A General Analytical Model for Head Response to Oscillatory Pumping in Unconfined Aquifers: Consider the Effects of Delayed Gravity Drainage and Initial Condition

Abstract

Abstract. Oscillatory pumping test (OPT) is an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters without net water extraction. There is a large number of analytical models presented for the analysis of OPT. The combined effects of delayed gravity drainage (DGD) and initial condition regarding the hydraulic head are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by OPT in an unconfined aquifer. The model contains a groundwater flow equation with the initial condition of static water table, Neumann boundary condition specified at the rim of a finite-radius well, and a free surface equation describing water table motion with the DGD effect. The solution of the model is derived by the Laplace transform, finite integral transform, and Weber transform. Sensitivity analysis is carried out for exploring head response to the change in each of hydraulic parameters. Results suggest the DGD reduces to instantaneous gravity drainage in predicting transient head fluctuation when dimensionless parameter a1 = εSyb/Kz exceeds 500 with empirical constant ε, specific yield Sy, aquifer thickness b, and vertical hydraulic conductivity Kz. The water table can be regarded as a no-flow boundary when a1