Download Design of Experiments or What to do when you donot have a clue

What to do when you don’t have a
clue.
Terry A. Ring
Chemical Engineering
University of Utah
First Job
• MS ChE at UC Berkeley, BS ChE Clarkson
– Well Educated in traditional unit operations
• 1st Project Develop Mass and Energy Balance
for Alumina from clay Acid Leach process
using a computer before ASPEN exists
• 2nd Project Al2O3 Nodules
Shaft
Kiln
1800C
Dryer
200C
Hot
Hot Gas
2nd Project
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Rotating Pan Nodulizer for Al2O3
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Control Pellet Size
Minimize Dust Generated
Minimize water Used
Minimize additives Used
Minimize Pore Volume
Process Variables
– Pan (1 m pilot, 5 m plant)
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RPM of Pan
Pan Angle
Spray Configuration
Alumina feed point
Ratio of Alumina to water fed
– Conveyor Dryer
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Drying Temperature
Airflow
– Shaft Kiln
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Sintering Temperature
Holding Time
Project finished in 6 mo.
Project 3
• Found Synergism between additives
– Decreased time/energy needed to sinter by ½
– Lowered Operating costs to produce
• US Patent 4,045,234 “Process For Producing High
Density Sintered Alumina”
• $1 million (1974 $s) in fuel savings
($4.83 million 2013 $s)
• How much was I paid for this work?
Getting Started
• Call Plant and Talk to Engineer
– Did not really know much
– Relies on Operator to run Pan Nodulizer
• Call Plant and Talk to Operator
– Everything controls Everything
• Call Technician who rate the Pilot Plant
– Water and pan angle and RPM control nodule size
• Literature Search
– 1 paper - P. Somasundaran and D. Feustenau
– 1 PhD thesis - P. Somasundaran and D. Feustenau
Fm (x,t) – Cumulative Mass Distribution
P. Somasundaran and D. Feustenau
Fm ( x, t )

t

a ( s, u )
 x Fm (u , t )  x Fm ( s, t )
s  0 u  x  s
u
with boundary conditions
 1 (t ) 
x
Fm ( x, t )  0
at
x  0,
Fm ( x, t )  1 at
and initial condition
Fm ( x, t )  Fm ,o ( x)
at
t 0
Agglomeration
x
What to do?
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Short Time for the Project – 6 months
No ChE Background that is useful!
No literature that is useful!
No people to help!
• So complain at lunch to fellow employees
Design of Experiments
• Lunch Companion
– I think you might try statistically designed
experiments or design of experiments
– We had a consultant come to talk about this two
years before you joined the company.
– I do not know much about what the consultant
said.
• Corporate Librarian Saved Me
Other Names
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Statistically Designed Experiments
Design of Experiments
Factorial Design of Experiments
ANOVA
– Analysis of variance : A mathematical process for
separating the variability of a group of
observations into assignable causes and setting up
various significance tests.
Comparison I
Design of Experiments
Traditional Experimentation
• Tests
– Theory
– Correlation
• Develop a new
– Theory
– Correlation
• End up with a mathematical
understanding of
experimental results based
on process variables
Comparison I
Design of Experiments
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Determines if Process Variables are
important (significant )
– compared to experimental errors
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Develops a mathematical
relationship for experimental
results based upon process
variables
– No Theory is developed or tested
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Allows Predictions of Results for all
process variables within ranges
used in experimentation
Allows Process Optimizations
Understand the requirements on
processing conditions needed to
meet production specifications
Traditional Experimentation
• Tests Theory
• Develop a new Theory
• End up with a mathematical
understanding of
experimental results
How is this approach different?
Design of Experiments
Traditional Experimentation
• Do a series of experiments
changing one variable at a
time
• 5 Process Variables (PV)
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RPM of Pan
Pan Angle
Spray Configuration
Alumina feed point
Ratio of Alumina to water fed
• 4 different values for PV
• Number of Experiments
– 5^4= 625 experiments
– 2 experiments/day ~ 1 yr work
How is this approach different?
Design of Experiments
Traditional Experimentation
• Do a series of experiments
changing all variables at the same
time
• 5 Process Variables (PV)
• Do a series of experiments
changing one variable at a
time
• 5 Process Variables (PV)
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RPM of Pan
Pan Angle
Spray Configuration
Alumina feed point
Ratio of Alumina to water fed
• 2 levels for PV plus multiples of
center point
• Number of Experiments
– 25+1= 64 experiments
– 2 experiments/day ~ 1 month work
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RPM of Pan
Pan Angle
Spray Configuration
Alumina feed point
Ratio of Alumina to water fed
• 4 different values for PV
• Number of Experiments
– 54= 625 experiments
– 2 experiments/day ~ 1 yr work
Different
Nomenclature
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Effects of PVs
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Process Variables
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Scaled PVs ( -1 to +1)
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original X value and converts to (X − a)/b, where a = (Xh + XL)/2 and b = (Xh−XL)/2
Effect Ei = [Σ Ri (+) – Σ Ri (-) ]/N
Responses, R’s
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RPM of Pan
Pan Angle
Spray Configuration
Alumina feed point
Ratio of Alumina to water fed
Diameter of Nodules
Water Content of Nodules
Pore Volume
Dust in Dryer
Sintering Temperature
Variance (StDEV2)
Software
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Stat-ease, MiniTab
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Response Surface
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Ri = E1 X1 + E2 X2 + E3 X3+ …
+E11 X12 + E22 X22 + E33 X32 + …
+E12 X1 X2 + E13 X1 X3 + E23 X2 X3 + …
+E123 X1 X2 X3
Response Surface Map
Bleaching Cotton
• Effects (PVs)
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% NaOH
%H2O2
Temp
Time
• Responses
– Reflectance
– Fluidity
• > 6 to be useful
Steps for DOE
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Identify process variables
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Identify the range for each process variable
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Often more PVs than you initially think are important
High
Low
Scale Process Variables
Set up experimental matrix
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Randomize Experiments
Identify Responses to be measured for each process variable
Run Experiments
Analyze Experimental results using ANOVA
Compare responses to experimental uncertainty (F-test)
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(+,-,-), (+,+,-),(+,-,+), (+,+,+)
Remove insignificant process variables
Calculate Response mathematics Ri = E1 X1 + E2 X2 + E3 X3+ … +E11 X12 + E22 X22 + E33 X32 + …
+E12 X1 X2 + E13 X1 X3 + E23 X2 X3 + … +E123 X1 X2 X3
Use for Process Optimization
Use for 6-sigma
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Identify the range that a PV can vary and keep product within specification
Nodulizer Results
• Nodule Diameter
– Important Effects (in order of importance)
• Water to alumina ratio
• RPM
• Pan angle
• Dust Production
– Important Effects (in order of importance)
• Water to alumina ratio
• Additive concentration
• RPM
Results
• Sintered Density
– Important Effects
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Sintering Time
Pan RPM
Water to alumina ratio
Additives
• Water Control is Critical
• IR water sensor and control system story