The elementary gas-phase reactionA+B → C + Dis carried out in a packed-bed reactor. Curren...

The elementary gas-phase reaction

A+B → C + D

is carried out in a packed-bed reactor. Currently, catalyst particles 1 mm in diameter are packed into 4-in. schedule 40 pipe (Ac = 0.82126 dm2). The value of ρn in the pressure drop equation is 0.001 atm/dm. A stoichiometric mixture of A and B enters the reactor at a total molar flow rate of 10 mol/min, a temperature of 590 K, and a pressure of 20 atm. Flow is turbulent throughout the bed. Currently, only 12% conversion is achieved with 100 kg of catalyst.

It is suggested that conversion could be increased by changing the catalyst particle diameter. Use the following data to correlate the specific reaction rate as a function of particle diameter. Then use this correlation to determine the catalyst size that gives the highest conversion. As you will see in Chapter 12, k’ for a first-order reaction is expected to vary according to the following relationship

where Φvaries directly with particle diameter, Φ= cDp. Although the reaction is not first order, one notes from Figure 12–5 the functionality for a second- order reaction is similar to Equation (P4-20.1).

(a) Show that when the flow is turbulent

and that a0 = 0.8 x 10−4 atm/kg and also show that c = 75 min ‘.

(b) Plot the specific reaction rate k’ as a function of DP, and compare with Figure 12–5.

(c) Make a plot of conversion as a function of catalyst size.

(d) Discuss how your answer would change if you had used the effectiveness factor for a second-order reaction rather than a first-order reaction.

(e) How would your answer to (b) change if both the particle diameter and pipe diameter were increased by 50% when

(1) the flow is laminar.

(2) the flow is turbulent.

(f) Write a few sentences describing and explaining what would happen if the pressure drop parameter a is varied.

(g) What generalizations can you make about what you learned in this problem that would apply to other problems?

(h) Discuss what you learned from this problem and what you believe to be the point of the problem.

Additional information:

Void fraction = 0.35 Solid catalyst density = 2.35 kg/dm3

Bulk density: ρB = (1 - Φ> ρc = (0.35) (2.35) = 0.822 kg/dm3

[Hint: You could use Equation (P4.20-1), which would include DP and an unknown proportionality constant that you could evaluate from the data. For very small values of the Thiele modulus we know T) = 1, and for very large values of the Thiele modulus we know that η= 3/ Φ = 3/cDp]