Oxygen sag equation for second-order BOD decay

A dissolved oxygen (DO) equation for a stream is developed in which the biochemical oxygen demand (BOD) deoxygenation rate is described as a second-order reaction. Rate constants for a second-order BOD equation may be evaluated by graphical or numerical methods. The DO sag equation incorporates exponential integral functions. These functions are available in tabular form or they may be calculated by exact or approximate series. The time at which the minimum DO concentration occurs is calculated numerically. The DO sag equation using a second-order BOD model fills a gap in the literature, as a number of investigators had explored describing BOD decay as a second-order reaction but the corresponding DO sag equation was not available to predict the impact of such wastes on a river.