Response of dual-zone heterogeneous wedge-shaped aquifers under steady-state pumping and regional flow

• Published in: Advances in water resources Vol. 147; p. 103823
• Main Author: Mahdavi, Ali
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2021
• Subjects: drawdown; finite element analysis; Flow net; head; Heterogeneity; hydraulic conductivity; rivers; seawater; Stagnation point; Stream depletion rates; streams; unconfined aquifer; Wedge-shaped aquifers; Stream depletion rates; Stagnation point; Heterogeneity; Flow net; Wedge-shaped aquifers
• ISSN: 0309-1708
• DOI: 10.1016/j.advwatres.2020.103823

•Analytical representation of flow net in heterogeneous wedge-shaped aquifers.•An explicit linkage between stream depletion rates and stream function.•Linear variation of stream depletion rates with angular position of the well.•Preservation of water balance at capture zone scale. Natural hydrogeological settings may delineate wedge-shaped aquifers that are sandwiched between streams, lakes or sea water bodies along arbitrary-oriented boundary lines. This is the case in multiple river basins, river deltas, alluvial fans, and coastal promontories and heterogeneity patterns are likely to arise because of sedimentation zoning. The aim of present study is to provide a steady-state analytical solution describing the nature of well extraction in heterogeneous wedge-shaped aquifers formed by intersection of arbitrary-oriented streams. This laterally bounded aquifer comprises two zones of constant but differing transmissivity (hydraulic conductivity) which are hydraulically connected through a common interface. First, the method of Green's function constructs a closed-form expression for the spatial distribution of dual-zone potential. Next, the stream function is derived from the integration of Cauchy-Riemann equations which in turn completes an analytical representation of the flow net. The stream depletion rates are shown to be explicitly linked to the stream function. This leads to simple expressions for the stream depletion rates, demonstrating that the lateral recharge from adjacent streams varies linearly with the angular position of pumping well without any dependency on the aquifer heterogeneity. The present solution encompasses a number of existing solutions for homogeneous aquifer system as subsets. Flow nets are generated for hypothetical test cases whereby stagnation points are identified semi-analytically. The present formulation ensures preservation of water balance for a capture zone subject to regional flow. Sensitivity analysis is conducted to address how drawdown at a certain observation point responds to a heterogeneity perturbation. Wider wedges appear more sensitive to variation of heterogeneity. The formulation is extended to account for rainfall-induced recharge over a dual-zone unconfined aquifer. In each case, the computed head profiles agree well with numerical counterparts from finite element method.