An Analytical Solution of Groundwater Flow in a Confined Aquifer With a Single-Well Circulation System

In this study, a general analytical model for the single-well circulation system is developed to analyze transient drawdown in a confined aquifer. The analytical solution of transient drawdown in the Laplace domain, which is numerically inverted into the time domain using the Stehfest method, is derived by employing a combination of the Laplace and Fourier cosine transforms. The characteristics of transient drawdown and the effects of different parameters related to the single-well circulation system on drawdown are investigated. Furthermore, the analytical solution under steady-state conditions is obtained using the Fourier cosine transform. The results show that steady drawdown contours are symmetric around a horizontal midplane of an aquifer and vary tremendously with distance from the well axis. The contours of drawdown around the sealed section are dense, meaning that the hydraulic gradient in this area is relatively large. The sensitivity analysis, performed to evaluate the characteristics of drawdown to changes in each parameter, indicates that the radial hydraulic conductivity and the length of the sealed section have a large impact on the drawdown and that each parameter has its influence period on the drawdown.