An Analytical Solution of Hydraulic Head due to an Oscillatory Pumping Test in a Confined, Unconfined or Leaky Aquifer

Abstract:

This study builds a mathematical model for three-dimensional (3D) transient hydraulic head induced by an oscillatory pumping test in a confined, unconfined or leaky aquifer. The aquifers are of a rectangular shape where the four sides are under the Robin conditions. The 3D flow governing equation with a line sink term representing a vertical well is employed. The sink term has a cosine function for the oscillatory pumping. A general equation describing the head on the top of the three kinds of aquifers is considered. The analytical head solution of the model is derived by the direct Fourier method and the double-integral transform and in terms of a double series with fast convergence. With the aid of the solution, we have found that the vertical component of flow vanishes when K_v d²/(K_hD²) > 1 where K_h and K_v are aquifer’s hydraulic conductivities, respectively, D is aquifer’s thickness, and d is a distance measured from the pumping well. Under the condition, temporal head distributions predicted by the present solution agree with those predicted by solutions developed based on two-dimensional flow by most previous researches.