MODELING TASK DESCRIPTION
In many groundwater models surface water bodies (rivers, streams, lake, ponds) are included that contribute to varying extent to the groundwater budget. Rivers sometimes even have sections with mainly infiltration and other sections with exfiltrating conditions. The classic approach to represent rivers in a groundwater model is the assignment of a 'Fluid-Transfer Boundary Condition' (3rd kind / Leakage / Cauchy BC). Such boundaries require a predefined reference head value (href) combined with a conductance parameter Φ (transfer rate of clogging layer).
For the correct implementation of a fluid-transfer boundary condition in a groundwater model, the following steps are required. The procedure is the same for lakes, ponds or any surface water bodies hydraulically connected to the aquifer:
Step #01 - Supermesh integration
The river course should be included as polyline in the Supermesh before the mesh generation. This will make it easier to refine the mesh near the river to cover potential high gradients in the zone of interaction between surface water and groundwater - see Fig. 1.
Fig. 1 - Supermesh view with a polygonial model area and a polyline representing the river
Step #02 - Mesh refinement
Choose a suitable mesh generator (e.g. Triangle) to be able to refine the river course. Activtate the 'Refine line' option in the Mesh Generator Properties Panel and specify the parameters 'Line Gradation' and 'Line Target Size' - see Fig. 2.
Fig. 2 - Mesh refinement along the river course
Step #03 - Select line feature
The supermesh line can be used to select the river nodes (double-click on 'Lines' in the Maps Panel and choose Select by Map Lines in the Selection toolbar) - see Fig. 3. Specify the Snap distance( ) for which the nodes will be selected apart from the line feature and click on the river course in the Map View or use the Select by all Map Geometries button (
) in the Selection toolbar - see Fig. 3.
The line selection can be done with multiple line features also at later stages of the model construction. It is good practice to include every possible structure that needs a refined mesh geometry during the initial supermesh editing, because remeshing at a later stage always comes with a re-assignment of parameters and boundary conditions.
Fig. 3 - Picture Choose Select by Map Line and Select by All Map geometries
Now, a nodal selection similar to the one shown in Fig. 4 should be visible.
Fig. 4 - Picture: Selected nodes on the river line to assign boundary conditions
Step #04 - Assign the fluid-transfer boundary condition
Fluid-Transfer boundary conditions can be assigned to element faces (3D models) or Edges (2D models). Depending on the way a river is represented in a model the element faces can be oriented horizontally or vertically - see Fig. 6. Accordingly, FEFLOW distinguishes two cases.
Fig. 6 - Picture Correctly assigned connected Fluid-Transfer BC-s
1D representation of rivers
If the river is narrow compared to the element sizes, a linear series of nodes assigned with the fluid-transfer BCs is sufficient to represent the river (Fig. 7). In this case, the assignment needs to be extended to the second slice as otherwise no faces are defined for the water exchange between river and aquifer. In case of deep river beds exceeding the thickness of the first model layer, the boundary condition can be extended to more than one underlying slices - see Fig. 8.
Fig. 7 - Fluid-transfer BC representing the river course from the top
Fig. 8 - 3D view of the model showing the carved-out area (in green) representing the connected faces of a fluid-transfer BC throughout the upper three slices
The water exchange between river and aquifer is calculated from the relevant area, the transfer rate and the difference between the reference head (href) and the calculated hydraulic head of the groundwater (h). The transfer rate is a conductance term related to the conductivity of the clogging layer. FEFLOW distinguishes between the in-transfer rate (surface water --> groundwater) and out-transfer rate (groundwater --> surface water). According to the calculated gradient direction, FEFLOW automatically chooses the correct value - see Fig. 9.
Fig. 9 - Transfer-rates assigned to elements shown in red color, the rest of the model is purple leaving the In-transfer rate at the default value of 0
2D areal representation of rivers
If the surface water body has a significant surface (wide rivers or lakes) fluid-transfer BCs are assigned to horizontal faces on top of the model. The user needs to select the nodes in the respective area covered by the surface water body for the assignment - see Fig. 10.
Fig. 10 - Fluid-Transfer BC-s representing a wide river line
The in-/and out-transfer rates should be assigned to the corresponding elements - Fig. 11.
Fig. 11 - In-/ and out-transfer rate
CONCLUSION
There are several ways to represent surface water and groundwater interactions inside FEFLOW. You can use the described methods individually or combine them to have a complex groundwater model including all surface water bodies apparent in the model domain.
Apart from the presented approach, there is another possibility to represent surface waters in FEFLOW: a native coupling between FEFLOW and MIKE 1D engines for integrated groundwater / surface water modelling through the plug-in piMIKE1D. More information you can find in the links below.
FURTHER INFORMATION AND USEFUL LINKS
Manuals and Guidelines
FEFLOW 10.0 Documentation - Fluid-Transfer BC
FEFLOW 10.0 Documentation - Material Properties Flow
FEFLOW 10.0 Documentation - FEFLOW piMIKE1D
Training Courses
DHI Training Portal - Getting started with groundwater modelling
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