# NEWTON RAPHSON SOLUTIONS OF BIOCHEMICAL OXYGEN DEMAND (BOD) KINETICS

## Main Article Content

## Abstract

As follow up on our previous studies,** t**his paper evaluated Newton-Raphson method (NRM) solutions of Biochemical Oxygen Demand (BOD) kinetics with the aim of ascertain error free solutions. Non-linear regression, logarithms difference, NRM, least square, daily difference, Thomas, two points, ratio and Fujimoto methods were used to determine constants in BOD kinetics. Microsoft Excel Solver was applied to all the methods. Accuracies of all the methods were evaluated using relative error, Coefficient of Determination (CD), reliability and Model of Selection Criterion (MSC). The study revealed that the values of ultimate BOD and BOD removal rate were in the range of 859 to 1911 mg/l and - 0.140/d to - 0.449 /d respectively. Average total error for the methods were 23.85, 25.7, 74.72, 88.68, 1066.5, 1016.33, 149.12, 78.1 and (61.45 and 59.10) for non-liner regression, logarithms difference, least squares, Thomas, Fujimoto, Ratio, two points, daily difference and NRM ( matrix and graphical).

Accuracy, validity and good fitness of these methods were in order of non-linear regression (8.16) > Logarithm difference (7.72) > NRM (6.26) > least square (6.03) >daily difference (5.42)> Thomas (5.04)> two points (4.14) > ratio (0.63) and Fujimoto (0.51) on basis of their average MSC values. It was concluded that NRM could be used for BOD kinetics. NRM is among the best options because of their simplicity and flexibility as graphical and numerical solutions.

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