On the Incorporation of Drains into Three‐Dimensional Variably Saturated Groundwater Flow Models

Abstract

Subsurface drains are important features in many problems involving shallow groundwater flow and have generally been represented in two-dimensional numerical models by specifying hydraulic head or fluid flux at one or more nodes in the computational grid. Here we describe a new approach for representing drains in threedimensional variably saturated flow models. The method is based on a one-dimensional flow equation for the drain which is analogous to a one-dimensional open-channel flow equation; the numerical contributions to the system of global equations from the onedimensional discretized equation are added to the three-dimensional, porous medium contributions. The inclusion of drain flow by this technique is readily adaptable to any three-dimensional numerical simulator. The accuracy of the method is demonstrated by comparing results obtained with the new method to steady state and transient results presented by Fipps et al. [1986]. The numerical formulation naturally accommodates flow in heterogeneous media and demonstrates excellent mass balance. Illustrative examples are presented which highlight the usefulness of the algorithm for studying the influence of drains in problems involving subsurface effluent disposal in heterogeneous aquifers and agricultural land drainage. The method will have application to many studies involving water and contaminant movement in drained soils.

Integrated modeling of groundwater–surface water interactions in a tile‐drained agricultural field: The importance of directly measured flow route contributions

“…K(h) is the tile drain conductivity and is be approximated by assuming shallow laminar flow: where μ is the fluid viscosity, ρ is the fluid density, and g is the gravitational acceleration constant. We refer to MacQuarrie and Sudicky [1996] for more details on the numerical implementation of tile drain flow in the model code, a verification of the approach, and some illustrative examples.…”

Interpretation of pumping tests in a mixed flow karst system

“…The second approach consists in using double‐continuum models to simulate flow exchanged between the systems based on differences in hydraulic head via linear exchange terms [ Barenblatt et al , 1960; Teutsch , 1988, 1989; Sauter , 1992]. A third approach couples discrete flow path networks to a continuum in order to model dualistic flows in MFKS (“hybrid models”) [ Kiraly , 1984; MacQuarrie and Sudicky , 1996; Arfib and de Marsily , 2004]. Liedl et al [2003] used such an approach by coupling a pipe network with a fractured system via linear exchange terms, with simulations of Darcian flow in the matrix done using a finite difference scheme.…”

Analysis and finite element approximation of a coupled, continuum pipe-flow/Darcy model for flow in porous media with embedded conduits

“…However, no mathematical theory is available to guarantee existence of solutions and the coupling condition of the form (1.4) is not incorporated. Combining the idea of dual porosity and mimicking the numerical schemes in [9,17], the model (1.5) in [10,11,16] is solved by the Carbonate Aquifer Void Evolution (CAVE) code [18]. CAVE solves the flow in the porous matrix by a finite difference scheme using MODFLOW [19] and the flow in conduit by a nonlinear finite difference discretization.…”

“…The model was originally borrowed from dual-porosity models [3][4][5][6]. The finite element discretization for the coupled nonlinear Richard's equation and pipe (or plane) flow is discussed in [9,17] for variably saturated porous media. However, no mathematical theory is available to guarantee existence of solutions and the coupling condition of the form (1.4) is not incorporated.…”

“…Alternatively, double-continuum or multicontinumm models have been applied wherein the cross flow between the two systems depends on the corresponding pressure differences via linear exchange terms [3][4][5][6]. As a third approach, discrete networks of flow paths can be coupled to a continuum model to model the dualistic flow patterns [7][8][9].…”