Consider one of the cylindrical channels of inner diameter d that run through an isomerization catalyst, as shown in the figure below. A catalyst coats the inner walls of each channel. This catalyst promotes the isomerization of n-butane (n-C₄H₁₀, species A) to isobutene (n-C₄H₁₀, species B):

n €“ C₄H₁₀ (g) †’ i €“ C₄H₁₀ (g)

The gas phase above the channels contains mixture of A and B maintained at a constant composition of 60 mol% A and 40 mol% B. Gas-phase species A diffuses down a straight channel of diameter d = 0.10 cm and length L = 2.0cm. The base of each channel is sealed. The surface reaction is rapid reaction so that the production rate of B is diffusion limited. The quiescent gas space in the channel consists of only species A and B.

a. State three relevant assumptions for the mass-transfer process. Based on your assumptions, simplify the general differential equation for the mass transfer of species A, leaving the differential equation in terms of the flux N_A.

b. Simplify Fick€™s flux equation for each coordinate of interest, and then express the simplified form of general differential equation from part (a) above in terms of the gas-phase concentration c_A.

c. Specify relevant boundary conditions for the gas-phase concentration c_A.

Transcribed Image Text:

Bulk gas phase -z=L=2.0 cm 0.01-cm-diameter (d) channels Catalytic surface A (g) – B (g) Inert support