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Nuclear Reactor Safety Technology of Accident Analysis J.T.Rogers Winter 2004 UNENE Topics ● Reactor Physics Review ● Fuel Behavior ● Thermalhydraulics ● Design-Basis Accidents ● Severe Accidents in CANDU Reactors Neutron Cycle Diagram Criticality Equation η.ε.p.f.Pf.Pth = keff = 1 η = fast neutrons emitted per absorption in fuel ε = neutrons produced by fast fission in U-238 p = resonance escape probability f = thermal neutrons absorbed in fuel Pf = fast neutron non-leakage probability Pth = thermal neutron non-leakage probability keff = effective multiplication factor kinf = η.ε.p.f Non-Leakage Probabilities Pf = exp(-B2 . τ) Pth= 1/(1+B2.L2) B2 = Buckling, cm-2 τ = Fermi Age, cm2 L = thermal diffusion length, cm Materials Buckling: B2m = (υ.Σf – Σa)/D Geometric Buckling, Cylindrical Geometry B2g = (2.405/R)2 + (π/H)2 where: υ = fast neutrons produced per fission Σf = macroscopic fission cross-section, cm-1 Σa = macroscopic absorption cross-section, cm-1 D = neutron diffusion coefficient, cm R = reactor core radius, cm H = reactor core length, cm CANDU Core Parameters Fresh Fuel Equilibrium Fuel η 1.2433 1.1990 ε 1.0277 1.0276 p 0.9036 0.9039 f 0.9315 0.9375 kinf 1.0755 1.0440 τ, cm2 155 155 L, cm 15.55 14.95 Neutron Diffusion Equation One energy group, one dimension, steady-state D.d2Φ/dx2 + [υ.Σf- Σa].Φ = 0 Φ = neutron flux, n/(cm2.s) Σa = macroscopic absorption cross-section, cm-1 Σf = macroscopic fission cross-section, cm-1 υ = neutrons per fission D = neutron diffusion coefficient, cm x = distance, cm Fuel Critical Mass and Implications Coolant Void Reactivity (CVR) ● CANDU “over-moderated” ● Voiding of channels in a LOCA reduces moderator/uranium ratio ● Core reactivity goes positive, power increases ● Requires two independent, reliable, diverse shutdown systems ● LWR “under-moderated”, opposite behavior ● ACR designed for negative CVR Point Kinetics Equations dN(t)/dt = (ρ-β).N(t)/l* +Σ [λi.Ci(t)] dCi(t)/dt = βi.N(t)/l* - λ iCi(t) β = Σ βi , i = 1 to 6 ρ = (k - 1)/k Importance of Delayed Neutrons ● Small fraction of neutrons (~ 0.6% in CANDU) are emitted by decay of fission products ● Characterized by six groups with half lives from 0.2 to 53.7 seconds, compared to prompt neutron lifetime of about 10- 4 seconds in CANDU ● Also, in CANDU, photoneutrons are produced in the moderator by core gamma rays, with average half life of 16.7 minutes ● Delayed neutrons make reactor control practical Neutron Flux Behavior in CANDU ● Neutron flux varies spatially in normal operation because of leakage, adjuster rods, zone controllers, fuelling, xenon ● Zone controllers needed to prevent xenon oscillations caused by on-power fuelling which could cause bundle power limits to be exceeded ● Neutron flux tilts occur in accidents because of voiding of one loop and insertion of shutoff rods (SDS1) from the top Analysis of Neutron Behavior ● Diffusion Theory: Simplified model, analogous to heat conduction. Neutron flux function of position only ● Transport Theory: Neutron flux function of position, energy, direction ● Diffusion theory breaks down at exterior boundaries, near or within strong absorbers and at interfaces between dissimilar materials. Industry Standard Toolset (IST) Computer Codes ● Single set of key computer codes for licensing and safety analysis ● Validation, quality assurance, maintenance ● Meet CNSC quality assurance standards: CNSC regulatory guides and CSA standards ● AECL responsible for certain codes, OPG for others CANDU Reactor Physics IST Codes WIMS, DRAGON ● Transport theory cell codes for fuel bundle, pressure tube, calandria tube, control mechanisms RFSP ● Diffusion theory core code; models neutron diffusion from cell to cell Decay Heat ● After reactor trip, power still produced by radioactive decay of fission products ● For trip after long operation, the decay power as a fraction of initial power can be approximated by: P(t)/Po = 6.6 x 10-2 t-2 , with t in seconds ● Relatively slow decay results in sizeable heat load for a long time after shutdown. Heat Flow in Fuel Elements (1) Conduction in fuel: -kf .[δ2T/δr2+1/r.(δT/δr)] = ρ.C.δT/δt + Qv (Transient) -kf .[d2T/dr2+1/r.(dT/dr)] = Qv (Steady state) To – Tfo = Qv.R2/(4.kf) (S.S., integrated, Qv & kf const.) Heat transfer across gap (fission product gases plus fill gas & contact conductance): q = hg.(Tfo – Tsi) Heat transfer across sheath: q = ks .(Tsi – Tso)/w (Steady state) Heat Flow in Fuel Elements (2) T = temperature, K Qv = heat generation in fuel,Wm-3 q = heat flux, Wm-2 r = radius, m w = sheath thickness, m t = time, s kf = fuel conductivity, Wm-1K-1 ks = sheath conductivity, Wm-1K-1 hg = gap conductance, Wm-2K-11 ρ = fuel density, kg.m-3 C = fuel specific heat, J.kg-1 Location of Fission Products • Fission products formed within fuel grains • Diffuse <10% >90% – Bound inventory Fission products – in grains move this way with – Grain boundary increasing inventory temperature & burnup – Gap inventory Fuel Behavior under Irradiation • Cracking • Swelling • Dishing/ridging • Gas pressure increase • Pellet-clad interaction Un-irradiated Irradiated Fuel Fuel (exaggerated) Fuel Behavior in Accidents Key Safety Parameters: ● Fuel temperature * Potential sheath failure * Potential pressure tube failure (Creep rupture, DHC) * Limited effect on physics ● Fuel sheath integrity ● Fission product inventory and release Fuel Behavior in Power Increase ● Temperature gradient across fuel pellet causes tensile stress in outer region. ● As power, and thus pellet temperature, increase, pellet cracks increase. ● As power and temperature rise further, central melting may begin. (UO2 MP = 2840 oC) ● Gas and volatile fission products release rates will increase. IST Codes for Fuel Behavior ELESTRES Models micro-structural, mechanical and thermal behavior of CANDU fuel element under normal operating conditions. Used to quantify pre- accident conditions. ELOCA Models thermo-mechanical behavior of a CANDU fuel element under accident conditions. Thermalhydraulics ● Two-Phase Flow Patterns ● System Thermalhydraulics Model ● Critical Heat Flux (DNB, Dryout) ● Post-Dryout Heat Transfer ● Two-Phase Critical Flow ● Two-Phase Flow Instabilities Two-Phase Flow Patterns Lamari & Rogers Horizontal Flow Regime Map Jg*= Gg/[g.d.ρg.(ρf-ρg)]0.5; X= (ρg/ρf)0.5.(μf/μg)0.1.[(1-x)/x]0.9 Two-Phase Flow Models ● Homogeneous model: Pseudo-fluid with averaged properties of vapor and liquid. Void fraction, α = Ag/At= 1/[1+ ρg .(1-x)/(ρf.x)] ● Slip flow model: allows for relative velocity (slip) between phases. α = 1/[1+ S.ρg .(1-x)/(ρf.x)] , S = ug/uf ● Separated flow model or two-fluid model (non- equilibrium model): vapor and liquid flow at different temperatures and velocities CANDU System Thermalhydraulics Model (1) ● Equations of mass, momentum and energy conservation for each phase in transient two- phase flow in a one-dimensional network + liquid and vapor plus non-condensable gases + non-equilibrium between phases + parallel and series paths ● Equations of state for each phase and n-c gases CANDU System Thermalhydraulics Model (2) ● Component models for fuel, fuel channels, feeders, headers, piping, valves, pumps, steam generators, secondary system, etc. ● Correlations for pressure drop, void fraction, heat transfer, critical heat flux ● Models of plant controllers Conservation of Mass Liquid phase: δ[ρf .A.{(1-α).uf}]/δz + δ[ρf.A.(1-α)]/δt = - Γ.A Vapor phase: δ[ρg.A.{α.ug}]/δz + δ[ρg.A.α]/δt = Γ.A Conservation of Momentum Liquid phase: δ[ρf.A.{(1-α).uf2}]/δz + δ[ρf.A.{(1-α).uf}]/δt = -(1-α).A.δp/δz + ρf.g.sinθ.(1-α).A - τwf.Pwf + τi.Pi -Γ.ufi.A Vapor phase: δ[ρg.A.{α.ug2}]/δz + δ[ρg.A.{α.ug}]/δt = -α.A.δp/δz + ρg.g.sinθ.α.A - τwg.Pwg - τi.Pi + Γ.ugi.A Conservation of Energy Liquid phase: δ[ρf.A.{(1-α).uf.hf}]/δz + δ[ρf.A.{(1-α).hf}]/δt = A.(1-α).δp/δt +qf".Phf + qif".Pi – Γ.hfi.A Vapor phase: δ[ρg.A.{α.ug.hg}]/δz + δ[ρg.A.{α.hg}]/δt = A.α.δp/δt + qg".Phg – qig".Pi + Γ.hgi.A Evaporation Term and Equation of State Γ = [(qig" – qif").Pi + τi.Pi.(ug – uf)]/[(hg – hf).A] ρf , ρg = f(p,T) Steam Tables for water, heavy water Closure Equations To solve the conservation equations, data or correlations are needed for void fraction (α), wetted and heated wall perimeters for each phase (Pwf, Pwg, Phf, Phg), interface perimeter (Pi), wall and interface shear stresses (τwf, τwg, τi), and wall and interface heat transfer rates (qf", qg", qif", qig"). Empirical correlations are available for void fraction, shear stresses and heat transfer rates. Conservation of Momentum Steady state, horizontal flow, no area change, no heat addition (i.e., no evaporation and thus no momentum change) Liquid phase: - (1-α).A.[dp/dz]FTP – τwf.Pwf + τi.Pi = 0 Vapor phase: - α.A.[dp/dz]FTP – τwg.Pwg – τi.Pi = 0 Wall and interface shear stresses can be expressed in terms of frictional pressure gradient Empirical Correlations for [dp/dz]FTP For convenience, the frictional two-phase pressure gradient, [dp/dz]FTP is generally expressed as: [dp/dz]FTP = Φfo2.[dp/dz]fo where [dp/dz]fo is the frictional pressure gradient for the liquid flowing alone at the same mass flow rate as the total two-phase flow rate and Φfo2 is the two-phase flow multiplier. Empirical correlations for Φfo2 include those of Lockhart & Martinelli (1949), Friedel (1979) and others. Friedel is recommended. Finite Difference Modelling of System ● System represented by nodes, containing mass and energy, and links joining the nodes ● Mass and energy conservation equations for nodes ● Momentum conservation equations for links Typical Link-Node Structure • Break the circuit up into – nodes containing mass – links joining the nodes • Mass & energy conservation equations for nodes • Momentum equation for links Wk, Lk, Ak f k, Dk, k etc. Mi, i, Pi, ei, Q i, Mj, j, Pj, ej, Q j, etc etc Thermalhydraulics Codes for CANDU Reactors CATHENA One-dimensional, steady-state or transient, two-fluid model of two-phase flow in piping networks, including allowance for one to four non-condensable gases. Also models heat transfer with solid surfaces. Used for design, licensing and safety analyses ASSERT (IST code) Models steady-state or transient single- or two-phase flows in sub-channels of fuel bundles. NUCIRC Models thermalhydraulic behavior of CANDU reactors using homogeneous model. Used for design and operational studies. Heat Transfer in Boiling Flows ● Effect of flow regime ● Nucleate boiling [Rohsenow (1952), Forster & Zuber (1955)] ● Forced convection boiling, nucleation suppressed [Chen (1963), Steiner & Taborek (1992)] Critical Heat Flux (CHF) ● Surface cooling changes from liquid cooling to vapor cooling ● In pool boiling or flow boiling at low velocities, increased vapor flow rate away from surface prevents liquid from reaching surface (Departure from nucleate boiling, DNB) ● In flow boiling at higher velocities, thickness of annular liquid film on wall decreases until film disappears (Dryout) Departure from Nucleate Boiling (DNB) Dryout in Flow Boiling (1) Dry Out in Flow Boiling (2) ● In annular flow, liquid film keeps surface well- cooled ● Film thickness controlled by evaporation (-), wave entrainment (-), droplet mass transfer (+) ● Dryout occurs when film thickness goes to zero [Hewitt (1970)] ● Integrated effect over boiling length (BLA method) ● Initiation of boiling length (saturation? OSV?). (OSV correlation Rogers & Li, 1992) Critical Heat Flux in CANDU Fuel Bundles ● Different power inputs, flow rates, qualities in different subchannels ● Flow and quality distribution also affected by mixing between subchannels, bundle end-plates, randomly aligned bundles ● Dryout initiates in one or more subchannels ● CHF data for CANDU bundles from experiments in full-scale electrically heated horizontal bundle strings with water or Freon Predictions of CHF in CANDU Fuel ● CHF Look Up tables developed by AECL and University of Ottawa. See handout for CHF in tubes, Groeneveld et al, 1986 ● CHF Look Up tables for CANDU 37-element and CANFLEX fuel channels ● CHF correlations for CANDU fuel channels. See handout for problem assignment. CHF in a CANDU Channel • CHF determined experimentally Heat flux – no reliable theory for (overpower) CHF needed accuracy • Local flux shape means Heat flux (normal) Dryout dryout is not at the end • How can we change the Quality flux shape to improve Distance along channel Inlet Outlet margins? Effects of Critical Heat Flux with Water Coolant ● For DNB, sheath temperature jump is very large, several thousand degrees. Surface “burn out” occurs. ● For dryout, sheath temperature jump is moderate for normal CANDU conditions. Sheath corrosion rate increases and sheath may fail. Post-Dryout (PDO) Heat Transfer ● Forced convection heat transfer to vapor ● Heat transfer by droplet impingement on wall ● Heat transfer to droplets in boundary layer ● Groeneveld correlation (1973) (conservative) ● AECL Look Up tables PDO Heat Transfer Critical Discharge in Two-Phase Flows ● For compressible gas flows, discharge rate through an opening is a maximum for sonic velocity. Further reduction of downstream pressure does not increase flow rate since pressure waves cannot penetrate upstream. ● Similar behavior for two phase flows. Moody (1965) diagram for thermodynamic equilibrium flows based on slip flow model. ● For two-phase discharge through very short paths non-equilibrium may exist (metastable flow); discharge rate will be much higher Moody Diagram for Two-Phase Critical Discharge Two-Phase Flow Instability ● Static Instability (Ledinegg instability) ● Dynamic Instability (Density wave instability) Density Wave Instability (1) ● Boiling channel with liquid at the inlet and inlet and outlet pressures fixed (e.g., many parallel channels). ● Frictional pressure drop in the liquid region in phase with any inlet flow perturbation. ● Friction and momentum pressure drops in the two-phase region not in phase with any inlet flow perturbation and impose a feedback effect on the liquid region that may enforce or attenuate the inlet flow perturbation. ● Flow is stabilized by high pressure, increase of liquid phase or inlet pressure drop, increase of liquid region length, high velocity. Density Wave Instability (3) Guido model: homogeneous flow, simplified assumptions Phase Change Number: NPCH = P.(ρf/ρg -1)/(w.hfg) Subcooling Number: NSUB = (hfs - hi).(ρf/ρg -1)/hfg Pressure Loss Coefficients: k = Δp/(ρ.u2) Flow Instability in a CANDU Power Plant ● CATHENA can predict flow instability. ● Flow instability not a problem in primary circuit under normal conditions because of high pressure and velocities ● Flow instability (oscillations) occurred (1986) on a Bruce steam generator secondary side because excessive fouling partially blocked TSP flow passages, thus reducing recirculation flow rates Design Basis Accidents in CANDU Reactors ● Single Failures (Failure of process system) + Loss of Regulation Accident (LORA) + Loss of Coolant Accident (LOCA) + Loss of Electric Power Accident (LOEPA) + Others ● Dual Failures (Failure of process system plus failure of Special Safety System) Special Safety Systems: Shutdown System 1, Shutdown System 2, Emergency Coolant Injection System, Containment System Loss of Coolant Accident (1) ● Break in PHTS, coolant undergoes critical discharge and local pressure falls rapidly. ● Rapid decrease in local saturation temperature. ● Flashing proceeds rapidly from break through fuel channel. ● Reactor power surges because of positive void reactivity, terminated by shutdown system ● Fuel sheath temperature rises, sheath strains and oxidizes, exothermic Zircaloy-steam reaction generates H2 Loss of Coolant Accident (2) ● Worst conditions during blowdown occur for “stagnation breaks” (Pump and break opposing). ● PHTS pumps cavitate when local pressure approaches saturation ● Emergency coolant injection is triggered by falling PHTS pressure. ● Emergency coolant flow quenches fuel and channel and prevents fuel sheath failure, fission product release and pressure tube failure. Analysis Methodology for LOCA plus LOECI Fuel Channel Behavior, LOCA + LOECI (1) ● Decay power plus heat from Zr + steam reaction ● Channel filled with stagnant steam ● Heat transfer from fuel fuel to pressure tube by radiation (and natural circulation) ● Above about 800oC, pressure tube begins to plastically deform. ● For 1 MPa > p< 6 MPa, PT balloons into contact with CT, for p <1 MPa, PT sags onto CT, for p > 6 MPa, PT bursts . Fuel Channel Behavior, LOCA + LOECI (2) Fuel Channel Behavior, LOCA + LOECI (3) ● Fuel bundle collapses into bottom of PT. Heat transfer from fuel bundle by radiation plus natural convection ● Heat transfer from PT to CT by contact (ballooned), by local contact plus radiation and natural convection (sagged) ● Heat transfer to moderator by nucleate boiling as long as CHF is not exceeded. Fuel Channel Behavior, LOCA + LOECI (4) ● Moderator cooling system removes heat. [3-d moderator circulation analyzed by MODTURC_CLAS, (IST code)] ● Fuel does not melt, fission product release low. ● With containment intact, dose to public is within CNSC requirements for dual failures. Fuel Channel Behavior, LOCA + LOECI (5) Heat Transfer by Radiation Qr = σ.A1. F12.(T14 – T24) kW σ is the Stefan-Boltzmann constant, 5.669x10-8 Wm-2K- 1 F12 is the radiation interchange factor, allowing for geometry (view factors) and emissivity of surfaces For example, for radiation between PT and CT: F12 = 1/[(1/ε1+ d1/d2.(1/ε2-1)] ε1, ε2 are emissivities of PT and CT d1, d2 are diameters of PT and CT Fuel Channel Behavior, LOCA + LOECI (6) Hydrogen from Zr + Steam Reaction Zr + 2.H2O -> ZrO2 + 2.H2 + heat ● Heat released raises fuel and PT temperatures ● Hydrogen escapes from PHTS to containment and may detonate or burn depending on local concentration, presence of steam, etc. ● If ECI is eventually restored, hydrogen may impede emergency water flow. ● If ECI is eventually restored, embrittled sheaths and PTs may shatter. Containment Behavior, LOCA + LOECI (1) ● Containment compartmentalized, 3-d flow in compartments ● Atmosphere consists of air, steam, water droplets, hydrogen. ● Heat added by steam, hot water, fission product decay. ● Heat removed by air-coolers, dousing spray, condensation on containment walls and equipment Containment Behavior, LOCA + LOECI (2) ● Heat may be added by hydrogen detonation (>10% H2, depending on steam fraction) or combustion (>4% H2). ● Hydrogen can be removed by AECL-designed passive catalytic recombiners. ● Containment pressure history established by balance of heat addition and removal rates Containment Behavior, LOCA + LOECI (3) ● Pressure affected by vacuum building, if present, leaks through cracks and venting through filters ● Containment codes include GOTHIC (IST code), for pressure, heat and flow analysis, and SMART (IST code) for fission product behavior. Severe Accidents in CANDU Reactors ● Severe accidents are those whose probability of occurrence is so low ( < 10-6 per year) that they need not be analyzed for licensing purposes. ● Examples of severe accidents are: + Loss of the moderator cooling system in a LOCA + LOECI, implying three coincident independent failures + Failure to shut down a reactor in a design-basis accident, requiring failure of both independent, diverse shutdown systems Dual Failure + Loss of Moderator Cooling (1) + CANDU-6, LOSWA +LOEPA + Moderator heats up, boils and is expelled through relief ducts after rupture disks break (Rogers et al., 1984). + As moderator expelled, uncovered channels sag onto submerged channels until they fail by shear. + Fuel in failed channels in solid state; quenched by remaining moderator. + Core disassembly end-state: debris bed of coarse pieces of UO2 , ZrO2 and re-solidified Zr at bottom of calandria (@ ~ 5 hours). Fuel Channel Disassembly (Blahnik et al 1993) Core Disassembly Transient (Blahnik et al, 1993) Dual Failure + Loss of Moderator Cooling (2) + Porous debris bed heats up to melting point + Melting occurs with accompanying geometry changes + Molten region superheats + Molten region cools as heat source decays and as heat is lost to shield-tank water + Molten region re-solidifies + Solidified regions cool as heat source decays further DEBRIS.MLT Model (Rogers & Lamari, 1997) ● Transient, 1-d, explicit finite difference model of porous debris bed and molten pool with crusts ● Porosity, pore size are inputs ● Decay heat (plus Zr + steam reaction as option) ● Allows for geometry changes on melting ● Models all heat transfer mechanisms in bed and from bed to shield-tank water ● Models all heat transfer mechanisms in pool and crusts and from crusts to shield-tank water ● Option for shield tank cooling system: on or off DEBRIS.MLT Heat Transfer Mechanisms DEBRIS.MLT Temperature Transients (Effects of Debris Bed Porosity; Pore Size 3 cm ) DEBRIS.MLT Additional Results ● Temperature transients also very insensitive to pore size over wide range ● Minimum crust thickness: ~ 8 cm top, ~ 13 cm bottom ● Maximum heat flux on calandria wall ~ 115 kW/m2 (Shield tank water CHF > ~ 6400 kW/m2) ● Maximum calandria wall temperature ~ 380oC (no concern about stress rupture) ● Results very insensitive to molten corium conductivity and viscosity ● Shield tank water boil off > 24 hours DEBRIS.MLT Conclusions ● While significant fraction of core melts, it is retained within crusts in the bottom of the calandria ● Calandria readily survives the accident as long as shield-tank water is available ● Significant time is available for emergency procedures ● Fission product releases from intact containment would be within regulatory limits for dual failure Application of DEBRIS.MLT to RASPLAV Experiments (1) ● International RASPLAV program, Moscow (OECD Nuclear Energy Agency) ● Experiments on interaction of molten corium on lower head of PWR pressure vessels ● Experimental geometry simulates CANDU core debris in calandria ● DEBRIS.MLT modification for RASPLAV conditions: DEBRIS.RAS Application of DEBRIS.MLT to RASPLAV Experiments (2) Application of DEBRIS.MLT to RASPLAV Experiments (3) Conclusions ● Comparisons of predictions to RASPLAV measurements provides confidence in DEBRIS.MLT ● Recommendations for improvements in DEBRIS.MLT MAAP-CANDU IST Severe Accident Code (OH, 1990) ● Incorporates mass, momentum and energy balances and models all chemical and other physical processes. ● Models all key structures and systems. ● Models all known severe accident phenomena. ● Physical models integrated to simulate all dynamic feedback effects at each time step. MAAP-CANDU Applied to Severe Accident in Pickering-A Reactor Unit (1) ● Accident: LOCA in inlet header, SDS1 and SDS2 both fail (triple failure) ● Power surges (+ve CVR), fuel melts, PTs and CTs fail, calandria fails, moderator discharges ● Loss of moderator terminates power surge (~ 4 s) ● Containment dome weld seal fails, opening = 0.073 m2 (quad failure) (~4 s) ● Core debris quenched by ECI flow (20-95 s) MAAP-CANDU Applied to Severe Accident in Pickering-A Reactor Unit (2) ● Containment pressures drop below atmospheric, due to VB (~ 200 s) Vacuum depleted (~ 260 m) ● EFADS activated to keep pressures below atmospheric (I and Cs fission products filtered) ● Noble gas fission products released ● Effective doses to public within CNSC limits for dual failure even for adverse weather conditions. (MACCS code) Summary ● Inherent passive safety of CANDU design help ensure public and operator safety. ● IST and other codes, validated by thorough, quality-assured experimental programs: + demonstrate CANDU safety in design-basis accidents. + show that even in low- probability severe accidents in CANDU reactors, public safety is maintained