New Semi-Analytical Model for an Exponentially Decaying Pumping Rate with a Finite-Thickness Skin in a Leaky Aquifer

Abstract

Pumping tests are commonly used to estimate aquifer parameters during field work. Classical pumping tests are mainly classified into two general types: constant-rate pumping tests and constant-head pumping tests. However, pumping rates can vary under different circumstances. In this paper, a semi-analytical solution is developed for an exponentially decaying-rate pumping test in an aquitard-aquifer system considering the effects of a finite-thickness skin. The solution was obtained in the Laplace domain and inverted numerically using the Stehfest method. The solution could be simplified to some special cases and was also compared to several previous work. The results show that drawdowns have asymptotic values similar to those of constant-rate pumping tests at early and late times but decrease for a short period at intermediate times. The presence of aquitards makes the drawdowns stable initially because larger transmissivity in aquitards generally leads to smaller drawdowns. It was also observed that the well skin had a significant impact on drawdown values within the skin zone but no impact in the formation zone. The new solution was validated by fitting it with aquifer parameters obtained from a field pumping test in in Jianghan Plain using a particle swarm optimization algorithm. This study provides new insights into aquifer parameter estimation and the impact of variable-rate pumping tests on drawdown phenomena, particularly in aquitard-aquifer systems.