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Delve into a journey of experimentation with Al2O3 powder in a chemical process, facing challenges to control variables, minimize pore volume, and optimize the drying and sintering stages. Explore the benefits of statistically designed experiments and how they can efficiently solve complex problems across industries. Learn about selecting variables, conducting experiments, analyzing data, and optimizing processes. Discover how this method saves time, cuts costs, and provides valuable insights for process improvement. Embrace the power of mathematical modeling and response surface mapping to enhance understanding, verification, and optimization of processes.
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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
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
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
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
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?
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.
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
Used today in • Pharma • Drug Development • Silicon Chip Processing • From Wafers to chips • It is the basis of 6 sigma’s statistical process analysis
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
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
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
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
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
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
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
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.
