The design of a nuclear reactor is many times hampered by contradictory criteria dominated by safety at the one hand and economical arguments at the other. Safety and economy are uneasy bedfellows and the resulting phase space is many times too small to yield a realistic reactor design. Fortunately, for the High Temperature Reactor (HTR) there seems to be a phase space window that provides sufficient degree of freedom for the designer to come up with a realistic reactor concept. This text tries to explain the criteria that determine roughly the design of an inherently safe HTR that is economical as well.
Nuclear safety can be defined in many ways, but we will classify a nuclear reactor as being safe if there is no hazard to the public or personnel. This implies that there should never be a need for a person near the boundary of the site to take shelter or be evacuated; that to ensure this target, no mechanical components are needed; and that the exposure to the plant personnel is always below the criteria set and lower than current international values.
The safety design philosophy of a nuclear power plant is based on criteria at three levels. First there are the limits on the exposure levels to the public and the personnel. These are usually set by the regulatory body. Clearly, the operator should always try to reduce these dose rates by applying the ALARA principle. In other words, the exposure levels set by the regulators are limits from which the operator should stay away as much as possible. Secondly, there are three fundamental functions to ensure the safety of the plant: 1) control of reactivity, 2) heat removal from the core and, 3) confinement of radioactive material. These three safety functions shall be performed both in normal and off-normal conditions. The ‘defense in depth’ principle is implemented to ensure these safety functions work properly in off-normal conditions. This principle is applied to prevent, control and mitigate any off-normal event.
The control of reactivity is done by control rods in the inner and outer reflectors and, if necessary, by a reserve shut-down system that mostly consists of B4C pellets or balls. The cooling of the reactor is usually done by the main cooling system, and by an auxiliary cooling system that starts up when the reactor is scrammed. Although modern HTR designs can dissipate their residual heat to the environment via conduction and radiation, the auxiliary system provides the flexibility to cool down the reactor much quicker than would be possible by passive means. The latter option is used when all forced cooling systems are no longer available, like in a Depressurized Loss of Forced Cooling (DLOFC) incident, caused for instance by a rupture of a primary circuit pipe. The reactor vessel cooling function is always in operation to cool the reactor shielding wall.
HTR’s employ so-called TRISO fuel particles embedded in graphite. The particles consist of a small fuel kernel made of uranium-dioxide with a typical diameter of 500 micrometers, surrounded with a buffer layer that can accommodate the gaseous fission products escaping from the fuel kernel, and three containment layers. The latter consist of an inner PyC layer, a SiC layer and an outer PyC layer. The SiC layer usually is under compression to assure the gas-tightness of the containment around the fuel kernel. The TRISO fuel particles can be embedded in a graphite sphere with a typical diameter of 5 cm surrounded with a 0.5 cm thick layer of graphite, or in small cylindrical pins with typical diameter of 1 cm, which are inserted in a graphite block. The first is called pebble-type fuel, while the second is called prismatic fuels.
The HTR differs from more conventional Light Water Reactors (LWRs) because the fission product containment is assured at the level of the TRISO fuel particles with a diameter of one millimetre contained in graphite spheres or cylinders (called compacts). In LWRs, the containment is enclosing the reactor pressure vessel, while in HTR’s the containment is surrounding every single TRISO particle. Although the Japanese authorities requested a containment for the HTTR reactor encapsulating the reactor pressure vessel, the fuel is performing so well that it is now generally accepted that future HTR’s don’t need containment vessels comparable to those of LWRs.
Experiments have shown that TRISO fuel particles behave very well up to temperatures of 1800 degrees Celcius. Below this temperature, the fuel failure fraction is very small and the fission product leakage negligible. Because the temperature limit depends on the fuel composition and fuel burnup, a generally accepted limit for the maximum temperature of TRISO fuel particles is 1600 degrees Celcius.
To ensure this limit is never exceeded the heat production during normal operation and the afterheat during shutdown (planned or unplanned) should always be assured. The decay heat is due to multiple components, like fission product decay (beta particles and gamma rays releasing about 15 MeV/fission), actinide decay (usually only important for MOX fuel), delayed neutron induced fission (a contribution of 10%, but only during a couple of minutes after shut down), spontaneous fission (more important for the shielding of spent fuel during transportation than a decay heat problem), and activation of structural materials (only few percents of fission product decay). From this list it is clear that the fission product decay contribution dominates the after heat problem. Decay heat removal is especially important at depressurized conditions with a loss of forced coolant flow.
The decay heat initially amounts up to 6% of the total power production. After half a day, about 0.0047 MWd of integral power has been produced, which amounts up to 400 full power seconds (FPS). If you compare this to the power needed to heat up the reactor core and coolant of a Boiling Water Reactor (BWR) from ambient temperature to operating temperature, which amounts to about 160 FPS, it is clear that the decay heat production is considerable and destructive to the fuel if not properly cooled. Passive removal of decay heat is one of the most important characteristics of an inherently safe HTR.
We can now start with the design of an HTR by inserting fuel pebbles into a cavity surrounded by a graphite reflector. The thickness of the reflector is determined by the reflector savings, which is the core size reduction obtained when a bare critical core is surrounded by a reflector and made critical again by reducing the core size. A reflector thickness of two times the neutron diffusion length is sufficient to maximize the gain. A thicker reflector would not reflect more neutrons back into the core, but absorbs the neutrons that would otherwise be lost by leakage. For a graphite reflector, this implies that the thickness should be one meter at least, while this would only be 6 cm for water!
Having fixed the reflector thickness, the neutron leakage from a bare cylindrical core can be minimized by minimizing the buckling of the neutron flux density. For a fixed core volume, one can determine that the ratio between the height and radius of a bare cylindrical core should be 1.85. In other words, a cylinder with height a little bit less than the diameter minimizes the neutron leakage from the core. This would give the optimal dimensions for a cylindrical core from the economic point of view.
However, there is one ‘but” in this result. A thick core is not able to conduct quickly enough the fission product decay heat to the environment in case of a Depressurized Loss of Forced Cooling incident (DLOFC), and the temperature at the centre of the core could easily exceed the limit of 1600 degrees Celcius. The total volume of a reactor core with optimal shape from the economical point of view would therefore be very small! Only very small reactors like the Chinese HTR-10 can have a small reactor core without violating the passive decay heat removal requirement. That’s why passive safe HTR cores with a large power output are usually long and thin. They need to be slender to remove the decay heat by conduction and radiation to the surroundings, while they are long to provide sufficiently large volume to produce enough power.
The maximum radius of the cylindrical core is usually fixed by practical considerations. The maximum radius of the Reactor Pressure Vessel (RPV), for example, is limited to somewhere between 6 and 6.5 m, because of transport considerations from the factory to the reactor site. The PBMR design team, for example, has opted for a vessel of 6.2 m in diameter. As explained before, in cylindrical core geometry it is not possible to increase the core radius to increase core power. If the radius increases, the average power density needs to reduce in order not to exceed the temperature limit in a DLOFC incident. For example, an increase of the radius from 3 to 4 meters, which almost doubles the core volume, would allow only for a 20% increase in reactor power. On the other hand, by actually applying a central fuel-free column and keeping the core volume constant, the power density and the total power output can be raised without exceeding the temperature limit in a DLOFC. This is possible because the power production in the core is concentrated near the outer reflector, which can easily dissipate and transport the decay heat to the surroundings.
Besides practical considerations, the maximum height of the reactor core is limited by reactor physics limits as well caused by the sensitivity of large cores to Xenon oscillations. Xenon is a highly absorbing fission product mainly produced by the decay of Iodine, which decays to Xenon with a half life of about 6.6 hours. Iodine is directly produced from fission with an effective yield of 6.6%. Xenon disappears by neutron capture, for which it has a high absorption cross section of several millions of barns, and by decay with a half life of 9.2 hours to a virtually stable and non-absorbing isotope. If the neutron flux density increases in one part of the core, the Iodine production increases, but the Xenon production remains virtually constant for a couple of hours due to the 6 hours half life of Iodine. The neutron capture by the Xenon, however, is directly proportional to the neutron flux density. As a result, a flux increase leads to a reduction of the Xenon concentration in the core, which leads to less neutron capture by Xenon and to an increase of the local power density. This is a positive feedback effect, which is usually taken care of by the reactor control system, but which can lead to reactor power oscillations between one part of the core and the other. For this reason, the maximum core size is limited to about 30 migration lengths, which corresponds to about 10 meters for a pebble-bed type HTR and to 8 meters for a prismatic type reactor core (the migration lengths for a prismatic and pebble-bed type HTR are about 20 and 30 cm, respectively). The limit of 30 migration lengths can be understood from the analysis based on micro-kinetics. The reactor power can be thought of as being built up by prompt fission chains induced by the emission of delayed neutrons. In a critical reactor, the average number of neutrons in a prompt fission chain equals 1 divided by the delayed neutron fraction beta (0.007 for U-235). As the mean squared distance a neutron travels from birth to absorption equals six times the migration area (migration length squared), the average distance travelled by the neutrons in a prompt fission chain, as the crow flies, equals 30 migration lengths.
Another parameter limiting the height of reactors is the pumping power required to pump the gas coolant, which is proportional to the pressure drop across the core, and the mass flow. For pebble-bed reactors, the pressure drop is proportional to the Q2 H3 where Q is the power density and H is the height of the reactor core. To limit the pressure drop, one either has to reduce the core height or the core power density.
A typical layout for an HTR core would look like the following figure. Cold helium enters the outer reflector from the bottom and flows upward to cool the reflector and other internals. Then it is directed towards the core through which it flows from the top to the bottom to remove the heat from the fuel (either pebbles or prisms). The central column of graphite, if present, will have a typical diameter of about 2 meters and can be made of fuel-free graphite pebbles or a solid central column. The first option leads to a large bypass flow through the central column, which needs extra pumping power. The advantage, however, is that the graphite pebbles can be cycled slowly through the core and replaced by fresh ones if needed. To replace the solid central column, the reactor would have to be stopped and the vessel be opened.
For all modern HTR’s, the choice for the coolant is helium. The optimum coolant is able to remove as much heat as possible from the core. Based on certain assumptions in mass flow, heat transfer, pressure drop, and pumping power, one can derive that the optimal coolant has a large molar heat capacity and small molar mass. The heat capacity of one gas molecule equals kT/2 for each degree of freedom, where k is Boltzman’s constant and T the temperature. The numbers of degree of freedom is three for a mono-atomic gas (only displacements in the three principal directions), five for a diatomic gas (two rotational degrees of freedom extra), and six for a polyatomic gas (one rotational mode extra).
A certain amount of power per unit frontal core area can be removed most efficiently by hydrogen molecules, because of the low molar mass of this gas and the relatively high heat capacity due to the fact it is a diatomic gas. Carbon dioxide is second best, but with a value only one half of that of hydrogen. Other optimization parameters like the heat transfer area for a fixed flow area, or the pressure losses in the core due to friction, show that helium is the best choice as a coolant. In conclusion, there is not a clear choice for the coolant gas, but helium is among the best ones. Combined with the inertness of this gas, both chemically and neutronically, helium seems to be a very good choice indeed.
At this point, it is interesting to look at the history of gas-cooled reactors. After the CP-1 pile in Chicago, which can be considered as an air-cooled reactor but with almost zero power production, the X-10 reactor in Oak Ridge, USA, was built and operated. It had a power of 3.5 MW and was cooled by air. Its successor was the Brookhaven atomic pile, which started operation in 1949. After that in Europe several prototype reactors were built like the nitrogen cooled reactor in Saclay, which was later on refurbished to carbon dioxide coolant, and the Calder Hall reactors in the UK which were also carbon dioxide cooled. All this experience culminated in the MAGNOX and AGR reactors which are still in operation in the UK and which are all cooled using carbon dioxide.
The history of High Temperature Reactors (HTR) starts with the DRAGON reactor in the UK, which operated from 1965 till 1976 and which was the first reactor to use TRISO fuel particles. Similar prototypes were built in Germany (AVR) and the US (Peach Bottom). Based on the experience gained with these prototypes, the Thorium High Temperature Reactor (THTR) and the Fort Saint Vrain reactor were built and operated. These reactors were medium sized reactors with a power output of 300-350 MW electric and a pre-stressed concrete vessel (PCRV). Because of this, they didn’t have the capability for passive removal of decay heat, like the early prototype reactors which had much smaller core size and steel vessels. Larger reactors with a power output of 3000 MW thermal and beyond were designed but never built. From that point on, the focus was on small modular reactors, like the German HTR-Modul and the MHTGR in the US. However, these reactors never operated either. From 1995 on, history seems to repeat itself with the design, construction and operation of small prototypes in Asia. In Japan, the HTTR has been put into operation, while in China the HTR-10 has been built and started.
Based on these experiences, medium sized modular reactors are being designed like the PBMR in South Africa and the HTR-PM in China. The first applies a Brayton cycle to convert the reactor power into electricity, while the latter uses the traditional Rankine cycle (steam water cycle). In the last couple of years, the PBMR design team has shifted from a cylindrical core to an annular core with a pebble column and, finally, to an annular core with a solid column. The latter has the advantage that the size and shape of the annular column is constant in time, and that there can be no fuel pebbles in the mixing zone that experience a too high power production. A disadvantage is that the graphite of the inner reflector is not refreshed on-line like the pebbles are. It is therefore necessary to replace the central column at mid-life to prevent radiation damage. An advantage of a central column of graphite is that the bypass flow rate of helium is reduced. The development in China focuses more on risk reduction by applying current technology. The HTR-PM has moved from an HTR-Modul design with a cylindrical core, via an intermediate annular core design, back to two smaller HTR modules with a cylindrical core.
What’s next? All the efforts are directing towards implementation of the Very High Temperature Reactor (VHTR), which should have a higher temperature outlet without jeopardizing the passive decay heat removal capability. This means that we should try to increase the outlet temperature without increasing too much the fuel temperature. Several options have been investigated by TU-Delft and her partners, like the design of a radial cooled pebble bed reactor, the optimization of the fuel recycling scheme in a pebble-bed reactor, and the application of so-called wall paper fuel, in which the fuel particles are not homogeneously distributed in the fuel zone of the pebble, but in an annular shell of the pebble. The zone with the highest temperature would be free of fuel in this concept. It is clear that further research is needed, but all the concepts look promising in achieving an inherently safe VHTR.
The slides can be downloaded here.
|For more information, please contact j.l.kloosterman (at) tudelft.nl