SIMPLIFIED DEVELOPMENT OF OXYGEN SAG MODEL

A dissolved oxygen sag equation is developed by use of the Laplace transform and the convolution integral for a stream in which the biochemical oxygen demand (BOD) deoxygenation rate is described as a second-order reaction. The Laplace transform method simplifies the mathematical solution of the model equation by avoiding difficult-to-evaluate integrals. The dissolved oxygen sag equation incorporates exponential integral functions which are calculated by exact or approximate series. The time at which the minimum dissolved oxygen concentration occurs is calculated numerically. The dissolved oxygen sag model is applied using BOD data collected from Douglas Fir needles in stream water. The Douglas Fir needles had a small reaction rate constant which results in the stream being able to carry a BOD load without exhausting its dissolved oxygen supply. The model is useful in calculating Total Maximum Daily Loads (TMDL) of streams. INTRODUCTION Water quality modeling in a river has developed from the pioneering work of Streeter and Phelps [1], who developed a balance between the dissolved oxygen *Financial support was provided by a Louisiana State University Board of Regents fellowship to the senior author.