# Lesson 6 – Exercise: Modeling Mass Transport in Two Flow-Through Tanks with Partitioning

In this Lesson, we will work on an Exercise to continue to become comfortable with simulating advective mass flux links. To do this, we will simply build on the previous Exercise. You should have saved this to the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop, and named it ExerciseCT4.gsm. If for some reason you do not have that model, open ExerciseCT4_Advection.gsm in the “Exercises” subfolder.

In this Exercise, we are simply going to make three changes:

• We will add a second species named Y;
• We will add a Solid named Sand that exists in each Tank; and
• We will add a partition coefficient for Y to Sand (X will not partition to Sand).

Although Y can partition onto the Sand, we will assume that the Sand is not transported out of the tanks.  The only contaminant mass (of Y) that is moved is mass that is dissolved in the Water.  Physically, we can imagine that the Sand is not suspended at all (it sits at the bottom of the tanks), but the Water is still well-mixed and in contact with the Sand so that it equilibrates instantaneously.  (Alternatively, we could assume that the Sand was indeed suspended, but a filter existed between the tanks so the suspended Sand could not be transported.) The key point is that we will not treat the Sand as if it is suspended in this model.

The new input parameters describing this system are summarized below:

Variable Value
Mass of Sand in each Tank 1 kg
Initial Mass of X and Y in first Tank 100 g
Density of Sand 1600 kg/m3
Sand Partition Coefficient for X 0 m3/kg
Sand Partition Coefficient for Y 5 m3/kg

To update this model, you should follow these steps:

1. Save the model it as ExerciseCT5.gsm in the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop (so as not to overwrite ExerciseCT4).
2. Edit the Species element to add a second species (Y).
3. Create Data elements for the inputs in the table above. Note that the initial mass and partition coefficients should be defined as vectors of species. Make sure you define the value for both items in these vectors.
4. Create (in the Material Container) a Solid named Sand and specify the partition coefficients.
5. Add Sand to the two tanks (there is no need to add it to the Sink).

Stop now and try to build 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 ExerciseCT5.gsm), as we will build upon this in a later Lesson. If, and only if, you get stuck, open and look at the worked out Exercise (ExerciseCT5_Advection_Partitioning.gsm in the “Exercises” subfolder) to help you finish the model.

Let’s walk through the model now.

These modifications to the model should have been straightforward, but let’s reiterate the key changes. First let’s look at the Sand:

The Partition Coefficients input should be linked to the Data element (a vector of Species) that you created.  Recall that in order to enter a link here, you need to press the Clear button first (since by default the values are locally defined).

Next, let’s look at Tank1:

The key point to note here is that the Sand is not marked as being suspended (the box is cleared). Tank2 should look identical (without the Initial Inventory).

Before we run the model, let’s edit the Time History Result element we created for the last Exercise.  If you double-click on it, it should look like this:

Recall that we are plotting X in the two tanks (as two separate Result items so they have different styles). Let’s change the Label for these to “X in Tank1” and “X in Tank2”.

Next, press the Add Result… button and browse to the [Y] item of Mass_in_Pathway output for Tank1:

Press OK and the Result Properties will now look like this:

Let’s make the following changes:

1. Change the Label to “Y in Tank1”.
2. Click on the line (under Style) to edit this.
3. Change the Line Color to red and the Line Style to a dashed line:

When you press OK the Result Properties will now look like this:

Now select the third item and press the Add Result… button. (By doing so, the item is added directly below.  Note, however, that if the item is not added where you wanted it, you can use the Move Up and Move Down buttons to change the order.)

Browse to the [Y] item of Mass_in_Pathway output for Tank2:

Press OK and the Result Properties will now look like this:

Let’s make the following changes:

1. Change the Label to “Y in Tank2”.
2. Click on the line (under Style) to edit this.
3. Change the Line Color to blue and the Line Style to a dashed line:

When you press OK the Result Properties will now look like this:

Press Close, run the model and double-click on the Result element:

What we see here illustrates a very important point about the impact of partitioning on the transport of contaminants.  We see that the species that does not partition to Sand (X) flushes out of each tank more rapidly than the species that does partition to Sand (Y). Partitioning slows the advective transport process, since the concentration being transported is reduced.

We can see this most clearly by looking at the Concentration_in_Water output of Tank1 (select the entire output so both species are plotted):

You will see how partitioning reduced the initial concentration of Y in the tank.  However, because X flushes so much faster, eventually the concentration of Y exceeds X.

Save your model to the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop (call it ExerciseCT5.gsm), as we will build upon this in a later Lesson.

In the next Lesson, we will revisit the equations that GoldSim solved to produce these results.