STACEY W Nuclear Reactor Physics (Wiley, 2nd ed. 2004) Chapter 6 - Fuel Burnup . 197 6 Fuel Burnup The long-term changes in the properties of a nuclear reactor over its lifetime are determined by the changes in composition due to fuel burnup and the manner in which these are compensated. The economics of nuclear power is strongly affected by the efficiency of fuel utilization to produce power, which in turn is affected by these long-term changes associated with fuel burnup. In this chapter we describe the changes in fuel composition that take place in an operating reactor and their effects on the reactor, the effects of the samarium and xenon fission products with large thermal neutron cross sections, the conversion of fertile material to fission- able material by neutron transmutation, the effects of using plutonium from spent fuel and from weapons surplus as fuel, the production of radioactive waste, the extraction of the residual energy from spent fuel, and the destruction of long-lived actinides. 6.1 Changes in Fuel Composition The initial composition of a fuel element will depend on the source of the fuel. For reactors operating on the uranium cycle, fuel developed directly from natural ura- nium will contain a mixture of 234U, 235U, and 238U, with the fissile 235Ucontent varying from 0.72% (for natural uranium) to more than 90%, depending on the enrichment. Recycled fuel from reprocessing plants will also contain the various isotopes produced in the transmutation–decay process of uranium. Reactors oper- ating on the thorium cycle will contain 232Th and 233Uor235U, and if the fuel is from a reprocessing plant, isotopes produced in the transmutation–decay process of thorium. During the operation of a nuclear reactor a number of changes occur in the composition of the fuel. The various fuel nuclei are transmuted by neutron cap- ture and subsequent decay. For a uranium-fueled reactor, this process produces a variety of transuranic elements in the actinide series of the periodic table. For a thorium-fueled reactor, a number of uranium isotopes are produced. The fission event destroys a fissile nucleus, of course, and in the process produces two inter- mediate mass fission products. The fission products tend to be neutron-rich and 198 6 Fuel Burnup Fig. 6.1 Transmutation–decay chains for 238Uand232Th. (From Ref. 3; used with permission of Taylor & Francis.) subsequently decay by beta or neutron emission (usually accompanied by gamma emission) and undergo neutron capture to be transmuted into a heavier isotope, which itself undergoes radioactive decay and neutron transmutation, and so on. The fissile nuclei also undergo neutron transmutation via radiative capture fol- lowed by decay or further transmutation. Fuel Transmutation–Decay Chains Uranium-235, present 0.72% in natural uranium, is the only naturally occurring isotope that is fissionable by thermal neutrons. However, three other fissile (fis- sionable by thermal neutrons) isotopes of major interest as nuclear reactor fuel are produced as the result of transmutation–decay chains. Isotopes that can be con- verted to fissile isotopes by neutron transmutation and decay are known as fertile isotopes. 239Pu and 241Pu are products of the transmutation–decay chain beginning with the fertile isotope 238U, and 233U is a product of the transmutation–decay 6.1 Changes in Fuel Composition 199 chain beginning with the fertile isotope 232Th. These two transmutation–decay chains are shown in Fig. 6.1. Isotopes are in rows with horizontal arrows rep- resenting (n, γ ) transmutation reactions, with the value of the cross section (in barns) shown. Downward arrows indicate β-decay, with the half-lives shown. Ther- mal neutron fission is represented by a dashed diagonal arrow, and the thermal cross section is shown. (Fast fission also occurs but is relatively less important in thermal reactors.) Natural abundances, decay half-lifes, modes of decay, decay energies, spontaneous fission yields, thermal capture and fission cross sections av- eraged over a Maxwellian distribution with kT = 0.0253 eV (σ th), infinite-dilution capture and fission resonance integrals (RIs), and capture and fission cross sec- tions averaged over the fission spectrum (σ χ ) are given in Table 6.1. Fuel Depletion–Transmutation–Decay Equations Concentrations of the various fuel isotopes in a reactor are described by a coupled set of production–destruction equations. We adopt the two-digit superscript con- vention for identifying isotopes in which the first digit is the last digit in the atomic number and the second digit is the last digit in the atomic mass. We represent the nm nm neutron reaction rate by σx ϕn , although the actual calculation may involve a sum over energy groups of such terms. For reactors operating on the uranium cycle, the isotopic concentrations are de- scribed by ∂n24 =−σ 24φn24 ∂t a ∂n25 = σ 24φn24 − σ 25φn25 ∂t γ a ∂n26 = σ 25φn25 − σ 26φn26 + λ36n36 ∂t γ a ec ∂n27 = σ 26φn26 + σ 28 φn28 − λ27n27 ∂t γ n,2n ∂n28 =−σ 28φn28 ∂t a ∂n29 = σ 28φn28 − λ29 + σ 29φ n29 ∂t γ a ∂n36 = σ 37 φn37 − λ36 + σ 36φ n36 ∂t n,2n a ∂n37 = λ27n27 − σ 27φn37 ∂t a ∂n38 = σ 37φn37 − λ38 + σ 38φ n38 ∂t γ a ∂n39 = λ29n29 − λ39 + σ 39φ n39 (6.1) ∂t a 200 6 Fuel Burnup ∂n48 = λ38n38 − σ 48φn48 ∂t a ∂n49 = λ39n39 − σ 49φn49 + σ 48φn48 ∂t a γ ∂n40 = σ 49φn49 − σ 40φn40 + σ 29φn29 + σ 39φn39 ∂t γ a γ γ ∂n41 = σ 40φn40 − λ41 + σ 41φ n41 ∂t γ a ∂n42 = σ 41φn41 − σ 42φn42 ∂t γ a ∂n43 = σ 42φn42 − λ43 + σ 43φ n43 ∂t γ a ∂n51 = λ41n41 − λ51 + σ 51φ n51 ∂t a ∂n52 = σ 51φn51 − σ 52φn52 ∂t γ a ∂n53 = λ43n43 − σ 53φn53 + σ 52φn52 ∂t a γ With respect to Fig. 6.1, a few approximations have been made in writing Eqs. (6.1). 239 240 Theneutroncapturein Utoproduce Ufollowedbythedecay(t1/2 = 14 h) 240 240 into Np and the subsequent decay (t1/2 = 7 min) into Pu is treated as the di- rect production of 240Pu by neutron capture in 239U, and the production of 240Np 239 by neutron capture in Np followed by the subsequent decay (t1/2 = 7 min) of 240Np into 240Pu is treated as the direct production of 240Pu by neutron capture in 239Np. These approximations have the beneficial effect for numerical solution tech- niques of removing short time scales from the set of equations, without sacrificing information of interest on the longer time scale of fuel burnup. For reactors operating on the thorium cycle, the isotopic concentrations are de- scribed by ∂n02 =−σ 02φn02 ∂t a ∂n03 = σ 02φn02 − λ03 + σ 03φ n03 ∂t γ a ∂n13 = λ03n03 − λ13 + σ 13φ n13 ∂t a ∂n22 =− λ22 + σ 22φ n22 ∂t a ∂n23 = σ 22φn22 + λ13n13 − σ 25φn23 ∂t γ a (6.2) ∂n24 = σ 23φn23 + σ 13φn13 − σ 24φn24 ∂t γ γ a 6.1 Changes in Fuel Composition 201 χ f f f 95 22 24 33 92 08 59 31 74 42 11 04 33 01 . σ (Continued) χ γ 072209 1 1 1 17 1 19 1 09 0 1107 0 0 93 0 11 1 091128 0 0 03 0 2 –– –– . σ 0 0 0 f f f − − – – – RI γ 84 94 –––– – – 864 RI − − − th f f f – – – σ 7 52 54 10 346 278 8 2 0 0 2 th γ 418887 469 6 507 138 631 133 774 278 7 0 0 0 35 64 66 173 364 0 144 20 661 7 0 621 2453 259 1032 0 392 1 1084399 49 1835 0 201 940 0 σ 1285 13 643 11 0 (barns) (barns) (barns) (barns) (barns) (barns) 9 9 9 9 8 10 5 − − − − − − − 10 10 10 10 10 10 10 – –– – –––––– – – – – – – –– –– × × × × × × × 6 1 7 0 6 2 . < < < Fission Yield (%) 9 91 77 69 35 0 94 49 1 2 52 3 2 27 57 4 3 39 . 4 4 4 4 4 5 0 0 4 2 0 1 1 0 0 5 1 0 ∗ ∗ α α α α α α α α β β β β β β β β β Mode (MeV) Decay Energy Spontaneous y y y y y y yec y 10 5 5 8 6 9 5 6 10 10 10 10 10 10 10 10 2 2 2 / / / 1 1 1 d d × × × × × × × × t t t h m d d y m h 41 7 59 46 04 34 75 47 54 14 12 3 1 0 9 5 1 . 1 6 1 2 7 2 6 4 1 2 2 22 24 27 68 23 14 Abundance Cross Section and Decay Data for Fuel Isotopes ThThThPa 100 Pa – U– – U– – U – UU– U– 0.0057 U 0.719 U– U– Np 99.27 NpNp – – – Isotope232 (%) 233 234 233 234 232 233 234 235 236 237 238 239 240 236 237 238 Table 6.1 202 6 Fuel Burnup χ f f f 08 99 80 65 36 38 13 46 . σ 1 1 χ γ 1510 2 05 1 12 1 1 09 1 10 23 19 1 –– . σ 0 0 f f f − – – RI γ – 445 RI 1130 − th f f f – – σ th γ 17 33 126458 146274264326 15 401 698532 53 938 154 59 182 8103 180 3 33 303 0 9 1305 576 0 0 0 0 14 0 σ (barns) (barns) (barns) (barns) (barns) (barns) 4 7 7 6 14 − 10 10 − − − − − − 10 10 10 10 10 –– – × 10 10 × × × × 5 . × × 7 4 9 2 . 5 < > Fission Yield (%) 23 35 0 22 72 64 91 61 02 – – –––––– .