The Physics of Energy, page 76
Heavy Water Reactors During World War II, Canada used its abundant hydroelectric power to produce many tons of heavy water (D2O) for the Manhattan project. Lacking domestic uranium enrichment facilities, Canadian nuclear engineers developed a reactor designed to run on natural, unenriched uranium, moderated and cooled by heavy water. Because the energy density of natural uranium is much less than enriched uranium (since the content is lower) these CANDU reactors required frequent fuel replacement. Thus, the design had to allow for in-service fuel replacement, and the core is held at lower pressure than a typical PWR. The resulting ingenious design, known generically as a pressurized heavy water reactor (PHWR), has proved safe and reliable, and even though it relies on large quantities of rare and expensive D2O, it remains a small but significant piece (see Table 19.3) of the nuclear power inventory, including recently completed plants in China.
When a deuterium nucleus absorbs a neutron it creates tritium, which is radioactive. Because of its value as well as its resulting radioactivity, the heavy water used for cooling is kept within a closed system, and its thermal energy is used to generate steam in a secondary cycle, similar to a PWR. As in LWRs all the radioactive materials are kept within a reinforced containment structure. Because of the relatively low power density of natural uranium, and the structural limits on the overall size of the system, CANDU reactors have typically about to the power rating (600–800 MWe compared to 1000–1300 MWe) of LWRs.
Gas-cooled Reactors Some of the first power reactors designed in Great Britain and France used natural uranium, were graphite-moderated, and used CO2 gas for cooling. They were named after the magnesium alloy cladding, Magnox, that encased the fuel. The graphite moderator and Magnox cladding, both of which would react with water at high temperature, motivated the use of a non-reactive gas such as CO2 as a coolant. Since the fuel could be inserted into and removed from channels in the graphite moderator, these reactors could be refueled in service, a requirement for natural uranium fuel (see CANDU reactors above). Since the fuel could be changed as often as desired, Magnox reactors were convenient sources of plutonium for weapons systems. (The reason that frequent fuel changes enhances the ability to weaponize plutonium is discussed in §20.6.3.) Indeed, Magnox reactors were originally designed for this purpose and the use of “waste” heat for electricity generation was considered a by-product.
Several design features, including the thermal instability of metallic uranium fuel, the cumbersome equipment needed for refueling, and the fact that Magnox-clad fuel elements could not be stored under water after use, led to the replacement of Magnox reactors by advanced gas-cooled reactors (AGR). AGRs use enriched uranium in the more stable form of uranium dioxide (UO2), with stainless steel fuel cladding. This allows for higher operating temperatures, leading to better thermodynamic efficiency, less frequent refueling, and easier spent fuel storage. Nevertheless, AGRs continue to suffer from design issues, and have not been widely deployed. Very high temperature (gas-cooled) reactors are descendants of this line of development and figure prominently among Gen IV reactor designs discussed below.
Water-cooled, Graphite-moderated Reactors As mentioned earlier, a graphite-moderated, water-cooled reactor has a potential safety problem: coolant loss can lead to higher reactivity, which could cause the reactor to go prompt critical. Reactors based on this model, known as RBMK reactors (a Russian acronym for high power channel-type reactor) were, nevertheless, designed in the former Soviet Union in the 1950s and built until 1986, when one of these reactors suffered a catastrophic failure at Chernobyl. The RBMK design was an attempt to capitalize on an existing Soviet military plutonium production reactor design. RBMK reactors typically employ uranium enriched to ~2%, formed into rods that are inserted in channels in the solid graphite moderator. The difficulties with this reactor design are surveyed in the discussion of the Chernobyl disaster (Box 19.2).
19.4.2 Generation IV Nuclear Reactors
Advanced nuclear fission reactor designs attract interest because of the still-unresolved issues that surround nuclear power, including (1) the need for improved safety and proliferation resistance; (2) the low thermodynamic efficiency of existing reactors (see §19.5); (3) limits on resources; (4) the quantity and radioactivity of nuclear waste; and (5) high capital costs for nuclear plant construction. A set of six advanced reactor concepts have been identified and studied by the Generation IV International Forum over the past decade [97]. Another concept, known as an energy amplifier, is sometimes put into the same category (Question 19.4). A very short description of these reactor concepts is given below. The goal of the Gen IV program is to develop these concepts over the next two decades. It is far from clear, however, whether any of these will find widespread deployment, and in any case the development and large-scale commercialization of a radically new reactor design would likely take several decades at least. (It took ~30 years for LWRs to reach widespread deployment in a climate that was quite conducive to the development of nuclear power.) The purpose of this summary is to give some idea of the range of options under consideration.
Generation IV Thermal Reactors Three of the Gen IV designs are basically thermal reactors and three make use of fast neutrons. The thermal reactors include:
Supercritical water reactor (SCWR) Similar to a boiling water reactor but operating above the critical point in the water phase diagram. Using a considerably higher temperature and pressure than existing PWRs or BWRs, and a single coolant loop, they aim for thermodynamic efficiencies of ~45% rather than ~30% characteristic of present-day reactors.
Very high temperature reactor (VHTR) Basically a gas-cooled, graphite-moderated reactor, this design relies on a very sophisticated fuel element design to achieve unparalleled temperatures (~1000℃ gas temperature at the reactor exit) and important inherent safety features. There are at least two variants: (1) spherical fuel modules, known as pebbles, around which the gas coolant circulates; and (2) hexagonal (prismatic) fuel columns that include channels through which coolant passes. In the pebble bed reactor, the enriched-uranium, plutonium, or thorium fuel (in the form of chemically and thermally stable oxides or carbides) is formed together with graphite moderator into heat-resistant spheres the size of tennis balls. The fuel particles themselves, which are smaller than a millimeter, are coated with several layers, including ceramic silicon carbide that is designed to maintain structural integrity up to temperatures above 1600℃ and prevent the release of fission fragments. A hypothetical pebble bed reactor is sketched in Figure 19.11. The individual pebbles are far too small to sustain a chain reaction. When they enter the reactor, the pebbles are assembled into a close-packed array and a chain reaction begins. The fuel quickly heats up, however, and due to its strong negative thermal coefficient of reactivity (§19.2.1), the chain reaction is stabilized at a temperature well below the limit of structural integrity of the pebbles. Only when a gas coolant circulates through the bed, carries away heat, and lowers the temperature of the fuel elements, does the chain reaction increase in power output.
Figure 19.11 A schematic diagram of a pebble bed reactor employing a secondary (steam) loop. Designs in which the coolant gas itself runs the turbine are also being considered.
In steady state the reactor produces only as much energy as can be carried away by the coolant. In the event of a catastrophic loss of coolant, the reactor simply heats up and runs at low power, awaiting restoration of cooling or dismantling, without damage to the pebbles or the rest of the system. One coolant under investigation is helium, which has the advantage of not becoming radioactive when exposed to neutrons. Thus, helium could be circulated directly through a gas turbine to produce electricity without making the mechanical systems radioactive.
In a pebble bed reactor, the individual fuel pebbles flow through the reactor bed, are recirculated several times, and eventually are removed for waste management. In addition to inherent safety and convenient fuel management, other advantages of the VHTR design include: (i) very high thermodynamic efficiency due to the high outlet temperature; (ii) proliferation resistance, since the plutonium isotope mixture in exhausted pebbles is unfavorable (see §20.6.3) and it would be difficult to disassemble the pebbles to obtain enough material for a bomb; and (iii) the possibility of making smaller, modular reactors with 100 MWe capacity, which could be produced and assembled with low capital costs. However, neither the pebble bed nor the prismatic alternative has yet been implemented in a commercial reactor.
Molten salt reactor (MSR) Using molten salt as a coolant has the advantage of access to very high temperatures without pressurization because molten salts have low vapor pressures even at temperatures above 1000℃. One version dissolves the fuel (uranium or thorium) in the circulating coolant. The nuclear reaction occurs when the coolant/fuel circulates through channels in a graphite core, which provides the necessary moderator. Fuel and actinides can then be separated from fission products by chemical processing of the circulating coolant. Other designs resemble pebble bed reactors with the gas coolant replaced by molten salt.
Generation IV Fast-neutron Reactors The fast-neutron reactor designs included in the Generation IV initiative are all intended to breed more fuel than they consume and thus fall in the domain of breeder reactors described in §19.3. The three fast reactor concepts in the Gen IV initiative are labeled by their different cooling systems:
Gas-cooled fast reactor (GFR) The circulating gas acts as a coolant and directly powers a Brayton cycle. Helium or CO2 have good thermodynamic and neutron-absorption properties. The gas cooling system would allow for high temperatures and good thermodynamic efficiency. A safety concern is that the absence of a moderator and the use of a gas coolant results in low heat capacity and a potential rapid rise in temperature after a loss of forced coolant.
Sodium-cooled fast reactor (SFR) Liquid sodium offers the same advantage as molten salt: low vapor pressure at high temperature, but also has a low neutron-absorption cross section, making it a suitable coolant for a fast reactor. Liquid sodium also has excellent heat transfer characteristics. Designs include many passive and inherent safety mechanisms. However the use of highly reactive liquid metal sodium is a significant concern: liquid sodium burns in dry air and oxidizes explosively in contact with water. The sodium-cooled BN-600 and BN-800 reactors at Beloyarsk mentioned above fall into this category and are being studied as prototypes for more advanced sodium-cooled fast reactors currently being designed.
Lead-cooled fast reactor (LFR) Another low-neutron-absorption coolant with low vapor pressure is lead or a lead-bismuth mixture with melting points as low at 123.5℃. The corrosive nature of liquid lead presents design challenges.
19.5Nuclear Reactor Power Cycles
Nuclear fission reactors are fundamentally heat sources, like fossil fuel power plants, that produce useable energy through a thermal power cycle. They can therefore be analyzed using the tools of §13. As thermodynamic systems, existing nuclear plants fall into two general classes: single-loop Rankine cycles, such as boiling water reactors (BWR), where the coolant is vaporized and used directly to run a steam turbine, and double-loop Rankine cycles, such as pressurized water reactors (PWR), where the coolant runs in a closed loop and transfers its heat to steam in a second loop that is used to run a steam turbine. Other cycles can be used in specific reactor systems; for example, the very high temperature reactor (VHTR) design described in §19.4.2 could use a single-loop Brayton (or Brayton/Rankine combined) cycle, where the coolant – helium or CO2 – from the reactor is fed directly into a gas turbine.
The temperature and pressure that can be tolerated by the materials in the reactor core limit the design and the thermodynamic efficiency of nuclear power plants compared to fossil fuel power plants. The structural integrity of the fuel and other components of the reactor core typically limit the water temperature and pressure in LWRs to well below the critical point, and MPa. For example, the US Nuclear Regulatory Commission (NRC) Design Certification [98] for a modern PWR indicates a coolant outlet temperature and pressure of MPa. This in turn heats water in the secondary loop to a saturated vapor (quality one) at , where the pressure is MPa. Boiling water reactors reach somewhat higher temperature and pressure in the turbine loop. The US NRC Design Certification [99] for an advanced BWR quotes MPa. These values also correspond to saturated steam at quality near to one. A modern version of the CANDU reactor has similar steam characteristics.
Nuclear Reactor Power Cycles
Commercial nuclear power reactors operate with steam temperatures lower than those achievable in conventional fossil fuel power plants, due to limits imposed by the structural integrity of materials in their cores. Turbines in nuclear plants are therefore designed to tolerate a mixed (water/steam) phase.
Using high-pressure and Rankine cycles that include regeneration and reheating, light-water reactors can reach efficiencies of 33–37%, comparable to conventional coal-fired power plants.
In §13 we concentrated on Rankine steam cycles with superheating, as shown in Figure 13.12. In the case of a water-cooled nuclear reactor, superheating is generally impractical because coolant from the reactor core cannot provide a high enough temperature. So the basic Rankine cycle appropriate to an LWR or CANDU reactor is more like the sketch of Figure 19.12(a), with the result that water droplets condense in the steam passing through the turbine as its quality drops below one. A nuclear power plant turbine must be specially designed to handle water droplets that may cause erosion of the metal blades. Similar considerations apply to geothermal power plants, where the steam drops below the saturation dome in the power cycle (see §32). In practice, LWR Rankine cycles usually employ reheating, as illustrated schematically in Figure 19.12(b). In such a cycle the steam is intercepted at an intermediate temperature and pressure, , after a high-pressure turbine, and reheated to before entering a second, low-pressure turbine. As shown in Figure 19.12(b), this not only increases the efficiency of the cycle, but also keeps the steam quality in the turbine relatively high and allows for more flexibility in turbine design.
Figure 19.12 (a) A Rankine cycle without superheating appropriate to an LWR. Compare with Figure 13.12(b). Note that the steam exiting the turbine is low quality, i.e. it contains considerable liquid water. (b) A Rankine cycle with the same maximum and minimum temperatures as (a), but with reheating. Note that the efficiency of the cycle and the quality of the steam exiting both turbines is higher than (a).
While nuclear power plants typically operate at lower temperatures and higher pressures than conventional coal-fired power plants, by using regeneration and reheating (see §13), LWRs can reach comparable efficiencies (33–37%). To reach efficiencies comparable to gas-fired combined cycle (CCGT) plants described in §13.5, nuclear plants must run at higher temperatures. This is the aim of the Gen IV VHTR project. With gas-coolant outlet temperatures conceivably in excess of 1000℃, directly employed in a Brayton cycle, efficiencies approaching those of CCGT power plants may be possible.
19.6Experiments in Thermonuclear Fusion
The possibility of virtually unlimited energy production from controlled nuclear fusion has raised great hopes, but encountered great difficulties. Notwithstanding the difficulties, the hopes have stimulated a decades-long quest to design and build a practical, economically viable energy source powered by controlled nuclear fusion.
The basic idea of fusion power is to bring matter to a high enough temperature and pressure to achieve a controlled fusion reaction that can be sustained over an extended period of time. As described in §18, deuterium–tritium (dt) fusion is considered most promising on physics grounds, though dd may also be feasible and avoids the use of the artificially created and radioactive isotope tritium. Typically must be about 15 keV for either dt or dd fusion, but the pressure and thermal energy confinement needed are much greater for dd than for dt fusion. Here we focus on dt fusion, which is much more likely to be achieved in the relatively near term.
At very high temperatures, atoms are completely ionized and the gas of ions and electrons forms a plasma. Thus, the study of nuclear fusion takes us into the realm of plasma physics.
The first efforts towards controlled fusion have made use of the fact that a charged particle travels in a helix in a magnetic field. The stronger the field, the smaller the radius of the helical orbit. Based on this effect, a strong magnetic field can confine even a very hot plasma in a relatively small volume. This is the fundamental idea behind magnetic confinement fusion (MCF), which is described in §19.6.3 below. Another possible approach, known as inertial confinement fusion, is described briefly in §19.6.4. Before describing either specific approach to plasma confinement, we examine the energy balance in a confined plasma undergoing fusion, and develop the criteria used to judge the performance of a fusion reactor.
19.6.1 Power Balance in a Fusion Reactor
In this section we suppose that a plasma consisting of fully-ionized deuterium and tritium with number densities and has been successfully confined and brought to a high temperature T where the fusion reaction
(19.19)
takes place in steady state. (The mechanism of confinement does not matter here.) dd and d fusion can be treated similarly. We assume that the deuteron and triton densities are equal, , where n is the electron density, and that the plasma can be approximated as an ideal gas with . The factor of two comes because the nuclei and the electrons contribute separately to the pressure.
The neutron and α particle are produced with energies in the ratio 4:1, MeV and MeV, as required by conservation of energy and momentum.4 The charged α particle loses its energy quickly in the plasma, whereas the neutron escapes the plasma and delivers its energy directly to the surrounding material. These energy production processes within the plasma are described in terms of the power density produced in α particles and produced in neutrons. Together and sum to the total fusion power production density . In addition to the energy carried by neutrons, the plasma loses energy to its surroundings by heat conduction and radiation, parameterized by averaged power densities within the plasma given by and respectively. The power deposited in the material surrounding the fusion reactor by neutrons and by radiation and conduction is, in principle, available to heat a working fluid and generate electricity. Finally, some power, parameterized by within the plasma, may be fed into the reacting plasma to maintain its temperature.
