Lesson 7 – Modeling Isotopes

When modeling radionuclides, you will almost always need to represent multiple isotopes for various chemical elements (e.g., Uranium 235 and Uranium 238). Care must be taken when entering input data for isotopes, and this will be discussed in this Lesson.

When you define your species using the Species element, there is a checkbox (labeled I in the main Species dialog and Isotope in the dialog for a particular species) that indicates whether the species is an isotope.  If you are using the ICRP database to define your species (which is strongly recommended), this input cannot be edited.

Note that the dialog for such a species looks like this:

What should specifically be noted here is that GoldSim lists both the Species ID and the Element for species that are isotopes.

You can also define species manually and specify that they are isotopes.  For example, instead of using the ICRP database, you could manually define a species named Pb210:

In this case, GoldSim does not know anything about the species named “Pb210” (since we are not using the ICRP database here).  So how does it know that it is an isotope of Pb?  The rule GoldSim uses is simple: if you define a manually-created species as an isotope, GoldSim defines the Element as the character(s) to the left of the first number in the Species ID.

The following points are worth noting:

• It is strongly recommended that you don’t do this (i.e., you should use the built-in ICRP species to model isotopes instead of manually defining them).  However, some models may have been developed before the ICRP functionality was added to GoldSim (2012), and these may still be using manually-defined radionuclides.
• You can always tell if a species is a built-in ICRP species or a manually-created species.  ICRP species have a light green background (instead of a white background) in the main Species dialog and the Species ID has a bright green background in the dialog for that specific species.
• GoldSim will not allow you to create a species if the ICRP species of the same name is already marked as being included (i.e., modeled).

Now that we see how species can be defined as isotopes, what are the implications of this? As discussed in detail in Unit 5, Lesson 5, there are two sets of Array Labels that are automatically added when the Contaminant Transport Module is activated (they would not be present if you deactivate the module).  These are named Elements and Species. The items in the Species Array Label set are the names of the species defined in the Species element.  The Elements array label set is created based on the names of the chemical elements that are assigned to the species when you define their properties.  (If a species is not defined as an isotope, the chemical element name is the same as the species name.)  The size of the Elements Array Label set is always less than or equal to the size of the Species Array Label set.

So why do we have these two sets and how do we use them? The reason is that some inputs vary by species, while others vary by chemical element. That is, some phenomena apply to chemical elements but not to radionuclides, and vice versa. In particular, some of the inputs for a model need to be a vector of species (we’ve done this multiple times in previous Units).  That is, they need to be specified for each species (e.g., an initial amount of mass in a pathway).  But some of the inputs for a model need to be a vector of elements.  This is because for these inputs, all the isotopes of the same element have the same value, and hence the value needs to be specified by element, not by species.

The inputs that vary by element (rather than species) are all media properties (i.e., properties defined in Fluid and Solid elements).  In particular, for species that are isotopes, the following inputs vary by element (i.e., all isotopes of the same element have the same value):

• Solubilities (Fluids)
• Reference Diffusivities (Fluids)
• Partition Coefficients (Solids and Fluids)
• Available Porosities (Solids)

If you are modeling isotopes, GoldSim treats these four properties in a special way: isotopes of the same element are assumed to have equivalent properties.  If the properties are defined by element (the default for these four fields), this is straightforward (as isotopes of the same element are represented by a single entry). 

However, you can also define these properties by species (although in general this is not advised).  In this case, it is possible that they could be entered inconsistently (i.e., isotopes of the same element could be assigned different values).  If properties are defined by species, GoldSim forces the properties for isotopes of the same element to be equivalent.  In particular, all isotopes of the same element take on the properties of the first of the element's isotopes in the species array label set.  For example, if the species array label set included U234, U235, and U238 (in that order), all three species would use the properties assigned to U234, regardless of what was specified for the other two species. 

An important effect of defining multiple isotopes of the same element is related to how solubilities are computed.  In particular, when computing solubility constraints (in a Cell pathway), the solubility is "shared" by (split among) all of the isotopes.

Note: This "sharing" of the solubility between the isotopes  results in the governing equation becoming non-linear (and hence a bit more difficult to solve).