Decay Heat & Power Density
History has shown the main cause of nuclear accidents is the inability to remove heat from the fuel after the nuclear chain reactions have been stopped. Heat piles up and temperatures rise until the fuel fails, releasing fission products and radiation. The major accidents have to do with what happens after the reactor has shut down.
As the fissions take place, uranium atoms are splitting and making periodic-table soup. The uranium isotopes usually split into fragments, and the distribution of new isotopes resembles has two hills. Many of these isotopes are not stable and will eventually decay to more stable isotopes through various decay processes that also release energy. This is the decay heat, and it is an appreciable amount of energy that can do a lot of damage if not carefully dealt with. The problem is that it cannot be stopped even after the nuclear chain reaction has been shutdown. In most cases, the decay heat is about 6-8% of the reactor power after shutdown, and will slowly fall away over the next few hours and weeks according to a power law.
6% of operating power right after shutdown doesn't seem like a big deal. But 6% of a 3 GWth reactor is 180 MWth - or 3 Boeing 777s (6 GE-90-115B engines) worth of power, pumped into the core. After 80 hours, even 0.2% decay heat presents a sizeable challenge because that heat needs to be removed or temperatures will rise.
Almost all nuclear reactor designs in use today use active systems to remove the decay heat of a reactor after it has shut down. This usually involves keeping the coolant flowing with electrically powered pumps. Those pumps can be powered by local electical grid or from emergency diesel genstes. Unscheduled interuptions in that emergency power supply are typically national news.
The problem is that maintaining that cooling capability is a finicky thing with many ways to fail. Possible failure modes include coolant leakage, partial or total; clogging; pump failure; power interruptions if the grid connection goes down or emergency back-up generators stop working for whatever reason. Any of these things can happen by accident such as during external events like weather, flooding, or earthquakes. Operators could accidentally trigger some events. They can also be intentionally triggered through malicious actions.
In the below accident simulation, we assume the reactor manages to shut down but loses all coolant and forced cooling capability. It has to deal with all the decay heat using only conductive and radiative heat transfer to the surrounding earth or building structures. This is also known as Class A passive cooling as opposed to Class B passive cooling which relies on natural convection of a fluid or moving parts. The simulation is highly approximate and for illustrative purposes only.
The advantages of high surface area to power ratio become clear – you can keep the core at safe temperatures with simple passive cooling! Not obvious from the visual above, is that if we constrain the reactor to a power level that can be safely cooled during accidents, smaller cores can have higher power densities. This suggests that smaller cores can have cost advantages.
It also becomes clear that some reactor types are much better suited to handling decay heat than others. In particular, the below simulations show how water cooled reactors experience rapid temperature increases in loss of coolant accidents.