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MODELING TASK DESCRIPTION

In groundwater modeling it is often of interest to identify capture and source zones of, for example, an ensemble of extraction wells. In FEFLOW, a rough estimation can be done with particle tracking using streamline or pathline analyses. These methods rely on the Darcy flow equation only and neglect effects like dispersion, effective porosity or other transport related terms. Particle tracking is thus limited to the interpretation of flow directions and the approximate range of flow times. 

If the modeling objectives require a more detailed calculation of capture zones, source partitioning or flow component budgeting, FEFLOW offers a quantitative method, the ‘groundwater age’ calculation. It calculates the groundwater travel times based on an advection-dispersion transport model. This toolbox is included in the mass transport license module (FM3 or FMH3). 

The 'groundwater age' module consists of three components respectively additional process variables: 

1) Groundwater Age: average time elapsed since the water has entered the model area at recharging boundaries. 

2) Lifetime Expectancy (LTE): expected travel time from the current location to the outflowing boundaries. 

3) Exit Probability: can be used to obtain information about the probability that groundwater will exit the model at a certain location.  

 
The following workflow describes how to use these parameters to delineate capture zones and calculate how much water enters an extraction originating from a specific source location. 


SOLUTION
 
To start the age calculation, the user has to activate the ‘Groundwater age’ module in the problem settings dialogue under Problem Class. Besides, the required age components must be added in the ‘Age Species’ tab. After applying the changes, additional parameters for each of the three age species are listed in the process variables and in the boundary conditions section of the Data Panel. For both ‘groundwater age’ and 'lifetime expectancy' (LTE), FEFLOW assigns an age/LTE boundary conditions (BC) of 0 to all inflow/outflow nodes automatically. The respective process variables for those parameters display the travel time from (age) or to (LTE) a certain location within the model domain. 

The following example illustrates how to use the third component ‘exit probability’ to identify the capture zone and to calculate how much water enters an extraction well EX, originating from an injection well INJ.


Step 1: Manually assigning an Exit Probability BC   
Exit probability BCs are not assigned automatically but manually defined by the user. For the capture zone of the extraction well EX, the exit probability is defined with a value of 1 for all screened multilayer well nodes (1 equals 100% probability). After running the simulation, the exit probability is limited to a range of 0.2 to 1.0 and the resulting distribution shows that the capture zone of extraction well EX includes the injection of well INJ - Fig. 1. 


Fig. 1 - Exit probability distribution (0.2 - 1.0) for the extraction well EX. 
 

Step 2: Creating a nodal selection of the capture zone
For further budget analyses it is important to store the capture zone as a nodal and/or elemental selection. This can be achieved with the expression editor. Press the sigma button in the Selection toolbar and insert an expression similar to this one, where the capture zone includes all water that will reach the well down to a probability of 20%. 


Please make sure to apply the expression in the 3D view to enclose nodes of the capture zone on all slices. 
This selection (Fig. 2) can be stored and converted into an elemental selection, which will be needed for water content analysis. 

Fig. 2 - Nodal selection of the previously calculated capture zone using the Expression editor.  
 
 
Step 3: Calculate the fluid volume and water transfers between source locations
To calculate the capture zone water content open the Content panel and activate the ‘Exit Probability Domain Fluid Volume’ under the EP - Exit tab. Set the element selection to the previously stored elemental selection of the capture zone to limit the volume to probability values > 0.2. The results are shown in Fig. 3.
 
Fig. 3 - Content Panel for the exit probability Domain Fluid Volume.   
 
Finally, we can use the elemental selection of the capture zone to qualify and quantify the sources of the pumped water. We can calculate the portion of fluid volume which is injected in INJ and pumped by the extraction well EX. Open the Rate Budget panel and switch to the EP - Exit tab. Start the simulation and activate the mass-budget calculation for the domain. The budget class Point-Source BC indicates the water transfer from INJ to EX - Fig. 4. 
 
Please note that the exit probability solution inverts the flow field, meaning negative values indicate inflow (INJ) and positive values outflow (EX). 

Fig. 4 - Rate Budget for the exit probability indicating water transfers from the injection (INJ) to the extraction well (EX) in the Point-Source BC class. 
 


FURTHER INFORMATION AND USEFUL LINKS

Manuals and User Guides

FEFLOW 11 Documentation - Groundwater Age Calculation
FEFLOW 11 Documentation - Process Variables: age
FEFLOW 11 Documentation - Age-Transport Boundary Conditions

Tutorials 
FEFLOW 11 Documentation - Tutorial Age
 

Keywords: FEFLOW, fluid budget, budget analysis, groundwater age, exit probability, source zone, origin of water, capture zone
Related Products: FEFLOW

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