Page 116 - Adsorption, Ion Exchange & Catalysis- 2007, Elsevier - Copy

Else_AIEC-INGLE_cH003.qxd 7/13/2006 1:45 PM Page 112
112 3. Heterogeneous Processes and Reactor Analysis

For a first-order reaction, in either reactant, the combination of these equations and the
elimination of the surface and liquid-phase concentrations lead to the formulation of an
This procedure is overall rate, e ulk gas-phase concentration. xpressed as a function of the b
essentially the same as the one presented analytically in Section 3.1.2 for the derivation of
v an oerall rate in three-phase systems.
Note that the gas-phase is flowing under plug-flow condition, and thus its concentration
will change with position C G,z . Thus, the procedure of the formulation of the oerall rate v
is made for a certain axial position (z) in the reactor where at steady state, the gas-phase
concentration is constant.
Following the procedure described in Section 3.1.2, the rate per unit volume of b ubble-
free liquid in terms of the concentration of the reactant in the gas phase is

( r u ) G,z (3.141)
K
C
where K o is an oicient (in s erall coef f v 1 ):

1 1 H 1  1 
H   (3.142)
K k a ka  ak m k 
gG L fgG L c f s s m

with a GL and a c being the gas–liquid and liquid–solid interfacial area per unit volume of
bubble-free liquid (in m 2 /m 3 ), respectiparameter . The ely v m s is the catalyst loading per
unit volume of bubble-free liquid (in kg/m 3 ).
v The oerall mass transfer coef icient f K L is

1 1 1
(3.143)
K Hk k
L g fg
If the gas-phase resistance is negligible (Section 3.1.2), then

1 H  1 1 1  (3.144)
K   ka fg GL k a f c s m k  
s m

Here, it is important to note that the v alue of K o ferent reac- is different if it is based on dif
ferent v tants due to the difalues of Henry’ s constant.

Reacting liquid-phase First-order in gas reactant and constant gas-phase concentration :
v The oerall rate is exactly the same as in the nonreacting liquid:

( r u ) C o G,i (3.145)
K
Note that here the gas-phase concentration is constant and thus its inlet concentration is
xpression. v present in the oerall rate e