Truncating Cross-Sectional Groundwater Models under Wetlands

Abstract

Cross-sectional models, which represent two-dimensional flow in the vertical plane, tend to have problematic aspect ratios since the aquifer thickness is often small compared to the lateral extent of the flow domain. For that reason, the model domain is usually limited to the immediate area of interest, for instance the aquifer section underneath a dam. We propose a Cauchy boundary condition to represent flow from remote wetlands that are left out of the truncated model. The resistance to flow inherent to such a boundary depends on the aquifer properties and the resistance to flow through the wetland bottom. While the Cauchy boundary condition is based on the Dupuit-Forchheimer approximation to flow underneath the remote wetlands, the error appears to be negligible ͑less than 0.6%͒ for most practical cases, including flow in stratified aquifers. For the case of multiple aquifers underneath the wetlands, the total flow in the truncated model can be a few percent in error, which is typically acceptable for most engineering applications. The approach is illustrated with an application near a levee-borrow canal setting in the Florida Everglades.

Modeling Flow into Horizontal Wells in a Dupuit‐Forchheimer Model

“…In the resulting one‐dimensional (1D) Dupuit‐Forchheimer model, the total flow Q [ L 3 /T] out of the river that enters the aquifer on one side of the horizontal well is given by Verruijt (1970), p. 30 Equation 4.10, as: where φ 0 is the river stage, φ w the head in the aquifer at the location of the horizontal well, and B [ L ] the length of the horizontal well being considered. The parameter λ [ L ] is referred to here as the characteristic leakage length defined as (Verruijt 1970): , with B = 1, represents the discharge Q x in the 1D Dupuit‐Forchheimer model for flow to one side of the horizontal well, hence the total discharge σ, per unit length of the horizontal well, is twice that amount: Following the same approach as in Haitjema et al (2010), we compare this total flow () with the inflow into a fictitious stream in a confined aquifer with a bottom resistance c DF (see Figure 1(b)), for which the total flow per unit length of the stream is, see also : Comparing yields a resistance c DF for the horizontal well that includes the resistance to flow through the river bottom and the resistance to horizontal flow in the aquifer: In order to obtain the resistance c ls for the Cauchy boundary condition on the horizontal well, the resistance c DF must be subtracted from c 2 defined by , hence A graph for c 2 is provided on http://www.haitjema.com/transfer/GW2010.zip…”

“…Following the same approach as in Haitjema et al (2010), we compare this total flow (Equation 21) with the inflow into a fictitious stream in a confined aquifer with a bottom resistance c DF (see Figure 1(b)), for which the total flow per unit length of the stream is, see also Equation 17:…”