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1 The Catalytic Muffler

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JAMES W E I Department of Chemical Engineering, University of Delaware, Newark, D e l . 19711

The catalytic

muffler represents

needs and research only effective cannot catalytic many

alternative

solutions

engine changes till the 1980's. This first

generation

muffler

pellet

by

has not been optimized

of experience Pioneering

our understanding

fail-safe

shallow

is the

challenged

effectively

improvements. and

society

pollution

years

further

solution

union of

This new technology

to automotive

be

through

a delightful

opportunity.

reliability,

and

of

(b)

is particularly

transport

beds and monoliths,

and reactors

for negative

transient

behavior

reactors.

and

through needed

to

design

modeling

(c) optimum order

and

tremendous

in (a) maintenance-free

catalysts

of

in design

is capable

research

today,

kinetics,

of

design

of

and

(d)

Τ η the f a l l of 1974 m i l l i o n s of cars t h a t w e n t o n sale w e r e e q u i p p e d A

w i t h o x i d i z i n g c a t a l y t i c converters to r e d u c e the emissions of c a r b o n

m o n o x i d e a n d h y d r o c a r b o n s ( 1 ). A r e d u c i n g c a t a l y t i c c o n v e r t e r f o r N O * m a y f o l l o w i n a f e w years. T h e terms " c a t a l y t i c m u f f l e r " a n d " c a t a l y t i c c o n v e r t e r " are sometimes u s e d i n t e r c h a n g e a b l y , w h i c h are s h o r t e n e d v e r sions for the m o r e c o m p r e h e n s i v e t e r m " K r a f t f a h r z e u g a b g a s e n t g i f t u n g s k a t a l y s a t o r . " H o w e v e r , the c a t a l y t i c muffler does n o t muffle engine noise a n d is l o c a t e d m u c h closer to the e n g i n e exhaust m a n i f o l d t h a n a r e g u l a r muffler. T h e r e are r e c e n t c o m p r e h e n s i v e r e v i e w s of t h e c a t a l y t i c muffler, c o v e r i n g b a c k g r o u n d , present t e c h n o l o g y , t h e r m o d y n a m i c s a n d k i n e t i c s , p h y s i c a l t r a n s p o r t processes, a n d d u r a b i l i t y (2, 3 ) .

T h e p u r p o s e of t h e

present r e v i e w is to concentrate o n the r e a c t i o n e n g i n e e r i n g a s p e c t s — a f e w past a c h i e v e m e n t s a n d a great m a n y u n s o l v e d p r o b l e m s . T h e C l e a n A i r A c t as a m e n d e d i n 1970 is the d r i v i n g force b e h i n d a n e w c h e m i c a l r e a c t i o n t e c h n o l o g y a n d the d e b u t of t h e c a t a l y t i c c o n v e r t e r as a n i t e m for mass c o n s u m p t i o n (4,5).

T h e conventional recipro-

1 Hulburt; Chemical Reaction Engineering Reviews Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

2

CHEMICAL

REACTION ENGINEERING

REVIEWS

e a t i n g s p a r k - i g n i t i o n gasoline e n g i n e c a n n o t m e e t t h e r e l a x e d f e d e r a l standards for 1975 m o d e l a u t o m o b i l e s i n C a l i f o r n i a w i t h o u t the use of the o x i d i z i n g c a t a l y t i c converter.

I n fact, the c a t a l y t i c c o n v e r t e r

l e a d to m o r e l e e w a y i n e n g i n e d e s i g n , w h i c h means u p to 2 0 %

will

improve-

m e n t i n v e h i c l e m i l e a g e p e r g a l l o n of gasoline a n d i n d r i v e a b i l i t y ( s u p p r e s s i o n of s t a l l i n g , h e s i t a t i o n , backfire, a n d other e n g i n e m a l f u n c t i o n s ) . T h e r e f o r e , the c a t a l y t i c c o n v e r t e r w a s i n s t a l l e d o n most 1975 m o d e l cars to m e e t the m o r e r e l a x e d f e d e r a l standards for the other 49 states. T h e d e b u t of the c a t a l y t i c converter is m a r r e d b y t w o controversies. G a s o l i n e n o r m a l l y contains 0 . 0 3 % less t h a n 1 %

sulfur b y weight, w h i c h contributes

of m a n - m a d e sources of s u l f u r i n the a i r . T h i s s u l f u r is

e m i t t e d as s u l f u r d i o x i d e i n t o the a t m o s p h e r e a n d is f u r t h e r o x i d i z e d to s u l f u r t r i o x i d e b y the c a t a l y t i c a c t i o n of m e t a l ions i n aerosols a n d b y sunlight (6).

T h e r e s u l t i n g s u l f u r i c a c i d a n d sulfates are

greater h e a l t h h a z a r d s t h a n s u l f u r d i o x i d e .

considered

T h e present a m b i e n t a i r

s t a n d a r d f o r s u l f u r d i o x i d e is 365 / x g / m , b u t the p r o p o s e d s t a n d a r d for 3

sulfates is 10 / x g / m . 3

input S 0

2

T h e catalytic converter oxidizes 1 0 - 3 0 %

of

the

to S 0 , w h i c h is o n l y a s m a l l a d d i t i o n a l b u r d e n w h e n p r o p e r l y 3

d i s p e r s e d ( 7 ) , b u t i t m a y give rise to h i g h l o c a l concentrations of sulfates a l o n g h e a v y traffic lanes. M u c h m o r e d e f i n i t i v e investigations are n e e d e d to d e t e r m i n e w h e t h e r the benefits of r e d u c i n g C O emission f r o m 30 to 3.4 g / m i l e , a n d h y d r o c a r b o n s f r o m 3.4 to 0.41 g / m i l e , is greater t h a n t h e h a r m of i n c r e a s i n g sulfate e m i s s i o n f r o m 0.001 to a p p r o x i m a t e l y 0.03 g / m i l e w h i l e r e c o g n i z i n g t h a t m u c h of the 0.16 g / m i l e e m i s s i o n of S 0

2

w o u l d o x i d i z e to sulfates i n the atmosphere later. T h e E n v i r o n m e n t a l P r o t e c t i o n A g e n c y is c o n t e m p l a t i n g a c o n t r o v e r s i a l v e h i c l e e m i s s i o n s t a n d a r d of sulfates at no m o r e t h a n 0.001 to 0.01 g / m i l e , w h i c h c o u l d l e a d to the d e m i s e of the c a t a l y t i c converter.

T h i s p r o p o s a l is c h a l l e n g e d b y t h e

F e d e r a l E n e r g y A d m i n i s t r a t i o n a n d the State of

California.

Existing

t e c h n o l o g y c a n save the c a t a l y t i c converter b y r e d u c i n g the s u l f u r c o n tent of gasoline, b y i m p r o v i n g the a b s o r p t i o n of sulfates i n the converter, a n d b y r e d u c i n g the excess a i r i n the converter to suppress S 0

3

forma-

t i o n , w i t h a cost increase. A n o t h e r source of c o n c e r n is the o u t s i d e s k i n t e m p e r a t u r e of the c a t a l y t i c converters, w h i c h m a y r e a c h 900° F after a h i l l c l i m b at f u l l t h r o t t l e . T h i s c o n v e r t e r t e m p e r a t u r e is o n l y

somewhat

h i g h e r t h a n a c o n v e n t i o n a l muffler at t h e same l o c a t i o n , a n d 400 degrees l o w e r t h a n t h a t r e a c h e d b y the exhaust m a n i f o l d of t h e engine, b u t t h e c o n v e r t e r is l o c a t e d closer to the g r o u n d a n d m a y cause fire a n d e x p l o s i o n o v e r t a l l grass a n d c o m b u s t i b l e s .

T h i s has l e d to the b a n n i n g of c a t a l y t i c

converters b y some o i l refineries a n d c h e m i c a l p l a n t s . A n e n g i n e c h a n g e is the o t h e r a p p r o a c h to m e e t the F e d e r a l s t a n d ards o n c a r b o n m o n o x i d e a n d h y d r o c a r b o n s

(8).

I t is f a r m o r e difficult

to m e e t the standards o n N O * . T h e d i e s e l engine emits smoke a n d o d o r

Hulburt; Chemical Reaction Engineering Reviews Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

1.

The Catalytic

WEI

a n d is 5 0 %

Muffler

3

l a r g e r a n d h e a v i e r t h a n the gasoline e n g i n e .

The rotary

e n g i n e is a l r e a d y i n mass p r o d u c t i o n f o r the s u b c o m p a c t M a z d a , w h i c h requires a thermal afterburner a n d provides a disappointing

gasoline

m i l e a g e . T h e stratified c h a r g e e n g i n e of H o n d a M o t o r s has s h o w n great p r o m i s e b u t needs p r o o f of d u r a b i l i t y . T h e r e are m a n y other i n t e r e s t i n g n e w engines i n the research a n d e a r l y d e v e l o p m e n t phase, i n c l u d i n g t h e steam engine, the S t i r l i n g e n g i n e , the R a n k i n engine, the gas t u r b i n e , t h e f u e l c e l l , a n d the storage b a t t e r y e l e c t r i c engines.

A l l have strong

p o i n t s , a n d a l l h a v e great weaknesses t h a t m u s t b e o v e r c o m e .

Experts

i n m a n u f a c t u r i n g e n g i n e e r i n g a n d i n customer service, w i t h i n a n d o u t side of the a u t o m o t i v e i n d u s t r y , b e l i e v e t h a t these engines cannot c a p t u r e a large p e r c e n t a g e of the t o t a l m a r k e t b e f o r e the 1980's. I n the r e m a i n d e r of this d e c a d e , the c h o i c e is a m o n g the c o n v e n t i o n a l e n g i n e w i t h t h e c a t a l y t i c converter, a n e n f o r c e d r e d u c t i o n of p e r m i s s i b l e v e h i c l e - m i l e a g e i n u r b a n areas, a n d a f u r t h e r r e d u c t i o n i n the standards of a m b i e n t a i r q u a l i t y . F o r the next d e c a d e , the best s o l u t i o n is the g o a l of a v i g o r o u s c o m p e t i t i o n b e t w e e n the investigators of n e w engines a n d the researchers of the c a t a l y t i c converter. P l a t i n u m a n d p a l l a d i u m are the a c t i v e i n g r e d i e n t s u s e d i n the first g e n e r a t i o n of c a t a l y t i c converters. I n one d e s i g n , these n o b l e metals are d e p o s i t e d o n 1 / 1 6 - to 1 / 8 - i n c h pellets of h i g h surface area a l u m i n a a n d placed i n a very shallow bed.

I n a n o t h e r d e s i g n , the n o b l e metals are

d e p o s i t e d o n a t h i n " w a s h c o a t " of a l u m i n a , w h i c h adheres to the w a l l s of c e r a m i c h o n e y c o m b m o n o l i t h s .

S i n c e space is at a p r e m i u m i n a n

a u t o m o b i l e , the r e a c t o r v o l u m e s h o u l d b e k e p t to a m i n i m u m so t h a t i t w i l l b e c o m p a c t e n o u g h to fit i n s i d e the a l r e a d y c r a m m e d e n g i n e h o o d , o r i t s h o u l d b e flat e n o u g h to fit u n d e r t h e f r o n t passenger's

seat.

T h e stated g o a l of the l a w is to m i n i m i z e emissions f r o m e a c h n e w c a r o v e r 50,000 m i l e s of use, subject to cost a n d r e l i a b i l i t y constraints. S i n c e u r b a n p o l l u t i o n is t h e m a i n target, the a u t h o r i z e d test c y c l e s i m u lates a n u r b a n c a r s t a r t i n g i n the m o r n i n g w i t h a c o l d e n g i n e a n d g o i n g t h r o u g h stop-and-go

traffic.

The

certification procedure

specifies

m a x i m u m p e r m i s s i b l e grams e m i s s i o n p e r m i l e t r a v e l e d , regardless

the of

a u t o m o b i l e w e i g h t or engine size.

(1) w h e r e m is the m o l e c u l a r w e i g h t of t h e p o l l u t a n t i n g / m o l e , F is

flow

r a t e of exhaust gas i n m o l e s / m i n , c is p o l l u t a n t c o n c e n t r a t i o n i n m o l e f r a c t i o n , a n d V is v e h i c l e s p e e d i n m i l e s / m i n . T h e c u r r e n t l y official C V S - C H p r o c e d u r e ( F e d e r a l C y c l e ) calls f o r a c y c l e f r o m a c o l d start, w i t h a r i g i d l y specified s c h e d u l e of v e h i c l e s p e e d as a f u n c t i o n of t i m e ,


4

CHEMICAL

REACTION

ENGINEERING

REVIEWS

c o v e r i n g 7.5 m i l e s i n 22.9 m i n u t e s . T h i s is f o l l o w e d b y a s h u t d o w n for 10 m i n u t e s a n d a re-start a n d r e p e a t of the first 8.4 m i n u t e s of the c y c l e . T h e d y n a m i c r a n g e of the i n p u t v a r i a b l e s to the c a t a l y t i c c o n v e r t e r is i m p r e s s i v e . T h e t o p s p e e d a t t a i n e d i n the F e d e r a l C y c l e is 56.7 m p h a n d c a n b e c o n s i d e r a b l y h i g h e r i n r o a d use. T h e i n l e t gas t e m p e r a t u r e varies f r o m a m b i e n t to 1 2 0 0 ° F i n the C y c l e a n d m a y go u p to 1 8 0 0 ° F i n r o a d use.

T h e c h e m i c a l heat c o n t a i n e d i n t h e exhaust gas c a n

c o n s i d e r a b l e since e a c h m o l e p e r c e n t of C O y i e l d s 140° F

be

temperature

rise u p o n o x i d a t i o n . T h e flow rate of gases v a r y f r o m 10 S C F M d u r i n g e n g i n e i d l e to 100 S C F M d u r i n g r a p i d a c c e l e r a t i o n i n the C y c l e a n d m a y g o u p t o 200 S C F M i n r o a d use. T h e gaseous c o m p o s i t i o n c a n v a r y f r o m a n o x i d i z i n g c o n d i t i o n w i t h a l e a n a i r - t o - f u e l r a t i o to a r e d u c i n g c o n d i t i o n w i t h a r i c h r a t i o . A s e c o n d a r y a i r p u m p is often n e e d e d w i t h e n o u g h c a p a c i t y to ensure a net o x i d i z i n g atmosphere. c a n v a r y f r o m b e l o w 0 . 1 % to a b o v e 8 % .

The C O

concentration

U n d e r these c o n d i t i o n s , t h e

gas has a reactor residence t i m e of 10 to 200 msec, a n d a c o n v e r s i o n l e v e l of 8 0 - 9 0 %

is n e e d e d .

M a n y c o m b i n a t i o n s of catalyst f o r m u l a t i o n s a n d reactor c o n f i g u r a tions are a d e q u a t e

w h e n t h e y are n e w l y i n s t a l l e d . T h e

performance

deteriorates w i t h use, m a i n l y b e c a u s e of h i g h t e m p e r a t u r e a n d poisons. I n s t e a d of today's gasoline w i t h 3.0 g of l e a d p e r g a l l o n , s p e c i a l gasoline w i t h less t h a n 0.05 g of l e a d w o u l d b e n e e d e d to a v o i d e a r l y d e a c t i v a t i o n . T h i s " l e a d - f r e e " gasoline r e q u i r e s m o r e r e f i n i n g a n d a n a d d i t i o n a l cost of a b o u t 0 . 1 0 / g a l ( 9 ) a c c o r d i n g t o a n i n d e p e n d e n t s t u d y , b u t o i l i n d u s t r y estimates are h i g h e r t h a n 1 0 / g a l .

T h e c a t a l y t i c converter

occasionally

fails f r o m p h y s i c a l a t t r i t i o n of the catalyst s u p p o r t a n d m e c h a n i c a l f a i l u r e of the a u x i l i a r y e q u i p m e n t s . I n a f e w years the d o l l a r sale of a u t o m o t i v e catalysts m a y e x c e e d the c o m b i n e d sale of catalysts to the c h e m i c a l a n d p e t r o l e u m i n d u s t r i e s (10).

T h e a p p l i c a t i o n of r e a c t i o n e n g i n e e r i n g p r i n c i p l e s to this e m e r g i n g

t e c h n o l o g y is s t i l l i n its i n f a n c y .

T h e o p t i m u m d e s i g n of a n i n d u s t r i a l

r e a c t o r evolves after m a n y years of experience.

T h e r e is v i r t u a l l y n o

experience w i t h the c a t a l y t i c muffler, a n d there is t r e m e n d o u s r o o m f o r improvement.

T h e c a t a l y t i c c o n v e r t e r also presents f o u r n e w challenges

to the art a n d science of r e a c t i o n e n g i n e e r i n g , w h i c h calls for p i o n e e r i n g research: ( a ) I t is mass p r o d u c e d a n d p l a c e d d i r e c t l y i n the h a n d s of t h e c o n s u m i n g p u b l i c , w h o c a n n o t a n d p e r h a p s h a v e n o i n c e n t i v e to p r o v i d e m o n i t o r i n g a n d m a i n t e n a n c e . A m a i n t e n a n c e - f r e e d e s i g n w i t h fail-safe r e l i a b i l i t y is n e e d e d . ( b ) Pressure d r o p across the c a t a l y t i c c o n v e r t e r m u s t b e severely l i m i t e d , r e q u i r i n g the u n f a m i l i a r s h a l l o w p e l l e t b e d , the c e r a m i c m o n o l i t h , a n d the m e t a l l i c screens. T h e t r a n s p o r t p r o p e r t i e s a n d m o d e l i n g of these reactors n e e d i n t e n s i v e s t u d y .


1.

WEI

The Catalytic

5

Muffler

( c ) T h e o x i d a t i o n of c a r b o n m o n o x i d e a n d h y d r o c a r b o n s o v e r p l a t i n u m a n d p a l l a d i u m exhibits a negative order kinetics. T h e o p t i m a l design of catalysts a n d reactors for s u c h k i n e t i c s s h o u l d be i n v e s t i g a t e d . ( d ) T h e p e r f o r m a n c e of the c a t a l y t i c converter is d e f i n e d o v e r a w i d e d y n a m i c r a n g e of i n p u t v a r i a b l e s a n d is d o m i n a t e d b y the first t w o m i n u t e s of transience f r o m a c o l d start of the engine. T h e t r a n s i e n t b e h a v i o r of converters s h o u l d b e better u n d e r s t o o d . T h e c a t a l y t i c muffler represents a d e l i g h t f u l u n i o n of society needs a n d research o p p o r t u n i t y . It deserves the a t t e n t i o n of some of the best talents i n our profession. Optimum

Policy

T h e o v e r a l l g o a l of the F e d e r a l C l e a n A i r A c t s h o u l d b e the best tradeoff b e t w e e n the benefits f r o m a decrease i n a i r p o l l u t i o n a n d the costs to the p u b l i c . L a w m a k e r s n e e d to h a v e t h e i r v i e w s b r o a d e n e d b y a r a n g e of p r o p o s e d p o l i c y alternatives, a n d t h e y n e e d to k n o w the p o s i t i v e a n d n e g a t i v e consequences of e a c h a l t e r n a t i v e . W i t h o u t the i n p u t s f r o m m a n y w e l l - i n f o r m e d , u n b i a s e d , a n d a b l y a r g u e d p o s i t i o n papers r e p r e s e n t i n g the t e c h n i c a l p o i n t of v i e w , the p u b l i c l a w s e n a c t e d m a y t u r n o u t to b e

w a s t e f u l , o b s t r u c t i v e , or c o u n t e r - p r o d u c t i v e .

The

optimal

d e s i g n of a set of p u b l i c l a w s , a i m e d at r e d u c i n g p o l l u t i o n at m i n i m u m cost to the n a t i o n , s h o u l d b e a h i g h o r d e r of business. R e a c t i o n engineers w h o s e l d o m v e n t u r e i n t o the c a l c u l u s of costs a n d benefits a n d i n t o the f o r m u l a t i o n of the o p t i m u m p o l i c y c o u l d p e r f o r m a n o t h e r

important

d u t y as experts a n d c o n c e r n e d citizens. A m b i e n t a i r q u a l i t y d e p e n d s o n the average e m i s s i o n p e r car a n d t h e t o t a l v e h i c l e m i l e a g e . I t does not seem reasonable to f o r b i d the sale of a v e h i c l e t h a t emits m o r e t h a n 9.0 g / m i l e of C O a n d to a c c e p t w i t h e q u a l pleasure t w o v e h i c l e s e m i t t i n g 1.0 a n d 8.9 g / m i l e . S u c h a l a w w i l l l e a d to the f o l l o w i n g d i s t o r t i o n s : e n c o u r a g i n g a d e s i g n for 8.9

g/mile,

w i t h a l l o w a n c e s f o r the v a r i a b i l i t y i n m a n u f a c t u r i n g q u a l i t y c o n t r o l a n d i n v e h i c l e testing e x p e r i m e n t a l scatter; c o n d e m n i n g to a j u n k y a r d a n automobile

t h a t emits 9.1 g / m i l e ; g i v i n g n o i n c e n t i v e to

l e a d i n g to v e r y l o w e m i s s i o n cars.

innovations

I n s t e a d , a l a w t h a t sets a p e n a l t y

t h a t is a c o n t i n u o u s a n d r a p i d l y i n c r e a s i n g f u n c t i o n of e m i s s i o n , c o u p l e d w i t h a p o s i t i v e r e w a r d for v e r y l o w e m i s s i o n , w o u l d i n d u c e the m a n u facturers to p r o d u c e better cars. I n a r e m a r k a b l e a r t i c l e , S h i n n a r a r g u e d t h a t to o b t a i n the h i g h e s t a i r q u a l i t y , the e m i s s i o n standards m u s t n o t b e set too l o w ( l i ) .

An

e m i s s i o n s t a n d a r d t h a t is too stringent w o u l d b e self-defeating since i t r e q u i r e s a n elaborate e n g i n e d e s i g n t h a t is m o r e p r o n e to f a i l u r e .

A

converter f a i l u r e m a y b r i n g a n e m i s s i o n t h a t is 1 0 - 2 0 times the a l l o w e d l i m i t . I f 5 % of the a u t o m o b i l e s o n the r o a d h a v e f a i l e d converters t h a t are not y e t d e t e c t e d a n d c o r r e c t e d , t h e n t h e a m b i e n t a i r q u a l i t y is d o m i -


6

CHEMICAL


REVIEWS

n a t e d b y t h e f a i l u r e rate. A m o r e s t r i n g e n t s t a n d a r d w o u l d l e a d to a h i g h e r f a i l u r e rate a n d d i r t i e r a i r . T h e r e are also m a n y r e l a t e d areas w h e r e r e a c t i o n engineers offer t h e i r t i m e a n d t a l e n t as c o n c e r n e d

citizens.

could

F o r instance,

why

s h o u l d the a i r q u a l i t y s t a n d a r d f o r C O s p e c i f y t h a t a n y w h e r e i n the U n i t e d States a n 8-hr average c o n c e n t r a t i o n of 9 p p m b y v o l u m e s h o u l d n o t o c c u r m o r e t h a n o n c e a year?

W h y s h o u l d the s t a n d a r d of

auto-

m o b i l e emissions, t a i l o r e d to c u r e u r b a n i l l s , b e i m p o s e d o n r u r a l d r i v e r s ? S i n c e 15 p p m is g o o d e n o u g h for h e a l t h y persons, w o u l d i t not b e sensible t o relocate h e a r t disease patients a w a y f r o m center c i t y ? T h e task of c u r b i n g a u t o m o b i l e

pollutants cannot

be

ended

by

r e g u l a t i n g o n l y the a u t o m o b i l e m a n u f a c t u r e r s . T h e r e is no c u r r e n t f e d e r a l l a w to r e q u i r e the p e r i o d i c i n s p e c t i o n a n d m a i n t e n a n c e of v e h i c l e s i n use.

I n the c h e m i c a l i n d u s t r y , a c a t a l y t i c reactor is often a m u l t i -

m i l l i o n d o l l a r i n v e s t m e n t t h a t is d e s i g n e d a n d c o n s t r u c t e d w i t h the exp e n d i t u r e of

many

engineering

man-hours.

To

m a x i m i z e profit,

an

i n d u s t r i a l r e a c t o r is m o n i t o r e d b y m a n y m e a s u r i n g a n d r e c o r d i n g i n s t r u m e n t s , u n d e r the w a t c h f u l eyes of p l a n t engineers r e a d y to m a k e c o r r e c t i v e measures.

I n contrast, the c a t a l y t i c muffler w i t h its accessories

has

a r e t a i l v a l u e of p e r h a p s $150 a n d is d e s i g n e d a n d c o n s t r u c t e d for the d a i l y use of the g e n e r a l p u b l i c .

T h e continued performance

of

the

c a t a l y t i c c o n v e r t e r m a y b e a m a t t e r of indifference to the average m o t o r i s t , w h o i n a n y case has n e i t h e r the i n s t r u m e n t a t i o n n o r the s k i l l to i n s p e c t a n d to m a i n t a i n .

T h e c a t a l y t i c muffler needs to b e f a i l u r e - p r o o f for 3

to 5 years w i t h o u t a t t e n t i o n — a feature n o t s h a r e d b y a n y

automobile

accessory. I t has b e e n p r o p o s e d t h a t the l a c k of m o t i v a t i o n to r e p a i r a m a l f u n c t i o n i n g c a t a l y t i c muffler m a y b e a u g m e n t e d b y the i n s t a l l a t i o n of a d e v i c e that emits l o u d noises w h i c h c a n n o t b e s i l e n c e d t i l l the c a t a l y t i c muffler is r e p a i r e d .

T h i s s o l u t i o n is s t i l l i n a d e q u a t e since the r e p a i r

service i n d u s t r y has n o t y e t b e e n o r g a n i z e d .

T h o u s a n d s of

mechanics

m u s t b e t r a i n e d to diagnose a n d to r e p a i r the v a r i o u s types of c a t a l y t i c mufflers, thousands of d i a g n o s t i c i n s t r u m e n t s m u s t b e mass

produced

a n d d i s t r i b u t e d , m i l l i o n s of spare parts m u s t b e p r o d u c e d a n d s t o c k p i l e d i n n u m e r o u s warehouses

(12).

T h e s e tasks h a v e n o t yet b e g u n .

Public

l a w is too serious a business to b e left to the l a w y e r s alone. Unusual

Catalytic

Beds

B e c a u s e of the concerns for engine p e r f o r m a n c e a n d f u e l e c o n o m y , the pressure d r o p across the c a t a l y t i c muffler m u s t b e k e p t to the m i n i mum.

T h e h i g h e s t pressure d r o p occurs o n w i d e - o p e n throttle e n g i n e

operations w h e n the exhaust gas flow rate a n d t e m p e r a t u r e are at the maximum.

A pressure d r o p of 5 - 8 inches of w a t e r is r e g a r d e d as the


1.

WEI

The Catalytic

7

Muffler

u p p e r l i m i t of a c c e p t a b i l i t y . T h i s r e q u i r e m e n t has l e d to the d e v e l o p m e n t of v e r y s h a l l o w p a c k e d b e d s a n d m o n o l i t h s . Shallow Packed Beds.

T h e c u r r e n t d e s i g n of p a c k e d b e d s

have

" p a n c a k e " aspect ratios, t y p i c a l l y 1-2 inches d e e p w i t h a cross-sectional a r e a of some 100 square inches.

S i n c e the pellets h a v e a d i a m e t e r of

1/16 to 1 / 8 i n c h , this means a b e d of 10 to 20 layers of p a r t i c l e s , w h i c h is a r a d i c a l d e p a r t u r e f r o m i n d u s t r i a l b e d s of h u n d r e d s or thousands of layers.

Pressure d r o p r e q u i r e m e n t s h a v e also l e d to t h e

development

of a n u m b e r of r a d i a l - f l o w reactors, w h e r e the catalysts are p l a c e d i n the a n n u l u s of t w o c o n c e n t r i c c y l i n d e r s a n d w h e r e the gas flows i n a d i r e c t i o n p a r a l l e l to the r a d i u s a n d transverse to the axis of the c y l i n d e r s Figure 1).

S i n c e b o t h a x i a l - f l o w a n d r a d i a l - f l o w reactors w i l l b e

(see con-

s i d e r e d , the t w o d i r e c t i o n s i n the reactor w i l l b e r e f e r r e d to as the " l o n g i t u d i n a l " a n d the " t r a n s v e r s e " d i r e c t i o n s to a v o i d c o n f u s i o n .

Figure

I.

Shallow pellet beds and

monoliths

W h e n a p a c k e d b e d is less t h a n 50 p a r t i c l e s d e e p , a step s i g n a l c r e a t e d b y a s u d d e n c h a n g e i n i n l e t c o n c e n t r a t i o n spreads as i t travels t h r o u g h the b e d

(13).

T h e l o n g i t u d i n a l s p r e a d i n g of a

s i g n a l is c o n s i d e r a b l y stronger (14, 15).

temperature

T h e s e m o d i f i c a t i o n s to the c o n -

c e n t r a t i o n a n d t e m p e r a t u r e profiles h a v e a s t r o n g effect o n the r e a c t o r performance.

D i s p e r s i o n of mass i n the transverse d i r e c t i o n is u n i m p o r -

tant i n a c a t a l y t i c muffler since the side w a l l s are i m p e r v i o u s a n d n o n c a t a l y t i c . T r a n s v e r s e d i s p e r s i o n of heat is i n s i g n i f i c a n t for the short a n d fat " p a n c a k e " reactors w h i c h a p p r o a c h a d i a b a t i c c o n d i t i o n s b u t is m o r e i m p o r t a n t f o r the l o n g a n d s l i m " c i g a r s " reactors.

Theories and experi-


8

CHEMICAL


REVIEWS

merits o n the m o d e l i n g of s u c h s h a l l o w p a c k e d b e d s u n d e r d y n a m i c c o n d i t i o n s are not w e l l

developed.

U s i n g the t e r m i n o l o g y of F r o m e n t , the m i n i m u m m o d e l to use is the

Pseudo-Homogeneous

Α.

II, where

i m p o s e d o n a p i s t o n flow r e a c t o r

l o n g i t u d i n a l dispersions

are

(16):

(2) λ -7-2 -

u{ c ) P

p

gas -τ-

+ Η · R =

0

T h e gases flow t h r o u g h a n exhaust p i p e of 2 to 3 inches i n d i a m e t e r i n a p u l s a t i n g flow, w i t h a f r e q u e n c y e q u a l to h a l f of the r p m of the e n g i n e , m u l t i p l i e d b y the n u m b e r of c y l i n d e r s a n d d i v i d e d b y the n u m b e r of converters. A r a p i d l y e x p a n d i n g cone connects the exhaust p i p e w i t h the c a t a l y t i c b e d of some 100 square inches i n cross-sectional area, a n d a s i m i l a r c o n t r a c t i o n cone gathers the exit gas i n t o a n exhaust p i p e . exhaust gas

flow

The

is t u r b u l e n t i n the exhaust p i p e u p s t r e a m f r o m

c a t a l y t i c b e d , w i t h a R e y n o l d s n u m b e r of 5000-80,000.

the

The Danckwerts

b o u n d a r y c o n d i t i o n s m a y b e i n a p p r o p r i a t e since l o n g i t u d i n a l dispersions of mass a n d heat o c c u r o u t s i d e of the reactor i n a n u n k n o w n m a n n e r . I n s i d e the p a c k e d b e d the R e y n o l d s n u m b e r of the gaseous

flow

i n the F e d e r a l C y c l e is f r o m 10 to 200, a n d the l o n g i t u d i n a l P e c l e t n u m b e r , w d p / D , f o r mass is almost constant at the v a l u e of 2 ( 1 3 ) .

T h i s is

v e r y f o r t u n a t e since one c a n t h e n use the same fixed P e c l e t n u m b e r at a l l flow rates. O n the other h a n d , the l o n g i t u d i n a l P e c l e t n u m b e r for heat, w d p ( p c ) g a s / A , is a p p r o x i m a t e l y constant w i t h a v a l u e of 0.3 p

(15).

T h i s s e v e n f o l d difference i n the values of mass a n d heat l o n g i t u d i n a l d i s p e r s i o n c o m p l i c a t e s the c o m p u t a t i o n s . The

Pseudo-Homogeneous

Cascade

model

is a g o o d d e a l

more

a m e n a b l e to n u m e r i c a l c o m p u t a t i o n . u ( C i _ i — Ci) — R = ( p c ) , u ( T . i - r ) + Rp

4

4

0

i = ο to Ν

H = 0

W h e n the n u m b e r of cells i n the C a s c a d e is chosen to b e Ν =

(3)

wL/2D,

the d i s t r i b u t i o n of gaseous r e s i d e n c e times is v e r y s i m i l a r b e t w e e n the t w o m o d e l s p r o v i d e d t h a t Ν is greater t h a n 10. T h e r e f o r e to s i m u l a t e mass d i s p e r s i o n w h e n the l o n g i t u d i n a l P e c l e t n u m b e r is 2, Ν s h o u l d b e chosen to e q u a l L/dp, or e a c h c e l l s h o u l d consist of one l a y e r of catalyst i n the b e d . O n the other h a n d , to s i m u l a t e t e m p e r a t u r e d i s p e r s i o n w h e n the l o n g i t u d i n a l P e c l e t n u m b e r f o r heat is 0.3, Ν s h o u l d b e c h o s e n to e q u a l L/7d

p>

or e a c h c e l l s h o u l d consist of seven layers. F o r t y p i c a l


1.

WEI

The Catalytic

b e d s w h e r e L/d

9

Muffler

is a b o u t 15, Ν s h o u l d b e e q u a l to 15 o r 2, d e p e n d i n g

p

o n w h e t h e r mass d i s p e r s i o n o r heat d i s p e r s i o n s h o u l d b e e m p h a s i z e d . W i t h s u c h a s m a l l v a l u e of N, t h e a n a l o g y b e t w e e n t h e D i s p e r s e d P l u g F l o w a n d C a s c a d e m o d e l breaks d o w n . C a u g h t b e t w e e n these t w o r e q u i r e m e n t s , o n e m i g h t a r g u e t h a t a n a c c u r a t e e v a l u a t i o n o f h e a t d i s p e r s i o n is m o r e i m p o r t a n t t h a n a n a c c u r a t e e v a l u a t e o f mass d i s p e r s i o n b e c a u s e o f t h e A r r h e n i u s expression f o r r e a c t i o n rate. T o b e m o r e precise, w e c a n define t h e r e l a t i v e s e n s i t i v i t y o f the r e a c t i o n rate to a p e r c e n t a g e change i n t e m p e r a t u r e c o m p a r e d w i t h a percentage change i n concentration as: ~

dR

. dR

d\nT when

dine

7

(4)

R = f(c)e-* '

/R T

_Q_ RT g

din/ dine

1

I f t h e r e a c t i o n rate is a s i m p l e n - t h o r d e r , din/ dine so t h a t S =

Q/R T g

= η

· 1 / n a n d has a v a l u e of a b o u t 20 f o r η < 1. I t is

justified to choose Ν a c c o r d i n g to t h e needs f o r t h e r m a l d i s p e r s i o n . T h e best v a l u e f o r iV w a s d e t e r m i n e d b y a set of transient e x p e r i m e n t s t o b e 2V =

( L / d p ) x ( 1 / 3 ) , o r e a c h c e l l s h o u l d consist of three layers of c a t a

lysts (17, 18).

E x p e r i m e n t a l values of t h e l o n g i t u d i n a l d i s p e r s i o n i n a

r a d i a l - f l o w reactor w e r e p u b l i s h e d b y H l a v a c e k et al. (19, 20). T h e Heterogeneous

C a s c a d e m o d e l is also u s e d f o r this p r o b l e m ,

w h e r e t h e t e m p e r a t u r e a n d c o n c e n t r a t i o n of t h e s o l i d a n d gas phases are a l l o w e d to b e different.

D i s p e r s i o n is r e l a t e d t o t h e gas t o s o l i d

transfer coefficients as w e l l as to N. ^(Ti.^

— Tf) = ha(Ti

g

— Ti ) +H

(5)

·R

s

H o w e v e r , t h e rates of mass a n d h e a t transfer b e t w e e n t h e s o l i d a n d t h e gas a r e n o t p r o p o r t i o n a l to gaseous flow rates. T h e j

H

and j

D

factors v a r y

a p p r o x i m a t e l y as —0.5 p o w e r of the R e y n o l d s n u m b e r so t h a t N u a n d S h v a r y as 0.5 p o w e r o f R e y n o l d s n u m b e r , l e a d i n g t o transference u n i t s t h a t v a r y w i t h —0.5 p o w e r o f R e y n o l d s n u m b e r .


10

CHEMICAL


REVIEWS

A l l the a b o v e t h e o r e t i c a l m o d e l s assume u n i f o r m flow d i s t r i b u t i o n s . I n p r a c t i c e , c h a n n e l i n g c o u l d b e a p r o b l e m i n v i e w of the s u d d e n e x p a n s i o n a n d c o n t r a c t i o n i n gas

flow.

I t c o u l d b e r e m e d i e d b y j u d i c i o u s use of

baffles a n d deflectors, at t h e expense of i n c r e a s e d pressure d r o p . T h e r m a l r a d i a t i o n effects are v e r y i m p o r t a n t for the " p a n c a k e " d e s i g n . Monolithic Catalytic Beds. A b u n d l e of p a r a l l e l tubes offers m u c h less resistance to a i r flow t h a n a r a n d o m p a c k e d b e d of spheres since the flow

does n o t h a v e to c h a n g e d i r e c t i o n r e p e a t e d l y a n d to s p l i t u p a n d

r e j o i n a r o u n d e a c h sphere.

T h e c e r a m i c m o n o l i t h is a n i n t e g r a l b u n d l e

of tubes w i t h a v a r i e t y of cross-sectional shapes i n c l u d i n g the c i r c l e , the h e x a g o n , t h e square, the e q u i l a t e r a l t r i a n g l e , a n d the s i n u s o i d . I n one process a m i x t u r e of fibers a n d c e r a m i c m a t e r i a l is e x t r u d e d f r o m a d i e a n d t h e n fired i n a k i l n . I n a n o t h e r process the m a t e r i a l is f o r m e d i n t o a l t e r n a t i n g sheets of flat a n d c o r r u g a t e d layers, a r r a n g e d i n t o a stack, a n d t h e n fired i n a k i l n .

S i n c e these c e r a m i c p r o d u c t s h a v e too

little

surface area to s u p p o r t a n d to disperse catalysts, a h i g h surface area a l u m i n a is d e p o s i t e d o n the t u b e surface as a " w a s h coat." A n u m b e r of o p e n m e t a l l i c catalyst s u p p o r t s h a v e also b e e n d e v e l o p e d i n the f o r m of o p e n - m e s h a n d r e i n f o r c e d w i r e structures a n d staggered layers of t a l l i c screens or saddles.

me-

T h e pressure d r o p t h r o u g h the m o n o l i t h s a n d

m e t a l l i c screens tends to b e l o w e r so t h a t these c a t a l y t i c b e d s m a y h a v e " c i g a r " aspect ratios, t y p i c a l l y 3 - 5 inches i n d i a m e t e r a n d 2 - 9 i n c h e s i n length. A t y p i c a l m o n o l i t h u s e d i n c a t a l y t i c mufflers has a c h a n n e l d i a m e t e r of 0.05 i n c h , a w a l l thickness of 0.01 i n c h , a n d a w a s h c o a t thickness of 0.001 i n c h w h e r e the a c t i v e p r e c i o u s metals are d e p o s i t e d . It is c o n t a i n e d i n a stainless steel c y l i n d e r 5 inches i n d i a m e t e r a n d 5 inches l o n g , c o n n e c t e d to the 2 % - i n c h exhaust p i p e s b y short cones.

Gas

flow

rates

g e n e r a t e d d u r i n g the F e d e r a l C y c l e w o u l d give R e y n o l d s n u m b e r r a n g i n g f r o m 20 to 400, w h i c h leads to a s t r e a m l i n e flow at a l l times e x c e p t p e r haps at the f r o n t o p e n i n g of the c h a n n e l w h e r e the gas m a y s t i l l

be

t u r b u l e n t . A great d e a l of c h a n n e l i n g takes p l a c e i n the m o n o l i t h , i n d u c e d b y the r a p i d l y e x p a n d i n g a n d c o n t r a c t i n g cones. T h e flow rate is m a n y times greater at the center of the axis, c a u s i n g faster w a r m u p f r o m a c o l d start, faster a g i n g , a n d l o w e r c o n v e r s i o n efficiency.

This channeling can

b e r e d u c e d b y u s i n g flow deflectors u p s t r e a m i n the e x p a n s i o n cone, w i t h a s i m u l t a n e o u s increase i n pressure d r o p . b e e n t r i e d a n d r e p o r t e d i n the l i t e r a t u r e (21,

A n u m b e r of devices

have

22).

T h e rates of mass a n d h e a t transfer f r o m gases i n s t r e a m l i n e

flow

to the w a l l s h a v e b e e n i n v e s t i g a t e d b y m a n y p e o p l e b e g i n n i n g w i t h G r a e t z a n d N u s s e l t , often i n c o n n e c t i o n w i t h the d e s i g n a n d o p e r a t i o n of c o m p a c t h e a t exchangers (23).

T h e rate of h e a t transfer is i m p o r t a n t

d u r i n g the w a r m u p , a n d also d u r i n g d e s t r u c t i v e o v e r h e a t i n g of the m o n o -


1.

WEI

The Catalytic

Muffler

11

l i t h at h i g h t e m p e r a t u r e operations. T h e e a r l y t h e o r e t i c a l solutions c o n sider c i r c u l a r c h a n n e l s w i t h f u l l y d e v e l o p e d v e l o c i t y profiles, n e g l e c t i n g l o n g i t u d i n a l d i s p e r s i o n i n the gas phase a n d r a d i a l c o n d u c t i o n i n the s o l i d phase.

(7) u(r)

=2m(1

-r7r

0

2

)

T h e s o l u t i o n is (8)

w h e r e the eigenvalues are β

0

=

2.705, β

χ

=

6.667, β

2

=

10.67, etc. a n d

the e i g e n f u n c t i o n ψ has i zeros a c c o r d i n g to the S t u r m i a n o s c i l l a t i o n {

t h e o r e m . W h e n χ is sufficiently large, a l l the terms i n the series b e c o m e insignificant c o m p a r e d w i t h the first t e r m , a n d the r a d i a l t e m p e r a t u r e profile reaches constant shape. It is c u s t o m a r y to define a heat transfer coefficient, h, i n terms of the m i x i n g c u p average t e m p e r a t u r e of gas a n d to c o m p u t e the N u s s e l t n u m b e r N u =

hd/λ.

the

A t the e n t r a n c e

of the c h a n n e l , the h i g h e r terms c o n t r i b u t e to a v e r y large v a l u e of N u ; w h e n the v a l u e of x/d · R e · P r > 0.05, N u reaches the a s y m p t o t i c v a l u e g o v e r n e d b y the e i g e n f u n c t i o n ψ alone. T h e s e solutions w e r e e x t e n d e d 0

to channels w i t h a p l u g flow e n t r a n c e a n d a d e v e l o p i n g v e l o c i t y profile. T h e t w o b o u n d a r y c o n d i t i o n s often u s e d are constant w a l l t e m p e r a t u r e a n d constant w a l l flux. T h e v a l u e of N u for d e v e l o p i n g flow a n d constant heat flux is greater t h a n N u for d e v e l o p i n g flow a n d constant w a l l t e m p e r a t u r e , w h i c h is i n t u r n greater t h a n N u for d e v e l o p e d flow a n d c o n stant w a l l t e m p e r a t u r e . T h e a s y m p t o t i c N u s s e l t n u m b e r s are i n d e p e n d e n t of the c h a n n e l d i a m e t e r or the R e y n o l d s n u m b e r .

W h e n the R e y n o l d s

n u m b e r is i n c r e a s e d , the o n l y effect is to l e n g t h e n the entrance r e g i o n of e n h a n c e d N u s s e l t n u m b e r . I n the c a t a l y t i c muffler, the l e n g t h of the e n h a n c e d r e g i o n is at most 0.7 i n c h vs. the c h a n n e l l e n g t h of 3 - 5 i n c h e s . T h e c o m p u t a t i o n of the G r a e t z - N u s s e l t p r o b l e m w a s e x t e n d e d

to

i n c l u d e a large v a r i e t y of c h a n n e l geometries, u s u a l l y r e q u i r i n g n u m e r i c a l t e c h n i q u e s . T h e a s y m p t o t i c N u s s e l t n u m b e r s w e r e the goals, a n d v e l o c i t y profiles w e r e sometimes o b t a i n e d . T h e d i a m e t e r , d, u s e d i n the d e f i n i t i o n of the N u s s e l t n u m b e r b e c o m e s the h y d r a u l i c d i a m e t e r , or f o u r times c h a n n e l cross-sectional area d i v i d e d b y the w e t t e d p e r i m e t e r . solutions are s u m m a r i z e d b y K a y s a n d L o n d o n (24) L o n d o n (25).

These

and by Shah and

T h e y r a n g e f r o m 2.5 for s i n u s o i d a l c h a n n e l s to 7.5 f o r

p a r a l l e l plates. T h e f u l l y d e v e l o p e d v e l o c i t y field i n sinusoids w a s s o l v e d b y S h e r o n y a n d S o l b r i g (26).

S c h o e n h e r r et al. h a v e s h o w n t h a t t r i -


12

CHEMICAL


REVIEWS

a n g u l a r a n d s i n u s o i d a l c h a n n e l s h a v e stagnant corners w h e r e the l o c a l heat transfer coefficient a l m o s t drops to z e r o

(27).

T h e r e is l i t t l e e x p e r i m e n t a l c o n f i r m a t i o n of these i n the l i t e r a t u r e . F o r the c a t a l y t i c muffler, the c o n d i t i o n s of these c a l c u l a t i o n s are n o t f u l f i l l e d : there is t u r b u l e n c e at the entrance of the c h a n n e l , a n d the w a l l is n e i t h e r at constant t e m p e r a t u r e n o r possesses constant h e a t flux. H e c k et al. h a v e a p a p e r i n this s y m p o s i u m , m e a s u r i n g the e x p e r i m e n t a l t e m p e r a t u r e profiles of a m o n o l i t h u n d e r w a r m u p c o n d i t i o n s (28).

They

f o u n d that the average N u s s e l t n u m b e r is a m i l d l y i n c r e a s i n g f u n c t i o n of the R e y n o l d s n u m b e r a n d falls b e t w e e n the a s y m p t o t i c values for constant w a l l t e m p e r a t u r e a n d for constant w a l l

flux.

The radial tem-

p e r a t u r e g r a d i e n t is n e g l i g i b l e . T h e entrance r e g i o n of d e v e l o p i n g t h e r m a l b o u n d a r y l a y e r is l o n g e r t h a n e x p e c t e d , p o s s i b l y because of entrance t u r b u l e n c e . K o c h s t u d i e d mass t r a n s p o r t i n m o n o l i t h s of v a r i o u s lengths b y e t h y l e n e o x i d a t i o n (29).

H e f o u n d g o o d agreement b e t w e e n his d a t a

a n d t h e f u l l y d e v e l o p e d l a m i n a r flow t h e o r y w h e n the t e m p e r a t u r e is sufficiently h i g h a n d mass t r a n s p o r t is rate l i m i t i n g . T h e m o n o l i t h u n d e r present muffler d e s i g n is v e r y s e l d o m u n d e r mass transfer l i m i t i n g c o n d i t i o n s , except for t u r n p i k e d r i v i n g c o n d i t i o n s w i t h v e r y h i g h s p e e d gas flow a n d f u l l y w a r m e d catalysts. A s s u m i n g a n i n f i n i t e l y fast k i n e t i c s , the exit c o n c e n t r a t i o n f r o m a m o n o l i t h is g i v e n b y

(9)

W h e n 9 0 % c o n v e r s i o n is d e s i r e d , the v a l u e n e e d e d for T U is 2.3.

The

v a l u e of the S h e r w o o d n u m b e r m a y b e a s s u m e d e q u a l to the N u s s e l t number.

U n d e r r e a c t i o n c o n d i t i o n s , the S c h m i d t n u m b e r is 0.23

h y d r o g e n , 0.81 for C O , a n d 1.60 for b e n z e n e .

for

A typical monolith with

0.05-inch c h a n n e l d i a m e t e r a n d 5 - i n c h l e n g t h has a v a l u e of 260 for T h u s e v e n w i t h the m o s t u n f a v o r a b l e c h a n n e l g e o m e t r y a n d S h = w e w o u l d b e mass t r a n s p o r t l i m i t e d o n l y w h e n R e =

ah. 2.5,

180, at the u p p e r

e n d r e a c h e d i n the F e d e r a l C y c l e . H o w e v e r , g o o d h e a t transfer is n e e d e d i n the w a r m u p p e r i o d f r o m a c o l d start. T h e m o d e l i n g of s i m u l t a n e o u s mass a n d heat t r a n s p o r t a n d c h e m i c a l r e a c t i o n o n c a t a l y t i c w a l l s m a y b e a p p r o x i m a t e d b y the

Heterogeneous

B . I m o d e l of F r o m e n t . T h e p r o b l e m is q u i t e c o m p l e x a n d c a n b e s o l v e d o n l y b y n u m e r i c a l t e c h n i q u e s e v e n i f the N u s s e l t n u m b e r is a s s u m e d constant t h r o u g h o u t the c h a n n e l l e n g t h . W h e n the r a d i a l g r a d i e n t i n the gas phase is also t a k e n i n t o account, w e a r r i v e at a m o d e l t h a t is n o t i n the classification scheme of F r o m e n t .

U n d e r isothermal conditions,

this p r o b l e m was t a c k l e d b y K a t z , b y S o l o m o n a n d H u d s o n , a n d b y L u p a a n d D r a n o f f , u s i n g e i g e n f u n c t i o n e x p a n s i o n (30, 31, 32).

These methods


1.

WEI

The Catalytic

13

Muffler

are n o t w i d e l y u s e d since the c a t a l y t i c muffler channels are not i s o Y o u n g a n d F i n l a y s o n s o l v e d this p r o b l e m b y u s i n g n u m e r i c a l i n t e g r a t i o n , and b y orthogonal collocation methods

(33).

T h e y discovered that a

spot m a y d e v e l o p o n the w a l l to i g n i t e the r e a c t i o n , a n d to rejuvenate the N u s s e l t n u m b e r for a short l e n g t h . I f the w a l l flux s u d d e n l y switches f r o m n e g a t i v e to p o s i t i v e , the N u s s e l t n u m b e r c a n d e c l i n e r a p i d l y to n e g a t i v e infinity a n d r e t u r n to the p o s i t i v e a s y m p t o t i c v a l u e b y of p o s i t i v e infinity.

This curious phenomenon

arises w h e n the

way

average

t e m p e r a t u r e of the gas is h i g h e r t h a n w a l l t e m p e r a t u r e , w h i c h is i n t u r n h i g h e r t h a n the gas t e m p e r a t u r e i m m e d i a t e l y adjacent to the w a l l ; this gives rise to a p o s i t i v e v a l u e for gaseous t e m p e r a t u r e g r a d i e n t at the w a l l b u t a n e g a t i v e v a l u e for T -T . s

E x p e r i m e n t a l investigations are

g

n e e d e d to evaluate the p r a c t i c a l significance of these

phenomena.

A n a p p r o x i m a t e e q u i v a l e n c e b e t w e e n the H e t e r o g e n e o u s D i s p e r s i o n B . I I m o d e l a n d the P s e u d o - H o m o g e n e o u s g i v e n b y V o r t m e y e r a n d Schaefer ( 3 4 ) . d /dx 2

2

(T -T ) s

g

Dispersion A . I I model

was

T h e y demonstrated that w h e n

= 0, m o d e l B . I I is e q u i v a l e n t to m o d e l A . I I w h e n

one

assigns A = A + ^ (pC )/Aa A

2

B

(10)

p

T h i s a s s u m p t i o n is v a l i d u n d e r m i l d c o n d i t i o n s b u t breaks d o w n u n d e r light-off c o n d i t i o n s . A f t e r t r a n s f o r m i n g the g a s - s o l i d heat transfer coeffi c i e n t i n t o a l o n g i t u d i n a l d i s p e r s i o n coefficient, one c a n take one m o r e step a n d t r a n s f o r m this A . I I m o d e l i n t o a C a s c a d e m o d e l . W h e n λ

Β

=0,

let

A

ud( c ) —λ P

en =

p

=

Α

dha r = (UpCp)

-,

iNU

a« — u

and, ^

Pe

r

2

n

L

d - ha

d ~~ 2upc

p

L d

U n f o r t u n a t e l y , h is p r a c t i c a l l y i n d e p e n d e n t of R e y n o l d s n u m b e r i n s t e a d of b e i n g p r o p o r t i o n a l to i t . T h u s , u n d e r l o w R e y n o l d s n u m b e r the m o n o l i t h m a y b e c o n s i d e r e d to be 60 cells i n series, b u t u n d e r h i g h R e y n o l d s n u m b e r the m o n o l i t h m u s t b e c o n s i d e r e d to b e six cells i n series, w h i c h makes c o m p u t a t i o n difficult. T h e best c h a n n e l cross-sectional shape, the best c h a n n e l d i a m e t e r , a n d the best c h a n n e l l e n g t h are the subjects of several i n v e s t i g a t i o n s . Sufficient g e o m e t r i c surface area m u s t be p r o v i d e d to disperse the a l u m i n a washcoat and platinum.

B e y o n d t h a t p o i n t , m o r e surface area w o u l d


14

CHEMICAL

REACTION

ENGINEERING

REVIEWS

m e a n a h e a v i e r m o n o l i t h a n d is n o t d e s i r a b l e . A s m a l l c h a n n e l d i a m e t e r w o u l d s i m u l t a n e o u s l y increase h e a t transfer coefficient h, a n d surface to v o l u m e r a t i o a since t h e N u s s e l t n u m b e r is p r a c t i c a l l y i n d e p e n d e n t of c h a n n e l d i a m e t e r ; i t w o u l d also l e a d to a m u c h h i g h e r pressure d r o p . T h e best d i a m e t e r is t h e r e s u l t o f a c o m p r o m i s e .

T h e optimum channel

shape is m o r e c o n t r o v e r s i a l since there is n o g e n e r a l l y a c c e p t e d set o f v a r i a b l e s to b e h e l d constant d u r i n g a c o m p a r i s o n . C i r c u l a r c h a n n e l s are not seriously c o n s i d e r e d since t h e y i n v o l v e t h i c k a n d h e a v y w a l l s . F o r fast w a r m u p , a set of i n f i n i t e l y w i d e p a r a l l e l plates w o u l d b e t h e best since i t w o u l d give t h e h i g h e s t transfer coefficient to t h e surface f o r the same gas f l o w rate a n d pressure d r o p . r u l e d o u t f o r its s t r u c t u r a l weaknesses.

This configuration must b e

T h e next best shape is a n e l o n

g a t e d rectangle, w h i c h is s t i l l difficult to m a k e a n d to protect.

Hegedus

m a d e a c o m p a r i s o n f o r v a r i o u s p r a c t i c a l shapes, b a s e d o n t h e same h y d r a u l i c d i a m e t e r a n d average gaseous v e l o c i t y ( 3 5 ) . H e s h o w e d t h a t f r o m t h e p o i n t o f v i e w of l o w e r surface area r e q u i r e m e n t a n d l o w e r pressure d r o p , t h e c i r c l e a n d h e x a g o n a r e s u p e r i o r to t h e s q u a r e , w h i c h is s u p e r i o r to t h e t r i a n g l e a n d s i n u s o i d . H i s results are g i v e n i n T a b l e I .

Table I.

Comparison of Monolith Geometries with the Same H y d r a u l i c Radius ° Circle

V o l u m e of w a l l needed, i n . Pressure d r o p , inch water

Hexagon

Square

Triangle

Sinusoid

10.2

10.2

12.9

15.7

15.7

4.1

3.9

4.5

5.1

5.0

3

Surface needed for 99% conversion under mass transfer limited conditions. A l l geometries have the same hydraulic radius of 0.062 cm, mass flow rate of 0.75 g / c m sec, wall thickness of 0.0305 cm, and temperature at 600°C. Hegedus defines the hydraulic radius as one-half of hydraulic diameter. α

2

Table II.

Comparison of Monolith Geometries with the Same Cross-Sectional A r e a a

Length, in. W a l l volume, i n . Δ Ρ , inch H 0 2

3

Circle

Hexagon

4.4 12.8 4.5

4.4 9.2 4.7

Square 4.1 9.8 5.0

Triangle 4.1 10.4 5.7

Sinusoid 3.7-4.0 11.6 5.5

° Length and surface area needed for 99% conversion under mass transfer limited conditions, with open area of 0.02 c m . 2

On

t h e other h a n d , J o h n s o n a n d C h a n g m a d e a c o m p a r i s o n b a s e d o n

the a s s u m p t i o n of e q u a l c h a n n e l o p e n

cross-sectional area

s i n u s o i d , i n c o m p a r i s o n w i t h a h e x a g o n w i t h t h e same

(36). A

cross-sectional


1.

WEI

The Catalytic

Muffler

15

area, has a s m a l l e r h y d r a u l i c d i a m e t e r a n d l a r g e r pressure d r o p b u t c a n be m a d e m o r e c o m p a c t .

T h e i r results are s h o w n i n T a b l e I I .

T h e s e differences are significant for the r e q u i r e m e n t of fast w a r m u p . D u r i n g the m a n u f a c t u r e of the c e r a m i c m o n o l i t h , s l u m p i n g of the w e t m a t e r i a l w i l l distort the exact g e o m e t r i c shapes; h o w e v e r , t h i c k coatings of washcoats w i l l r o u n d out t h e s h a r p corners a n d i m p r o v e

the

performance. Negative

Order

Kinetics

F o r m o s t reactions u n d e r i s o t h e r m a l c o n d i t i o n s , t h e r e a c t i o n rate is a n i n c r e a s i n g f u n c t i o n of the c o n c e n t r a t i o n of e a c h r e a c t a n t c o n s u m e d . M o s t of o u r r e a c t i o n e n g i n e e r i n g l i t e r a t u r e is r o o t e d o n the G u l d b e r g W a a g e mass a c t i o n l a w , o n reactions of p o s i t i v e f r a c t i o n a l o r d e r , o n rates i n v o l v i n g a quotients of p o l y n o m i a l s , a l l o b e y i n g the r e l a t i o n dR/dC w h e r e C is the c o n c e n t r a t i o n of a reactant c o n s u m e d .

^

0

M a n y of the r e a c -

t i o n e n g i n e e r i n g rules t h a t h a v e b e e n w o r k e d out a n d a p p l i e d w i d e l y are b a s e d o n the p o s i t i v e o r d e r k i n e t i c s , s u c h as the e c o n o m y of the p i s t o n flow reactor over the s t i r r e d t a n k reactor i n reactor v o l u m e r e q u i r e m e n t s , the s u p e r i o r i t y of the o n c e - t h r o u g h reactor over the r e c y c l e reactor, a n d the d e c l i n e of the effectiveness

of porous

diffusion effects are e n c o u n t e r e d .

catalysts w h e n i s o t h e r m a l

T h e s e rules are r e v e r s e d w h e n

one

encounters n e g a t i v e o r d e r k i n e t i c s . N e g a t i v e o r d e r k i n e t i c s are rare b u t are i n d u s t r i a l l y i m p o r t a n t . A u t o c a t a l y t i c a n d free r a d i c a l reactions are often c i t e d b u t are i m p r o p e r examples since a d e c l i n e i n r e a c t a n t c o n c e n t r a t i o n is n o t a l w a y s assoc i a t e d w i t h a n increase i n c a t a l y t i c or r a d i c a l concentrations.

Hydro-

genolysis, o r the s p l i t t i n g of a s a t u r a t e d h y d r o c a r b o n i n t o t w o s a t u r a t e d hydrocarbons

by

hydrogen,

exhibits negative

order

with

respect

to

h y d r o g e n concentrations over m a n y s u p p o r t e d metals. AB + H , = A H + B H M o r i k a w a , B e n e d i c t , a n d T a y l o r h a v e f o u n d the r e a c t i o n to b e —1.2 to —2.5 o r d e r d e p e n d e n t o n c o n c e n t r a t i o n ( 3 7 ) .

S i n f e l t gave t h e r e a c t i o n

orders of ethane h y d r o g e n o l y s i s o v e r the t r a n s i t i o n metals as —0.8 to -2.5

(38).

T h e k i n e t i c s of C O o x i d a t i o n o v e r p l a t i n u m a n d p a l l a d i u m h a v e b e e n i n v e s t i g a t e d b y n u m e r o u s scientists, b e g i n n i n g w i t h the p i o n e e r i n g w o r k of I r v i n g L a n g m u i r ( 3 9 ) .

H e showed that the kinetics can be repre-

sented b y the expression rate =

/c(0 )/(CO) 2


(11)

16

CHEMICAL REACTION ENGINEERING

REVIEWS

H e s p e c u l a t e d t h a t the r a t e - c o n t r o l l i n g m e c h a n i s m is t h e c o m b i n a t i o n of the a d s o r b e d o x y g e n atoms a n d a d s o r b e d C O . T h e p l a t i n u m surface is i n t e n s i v e l y c o v e r e d w i t h a d s o r b e d C O so that a n increase o f C O c o n c e n t r a t i o n w o u l d decrease t h e a d s o r b e d

concentration of oxygen

and

the rate o f r e a c t i o n . T h i s k i n e t i c p h e n o m e n o n has b e e n c o n f i r m e d m a n y times b y v a r i o u s investigators (40, 41, 42, 43,44).

Baddour and Cochran

s t u d i e d C O o x i d a t i o n over p a l l a d i u m a n d p l a t i n u m w i t h s i m u l t a n e o u s i n f r a r e d measurements

T h e y d i s c o v e r e d t h a t the k i n e t i c s are d i

(45).

v i d e d i n t o t w o r e g i m e s : a " n o r m a l r e g i m e " w h e r e the C O c o n c e n t r a t i o n is a b o v e a c r i t i c a l v a l u e , w h e r e the k i n e t i c s has a n e g a t i v e d e p e n d e n c e o n CO

c o n c e n t r a t i o n , a n d w h e r e there is significant i n f r a r e d a b s o r p t i o n

at 2100 c m " ; a n d a " l o w surface c o v e r a g e r e g i m e " w h e r e the C O c o n 1

c e n t r a t i o n is b e l o w a c r i t i c a l v a l u e , w h e r e the k i n e t i c s is first o r d e r t o C O c o n c e n t r a t i o n , a n d w h e r e the i n f r a r e d a b s o r p t i o n p e a k is absent. ι ι

1

1

i oo (NEGATIVE \ ORDER)

/io\ \

1 FIRST

\ \

ε-

k

2

c

0

/SNA

/

^ ζ = 0 ι

Figure

2.

(FIRST ORDER)

1

The himolecular netics

1

1

Langmuir

ki

A c a r e f u l e x p e r i m e n t a n d q u a n t i t a v e analysis o f t h e k i n e t i c d a t a w a s p e r f o r m e d b y V o l t z et al. (46). T h e i r e x p e r i m e n t w a s d o n e over i m p r e g n a t e d p l a t i n u m catalysts o n pellets, w i t h t e m p e r a t u r e s a n d gaseous c o m positions s i m u l a t i n g exhaust gases.

T o m i n i m i z e d i f f u s i o n effects,


most

1.

WEI

The Catalytic

17

Muffler

of the p l a t i n u m w a s d e p o s i t e d i n t h e outer p o r t i o n s o f the p a r t i c l e . T h e y f o u n d that t h e i r C O o x i d a t i o n d a t a c a n b e fitted b y fei(CO) [l +

rate =

(Q ) fc (CO)]

(12)

2

2

2

where ( C O ) a n d ( 0 ) are i n mole % - a t m a n d fci — 1.83 X 1 0 e x p ( - 2 2 , 5 0 0 / 7 ) , (secKMOo)" k = 6.55 X 1 0 " e x p ( + l , 7 3 0 / D , (CO)" Τ = t e m p e r a t u r e , degrees R a n k i n . 2

7

1 2

1

2

1

1

T h e d e n o m i n a t o r t e r m i n E q u a t i o n 12 contains c o n t r i b u t i o n s f r o m N O a n d h y d r o c a r b o n s w h e n t h e y a r e present.

T h e propylene oxidation

rate has t h e same f o r m as E q u a t i o n 12. T h e f o r m of these k i n e t i c s is g i v e n i n F i g u r e 2 w h i c h is s t r i k i n g l y different f r o m t h e f o r m of a firsto r d e r k i n e t i c s . H e r e , C is t h e c o n c e n t r a t i o n o f C O . T h e m a x i m u m rate is a t t a i n e d at C =

l/k . 2

M a n y peculiar properties result from t h e bimolar L a n g m u i r kinetics of E q u a t i o n 12. F o r instance, t h e c o n c e n t r a t i o n profile of a

first-order

k i n e t i c s i n a n i s o t h e r m a l p i s t o n flow reactor f o l l o w s a n e x p o n e n t i a l c u r v e s h o w n i n F i g u r e 3. T h i s c o n v e x f u n c t i o n i n d i c a t e s t h a t a n y b a c k m i x i n g w o u l d h a r m t h e p e r f o r m a n c e so t h a t a constant s t i r r e d t a n k reactor o r a r e c y c l e reactor of the same v o l u m e w o u l d b e f a r less efficient t h a n a p i s t o n flow reactor.

H o w e v e r f o r a b i m o l e c u l a r L a n g m u i r k i n e t i c s i n t h e same

reactor, t h e c o n c e n t r a t i o n profile is g i v e n b y i n t e g r a t i o n of E q u a t i o n 12 to y i e l d : M0 )r 2

- I n y + 2ζ(1 -

y) + ζ\1 -

y )/2 2

(13)

ζ=ο (FIRST ORDER)

0.0

20

40

60 k,(0 ÎT 2

Figure 3.

Conversion

in piston flow reactor


100

18

CHEMICAL


where τ is the residence t i m e , y is the r a t i o ^Ciniet-

REVIEWS

( C O ) / ( C O ) i t , a n d ζ is i n

e

T h e c o n c e n t r a t i o n profiles g i v e n i n F i g u r e 3 a r e c o n c a v e so t h a t backmixing w o u l d be beneficial ( 3 ) . W h e n the bimolecular L a n g m u i r k i n e t i c s o c c u r i n a n i s o t h e r m a l C S T R , t h e reactor p e r f o r m a n c e

is de

scribed b y Μ0 )τ=(1-ν)(1

(14)

+ ζν) /ν 2

2

A b o v e a c r i t i c a l v a l u e o f ξ = 8, t h e r e w i l l b e three steady-state s o l u tions f o r e a c h v a l u e of & ι ( 0 ) τ . T h u s i n a n e x p e r i m e n t w h e r e t h e v a l u e 2

of & ι ( 0 ) τ is v a r i e d b y c h a n g i n g t h e flow rate o f gases or b y c h a n g i n g 2

t h e flow rate o f gases o r b y c h a n g i n g t h e reactor t e m p e r a t u r e , t h e d e g r e e of c o n v e r s i o n w o u l d t a k e s u d d e n leaps a n d w o u l d e x h i b i t hysteresis

(see

F i g u r e 4 ) . F o r t h e r e c y c l e reactor w i t h a r e c y c l e r a t i o of R , t h e reactor equation i s : M 0

2

) T =

(l+fl){lnz+2ft/(*-l) +£V(2 -D/2} 2

where 2 = (1 + Ry)/(1

+

(15)

R)y

S i m i l a r i n s t a b i l i t i e s c a n b e o b s e r v e d i n F i g u r e 5. T h u s , t h e C S T R a n d t h e r e c y c l e reactors are s u p e r i o r i n p e r f o r m a n c e to t h e p i s t o n flow r e a c t o r w h e n t h e k i n e t i c s are of t h e b i m o l e c u l a r L a n g m u i r t y p e . G r e a t care m u s t b e t a k e n t o a v o i d t h e i n s t a b i l i t i e s w h i c h c a n arise d u r i n g t h e a c c e l e r a t i o n o f a n a u t o m o b i l e w h e n t h e residence t i m e c a n rise b y a f a c t o r of 20, w h e n t h e C O i n l e t c o n c e n t r a t i o n m a y v a r y f r o m 8 to 0 . 1 % , a n d w h e n t h e t e m p e r a t u r e m a y v a r y f r o m 900° to 1800°F ( 3 ) . A n e v e n m o r e i n t e r e s t i n g p h e n o m e n o n arises w h e n t h e b i m o l e c u l a r L a n g m u i r k i n e t i c s t a k e p l a c e w i t h s i m u l t a n e o u s d i f f u s i o n across a porous catalyst. T h e c l a s s i c a l T h i e l e analysis s h o w e d t h a t a d r o p of c o n c e n t r a t i o n i n t h e i n t e r i o r o f a catalyst w o u l d l e a d t o a decrease i n o v e r a l l r e a c t i o n rate—as l o n g as there is a p o s i t i v e d e p e n d e n c e o f l o c a l r e a c t i o n rate o n l o c a l c o n c e n t r a t i o n .

F o r the bimolecular L a n g m u i r kinetics the

same c o n c e n t r a t i o n d r o p i n t h e i n t e r i o r w o u l d l e a d t o a n increase i n o v e r a l l r e a c t i o n rate (47, 48).

W e i a n d B e c k e r (49)

i n a n i s o t h e r m a l reactor t h e o v e r a l l effectiveness

showed that even

f a c t o r c a n b e greater

t h a n 1 a n d t h a t m u l t i p l e steady-state solutions c a n b e e x p e c t e d

when

t h e v a l u e o f ζ exceeds 8. T h i s means t h a t f o r a g i v e n q u a n t i t y o f p l a t i n u m i t is better t o s p r e a d i t o v e r a t h i c k e r s u p p o r t l a y e r t h a n to concentrate i t o n a n a r r o w l a y e r n e a r t h e p e l l e t surface.

A n even deeper placement

of p l a t i n u m is advantageous i n a v o i d i n g l e a d a n d p h o s p h o r u s

deposition

o n t h e catalyst pellets, w h i c h t e n d to concentrate o n t h e surface ( 5 0 ) .


1.

WEI

The Catalytic

19

Muffler

k,(0 )T 2

Figure 4.

Figure 5.

Conversion

Conversion

in CSTR

in recycle reactor

T h e s e t h e o r e t i c a l advantages h a v e b e e n c o n f i r m e d b y t h e e x p e r i m e n t a l d a t a of D o e l p et al. (51)

and by Michalko (52).

T h e s e observations c a n

l e a d to a c o m p l e t e r e v e r s a l of t h e c o n v e n t i o n a l p o l i c y of o p t i m a l c a t a l y s t d e s i g n : d e p o s i t i o n of t h e catalyst o n t h e v e r y e d g e of t h e s u p p o r t to f o r m the s o - c a l l e d " e g g s h e l l " catalyst s h o u l d b e r e p l a c e d b y

deeper

d e p o s i t i o n to f o r m " e g g y o l k " catalysts. A h i g h l y e x o t h e r m i c r e a c t i o n c a n g i v e r i s e to m u l t i p l e steady-state solutions, hysteresis, a n d i n s t a b i l i t y i n a reactor.

Davies and Buben

o b s e r v e d these i n s t a b i l i t i e s i n t h e o x i d a t i o n of h y d r o g e n a n d a m m o n i a


20

CHEMICAL

on p l a t i n u m wires (53).


REVIEWS

H i g h l y self-poisoned b i m o l e c u l a r L a n g m u i r k i -

netics c a n g i v e rise to a l l these i n s t a b i l i t y p h e n o m e n a e v e n i n a n isot h e r m a l system. C a r d o s o a n d L u s s (43)

h a v e s t u d i e d the o x i d a t i o n of b u t a n e a n d

C O over c o i l e d p l a t i n u m w i r e s . W h e n the t e m p e r a t u r e of the gas w a s r a i s e d a n d t h e n l o w e r e d , t h e t e m p e r a t u r e of the w i r e d e m o n s t r a t e d t w o b r a n c h e s of steady-state solutions w i t h hysteresis. T h e s e i n s t a b i l i t i e s are associated w i t h r e a c t i o n h e a t effects since the t e m p e r a t u r e

difference

b e t w e e n the w i r e a n d t h e gas c a n b e several h u n d r e d degrees. a n d J a k u b i t h (44)

Hugo

o b s e r v e d m u l t i p l e steady-state c o n d i t i o n s a n d h y s -

teresis w i t h C O o x i d a t i o n o n a w i r e m e s h of p l a t i n u m .

They believed

t h e system to be i s o t h e r m a l a n d h y p o t h e s i z e d t h e cause of oscillations as a n a l t e r n a t i o n of a d s o r b e d C O b e t w e e n a l i n e a r a n d b r i d g e f o r m . Luss and Amundson

(54)

h a v e p o i n t e d out t h a t for i s o t h e r m a l

reactions i n s i d e a p o r o u s catalyst, m u l t i p l e steady states c a n n o t t a k e p l a c e i f the m a x i m u m rate occurs at the surface. computed

Luss and Lee

(55)

m u l t i p l e steady states i n a n i s o t h e r m a l catalyst slab w h e n

t h e diffusivities of the t w o reactants are m a r k e d l y different a n d w h e n the r e a c t i o n rate d e p e n d s o n one r e a c t a n t p o s i t i v e l y a n d o n t h e other r e actant negatively.

A

case of i s o t h e r m a l i n s t a b i l i t y w a s

Beusch, Fieguth, and W i c k e

(56)

observed

d e p o s i t e d o n a l u m i n a pellets of 3 - m m d i a m e t e r .

A s the c o n c e n t r a t i o n

of C O i n the gas p h a s e w a s i n c r e a s e d , t h e p r o d u c t i o n rate of C 0 tially

by

w i t h C O oxidation over p l a t i n u m

2

ini-

increases a n d t h e n a b r u p t l y descends to a l o w e r b r a n c h ; w h e n

t h e C O c o n c e n t r a t i o n w a s decreased, the C 0

2

p r o d u c t i o n rate s t a y e d

o n t h e l o w e r b r a n c h f o r a w h i l e , a n d t h e n a b r u p t l y a s c e n d e d to t h e u p p e r branch.

O s c i l l a t i o n s w e r e also o b s e r v e d .

T h e i r data can be explained

q u a l i t a t i v e l y b y the t h e o r y of W e i a n d B e c k e r

(49).

T h e p e c u l i a r i t i e s of t h i s n e g a t i v e o r d e r k i n e t i c s has l e d to

many

r e - e v a l u a t i o n s i n r e a c t i o n e n g i n e e r i n g p r a c t i c e s , a n d t h e y are i m p o r t a n t i n d e s i g n i n g t h e c a t a l y t i c mufflers. T h e i n s t a b i l i t i e s m a y b e r e l a t e d to t h e s u d d e n m o n o l i t h m e l t i n g a n d to t h e p h e n o m e n o n of " b r e a k t h r o u g h " — s u d d e n t r a n s i e n t e m i s s i o n of u n c o n v e r t e d C O a n d h y d r o c a r b o n s i n a a f u l l y w a r m e d - u p converter. Transience

and

Dynamics

M o s t i n d u s t r i a l c a t a l y t i c reactors are d e s i g n e d to operate w i t h i n a v e r y n a r r o w r a n g e of i n l e t t e m p e r a t u r e s , flow rates, a n d concentrations. E x c e p t f o r s t a r t - u p , a c h a n g e i n feedstock, or a n o c c a s i o n a l upset, steadystate c o n d i t i o n s p r e v a i l .

O n the other h a n d , r a p i d transience a n d w i d e

d y n a m i c ranges are t h e r u l e w i t h t h e c a t a l y t i c muffler.

The

proper

e n g i n e e r i n g of the c a t a l y t i c muffler r e q u i r e s a n a c c u r a t e transience a n a l y -


1.

WEI

The Catalytic

21

Muffler

sis a n d a n o p t i m a l reactor d e s i g n over a w i d e r a n g e of i n p u t v a r i a b l e s w i t h a g i n g catalysts. T h e r e q u i r e d l e v e l of c o n v e r s i o n over the entire F e d e r a l C y c l e is i n t h e r a n g e of 7 0 - 9 0 % .

Since t h e c a t a l y t i c converter is not h o t

enough

d u r i n g the first t w o m i n u t e s to b e effective, the c o n v e r s i o n after the first t w o m i n u t e s m u s t b e m u c h better t h a n the average v a l u e of 9 0 % . converter t h a t effects better t h a n 9 0 %

A

c o n v e r s i o n at a h i g h flow rate

a n d l o w t e m p e r a t u r e w i t h a n a g e d catalyst m u s t b e o v e r d e s i g n e d d u r i n g a l o w flow rate a n d h i g h t e m p e r a t u r e w i t h f r e s h catalyst.

Homogeneous

gas phase o x i d a t i o n m a y b e c o m e i m p o r t a n t at t e m p e r a t u r e s a b o v e 1600 ° F . A n o t h e r area w h e r e transient analysis is sorely n e e d e d is d e s t r u c t i v e m e l t i n g of m o n o l i t h s , w h i c h occurs a b o v e 2 5 0 0 ° F .

These

temperatures

c a n n o t b e a c h i e v e d b y t h e sensible heat of t h e exhaust gases alone a n d must involve combustion exhaust gas.

of

unburned C O

and hydrocarbons

i n the

T h e r m a l r a d i a t i o n m u s t p l a y a c e n t r a l r o l e i n the

b a l a n c e l e a d i n g to s u c h d a m a g e .

I n t h e absence of t r a n s p o r t

heat

effects,

the m a x i m u m t e m p e r a t u r e a t t a i n e d i n a c o m b u s t i b l e m i x t u r e is the a d i a b a t i c flame t e m p e r a t u r e . H o w e v e r , i f the c o m b u s t i o n takes p l a c e e x c l u s i v e l y o n t h e w a l l , t h e m a x i m u m w a l l t e m p e r a t u r e is g o v e r n e d b y the ratio of mass transfer coefficient of the c o m b u s t i b l e to t h e h e a t transfer coefficient.

W h e n the v a l u e of the L e w i s n u m b e r c pD/\ p

is greater t h a n

1, w h i c h is the case for h y d r o g e n , the m a x i m u m w a l l t e m p e r a t u r e m a y exceed t h e a d i a b a t i c flame t e m p e r a t u r e . T h i s p h e n o m e n o n w a s p r e d i c t e d b y H e c k (57)

a n d experimentally confirmed by Hegedus

V a r d i and Biller (59)

(58).

are t h e first to r e a l i z e the c e n t r a l i m p o r t a n c e

of m o d e l i n g the reactor b e d t e m p e r a t u r e d u r i n g a c o l d start. T h e i r m o d e l of t h e reactor is one d i m e n s i o n a l w i t h separate t e m p e r a t u r e s for

gas

a n d solid but w i t h o u t longitudinal dispersion a n d w i t h o u t chemical reaction.

T o p e r f o r m the c o m p u t a t i o n , t h e y r e p l a c e d t h e c o n t i n u u m i n the

longitudinal direction w i t h

finite

i n t e r v a l s w h i c h reduces

the

reactor

to a series of 10 to 30 t i r r e d t a n k s . T h e i r i n p u t c o n d i t i o n s d e r i v e f r o m the seven m o d e C a l i f o r n i a C y c l e of t h e 1960's.

They concluded

that

most of t h e transience takes p l a c e i n the first t w o m i n u t e s a n d t h a t t h e t e m p e r a t u r e b e t w e e n the gas a n d t h e s o l i d is s e l d o m h i g h e r t h a n 50 ° F . T h e first successful m o d e l t h a t describes t h e c o m p l e t e

performance

of a c a t a l y t i c muffler d u r i n g a cold-start F e d e r a l C y c l e w a s g i v e n b y W e i (17)

a n d b y K u o et al

(18).

I t describes a r a d i a l - f l o w p e l l e t b e d

w i t h base m e t a l o x i d e e g g s h e l l catalyst, b y u s i n g a C a s c a d e m o d e l w h e r e e a c h c e l l comprises t h r e e to f o u r r o w s of pellets. A c o m p l e t e h i s t o r y of t h e i n l e t gas flow rates, t e m p e r a t u r e s , a n d gaseous c o m p o s i t i o n s e n t e r i n g the c a t a l y t i c muffler constitutes t h e i n p u t . T h e t e m p e r a t u r e a n d gaseous concentrations i n e a c h c e l l are c o m p u t e d

as f u n c t i o n s of t i m e .

This

m o d e l has b e e n u s e d to p r e d i c t muffler outlet concentrations a n d b e d


22

CHEMICAL


REVIEWS

t e m p e r a t u r e s w h i c h fit t h e e x p e r i m e n t a l d a t a a c c u r a t e l y . T h i s m o d e l has b e e n extensively u s e d to e x p l o r e t h e r e l a t i v e i m p o r t a n c e of

numerous

v a r i a b l e s of d e s i g n a n d o p e r a t i o n a n d to p o i n t to p r o m i s i n g avenues for n e w design. H a r n e d i n v e s t i g a t e d t h e m o d e l i n g of m o n o l i t h i c beds w i t h m e t a l a n d p r e c i o u s m e t a l catalysts ( 6 0 ) .

base

T h e b e d is a s s u m e d to

be

heterogeneous p i s t o n flow w i t h o u t a x i a l d i s p e r s i o n , a n d the k i n e t i c u s e d is s i m p l e n e g a t i v e first o r d e r .

F i n i t e difference m e t h o d s w e r e u s e d so

that the a x i a l l e n g t h is effectively d i v i d e d i n t o 10 to 40 zones.

This

creates a C a s c a d e m o d e l , w h e r e t h e n u m b e r of cells is a s s u m e d to be i n d e p e n d e n t of a t e n f o l d c h a n g e i n flow rate.

N o attempt w a s

made

to c o m p a r e these c a l c u l a t i o n s w i t h e x p e r i m e n t a l d a t a , a n d the v a l i d i t y of this m o d e l is y e t to b e e s t a b l i s h e d .

Ferguson a n d F i n l a y s o n have

d e m o n s t r a t e d that q u a s i - s t a t i c solutions are close to d y n a m i c solutions (61).

Bauerle and Nobe

piston

flow

firmation

also m o d e l e d

p e l l e t b e d s as heterogeneous

without axial dispersion, again without experimental con-

(62).

Y o u n g a n d F i n l a y s o n c h a l l e n g e d the v a l i d i t y of

these

m o n o l i t h i c m o d e l s for n e g l e c t i n g r a d i a l gaseous t e m p e r a t u r e g r a d i e n t (33).

T h e y s h o w e d that the N u s s e l t a n d S h e r w o o d n u m b e r s c a n n o t b e

c o n s i d e r e d passive p a r a m e t e r s that are assigned a h e a d of t i m e t h e y d e p e n d o n the rate of c h e m i c a l r e a c t i o n .

O u r great n e e d

since today,

as a l w a y s , is a r a p i d , c l o s e d l o o p b e t w e e n t h e o r e t i c a l p r e d i c t i o n s a n d e x p e r i m e n t a l testing. T h e d u r a b i l i t y of the c a t a l y s t is l i m i t e d b y t h e r m a l a g i n g a n d b y p o i s o n i n g ( 6 3 ) . T h e d e p o s i t i o n of l e a d a n d s u l f u r i n a m o n o l i t h is h e a v i l y c o n c e n t r a t e d at t h e reactor i n l e t ( 5 0 ) .

A s i m i l a r t e n d e n c y is u s u a l l y not

o b s e r v e d i n a p a c k e d b e d , p o s s i b l y because of a s l o w catalyst c i r c u l a t i o n d r i v e n b y the p u l s a t i n g gas

flow.

L e a d a n d s u l f u r penetrations i n s i d e a

p o r o u s s u p p o r t are m a i n l y c o n f i n e d to a d e p t h of 0.6 m m . T h e o p t i m a l reactor d e s i g n for s u c h a g i n g characteristics is a f e r t i l e field for i m a g i n a tive optimization.

Conclusion

T h i s r e v i e w has d e s c r i b e d the c a t a l y t i c muffler as: n e w — l o t s of r o o m for i m p r o v e m e n t , b i g — a n n u a l sales of s e v e r a l h u n d r e d m i l l i o n d o l l a r s , h e r e to s t a y — n o effective c o m p e t i t i o n t i l l 1980s. A f e w past achievements are d w a r f e d b y t h e m a n y u n s o l v e d p r o b l e m s w h i c h pose a c h a l l e n g e w e c a n n o t i g n o r e .


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23

Muffler

Nomenclature a surface to v o l u m e r a t i o C pollutant concentration c heat c a p a c i t y Ό d i s p e r s i o n coefficient d h y d r a u l i c d i a m e t e r of c h a n n e l dp d i a m e t e r of pellets F flow rate of gas H heat of r e a c t i o n h heat transfer coefficient b e t w e e n gas a n d s o l i d k mass transfer coefficient b e t w e e n gas a n d s o l i d L l e n g t h of b e d m m o l e c u l a r w e i g h t of p o l l u t a n t Ν n u m b e r of cells i n C a s c a d e m o d e l η reaction order Nu N u s s e l t n u m b e r , hd/λ Pe P e c l e t n u m b e r ud/D and udpC /\ Pr P r a n d t l n u m b e r c p./\ Q activation energy R reaction speed R gas constant r distance i n radial direction r r a d i u s of t u b e Re R e y n o l d s n u m b e r dup/λ Sc S c h m i d t n u m b e r , μ/ρΌ Sh S h e r w o o d n u m b e r , kd/D Τ temperature TU transfer units, N u · a L / R e · P r or S h · ah/Re • S c t time u gas v e l o c i t y i n b e d V vehicle speed W g m / m i l e of p o l l u t a n t e m i s s i o n i n F e d e r a l C y c l e χ distance, l o n g i t u d i n a l d i r e c t i o n v

v

v

g

c

a. β λ μ. ζ ρ τ ψ

t h e r m a l d i f f u s i v i t y , \/pc i n gas eigenvalue i n Graetz p r o b l e m heat c o n d u c t i o n coefficient viscosity k C inlet density residence time eigenfunction i n Graetz problem v

2

Literature

Cited

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24

C H E M I C A L REACTION ENGINEERING

REVIEWS

3. Wei, James, "Catalysis for Motor Vehicle Emissions," Advan. Catalysis (1975) 24, 57. 4. Federal Register 35 (219) Nov. 10, 1970; 36 (128) July 2, 1971. 5. "Report by the Committee on Motor Vehicle Emissions," National Academy of Sciences, Washington, D.C., Feb. 15, 1973. 6. Williamson, S. J., "Fundamentals of Air Pollution," Chap. 8, Addison -Wesley, 1973. 7. Pierson, W. R., Hammerle, R. H., Kummer, J. T., Soc. Auto. Eng. (1974) paper 740287. 8. "An Evaluation of Alternative Power Sources for Low Emission Auto mobiles," Panel Report of the Committee on Motor Vehicle Emissions, National Academy of Sciences, April 1973. 9. Oil Gas J. (June 10, 1974) p. 105. 10. Burke, D. P., Chem. Week (Nov. 1, 1972) p. 23. 11. Shinnar, R., Science (1972) 175, 1357. 12. "Feasibility of Meeting the 1975-76 Exhaust Emission Standards in Actual Use," Panel Report of the Committee on Motor Vehicle Emission, Na tional Academy of Sciences, June 1973. 13. Kramers, H., Westerterp, K. R., "Elements of Chemical Reactor Design and Operation," Chap. 3, Netherlands University Press, 1963. 14. Yagi, S., Kunii, D., Wakao, N., AIChE J. (1960) 6 (4) 543. 15. Votruba, J., Hlavacek, V., Marek, M., Chem. Eng. Sci. (1972) 27, 1845. 16. Froment, G. F., ADVAN. C H E M . SER. (1972) 109, 1.

17. Wei, J., Chem. Eng. Progr., Monograph Ser. (1969), Ser. 6, No. 65. 18. Kuo, J. C. W., Morgan, C. R., Lassen, H. G., Soc. Auto. Eng. (1971) paper 710289. 19. Votruba, J., Hlavacek, V., Chem. Eng. J. (1972) 4, 9. 20. Hlavacek, V., Kubicek, M., Chem. Eng. Sci. (1972) 27. 21. Lemme, C. D., Givens, W. R., Soc. Auto. Eng. (1974) paper 740243. 22. Howitt, J. S., Sekella, T. C., Soc. Auto. Eng. (1974) paper 740244. 23. Eckert, E. R. G., Drake, R. M., Jr., "Analysis of Heat and Mass Transfer," Chap. 7, McGraw-Hill, New York, 1972. 24. Kays, W. M., London, A. L., "Compact Heat Exchangers," 2nd ed., McGraw-Hill, New York, 1964. 25. Shah, R. K., London, A. L., Technical Report No. 75, Contract 225 (91) for Office of Naval Research, Dept. of Mech. Eng., Stanford University, 1971. 26. Sherony, D. F., Solbrig, C. W., Int. J. Heat Mass Transfer (1970) 13, 145. 27. Schoenherr, R., Woolley, J. Α., Chow, W., presented ACS, April 1974. 28. Heck, R. H., Wei, J., Katzer, J. R., ADVAN. CHEM. SER. (1974) 133, 34. 29. Koch, H., Ph.D. Thesis, Technical University of Munich, 1973. 30. Katz, S., Che.m Eng. Sci. (1959) 10, 202. 31. Solomon, R. L., Hudson, J. L., AIChE J. (1967) 13, 545. 32. Lupa, A. J., Dranoff, J. S., Chem. Eng. Sci. (1966) 21, 861. 33. Young, L. C., Finlayson, Β. Α., ADVAN. CHEM. SER. (1974) 133, 629. 34. Vortmeyer, D., Schaefer, R. J., Chem. Eng. Sci. (1974) 29, 485. 35. Hegedus, L. Louis, "Abstracts of Papers," 166th National Meeting, ACS, Chicago, 1973, PETROL 008. 36. Johnson, W. C., Chang, J. C., Soc. Auto. Eng. (1974) paper 740196. 37. Morikawa, K., Benedict, W. S., Taylor, H. S., J. Am. Chem. Soc. (1936) 58, 1795. 38. Sinfelt, J. H., J. Catalysis (1972) 27, 468. 39. Langmuir, I., Trans. Faraday Soc. (1922) 17, 621. 40. Schwab, G. M., Gossman, Κ., Z. Phys. Chem. (1958) 16, 39. 41. Tajbl, D. G., Simons, J. B., Carberry, J. J., Ind. Eng.Chem.,Fundamentals (1966) 5, 171.


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Muffler

25

42. Sklyarov, Α. V., Tretyakov, I. I., Shub, B. R., Roginskii, S. Z.,Dokl.Akad. Nauk. SSSR (1969) 189, 1302. 43. Cardozo, Μ. Α. Α., Luss, D., Chem. Eng. Sci. (1969) 24, 1699. 44. Hugo, P., Jakubith, M., Chem-Ing.-Tech (1972) 44, 383. 45. Cochran, H. D., Ph.D. Thesis, Chemical Engineering, MIT, 1972. 46. Voltz, S. E., Morgan, C. R., Liederman, D., Jacob, S. M., Ind. Eng. Chem., Prod. Res. Develop. (1973) 12, 294. 47. Roberts, G. W., Satterfield, C. N., Ind. Eng. Chem., Fundamentals (1966) 5, 317. 48. Satterfield, C. N., "Mass Transfer in Heterogeneous Catalysis," MIT Press, Cambridge, Mass., 1970. 49. Wei, J., Becker, E. R., ADVAN. C H E M . SER. (1975) 143, 116. 50. MacArthur, D. P., ADVAN. C H E M . SER. (1975) 143, 85.

51. Doelp, L. C., Koester, D. W., Mitchell, M. M. Jr., ADVAN. CHEM. SER. (1975) 143, 133. 52. Michalko, E., U.S. Patent 3,259,589 (July 1966). 53. Frank-Kamenetskii, D. Α., "Diffusion and Heat Exchange in Chemical Kinetics," translated by N. Thon, Chap. 9, Princeton University Press, 1955. 54. Luss, D., Amundson, N. R., AIChE J. (1967) 13 (2), 279. 55. Luss, D., Lee, J. C. M., Chem. Eng. Sci. (1971) 26 (9), 1433. 56. Beusch, H., Fieguth, P., Wicke, E., ADVAN. CHEM. SER. (1972) 109, 615. 57. Heck, R. H., Ph.D. Thesis, Chemical Engineering, University of Delaware, 1974. 58. Hegedus, L. L., "Temperature Excursions in Catalytic Monoliths," AIChE Meeting, Washington, D.C., December 1974. 59. Vardi, J., Biller, W. F., Ind. Eng. Chem., Process Design Develop. (1968) 7, 83. 60. Harned, J. L., Soc. Auto. Eng. (1972) paper 720520. 61. Ferguson, Ν. B., Finlayson, Β. Α., AIChE J. (1974) 20, 539. 62. Bauerle, G. L., Nobe, K., Ind. Eng. Chem., Process Design Develop. (1973) 12 (4), 407. 63. Hegedus, L. L., Ind. Eng. Chem., Fundamentals (1974) 13, 190. RECEIVED December 4, 1974. This review was written with the support of the National Science Foundation grant GK 38189 and the support of the Minnesota Mining and Manufacturing Co.


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