Gone Fission

This week, Marika and I watched HBO's Chernobyl series. In spite of the depressing topic, and the at times gruesome imagery, we found it extremely interesting. I was (of course) most drawn to the explanation of how the reactor operated, and then failed. I've never studied nuclear physics in detail, but I had a rudimentary understanding of how reactors work:

• Uranium atoms radiate particles which can hit other uranium and cause them to split
• When uranium splits, it releases energy, which heats the fuel
• The fuel is cooled by water, which drives a turbine to generate power
• Control rods block the radiated particles, slowing down the reaction

The final episode of the series shows the trial of the technicians in charge of the plant, and a scientist gives an excellent explanation of how their decisions and flaws in the design caused the disaster. There are a number of interconnected systems that control the behavior of the reactor, including the control rods and the cooling water, but also buildup of gasses and the power output of the reactor when any of these properties change.

I was curious if I could create a rudimentary simulation of these systems to see if I could cut it as a Soviet reactor tech. I decided to base my model on a boiling water reactor, which seemed to be nearest to my previous understanding of how these plants work. A bit of searching turned up this document describing exactly the type of setup I was imagining, intended for training power station operators!

I wasn't interested in reimplementing a product developed by the International Atomic Energy Agency, but their description was a good starting point to identify the variables, and pare down the complexity. The elements I chose were: Reactor power output P, which increases or decreases as the control rods are removed or inserted; the heat transferred to the water ΔQ, which corresponds to the electric power produced by the plant; the volume of water surrounding the fuel V; the rate water is pumped into the reactor F; and the temperature of the fuel T. These are related by some differential equations. The heat transferred from the fuel to the water is proportional to the temperature of the fuel, and how much water is in contact with it:

That heat is taken out of the fuel, which cools it, while the nuclear reactions I described above are heating it:

The heat is also causing water to evaporate, but we're pumping water in to compensate:

I've played a bit loose with the units here – There should be conversion factors to go from energy to temperature, and energy to volume. I just wanted to get a feel for how these parameters interact, and I did! Below, you'll find another HTML5 simulation, where you can control how far the control rods are inserted, and how much feed water is entering the reactor. If the reactor gets too hot, it will meltdown, and you'll need to reset. I don't think it's very realistic, so aspiring nuclear technicians should not include this on their resume, but you can see some interesting behavior. Have fun!

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Control Rods %

Feedwater %