A sewage lagoon that has a surface area of 100,000 m2 (10 ha) and a depth of 1 m is receiving 8,640 m3/d of sewage containing 100 mg/L of biodegradable contaminant. At steady state, the effluent from the lagoon must not exceed 20 mg/L of biodegradable contaminant. Assuming the lagoon is well mixed and that there are no losses or gains of water in the lagoon other than the sewage input, what biodegradation reaction rate coefficient (d-1) must be achieved?

The biodegradation reaction rate coefficient that must be achieved for the required concentration of exit stream = 0.003456 / day

Explanation:

The lagoon can be treated as a continuously stirred tank reactor.

Let C₀ represent the initial concentration of the biodegradable organic material = 100 g/L = 100 g/m³

Let C be the concentration of biodegradable organic material that leaves the lagoon (reactor) = 20 mg/L = 20 g/m³

Let the rate constant be k

Let V be the volume of the lagoon = 10 hectares * 1 m = 100000 * 1 = 100000 m³

Let F₀ be the flowrate of influent into the first lagoon = 8640 m³/day

The performance equation for a CSTR with a first order reaction going on for the lagoon reactor

(kC₀V/F₀) = (C₀ - C) / C

(k*100*100000/8640) = (100-20) / 20

k = (4*8640) / (100*100000) = 0.003456 / day