Abstract. Oscillatory pumping tests (OPTs) provide an alternative to constant-head and
constant-rate pumping tests for determining aquifer hydraulic parameters when
OPT data are analyzed based on an associated analytical model coupled with an
optimization approach. There are a large number of analytical models presented
for the analysis of the OPT. The combined effects of delayed gravity
drainage (DGD) and the 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 the OPT in an
unconfined aquifer. The model contains a groundwater flow equation with the
initial condition of a static water table, Neumann boundary condition specified
at the rim of a partially screened well, and a free surface equation
describing water table motion with the DGD effect. The solution is derived
using the Laplace, finite-integral, and Weber transforms. Sensitivity
analysis is carried out for exploring head response to the change in each
hydraulic parameter. Results suggest that the DGD reduces to instantaneous
gravity drainage in predicting transient head fluctuation when the 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<10-2 and P<104 s, with P being
the period of the oscillatory pumping rate. A pseudo-steady-state model without
the initial condition causes a time-shift from the actual transient model in
predicting simple harmonic motion of head fluctuation during a late pumping
period. In addition, the present solution agrees well with head fluctuation
data observed at the Savannah River site. Highlights. An analytical model of the hydraulic head
due to oscillatory pumping in unconfined aquifers is presented. Head
fluctuations affected by instantaneous and delayed gravity drainages are
discussed. The effect of the initial condition on the phase of head fluctuation
is analyzed. The present solution agrees well with head fluctuation data taken
from field oscillatory pumping.
A general analytical model for head response to oscillatory pumping in unconfined aquifers: effects of delayed gravity drainage and initial condition
