Inertial and storage effects in well‐aquifer systems: An analog investigation

Abstract

Equations for nonsteady groundwater flow are based upon Darcy's law, which is equivalent to assuming that the forces of inertia in the aquifer are negligible. Futhermore, derivation of these equations commonly assumes that the diameter of the pumped well is infinitesimal, which is equivalent to neglecting the additional storage in the well. The inertia of the column of water in the pumped and observation wells is also generally neglected in the derivation of these equations and in the analysis of drawdown measurements. However, for problems involving rapid acceleration of the water in the well and in the aquifer there is the possibility that the inertial forces and/or well storage may be significant. The effects of inertia in both the aquifer and the well, along with the effect of storage of water in the well, were investigated by electric analog. The results indicate that: (1) Some equations of groundwater flow are not applicable when the inertia of the water in the well and/or the storage of water within the well are taken into account; (2) A well can behave as an underdamped simple harmonic oscillator; i.e., it will oscillate following a sudden disturbance. The critical damping curves for 6‐inch‐diameter wells are presented. The ‘resonant’ frequency of the well‐aquifer system is to a large extent determined by the mass of ‘water’ in the well; (3) Except where changes in velocity occur very rapidly, as in forced oscillation, the effects of the inertia of water in the acquifer are negligible when compared with frictional (viscous) losses.