A non-penetrating well in a confined aquifer. An approximate closed solution

The non-steady flow towards a non-penetrating well in a closed aquifer with storativity is studied theoretically. A closed solution can be derived, if the boundary condition at the interface between the well and the aquifer is properly approximated. The analysis shows that if the thickness of the aquifer is much bigger than the radius of the well, the approxiamtion is good and that the flow in the aquifer is concentrated to the top of the aquifer, leaving the water at the bottom effectively stagnant, if the distance from the well far exceeds the diameter of the well but is far below the thickness of the aquifer. The solution together with the well-known solution for a complete well can serve as limits for the practically important case of a partially penetrating well.