Effect of Flow Velocity on Sediment Oxygen Demand: Theory

Abstract

A model of sediment oxygen demand (SOD) is presented that relates the SOD to flow velocity over the sediment. Previous analyses emphasize, almost exclusively, the relationship between SOD and sediment composition, i.e., their chemistry and biology. Herein a quantitative relationship is established between SOD and the velocity and dissolved oxygen concentration in the bulk water. Oxygen consumption in the sediment is expressed as the sum of biological consumption with Michaelis‐Menten kinetics, and the chemical consumption assumed to be a first order reaction of oxygen. At very low flow velocities, transport through the diffusive water boundary layer is the limiting factor of SOD, and SOD is expressed as a linear increasing function of velocity. On the other hand, when flow velocities are increased, SOD becomes independent of velocity, since the reactions in the sediment become rate‐limiting. The model also suggests that SOD is an increasing function of dissolved oxygen concentration in the water overlying the sediment. Combined with the linear theory of internal seiche motion, an average SOD in a rectangular, two‐layered lake is derived as a function of the wind velocity, aspect ratio of the lake and the depth of the thermocline. The average SOD has a minimum when the thermocline depth is one‐quarter of the total depth.