Construction of a Construction of a 21-Component Layered 21-Component Layered Mixture Experiment Mixture Experiment Design Design Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones, SAS Institute Inc. Fall Technical Conference Valley Forge, PA October 17-18, 2002 PNNL-SA-37314
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Construction of a 21-Component Layered Mixture Experiment Design
PNNL-SA-37314. Construction of a 21-Component Layered Mixture Experiment Design. Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones, SAS Institute Inc. Fall Technical Conference Valley Forge, PA October 17-18, 2002. Introduction. - PowerPoint PPT Presentation
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Construction of aConstruction of a21-Component Layered 21-Component Layered
Hanford Site in WA state has 177 underground waste tanks
Wastes will be retrieved from the tanks, separated into high-level waste (HLW) andlow-activity waste (LAW) fractions, and separately vitrified (i.e., made into waste glass)
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Experimental Design for GlassExperimental Design for GlassProperty-Composition ModelsProperty-Composition ModelsExperimental Design for GlassExperimental Design for GlassProperty-Composition ModelsProperty-Composition Models
Need data to support fitting glass property-composition models (used for many things)Use mixture experiment designs that cover the constrained experimental regionsWant design points on the boundary and interior of the glass experimental region Boundary glass compositions less likely, but
still need models able to predict Interior compositions more likely, so must
Liquidus temperature (TL) is the highest temperature at which crystalline phases exist in a glass melt
TL will limit the waste loading in nearly all Hanford HLW glassesSpinel (Ni,Fe,Mn)(Cr,Fe)2O4 crystals of concern
Property-composition models are required to implement spinel TL constraints
Hence, data are required to develop models
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Overview of Experiment Design Overview of Experiment Design Approach for Spinel TApproach for Spinel TLL Problem ProblemOverview of Experiment Design Overview of Experiment Design Approach for Spinel TApproach for Spinel TLL Problem Problem
144 existing glass compositions relevant to Hanford HLW were selected and augmented
A layered design approach for mixture experiments was used Outer layer Inner layer Center point
Non-radioactive and radioactive glasses 40 glasses not containing uranium (U3O8) and
thorium (ThO2) 5 glasses containing U3O8 and ThO2
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Step 1: Define the HLW Glass Step 1: Define the HLW Glass Composition Experimental RegionComposition Experimental Region
Step 1: Define the HLW Glass Step 1: Define the HLW Glass Composition Experimental RegionComposition Experimental Region
Glass scientists selected 21 HLW glass components to study their effects on spinel TL (see Table 1 in handout)
The 21 components included two radioactive components, U3O8 and ThO2
A 22nd component “Others” (a mixture of the remaining minor waste components) was to be held constant at 0.015 for new design glasses
Hence
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1
22
11 and 985.0
i iii XX
015.0 21,...,110 22 XiX i
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Step 1: Define the ExperimentalStep 1: Define the ExperimentalRegion (cont.)Region (cont.)
Step 1: Define the ExperimentalStep 1: Define the ExperimentalRegion (cont.)Region (cont.)
Single- and multi-component constraints on the proportions of the 21 glass components were specified to define outer and inner layers of the experimental region
Single-component constraints 38 outer- and inner-layer, nonradioactive 42 inner-layer, radioactive
6 multi-component constraints
See Tables 1 and 2 at the end of the handout for the specific constraints
iii UxL
01
0 axa i
q
ii
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Step 2: Screen the Existing DatabaseStep 2: Screen the Existing DatabaseStep 2: Screen the Existing DatabaseStep 2: Screen the Existing Database
More than 200 existing glasses with spinel TL values from many other studies
Insufficient glasses inside the single- and multi-component constraints defining the outer layer in Step 1Expanded the outer-layer single-component constraints by 10% (see Table 3 in handout)144 glasses satisfied the revised constraints and were selected for design augmentation
Compositions graphically assessed using dot plots and scatterplot matrix
Existing data spanned ranges of some components fairly well
For B2O3, Cr2O3, F, K2O, MnO, P2O5, SrO, TiO2, and ZnO there were limited data for larger values within component ranges
None of the 144 glasses contained Bi2O3 or ThO2
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Conversion to 19 Components for Conversion to 19 Components for Nonradioactive Portion of DesignNonradioactive Portion of DesignConversion to 19 Components for Conversion to 19 Components for Nonradioactive Portion of DesignNonradioactive Portion of Design
The 144 existing glass compositions were expressed as normalized mass fractions of the 19 components w/o U3O8 and ThO2
The single-component constraints were adjusted by li = Li /0.985 and ui = Ui /0.985
The multi-component constraints were adjusted as described in the paper
Initially tried generating the outer-layer vertices with the goal of selecting a subset using traditional candidate-point optimal designHowever, too many vertices to generateIdeas for generating a “random” subset of vertices to select from were unsuccessfulJMP no-candidate-point D-optimal design capability was used (Brad will discuss later)8 outer-layer glasses were selected to augment the 144 existing glasses
Again used JMP no-candidate D-optimal design capability to select 27 inner-layer nonradioactive glasses to augment144 existing glasses8 outer-layer glasses from Step 4
Steps 4 and 5 performed several timesCompared compositions and predicted
property values (from preliminary models) using dot plots and scatterplot matrices
Selected the set of 8 outer + 27 inner glasses judged best
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Step 6: Add Overall Centroid and Step 6: Add Overall Centroid and Replicates to the Experimental DesignReplicates to the Experimental Design
Step 6: Add Overall Centroid and Step 6: Add Overall Centroid and Replicates to the Experimental DesignReplicates to the Experimental Design
A center point for nonradioactive glasses was formed by averaging the 8 outer-layer and 27 inner-layer glasses4 replicates chosenCenter point3 existing nonradioactive glasses
Replicates chosen to “span” composition as well as property spaces
Radioactive glasses selected within a 21-component (19 + U3O8 + ThO2) glass composition region defined by: inner-layer single-component constraintsmulti-component constraints
5 radioactive glasses (containing U3O8 and ThO2) selected to augment144 existing glass8 + 27 + 5 = 40 new nonradioactive glasses
using JMP no-candidate D-optimal design
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Step 8: Assess the Existing Glasses & Step 8: Assess the Existing Glasses & New Experimental Design GlassesNew Experimental Design Glasses
Step 8: Assess the Existing Glasses & Step 8: Assess the Existing Glasses & New Experimental Design GlassesNew Experimental Design Glasses
Dot plots and scatterplot matrices used to assess 1-D and 2-D projective properties of the existing and new glasses, e.g.
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SummarySummarySummarySummary
Challenging problem to construct a constrained mixture experiment design for studying spinel TL in nuclear waste glass
Separate design portions for nonradioactive glasses (19 components) and radioactive glasses (21 components)Existing data to select and augmentLayered design approach with separate outer- and inner-layer experimental regionsHad to use no-candidate optimal design capability of JMP because problem was too big to use traditional approach of selecting design from candidate points ( Brad)
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Electronic Copy of PaperElectronic Copy of PaperElectronic Copy of PaperElectronic Copy of Paper
If interested in receiving a copy of the paperPiepel, G.F., S.K. Cooley, and B. Jones (2002), “Construction of a 21-Component Layered Mixture Experiment Design”, PNNL-SA-37340, Rev. 0, Pacific Northwest National Laboratory, Richland, WA.
email to [email protected] to receive a PDF electronic copy by return email