Operational Reactor Safety
22.091/22.903
Professor Andrew C. Kadak
Professor of the Practice
Lecture 3
Reactor Kinetics and Control
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 1
Topics to Be Covered
• Time Dependent Diffusion Equation
• Prompt Neutrons
• Delayed Neutrons
• Point Kinetics Equation
• Reactivity
• Inhour Equation
• Feedback - Fuel-Doppler, Moderator, Power
• Reactor Control
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 2
Key Concepts
• Time Dependent Diffusion Equation
– Rate of change = rate of production – rate of
absorption – rate of leakage
• Prompt neutron keff
• Reactivity – ρ = (k -1)/k
• Mean neutron generation time l* = 10-7 sec
• Reactor Period – T = l*/ρ
– Time to increase power by factor of e
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 3
Impact of Delayed Neutrons
• 99 % of Neutrons are Prompt – released at time of fission
• Fission Products also release neutrons with some delay
based on half life - Precursors
• 20 Precursors grouped into 6 groups with half lives
ranging from 0.25 sec to 1 minute
• Delayed neutron fraction
– ßi = delayed neutrons from precursor group Ci /v
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 4
Delayed Neutrons
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Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 5
Neutron Balance
• Prompt source
• Delayed source
• Time Dependent Neutron Balance Equation
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 6
Key Kinetics Equations
• Point Kinetics Equations
• Inhour Equation
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 7
Average Delayed Neutron from
Uranium and Plutonium
Delayed neutrons are produced at about ½ the energy of prompt neutrons
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Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 8
Reactivity Insertions
• Reactor follows point kinetics equations
• Prompt jump – drop
• Asymptotic Period – considering delayed neutrons
• Prompt critical – transition to prompt from delayed
control ρ = ß
• Period of core used to start up reactor – 80 sec.
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 9
$ = ρ/ß
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 10
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Reactivity Feedbacks
• Fuel Temperature
– Thermal expansion
– Doppler
• Moderator/Coolant
• Fuel Motion – bowing
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 11
Reactivity Coefficients
• Fuel Temperature
• Moderator Temperature
• Moderator Density
• Void Coefficient
• Power Coefficient
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 12
Doppler Broadening
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Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 13
Reactivity Feedback
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Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 14
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 15
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Reactor Control
• Inherent feedback mechanism
– Fast – fuel
– Slow – moderator
• Control Rods
– Relatively fast but rod worth an issue
- Rod ejection
- Rapid withdrawal
• Soluable Boron – effect on Moderator Temp. Coefficient
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 16
Homework Assignment
• Knief Chapter 5
– Problems: 1,4,6,9
• Read Chapter 6 for next class
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008
Page 17
MIT OpenCourseWare
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22.091 Nuclear Reactor Safety
Spring 2008
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