First-Order Contaminant Removal in the Hyporheic Zone of Streams: Physical Insights from a Simple Analytical Model

A simple analytical model is presented for the removal of stream-borne contaminants by hyporheic exchange across duned or rippled streambeds. The model assumes a steady-state balance between contaminant supply from the stream and first-order reaction in the sediment. Hyporheic exchange occurs by bed form pumping, in which water and contaminants flow into bed forms in high-pressure regions (downwelling zones) and out of bed forms in low-pressure regions (upwelling zones). Model-predicted contaminant concentrations are higher in downwelling zones than upwelling zones, reflecting the strong coupling that exists between transport and reaction in these systems. When flow-averaged, the concentration difference across upwelling and downwelling zones drives a net contaminant flux into the sediment bed proportional to the average downwelling velocity. The downwelling velocity is functionally equivalent to a mass transfer coefficient, and can be estimated from stream state variables including stream velocity, bed form geometry, and the hydraulic conductivity and porosity of the sediment. Increasing the mass transfer coefficient increases the fraction of streamwater cycling through the hyporheic zone (per unit length of stream) but also decreases the time contaminants undergo first-order reaction in the sediment. As a consequence, small changes in stream state variables can significantly alter the performance of hyporheic zone treatment systems