NUCLEAR POWER PLANTS

• Heat source is the nuclear reactor with the heat coming from nuclear reactions (fission of uranium or other fissionable material) • Working fluid is water. Most plants use H2O (light water) and some use D2O (heavy water)

• Water acts as working fluid as well as “moderator” of the nuclear reaction (to be explained)

• Nuclear power plants are expensive (high capital costs).

• Cost of fuel is low

• Estimates of “overnight cost” (construction cost without including financing) is $5945 per kW (from world-nuclear.org) • Including financing, cost can vary between $6500 to $12,250 per kW for a 2GW plant (world-nuclear.org)

https://www.world-nuclear.org/information-library/economic-aspects/economics-of-nuclear-power.aspx Capital costs Costs are incurred while the generating plant is under construction and include expenditure on the necessary equipment, engineering and labour, as well as the cost of financing the investment. The overnight cost is the capital cost exclusive of financing charges accruing during the construction period. The overnight cost includes engineering, procurement and construction (EPC) costs, owners' costs (land, cooling infrastructure, associated buildings, site works, switchyards, project management, licences, etc.) and various contingencies. Construction/investment cost is the capital cost inclusive of all capital cost elements (overnight cost, cost escalation and financing charges). The construction cost is expressed in the same units as overnight cost and is useful for identifying the total cost of construction and for determining the effects of construction delays. In general the construction costs of nuclear power plants are significantly higher than for coal- or gas-fired plants because of the need to use special materials, and to incorporate sophisticated safety features and backup control equipment. These contribute much of the nuclear generation cost, but once the plant is built the cost variables are minor. About 80% of the overnight cost relates to EPC costs, with about 70% of these consisting of direct costs (physical plant equipment with labour and materials to assemble them) and 30% indirect costs (supervisory engineering and support labour costs with some materials). The remaining 20% of the overnight cost is for contingencies. Financing costs will be dictated by the construction period and the applicable interest charges on debt.

• Most common nuclear reactors • BWR (Boiling Water Reactors). Mostly older reactors.

• PWR (Pressurized Water Reactors). More recent and new reactors for electricity productions are all PWRs • Both of them use light water as coolant and moderator

• Both of them use a reactor core of enriched uranium (3.5% - 4.5%)

235 2.42U n A B n+ ⇒ + + • Fission of uranium is induced by a neutron “n” • Most common reaction products A, B are iodine, caesium, strontium, xenon, kripton and barium • On average, fission of U235 releases 2.42 neutrons that are used to induce other fission reactions (chain reaction) • Typical fission reactions of U release 200MeV of energy per reaction

MeV= megaelectronvolt= 106 eV = 1 million eVs 1eV =1.6× 10-19 Joules • Typical chemical oxidation reactions (burning of coal) release few eV per reaction • Nuclear reaction release ~ 106× more energy than chemical reactions • Most of the energy from a nuclear fission reaction is in the form of kinetic energy of the reaction products A and B

Typical fission reaction of uranium-235 used in nuclear reactors On average

235 2.42U n A B n+ ⇒ + +• Most common Uranium isotope is U238 (235 and 238 are the mass numbers, i.e. number of nucleons (protons+neutrons). All uranium isotopes have the same atomic number (of course) of 92 (92 protons) but differ in the number of neutrons 143 in U235 and 146 in U238

• The probability of a fission reaction to occur (fission cross section) is highest for the isotope U235 • The isotope U235 is only about 0.7% of the natural uranium. Most of uranium is U238

• Reactors like BWR and PWR requires enriched uranium with 3.5%-4.5% of U235

• Enrichment is done in centrifuges by exploiting the mass difference between U235 and U238

• Countries with largest uranium reserves are: Australia, Kazakhstan, Russia, Canada, South Africa, Niger, Namibia, China

235 ( ) 2.42 ( )U n slow A B n fast+ ⇒ + +

• The fission cross section for U235 is highest for “thermal” neutrons.

• Thermal neutrons are slow neutrons with an energy corresponding to room temperature: 1eV = 11606 Kelvin 290 K = 0.025eV typical energy of thermal neutrons • However, the neutrons produced in a fission reaction of U235 are fast with a mean energy of 2 MeV • Therefore, a “moderator” is required to slow down the fast neutrons (thermalization)

• Use elastic collisions with another nucleus (A) to slow down neutrons

• Momentum conservation

• Energy conservation

mn is the mass of the neutron and mA is the mass of nucleus A vn is the velocity of colliding neutron before collision vn’ is the neutron velocity after collision vA is the velocity of nucleus A after collision (A was initially at rest)

• From momentum conservation

• Substitute into energy conservation

• Define energy of neutron after and before collision

• The neutron energy is greatly reduced by elastic collision if mA≈mn

• The neutron energy is greatly reduced if hydrogen is the moderating agent It follows that water (H2O) is an excellent moderator

Reactor core

Some neutrons escape without causing fission

Some neutrons are absorbed without causing fission

235 2.42U n A B n+ ⇒ + +

Some neutrons trigger fission reactions. Higher enrichment more reactions

• This loss of neutrons depends on the surface to volume ratio. • The bigger the Surface/Volume ratio the greater the losses • Since

• These losses can be reduced by making the core big enough (i.e. critical mass)

1~linear size

SV

A steady state chain reaction requires a critical size of the reactor core which Depends on the enrichment of the fuel. The higher the enrichment level the smaller is the critical size (and the power density)

Reactor cores are designed to maintain the chain reaction at steady state. More complex phenomena such as delayed neutrons enable control of the fission chain reactions (not discussed here)

The reactor core

Fuel rod

Fuel Assembly

Reactor core has a cylindrical shape with vertical axis. The core is made up of hundreds of fuel elements of squared cores section. Each fuel elements supports many (<100) fuel rods of circular cross section. A neutron absorbing rod (boron) is placed between elements. Boron is a good neutron absorber and used to control the power level inside the reactor as well as for emergency shutdown (SCRAM). The shroud of each fuel rod is made of zirconium (material with low absorption of neutrons). The gap in each rod is filled with He. The rods are several meters long

Control rod (boron)

Reactor vessel for PWR Open vessel. View of fuel Elements. Glow from Cherenkov radiation

BOILING WATER REACTORS (BWR)

Layout of a BWR nuclear power plant

Control rods

pump pump

Jet pump

Steam separators

Saturated water at 70 bar

Steam separator

High Pressure Turbine

Low Pressure Turbine

Condenser Feedwater heater

Feedwater pump

Layout of a BWR nuclear power plant (NRC)

PRESSURIZED WATER REACTORS (PWR)

T

C P

PRESSURIZED WATER REACTORS. Primary loop (subcooled water) and secondary loop (steam cycle)

PRIMARY (high pressure subcooled water)

Secondary (steam cycle)

Water enters through the bottom of the reactor's core at about 548 K (275 °C; 527 °F) and is heated as it flows upwards through the reactor core to a temperature of about 588 K (315 °C; 599 °F). The water remains liquid despite the high temperature due to the high pressure in the primary coolant loop, usually around 155 bar (15.5 MPa 153 atm, 2,250 psi). In water, the critical point occurs at around 647 K (374 °C; 705 °F) and 22.064 MPa (3200 psi or 218 atm). [Wiki,international Association for the Properties of Water and Steam,

Reinforced concrete containment and shield

Control rods Pressurizer

Steam generator

Steel pressure vessel

Fuel elements Reactor core

Water

Steam

Wikipedia: layout of a PWR nuclear power plant

Layout of a PWR nuclear power plant (NRC)

Typical steam generator for PWR

Most PWRs have several steam generators fed by one reactor. There can be more than one reactor in a nuclear power plant

Reactor vessel

Steam generator Steam

generator

Steam generator

pump

pump

pump

Pressu- rizer