Abstract

Subsurface tidal analysis requires only continuous pressure monitoring data and therefore can be a cost-effective technique for estimating aquifer properties. The tidal behavior of a well in a semiconfined aquifer can be described by a diffusion equation that includes a leakage term. This approach is valid for thin aquifers, as long as the overlying layer has low permeability relative to the main aquifer. However, in cases where the aquifer is not thin and the permeability of the overlying layer is not low, using the existing solutions based on these approximations may lead 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. Furthermore, a nondimensional number was derived mathematically, which forms the basis for a quantitative criterion to assess the applicability of the existing solutions. In the case of a vertical well, the existing solution exhibits acceptable error only if the nondimensional number is less than 0.245. Our new solution extends this upper limitation to 0.475. However, when the number is greater than 0.475, both the existing solution and our 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.