design of experiments for real world chemical systems
TRANSCRIPT
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Design of Experimentsfor
Real World Chemical Systems
James N Cawse
Cawse and Effect LLC
www.cawseandeffect.com
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Chemistry offers unique challenges.
• Mixtures
• Kinetics• Reactor systems
• Nonlinear relationships• Nonquantitative factors and responses
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Why use Design of Experiments?
• Coverage
• Efficiency
• Signal to Noise
• Interactions
• Mathematical models
[a‐,b‐,c‐] A
C
[a+,b‐,c‐]
[a‐,b+,c‐]B
[a‐,b‐,c+]
BC [a‐,b+,c+] ABC[a+,b+,c+]
AC [a+,b_,c+]
AB[a+,b+,c‐]
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Why use Design of Experiments?
• DOE is great for many scientific disciplines. Because…
• Factors are ordered
• Simple interactions
• Not too many dimensions
• Space is relatively smooth
• Linear models hold!Y = B0 + B1x1 + B2x2 + B12x1x2 + B11x1
2 +…
[a‐,b‐,c‐] A
C
[a+,b‐,c‐]
[a‐,b+,c‐]B
[a‐,b‐,c+]
BC [a‐,b+,c+] ABC[a+,b+,c+]
AC [a+,b_,c+]
AB[a+,b+,c‐]
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Why…?
• DOE is great for many scientific disciplines. Because…
• Factors are ordered
• Simple interactions
• Not too many dimensions
• Space is relatively smooth
• Linear models hold!Y = B0 + B1x1 + B2x2 + B12x1x2 + B11x1
2 +…
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Mixtures
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Mixtures
• Chemists make mixtures of “stuff”• Catalysts• Drugs• Personal care• Other chemicals…
Active Ingredients Citric Acid 1000 mgAspirin 325 mgSodium Bicarbonate 1916 mg
Active Ingredients Sodium Fluoride 0.24%Triclosan 0.30%
Inactive Ingredients water, hydrated silica, glycerin, sorbitol, PVM/MA copolymer, sodium lauryl sulfate, cellulose gum, flavor, sodium hydroxide, carrageenan, propylene glycol, sodium saccharin and titanium dioxide,
EO catalyst Ingredients SilverChlorideSodiumPotassiumCesium…
Black ink composition WO 2016048234 A1A black ink composition for post print and preprint, obtainable by adding (colour concentrate mixture) solid red concentrate, blue concentrate, and green concentrate to a carbon black ink …, and the colour pigments are made up 75‐90% by weight.
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BUT... Real Components may…
• Not range 0 to 100%
• have proportional constraints
• have one component which is a solvent
Extreme VerticesA
B
CC
B
B < 60%
A < 80% C < 75%
C > B
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Mixture Systems may….• have an effect proportional to amount
• be in a system where process variables count
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Mixture Systems may….• have an effect proportional to amount
• be in a system where process variables count
Low
High
Fertilizers or Insecticides
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Catalyst Mixture Study
• Screening: 8 components• B, Fe, Ga, La, Mg, Mn, Mo, and V
• Select in groups of 4 at constant total concentration• e.g. {B, Fe, Ga, La}; {Ga, La, Mg, Mn}; {La, Mg, Mn, Mo}
• Combin(8,4) = 70
• xMixture(4) ≈ 20
• Total runs ≈ 1,400
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Catalyst Study
100% Mg
100% Ga
100% V
100% Mo
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In Design‐Expert:
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Basic Chemistry: Kinetics
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Basic Chemistry
• What is being made?
• Where is the reaction going?
• How fast is it getting there?
• Fundamental kinetics:
• Rate = f(concentrations, temp)
• Order• Rate = k*C1
• Rate = k*C1*C2 …
• Synthesis
• Equilibrium
• Kinetics
Multiplicative, not additive!
Remember: Linear Models!:Y = B0 + B1x1 + B2x2 + B12x1x2 + B11x1
2 +…14
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“Simple” Chemical Kinetics
When do you take your data??
0
0.2
0.4
0.6
0.8
1
0 1 2 3
fraction complete
Reaction time (hrs)
Second Order reaction
0
0.2
0.4
0.6
0.8
1
0 1 2 3
Fraction complete
Reaction Time (hrs)
First Order Reaction
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“Simple” Chemical Kinetics
When do you take your data??
0
0.2
0.4
0.6
0.8
1
0 1 2 3
fraction complete
Reaction time (hrs)
Second Order reaction
0
0.2
0.4
0.6
0.8
1
0 1 2 3
Fraction complete
Reaction Time (hrs)
First Order Reaction
Reaction too fast! Noisy data!
Reaction over! No useful data!
Fraction complete
Time
ABC
Two Stage reactionA B C
What (and when) do you sample?
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Kinetics in a Reactor
• Batch
• Tubular
• Continuously stirred tank
Feed
Product
Cooling JacketFeed Product
Feed
Feed
Product
Product
Cooling Jacket
Cooling Jacket
Flow
Flow
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Nonlinear Reactor kinetics
• Batch
• Tubular
• Continuously stirred tank
190 230 270
Feed Product
Flow
0
0.2
0.4
0.6
0.8
1
0 1 2 3
completion
Time (hrs)
Temperature
Da = reaction rate Flow
Conversion = Da1+ Da
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Tubular Example
• Butyrolactone hydrogenation
H2, catPBT polyester
Reactant
FLOW RATE
Product
Residence time
Completion
Reactant
Mass Transfer
Mass Transfer
Product
Diffusion Zone
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Hard Core Gas‐Solid Kinetics
• Langmuir‐Hinshelwood Equation
• Standard linear regression hopeless interactions
• Better bet: modified exponential model regression• Ln(rate) = f(ln PA, lnPb, ln PA* lnPb…)
A
BAB
Catalyst particle
krKA
KB
Rate(A + B ‐> AB) =kr KA KB PA PB
(1+ KA PA + KB PB )
… Jean Cropley
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Basic Chemistry: Catalysis
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Catalyst Chemistry: Increasing Complexity and Decreasing Returns
• Ethylene Oxide Reaction
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Ethylene Oxide: Chemistry and History
U.S Patent April 10, 1990 4,916,243
1980’s: Silver, Potassium, Cesium%K
%Cs
Two‐factor interaction
1940 1950 1960 1970 1980 1990 2000 2010 2020
Catalyst Selectivity100
90
80
70
60 Ag
Theoretical limit?
+Na
+Cl
+Na/K+Mn… +Mn+1…+Re
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2016: High Level Interactions
• Modeling five cocatalysts!!• All main effects
• 7 of 10 2‐way interactions• But…
Term t Ratio Prob>|t|
Intercept 94.33 <.0001*
M1(M2) 3.25 0.0030*
M2 4.71 <.0001*
M3 0.61 0.5484
M4 9.71 <.0001*
M5 ‐9.4 <.0001*
(M1)*(M3) ‐7.73 <.0001*
(M1)*(M4) 7.73 <.0001*
(M1)*(M5) ‐11.94 <.0001*
(M2)*(M3) ‐2.56 0.0163*
(M2)*(M5) ‐1.61 0.1182
(M3)*(M4) ‐3.13 0.0041*
(M3)*(M5) 9.19 <.0001*
M1 M1*M3
M3 M3*M5 M1*M3*M5
M5 M5*M1
(M1)*(M3)*(M5) 7.48 <.0001*
(M2)*(M3)*(M5) 9.27 <.0001*
(M1)*(M1) 3.59 0.0013*
(M3)*(M3) 3.23 0.0032*Ignore 3‐way interactions….!!??
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It gets worse…The Law of diminishing returns
• As you get closer to the theoretical limit – any improvement disappears in the noise!
Remaining improvement!
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Multistep Reactor Study
• New Zeolites:
• Every vessel is a reactor... and an experiment!
Mix
Zeolite sub‐typeBinder type
Exchange
TimeTemperatureNo. of exchanges
Calcination
Order
Steaming
Mix
Zeolite
Binder
Exchange
Temperature
No. Exchan
ges
Order Calcination Steaming
Loss of Information!
Measurement
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Nested Design
Mix
Zeolite sub‐typeBinder type
TimeTemperatureNo. of exchanges
Order
Z1B1 Z1B2 Z2B1 Z2B2
Temp
No. Exc
Temp
No. Exc
Temp
No. Exc
Temp
No. Exc ….
….
4 runs x 4 runs x 2 runs = 32 Run Experiment
Exchange
Calcine
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Basic ChemistryQualitative vs. Quantitative
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Numbers = Continuous Factors
• Soap side chains
• What’s wrong here?• This is not a continuous factor!• These are distinct compounds – hence qualitative!
• In Design‐Expert: “Discrete Numeric”
/
CH2‐CH2‐CH3 CH2‐(CH2)3‐CH3 CH2‐(CH2)5‐CH3 CH2‐(CH2)7‐CH3
Factor (units) Type(qualitative, quantitative, formulation)
Normal level & range
Measurement precision & setting error
Proposed settings Ease of Adjust.
Chain Length Quantitative 3, 5, 7, 9
Control Factors
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Osha.gov
Complex Natural Products
Gasoline
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Factors from “natural”Mixtures• Petroleum impurities problem
• Sample and model an experimental space in two chemical factors using blends of existing oils. All oils must be used!• Oils are clustered at low levels
• Spread out at high levels
0.00
1.00
2.00
3.00
4.00
5.00
0.00 1.00 2.00 3.00 4.00 5.00 0.01
0.10
1.00
10.00
0.01 0.10 1.00 10.00Impurity 1
Impurity 2
1. Transform to a log scale!2. Fit a RSM design3. Perform an iterative search for blends
Impurity 1
Impurity 2
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MoralBeware force fitting chemistry
into a statistical box!
• In Chemistry:
3+ factor interactions
Nonlinear models
Reactor dependence
Natural product factors
A B
C
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