Analytical solution of capture time to a partially penetrating well in a semi-infinite aquifer

Calculating the capture time of contaminant to a well is important in the context of both groundwater protection and aquifer remediation. Although partially penetrating wells are much more commonly used than fully penetrating wells, there is no analytical solution for capture time calculations, probably due to the challenges of mathematically modeling such types of wells. In this study, an analytical solution of capture time was developed, based on the assumption that a partially penetrating well was installed in a homogeneous and semi-infinite aquifer. For an example case, the capture time result by the analytical solution fitted well with result by a high-resolution particle tracking method established according to the fourth-order Runge-Kutta algorithm. The impacts of different parameters are analyzed, and results indicate that the effects of both screen length L and anisotropic ratio a on capture time T are spatially dependent. Such comparisons also demonstrate that the influence of the lower boundary is stronger as penetration increases. In the end we compare the analytical solution for a line sink with that for a point sink, and demonstrate that larger differences occur near the wellbore, however, at a sufficiently large distance from the wellbore, the capture time distributions become the same for both source types.