CHEMICAL ENGINEERING

282 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The mass transfer coefficienthDis proportional to the velocity raised to the power of 0.6.
What is the value ofhDat the original velocity?

kD 1. 6 ð 10 ^3 s^1 ,DeD 10 ^8 m^2 /s

catalyst pellet thickness 2 L
D10 mm.

Solution

(i) The partial differential equation for unsteady-state diffusion accompanied by chem-

ical reaction is derived in Volume 1 as equation 10.170

(ii) The molecular diffusivityDmust be replaced by an effective diffusivityDebecause

of the complex internal structure of the catalyst particle which consists of a multi-

plicity of interconnected pores, and the molecules must take a tortuous path. The

effective distance the molecules must travel is consequently increases. Further-

more, because the pores are very small, their dimensions may be less than the

mean free path of the molecules and Knudsen diffusion effects may arise

(iii) Equation 10.170 is solved in Volume 1 to give equation 10.199 for a catalyst

particle in the form of a flat platelet

(iv) The effectiveness factor is the ratio of the actual rate of reaction to

that which would be achieved in the absence of a mass-transfer resistance. For a

platelet, it is evaluated in terms of the Thiele modulus as equation 10.202

(v) For the case, where there is an external mass transfer resistance, the reaction rate

is expressed in terms of the bulk concentration as equation 10.222:

RvD

kCAo

 1 /;

CkL/hD

ForkD 1. 6 ð 10 ^3 s^1 , DeD 10 ^8 m^2 /s, LD 5 ð 10 ^3 m:

DL

√

k

De

D 5 ð 10 ^3

√

1. 6 ð 10 ^3

10 ^3

D 2

;D

1

f

tanhfD

1

2

tanh 2D

0. 96

2

D 0. 48

∴

1

;kL

D

1

0. 48 ð 1. 6 ð 10 ^3 ð 5 ð 10 ^3

D

1

3. 84 ð 10 ^6

D 0. 260 ð 106.

If the original value of mass transfer coefficient ishD, the new value at twice original
velocityDhD 2
0.^6 D 1. 516 hD. Given that the overall rate is increased by a factor of 1.2:





1

0. 260 ð 106 C

1

1. 516 hD









/









1

0. 260 ð 106 C

1

hD







D^1.^2

(

0. 260 ð 106 C

1

hD

)

(

0. 260 ð 106 C 0. 66

1

hD

)D 1. 2