Question 1. The first order irreversible gas phase reaction Normal Pentane-> Iso-pentane is to be carried out in a packed bed reactor. Currently 1,000 kg of reforming catalyst are packed in a 4 cm diameter pipe. The catalyst particles are 0.5 cm in diameter and the bulk density of the packed catalyst is 1,000 kg/m3. Currently 14.1% conversion is realized. The entering pressure is 20 atm and the pressure at the exit of the reactor is 9.0 atmospheres. It is believes that this reaction is internal diffusion limited. For internal diffusion limitations, the rate of reaction varies inversely with the catalyst particle size. Consequently, one of the engineers suggests that the catalyst be ground up into a smaller size. She also notes that the smallest size to which the catalyst may be ground is 0.01 cm. and that there are 3 other pipe sizes available into which the catalyst could be packed. These non-corrosive heat-resistant pipes, which can be cut to any length, are 2 cm, 3 cm, and 6 cm in diameter.
a. What conversion could be achieved in a CSTR with the same catalyst weight and no pressure drop?
b. Calculate the maximum value of the pressure drop parameter alpha that you can have and still maintain an exit pressure of 1 atm.
c. Should you change the catalyst size and pipe diameter in which 1,000 kg of the catalyst is packed while maintaining the catalyst weight?
d. Next consider how alpha would change if you changed both pipe size and particle size. Can you change pipe size and particle size at the same time such that alpha remains constant at the value calculated in part b?
Question 2. The gas-phase reaction A + 2B -> 2D is to be carried out in an isothermal plug-now reactor at 5.0 atm. The mole fractions of the feed streams are A = 0.20, B = 0.50, and inerts = 0.30.
a. What is the steady-state volumetric flow rate at any point in the reactor if the pressure drop due to fluid friction can be ignored?
b. What are the expressions for the concentrations of A, B, and D as a function of conversion at any point along the reactor?
c. What is the feed concentration (units: mol/ dm3) of A if the feed temperature is 55°C?
d. Determine how large the plug-flow reactor must be to achieve a conversion (based on A) of 0.70 if the temperature in the reactor is uniform (55°C), the volumetric feed rate is 50 dm3//min, and the rate law at 55°C is -r = 2.5 C A(1/2)C B kmol/m3 min
e. Plot the concentrations, volumetric flow rate, and conversion as a function of reactor length. The reactor diameter is 7.6 cm.
f. How large would a CSTR have to be to take the effluent from the PF reactor in part (d) and achieve a conversion of 0.85 (based on the feed of A to the plug-flow reactor) if the temperature of the CSTR is 55°C?
g. How many 1-in.-diameter pipe tubes, 20 ft in length, packed with a catalyst, are necessary to achieve 95% conversion of A starting with the original stream? Plot the pressure and conversion as a function of reactor length. The particles are 0.5 mm in diameter and the bed porosity is 45%.
h. Calculate the PFR size to achieve 70% of the equilibrium conversion and the CSTR size necessary to raise the conversion of the PFR effluent to 85% of the equilibrium conversion if their temperatures were uniform at 100°C.
The activation energy for the reaction is 30 kJ/mol, and the reaction is reversible with an equilibrium constant at 100°C of 10 (m3 /kmol) 1/2.