Author(s): Saumava Dey; Anirban Dhar

Linked Author(s): Saumava Dey, Anirban Dhar

Keywords: Partially penetrating well; Confined aquifer; Laplace domain solution; Finite Volume method; Reduced-order model

Abstract: Well flow problems through porous media are of great importance in assessing the groundwater dynamics and parameter characterization of natural aquifer systems. The characteristics of well flow are different in confined and phreatic aquifer systems depending on the mechanism of water released from storage. A confined aquifer is bounded by impermeable surfaces on both the upper and lower boundaries and hence no vertical inflow is assumed to occur into the aquifer. In response to extraction through wells, water gets released from the storage due to compression of the aquifer matrix and subsequent expansion of water. The drawdown also depends on the extent of the well’s penetration into the aquifer. When the extraction well completely penetrates the depth of the confined aquifer, the flow toward the well is completely horizontal. On the other hand, in a partially penetrating well, both horizontal and vertical flow components are dominant and hence, the anisotropy of the porous media has to be considered for estimating well hydraulics. However, a partially penetrating well yields less than a fully penetrating one and hence, the drawdown in the former is more than the later for a constant rate of extraction from the confined aquifer. In this work, we have developed a computationally inexpensive and efficient mathematical framework for simulating the hydrodynamics of a randomly heterogeneous confined aquifer system subjected to constant extraction through a partially penetrating well. We have modelled the drawdown in the extraction well and its neighbouring locations by numerically inverting the Laplace Transform of the analytical solution of the well hydraulics problem developed by Dougherty and Babu (1984). Assuming homogeneity of the aquifer parameters in the vicinity of the extraction wells, we have discretized the aquifer domain defining a circular time-varying Dirichlet boundary around each extraction well. We have specified the hydraulic head calculated by numerical inversion of the Laplace domain solution at every time step along the internal circular well boundary. We have estimated the transient groundwater response of the aquifer system by a Finite Volume (FV) method-based mathematical model on an irregular-unstructured grid system subjected to the internal well boundary condition and external domain boundary conditions. The proposed approach also satisfies the grid-convergence criterion yielding consistent results with varying grid dimensions. The numerical results confirm the potential applicability of the above methodology for evaluating well hydraulics and aquifer dynamics on a catchment-scale. Furthermore, we have implemented a Proper Orthogonal Decomposition (POD) based reduced-order modeling technique to cut down the computational expenses incurred in full-system modeling of groundwater flow systems. The performance evaluation of the reduced-order model also justifies its capability of replicating the full-system model with the desired accuracy.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022253

Year: 2022