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Oklo: the Fossil Nuclear Reactors. Physics Study

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Oklo: the Fossil Nuclear Reactors. Physics Study Illlllllllllllllllllililllllll SE9700079 TECHNICAL REPORT 96-14 Oklo: Des reacteurs nucleates fossiles (Oklo: The fossil nuclear reactors). Physics study (R Naudet, CEA) -Translation of chapters 6,13, and conclusions V O Oversby VMO Konsult September 1996 SVENSK KARNBRANSLEHANTERING AB SWEDISH NUCLEAR FUEL AND WASTE MANAGEMENT CO P.O.BOX 5864 S-102 40 STOCKHOLM SWEDEN PHONE +46 8 665 28 00 FAX +46 8 661 57 19 OKLO: DES REACTEURS NUCLEAIRES FOSSILES (OKLO: THE FOSSIL NUCLEAR REACTORS). PHYSICS STUDY (R NAUDET, CEA) TRANSLATION OF CHAPTERS 6,13, AND CONCLUSIONS V O Oversby VMO Konsult September 1996 This report concerns a study which was conducted for SKB. The conclusions and viewpoints presented in the report are those of the author(s) and do not necessarily coincide with those of the client. Information on SKB technical reports froml977-1978 (TR 121), 1979 (TR 79-28), 1980 (TR 80-26), 1981 (TR 81-17), 1982 (TR 82-28), 1983 (TR 83-77), 1984 (TR 85-01), 1985 (TR 85-20), 1986 (TR 86-31), 1987 (TR 87-33), 1988 (TR 88-32), 1989 (TR 89-40), 1990 (TR 90-46), 1991 (TR 91-64), 1992 (TR 92-46), 1993 (TR 93-34), 1994 (TR 94-33) and 1995 (TR 95-37) is available through SKB. Oklo: Des Reacteurs Nucleates Fossiles (Oklo: The Fossil Nuclear Reactors) Physics study Roger Naudet Commissariat a I'Energy Atomique Translation of chapters 6,13, and Conclusions V. O. Oversby VMO Konsult September, 1996 Keywords: Oklo, nuclear reactors, uranium ore, criticality. Produced with the permission of the Commissariat a l'Energy Atomique, Direction de l'lnformation Scientifique et Technique, Centre d'fitudes de Sad ay. TABLE OF CONTENTS Page CHAPTER 6 1 CHAPTER 13 46 CONCLUSIONS 88 111 CHAPTER 6 - STUDY OF CRITICALITY The study of neutron balance has shown that this depends on many factors and that there are many ways of reaching the critical state, that is to say obtaining a stable chain reaction. For example, the concentration of uranium in the ore is a fundamental parameter, but a very rich ore is not necessarily favored if the deposit is too thin or there is not enough water. There are not, therefore, limits imposed on each parameter (although there are, in general, thresholds); it is the combination of the ensemble thatmust be considered. In the reactor zones, criticality was achieved throughout, at any time, in all circumstances, and despite the great diversity of characteristics and situations: to seek how this was obtained and maintained for Oklo is the fundamental physical problem. One will only begin this study in the present chapter: for the time being one leaves to the side the problems of equilibration of activity during functioning (the subject of chapter 9), and the spatial interferences between reactors (chapter 10 studies). One considers here only the initial and final states of isolated reactors. We also limit ourselves to analysis and comparison of situations, leaving for later interpretations concerning the origin of the situations and the progress of the phenomenon in its entirety. In the first part of thechapter, we approach theproblem from a very general manner, only taking into consideration a small number of parameters in order to establish equivalences and ranges of compatible values. In particular, this allows comparison of the initial and final conditions of the reactors. On the other hand, after supposing in the first case that there was, from the beginning, the argillaceous gangue and the geometry we now have, we take into account that these reactions were able to start in sandstones thatwere more or less desilicified, from which we get new equivalences. We then examine more concretely a certain number of situations typically encountered at Oklo, in order to determine if we can justify criticality in a homogeneous manner, or if we must admit, on the contrary, that it was reached under conditions that were not identical everywhere. Moreover, it is interesting to inquire to what extent criticality could have been reached in uranium ore deposits with origins younger or older than those of Oklo. A reflection on the phenomenon of "natural reactors" is discussed in the appendix to the chapter. 1 TABLE OF CONTENTS OF THE CHAPTER 1 Parametric study in argillaceous medium 3 1.1 Choice of parameters . Definition of an equivalent thickness 3 Simplification of the geometry 4 Advantage of the reflector 6 1.2 Initial criticality - equivalences among the parameters 8 1.3 Criticality at the time of stoppage of the reactors . 11 2 Criticality in the sandstones 15 2.1 Sandstones in the process of desilicification 15 2.2 Initial starting of the reactors 19 3 D etailed examination of situations encountered at Oklo 25 3.1 Examination of zone 2; discussion 26 3.2 Examination of other zones 31 zones 1 and 6 31 zones 3 to 5 32 zones 7 to 9 35 Appendix: Importance of age in the phenomenon of "natural reactors " 39 Deposits of uranium more recent than Oklo 40 Deposits of uranium older than Oklo 44 2 1 Parametric Study in Clay medium i.i Choice of parameters - Definition of an ’’equivalent ” THICKNESS The three principal parameters that characterize the composition of the ore deposits for a given environment are the relative amounts of uranium, of gangue, and of water, as well as theneutron capture capacity of the gangue. In practice, we use the parameters t, x, and m defined in chapter 5, and reviewed briefly here, "t" is the concentration of uranium (or grade) of the ore, translated to present day (to adjust for radioactive decay), "x" represents the neutron poisons (rare earth elements, boron) and more generally, an increment of capture capacity of the gangue in comparison with a "standard" composition (in the following material, we keep the composition given in the preceding chapter, which represents suitably the average of zones 1 and 2). Finally, "m" defines the "free volume" occupied by water (m/(l+m) is the porosity of the deposit). The total quantity of water present is fixed when, in addition, the fraction of structural water in the clay is given and the densities are given. We will only consider the initial and final conditions, and assume that the temperature is still - or again - that of the environment. In the following, we adopt, as in the reference example, T = 160°C; the margin of error in this value (which might need to be lowered by about 20°C) is of little consequence with respect to criticality. We will also not vary the parameters related to heterogeneity, the "standard" hypotheses defined in thepreceding chapter being considered as representative of the mean. Finally, in nearly all the calculations, we adopt an age of 1950 MA, considered as the best value; we examine only the effect of variation of this parameter, this question being reviewed more thoroughly in the appendix. Two other parameters will eventually be used: in the initial condition, we consider either a deposit completely argillaceous - that is with a gangue such as we now see - or a sandstone, more generally a sandstone in the process of being desilicified - that is a deposit with some quartz remaining. There is then a supplementary parameter "Q", which designates the ratio of quartz to clay in the gangue. In the final condition, the irradiated deposit will be characterized by the parameter "e", defining theisotopic depletion of the uranium (transposed to present time). This result implies a calculation of the residual poisons and fission products accumulated at the end of reaction. 3 There remains, finally, to characterize the dimension of the multiplication medium and then the escape of neutrons: a certain number of conventions and simplifications are needed to represent this complex ensemble of results by means of a single parameter. This is what we will now examine; this will also be the occasion to note that the geometry of the reactors at Oklo poses certain problems. Simplification of the geometry To proceed in a simple manner, it would be necessary to suppose thatthe multiplication medium is homogeneous, that it has a definite geometric form, and that it is surrounded by a void. In reality, one is very far from this abstract concept; the characteristics of the terrain vary in all respects without precise limits. We can in the first instance adopt themodel of a "flat cake reactor" in whichwe suppose the escape of neutrons to be important only in a single dimension. The distribution revealed along a core that crosses a reactor zone is then considered to represent the small dimension and we assume that the properties in the core are uniform in the other two dimensions. In reality it is not at all like this, of course, and the exchanges of neutrons with the lateral environment is often important. The situation will be different depending on whether the core is surrounded by rich ore or by poor ore and whether it is in the center of the reactor zone or on the edge. Another difficulty comes from the fact that vertical drill cores cut the strata obliquely to the bedding. (It is the same problem with samples taken from horizontal faces of a mining face). To be consistent with the hypotheses used, one must multiply all the distances in the drill core by the cosine of thedip of the strata. This "recipe" is hard to apply because the dips are poorly known, and moreover the dips are poorly defined because the beds are deformed and the thicknesses of each partial environment is not constant. Another adaptation is needed to recover the geometry of the reactors; since that time, therehas been a compaction of the terrain.
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