Keywords: dimensionless analysis, cubic spline, least squares, Thomas, geometric–logarithm series, BOD kinetics, BOD first–order model, biochemical oxygen demand, waste management
A dimensionless approach for the determination of BOD first–order model coefficients
A new method based on a dimensionless analysis of the BOD first order model is used to determine the model coefficients (k and L). Curves for the theoretical first order model for the first five days of BOD divided by the theoretical BOD5 for different k values are drawn. The experimental BOD1 through BOD5 are made dimensionless by dividing them with the experimental BOD5. These values are connected smoothly using cubic spline method and MATLAB. The area below these cubic spline equations is compared to the area below the theoretical curves for different k values. The curve with the same area below it as that with the cubic spline curves is used for the determination of k and L values. The closeness of the experimental data to the first order model is easier to observe in this method. Data from the literature have proven the validity of the new method.