Chemical Engineering 412

Transcription

1 Chemical Engineering 412 Introductory Nuclear Engineering Final Exam Review

2 Spiritual Thought 2

3 Exam 3 Performance 3 Part a Part b Part c Part d Total Average High Low Median StDev

4 Chapter 1 Units and Constants Conservations (when apply and when don t) Mass Energy Equivalence Elementary Particles Bozons, Quarks, Leptons Compositions of neutrons, protons, electrons, etc. Isotopes Nomenclatures and chart of nuclides Abundances and properties Summary of Isotopes Atomic Weight Mixtures and single element Traditional chemistry vs. nuclear chemistry

5 Chapter 2 Quantum Theory Newtonian vs. Maxwellian physics Special Relativity Time, Length, Mass alterations Mass/Energy Equivalence + Implications Momentum and Kinetic Energy (Classical vs. Relativistic) Particle Wave Duality Schrödinger Wave Equation Assumptions and Boundary Conditions Solution (1D particle + Hydrogen Atom) Uncertainty Implications and Conclusions

6 Chapter 3 Atomic Theory & Atomic Structure Nuclear Energy Levels Liquid Drop Model Repulsive vs. Attractive Forces Calculations of total Mass Shell Model Stability Binding Energy Calculations Modern Nuclear Concepts Interesting Nucleii

7 Chapter 4 Nuclear Energetics (mass/energy) Terminology Mass Defect vs. Binding Energy Nuclear Reactions (1, 2, 3 particles, etc.) Nuclear Conservations (charge!!) Parallel Reactions Q-Value Definition Calculations Implications Z-Changes Excited Nucleii

8 Decay Mechanics Chapter 5 Conservations Mechanisms Reading Chart of Nuclides Energy Diagrams Decay Types & Details Decay Constants/Half Lifes Kinetics (single & parallel reactions) Decay Chains Primary chains (4n, 4n+1, 4n+2, 4n+3) Secular Equilibrium, Daughter product analysis Carbon Dating & Inorganic Dating

9 Chapter 6 Binary Nuclear Reactions Major Types & Definitions Mechanisms Kinematics Threshold Energies Nuclear Scattering Reactions Nuetron Interactions Slowing Down Absorption Fission Reactions Mechanism and products Energies & Decay Heat Prompt vs. Delayed

10 Chapter 7 Radiation Interactions with Matter Types Linear Interaction Coefficient Total Probability of Interaction Conceptual Interpretations Cross Section (vs. interaction coefficient) Macroscopic vs. Microscopic Interaction specific vs. total Energy Dependence, material dependence, etc. (plots) Nuetron Flux & Fluence (collided vs. uncollided) Photon Interactions (+photoelectric) Stopping Power

11 Chapter 10 (I) Chapter 10 Criticality Six factor formula Multiplication factor Cross Sections Neutron Life Cycle Moderation Common moderators Most effective moderators Bare Reactor Flux profiles Boundary conditions Diffusion Equation Problems

12 Chapter 10 (II) Homogenous vs. heterogeneous Buckling Geometric Material Constituents How to size reactor Transient Reactor Behavior Delayed neutrons reactivity δk Reactor worth ($) Reactor operation Period and times

13 Chapter 10 (III) Poisons Reactivity insertions Reactivity swing Reactor control methods Long term reactivity changes and countermeasures Changes in time Reactivity Coefficients Doppler Void (moderator expansion) Axial Expansion Radial Expansion Control Rod Drive Expansion Calculate change in reactivity based on given coefficients

14 Chapter 11 (I) Nuclear Energy Conversion Key Components General layout of nuclear plant systems Light Water Reactors Components Configurations Design Challenges Operation BWR vs PWR Operation Perturbations Thermal Changes Load Changes Fuel Changes Accidents

15 Chapter 11 (II) Gen IV Reactors Know types Benefits/Disadvantages Evolution of Nuclear Power Generations Characteristics Other Non-LWR (non Gen IV) Fast Reactors Breeder vs. Burner Key Components Challenges World-wide use

16 Chapter 12 heat output of radioactive isotopes. GPHS Characteristics Table 12.2 RTGs Types Differences & Similarities Electricity generation at any point in the life of an RTG. Space reactor concepts

17 Example 1: Back to the Future 17 Equate Bucklings Geometric Easy Material significantly harder (why?) Simplest approach Assume homogenous core Assume single energy Assume number density ratio based on movie Find B 2 using the 6 factor formula (k eff =1)

18 Example 2: Rod Ejection Accident 18 A control rod is ejected from the core instantly adding $ reactivity to the core. Assuming we want a temperature increase of no more than 10 ºC, what is the minimum overall reactivity feedback coefficient (in %mil/ºc)? If water contributes 1 %mil/ºc of negative feedback, how much should the soluble Boron provide?

19 Chapter Nuclear Fuel Cycle: front and back end Enrichment Calculations Waste factor, feed factor, separation potentials Use these factors to determine cost given price Grades and forms of Uranium Separation Techniques LWR Fuel compositions Radiopharmaceuticals Once-through cycle Other fuel cycles recycle, mixed oxides, etc.

20 Chapter 8 Detector Types Dead times, interaction rates, performance, paralyzable, etc. Examples & Diagrams, etc. Fundamental operation principles Detection and Operation Modes Spectroscopy Efficiency Related equipment (PMTs, SCPHA, MCA)

21 Chapter 9 Know Big picture of Radiation Doses Know various measurements, units conversion from one to another KERMA, exposure, Absorbed Dose, etc. Know how to correlate to biological impacts Calculation of dose Hazards of Radiation (Table usage) Exposure limits amounts, history, etc. Perspective on radiation effects Acute and latent effects/symptoms Does model Linear, threshold, hormesis

22 Chapter 13 Beneficial Uses of Radiation +Applications Specific isotopes and production Advantages/Disadvantages of radioactive Uses of Tracers (calculate amount needed) Uses of Materials affecting Radiation Uses of Radiation affecting Materials Particle Accelerators Economics and Widespread applciations

23 Chapter 14 Medical Uses of Radiation Diagnostic vs. theraputic X-Rays Mammography & Densitometry CT Scan SPECT PET MRI

24 New Material 24 Thermal Analysis of Nuclear Fuel Fuel pellet of all shapes Several layers Different materials Accidents Three Mile-Island Chernobyl Fukushima Dai-ichi Nuclear Regulations

25 Example 1 25 How long will it take a reactor operating at 100 MW to increase to 1 GW after a $0.15 increase in reactivity? TT = ββββ δδδδ = ββββ kk eeeeee 1 = ββββ kk eeeeee ρρ = ττ kk eeeeee ρρ $ ττ ρρ $ = 12.8ss 0.15 PP = 85.3ss ln 1000 MMWW ee 100 MMWW ee = 196 ss = 85.3 ss

26 Example 2 26 The pebble bed reactor packages fuel in spheres that are coated with various structural and moderating layers. Determine the steady-state temperature profile of a spherical particle with a constant heat source. The energy transport equation for this geometry is: 1 dd rr 2 dddd rr2 kk dddd dddd + qq = 0 where qq is a constant heat source (positive means heat is generated). a) Derive an expression for the temperature profile in the fuel sphere assuming that the temperature at the edge of the fuel is TT rr and is known. b) If the maximum temperature in fuel (to prevent melting) is TT mm, determine the maximum size of the sphere in terms of TT rr, qq, kk and TT mm.

27 Example 2 Solution 27 BC1: dddd = 0 BC2: TT dddd rr=rr = TT rr rr=0 1 dd rr 2 dddd dd dddd rr2 kk dddd dddd + qq = 0 rr2 kk dddd dddd = rr2 qq rr 2 kk dddd dddd = rr3 qq + CC 3 dddd = rr CC qq + By BC1, C = 0 dddd 3kk rr 2 kk rr = RR = TT rr = RR2 qq 6kk + DD DD = TT rr + RR2 qq 6kk TT rr = TT rr + qq 6kk RR2 rr 2 TT mm = TT 0 = TT rr + RR2 qq 6kk RR mmmmmm = 6 TT mm TT rr kk qq (BC2)

28 Example 3 28 The health effects from 222 Rn exposure are associated primarily with its decay products, not the radon itself. Assume an air-borne radon concentration of 4 pci/l (the EPA threshold action value) that is constantly being replenished. Also, assume radon decays only by alpha emission. If the initial concentrations of the daughter products in a lung containing 1 L of air are zero, determine the concentration of the first daughter product after 1 year assuming none of the daughter product (which is a solid) leaves with the exhaling air. The half-life data are in Appendix D of the text.

29 Example 3 Solution (I) 29 In this case, there is a non-changing (continuously replenished) initial amount of 222 Rn, which we will call NN 0 RRRR that produces 218 Po. The 218 Po experiences first-order decay. The amount of Po at any given time is given by the solution to the following differential equation, subject to the initial condition that NN PPPP tt = 0 = 0. ddnn PPPP = λλ dddd RRRR NN 0 RRRR λλ PPPP NN PPPP The first term right of the equal sign is constant with respect to time while the second is not. The solution to this equation is NN PPPP = NN RRRR 0 λλ RRRR + CC exp λλ λλ pppp tt PPPP Applying the boundary condition NN PPPP tt = 0 = 0 NN PPPP = NN RRRR 0 λλ RRRR 1 exp λλ λλ pppp tt PPPP = 4 pppppp LL 2.098xx10 6 ss xx10 3 ss 1 1 exp 3.788xx10 3 ss ss = xx10 3 pppppp LL = xx10 3 pppppp 1CCCC 3.7xx10 10 dddddddddddd/ss LL = 8.19xx10 5 dddddddddddd pppppp CCCC LL

30 Example 3 Solution (II) 30 One year substantially exceeds the half-lives of both Rn and Po, so the term in square brackets above is essentially unity and this step of the system has reached dynamic equilibrium. If one recognizes this, the problem could be more easily solved as ddnn PPPP dddd NN PPPP = λλ 0 RRRRNN RRRR λλ PPPP = λλ RRRR NN 0 RRRR λλ PPPP NN PPPP = 0 = 2.215ee 3 pppppp LL = 8.19xxxx 5 dddddddddddd/ll