Sectional 2D numerical modelling method for steady state well-flow in an unconfined aquifer

Abstract

Objective Both the classical Dupuit model and the modified Dupuit model including infiltration are influenced by Dupuit's assumption and have potential systematic errors. Building a numerical model of well flow in an unconfined aquifer by characterizing the three-dimensional or axisymmetric two-dimensional (2D) flow is an essential approach to verify the performance of Dupuit-type models. Methods In this study, a 2D numerical model is proposed for the steady state well-flow in an unconfined aquifer, in which the control equation of seepage in the cylindrical coordinates is transformed equivalently to the Cartesian coordinates through parameter transformation, and the sectional 2D modelling is implemented via the MODFLOW finite-difference grid of cubic blocks. In the numeric model, the water level in the pumping well is a given condition, the flux across the seepage face is estimated by difference equation according to Darcy's law, the phreatic surface is identified by the treatment of dry and wet cells in MODFLOW, and the pumping rate is determined from the water debug calculation. Results Fine grids are constructed innumerical models of typical cases to obtain high-precision results, in which the relative error of the backwards estimated pumping rate is no more than 0.2%. This numerical model is used to check the Dupuit-type well-flow models. As indicated, the groundwater level estimated from the analytical formulas generally agrees well with the numerical modelling results, except that near the well, where the analytical solution underestimates the groundwater level due to ignoring the waterjump and the errors depend on the anisotropic permeability of the aquifer. When infiltration exists, the flow in the vicinity of watershed does not follow Dupuit's assumption. However, the estimated groundwater level on the watershed by modified Dupuit well-flow equation has a low level of relative error, which is less than 1%. Conclusion This numerical method is simple and practical however it is also influenced by limitations in MODFLOW.

Keywords

• dupuit's assumption
• pumping well
• infiltration recharge
• seepage face
• phreetic surface
• anisotropic
• finite difference method