What to do when you haven’t got a clue.

1. What to do when you haven’t got a clue. Terry A. Ring Chem. Eng. University of Utah www.che.utah.edu/~ring/Statistically Designed Experiments

2. My First Job Al2O3 Powder Water spray • My First Task • Process that I knew nothing about. • Nodulization • Drying • Sintering • Plant • 3m (0.5m tall) • Pilot Plant • 1m(0.3m tall) Drying Oven Conveyor Belt Shaft Kiln 1800C

3. Process Al2O3 powder • Problem • Control Ball Size • Minimize H2O • Minimize Pore Volume • Low Dust Emissions • 6 mo. to solve problem Water Spray 3 cm Drying Oven Conveyor Belt Shaft Kiln 1800C 2.5 cm

4. Variables Al2O3 powder • Variables • Water flow rate • Concentration of additives • Powder Flow Rate • RPM • Time in Dryer • Temp Dryer • Time in Shaft Kiln • Temp of Shaft Kiln • 6 mo. to solve problem Water Spray 3 cm Drying Oven Conveyor Belt Shaft Kiln 1800C 2.5 cm

5. What to do? • Literature Review on Nodulization • 1 paper • 1 PhD thesis • m(d,t) is the mass of sphere of diameter d • How do I solve this? • What do I do now?

6. Now what do you do? • Get Help • Plant Operator in Baton Rouge, Louisiana • Nothing Useful • Technician that last ran the Pilot Plant • Water flow rate seemed to be critical. • Talk to others at the research site • Idea at lunch to use statistically designed experiments • Consultant gave lecture 2 years ago at site.

7. Statistically Designed Experiments • Save time and money • Find out what variables are important • Tell you if you have all the important variables • Tell you if some variables are not important • Tell you if variable interact • Non-linear effects • Gives a Model for prediction purposes • Allows optimization of the process

8. Used today in • Pharma • Drug Development • Silicon Chip Processing • From Wafers to chips • It is the basis of 6 sigma’s statistical process analysis

9. Traditional Experimentation • Move one variable at a time • Keep other variables constant • No of experiments = LV • V=Variables • L=Levels • Traditional Experimentation • 57=78,125 experiments • 37=2,187 experiments • Need to reduce the number of variables y Response Levels of x2

10. Saves Time and Money • No of experiments = LV • V=Variables • L=Levels • Traditional Experimentation • 53=125 experiments • Statistically Designed Experiments • 23= 8 experiments + 2 (repeats)=10 expts. • 23= 8 experiments x 2 (repeats)=16 expts. • Vary all variables simultaneously then mathematically sort things out yi Response Levels of x2

11. Process for Design of Experiments • Select Variables – RMP, Water Flow, Drying Time, Sintering Time • Select range of to manipulate the variables • Low value (-) sometimes scaled variable -1 • High value (+) sometimes scaled variable +1 • Select Measurements to be made • Ball Diameter, Pore Volume, H2O content, Dust • Run Experiments in a Randomized Order

12. Variables for 23 Design

13. Mathematics • Calculate Effects of each variable on each measurement • Ei=Σyi(+)- Σyi(-) • Prediction Equation • y(x)=E1x1+ E2x2+ E3x3+ … • E1E2x1x2+ E1E3x1x3+ E2E3x2x3+ • E123 x1x2x3 • Generate Response Surface Map • Optimize

14. Response Surface Map

15. Various Software to do this • ** Stat-ease from Stat-ease Inc. • (3 mo free license) • DOE from BBN Software Products • Reliasoft • MiniTab • Statistica from Statsoft • DoE from Camo • Others

16. Why do you do experiments? • Understand how process responds to changes in variables • Develop a mathematical description of the process • Verify a model • Determine various coefficients in the model

17. Physical Model vs DoE model • Physics based Model • Often physics is too difficult to model • Often equations are too difficult to solve • Use of simplified model is all too often occurrence • DoE Model • Little physical significance to Effects in equation • Good only inside box • Minor extrapolation is possible

18. Use Physics to guide variable choice • Suppose you know the physics behind the model • Choose a variable and response that are linearly related. • Suppose we vary temperature and are looking at the output from a bleaching operation • Use 1/T as a variable • Use Cbleach as a variable • Use ln[whiteness] as measured response • This approach will determine the activation energy as the temperature effect and the rate constant as the concentration effect. • The standard errors will be determined giving the error on the activation energy and the rate constant.