Modeling nitrogen–carbon cycling and oxygen consumption in bottom sediments

A model framework is presented for simulating nitrogen and carbon cycling at the sediment–water interface, and predicting oxygen consumption by oxidation reactions inside the sediments. Based on conservation of mass and invoking simplifying assumptions, a coupled system of diffusive–reactive partial differential equations is formulated for two-layer conceptual model of aerobic–anaerobic sediments. Oxidation reactions are modeled as first-order rate processes and nitrate is assumed to be consumed entirely in the anoxic portion of the sediments. The sediments are delineated into a thin oxygenated surface layer whose thickness is equal to the oxygen penetration depth, and a lower, but much thicker anoxic layer. The sediments are separated from the overlying water column by a relatively thin boundary layer through which mass transfer is diffusion controlled. Transient solutions are derived using the method of Laplace transform and Green’s function, which relate pore-water concentrations of the constituents to their concentrations in the bulk water and to the flux of decomposable settling organic matter. Steady-state pore-water concentrations are also obtained including expressions for the extent of methane saturation zone and methane gas flux. A relationship relating the sediment oxygen demand (SOD) to bulk water oxygen is derived using the two-film concept, which in combination with the depth-integrated solutions forms the basis for predicting the extent of oxygen penetration in the sediment. Iterative procedure and simplification thereof are proposed to estimate the extent of methane saturation zone and thickness of the aerobic layer as functions of time. Sensitivity of steady-state solutions to key parameters illustrates sediment processes interactions and synergistic effects. Simulations indicate that for a relatively thin diffusive boundary layer, d, oxygen uptake is limited by biochemical processes inside the sediments, whereas for a thick boundary layer oxygen transfer through the diffusive boundary layer is limiting. The results show an almost linear relationship between steady-state sediment oxygen demand and bulk water oxygen. For small d methane and nitrogen fluxes are sediment controlled, whereas for large d they are controlled by diffusional transfer through the boundary layer. It is shown that the two-layer model solution converges to the one-layer model (anaerobic layer) solution as the thickness of the oxygenated layer approaches zero, and that the transient solutions approach asymptotically their corresponding steady-state solutions.