An analytical model for a single‐well circulation system in a confined aquifer with a finite thickness well skin

Abstract

AbstractIn this study, a general analytical model of a single‐well circulation system is developed to analyze transient drawdown in a confined aquifer considering the effects of a finite thickness well skin. The analytical solutions in the Laplace domain of transient drawdown in the skin and formation zones are obtained by applying the Laplace and Fourier cosine transforms. The Stehfest method is employed to numerically invert transient drawdown in the Laplace domain into the time domain. Meanwhile, the steady‐state solutions in the time domain for the skin and formation zones are also derived by using the Fourier cosine transform. The influence of different parameters on transient drawdown is investigated. The results show that the skin type and thickness have an enormous impact on drawdown in the skin zone, while their influence on drawdown in the formation zone is small and can be neglected. The sensitivity analysis, carried out to investigate the characteristics of drawdown with respect to each parameter, indicates that drawdowns in the skin and formation zones are highly sensitive to the sealed section's length.