Operational Reactor Safety

22.091 /22.903

Professor Andrew C. Kadak Professor of the Practice

Lecture 3

Reactor Kinetics and Control

Prof. Andrew C. Kadak, 2008 Page 1

Department of Nuclea r S c ien ce & Engineering

Topics to Be Covered

• Time Dependent Diffusion Equation

• Prompt Neutrons

• Delayed Neutrons

• Point Kinetics Equation

• Reactivity

• Inhour Equation

• Feedback - F uel-Doppler, Moderator, Power

• Reactor Control

Prof. Andrew C. Kadak, 2008 Page 2

Department of Nuclea r S c ien ce & Engineering

Key Concepts

• Time Dependent Diffusion Equation

– R ate of change = rate of production – r ate of absorption – r ate 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

Prof. Andrew C. Kadak, 2008 Page 3

Department of Nuclea r S c ien ce & Engineering

Impact of Delayed Neutrons

• 99 % of Neutrons are Prompt – r eleased at time of fission

• Fission Products also release neutrons with some delay based on half life - P recursors

• 20 Precursors grouped into 6 groups with half lives ranging from 0.25 sec to 1 minute

• Delayed neutron fraction

– ß i = delayed neutrons from precursor group C i /v

Prof. Andrew C. Kadak, 2008 Page 4

Department of Nuclea r S c ien ce & Engineering

Delayed Neutrons

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Prof. Andrew C. Kadak, 2008 Page 5

Department of Nuclea r S c ien ce & Engineering

Neutron Balance

• Prompt source

• Delayed source

• Time Dependent Neutron Balance Equation

Prof. Andrew C. Kadak, 2008 Page 6

Department of Nuclea r S c ien ce & Engineering

Key Kinetics Equations

• Point Kinetics Equations

• Inhour Equation

Prof. Andrew C. Kadak, 2008 Page 7

Department of Nuclea r S c ien ce & Engineering

Average Delayed Neutron from Uranium and Plutonium

Delayed neutrons are produced at about ½ t he energy of prompt neutrons

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Prof. Andrew C. Kadak, 2008 Page 8

Department of Nuclea r S c ien ce & Engineering

Reactivity Insertions

• Reactor follows point kinetics equations

• Prompt jump – d rop

• Asymptotic Period – c onsidering delayed neutrons

• Prompt critical – t ransition to prompt from delayed control ρ = ß

• Period of core used to start up reactor – 80 sec.

Prof. Andrew C. Kadak, 2008 Page 9

Department of Nuclea r S c ien ce & Engineering

2008

De

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Reactivity Feedbacks

• Fuel Temperature

– T hermal expansion

– D oppler

• Moderator/Coolant

• Fuel Motion – bowing

Prof. Andrew C. Kadak, 2008 Page 11

Department of Nuclea r S c ien ce & Engineering

Reactivity Coefficients

• Fuel Temperature

• Moderator Temperature

• Moderator Density

• Void Coefficient

• Power Coefficient

Prof. Andrew C. Kadak, 2008 Page 12

Department of Nuclea r S c ien ce & Engineering

Doppler Broadening

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Prof. Andrew C. Kadak, 2008 Page 13

Department of Nuclea r S c ien ce & Engineering

Reactivity Feedback

Figures © Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse .

Prof. Andrew C. Kadak, 2008 Page 14

Department of Nuclea r S c ien ce & Engineering

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Reactor Control

• Inherent feedback mechanism

– Fast – f uel

– Slow – moderator

• Control Rods

– R elatively fast but rod worth an issue

- Rod ejection

- Rapid withdrawal

• Soluable Boron – e ffect on Moderator Temp. Coefficient

Prof. Andrew C. Kadak, 2008 Page 16

Department of Nuclea r S c ien ce & Engineering

Homework Assignment

• Knief C hapter 5

– P roblems: 1,4,6,9

• Read Chapter 6 for next class

Prof. Andrew C. Kadak, 2008 Page 17

Department of Nuclea r S c ien ce & Engineering

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22.091 Nuclear Reactor Safety

Spring 200 8

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