Interpreting Step-Drawdown Pumping Test Undergoing Confined-Unconfined Conversion with Well Loss

Abstract

The step-drawdown pumping test often experiences a transition from confined to unconfined conditions due to the continuously increasing pumping rate. However, the current well hydraulics model has not accurately interpreted this phenomenon. In this study, we developed an analytical solution to address the confined-unconfined conversion in step-drawdown pumping tests based on Girinskii's potential and superposition theory. Additionally, a field step-drawdown pumping test featuring confined-unconfined conversion was conducted to apply the proposed analytical solution. The particle swarm optimization algorithm was employed to simultaneously estimate multiple parameters. The results demonstrate that the newly proposed solution provides a better fit to the observed drawdown in the pumping well compared to previous models. The hydrogeological parameters (K, S), well loss coefficient (B), and critical time for confined-unconfined conversion (t_c) were estimated to be K = 7.15 m/d, S = 6.65 × 10⁻⁵, B = 7.48 × 10⁻⁶, and t_c = 1152 min, respectively. Neglecting the confined-unconfined conversion in step-drawdown pumping tests leads to underestimation of drawdown inside the pumping well due to an overestimation of the aquifer thickness. After the conversion from confined to unconfined conditions, the estimated well loss coefficient decreased by 88% compared to its pre-conversion value. This highlights the necessity of adjusting the well loss coefficient in the step-drawdown pumping test model to account for confined-unconfined conversion. In summary, this study introduces a new method for interpreting parameters in step-drawdown pumping tests and provides field validation for its effectiveness.