dynamic modeling and recipe optimization of polyether...

Dynamic Modeling and Recipe Optimization ofPolyether Polyol Processes

Fall 2012 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

September 27, 2012

Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 1 / 12

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)

Basic proceduresI 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

Basic proceduresI 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

Reaction scheme: Polypropylene glycol

Hydrolysis:

W + Mkh−→ D0

Initiation:

G0 + Mki−→ G1

Q0 + Mki−→ Q1

Propagation:

Gn + Mkp−→ Gn+1 (n > 1)

Qn + Mkp−→ Qn+1 (n > 1)

Transfer:

Gn + Mkt−→ Dn + Q0 (n > 0)

Qn + Mkt−→ Rn + Q0 (n > 0)

Exchange:

Gn + Dmke−→ Dn + Gm (n,m > 0)

Qn + Rmke−→ Rn + Qm (n,m > 0)

Gn + Rmke−−⇀↽−−ke

Dn + Qm (n,m > 0)

MaterialStarter Propylene glycol (PG)

WaterCatalyst KOHMonomer PO

NotationM monomers (PO)W water

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


Process Dynamic ModelingA first-principle dynamic model

Model equations

Population balancesd(V [Gn])

dt= V (kp([Gn−1]− [Gn])[M]− kt [Gn][M]− ke [Gn]

N∑m=0

([Dm] + [Rm]) + ke [Dn]N∑

m=0

([Gm] + [Qm]))

d(V [Dn])

dt= V (kh [W][M]+kt [Gn][M] + ke [Gn]

N∑m=0

([Dm] + [Rm])− ke [Dn]N∑

m=0

([Gm] + [Qm]))

Similar balances for unsat populations (Q and R)

Monomer balance

Total mass balance

Volume determination

Vapor-liquid equilibriumI Liquid phase activities: Flory-Huggins theoryI Vapor pressures: Antoine equation


Process Dynamic ModelingReformulation of the first-principle model

Characteristics of the obtained model

A large-scale differential-algebraic equation (DAE) system

Synergistic fast and slow dynamic modesI Caused by fast exchange reactions− Stiff differential equations− Numerical difficulties in optimizationI A reformulation procedure

A nullspace projection method for equilibrium reactions

Separating fast and slow dynamic components

Modeling fast dynamics as algebraic equations

+ Systematic procedure based on linear algebra


Process Dynamic ModelingReformulated propoxylation model

Two pseudo-species introduced: X = G + D Y = Q + R

Population balances

d(V [Xn])

dt= Vkp([Gn−1]− [Gn])[M]

d(V [Yn])

dt= Vkp([Qn−1]− [Qn])[M]

Quasi-steady states of the equilibrium reactions

Xnnc = Gi (ni + nu)

Ynnc = Qi (ni + nu)

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

Important remarksI Complete with additional equations: monomer balance, VLE, etc.I An index-one DAE system

+ Fewer differential variables and equations+ Less stiff differential equations


Process Recipe OptimizationA dynamic optimization formulation

Objective function Minimizing the batch time of polymerizationConstraints Reformulated process model

Product quality constraintsI Target molecular weightI Requirement on the unsaturation valueI Final time monomer concentration

Process safety constraintsI Heat removal dutyI Adiabatic end temperature due to loss of cooling

+ =

Rxr temp

Adiabatic temp rise

Adiabatic end temp

Control variables Reactor temperature and monomer feed rate


Case StudyProduction of polypropylene glycol

Process specifications

Initial charge conditionInitiator: PG and WaterCatalyst: KOHMonomer: PO

Process constraintsI Product molecular weight > 950 g/molI Product unsaturation value 6 0.032 mmol/g polyolI Unreacted PO 6 120 ppmI Heat exchanger load 6 Hmax kWI Adiabatic end temperature Tad − Tb 6 80◦C

Model validation on reactor pressure: model prediction vs. plant data

0.00

0.20

0.40

0.60

0.80

1.00

0 0.2 0.4 0.6 0.8 1

Rea

ctor

pre

ssur

e [P

max

]

Normalized time

PredictionPlant data


Case StudyProduction of polypropylene glycol

Optimization results

Optimization model statistics and solutionOpt. soln MW (g/mol) Unsat (mmol/g) PO(ppm) # of var. # of con.

0.575 950 0.028 120 10946 11043

I Batch time reduced by 42.5% (base case batch time is normalized to 1)I Product quality constraints are satisfied at the end of the operation

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

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Tem

pera

ture

[T-T

b]

Normalized time

OptimizedRecipe

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.2 0.4 0.6 0.8 1

Sca

led

feed

rat

e

Normalized time

OptimizedRecipe

Important remarksI Piecewise linear control profiles with continuity on finite element boundariesI U-shape temperature profile and higher average feed ratesI Merging the feeding and digestion periods


Case Study ResultsOptimal product molecular weight distributions (MWD)

MWD of the product (top) and unsat (bottom) polymers

0

2000

4000

6000

8000

10000

12000

0 2 4 6 8 10 12 14 16 18

Pop

ulat

ion

[mol

]

Number of repeating units

Product chains

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14 16 18

Pop

ulat

ion

[mol

]

Number of repeating units

Unsat chains

Important remarksI Near Poisson distribution for the product polymersI Flat distribution for the unsat polymers


Case Study ResultsOptimal product polymer property profiles

Unsat number, functionality, HEW, and OH number

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0 0.2 0.4 0.6 0.8 1

Uns

atur

atio

n va

lue

[meq

/g]

Normalized time

OptimizedRecipe

1.93

1.94

1.95

1.96

1.97

1.98

1.99

2.00

0 0.2 0.4 0.6 0.8 1

Fun

ctio

nalit

y

Normalized time

OptimizedRecipe

50

100

150

200

250

300

350

400

450

500

0 0.2 0.4 0.6 0.8 1

HE

W [g

/mol

]

Normalized time

OptimizedRecipe

100

150

200

250

300

350

400

450

500

550

600

0 0.2 0.4 0.6 0.8 1O

H#

[mg

KO

H/g

]

Normalized time

OptimizedRecipe

Important remarksI All widely used property indexesI All in proper ranges at final time


Conclusions and acknowledgmentsProject timeline

Nov. 2009 - Dec. 2011I Proof-of-concept: integration of scheduling and dynamic optimization

Jan. 2012 - May. 2012I Application at Dow: polyether polyols

F First-principle reactor model developmentF Optimization case study: 3000-MW product of PO and glycerol

Jun. 2012 - Aug. 2012I Polyol process: reactor model development con’t

1 VLE model and reactor pressure calculations2 Model calibration against plant data3 Copolymerization of EO and PO and multi-step products

I Optimization case study: polypropylene glycolF Recipe design pattern change

Sep. 2012 - Dec. 2013I Modeling and optimization of copolymers, multi-step productsI 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 any questions


Backup SlidesThe nullspace projection method

Method developmentA generic reaction system with irreversible and equilibrium reactions

x =[A1 A2

] [ r1(x)σr2(x)

]+ g(t)

Multiplying with a non-singular matrix[YT ZT

]T(ZTA2 = 0)YT

a

YTb

ZT

x =

YTa

YTb

ZT

A1r1(x) +

0σf (x)

0

+

YTa

YTb

ZT

g(t)

Stable solution needs f (x) = 0, when σ →∞Reformulated system

YTa x = YT

a A1r1(x) + YTa g(t)

f (x) = 0

ZTx = ZTA1r1(x) + ZTg(t)



A toy example

Reaction system Ak1−→ B

k2−⇀↽−k3

C

Mass balance equations

a = −k1a a(0) = a0

b = k1a− k2b + k3c b(0) = 0

c = k2b − k3c c(0) = 0

Analytical solution

t

a∗(t)

b∗(t)

c∗(t)

a0

0

Ke =k3

k2

= 2k2

k1

= 2



A toy example

Reformulation matrix YT =

[1 0 00 1 0

]ZT =

[0 1 1

]Reformulated system

a = −k1a

b = k1a− k2b + k3c

c = k2b − k3c

=⇒a = −k1a a(0) = a0

s = k1a s(0) = 0

s = b + c k2b = k3c

Analytical solution

t

a∗(t)

b∗(t)

c∗(t)

a(t)

b(t)

c(t)

a0

0

Ke =k3

k2

= 2k2

k1

= 2



A toy example

Reformulation matrix YT =

[1 0 00 1 0

]ZT =

[0 1 1

]Reformulated system

a = −k1a

b = k1a− k2b + k3c

c = k2b − k3c

=⇒a = −k1a a(0) = a0

s = k1a s(0) = 0

s = b + c k2b = k3c

Analytical solution

t

a∗(t)

b∗(t)

c∗(t)

a(t)

b(t)

c(t)

a0

0

Ke =k3

k2

= 2k2

k1

= 20


Backup SlidesProcess constraint profiles

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

40

45

50

55

60

65

70

75

80

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

End temp.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6

Hea

t rem

oval

[Hm

ax]

Normalized time

DutyCapacity

Important remarksI Heat exchanger capacity is the main constraining factorI The adiabatic end temperature constraint is also limiting process

performanceYisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 16 / 12

dynamic modeling and recipe optimization of polyether...

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