Law of substitution for mixed arrays

The nuclear safety justification of a mixed array of dissimilar fissile units of metal units and dilute solution units, according to Clayton, has been a persistent and nagging problem. Dissimilar uranium metal or dissimilar uranium solution units in a mixed array can also create a modeling nightmare for the nuclear criticality safety engineer. Now, a calculational method known as the Law of Substitution has been developed to ensure that the k/sub eff/ of an array of uranium metal and uranium solution units will satisfy any k/sub eff/ limit set by the nuclear safety engineer. The nuclear criticality safety engineer can utilize the Law of Substitution to safely mix or substitute different uranium metal units, different uranium solution units, and more importantly, uranium metal and dilute UO2 solution units in an array. The Law of Substitution is as follows: (1) calculate the k/sub eff/ of each unit type in its own infinite planar array. (2) Determine the edge-to-edge spacing of the infinite planar array of each type of unit to satisfy a desired k/sub eff/. (3) Select the largest edge-to-edge spacing from among the similar units in their infinite planar arrays and use that spacing for the finite or infinite planar array of mixed units