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5 | TRANSPORT AND ADSORPTION
Equation 2 defines the units of the rate constants k
ads
and k
des
. The initial condition is
that the concentration of adsorbed species is zero at the beginning of the process:
The equation for the surface-reaction expression includes the concentration of the bulk
species, c, at the position of the catalyst surface. Thus you must solve the equation for the
surface reaction in combination with the mass balance in the bulk. The coupling between
the mass balance in the bulk and the surface is obtained as a boundary condition in the
bulk’s mass balance. This condition sets the flux of c at the boundary equal to the rate of
the surface reaction and is presented below. The transport in the bulk of the reactor is
described by a convection-diffusion equation:
(3)
The initial condition sets the concentration in the bulk at t = 0:
In the above equation, D denotes the diffusivity of the reacting species, c is its
concentration, and u is the velocity. In this case, the velocity in the x direction equals 0
while the velocity in the y direction comes from the analytical expression for fully
developed laminar flow between two parallel plates:
Here, δ is the distance between the plates, v
max
is the maximum local velocity, and x = 0
at the left boundary of the 2D model geometry shown on the right in Figure 1.
BOUNDARY CONDITIONS
The boundary conditions for the surface species are insulating conditions according to:
(4)
For the bulk, the boundary condition at the active surface couples the rate of the reaction
at the surface with the flux of the reacting species and the concentration of the adsorbed
species and bulk species:
(5)
c∂
t∂
-----
∇+ Dc cu+∇–()⋅ 0=
u 0 v
max
1
x 0.5δ–()
0.5δ
-------------------------
2
–(, )=
n Dc cu+∇–()⋅ k–
ads
c Γ
s
c
s
–()k
des
c
s
+=