Page 175 - Adsorption, Ion Exchange & Catalysis- 2007, Elsevier - Copy

Else_AIEC-INGLE_cH003.qxd 7/13/2006 1:46 PM Page 171
3.7 Three-Phase Fixed Beds: Trickle-Bed and Ped Bubble-Bed Reactors ack 171

For reactant A in the liquid phase, at steady state, and for a v xtends olume element that e
across the reactor ,
2 C d C d C  
D AL u AL Ka ( )  AG C  k a ( C ) [ C ] 0 (3.367)
L 2 sL LG A AL f u A AL AS A
L
z d z d  H A 
where C AS is the concentration of A in the liquid–solid interf ace u sL the superficial liquid
velocity.
The third mass conservation equation needed is that for reactant B in the liquid phase.
2 C d C d
D L 2 BL u sL BL ka ( fu B C ) [ BL C ] 0 (3.368)
BS
z d z d
Here, it has been assumed that B is nonThe v olatile. v elocity u sL is the superficial liquid
velocity.
The reaction rate expressed in terms of surface concentrations provides the relationship
,
between C S and C L . From the definition of the efeness f we may express the
v
actor
fecti
required equality of mass transfer and reaction rates as
( ka fu A ) [C AL C ] (R b m A (r ) (3.369)
)
A
AS
( ka ) C C ( R ) ( A ) R b ( r ) (3.370)
fu A BL BS B mA
a a
where is the bulk density of the bed, a the stoichiometric coef (– icient, f r ) A represents
m
b
the rate of reaction per unit mass of catalyst, and – R A and – R B represent the rate of reac-
olume of reactor tion per unit v. Note that subscripts A and B denote that the mass transfer
coefficient could be different for different species due to the difference in the dif fusion
coefficients.
As in the case of two-phase fed beds, the material balances of trickle beds are
ix
expressed in terms of the reactor v olume V R (see Section 3.1.1 for the deriation) and the v
following relationship holds:
1d N
( R ) (1 ) r vs s b ) r s ( r ) m (3.371)
)(
( S
b
V d t
R
Example 7
An interesting case is a reaction with 1. A typical example is the catalytic reaction
R
of the form
A(g) B(
C(l)
l)
where the gas feed is pure A and it is the limiting reactant. Analogous to batch systems,
Q
G 1 x 1 x
Q G,i RA A