COMSOL NEWS 2010
Figure 1. Schematic illustration of a final repository. Spent nuclear fuel bundles are placed within a copper canister that can measure 8 meters in height. This is then surrounded by the bentonite buff er material, along with filler material and placed in the final repository, 500 meters under the Earth’s surface. Copyright© SKB. Illustrator: Jan M Rojmar — Grafiska Illustrationer.
Nuclear energy has been touted as being one possible source of alternative clean energy to carbon-based energy, where the gains in the reduction of greenhouse gases from burning fossil fuel is evident. Yet, while producing this energy, the nuclear industry is also committed to safe waste management, and is now reaping the benefits from half a century of advanced research and billions of Euros in investment in robust geological repositories.
The scientific consensus is that the disposal of spent nuclear fuel rods in deep geological structures is an acceptable and safe method for long-term management of them. Many sites throughout the world, which have remained geologically stable for millions of years and are likely to do so in the future, are being considered as repositories.
“As time goes on, more research groups and institutions will turn to modeling to adequately simulate the behaviour of their nuclear waste and repositories.”
Sweden and Finland are the two countries that have progressed furthest with respect to developing such repositories. And the work is indeed immense. Nuclear power companies in Sweden jointly established the Swedish Nuclear Fuel and Waste Management Company (SKB) in the 1970s and a fund to finance it in 1982. Companies that use radioactive fuel that will someday be placed in their repositories pay an annual fee to this fund, which, in 2008, was almost 3 billion Swedish kronor (300 MEUR). At the beginning of 2010,the fund was worth approximately SEK 42 billion. Finland through her equivalent, Posiva Oy, assumes that the total cost of their repositories and maintenance will also be in the scale of billions of Euros.
The repositories consist of, among others, two important containment barriers, each contributing to the required longterm isolation of the nuclear waste from the biosphere (see Figure 1). One is the containers or canisters that protect the waste and prevent any water reaching it for hundreds of thousands of years. Made of copper and specially welded and treated, a lot of research has been made on the choice of material and design. Another is the bentonite buffer material that protects the canisters, preventing water from fl owing through to them, as well as mitigating any deep-earth movement, and binding any radionuclides that eventually escape from the canisters.
Bentonite has long been used in the drilling and mining engineering industries due to its unique rheological properties. It is a naturally occurring type of clay that expands when coming into contact with water, but on the other hand, allows almost no water fl ow through it at all. Expanding bentonite fills the space surrounding the final disposal canisters; cracks that already exist and cracks that may open up in the future. It also behaves somewhat like modeling clay by buckling when necessary, and recovering its shape because of its elasticity. In the event of a possible canister leak, it also retards the radioactive substances from coming into contact with the rock through its sizable resistance to radionuclide diffusion.
A number of research groups throughout the world are studying the effectiveness of bentonite as a barrier of containment. These activities consist of work with mathematical models, since testing is extremely difficult due to the the timescales involved. Both SKB and its Finnish equivalent, Posiva Oy, have collaborated with several research groups in Sweden and Finland to model and study the repositories. These include a group led by Docent Markus Olin at VTT Technical Research Centre of Finland (VTT), and a group led by Professor Ivars Neretnieks and Dr. Luis Moreno at the Division of Chemical Engineering at the Royal Institute of Technology, Sweden (KTH).
Markus Olin and his colleagues at VTT have a number of different phenomena that they are looking at. If we were to consider the application according to time-scales, three significant stages occur. They are investigating what happens during the excavation of the tunnels and placement of the canisters (days to months), the saturation of bentonite by water (months to hundreds of years), and the long-term safety where breaches can occur such that the surrounding system will have to retard radioactive material reaching the biosphere (many thousands of years). They are also considering a number of different but interacting physical phenomena that influence the repositories; hydrological, thermal, mechanical and chemical phenomena.
Figure 2. Modeling domains. Radionuclides seep from a defect in the canister and are transported by diffusion through the bentonite, rock fractures, the tunnel and the excavation damaged zone (EDZ).
Veli-Matti Pulkkanen at VTT has produced 3D models over the whole bentonite and surrounding rock including fractures that cut through it where a hypothetical leak of radionuclides from a canister is simulated. When the tunnels and holes are excavated, a thin layer of bedrock surrounding them may be damaged (known as the excavation damaged zone — EDZ), and it is easier for water to fl ow through the small pores and fractures that have resulted from this excavation. It may be even easier for fluid to fl ow in the EDZ than through the original tunnel, which has been backfilled with bedrock (see Figure 2).
Figure 3. The concentration profile in the bentonite, backfill, rock fracture, EDZ, and tunnel after 20, 200 and 2,000 years.
COMSOL Multiphysics is particularly useful in his modeling as he is able to define the source of radionuclide leaking from the canister using a simple 1D initial boundary-value problem, and couple this to the natural 3D geometry. The same technique is also used to define the flow physics in 2D for thin fractures and couple this to 3D flow. This ability to couple physics defined in different dimensions comes as an automatic interface in the software and requires nothing more than specifying the relevant material properties — the coupling between the different geometries is done automatically and the meshing is simple to manipulate. His results indicate that the bentonite layer is an important hindrance to the transport of leaking radionuclides (see Figure 3).
On another level, Markus Olin at VTT has simulated the chemical stability of bentonite using the Reaction Engineering Module. The susceptibility of bentonite to dissolve in relatively low-saline water, which could reach the repositories after postglacial periods, is far greater if its cation makeup is dominated by sodium ions as opposed to calcium ions. Even if the bentonite is in contact with saline water, the exchange of calcium ions with sodium ions can also occur.
Figure 4. Chemical reactions and equations involved in describing the transfer of sodium and calcium ions between the bentonite and water.
He was able to define and simultaneously solve three chemical equations and their corresponding non-linear mass-action laws, three mass balance equations, two charge balance equations and an activity coefficient model (see Figure 4). From this simplest possible chemical model of bentonite, he was able to determine the equivalents of the two ions in the bentonite as a function of the equivalent of calcium ions in water, and show that the relationship is nonlinear — a property that must be considered when considering transport models of the system (see Figure 5). Olin hopes to later incorporate his reaction model into a model of transport between a fracture and the bentonite by also the structural behaviour of saturated and swelling bentonite.
Figure 5. The equivalent ratio of sodium ions (green line) and calcium ions (blue line) in bentonite in relationship to the equivalent ratio of calcium ions in the external water. When the water is low in calcium ion concentation, then the amount of calcium in the bentonite is also low, leading to the increased risk of bentonite dissolution as colloids.
The group led by Ivars Neretnieks is investigating how the structural properties of bentonite affect its dissolution. When bentonite in contact with a water stream dissolves in this stream, it reduces its material volume. Yet, because bentonite expands in the presence of water, it will also continue to replenish its volume, as other parts come in contact with the water. It therefore grows towards the region of dissolution and promotes its own dissolution. Being able to couple these mechanisms has required the flexibility of COMSOL Multiphysics.
As time goes on, more research groups and institutions will turn to modeling to adequately simulate the behaviour of their nuclear waste and repositories. The time-scales associated with the behaviour make experiments and testing rather limited, so that highly accurate estimations of the future consequences are required. The more physics you can incorporate into a model, the more accurate it will become. And by keeping the models equationbased, just as COMSOL Multiphysics does, and not hidden in the intricacies of code, then this will allow future generations to build on the simulations that are being conducted today.
The research group at VTT consists of Anniina Seppälä, Veli-Matti Pulkkanen and Markus Olin.