Periodic Diffusional Mass Transfer near Sediment/Water Interface: Theory

Time-variable (periodic) flow over a lake bed, and the associated boundary layer development, have the potential to control or at least influence rates of mass transfer across the sediment/water interface. An analysis for instantaneous and time averaged flux of a material across the sediment/water interface for infinite supply in the water and infinite sink in the sediment is presented. The water flow above the interface is characterized by the shear velocity (U?) which is a periodic function of time with a maximum amplitude of (U?0) as may be typical of an internal seiche (internal standing wave) motion in a density stratified lake. The relationship between the shear velocity on the lake bed and the wind shear on the lake surface is illustrated for an extremely simplified two-layered lake of constant depth. For a less restrictive analysis, shear velocities on a lake bed have to be obtained either from field measurements or from a three-dimensional lake circulation model driven by atmospheric forcing including wind. Smaller and wind-sheltered lakes will have lower (U?0) and periodicities (T). The response of the diffusive boundary layer was related to the period of the periodic motion (T), Schmidt number (Sc), and shear velocity (U?). The vertical diffusive flux at the sediment/water interface was expressed by a Sherwood number (Sh), either instantaneous or time averaged. The mean Sherwood number (Shave) varies with shear velocity of the wave motion over the sediment bed, Schmidt number (Sc) and the period (T) due to the response of the diffusive boundary layer to the time variable water velocity. Effective diffusive boundary layers develop only at low shear velocities. Where they do, maximum and minimum boundary layer thickness depends on all three independent variables (T, Sc, and U?0). The diffusive boundary layer strongly affects sediment/water mass transfer, i.e., Sherwood numbers. Mass transfer averaged over a period can be substantially less than that produced by steady-state flow at the same U?0 and Sc. At Sc = 500, typical for dissolved oxygen, the mass transfer ratio can be reduced to 60% of steady state, depending on the internal wave period (T).     

Dissolved Oxygen Demand at the Sediment-Water Interface of a Stream: Near-Bed Turbulence and Pore Water Flow Effects

A microbial dissolved oxygen (DO) uptake model was developed for a stream bed, including the effect of turbulence in the flow over the bed and pore water flow in the porous bed. The fine-grained sediment bed has hydraulic conductivities 0.01 ≤ k ≤ 1??cm/s, i.e., sediment particle diameter 0.006 ≤ ds ≤ 0.06??cm. The pore water flow is driven by pressure fluctuations at the sediment-water interface, mostly attributable to near-bed coherent motions in the turbulent boundary layer above the sediment bed. An effective mass transfer coefficient (De) coupled to a pore water flow model was used in the DO transport and DO uptake model. DO flux across the sediment-water interface and into the sediment, i.e., sedimentary oxygen demand (SOD), was related to hydraulic conductivity and microbial oxygen uptake rate in the sediment and shear velocity at the sediment-water interface. Simulated SOD values were validated against experimental data. For hydraulic conductivities of the sediment bed up to k ≈ 0.01??cm/s, the pore water flow effect on SOD was found negligible. Above this threshold, the effective mass (DO) transfer coefficient in the sediment bed (De) becomes larger as the hydraulic conductivity (k) becomes larger as the interstitial flow velocities increase; consequently, DO penetration depth increases with larger hydraulic conductivity of the sediment bed (k), and SOD increases as well. The enhancement of vertical DO transport into the sediment bed is strongest near the sediment-water interface, and rapidly diminishes with depth into the sediment layer. An increase in shear velocity at the sediment-water interface also enhances DO transfer. Shear velocity increases at the sediment-water interface will raise SOD regardless of the maximum oxidation rate if the hydraulic conductivity is above the threshold of k ≈ 1??cm/s. The relationship is nearly linear when U*<0.8??cm/s. At shear velocity U* = 1.6??cm/s, SOD for oxidation rates μ = 1000 and 2000??mg?l-1?d-1 are almost five times larger than those with no pore water flow. When pore water transport of DO is not limiting, SOD is a linear function of oxygen demand rate μ in the sediment when 0 ≤ μ ≤ 200??mg?l-1?d-1.     

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?cm/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+ = 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.     

Effects of Hydrodynamic Conditions on Sediment Oxygen Demand: Experimental Study Based on Three Methods

The quantitative effects of hydrodynamic conditions on sediment oxygen demand (SOD) under smooth surface conditions were investigated using the following three practical and compact experimental systems: (1) a continuous flow system containing sediment core samples; (2) a rectangular flume system; and (3) a system combining the first two. Experimental results demonstrated that SOD showed a monotonically increasing tendency as the flow velocity increased with reduction of the thickness of the diffusive boundary layer. The experimental results were compared with numerical models theoretically relating SOD and flow velocity under smooth surface conditions. The features of each experimental system are discussed. The continuous flow system is advantageous because it simultaneously produces a steady state and different dissolved oxygen (DO) conditions. The rectangular flume system is suitable for fundamental studies of hydrodynamic effects on SOD because it makes controlling hydrodynamic conditions easy, while the combined system is appropriate for studying the effect of microscopic phenomena on exchange rates, as it can reproduce natural microscopic physicochemical processes.     

Long-Term Dynamic Modeling Approach to Quantifying Attached Algal Growth and Associated Impacts on Dissolved Oxygen in the Lower Truckee River, Nevada

Nutrient loads enter the lower Truckee River of western Nevada, affecting the growth of attached algae (periphyton) which causes depressed nighttime dissolved oxygen (DO) levels. The lower Truckee River is home to the endangered cui-ui and threatened Lahontan cut-throat trout, with DO standards being established to in part protect these species. Hydrodynamics, nutrient concentrations, periphyton biomass, and DO data spanning August 2000–December 2001 were used to calibrate and verify a modified version of the Water Quality Analysis Simulation Program Version 5 (WASP5). Under typical loading conditions the periphyton community is nitrogen limited, however nitrogen loading from an upstream wastewater treatment facility increased greatly during the analysis period due to approved site construction activities (discharge permit excursion) causing the periphyton community to temporarily become phosphorus limited. The developed modeling approach, with limited calibration, was able to accurately track dynamic system responses. Removing the impact of the noted discharge permit excursion resulted in a minimum computed DO value of 4.13?mg/L, occurring at the downstream end of the modeling domain on August 8, 2001. Additionally removing the impact of all nutrient loads from area agriculture resulted in a predicted minimum DO value of 4.54?mg/L, while also shifting its location significantly upstream and its timing to April 26, 2001. Meeting all prescribed DO standards required establishing a minimum in-stream flow value of 1.81?m3/s (64.0?ft3/s) downstream of Derby Dam.     

In Situ Characterization of Resuspended-Sediment Oxygen Demand in Bubbly Creek, Chicago, Illinois

Sediment oxygen demand (SOD) can be a significant oxygen sink in various types of water bodies, particularly slow-moving waters with substantial organic sediment accumulation. In most settings in which SOD is a concern, the prevailing hydraulic conditions are such that the impact of sediment resuspension on SOD is not considered. However, in the case of Bubbly Creek in Chicago, the prevailing slack water conditions are interrupted by infrequent intervals of very high flow rates associated with pumped combined sewer overflow (CSO) during intense hydrologic events. These events can cause resuspension of the highly organic, nutrient-rich bottom sediments, resulting in precipitous drawdown of dissolved oxygen (DO) in the water column. To address this issue, a new in situ experimental apparatus designed to achieve high flow velocities was implemented to characterize SOD, both with and without sediment resuspension. In the case of resuspension, the suspended sediment concentration was analyzed as a function of bed shear stress, and a formulation was developed to characterize resuspended-sediment oxygen demand (SODR) as a function of suspended sediment concentration in a form similar to first-order biochemical oxygen demand (BOD) kinetics with the DO term in the form of Monod kinetics. The results obtained can be implemented into a model containing hydrodynamic, sediment transport, and water-quality components to yield oxygen demand varying in both space and time for specific flow events. The results are used to evaluate water quality improvement alternatives that take into account the impact of SOD under various flow conditions.