Question

The following reaction of great industrial importance A rightarrow B is to be carried out under the following reaction conditions: T = 25 degree C, C_A0 = 0.15mol/lt and volumetric flow rate 0.5lt/min. The reaction is first order with respect to A and the rate constant, k = 0.158min^-1. The process engineer suggests the following plausible reactor configurations. Using the concept of Damkohler number, find which of these configurations will give the maximum conversion?

Answer 1

Damkohler number can be defined in number of ways.

For a general chemical reaction A → B of nth order, the Damköhler number for a convective flow system is defined as:

{\displaystyle \mathrm {Da} =kC_{0}^{\ n-1}\tau }

Where

k = kinetic reaction rate constant

Co = Initial concentration

n = reaction order

= Mean residence time or space time

Given data:

k = kinetic reaction rate constant = 0.158 min-1

Co = Initial concentration = 0.15 mol/lt

n = reaction order = 1

vo = Volumetric flow rate = 0.5 lt/min

For a first reaction, Damkohler number is given as

Calculation of Conversion

a)

= Mean residence time or space time = V/vo=5/0.5 = 10 min

Damkohler number