Chemical Reaction Engineering Reviews

4 Physical Processes in Chemical Reactor Engineering

Downloaded by UNIV OF NORTH CAROLINA on June 17, 2013 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1975-0148.ch004

E.

WICKE

Institut für Physikalische Chemie, Westfälische Wilhelms-Universität, 4400 Münster, Germany

The

scope

of this review

examination

of the

pseudo-homogeneous systems. SLP

catalysts,

are discussed this principle processes

this principle in detail.

Taylor

are indicated

with

the mass transfer beds.

of mass in packed This difference

boundary

and Wilhelm,

heat transfer

its

flow The

conditions

at the bed

ad-

systems, elementary

are

illustrated; in f l u i d i z e d

in packed

problems

Differentiation

and

applicability

The limits of pseudo-homogeneous

and of shallow

emphasized. known

dispersion

the

gas-solid

diffusivity;

For heterogeneous

the

critical

multiphase

and the limits of its

beds as well as to interphase

dispersion

i.e. porous

in

to gas phase and to solids dispersion

are presented. screens

processes

is effective

and

that underlie

is radial and axial dispersion.

including

applications

for

systems,

its shortcomings,

presentation

principles

models

For diffusion

vantages,

is the

physical

beds

modeling of

catalyst

between

axial

beds and real backmixing requires

a change

of Dankwerts,

of the

and of

is well

Wehner

entrance.

A l t h o u g h the papers i n the session o n " P h y s i c a l Processes" (see A D V A N C E S I N C H E M I S T R Y S E R I E S N O . 1 3 3 ) are different i n scope a n d n a t u r e , t h e y c o n t a i n a n u m b e r of c o m m o n v i e w p o i n t s that m a y serve as a basis f o r this r e v i e w .

O n e of t h e most i m p o r t a n t v i e w p o i n t s seems to b e t h e

o b v i o u s t e n d e n c y to d e s c r i b e processes t h a t r u n i n heterogeneous m u l t i p h a s e systems b y p s e u d o - h o m o g e n e o u s

m o d e l s a n d to c o m p r e h e n d t h e

b e h a v i o r of s u c h processes, s t a t i o n a r y o r d y n a m i c , i n terms of s i n g l e p h a s e concepts. principles

H e n c e t h e t h e m e of this r e v i e w w i l l b e to i n d i c a t e t h e

a n d the methods

of d e v e l o p i n g h o m o g e n e o u s

models for

heterogeneous processes a n d to present t h e usefulness of those concepts as w e l l as t h e l i m i t s of t h e i r a p p l i c a b i l i t y . 75 In Chemical Reaction Engineering Reviews; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

76

CHEMICAL

REACTION ENGINEERING REVIEWS

T h e r e are t w o p r i n c i p a l types of heterogeneous systems i n c h e m i c a l reactors ( T a b l e I ) : the f l o w systems w h e r e h y d r o d y n a m i c flow is t h e p r e d o m i n a n t process of mass transport, a n d the d i f f u s i o n systems w h e r e

Table I. Type of System


Flow

Two

Heterogeneous Reaction Systems Three

Phases

Phases

t r i c k l e beds bubble columns ( w i t h suspended c a t a l y s t s )

p a c k e d beds fluidized beds

macroheterogeneity:

e

m

microheterogeneity :

u

i j s

o

n

\ p h a s e - b u b b l e phase

grains-fluid

grids, screens, gauzes Diffusion

porous solids

| S L P catalysts

m a c r o p o r e a n d m i c r o p o r e systems

m o l e c u l a r d i f f u s i o n p r e v a i l s . T y p i c a l flow systems are r e p r e s e n t e d b y p a c k e d beds,

fluidized

b e d s , g r i d s , a n d screens, a n d those w i t h three

phases b y t r i c k l e beds a n d b u b b l e c o l u m n s w i t h s u s p e n d e d catalysts. D i f f u s i o n systems are the porous gas—solid catalysts a n d t h e s u p p o r t e d l i q u i d p h a s e ( S L P ) catalysts. I n some cases, different levels of h e t e r o geneity can be discerned. I n

fluidized

beds a n d i n three-phase b u b b l e

c o l u m n s there are the m a c r o l e v e l of h e t e r o g e n e i t y ( d e n s e or e m u l s i o n phase a n d b u b b l e p h a s e )

a n d the m i c r o l e v e l ( g r a i n s a n d

fluid);

in

d i f f u s i o n systems, these levels of h e t e r o g e n e i t y are t h e m a c r o p o r e a n d the m i c r o p o r e arrays. I n flow systems, the h e t e r o g e n e i t y leads to the w e l l k n o w n d i s p e r s i o n effects.

P a r a l l e l to the m a i n flow d i r e c t i o n — a x i a l or l o n g i t u d i n a l — t h e

d i s p e r s i o n is a p p r e c i a b l y b r o a d e r t h a n i t is n o r m a l to i t — r a d i a l or transversal. I n o r d e r to d e s c r i b e these effects i n a n a l o g y w i t h d i f f u s i o n p r o c esses, m e a n i n g f u l coefficients

for r a d i a l a n d a x i a l d i s p e r s i o n m a y

be

m e a s u r e d a n d defined o n l y i f t h e system is l a r g e e n o u g h to c o v e r the l e n g t h of at least 10 c h a r a c t e r i s t i c d i s p e r s i o n p a t h w a y s i n either d i r e c t i o n . I f this c o n d i t i o n is n o t satisfied, t h e m o d e l of t h e i d e a l single m i x i n g stage or the cascade of m i x i n g cells m a y b e a p p l i c a b l e to t h e system. I f this fails also, t h e n a p s e u d o - h o m o g e n e o u s

m o d e l does not seem to b e

a d e q u a t e for the flow system. T h i s is t r u e , for instance, for screen c a t a lysts a n d for s h a l l o w p a c k e d beds as w e l l as for c e r t a i n (see

fluidized

below).

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

beds

4.

Physical

wiCKE

Diffusion

Processes

Systems

T h e pseudo-homogeneous m o d e l can be a p p l i e d

i n heterogeneous

diffusion systems i f the units of h e t e r o g e n e i t y — p o r e s ,

holes, p a r t i c l e s ,

e t c . — a r e s m a l l c o m p a r e d w i t h the l e n g t h of the diffusion p a t h s , i.e. t h e extension of the c o n c e n t r a t i o n profiles. T h e most s i m p l e a p p l i c a t i o n of this m o d e l is to m a k e use of a n effective diffusion coefficient:


D

e f

, =

ψ · An

(la)

w h e r e φ is the p e r m e a b i l i t y of the porous b o d y a n d D coefficient i n the free gas phase.

is t h e d i f f u s i o n

m

I n o r d e r to measure D

accordingly,

ett

steady state d i f f u s i o n m u s t be a p p l i e d ( t h e t e r m p e r m e a b i l i t y i n d i c a t e s steady state c o n d i t i o n s ) , a n d the gas pressure m u s t b e sufficiently h i g h i n o r d e r to justify the neglect of K n u d s e n diffusion.

T h e permeability

c a n t h e n b e u s e d to define a l a b y r i n t h f a c t o r χ (or t o r t u o s i t y factor l / χ ) by: φ =

c · χ w h e r e c is t h e p o r o s i t y . T h e system of transport pores p

p

for p e r m e a t i o n t h r o u g h the porous b o d y is n o r m a l l y the same as t h e macropore

system a n d has a f a i r l y w e l l defined m e a n p o r e r a d i u s , r;

the m i c r o p o r e s are t h e n s i m i l a r to pockets i n t h e w a l l s of the m a c r o p o r e s . I n s u c h a case, the p e r m e a b i l i t y i n t h e K n u d s e n r e g i o n , a c c o r d i n g to ϋ\

=

ΐ ί

φ

κ

(lb)

· D (r) K

w i t h D ( r ) = K n u d s e n diffusion coefficient, c a n b e c o n s i d e r e d e q u a l to K

t h e p e r m e a b i l i t y for b u l k d i f f u s i o n : ψ

κ

«

φ.

I f o n the other h a n d , t h e

m i c r o p o r e s c o n t r i b u t e m a r k e d l y to the d i f f u s i o n resistance for p e r m e a t i o n , ψ =τ^ψ h o l d s , w h i c h means t h a t the p e r m e a b i l i t y i n the t r a n s i t i o n r e g i o n κ

b e c o m e s d e p e n d e n t o n t o t a l gas pressure a n d o n the t y p e of m o l e c u l a r species t h a t is diffusing. F o r n o n s t e a d y state diffusion i n porous systems, the mass

balance

e q u a t i o n is

—

(c c + n ) &

p

=

d i v (xf/D · g r a d c)

(2)

m

w h e r e n is the a m o u n t of gas a d s o r b e d at the p o r e w a l l s p e r u n i t v o l u m e a

of the porous b o d y . P s e u d o - h o m o g e n e o u s

treatment is possible i f n

a

can

b e t a k e n as the v a l u e i n a d s o r p t i o n e q u i l i b r i u m w i t h c. I n the r e g i o n of linear adsorption isotherm and w i t h D

m

i n d e p e n d e n t of

concentration,

E q u a t i o n 2 t h e n simplifies to

IT dt

=

, ^ / τ div grad c = c + dn /dc m

p

D'

e f f

· div grad c

a

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

(3)

78

CHEMICAL

w i t h a n effective coefficient D '

e f f

REACTION ENGINEERING REVIEWS

for n o n s t e a d y state d i f f u s i o n .

When

a d s o r p t i o n is n e g l i g i b l e

D ' e f f - ^ D m - — C

P

C

=χΑη

P

(4)

r a t h e r t h a n E q u a t i o n l a for steady state c o n d i t i o n s . If, o n the other h a n d , a d s o r p t i o n w i t h c u r v e d isotherms has to be c o n s i d e r e d , t h e mass b a l a n c e i n t h e g e n e r a l f o r m of E q u a t i o n 2 m u s t b e u s e d , a n d the s o l u t i o n of


diffusion problems becomes very complicated although still w i t h i n the c o n c e p t of

pseudo-homogeneity.

Wakao's paper ( I )

starts w i t h the q u e s t i o n i f the b i n a r y c o u n t e r -

diffusion of inert, n o n a d s o r b a b l e gases t h r o u g h p o r o u s m e d i a r u n s for steady state a n d for n o n s t e a d y state c o n d i t i o n s w i t h effective d i f f u s i o n coefficients t h a t differ o n l y b y the f a c t o r e , i.e. D f = p

to E q u a t i o n 4.

e

e · D' f

f

p

e

£

according

I n fact, the v a l i d i t y of this r e l a t i o n c o u l d b e c o n f i r m e d

b y measurements w i t h N - H 2

2

m i x t u r e s i n p o r o u s r e f r a c t o r y m a t e r i a l as

w e l l as b y c a l c u l a t i o n s of t h e d i f f u s i o n t h r o u g h a t w o - d i m e n s i o n a l n e t w o r k of i n t e r c o n n e c t e d m a c r o - a n d m i c r o p o r e s . T h i s n e t w o r k m o d e l w a s also u s e d b y W a k a o to discuss the b a s i c q u e s t i o n i f t h e effective d i f f u s i o n coefficient, as m e a s u r e d b y m e t h o d s of steady state p e r m e a t i o n t h r o u g h the porous m e d i u m , D

D

e f £

— b i n a r y b u l k d i f f u s i o n or K n u d s e n d i f f u s i o n —

w i l l b e t h e same as the coefficient, D f , that c a n be o b t a i n e d f r o m t h e R

effectiveness

f a c t o r of a

first-order

e

f

r e a c t i o n r u n n i n g at the p o r e w a l l s .

I n fact, t h e c a l c u l a t i o n y i e l d s differences for the same m o l e c u l a r species w i t h and without reaction: D

R

e f f

Chemical Reaction Engineering Reviews

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