How low-velocity non-Darcian flow in low-permeability media controls the leakage characteristics of a leaky aquifer system

The distribution of saline water in the upper aquifer and freshwater in the lower aquifer is a characteristic of groundwater resources in the North China Plain (NCP). The phenomenon of groundwater depression cones in confined aquifers, primarily caused by excessive groundwater extraction, has been extensively documented. In line with Darcy’s law, it is noteworthy that the migration of shallow groundwater into confined aquifers can occur due to a substantial difference in hydraulic head between the unconfined and confined aquifer systems. However, based on the monitoring data, the quality of deep groundwater generally remains good. This paper attempts to explain this phenomenon from the perspective of non-Darcian flow in aquitards. A finite difference method is used to solve low-velocity non-Darcian flow to a well in the NCP. The mathematical model considers the threshold pressure gradient to describe non-Darcian flow in the aquitard and assumes Darcian and horizontal flows for both shallow and confined aquifers. The comparison with traditional Darcian flow indicates that the leaky area decreases rapidly when considering the threshold pressure gradient. The leaky area is negatively correlated with the aquitard thickness and the transmissivity of the confined aquifer, and positively correlated with the pumping rate. The non-Darcian vertical flow velocity is significantly lower than that obtained from Darcian theory. The vertical velocity difference between Darcian and non-Darcian flows is significant under the situation of a small aquitard thickness, large pumping rate, low transmissivity and large leakage coefficient when the threshold pressure gradient is large.