### 1. Introduction

##### (1)

$$D={D}_{0}\hspace{0.17em}{e}^{-{k}_{a}t}+\frac{{k}_{d}{L}_{0}}{{k}_{a}-{k}_{d}}({e}^{-{k}_{d}t}-{e}^{-{k}_{a}t})$$##### (2)

$$D={D}_{0}{e}^{-{k}_{a}t}+\frac{{k}_{d}{L}_{0}}{{k}_{a}-{k}_{r}}({e}^{-{k}_{r}t}-{e}^{-{k}_{a}t})+\frac{{k}_{n}{L}_{n0}}{{k}_{a}-{k}_{n}}({e}^{-{k}_{n}t}-{e}^{-{k}_{a}t})$$*D*is the oxygen deficit after travel time ‘

*t*’;

*D*

*is the initial oxygen deficit;*

_{o}*k*

*is the reaeration rate coefficient;*

_{a}*t*is the travel time. For Eq. (1),

*k*

*is the BOD decay rate coefficient;*

_{d}*L*

*is the ultimate BOD in the river. For Eq. (2),*

_{o}*k*

*is the CBOD decay rate coefficient,*

_{d}*k*

*is the NBOD or AN decay rate coefficient,*

_{n}*k*

*is the CBOD removal rate coefficient,*

_{r}*L*

*is the ultimate CBOD in the river after mixing,*

_{o}*L*

*is the ultimate NBOD in the river after mixing.*

_{no}### 2. Materials and Methods

*C*is the concentration of pollutant after a time ‘

*t*’;

*C*

*is the initial concentration of pollutant;*

_{0}*t*is the time in days;

*k*is the decay rate in day

^{−1.}

*k*’ value was solved for minimum Root Mean Square Error (RMSE). The decay rates obtained from the curve fitting method were extrapolated to rates at 20°C by using Eq. (4).

*k*

*is the BOD or CBOD decay rate at 20°C;*

_{20}*θ*is the temperature correction factor;

*T*is temperature;

*k*is the BOD or CBOD decay rate at

*T*°C.

*θ*= 1.047 [21].

### 3. Results and Discussion

^{2}. In the case of BOD, minimum RMS error was found to be 0.08 mg/L for experiment 11, whereas initial concentration was 6 mg/L. Experiment 5 produced maximum RMS error, i.e. 12.6 mg/L, which also has the highest initial concentration, i.e. 266 mg/L. The final concentrations of experiment 11 and 5 are 4.6 mg/L and 206.4 mg/L, respectively. Therefore, maximum and minimum errors are insignificant compared to the initial and final concentrations of BOD. The RMS errors of the remaining experiments were also low compared to their corresponding initial and final concentrations except experiment 2. Initial and final BOD concentrations of experiment 2 were 76 mg/L and 24.7 mg/L, respectively, whereas the RMS error was 9.24 mg/L. Though, RMS error for experiment 2 is comparatively high in terms of corresponding initial and final concentrations, it is still within fair margin of acceptable limit. R

^{2}values ranged between 0.74 and 0.99 for BOD, which is satisfactory.

^{2}value was estimated to be more than 0.8 except experiment 11 implying strong agreement between observed and predicted data.

*k*

*) and BOD decay rate (*

_{CBOD}*k*

*) gives a linear relationship. R*

_{BOD}^{2}value for this plot was found to be 0.81.

### 4. Conclusions

*k*

*= 0.8642*

_{CBOD}*k*

*− 0.0349. Such relations will assist the water quality professionals to conduct additional analysis and verifications related to BOD decay rates.*

_{BOD}### Nomenclature

*C*_{0}

*C*

*D*_{o}

*D*

*k*_{a}

*k*_{CBOD}

*k*_{BOD}

*k*_{d}

*k*_{20}

*°*C

*L*_{o}

*L*_{no}

*k*_{n}

*k*_{r}

*t*

*T*

θ