Lesson 8 – Exercise: Boundary Conditions for an Aquifer Element
In this Lesson we will work through a simple Exercise to use the boundary condition options we discussed in the previous Lesson.
This example is shown schematically below:
Waste material is placed in a trench at the ground surface a small distance above the water table. The trench is 100 m long. A single contaminant (X) is spread out along the entire length of the trench. It is assumed that this contaminant trickles downward and eventually reaches the water table, where it enters a sandy aquifer (at a constant rate). In this simple model, we will not simulate the vertical transport downward; instead we will simply assume mass enters the water table at a fixed rate over the length of the trench.
The contaminant plume subsequently flows along the water table. The contaminant is not sorbed onto the sand. The entire plume eventually discharges to a stream and is quickly mixed across the width and depth of the stream. For the purpose of this simple Exercise, we will assume that the flow rate through the aquifer and in the stream is constant. Our objective is to predict the concentration of the contaminants just downgradient of where the groundwater plume discharges into the stream (where the stream is assumed to be well-mixed).
The various input parameters describing this system are summarized below:
|Rate at which X enters groundwater||10 g/day|
|Dispersivity Fraction (fraction of length)||10%|
|Sand Saturated Hydraulic Conductivity||5E-4 m/s|
|Sand Density||1600 kg/m3|
|Distance to Stream||200 m|
|Hydraulic Gradient in Aquifer||1%|
|Plume Thickness||10 m|
|Trench Length||100 m|
|Trench (and Plume) Width||5 m|
|Stream Flow Rate||300,000 m3/day|
|Stream Reach Volume downstream of plume||75 m3|
To create this model, you should start with a new model and follow these steps:
- Edit the Species element and make sure there is a single species (X).
- Create Data elements for the inputs in the table.
- Add a Solid called Sand and define the density and porosity.
- Create a Cell representing the stream and assign it the reach volume in the table. This simply represents the volume of water in the reach downstream of where the groundwater plume discharges (and the mass becomes well-mixed).
- Create a Cell representing the Sink (assign it a volume of 1 m3).
- Create an Aquifer element and define all of its properties as specified in the table. The Length is the distance to the stream. Define the Area as the plume thickness multiplied by the trench width (we will discuss this assumption below). The Dispersivity should be the distance to the stream multiplied by the dispersivity fraction. You can leave it at the default value of using 10 Cells.
- Define the appropriate Source Term Length.
- Since we are discharging into a low concentration stream, check the box to Enable dispersive and diffusive outfluxes to downstream pathway(s).
- Create an advective mass flux link from the Aquifer element to the stream. The flow rate can be computed as the pathway Area multiplied by the hydraulic conductivity multiplied by the gradient.
- Create an advective mass flux link from the stream to the sink (using the stream flow rate).
- Finally, in the Time Settings, set the Duration 400 days, and the timestep to 1 day.
Stop now and try to build and run the model.
Once you are done with your model, save it to the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop (call it ExerciseCT13.gsm). If, and only if, you get stuck, open and look at the worked out Exercise (ExerciseCT13_Aquifer_Source_Length.gsm in the “Exercises” subfolder) to help you finish the model.
Let’s walk through the model now.
If you organized all of your inputs in one Container and the pathways in another, the pathways Container should look similar to this:
Let’s look at the Aquifer element (named Saturated_Zone here):
Note that you should have specified a Source Term Length, defined an Input Rate, and checked the box to Enable dispersive and diffusive outfluxes to downstream pathway(s).
As we did in the previous Exercise (for the reasons discussed there), we are assuming that the vertical and transverse spread of the plume along the flow path is negligible (i.e., the Area of the pathway remains constant along its length). We’ve assumed a (somewhat arbitrary) plume area controlled by an assumed mixing depth for the plume and the width of the overlying trench.
Note that the plume flow rate (the flow rate leaving the Aquifer and entering the stream Cell) is computed as follows:
The stream Cell is defined in exactly the same was as it was in the previous Exercise (by assuming a small volume that turns over rapidly).
If we run this model and plot the concentration in the stream it should look like this:
How much did the specification of a (non-zero) Source Term Length impact the breakthrough? You can see this by simply clearing the Source Term Length field.
The plot below shows the concentration in the stream with and without the Source Term Length specified:
As you would expect, when the mass enters over 100 m of the pathway (as opposed to only at the beginning), it reaches the stream faster.