Question 6 of 6: Fuel Characteristics

Question 6: Fuel Characteristics (15 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 I — Fossil Fuel (9 marks)

Part I (a) — heating value, higher and lower. The heating value of a fuel is the quantity of heat released when unit mass (or unit volume, for a gas) is burned completely with the products returned to the initial temperature, conventionally 25 °C. It is measured in a bomb calorimeter for solids and liquids and quoted in MJ/kg. The ambiguity that gives rise to two values concerns the water in the products. Every hydrocarbon produces water vapour on combustion, both from the hydrogen it contains and from any moisture it carried. If the products are cooled far enough for that water to condense, its latent heat is recovered and appears in the measurement: this is the higher heating value (HHV), or gross calorific value, and it is what a bomb calorimeter naturally reports. If the water is left as vapour, as it is in every real furnace and boiler that discharges to a stack above the acid dew point, that latent heat leaves up the chimney and the useful release is the lower heating value (LHV), or net calorific value. The two differ by the latent heat of the product water, $\mathrm{HHV} - \mathrm{LHV} = m_{H_2O}\,h_{fg}$, with $h_{fg} = 2442\ \text{kJ/kg}$ at 25 °C. For methane, which yields 2.25 kg of water per kilogram burned, the gap is $2.25 \times 2442 = 5.5\ \text{MJ/kg}$ — the difference between 55.5 and 50.0 MJ/kg, some 10 %. For coal, with far less hydrogen, the gap is nearer 4 %. Practice in North America, including Canadian utility and regulatory reporting, is to quote and to base efficiency on the higher heating value, so a Canadian station heat rate is an HHV figure; European practice and most gas-turbine vendors use the LHV, which is why a manufacturer's quoted efficiency is always several points above the same machine's HHV efficiency. Comparisons between sources are meaningless unless the basis is stated.

Part I (b) — coals of different rank. Coal is not one substance but a continuum produced by the progressive burial, compaction and heating of accumulated vegetal matter. Coalification drives off first water, then the oxygen-rich and hydrogen-rich volatile fractions as carbon dioxide, methane and tars, leaving a residue progressively richer in fixed carbon. Rank measures how far that transformation has gone, and essentially every property of interest to a power engineer follows from it. Peat, the precursor, carries 70–90 % moisture as dug and only 8–15 MJ/kg dry. Lignite or brown coal has 30–50 % inherent moisture, high volatile matter and a heating value of 10–20 MJ/kg; it is friable, prone to spontaneous combustion and uneconomic to transport, so it is burned at the mine mouth (Estevan in Saskatchewan, Genesee in Alberta). Sub-bituminous coal holds 15–30 % moisture at 18–24 MJ/kg. Bituminous coal is the classic steaming and coking coal, 2–15 % moisture, 20–35 % volatile matter and 24–35 MJ/kg, with good grindability and stable ignition — the reference fuel for most pulverised-fuel boiler designs. Anthracite is the highest rank, over 90 % fixed carbon, under 10 % volatile matter and 30–35 MJ/kg. The trends are systematic: moisture and oxygen fall, fixed carbon rises, heating value rises, and hydrogen falls slightly. But high rank is not simply better for combustion. Volatile matter is what ignites first and anchors the flame, so anthracite's scarcity of it makes ignition difficult and demands finer grinding, higher furnace temperatures and often support firing; low-rank coals ignite readily but carry water that must be evaporated by the fuel itself, cutting boiler efficiency and swelling the flue-gas volume. Ash and sulphur content vary with the depositional environment rather than with rank, and independently govern fouling, slagging, erosion and the sulphur dioxide load on the flue-gas treatment. Boiler furnace sizing, mill selection, burner design and emission control are therefore all specified against a particular coal or a narrow band of them.

Part I (c) — proximate and ultimate analysis. The two standard analyses answer different questions. The proximate analysis is an empirical, procedural test that reports four fractions summing to 100 %: moisture, driven off by heating to about 105 °C; volatile matter, released on further heating to about 950 °C out of contact with air; fixed carbon, the combustible residue remaining; and ash, the incombustible mineral matter left after burning that residue. It is cheap, quick and repeatable, and it maps directly onto the questions an operator asks — how readily will this coal ignite and hold flame (volatile matter), how much of the fuel is inert freight and future ash handling (moisture and ash), how long will the char take to burn out (fixed carbon). It is the basis for rank classification and for routine contract and quality control on delivered coal, usually accompanied by the calorific value and a grindability index. The ultimate analysis is a chemical determination of the elemental composition — carbon, hydrogen, oxygen, nitrogen and sulphur, with ash and moisture reported separately. It is more expensive but it is the only basis on which combustion can actually be calculated: stoichiometric air requirement, flue-gas mass and composition, dew point, theoretical flame temperature and the sulphur dioxide and thermal-nitrogen-oxide loading all follow from the elemental split, and the hydrogen figure is what converts a measured HHV into the LHV. In short, the proximate analysis characterises the fuel as handled and fired, and the ultimate analysis characterises it as a chemical reactant; a boiler designer needs both, and the performance guarantee will be written against a specified range of each.

Part II — Nuclear Fuel (6 marks)

The reactor chosen is the CANDU pressurised heavy-water reactor, the Canadian design that supplies the great majority of nuclear generation in this country and whose distinguishing features make the argument about fuel characteristics unusually clear.

Part II (a) — the fission process, the fuel, and what fission requires of it. Fission is the splitting of a heavy nucleus into two lighter fragments after it absorbs a neutron. In uranium-235 the absorbed neutron forms a highly excited uranium-236 nucleus which is unstable against deformation and divides, typically asymmetrically, into two fission products of mass number near 95 and 138, releasing on average 2.4 fast neutrons, several prompt gamma rays, and about 200 MeV of energy — overwhelmingly as kinetic energy of the two charged fragments, which is deposited within a fraction of a millimetre in the fuel itself and appears immediately as heat. The remainder arrives as beta and gamma decay of the fission products, which is why a shut-down core still produces several per cent of full power and must go on being cooled. The chain reaction is initiated by these neutrons: fission of uranium-235 is far more probable at thermal energies (a cross-section near 580 barns) than at the megaelectronvolt energies at which the neutrons are born, so the fast neutrons must be slowed by elastic scattering in a moderator before they can sustain the reaction. Startup neutrons come from spontaneous fission and from photoneutron and beryllium-antimony sources.

The fuel used in a CANDU is natural uranium dioxide, 0.72 % uranium-235 and the balance uranium-238, in the form of sintered ceramic pellets sealed in thin Zircaloy sheathing and assembled into 37-element bundles about half a metre long. Natural uranium is usable only because heavy water is such an efficient moderator with so small a parasitic absorption cross-section that the neutron economy still closes; in a light-water reactor the same fuel could not sustain a chain reaction and 3–5 % enrichment is required. The characteristics demanded of any reactor fuel are: a sufficient density of fissile atoms; a high melting point (UO₂ melts near 2865 °C, giving a very large margin over the roughly 2000 °C centreline temperature at full power); chemical and radiation stability, so it neither reacts with the sheathing and coolant nor swells excessively as gaseous fission products accumulate; adequate thermal conductivity to carry the heat out; and a capacity to retain fission products within the pellet and the sheath, which together with the pressure tube, the calandria and the containment form the defence in depth. UO₂ buys its excellent stability at the price of poor thermal conductivity, which is why the pellets are made small and the fuel elements thin.

Given. Natural UO₂, $\gamma = 0.0071$, $\rho = 10.6\ \text{g/cm}^3$, $M = 270$, $\sigma_f = 580$ barns, thermal flux $\phi = 10^{14}\ \text{n/cm}^2\text{s}$, $E_f = 3.2\times10^{-11}$ J. Find. The volumetric heat release rate in the fuel, using the three nuclear relations printed on page 18.

1. Fissile nuclei per unit volume, then heat release. $$N = \frac{N_A}{M} = \frac{0.602\times10^{24}}{270} = 2.23\times10^{21}\ \text{nuclei/g}$$ $$N_f = \gamma\,\frac{N_A}{M}\,\rho = 0.0071 \times 2.23\times10^{21} \times 10.6 = 1.68\times10^{20}\ \text{cm}^{-3}$$ $$q^{*} = N_f\,\sigma_f\,\phi\,E_f = 1.68\times10^{20} \times 580\times10^{-24} \times 10^{14} \times 3.2\times10^{-11} = \boxed{311\ \text{W/cm}^3}$$ That is 311 MW per cubic metre of fuel — the reason a reactor core is small, and the reason its cooling can never be interrupted.

Part II (b) — design requirements and the main internal components. A power reactor must do four things at once: sustain a controlled chain reaction, extract the heat, contain the radioactivity, and remain safe under every credible fault including loss of coolant and loss of control. Those requirements map directly onto the components. The fuel in its Zircaloy sheathing provides the fissile material and the first barrier. The moderator — in a CANDU, heavy water held cool and near atmospheric pressure in the calandria — slows the fast fission neutrons to thermal energies; keeping it physically separate from the coolant is the design's central choice, because it means the moderator can be a large, cold, unpressurised heat sink of last resort as well as the neutron economiser. The coolant, pressurised heavy water at about 10 MPa and 310 °C, flows through the horizontal pressure tubes over the fuel bundles and carries the heat to the steam generators, where it boils ordinary light water on the secondary side; the pressurizer holds the primary pressure above saturation so the coolant stays liquid. Control and shutdown devices manage reactivity: adjuster and control absorber rods and light-water zone controllers for routine regulation and xenon override, and two independent, diverse fast shutdown systems — gravity-dropped shutoff rods and high-pressure injection of gadolinium nitrate into the moderator — for trips. A reflector of moderator around the core returns escaping neutrons and flattens the flux; shielding and the concrete containment protect the operators and the public. Two consequences of the design deserve emphasis. Because the channels are individually accessible, CANDU refuels on power, which is what makes a very low fuel burnup economically tolerable and avoids the reactivity swing that forces enriched-fuel reactors into burnable-poison chemistry. And because reactivity control ultimately depends on engineered systems rather than on a large negative void coefficient, redundancy and diversity in the shutdown systems are central to the Canadian licensing case administered by the Canadian Nuclear Safety Commission.