JTATINRID - S 3 4456 D360L0O3 3 2 é ORNL 1368 Reactors-Research and Power fd./ @ ) 1@‘? | SO en e QN A Myl .fiw-__ SOME EFFECTS OF TRANSMQT)*%TQN‘ PRODUCTS ON U233 BREEDER PILE OPERATION CENTRAL RESEARCH LIBRARY DOCUMENT COLLECTION LIBRARY LOAN COPY DO NOT TRANSFER TO ANOTHER PERSON If you wish someone else to see this document, send in name with document and the library will arrange a loan. OAK RIDGE NATIONAL LABORATORY OPERATED BY CARBIDE AND CARBON CHEMICALS COMPANY A DIVISION OF UNION CARBIDE AND CARBON CORPFPORATION T = POST OFFICE BOX P OAK RIDGE. TENNESSEE ORNL~-1368 . This document consists of 40 pages, Copy é? of 158 , Series A. Contract No. W-740S5, Eng. 26 SOME EFFECTS OF TRANSMUTATION PRODUCTS ON U233 BREEDER PILE OPERATION CHEMISTRY DIVISION J. Halperin and R. W. Stoughton | DECLASS’HEU CLASSIPICATION CRANGRD To: - - - s AEC 7 BN il teT .zl .-i? BY - W iy - "‘-"_"--““ - Date Issued: SEe g OAK RIDGE NATIONAL LABORATORY Operated by CARBIDE AND CARBON CHEMICALS CCMPANY A Division of Union Carbide and Carbon Corporation Post Office Box P Oak Ridge, Tennessee d 4456 03L0L0O3 3 =ii- ORNL 1368 Reactors-Research and Power INTERNAL DISTRIBUTION 1. . Felbeck (C&CCC) 18. L. B. Emlet (Y¥-12) 31. K. Z. Morgan 2~3. Chg stry Library 19. A, M. Weinberg 32. J. S, Felton 4. Ph} s Library 20. E. H. Taylor 33. A. S. Householder 5. Biol} Library 21, E. D. Shipley 34. C, S. Harrill 6. Healt@Physics Library 22. S. C., Lind 35. C. E, Winters 7. Metal Ny Library 23. F. C. Vonderlage 36. D. W. Cardwell 8-9. Trainir\@@School Library 24. R, C, Briant 37. E. M. King 10. Reactor \@Werimental 25. J. A, Swartout 38, J. A. Wethington Engineer\g Library 26, F. L. Steahly 39. D. D. Cowen 11-14. Central Fi¥WRe 27. A. H. Snell 40. F, R. Bruce 15. C. E. Centé} 28, A. Hollaender 41. D. E. Ferguson 16, C. E. Larso 29, M. T. Kelley 42-43. J. Halperin 17. W, B. Humes (\g@5) 30. G. H. Clewett Lih=~45, R, W, Stoughton L6-58, 29. 60-68. 69. 70-73. Th. 75-76. 77-82. 83. 8. 85-89. 90-92. 93-96. 97. 98-104. 105. 106-109. 107-112. 113. 114. 115-117. 118. 119, 120-121. 122-123. 124. 125, 126. 127. 128, 129-130. 131. 132-135. 136-143. 1,4-158. EXTERNAL DISTRIBUTION ArgonrN@llational Laboratory (1 copy to W. M. Manning and 1 copy WA John Huizenga) Armed FOjles Special Weapons Project (Sandia) Atomic ErN§ Commission, Washington (1 copy to J. A. Lane) Battelle M@gerial Institute Brookhaven R@ional Laboratory (1 copy to D. E. Koshland, Jr.) Bureau of Sh¥s ch and Development Company Carbide and CaX@n Chemicals Company (Y-12 Area) Chicago Patent Sip Chief of Naval Rege duPont Company % General Electric C-d General Electric Conig Hanford Operations Off Idaho Operations Offlc _ Iowa State College “* Knolls Atomic Power LaboX Los Alamos Massachusetts Institute of Massachusetts Institute of Mound Laboratory e National Advisory Committee foh sleronautics, Cleveland National Advisory Committee for "fronautics, Washington New York Operations Office o North American Aviation, Inc. k. Nuclear Development Associates (NDA Patent Branch, Washington Rand Corporatlon Savannah River Operations Offlce, Auvgu Savannah River Operations Office, Wilmln- University of California Radiation Laborat# Vitro Corporation of America Westinghouse Electric Corporation Wright Air Development Center Technical Information Service, Oak Ridge 2 - e 2 2 P ; - SRR L B 5 i, - v . N N -~ s M ‘ - L . ™ N RS California ReW rch any (ANPP) ;‘ Richland ry B hrology (Kaufmann) ;?;f ology (Benedict) INTRODUCTION * Two mutually dependent factors influencing the‘feasibility of breeding are the losses of fuel atoms in chemical processing and the losses of neutrons due to absorption by fission producta. If the fission products are removed by processing exceedingly frequently, the neutron losses mentioned would ge low.but the fuel atoms lost would be exhorbitant; con- versely if processing were conducted less and less frequently, the fuel atoms lost in pro- cessing would diminish but the neutrons absorbed by fission products would become prohibitive. Hence it seems desirable to minimize the sum of these two losses with respect to processing period and to estimate the magnitude of the losses around the optimum value. It is felt that sufficient data are available on certain processing losses and cross-section values to glve a reasonable estimate of the probable range of these combined losses and of the optimum processing periods. J. A Lane, et al,(l) have considered the various factors influencing the financial and neutron efficiencies of a UPJDJ breeder. For a particular pile configuration; they com- puted the U233 production as a fudction of processing period. ; The purpose of the first part of the current paper was to comstruct an expression for the fuel losses due to chemical processing plus the neutron losses due to absorption by fission products and to investigate the influence of the various parameters on the magnitude of the losses and on the optimum processing period. | In these calculations the fission products have been divided into three classes: those removed continuously as rare gases, those with relatively low cross-sections and those with quite high cross-sections. Then the sum of the two types of losses under consideration has been minimized with respect to processing period. Our interest here has been limited largely to the 0233 breeder although the treatment should hold for any homogeneous thermal reactor. The second part of the paper deals with the build-up of heavy isotopes both in the reactor and blanket of a U233 breeder and the effects of these species on neutron economy and chemical processing. The build-up and the effects of U25h, U255, and U256 have been (2) quite thoroughly considered by S. Viener . Some of these higher isotope computations (1) (2) ~ o . __. AT - - % A a9A fA_4 T M\ ORNL-1096, Part IV (Dec. 10, 1951); also see ORNL-855, pp. 50-55 (Oct. 16, 1950). have been repeéted here, however, since it was felt desirable to include effects of U237 and some still higher species. I. Fiesion Product Poison lLosses vs Pfocessing Losses In considering the factors determining reactor efficiency, one must optimize with re- spect to some pertinent parameter. For converter and power reactors onme wants the cost per unit product optimized. However, for breeder piles, until we are comvinced that breeding is feasible, it seems more reasonable to minimize neutron plus fuel losses. A calculation of the optimum processing period was carried out on the basis of a num- ber of simplifying assumptioms. All the variables considered have been extended through a reasonable range of values, and 1t is felt that the actual values to be realized in a given reactor system should lie within the range covered. The fission products were rather arbitrarily divided imto three groups: Average Fission yield Neutron capture cross-section symbol value symbol value G: Bemoved from reactor as rare gases -- 0.385 - -- R: Highly capturing Rare Eerths ¥y 0.015 - 50,000 b A; Remaining Yo 1.6 (, 50 b The values of y. and.d; for the highly ebsorbing rare earths are rounded off figures from the results of Ingraham, Hayden and Hess LEhys. Rev. 79, 271 (195017, end consist mainly of Smlhg (y = 0.011, ¢ = 47,000) and sm1”1 (y = 0.004%, 0 = 7200). The actual value of 6; is not very important as this group is essentially entirely removed by neutron capture, and this condition would mot be altered significantly by rather large changes in 6;. The yield for all the fissiom products with rare gas ancestors was estimated by Coryell, Turkevich et al. in 1944k to be about 30%; it was estimated that this fraction of all the - fission products could in primciple be removed as gases leaving T0% or 1.4 atoms per fission in a fiqmogeneous reactor solution. A yield of 0.6 for the removable fiéeion products 1s probably optimistic under amny practical conditiofiss perhaps 0.4 is more realistic. The actual value used was 0,385 (i. e. 0.4 less 0.015) so the total yield per fission would be exactly two. The cross-section value of 50 barnms is somewhat larger than the value of ~3- (3) E, P. Steinberg 0 10.0 z 30 — Oy - - 0 " Oo_~o==% | :-3 00 ® i e) i ’,/, » ,,__.-‘ . 300 b - i =~ ’ —?““—’” -—'; ; - o —— g’ - ’.—"‘— b _ R N I L 1 ] I ! ] ] I t ] 1 ] { 10 20 30 40 50 60 4 70 80 90 {00 1O - r(days) at f = 10 ) 0 | | : | 1 | I | I | ! | i | I | I | 1 { 10 20 30 40 50 60 70 80 S0 {00 fr x 10-19( necu;]rzons) FIG. 6 LOSSES AS A FUNCTION OF THE AVERAGE CROSS—SECTION OF GROUP B FISSION PRODUCTS, a <1k the advantages of batch processing may well outweigh the disadvantages. Tt has been pointed out that the assumption that the processing losses will be proportional to the fuel atoms processed may not be valid for all mefhods of processing. For example, with an ion exchange method, fuel solution could be poured through an absorption column until the radiation had destroyed the usefulness of the resin or until the column was loaded with fission products and the urenium losses on the column might be essentlally 1ndependent_of the rate of throughput. This might be true and in such a case the treatment given here would not nec- essarily be expected to hold for ion-exchange processing; it is8 not entirely clear, however, exactly how an ion-exchange continuous process would be carried out. It is felt thaf the calculations made in this report would be pertinent to a solvent extraction process vwhether conducted in 1light water or directly in heavy water. -15- TABLE 1 Minimum Losses in % Due to Chemical Proceasing Plus Fission Product Neutron Absorption Per Fuel Atom Destroyed. (Fuel Atom Lost Assumed Equivalent to Neutron Lost). T (Days) T (Days) std. ariable | value | value | Ly |trx 10719 | at £ = o | 1, |erx107 |at £ = 10%Y o= - std. | 2.9 21 24 3.5 15 18 1, 0.001 | 0.0003 | 2.0 10 12 2.h 10 12 1 .01 | .005 | 5.0 50 58 6.5 35 b1 67 |500 800 2.5 16 19 3.0 12 14 Yy 015 | .005 | 2.0 22 26 2.6 15 17.5 Yy 015 | .03 b1 19 22 n,7 14 16 6 150,000 | 10,000 2.4 18 21 3.1 14 16 @ |50,000 [150,000 3.0 20 23 3.6 16 19 yafa | 80 20| 2.1 4o 47 2.k 30 35 yafa | 80 200 | 3.8 13 15 %8 | 10 | 12 6o 0 300 | 3.0 19 22 3,7 m 16 6o 0 3000 | 3.8 14 16 b7 10 12 -16- II. The Effects of Bulld-Up of Heavy Isotopes In a U233 thermal breeder the U233 concentration in the core will refiain essentially constant by addition of new material as the fuel is burmed, and the isotopes U234, y235 and U236 will 8lovly grow in and attaln concentrations of roughly the same order of magni- tude as that of the U233, Other species, e. g. U237, Np237, Wp238, Pu238, pu239, y231, U232, etc., will also grow in in smaller amounts and the methods and schedule of processing the fuel will determine the maximum levels of the Np and Pu isotopes. The following seche- matic diagram indicates moet of the pertinent reactions which will occur in the core. Neutron fission reactions are omitted although U231, 0932, 0255, U235, U237 and Pu?39 are known or expected to undergo fission with thermal neutrons. Pu38(n,y)Pu239 .0d 2.3d s‘r B-’T ’ 239 p>37(n,7) ¥p238(n,7)Np 6. U231(n,2n) U232(n,2n) U233(n,y) U234(n,y) U235(n,y) UR36(n,y) UR37(n,y) U238(n,r) U39 The nuclides U231, 0238, U239, Np239 and Pu239 will not be discussed subsequently g8ince they will exist in rather small concentrations and ainfie calculations concerning their build-up would be very unreliable. The effects of the uranium isotopes consiet largely of 1ncreasing the total uranium concentration and specific alpha activity. The total uranium concentration at equilibrium becomes about 2.18 times that at the start-up of the pile. The alpha activity change will depend largely on the U232/UR33 ratio as discussed below. In addition, the U237 growing in will cause even the "decontaminated" fuel to contain apprecisble quantities of beta and gamma radioactivitlies. The effect on neutron economy is small, -17- Considering first the major heavy isotopes, the differential equations for growth are dNok dt Noz£6c(23) - Nouflc(2h) 25 at Nouflc(2h) - Nostla(25) dN26 ———— dat Nos£(c(25) - Nagede(26) Where f represents the neutron flux, 0? and 0’;3. indicate respectively cross-sections for neutron capture and for meutrom absorption (1. e. fission plus capture). The N's indi- cate the concentrations of the various species; the subscript and parenthetical numbers are the usual code symbols for the heavy isotopes, e. g. 23 represents elément 92, masse 232.‘ The fission cross-sections for both Uejh and U’256 are negligibly small. The final equilibrium values of the relative concentrations of U233, U234, ¥235, and U236 are obtained by equating these differential equations to zero and solving for the vari- ous isotopic ratios. The following ratios are obtained using the cross-sections given in Table II. Mol 6c(23) 50 et =7 ‘= 0.71L Moz Gc(oh) 70 Nas _ €c(23) _ 50 = 0.078 Nos (a(25) 6ho N 25) 06 26 _ (c(25)0e(23) _ 100 x 50 _ 0.391 Nps Go(26)0a(es) 20 x 6h0 From these values one sees that the final equilibrium number of uranium atoms per atom of UPDD is 2.18, 1. e. the uranium concentration increases by this factor. -18- TABLE II Thermal Neutron Cross-Sections of Heavy Isotopes Used in this Report. (Values Given in Nuclide Th232 The33 Pal3l Pa233 uR32 ye33 yash @35 1236 237 Np237 pu238 (. 7.0 1350 150 50 50 50 70 100 20 180 460 T.0 1350 100 250 TO 640 20 - 8ho 480 Barns). Remarks Value from HE. S. Pomerance, ORNL-51, p. 16 (19.48). Hyde, et al. ANL-4165, 6-25-48 reports 0, = 1350 § 100 barns. G, assumed equal to (. A better value is probably (; = 290 + 20k, reported by R. E. Eleon and P. Sellere, ANL-4112, p. 27 (1947). L. I. Katzin and F, Hagemann, CC-3699 (1946), report 37 + 14 for O'C(lj) , but there is evidence from Hanford irradiatione of Th that their figure is too Jlow A. Van Winkle, R. Olson, W. C Bentley and A. Ghiorso, CF-3795 (1947), obtained U ¢(22) = The value of (g (22) used here is purely a guess G. Haines and K. Way, ORNL-86, report as a consistent set of values, 0o = Th, Og = 564, N = 2.35. (r (24) = 88 was reported by H. Pomerance, Reactor Sci- ence and Technology 2, Fo. 1, p. 83 (April 1952); this is probably the best value. G. Haines and X. Way, ORNL-86, report as a consistent set of values, ¢, = 98, (O = 644, n = 2.12. P. R. Fields and G L. Pyle ANL-4490, p. 5 (1950) give Jc = 23.5.H. Pomerance, ibid., gives 5.8 . A guess, giving 3(27) + 227 /f 2 x 10°°L at £ = 1015, T1/2(27) = 6.9 4. Value quoted for pile neutrons by P. R. Fields and G. L. Pyle, ibid. G. Reed and W. Bentley, cc-3780(19h7) report (@ = 300 - 800. -19- On solving the differential equations, the isotopic ratios as a function of time become ok Go(3) | T@ITy ogsm (1 - e Setehiee, No3 Oc(2h) v Oe(2) Geen) Teemre ge(z) oY) _ -Ga(es)se N, 0aes) Ta(@5)-le(2h) Oa(25)/07a(25)-0c(24)] | - Oc(ak)ft fa(25)ft - 0.078125 - 0.0877192982 e + 0.0095942982ke | Mo _ 6e(23)0c(25) (1;e'°2(26)fl5+0:’(23)0:(25) [;-63(21&)&_;06(26):?1:] N,s Ca(25)0c(26) [Ba(25)-Ge(24)] [Tclan)-Tc(26)] - _0c(23) 0c(24) Gc(25) -0a(25)ft -Jc(26)ft, [33125).63(26)7[33(25)-62(2&)]63(25) e - ) ~fc(eh)tt _Ga(25)ft Fec(26) £t = 0.390625 + 0.1754385965 e -0.001547467458e -0.02052785923ke Values of méh/u23; H25/H23 and N26/né3 as a function of £t are given in Teble III. At short times, 1. e. up to ft = 1021 neutrons/cm?, the approximation 2 26 ———— —— — 5 Go(23)0c(24)0c(25) £t mfl N\ may be used with a maximum error of 20% at the highest ft. -20- TABLE III Relative Concentrations of U25317023h, U235 and 0256 as a Function of Flux times Time, ft ft x 10-19 1 3 10 30 100 300 1000 3000 5000 7000 10,000 15,000 20,000 30,000 Nok/Nps ¥.998 x 10~ 1.498 x 1073 1.983% x 1077 1.484 x 1072 4.829 x 1072 0.1353 .3596 .6268 .6927 . 7090 L7143 .T143 7143 .T1h43 Nos/Nos 1.746 x 107" 1.564 x 1076 1.709 x 1072 1.468 x 10-% 1.395 x 1072 8.428 x 107 0.03458 06738 .0T548 LOTTHT .07812 .07812 .07812 .07812 N26 /Mo 5,845 x 10"11 1.567 x 1077 5.728 x 10-5 1.492 x 10"6 h.89% x 1077 9.646 x 107 1.556 x 1072 .10230 .1882 .2527 314k .3625 .3803 .3892 .391 ~21- In view of the beta and gamma activity associated with 0237 ag well as its possible fissionability, the concentration of this isotope as a function of time was also determined ag follows: Symbolic forms of the equations for Ny Ny; and Naq/w,, - oe(24)ft - Ga(25)ft - Ge(26)1¢, 1. e Egé =8+Dbe e(24) +ce ' +de N , -Cc(ak)rt -0a(25)ft -O0c(26)ft - q ft and 2T - ai + bt e +c’2 +d' e + gl e NQ} were put into the differential equation, N . where q = 6_:E;,(Q"{) + AET/f’ 227 being the radioactive decay constant of U237. The values of a', b', c', d' and g' were obtained in terms of g, the various cross- sectiona, and the values of a, b, ¢, and 4; the latter numerical values are those in the last form of the equation for N,./N»-z presented previously. | 26/ 723 at =~ 80¢(26) ; b' =bCe(26) ; c' =cOc(26) ; d' =a0e(26) ; g = -a'-b'-c'-d'. qa q - Oc(24) q -0a(25) q -G c(26) Then at £ = 1015, N | - Cc(2k)ft -0a(25)rt 27 = 0.00390625 + 0.00181801654395 e - 0.000022756874378 e + Koz -G c(26)ft -q ft - 0.0057021831206 e + 0.000000673451984 e The value of q used for f = 101 was 2 x 10721 om”. While these calculations are quite elaborate, the methods used here are'conaidered better, if a desk calculator is available, then using sufficiently precise approximate expressions. Values of H2.T/N23 and curies of U~ per gram of U7 are shown in Table IV. The subsequent approximate expresaions were used to obtain the values of Né7/flé3 at the shortest times and to check the values at t x 107 = 1, 3 and 10 and at the longest times. -22- The first involves substituting the approximate expression for H26/H23, i.e., the expression proportional to 33, into the differential equation, for H27 growth glven previously, solving the resulting equation, expanding the exponential term in the solution and dropping off higher terms. aN '&'%I = Npgf 05(26) - Npp q f - 2 G(23) 05(21) 03(25) a5(26)2"7 - Mpq q £ Ny =1 Gi(23) 0G24 GG(25) G(e6)e T - LT The second approximation, which actually can be as accurate as one wishes with enough works providing N26/N23 is known as a function of time, utilizes the assumption that N2§ can be considered constant over small increments of ft at the higher values of the latter. On this assumption the differential equation becomes dNg7/at = Wog £0(26) - Nop q £, where Nog is the average value of N26 over the time increment in question At = t-t!. If now No7 is the concentration of U237 at time t, N£7 the value at t' and ANp7 = No7 - N£7, the solution may be expressed alternatively Ne7 | N2 Tc(26) [1 _ (1 _ 1 N§7/N23 ) o=d A(ft)J N2j Noj q 0-c(26)-1\T;6-/N25 ! _ or ANz . {E&E_‘i@fl - N_?z} {1 ) e-qA(ft)} N23 N23 q N23 The equilibrium value of Np7/N,j, unlike the ratios of the lower uranium isotopes, is flux dependent. N2y _ N26 o c(26) - N2g fa-e(26) Ne3 Nej q Na3 (g7 + £0(27)) 0.00391 at a flux of 1015 Table IV U237 /4233 Ratios as a Function of Irradiation Time at Flux of 1015 t(sec x 10-5)* Oel o3 1.0 10 30 100 300 1,000 3,000 10,000 N26/No3 5.83 x 10-11 1.57 x 10=7 5,73 x 1078 1.49 x 1076 L.89 x 10-5 9.65 x 10~k 1.56 x 10~2 0.102 314 0389 2391 391 3 One day is 0.86L x 10° sec. sz/N23 2,91 x 10715 2.36 x 10713 2.8 x 10-11 2,01 x 10-9 1,77 x 10=7 6.6 x 10-6 1.40 x 10~k 9.99 x 10-4 j.lh x 10-3 3.89 x 10-3 3,90 x 10-3 3.91 x 1073 Curies y237/g y233 2,35 x 10-10 1.91 x 10-8 2.27 x 106 1.63 x 10-b 1.43 x 10-2 5.22 x 10~1 11.3 80.8 25k. 31L. 315. 316. —2l- The concentration of Np237 will depend on the processing method, 1.e. whether or not neptunium is removed from the fuel during processing. If it is not removed it will continue to build up with time and its relative concentration will be given by t N7 . A27N27dt No3 N3 ° until its destruction rate by neutron absorption becomes significant. The accurate expression for N27/N23 ‘given previously may be put into this equation and integrated, thereby giving an accurate expression for N37/N23 for shorter times. At longer times the concentration would be cbtained by integrating the equapion N3 T - ?\27 N27 - N37 £ 06(37) If the neptunium isrpartly removed in chemical processing the differential equation becomes dN —E‘gl = )\27 No7 = N3, (£ 08(37) + a/7) Where 7 is the processing period and a is the fraction of Np removed from the fuel in processing. (Complete removal in processing corresponds to as 1), The maximum possible relative concentration of Np237 at equilibrium, assuming a = O and assuming the values of cross-sections given in Table II, would then be N3z 25 ‘N7 qf%c(37) or Ny . Nyg Moy _ Nps DBy oo(26) 23 Np7 Np3 Np3 q°f2Cc(37) = 0.037 at £ = 1015, g = 2 x 10721 ~25. Considering the growth of Np237 for intermediate and long times inder the con- dition where none of it is removed by chemical processing, it may be assumed that the production of Np237 is equal to the neutron capture by U236 1ess the neutron absorption by v237 and Np237, i.e., dN37 ~ ot - T, O Ll | -4 - Nog £ c(26) q £ N37f 0 e(37) where Nog is the average concemtration of 0236 over any interval At or A(ft). On integration the increase of Np237 in any interval becomes E?l {N% 0_6(26).' ;{27 i NB'Y} {1 ) e-G'c(BT)A(ft)J No3 (N23 ©Oe(37) af N3 where Né-? is the concentration of Istz37 at the beginning of the interval A (£t). This expression should be quite accurate for longer times of reactor operation providing the Np237 is not removed by chemical processing. If the Np is removed by processing then A N37 may be taken as the amount of Np237 produced since the end of the last processing period if the processing is conducted batchwise. In the latter case, N;7/N23 = 0 and A (ft) becomes £7 at the engl of a processing period; with these substitutions the above equation gives N37/N23 at the end of a period (providing the period is long compared to the 7 day half life of U237): N37/N23 ={N_23 oe(20) 327} {1 - e'°_°(37)f7} (1) N23 Oc(37) af If continuous processing is employed and Np is removed with high chgmi’cal -ef ficiency, an approximate expression for N37/N23 is Ny Aer 1 = 56 £ Tc(26) — N37 {f c(37) +T}' 0 ~26- or N37 _ m A37 Ge(26) £ 7 (2) " No3 N23 aqf 1.40¢(37)f7T where 7T 1s the processing period. In view of the uncertainty in the factors which determine the Np237 concen- 238 tration, it was not felt meaningful to calculate the Pu concentrations except under certain extreme conditions. It seems pointless to carry out more calcu- lations on Pu until a given reactor system is designed. As an example, however, the N),g in a reactor where equation (2) holds and where Pu is also removed Ly continuous chemical processing may be obtained in a manner similar to the N37: WS - N3y £0(37) - Myg(£oa(ll) 4 =) = o at i Mg | Ny oONET | Wag A2 (we(26):T) op(3DET N23 Np3 14ca(U8)ET Moz qf (L4oe(3NET) (L +0,(L8)E T) (3) Table V shows the relative concentrations of Np237 and Pu238 compared to ye33 as a function of ft (flux times time of pile operation) for two different values of fT for continuous processing. Column five shows corresponding N37/N23 ratios for batch processing at £T = 1022, The neutron loss due to the absorption by U23h, U235 and U236 less the re- production of neutrons by fission of 1 is given by equation (L). L, = neutron loss - N2), - 6 e(2h) + (1 Npga(25) . N2 Go(26) U233 atoms destroyed N23 G a(23) No3oa(23) N23zoa(23) = 25) -Co(2L) £t -0 ,(25)ft 0,0032954545) 4+ 0.02979266347 e - 0,01256025877 e 0.02052785923) e~ Tc(20)ft (L) 'Here,szs = neutrons emitted per neutron absorbed by U235 and is here assumed equal to 2.12. A plot of L, vs. ft is shown in Fig. 7. The losses are seen to increase to a maximum value of 0.0063 (i.e. 0.63%) at about ft = 3 x 1021, then decrease to o g { ] IR | { F T T T I { F T yTd [ | T TT1T1] I IDV\I,G'I“IGCI)AIH O az j— 0 o +.006 + 006 s O — Njf + 004} +004 N aJ > E:u + 002 +.002 Qa w Ll @ 0 0 O - 5 S -002f -002 — - = Ll £ ._IC 19 1 IItIIlll20 1 IIIlIIII2| 1 lIIIIlIl2 I lllIlllI ] L1 11t 2 2 10 10 10 10 0 0= FLUX-TIME (ft) FIGURE 7. NET NEUTRON LOSSES DUE To UZ>* (239 AND U%® BUILD-UP “LZ— Table V Concentrations of Np237 [Equation (2)] and Pu230 E‘L’quation (3)_] as a Function of ft for Continuous Processing Where Both Np and Pu Are Chemically Removed by Processing. (t is time after reactor first starts up. ) 3t Ny7/N23 N37/No3 Ny,g/N5 £t x 10-21 No6/No3 £7 =100 £7 = 1022 £T =102 £T = 1020 £7 = 1022 % 1.9 x 105 5.7 x 108 2,0 x 1070 2.6 x 10~ 9.7 x 10~10 6.3 x 10~7 3 9.6 x 104 1.1 x10® 4.0 x 1075 5.2 x 10-5 1.9 x 108 1.2 x 10-5 10 1.6 x 1072 1.9 x 107 6.6 x 1074 8.6 x 10-L 3.2 x 10°7 2.0 x 10~k 30 0,102 1.2 x 104 1.2 x 10-3 5.5 x 10-3 2.0 x 10~ 1.3 x 10~3 100 .31 3.6 x 1074 1.3 x 1072 1.7 x 1072 6.1 x 100 4.0 x 10-3 300 .39 LS x 1007% 1.6 x 1072 2,1 x 1072 7.7 x 10~6 5.0 x 10™3 O .39 L5 x 1074 1.6 x 107 2.1 x 1072 7.7 x 10°° 5.0 x 107> *Batch processing, calculated by Equation (1). $#nity here would be about 11.6 days at £ = 1015 or 116 days at f = 101k, -Q2- ~29 - a minimum of -0.00L43 (i.e. a net neutron gain) at about 3 x 1022 and then increase again and level off at an equilibrium value of 0.0033 above 3 x 1023, The equili- brium value alone, of course, can be obtained from the above equation in its first form by insertion of the equilibrium values of the relative concentrations N2h/N23 s N25/N23 and N26/N23. It is interesting that while the total uranium atoms per atom of Y233 approaches 2,18, the maximum neutron loss is only about 0.6% and the equili- brium value is only about 0.3%. Breeder Blanket In the blanket the following scheme was considered: he3h A7 X A 2L4.1 4 7 (n,7) 233 B Th \ A 23.5 m (n,‘)’) Th232 (n,2n) ¥ the3l B- 25.6 h The primary reaction sequence, of course, is Th232(n, )Th233 e pa®33 — pe33 Pa23,4 /5’ U23h ___fi_.____> flk T.1 m; 6.7 h 2.3 x 105 y (n:7) (n,%) pa233 y233 oL 27ah d i (n,fiSSo) (n,2n) l (ny2n) v pa32 § y232 oL 3 P.:-1231 | oL and the other reactions may be considered according to their effects on the production of U233. Neutron capture by the members of the 233-chain involves a double loss, i.e. a neutron is lost and an actual or a potential U233 atom is converted into a non- fissionable U23h atom. Higher isotopes may be built up by neutron capture if the blanket is not processed very frequently. Fission of U233 need not involve a net -30- loss since most of the resulting fission neutrons should be abscrbed in the blanket, especially since most of the fissions will occur toward the inner edge of the blanket (i.e. the edge nearer the reactor). It may be reasonable to assume then that absorption by U233 results in neither 'a neutron‘loss or gain. Should some fast neutrons come in contact with the blanket, the (n,2n) reactions will occur to a small extent. These will involve a small neutron gain (a negative loss). The principle (n,2n) reaction may be expected to be Th232(n,2n) Th?3L _B7 pa23l in view of the high relative concentration of Th2320 The net gain would obviously - be equal to the number of (n,2n) reactions by thorium less the number of neutrons absorbed by the Pa231. | The principle effect of the U232 will be to increase the specific alpha activity of the product. U232 decays to the 1.9 y ThZ28, all the daughters of which are much shorter than 1.9 y. Hence‘the activity resulting from any U232 win grow with a2 1.9 y half life amd finally attain a disintegration rate six times that of the parent U232 (i.e. five additional alphas from the daughters). The effect of U23h, in addition to the losses mentioned above, is merely one of diluting the mroduct ?ith a non-fissioning isctope. All the calculations madé here assume constant flux, i.e. invariant in time and independent of position. While this assumption is reasonably good for the reactor, it is much poorer for the blanket. Should the fuel and blanket be intimately mixed in a one core reactor, the results here would‘be somewhat better for the blanket reactions and somewhat poorer for the reactions con- cerning the fuel. In the cases of the (n,2n) reactions the calculations are based upon cross-sections for (n,2n) reaction per unit thermal flux; obviously any particular value for such a cross-section can hold only for a particular geometrical configuration. Hence the (n,2n) calculations are particularly poor -31- unless an appreciable amount of fissioning of U233 occurs in the blanket or unless a one region breeder reactor is being considered. The losses due to capture by merbers of the 233-chain may be estimated as follows: For any reasonable irradiation time, the Th233 concentration will be at its steady state value because of the short half-life of this species (23.5 m). ~ Hence i‘g.s."z = Ngpf 5(02) =Aqalg3 = O or NO3 = w A03 The resulting loss of Th233 atoms per U233 atom produced will then be approximately No3f 0(03)t _ £0,(03) Noof ca(02)t 03 and will remain independent of irradiation time as long as the U233 production is directly proportional to irradiation time, As long as the fraction of Pa?33 and 1233 atoms absorbing neutrons is small, the concentrations of these two species may be simply expressed: dN]_3 dt neutrons absorbed by Th less decay of P3233 Noof Ta(02) - A3 Ni3 = N W 1 Noof G.(02)t [1 - -5\—;; (l-e'h3til =32= For long irradiation times or very high fluxes, more accurate expressions will be required which take into account the loss of Pa233 and U233 atoms by neutron absorption. For the present purposes, however, this is not thought necessary especially in view of the question concerning the value of the capture cross-section of Pa¢33, 1In any case, the methods employed here will be satisfactory for checking more accurate calculations; also in combination with successive approximations for the neutron absorptions mentioned the methods used here can be made essentially as accurate as one wishes. The total loss (of neutrons and neutron-equivalence of 233-chain atoms) per U233 atom produced is then t t " | o (1 4 h) [£076(03)/X ¢y + IR 0 2,2 [fo-c(03)//\03 $ -—‘:9—;%(-23 (1~ —tpe(l =€ A13"'):| 13 A13 - where h is the breeding gain (i.é; the U233 atoms produced per 1233 atom des- troyed) and may be assumed equal to about 1.2. The absorption of neutrons by U233 while producing little or no net neutron losses will cause a time loss in that for each U233 atom destroyed a Thé33 atom is assumed to be produced and this atom must deczy through Pa233 to U233, The U23h formed is produced by capture by Th233hand Pa233 and U233, the U23h‘to U233 ratio being given approximately by the equation N t ’ “EE = —_— ' fdt N 23)fdt o fc-c(03)/>\03 1 oy o(0) % / N3O o(13)8dt ¢ [ Np3G(23) 0 0 = fO—e(O3)/AOB ¥ f—%:%](-?-)- [1 - -Xi-’gg (1 - e‘=‘7\13t-{] %G‘c(23)fl" [-]é'- = 7%375 1 _=A13t + —T—” " (1-e 3 ):l =33=- If now Ug(13) = 0g(23) = G3 N2), — I £fTL(03)/A,. +1 ot Thus within the accuracy of the above assumptions the U234 produced by Th233 capture per 233 produced depends on flux only while the y23k produced from the other two members of the 233-chain per U233 atom produced depends directly on the product ft. The ye3L/ye33 at ény given irradiation time is, of course, directly proportional to the neutron flux. | Some figures on y233 roduction, U23,4/U233 ratios and losses due to U23h production are given in Table VI. The production of Pa23l and 0232 will now be considered. In these calcu- lations some of the cross-sections are either unknown or poorly known, and hence the results may be considered as very rough estimates or guesses. Since the half life of Th@3l is short compared to the probable irradiation tixfie, THh3? may be considered to be transformed directly to Pa231 by (n,2n) reaction. dN11 —= = Nop Sh,2n(02)f - N3G (11)E or Ny _ dn,2n(02) - e=Q‘c(ll)ft) No, Qe(11) 1.0 x 107U (1 - e Te(11)ft, The symbol*crh,gn(02) stands fa a number which when multiplied by the thermal neutron flux gives the specific rate of transformation of Th232 4o Th23l, Actually this {n,2n) reaction can occur only with neutrons of kinetic energy greater than the binding energy of one neutron in Th232, and hence the value of the cross-section can vary greatly at constant thermal neutron flux. In a given pile assembly, however, the value of (Sa’zn(02) will be constant in time, “fiafleVI 4233 and U234 Production in U233 Breeder Blanket Losses Resulting from Neutron Capture by Th?33 and Pa®33 (A1l figures are for flux of 104 and are directly proportional to flux) No),/N°>% Resulting Fr om . 3368t t(days) N13/N02 N23/N02 Elé_iifial Pa233 Capture 1233 Capture AfTEE:}n§£3 i?ef }g?%) Nop 1 $.97 x 105 0.08 x 105 6,05 x 10°5 2.1 x 10k 1.82 x 10-6 5.0L x 10k 0.110 3 1.76 x 10-4 0.06 x 104 1.82 x 10k 6,35 x 1078 1.56 x 10-5 9.38 x 104 .203 1Q 5.35 x 104 0.70 x 1074 6,05 x 10-4 1.99 x 1073 1.68 x 1074 2.45 x 1073 .501 30 1.28 x 10-3 0.5L x 10-3 1.82 x 103 5.13 x 1073 1.37 x 10=3 6.79 x 1073 1.19 50 1.72 x 10-3 1.30 x 103 3.02 x 10-3 7.43 x 1073 3,37 x 103 1.11 x 102 1.70 70 2.00 x 103 2.24 x10-3 kL.2L x 103 9.15 x 1073 6.00 x 103 1.53 x 1072 2,07 100 » 21 x 103 3.8Lx 1073 6.05 x 107 1.09 x 1072 1.07 x 102 2.19 x 102 2.L6 150 2.37 x 10-3 671 x 1073 9.08 x 107 1.28 x 1072 1.96 x 1072 3,27 x 102 2.88 200 2.40 x 1073 9.7 x103 12,1 x1073 1.38 x 1072 2,93 x 1072 L.35 x 1072 3.10 300 ol x 103 15.8 x 1023 18,2 x 1073 1.51 x 1072 5,00 x 1072 6.53 x 1072 3.39 *Ratios given are for complele decay of the Pa233° 3t constant value of 2.88 x 10-l4 is included in this column for neutr ##tyeutron plus fuel atom losses due to neutron capture by T on capture by 233, n233 and Pa?33. =35~ at constant power, and will vary somewhat with the space coordinateé; in an external blanket the value will vary to a greater extent with space coordinates, decreasing rather rapidly with increasing distance from the source of fast neutrons. The value of Crh,2n(02) used here is 0,015 barns which is approximately the value for the 238 (n,2n) reaction on U in the Hanford piles. I. Perlman (MB-IP-62L, November 15, 1952) gives a figure of 0,007 barns for the U238 (n,2n) reaction for pile neutrons and suggests that the Th232 (n,2n) may be a little lower. O the other hand Perlman suggests a higher wvalue, i.e., 290 rather than 150 bams, for the cross- section for the subsequent Pa231 (n, ¥) reaction. For the U232 formed by neutron capture by Pa?3l followed by beta decay of Pa232 dN _E%g = N11Q(11)f - Noowp(22)f N - sz : Un,2n駧)+ G;,zn(ozzr e S o 5n(02) Gp(1) - (222 02 U'a( Gc(ll)" a( ) 0-3.(22)[06(11)' %(22)] 105 X lO"h (1 } 2.0 e-G-c(ll)ft - 3.0 e-Fa(ZZ)ft) At small wvalues of t g%: ~ 1.5 x 10~k [(g—g(ll)- %6‘32(22)) £242 (%5-&2(22) - %0_03(11)) f3t3:] The relative concentrations Nll/NOQ and'N22/N02 at various values of ft are given in Table VII. Tt does not seem feasible to estimate with any accuracy the amount of U232 produced by (n,2n) reaction on ye33 or by (n,2n) reaction on Pa233 followed by beta decay of the Pa232, as thesg (n,2n) cross-sections for pile neutrons are entirely unknown. If, however, the (n,2n) cross-sections fér Pa233 and 7233 232 are the same as for‘Th232, then the amount of U produced from these two species ~36- will be about 1/20 that calculated in Table VII as formed from Th232 via pa®3l up to about £t = 10%2; above this ft value the U232 formed from Pa?33 plus U233 approaches about 3£§ that shown in Table VII. Table VII pa23l/pn232 ang y232/7n232 Ratios Formed in Blanket Due to Reactions ft 1019 3 x 1019 1020 3 x 1020 1021 3 x 1041 1022 3 x 1022 1023 N11/Noo 1.50 x 10~7 4.50 x 10-7 1.50 x 106 L.ko x 10~ 1.39 x 1075 3.62 x 1075 7.77 x 10~ 9.89 x 10=> 1.00 x 1074 1.00 x 10~k Th232 (n,2n) Th231-1£i;9Pa231(n,6)Pa2327fi5::> y232 N22/N02 1.12 x 10-10 1,01 x 10-9 1.12 x 1078 0.99 x 10~7 1.04 x 1076 7.92 x 10-6 5.1k4 x 1075 1.31 x 107k 1.50 x 107b 1.50 x 10~k -37- Appendix A Relative Losses for Batch and Continuous Processing It might be argued that with some combination of half lives and cross-sections of the shorter lived fission products it is conceivable that continuous processing might afford lower losses than batch processing. It can easily be shown that this is not possible, Consider a hypothetical fission product of yleld ¥, capture cross-section of T3, decay constant A, and concentration Ny; and define A= Ay + fay- Then in the batch case, at time t after the last processing Ni becomes Ny =M (1 - e=NY), and the contribution of this species to the overall loss per fission 1 T y1O1f A Lo! = frogt f o - [ —= ) O In the continuous case the steady state concentration Ny and the contribution to the overall losses L, become NeOpf T . NS, f ) £ =.Z;_£_;£___ and Lcw - —;—_;h:E - Z}EZE_:E 14+ NT | NeOpf T L4AT Now consider the total losses Ly and L; with the contribution from the species Nj: h 1 1 1 o fTy |, Y1S 1 | } Iy = ¢ +lyag by |1t (- O )4 1 L (16T e = Ple 4y oers T 4T Opf 7 1L+GSET 14 AT ~38- Comparing these equations term by term at T = optimum processing period for continuous processing, it is readily seen that the two first terms are equal. Each of the other terms is smaller in the batch case than the corresponding term in the continuous case; this is obvious for the two second terms. The third terms are very similar to the fourth ones (i.e. they become exactly similar in the limiting case where )\i = 0); hence the argument to be made for fourth terms will also hold for the third ones. Take the ratio It 1 4+AT —pi- - l l (l_ e-AT) . Le! AT NT This ratio is equal to 1/2 at AT =0 , cor;tinues to increase as /\‘Tincreases and finally approaches unity as /A7 gets indefinitely large. Hence it is always lesa than unity for finite AT . Any further breaking up of fission products into additional groups will give further terms like those already considered, and therefore would not alter the conclusions drawn here. A possibility not explicitly covered so far is the production of a highly absorbing species from a moderat.eiy long-lived fission product of lower cross- section; such a case would tend to favor batch processing even more than those considered above. The argument so far proves that if the optimum ‘T for continuous processing is employed for both types of processing the batch method af fords lower losses, Obviously if the batch case were optimized indeiaenden_tly with fespect t:o T it would afford even lower losses.