Modeling flow into horizontal wells in a Dupuit-Forchheimer model

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.