Oxygen Demand by a Sediment Bed of Finite Length

A model of sedimentary oxygen demand (SOD) for a sediment bed of finite length is presented. The responses of diffusive oxygen transfer in turbulent flow above the sediment surface and of microbial activity inside the sediment to a developing diffusive boundary layer are modeled numerically. The developing diffusive boundary layer above the sediment/water interface is modeled based on shear velocity and turbulent boundary layer concepts, and dissolved oxygen (DO) uptake inside the sediment is modeled as a function of the microbial growth rate. The model predicts that the diffusive boundary layer above the sediment/water interface thickens in flow direction, and that DO penetration depth into the sediment is practically constant over the length of the sediment bed. The effect of the developing diffusive boundary layer on SOD is minor, except at very low shear/flow velocities (shear velocity $U_{*}<0.01\mathrm{cm}∕\mathrm{s}$ ) and/or high microbial density inside the sediment. The average SOD over the sediment bed therefore varies only slightly with its length. SOD varies somewhat in flow direction, i.e., SOD is largest near the leading edge $(x=0)$ , decreases with distance, and finally, approaches a nearly constant value for fully developed boundary layer. Including microbial activity in the sediment makes the change of SOD in flow direction much smaller than is predicted by a pure vertical diffusive flux model. The diffusive boundary layer is nearly fully developed at a dimensionless distance $x^{+}=\mathrm{10,000}$ , regardless of microbial activity inside the sediment. Longer sediment beds are required to eliminate the small leading edge effect on any measured average SOD value. SOD depends strongly on the diffusion coefficient of DO inside the sediment bed. This effect becomes more significant as shear/flow velocity is increased. Overall, SOD is found to be controlled principally by shear velocity of the water flowing above the sediment/water interface, microbial activity inside the sediment, and diffusion of DO inside the sediment. The length of the sediment bed is of lesser influence.