Estimation of Groundwater Flow Velocity via Single-Well Push–Pull Tests with Multimethod Approaches

Abstract Accurate determination of groundwater flow velocity (GFV) is essential for resource management and contamination control. The single-well push–pull (SWPP) test is widely used for GFV estimation due to its cost effectiveness, but its accuracy is influenced by operational and hydrogeological factors. This study conducted controlled sand tank experiments under varying free-drift times, defined as the interval between the end of tracer injection and the start of extraction, as well as different extraction rates and hydraulic gradients. Measured breakthrough curves (BTCs) were interpreted using two traditional analytical models (Leap model and Paradis model), and a three-dimensional numerical model to examine GFV inversion accuracy and compare model performance under different scenarios. The results show that drift time primarily governs BTCs morphology and is therefore critical for GFV estimation, with extraction rate and hydraulic gradient playing counteracting and reinforcing roles, respectively. Compared to the numerical solution, which offers robust and accurate results, both analytical solutions show significant errors, first negatively and then positively correlated with drift time. The position of the solute plume relative to the velocity distortion, capture, and detachment zones primarily governs these errors. By incorporating centroid displacement during injection, the Paradis model partially corrects the overestimation of GFV from preferential flow in the distortion zone but amplifies relative error in groundwater flow velocity estimation when solute trapping does not occur. These results indicate that in actual SWPP tests, the free-drift time should be strictly controlled, solute recovery should be enhanced by increasing the extraction rate, and the influence of the velocity distortion zone must be carefully considered.