Polymerization Modeling for Relief Systems Design

8/7/2019 Polymerization Modeling for Relief Systems Design

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Polymerization Modeling for Relief Systems Design

1,3-Buatadiene Polymerization Case Study

By

G. A. Melhem, Ph.D.

[email protected]

A Presentation to the

DIERS USERS GROUP

April 28-30, 2003, Philadelphia, PA

www.iomosaic.com

2003, ioMosaic Corporation, 93 Stiles Road, Salem, New Hampshire 03079, USA. All rights reserved


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GAM/Spring 2003 DIERS 2

Incident statistics of reactive storage

Survey recently completed bythe chemical safetyinvestigation board

Storage vessels and drumsaccount for 32 % of allaccidents surveyed

Source: J. Murphy, CSIB Public Hearing Staff Preliminary Conclusions, May 2002, Paterson,New Jersey.


3/28


Polymerizations: How much do we know ?

Free radical polymerizations are the best studiedreactions in all of chemistry[1]

The kinetics of alkyllithium initiation for styrene anddiene polymers in hydrocarbon solutions has beeninvestigated extensively[10]

In 1998, the chemical and petrochemical industries

produced 87 Billion lbs of polymers including

thermoplastics, thermosets, synthetic fibers, andsynthetic rubber[2]

Many companies have developed and tunedpolymerization models (anionic, free radical, etc.)that can be coupled with thermally initiated

polymerization kinetics for relief design underrunaway reaction scenarios[3][4][5]

Millions of lbs

Thermoplastics

Polyethylene - Low Density 7,578

Polyethylene - Linear Low Density 7,227Polyethylene - High Density 12,924

Polyvinyl Chloride and Copolymers 14,502

Polypropylene 13,825

Polystyrene 6,327

Acrylonitrile-Butadiene-Styrene 3,086

Thermosets

Phenolic 3,940

Urea 2,581

Unsaturated Polyester 1,713

Epoxy 639

Melamine 290

Synthetic Fibers

Polyester 3,911

Nylon 2,847

Olefin 2,800

Acrylic 346

Acetate and Rayon 365

Synthetic Rubber

Styrene-Butadiene 960

Polybutadiene 580

Ethylene-Propylene 321

Nitrile 89

Polychloroprene 72

Totals 86,923


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The heats of reaction/polymerization are well known[6]

Monomer Bond Polymer Bond

Heat of

Polymerization

(Kcal/gmol)

Heat of

Polymerization

(BTU/lbmol)

C=C -C-C -20 -35,977

C=O -C-O -5 -8,994C=N -C-N -1.4 -2,518

CN -C=N- -7.2 -12,952

C=S -C-S- -2 -3,598

S=O -S-O- -7 -12,592


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The heats of reaction/polymerization are well known[7][8][9]

Monomer

Heat of

Polymerization

(kcal/gmol)

Heat of

Polymerization

(BTU/lbmol)

Heat of

Polymerization

(cal/g)

Heat of

Polymerization

(BTU/lb)

LOWMethyl Styrene -8.4 -15,110 -71 -128

Methyl Methacrylate -13.5 -24,284 -135 -243

Styrene -16.7 -30,041 -160 -288

Vinylidene Chloride -18 -32,379 -186 -334

Methyl Acrylate -18.8 -33,818 -218 -393

Isobutene -12.3 -22,126 -219 -394Vinyl Acetate -21 -37,776 -244 -439

Isoprene -17.8 -32,019 -261 -470

1,3-butadiene -17.4 -31,300 -322 -579

Vinyl Chloride -22.9 -41,193 -366 -659

Tetrafluoroethylene -37.2 -66,917 -372 -669

Propylene -20.5 -36,876 -487 -876

Ethylene -22.7 -40,834 -809 -1,456

HIGH


6/28GAM/Spring 2003 DIERS 6

The mechanism of free radical polymerization involves three steps:initiation, propagation, and termination[1][2][8][10]

[ ]2 [ ]

dk

d

d I I R k I

dt

=Initiation

1

[ ][ ][ ]

pk

n n p

d MM M k M M

dt

++ =Propagation

2[ ]dead polymer 2 [ ]tk

n m t

d MM M k M

dt

+ =Termination

At steady-state (> 1 min), the net rate of production of free radicals iszero so that the initiation and termination rates are equal



Other important data can be estimated using the steady state assumptionsuch as termination rates and average degree of polymerization [1][2][8][10]

2[ ]dead polymer 2 [ ] 2 [ ]tk

n m t d

d MM k M k f I

dt

+ = =

Termination

[ ]where

[ ] 2

p

d t

kM DP k k

I k k f = =

Average Degree of Polymerization*

* Molecular weight of polymer / molecular of monomer



Often, the free radical rate expression is simplified such that the rate ofpolymerization is represented using a composite form[1][2][8]

( )

3

1

2

1[ ] [ ]

is the number of moles in ( )and[] in ( / )

where f is theinitiatorefficiency

1exp where and

2

exp an

monomerc monomer

l

dc p

t

c dc c c p c p d t

t

dd d

dNk N I

V dt

N kmol is kmol m

kk k f

kE A

k A A A f E E E E T A

Ek AT

=

=

= = = +

=

3 3 1

d

Total liquid volume in , and are in ( / / ) and is in

d

l p t d

dI k Idt

V m k k m kmol s k s

=

=


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There are many published values for kd[1][8][11]

INITIATOR REFERENCE SOLVENT Ad Ed (/K) Kd at 50 C

sqrt(Kd/K*)

at 50 C

2,2-Azo-bis-isobutyronitrile (AIBN) Polymer Handbook Benzene 1.438E+15 15,449 2.485E-06 1.189

2,2-Azo-bis-isobutyronitrile (AIBN) Principles of Polymerization Benzene 1.881E+14 14,842 2.129E-06 1.100

Benzoyl peroxide Polymer Handbook Benzene 5.281E+12 13,990 8.349E-07 0.689Benzoyl peroxide Principles of Polymerization Benzene 7.390E+13 14,950 5.983E-07 0.583

Benzoyl peroxide ATOFINA Catalogue 3.184E+14 15,318 8.254E-07 0.685

Butadiene Polyperoxide Butadiene Safety Manual 2.400E+07 9,864 1.329E-06 0.869

Cumyl peroxide Polymer Handbook Benzene 1.318E+18 20,481 3.933E-10 0.015

Cumyl peroxide Principles of Polymerization Benzene 1.290E+18 20,482 3.832E-10 0.015

Lauroyl Peroxide Polymer Handbook Benzene 2.142E+15 15,298 5.907E-06 1.833

Lauroyl Peroxide* ATOFINA Catalogue 1.300E+16 16,272 1.759E-06 1.000

tert-Butyl hydroperoxide Polymer Handbook Benzene 3.223E+15 20,531 8.228E-13 0.001

tert-Butyl hydroperoxide Principles of Polymerization Benzene 2.868E+15 20,531 7.342E-13 0.001

tert-Butyl hydroperoxide ATOFINA Catalogue 1.523E+12 17,321 8.033E-12 0.002

tert-Butyl perbonzoate Polymer Handbook Benzene 2.314E+15 17,462 7.886E-09 0.067

tert-Butyl perbonzoate ATOFINA Catalogue 1.754E+14 16,465 1.307E-08 0.086

tert-Butyl peroxide (TBP) Polymer Handbook Benzene 8.568E+13 17,110 8.685E-10 0.022

tert-Butyl peroxide (TBP) Principles of Polymerization Benzene 3.236E+14 17,668 5.825E-10 0.018


10/28


There are many published values for kp, and kt[1][8]

Kp = Ap exp ( -Ep/T)

Kt = At exp (-Et/T)

Ep and Et are in /K

Ap and At are m3/kmol/s

References [1] and [8] provide guidance and typical values on activation energies, pre-exponential factors, rateconstants, and rate constant ratios

Monomer Ap Ep kp at 60 C At Et kt at 60 C kp/kt

Vinyl Chloride 3.300E+06 1,924 10,231 1.474E+12 2,117 2.564E+09 3.990E-06

Vinyl Acetate 1.532E+06 2,165 2,307 7.899E+10 2,634 2.910E+07 7.926E-05

Acrylonitrile 6.813E+05 1,948 1,965 2.719E+11 2,717 7.800E+07 2.519E-05

Methyl acrylate 1.000E+08 3,572 2,205 2.884E+10 2,670 9.534E+06 2.313E-04

Methyl methacrylate 8.700E+06 3,175 631 1.876E+09 1,431 2.555E+07 2.471E-05

Styrene 4.500E+06 3,127 377 1.079E+09 962 6.008E+07 6.281E-06

Ethylene 1.862E+05 2,213 243 8.636E+08 156 5.401E+08 4.494E-07

1,3-Butadiene 1.200E+07 2,923 1,8591,3-Butadiene [15] 8.050E+07 4,292 205 1.130E+10 711 1.337E+09 1.530E-07


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1,3-Butadiene thermally initiated polymerization occurs in both thevapor and liquid phases[16][11]

Thermal dimerization of butadiene to form vinylcyclohexene proceedsaccording to the rate equation (dominant dimerization reaction at 600BTU/lb of BD) and is second order in BD.

7 21 12,3443.47 10 exp [ ]BD BDdN

CV dt T

=

Thermal dimerization of butadiene to form 1,5-cyclooctadiene proceedsaccording to the rate equation (a few percent of COD typically formed)

8 21 14,3121.8 10 exp [ ]BD BDdN

CV dt T

=

Where N is the number of moles (kmol), V is the total liquid volume (m3), T is the temperature in (K), t is the timein (s), and CBD is concentration of butadiene in (kmol/m3).

Thermal trimerization of butadiene to form 3,3-octahydro diphenylproceeds according to the rate equation

131 19,1228 10 exp [ ][ ]BD BD VCH

dNC C

V dt T

=


12/28


We conducted several adiabatic calorimetry tests to verify thebutadiene kinetics reported in the literature

The TBC was removed by vacuum distillation

Test A, B, and C were conducted in the accelerating rate calorimeter

(ARC) Test D was conducted in the advanced pressure tracking adiabatic

calorimeter (APTAC)

Lauroyl peroxide was used to simulate the effect of butadiene

polyperoxide on butadiene polymerization

The test data clearly shows (as stated in various literature sources) thatthe onset temperature of the butadiene polymerization is loweredconsiderably in the presence of active oxygen


13/28



14/28


TEMPERATURE (C)

0 100 200 300 400 500

dT/dt(C/MIN)

0.01

0.1

1

10

100

Test A

Test B

Test C

Test A Test B Test C

Inert gas Argon Argon Argon

1,3-Butadiene Sample Mass (g) 2.089 2.057 4.345

Active Oxygen Concentration (ppmw) 0 557 2,682

Test Cell Weight (g) 10.447 10.414 6.834

Test Cell Volume (ml) 9 9 9

Test Cell + Fittings Weight (g) 21.157 21.087 17.55

Detection Sensitivity (C/min) 0.02 0.02 0.02

Start Temperature (C) 28.8 18.65 23.2

Heat Step (C) 3 3 3

Wait Time (min) 20 20 20

Starting Pressure (psia) 40.5 33.4 38.1

Detected Onset Temperature (C) 112 73 55


15/28


TIME (MIN)

0 1000 2000 3000 4000

TE

MPERATURE(C)

0

100

200

300

400

500

Test A

Test B

Test C


16/28


TIME (MIN)

0 1000 2000 3000 4000

PR

ESSURE(PSIA)

0

500

1000

1500


Inert gas Argon Argon Argon

1,3-Butadiene Sample Mass (g) 2.089 2.057 4.345

Active Oxygen Concentration (ppmw) 0 557 2,682






Heat Step (C) 3 3 3




Test ATest B

Test C


17/28


TEMPERATURE (C)

0 100 200 300 400

PR

ESSURE(PSIA)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200


Inert gas Argon Argon Argon1,3-Butadiene Sample Mass (g) 2.089 2.057 4.345

Active Oxygen Concentration (ppm) 0 557 2,682






Heat Step (C) 3 3 3




Test C

Test A

Test B


18/28


TEMPERATURE (C)

0 50 100 150 200

dT/dt(C/MIN)

0.01

0.1

1

10

100 Test DInert gas None

1,3-Butadiene Sample Mass (g) 60.31

Active Oxygen Concentration ppmw 570

Test Cell Weight (g) 34.82

Test Cell Volume (ml) 133

Test Cell + Fittings Weight (g) 38.88

Detection Sensitivity (C/min) 0.06

Start Temperature (C) 25

Heat Step (C) 2Wait Time (min) 20

Starting Pressure (psia) 56

Detected Onset Temperature (C) 50Dead End

Polymerization

Dimerization


19/28


TEMPERATURE (C)

0 50 100 150 200

dP

/dt(PSI/MIN)

0.01

0.1

1

10

100

1000 Test DInert gas None

1,3-Butadiene Sample Mass (g) 60.31

Active Oxygen Concentration ppmw 570

Test Cell Weight (g) 34.82

Test Cell Volume (ml) 133

Test Cell + Fittings Weight (g) 38.88

Detection Sensitivity (C/min) 0.06

Start Temperature (C) 25

Heat Step (C) 2Wait Time (min) 20

Starting Pressure (psia) 56

Detected Onset Temperature (C) 50


20/28


Model fit for free radical and thermally initiated 1,3-butadiene kinetics

TEMPERATURE. F

0 100 200 300 400 500

dT/dt(C

/MIN)

0.001

0.01

0.1

1

10

100

1000

Model Predictions

Experimental

10

,

1

210

1 13,7862.7815 10 exp [ ]

where

13,786

2.7815 10 exp

BD BD active ppmw

d

pt

dNC C

V dt T

k

k fT k

=

=

Where N is the number of moles (kmol), Vis the total liquid volume (m3), T is thetemperature in (K), t is the time in (s), CBDis concentration of butadiene in (kmol/m3),and Cactive is the concentration of activeoxygen/free radicals in ppm

Dimerization

Note that dimerization kineticsare based on knownliterature data and were not fitfrom this data set.

Dead EndPolymerization

Source: SuperChems Expert Version 5.2


21/28


Model fit for free radical and thermally initiated 1,3-butadiene kinetics

TEMPERATURE. F

0 100 200 300 400 500

dP/dt(PS

I/MIN)

0.01

0.1

1

10

100

1000

10000

Experimental

Model Predictions

Source: SuperChems Expert Version 5.2


22/28


Dilute concentrations of butadiene polyperoxide decompose at highertemperatures than Lauroyl peroxide[11][12]

TEMPERATURE. F

0 100 200 300 400

C/CoAFTER

60MINUTES

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

BDP

LP

Where C is in ppm, k is in /s and T is in Kelvins.

7

16

9,8642.4 10 exp

16,1721.3 10 exp

BDP

LP

dC k Cdt

kT

kT

=

=

=

The decomposition rate of Lauroyl (LP) andbutadiene polyperoxide (BDP) at diluteconcentrations are give by the following rateexpressions:


23/28


The presence of active butadiene popcorn polymer increases the ratesof the butadiene free radical polymerization and lowers its onsettemperature[15]

Active butadiene popcorn polymer always contains peroxides, which areformed by the peroxidation of butadiene by dissolved oxygen

The peroxide, required for the formation of popcorn polymer, and theperoxide containing butadiene popcorn polymer itself are known to initiatethe free radical polymerization of butadiene at low temperatures

Adiabatic data indicate the potential for a runaway reaction at atemperature at least 50 C lower than would be expected for neatbutadiene


24/28


Popcorn kinetics model predictions based on 1950s data[11][13][14]

EXPERIMENTAL POPCORN MASS RATIO. M/Mo

0 10 20 30 40

PR

EDICTED

POPCO

RN

MASSRATIO.

M/Mo

0

10

20

30

40

where T is in Kelvins, k is in /s, andM is the BD popcorn mass

7 10,1318.0 10 exp

dM

k Mdt

kT

=

=


25/28


The free radical model established for 1,3-butadiene using lauroylperoxide can easily be extended to other free radical initiators

1

210

,

,

,

1

2

,

1 13,7862.7815 10 exp [ ]

exp

For 2,2-Azo-bis-isobutyronitrile,benzoyl peroxide,and butadiene polyperoxide

1 at 50C

dBD BD active ppmw

d LP

active ppmw dd

d

d LP

kdNC C

V dt T k dC E

kdt T

k

k

=

=


26/28


An Example of an anionic radical polymerization for acrylonitrile

TEMPERATURE (C)

0 100 200 300

dT/dt(C

/MIN)

0.01

0.1

1

10

100Test cell becomesliquid full due to expansion

Thermally initiatedpolymerization

Anion initiatedpolymerization

ARC test / Thermal Inertia = 1.81Total sample mass = 3.6 g (20 % Active A)Anionic species mass = 0.6 g


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Summary / Conclusions

Polymerization reactions are the best studied reactions in all of chemistry

Well known heats of polymerization and thermal polymerization models

Free radical and anionic polymerizations of many common polymer systemscan easily be established and modeled: (a) using literature data, or

(b) Established experimental techniques of adiabatic/isothermal calorimetry, or

(c) in-house proprietary production kinetic models.

Free radical polymerization models should be run in parallel with thermallyinitiated polymerization models

It is possible for a free radical/anion initiated polymerization to jump-startthermally initiated polymerizations if sufficient initiator is present

Polymerization models are simple and can easily be applied in SuperChemsfor DIERS or other simulation computer codes for performing relief design forreactive systems and process optimization as well


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References

[1] Polymer Chemistry, An Introduction, R. B. Seymour and C. E. Carraher, Jr., Mercel Dekker, NY, 1981

[2] http://www.stanford.edu/class/cheme160/lectures/lecture1.pdf

[3] Identification and Validation of a VSL Polymerization Reactor Model, Bayer Inc., Sarnia, Canada, 1998-2002,

http://www.uni-bayreuth.de/departments/math/~kschittkowski/proj_bay.htm

[4] Styrene-butadiene rubber synthesized by anionic polymerization, M. C. Iovu et al., 2000,

http://www.sun.ac.za/unesco/Conferences/Conference2000/Abstracts2000/Iovu/IOVU.pdf[5] Modeling of ionic polymerization process: styrene and butadiene, A. Sirohi and K. Ravindranath, AIChE Spring 1999 Meeting, Houston.

[6] http://www.stanford.edu/class/cheme160/lectures

[7] G. Moad and Solomon, The Chemistry of Free Radical Polymerization, Pergamon, ISBN 0080420788

[8] G. Odian, Principles of Polymerization, 3rd Edition, Wiley, 1991

[9] http://www.chem.warwick.ac.uk/ug/ugcourses/year3/ch3a4/downloads/Background.pdf

[10] Anionic Polymerization, Principles and Practical Application, H. L. Hsieh and R. P. Quirk, Mercel Dekker, 1996

[11] Butadiene Safety Manual, D. G. Hendry and F. R. Mayo, Stanford Research Institute, 1966

[12] ATOFINA Peroxide Catalogue

[13] Butadiene Popcorn Polymer, G. H. Miller et al., Journal of Polymer Science, 1952, pp. 453-462

[14] Proliferous Polymerization, Encyclopedia of Polymer Science and Engineering, Wiley, 1988, 2nd Edition, pp. 453-463

[15] H. G. Fisher, DIERS Users Group Presentation, May 11, 2002

[16] International symposium on runaway reactions, effluent handling and pressure relief design, G. A. Melhem and H. G. Fisher, Editors,AIChE, 1998.

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