Transient radial movement of a confined leaky aquifer due to variable well flow rates

The present paper investigates aquifer horizontal movement driven by hydraulic forces. New analytic solutions are found for the velocity and displacement fields describing aquifer radial transient movement caused by well discharge and recharge within a confined leaky aquifer. The development of the new solutions is based on linear momentum of bulk mass flux, mass conservation of bulk mass flux, the Darcy–Gersevanov law, and the analytic hydraulic drawdown. If the Hantush–Jacob, Carslaw–Jaeger, and Theis analytic drawdowns are applied respectively, a corresponding aquifer transient movement is found within the new solutions. Three sets of simplified solutions based on the Carslaw–Jaeger drawdown have been applied to three schemes of well flow rates that are power, periodic and exponential functions of time. For all three schemes, the dimensionless relations of aquifer displacement versus radial distance show the zones and locations where possible tensile stress may occur and cause potential earth fissuring. For the well flow rates varying as a power or periodic function, tensile stress may be generated when inertial forces change directions based on the dimensionless relations of aquifer velocity versus time. Analysis of effects that vertical leaky flow have on aquifer horizontal movement shows that the vertical water flow plays a significant role in aquifer radial movement, and that aquifer radial velocity is much more responsive to the vertical flow than is aquifer displacement.