Mixed-well model of the relation between drawdown and water inflow in a pumping well with variable-diameter

Objective Pumping tests are an important method for determining the hydrogeological parameters of aquifers and evaluating groundwater resources. For the analysis of single-well pumping tests, existing models assume that the well diameter remains constant with depth and that the aquifer is either unconfined or confined. They do not consider situations where the well diameter varies or when multiple aquifers are encountered. Methods In this study, we developed a steady-state mixed-well flow model to account for a pumping well with a variable diameter that penetrates multiple aquifers with the assumption of horizontal flow within the aquifers. The analytical solutions for the relation between pumping discharge and drawdown were derived. This study explores the methodology of using single-well steady-state pumping tests with variable-diameter wells to obtain aquifer parameters. Additionally, accurate solutions for the equivalent radius of a confined aquifer segment and alternative radius calculation formulas are proposed. Results The mixed-well flow model was applied to analyze pumping tests near the Zihe River. Based on the data from three stepped pumping tests, a parabolic relationship between pumping discharge Qw and drawdown sw was established.The model predicted a pumping discharge of 4 093.8 m3/d when the maximum drawdown sw was 25 m. The hydraulic conductivity of the unconfined aquifer was estimated to be 1.88 m/d, and the hydraulic conductivity of the confined aquifer was estimated as 0.43 m/d, with a relative error of less than 5%. Conclusion The mixed-well model serves as a theoretical foundation for predicting water yield from pumping wells in multiple aquifers system. However, it is important to acknowledge that the model's applicability is constrained by certain assumptions. In situations where rivers fully penetrate aquifers, there is a possibility of overestimating the hydraulic conductivity. On the other hand, when rivers only partially penetrate aquifers, the analytical solution may underestimate the hydraulic conductivity.