Question

The gas-phase reaction, A + 0.5 B -> 3P occurs in a packed bed reactor. The rate law is –rA = kCA^2CB where k = 40 L^3/(g-min-mol^2). The superficial gas velocity (‘G’) is 1.8 kg/m^2-s with a density of 1.26 kg/m^3 and a viscosity of 2.2x10-5 kg/m-s. The porosity, catalyst density, and particle diameter are, respectively, 0.45, 2.3 g/cm^3, and 4 mm. The cross sectional area of the reactor is 60 cm^2. The inlet pressure and temperature are, respectively, 200 kPa and 400K. The feed composition consists fo 80 mole % of A and 20 mole% of B. Calculate the conversion (X) of component A when the catalyst weight in the reactor is 30 kg. Assume that the system operates isothermally.

Note that this problem requires a solver (Matlab, Polymath, etc). You will need multiple equations - one is your regular PBR design equation, the other is the Ergun equation.

Answer 1

Given Data: ra = KCa^2* Cb k =40 unit

G= 1.8unit , density = 1.26 unit

viscosity= 2.2 * 10^(-5) porosity =0.45

solution : By using PBR equation

1.    t/ca0 =  
   dra/(-ra)
   

put all the data in this eqaution and integrate from 0 to xa then you will get xa =0.86 conversion