Evaluating BOD and the coefficient of oxidation rate: Monitoring, direct and inverse problems, formulas, calculations and tables

Abstract

It is proposed to evaluate two theoretical characteristics, i.e., BOD (biochemical oxygen demand) and k₀ (the coefficient of oxidation rate by new formulas based on two experimental variables: BOD_T and BOD_2T (biochemical oxygen consumption in two periods T and 2T day, respectively). The formulation and an analytical solution are given for a direct problem describing the process of biochemical oxidation of organic matter (OM) in a water volume in the absence of aeration (e.g., in a water body under ice or in a sealed flask used to measure biochemical oxygen consumption). The problem is solved based on the closed (modified) Streeter–Phelps system. Unlike the classical Streeter–Phelps system, the closed system excludes physically incorrect solutions (e.g., negative concentrations of dissolved oxygen (DO)) [4]. The solution of the direct problem is used to formulate an inverse problem, whose solution is given in the form of formulas for evaluating BOD and k₀. These formulas are used to compile tables to illustrate the essence of the proposed method.