The kill of pathogens by disinfection in water treatment can be described by a f

Question

The kill of pathogens by disinfection in water treatment can be described by a first order reaction. Complete a reactor comparison for a batch reactor, CSTR and PFR for disinfection. The treatment plant produces 100 L/s of water. The starting concentration of pathogens is 20,000 organisms/L and the desired final concentration is 5 organisms/L. The reaction rate constant is 0.05 per second.

a)   Determine the volume of reactor needed for each hydraulic regime.

b)   From the volume, calculate a possible L x W x H for each tank. Are the tanks sizes reasonable?

c)   Which design would you choose and why? (For the batch system, assume one batch reactor is filling while the other is reacting).

Explanation / Answer

Final concentration = Initial Concentration * exponential^(-rate constant * time)

thus,

5 = 20000 * e^(-0.05*time)

e^(0.05*time) = 20000/5 = 4000

Taking logarithm to the base e on both sides of the equation,

0.05 * time = ln(4000) = 8.294

time = 8.294/0.05 = 165.881 seconds = 166 seconds approximately

Minimum volume of reactor required = 166 * 100 litres = 16600 Litres = 16.6 cubic metres.

For the batch reactor, one gets filled when the other reacts. Thus, we need two such reactors.

Hence, the total volume of the reactor = 16.6*2 = 33.2 cubic metres = 33200 litres.

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