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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 2 / 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)
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 2 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 3 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 4 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 5 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 5 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 6 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 7 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 8 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 8 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 9 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 9 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 10 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 11 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 12 / 12
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 12 / 12
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)
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 13 / 12
Backup SlidesThe nullspace projection method
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 14 / 12
Backup SlidesThe nullspace projection method
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 15 / 12
Backup SlidesThe nullspace projection method
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
Yisu Nie (Carnegie Mellon University) Fall 2012 EWO Meeting September 27, 2012 15 / 12
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