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Construction of a 21-Component Layered Mixture Experiment Design

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## Construction of a 21-Component Layered Mixture Experiment Design

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### Construction of a21-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

- 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 data
- a layered design developed in stages
- a no-candidate-point optimal design approach

Greg

Brad

2

Mixture 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

3

Tried (Tired?) But True Mixture Experiment Examples

Pu

Th

U

Sheepshead

Croaker

Mullet

Etc.

Si

B

Al

Waste Glass

Piepel

Cornell

Fish Patties

4

Waste 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) and

low-activity waste (LAW) fractions, and separately vitrified (i.e., made into waste glass)

5

Experimental Design for GlassProperty-Composition Models

- Need data to support fitting glass property-composition models (used for many things)
- Use mixture experiment designs that cover the constrained experimental regions
- Want 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

6

Layered Design

- A layered design (LD) consists of points on:
- an outer layer
- one or more inner layers
- one or more center points
- May also contain replicates

Outer Layer

Center

Point

Inner Layer

7

Spinel Liquidus TemperatureExperimental 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 glasses

- Spinel (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

8

Overview of Experiment Design Approach for Spinel TL 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

9

Step 1: Define the HLW Glass Composition 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

10

Step 1: Define the ExperimentalRegion (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

11

Step 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 1
- Expanded 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

12

Step 3: Assess 144 ExistingData 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

13

Conversion to 19 Components for Nonradioactive 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

14

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

- Initially tried generating the outer-layer vertices with the goal of selecting a subset using traditional candidate-point optimal design
- However, too many vertices to generate
- Ideas for generating a “random” subset of vertices to select from were unsuccessful
- JMP 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

15

Step 5: Select 27 Inner-LayerNonradioactive Glasses

- Again used JMP no-candidate D-optimal design capability to select 27 inner-layer nonradioactive glasses to augment
- 144 existing glasses
- 8 outer-layer glasses from Step 4
- Steps 4 and 5 performed several times
- Compared 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

16

Step 6: Add Overall Centroid and Replicates to the Experimental Design

- A center point for nonradioactive glasses was formed by averaging the 8 outer-layer and 27 inner-layer glasses
- 4 replicates chosen
- Center point
- 3 existing nonradioactive glasses
- Replicates chosen to “span” composition as well as property spaces

17

Step 7: Select 5 NewRadioactive Glasses

- Radioactive glasses selected within a 21-component (19 + U3O8 + ThO2) glass composition region defined by:
- inner-layer single-component constraints
- multi-component constraints
- 5 radioactive glasses (containing U3O8 and ThO2) selected to augment
- 144 existing glass
- 8 + 27 + 5 = 40 new nonradioactive glasses

using JMP no-candidate D-optimal design

18

Step 8: Assess the Existing Glasses & New 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.

19

Summary

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 augment
- Layered design approach with separate outer- and inner-layer experimental regions
- Had 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)

20

Electronic Copy of Paper

- If interested in receiving a copy of the paper

Piepel, 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 greg.piepel@pnl.gov to receive a PDF electronic copy by return email

21

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