First and second stage BOD

First-stage BOD (carbonaceous)

In the first stage, bacteria oxidise the carbonaceous organic matter into CO₂ and water. It is practically complete in about 20 days at 20°C (with $k=0.1$ day⁻¹, about 68% in 5 days and 99% in 20 days). The first stage is called carbonaceous BOD (CBOD).

Second-stage BOD (nitrogenous)

After about 8-10 days, nitrifying bacteria (Nitrosomonas, Nitrobacter) oxidise ammonia to nitrite and then to nitrate, using more oxygen:

$$NH_4^+\xrightarrow{\text{Nitrosomonas}}NO_2^-\xrightarrow{\text{Nitrobacter}}NO_3^-$$

This is the nitrogenous BOD (NBOD). Because the nitrifiers grow slowly, it does not appear in the standard 5 day test at 20°C.

 BOD exerted
   |                  ______ second stage
   |            _____/ (nitrification)
   |      _____/___ 
   |   __/ first stage ends (L)
   |  /
   | /
   +----+----+----+----+----> days
   0    5   10   15   20

The first-stage curve is $y_t=L(1-10^{-kt})$. The second-stage curve starts at about the 8th-10th day and rises above it.

Ultimate BOD calculation

The rate constant is not given, so the standard value $K_{20}=0.1$ day⁻¹ (base 10) is assumed.

$$L=\frac{y_5}{1-10^{-kt}}=\frac{400}{1-10^{-0.1\times5}}=\frac{400}{1-0.3162}=585.0\ \text{mg/L}$$

Answer: Ultimate first-stage BOD = 585.0 mg/L (with $K=0.1$/day base 10; with the equivalent $K=0.23$/day base $e$ the result is nearly the same, 585.3 mg/L).