Inception and evolution of Oklo natural nuclear reactors

Abstract

Version franc ¸aise abre ´ge ´eLa zone de re ´action 9 (RZ9) repre ´sente ´e sur la Fig. 1 fait partie de la quinzaine de re ´acteurs nucle ´aires naturels de ´couverts depuis 1972 dans les mines d'uranium d'Oklo et Okelobondo au Gabon. Plus connu sous le nom

Modeling the short-term and long-term behaviour of the Oklo natural nuclear reactor phenomenon

“…The reactor collapses vertically as silica is removed under the weight of the rock above it (see Section 2.5.3). These assumptions are consistent with those found in Naudet (1991); Petrov et al (2006); Bentridi et al (2011a). The possibility of the reactor spreading radially as it collapsed vertically was also considered, but this hypothesis was rejected on the basis of the constraining effect of the surrounding rocks.…”

“…The material inside the reactor consists of gangue and uraninite (UO 2 ). Uraninite makes up 5-7% of the volume of the reactor (Bentridi et al, 2011a); in this model the initial uraninite volume fraction is assumed to be 6%. The material in both the reactors and surroundings is assumed to be homogeneous.…”

“…The sixteen different Oklo reactor zones vary widely in size, but are now typically lensshaped (Gauthier-Lafaye, 2002). Geological changes mean it is not possible to say with certainty what the geometries of the reactor zones were when they operated 2 billion years ago, but they are taken to be a horizontally-oriented cylinder, as they are in Bentridi et al (2011a). Particularly for the larger reactors, the precise shape does not make a significant difference to their operation, so this simple geometry is a reasonable approximation.…”

“…The main cause of variation in the geometry of the reactor over time is the removal of silica (Naudet, 1991). Given the pressure exerted by surrounding rocks, reported as 200 bars in Bentridi et al (2011a), it is assumed that for every unit volume of silica removed, the reactor contracts by the same volume. Though there might have been some time delay between the removal of silica and the shrinking of the reactor to fill the void created, it is deemed appropriate to assume in the model that the reactor shrinks immediately as silica is removed.…”

“…Uraninite may have been deposited gradually over the duration of the GOE (hundreds of millions of years) until criticality occurred, or it may have been deposited in a short period of time (perhaps 10,000 years; see Klinkhammer and Palmer (1991)) after a seismic event that caused fracturing of the reactor region and an influx of uranium-carrying water. Given this uncertainty, the model is started at 1.95 billion years ago, the end of the GOE and the most precise estimate of first criticality used in the literature (Gauthier-Lafaye and Weber, 2002;Bentridi et al, 2011a), with the uraninite already in place and disregarding how it accumulated. At this time the natural enrichment of uranium was 3.53%.…”