Dynamics & Control Processes Modeling and Control of Molecular Weight Distribution in a Liquid-phase...

Dynamics & Control Processes

Modeling and Control of Molecular Weight Modeling and Control of Molecular Weight Distribution in a Liquid-phase Polypropylene Distribution in a Liquid-phase Polypropylene

ReactorReactor

Mohammad Al-haj Ali, Ben Betlem, Günter Weickert & Brian Roffel

Research groups Dynamics & Control Processes-Industrial Polymerization Processes - Faculty of Science and technology

University of Twente11/11/2005

2


Project goalsProject goals

Producing tailor-made polypropylenes, including bimodal grades, by using a single reactor

1 2 3 4 5 6 7 80

5

10

15

20

25

log(j*Mw)

GP

C

3


to improve the understanding of the relationship between polypropylene molecular weight and MWD and hydrogen concentration in liquid propylene as well as model this dependency.

to develop a simple and efficient nonlinear model-based control scheme.

to study the optimal grade change of polypropylene. to perform a feasibility study of the optimal broadening of MWD. to build hollow shaft reactor set-up.

to develop a predictive kinetic model for propylene polymerization in liquid pool.

4


Experimental set-upExperimental set-up

• 5.0 L batch reactor.

• Max. operating Pressure = 60 bar.

• Liquid and gas polymerization

reactions.

Ziegler-Natta catalyst:

MgCl2/TiCl4/phthalate – AlEt3/Silane

6 wt % TiCl4

5


Experimental ResultsExperimental Results

Reproducibility

0

20

40

60

80

100

120

0 5 10 15 20 25 30

Time, min

Rp, k

g/gc

at. h

r

Exp. 1

Exp. 2

Exp. 3

Experimental conditions: T = 70 °C, mass of catalyst = 3.78 mg, mass of cocatalyst = 1000 mg, hydrogen added = 150 mg

6


Effect of reactor filling on polymerization kinetics

Run T, °C

Catalyst, mg

Cocatalyst mg

Donor, mg

H2, mg

Yield, kg/gcat. hr

Filling degree

1 70 3.78 500 30 0 12.6 H

2 70 3.78 1040 50 0 15.6 T

3 70 3.78 500 30 150 59.8 H

4 70 3.78 1040 50 150 82.5 T

7


Run T, °C

Catalyst,

mg

Cocatalyst, mg

Donor, mg

H2, mg

Yield, kg/gcat. hr

Filling degree

3 70 3.78 500 30 150 59.8 H

4 70 3.78 1040 50 150 82.5 T

5 80 1.54 1040 50 150 119.8 T

6 80 1.54 500 30 120 52.5 H

Effect of reactor filling on polymerization kinetics

8


Kinetics and Molecular weight distribution Kinetics and Molecular weight distribution

Experimental recipe:

Liquid-pool polymerization in a fully-filledfully-filled reactor. Different hydrogen amounts.

0.0 mg - 2500 mg Hydrogen Different reaction temperatures.

60 °C - 80 °C

9


Run H2, mg X*10-3 tr, min Rpo, kg/gcat. hr kd, hr-1

1 0.0 0 60 16.1 0.34

2 25 0.24 60 62.5 0.80

3 150 1.44 47 121.6 1.19

4 250 2.47 45 145.1 1.50

5 1000 9.94 45 139.6 1.93

6 2500 26.7 30 125.9 2.81

Kinetics: hydrogen and temperature effects

T = 70 °C

10


Kinetics: hydrogen and temperature effects

0

50

100

150

200

250

300

0 0.005 0.01 0.015 0.02 0.025 0.03

X

Rpo

, kg/

g cat

. hr

60 °C 70 °C 80 °C0

0.5

1

1.5

2

2.5

3

3.5

0 0.005 0.01 0.015 0.02 0.025 0.03

X

k d, 1

/hr

60 °C 70 °C 80 °C0

0.51

1.52

2.53

3.5

0 50 100 150 200 250 300

Rpo, kg/gcat. hr

k d, 1

/hr

60 °C, variable H2

70 °C, variable H2

80 °C, variable H2

varying H2

varying H2

varying H2

11


Kinetics: modeling

0

50

100

150

200

250

300

0 0.01 0.02 0.03

X

Rpo

, kg/

g ca

t. hr

Exp, 70 ºC

Model, 70 ºC

Exp, 60 ºC

Model, 60 ºC

Exp, 80 ºC

Model, 80 ºC

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300

Rpo, kg/gcat . hr

k d, 1

/hr

exp 70 ºC

model, 70 ºC

exp 80 ºC

model 80 ºC

exp 60 ºC

model 60 ºC

)TR

1022.67exp()k1(1041.6k

02.8k

1086.3T1026.2T8.32k

Xkk1

)Xk1(CkR

3

28

p

2

6421

12

1maxmppo

3k

3,d

42,d

31,d

3,dk

2,dpo1,dd

1020E

288k

107.1k

1038.8k

)Xk1(TR

EexpkRkk

d

d

12


Molecular weight distribution

3 3.5 4 4.5 5 5.5 6 6.5 7 7.50

0.2

0.4

0.6

0.8Model parameter optimization

Log(Mw)G

PC

experimentmodel 4 sitesSite1Site2Site3Site4

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5-0.03

-0.02

-0.01

0

0.01

0.02

Log(Mw)

GP

Cex

p-G

PC

mod

el

4

1ii

dj

2dj

)yw(GPC

)qjexp(qjy

13


Process modelProcess model

)u,x(hy

)d,x(l)u,x(fdt

dx

]FF[d

]TF[u

]YPPMITC[y

]YPPMITyyyym[x

inHT

jHT

jncwcT

jncwccdcHmT

2

2

2

14


Design of Control SchemeDesign of Control Scheme

Polymerization Reactor

FH2,in

Tj

F

FinFc,in

MIc

T

P

C

15


Design of ControlDesign of Control SchemeScheme

Nonlinear Multivariable Controller:

Generic model control (GMC)-based controller

0dt)()(dt

d t

0

sp2sp1 yyKyyKy

= 0

h(x)y

l(x)dg(x)u)f(x,dt

dx

dl(x)ug(x))f(x,dx

dh(x)y

1

16





Δt

e

Δt

yyy kksp

k

))g(x(dh/dx

d)l(x),f(x)/dxdh(x)y(yKu

spsp

spspspspksp1k

T

r211 Δt

1

Δt

1

Δt

1K

17





sp,m

p

sp,m

in,minspHH

p,Rpininspj

y

R

y

yF

t

MIMI

MI

myF

H.R)HH(FA.U

1TT

2in,2

18



Nonlinearcontroller

Delayed labmeasurementsPlant

Nonlinearsimplified model

Delayedmeasurements

Updatealgorithm

+

+-

-ysp ym

y

Filter

θ//dtyd

yy

τ

1

dt

θd2

19



0 5 10 15 2010

15

20

25

30

35

40

Time, hrs

MIc

(a) NLMVC-Rigorous model (b) NLMVC-Simplified model(c) PI controller (d) Setpoint

(a) (c)

(b)

(d) a

0 5 10 15 20

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

Time, hrs

y H2

,in*F

in,

g/h

r(a) NLMVC-Rigorous model (b) NLMVC-Simplified model (c) PI controller

(b)

(c)

(a)

b

02.102.0

02.002.1Λ

20



8.02.0

2.08.0Λ

21


Optimal Grade TransitionOptimal Grade Transition

Objective function:

2

sp

spf5

t

t

4

1i

2

sp,i

ii C

C)t(Cwdt

q

q1w

f

0

J

Solution methods:

1. Pontryagin’s Minimum Principle

2. Simultaneous method

3. Control Parameterization technique

22



Model Solvercalculate states (x)

and outputs(y)

Evaluate* Objective function* Constraints

Optimization algorithm(NLP)

Calculate parametersai

Checktolerance

Set initial conditionsGuess initial control parameters

Optimal control parametersai

Calculate inputu(t)

u(t)

ai

x(t), y(t)

Control Parameterization technique

23



Pontryagin’s Minimum Principle

4,,1iGFE

DFCFBAq

dt

dq

iin,Hi

iin,Hiin,Hiii,i

i,ii

2

2

2

4,,1i,qqdt

dqi,ci,i

i,c

0

0.002

0.004

0.006

0.008

0.01

0 0.1 0.2 0.3 0.4

FH2,in

q1

data

model

24



8 10 12 14 162

2.5

3

3.5

4

4.5

5x 10

5

Time, hrs

Mw

c, g

/mol

PMP

Control parameterization

GMC-based controller

10 12 14 160

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time, hrs

FH

2in

, g/h

r

Control parameterization

PMP

GMC-based controller

25


Optimal Broadening of MWDOptimal Broadening of MWDBatch mixing of two polypropylene samples

00.10.20.30.40.50.60.70.80.9

0 1 2 3 4 5 6 7 8

Log(Mw)

GPC

X = 0.05 X = 0.0 Cumulative

26


Optimal Broadening of MWDOptimal Broadening of MWDBroadened polypropylene produced in the continuous reactor

Objective function:

dtC

C)t(Cw)

PDIPDI

PDI(w

f

0

t

t

2

sp

sp2

2

avginitial

initial1

J

27



2 4 6 80

0.5

log(j*mw)G

PC

10 15 20 256

8

10

PD

I

10 15 20 250

0.05

X

10 15 20 250.2

0.22

C

10 15 20 25342.8

343

343.2

Time, hrs

T, K

10 15 20 255000

10000

15000

Time, hrs

Mn

c, g/m

ol

10 15 20 250

1

2

3

FH

2in,

g/h

r

10 15 20 250

0.005

0.01

Fca

t,in,

g/h

r

t = 8 hrs t = 16 hrs

a b

c d

e f

g h

28



2 4 6 80

0.5

log(j*mw)

GP

C

10 15 20 256

8

10

12

PD

I

10 15 20 250

0.01

0.02

X

10 15 20 25

0.28

0.3C

10 15 20 250

1

FH

2in

, g/h

r

10 15 20 256

7

8x 10

-3

Fca

t,in

, g/h

r

10 15 20 250

10

20

30

Time, hrs

Mn

c, kg

/mo

l

10 15 20342

343

344

Time, hrs

T, K

t = 8 hrs t = 16 hrs

a b

c d

e f

g h

29


Hollow Shaft ReactorHollow Shaft Reactor

2.0 L reactor.

Max. operating Pressure = 250 bar

Max. operating Temperature = 250° C

Minimum dead volume.

Can be modeled as CSTR.

30


Monomer supply unit

P

P

P P

TI TI

P P

P

PIPI

Monom

er Storage V

essel

P

P P

P

TC

PropyleneHPLC pump

P

P

P

P

H

TI

Nitrogen

Monom

er Storage V

essel

Purge

Water Bath

HSR


31


Syringe pump

N2

Catalystvessel

HH

H

H

H

H

P

P

H

H

H

H

H

H

Hexane

Hexane

Purge

Purge

HSR

William pump

Cocatalystvessel

Purge


Catalyst injection unit

32


The reactor


HSR

Purge

P

P

P

PC

P

P

Hydrogen

P

P

33


Experimental results


60

65

70

75

80

85

90

95

100

7000 7500 8000 8500 9000 9500 10000 10500

Time, Sec

T, °

C

45

50

55

60

65

70

75

80

85

P, b

ar

Ts_up Ts_down P

34


35


Pressure-drop dilatometry

H2, mg 0.0 50 250 1000

M1 1.85 1.57 1.62 3.10

M2 2.01 1.99 2.05 4.80

Experimental conditions: T = 70 °C, mass of catalyst = 3.78 mg, mass of cocatalyst = 1000 mg, H2 = 150 mg

Experimental conditions: T = 70 °C, mass of catalyst = 3.78 mg, mass of cocatalyst = 1000 mg, H2 = 1000 mg

1000

3.2

4

ExtrapolatedExtrapolated

Dynamics & Control Processes Modeling and Control of Molecular Weight Distribution in a Liquid-phase...

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