The collision probability treatment for regions comprised of a uniform background medium with a random dispersion of small heterogeneities is analyzed using recently-developed statistical techniques. By assuming that the chord length distributions in such regions follow a renewal process we obtain an exact expression for the equivalent homogeneous cross section. Numerical comparisons show that the collision probability value for this cross section can be significantly in error in most cases, with an error of ∼8% for typical PWR poisoned fuel consisting of a mixture of uranium oxide and gadolinia grains. Renewal theory is generalized to the case of materials with internal structure allowing us to justify the central assumption on which the collision probability treatment is based. Also, new formulas are proposed for the calculation of the collision probabilities between matrix and grains in terms of the collision probabilities for the homogenized regions. © 1991.
Sanchez, R., & Pomraning, G. C. (1991). A statistical analysis of the double heterogeneity problem. Annals of Nuclear Energy, 18(7), 371–395. https://doi.org/10.1016/0306-4549(91)90073-7