A completely mixed reactor (CSTR or CMRF) is to be used to treat an industrial w

Question

A completely mixed reactor (CSTR or CMRF) is to be used to treat an industrial wastewater.

A tracer study is conducted to determine the true hydraulic residence time of the reactor. A slug of tracer (NaBr) is added to the reactor and allowed to wash out over time. The flow to the reactor is 10,000 L/d and the reactor volume is 40,000 L. The tracer data are given below. Using our mass-balance approach, determine the true hydraulic residence time of the reactor.

If the pollutant to be removed has a concentration of 100 mg/L and decays by 1st-order kinetics with a rate coefficient (k1 value) of 2.25 d-1, what percent removal is achieved if one uses the theoretical hydraulic retention time of the reactor?

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What percent removal is achieved using the true hydraulic residence time determined in part (a) of this problem?

Time (day) Tracer Concentration (mg/L)

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50 1 30 2 18 3 11 4 6.8 5 4.1 6 2.5 7 1.5 8 0.9 9 0.6 10 0.3

Explanation / Answer

Hydraulic residence time

Using the equation,

ln (Ct/Co) = -t/HRT ans =

where Ct = concentation at time t, Co= initial concentration, t = time and HRT = hydraulic residence time

using Ct = 30mg/L, t = 1 day (you can use any set) and Co = 50mg/L

ln (30/50) = -1/HRT

HRT = 1.955 days

% removal

We know that HRT=V/Q

HRT= 40,000L/10,000 L/d = 4 days

Also, Ct/Co = 1/(1+kHRT)= 1 + (1+ 2.25 x4) = 1/10 = 0 .10

removal = 1- 0.10= 0.9 which means 90%

% removal for (a)

HRT = 1.955 days

Now, Ct/Co = 1/(1+kHRT)= 1 + (1+ 2.25 x1.95) = 1/5.39875 = 0 .185

removal = 1- 0.185 =81.48 which means 81.48%

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