FBR eutronics: Breeding potentil, Breeding Rtio, Breeding Gin nd Doubling time K.S. Rjn Proessor, School o Chemicl & Biotechnology SASTRA University Joint Inititive o IITs nd IISc Funded by MHRD Pge 1 o 7
Tble o Contents 1 BREEDIG... 3 1.1 BREEDIG RATIO... 4 1.2 BREEDIG GAI... 4 1.3 DOUBLIG TIME (DT)... 5 2 REFEREES/ADDITIOAL READIG... 7 Joint Inititive o IITs nd IISc Funded by MHRD Pge 2 o 7
In this lecture, we shll discuss bout the clcultion o breeding rtio nd doubling time At the end o this lecture, the lerners will be ble to (i) (ii) (iii) deine conversion or breeding rtio determine breeding potentil nd breeding gin determine the time required or doubling the uel inventory (doubling time) 1 Breeding Breeding in nucler rectors reers to the process in which signiicntly mount o ertile mterils re converted to issile mterils by nucler trnsmuttion. This requires the ertile isotope to hve lrge cross section or neutron cpture. Since the min purpose o nucler rector is to produce electricity, breeding is considered s n o-shoot o excess neutrons produced during ission bove the ones required or sustennce o chin rection. The possibility o breeding in nucler rector, tking into ccount o the type o issile mteril used, depends on the number o neutrons produced or every neutron bsorbed in the uel. This is denoted by reproduction ctor η. This is relted to the cross sections s ollows: σ η ν (1) σ The probbility o breeding is enhnced when the vlue o η exceeds two by lrge rction. For exmple, the vlue o η or U-235, Pu-239 nd U-233 when bombrded by therml neutrons is 2.07, 2.11 nd 2.30 respectively. Breeding with therml neutrons using U-235 nd Pu-239 uels is virtully impossible due to neutron bsorption in structurl mterils nd modertor. However, with U-233 uel, it is possible to chieve breeding using therml neutrons. The scenrio is dierent or the cse o bombrdment with st neutron. The vlue o η or U-235, Pu-239 nd U-233 when bombrded by st neutrons is 2.3, 2.7 nd 2.45 respectively. Hence, breeding is possible with ll the bove issile nuclei due to bombrdment with st neutron. Conversion rtio is widely used term to denote the bility o rector to convert ertile to issile mteril. Conversion rtio is deined s the rtio o number o issile nuclei produced to the number o issile nuclei consumed. When rector is operted without ny ertile mteril, the conversion rtio is zero. In this cse, the rector is reerred to s burner s it burns ll the uel without producing ny issile mteril. Joint Inititive o IITs nd IISc Funded by MHRD Pge 3 o 7
It my be reclled tht the urnium uelled therml rectors either use nturl urnium or enriched urnium. In both these cses, isotopic bundnce o U-238, ertile mteril, is very high. It is possible to chieve higher conversion rtio by cilitting higher neutron cpture in U-238 reltive to neutron bsorption in U-235. This must be crried out without the loss o criticlity. To ensure tht suicient neutrons re vilble or chin rection, the neutron losses in structurl elements nd modertor must be reduced. Also, the use o modertors like hevy wter nd crbon require more collisions or neutron thermliztion nd hence require lrger core. This improves the contct between neutron nd U-238 contct, thereby improving the conversion rtio. The conversion rtio cn be predicted pproximtely s ollows: Conversion Rtio (CR) η 235 ε-1-l (2) η 235 corresponds to reproduction ctor o pure U-235. Hence to improve the conversion rtio, lekge o neutrons (l) must be reduced. For most therml rectors, CR is between 0.4 nd 0.7 nd these rectors re clled converters (0<CR<1). ε is the st ission ctor tht indictes the contribution due to st neutrons in therml rector. 1.1 Breeding Rtio The rector with conversion rtio greter thn 1 is clled breeder rector. This is the rector tht produces more uel thn tht it consumes. For breeder rectors, the term breeding rtio (BR) is used. The breeding rtio is mximum when the lekge o neutrons (l) is zero. This is clled mximum breeding rtio (BR mx ) nd is lso clled Breeding Potentil o the uel. Breeding Potentil BR mx η-1 (3) Plese note tht in Eq. (3), ε the st ission ctor is tken s unity s most o the breeders re st breeders. The reproduction ctor is to be clculted or Pu-239, the predominnt issile isotope in st rectors. 1.2 Breeding Gin Another term widely used in breeder rector is Breeding Gin (BG). reltionship between BG nd BR is The BG BR 1 (3) This represents the extr issile mteril produced or every tom o uel (issile isotope) consumed. For Pu-239 uelled st rector, BR η 239-1-l (4) Joint Inititive o IITs nd IISc Funded by MHRD Pge 4 o 7
CR σ BR ν 1 l σ 239 (5) Exmple -1: Determine Breeding Rtio or Pu-239 uelled st rector. Tke ν 2.975; σ 1.850; σ 2.11 nd l 0.405. 1.85 Using Eq. (5), BR 2.975 1 0. 405 2.11 BR 1.203 Exmple 2: Consider st breeder rector operting with Breeding Rtio o 1.3. I it is desired to ccumulte n dditionl 1500 kg o issile mteril, determine the mount o pure Plutonium uel to be burnt. By deinition o Breeding Rtio, BR number o issile nuclei produced/number o issile nuclei consumed BR mss o issile nuclei produced/mss o issile nuclei consumed Let x be the mss o issile nuclei consumed, then BR (x+1500)/x1.3 Solving the bove or x gives x 5000 kg Hence 5000 kg o Plutonium must be burnt to produce n dditionl 1500 kg o issile mteril. 1.3 Doubling time (DT) It is deined s the time required to ccumulte mss o uel equl to tht loded initilly in rector system. When the initil inventory o issile mteril is low, doubling time is reduced. In other words, doubling is chieved in shorter period o time with initil lower loding o issile mteril. Let us derive n expression or clcultion o Doubling Time (DT). The rector power per unit mss o uel (P ) my be relted to the number o uel nuclei per unit mss o the uel ( ) s P E φ - σ (6) The bove eqution my be rewritten s: Power per unit mss o uel (W/kg) Energy relesed per ission (J) * umber issions per unit time per unit mss o uel (s -1 kg -1 ) The number o issions per unit time per unit mss o uel represents the rte o consumption o unit mss o uel. Joint Inititive o IITs nd IISc Funded by MHRD Pge 5 o 7
Thereore, I M F is the mss o uel loded, then the rte o consumption (R C ) o uel o mss M F is given by R C M F φ - σ (toms/s) (7) I BR is the Breeding Rtio, then the rte o production (R P ) o issile mss is given by R P BR*M F φ σ (toms/s) (8) The net increse in uel Rte o Production Rte o consumption et increse R net (BR-1)*M F φ σ (toms/s) (9) I DT is the Doubling Time, then DT*R net M F (10) Thereore, DT M F R net M F ( BR 1) M F φ σ ( BR ) φ σ 1 1 (11) An expression my be obtined or DT In terms o rector power (P ) s ollows: Recll, P E φ - σ φ - P / ( E σ ) (12) Substituting the bove in the eqution or Doubling Time, we get DT E σ (13) ' ( BR 1) σ P ow let s discuss the ctors tht inluence Doubling Time. (i) Breeding Rtio: Higher the Breeding Rtio, greter is the mount o issile mteril produced. Hence, the time required or doubling the mss is reduced t higher Breeding Rtios. We hve seen erlier tht Breeding Rtio depends on the reproduction ctor η, which inturn is inluenced by bsorption cross section, ission cross sections nd ν'. As the cross sections re unctions o neutron energies, pproprite choice o neutron energy nd steps to minimize neutron lekge will result in incresed Breeding Rtio (BR). (ii) Power per unit mss o the uel: When this quntity is high, the verge neutron lux is lso high mong other vribles. As evident rom Eq. (11), with incresed neutron lux, the Doubling Time is reduced. Hence the Doubling time decreses with incresed rector Power per unit mss o the uel. Joint Inititive o IITs nd IISc Funded by MHRD Pge 6 o 7
Exmple 4: Determine the doubling time o Pu-239 st breeder rector. The rector is operted t 400 MW/tonne Pu-239 with Breeding Rtio o 1.2. The bsorption nd ission cross section re 2.16 nd 1.81 b respectively. The number o Pu-239 per unit mss is 2.52x10 21 (toms/g). Dt: E 3.2x10-11 J; 2.52x10 21 ; P 400 MW/tonne 400 J/gs; σ 2.16 b; σ 1.81 b Substituting the bove in Eq. (13), DT E σ 2.52x10 *3.2x10 11 ' ( BR 1) σ P ( 1.2 1) 2.16 * 400 21 *1.81 DT 9776 dys ~ 27 yers 2 Reerenes/Additionl Reding 1. ucler Energy: An Introduction to the Concepts, Systems, nd Applictions o ucler Processes, 5/e, R.L. Murry, Butterworth Heinemnn, 2000 (Chpter 13). Joint Inititive o IITs nd IISc Funded by MHRD Pge 7 o 7