phase

maleic

anhydride

51 |* — g Emulsion

phase

[

g Maleic

Bubble phase

anhydride Catalytic oxidation of Benzene

Figure 5. Model of thefluidizedbed. Benzeneflowisshown by the heavy solid line and maleic anhydrideisrepresented by the heavy dashed line.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

68

CHEMICAL REACTORS

1/2 k

k

P

where k_ = 11900

P

B O B 0

D

k k

P

0 0

1 / 2

+

e

4 k

-58100/RT (20)

65900/RT = 2900 e"

Q

P

B B

f o r the c a t a l y t i c o x i d a t i o n , and

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r

™ M

=

k

ι 1/2 -30000/RT ™P™ > where k , = 237000 e M M M ,

0

0

7

Λ Λ Λ

(21)

x

I m p l i c i t in these equations are the s u c c e s s i v e o x i d a t i o n s of benzene and maleic anhydride. The d i r e c t o x i d a t i o n of benzene to water and carbon oxides is not permitted. The o p t i m i z a t i o n r e s u l t s reported in t a b l e I I i n d i c a t e that the a c t i v a t i o n energies are almost independent of the model chosen to represent the fluidized bed r e a c t o r . Furthermore, the a c t i v a ­ t i o n energy obtained in this manner agree with those reported by Holsen, Steger and Germain et a l while those given by Quach are much s m a l l e r . The data are summarized in table I I I below. More­ over, it is known from the c a t a l y s t f a b r i c a t o r that f i x e d bed reactors having an i n l e t benzene c o n c e n t r a t i o n of 1.5% and a r e s i ­ dence time of O.72 s. give conversions on the order of 93 to 95%. The k i n e t i c s r e q u i r e d f o r this r e s u l t c o i n c i d e with the k i n e t i c s obtained from the numerical experimentation. F i n a l l y , we note that the energy of a c t i v a t i o n f o r the homogeneous decomposition of maleic anhydride obtained from the o p t i m i z a t i o n is in good agree­ ment with the work of Quach et a l . TABLE I I I COMPARISON OF ACTIVATION ENERGIES Worker

Catalyst

Holsen

V 0 /A1 0

Steger

Ag 0, V 0 , Al 0 /SiC

2

5

2

2

2

2

325-450

3

5

Temperature range °C

MoO

Activation energy kJ/mole 81-82

450-530

63

380-500

92-42

3

Germain et a l

V 0 /Mo0

Quach et a l

V 0 /Si0

2

280-430

24

Our numerical optimization

V 0 /Si0

2

430-490

60-67

2

2

2

5

5

5

b i s c u s s i o n and Conclusion:

3

F l u i d i z e d Bed Model

The optimized values given in t a b l e I I i n c l u d e the values of the mean bubble diameter. These values are c o n s i s t e n t l y smaller than those c a l c u l a t e d from the Mori and Wen equation. For example, at the c e n t r a l p o i n t of the f a c t o r i a l p l a n , a value of = 2.1 cm is p r e d i c t e d by Mori and Wen's equation while the "optimized 11

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

4.

JAFFRÈS ET A L .

69

Maleic Anhydride Production

values f o r vary between 1 . 2 2 and 1 . 7 1 cm depending on the simul a t i o n case. This discrepancy is not e n t i r e l y unexpected s i n c e the bubble diameters i d e n t i f i e d from the fluidized bed models are apparent or e f f e c t i v e values i n t i m a t e l y l i n k e d to the mass t r a n s f e r mechanism of the model. The smaller bubble s i z e values obtained by our procedure may simply mean that the a c t u a l mass t r a n s f e r is l a r g e r than that suggested by the Orcutt-Davidson models. This is compat i b l e with the f a s t r e a c t i o n assumption that implies a disproport i o n a t e l y high conversion c l o s e to the d i s t r i b u t e r and a much higher mass t r a n s f e r rate in this zone. C a l c u l a t i o n s o f conversion and s e l e c t i v i t y have good general agreement with K i z e r s r e s u l t s as shown in F i g u r e 6. An exception is the s e l e c t i v i t y - b e d height r e l a t i o n s h i p . Our c a l c u l a t i o n s show s e l e c t i v i t y to be i n s e n s i t i v e to bed height, but K i z e r found a strong inverse r e l a t i o n between s e l e c t i v i t y and . K i z e r explains this by proposing a d i r e c t o x i d a t i o n of benzene to water and carbon oxides which is in compet i t i o n with the o x i d a t i o n to maleic anhydride. We note that the heterogeneous d e p l e t i o n of maleic anhydride may a l s o e x p l a i n the above behaviour. K i z e r e t a l ( 1 4 ) claimed that the combined e f f e c t s of bed height and flow r a t e could be replaced by the residence time. This implies that simple f i x e d bed models could be used to adequately describe this r e a c t o r . Table I I and Figure 4 shows that this could be the case f o r the Orcutt-Davidson PM model, however the model demands the u n r e a l i s t i c value of D^Q = O.043 cm (case A). The PF model requires operation away from the l i m i t i n g conv e r s i o n s and is thus in c o n f l i c t with K i z e r s claim, although more r e a l i s t i c values o f D are estimated. I t seems probable that the r e a c t o r operation is somewhere between that of a single-phase p e r f e c t l y mixed r e a c t o r and plug flow in the same r e a c t o r . I t is p r e c i s e l y in this region that both bed hydrodynamics and k i n e t i c s are important. Thus, it is not u s e f u l to f u r t h e r analyse our r e s u l t s without possessing indépendant knowledge o f the hydrodynamic or k i n e t i c parameters. A number of points have become apparent as a r e s u l t o f our e f f o r t s to simulate the fluidized-bed reactor-preheater system s t u d i e d by K i z e r . Two of the most important are: it is imperat i v e to have good k i n e t i c data f o r the r e a c t i o n ( s ) that occur. I t has been demonstrated that the i n t e r p r e t a t i o n o f the r e s u l t s is profoundly a f f e c t e d by r e l a t i v e l y small changes in the k i n e t i c s . The second important point is the r e c o g n i t i o n that there are r e gions of operation where both the r e a c t i o n k i n e t i c s and the bed hydrodynamics i n f l u e n c e the o v e r a l l performance o f the r e a c t o r . The coupling o f k i n e t i c and hydrodynamic e f f e c t s is strong such that both must be known to properly describe the r e a c t o r behaviour . We note that this model is not s u i t e d to process c o n t r o l purposes. The computational resources and time r e q u i r e d are simply too great to allow r e a l - t i m e c o n t r o l algorithms to use this

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T

1

b o

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

65

4 0

4 5

460

460

490

490

T,°C

e

T, C

a

3

1

m /

mf,cm

mf,cm

Figure 6. Conversion and selectivity vs. catalyst temperature, airflowrate,and bed height. The results of Kizer et al. are the solid lines and our calculations are shown as the hatched area. Operating conditions are: F = 6m h' , H = 5 cm, Τ = 460°C, benzene concentration, c == 1 mol percent except when the variable appears on the abscissa.

430

55

- 5 0

ο

1

430

65 "

70

^60 > %

ο

1

~ 85^

c ο

c= 1%

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8

H

M

ο

4. JAFFRÈS E T AL.

Maleic Anhydride Production

71

model in s p i t e o f the many s i m p l i f y i n g assumptions made to reduce the computer l o a d .

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Legend of Symbols A a C c D Ε F, f G h H H ΔΗ K k, k Pr p Q Re R r Τ U V w X

= =

T

1

x

= -

-

a i r (at NTP; 20°C and 1 atm) benzene bubble, initial, mean convection fluid inlet

-

Y , Yp, Y 3 η λ y V ξ p c

s

z

c r o s s - s e c t i o n a l area o f r e a c t o r , m h e a t - t r a n s f e r area, m^ s p e c i f i c heat, c a l * g ~ l c o n c e n t r a t i o n , mol percent diameter, m a c t i v a t i o n energy, J · mol"*l volumetric flow r a t e , m^ · h~ mass flow r a t e , g · h " l heat t r a n s f e r c o e f f i c i e n t , c a l · m · s"" °C enthalpy, c a l · g " l height, m heat o f r e a c t i o n , c a l · mol~"l (kgRTW )/(AU), dimensionless r e a c t i o n r a t e r e a c t i o n r a t e constant, s e c ~ l P r a n d t l number, dimensionless ( p a r t i a l ) pressure, Ν · m~2 heat, c a l Reynolds number, dimensionless gas constant r e a c t i o n r a t e , mol · h " l temperature, °C v e l o c i t y , m · sec~"l volume, m^ mass, g (xH)/(U Vb)* number o f t r a n s f e r u n i t s , equations (10) and (11) o v e r a l l r a t e of exchange between bubble and dense phase r e a c t o r conversion, production and s e l e c t i v i t y 1 - ( U / U ) , equations (10) and (11), dimensionless parameter of equation (16) _^ thermal c o n d u c t i v i t y , c a l · sec · m~l · °C~1 v i s c o s i t y , Pa · sec""i s t o i c h i o m e t r i c c o e f f i c i e n t , dimensionless parameter of equation (16) d e n s i t y , g · cm"3 s

1

b

mf

Subscripts a Β b , bo, bm c f in

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

72

CHEMICAL REACTORS

summation i n d i c e s lost maleic anhydride mean minimal fluidization particle reactor, reaction separation solid

I M m mf

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Ρ R S s

Acknowledgements The authors g r a t e f u l l y acknowledge the research grants pro­ vided by the Province of Quebec (FCAC), the N a t u r a l Sciences and Engineering Research C o u n c i l of Canada and the I n s t i t u t du génie chimique de Toulouse.

Literature Cited 1.

De Maio, D.A., " W i l l Butane Replace Benzene as a Feedstock for M a l e i c Anhydride", Chem. Eng., 1980, May 19, p. 104. 2. Germain, J.E., Graschka, F., Mayeux, Α., "Cinétique de l'oxyd a t i o n c a t a l y t i q u e du benzène sur oxydes de vanadium-molybdène", Bull. Soc. Chim. F r . , 1965, p. 1445. 3. Vaidyanathan, K., Doraiswamy, L.K., " C o n t r o l l i n g Mechanism in Benzene O x i d a t i o n " , Chem. Eng. Sci., 1968, 23, 537. 4. Badarinarayana, M.C., Ibrahim, S.M., Kuloor, N.R., " S i n g l e Step C a t a l y t i c Vapor Phase O x i d a t i o n of Benzene", Ind. J. Techn., 1967, 5, 314. 5. K u l l a v i n a j a y a , P., "Statistical Study of the Benzene O x i d a t i o n Process in a F l u i d i z e d Bed Reaction", Ph.D. t h e s i s , Ohio State U n i v e r s i t y , Columbus, 1966. 6. Ahmad, S.I., Ibrahim, S.M., Kuloor, N.R., " K i n e t i c Studies on the Oxidation of Maleic Anhydride", Ind. J. Techn., 1971, 9, 251. 7. K i z e r , O., Laguérie, C., Angelino, Η., "Experimental Study of the C a t a l y t i c Oxidation of Benzene to Maleic Anhydride in a F l u i d i z e d Bed", Chem. Eng. J o u r n a l , 1977, 14, 205. 8. Quach, T.Q.P., Rouleau, D., Chavarie, C., Laguérie, C., "Catalytic Oxidation of Benzene to M a l e i c Anhydride in a Continuous S t i r r e d Tank Reactor", Can. J. Chem. Eng., 1978, 56, 72. 9. Hammar, C.G.B., "Reaction K i n e t i c s of the C a t a l y t i c Vapor-Phase Oxidation of Benzene to Maleic Anhydride", Svensk. Kem. Tid., 1952, 64, 165. 10. Holsen, J.N., "An I n v e s t i g a t i o n o f the C a t a l y t i c Vapor Phase Oxidation of Benzene", Ph.D. t h e s i s , Washington U n i v e r s i t y , S t . L o u i s , M i s s o u r i , 1954.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

4.

JAFFRÈS ET

AL.

Maleic Anhydride Production

73

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11. I o f f e , I . I . , L y u b a r s k i , A.G., " K i n e t i c s of C a t a l y t i c Oxidation of Benzene to M a l e i c Anhydride", K i n , i Kat., 1963, 3, 261. 12. Dmuchovsky, Β., F r e e r k s , M.C., P i e r r o n , E.D., Munch, R.H., Z i e n t y , F.B., " C a t a l y t i c O x i d a t i o n of Benzene to M a l e i c Anhy­ d r i d e " , J. C a t a l y s i s , 1965, 4, 291. 13. Steger p u b l i s h e d in C a t a l y s i s , e d i t e d by P.H. Emmet, Reinhold, New York, 7, Chap. 3, 1960, pp. 186-194. 14. K i z e r , O., Chavarie, C., Laguérie, C., C a s s i m a t i s , D., "Quad r a t i c Model of the Behaviour of a F l u i d i z e d Bed Reactor: C a t a l y t i c O x i d a t i o n of Benzene to Maleic Anhydride", Can. J. Chem. Eng., 1978, 56, 716. 15. Chavarie, C., Grace, J.R., "Performance A n a l y s i s of a Fluidized Bed Reactor", IEC Fund., 1975, 14, 75, 79, 86. 16. K u n i i , D., L e v e n s p i e l , O., "Bubbling Bed Model f o r K i n e t i c Processes in F l u i d i z e d Bed-Gas-Solid Mass and Heat T r a n s f e r and C a t a l y t i c Reactions", IEC Proc. Des. Dev., 1968, 7, 481. 17. O r c u t t , J.C., Davidson, J.F., P i g f o r d , R.L., "Reaction Time D i s t r i b u t i o n s in F l u i d i z e d C a t a l y t i c Reactors", Chem. Eng. Progr. Symp. Ser., 1962, 58, 1. 18. Mori, S., Wen, C.Y., " E s t i m a t i o n of Bubble Diameter in Gaseous F l u i d i z e d - B e d s " , AIChE J o u r n a l , 1975, 11, 109. 19. Yacono, C., Angelino, Η., "The Influence of Gas D i s t r i b u t o r on Bubble Behaviour; Comparison between B a l l D i s t r i b u t o r and Porous D i s t r i b u t o r " , published in F l u i d i z a t i o n , Cambridge Uni­ v e r s i t y , Cambridge, 1978, p. 25. 20. Froment, G.F., "Fixed-Bed C a t a l y t i c Reactors - Current Design Status", Ind. Eng. Chem., 1967, 59, 18. 21. Wen, C.Y., Leva, Μ., " F l u i d i z e d - B e d Heat T r a n s f e r - a Genera­ lized Dense Phase C o r r e l a t i o n , AIChE J o u r n a l , 1956, 2, 482. 22. Pohlhaussen, K. p u b l i s h e d in P r i n c i p l e s of Heat T r a n s f e r , 3rd ed. Intext Press, New York, 1976, p. 442. 23. Mac Adams, W.H., Heat Transmission 2nd ed. MacGraw Hill Book Company, New York, 1942, p. 241. 24. Perry, R.M., C h i l t o n , CH., Chemical Engineers Handbook, 5th ed., 1973, p. 10-15. 25. Marquardt, D.W., "An A l g o r i t h m f o r Least Squares E s t i m a t i o n of Non-Linear Parameters", Journ. Soc. Ind. Appl. Math., 1963, 11, 431. 26. Grace, J.R., De Lasa, H.I., "Reaction near the G r i d in Fluidi­ zed Beds", AIChE J o u r n a l , 1978, 24, 364. RECEIVED JUNE 30,

1981.

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.