In a fixed (packed) or fluidized bed reactor, a fluid containing one or more reactants flows by
catalyst pellets. The diffusion and reaction process within the reactor can be thought of as a
5-step process: (1) the reactants diffuse from the bulk fluid to the surface of pellets, (2) the
reactants diffuse into the pellets, (3) the reaction proceeds inside the catalyst, (4) the products
diffuse out of the pellets, and (5) the products diffuse from the pellets to bulk. Jim, a new
chemical engineer at San José Petroleum, has been hired to design a fluidized bed reactor that
will be used to facilitate the gas-phase reaction, A  2B. The reaction is highly exothermic,
only occurs within the catalyst, and is first order with a reaction rate constant of k”a. The
feed stream consists of 80% nitrogen and 20% A at 300K and 200kPa. You are tasked with
approving Jim’s designs. The following is a selection of excerpts from Jim’s notes detailing
how he is modeling the diffusion between the bulk and a catalyst pellet (the first and fifth
steps of the process). Indicate, explain, and if possible, fix any errors. Hint: There are 6
errors. (You will get 4 points for each error you fully explain and correct if possible.)

The catalysts can be approximated as spheres with radius R.
To calculate the molar flux of A from the bulk, I use Fick’s 1 st Law:
N Ar = −D AB
dc A
dr
I assume axisymmetry, so I only look at diffusion in the radial direction. (** Note to test-
taker: assume Jim is correct here **).
To find the concentration profile, I use the continuity equation,
d 2 c A
∇ ⋅ N A = −D AB
= −k"ac A
dr 2
I will treat the bulk as being infinitely far from a pellet, so the boundary conditions would be
200 × 10 3 Pa
c A (r → ∞) = 0.2 ⋅
≈ 16 mol/m 3
J
8.314
× 300K
mol K
dc A
(r = 0) = 0
dr