Steady state analytical solutions for pumping in a fully bounded rectangular aquifer

Abstract

Using the Schwartz-Christoffel conformal mapping method together with the complex variable techniques, we derive steady state analytical solutions for pumping in a rectangular aquifer with four different combinations of impermeable and constant-head boundaries. These four scenarios include: (1) one constant-head boundary and three impermeable boundaries, (2) two pairs of orthogonal impermeable and constant-head boundaries, (3) three constant-head boundaries and one impermeable boundary, and (4) four constant-head boundaries. For these scenarios, the impermeable and constant-head boundaries can be combined after applying the mapping functions, and hence only three image wells exist in the transformed plane, despite an infinite number of image wells in the real plane. The closed-form solutions reflect the advantage of the conformal mapping method, though the method is applicable for the aspect ratio of the rectangle between 1/10.9 and 10.9/1 due to the limitation in the numerical computation of the conformal transformation from a half plane onto an elongated region (i.e., so-called ''crowding'' phenomenon). By contrast, for an additional scenario with two parallel constant-head boundaries and two parallel impermeable boundaries, an infinite series of image wells is necessary to express the solution, since it is impossible to combine these two kinds of boundaries through the conformal transformation. The usefulness of the results derived is demonstrated by an application to pumping in a finite coastal aquifer.

Experiment and Numerical Simulation of Seawater Intrusion under the Influences of Tidal Fluctuation and Groundwater Exploitation in Coastal Multilayered Aquifers

“…The farther the position is from the sea, the smaller the fluctuation of the groundwater level is, which is similar to the results of previous studies [36,49]. However, the groundwater level fluctuation is complex when considering the effect of pumping (e.g., [39,42,52,53] 14 Geofluids pumping test, due to the groundwater level dynamics jointly induced by tidal forcing and groundwater pumping. In contrast to those previous studies, this study concentrates on the comprehensive effects of the fluctuating sea level and inland recharge on the pumping-induced groundwater level.…”

Preventing Seawater Intrusion and Enhancing Safe Extraction Using Finite‐Length, Impermeable Subsurface Barriers: 3D Analysis

“…The scale of the studied area was selected to limit adverse influences of boundaries on freshwater‐saltwater distributions (Lu et al, 2015). Preliminary simulations indicated that domain dimensions L × W × H (see Figure 1) of 1,120 m × 2,250 m × 30 m were a reasonable trade‐off that minimized both the computational load and boundary effects and allowed for a relatively fine grid resolution.…”

Preferential Flow Enhances Pumping‐Induced Saltwater Intrusion in Volcanic Aquifers

“…In most cases, particularly in homogeneous aquifers, it is assumed that onshore freshwater pumping causes underlying saltwater to migrate vertically upward, termed saltwater upconing (Lorentz, 1912; Muskat, 1946; Werner et al, 2013; Zhou et al, 2005) (Figure 2a). Therefore, monitoring and management strategies typically target upward or lateral movement of deep saline groundwater between the freshwater‐saltwater interface and the well (Abarca & Clement, 2009; Cheng et al, 2000; Cummings, 1971; Lu et al, 2015; Morell Evangelista et al, 2016).…”