The irreversible reactionis taking place in the porous catalyst disk shown in Figure P12-9...

The irreversible reaction

is taking place in the porous catalyst disk shown in Figure P12-9A. The reaction is zero order in A.

(a) Show that the concentration profile using the symmetry B.C. is

where

(b) For a Thiele modulus of 1.0, at what point in the disk is the concentration zero? For ϕ0 = 4?

(c) What is the concentration you calculate at z = 0.1 L and ϕ0= 10 using Equation (P12-10.1)? What do you conclude about using this equation?

(d) Plot the dimensionless concentration profile Ψ = CA/CAs as a function of λ = z/L for ϕ = 0.5, 1, 5, and 10. Hint: there are regions where the concentration is zero. Show thatλc = 1 - l/ϕ0 is the start of this region where the gradient and concentration are both zero. [L. K. Jang, R. L York, J. Chin, and L. R. Hile, Inst. Chem. Engr., 34, 319 (2003).] Show that Ψ=  λ2 - 2ϕ0(ϕ0 - 1) λ + (ϕ0 - 1)2 forλc ≤ λ<1.

(e) The effectiveness factor can be written as

where zc (λc) is the point where both the concentration gradients and flux go to zero and Ac is the cross-sectional area of the disk. Show for a zero-order reaction that

(f) Make a sketch for η versus ϕ0 similar to the one shown in Figure 12–5.

(g) Repeat parts (a) to (f) for a spherical catalyst pellet.

(h) What do you believe to be the point of this problem?