Chemical Engineering 412

Transcription

1 Chemical Engineering 412 Introductory Nuclear Engineering Lecture 18 Nuclear Reactor Theory IV Reactivity Insertions 1

2 Spiritual Thought 2 Mosiah 2:33 33 For behold, there is a wo pronounced upon him who listeth to obey that spirit; for if he listeth to obey him, and remaineth and dieth in his sins, the same drinketh damnation to his own soul; for he receiveth for his wages an everlasting punishment, having transgressed the law of God contrary to his own knowledge.

3 Reactivity and Δk ρ = k ( $ ) keff k eff ρ = β 1 = k( $ ) = worth δk k eff ρ = reactivity δk = delta k β = delayed neutron kk oo = fraction ll ββ + ii=1 GG aa ii λ ii + ωω Inhour equation

4 φ T φ T T = = = ρ = A 1 1+ ωl Reactivity Equation Solutions 1 1 dominant term as t 1 ω exp exp ωl p t T p ( ω t ) + A exp( ω t ) ω + 1+ ωl 2 2 approaches 0 rapdily p 6 i = 1 βi ω + λ i General solution for single group of delayed neutrons Definition of reactor or stable period General solution for single group of delayed neutrons Reactivity equation for six group model graphical solution on next page

5 Reactivity Equation Solutions TT = ll kk eeeeee 1 = ll δδδδ = ββββ δδδδ = Reactor period - The time required for a neutron population to change by a factor of e kk eeeeee = 1 + δδδδ = 1 + ββββ TT ττ =Lifetime of delayed neutrons ~12.8s (U235) TT = ββββ δδδδ = ββββ kk eeeeee 1 = ββββ kk eeeeee ρρ = ττ kk eeeeee ρρ($) ττ ρρ $ ϕ(tt) = eeeeee tt TT Remember, Flux is proportional to power. CC PP(tt) = eeeeee tt TT TT = eeeeee PP(tt) CC PP(0) CC TT = eeeeee PP(tt) PP(0)

6 1-level Model Parameters ββ TT1 2,dd(ss) ττ dd (ss) 232 Th U U U Pu Pu Am Am Cm Source: Laboratoire de Physique Subatomique et de Cosmologie

7 Exploration 1 7 What if we add -$0.1 to AP1000 core? P.i ( i s) 3 P( j s) 2 P.f ( k s) i, j, k t.e

8 Exploration 2 8 What if we add $0.1 to AP1000 core? P.i ( i s) P( j s) 10 P.f ( k s) i, j, k t.e

9 Exploration 3 9 What if we add $0.1 to AP1000 core, then after 10 seconds we add -$0.1? P.i ( i s) 3 P( j s) 2 P.f ( k s) i, j, k t.e

10 Reality 10

11 Kinetics 11 This is how reactor power is controlled Control rods add/subtract worth The circumstances we ve seen so far are not a real, however. Why? Often a balancing influence is experienced Feedback Mechanisms!

12 Isotopic Feedbacks (slow) Fuel Burnup (slow) Decrease in reactivity Fuel breeding (slow) Increase in reactivity Fission product poisons (moderate hours) 135 Xe and 149 Sm Decrease reactivity until decay away Burnable Poisons (slow) Decrease reactivity until transmuted away

13 Temperature Feedbacks (fast) Atomic concentration changes Moderator coolant density Void coefficient fuel expansion Neutron energy distribution changes harden spectrum with increased T TRIGA reactor is extreme example Resonance interaction changes Doppler dominant feedback Burnable Poisons Geometry changes

14 Feedback Effects 14 What if we add $0.1 to AP1000 core with void feedbacks included? P.i ( i) P( j) 3 P.f ( k) i, j, k t.f

15 Exotic Reactors Prompt critical (supercritical) behavior refers to reactors that are critical based on prompt neutrons only and hence have very short periods. Reactors can be designed with inherent shutdown characteristics when they become supercritical. General Atomics TRIGA reactor is an example. Such reactors can produce short but intense pulses of neutrons (see chart at left).

16 Ramifications For positive reactivity (increases in power), which necessarily must be small, prompt neutron jump is negligible, (flux essentially unchanged in the short term) For negative reactivity (decreases in power) can be arbitrarily large prompt neutron change can be very large Up to 96% in the case of a scram over about 80 seconds. Fission product decay accounts for up to 6% of total power (for an equilibrium reactor) not affected by the reactivity change cannot reduce by more than about 93% the power output

17 Cluster Control Rods

18 Cruciform Control Rods

19 α T d = ρ = dt d dt Temperature Dependence k 1 = k 1 k dk dt 2 1 k dk dt α T = temperature reactivity feedback coefficient If α T > 0, Unstable increases and decreases in temperature run away to meltdown or shutdown without operator response. If α T < 0, Stable Increases and decreases in temperature self regulate and the reactor stabilizes. reit-wigner describes absorption profile at 0 but Doppler effect broadens peaks, with Different α s for fuel/moderator ittle change in area, at higher temperatures. Different timescales 2 λ Γ Γ Fuel is most rapid r g n γ σ γ ( E) = 2 α 4π prompt 2 Γ ( E Er ) + NRC requires negative α 4 prompt values for licenses

20 Xenon (Iodine, Tellurium) Xenon-135 has a high absorption cross section (2.65x10 6 b in thermal region) and is the most significant absorbing poison. 135 Te β 11sec Fission d X dt 135 = I 6.7 hr Fission λ I I = λ I I β d I dt Iodine decay + γ + γ X ( T ) 1/ = Σ f Xe 9.2 sec Fission γ Σ φ I f T fission yield X f T fission yield Cs λ I I λ X X C ( t ) φ ( t ) ( λ + σ φ ) X, eff Σ φ T = β λ X 135 natural natural decay X σ φ ax 2.3x10 decay T β ax ( t ) 6 T yr 135 σ axφt X X Ba ( stable) absorption decay

21 Fuel Loading Patterns

22 Burnable (absorbing) poisons Burnable poison forms products with lower adsorption cross sections, compensating for accumulation of other poisons. Boron and gadolinium oxides (gadolina) are examples.

23 Typical Control Worths