Question 6 of 8: Nuclear Reactor Principles

Question 6: Nuclear Reactor Principles (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — the process illustrated, and where the energy comes from. The diagram shows a self-sustaining thermal-neutron fission chain reaction. A neutron surviving from the previous generation enters a fuel rod and is captured by a fissile nucleus, which becomes so unstable that it splits into two lighter fragments and releases two or three further neutrons. For uranium-235 the reaction is written $${}^{235}_{\ 92}\text{U}+{}^{1}_{0}n\ \longrightarrow\ {}^{236}_{\ 92}\text{U}^{*}\ \longrightarrow\ {}^{141}_{\ 56}\text{Ba}+{}^{92}_{36}\text{Kr}+3\,{}^{1}_{0}n+\text{energy},$$ one of many possible fragment pairs; the fragments always straddle mass numbers of roughly 95 and 140, and the average yield is about 2.4 neutrons per fission. Energy appears because the binding energy per nucleon of the fragments exceeds that of the parent nucleus by roughly 0.9 MeV, so about 200 MeV is released per fission. Around 165 MeV of that, more than four fifths, appears immediately as the kinetic energy of the two highly charged fission fragments, which are stopped within a few micrometres of where they were born. That is the crucial practical point: the great majority of the reactor's heat is generated inside the fuel pellets themselves, so the fuel runs far hotter than the coolant and the whole thermal design of the core is a problem of getting heat out of small ceramic cylinders. The balance is shared between the kinetic energy of the prompt neutrons (about 5 MeV, deposited in the moderator as they slow down), prompt and delayed gamma radiation, and the beta decay of the fission products, which continues after shutdown and is the reason a reactor needs decay-heat removal for days after it is tripped. On a mass basis the result is spectacular: 200 MeV per fission of uranium-235 works out at about 82 TJ per kilogram, some 2.7 million times the 30 MJ/kg of the coal in Question 3, which is why a CANDU refuels with tonnes a year where a coal station of the same output consumes the 1.5 million tonnes computed in Question 4.

Part (b) — the four main components and why the core is laid out as shown. The fuel supplies the fissile nuclei and contains the fission products; it is the heat source and, because the fragments stop within it, it is also the hottest material in the plant. The moderator slows the fast neutrons born from fission down to thermal energies. This is necessary because the fission cross-section of uranium-235 is a few hundred times larger for a thermal neutron than for a fast one, so without moderation a chain reaction could not be sustained at natural or low enrichment. Moderation works by elastic scattering, and a light nucleus takes more energy per collision than a heavy one, which is why hydrogen, deuterium and carbon are the practical choices. The control rods hold the multiplication factor at unity: they contain a strong thermal-neutron absorber, and inserting them removes neutrons from the chain, letting the operator raise, lower or shut down power and compensate for fuel burn-up and xenon poisoning over the cycle. The coolant flows past the fuel surfaces and carries the fission heat out of the core to the steam-raising plant; it fixes the fuel temperature and hence the margin to melting, and it sets the steam conditions available to the turbine.

The geometry follows from those functions. The fuel is divided into many slender rods rather than cast as a single block for two reasons at once: a small diameter keeps the centreline temperature of a poorly conducting ceramic within limits, and a large surface-to-volume ratio gives the coolant enough area to remove the heat. The rods are spaced in a regular lattice with the moderator filling the gaps, so that a fast neutron born in one rod must traverse the moderator — and be thermalised — before it reaches the next; the lattice pitch is chosen to maximise the probability that it arrives thermal. This separation of fuel and moderator is what makes a heterogeneous reactor, and it also reduces resonance capture in uranium-238, because the neutron does most of its slowing down outside the fuel where the resonances cannot reach it. The control rods sit in guide tubes within the same lattice so that they see the same thermal flux as the fuel, and the coolant is routed along the rods in the direction of the lattice channels. Finally the core is made large enough that leakage — the neutrons shown escaping from the edge — remains a small fraction of the population, since leakage is a surface effect and production a volume one.

Part (c) — materials and construction of a CANDU system. Taking the Canadian design, the fuel is natural uranium dioxide, about 0.71 per cent uranium-235, pressed and sintered into ceramic pellets roughly 12 mm in diameter and stacked in thin-walled Zircaloy-4 sheathing to form elements about half a metre long. Thirty-seven such elements are welded into a bundle around 10 cm across, and twelve or thirteen bundles sit end to end in each fuel channel; a CANDU 6 core holds about 380 channels and some 4500 bundles. Zirconium alloy is used because its absorption cross-section for thermal neutrons is very low, which matters enormously when the fuel is unenriched, and uranium dioxide is used because it is chemically stable, has a very high melting point and retains its fission gases. The moderator is heavy water, deuterium oxide, held at low temperature and near-atmospheric pressure in a large horizontal cylindrical tank — the calandria — which the fuel channels penetrate. Heavy water is chosen because deuterium absorbs so few neutrons that a chain reaction can be sustained on natural uranium with no enrichment at all; the price is a somewhat larger core, because deuterium is heavier than hydrogen and takes more collisions to thermalise a neutron. The coolant is separately circulated heavy water at about 10 MPa, entering each channel near 265 °C and leaving near 310 °C, contained in zirconium–2.5 per cent niobium alloy pressure tubes that are isolated from the cool moderator by an annular carbon dioxide gas gap inside a surrounding calandria tube. Because each channel is its own small pressure boundary, CANDU needs no large pressure vessel and can be refuelled on power by fuelling machines that latch onto both ends of a channel — the design's defining feature. Reactivity control is shared among several devices rather than concentrated in rods: vertical zone compartments filled with ordinary water provide fine, spatially distributed control, cobalt or stainless steel adjuster rods shape the flux and provide xenon override, mechanical cadmium control absorbers give bulk control, and two independent fast shutdown systems — spring-assisted cadmium shut-off rods dropped into the calandria, and the injection of gadolinium nitrate poison directly into the moderator — provide the safety function. The heat is delivered to inverted vertical U-tube steam generators with Incoloy-800 tubing, raising ordinary light water to saturated steam at about 4.7 MPa for the turbine.