Nuclear Power Plants

Table of Contents
1. NUCLEAR POWER PLANTS
2. PRESSURISED WATER REACTOR (PWR)
3. BOILING WATER REACTOR (BWR)
4. GAS-COOLED REACTORS
5. LIQUID-METAL FAST BREEDER REACTOR (LMFBR)
6. HEAVY WATER REACTORS (HWR)
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NUCLEAR POWER PLANTS

Basic structure of atom and nuclear quantities

All matter is composed of unit particles called atoms. An atom consists of a relatively heavy, positively charged nucleus and much lighter negatively charged electrons orbiting the nucleus. The nucleus is made up of protons (positively charged) and neutrons (neutral); protons and neutrons are collectively called nucleons. The atom as a whole is electrically neutral because the number of protons equals the number of electrons.

The atomic number Z is the number of protons in the nucleus. The mass number A is the total number of nucleons (protons + neutrons). A nuclear symbol is commonly written as A _ZX (mass number as superscript, atomic number as subscript).

Most of the mass of an atom is concentrated in the nucleus. Typical length scales are:

• Radius of nucleus ≈ 10^-15 to 10^-14 m (order of 10^-16 m given in some texts)
• Radius of atom ≈ 10^-10 to 10^-11 m

Masses of primary sub-particles:

• Neutron mass, m_n = 1.008665 u = 1.674 × 10^-27 kg
• Proton mass, m_p = 1.007277 u = 1.673 × 10^-27 kg
• Electron mass, m_e = 0.0005486 u = 9.109 × 10^-31 kg

The atomic mass unit (amu or u) is approximately 1.66054 × 10^-27 kg.

• Hydrogen (¹H): nucleus contains one proton, zero neutrons (Z = 1, A = 1).
• Deuterium (²H): nucleus contains one proton and one neutron (Z = 1, A = 2).
• Helium (⁴He): nucleus contains two protons and two neutrons (Z = 2, A = 4).

Isotopes

Atoms that have the same number of protons (same Z) but different numbers of neutrons are called isotopes. Examples: ²³⁵U and ²³⁸U; ¹H, ²H, ³H.

Chemical reactions versus nuclear reactions

In a chemical reaction, atoms act as whole units and only the electrons participate; nuclear composition (protons and neutrons) remains unchanged. In a nuclear reaction, nuclei are involved and the numbers of nucleons can change, producing different nuclides.

Mass defect and binding energy

When nucleons (protons and neutrons) combine to form a nucleus, the mass of the nucleus is less than the sum of individual nucleon masses. This difference is called the mass defect, Δm.

The mass defect is converted to energy according to Einstein's mass-energy relation:

ΔE = Δm c²

The energy associated with the mass defect that binds the nucleons together is called the binding energy. Binding energy per nucleon indicates nuclear stability. The energy equivalent of 1 u mass is approximately 931 MeV (≈ 1 u × c² ≈ 931 × 10⁶ eV). One electron volt (eV) = 1.6021 × 10^-19 J.

Radioactivity: types of emission and properties

Common types of radioactive emissions:

• Alpha (α) radiation: Emission of a helium nucleus (⁴He: two protons and two neutrons). α-decay reduces the mass number by 4 and the atomic number by 2.
• Beta (β) radiation: Emission of an electron (β⁻) or positron (β⁺). In β⁻ decay a neutron converts to a proton and an electron is emitted; atomic number increases by 1 while mass number remains unchanged. Beta emission is often accompanied by emission of a neutrino.
• Gamma (γ) radiation: Electromagnetic radiation of very short wavelength and very high frequency emitted when an excited nucleus falls to a lower energy state. γ-decay does not change atomic or mass numbers; it only carries away excess energy.
• Neutron emission: A highly excited nucleus may emit one or more neutrons; mass number of daughter nucleus decreases by the number of neutrons emitted.

Penetrating power: γ > β > α.

Radioactive decay law and half-life

For a large number of identical radioactive nuclei, the decay rate (activity) is proportional to the number of undecayed nuclei present at time t. Let N(t) be the number of nuclei at time t and λ the decay constant (s^-1).

Derivation (stepwise):

The rate of change of N with time is proportional to N:

-dN/dt = λ N

Separate variables and integrate:

∫(dN/N) = -∫ λ dt

Integration gives:

ln N = -λ t + constant

Using initial condition N(0) = N₀:

ln N₀ = constant

Therefore:

N(t) = N₀ e^{-λ t}

The activity A(t), defined as the decay rate (disintegrations per second), is:

A(t) = -dN/dt = λ N(t) = λ N₀ e^{-λ t}

The half-life t_1/2 is the time for which N reduces to N₀/2. From N(t) = N₀ e^{-λ t} we get:

At t = t_1/2, N = N₀/2 = N₀ e^{-λ t_1/2}

Therefore:

1/2 = e^{-λ t_1/2}

Taking natural logs:

ln 2 = λ t_1/2

Thus:

t_1/2 = (ln 2) / λ ≈ 0.693 / λ

Some half-lives

Units of radioactivity:

• Curie (Ci) - historical unit. 1 Ci ≈ 3.7 × 10¹⁰ disintegrations per second (dis/s).
• Becquerel (Bq) - SI unit. 1 Bq = 1 disintegration per second.

Nuclear fission

Nuclear fission occurs when a heavy nucleus absorbs a neutron (or other particle), becomes unstable and splits into two (or more) lighter nuclei, releasing energy, neutrons and other particles. Fission can be spontaneous for some nuclides but is most often induced by neutron absorption.

• Common fissionable fuels: ²³³U, ²³⁵U, ²³⁹Pu (²³⁹U is not a common designation; plutonium-239, ²³⁹Pu, is commonly used in reactors and breeders).
• Fission releases several neutrons; these neutrons can induce further fissions - this is the basis of a chain reaction.
• Moderator: Material used to slow down fast neutrons to thermal energies (thermal neutrons), increasing the probability of fission in certain fuels (e.g. light water, heavy water, graphite).
• Fuel burnup is the amount of energy produced per unit mass of nuclear fuel, typically expressed in MW-days per metric ton of fuel.

Basic reactor components and functions

• Fuel: Fissile material (e.g. enriched uranium or mixed oxide fuel) arranged in fuel assemblies.
• Moderator: Slows down neutrons (e.g. light water, heavy water, graphite).
• Coolant: Transfers heat from the core to the heat exchanger/steam generator (e.g. water, CO₂, helium, liquid sodium).
• Control rods: Inserted/withdrawn to absorb neutrons and control reactivity (typically made of boron, cadmium or hafnium alloys).
• Pressure vessel / reactor vessel: Contains the core and coolant at required pressure.
• Heat exchanger / steam generator: Transfers thermal energy to a secondary circuit to drive turbines.
• Shielding: Protects personnel and environment from ionising radiation.

PRESSURISED WATER REACTOR (PWR)

PWRs are light-water moderated and cooled reactors that use enriched uranium fuel. The primary coolant (water) is kept at high pressure so it does not boil in the core; heat from the primary circuit is transferred to a secondary circuit where steam is produced to drive the turbines.

Main components commonly associated with the PWR primary system:

• Reactor core (fuel assemblies)
• Reactor pressure vessel
• Primary coolant pump(s)
• Steam generator (primary-to-secondary heat exchanger)
• Pressurizer
• Control rods and drive mechanisms

Function of the pressurizer: It maintains the primary circuit pressure within the required range throughout the load cycle. Electric heaters in the pressurizer produce a small volume of steam collected in the pressurizer dome to set the pressure. Water spray can condense steam to reduce pressure when required.

Operation summary:

• Heat from fission in the reactor core is absorbed by the primary coolant (water) circulating through the core.
• The hot primary coolant flows through the steam generator where it transfers heat to the secondary water circuit, producing steam for the turbine.
• The primary coolant remains liquid (no phase change) and is recirculated by pumps at pressures typically in the range 100-160 bar (typical commercial PWRs operate near 150 bar).

Precautions and safety considerations:

• Primary coolant becomes radioactive due to neutron activation and must be contained and shielded; this requires robust shielding of the primary circuit.
• Secondary steam is normally non-radioactive since it is separated from the primary coolant by the steam generator. However, leaks or failures require careful design and monitoring.

Advantages of PWR:

• Water as coolant/moderator is readily available and well understood.
• Compact core and relatively high power density.
• Complete separation of primary and secondary circuits allows optimisation of the turbine and steam cycle and easier maintenance of turbine plant during operation.
• Good fuel utilisation with high burnups possible in some designs.
• Negative temperature coefficient of reactivity contributes to safe and stable operation.

Disadvantages of PWR:

• High primary circuit pressure requires a strong pressure vessel and associated high capital cost.
• High-pressure systems increase corrosion and material degradation issues.
• Thermal efficiency is limited by operating temperatures and pressures; typical thermal efficiency for some PWR plants is lower than certain other reactor types.

BOILING WATER REACTOR (BWR)

In the BWR, water acts as coolant and moderator and is allowed to boil in the core. Steam produced in the reactor vessel is sent directly to the turbine (single circuit). BWRs use enriched uranium fuel as well.

Advantages of BWR:

• Lower operating pressure in the reactor vessel compared with PWRs, reducing pressure vessel cost.
• No separate steam generator or pressurizer is required, simplifying the primary circuit.
• Lower metal temperatures for given output conditions in some designs.
• BWRs exhibit self-stabilising behaviour: increased reactivity → increased steam formation → reduced moderation and consequently reduced reactivity (often described as partial self-control).
• Higher thermal efficiency compared with some PWR designs (typical LWR efficiencies around 30% depending on cycle conditions).

Disadvantages of BWR:

• Steam passing through the reactor becomes in direct contact with fuel: possibility of radioactive contamination of turbine and turbine plant if fuel cladding fails.
• More elaborate and costly safety systems may be required for certain scenarios.
• Power density and boiling limits can constrain design; only a small fraction of coolant mass may change phase per pass through the core.
• Risk of local dryout or "burn-out" (departure from nucleate boiling) if heat flux from fuel surfaces becomes excessive.

GAS-COOLED REACTORS

Gas-cooled reactors use a gas coolant (e.g. carbon dioxide, helium, or even air/hydrogen in early designs) and graphite as moderator. These reactors are typically more tolerant to certain accident conditions and can operate at higher temperatures than water-cooled reactors, allowing potentially higher thermal efficiencies.

Two common gas-cooled reactor classes:

• Gas cooled, graphite moderated (GCGM) - traditionally used natural uranium fuel and CO₂ coolant with graphite moderator.
• High temperature gas cooled reactor (HTGR) - uses helium coolant and graphite moderator, often with ceramic fuel forms; operates at much higher outlet temperatures for process heat applications.

LIQUID-METAL FAST BREEDER REACTOR (LMFBR)

Fast breeder reactors are designed to produce (breed) more fissile material than they consume while producing power. A typical breeding reaction converts fertile ²³⁸U to fissile ²³⁹Pu by successive neutron captures and β decays. Fast reactors operate with little or no moderator so neutrons remain at high energy (fast).

Definitions and relationships:

When a fission produces on average ν neutrons per fission, and losses due to leakage and parasitic captures are L, the conversion or breeding ratio C is:

C = ν - 1 - L

The maximum possible breeding ratio, if L = 0, is:

C_max = ν - 1

A reactor with C < 1 is a burner.

A reactor with C = 1 produces as many fissile nuclei as it consumes (a converter operating at unity conversion).

A reactor with C > 1 is a breeder and produces net fissile material.

The breeding gain G is defined as the net increase of fissile nuclei per fissile nucleus consumed:

G = C - 1 = ν - 2 - L

Doubling time is the time required to produce twice the number of fissile nuclei originally present (important for fissile-material growth in a breeder programme).

• Fast reactors typically have smaller cores for a given power because of the high concentration of fissile fuel and absence of moderator; high power density is common.
• Thin fuel pins and an efficient coolant are used to minimise temperature drops and remove heat effectively.

Coolants for fast reactors should have excellent heat transfer, low moderation (do not slow neutrons) and a high boiling point so the reactor can operate at low pressure. Liquid metals such as sodium (Na) are commonly used. Sodium has a high boiling point and good thermal conductivity, allowing unpressurised operation at high temperature.

However, sodium becomes radioactive by neutron activation (produces ²⁴Na), so an intermediate circuit is commonly used to isolate the primary radioactive sodium from the steam cycle.

²⁴Na is radioactive and decays with a half-life of about 14.8 hours, emitting β and γ radiation; it decays to stable ²⁴Mg.

• Because of the induced radioactivity of liquid sodium, many plant designs use an intermediate sodium loop (Na or NaK) between the primary radioactive sodium and the steam generator to reduce radiological risk.

Primary loop designs for liquid-metal fast reactors are commonly:

• Pool type: Reactor core, primary pumps and intermediate heat exchangers are placed in a large pool of liquid sodium inside the reactor vessel.
• Loop type: The intermediate heat exchanger and pumps are located outside the reactor vessel, with piping connecting these components to the vessel.

HEAVY WATER REACTORS (HWR)

Heavy water reactors use heavy water (D₂O) as moderator and usually also as coolant. Heavy water is a very effective moderator and allows the use of natural uranium (≈0.7% ²³⁵U) as fuel in many designs because heavy water absorbs fewer neutrons than light water. Examples include the CANDU family of reactors.

Activation and radiological notes

Radioactive products and activation of structural materials and coolant require suitable shielding, containment and waste management systems. Reactor designs include engineered barriers, multiple containment zones and radiation monitoring to protect personnel and the public.

Location considerations for nuclear power plants

• Availability of adequate cooling water (rivers, lakes, sea) for condenser and heat rejection.
• Good transport facilities for construction materials, fuel and personnel.
• Safe distance from major population centres; access to transmission lines and load centres.
• Seismic stability and suitable geology for reactor foundations and containment structures.
• Facilities and plans for radioactive waste handling, storage and disposal.
• Environmental impact, emergency planning zones and public safety considerations.

Summary and applications

Nuclear power plants convert energy released by nuclear reactions (primarily fission) into electrical power by heating a working fluid to produce steam that drives turbines. Reactor design choices - choice of coolant, moderator and fuel - determine operating conditions, safety features, efficiency and fuel utilisation. Understanding atomic and nuclear fundamentals (mass defect, binding energy, types of radiation and radioactive decay) is essential to analyse reactor behaviour, shielding, and radiological safety.