Lesson 9 – Exercise: Modeling Transport of Suspended Particulates
In this Lesson, we will work on an Exercise to become comfortable with simulating suspended Solids. To do this, we will simply build on a previous Exercise we completed in Unit 6, Lesson 9. You should have saved this to the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop, and named it ExerciseCT6.gsm. If for some reason you do not have that model, open ExerciseCT6_Boundary_Condition.gsm in the “Exercises” subfolder.
Recall that this model consists of two tanks containing Water and Sand (and the Sand is not suspended):
There are two species: X (which does not partition onto the Sand) and Y (which does partition onto the Sand). Water flowed through the entire system (with clean water entering from upstream) so that the volume in the tanks did not change. Mass was input at a constant rate at a rate equal to 5 g/day for each species.
In this Exercise, we are simply going to make the following changes:
- Add a new species (Z).
- Z is added to Tank1 at the same rate as the other two species.
- Add a new Material (named Clay), which is suspended in the water. The Clay flows through the entire system (it enters at a particular concentration of clay per unit volume of water, and that concentration stays constant throughout the system).
- Neither X nor Y partitions onto the Clay. Z, however, partitions onto the Clay and onto the Sand.
The new input parameters describing this system are summarized below:
|Suspended Clay Concentration in Water||0.025 kg/m3|
|Density of Clay||2000 kg/m3|
|Mass Input Rate for Z||5 g/day|
|Clay Partition Coefficient for Z||100 m3/kg|
|Sand Partition Coefficient for Z||10 m3/kg|
Conceptually, the new schematic for the model looks like this (note the suspended particulates):
To update this model, you should follow these steps:
- Save the model it as ExerciseCT9.gsm in the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop (so as not to overwrite ExerciseCT6).
- Add a third species (Z).
- Edit the existing Data elements for the Sand Partition Coefficients and Mass Input Rate and add the appropriate values for Z.
- Create Data elements for the new inputs in the table above (Clay Partition Coefficients, Suspended Clay Concentration, and Clay Density). Note that the Clay Partition Coefficients must be defined as a vector (and only has a non-zero value for Z).
- Create a Clay Solid and define its properties (Partition Coefficients and Density) appropriately.
- In Tank1, Tank2 and the Sink, add Clay, and mark it as suspended. The mass should be defined as the volume of water times the clay concentration.
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 ExerciseCT9.gsm). If, and only if, you get stuck, open and look at the worked out Exercise (ExerciseCT9_Suspended_Solids.gsm in the “Exercises” subfolder) to help you finish the model.
Let’s walk through the model now.
Tank1 should look like this:
Tank2 should look similar (without the Mass Input Rate).
The Sink should look like this:
The key point to notice here is that it must contain Clay (although the amount does not matter, and it does not necessarily need to be suspended). This is because, as pointed out in the previous Lesson, particulates are only advected into the downstream Cell if the Solid exists in that Cell.
Let’s run the model and look at the results. In particular, let’s plot the mass in the Sink. If you do that, the plot will look like this:
As an aside, when GoldSim plots vectors (as we are doing here), it chooses default styles (in this case solid red for the first item, dashed blue for the second item, and dotted green for the third). We don’t need to stick to these default styles. To illustrate how to do this, close this result, return to Edit Mode, and select Model|Array Labels… from the main menu. Double-click on Species:
Click on the Style for Z:
In this dialog, edit the Style drop-list to make this line solid (rather than dotted).
Close the three dialogs, rerun the model, and plot the mass in Sink again:
What we see clearly here is that the amount of mass of X that has been flushed to the Sink is greater than that of Z, which in turn is greater than that of Y. Y and Z both flush slower than X, because they are associated with the immobile Sand. Z flushes a bit faster than Y (but slower than X) since it is also associated with the mobile Clay.