Evaluation of alluvial well depletion analytical solutions from a stream-aquifer analysis test along the North Canadian River in Oklahoma

Extracting ground water from pumping wells located adjacent to streams can reduce streamflow, a result that is known as alluvial well depletion. Primary factors influencing stream-aquifer interaction during alluvial well depletion are the hydrologic properties of the aquifer, the degree of penetration of the stream into the aquifer, and a potential streambed layer with a hydraulic conductivity different than the aquifer conductivity. Research over the past decade has developed analytical solutions for streams that account for more site-specific features but become mathematically complex. Evaluation of these analytical solutions using field data from multiple regions is needed to assess existing and recently proposed solutions' applicability and predictive capability. At a well site located adjacent to the North Canadian River in central Oklahoma, a stream-aquifer analysis test was performed. Observation wells were installed between the stream and the pumping well and were instrumented with automated water level sensors to measure water levels every 5 minutes. During the stream-aquifer analysis test, a discharge well located approximately 85 m from the North Canadian River was pumped at a constant rate (2180 m³/d) for 90 hrs. Predicted drawdown from several analytical solutions were fit to the measured drawdown to inversely estimate the aquifer transmissivity, T = 790 to 950 m²/d, specific yield, S_y = 0.19 to 0.28, and streambed conductance, λ > 1500 m/d, and then to estimate stream depletion caused by the pumping well. The stream-aquifer analysis test suggested that the stream was behaving similar to a fully penetrating stream with streambed conductivity equivalent to the alluvial aquifer conductivity. For this system, simple analytical solutions were adequate to inversely estimate the aquifer and streambed hydrologic parameters, especially since early-time delayed yield effects were ignored. After only one day of pumping, estimated stream depletion ranged between 30 and 35% of the pumping rate. After five days of pumping, the estimated stream depletion was 60 to 70% of the pumping rate. These results highlight the intense degree of stream-aquifer interaction in this system, which should be accounted for in allocating future water rights.