Lesson 12 – Advanced Source Concepts
In this Lesson we will discuss several advanced Source concepts.
Before discussing several advanced features that we have not yet addressed, it is first important to reiterate a point we made in an earlier Lesson. In this Unit we have used Examples and Exercises in which our representation of the mass transport processes has been quite simple. While we did consider processes such as solubility and partitioning, we almost always used only a single Associated Cell (in one case, we used two). But it is important to understand that your representation of the package interior can be quite complex (using many Cell pathways).
As an example of this, you should recall that in Unit 8, Lesson 8 we described a system involving a cylindrical waste package disposed of in a borehole:
From the top of the borehole looking down, the system looked like this:
We represented this system using a series of Cells. One Cell represented the cylinder (containing contaminants) and others represented nested cylinders of bentonite and fractured rock:
We simulated diffusion outward from the cylinder. In most situations where such a disposal method would be used (e.g., a radioactive waste repository) there would be hundreds or thousands of such packages. The cylinder itself would need to fail before releasing any mass (and the mass would likely be bound in a matrix). This would obviously be straightforward to model using a Source element. We would specify multiple packages with an Inventory bound in a matrix. The Cells representing the cylinder, bentonite and surrounding fractured rock would all be Associated Cells inside the Source container. Only the cylinder Cell would be defined as an Inventory Cell. The mined drift would represent the first pathway outside of the Source (the Associated Cell representing the fractured rock would release mass into this pathway).
One other point is worth noting here regarding defining Associated Cells for Sources. Mass cannot move from one failed package in a Source into another one. In the two Exercises with multiple vaults that we worked on earlier in this Unit this was not an issue as the flow was vertical and the mass leaving one failed vault did not interact with other vaults. And in many other situations, this assumption will be appropriate (e.g., for the cylindrical waste packages discussed above, mass being transported in the mined drift – which presumably has a high transmissivity – would be unlikely to flow back into the boreholes).
But what if multiple vaults that we wanted to represent as packages within a Source were stacked on top of each other so that the mass leaving one vault (i.e., package) flowed into the one below it? Representing such a system must be done with great care. Recall how the Associated Cells are defined (representing a single package that is scaled based on the number of failed packages). Given this, how would you define the flow logic for one package to flow into another? Among other things, to do this, you would need to track where the failed package was in the stack (e.g., top or bottom, or in between). But, unfortunately, a Source knows nothing about the location of the various packages.
As a result, to represent such a system, you would need to take an approach that was similar to one of these:
- Assume that any mass leaving a package flows only in between the other packages (and never flows into them). This could be appropriate if the transmissivity of the “gaps” between packages was very high.
- Treat each layer as a separate Source. Any mass flowing out of the top layer flows into a normal Cell (not an Associated Cell) representing the region in between the two layers, and then from that Cell into the Associated Cells representing the failed packages in the bottom layer.
Before we finish this Unit, it is worthwhile to discuss two advanced features of Sources that we have not yet explored.
We noted at the beginning of the Unit that for each individual package, zero, one or two layers of containment (barriers) can be explicitly considered to exist. So far, we have considered only a single barrier (the Outer Barrier). However, for some types of systems, you may want to specify two barriers. For example, for a package containing used (nuclear) fuel rods, we might need to specify two barriers (the waste package itself and the cladding surrounding the fuel rods).
To understand the implications of this, let’s look at a simple example. Open ExampleCT35_Two_Barriers.gsm from the “Examples” subfolder of the “Contaminant Transport Course” folder you should have downloaded and unzipped to your Desktop.
In this model, we are simulating 10,000 buried drums. Each drum contains species X and Y (neither of which decay). We will just look at this exposure process: once the mass is exposed, it remains inside the drums; there is no mass transport out of the drums. However, we will assume that there are two barriers: the drum wall itself, and an interior liner.
Open up the Drums Source element:
You can see that the Number of Packages is defined by a Data element (that is equal to 10,000).
There are two barriers defined. If you press Outer Barrier… to see how it is defined, you will note that is simply a Weibull distribution that starts immediately with a Slope of 2 and a Mean lifetime of 3 years. Press Inner Barrier… to see how this is defined:
In this case, we have specified a Weibull distribution that starts when the Outer Barrier fails with a Slope of 2 and a Mean lifetime of 2 years.
Note that this dialog is similar to the Outer Barrier Failure dialog with one key difference. Rather than defining an Effective Time, you specify that either 1) failure starts when the outer barrier fails (which we have done here); or 2) failure starts at a specified Start Time.
A key point here is that whereas the outer barrier failure distribution is applied to a specified number of packages which are present in the Source, the inner barrier failure distribution is applied to each individual package. That is, it represents the failure distribution of the inner barrier(s) within a given package. One very important implication is that unlike the outer barrier, failure of the inner barrier is not discretized. That is, you do not specify the number of inner containers within each package. Hence, if your conceptual model is that a single inner container exists in each package (e.g., a liner within a drum), the failure distribution represents the fraction of the single inner container that has failed as a function of time. If your conceptual model is that multiple inner containers exist in each package (e.g., multiple drums within a large concrete container), the failure distribution represents the fraction of the inner containers that have failed as a function of time.
Close the Inner Barrier Failure dialog and open the Inventories dialog. We have defined two Inventories. Recall that when defining inventories, it is necessary to specify a Location. The Location is defined relative to the barriers. As such, it is a drop-list whose options depend on how many barriers you have specified. If you have specified a double barrier (as we have done), there are two options available: “Outer” and “Inner”. “Inner” means that the mass is inside both barriers. “Outer” means that the mass is inside the “Outer” barrier but outside the “Inner” barrier (i.e., it is located between the barriers).
You will note that we have defined two Inventories (neither of which is bound in a matrix). The first (which contains only X) is located inside the “Outer” barrier but outside the “Inner” barrier (and as such is unaffected by the inner barrier failure distribution). The second (which contains only Y) is located inside the “Inner” barrier (and as such is affected by both the inner and outer barrier failure distributions).
Run the model and plot the Exposure Rates (this model was run for 100 realizations, and we are looking at the mean):
As can be seen, the exposure rate for X (which is affected only by the outer barrier failure distribution) is simply the Weibull distribution. The exposure rate for Y (which is affected by both the inner and outer barrier failure distributions) is delayed and dispersed due to the presence of the inner barrier.
Before closing this model, return to Edit Mode and open the Drums Source element again. In the middle of the dialog, you will notice a field named # Packages failed by events:
What is this input? In addition to failing packages by defining failure distributions, you can also fail packages instantaneously via discrete events (e.g., an earthquake or perhaps intentional human intrusion). The input field accepts discrete change signals (produced, for example, by a Discrete Change element). Such a signal includes a value. When a discrete change signal is received by the Source, the specified number of packages (the discrete change signal’s value) is instantaneously disrupted (both outer and inner barriers are failed). Discrete change signals were discussed in Unit 13, Lesson 6 of the Basic Course.