Question

What is the Damkohler number? b) What is the significance of a system with a low Damkohler number?

Answer 1

Explanation:

(a)  A number which is dimensionless and provides us an estimate of the degree of conversion which can be achieved in CSTR, that is, continuous stirred tank reactor is known as Damkohler number.

This number is denoted as Da.

Mathematically,     Da = $\frac{\text{reaction rate}}{\text{convection rate}}$

             Da = $\frac{-rA \times V}{Fa_{o}}$

Now, for first order system, Da = $\frac{-rA \times V}{Fa_{o}}$

                        = $\frac{k \times CA_{o} \times V}{v \times CA_{o}}$ = Tk

where,      rA = rate of reaction

                V = volume of reactor

                $Fa_{o}$ = molar flow rate of component A

                 k = rate constant

               $CA_{o}$ = initial concentration of A

                  v = volumetric flow rate of A

                  T = residence time

(b)   Since, from a given Damkohler number we can figure out the possible conversion of CSTR, that is, continuous stirred tank reactor.

So, if we have a low Damkohler number then the system will give us a less conversion formula. As the conversion is as follows.

                       X = $\frac{Da}{Da + 1}$

Hence, we can conclude that $Da \leq 0.1$ will give less than 10% conversion as calculated by using above formula.