Transport Phenomena in Packed Bed Reactors - American Chemical

4 Transport Phenomena in Packed Bed Reactors

Downloaded by UNIV OF PITTSBURGH on August 13, 2015 | http://pubs.acs.org Publication Date: January 19, 1978 | doi: 10.1021/bk-1978-0072.ch004

E. U. SCHLÜNDER Institut für Thermische Verfahrenstechnik, Universität Karlsruhe, F.R.G., West Germany

I. Preface The performance of packed bed reactors may be influenced and sometimes even controlled by transport phenomena in the voids between the particles as well as inside the particles. This paper is restricted to transport phenomena mainly between the particles. There occurs heat, mass and momentum transfer between the fluid and the particles. Moreover, transport of heat and mass also occurs between the voids themselves. While mass transport through the particles is negligible, heat conduction through the particles is always involved with transport of heat between the voids and therefore must be considered simultaneously. In this paper emphasis is put on recent developments rather than on a more or less complete literature survey. However, experimental data w i l l be thoroughly reported, because they are the basis of any theoretical analysis. II.

Outline

Since transport of heat and mass in the voids of a packed bed cannot be understood without knowing the movement of the f l u i d , hydraulic phenomena w i l l be treated f i r s t . Second the heat and mass transfer between the fluid and the particles w i l l be discussed. Third the radial transport of heat and mass through the voids (and the particles) w i l l be treated. In the past these transport phenomena usually have been treated assuming that the fluid passes through the reactor in plug flow. This assumption then has been revised after careful studies have revealed, that there is not only a microscopic but also a macroscopic void fraction distribution. Consequently,there is a certain 0-8412-0432-2/78/47-072-110$12.80/0 © 1978 American Chemical Society In Chemical Reaction Engineering Reviews—Houston; Luss, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Transport in Packed Bed Reactors

4. SCHLUNDER

111

macroscopic flow rate distribution i n a tubular reactor. But only recently the consequences o f this macroscopic non-uniform d i s t r i b u t i o n of flow rate have been e v a l u a t e d w i t h r e g a r d t o heat and mass t r a n s f e r between t h e f l u i d and t h e p a r t i c l e s . This e f f e c t w i l l b e t r e a t e d i n t h i s p a p e r t o some e x t e n t . Another problem, which s t i l l has not been solved i s the heat t r a n s f e r between p a r t i c l e s and r i g i d w a l l s . However, some a c h i e v e m e n t s c a n b e r e p o r t e d a l r e a d y now.


III.

Flow rate d i s t r i b u t i o n tubular reactors

and pressure

drop

i n

It i s w e l l known t h a t t h e v o i d f r a c t i o n i s larger near the walls of a tubular reactor than i n the central p a r t s . F i g . 1 shows e x p e r i m e n t a l d a t a o f B e n e n a t e and Brosilow (1). The v o i d f r a c t i o n ψ decreases from 1 a t t h e w a l l t o a minimum o f 0 , 2 3 a n d f o l l o w s a damped o s c i l l a t i o n f u n c t i o n towards the center of the tube. The a b s c i s s a y / d i s t h e d i s t a n c e from t h e w a l l divided by the p a r t i c l e diameter. A semitheoretical analysis of t h i s d i s t r i b u t i o n has been given by R i d g e w a y a n d T a r b u c k (2.) . F o r p r a c t i c a l p u r p o s e s Martin (3) gave a n e m p i r i c a l e x p r e s s i o n a s shown i n Fig. 1. T h e a v e r a g e v o i d f r a c t i o n r e m a i n s practically c o n s t a n t f o r y / d > 0 , 5 and i s about 0 , 4 0 f o r a random packed bed o f equal s i z e d s p h e r e s . However, near t h e r e t a i n i n g w a l l the average v o i d f r a c t i o n i s about 0,50. T h i s means t h a t m o d e l s o f p a c k e d b e d r e a c t o r s intro d u c i n g an average h y d r a u l i c diameter must be based a t l e a s t o n two a v e r a g e d i a m e t e r s . In t h i s case one o b t a i n s a h i g h e r f l o w r a t e V2 n e a r t h e w a l l a n d a l o w e r o n e V3

2 2 c ρ

κ

( 3 0 )

at ^

low

10~4

pressure which

same o r d e r o f m a g n i t u d e a s h a s b e e n f o u n d state experiments, see e . g . F i g . 12.

i s

and in

from

short

the steady


Eq. 27 g i v e s a v e r a g e w a l l h e a t t r a n s f e r c o e f f i c i e n t s obtained by i n t e g r a t i n g over the l o c a l heat transfer rates, which reach a rather high value near the contact point, see F i g . 9. T h i s l a r g e variation of the l o c a l heat flux with respect to the particle r a d i u s may become o f p r a c t i c a l i m p o r t a n c e , too. E . g . s h o u l d a wet porous c a t a l y s t be d r i e d i n an indirectly heated rotary dryer, one would expect t h a t the drying rate during the constant rate period i s controlled by the wall heat transfer coefficient c* a c c o r d i n g E q . 2 7 . Experiments, however, have shown that! t h e d r y i n g rate i s much l o w e r . F i g . 23 s h o w s e x p e r i m e n t a l data (Uni versity of Karlsruhe, s t i l l unpublished) for magnesium w

s i l i c a t e s p h e r e s o f 6 mm d i a m e t e r d r i e d i n an agitated packed bed c o n t a c t i n g a hot p l a t e . The o^-controlled d r y i n g r a t e can be m a i n t a i n e d o n l y d u r i n g the f i r s t few s e c o n d s . L a t e r when a c o n s t a n t r a t e p e r i o d is o b s e r v e d , the d r y i n g r a t e i s much l o w e r . The reason for this considerable rate reduction i s , that the particles immidiately dry off near the contact point, because the l o c a l heat flux i s so h i g h , t h a t the equivalent amount o f l i q u i d c a n n o t be b r o u g h t t o the surface of the p a r t i c l e s at t h i s point. T h i s means that the dry longer control forces

ing rate durin heat transfer led according i n the porous

g the constant rate period i s no c o n t r o l l e d , but a l s o mass transfer to the strength of the capillary granules.

Wall heat transfer coefficients in tubular reactes w i t h a f l u i d p a s s i n g through can be determined either by d i r e c t e v a l u a t i o n of temperature p r o f i l e s in the packed bed or by a n a l y z i n g over a l l heat transfer c o e f f i c i e n t s , s o far the apparent heat conductivity i s k n o w n . R e c e n t l y H e n n e c k e a n d S c h l u n d e r (6J5) have e v a l u a t e d a b o u t 5 0 0 0 d a t a c o l l e c t e d f r o m 14 authors, who h a v e p u b l i s h e d o v e r a l l h e a t t r a n s f e r coefficients a p p l y i n g E q . 22 a a n d t h e f o l l o w i n g o n e s f o r the p r e d i c t i o n of the apparent heat conductivity of packed bed A . Assuming plug flow they obtained heat transfer c o e f f i c i e n t s depending not only on P e c l e t number (Pe = u d / κ ) b u t a l s o o n t h e r a t i o tube diameter D t o t u b e l e n g t h L as shown i n F i g where the w a l l N u s s e l t number Nu.. = d / A i s pl against Pe. u i s the s u p e r f i c i a l v e l o c i t y of the a

w

In Chemical Reaction Engineering Reviews—Houston; Luss, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

the wall the of . 24, otted gas,

;

CHEMICAL REACTION ENGINEERING REVIEWS—

Plate surface temperature [•c]

Stirrer speed


60.9

•

70.7

Δ

81.5

Ο

91.3

Init. moisture content Ug/kg]

2

[l/min]

50.3 Ο

maximum drying rate [kg / m h ]

15.4 15.4

154 10' 219 10'

15,4 15.4

3

0.166 0.221

3

262 1 0 ' 324 10-3

0.201

3

0.199

3

zero

364 10"

0.211

Ρ s 21mbar

0.05

0.10

0.15

0.20 kg

Moisture

content

025

0.30

H 0 2

Y kg dry m a t .

Figure 23. Contact drying of magnesium silicate spheres of 6mm diameter in an agitated packed bed. Drying rate m vs. moisture content Y. Pressure 21 mbar.



Figure 24. Wall heat transfer coefficients Nu* — «w/dA vs. particle Peclet number Pe — ud/κ obtained by evaluation of overall heat transfer coefficients in tubular reactors assum ing plug flow according to Ref. 65. D — tube diameter, L — tube length.


CHEMICAL REACTION ENGINEERING REVIEWS—HOUSTON


156


d i s the p a r t i c l e and λ the thermal the

157


SCHLUNDER

4.

N u - d a t a

not

also turned out the r a d i a l flow

diameter, κ the conductivity of only

tend

thermal d i f f u s i v i t y t h e g a s . Some o f

towards

i n f i n i t y

but

to be n e g a t i v e ! Taking i n t o account rate d i s t r i b u t i o n as given i n F i g . 3

t h e same e v a l u a t i o n y i e l d e d w a l l h e a t transfer c o e f f i c i e n t s Nu.. (Pe, L/D) d e p e n d i n g much l e s s ratio


have heat

L/D

as

shown

in

F i g .

25.

Also

no

on

negative

the

values

been o b t a i n e d . However, for long tubes the wall transfer c o e f f i c i e n t s are s t i l l lower by o r d e r s

of magnitude than those for short tubes. This effect is s t i l l not r e a l l y u n d e r s t o o d . It may b e t h a t t h i s i s due to the by pass e f f e c t d e s c r i b e d i n s e c t i o n IV. However, t h i s i s an assumption and i s s t i l l subject to further i n v e s t i g a t i o n . For p r a c t i c a l purposes Hennecke (65) has developed semi-empirical correlations to predict both wall heat transfer c o e f f i c i e n t s as shwon i n F i g . 25 a s w e l l a s f l o w r a t e d i s t r i b u t i o n s i n p a c k e d b e d r e a c t o r s as shown i n F i g . 3. At

the

present

state

these

correlations

together

w i t h E q . 23 f o r t h e p r e d i c t i o n o f t h e a p p a r e n t heat c o n d u c t i v i t y and E q . 6, 7 for the p a r t i c l e - t o - f l u i d h e a t t r a n s f e r may b e r e c o m m e n d e d f o r a p p l i c a t i o n in tubular reactor design. These correlations give f a i r l y r e l i a b l e parameters for either homogeneous o r hetero g e n e o u s one o r two d i m e n s i o n a l t i c a l simulation of packed bed Symbols A a

v

Cg

surface surface

area area

radiation

d

particle

D,4^,

bed

per

of

the

unit black

models for reactors.

mathema

volume body

diameter

diameter

f

cross

L ΔΡ q

bed height ; pressure drop Heat flux

r,p

radial

S

gap

Τ u

temperature s u p e r f i c i a l

sectional

area 1

p a r t i c l e

length

coordinate

width ; velocity

t

V

flow

y

distance

α ε η,ν

heat transfer coefficient radiation emissivity dynamic and kinematic v i s c o s i t y ,

λ

void

time

rate from

the

tube

wall

resp.

fraction

Λ κ

apparent thermal

0

mean

o

the

free

heat conductivity d i f f u s i v i t y path

of

the

molecules


158


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Transport Phenomena in Packed Bed Reactors - American Chemical

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