The issue of nuclear waste is one of the most commonly raised objections to nuclear energy, and one that many of us who were formerly opposed to nuclear energy were troubled with. It is an area where public perception is widely separated from the reality.
A lot of materials we deal with, and dispose of as waste, in our industrialised civilisation are hazardous, including lead, mercury, arsenic, cadmium, chromium, chlorine, hydrofluoric acid, cyanide, asbestos, silica, PCBs, dioxins, many other carcinogens, clinical wastes and various pathogens. Like nuclear waste they must be managed carefully to avoid danger to humans and other living creatures. Not all wastes are treated as carefully as those from nuclear energy and some do cause harm. (Abandoned medical nuclear material has also caused harm.) Also unlike nuclear, most other wastes remain dangerous forever, whereas nuclear wastes become exponentially less hazardous over time.
Nuclear energy produces very small quantities of waste, especially the most hazardous: spent nuclear fuel.
Wastes are classified as high level, medium (or intermediate) level, and low level, according to how radioactive they are. Low and intermediate level wastes include items such as radiation workers' used protective clothing, and building materials from decommissioned power stations, which have slighly higher than background radiation levels. The most hazardous - high level - includes spent nuclear fuel.
Conventional nuclear reactors use solid fuel, made up of pellets of uranium oxide (or sometimes MOX: mixed uranium and plutonium oxides) clad in zirconium in long tubes, and made into bundles. When they are fresh and unused they have very low radioactivity and can be handled easily, but once in a working reactor their fissile isotopes, such as uranium 235, get transmuted into many other isotopes, many of which have very short half lives and are thus very radioactive. Some of these "fission products" are good at absorbing the neutrons which are needed to keep the chain reaction going.
Over the years in a reactor the proportion of such neutron-absorbing fission products builds up, and the proportion of 235-U in the fuel, which started out enriched to 3–5%, decreases, until it gets to a point where the fuel is no longer productive. At this point it is removed. In light water reactors such as PWRs and BWRs the reactor is shut down for refuelling outages; this typically happens every 18 months or so, although only a proportion of the reactor's total fuel is replaced at each stop. In other designs such as CANDU reactors and the British AGRs refuelling can be done while the reactor is still running.
When a reactor is shut down, the fuel still produces heat at around 7% of the thermal power the reactor had while it was running. In an hour this heat production drops to 1.5%, and in a week it drops to 0.2%. For a reactor which produces 3 GW (3,000 MW) of thermal power (which would generate about 1 GW of electrical power) its heat output would have dropped to about 60 megawatts one week after shutdown. (That's still about as much as some Small Modular Reactors are designed to give at full power.)
When a fuel assembly is removed from a rector it is extremely hot, both radioactively and thermally, due to the heat produced by highly radioactive fission products (i.e. ones with short half lives). This fuel is immediately transferred to a pool (also known as a pond) which cools the fuel and shields its radioactivity from its surroundings (including people). It usually remains in the pool for between 2 and 10 years.
In some countries spent nuclear fuel is reprocessed to recover unburned uranium, and plutonium, which are used to make new Mixed Oxide (MOX) fuel. This leaves a relatively small amount of radioactive material as waste to be disposed of.
This video describes the process:
After cooling the spent fuel is moved to interim storage. This can be another pool, or "dry-cask" storage, where it can be stored safely for decades. At this point, air cooling is enough to keep the spent fuel from overheating, and it poses no danger to people near it.
Various options have been proposed for final disposal of spent nuclear fuel and other high level nuclear wastes. The mainstream option is burial in deep geological repositories, but deep boreholes have been proposed as an alternative. A different approach is to "burn up" highly radioactive isotopes by transmutation in fast neutron reactors, which produce much smaller quantities of waste which has a much shorter lifetime: of the order of decades rather than centuries.
This type of repository consists of an underground mine into which waste to be disposed of (nuclear or otherwise) is packed. The mine may be excavated for the purpose of constructing the repository or may be re-purposed from a disused existing mine.
The waste is held in suitable containers which are surrounded by material such as Bentonite clay, which strongly binds to any radioactive material which might escape the container. The mine is divided into many passages or caverns and when one is filled it is sealed shut.
The scientific consensus is that deep geological repositories are a safe and effective approach to permanently disposing of spent nuclear fuel and high-level radioactive waste.
Deep geological repositories are an accepted method of long-term disposal of waste containing arsenic, cyanide, mercury, and other toxic chemicals.
There are currently no long term disposal facilities for civilian high level nuclear waste (although there is a repository for military nuclear waste in the USA and two repositories for low- and medium-level waste in Germany). This is largely for political rather than technological reasons, including opposition from many of the same groups who oppose nuclear energy in part because they object to the lack of long term waste disposal facilities.
A deep geological repository for spent nuclear fuel is currently under construction at Onkalo in Finland, and others are at various stages of planning in Sweden, the UK and elswehere.
The Finnish Radiation Safety Authority (STUK) assessed several safety evaluations during the preparations for the Onkalo repository. The the worst-case scenario from the externally reviewed Posiva 2009 Biosphere Assessment Report requires:
The resulting maximum exposure of 0.00018 milli-sieverts per year (much less if any one of the above requirements aren’t met) also requires that the copper canisters which house the spent fuel effectively vanish after 1,000 years, while the bentonite clay barrier (which, alone, is a very effective catcher of radioactive particles) must also disappear somewhere, and the groundwater must move towards the surface. Note that even if the canisters begin to leak immediately, the maximum exposure occurs only after some 10,000 years as it will take time for the radioactive materials to migrate to the surface. After AD 12,000, doses will fall steadily.
Even allowing for reasonable scepticism about assessments made by the company responsible for building the repository, it seems that safety margins are nevertheless considerable. The Finnish Radiation Safety Authority (STUK) agreed, and gave Posiva a permit to proceed with construction in 2015.
Note that this worst-case scenario already accounts for the most common arguments against deep geological repositories for nuclear waste: that the canisters might fail, that surrounding bentonite clay might erode, and that groundwater movement toward the surface might be faster than expected.
Deep borehole disposal proposes disposing of spent nuclear fuel in extremely deep boreholes (as much as 5Km underground), relying primarily on the thickness of the natural geological barrier to safely isolate the waste from the biosphere for long enough that it would not pose a threat to living beings.
Wikipedia's article has more information on this approach.
Although "spent" nuclear fuel can no longer be used productively in the type of reactor it has been removed from, it still contains fissionable Uranium-235 and Plutonium isotopes, and various other radioactive isotopes which emit energy as they decay. These can be used in fast neutron reactors to produce more energy. The fast reactor still produces its own spent fuel waste but it is smaller in quantity and shorter-lived in activity.
This approach has not been used to date because fast reactors are significantly more expensive to build than regular (so called "thermal" or "thermal neutron") reactors, and the cost of Uranium fuel has been so low that it has not justified building fast breeder reactors to "close the fuel cycle" by breeding fuel from waste, on economic grounds.
The UK has a stockpile of over 100 tonnes of reactor grade Plutonium which the British government has yet to make a decision on what to do with. A consortium of General-Electric (GE) and Hitachi has proposed using its PRISM reactor – a design based on the successful US prototype EBR-II – to burn up this fuel, producing a modest 600MW of electricity over the following 55 years. The plant could later be used to recycle fuel from other reactors.