Title: Cubic spline use for the determination of BOD first-order model coefficients in the presence of a lag phase
Authors: Bashaar Y. Ammary; La'aly A. Al-Samrraie
Addresses: Water and Environmental Engineering Department, Huson College, Balqa Applied University, Huson 21510, Jordan ' Water and Environmental Engineering Department, Huson College, Balqa Applied University, Huson 21510, Jordan
Abstract: A new method for the detection of the presence of a lag phase and the determination of the corresponding coefficients (k and L) of the BOD first order model equation is introduced. The new method is based on a dimensionless approach to the first order equation with a lag phase and the use of cubic spline interpolation and MATLAB. Curves for the theoretical first order model with a lag phase for the first five days of BOD divided by the theoretical BOD5 with a lag phase for different k values are drawn. The experimental BOD values of the first five days are made dimensionless by dividing them by the experimental BOD5. These values are connected smoothly using cubic spline method for different lag periods. Using MATLAB, the closest theoretical curve to the cubic spline curve when both have the same lag phase is selected and used for the determination of k, L, and the lag period values. The closeness of the experimental data to the first order model with a lag phase can be clearly observed in this method.
Keywords: dimensionless method; cubic splines; BOD kinetics; biochemical oxygen demand; lag phase; first-order coefficients; modelling.
International Journal of Environmental Engineering, 2015 Vol.7 No.3/4, pp.226 - 235
Received: 25 Jan 2015
Accepted: 20 Jul 2015
Published online: 24 Feb 2016 *