Slug tests for determining the hydraulic parameters of an unconfined aquifer considering delayed drainage effect

A mathematical model describing the hydraulic head variation distributions is presented for a slug test performed in an unconfined aquifer system considering delayed drainage. A closed-form solution for the model is derived by Laplace transform and Bromwich integral. The new solution is employed to study the characteristics of water release in the well and unconfined aquifer, and investigate the impacts of the dimensionless dewatering factor alpha D, the water release coefficient ratio ; on the distributions of dimensionless well hydraulic head variation. Besides, slug tests were conducted in an unconfined aquifer to estimate hydraulic parameters. The results indicate that the distributions of dimensionless hydraulic head variation in the well or unconfined aquifer are significantly different from those in a confined aquifer. The dimensionless hydraulic head variation versus dimensionless time exhibits five distinct stages, with the dimensionless dewatering factor alpha D having a notable influence. The dimensionless well hydraulic head variation increases with alpha D increases before the relatively gentle stage and gradually coincides with the curve presented by Cooper et al. (1967) with a high storativity. In addition, the water release coefficient ratio ; mainly affects the gravity drainage phase, where the dimensionless well hydraulic head variation increases as ; increases. The proposed method in this paper improves calculation accuracy. For the clay or low-permeability aquifers, the gravity delayed drainage effect is negligible.