Sedimentary microbial oxygen demand for laminar flow over a sediment bed of finite length

Dead organic material accumulated on the bed of a lake, reservoir or wetland often provides the substrate for substantial microbial activity as well as chemical processes that withdraw dissolved oxygen (DO) from the water column. A model to estimate the actual DO profile and the "sedimentary oxygen demand (SOD)" must specify the rate of microbial or chemical activity in the sediment as well as the diffusive supply of DO from the water column through the diffusive boundary layer into the sediment. Most previous experimental and field studies have considered this problem with the assumptions that the diffusive boundary layer is (a) turbulent and (b) fully developed. These assumptions require that (a) the flow velocity above the sediment bed is fast enough to produce turbulent mixing in the boundary layer, and (b) the sediment bed is long. In this paper a model for laminar flow and SOD over a sediment bed of finite length is presented and the results are compared with those for turbulent flow. Laminar flow near a sediment bed is encountered in quiescent water bodies such as lakes, reservoirs, river backwaters, wetlands and ponds under calm wind conditions. The diffusive oxygen transfer through the laminar diffusive boundary layer above the sediment surface can restrict the microbial or chemical oxygen uptake inside the sediment significantly. The developing laminar diffusive boundary layer above the sediment/water interface is modeled based on the analogy with heat transfer, and DO uptake inside the sediment is modeled by Michaelis-Menten microbial growth kinetics. The model predicts that the rate of SOD at the beginning of the reactive sediment bed is solely dependent on microbial density in the sediment regardless of flow velocity and type. The rate of SOD, and the DO penetration depth into the sediment decrease in stream-wise direction over the length of the sediment bed, as the diffusive boundary layer above the sediment/water interface thickens. With increasing length of the sediment bed both SOD rate and DO penetration depth into the sediment tend towards zero if the flow is laminar, but tend towards a finite value if the flow is turbulent. That value can be determined as a function of both flow velocity and microbial density. The effect of the developing laminar boundary layer on SOD is strongest at the very lowest flow velocity and/or highest microbial density inside the sediment. Under quiescent conditions, the effective SOD exerted by a reactive sediment bed of a lake or wetland approaches zero, i.e. no or very little oxygen demand is exerted on the overlying water column, except at the leading edge.     

Unsteady diffusional mass transfer at the sediment/water interface: Theory and significance for SOD measurement

Dissolved oxygen uptake at a sediment/water interface (SOD) is controlled by mass transport and/or biochemical reactions in two adjacent boundary layers: the diffusive boundary layer delta(D) in the water and the penetration depth delta in the sediment. Either one of those boundary layers or both can be controlling. The transition from sediment control to water control is a function of shear velocity at the sediment/water interface (U(*)) and biochemical activity rate (micro(0)) in the sediment. A model was developed for the unsteady response of SOD and DO profiles near the sediment/water interface. Michaelis-Menten kinetics were used initially, but zero order kinetics work just as well when the half saturation coefficient K(O(2)) is small as was suggested by field data. Beginning with zero DO in the sediments the times required to reach steady state DO profiles and SOD was on the order of minutes to hours, faster where biochemical activity is strong. The values of SOD estimated by the model were compared with experimental data to verify the reliability of the model. The model can reproduce observed penetration depths and diffusive boundary layer thickness. Values of SOD estimated by the model were of same magnitude as observed data. The unsteady DO uptake model can be used to provide guidance for field measurements of SOD. Placing a chamber (with a stirrer) into the sediments disturbs the DO equilibrium at the sediment/water interface. A new equilibrium will be reached within a time that can be measured in terms of cumulative DO consumption in the chamber (SOD exerted). Upper bounds for (SOD exerted) are larger when biochemical activity in the sediments is smaller. Values of SOD exerted are less than 0.1gm(-2) when micro(0) is less than 50mgl(-1)d(-1) and U(*)>0.1cm/s. In other words, steady state conditions are easier to reach for high SOD values. Actual times required to reach steady state can be from minutes to hours. If flow conditions in the chamber and at the natural sediment/water interface are much different, measured SOD values have to be adjusted. A procedure for the adjustments, which can be substantial, has been developed.