Multiregion Concentration Diffusion Coefficient Determination Using Davidon’s Variable Metric Method

An analytic solution of the one-dimensional steadystate multiregion concentration diffusion decay equation is constructed. The solution is used to determine the diffusion coefficients of metallic fission products in high-temperature gas-cooled reactor fuel particles from experimental measurement of the concentrations using Davidon’s variable metric method for chi-square minimization. Typically, for two to four material regions with 50 measured concentration data points, the diffusion coefficients and their associated uncertainties can be determined rapidly (<8 s on the AMDAHL 470/V6). Using analytical solutions, the diffusion coefficients can be determined ∼25 times faster than using finite difference solutions. The methodology is applied to Zoller’s concentration measurements of ¹³⁷Cs and ⁹⁰Sr.