Page 147 - Adsorption, Ion Exchange & Catalysis- 2007, Elsevier - Copy

Else_AIEC-INGLE_cH003.qxd 7/13/2006 1:45 PM Page 143
3.6 T w o-Phase Fix ed Beds 143

Dividing by the term ( A z ) we ha e v

D  C C  Q
L C ( C )
z   z W z E   A z W E (3.282)
C ( C )

(1 ) p m r ) E W
(
t
v
Setting z → 0, we can derie the differential form of equation (3.282). Taking into
account that
z z
t t
C W C E C
C C  C 
 
z z  z 
E W
 C 
  z    2 C (3.283)

 C 
z zz  z  z 2
eq. (3.282) becomes

 C  Q C C
)
D   (1 ( r ) (3.284)
L z  z  A z p m t
or
2 C C C
D L u s ( R ) (3.285)
z 2 z t
The material balance including the effect of incomplete mixing in the radial direction is
(Perry and Green, 1999)

 C 2 C   2 C 1 C  C
(
  u s z D L z 2   D R   r 2 r   R ) t (3.286)
r
where:
the bed v oidage
the bulk density
b
u the superficial fluid v elocity
s
D the axial dispersion coef icient f
L
D the radial dispersion coef icient f
R
C the solution concentration.