# Lesson 4 – Exercise: Simple Decay and Ingrowth

In order to become more comfortable with specifying decay rates and daughter products, in this Lesson we will work through a very simple Exercise.

We will model four different species (A, B, C and D).

These species decay in a “chain” as follows:

A => B => C + D

100 g of A is added to a tank with 10 m3 of water. The data describing the species is as follows:

Species Molecular Weight (g/mol) Half-life (days)
A 50 20 days
B 50 50 days
C 25 10 days
D 25 Does not decay

1. Edit the Species element and add the four species (with the appropriate Molecular Weights, Half-lives, Daughters and Stoichiometry (as determined from the reaction equation).
2. Create a Cell and assign it a volume of water of 10 m3.
3. Add an Initial Inventory to the Cell of 100 g of A (and 0 g of the other species). Make sure you specify that the Time History of the mass in the Cell is saved.
4. The Time Settings can remain unchanged (100 days, 1 day timestep).

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 ExerciseCT15.gsm). If, and only if, you get stuck, open and look at the worked out Exercise (ExerciseCT15_Decay.gsm in the “Exercises” subfolder) to help you finish the model.

Let’s walk through this very simple model now.

Note: As we have emphasized in previous Examples and Exercises, it is best practice to define all the input parameters (in this case, half-lives, molecular weights, water volume, initial inventory) as separate Data elements.  Because this model is so simple, this is not done below (these inputs are entered directly in the various dialogs).  However, you should not do this for real-world models!

The Species element should look like this:

Species A should look like this:

And Species B should look like this (note the Stoichiometry for the two daughters):

The Cell representing the tank should look like this:

If we run the model and plot the mass in the tank, the result looks like this:

We see A decaying, B and C ingrowing and decaying, and D ingrowing.

Note: Your chart will not look like this (the line styles will be different).  You can change the line styles for the items in the vector by selecting the Edit Properties button for the chart, and then pressing the Edit... button under Style in the list of Results.