Lesson 11 – Exercise: Modeling a Tank with Multiple Fluids
We will finish this Unit by doing a simple Exercise. This is very similar to the Example we worked on together earlier in this Unit, but this time you will attempt to build the model on your own. Admittedly, this is not a very interesting problem (as nothing is being transported). However, in order to use the Contaminant Transport Module (and work through the Examples and Exercises we will discuss in the remainder of the Course), it is critical that you are comfortable with creating and editing the Materials (i.e., editing the Species element and Reference Fluid element, and creating and editing Fluids and Solids). This Exercise provides a way for you to practice that.
Once again we will consider a large tank containing water. However, the tank is not completely filled. The top portion of the tank contains air. Suspended in the water is a fine-grained sand (that stays suspended in the water). A small quantity of two chemicals (named X and Y) is introduced into the tank. X partitions between water and the sand, but does not partition into air (it is not volatile). Y partitions into the air (it is volatile) but does not partition onto the sand.
The tank is assumed to be continuously and instantaneously mixed. This means that when we add the two chemicals they are instantaneously mixed throughout the tank. Moreover, we are assuming that the partitioning of the chemicals between water, air and the sand can be treated as equilibrium (instantaneous) reversible linear partitioning. That is, it is assumed that when the chemicals enter the tank, they are immediately partitioned between the water, air and the sand everywhere in the tank according to equilibrium partition coefficients.
Finally, we will assume that X and Y decay according to a first-order reaction.
Our goal is to compute the total mass of X and Y in the tank, and the concentration of X and Y in water, in air and on the sand. The concentration (and mass) of X and Y change with time due to decay.
The various input parameters describing this system are summarized below:
|Volume of Water in Tank
|Volume of Air in Tank
|Mass of Sand in Tank
|Initial Mass of X and Y
|Sand Partition Coefficient for X
|Sand Partition Coefficient for Y
|Air Partition Coefficient for X
|Air Partition Coefficient for Y
|Half-Life of X
|Half-Life of Y
|Density of Sand
To create this model, you should follow these steps:
- Edit the Species element to create 2 species (X and Y).
- Create Data elements for all of the inputs in the table above. Note that partition coefficients and the initial mass should be defined as vectors of species.
- Return to the Species element and add the half-lives for X and Y.
- Create the Solid Sand and assign partition coefficients (and density).
- Create the Fluid Air and assign the partition coefficients.
- Create the Cell representing the tank and define the Media and Initial Inventory appropriately. For reasons we will explain below, add Sand before you add Air to the Cell.
- Run the model. You can keep the Duration (100 days) and Timestep (1 day) unchanged.
Stop now and try to build and run the model.
If, and only if, you get stuck, open and look at the worked out Exercise (ExerciseCT3_Materials.gsm in the “Exercises” subfolder) to help you finish the model.
Let’s walk through the model now.
Note that the first thing you should have done was edit the Species element and create the two species. You needed to do this first because by doing so, you populated the Species array label set. This was necessary in order to define any inputs that were vectors of species.
After doing so, you should have created all of the input Data elements. Generally, you would want to put these in a separate Container (e.g., named Inputs):
After doing so, you should have 1) gone back to the Species element and added the half-life input to the two species, and 2) created Air and Sand.
Air should look like this:
Note: You will note that the Reference Diffusivity here is 1E-09 m2/s. This is the default value when you create a new Fluid. This value is actually appropriate for water, but not for air (for air, it is about four orders of magnitude higher). However, since we are not simulating diffusion in this example, there is no reason to change it (i.e., it is not used in the model).
Sand should look like this:
Your Cell pathway should look like this:
The following points should be noted:
- It is important that the Media appear in the exact order you see here. Why? It is because Sand is specified as being suspended (the S box is marked). When this is done, GoldSim assumes that the Solid is suspended in the first Fluid directly above it. If you entered Air as the second Medium and Sand as the third, the Sand would be assumed to be suspended in the Air, not the Water.
- The F and H boxes should be checked for the three Media in order to save the concentration results. Final Values and Time History should be checked at the bottom of the dialog in order to save the mass results.
- The Initial Inventory should be specified.
If you run the model and plot the mass it should look like this:
Because X has a shorter half-life than Y it decays faster.
The concentration in Sand should look like this:
Because Y does not partition onto the Sand, the concentration in Sand is zero.
The concentration is Air should look like this:
Because X does not partition into Air, the concentration in Air is zero.