An analytical and meshless model for 3D transient flow in a confined aquifer with nonuniform thickness: Application to stream depletion due to groundwater extraction

This study proposes an analytical and meshless model for three-dimensional transient flow induced by multiple wells in a stream-confined aquifer system with arbitrary nonuniform aquifer thickness. The model involves allocating external image wells near the aquifer boundary. The aquifer drawdown is defined as Theis’ solution plus a simple series expanded by complementary error functions reflecting the boundary effects of the stream and impervious stratum. The solution for stream depletion rate (SDR) can be derived based on the drawdown solution. Results suggest the Dupuit assumption of no vertical flow is valid to estimate SDRs affected by the landward exponentially decreasing thickness. The SDR induced by multiple wells is the same as that by a single well if the total well discharge rate and stream-well distances in the multiple well case are identical to those in the single well case. The present solution outperforms a finite difference solution in computational efficiency.