Additional Problems Effects of Transport Limitations on Rates of Solid Catalyzed Reactions

King Saud University College of Engineering Chemical Engineering Department

ChE 426: Heterogeneous Reaction Engineering

     :

Additional Problems

Summer 1430/1431 (2010)

Prof. Ibrahim S. Al-Mutaz

Effects of Transport Limitations on Rates of Solid Catalyzed Reactions -1

1- A

-1

second-order, irreversible reaction with rate constant k = 1.8 L mol  s  takes place in a catalyst particle that can be considered to be a one-dimensional one-dimensional slab of half width = 1 cm. The concentration of -1 -1 reactant in the gas phase is 0.1 mol L  and at the surface is 0.098 mol L . The gas-phase gas-phase mass-transfer -1 coefficient is 2 cm s . Determine the intra-phase effectiveness factor. ----------------------------------------------------------------------------------------2- The

irreversible, first-order reaction of gaseous A → B occurs in spherical catalyst pellets with a -1 2 -1 radius of 2 mm. The molecular diffusivity of A is 1.2 x 10  cm  s  and the Knudsen diffusivity is 9 x -3 2 -1 10 cm s . The intrinsic first-order rate constant determined from detailed laboratory measurements -1 -1 was found to be 5.0 s . The concentration concentration of A in the surrounding surrounding gas gas is 0.01 mol L . Assume the porosity and the tortuosity of the pellets are 0.5 and 4, respectively. (a) Determine the Thiele modulus for the catalyst pellets. (b) Find a value for the internal effectiveness factor. -1 (c) For an external mass-transfer coefficient of 32 s  (based on the external area of the pellets), determine the concentration of A at the surface of the catalyst pellets. (d) Find a value for the overall effectiveness factor. ----------------------------------------------------------------------------------------3- The

importance of diffusion in catalyst pellets can often be determined by measuring the effect of pellet size on the observed reaction rate. Consider an irreversible first-order reaction occurring in catalyst pellets where the surface concentration concentration of reactant A is C AS = 0.15 M. Data: Diameter of sphere (cm) 3

robs(mol/h/cm )

0.20

0.06

0.02

0.006

0.25

0.80

1.80

2.500

(a) Calculate the intrinsic rate constant and the effective diffusivity. (b) Estimate the effectiveness factor and the anticipated rate of reaction (r obs) for a finite cylindrical cylindrical catalyst catalyst pellet of dimensions 0.6 cm x 0.6 cm (diameter = length). ----------------------------------------------------------------------------------------4- A

first-order irreversible i rreversible reaction is carried out on a catalyst of characteristic dimension 0.2 cm and 2 effective diffusivity of 0.015 cm  /s. At 100°C the intrinsic i ntrinsic rate constant has been measured to be 0.93 -1 s  with activation energy of 20 kcal/mol. -2

(a) For a surface concentration of 3.25 x 10  mol/L, what is the observed rate of reaction at 100°C? (b) For the same reactant concentration, what is the observed rate of reaction at 150°C? Assume that the effective diffusivity is independent of temperature. (c) What value of the activation energy would be observed? (d) Compare values of the Thiele modulus at 100°C and 150°C.