Process Optimization Using Statistical Methods

Process Optimization Using Statistical Methods

Prof. Attilio Citterio

Dipartimento CMIC “Giulio Natta”

http://iscamap.chem.polimi.it/citterio/dottorato//

PhD

IN INDUSTRIAL CHEMISTRY AND

CHEMICAL ENGINEERING (CII)

Correlation Effect Temperature & pH

0 Temperature (°C) 100

Y ield (%)

100

pH 10

pH 7

Efficiency in Research Development and

Production:

The Statistical Design and Analysis of Chemical Experiments

Leslie Davies

Department of Chemistry and Applied Chemistry,

University of Salford

ROYAL SOCIETY OF CHEMISTRY

Some Difficult Decisions

Design and

Optimisation in Organic Synthesis Rolf Carlson

Department of Organic Chemistry, Umea University, S-901 37 Umea, Sweden

ELSEVIER 1992

EXAMPLE

• Reaction is thought to depend on 3 variables - Temperature (T)

- Concentration (C) - Catalyst (K)

• Set an initial range for each variable:

- Temperature 160-180°C - Concentration 20-40%

- Catalyst A or B

Factorial Design

Data from a 2

Factorial Design

a) Original units of variables

Test Condition

Number

Temperature (°C)

T

Concentration (%)

C

Catalyst (A or B)

K

Yield (grams)

y

1 160 20 A 60

2 180 20 A 72

3 160 40 A 54

4 180 40 A 68

5 160 20 B 52

6 160 20 B 83

7 160 40 B 45

8 180 40 B 80

b) Coded units of variables

Test Condition

Number

Temperature (°C)

T

Concentration (%)

C

Catalyst (A or B)

K

Yield (grams)

y

1 - - - 60

2 + - - 72

3 - + - 54

4 + + - 68

5 - - + 52

6 + - + 83

7 - + + 45

8 + + + 80

Data from a 23 Factorial Design

Effect of Temperature Change

Condition at which Comparison is made Individual measure of the effect of Concentration Catalyst

Changing concetration from 20 to 40 C K

y

– y

= 72 - 60 = 12 20 A

y

– y

= 68 - 54 = 14 40 A

y

– y

= 83 – 52 = 31 20 B

y

– y

= 80 - 45 = 35 40 B

Main effect of concentration C = 23

Effect of Concentration Change

Condition at which Comparison is made Individual measure of the effect of Temperature Catalyst Changing temperature from 160 to 180°C T K

y

– y

= 54 - 60 = -6 160 A

y

– y

= 68 - 72 = -4 180 A

y

– y

= 45 – 52 = -7 160 B

y

– y

= 80 - 83 = -3 180 B

Main effect of temperature T = -5

Effect of Catalyst Change

Condition at which Comparison is made Individual measure of the effect of Temperature Conc Changing from catalyst A to catalyst B T C

y

– y

= 52 - 60 = -8 160 20

y

– y

= 83 - 72 = 11 180 20

y

– y

= 45 – 54 = -9 160 40

y

– y

= 80 - 68 = 12 180 40

Main effect of catalyst K = 1.5

b) Coded units of variables

Test Condition

Number

Temperature (°C)

T

Concentration (%)

C

Catalyst (A or B)

K

Yield (grams)

y

1 - - - 60

2 + - - 72

3 - + - 54

4 + + - 68

5 - - + 52

6 + - + 83

7 - + + 45

8 + + + 80

Calculation of Interaction Effects

Average

Concentration Temperature effect

(+) B -5.0 C × K interaction = 0/2 = 0

(-) A -5.0

difference 0.0 Average

Concentration Temperature effect

(+) 40% 24.5 T × C interaction = 3/2 = 1.5

(-) 20% 21.5

difference 3.0

Average

Catalyst Temperature effect

(+) B 33 T × K interaction = 20/2 = 10

(-) A 13

difference 20

Interaction Effects

Effect Estimate +/- standard error Average 64.25 ± 0.7 *

Main effects

Temperature T 23.0 ± 1.4 * Concentration C -5.0 ± 1.4 * Catalyst K 1.5 ± 1.4 Two-factor interactions

T × C 1.5 ± 1.4 T × K 10 ± 1.4 * C × K 0.0 ± 1.4 Three-factor interactions

T × C × K 0.5 ± 1.4

Estimated Effects

• Effect of concentration is to reduce yield by ca. 5 units, regardless of other variables

• Effects of temperature and catalyst cannot be interpreted separately - large T × K interaction

- Difference in sensitivity to temperature change for each catalyst - Catalyst A : 13 units; catalyst B : 33 units

• Catalysts obtained from different suppliers, but were supposed identical

• Yield from catalyst B at 180°C highest so far seen

• Careful study of catalyst in further iterations

Conclusions

A + B + C D + other products Solvent E

• Object - Maximize yield of D with respect to A

• Known conditions give ca. 45% yield

• Reactions of this type should give ca. 75%

• Experimental error < 1%

• Five factors varied

- Amount of solvent E x

- Amount of C x

- Concentration of C x

- Reaction time x

O.L. Davies, “The design and Analysis of Industrial Experiments”, 2^nd Edn, Longmans, London, 1979

Example of Steepest Ascent

Factor Levels for 1

Experiment

Factor ----Factor

- 1

Level----

+ 1

X

Amount of solvent E (ml) 200 250

X

Amount of C (mol/mol A) 4.0 4.5

X

Concentration of C (%) 90 93

X

Reaction time (hours) 1 2

X

Amount of B (mol/mol A) 3 3.5

Selection of Initial Trials

• Full factorial requires 2

(32) trials

• Analysis will give 32 parameters

- Average yield (1)

- Main effects (5)

- 2-variable interactions (10) - 3-variable interactions (10) - 4-variable interaction (5) - 5-variable interaction (1)

• Many effects will be insignificant

• Should be able to get important information from fewer

trials

Trial Factor level Yield (%)

X

X

X

X

X

y

1 - 1 - 1 - 1 - 1 - 1 34.4

2 - 1 - 1 - 1 1 1 51.6

3 - 1 1 - 1 1 1 31.2

4 - 1 1 1 - 1 - 1 45.1

5 1 - 1 - 1 1 - 1 54.1

6 1 - 1 1 - 1 1 62.4

7 1 1 - 1 - 1 1 50.2

8 1 1 1 1 - 1 58.6

Fractional Factorial Design - First

Experiment

Calculation of Parameters - (1)

b

48.5 β

−β

−β

−β

b

7.9 β

−β

β

−β

b

-2.2 β

−β

β

−β

b

6.0 β

−β

β

−β

b

0.4 β

−β

β

−β

b

0.4 β

−β

−β

β

b

-1.8 β

β

−β

−β

b

0.2 β

β

−β

−β

Real para- meters

Estimated parameters

Path of Steepest Ascent

x

(ml)

x

(mol)

x

(%)

x

(hr)

x

(mol)

Yield (%)

6 Path of steepest ascent

represented by a series of possible trials on it

225 4.25 91.5 1.5 3.25 235 4.22 92.0 1.5 3.25 245 4.19 92.4 1.5 3.26 255 4.17 92.9 1.5 3.26 265 4.14 93.3 1.5 3.27

Trial (9) 275 4.11 93.8 1.6 3.27 80 285 4.08 94.2 1.6 3.28

Trial (10) 275 4.06 94.7 1.6 3.28 79.4

395 4.03 95.1 1.6 3.29

Factor ----Factor - 1

Level----

+ 1

X

Amount of solvent E (ml) 280 310

X

Amount of C (mol/mol A) 3.85 4.15

X

Concentration of C (%) 94 96

X

Reaction time (hours) 2 4

X

Amount of B (mol/mol A) 3.5 5.5

Factor Levels for 2

Experiment

Trial Factor level Yield (%)

X

X

X

X

X

y

11 - 1 - 1 - 1 - 1 1 77.1

12 - 1 - 1 1 1 1 69.0

13 - 1 1 - 1 1 - 1 75.5

14 - 1 1 1 - 1 - 1 72.6

15 1 - 1 - 1 1 - 1 67.9

16 1 - 1 1 - 1 - 1 68.4

17 1 1 - 1 - 1 1 71.5

18 1 1 1 1 1 63.4

Second Experiment

b

+ β

(+ β

+ β

+ β

+ β

+ β

) = 70.7 b

+ β

(+ β

) = -2.9

b

+ β

(+ β

) = 0.1

b

+ β

(+ β

) = -2.3

b

+ β

(+ β

) = -1.7

b

+ β

(+ β

+ β

) = -0.4 b

0 (+ β

+ β

) = 0.4 b

0 (+ β

+ β

) = -0.4

Calculation of Parameters

Enamine synthesis

R. Carlson, L. Hansson & T. Lundstedt, Acfa. Chem. Stand., 1986 (40), 444-452

Works well for most ketones

Self-condensation with hindered ketones

Carlson’s philosophy: Optimise reaction BEFORE searching for new reagents

Design for Competing Reactions

O

HN O

N

O O

heat

+

TiCl

Response Surface Design

Variables Levels

-1.414 -1 0 1 1.414 x

: Ratio morpho-

line/chetone (mol/mol)

3.00 3.59 5.00 6.41 7.00

x

: Ratio TiCl

/chetone (mol/mol)

0.50 0.57 0.75 0.93 1.00

x

: Temperature (°C) 60 60 80 100 108

Entry X₁ X₂ X₃ Y₁ Y₂

1 -1 -1 -1 41.6 14.6

2 1 -1 -1 45.1 6.7

3 -1 1 -1 51.7 26.2

4 1 1 -1 64.7 17.7

5 -1 -1 1 47.8 11.9

6 1 -1 1 57.1 17.5

7 -1 1 1 63.6 26.1

8 1 1 1 77.8 11.0

9 1.414 0 0 66.7 8.1

10 -1.414 0 0 49.5 22.2

11 0 1.414 0 70.4 18.9

12 0 -1.414 0 43.9 80.0

13 0 0 1.414 66.4 9.0

14 0 0 -1.414 52.4 17.3

15 0 0 0 56.5 13.6

16 0 0 0 60.0 12.3

17 0 0 0 56.6 12.6

18 0 0 0 57.2 13.6

Response Surface Design - Results

Ratio Molpholine/ketone

(3) (5) (7)

0

-1 1 2

-2

20

30

40

40 50 60 70 80

10

Yield of enamine

Yield of

by-products

Isocontour Projection

purified by batch distillation to remove various by-products

Factorial Design in a Continuous Process

N O

Et

HS NHCOEt

N HN

OH

N HN

S

NHCOEt O N

Et

NHCOEt

RO S NHCOEt

By-products H

S, 180-220°C

BMEP

BMEP

R

Factorial Design in a Continuous Process

• Because process continuous, experiment had to be run on plant

• Factors varied - Flow rates

- Temperatures at various sections of reactor - Length of reactor

• Optimised for yield and quality

- Complex because some impurities react in 2nd step to give correct product

• Yield increased from 85% to 91% in 1 week

x

(ml)

x

(mol)

x

(%)

x

(hr)

x

(mol)

Yield (%) 295 4.0 95.0 3.0 4.5

Trial (19) 285 4.0 94.5 2.6 4.4 80.8 275 4.0 93.9 2.2 4.3

Trial (20) 265 4.0 93.4 1.8 4.2 84.0 Trial (21) 255 4.0 92.8 1.4 4.1 81.5

Path of Steepest Ascent -

2nd Experiment

Ratio Molpholine/ketone

(3) (5) (7)

0

-1 1 2

-2 -1 0 1 2

20 50

60 70

10

Yield of enamine

Yield of

by-products

Isocontour Projection

Temperature

Ratio TiCl

/ketone (52)

(80) (108)

0

-1 1 2

-2

(0.5) (1.0)

-1 0 1 2

20 40

50 60 70 80

10

Yield of enamine

Yield of

by-products

0

Isocontour Projection

Preparative Scale Run

 To 1L 3-neck flask, Herschberg stirrer, condenser, dropping funnel, cooled in ice-bath

 180 ml (2.05 mol, 10 eq.) morpholine added in 220 ml petr. ether

 22.5 ml (0.206 mol, 1 eq.) TiCI

in 80 ml pet ether added over 10 min with vigorous stirring

 Heated to reflux (ca. 120°C)

 20.09 (0.20 mol, 1 eq.) MTBK in 80 ml petr. ether added rapidly

 Refluxed one hour; mixture became very thick

 100 ml petr. ether added to help agitation

 Mixture cooled, filtered through sintered glass

 Solvent & excess morpholine removed under reduced pressure

 Crude product fractionated over 25 cm Vigreux column

 Yield 28.9 g enamine (85%) at 70-71°C/8 mmHg

Two Pats for OVAT Optimization

20 40 60 80 100

Conc. (g/g)

20 40 60 80 100

Temperature °C 40 60 Path 1 80

Path 2

50 70 90

Number of factors

k

Treatment Three-level

factorials 3

Combinations Composite

2

+ 2k + 1

2 9 9

3 27 15

4 81 25

5 243 43

5 81 (1/3 fraction) 27 (1/2 fraction)

6 729 (1/3 fraction) 77

6 243 (1/3 fraction) 45 (1/2 fraction)

Experiments Required for 3k Factorial

& Central Composite Designs

Star points &

centre points

(-1,1,1) (1,1,1)

Factorial points

(1,1,-1)

(1,-1,-1)

(s,0,0)

(0,-s,0) (0.0,-s)

(0,s,0)

A B C

Central Composite Design

3 (desired product)

Case Study - X-ray Contrast Agent

N O OH O

I

HN OH

OH

O O

O

O I HN

O

I

HN OH

OH

O I

HO

OH

O I

OH HO

O

N O OH O

I N

HO

OH OH

O

O HO

OH

O

I N

O OH O

I

HN OH

O O

OH

O HO

OH

O I MeOH

NaOH CaCl₂

+ etc.

+

I

I I

 Determine which variables influence yield

 Determine which variables influence selectivity

 Increase yield (Y

) to > 95%

 Decrease total by-products (Y

) to < 2.5%

 Find optimum conditions

Objectives

Response Surface Design

Variables Levels

-2 -1 0 1 2

x

: equiv. NaOH 1.15 1.30 1.45 1.60 1.75

x

: equiv. CaCl

0.45 0.80 1.15 1.40 1.85

x

: Temperature (°C) 17.5 25.0 32.5 40.0 47.5

x

: subs. conc (g/ml) 0.65 1.00 1.35 1.70 2.05

x

: equiv. reagent 1.25 1.40 1.55 1.70 1.85

Entry X₁ X₂ X₃ X₄ X₅ Y₁ Y₂

NaOH CaCl₂ Temp. Substrate Reagent (3) (by-products)

1 -1 -1 -1 -1 1 81.3 1.39

2 1 -1 -1 -1 -1 90.8 1.49

3 -1 1 -1 -1 -1 89.3 2.24

4 1 1 -1 -1 1 94.1 3.62

5 -1 -1 1 -1 -1 87.9 2.42

6 1 -1 1 -1 1 93.9 3.21

7 -1 1 1 -1 1 90.9 2.21

8 1 1 1 -1 -1 93.4 4.41

9 -1 -1 -1 1 -1 66.2 1.58

10 1 -1 -1 1 1 83.9 2.02

11 -1 1 -1 1 1 85.8 1.43

12 1 1 -1 1 -1 90.0 2.30

13 -1 -1 1 1 1 58.0 1.29

14 1 -1 1 1 -1 89.8 4.06

15 -1 1 1 1 -1 89.8 2.23

16 1 1 1 1 1 93.6 3.41

Response Surface Experiments & Results - (1)

Entry X₁ X₂ X₃ X₄ X₅ Y₁ Y₂

NaOH CaCl₂ Temp. Substrate Reagent (3) (by-products)

17 -2 0 0 0 0 73.4 1.12

18 2 0 0 0 0 91.1 3.27

19 0 -2 0 0 0 59.2 1.26

20 0 2 0 0 0 92.7 2.59

21 0 0 -2 0 0 79.8 0.96

22 0 0 2 0 0 94.0 3.36

23 0 0 0 -2 0 91.2 2.53

24 0 0 0 2 0 83.1 1.39

25 0 0 0 0 -2 90.0 2.73

26 0 0 0 0 2 86.1 1.59

27 0 0 0 0 0 88.7 2.43

28 0 0 0 0 0 89.8 2.57

29 0 0 0 0 0 90.4 2.49

30 0 0 0 0 0 88.8 3.48

Response Surface Experiments &

Results performed in random order - (2)

Y

Y

Average 88.21 2.40

Linear effects x

(NaOH) -4.87 +0.75 x

(CaCl

) +5.86 - x

(temp) - +0.50 x

(Substrate) -3.41 -0.21 x

(Reagent) - - Interactions x

x

-3.02 - x

x

+2.89 - x

x

- +0.32 x

x

-2.00 - Quadratic

Effects x

x

-2.75 -

Response Surface Analysis -

Significant Effects

Temperature (C) = 32.50 Substrate (g/ml) = 1.350 alkyl agent = 1.550

P r o d u c t

Ca Cl

(e q )

1.2 1.4 1.6

1.0 1.5

0.5

90

95

Example of Contour Plot - Product

Temperature (C) = 32.50 Substrate (g/ml) = 1.350 alkyl agent = 1.70

Ca Cl

(e q )

NaOH (eq)

1.2 1.4 1.6

1.0 1.5

0.5

3

2

1

0

Example of Contour Plot - Product

Optimum Conditions

• NaOH 1.70 equiv.

• CaCl

1.40 equiv.

• Temperature 10°C

• Substrate 0.91 g/ml

• Reagent 1.60 equiv.

• Yield of product (calcd) 99.2%

• Yield of product (obs) 96.8%

• By-products (calcd) 2.49%

• By-products (obs) 2.31%

Temperature (C) = 10.00 Substrate (g/ml) = 0.910 alkyl agent = 1.600

P r o d u c t

Ca Cl

(e q )

NaOH (eq)

1.2 1.4 1.6

1.0 1.5

0.5

90

95

100

Chosen conditions

Response Surface Around Chosen

Conditions

Temperature (C) = 10.00 Substrate (g/ml) = 0.910 alkyl agent = 1.600

B y - p r o d u c t s

Ca Cl

(e q )

1.2 1.4 1.6

1.0 1.5

0.5

90

100

Chosen conditions

Response Surface Around Chosen

Conditions

NaOH (eq) = 1.700 CaCl

(eq) = 1.400 alkyl ag. = 1.600 P r o d u c t

S ub s tr a te ( g/ ml )

Temperature (°C)

10 20 30

1.2 1.5

0.9

95 96

Chosen conditions 1.8

+

97 98

99.5

Response Surface Around Chosen

Conditions

Evolutionary Operations

 IS the process operating under OPTIMUM conditions?

• production processes

• continuous or batch (large number of batches)

 DELIBERATE programme of replacing the STATIC operation of a plant by CONTINUAL PROCESS MODIFICATION

 LEADS EVENTUALLY TO IMPROVED

PROCESS

Optimize on: Time 19-31 h Responses: % Product

temp 10-30°C % SM

Stoichiom 1-1.68 moles % By-products

conc. 3-7 vol. of solvent

impurity

%

time lactone

Starting material

product

Silyl Group Hydrolysis

Et₃N×3HF O N

R

OSiMe₂Bu^t

R₁

O N R

OSiMe₂Bu^t

R₁ HN

O O

R OH

R₁

NMP +

Product

Impurity Time

86% 89%

92%

95%

92%

Time

34 1 2

0.5

Temp Temp

Temp

SM

After optimization 94.2% yield 1.9% impurity Solvent 3.5 vol

TEA•HF 1.18 Time 23 h Temp 10°C

Analysis

20

40 60

80

60

40

A B 20

C

Temperature Concentration

Simplex

20

40 60

80

60

40

A B 20

C Concentration

D F E

G H

Simplex (2)

F. L. Chubb, J.T. Edward & S.C. Wong J.Org. Chem. 1980, 45, 2315-2320

Bucherer-Bergs Reaction

OH

C N O

NH₃

NH

HCN

C N N

O SH H

C N

OH NH₃

S N H

O

N H

NH N

H

O

N H NH₃

NH₂ S

N C O

NH N

H

O

S

Yield in Bucherer-Bergs Reaction

Experiment N° 1 2 3 4 5 6 7

Solvent (% EtOH) 50 75 50 50 50 50 50

[NH

] 4 4 6 4 4 4 4

[COS] 2 2 2 1 2 2 2

[HCN] 2 2 2 2 4 2 2

Temperature (°C) 53 53 53 53 53 43 53

Time (hr) 4 4 4 4 4 4 2

Yield (%) 49 69 57 31 32 36 59

Calculation of Next Vertex

Variable 1 2 3 4 5 6

(i) Sum of values (excluding rejected)

325 26 12 14 308 22

(ii) Centroid of retained levels = sum/n*

54.16 4.33 2 2.33 51.33 3.67 (iii) Rejected vertex

50 4 1 2 53 4

(iv) Displacement = (ii)-(iii)

4.16 0.33 1 0.33 -1.67 -0.33 (vi) New vertex (8) = (ii) + (iv)

58.32 4.66 3 2.66 49.84 3.34

Second Simplex

Experiment N° 1 2 3 4 5 6 7 8

Solvent (% EtOH) 50 75 50 50 50 50 50 58

[NH

] 4 4 6 4 4 4 4 4.7

[COS] 2 2 2 1 2 2 2 3

[HCN] 2 2 2 2 4 2 2 2.7

Temperature (°C) 53 53 53 53 53 43 53 50

Time (hr) 4 4 4 4 4 4 2 3.3

Yield (%) 49 69 57 31 32 36 59 65

Progress of Simplex

30 50 70 90

5 10 15 20

Experiment N°

Y ield (%)

Initial trials

Subsequent

Bucherer-Bergs Reaction - Conclusions

 Effect of [C] on yield

- Organic chemist’s instinct is to increase concentration to improve yield

- Simplex shows this would not be effective

 Reaction time

- Increasing reaction time gives lower yield

- Despite unreacted cyanohydrin and ammonia

- Degradation to imino compound?

C E

E

E

B A D

Modified Simplex Method

 Reflected point gives best response

- Move further in same direction - E

 Reflected point worse than all retained points

- Move a little in reverse direction - E

 Reflected point worse even than discarded point

- Move back towards discarded point - E

Calculation of Next Vertex

A B C D E F G

(i) Sum of levels (excluding rejected)

36 195 766 470 2.7 10,000 465

(ii) Centroid of retained levels = sum/n*

5.14 27.9 109 67.1 0.386 1430 66.4 (iii) Rejected vertex

4 45 122 50 0.5 1200 55

(iv) Displacement = (ii)-(iii)

1.14 -17.1 -13.0 17.1 -0.114 230 11.4 (vi) New vertex (8) = (ii) + (iv)

6.28 10.8 96 84.2 0.272 1600 77.8

Case Study - Boots (UK)

 Example

A +B +C product A+B by-product B is expensive

 Object - to reduce cast without jeopardising quality

 Current operating conditions

- Solvent 7500 kg

- Reagent C 1 equivalent

- Quality < 0.8% residual C - Cost £3.10 per kilo

 Experimental design

- 16 experiments

- 2 variables (equivalents of C, amount of solvent)

- 2 responses (residual C, material cost)

Expt Solvent Kg

Reagent C Quality (res. C)

Cost (£/Kg)

1 7000 1 0.41 3.078

2 5000 1 1.65 3.161

3 7000 2 3.50 3.099

4 5000 2 7.01 3.314

5 5207 1.5 4.19 3.233

6 6793 1.5 1.46 3.056

7 7500 1.207 0.46 3.260

8 7500 0.793 0.61 3.132

9 7500 1.5 1.60 3.080

10-16 repeats of 1 & 9

1 repeats 0.39-0.51 3.076-3.084

Boots Case Study - Experimental Design

Boots Case Study - Quality Response Surface

6000 7000 8000 9000

Kg of solvent 0.5

1.0 1.5 2.0

M oles of C

0.5 1.0 2.0 3.5 5.0 6.0

Boots Case Study - Cost Response Surface

6000 7000 8000

Kg of solvent 0.5

1.0 1.5 2.0

M oles of C

3.05 3.10 3.15 3.20

Original

Operating

Conditions

Solvent C(mol) %C

predicted actual

7000 1.75 2.37 1.99

7000 1.75 2.37 2.10

7000 1.25 0.72 0.69

6750 2.21 4.75 5.81

6750 1.75 2.12 2.29

6750 1.75 2.12 2.15

Boots Case Study - Conclusion

 Optimum conditions

- 6800 kg solvent

- 1.4 equivalents reagent C

- extra cast of reagent C was taken into account in the design

 Confirmatory Experiments

Boots Case Study - Final Conditions

 Solvent 6750 kg

 Reagent C 1.5 equivalents

 Cost € 2.46 / kg

 Quality 1.3% C

 Saving € 0.065 /kg

(€ 81,000 per year)

Evolutionary Operation

 IS the process operating under OPTIMUM conditions?

• production processes

• continuous or batch (large number of batches)

 DELIBERATE programme of replacing the STATIC operation of a plant by CONTINUAL PROCESS MODIFICATION

 LEADS EVENTUALLY TO IMPROVED

PROCESS

Evolutionary Operation

 Box 1956

 Manufacturing process should yield INFORMATION as well as PRODUCT

 Effect of process variables on PERFORMANCE

 Carried out on plant

 Requires process operators to change the process for

EVERY batch

Evolutionary Operation

Process operating at 85% yield

 Assume that this is NOT optimum

 Don’t know contours

 Choose 4 new conditions

 Run A → D + X several times

 Some runs give >85%, some less

- (plant manager note!)

 Soon established STATISTICALLY that conditions B are

better than X

170 180 190 190 190 190 190 190 1.0

1.01 1.02 1.03 1.04 1.05 1.06

S toic hiom et ry

A B

X

C

E F

G D

93 92 90 85

80

70

Response Surface

Evolutionary Operation

• Repeat cycle with B and X and 3 new points

• E gives best results

• Repeat cycle with E (can use 4 new points if desired)

• Continue until optimum (93%) is reached

• May take up to 8 cycles of 5 × (say) 5 experiments = 200 batches

• Once optimized on these 2 parameters, choose 2 more to

optimize

Response Surface

170 180 190 190 190 190 190 190 1.0

1.01 1.02 1.03 1.04 1.05 1.06

S toic hiom et ry

B X E

93 92 90 85

80

70

Disadvantages/Advantages

Disadvantages:

• Cost in time / money

- Training - record keeping

• Changes can only be small to avoid “failed batches”: thus large number of batches required to statistically prove results

• More COMPLEX production routine; errors may occur

• If process already at optimum changes will lead to poorer performance

Advantages

• Uses actual plant equipment / scale

• Observed changes are real!

• Gain improved knowledge of process

• Process operators become MORE INVOLVED and motivated

Which Processes are Suitable?

 High volume production

 Where potential benefits are large

 Process NOT at optimum

 Variables can be altered readily

 Process stabilises rapidly after a process change

 Response (yield, cast, quality, throughput) can be rapidly obtained and measured

G. P. Rangaiah (Ed.), Multi-Objective Optimization : Techniques and Applications in Chemical