Page 70 - Adsorption, Ion Exchange & Catalysis- 2007, Elsevier - Copy

Else_AIEC-INGLE_cH003.qxd 7/13/2006 1:44 PM Page 66
66 3. Heterogeneous Processes and Reactor Analysis

metals, if the same v alue of turnover frequency is obtained for a specific reaction at fixed
conditions on two catalytic samples containing different amounts of metal on the porous
support, the kinetic data are not obscured by heat or mass transfer phenomena.

3.1.2 The concept of the overall reaction rate in heterogeneous reactions

General
In heterogeneous reactions, phase boundaries exist between phases and transport
processes; the intrinsic rate of reaction should be taken into account simultaneously in
reactor design. The combination of mass transfer rates and reaction rates leads to the so-
called oerall rate. The goal is to express the global rate in terms of the bulk properties of v
the phases, eliminating the interphase properties.
v If the oerall phenomenon requires that a number of steps take place in series , then, at
steady state, all these steps will proceed at the same rate, which is equal to the o erall rate v
(Levenspiel, 1972):

r
r overall 1 r r ... n (3.28)
2
There are cases, as in catalysis, where some steps are in par allel . In these systems, the
overall rate is greater than the rate of each individual step. If these steps are independent
of each other the oerall rate is the sum of all individual rates (Le 1972). enspiel, v
,
v
n
r overall ∑ r i (3.29)
n 1
The elimination of the interphase concentrations could be done easily if the rate e xpres-
xpressions,
v
sions of all steps are linear in concentration. Ho for nonlinear e it is
we
er
,
difficult to evaluate and handle the overall rate. We will examine some simple cases in two-
and three-phase systems.
Two-phase systems
one for each fluid, o f In the case of two fluids, twilms are developed, and the corresponding
mass-transfer coefficients are determined (Figure 3.2). In a fluid–solid system, there is only
one film; whereas the resistance within the solid phase is expressed by the solid-phase dif-
fusion coefficient, ho in many cases an “ef mass-transfer coef e” v fecti icient is used f
,
v
we
er
in the case of solids as well. Consider the irreversible catalytic reaction of the form
A(g) B(g)
Here, we consider the general case of a porous catalyst, where the internal dif fusion ef fect
eness f actor ( v fecti is included in the ef ).
s
The intrinsic rate of reaction per unit mass of catalyst is (in mol/m 2 s)
1d N

( r ) kC (3.30)
s s s s
S d t