An Empirical Formula that Predicts the Critical Parameters of a Uranium Solution Slab-Cylinder System

An empirical formula has been developed for the criticality specialist who does not have readily available a computer that calculates the individual cylinder diameter for a critical uranyl nitrate solution slab-cylinder system. The formula is used to calculate the criticality condition for an accidental leak in an array of fissile-containing vessels which forms a solution slab under the array. The critical system consisted of a square array of 1, 4, 9, or 16 vertical, equal-diameter cylinders resting on and interacting with a horizontal slab. Both the array and the slab were filled with ∼495 g U/liter uranyl nitrate solution with the uranium enriched to 93.2 wt% ²³⁵U. The empirical formula, which predicts the critical unit cylinder diameter of the slab-array system, is where D_a is the critical unit cylinder diameter of the array alone at 500 g U/ liter. The independent variables are the number of cylinders, N; the edge-to-edge spacing between nearest neighbored cylinders in cm, S; the array solution height in cm, H; the solution concentration in g U/liter, C; and the solution slab thickness in cm, T. The calculated unit cylinder diameter, D_s, in cm, is within ±11% of the experimentally measured diameter for 65 critical slab-array systems. This accuracy is sufficient for calculating the accident condition for nuclear safety purposes. Monte Carlo calculations were performed on some typical experimental configurations. The average k_eff ranges from 0.977 ± 0.017 to 0.996 ± 0.012. By increasing the slab thickness by the experimental error, the low k_eff was increased to 0.998 ± 0.012.