1. REP/ - page 1 - PWR Nuclear Reactor Core Design Power and Reactivity Elements on Reactor Kinetics and Residual Power G.B. Bruna FRAMATOME ANP

2. REP/ - page 2 - Foreword  Neutron Balance Equation of a multiplying system at time t:

3. REP/ - page 3 - Foreword  Steady State Conditions  At any time t :

4. REP/ - page 4 - Foreword  Steady State Conditions  At any time t :  The number of neutron in any generation equals the number of neutrons in the previous and following generation;  The prompt-neutron lifetime equals exactly the generation-time.

5. REP/ - page 5 - Foreword  Steady State Conditions  At any time t, any explicit dependence on the variable time can be dropped out :

6. REP/ - page 6 - Foreword  Steady State Conditions  In steady state conditions, the neutron balance of the system changes  Very slightly due to:  Xenon oscillations,  Fuel burn-out,  With a time-constant which is quite long against observation-time.

7. REP/ - page 7 - Power and Reactivity  Main Parameters in Reactor Core Design  Power  It is a physical observable which measures the energy released under different forms (kinetic energy of fission fragments, kinetic energy of fission neutrons, gamma) within the system by neutron fission, capture and slowing-down.  Reactivity  It is not a real physical observable because it measures the reset that is to be applied to the fission operator to restore criticality of a given multiplying system, generally not critical after any perturbation (change of the state Boltzmann operator).

8. REP/ - page 8 - Power and Reactivity  Power  Total Fiss Power  Total Power  Local Fiss Power

9. REP/ - page 9 - Power and Reactivity  Power  Power Peak  Axial Offset

10. REP/ - page 10 - Power and Reactivity  Reactivity

11. REP/ - page 11 - Power and Reactivity  Control of Power  Power distribution within the reactor core is not flat because of :  Neutron gradient (leakage),  Short-life fission-product poisoning,  Burn-up and breeding effects,  Reflector gain,  Fuel and moderator temperature feed-back,  Control rod effect; ...

12. REP/ - page 12 - Power and Reactivity  Control of Power  Power distribution can be controlled both  At the design stage (assembly and core layout, burnable poisons, reflector, reloading strategy),  In operation (mainly by control rods positioning);  Several strategies of control rod management can be adopted (e.g., in French PWRs : A mode, G mode, X mode).

13. REP/ - page 13 - Power and Reactivity  Control of Power  Core design and operation : Typical MOX reloading strategy

14. REP/ - page 14 - Power and Reactivity  Control of Power  Core design and operation : X mode operating Control of AO Control of Temperature

15. REP/ - page 15 - Power and Reactivity  Control of Reactivity  Reactivity of the core is sensitive to :  Reactor life:  Fuel burn-up,  Breeding process,  Fission-product and actinides build-up,  Burnable poison burn-out,  Short-lifetime fission-product poisoning,  Power and temperature feed-back.

16. REP/ - page 16 - Power and Reactivity  Control of Reactivity  Core reactivity is also sensitive to any external perturbation of Boltzmann operator :  Soluble boron concentration change,  Position of control banks,  Power output,  Any incident and/or reactivity accident.

17. REP/ - page 17 - Power and Reactivity  Control of Reactivity  In normal operation, reactivity is to be kept constant (no measurable reactivity change);  To guarantee respect of this condition, reactivity NEEDS (sources of reactivity changes and design margins) must be compensated exactly by reactivity AVAILABILITIES (worth of control devices).

18. REP/ - page 18 - Power and Reactivity  Control of Reactivity (NEEDS)  Reactivity NEEDS (normal operation) :  Respect of safety criteria,  Respect of margins,  Compensation of fuel burn-up and breeding,  Compensation of burnable poison burn-out,  Compensation of Xenon and Samarium build-up,  Compensation of power and temperature effect.

19. REP/ - page 19 - Power and Reactivity  Control of Reactivity (NEEDS)  Criteria and margins  The main objective of a nuclear is producing a cheap energy in safest way;  In order to achieve this goal, design and exploitation of the plant must :  Guarantee respect of the safety criteria at any time,  Maximize energy release from the fuel, according to a given exploitation strategy.

20. REP/ - page 20 - Power and Reactivity  Control of Reactivity (NEEDS)  Criteria and margins  In order to guarantee respect of the maximum allowed values (criteria), uncertainty is affected to design parameters;  Uncertainty must account for:  Computational precision (base-data, qualification,..),  Technology of the fuel (fabrication tolerance, …),  Measurement device precision,  Alea (power tilt,...);  Margins can also be enforced to account for future changes of loading strategies and new fuel features.

21. REP/ - page 21 - Power and Reactivity  Control of Reactivity (NEEDS)  Fuel burn-up and breeding  Fissile isotopes burn-out,  Plutonium build-up,  Minor Actinides build-up,  Fission-Products build-up.

22. REP/ - page 22 - Power and Reactivity  Control of Reactivity (NEEDS)  Burnable poison burn-out  Burnable poisons contribute to :  Compensate reactivity,  Flatten core power;  When they disappear :  Fuel reactivity can increase,  Power pick can appear.

23. REP/ - page 23 - Power and Reactivity  Control of Reactivity (NEEDS)  Xenon and Samarium build-up  Short-lifetime Fission Products as Xenon and Samarium build-up as a consequence of production of power,  Any power change engenders a variation of their concentrations which affects the reactivity of the system,  Local power variation engender spatial discontinuities in concentration which produce power tilt.

24. REP/ - page 24 - Power and Reactivity  Control of Reactivity (NEEDS)  Power and temperature effect :  Doppler broadening of wide epi-thermal resonances:  Fissile isotopes do not contribute significantly to Doppler effect owing to compensation among capture and fission reaction-rates,  Fertile isotopes (mainly U238 and Pu 240) have major contribution to the effect;  Moderator effect :  When moderator density varies, neutron spectrum either hardens-up or soften-down and reactivity changes;  Soluble boron poisoning effect :  When moderator density varies, amount of boron atoms per unit volume is modified.

25. REP/ - page 25 - Power and Reactivity  Control of Reactivity (NEEDS)  Power and temperature effect : Doppler broadening  Broadening of epi-thermal resonances of heavy isotopes (at first order, only even ones contribute),  Very fast action (sensitive to temperature changes inside the pellet),  About -3°pcm (1 pcm = 1 E-5) par degree Celsius.

26. REP/ - page 26 - Power and Reactivity  Control of Reactivity (NEEDS)  Power and temperature effect : Moderator effect  Variation of the water moderating power (neutron spectrum changes),  Long term action (sensitive to the coolant temperature),  Worth sensitive to isotopic composition of the fuel (stronger for MOX).

27. REP/ - page 27 - Power and Reactivity  Control of Reactivity (NEEDS)  Power and temperature effect: Moderator effect MOX UOX Reactivity Void rate 0 100

28. REP/ - page 28 - Power and Reactivity  Control of Reactivity (AVAILABILITIES)  Reactivity AVAILABILITIES (normal operation) :  Soluble boron,  Control and scram clusters :  Black rods,  Gray rods,  Burnable poisons :  Fixed,  Extractable  Extractable poisons.

29. REP/ - page 29 - Power and Reactivity  Control of Reactivity (AVAILABILITIES)  Soluble boron  Soluble boron is mainly used to compensate the fuel burn-up,  Power shape is quite insensitive to soluble boron poisoning the primary leg,  Soluble boron worth is very sensitive to fuel nature (ranging from 10 pcm/ppm to 4 pcm/ppm and less),  Concentration of boric acid in primary leg is limited by :  Crystallization (clad rupture),  Moderator density dependence of poisoning effect.

30. REP/ - page 30 - Power and Reactivity  Control of Reactivity (AVAILABILITIES)  Control and scram clusters  Control clusters can be either homogeneous (AIC) or mixed (axially heterogeneous B4C - AIC),  If needed, boron in boron carbide can be enriched in B10,  The mixed clusters can be more effective then AIC ones, but they posses the inconvenient to bow-up under pressure of He gas produced by B10 neutron capture.

31. REP/ - page 31 - Power and Reactivity  Control of Reactivity (AVAILABILITIES)  Control and scram clusters  Control clusters are used to  Finely adjusting the primary leg output temperature,  Controlling Xe oscillations,  Maintaining AO inside the operating range;  When inserted into the core control clusters cannot must respect a threshold to avoid prompt criticality in presence of a rod-ejection reactivity accident.  They can (partially) contribute to scam.

32. REP/ - page 32 - Power and Reactivity  Control of Reactivity (AVAILABILITIES)  Burnable poisons  Burnable poisons are used to :  Compensate fuel burn-out,  Contribute to power flattening;  Burnable poisons can be :  Introduced into guide tubes of some unclustered assemblies (Pyrex),  Integrated to the fuel (Gadolinium Oxide)  Thy engender a spectrum hardening,

33. REP/ - page 33 - Power and Reactivity  Control of Reactivity (AVAILABILITIES)  Extractable poisons  Extractable poisons are introduced at beginning of cycle into guide tubes of assemblies not receiving control and safety clusters,  Their position is not axially adjustable (they can be either OUT or IN),  They engender a spectrum hardening,  When they are dropped out, a spectral-shift is produced.

34. REP/ - page 34 - Reactor Kinetics  Neutron Balance Equation of a multiplying system at time t[inhomogeneous equation]:

35. REP/ - page 35 - Reactor Kinetics  Lifecycle inside a reactor system (recall) Production Neutrons Diffusion Slowing-down Capture Leakage

36. REP/ - page 36 - Reactor Kinetics  Lifetime and generation-time (recall)  During transients prompt-neutron lifetime differs from generation time.

37. REP/ - page 37 - Reactor Kinetics  Lifetime and generation-time  Typical values for L / L*  Vacuum20 mm (L* )  PWR (UOX)25  s(L* same)  PWR (UOX - MOX)10  s "  PWR (MOX) 7  s "  FBR (MOX) 5  s "  Critical sphere (U) 6 ns "  Critical sphere (Pu) 3 ns "

38. REP/ - page 38 - Reactor Kinetics  Point Kinetics  Heuristic approach  Reactor is homogenized in space and collapsed to a space-point system (no explicit dependence of variables on space),  Neutrons are collapsed in energy to one group (no explicit dependence of neutrons on energy),  Simplified statistical approach:  The number of neutron in the system is quite large,  The behavior of the system is described by averaged values of reaction-rates.

39. REP/ - page 39 - Reactor Kinetics  Point Kinetics  Heuristic approach : Principle  A quite simple demography problem where, every generation-time L, the neutron population is multiplied by a factor  In a conventional PWR there are about 40 neutron generations per millisecond, i.e. 40 000 per second.  Time Neutron population  0N0  LN0 *  2LN0 * *  3LN0 * * *

40. REP/ - page 40 - Reactor Kinetics  Point Kinetics  Heuristic approach : Application  Keff = 1.00010 L= 25  s  Neutron generation per second = 1/25E-6 = 40 000  Time (s) Neutron population  0N0  1N0*E+40 000 = N0*55  2N0*E+80 000 = N0*2980  3 N0*E+120 000 = N0*162 000  Simple but catastrophic scenario!

41. REP/ - page 41 - Reactor Kinetics  Point Kinetics  Heuristic approach : Application  Keff = 0.900 L= 25  s  Neutron generation per millisecond = 1E-3/25E-6 = 40  Time (ms) Neutron population  0N0  1N0*E+40 = N0*0.0150  2N0*E+80 = N0*0.0002  3 N0*E+120 = N0*0.000003  Simple but catastrophic scenario!

42. REP/ - page 42 - Reactor Kinetics  Point Kinetics  Heuristic approach : Sub-critical system with external source  Gain amplifying factor  Time Neutron population  LS  2LS(1+ )  3LS(1+ + *)  4L ……… 

43. REP/ - page 43 - Reactor Kinetics  Delayed neutrons  Stability of the nucleus :  The Electromagnetic field inside nucleus :  Effect on protons,  The Nuclear Force field :  Contribution of neutrons to nucleus stability,  The Fission process :  Compound activated nucleus,  Production of fission fragments (Fission Products)  Neutron emission.

44. REP/ - page 44 - Reactor Kinetics  Delayed neutrons  Delayed neutron fraction per fission (UOX fuel) :  U2350.65%  U2381.48%  Pu2390.21%  Delayed neutron emission time :  Br87 -> Kr87 -> Kr86+n80.6 s  I137 -> Xe137 > Xe136+n32.8 s

45. REP/ - page 45 - Reactor Kinetics  Back to the Fission process Incident neutron Fission Delayed neutrons Prompt neutrons Bv (1-B)v Diffusion & slowing-down Delay >0.3 sec Delay>03 sec.

46. REP/ - page 46 - Reactor Kinetics  Point Kinetics  Thermal feed-back : Power and temperature effect (recall):  Doppler broadening :  Fissile isotopes do not contribute significantly to Doppler effect,  Fertile isotopes (mainly U238 and Pu 240) have major contribution to the effect;  Moderator effect :  When moderator changes, neutron spectrum is affected;  Soluble boron poisoning effect :  When moderator density varies, amount of boron atoms per unit volume is modified.

47. REP/ - page 47 - Residual Power  Time-dependence  After shut-down, power does not go immediately to zero:  The system undergoes a fast transient during which power decrease is driven by decay of residual neutron precursors (Fission Products) [kinetics],  Afterwards, power goes-on decreasing very slowly [activity, residual power].

48. REP/ - page 48 - Residual Power  Sources of activity  Radioactive decay of:  Fission Products (B+y),  U239, Np239 and daughters (B+y),  Minor Actinides (a),  Other Activation Products (B+y),  Spontaneous Fission,  Induced neutron emission.

49. REP/ - page 49 - Residual Power  Sources of activity  In order to explain origin of different contributions to the activity, several items must analyzed :  The fuel burn-up breeding process described by Heavy-Isotope Depletion Chain,  The decay process of nuclei described in Base-Data Libraries.

50. REP/ - page 50 - Residual Power  Sources of activity  Activity is also due to the multiplication in sub-critical conditions of the inherent neutron source :  Spontaneous Fission,  Neutron emission by Oxygen 18 :  Actinide decay produces a particles,  Free neutrons are generated by stripping by a particles on O18.

51. REP/ - page 51 - Residual Power  Computation  In calculation, contributions to residual power are packed into three groups :  Term A includes contribution from residual Neutron Source,  Term B includes contribution from decay of U239, Np239 and daughters,  Term C includes contribution from decay of :  Fission Products and and Activation Products others than U239, Np239 and daughters,  Minor Actinides.

52. REP/ - page 52 - Residual Power  Computation  Several solutions can be adopted to account for burn-up:  Using fuel burn-up averaged values,  Maximize burn-up of the fuel via infinite irradiation.  Uncertainty  Can be accounted for in different ways depending on computational procedure and / or data - library adopted.

53. REP/ - page 53 - Keyword Survey  Neutron Balance Equation  Steady state Conditions  Power and Reactivity  Power  Reactivity  Control of Power  Control of Reactivity

54. REP/ - page 54 - Keyword Survey  Reactivity NEEDS  Criteria and Margins  Fuel Burn-up and Breeding  Burnable Poison Burn-out  Xenon and Samarium Build-up  Power and Temperature Effect  Doppler Broadening  Moderator Effect  Reactivity AVAILABILITIES  Soluble Boron  Control and Safety Clusters  Burnable Poisons  Extractable Poisons

55. REP/ - page 55 - Keyword Survey  Reactor Kinetics  Neutron Balance Equation  Lifecycle  Lifetime and generation-time  Point Kinetics  Heuristic approach  Application  Delayed neutrons  Point kinetics  Heuristic approach,  Thermal feed-back,

56. REP/ - page 56 - Keyword Survey  Residual Power  Time dependence  Sources of activity  Radioactive decay  Actinide depletion  Fission Products  Sub-critical conditions  Computation