Water containing a hazardous chemical is being treated in a completely mixed flo

Question

Water containing a hazardous chemical is being treated in a completely mixed flow reactor (CMFR). The volume of the reactor is V, we are treating a volumetric flow rate Q, and the system operates at steady state. The hazardous chemical is converted to a harmless by-product in a chemical reaction that obeys first order kinetics.

Unfortunately, the process isn't working well, and we are only removing 40% of the hazardous chemical, 60% makes it through the reactor and comes out in the effluent stream. We want to adjust the detention time in the reactor to improve the process. Suppose we want at least 80% conversion of hazardous chemicals.

Should we increase or decrease the HRT? by how much?

Explanation / Answer

First order Kinetic equation

[At]= [A0]e^(-kt) where [At] denotes concentration of hazardous chemical at some time t and [A0] denotes initial concentration.

Thus let t1 be time for 40% removal

0.4= e^-kt1 thus t1= 0.916/k ......(a)

Let t2 be time for 80% conversion

0.2= e^-kt2 thus t2= 1.609/k ........(b)

From equations a and b

t2= 1.756 t1

Thus we need to increase HRT or hydraulic retention time so that 80% removal of hazardous chemical is possible

Percentage increase in HRT from earlier time t1 is given as =( t2-t1)*100/t1= 75.6%

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