Comprehensive PWR & Nuclear Power Study Notes

PRESSURIZED-WATER REACTOR (PWR)

• Light-water, thermal-neutron power plant; two separate water loops keep radioactive primary circuit isolated from turbine side.
• Nominal core outlet ≈ $330\,^{\circ}\mathrm C$; pressure $\approx155\,\text{bar}$ (design ≈ 180 bar) keeps water sub-cooled.
• Core geometry ≈ right cylinder (H≈D) → minimum neutron leakage, simpler machining than sphere.
• Fuel: low-enriched UO$_2$ (3–5 % $^{235}\mathrm U$) formed into pellets → rods → square lattices $\;70\times70\;–\;90\times90$ rods/assembly.
• Gap between pellets/cladding filled with He (high k, inert, accommodates thermal expansion).
• Control rods (B, Ag-In-Cd, Hf) inserted from vessel head by step-type electromagnetic drive (15 mm per step). Gravity-insertion = SCRAM.
• Primary coolant also borated (soluble poison) for coarse reactivity swing; concentration tracked by Chemical & Volume Control Sys.

Two-Circuit Heat Removal

• Primary: RPV → hot-leg → steam generator (SG) tubes → cold-leg → RPV; 4 identical loops typical.
• Secondary: feedwater downcomer → boil on shell‐side of SG → moisture separators & dryers → turbine → condenser (≈ 40 ° C) → BFP → SG.
• Pressurizer attached to hot-leg nozzle; maintains pressure via electrical heaters + spray nozzles + relief/safety valves; liquid level instrumented to keep heaters flooded.

Start-up / Load-follow

1. Pressurize primary loop (heaters ON).

2. Withdraw control rods slowly; reach criticality; power ramp to 100 % over ≈ 24 h.

3. Load reduction (PWR): throttle turbine admission valve ⇒ SG pressure ↑ ⇒ secondary saturation T↑ ⇒ ΔT (primary–secondary) ↓ ⇒ fuel/coolant T↑ ⇒ density ↓ ⇒ moderation ↓ ⇒ negative reactivity (self-regulation). BWR behaves oppositely.

4. Hot-shutdown: rods in, T and P nominal, no steam production (SG ≈ 80 bar to limit wall-thickness).

Safety Containers

• Primary containment: spherical steel shell, designed for peak LOCA pressure & H$_2$ detonation; uniform stress field.
• Secondary containment: reinforced concrete cylinder/hemisphere; aircraft/quake protection, radiation shielding.
• All penetrations (4–8 per loop) fitted with redundant isolation valves (internal + external); feedwater & steam lines have isolation + check valves.
• Key principle: separation & redundancy – probability(all-valves-fail) ≈ 0 but not 0.

Design Basis Accidents

• Decay heat: 6 % of full power at t=0 s-shutdown, $\approx1\%$ at 1 h, tail to months ⇒ ECCS must remove.
• Loss-of-Coolant Accident (LOCA): flashing steam raises containment P,T. Spray, passive pools, or steel shell conduction condense steam.
• Hydrogen risk: Zr-steam reaction → H$_2$. Mitigation: recombiners, igniters, or inerted containment.

STEAM GENERATOR TECHNOLOGIES

• Vertical U-Tube (Westinghouse/EPR): primary inside tubes; secondary outside.
– Regions: tube sheet, tube support plates, down-comer, swirl-vane separators, dryers, steam nozzle (design ΔP).
• Once-Through (Babcock-Wilcox, Siemens): straight tubes; complete phase change; superheated steam; no recirculation.
• Horizontal (Russia VVER): U-tubes horizontal between inlet/outlet headers; larger shell.
• Issues: SCC & denting of Inconel-600 → modern Inconel-690; tube plugging acceptable up to ≈ 2 % before SG replacement (3 y outage).

PRESSURE VESSEL & INTERNALS

• Forged low-alloy carbon-steel, 15–25 cm wall, stainless-steel cladding 5–10 mm.
• Height ≈ 12 m, Φ ≈ 3–5 m. Upper head bolted to flange; CRDM penetrations.
• Neutron embrittlement: fast-flux displacements → ductile-to-brittle shift; managed via surveillance capsules and replaceable core shroud/reflectors (water+steel, bypass 1–3 %).

PRIMARY PUMP

• Vertical single‐stage centrifugal; shaft-seal sets; motor ≈ 5–7 MW-e; handles 155 bar, 292 ° C.
• Cooling & lubrication via heat exchanger; multiple seals in series.

REACTOR PHYSICS ESSENTIALS

• Fission of $^{235}\mathrm U$ by thermal n → $200\,\text{MeV}$, release $\nu\approx2.43$ n (normalised).
• Prompt n (99 %) $t_{em}\sim10^{-14}\,\text s$, delayed n (≈1 %) 6 groups $0.2–55\,\text s$; vital for control.
• Fission vs fissile: fissile (U-233, 235, Pu-239, 241) – fission w/ slow n; fissionable (Th-232, U-238) need fast n.

Neutron Cross-Sections

• $\sigma$ units: 1 barn = $10^{-24}\,\text{cm}^2$.
• $\sigma<em>t = \sigma</em>s + \sigma<em>a$; $\sigma</em>a = \sigma<em>f + \sigma</em>{n,\gamma} + …$
• Dependence on target, reaction, n-energy (resonances in U-238).

Neutron Balance & Multiplication

• Four-Factor (infinite) $k<em>{\infty}=\nu f \epsilon p$ where – $\nu$: n per absorption in fuel, – $f$: thermal fission probability, – $\epsilon$: fast-fission factor, – $p$: resonance-escape probability. • Six-Factor (finite) $k</em>{eff}=\epsilon\;P<em>{nf}\;p\;P</em>{tf}\;f\;\eta$ with $P<em>{nf},P</em>{tf}$ fast/thermal non-leakage.
• Critical when $k_{eff}=1$; control rods/boron vary $\rho=(k-1)/k$.

MODERATOR & COOLANT CHOICES

• Goal: maximise scattering, minimise absorption, high number density, low A.
• Candidates:
– Light water H$<em>2$O: high $\sigma</em>s$, cheap; high $\sigma<em>a$ ⇒ needs enrichment. – Heavy water D$</em>2$O: low absorption ⇒ can run on natural U; expensive.
– Graphite & Be: solid, low capture; larger core.
• Coolants: low macroscopic capture ⇒ water (requires enrichment), gas (CO$_2$, He), liquid metals (Na).

NUCLEAR FUEL CYCLE

Mining & Milling

• Ore bodies: open-pit, underground, ISL (acid/alkali), heap leach for low grade.
• Major producers: KZ (ISL), CA (high-grade), RU, AU.
• Tailings stored in water-covered dams; reclamation w/ clay+topsoil cap.

Conversion

• Yellowcake → UO$<em>3$ → UO$</em>2$ → UF$<em>4$ → UF$</em>6$ (wet or dry fluorination). UF$_6$ is volatile (subl 56 ° C) & single-isotope F.

Enrichment (3–5 % $^{235}\mathrm U$)

• Gas centrifuge dominant; separative work unit (SWU) metric.
– Centrifuge: UF$<em>6$ rotated; heavier $^{238}$UF$</em>6$ migrates outward; cascade stages.
– Ultra-centrifuge challenges: frictionless magnetic bearings, carbon-fibre rotors, resonance control.
• Gaseous diffusion obsolete (50-60× energy of centrifuge).

Fuel Fabrication

• UF$<em>6$ → UO$</em>2$ powder (ADU/AUC/dry); pressed at 400–500 MPa; sintered 1700–1800 ° C → 95 % TD.
• Pellets chamfered, central hole; loaded in Zircaloy cladding; filled He + spring.
• Rods sealed w/ end-plugs; assembled with guide‐ & instrumentation tubes, spacer grids, debris filters.

Burn-up & Reloading

• Burn-up (BU): $\text{MWd/tonU}$. Modern PWR ≈ 50–60 GWd/t.
• Refuelling every 12–18 mo; 20–25 % bundles replaced, others shuffled to even out flux.

Reprocessing & MOX

• PUREX: chop, dissolve in HNO$<em>3$, TBP solvent extraction separates U, Pu. • MOX: blend 5–10 % PuO$</em>2$ + UO$_2$ → pellets → PWR use (≈ 30 % core fraction).
• Closed cycle reduces HLW mass/heat, consumes plutonium; proliferation concerns → safeguards.

Waste Management

• Classification (IAEA GSG-1): VLLW, LLW, ILW, HLW; ~97 % volume is VL/LL.
• Interim wet pool storage (heat removal) then dry cask.
• HLW destined for Deep Geological Repository (DGR) 200–1000 m in stable host rock (e.g., Onkalo FIN 2026).

ECONOMICS & FINANCE

• Cost structure (nuclear): Capital > 50 %, Fuel < 30 %, O&M ≈ 15 %.
• High sensitivity to discount rate: $\text LCOE\uparrow$ 50 % when interest from 5 %→10 %.
• Learning curve: China/UAE build on continuous fleet – lower cost & schedule vs isolated Western builds (e.g., OL3 over-run from €3.2 → 12 bn).
• SMR rationale: lower absolute capital, factory fabrication but counters economies-of-scale.
• Financing models:
– Mankala (Olkiluoto): 25 % equity + 75 % debt; offtakers = shareholders, cost-price electricity.
– CfD (Hinkley C): strike £92.5/MWh (2012£) for 35 y; top-up/ claw-back protects investors & consumers.
– Regulated Asset Base (RAB) under consideration for Sizewell C.

ENVIRONMENTAL & LCA FINDINGS

• Full LCA GHG emissions: nuclear 5–12 g CO$_2$-eq/kWh (similar hydro/wind, lower than solar ≈ 45 g).
• Land use: 1 GW(e) nuclear ≈ 3 km$^2$ vs wind/solar hundreds km$^2$.
• Water: once-through vs cooling tower; thermal discharge managed under $\Delta T$ limits.
• LCA impact categories: acidification & eutrophication lowest for nuclear among dispatchable technologies; ecotoxicity driven by mining.

OTHER REACTOR CONCEPTS

• Gas-cooled: Magnox (CO$<em>2$ / Mg-Al cladding), AGR (SS cladding, UO$</em>2$, $650^{\circ}\mathrm C$), HTGR (He, TRISO pebbles).
• Heavy-water: CANDU – pressure tubes, natural U, on-power refuelling, good plutonium recycle.
• Gen-IV: SFR (Na coolant, fast spectrum, breeding), MSR (fuel salt, online processing).
• TRISO particles: UCO/UC kernel, porous C buffer, inner pyrolytic C, SiC barrier, outer PyC – retains fission products up to $1600^{\circ}\mathrm C$.

SPACE NUCLEAR APPLICATIONS

• RTG: Pu-238 decay heat → thermoelectric; used in Voyager, Curiosity; power O(100 W).
• Fission power (Kilopower, 10 kW) for lunar/Mars bases: U-235, NaK loop, Stirling conversion.
• Nuclear Thermal Propulsion (NTP): U-carbide fuel, LH$<em>2$ coolant/propellant; specific impulse $I</em>{sp}\approx900\,\text s$ (×2 chemical).
• Nuclear Electric Propulsion (NEP): fission ↠ Brayton or thermoelectric ↠ ion thrusters.

LEGAL & REGULATORY FRAMEWORK

• International: IAEA Safety Standards, NPT, Joint Convention, Convention on Nuclear Safety.
• EU: EURATOM Treaty; 2013 BSSD (\gamma, neutron dose limits); 2014 Nuclear Safety Directive – licensee primary responsibility.
• Safety review instruments: OSART, IRRS, IRS, REPA, WENRA reference levels.

SUMMARY EQUATIONS & DEFINITIONS

• Binding energy: $E=\Delta m c^2$.
• Multiplication factor: $k=\dfrac{\text{neutrons in gen }n+1}{\text{neutrons in gen }n}$.
• Four-factor: $k<em>{\infty}=\nu f \epsilon p$. • Six-factor: $k</em>{eff}=\epsilon P<em>{nf} p P</em>{tf} f \eta$.
• Burn-up: $BU=\dfrac{\text{MWd}<em>{thermal}}{\text t</em>{U}}$.
• Net cycle efficiency $\eta<em>{net}\approx33\%$ (Rankine). • Load factor: $LF=\dfrac{\sum</em>{year} P<em>{actual}}{P</em>{rated}\times8760\,h}$.

Study these bullet-points together with diagrams, timing curves, and numerical examples to master the full chain from neutron physics to plant economics and waste disposal.