Question

Waste water treatment plant. A municipal water treatment plant for a small community. Waste water 32,000 m3/day, flows through the treatment plant with a mean residence time of 8 hr, air is bubbled through the tanks and microbes break down the organic materials. An entering feed has a BOD of 200 mg O2/liter and the effluent has a negligible BOD. Find the rate of reaction in the treatment tanks.

Answer 1

The reaction rate k is 0.0012563 (1/hour).

Step-by-step explanation:

We considered the reactions occurring in the plant as first order, and represented by this equation:

`y = L (1- e^(-kt))`

where y is the BOD at time t, L is the initial value of BOD and k is the reaction rate.

If we replaced with the values

y = 2 mg O2/l (1% of the initial value)

L = 200 mg 02/l

t = 8 hr

We can calculate k

`y=L(1-e^(-kt))\\\\k=-(1/t)*ln(1-y/L) = -(1/8)*ln(1-2/200)=-(1/8)*(-0.01)=0.0012563 \, hour^(-1)`

The reaction rate k is 0.0012563 1/hour.