Exercise 7.4: Thiele modulus and a second-order reaction The following second-or

Question

Exercise 7.4: Thiele modulus and a second-order reaction The following second-order catalytic reaction is currently carried out in a fixed-bed reactor operating isothermally at 650 K. cm3 mol s 'B k=4.54 × 107 A Pure A is fed to the reactor and a conversion of 93% is achieved at a pressure of 2.0 The catalyst vendor has changed fabrication procedures and has verified that the trinsic rate constant listed above is unchanged. Using the following data, determine if the mass of catalyst needs to be changed for production rate of B. The pressure drop in the tube is negligible for both catalysts at m. the new catalyst to maintain the same New catalyst 0.0072 cm2/s 1.79 g/cm3 0.96 g/cm3 Old catalyst Property effective diffusivity 0.0095 cm/s particle density 1.75 g/cm3 bed density shape 0.84 g/cm3 sphere (0.635 cm diam) cylinder (0.48 cm diam, 0.79 cm length)

Explanation / Answer

Effective Diameter of cylinder pellet = 6*volume/area =6*3.14/4*.48^2*.79/(2*3.14/2*.48*.79) =0.72

R, Reaction Rate proportional to (1/(Diameter*Diffusivity)

=>Rsphere/Rcylinder = (.72*.0072)/(.63*.0095) =0.86

=>Rcylinder*.86= Rsphere

Therefore, Mass of cylindrical catalyst need to reduce to maintain same reaction rate.

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