Chapter 15, Problem 15.2Q

Suppose someone had used the false kinetics (i.e., wrong E, wrong n)? Would the catalyst weight be overdesigned or underdesigned? What are other positive or negative effects that occur?

Interpretation Introduction

Interpretation:

Whether the catalyst weight be overdesigned or underdesigned if false kinetics is used or not is to be stated. The other positive and negative effects of false kinetics are to be stated.

Concept introduction:

The effectiveness factor is the division of the average rate of the reaction with rate of reaction at the bulk-stream point that is at boundary conditions or without diffusion. It is denoted by $\text{η}$. The overall effectiveness is denoted by $\Omega$.

Answer to Problem 15.2Q

The catalyst weight will be overdesigned if false kinetics is used. The other positive and negative effects of false kinetics have been stated below.

Explanation of Solution

If kinetics like activation energy, number of moles is taken wrong then it is known as false kinetics. In case of decreased particle size, the activation energy and temperature of the reaction becomes higher. Due to this reason reaction becomes much more temperature sensitive. This causes the runaway reaction due to which explosion occurs.

These are effects of applying the false kinetics.

The weight of the catalyst is inversely proportional to the overall effectiveness and the rate constant according to the equation given below.

    $W=\frac{v_0}{\Omega k_1^{\text{'}}}\ln \frac{1}{1-X}$

Where,

$\Omega$ is the overall effectiveness.

$W$ is the weight of the catalyst.

$k_1^{\text{'}}$ is the rate constant.

$v_0$ is the volumetric flow rate.

$X$ is the conversion.

If the false kinetics is applied then the overall effectiveness becomes lower due to which rate of the reaction becomes higher which corresponds to the overdesigned catalyst weight.

Conclusion

The catalyst weight will be overdesigned if false kinetics is used. The other positive and negative effects of false kinetics have been stated above.