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WOLFRAM|DEMONSTRATIONS PROJECT

Surface Kinetics with Pore Diffusion Resistance

​
Thiele modulus
1
Consider a first order reaction
A→B
taking place on the surface of a catalyst with cylindrical pores. The relevant equation is
2
d
C
A
d
2
x
-
k
C
A
=0
.
with the following boundary conditions:
at
x=0
,
C
A
=
C
AS
,
at
x=L
,
d
C
A
dx
=0
,
Here
L
is the pore length and
C
AS
is the surface concentration of species
A
. The second boundary condition specifies that there is no flux of material through the interior end of the cylindrical catalyst pores. The concentration of reactant within a pore is given by
C
A
C
AS
=
cosh(mL(1-x/L))
cosh(mL)
, where
mL
is the Thiele modulus and
m=
k
.
This Demonstration plots the dimensionless concentration versus the dimensionless distance within the pores for user-set values of the Thiele modulus. It also gives the value of the effectiveness factor
E=
tanh(mL)
mL
=
-
C
A
C
AS
, where
-
C
A
is the average concentration of species
A
in the catalyst pores.
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