Analytical Solutions for Groundwater Response to Earth Tides in Thick Semiconfined Aquifers

Abstract

The tidal behavior of a well in semiconfined aquifers can be described by a diffusion equation including a leakage term. This approach is valid for thin aquifers, as long as the aquitard has low permeability relative to the aquifer. However, in cases where the aquifer is thick and the permeability of the aquitard is not low, using the existing solutions based on these approximations leads to unsatisfactory outcomes. Alternative solutions for both vertical and horizontal wells were obtained by solving the standard diffusion equation, with leakage expressed as a boundary condition. The solutions can be used to estimate any one of wellbore storage coefficient, skin effect, hydraulic diffusivity, and vertical leakage, given the other three. Furthermore, a nondimensional number, named hydraulic Biot number, was derived mathematically, which forms the basis for a quantitative criterion to assess the applicability of existing solutions. In the case of a vertical well, the existing solution exhibits acceptable error only if the hydraulic Biot number is less than 0.245. The new solution extends this upper limitation to 0.475. However, when the number is greater than 0.475, both the existing solution and new solution are invalid due to the invalid uniform flowrate assumption. For a horizontal well, when the number is less than 0.245, the existing solution is suitable with acceptable error. Our new solution effectively overcomes this limitation. Finally, the new solution was applied to the case of the Arbuckle aquifer to demonstrate the improved validity of the new solution compared to the existing one.