Steady-State Shape Factor for a Slug Test in an Unconfined Aquifer

A new solution is presented for the steady-state shape factor of a partially penetrating well in an unconfined aquifer. The problem is solved by taking into account mixed boundary conditions at the well, i.e., zero flux at the well casing and constant head at the well screen equal to the head in the well so that the flow through the well screen is non-uniform. The new method is compared with established methods, such as those of Bouwer and Rice and Zlotnik et al., demonstrating that the new approach provides more accurate results under certain conditions. The comparison highlights that the new method is particularly effective in scenarios where the assumptions of uniform flow through the well screen do not hold. This study assumes idealized conditions, such as homogeneity, isotropy, and negligible storativity in the aquifer, which may limit the method’s applicability in more complex environments. The computational demands of the iterative solution process may pose challenges for practical use, especially in resource-constrained settings.