A “superficially porous” catalyst particle, sketched in Fig. P.11.12, consists of a solid spherical catalytic core surrounded by a spherical macroporous shell. The reaction 2 C₂H₄ → C₄H₈ occurs only on the surface catalytic core. The particle is placed in a rapidly flowing stream of pure C₂H₄ gas, which diffuses in the porous shell and reacts instantly as soon as it reaches the catalytic core. The absolute pressure is 2 atm, and the temperature is 400 K. The shell porosity is 0.5, and the tortuosity factor is 4. The system is isothermal. Assuming that the reaction is irreversible and that the overall process is diffusion-controlled:

(a) Write an equation to describe the steady-state flux of C₂H₄ in the shell for these conditions. (b)

Write a steady-state differential material balance for C₂H₄ along with boundary conditions needed to describe diffusional mass transfer in the shell.

(c) Integrate your material balance in part

(b) to determine the rate of mass transfer of C₂H₄.

(d) Calculate the rate of C₄H₈ production in mole/s.

FIGURE P.11.12:

Transcribed Image Text:

Macroporous shell, radius R = 1 cm Catalytic core, radius R=0.5 cm