On The Criticality Conditions of Oklo Natural Reactors in Gabon: Realistic Model of the Reaction Zone 9. Salah-Eddine BENTRIDI 1,3 , Benoît GALL 2 , François GAUTHIER-LAFAYE 3 , Abdeslam SEGHOUR 4 IEEE Nuclear Science Symposium & Medical Imaging Conference, 23-29 October-Valencia, Spain I. Introduction Natural occurrence of criticality, known as the “Oklo phenomenon”, took place 1950 million years ago 2, 3, 5) in Oklo uranium deposit (fig. 1) The present day geometry of the considered natural reactor can be assimilated to a few centimetres thick lens with extension of 12 m x 7 m along the geologic layer. (fig. 2) The special interest for this reactor come from the difficulty encountered to explain the occurrence of the criticality in such site. Today, the possibility offered by the Monte-Carlo code MCNP 11, 12, 13) , allows us to make more realistic and detailed numerical computations to study criticality in such a system. For this purpose the minimal size needed for criticality was studied with respect to a realistic porosity, organic Matter (O.M.), water, Uranium (U) and poisons content. Several geometries have been defined in order to consider also the effect of surrounding rocks. Criticality in RZ9 can be explained by the present work. Fig. 1 Geological map of the Franceville basin in Gabon1) 2. Why the Reaction Zone n°9? Compared to the northern sector (RZ’s 1 to 6) the RZ9 is characterized by an important abundance of degraded organic matter in form of bitumen was observed in the RZ9. besides that, the present time U content obtained from analysed samples, range between 25 and 30% wgt (considered on dehydrated ore). 8) In previous studies, this geometry was considered to be too thin to allow criticality due to important geometrical induced leakage of fission neutrons and the low U content was considered to be insufficient to assure a criticality in such case. 2,8) 3. Modeling of the Reactor The Oklo deposit is the oldest high-grade uranium deposit located in a sedimentary sequence and it can be considered as an ancient hydrocarbons field prior to be an uranium deposit 4, 8) . Realistic rock porosity in such sandstone rock reservoir may therefore range from 20% to 40% 14) . The typical ore sample used in this study is numerically defined by two main volumes (i) a solid volume (clay, UO 2 , silica) and (ii) a fluid volume fraction V free located in all forms of porosity even the intrinsic porosity of clay (moderator: water and/or Hydrocarbons designed by φ T . (fig. 3) • The parameter used to define the ore enrichment is designed by V UO2 . It represents the volume of the uraninite in a volume of 1 cm 3 of the hydrated ore. • The gangue is defined to be : 90% of silica + 10% of clay • Using a detailed composition of clay and assuming incompressible materials, we define the solid part density, including the Mineralised Hydrocarbons Sandstone (MHS) density 1) : MHS UO MHS vol MHS UO vol UO solid f f + = × + × = 2 2 2 % % ρ ρ ρ The contribution of initial poisons like Sm and Gd, present before occurrence of criticality, is considered in order to be realistic. Introducing in this static model an equivalent Bore-10 content, given in ppm of the ore weight density, simplify the treatment of the influence of these poisons. According to geological statements 6, 16) , we consider in the model a cylindrical geometry for the RZ9 with reflectors. This assumption reduces the geometrical parameters to the radius “R” and the thickness of a cylinder “e”. To be consistent with geological conditions lateral reflector has 15% porosity where the top/bottom has only 10% (fig.4). 4. Results The MCNP5 code is used here to compute the effective multiplication factor k eff to find critical configurations. Isocritical lines connect all the critical configurations in a multiparametric representation 1) . First approach : results are obtained for two poisons-free cases, respectively: Reflector-less Core (RC) and Core with Reflectors without Uranium (CRwU) 1) as shown in. Figure 5 shows all possible critical configurations at a given reactor thickness (e = 70 cm) with respect to core radius RC and ore porosity φ T 15 20 25 30 35 40 45 0 50 100 150 200 250 300 350 Rc (cm) φ T (%)     V UO2 = 5% e = 70cm In a second approach , all reflectors are considered having a uranium content (VUO2 = 1,25%). The top/bottom reflectors are considered with 1/5 of core’s poison content (1 ppm) and the lateral one with the same as the core itself. Figure 6 (CRUP[5ppm] line). the criticality may occur with reasonable initial size, even by considering initial poisons, prior to the operating of those natural reactors. 15 20 25 30 35 40 45 0 50 100 150 200 250 300 350 V UO2 = 5% e = 70cm      R C (cm) φ T (%)  References 1) S. Bentridi, B. Gall, F. Gauthier-Lafaye & A. Seghour, “Monte-Carlo Based Numerical Modeling and Simulation of Criticality Conditions Occurrence in Nautral Reactor Zone 9 in Oklo Deposit (Gabon).” Progess Nuclear Science and Technology, 2011, in press). 2) F. Gauthier-Lafaye, “The constraint for the occurrence of uranium deposits and natural nuclear fission reactors in the paleoproterozoic Franceville Basin (Gabon),” Geol. Soc. Am. Mem 198, 157-167 (2006) 3) F. Gauthier-Lafaye, F. Weber, “Natural nuclear fission reactors: time constraints for occurrence, and their relation to uranium and manganese deposits and to the evolution of the atmosphere,” Precamb. Res. 120, 81-100 (2003). 4) F. Gauthier-Lafaye, “From nuclear fuels to waste: current research: 2 billion year old natural analogs for nuclear waste disposal: the natural nuclear fission reactors in Gabon (Africa),” C. R. Physique 3, 839-849 (2002). 5) F. Gauthier-Lafaye, “The last natural nuclear fission reactor,” Nature 387, p337 (1997). 6) F. Gauthier-Lafaye, P. Holliger and P.L. Blanc, “Natural fission reactors in the Franceville basin, Gabon: A review of the conditions and results of “critical event” in a geological system,” Geo. & Cosmo. Acta. 60[23], 4831-4852 (1996). 7) R. Naudet, Oklo : Des réacteurs nucléaires fossiles – Etude physique, Série Synthèses : C.E.A, éditions Eyrolles 685 (1991). 8) F. Cortial, F. Gauthier-Lafaye, A. Oberlin, G. Lacrampe-Couloume and F. Weber, “Charaterization of organic matter associated with uranium deposits in the Francevillian Formation of Gabon (Lower Proterzoic)”, Org. Chem. 15[1], 73-85 (1990). 9) H. Hidaka et al. “Abundance of fissiogenic and pre-reactor natural rare-earth elements in a uranium ore sample from Oklo,” Geoch. J. 22, 47-54 (1988). 10) R.D. Loss et al. “The Oklo natural reactors: cumulative fission yields and nuclear characteristics of Reactor Zone 9,” Earth and Plan. Sci. Lett. 89, 193-206 (1988). 11) J. K. Shultis & R. E. Faw, “An MCNP Primer,” Kansas State University, (2006). 12) C. D. Harmon et al; Los Alamos National Laboratory, X-5, “Criticality Calculations with MCNP5: A Primer 2nd Edition”, LA-UR-04-0294, (2004). 13) X- Monte-Carlo Team, “MCNP Manual: A General Monte-Carlo N-Particle Transport Code, Version 5”, Los Alamos National Laboratory, (2003). 14) P. H. Nelson, J. E. Kibler, A Catalog of Porosity and Permeability from Core Plugs in Siliciclastic Rocks, USGS, Open-file Report 03-420 (2003). 15) J-P. Tchebina-Makosso, “Effets, sur l’encaissant, des reactions de fission naturelles d’Oklo (République Gabonaise) Evolution minéralogique des phyllosilicates et bilans géochimiques” Thèse de Doctorat (3ème cylce), U.E.R des Sciences de la vie et de la terre, Institut de Géologie Strasbourg (1982). 16) F. Gauthier-Lafaye, Contrôle Géologique de l’exploitation des zones de réaction 7 à 9, Oklo, Gabon, Geology Institute, Louis Pasteur University, Apr.1978 – Sep. (1979). Fig. 2 East-West outcrop of the RZ9 reactor area 5. Conclusion The “isocritical line" was introduced to represent the critical configurations in a suitable parametrical space. The criticality computations performed within this study using MCNP code, have allowed the identification of the main influent parameters on the criticality and their influence on different systems. Since those systems had undergone an expected compaction due to lithostatic pressures to which they were subject, especially after considerable mass departure of silica due to thermo-hydraulic processes induced by the natural reactors in operation, it is now relatively difficult to determine the initial conditions from the present-day observations. The start-up of the reactions in the core may have taken place between two limits: one is related to favorable zones with very large dimensions (like is the case for the RZ2) and the other case is related to a little favorable zone with smaller extension, which experienced a relatively low operating rate and a shorter period of operating. Until now start-up of these latter reactors was not explained yet. This study is far from being finished even if it has already significantly contributed to the explanation of the start-up and evolution of the “Oklo" phenomenon. The static simulations done give snapshots of the reactor situation in a chosen configuration. Thus major perspective of this study would be to run fuel depletion simulations in order to monitor reactor evolution during the time of their operation, and follow realistic scenarios. Abstract : The occurrence of more than fifteen natural nuclear Reactor Zones (RZ) in a geological environment remains a mystery even forty years after their discovery. The present work gives for the first time an explanation of the chemical and physical processes that caused the start-up of the fission reactions with two opposite processes, uranium enrichments and progressive impoverishment in 235U. Based on Monte-Carlo neutronics simulations, a solution space was defined taking into account realistic combinations of relevant parameters acting on geological conditions and neutron-transport physics. This study explains criticality occurrence, operation, expansion and end of life conditions of Oklo natural nuclear reactors, from the smallest to the biggest ones. 1 Laboratoire de l’Energie et des Systèmes Intelligents, C.U.K.M, Route de Theniet El-Hed 44225, Algérie; 2 Institut Pluridisciplinaire Hubert Curien, UMR 7871, 23 rue du Loess 67037 Strasbourg, France; 3 Laboratoire d’Hydrologie et de Géochimie de Strasbourg, 1 rue Blessig, 67084 Strasbourg, France; 4 Centre de Recherches Nucléaires d’Alger CRNA, 2 Bvd Frantz Fanon 16002 Alger, Algérie. Fig. 5 Isocriticality lines for Fresh core including poisons with Reflectors without Uranium Fig. 6 Isocriticality lines for more realistic fresh core with reflectors including poisons and Uranium Fig. 4 Cylindrical model of the core reactor with reflectors R e SiO2 Clay UO2 (~5%) porosity (20-40%) Fig. 3 Composition of initial rich ore View publication stats View publication stats