A dispersed plug-flow reactor has an influent flow with a concentration of 150 m

Question

A dispersed plug-flow reactor has an influent flow with a concentration of 150 mg/L of A and a flow rate of 100 gal/min. The reaction is first-order: the rate expression is: and the rate constant is 0.40 hr-1. The axial or longitudinal dispersion number, D/v L, is 1.0. Determine the following: The required detention time and the required volume of the reactor if the conversion of A is 90%. Express the volume as gallons and liters. The required detention time and the required volume of the reactor if the conversion of A is 80%. Express the volume as gallons and liters.

Explanation / Answer

Flow rate = 100 gallon/min = 6000 gallon/hr = 22710 litres/hr.

For 1st order reactions the govrning equation is :-

k*t = ln(A0/A) ; where A0 = initial activity and A = activity after time 't' & t = detention time

a) k = 0.4 hr-1 ; A0 = 100 ; A = 10

Thus, 0.4*t = ln(100/10)

or, t = 5.756 hr.

Volume of the reactor required = flow rate*detention time = 6000*5.756 = 34536 gallons = 130718.76 litres

b) k = 0.4 hr-1 ; A0 = 100 ; A = 20

Thus, 0.4*t = ln(100/20)

or, t = 4.023 hr.

Volume of the reactor required = flow rate*detention time = 6000*4.023 = 24138 gallons = 91362.33 litres

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