A numerical study on the occurrence of flowing wells in the discharge area of basins due to the upward hydraulic gradient induced wellbore flow

The occurrence of flowing wells in basins has been found to be closely related to the discharge area with an upward hydraulic gradient. Unfortunately, previous studies on upward gradient induced wellbore flow with equaling total inflow (Q_in) in the deep and total outflow (Q_out) in the shallow could not explain the occurrence of flowing wells. By representing wells using the MNW2 Package imbedded in MODFLOW 2005, we obtain the exchange of groundwater between the aquifer and the well in the discharge area of 3D unit basins and identify three scenarios: Q_in = Q_out, Q_in > Q_out > 0 and Q_in > Q_out = 0. The relationship of Q_in > Q_out well explains why flowing wells only develop in a limited part of the discharge area. Sensitivity analysis shows that well location, water table undulation, and basin length–depth ratio do not change the profile of the ratio of cumulative flow rate in a flowing well to total inflow (Q_v/Q_in) versus the relative elevation in the inflow segment, z_in*, but could significantly change the length of the inflow segment; well depth could change both the length of the inflow segment and the profile of Q_v/Q_in versus z_in*. Based on the numerical results in homogeneous and isotropic basins with different basin length–depth ratios in the current study, the ratio of inflow in the lower half part of a flowing well to the total inflow is found to be at least 67% and could be close to 100%, indicating that water at the outlets of flowing wells with long open sections is mainly from the deep part of the well.