Analytical Dissolved Oxygen Model for Sinusoidally Varying BOD

Abstract

An analytical solution is developed for biochemical oxygen demand (BOD) and dissolved oxygen concentration (DO) in a river for the case when BOD loading concentration and DO loading concentration each vary sinusoidally. The analytical solution is for the quasi-steady-state (periodic) case as the initial condition is ignored, but the boundary conditions are satisfied. Thus, the analytical solution is applicable from the BOD and DO loading locations to the concentration front. This distance is calculated by making use of the memory length concept. The solution is developed by breaking the BOD and DO equations into three subproblems, which are solved separately, then combined by applying the superposition principle. The solution is tested against published solutions from the literature, which include an integral equation, a perturbation solution, and a numerical solution. The analytical solution is easy to apply and extends the cases with which engineers can compare their numerical models. The results suggest the importance of considering time variable wastewater loadings to a river when designing water quality monitoring networks.