RBMK reactor 4 at the Chernobyl Nuclear Power Plant was due to temporarily close for routine maintenance on April 25 1986. The personnel decided this would be the perfect opportunity to run a particular test on this reactor. This test was to ensure that during a shutdown, enough electrical power would be available to run the emergency equipment and the water cooling supply until the diesel power came on. Here is the sequence of events on April 25 and 26 which ended in the disaster.
The test started in the morning of April 25. Part of the test was to shutdown the emergency core cooling system (ECCS) so it wouldn't interrupt to the test later on. This shutdown of the ECCS was not a cause of the accident, although, had it not been shut down the severity of the accident may have been reduced. With this shutdown the reactor was carried on at half the power. At about 23.00h on April 25 the power was reduced further. The reason it was so late on in the day was because the grid controller had requested the reactor operator to keep delivering electricity throughout the working hours causing a delay of the test.

Once the reduction of power had recommenced the reactor should have been stabilised at 1000MW before it was shutdown, but an operational error made the power drop to about 30MW where the positive void coefficient became a problem (this is additional steam in the cooling channels) . The operators did their best to redeem the problem by freeing the control rods manually, this way they managed to stabilise the reactor at 200MW.

Shorly after that, the coolant flow increased and the steam pressure dropped requiring the operators to remove almost all the rods, making the reactor very unstable. There is a minimum requirement of 20 rods that need to be inserted in the reactor at any time. There were probably only about 6 left after the operators had finished removing them but the automatic rods in the reactor increase this number towards 20. The operators had to maintain the steam pressure, they managed to do this by reducing the flow of feedwater. The cooling of the reactor became less and less because the pumps powered by turbine were slowing down as the turbine was slowing down. This meant the positive void coefficient occurred and the operators were now unable to control the power surge.
The temperature increased rapidly causing part of the fuel to rupture. This fuel then got into the water and fuel particles started reacting with the water causing a steam explosion, this then destroyed the core of the reactor and 2 minutes later a second explosion due to expansion of fuel vapour occurred causing more destruction to the reactor. These 2 explosions resulted in the pile cap lifting up allowing air to enter the reactor and to react with the graphite moderator blocks producing carbon monoxide (CO). CO is a very flammable gas and ignited easily causing a fire in the reactor.
About 8 of the 140 tonnes of fuel, containing plutonium and other highly radioactive fission products, were released from the reactor along with the graphite moderator which is was also highly radioactive. Along with this vapours from caesium and iodine were released with the explosion and the fire which burnt long after.
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Pictures of reactors are from Chernobyl - The accident and progress since 1986 website.