An improved analytical model for estimating ambient groundwater velocity from a single-well push-pull test through consideration of the velocity distortion zone

The single-well push-pull (SWPP) test is an effective in situ method for estimating ambient groundwater flow (AGF) velocity. Classical analytical models previously developed for AGF velocity estimation using SWPP tests often rely on the idealized assumptions of a uniform flow field and negligible dispersion effects. However, a velocity distortion zone (VDZ) exists around the well, where higher flow velocities within this region can impact the displacement of the center of mass of the tracer plume during SWPP tests. This study introduces a modified analytical model for estimating AGF velocity concerning the effects of the VDZ. A series of laboratory SWPP experiments were conducted to investigate the influence of test parameters on the AGF velocity estimation. Meanwhile, classical analytical models for AGF velocity estimation were applied to experimental data, using the recovery time of the tracer plume's center of mass. Comparative results indicate that drift time, pumping rate, and hydraulic gradient might amplify the errors caused by idealized assumptions, significantly impacting the parameter estimation due to the VDZ and tracer recovery. Numerical simulations were then employed to derive a correction factor in the modified analytical model. The effectiveness of the modified model was validated by comparing breakthrough curves and benchmark AGF velocities obtained from laboratory experiments and numerical simulations. The modified analytical model outperforms the classical model when the tracer is completely recovered. This study aims to enrich the theoretical and methodological understanding of SWPP tests, providing insights into the effects of the VDZ and improving AGF velocity estimation accuracy.