On the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells in unconfined aquifers

Abstract

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated–saturated flow process and the well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in the Laplace domain is derived by the Laplace–finite-Fourier-transform and the method of separation of variables, and the semi-analytical solutions are obtained using a numerical inverse Laplace method. The solution is verified by a finite-element numerical model. It is found that the effects of the unsaturated zone on the drawdown of a pumping test exist at any angle of inclination of the pumping well, and this impact is more significant in the case of a horizontal well. The effects of the unsaturated zone on the drawdown are independent of the length of the horizontal well screen. The vertical well leads to the largest water volume drained from the unsaturated zone (W) during the early pumping time, and the effects of the well orientation on W values become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for the parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

Base flow recession from unsaturated‐saturated porous media considering lateral unsaturated discharge and aquifer compressibility

“…This model is chosen based on two considerations. First, it has been commonly employed in previous related investigations [ Liang et al ., ; Malama , ; Mathias and Butler , ; Mishra and Neuman , ; Tartakovsky and Neuman , ]. Second, it has been proven in multiple previous studies that this model is physically sound and is amendable to analytical treatment.…”

“…Kroszynski and Dagan [] proposed a first‐order linearized method by expanding the dependent variable in Richards' equation as a power‐function series. This linearized method was widely adopted by previous studies to solve the problems of the coupled unsaturated‐saturated flow [ Liang et al ., ; Mathias and Butler , ; Mishra and Neuman , ; Tartakovsky and Neuman , ]. The details of the linearized equation derivation can be found in previous studies [ Kroszynski and Dagan , ; Tartakovsky and Neuman , ].…”

Analysis of three-dimensional unsaturated–saturated flow induced by localized recharge in unconfined aquifers

“…Kroszynski and Dagan (1975) employed the approach of perturbation expansion to simplify Richards' equation as a first-order linearized equation and developed an approximate solution for unsaturated-saturated flow induced by well pumping. The approach is extensively used in many studies on unsaturated-saturated flow (e.g., Mathias and Butler, 2006;Tartakovsky and Neuman, 2007;Mishra et al, 2012;Liang et al, 2017a). The linearized version of Richards' equation is written as…”

A General Analytical Model for Head Response to Oscillatory Pumping in Unconfined Aquifers: Consider the Effects of Delayed Gravity Drainage and Initial Condition

“…The Laplace transform and finite integral transform are applied to solve Eqs. (8) -(13) (Liang et al, 2017). The former converts ℎ ̅ ( ̅ , ̅ , ̅ ) into ĥ( ̅ , ̅ , ), ℎ ̅ / ̅ in Eq.…”