Workshop 09: External and internal diffusion effects

Lecture notes for chemical reaction engineering

Solutions

Solutions to these problems are uploaded at Workshop 9 solutions

P 14-9

The irreversible gas-phase reaction

$\ce{ A ->[ cat ] B}$

is carried out adiabatically over a packed bed of solid catalyst particles. The reaction is first order in the concentration of A on the catalyst surface

$$-r_{As}' = k' C_{As}$$

The feed consists of 50% (mole) A and 50% inerts, and enters the bed at a temperature of 300 K. The entering volumetric flow rate is 10 dm³/s (i.e., 10,000 cm³/s). The relationship between the Sherwood number and the Reynolds number is

$$Sh = 100 Re^{1/2}$$

As a first approximation, one may neglect pressure drop. The entering concentration of A is 1.0 M. Calculate the catalyst weight necessary to achieve 60% conversion of A for

1. isothermal operation.

2. adiabatic operation.

Additional information:

• Kinematic viscosity: $\mu/\rho = 0.02 cm^2/s$
• Particle diameter: $d_p = 0.1 cm$
• Superficial velocity: $U =10 cm/s$
• Catalyst surface area/mass of catalyst bed: $a= 60 cm^2/g-cat$
• Diffusivity of A: $D_e = 10^{-2} cm^2/s$
• Heat of reaction: $\Delta H_{Rx}^{\circ} = 10,000 cal/g mol A$
• Heat capacities: $C_{pA} = C_{pB} = 25 cal/g mol \cdot K, C_{pS}\, \text{(solvent)} = 75 cal/g mol \cdot K$
• $k' (300 K) = 0.01 cm^3 /s \cdot g-cat \; \text{with}\; E = 4000 cal/mol$