Tutorial Results

In the following exercises we use a simulation record to evaluate the mode­ling results after the simulation. Start FEFLOW and click  Open to load the file results.dac. The file contains the complete results for every calculated time step of a transient flow and mass transport simulation.

Tools

 

 Simulation toolbar.

Observation Points

For the loaded simulation record, nine different charts can be displayed: Time Steps, Hydraulic Head, Pressure, Local and Average Concentration, Fluid-Rate and Fluid-Period Budget, and Mass-Rate and Mass-Period Budget.

To open a chart, right-click in an empty part of the FEFLOW workspace, select  Charts and then the chart that is to be displayed. For each obser­vation point a curve is plotted so that the hydraulic head, concentration and pressure changes at these locations can be monitored during and after the simulation.

 

Observation points with error bars and labels and hydraulic-head scat­ter plot.

To compare the field data for Hydraulic head to the calculated head results at observation-point locations, activate the Slice view first, switch to slice 2 and select Model Locations > Observation Points in the  Entities panel. Next, double-click on Process Variables > Fluid flow > Hydraulic head in the  Data panel. The deviations between measured and computed water levels are now shown as colored bars and as labels next to the observation-point locations. The error bars and labels always refer to the currently selected simulation time. Use the tools in the  Simulation toolbar to switch to different simulation steps to check how the deviations change. Green bars indicate deviations within the confidence interval, red bars indicate that the deviations exceed the confidence interval. The position of an error bar indicates whether the deviation is positive or negative.

In addition to displaying the water-level deviations in the active view, we open a scatter plot to compare measured and computed data. Open the context menu of the Hydraulic-head chart and select  Scatter plot. The plot always reflects the results at the currently selected simulation time, displayed in both the  Simulation toolbar and the view windows.

 Budget Analysis

We can use the  Rate-Budget panel to monitor the fluid and mass flows that enter and leave the model domain, or only specific areas.

For mass-transport simulations, the  Rate- and  Period-Budget panels contain two tabs, one for fluid and one for mass. To start the budget calculation for the entire model domain set the check mark for  Active in the respective tab for fluid and mass. After a brief computation, the  Rate-Budget panel shows the flow rate for each boundary condition type, for sources and sinks, storage capture and release and the imbalance term representing the remaining residual error. Flows that leave the model have a negative algebraic sign while flows that enter the model have a posi­tive algebraic sign.

Use the  Period-Budget panel to calculate the time-integrated budget the first 1000 days of the simulation: Switch to day 1000 via the drop-down list of stored time steps in the  Simulation toolbar and then click on the integral icon in the panel to start the calculation.

We now calculate the fluid budget for the border in the south instead of taking the entire model as budget domain. Go to the  Selections panel, open the context menu of Southern Border and select  Use Selection as Budget Domain. The domain of interest is automatically switched from  Domain to  Southern Border in both the  Rate and the  Period-Budget pan­els. Start the rate-budget calculation with  Active. The rate budget is now calculated for the selected nodes only. The budget shows that water is leav­ing the model domain through the border in the south.

 

Scaled budget spheres along the southern border.

Additionally, the in- and outgoing flows can be visualized as scaled spheres. Set the 3D view as active view and click on Southern Border in the   Selections panel.

Now, double-click on Fluid flow > Rate Budget in the  Data panel. Blue and green spheres of different sizes are plotted at nodes along the southern border where water leaves the model. We now increase the relative size of the spheres in order to make smaller spheres visible. Open the context menu of Fluid rate budget > Scaled Spheres in the  View Components panel and select  Properties. In the Size tab increase the relative size to  3.0 and click  Apply.

To check how much mass has left the model via the border in the south over time, we use the Mass-Period Budget chart. Open the chart via  View > Charts > Mass-Period Budget History and check the curve Southern Bor­der.

Subdomain-Boundary Budget

To evaluate how much mass enters the lower aquifer via the two contamina­tion sources, we apply the Subdomain Boundary Budget panels.

First, we define layer 5 as domain of interest for the budget calculation. In a subsequent step, we create a second element selection to apply as masking domain. This step is required as we would like to compute the mass flow through only those boundary parts of layer 5 which are in direct contact with the contamination sites.

Activate the Slice view and switch to Layer 5 in the  Entities panel. Make sure that the geometry type is set to  Select Elements in the  Selection toolbar and select the entire bottom layer with a click on  Select All. Right-click into the Slice view and select  Store Current Selection. Rename the selection to Lower Aquifer and finish with <Enter>. The stored selection now appears in the  Selections panel. To use this selection as domain of interest in the Subdomain Boundary Bud­get panels, right-click on Lower Aquifer and select  Use Selection as Boundary-Budget Domain. The selection is now available as domain of interest in both the  Subdomain Boundary Rate and Period Budget pan­els. In the  Subdomain Boundary Rate Budget panel, switch to the Mass tab and start the budget calculation with the  Active check box. The panel now displays the mass rate entering and leaving this subdomain at the cur­rently selected simulation time.

As we are only interested in the amount of mass entering the lower aquifer via the bottom sections of the two contamination sites, we now apply a sec­ond selection as masking domain. First, clear the current selection with a click on  Clear Selection. Now switch to Layer 4 in the  Entities panel and activate the Supermesh Polygons map for selection via a double-click on this entry in the  Maps panel. Then, reduce the Snap distance to  1 m in the  Snap-Distance toolbar and switch to the  Select by Map Polygon tool in the drop-down list in the  Selection toolbar. Move the mouse cursor over the model domain and create the two selections with a single click into the two contamination sites. Use the context menu of the Slice view to store the selection as  Contaminations. To apply this sec­ond selection as masking domain, click on Contaminations in the  Selections panel and then click on the green check-mark symbol in the Masking Domain section in the  Subdomain Boundary Rate Budget panel. The mass-flow calculation is now limited to these element faces which are shared by both selections.

The settings of the  Subdomain Boundary Period Budget panel follow those of the Rate panel. To invoke the time-integrated budget calculation, set the check mark in front of  Active, enter the starting time for the budget calculation and click on Integral Symbol. After a brief computation time, the mass enter­ing and leaving the domain of interest via the selected subdomain boundaries is displayed.

 

Subdomain Boundary Rate and Period Budget panels with results for the selected DOI and MD.

 Content Analysis

To check how much mass the model domain contains at different time steps we use the  Content panel. Switch to the tab Mass and activate the con­tent calculation for  Dissolved Species Mass. The currently contained amount of mass is now displayed in grams. Browse the time-step list in the  Simulation toolbar to check how the mass content changes with time.

Streamlines, Pathlines

To visualize the steady and transient flow fields we plot both streamlines and pathlines. Start with a 3D plot of streamlines that start at the two well loca­tions.

First, set the 3D view as active view and deactivate Geometry > Faces in the  View Components panel as otherwise the streamlines located below slice 1 would be concealed.

Now, click on Node Selection > Wells in the  Selections panel and dou­ble-click on Streamlines > Backward in the  Data panel. Start the plot by checking  Traces in the  View Components panel. After a brief compu­tation the streamlines are shown in the 3D view.

To visualize the flow field in the vicinity of the wells we increase the radius for the streamline seeds around the wells. To change the radius and other streamline properties, open the context menu of Travel time, backward streamlines seeded@Wells in the  View Components panel and select  Properties. In the upcoming  Properties panel type 30 m as radius, hit <Enter> and click  Apply. Several streamlines are now plotted around the two wells. Figure below shows a 3D plot of stream­lines around the wells.

 

3D Streamlines around the wells.

To visualize the transient flow field with pathlines, go back to the  Data panel and double-click on Pathlines > Backward. To start the plot, repeat the same steps as previously described for the streamlines. Furthermore, select time step #66 in the  Simulation toolbar.

We also add Period Sections to visualize particle travel times. In the  View Components panel, uncheck  Traces and check  Travel time, backward pathlines seeded@Wells > Period Sections and then double-click on this entry to edit the period-sections settings in the  Properties panel. On the Iso tab, deactivate the  Automatic option, enter an interval of  365 d and confirm the changes with  Apply.

To plot each period section in a different color, open the  Properties panel of Travel time, backward pathlines seeded@Wells via its context menu in the  View Components panel. Right-click into the color bar on the left-hand side of the panel and select  Presets > Rainbow. Figure below shows the resulting plot.

 

Period sections.

Streamlines or pathlines can also start from polylines. To draw a polyline for streamline plotting, open the context menu of Streamlines > Forward and select  Draw seed line/points > Draw a 3D Line. Start an arbitrary line on the top slice of the model with a single click. Extend the line by adding points and finish with a double-click.

The line is now displayed in the active view and is shown as Domain Loca­tions > 3D Polyline #1 in the  Entities panel.

Now, click on 3D Polyline #1 in the  Entities panel and start the streamline plot with a double-click on Streamlines > Forward in the  Data panel. Fig­ure below shows an example for a streamline plot from a polyline.

 

Streamlines starting at a polyline.

Random-Walk Particle-Tracking (RWPT)

To illustrate RWPT select Backward Random-Walk Tracks in the  Data panel, for the same node locations as in the previous section.

Go to  Edit > Problem Settings > Field-Line Computation > Random-walk tracks and use the default, homogeneous dispersive parameters for molecular diffusion and the coefficients of dispersivity.

 

Defining RWPT parameters.

Note that dispersivity values are small. As opposed to standard advection-dispersion solution techniques, the RWPT does not suffer from numerical dis­persion effects and stability constraints. Thus, there is no need to artificially increase dispersion coefficients according to mesh size. In other words, RWPT can be solved with arbitrary dispersive coefficients, in preference close to their physical values, even if the mesh is very coarse.

In order for RWPT solutions to be consistent with advection-dispersion solu­tions, a sufficiently large number of input particles must be used. The greater the amount of used particles the more the RWPT and advection-dispersion solutions will be comparable. However, RWPT solutions can be very memory-demanding when many particles are used so it is recommended to (i) start with a relatively small amount of particles (e.g., 100), (ii) analyze the runtime and memory demand, and (iii) subsequently increase the number of used particles if possible. Most problems will require a minimum number of about 10,000 particles for RWPT solution to be able to explore all possible advec­tive-diffusive/dispersive paths and thus be consistent with advection-disper­sion solutions. Note that there is a control during the RWPT solution phase on memory usage to avoid memory overflow situations.

 

Backward RWPT solution seeded at the wells.

Export of Results

To export the mass distribution obtained at the end of the simulation browse to the last time step in the  Simulation toolbar and double-click on Mass concentration in the  Data panel. Open the context menu of Mass con­centration in the  View Components panel and select  Export Data > Current Time #116 7300 d > All Nodes. Select a file name and choose the ESRI Shape File 3D format (*.shp). The exported data can be loaded again as a map and assigned as initial mass distribution in subsequent simulations. To automatically add the exported map to the current model, confirm with  Yes in the dialog appearing after the map export.

Plots can be exported in the same way as data. To export the isolines plot open the context menu of Mass concentration > Isolines in the  View Components panel and select  Export Plot. Choose a file name and for­mat for the exported isolines and finish the export with  Save.

A further option to export simulation results is to take snapshots of the active view window. Click  Snapshot of the Active View in the  View tool­bar and choose a resolution enhancement factor for the exported snapshot. After clicking  OK, choose a name and file format for the snapshot.