UCN-2383 (3 11-60) OAK RIDGE NATIONAL LABORATORY Operated by For Internal Use Only UNION CARBIDE NUCLEAR COMPANY ’ Division of Union Carbide Corporation 0 R N l uee | CENTRAL FILES NUMBER Post Office Box X Oak Ridge, Tennessee | | 6 l _ 1 O ",i__g.... DATE: October 11, 1961 COPY NO. j / SUBJECT: Delayed Neutron Losses in Circulating Fuel Reactors — MSCR Memo No. 6 TO: Distribution FROM: T. W. Kerlin, Jr. Abstract Equations which describe delayed neutron losses in external loops of circulating fuel reactors were derived. A working equation - | and the necessary input data for calculating delayed neutron losses ' by an equilibrium reactor code such as ERC-5 are given. NOTICE : This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It is subject to revision or correction and therefore does not represent a final report. The information is not to be abstracted, reprinted or otherwise given public dissemination without the approval of the ORNL patent branch, Legal and Information Control Department. DELAYED NEUTRON LOSSES IN CIRCULATING FUEL REACTORS Circulating fuel reactors lose neutrons because some of the delayed neutrons are emitted outside of the core. These losses depend on core residence time, external loop residence time, and decay characteristics of the precursors. A symbolic representation of the system is MVefeVe MV ETRE Tl 1 Core > Heat & Exchanger ~ Bivzf¢fcvc where )ij = decay constant of the ith precursor from fissionable material j, Bij = number of ith precursors formed per fission neutron from fis- sionable material j, Nijc = atoms of ith precursor per unit volume of fuel stream in the core resulting from fissions in material j, | NijE = gagtoms of ith precursor per unit volume of fuel stream in the external loops resulting from fissions in material j, fc = volume fraction of fuel in the core, fE = volume fraction of fuel in the external loops, V. = core volume, ¢ VE = eXternal loop volume, pjzfj¢finflz = rate of production of fission neutrons in the core from fissionable material J. The precursor concentrations are described by these equations: dN, . I [ . e Pig¥ P - Mige > (1) dNi‘E dt, - MisE 2 (2) where tc = +time in the core, tE‘ = +time in the external loops. The boundary conditions are: Nijc(TC) = NijE(O) , (3) where Tc = time for the fuel stream to pass through the core, TE = +time for the fuel stream to pass through the external loops. The solutions to Egs. (1) and (2) are: B, V.20 A, st “A o b _ 1 J 1’ _ ij e ij ¢ ...)\ t _ ij E Note that the precursor production rate is assumed constant for the fuel stream during its stay in the core. This idealized case would exist only for uniform power density along the fuel stream or for core residence times which are short compared to the half-life of the precursor. The boundary conditions become: B, V. 2.0 -A; ;T -A; T _i%zfi—gi—(mR‘ e 1Y ) + Nijc(o) e C - NijE(O) ’ (7) -A; 5T | Nijc(o) = NijE(O) e 1IE (8) Eliminating Nijc(o) in Egs. (7) and (8) and substituting the result in Eq. (6) gives: =N ;T -\ .t Pl o e MY WE ijE Aij [1 ] e-Rij(Tc + TE)] | . (9) The rate of decay of precursors in the external loops is: LN B, .w 2, PV (1 - e-%%fiTé)(l - efixijTE) EE TE * A (T + T ) ijt e E xijTE[l - e ] The total rate of precursor decay (at equilibrium)is Bijvjzfj¢fcvc' Thus the fraction of the delayed neutrons which appear in external loops is: N f_V "1JEE'E A 5T, N TR T, £ Vp(l - e (1 -2 ) (11) _ _ S 11 B. V.2 . QT V “As AT+ To)q ° 13t e _ ij e E 'fcvcxijTE [l e } £V, T Since Ez-fig , Eg. (11) becomes: c TV “ce g 5T AT PigE _ (1-e MYOG@-e T (12) B, Ay (T + T) 13 Nl [1 L 13te E] ij c For using these results in an equilibrium reactor code such as ER.C-B,l the term.vjzfj¢ may be replaced by a neutron production rate given by f N.C’ 3 3¥3 where Cf = reaction rate coefficient for fissions in material j. J Using this in Eq. (12) gives the following result for the number of neutrons lost in the external loops per neutron produced: -A, T N, T Bij(l - € 1J C)(l - € ij E) £ losses = Z Njijj Z ' (T % T (13) 3 1 [ 13 e E] Ki.T 1 -e Jgc The necessary constants for Th252, U235, U235, U238, and Pu259 arez2 Group A (sec-l) ’ _ | o Th232 233 P PP 239 1 0.0128 0.00085 0.00020 0.0003 0.00015 0.0001 2 0.0315 0.003%5 0.00075 0.0018 0.0017 0.0006 3 0.125 0.0045 0.00105 0.0022 0.0028 0.00045 L 0.325 0.0120 0.00075 0.0023 0.0071 0.00085 5 1.55 0.0045 0.00025 0.0007 0.0042 0.0003 6 4.5 0.0009 - 0.0002 0.0015 - 0.02625 o;ooso 0.0075 0.01745 0.0023% L. G. Alexander, ERC-5 Program for Computing the Equilibrium States of Two-Region, Thorium Breeder Reactors, ORNL-CF-60-10-87 (Oct. 20, 1960). ?A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors, p. 1%6, The University of Chicago Press, Chicago, 1958. DISTRIBUTION 1-10. L. G. Alexander 3. J. A. Lane 11. S. E. Beall 37. J. L. Lucius 12, L. L. Bennett 38. R. N. Lyon 135, A. L. Benson, ORO 39. H. G. MacPherson 14, E. S. Bettis 40, W. B. McDonald 15. A. L. Boch 41. R. P. Milford 16, F. E. Blankenship 4o, A. M, Perry 17. R. B. Briggs 43, D. Scott 18. D. 0. Campbell 4. E. P. Self, ORO 19. W. L. Carter 45, M, J. Skinner 20. R. H. Chapman 46. 1I. Spiewak 21, F. L. Culler Y7, J. A, Swartout 22, J. G. Delene 48. W. C. Thurber 2%3. D, E. Ferguson 49, J. W. Ullmann 24k, H. E. Goeller 50. R. Van Winkle 25. W. R. Grimes 51. G. M. Watson 26. C, E. Guthrie 52. A. M. Weinberg 27. dJ. P, Hammond 53. dJ. H, Westsik 28, F. E. Harrington 54-55. Central Research Library 29, W. H., Jordan 56. Document Reference Section 30. P. R. Kasten 57-59. Laboratory Records 31-35, T, W. Kerlin 60. Laboratory Records (LRD-RC)