Reactor Modeling and Recipe Optimization of Polyether...

Reactor Modeling and Recipe Optimization ofPolyether Polyol Processes

Spring 2013 EWO Meeting

Yisu Nie1 Lorenz T. Biegler1 Carlos M. Villa2 John M. Wassick2

1Center for Advanced Process Decision-makingDepartment of Chemical Engineering

Carnegie Mellon University

2The Dow Chemical Company

March 13, 2013

Yisu Nie (Carnegie Mellon University) Spring 2013 EWO Meeting March 13, 2013 1 / 12

IntroductionProject timeline

Development of systematic optimization methods of batch processes

Nov. 2009 - Dec. 2011I Proof-of-concept: integration of scheduling and dynamic optimizationI Y. Nie, L.T. Biegler, and J.M. Wassick. Integrated Scheduling and Dynamic Optimization of Batch Processes Using

State Equipment Networks. AIChE Journal, 2012.

Jan. 2012 - Dec. 2012I Application on polyether polyol processes at DowI Homopolymerization: polypropylene glycol

1 First-principle reactor model: population balances, kinetics, VLE, etc.2 Hypothetical optimization case study: over 40% batch time reduction

I Y. Nie, L.T. Biegler, C.M. Villa, and J.M. Wassick. Reactor Modeling and Recipe Optimization of Polyether Polyol

Processes: Polypropylene Glycol. submitted for publication, 2013.

I Copolymerization: block copolymer polyol1 Reactor modeling with the method of moments2 Hypothetical optimization case study: over 40% batch time reduction


IntroductionPolyether polyol process description

Key ingredientsI Epoxides (ethylene oxide (EO), propylene

oxide (PO))

OO OOI Molecules containing active hydrogen atoms

(alcohols, amines)

OH N

H

HI A basic catalyst (KOH)

Typical procedures usedI Starters are first mixed with catalyst in the liquid phaseI Alkylene oxides in the liquid phase are fed in controlled ratesI The reactor temperature is controlled by the heat exchangerI Allowed maximum reactor pressure guarded by the vent system control valve


IntroductionPolyether polyol process description

Key ingredientsI Epoxides (ethylene oxide (EO), propylene

oxide (PO))

OO OOI Molecules containing active hydrogen atoms

(alcohols, amines)

OH N

H

HI A basic catalyst (KOH)

N2

Monomer

Reactor

Typical procedures usedI Starters are first mixed with catalyst in the liquid phaseI Alkylene oxides in the liquid phase are fed in controlled ratesI The reactor temperature is controlled by the heat exchangerI Allowed maximum reactor pressure guarded by the vent system control valve


Process Dynamic ModelingModeling reaction kinetics

Many polyether polyol products are copolymersI Example: EO capped diols

H2C

H2C

O OOH

nP nE

O OOH

nP nE

PO block EO block

EO/PO block copolymer

Challenge: the effect of chain ends on chain growth

Propagation scheme Rate constant

. . .EO∗ + EO→ . . .EO∗ kEEp

. . .EO∗ + PO→ . . .PO∗ kEPp

. . .PO∗ + EO→ . . .EO∗ kPEp

. . .PO∗ + PO→ . . .PO∗ kPPp

Terminal unit is designated by ∗

kEEp > kEP

p > kPEp > kPP

p


Process Dynamic ModelingModeling EO/PO copolymerization processes

Reaction scheme: EO/PO copolymerInitiation:

G0,0 + EOkEi−→ GE

0,1

Q0,0 + EOkEi−→ QE

0,1

G0,0 + POkPi−→ GE

1,0

Q0,0 + POkPi−→ QE

1,0

Propagation:

GPnP,nE

+ POkPPp−→ GP

nP+1,nE(nP + nE > 1)

QPnP,nE

+ POkPPp−→ QP


GPnP,nE

+ EOkPEp−→ GE

nP,nE+1 (nP + nE > 1)

QPnP,nE

+ EOkPEp−→ QE

nP,nE+1 (nP + nE > 1)

GEnP,nE

+ POkEPp−→ GP


QEnP,nE

+ POkEPp−→ QP


GEnP,nE

+ EOkEEp−→ GE

nP,nE+1 (nP + nE > 1)

QEnP,nE

+ EOkEEp−→ QE

nP,nE+1 (nP + nE > 1)

Transfer:

GPnP,nE

+ POkt−→ DP

nP,nE+Q0,0 (nP,nE > 0)

GEnP,nE

+ POkt−→ DE


QPnP,nE

+ POkt−→ RP


QEnP,nE

+ POkt−→ RE


Exchange:

GPnP,nE

+DPmP,mE

ke−→ DPnP,nE

+GPmP,mE

(nP,nE,mP,mE > 0)

GPnP,nE

+DEmP,mE

ke−⇀↽−ke

DPnP,nE

+GEmP,mE

(nP,nE,mP,mE > 0)

GEnP,nE

+DEmP,mE

ke−→ DEnP,nE

+GEmP,mE

(nP,nE,mP,mE > 0)

QPnP,nE

+RPmP,mE

ke−→ RPnP,nE

+QPmP,mE

(nP,nE,mP,mE > 0)

QPnP,nE

+REmP,mE

ke−⇀↽−ke

RPnP,nE

+QEmP,mE

(nP,nE,mP,mE > 0)

QEnP,nE

+REmP,mE

ke−→ REnP,nE

+QEmP,mE

(nP,nE,mP,mE > 0)

GPnP,nE

+RPmP,mE

ke−⇀↽−ke

DPnP,nE

+QPmP,mE

(nP,nE,mP,mE > 0)

GPnP,nE

+REmP,mE

ke−⇀↽−ke

DPnP,nE

+QEmP,mE

(nP,nE,mP,mE > 0)

GEnP,nE

+RPmP,mE

ke−⇀↽−ke

DEnP,nE

+QPmP,mE

(nP,nE,mP,mE > 0)

GEnP,nE

+REmP,mE

ke−⇀↽−ke

DEnP,nE

+QEmP,mE

(nP,nE,mP,mE > 0)

1

MaterialStarter Low MW diolCatalyst KOHMonomer EO and PO

Notation

Gn growing product chains (PnO−K+)

Dn dormant product chains (PnOH)

Qn growing unsat chains (UnO−K+)

Rn dormant unsat chains (UnOH)

Pn CH3(PO)nUn CH2 = CHCH2(PO)n

Indexn,m repeating units (PO and EO)

SuperscriptE,P terminal units

Polyol chains in the reactorliving dormant

normal GP,GE DP,DE

unsaturated QP,QE RP,RE

total products X = GP + GE + DP + DE

total byproducts Y = QP + QE + RP + RE


Process Dynamic ModelingPopulation balances vs. method of moments

Population balance model (PBM)I Differential equations

d(V [XPnP,nE

])

dt=V (k

PPp [G

PnP−1,nE

] + kEPp [G

EnP−1,nE

])[PO]− V (kPPp [PO] + k

PEp [EO])[G

PnP,nE

]

d(V [XEnP,nE

])

dt=V (k

PEp [G

PnP,nE−1] + k

EEp [G

EnP,nE−1])[EO]− V (k

EPp [PO] + k

EEp [EO])[G

EnP,nE

]

d(V [YPnP,nE

])

dt=V (k

PPp [Q

PnP−1,nE

] + kEPp [Q

EnP−1,nE

])[PO]− V (kPPp [PO] + k

PEp [EO])[Q

PnP,nE

]

d(V [YEnP,nE

])

dt=V (k

PEp [Q

PnP,nE−1] + k

EEp [Q

EnP,nE−1])[EO]− V (k

EPp [PO] + k

EEp [EO])[Q

EnP,nE

]

I Algebraic equations

XSnP,nE

nc = GSnP,nE

(ni + nu), S ∈ {P,E}

YSnP,nE

nc = QSnP,nE

(ni + nu), S ∈ {P,E}

nc total moles of catalystni total moles of initiatornu total moles of unsaturated chains

Pros and cons

+ Revealing full MWD spectrum− Computationally demanding

2000 MW diol > 1400 differential equations + 1400 algebraic equations


Process Dynamic ModelingPopulation balances vs. method of moments

Definition of moments: kth order moment of polymeric species

λk =

∞∑nP+nE>1

(nP + nE)kXnP,nE , ζk =

∞∑nP+nE>1

(nP + nE)kGnP,nE , k = 0, 1, . . .

µk =

∞∑nP+nE>1

(nP + nE)kYnP,nE , νk =

∞∑nP+nE>1

(nP + nE)kQnP,nE , k = 0, 1, . . .

Moment model (MM)I Differential equations

dλPkdt

= V −1(kPi G0PO+ kPPp

k−1∑i=0

(ki

)ζPi PO+ kEP

p

k∑i=0

(ki

)ζEi PO− kPE

p ζPk EO)

dλEkdt

= V −1(kEi G0EO+ kEEp

k−1∑i=0

(ki

)ζEi PO+ kPE

p

k∑i=0

(ki

)ζPi EO− kEP

p ζEk PO)

dµPkdt

= V −1(kPi Q0PO+ kPPp

k−1∑i=0

(ki

)νPi PO+ kEP

p

k∑i=0

(ki

)νEi PO− kPE

p νPk EO)

dµEkdt

= V −1(kEi Q0EO+ kEEp

k−1∑i=0

(ki

)νEi PO+ kPE

p

k∑i=0

(ki

)νPi EO− kEP

p νEk PO)

I Algebraic equations

λSknc = ζSk (ni + nu), S = {P,E}

µSknc = νSk (ni + nu), S = {P,E}

Pros and cons

+ Model size does not increase with polymer MW

0th − 2nd moments = 12 differential equations + 12 algebraic equations

− No detailed distribution


Copolymerization Case StudyProduction of EO capped diol

Process specifications

I Charge conditionInitiator: PPGCatalyst: KOHMonomer: PO and EO

I Process constraints*F Product molecular weight > 2000 g/molF Product unsaturation value 6 0.02 mmol/g polyolF Heat exchanger load 6 UA(T − Tw) kWF Adiabatic end temperature 6 (Tb + 90)◦CF Capping ratio > 70% (% of EO ended chains in total chains)

* The set of constraints has been chosen to illustrate the use of dynamic optimization technology and does not include all

possible constraints or necessarily reflect the true capability of the plant.

Model calibration

0.0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1

Sca

led

reac

tor

pres

sure

Normalized time

Pressure (MM)Pressure (PBM)Plant data


Copolymerization Case StudyProduction of EO capped diol

Process specifications

I Charge conditionInitiator: PPGCatalyst: KOHMonomer: PO and EO

I Process constraints*F Product molecular weight > 2000 g/molF Product unsaturation value 6 0.02 mmol/g polyolF Heat exchanger load 6 UA(T − Tw) kWF Adiabatic end temperature 6 (Tb + 90)◦CF Capping ratio > 70% (% of EO ended chains in total chains)

* The set of constraints has been chosen to illustrate the use of dynamic optimization technology and does not include all

possible constraints or necessarily reflect the true capability of the plant.

Optimization resultsI Optimization model statistics and solution

Opt. soln MW (g/mol) Unsat (mmol/g) Capping(%) # of var. # of con. CPU (s)

0.580 2000 0.02 70 11, 248 11, 121 22

F Optimized with the moment modelF Batch time reduced by 42.0% (base case batch time normalized to 1)F Product quality constraints are satisfied at the end of the operationF More details...


Copolymerization Case Study ResultsOptimal control profiles of the process

Reactor temperature (top) and monomer feed rate (bottom) profiles

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0 0.2 0.4 0.6 0.8 1

Tem

pera

ture

[T−T

b]

Normalized time

End of optimized recipe

OptimizedBase case

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.2 0.4 0.6 0.8 1

Sca

lued

feed

rat

e

Normalized time

Optimized POOptimized EOBase case POBase case EO

Important remarksI Piecewise linear control profiles with continuity on finite element boundariesI Rising temperature for PO digestion and EO feedingI Flat feed rates for both monomers: no need for ramping


Copolymerization Case Study ResultsProcess constraint profiles

Adiabatic temp. (top) and hxn duty (bottom)

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6

Adi

abat

ic e

nd te

mp.

[T−T

b]

Normalized time

Adiabatic end temp.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5 0.6

Sca

led

heat

rem

oval

Normalized time

Heat removal dutyCooling capacity

Important remarksI Constraint on the adiabatic temp. is inactiveI Heat exchanger capacity is the major constraining factor


Copolymerization Case Study ResultsOptimal product molecular weight distributions (MWD)

MWD of the product (left) and unsat (right) polymers

0 5

10 15

20 25

30 0 2

4

6

8

10

12

14

0

50

100

150

200

250

Product population

[mol]

Number of PO

Number of EO

Product population

[mol]

0

50

100

150

200

250

0 5

10 15

20 25

30 0 2

4

6

8

10

12

14

0

1

2

3

4

5

6

7

Unsat population

[mol]

Number of PO

Number of EO

Unsat population

[mol]

0

1

2

3

4

5

6

7

Important remarksI Similar optimal solution obtained from the PBM

Opt. soln MW (g/mol) Unsat (mmol/g) Capping(%) # of var. # of con. CPU (s)

0.588 2000 0.02 70 191, 408 185, 147 5221

I Optimization over PBM is computationally expensive


ConclusionsProject timeline

Development of systematic optimization methods of batch processes

Jan. 2012 - Dec. 2012I Application on polyether polyol processes at DowI Homopolymerization: polypropylene glycol

1 First-principle reactor model: population balances, kinetics, VLE, etc.2 Hypothetical optimization case study: over 40% batch time reduction

I Copolymerization: block copolyol1 Reactor modeling with the method of moments2 Hypothetical optimization case study: over 40% batch time reduction

Jan. 2013 - May. 2014I Simultaneous scheduling and dynamic optimization

F Multiple reactors and possible incorporation of finishing trainsF Real-time constraints on shared resources

I Methodology generalization and further extensions

Thank you

I am glad to take your questions


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