Lesson 14: Reactivity Variations and Control

Transcription

1 Lesson 14: Reactivity Variations and Control Reactivity Variations External, Internal Short-term Variations Reactivity Feedbacks Reactivity Coefficients and Safety Medium-term Variations Xe 135 Poisoning (Thermal Reactor) Long-term Variations Fuel Composition Changes with Burnup Means of Control Laboratory for Reactor Physics and Systems Behaviour Reactivity Variations and Control.. 1

2 General Different mechanisms cause variation of k eff, i.e. of reactivity Effects need to be compensated so as to maintain k eff = 1 Reactor power needs to be closely monitored and regulated (reactor control) In an anamolous situation, automatic reactor shutdown needs to be guaranteed Means of reactor control Poisons : neutron absorbers (control rods, burnable poisons, soluble poison, ) Refuelling (renewal of core loading) Auto-control mechanisms (limited possibilities) Reactivity Variations External causes (modification of poison, change of fuel, ) Internal causes (modifications in i values, and hence in neutron balance, ) Reactivity feedbacks Short-, medium-term effects (temperature, Xe, etc.) Long-term effects ( evolution of fuel composition) Reactivity Variations and Control.. 2

3 Reactivity Variations In reality, reactivity changes not sudden and constant, i.e. not step functions, function of time (also, spatial effects) kinetics eqns. need to be solved numerically Various time constants involved (e.g. time for power change to affect temperature, ) Values quite different for different types of feedbacks Short-term causes for -variation Fuel temperature (Doppler effect), < 1 sec (effect ~ prompt most important ) Moderator temperature, secs - mins Voidage of liquid moderator/coolant, secs (boiling, bubble formation, effect on density ) Medium-term causes Principal effect: Fission product Xe 135 in a thermal reactor, hours - days Long-term effects Fuel composition changes with irradiation (burnup), days - months Largest effect in power reactors ( burning of fissile, Pu-production, accumulation of FPs, ) Reactivity Variations and Control.. 3

4 Doppler Effect (T c ), Fuel Temp. Coeff Laboratory for Reactor Physics and Systems Behaviour When T c, U 238 resonances broadened due to increased thermal agitation of nuclei Area under resonance constant, but flux is less depressed Effective resonance integral, I eff In, where with Fuel Temperature Coefficient of Reactivity (Doppler Coeff.) Reactivity Variations and Control.. 4

5 Comments, c For a fast reactor, Doppler effect more difficult to calculate Very large number of resonances at high energies (very narrow, partly overlapping) Fissions also largely of resonance nature T c implies, e.g., increase of radiative captures in U 238, as well as of Pu 239 fissions Globally negative effect needs to be guaranteed Fissile enrichment (Pu-content) is limited Negative Doppler usually no problem (enough U 238 present), but if Pu-burner desired instead of a breeder, high Pu-contents needed (safety provides constraints ) Other effects of T c Fuel expansion (reduction of density: s, M 2 and leakage ) Important in small reactors, particularly fast reactors (fuel much more important for M 2 ) Reactivity Variations and Control.. 5

6 Moderator (Coolant) Temperature Coefficient, m m = Neutron spectrum effects Maxwellian part shifted to right when T m th s ~ 1/v (i.e. 1/ E ), but not exactly For, individual changes of important For U nat, c when T m In presence of Pu, this changes (Pu 239 resonance at 0.3 ev: +ive effect) Partly compensating effect from Pu 240 (large capture resonance at 1ev) Spectrum effect most important for solid moderator, e.g. graphite For a liquid moderator (coolant), density variation more important effect Undermoderation crucial for safety Reactivity Variations and Control.. 6

7 Void Coefficient, v v = (v : volumetric fraction of void ) Very important to have negative v for liquid moderator/coolant (Chernobyl!) Boiling implies a strong reduction of density As for m, thermal reactor needs to be undermoderated Sodium (coolant) voidage in fast reactor complex effects Moderation reduced, spectrum harder ( E ) Pu : positive effect Na absorptions : positive effect Na density neutron leakage : negative effect Effect particularly important for small reactors, or for pancake cores In practice, for a sodium-cooled fast reactor, v often slightly positive Not serious, because c negative and has more immediate impact Reactivity Variations and Control.. 7

8 Comments For the short-term effects, one may write: However, this does not give the true dynamic behaviour No consideration of the time constants One needs proper time-dependent modelling of the power reactor (including the secondary cooling system), with coupling betn. neutronics, thermal-hydraulics Safety studies: Numerical simulation and analysis of hypothetical accident situations In general, if all the s are negative, reactor inherently safe from viewpoint of automatic shutdown Calculation of s generally very delicate Compensation of individual effects, e.g. sodium v, or m in HTR (graphite) Necessary to carry out checks on power reactor before start-up Reactivity Variations and Control.. 8

9 Consequences for Reactor Control Strongly negative s demand large reactivity reserve Complex control system (economics aspect) Laboratory for Reactor Physics and Systems Behaviour After reactor shut-down, one needs to be able to compensate the important s corresponding to different reactor states: (1) Hot full power (HFP) (2) Hot zero power (HZP) (3) Cold zero power (CZP) For such considerations, one may use: Reactivity Variations and Control.. 9

10 Medium-term Reactivity Variations Laboratory for Reactor Physics and Systems Behaviour For a power reactor, the FP s accumulate and influence the neutron balance In general, long-term poisoning effect (~ 50 b extra a added per fission (thermal reactor)) Special case (thermal reactor) ~ 2-3 days after start-up, one obtains an equilibrium Reactivity Variations and Control.. 10

11 Efect of a Poison on In, the FP s (thermal reactor) mainly influence f One has (1) For a large reactor, (2) From (1) and (2), Reactivity Variations and Control.. 11

12 Equilibrium-Xenon Poisoning At equilibrium, Laboratory for Reactor Physics and Systems Behaviour Equilibrium-Xe effect depends on Ex. For a system with U 235 as fuel (p = = 1), By far, most important FP effect in a thermal reactor Reactivity Variations and Control.. 12

13 Xenon Transients Equilibrium betn. production, destruction mechanisms: If reactor is shutdown, destruction by absorption stops, but principal production (I 135 decay) continues At equilibrium, After t = 0, For a reactor at high power, it is possible that the reactivity reserve is insufficient for restarting very soon after the shutdown Reactivity Variations and Control.. 13

14 Comments Changes in reactor power produce reactivity variations due to xenon In large-sized reactors, one has possibility of xenon oscillations Instabilities, not serious quite large time constant N.B.: Another quite important, individual FP: Sm 149 (stable, more of a long-term effect ) Reactivity Variations and Control.. 14

15 Long-term Effects -variation of largest magnitude in power reactor, also slowest (not really, kinetics ) Fuel composition changes with burnup (fuel evolution ) Determines, for given initial -excess, max. burnup achievable (from neutronics viewpoint) Involved phenomena: Consumption of fissile material (U 235, ) Production of new fissile material from fertile (Pu 239 from U 238, etc.) Appearance of non-fissile nuclides such as U 236 ( also transuraniums ) Accumulation of stable FP s All the above (except 2 nd ) cause One needs to determine the fuel composition as function of irradiation time, via Fuel Evolution Equations (Bateman Equations) analysis, corresponding to each different reactor state, gives new values for: k eff, -coefficients, control rod worths, power distribution, etc. Reactivity Variations and Control.. 15

16 Fuel Evolution Equations For thermal reactor burning enr. U : Even if power is constant, (t) varies because of variation of f Preferable to consider the variable fluence (time-integrated flux): Equation for U 235 becomes with solution: (units: cm -2 ) (analogy with radioactive decay : time, a5 : decay constant) Considering other reactions, one has for the other nuclides etc., etc. N.B.: For the fissiles, a = c + f Reactivity Variations and Control.. 16

17 Comments For the FP s, fuel evolution equations more complex Radioactive decay chains also need to be considered Only few FP s need to be treated explicitly Fuel burnup: (contributions of all fissile isotopes to be considered) Average values: One can express all parameters ( k eff, -coefficients, etc.) in function of W sp Reactivity Variations and Control.. 17

18 Example LWR fuel ~ 3.4% U enr W sp ~ 30,000 MWd/t (today, > 4% enr, W sp ~ 50,000 MWd/t) Solution of Fuel Evolution Equations gives In example, ~ 30% of fissions in Pu (in-situ) For a U nat reactor (CANDU) can be ~ 50% Pu- quality at discharge (~ 70% fissile) poor for nuclear explosive ( civil Pu ) For production of military Pu, one needs to strongly reduce W sp (< 5000 MWd/t) Nuclear power plants too costly for this (one uses cold power reactors) Reactivity Variations and Control.. 18

19 Consequences for Reactor Control Laboratory for Reactor Physics and Systems Behaviour For considered example (U enr, LWR): For a U nat reactor (CANDU, ): N.B.: Scales different Large reactivity variation in LWR case demands partial charging, discharging of core e.g. with 3 segments (zones) in the equilibrium situation: 1 new fuel (at t = 0) 2 fuel with one cycle of residence in core 3 fuel with 2 cycles of residence Reactivity Variations and Control.. 19

20 Consequences for Control (contd.) Laboratory for Reactor Physics and Systems Behaviour After time T/3, one discharges Segment 3 and displaces the fuel between the zones Reactivity variation: Reactivity Variations and Control.. 20

21 Comments Reactivity variation reduced by factor of ~ 3 (in case considered) Initial enrichment needed ( as also control ), significantly reduced Fuelling, refuelling needed more frequently (but each time quantity ~ 1/3) In the limit, one can have continuous refuelling (not possible in LWR ) One can profit also from flux flattening Material properties deteriorate with irradiation One has technological constraints to maximum burnup in LWRs (fuel, cladding), i.e. increase in enrichment not meaningful beyond certain value For systems using U nat, neutronics provides principal constraint to burnup (even with on-line refuelling, as in CANDU) Reactivity Variations and Control.. 21

22 Means of Control Control rods (of different types) Compensation rods, e.g. for Xe-buildup, cold-to-hot, etc. Higly absorbing materials (B 4 C, Ag-In-Cd, ) Pilot rods, for power regulation, automatic piloting, etc. (low -worths, steel often used) Safety rods, (normally withdrawn, fall rapidly in accidental situation ( scram ), B 4 C, etc. Soluble poison (liquid moderator/coolant) For long-term effects, adjustable concentration (H 3 BO 3 in PWRs) Not used in BWRs (influence too large on v ) Reduces need for compensation control rods (advantage also of better power distribution) Requires special chemical processes and control Burnable poison Solid, strong absorbers (Gd, B, ), mixed with a certain fraction of fuel rods (BWRs, ) Disappears (is burnt) during irradiation, with density reduction: Again, mainly for long-term effects (fuel evolution) Can be optimised to flatten -curve (cf. Slide 19) Reactivity Variations and Control.. 22

23 Reactor Instrumentation, Power Regulation Power of NPP known via thermal balance for coolant, bur power regulation needs rapid monitoring (possible via neutron flux measurements, with prior calibration ) Neutron detectors: fission chambers, BF 3 counters, etc. (with, without -compensation) Start-up chains (< 10-6 P 0 ) Minimal count-rate necessary at start (sensitive detectors, external n-source if necessary ) Logarithmic chains (~ 10-7 P 0 to P 0 ) Several decades covered, current mode; derivative provides period measurement Linear chains (~ 10-2 P 0 to 10 P 0 ), for piloting reactor Allow fine regulation; feedback loop (connected to pilot rods) and servo-mechanism Safety chains, for triggering insertion of safety rods (often in mode 2-out-of-3 ) Fixed criteria, e.g. P 1.15 P 0, T T min, N.B.: Detectors often in reflector; however NPPs also have in-core instrumentation, e.g. series of miniature chambers, which can provide a detailed flux map. Reactivity Variations and Control.. 23

24 Summary, Lesson 14 External, internal reactivity variations Short-term variations Reactivity feedbacks (fuel temperature, moderator temperature, coolant voidage, etc.) Importance for inherent safety Medium-term variations Xe 135 poisoning (equilibrium, transients, ) Long-term variations Fuel composition changes with burnup Evolution equations Consequences for control Means of control, instrumentation Reactivity Variations and Control.. 24