Optimization of waste loading in high-level glass in the presence of uncertainty

Hanford high-level liquid waste will be converted into a glass form for long-term storage. The glass must meet certain constraints on its composition and properties in order to have desired properties for processing (e.g., electrical conductivity, viscosity, and liquidus temperature) and acceptable durability for long-term storage. The Optimal Waste Loading (OWL) models, based on rigorous mathematical optimization techniques, have been developed to minimize the number of glass logs required and determine glass-former compositions that will produce a glass meeting all relevant constraints. There is considerable uncertainty in many of the models and data relevant to the formulation of high-level glass. In this paper, we discuss how we handle uncertainty in the glass property models and in the high-level waste composition to the vitrification process. Glass property constraints used in optimization are inequalities that relate glass property models obtained by regression analysis of experimental data to numerical limits on property values. Therefore, these constraints are subject to uncertainty. The sampling distributions of the regression models are used to describe the uncertainties associated with the constraints. The optimization then accounts for these uncertainties by requiring the constraints to be satisfied within specified confidence limits. The uncertainty in waste composition is handled using stochastic optimization. Given means and standard deviations of component masses in the high-level waste stream, distributions of possible values for each component are generated. A series of optimization runs is performed; the distribution of each waste component is sampled for each run. The resultant distribution of solutions is then statistically summarized. The ability of OWL models to handle these forms of uncertainty make them very useful tools in designing and evaluating high-level waste glasses formulations