
339Heterogeneous Reactors
where
D
A
: effective diffusivity of A through the solid slab
Consider a section of the catalyst pellet of thickness Δx at a distance x from the central
axis (x = 0).
Taking a steady-state balance of A across this section, we have
Rateof transfer
ofintothesection
Rateof transfer
A
=
+xx∆
of outofthesection
Rateof conversion
ofinthesect
+
x
iion
(4.135)
SD
dC
dx
SD
dC
dx
kC Sx
A
A
xx
A
A
x
⋅=⋅+
+∆
∆ρ
(4.136)
Dividing the terms in the above equation by (Δx ⋅ D
A
) and taking limits as Δx → 0, we get
the second-order differential equation
dC
dx
kC
D
A
pA
A
2
2
0
ρ
(4.137)
With boundary conditions dened at x = ± L and x = 0 as
At ; ...