Question

It is desired to reduce the bacterial count of polluted water from 30 million organisms per ml to 5 organisms per ml. Calculate the number of completely mixed chlorine contact chambers in series, each having a detention time of 120 min, that would be required if the first order removal rate is 2.6 / hr ? Answer: 9 chambers

Answer 1

for CSTR and for first ordee reaction

(CO-C1)/ KC1= T, T =detention time ( for 1st reactor)

CO/C1= 1+KT (1)

for 2nd reactor C1/C2= 1+KT (2) ( since they are equal sized and T is same)

C2/C3= (1+ KT) (3) so on and so forth and for N the reactor CN-1/CN= (1+KT) (9)

multiplying all the above equations give

C0/CN= (1+KT)^N

where cN= 5 mg/L =concentration in the Nth reactor

Co = Initial concentration = 30*106 mg/L

CO/CN= 30*10⁶/5= 6*10⁶

K= 2.6/hr= 2.6/60 min

KT= 120*2.6/60= 5.2

6*10⁶= (1+5.2)^N

taking log

log (6*10⁶)= N* log (6.2)

6.78= N*0.79

N= 8.55 = 9 reactors