Construction of a 21-Component Layered Mixture Experiment Design Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory Bradley Jones,

Construction of aConstruction of a21-Component Layered 21-Component Layered

Mixture Experiment DesignMixture Experiment Design

Construction of aConstruction of a21-Component Layered 21-Component Layered

Mixture Experiment DesignMixture Experiment Design

Greg F. Piepel and Scott K. Cooley Pacific Northwest National Laboratory

Bradley Jones, SAS Institute Inc.

Fall Technical ConferenceValley Forge, PA

October 17-18, 2002

PNNL-SA-37314

2

IntroductionIntroductionIntroductionIntroduction

We discuss the solution to a unique and challenging mixture experiment design problem involving:

19 and 21 components for two different parts of the design

many constraints, single- and multi-component

augmentation of existing dataa layered design developed in stagesa no-candidate-point optimal design

approach

Greg

Brad

3

Mixture ExperimentMixture ExperimentMixture ExperimentMixture Experiment

End product is a mixture of q components, with proportions xi such that

(1)

May have additional constraints

(2)

Experimental region for: (1) a simplex, (2) generally an irregular polyhedron

q

iii xx

11 and 10

ii

q

iiiiii DxACUxL

1 and/or

4

Tried (Tired?) But True Mixture Tried (Tired?) But True Mixture Experiment ExamplesExperiment Examples

Tried (Tired?) But True Mixture Tried (Tired?) But True Mixture Experiment ExamplesExperiment Examples

PiepelCornell

Th U Pu

BAlSi

Sheepshead

Croaker

Mullet

Etc.

5

Waste Glass BackgroundWaste Glass BackgroundWaste Glass BackgroundWaste Glass Background

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)

6

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

explore adequately to support models

7

Layered DesignLayered DesignLayered DesignLayered Design

A layered design (LD) consists of points on:an outer layerone or more inner

layersone or more center

points

May also contain replicates

Inner Layer

Outer Layer

Center

Point

8

Spinel Liquidus TemperatureSpinel Liquidus TemperatureExperimental Design ProblemExperimental Design ProblemSpinel Liquidus TemperatureSpinel Liquidus TemperatureExperimental Design ProblemExperimental Design Problem

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

9

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

10

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

21

1

22

11 and 985.0

i iii XX

015.0 21,...,110 22 XiX i

11

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

12

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

13

Step 3: Assess 144 ExistingStep 3: Assess 144 ExistingData PointsData Points

Step 3: Assess 144 ExistingStep 3: Assess 144 ExistingData PointsData Points

Of the 144 existing glasses: 14 contained U3O8

None contained ThO2

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

14

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

1 where 19 ..., 2, 1, ,19

119

1

ii

ii

ii gi

X

Xg

15

Step 4: Augment 144 Existing Glasses withStep 4: Augment 144 Existing Glasses with8 Outer-Layer Nonradioactive Glasses8 Outer-Layer Nonradioactive Glasses

Step 4: Augment 144 Existing Glasses withStep 4: Augment 144 Existing Glasses with8 Outer-Layer Nonradioactive Glasses8 Outer-Layer Nonradioactive Glasses

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

16

Step 5: Select 27 Inner-LayerStep 5: Select 27 Inner-LayerNonradioactive GlassesNonradioactive Glasses

Step 5: Select 27 Inner-LayerStep 5: Select 27 Inner-LayerNonradioactive GlassesNonradioactive 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

17

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

18

Step 7: Select 5 NewStep 7: Select 5 NewRadioactive GlassesRadioactive GlassesStep 7: Select 5 NewStep 7: Select 5 NewRadioactive GlassesRadioactive Glasses

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

19

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.

20

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)

21

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