Chapter 17: Distributions of Residence Times for Chemical Reactors

Example: Calculate X_mm and X_seg

Calculate the conversion in a real reactor using the segregation and the maximum mixedness model.  The reaction A -> B is carried out in a real reactor that has the following F-curve. The entering concentration of A is 8 mol/dm³. The following F(t) was determined from a trace test

 

For 10<t<20

For 20<t<30

The reaction rate also varies with time as per below equation

For 10<t<20 -r_A = k * C_A^0.6

For 20<t<30 -r_A = k * C_A^2.7

Where, k=0.1

Calculate the conversion using

1)   the segregation model

2)   the maximum mixedness model

Also explain the difference in conversions between the two models.

 

Solution

1)   X _seg = 0.796 [Polymath code]

2)   X _mm = 0.796 [Polymath code]

 

Both models predict the same conversion!

The reason is: for reaction order 0 < n < 1, max mixedness predicts higher conversion and for n > 1, segregation predicts higher “X”. In this case, the reaction goes from 0.6 to 2.7 as C_A decreases. Thus, the predictions of the two models average out.

 

 

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