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چکیده
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A steady-state analytical solution based on the method of Green’s function is presented for the analysis of hydraulic interference between pumping wells and ambient flow in a heterogeneous wedge-shaped aquifer. Two intersecting streams with spatially variable head form the boundaries of the wedge and establish non-uniform distribution of ambient flow across it. The dual-zone aquifer consists of two porous media of constant but contrasting transmissivities and refraction conditions are exactly satisfied along their common interface. The method of Green’s function affords an integral representation of boundary heads which is readily evaluated in terms of Lerch transcendent function. Integration of Cauchy-Riemann equations gives the associated stream function in closed-form which in turn completes analytical description of the flow net. A systematic way for the assessment of mass balance at both aquifer and sub-aquifer (well capture zone) scales is discussed which also helps identifying whether a certain reach of the boundary stream is losing or gaining water to or from the adjoining aquifer. The solution is general in the sense that the wedge angle, location and discharge of the wells, dual-zone transmissivities and slopes of boundary head variation can be arbitrary chosen. The solution encompasses the case of stream-barrier wedge as a subset. Hypothetical examples demonstrate the complex interaction between surface–subsurface waters showing formation of stagnation point on the capture zone envelopes. In each case, head profiles are in excellent agreement with numerical counterparts from adaptive finite element method. Finally, uncertainty analysis quantifies the extent to which stochastic nature of dual-zone transmissivities and boundary head slopes (model inputs) affects hydraulic head at specific observation points (model output).
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