Chapter 14: External Diffusion Effects on Heteregeneous Reactions
Self Test: What 4 things are wrong with this solution?
Problem
The isomeriation A -> B follows an elementary rate law and is carried out in a packed bed reactor where 63.2% conversion is achieved. What would be the conversion if the particle size were doubled and the entering pressure is doubled, but there is no pressure drop?
Solution
\( X = 1 - e^{\frac{k_c a_c W}{v_o}} \)
For Case 1 and Case 2:
\( \ln \left( \frac{1 - X_1}{1 - X_2} \right) = \frac{k_c a_c|_h}{k_c a_c|_l} \)
\( k_c \approx \frac{1}{d_\rho}, \quad a_c \approx \frac{1}{d_\rho^{3/n}} \)
\( k_c \approx P, \quad a_c \ne f(P) \)
\( \frac{k_c a_c|_h}{k_c a_c|_l} = \frac{P_1}{P_2} \left( \frac{d_2}{d_1} \right)^{1/n} = (2)(2)^{1/2} = 2.82 \)
\( \ln \left( \frac{1 - 0.63}{1 - X_2} \right) = 2.82 \)
\( \boxed{X_2 = 0.55} \)
Answer
You'll have to figure this one out on your own!