Modeling Flow into Horizontal Wells in a Dupuit‐Forchheimer Model

Abstract

Horizontal wells or radial collector wells are used in shallow aquifers to enhance water withdrawal rates. Groundwater flow patterns near these wells are three-dimensional (3D), but difficult to represent in a 3D numerical model because of the high degree of grid refinement needed. However, for the purpose of designing water withdrawal systems, it is sufficient to obtain the correct production rate of these wells for a given drawdown. We developed a Cauchy boundary condition along a horizontal well in a Dupuit-Forchheimer model. Such a steady-state 2D model is not only useful for predicting groundwater withdrawal rates but also for capture zone delineation in the context of source water protection. A comparison of our Dupuit-Forchheimer model for a radial collector well with a 3D model yields a nearly exact production rate. Particular attention is given to horizontal wells that extend underneath a river. A comparison of our approach with a 3D solution for this case yields satisfactory results, at least for moderate-to-large river bottom resistances.

A Modeling Framework for the Design of Collector Wells

“…This approach is useful when localized aquifer layering is known or when detailed vertical flow paths are needed to make regulatory or treatments decisions. Our regional model applied the method described by Haitjema et al (2010) to simulate effects of the collector wells. We represented the lateral screens of the collector wells in the regional 2D ModAEM model using the equivalent resistance provided in Haitjema et al (2010).…”

Recent advances in modeling of well hydraulics

“…Mohamed and Rushton [252] presented a finite different model based on MODFLOW for describing groundwater response in a horizontal well system at a field test site in Malaysia with considering three flow regimes: flow within the aquifer, flow from aquifer to the well screen, and flow through the horizontal well. Haitjema et al [253] used MODFLOW and the analytic element model, GFLOW, to simulate a Dupuit-Forchheimer flow underneath a river or in a confined aquifer with a Cauchy boundary along a horizontal well in shallow aquifers.…”

Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

“…Most existing models assume 2-D flow by neglecting the vertical flow for pumping at a horizontal well (e.g., Mohamed and Rushton, 2006;Haitjema et al, 2010). The head distributions predicted by those models are inaccurate if an observation point is close to the region where the vertical flow prevails.…”