Analysis of radial movement of a confined aquifer due to well pumping and injection

Three aspects of radial motion of an aquifer solid matrix, driven by hydraulic forces due to well recharge and discharge, have been investigated mathematically. Firstly, the analytic solutions in the velocity and displacement fields were found using the definition of bulk mass flow, conservation of water and solid mass, the Darcy-Gersevanov law, and the drawdown of hydraulic head for unsteady flow. Secondly, the radial velocity and displacement of aquifer solid matrix were investigated with respect to time and location in response to three pumping-injection schemes (i.e., linear, nonlinear, and sinusoidal well flow rates). Aquifer movement was found to be more responsive to linear and nonlinear pumping rates than to constant pumpage. Aquifer movement in response to periodic well discharge and recharge was governed by an integral sinusoidal function. Finally, the potential risk of earth fissuring at a given location caused by tensile stress, in turn induced by well discharge-recharge activity, has been discussed using the analytic solution. The deformation compression and extension zones derived from analysis of the results indicated the possible occurrence of tensile stress that may cause earth fissures. Sample computations, using assumed parameters, provided a first-hand evaluation of the location of potential fissuring in relation to the well.