Multi-Criteria Assessment of Biochemical Oxygen Demand Kinetic Parameter Estimation: Evidence from Seven Wastewater Assays

Abstract

Biochemical oxygen demand (BOD) kinetics are widely used to describe oxygen consumption during biodegradation of wastewater organic matter and to support wastewater-treatment and receiving-water assessments. This study presents a seven wastewater BOD assays and comparing least-squares, Thomas and nonlinear regression approaches using kinetic parameters and three goodness-of-fit measures: sum of squared errors (SS), coefficient of determination (CD), and model selection criterion (MSC). The waste water came from food-processing effluents with BOD₅ values of 629–938 mg L⁻¹. Across the seven curves, nonlinear regression produced the lowest mean SS (2,423.0), compared with 4,131.1 for least squares and 4,847.2 for Thomas; the highest mean CD (0.99708); and the highest mean MSC (5.411). A Friedman test applied to the paired method comparisons indicated a significant overall difference among methods (χ² = 10.571, p = 0.005), with Kendall’s W = 0.755, indicating a large method effect. Exact paired post-hoc Wilcoxon tests showed that nonlinear regression outperformed both least-squares and Thomas methods for all three criteria. The analysis supports nonlinear estimation as the most consistently accurate of the three approaches, while also demonstrating that reliance on a single goodness-of-fit statistic can obscure method differences.