Surface Kinetics with Pore Diffusion Resistance
Surface Kinetics with Pore Diffusion Resistance
Consider a first order reaction taking place on the surface of a catalyst with cylindrical pores. The relevant equation is
A→B
2
d
C
A
d
2
x
k
C
A
with the following boundary conditions:
at , =,
x=0
C
A
C
AS
at , =0,
x=L
d
C
A
dx
Here is the pore length and is the surface concentration of species . 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 =, where is the Thiele modulus and .
L
C
AS
A
C
A
C
AS
cosh(mL(1-x/L))
cosh(mL)
mL
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 , where is the average concentration of species in the catalyst pores.
E==
tanh(mL)
mL
-
C
A
C
AS
-
C
A
A