In this presentation, the Streeter-Phelps formulation for river self purification will be examined from a modelling perspective. The physical modelling issue of first versus second order kinetics will be treated at the outset. Then, we will study the mathematical modelling issue of the Eulerian versus the Lagrangian approach. Finally, we will investigate the numerical modelling issue of central differencing versus exponential fitting in the presence of small diffusion. These issues will discussed in the context of accurate simulation of the oxygen sag curve.