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

Abstract

In the process of groundwater recharge, surface water usually enters an aquifer by passing an overlying unsaturated zone. Little attention has been given to the development of analytical solutions to a coupled unsaturatedsaturated flow model due to localized recharge up to now. This paper develops a mathematical model to depict threedimensional transient unsaturated-saturated flow in an unconfined aquifer with localized recharge on the ground surface. The model contains Richards' equation for unsaturated flow, a flow equation for saturated formation, and the Gardner constitutive model describing the behavior of unsaturated soil properties. Both flow equations are coupled through the continuity conditions of the head and flux at the water table. The semi-analytical solution to the coupled flow model is derived by the methods of Laplace transform and Fourier cosine transform. A sensitivity analysis is performed to explore the head response to the change in each of the aquifer parameters. A quantitative tool is presented to assess the recharge efficiency signifying the percentage of the water from the recharge to the aquifer. We found that the effect of unsaturated flow on the saturated hydraulic head is negligible if two criteria associated with the unsaturated soil properties and initial aquifer thickness are satisfied. The head distributions predicted from the present solution match well with those from finite-difference simulations. The predictions of the present solution also agree well with the observed data from a field experiment at an artificial recharge pond in Fresno County, California.

Effects of Unsaturated Flow on Hydraulic Head Response to Earth Tides–An Analytical Model

“…The GK model has been verified in previous studies (e.g., Mishra and Neuman. 2010) and widely adopted in analytical solutions of the linearized Richards equations (Chang et al., 2018; Liang et al., 2017a, 2017b, 2018a, 2018b; Lin et al., 2017; Mathias & Butler, 2006; Mishra & Neuman, 2010; Tartakovsky & Neuman, 2007). Although the GK model is widely used in previous studies, its exponential form limits its flexibility in representing of some soil properties (Assouline & Or, 2013), for example, it cannot describe the S e ∼ ψ curve of silts well when S e is small, which will be discussed later.…”

“…Kroszynski and Dagan (1975) proposed a perturbation method to linearize Richards equation, which is a feasible approach to approximately resolve this challenge. On the basis of this linearized method, a number of analytical solutions for coupled unsaturated‐saturated flow in different setting were developed, for example, groundwater flow into pumping wells (Liang, Zhan, Zhang, & Liu, 2017; Lin et al., 2017; Malama, 2014; Mathias & Butler, 2006; Mishra and Neuman, 2010, 2011; Tartakovsky & Neuman, 2007), slug test (Liang et al., 2018b), groundwater flow near infiltration wells (Liang, Zhan, & Zhang, 2018; Qi et al., 2020), and groundwater flow induced by recharges (Chang et al., 2018; Liang, Zhan, Zhang, & Schilling, 2017).…”

Mathematical Modelling of Surface-Groundwater Interactions under Varying Hydrological Conditions: Review of Past Works

“…Finite volume method is applied to obtain solution of two-dimensional unsaturated flow in regions of irregular shapes, for the prediction of two-dimensional transient ground water flow over unconfined slanting aquifer [60] to estimate depletion rates of a stream caused due to well pumping [61]. Seedpanah et al [62] studies tidal fluctuations induced by ground water flow in coastal aquifers for studying ground water flow mechanism in porous medium of heterogeneous type.Three-dimensional analytical studies of the ground water flow is carried out by Haunget al [63] and Chang et al [64].…”

Aquifer Recharge Using a Vadose Zone Infiltration Well

“…This treatment eventually leads to a first‐order linearized unsaturated flow equation and a known position for the water table. This linearized method was widely adopted in previous studies to solve the coupled unsaturated‐saturated flow problems (Chang et al, ; Liang et al, ; Liang, Zhan, Zhang, & Liu, ; Lin et al, ; Mathias & Butler, ; Mishra & Neuman, ; Tartakovsky & Neuman, ). The details of the linearized equation derivation can be found in previous studies (Kroszynski & Dagan, ; Tartakovsky & Neuman, ).…”