EIR-Bericht Nr. 270 EIR-Bericht Nr. 270 Eidg. Institut far Reaktorforschung Wirenlingen Schweiz The transmutation of fission products (Cs-137, Sr-90) in a liquid fuelled fast fission reactor with thermal column M. Taube, J. Ligou, K.H. Bucher l I B Wilrenlingen, Februar 1975 EIR-Bericht Nr. 270 The transmutation of fission products (Cs-137, Sr-90) in a liquld fuelled fast fission reactor with thermal column M. Taube, J. Ligou, K.H. Bucher February 1975 sSummary The possibilities for the transmutation of caesium—-137 and strontium-90 in high-flux fast reactor with molten plutonium chlorides and with thermal column 1s discussed. The effecitve half 1life of Cs-137 could be decreased from %0 years to 4-5 years, and for Sr-90 to 2-3 years. Introduction The problem of management of highly radiocactive fission product waste has been intensely and extensively discussed in the recent paper WASH - 1297 and especially in BNWL 1900 (Fig. 1). Here only tne transmutation of Fission Products (F.P.) without the recycling of the actinides 1s discussed, making use of neutron irradiation by means of a fission reactor (Fig. 2). A short outline of this paper 1s as follows 1) Why, contrary to many assertions, is neutron transmutation in a fusion reactor not feasible. 2) Why recent discussions concerning transmutation in fission reactors are rather pessimistic. %3) Could the transmutation in a fission reactor be possible taking into account the neutron balance in a breeding system? 1)y Which are the F.P. candidates for irradiation in a fission reactor? 5) Is the rate of transmutation sufficiently high in a fission reactor? 6) In what type of fission reactor is the transmutation physically possible? 7) What are the limiting parameters for transmutation in a solid fuelled fission reactor? 8) Is a very high flux fission reactor possible if the fuel is in the liquid state instead of the solid state? 9) How could such a high flux fast reactor with circulating liquid fuel and a thermal column operate as a 'burner' for some F.P. (Cs-137 Sr~90 etc) transmutation.’ 10) What engineering problems must be solved for this to be realised? Radiocactive Waste — . nigh active low active waste vaste /N any management A (ferbiaden direct controlled storage on tihe surface litosphere inydrosphere {underground) salt rocks water ice mines (deep sheet see (polar) floor stable geologic conditions nonstable conditiocns c norn controlled storage solar deep impact ¢ management dissipation transnutation without witn cnanging changing L and 4 A {but no Z) coculomb exitation (r,v) {(n,2n) continously with cnanging - (p,Y) periodical fission . underground xplosion csmic escape neutrons neutrons (primary) (secondary) fusion fission accelerator reactor reactor A /\ fast thermal thermal fast neutron reutron with without thermal tnermail column column (p,spallation) thermonuclear urcerground slosion Fig. 2 10 10 Transmutations of fission products gquasi stable F.P,. Half-1ife, years 1074 stable nuclides [Living \E.P. . D, r__\ \Gpontaneouse beta decay \ \ sShort 10 long 1L i 10~ / / 10 Cransmuta iving 10 1. Why the transmutation of F.P., is not feasible in a controlled thermonuclear reactor (CTR): The recent studies of the use of a C.T.R. as a transmutation machine for at least the conversion of Cs-137 have been to some extent optimistic. Table 1 gives a summary of the most important data and results from BNWL 1900. Comments 1 Wolkenhauer (BNWL 4232) calculated the values with a nominal one energy group cross sectlon and fast neutron {lux 5 X lOl5n cmdgs—l. (The primary flux of 14 MeV neutrons for 10 MW/m2 wall loading equals 5 x 101un cm—zs_l, but such a high loading 1s very optimistic!) Cs-137 Sr-90 o{barns) 2 O(S—l) o(barns) 7+ o(s H (ngY) 0.44 2.0 loulo 0.0188 0.94 - 10-10 (n,2n) 0.147 7.3 - 1070 0.148 7.40 - 107 %Y (g~-decay) - 8 25. 10 %Y _ 763 1710 The results obtalned are rather pessimistic since the values of the reduction of the steady state amount due to the trans- formations are given Dby: . ~-10 for Cs-137 Atofal 17.76°10 - 2.15 Adecay g 06, 10—10 Atotal 15 97.10‘1O for Sr-90 —_— = - = 2.09 rdecay 7.63'10—10 rtotal = Adecay + g« 9 Table 1 Transmutation possibilities for different devices (from BNWL-1900, WASH=-1297) r Machine Flux/ Reactions, and remarks of authors See Energy of original reports. Comments Accelerator of Protons Reaction (p,xn.) Not promising. Ruled out _ medium and high 100 MeV on basis of energy balance criteria energy protons Protons Spalation (p,xn) and (n,2n) {(n,vy) 1-10 GeV with secondary neutron flux Cs=137 as Not feasible within limits of current - target and/or technology. The capital cost 1is thermalised prohibitive. fflux of neutrons Fusion (thermonuclear) reactor in all cases with wall Fast flux of Neutron reactions (n 2n) and &n,y) Fast Flux of 5 x 10 5n cm~ s 14 MeV neutrons 2 from. (D-T) @ = 5x107 'n cm'ZS_l Thermalised Practically only (n,y) flux in Thermal flux 6.7 x 1015n em— 2t 2 beryllium trap Attractive transmutation rate has not been demonstrated but possible to transmutate 3 all Cs-137 and Sr-90 created by fission reactors Nuclear Fissile Technically not feasible. No. of explosions explosions explosive or per year very high. Appr. 3900 p.a. each of thermonuclear 100 k ton. (For USA in year 2000 Cs-137 and| — explosive Sr-90) Probably not acceptable to public! Fission See table 2 reactor and are clearly too small for justifying such a complicated technology as transmutation in a CTR. In spite of this Wolken- hauer writes: "the flux level is somewhat higher than that usually associated with CTR power plants. This value was selec- ted based upon the hope that by the time transmutation 1s applied in a CTR that technology will have advanced far enough to allow for the implied vacuum wall lcocading. If this high a value proves to be unrealistic longer irradiation times will be required" "attractive transmutation rates have not been demon- strated up to this point". Also all these calculations were done on the basis of isotopically pure Cs-137 and Sr-90. Later Wolkenhauer writes, "any practical scheme would probably involve elemental rather than isotopic loadings" Comment 2 In BNWL-1900 it was noted that the calculation (in a moderating blanket of the CTR) represents a more realistic blanket configu- ration with a neutron wall loading of 10 MW/mz. (This is still a very optimistic value. M.T.) In this case the following date have been obtalned for a therma- lised neutron flux from a CTR w1th a 10 MW/m wall locading. ¢ thermal ¢.0 .o total n.cm_2s_l (n,vy) (n,2n) tl1/2 eff. for 807% 6.71-1015 I ):0.117 (n.2n) 20,104 {a=22.2°10 ts7t fraction > (barn) (barn) - -10 ~291 kg 7.91-10 U 7.0-10 1 9.9 years Cs/yr The conclusions of fthis study are that useful quantities of Cs=137 could be transmuted under the projected CTR blanket loading conditions. The reduction in Cs-137 "toxdicity" 1s still expected to be at most a factor 3 down. In addition a study of the bulld-up of fission product nuclei in order to establish the requirements of periodic chemical processing and associated costs has not been carried out. Comment 3 H.W. Lefevre (appendix to BNWL-1900) makes an interesting comment on the study of the transmutation of Cs-137 and Sr-90 in CTR: 'Everyone knows that a CTR will be "clean". Don't spoil that illusion. I think that I would worry some about a CTR loaded with 50 kg of Cs-13%7"'. 2. Why recent remarks about transmutations in a fission reactor are rather pessimistic A recent and most intensive study of the use of a fission reactor for the transmutation of fission products has been published by Claiborne (1972). He writes: "The problem fission products cannot be eliminated by any system of fission power reactors operating in elther a stagnant or expanding nuclear power economy since the production rate exceeds the elimination rate by burnout and decay. Only a equilibrium will the production and removal rates be equal, a condition that 1s never attalned in power reactors. Equilibrium can be obtained, however, for a system that includes the stockpile of fission products as part of the system inventory since the stock- pile will grow until its decay rate equals the net production rate of the system. For the projected nuclear power economy, however, this will require a very large stockpile with 1ts associated potential for release of large quantitites of hazardous radio- isotopes to the environment. It is this stockpile that must be greatly reduced or eliminated from the blosphere. A method suggested by Steinberg et al. is transmutation in "burner reactors”, which are designed to maximize neutron absorption in separated fission products charged to a reactor. If sufficlent numberes of these burners are used, the fisslon products inventory of a nuclear power system can then reach equilibrium and be maintained at an irreducible minimum, which is the quantity contained 1in the reactors, the chemical processing plants, the transportation system, and in some industrial plants. If the assumption is made that burner reactors are a desirable adjunct to a nuclear economy, what are the design requirements and limitations: It 1s obvious that they must maximize (with due regard to economics) the ratio of burnout of a particular fission product to 1its production rate in fission reactors, and the neutron flux must be high enocugh to cause a significant decrease in its effective half-life. Of the fission types, the breeder reactor has the most efficient neutron economy and in principle would make the most efficient burner if all or part of the fertile material can be replaced by a Sr-Cs mixture without'causing chemical processing problems or too large a perturbation in the flux spectrum because of the different characteristics of these fission products. The cost accounting in such a system would set the value of neutrons absorbed in the fission product feed at an accounting cost equal to the value of the fuel bred from those neutrons. The maximum possible burnout of fission products would occur when the excess neutrons per fission that would be absorbed in a fertile material are absorbed instead in the fission product feed. The largest possible burnout ratio would then be the breeding ratio (or conversion ratio for non-breeders) divided by the fisslon product yield. The estimated breeding ratio for the Molten Salt Breeder Reactor (MSBR), a thermal breeder, is 1.05 and for the Liquid Metal Fuelled Fast Breeder Reactor (LMFBR), 1.38. The yield of 13705 + 9OSr is 0.12 atom/fission, but a number of other isotopes of these elements are produced which would also absorb neutrons. However, 1f the fission product waste is aged two years before separation of the cesium and strontium, the mixture will essentially be composed of about 80% 137Cs + 908r and 207% 155 136Cs that decays with a 13-day half-1ife (M.T. see Comment 4): consequently 137CS 950 + Sr will be decreased by Cs (which will capture neutrons to form the maximum burnout ratioc for 20%. This leads to a maximum possible burnout ratio of about 7 for the MSBR and about 9 for the LMFBR. Unfortunately, however, the neutron fluxes 1n these designs are well below lOl6n cm_zs_l. Any modiflications of these designs to create high neutron fluxes will increase the neutron leakage and decrease the burnout ratios significantly." (Claiborne 1972) 10 Comment 4 It is not clear why Claiborne claimed that after 2 years ageing and separation of strontium and caesium the isotope composition will be Cs=1357 807 Sr-90 20% Cs-13%5 From Crouch (1973%) the fission products of U-23%% have the following composition (2 years ageing) (in at % per fissioned nucleous) (see Table 3). Sr-88 (stable) 3,63 Sr-90 (28 years) 4,39 Cs-1%% (stable) 6.57 Cs-134 (2 years) 3.5 (7.09+0.5 from independent yield) Cs-135 6.26 Cs-137 5.99 Subtotal 30, 34 "he realistic data are unfortunately more than twice those cited by Clalborne. The same negative opinions concerning the use of Fission Reactors for F.P.-transmutation are given by the following authors: - A.S. Kubo (BNWL - 1900): "Fission products are not conductive to nuclear transformation as a general solution to long term waste management'. - BNWL - 1900, itself: "In summary it is improbable that transmutation of fission products in fission reactors could meet any of the technical feasibility requirements for the production of stable daughters'. - Claliborne (1972): "Developing special burner reactors with the required neutron flux of the order of 1017n em™¢s™1 is beyond the limits of current technology'. 5. 11 Is the transmutation in a fissilon reactor possible taking into account the neutron balance in a breeding system? In spite of all these pessimiétic opinions on the transmutation of F.P. (especilally Cs-13%7 and Sr-90) in a fissilon reactor the dis- cussion below points to a more optimistic conclusion. The calculation of the transmutations of F.P. nuclides 18 made on the basis of the following more or less arbitrary assumptions: 1) The total number of fission power reactors installed must form a self sustaining system (a breeding system) with a compound doubling time TS of about 30 years (at a later date in the development of cur civilization this may be satisfied). T . 2.75 - M - (1L + ) . 1y D 5 (BR-1) + (1 + a) C TS = compound doubling time (years) M = 1initial fuel loading (kg/MW th) C = fraction of time that reactor is at full power F = ratio of the fertile isotope fission rate o = capture to fission ratio for the fissile material BR = breeding ratio From this BR = 1 + exf2 * M (L + F) r 1In?2 We have postulated: TS = 30 years and we know that the mean values for 'our reactor' are I3 = 0.20 (instead of 0.3, see Beynon 1974) a = 0.24 M = 1 kg Pu/MWth C = 0.8 and we obtain 2) if 12 We know that the breeding ratio can be defined as (v=1-a) + (F(v'-1)) - (A+L+T) BR = (L + a) v and v' = number of neutrons per fission A = ratio of parasitic capture rate in structural material to fission 1n fissile material T = ratio of parasitic capture rate in transmutated F.P. to fission in fissile material L = leakage ratio In this paper the following rather For illustration only conservative data are postulated (ref. Beynon, 1974) GCFR LMFBR MSBR L = 0.06 0.05 0.04 0.0244 A = 0.30 (instead of 0.23) 0.0067 0.09 0.163% v = 2.96 2.95 2.93 vi = 2.70 2.92 2.77 F = 0.20 (instead of 0.30) 0.25 0.19 o = 0.24 0.22 0.28 we obtain T = v-1-x-BR (1+x)-A-L + F (v'-1) T = 0.364 T = 0 T=0 T =0 T = 0 then BR max. = 1.371 1.47 1.21 1.06 Table 2 Possibility for transmutation of F.P. - particularly Sr-90 in a fission reactor according to BNWL - 1900 Cs=-13%7 and Reactor Reference Flux Remarks thermal power reactor Steinberg Wotzak Manowitz,l1964 The authors use a wrong value: Kr-85 with large 83 = 15 Dbarns instead of 65 = 1.7 barns. Isotopic separation of Kr- isotopes 13 310 thermal Only I-129 can be transmuted. high flux (trap) Steinberg, 1964 1016 in the trap smaller 1n the presence of the F.P. target An equal or greater no., of F.P. would be formed in the fission process per transmutation event. Claiborne, 1972 15 2+10 thermal This reactor does not meet the criteria of overall waste ba- lance and of total transmuta- tion rate. ffast ligquid metal fast breeder Claiborne, 1972 15 1-10 fast Neutron excess 0.15 - 0.3 at the expense of being no longer a viable breeder of fissile material. Also this flux does not allow the attainment of a sufficiently high transmutation rate and is, therefore, not a feasible concept. fast with thermal Liguid fuel fast reactor with thermal column this paper. ¢T 14 The result can be checked as focllows: In a mixed breeder/burner system let the ratio of the power be X Breeder reactors power Burner reactors power From this X-BR = (X + 1) BR max in also BR = BR . + i max min 1l + a T £ (Blen 1l + a) B Blen _ 1+ a X = BRmin T = 3,607 Conclusions BR_ . min Tt is clear that a breeding-self transmutating system with T >>0 1is possible only for a fast reactor in which the value of breeding ratio BR is >1.3 and not for a thermal reactor in which BR <1.06 (see Fig. 3). 15 Fig. 3 Burning of F.P. 1in steady state Sr—=90 Cs-137 beta decay only 1 B tnermal 1074 Q) — ¢, O ) © C per ic recharging, 1 year 5 , 0 10 ™ 2 o 3 Q0 - = @ Q o 43 s - — O £ -3 . . 10 74 contlnouse reprocessing i dwelling time: 10 days 16 4. Which fission products are candidates for transmutation? In our case the amount of transmutatable nuclide can equal T = 0.307 The tables of (BNWL-1900) provide the data for Fig. 4 in which the radiloactivity of a I'.P. after a very short 'cooling' time is seen, from which it is clear that the main hazard arises from only a few radionuclides. But these radionuclides nevertheless constitute the global hazard even taking the amounts produced during the next period of nuclear energy development. The crucilal nuclides are characterised in Table 3 together with other 1isctopes. All this data now makes i1t possible to estimate the number of candidates for transmutation in our breeder/ burner system. The criterilia are as follows - the total amount of all transmutated nuclides cannot be bigger than the estimated value of T = 0.367, that is ~3%6 atoms of F.P. nuclides for each 100 fissioned nuclides. - fthe priority of transmutation is given as follows Cs>Sr>I>Te>Kr Total equals: T = 0.3318 - in the first instance no isotopic separation process is postulated. Table % shows the F.P. nuclides selected for transmutation. (see also Fig. 4). Table 3 The priority for the transmutation of fissioned products Selected Yield for fission of Atom/100 atom Pu-239 Assuming isotopic 100 atoms of Pu-239 Subtotal separation atoms/100 atoms Pu-239 Cs=-13%3% (stable) 6.91 6.91 0.14 Cs=-13%5 7.54 21.140 14.450 7.54 14,37 Cs-137 6.69 ' 21.140 6.69 Sr-90 2.18 25.32 2.18 Sr-88 (stable) 1.44x0.02 = 0.029 2.203 23,349 0.029 2.209 (2% isotopic separation efficiency) I-129 1.17 } 24,519 1.17 I-127 (stable) 0.38 1.55 24,899 0.01 J 1-1° Te-99 5,81 5.81 30.709 5.81 5.81 Kr-83% (stable) 0.36 h Kr-84 (stable) 0.56 Kr-85 0.672 2. 14Th 0.67 0. Krf86 (stable) 0.882 ) 3%.183 0.04 rt Total 3%.18% 24,28 LT curie/watt Aectivity 18 1 day ] 10 days 100 days 1 year 10 years 100 years 1000 y. i | | | 1 1 time, seconds 19 5. Is the rate of transmutation good enough? 1t 1s clear that the rate of radiocactive nuclide removal in a field of particles is given by: ln 2 eff Adecay ¥ Atransmutation (s l) = t 1/2 (eff) where A = g @ trans trans . 2 ) . o = c¢ross section (ecm ) for a given reaction ¢ = flux of the reacting particles (cmngs_l) Let us assume that the energy production 1s based on a set of n burners and nX breeders (see §3). At time tn (see Fig. 5) when 1t 1s declded to stop fission energy production in favour of other sources the total amount of a selected fission product is (1) (k) = (X + Ln< el with K = YP/E Y = yield of the selected F.P. P = power per burner (or breeder) (watt) E = energy per fission (Joule) This amount of F.P. 1s located only in the burners, therefore, each burner can receive (X + 1)%eff although their own produc- tion should represent only T in the steady state. elfl At time tn the nX breeders are shut down and only n burners are in operation. Later on (time tn_l) the nuclide removal 1s such that a rearrangement 1is possible and one burner can be stopped, 1ts F.P. content will be loaded in the remaining burners etc. At the beginning of each time step, tp, the p burners which 0c A Fig. 5 (X + 1) V- . K - , \\ oo = 75 amount of F.P. produced by one burner (n,1)(X+1) \\ eff in steady state N\ N \\ AN X+1 \ p( ) \ N N\ 3(X+1) \ N\ \\ 2(X+1 ' ( ) N N I N N (X+1) N \\ 1.2 T~ 1.0 4 — 4+ e 5 — e e — 11 D DL 5 o N 0 Burner number n n.l? P 3 2 = O %EESS;P X-n 0 0 0 0 0 0 21 are stl1ll working contain the max. possible amount of F.P.: where N(t) represents the total amount of the selected F.P. One could imagine other schemes: for example one could make the re- arrangement only when 2 burners can be shutdown. From the reacti- vity point of view this solution is worse than the proposed one. Coming back to the original proposal one has still to solve at each time step (tp, tp_l) the burn up equation. (3) ai Keff N = K.p where the right hand side is the F.P. at production Then the solution is (4) N(t) = 22+ (e ) - using (2) one deduces the time needed to go from p burners to (p-1). (5) Agrp (tp—l ~ tp) = 1ln with a summation one gets the time t, after which one burner only 1 is 1in operation (6) A (b = &) eff 1 I Ho™H }._I 3 22 A more direct evaluation can be obtained if n is so large that the number of operating burners changes continuously with time (p = n(t)) then by a single elimination of p between (2) and (3) one gets dN . gt T rere N7 NApp or X+ 1 A (t -t ) ! (4 ) N(t) = N(t ) e erf =171 1 _ X + 1 N(tn) _ L+ 1 (6 ) )\eff(tl tl’l) = < 1In N‘(t ) = ——'X—'— 1n ( 1’1) The two approaches give similar results except at the end when few burners are in operation (see Fig. 5) For times longer than £, only one burner is operated and the 1 amount of F.P. would decrease from (X + 1) % to % the el f We shall postulate that it has no sense to operate this last burner when the amount of F.P. is only 1.2 times longer than the asymptotic wvalue which requires a new time interval (eq. 4 p =1) A (to - tl) = 1In b X The total time to - tn will be the sum (6) + (7) which corres- n{x + 1) 1.2 only be obtained by natural decay (t>to). ponds to the reduction factor Further reductions can Numerlcal application: With x = 4,n = 100 which means the economy was based before tn on 400 breeders, the initial F.P. amount is reduced 415 times when the last burner is shutdown. Then the required time is defined _ : . 1 by Aorr (tO tn) = 8.9% (8.76 with the approx expression (67 ). It this time is to be less than say 60 years (2 reactor generations) 23 then Aeff Since the most hazardous F.P. nuclides are those which apart from > 4.7-10"95_l(t 1/2 eff = 4,7 years). their high metabolic activity and high retention in living organisms also have a half life of the same order as a human life span of 60-70 years we arrive at the following list of hazardous isotopes which are the most important for transmutation. Kr-85 t 1/2 = 10 years Adec = 20.9 ].O“los_l -10 -1 Sr-90 6 1/2 = 28.2 years Adec _ 7.76 - 10 S Cs-137 t 1/2 = 30 years Mo = T-32 ¢ 10”0571 . : -9 -1 1 1 - = . = desired 'half 1life L.7 years Adesired b7 10 S = A + dec Ktrans The most important problem arises from the fact that the two nuc- lides Sr-90 and Cs=137 have very small cross sections for neutron absorption in both the thermal and fast regions. thermal fast Sr-90 0.6 Dbarns 0.007 barns Cs=-137 0.06 " 0.010 " therefore to achieve A . = 4.7 - 10_93"1 the neccessary fluxes desired should be . A e fast flux Cs-137 @fast = -S&sired decay _ _4.10 2 cCs-137 fast 0.01-10 u = = 4.0-1017(n cm_gs—l) 24 4+1077 16 —2 -1 thermal flux Cs=-13%7 gth: ...... 5T T 6-10 (n em “s ) 0.06+10 4001077 ) 15 -2 -1 Sr-90 ) T = 6.6°107"(n cm “s ) th 0.6-10°" The question then arises, in what device are such fluxes possible - a fast flux of Ll'lO17 or a thermal flux 6~1016. It is interesting to point out that during the period of 60 years which provides the reduction factor of 415 (if the Aeff = H.?-lo_gs_l can be achieved) the natural decay of Cs=137 would have reduced it only by a factor 4 which demonstrates the efficiency of the burner. Also the burning which cccurs during the first period (t € tn) reduces the amount of F.P. R times = 6.7 times for Cs-137 6. In what reactors are the transmutations possible? From the point of view of this paper the most important process is the transmutation of some of these nuclides by neutrons in a fission reactor. The criteria given in chapter 2 1limit the choilce of system. That is a) the number of F.P. nuclei cannot be too large in relation to the number of fissioned atoms in the burner reactor (reactor for transmutation) because the latter process also produces new fission products. b) the fission reactor should be self-sustaining - that is a breeding system. 25h c) the specific power of the reactor is proportional to the neutron flux. High neutron flux means high specific power which 1s controlled by the erfectiveness of the core cooling. d) the specific power P and the neutron flux ¢ are coupled by the fission cross section and the concentration of fissile nuclide (Nf) For thermal neutrons Of is approx. 700 barns and for fast neutrons only 1.0 barns, that is 400 times smaller. Yor the gilven total power and the same specific power the product N Y for the thermal reactor must be approx. 400 times smailer than for a fast reactor. Since the critical concentration of fissile nuclides in a thermal reactor can only be 10 times smaller than for a fast reactor then for a given specific power the neutron flux in a fast reactor can be about 40 times higher than that of a thermal reactor. The cross section for thermal neutrons for the nuclides con- sidered here 1s from 3 to 10 times larger than in a fast flux and this must be taken into account. All these factors bring us to the following solution of the problems under discussion. a) The highest specific power and hence the highest neutron flux is possible if the cooling process is carried out by the fuel itself and not by a separate cooling agent only. This directs our interest towards a reactor with molten fuel in spite of the exotic nature of this solution. 26 b) The high flux reactor must be a fast reactor (small o for fast fission) ¢) Because Oth >Gfast the fthermalisation of the high flux 1n a thermal (column) 1s postulated, then 1t 1is possible that @column core therm. ffast d) The first approximation is made for an isotopically pure radio- nuclide e.g. Cs-137 without Cs-133% (stable) and Cs-135 and also Sr-90 without Sr-88 (stable) The discussion then results in: - transmubtation of Cs-137 (and some other nuclides) in a therma- lised trap of high flux neutrons: @ thermal = 5'1Ol6n cmmzs_l § -1 - production of a high flux of fast neutrons >5-lOl n cm_gs 5 and the high specific power of 15 KW cm ° is achieved by means of liquid fuel circulating through an external cooler. - transmutation of other selected fission products in an external thermalised region with a thermal flux of 5 -2 -1 5-1()1b or 1-1015n cm 28 . - coupling of one burner - high flux fast burner reactor with a system of 'nmormal' power breeder reactors, 27 7. What are the limits of specific power Iin a solid fuelled reactor? Is the specific power of 15 KWcm_3 achievable in a solld fuel reactor? These are the self-evident limits in solid fuelled reactors: a) rate of burning of fissile nuclides limited due to depletion of fissile or an increase of F.P. nuclides. b) heat transfer limitation of fuel/clad to coolant c) temperature and temperature gradients in the fuel and cladding (melting, mechanical properties) d) bolling of coolant e) limitation of coolant velocity, pumping power, stabllity Now we discuss these limitations in more detail a) the dwell time in a solid fuelled reactor in core for the fissile nuclides must not be too short. concentration of fissile nuclide * maximum burn-up £ dwell fission rate We could write: 28 where N = concentration of fissile nuclide N = g : g and £ = 3.1 X lOlO fissions/joule s = power (watts) R = fission rate (fission s l) R =P " 7f from this: tdwell ) T G 0 o . For a thermal reactor (some arbitrary values) D = 0.03 6§h = 700 - 10‘2Ll em® Y = 5 1016 n cm_zs_l tdwell = 850 s = 14.3% minutes but also for b = 0.10 we achieve ¢t = 47.6 minutes dwell For a fast reactor (some arbitrary values) D = 0.10 6£a5t - 1.8 x 102" en? @ = 5 1016 n cm—gs—l _ 6 - tdwell = 1.1 10" sec = 12.9 days Conclusion: - the dwell time in a thermal reactor i1s prohibitive short; - in a fast reactor it 1s more reasonable but still very short, especially in the case a of solid fuel reactor 29 b) The limitation of specific power by heat transfer 1s the following: a o . . . Speciflc power PspeC in a 'good!' 3 thh power reactor and with the appropriate flux can be taken from literature is: .05 kW/cmB; 2 spec th 5 fast Pspec =1 kW/cm™; @f 15 5 x 10 t thermal P 5 b X lOl In a high flux reactor: (see LANE 1969, FEINBERG 1970) (see also Fig. 6) thermal thermal: P = 2.0 kW/cmB; 2z = 3 x 1015n cm S spec th 5 16 -2 -1 = [N . = Popee © 1e0 kW/cm” ; ¢, = 3 x 107'n fast: P = 1.0 KW/cmB; @ = 1.5 x 1016n cm—gs_l spec f With the same geometfry the very high flux reactor desired here would have the following flux for Cs-137 transmutation: 16 5 5.0 x 10 the specific power Pth = 22.5 kW/cm for @th .0 x 1017 the specific power P, = 20 kW/cm3 f for @th 30 Eifi;_é Fuel cycle o Feinberg's C calculation Fast reactor for 2 GW with thermal column 1016- @ HFIR ATR @ 15 w10 e !FBR 5 ® ETR = ® ; MSBR 3 14 (continuous) — WR a 7 " S () e = 1013 T T 1 T T 0.01 0.1 1 10 100 500 Fuel cycle, days 1004 Specific power einberg's calculation 1 GW(th) 4o M/s 20 M Thermal E 10 column in ; 1 fast reactor X L.fl 0] = O 2 5 HFIR 3 CM-2 (Feinberg) h O ) 1 - o |92] 0.5 FFTFEF 4hoo MW 0.2 - 0.1 . 1ot R 1010 1017 Thermal flux,lq/cmzs For a solid fuel we Jlmension Cell: D.9x0.9x1.0 cm Fuel: f = 0.6 cm Cladding: 2. = 0.6 cm i s = 0.03% cm 2 = 0.6 cm ol Coolant: 0 - 31 volume .81 cm5 Z .283% em” .568-10H20m5 .5 e 1 cim 5 postulate the following "unit-cell" cCross-—= surface- section area area 0.81 cm2 3.60 cm2 9! 0.28% cm2 1.885 em” 0.568-10h2 cm2 1.904 cma 0.521 Cm2 In this specified cell of a "desired" high-flux-reactor, we would achieve a heat-flux, per unit fuel element surface area: (for both types of reactors, thermal and fast) b z 21 kW/cem” }{ — = Fasn 2] , A 0.51 cm” f's D) - j— Fan 1.685 cm ) 9 kW/em © 52 Using now a simplified model for the first guess of the tempera- ture gradlent we can say: the amount of heat generated in the fuel must be the same as leaving the surface of the cladding- material. ' - . 5 Alclad - Hfs i\ Where s = wall thickness and A = heat conductivity (w-cm_l-K_l) an optimistic value for stainless steel is A = 0.4 W-cm_l'K"l. ATclad = 9000 - —;T— = 0675 “C It is evident that this result 1is not realistilc. The solution of this problem may be the thermalisation of neutrons in a high flux fast core and the irradiation of Cs-137 in a thermal trap (see Fig. 7). In such a thermal trap we postulate (which must be based later on core calculation) @th = 1.2~ Qjfast _ 16 . _ 16 -2 -1 to reach @th = 6.0-10 we reguire ®fast = 5.0-10 n cm S For this fast flux the specific power can be assumed, 1f we take into account the effective increase of the fisslon cross section because of the influence of the thermal trap. The simpli- 30 fied calculation results in a specific power of ~10 KW/cm The corresponding heat-flux 1s therefore reduced to P B H _ _Spec cell