Utilization of Weibull Techniques for Short-Term Data Analysis in Environmental Engineering

Abstract

Failures and disadvantages of biological treatment plants reported in the literature indicates that there is a need to apply extreme value distributions in the establishment of design parameters including ultimate biochemical oxygen demand (BOD) and the BOD removal rate constant. This paper presents the application of extreme value distributions in environmental engineering. Wastewater samples were collected from a domestic-institutional wastewater treatment plant weekly for 15 months. BOD concentrations were determined for the first 6 days using respirometric method. Ultimate BOD (L_o ) and BOD removal rate constant (k) were determined using nonlinear regression method. L_o and k were used in the application of extreme value distribution and environ–economics analysis. The study revealed that extreme value distributions can be used in environmental pollution control to select design parameters. The values of a and b in a reliability function were 0.192 and 9.638, 0.333 and −6.867 for k and L_o, respectively. Prediction of reliability agreed with the practical values using a Weibull plot, F(1,59) = 1.75 and 0.273 for k and L0 , respectively. The design parameters at 90, 95, 99, and 99.5% reliability for k and L_o were 0.275, 0.288, 0.226, and 0.208/day and 2106.10, 2130.46, 2155.97, and 2158.62 mg/L, respectively. K_k values were 102,030 and 0.000005 for k and L_o , respectively. In environ–economics analysis reliability of 0.986 (98.6%) was found to be economical for the design of a domestic–institutional wastewater treatment plant studied with a risk cost of 706.2 Euro (12.36 × 10⁴ Naira) per annual per 1,000 mg of BOD. It was concluded that utilization of extreme value distributions in the selection of design parameters such as L_o and k will help in simulation and improve design of biological treatment plants.