Submixture model to predict nepheline precipitation in waste glasses

Abstract

99354High-alumina high-level waste (HLW) glasses are prone to nepheline precipitation during canister centerline cooling (CCC). If sufficient nepheline forms, the chemical durability of the glass will be significantly impacted. Overly conservative constraints have been developed and used to avoid the deleterious effects of nepheline formation in U.S. HLW glasses. The constraints used have been shown to significantly limit the loading of waste in glass at Hanford and therefore the cost and schedule of cleanup. A 90-glass study was performed to develop an improved understanding of the impacts of glass composition on the formation of nepheline during CCC. The CCC crystallinity data from these glasses were combined with 657 glasses found in the literature. The trends showed significant effects of Na on the propensity for nepheline formation. A pseudoternary submixture model was proposed to identify the glass composition region prone to nepheline precipitation. This pseudoternary with axes of SiO 2 + 1.98B 2 O 3 , Na 2 O + 0.653Li 2 O + 0.158CaO, and Al 2 O 3 was found to divide glasses that precipitate nepheline during CCC from those that do not. Application of this constraint is anticipated to increase the loading of Hanford high-alumina HLWs in glass by roughly one-third.

Nonlinear logistic regression mixture experiment modeling for binary data using dimensionally reduced components

“…In Equation (10), the correspondence between the i and j subscripts on the g's and their numerical values is 1 = Alk, 2 = AlFe, and 3 = SiB. Further, setting α Alk;Na 2 O ¼ 1:0 makes α Alk,j the effect of the j th component relative to Na 2 O in the k = Alk group.…”

“…This example is used in the rest of the article to illustrate fitting mixture experiment models expressed in terms of DRCs using NLR (ie, NLR-DRC models). 10,16,17 Should one of the remaining components (occurring at higher concentrations but not included in a group) prove important to modeling nepheline formation, it would lead to poor model performance and be detected via partial residual plots. The binary response variable is whether or not nepheline crystals (nominally NaAlSiO 4 ) formed during canister centerline cooling (CCC) of the HLW glass.…”

“…10,11 For the first time, this article proposes and illustrates statistical frameworks for mixture experiment modeling and prediction uncertainty using DRCs. UDRCs do not necessarily sum to one.…”

“…The right sides of Equations(8) to(10) are expressed in terms of the proportions of the three DRCs (g Alk,h , g AlFe,h , and g SiB,h ) and the parameters γ i , γ ii , and γ ij . The subscript h denotes the data point (HLW glass) index, where h = 1, 2, …, 747.…”

“…, p h is the probability of nepheline forming in the h th HLW glass melt during CCC, and the left sides of the equations are the logistic transformation of p h . However, via Equations (3) to (5), the right sides of Equations(8) to(10) are also functions of the original proportions of components in the three groups ðx Na 2 O The right sides of Equations(8) to(10) are expressed in terms of the proportions of the three DRCs (g Alk,h , g AlFe,h , and g SiB,h ) and the parameters γ i , γ ii , and γ ij .…”