Question 5 of 6: Fuel Characteristics

Question 5: 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 (a) — Heating value, higher and lower

The heating value, or calorific value, of a fuel is the quantity of heat released when unit mass (or unit volume, for a gas) is burned completely with stoichiometric air, the products being returned to the same temperature as the reactants entered — conventionally 25 °C. It is measured in a bomb calorimeter at constant volume for solid and liquid fuels, and it is the single number on which every fuel purchase, every boiler efficiency calculation and every plant heat rate ultimately rests.

The ambiguity that gives rise to two values concerns the water in the products. Every hydrocarbon fuel contains hydrogen, which burns to water vapour, and most solid fuels also carry free moisture that is evaporated during combustion. If the products are cooled far enough for that water to condense, the latent heat of condensation — about 2440 kJ per kilogram of water — is recovered and appears in the measurement. That figure is the higher heating value (HHV), also called the gross calorific value: it is what the bomb calorimeter reads, because the bomb and its water jacket cool the products right back to ambient. If instead the water is allowed to leave as vapour, as it does up a real chimney, that latent heat is lost with the flue gas and the useful release is smaller. That figure is the lower heating value (LHV), or net calorific value.

The two are related by the mass of water formed and evaporated per kilogram of fuel:

where \(m_{H_2}\) is the mass fraction of hydrogen in the fuel (each kilogram of hydrogen produces nine kilograms of water) and \(m_{H_2O}\) the free moisture. For a bituminous coal with 5 % hydrogen and 5 % moisture the difference is about 1220 kJ/kg, roughly 4 % of the heating value; for natural gas, which is 25 % hydrogen by mass, it is nearly 11 %; for wood or lignite carrying 30–50 % moisture it can exceed 15 %.

Which is "commonly used" depends on the tradition. In North America — and in this examination, where the Nanticoke coal is quoted at 30 240 kJ/kg (13 000 Btu/lb) — the higher heating value is the customary basis: coal and gas are bought and sold on HHV, boiler efficiencies are quoted on HHV, and utility heat rates in Btu/kWh are HHV figures. European practice and most gas-turbine and engine manufacturers quote LHV instead, which flatters efficiency by several percentage points. The practical rule is simply that the basis must be stated: an efficiency quoted on LHV and compared against one on HHV is a comparison of nothing. Since a conventional boiler exhausts above the acid dew point and therefore cannot recover the latent heat, LHV arguably describes the available energy better — but a condensing boiler or a flue-gas condenser does recover part of it, which is why such units are legitimately advertised at efficiencies above 100 % on an LHV basis.

Part I (b) — Coals of different rank

Coal begins as accumulated vegetal matter in a swamp. Burial under sediment applies pressure and, more importantly, geothermal heat over geological time, and the biochemical and then geochemical process known as coalification progressively expels water, carbon dioxide and methane, leaving a residue steadily richer in carbon. The rank of a coal is a measure of how far that process has gone, and essentially every property of the fuel follows from it.

In ascending order of rank:

• Peat — barely coal at all: 75–90 % moisture as dug, 55 % even after field drying, heating value about 8–12 MJ/kg. Fibrous plant structure still visible. Used only where it is locally abundant.
• Lignite (brown coal) — 25–45 % moisture, 25–35 % volatile matter, 25–30 % fixed carbon, heating value 14–19 MJ/kg. Friable, prone to spontaneous combustion in storage, and uneconomic to transport far, so lignite plants sit on the mine.
• Sub-bituminous — 15–30 % moisture, heating value 19–26 MJ/kg. The staple of many western North American stations; low sulphur is its commercial attraction.
• Bituminous — 2–15 % moisture, 20–35 % volatile matter, 45–70 % fixed carbon, heating value 27–34 MJ/kg. The classic utility and coking steam coal, and the grade assumed for Nanticoke at 30.2 MJ/kg.
• Anthracite — under 5 % moisture, under 8 % volatile matter, 85–95 % fixed carbon, heating value 32–35 MJ/kg. Hard, lustrous, nearly smokeless.

Three trends run through that list, and all three have the same cause. Moisture falls because water is squeezed out mechanically and driven off thermally; since water contributes nothing to combustion and must itself be evaporated, its removal alone lifts the heating value. Volatile matter falls because the oxygen- and hydrogen-rich functional groups of the original cellulose and lignin are progressively cracked off as water, carbon dioxide and methane. Fixed carbon rises as the inevitable complement. The heating value therefore climbs monotonically with rank — except at the very top, where anthracite's near-total loss of hydrogen slightly offsets its carbon content, so the highest heating values per kilogram belong to low-volatile bituminous coals rather than to anthracite itself.

These characteristics govern how the coal must be burned. High-volatile coals ignite readily and hold a stable flame close to the burner; anthracite is hard to ignite and needs high preheat, a longer furnace and often a supporting oil flame. Low-rank coals need larger mills and larger furnaces for the same heat release, because so much of the mass throughput is water and ash, and they demand higher air-heater duty to dry the fuel. Ash content and ash-fusion temperature, which vary with the depositional environment rather than with rank, then decide whether the boiler can be a dry-bottom or a slagging design. Sulphur, largely inherited from the original swamp chemistry, sets the flue-gas desulphurisation requirement under Canadian federal and provincial air-quality standards.

Part I (c) — Proximate and ultimate analysis

Coal is characterised by two standard analyses, and the distinction between them is the distinction between an operational and a chemical description of the fuel.

The proximate analysis divides the coal into four operationally defined fractions, determined by successively heating a sample under controlled conditions: moisture (mass lost at 105–110 °C), volatile matter (further mass lost on heating to 950 °C out of contact with air), ash (the incombustible residue after burning off in air at 750 °C), and fixed carbon (obtained by difference: 100 % less the other three). The four sum to 100 %, and the analysis is usually reported alongside the heating value and the sulphur content. It is quick, cheap and directly useful to the plant: volatile matter predicts ignition behaviour and flame stability and therefore burner and furnace design; moisture sizes the mills and the air heater and depresses the heating value; ash sizes the ash-handling plant, drives fouling and slagging, and abrades mill and burner components; fixed carbon indicates the char that must burn out in the furnace residence time. The proximate analysis is what a station uses day to day to check that the delivered coal matches the design coal.

The ultimate analysis instead reports the elemental composition by mass — carbon, hydrogen, oxygen, nitrogen, sulphur, plus ash and moisture — determined by combustion and gravimetric or instrumental chemistry. It is the analysis needed for any calculation involving combustion stoichiometry: the theoretical air requirement, the mass and composition of the flue gas, the dew point of the flue gas, the carbon dioxide emitted per unit of energy, the sulphur dioxide loading on a scrubber, and the hydrogen content required to convert between higher and lower heating value as in Part I (a). It also allows the heating value to be estimated where it has not been measured, through correlations such as Dulong's formula:

with the elements as mass fractions. In short, the proximate analysis tells the operator how the coal will behave; the ultimate analysis tells the engineer what the coal is, and is the only basis on which air, flue gas and emissions can be computed. A complete fuel specification quotes both, together with the calorific value, the ash-fusion temperatures and the grindability index, and states the basis — as-received, air-dried, dry, or dry-ash-free — since the same coal yields quite different numbers on each.

Part II (a) — The fission process (CANDU reactor)

The reactor chosen here is the CANDU pressurised heavy-water reactor, the Canadian design that generates the majority of Ontario's electricity and the plant the previous question's nuclear station represents.

Nuclear fission is the splitting of a heavy nucleus into two lighter fragments. In a CANDU the fissile nuclide is uranium-235, present at its natural abundance of 0.72 % in fuel that is otherwise uranium-238, pressed and sintered as uranium dioxide (UO₂) pellets. When a slow — "thermal" — neutron is absorbed by a U-235 nucleus, the resulting U-236 compound nucleus is left in an excited state that it cannot accommodate, and within about 10⁻¹⁴ s it deforms and splits. A representative reaction is

The products are therefore of three kinds. Fission fragments — typically one nucleus of mass 90–100 and one of mass 135–145 — carry about 168 MeV as kinetic energy and are stopped within microns inside the fuel pellet, which is where essentially all the heat appears. Neutrons, on average 2.4 per fission, are emitted at about 2 MeV; these sustain the chain reaction. Radiation — prompt gamma rays, and beta and gamma decay of the radioactive fission products — accounts for the remaining energy, part of it deposited outside the fuel and part released with a delay of seconds to years, which is the origin of decay heat and of the requirement to cool a shut-down reactor. Total recoverable energy is about 200 MeV per fission, or roughly 3.2 × 10⁻¹¹ J: one gram of U-235 fissioned yields about 1 MW-day, some three million times the energy of a gram of coal.

Fission is initiated in a fresh core by a neutron source (an antimony–beryllium or californium source), and thereafter by the neutrons of the previous generation. The essential difficulty is that the neutrons are born fast while the U-235 fission cross-section is large only at thermal energies — 585 barns at 0.025 eV against a fraction of a barn at 2 MeV. They must therefore be slowed by elastic collision with a light nucleus, the moderator, without being absorbed on the way. This is the whole reason CANDU uses heavy water (D₂O): deuterium's neutron absorption cross-section is some 600 times smaller than that of ordinary hydrogen, so the neutron economy is good enough to sustain a chain reaction in natural uranium and no enrichment plant is needed — a decisive strategic advantage for Canada, which has uranium but chose not to build enrichment capacity.

The basic requirements of a nuclear fuel follow from the environment it must survive. It must contain enough fissile material for the lattice to reach criticality with the chosen moderator; it must have a high melting point (UO₂ melts at about 2800 °C) and remain dimensionally and chemically stable under intense radiation, since the fuel is the hottest component and any melting releases the fission-product inventory; it must retain gaseous fission products (xenon, krypton) within the pellet and accommodate the swelling they cause; it must resist corrosion by the coolant should the sheath fail; it must have adequate thermal conductivity to conduct heat out of the pellet centre, which is UO₂'s principal weakness and the reason CANDU pellets are small and the fuel bundles thin; and it must be economical to fabricate and to reprocess or dispose of. UO₂ meets these criteria well enough to be the near-universal choice, clad in a thin Zircaloy sheath — zirconium being chosen for its very low neutron absorption, its strength at temperature and its corrosion resistance in hot water.

Part II (b) — Reactor design requirements and internal components

A power reactor must satisfy four simultaneous requirements: it must be able to sustain a controlled chain reaction over a full fuel cycle; it must remove heat from the fuel fast enough that no part of it approaches its melting point under any credible condition, including after shutdown; it must shut down reliably and rapidly on demand; and it must contain its radioactive inventory against the whole spectrum of postulated accidents. Every internal component exists to serve one or more of these.

The core of a CANDU is a horizontal cylindrical tank, the calandria, pierced by several hundred horizontal fuel channels. Each channel contains a pressure tube of zirconium–niobium alloy holding twelve or thirteen fuel bundles, and each pressure tube is separated from the calandria by an insulating gas annulus. This separation of the high-pressure coolant from the low-pressure moderator is CANDU's defining feature, and it has two consequences: it removes the need for a single massive pressure vessel, and it makes on-power refuelling possible, which in turn allows the reactor to run at high capacity factor on natural-uranium fuel whose reactivity margin is small.

The fuel is natural UO₂ in Zircaloy-sheathed bundles. The moderator is heavy water at low temperature and near-atmospheric pressure, filling the calandria and surrounding the channels; its job is purely neutronic — to thermalise the fission neutrons — and because it is cool and separate it also constitutes a large heat sink in an accident. The coolant is separate heavy water, pumped at about 10 MPa through the pressure tubes, entering at roughly 265 °C and leaving at 310 °C; it carries the fission heat to the steam generators, where it boils ordinary light water in a secondary circuit to raise steam at about 4.6 MPa. Because that steam is saturated rather than superheated, the cycle efficiency is limited to about 33 %, which is precisely the figure Question 4 uses.

The chain reaction is maintained by keeping the effective multiplication factor \(k_{eff}\) at unity, so that exactly one neutron from each fission goes on to cause the next. That balance is held by reactivity control devices inserted into the moderator between the channels — light-water zone-control compartments for fine, continuous adjustment, together with adjuster rods and, for shutdown, cadmium shut-off rods that drop by gravity and a wholly independent system that injects gadolinium nitrate poison into the moderator. Two independent, diverse, fast-acting shutdown systems are a licensing requirement of the Canadian Nuclear Safety Commission. Control is made practicable by the small fraction — about 0.65 % — of neutrons that are emitted not promptly but over seconds by decaying fission products: these delayed neutrons stretch the reactor's response time from microseconds to tens of seconds and are what make a nuclear reactor controllable at all. Additional stability comes from the negative fuel temperature coefficient arising from Doppler broadening of the U-238 resonances, so that a rise in fuel temperature immediately absorbs more neutrons and reduces reactivity.

Around all of this sit the reflector (surplus moderator, returning leaking neutrons to the core and flattening the flux), the biological shield of concrete and water, the calandria vault, and the containment building with its vacuum-building pressure-suppression system unique to multi-unit Canadian stations. Energy removal, finally, is a chain of thermal resistances that the designer must respect at every link: heat is generated volumetrically in the pellet, conducted to the pellet surface against UO₂'s poor conductivity, crosses the pellet-to-sheath gap, conducts through the Zircaloy, and is finally convected to the coolant. The limiting condition is the critical heat flux, at which boiling on the sheath becomes film boiling and the surface temperature jumps by hundreds of degrees; operating margin to that point governs the permitted channel power. Emergency core cooling and long-term decay-heat removal — the fission products continue to release about 7 % of full power immediately after shutdown, decaying to under 1 % after an hour — must remain available on loss of the main coolant, and it is that requirement, more than any other, that shapes the safety systems of the plant.