An analytical solution for non-Darcian flow induced by variable-rate pumping in a radially heterogeneous confined aquifer

A proposed analytical solution for non-Darcian flow is applied to a variable-rate pumping test for a radially heterogeneous confined aquifer. By using the Izbash equation to describe the non-Darcian flow, the analytical solution is derived by the Boltzmann transform and the principle of superposition. The anisotropy of the confined aquifer, represented by the non-Darcian index, quasi-hydraulic conductivity, storativity and thickness of the radially heterogeneous aquifer region, is further investigated. Based on the proposed solution and the measured time-drawdown curves, a practical method for parameter assessments is proposed and validated through an application to field data from the city of Wuxi, Jiangsu Province, China. Using parameter inversion and comparing the simulated data with the measured data, it is found that the influence of the radially heterogeneous aquifer region on hydraulic conductivity should be considered when the thickness of the radially heterogeneous aquifer is less than 6 m. The effects of the non-Darcian index, quasi-hydraulic conductivity and storativity on the radially heterogeneous aquifer region in three cases are analyzed. The results show that the aforementioned parameters are negatively correlated with the drawdown-time value. This paper provides insights for greater understanding of the non-Darcian flow mechanism in a radially heterogeneous, confined aquifer.