You are designing a reactor that uses chlorine in a PFR or CMFR to destroy patho

Question

You are designing a reactor that uses chlorine in a PFR or CMFR to destroy pathogens in water. A minimum contact time of 30 min is required to reduce the pathogen concentration from 100 pathogens/L to below 1 pathogen/L through a first – order decay process. You plan on treating water at a rate of 1,500 gal/min.

(a) What is the first – order decay rate constant?

(b) What is the minimum size (in gallons) of the reactor required for a PFR?

(c) What size (in gallons) of CMFR would be required to reach the same outlet concentration?

(d) Which type of reactor would you select if your treatment objective stated that “no discharge can ever be greater than 1 pathogen/L”? Explain your reasoning.

(e) If the desired chlorine residual in the treated water after it leaves the reactor is 0.20 mg/L and the chlorine demand used during treatment is 0.15 mg/L, what must be the daily mass of chlorine added to the reactor (in grams)?

Explanation / Answer

Given T= 30 min =V/Vo. For a given reactor size, T will be minimum when the volumetric flow rate is maximum. This is possible in PFR.

Hence for a PFR for a 1st order system, KT= -ln(1-XA)

Where K= rate constant and T=30min, XA =conversion = 1-CA/CAO =1-1/100 =1-0.01=0.99, -ln(1-0.99)= 30*K, K= 0.000335/min

b) for a PFR, T= V/Vo= -ln(1-XA)/K

given T= 30 min and Vo= 1500gal/min

30 = V/1500 , V= 1500*30 =45000 Gallons

c) for a CMFR, KT= XA/(1-XA)= 0.99/(1-0.99)= 99

K =0.000335, T= 99/0.000335 min=295522 min

For T= V/Vo, V= Vo*T= 1500*295522 Gal=4.43*108 gallons

d) The data suggests the requirement of PFR compared to CMFR since the volume of PFR is less than CMFR for achieving the same conversion,

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