Two-region Darcian and non-Darcian flow towards a well with exponentially decayed rates considering time-dependent critical radius

•A new two-region Darcian and non-Darcian flow towards a well with exponentially decayed rates;•The critical radius separating the Darcian and non-Darcian regions varies with time;•The wellbore storage effect is considered;•A new deflection point method yields robust parameter estimates of Darcy and non-Darcy flows. Field pumping tests are frequently encountered with variable pumping rates, and the high-velocity non-Darcian region near the pumping well is often time-dependent, leading to special drawdown behaviors that could not be soundly explained by the classical analytical well hydraulics models. Considering the commonly encountered situation of exponential decay in rates, a two-region Darcian and non-Darcian flow model with time-dependent critical radius, which separates the Darcian and non-Darcian regions, is constructed and the corresponding numerical method is applied to analyze the characteristics of aquifer drawdown and the critical radius. Simulation results revealed that the critical radius and drawdown may reach their local maximum value at the intermediate times, and then decrease for a period of time. A larger decay coefficient leads to an earlier deviation in the drawdown and critical radius. For the near-well non-Darcian region, the time-drawdown curves for different decay coefficients have a common critical point (i.e., the early deflection point), while the curves for different inertial force coefficients have different critical points and a larger inertial force coefficient results in a larger critical time. Besides, a larger inertial force coefficient may result in larger extreme points of drawdowns and experience a shorter time from the critical point to the extreme points. Considering the special deflection characteristics of drawdown, a new deflection point method is proposed to estimate the inertial force coefficient, storage coefficient, and hydraulic conductivity of the confined aquifer. The applicability and robustness of this new method were demonstrated by a synthetic pumping test.