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Polymerization Modeling for Relief Systems Design 1,3-Buatadiene Polymerization Case Study
By
A Presentation to the
G. A. Melhem, Ph.D.
DIERS USERS GROUP
[email protected]
April 28-30, 2003, Philadelphia, PA
© 2003, ioMosaic Corporation, 93 Stiles Road, Salem, New Hampshire 03079, USA. All rights reserved
Incident statistics of reactive storage • Surv Survey ey rec recen entl tly y comp comple lete ted d by the chemical safety investigation board • Stor Storag age e ves vesse sels ls and and dru drums ms account for 32 % of all accidents surveyed
Source: J. Murphy, CSIB Public Hearing Staff Preliminary Conclusions, Conclusions, May 2002, Paterson, New Jersey.
Millions of lbs Thermoplastics
Polymerizations: How much do we know ? • “Free radical polymerizations are the best studied reactions in all of chemistry”[1] • “The kinetics of alkyllithium initiation for styrene and diene polymers in hydrocarbon solutions has been investigated extensively”[10] • In 1998, the chemical and petrochemical industries produced 87 Billion lbs of polymers including thermoplastics, thermosets, synthetic fibers, and synthetic rubber [2] • Many companies have developed and tuned polymerization models (anionic, free radical, etc.) that can be coupled with thermally initiated polymerization kinetics for relief design under runaway reaction scenarios [3][4][5]
Polyethylene - Low Density Polyethylene - Linear Low Density Polyethylene - High Density Poly viny l Chloride and Copoly mers Polypropylene Polystyrene Acrylonitrile-Butadiene-Styrene
7,578 7,227 12,924 14,502 13,825 6,327 3,086
Thermosets Phenolic Urea Unsaturated Polyester Epoxy Melamine
3,940 2,581 1,713 639 290
Synthetic Fibers Polyester Nylon Olefin Acrylic Acetate and Rayon
3,911 2,847 2,800 346 365
Synthetic Rubber Styrene-Butadiene Polybutadiene Ethylene-Propylene Nitrile Polychloroprene Totals
960 580 321 89 72 86,923
The heats of reaction/polymerization are well known[6]
Heat of Polymerization Monomer Bond Polymer Bond (Kcal/gmol) C=C C=O C=N C≡N C=S S=O
-C-C -C-O -C-N -C=N-C-S-S-O-
-20 -5 -1.4 -7.2 -2 -7
Heat of Polymerization (BTU/lbmol) -35,977 -8,994 -2,518 -12,952 -3,598 -12,592
The heats of reaction/polymerization are well known[7][8][9]
Monomer Methyl Styrene Methyl Methacrylate Styrene Vinylidene Chloride Methyl Acrylate Isobutene Vinyl Acetate Isoprene 1,3-butadiene Vinyl Chloride Tetrafluoroethylene Propylene Ethylene
Heat of Polymerization (kcal/gmol) -8.4 -13.5 -16.7 -18 -18.8 -12.3 -21 -17.8 -17.4 -22.9 -37.2 -20.5 -22.7
Heat of Heat of Heat of Polymerization Polymerization Polymerization (BTU/lbmol) (cal/g) (BTU/lb) LOW -15,110 -71 -128 -24,284 -135 -243 -30,041 -160 -288 -32,379 -186 -334 -33,818 -218 -393 -22,126 -219 -394 -37,776 -244 -439 -32,019 -261 -470 -31,300 -322 -579 -41,193 -366 -659 -66,917 -372 -669 -36,876 -487 -876 -40,834 -809 -1,456 HIGH
The mechanism of free radical polymerization involves three steps: initiation, propagation, and termination[1][2][8][10]
Initiation
Propagation
Termination
k d
•
I 2 R →
• n
•
−
k p
+ M → M n•+1
•
k t
M n + M m → dead polymer
−
−
d [ I ] dt
d [ M ] dt
= d k[ ]I
= k p [ M • ][ M ]
d [ M • ] dt
= 2kt [ M • ]2
At steady-state (> 1 min), the net rate of production of free radicals is zero so that the initiation and termination rates are equal
Other important data can be estimated using the steady state assumption such as termination rates and average degree of polymerization [1][2][8][10]
Termination • n
•
k t
+ M m → dead polymer
−
d [ M • ] dt
= 2 kt [ M • ] 2 = 2 k d f [ I ]
Average Degree of Polymerization* = DP
[ M ] [ I]
′′k where
′′k=
k p 2 kd kt f
* Molecular weight of polymer / molecular of monomer
Often, the free radical rate expression is simplified such that the rate of polymerization is represented using a composite form[1][2][8]
−
1 dN monomer
Vl
dt
= kc [ N monomer ] [ I ]
isNthe number of moles in (
) and [ ] inis( kmol
/ 3 )m kmol
1
k d 2 kc = k p f where f is theinitiator efficiency k t Ec where Ac = Ap T
kc = Ac exp −
f
Ad At
and Ec = E p +
1 2
( Ed − Et )
dI E d = − kd I an d dt T
kd = Ad exp −
Vl = Total liquid volume in m3 , k p and kt are in (m3 / kmol / s ) and k d is in s −1
There are many published values for kd[1][8][11] SOLVENT
Ad
Ed (/K)
Kd at 50 C
sqrt(Kd/K*) at 50 C
INITIATOR
REFERENCE
2,2-Azo-bis-isobutyronitrile (AIBN) 2,2-Azo-bis-isobutyronitrile (AIBN)
Polymer Handbook Benzene Principles of Polymerization Benzene
1.438E+15 1.881E+14
15,449 14,842
2.485E-06 2.129E-06
1.189 1.100
Benzoyl peroxide Benzoyl peroxide Benzoyl peroxide
Polymer Handbook Benzene Principles of Polymerization Benzene ATOFINA Catalogue
5.281E+12 7.390E+13 3.184E+14
13,990 14,950 15,318
8.349E-07 5.983E-07 8.254E-07
0.689 0.583 0.685
Butadiene Polyperoxide
Butadiene Safety Manual
2.400E+07
9,864
1.329E-06
0.869
Cumyl peroxide Cumyl peroxide
Polymer Handbook Benzene Principles of Polymerization Benzene
1.318E+18 1.290E+18
20,481 20,482
3.933E-10 3.832E-10
0.015 0.015
Lauroyl Peroxide Lauroyl Peroxide*
Polymer Handbook ATOFINA Catalogue
Benzene
2.142E+15 1.300E+16
15,298 16,272
5.907E-06 1.759E-06
1.833 1.000
tert-Butyl hydroperoxide tert-Butyl hydroperoxide tert-Butyl hydroperoxide
Polymer Handbook Benzene Principles of Polymerization Benzene ATOFINA Catalogue
3.223E+15 2.868E+15 1.523E+12
20,531 20,531 17,321
8.228E-13 7.342E-13 8.033E-12
0.001 0.001 0.002
tert-Butyl perbonzoate tert-Butyl perbonzoate
Polymer Handbook ATOFINA Catalogue
Benzene
2.314E+15 1.754E+14
17,462 16,465
7.886E-09 1.307E-08
0.067 0.086
tert-Butyl peroxide (TBP) tert-Butyl peroxide (TBP)
Polymer Handbook Benzene Principles of Polymerization Benzene
8.568E+13 3.236E+14
17,110 17,668
8.685E-10 5.825E-10
0.022 0.018
There are many published values for kp, and kt[1][8] Monomer
Ap
Vinyl Chloride Vinyl Acetate Acrylonitrile Methyl acrylate Methyl methacrylate Styrene Ethylene 1,3-Butadiene 1,3-Butadiene [15]
3.300E+06 1.532E+06 6.813E+05 1.000E+08 8.700E+06 4.500E+06 1.862E+05 1.200E+07 8.050E+07
Ep
kp at 60 C At 1,924 2,165 1,948 3,572 3,175 3,127 2,213 2,923 4,292
10,231 2,307 1,965 2,205 631 377 243 1,859 205
1.474E+12 7.899E+10 2.719E+11 2.884E+10 1.876E+09 1.079E+09 8.636E+08 1.130E+10
Et 2,117 2,634 2,717 2,670 1,431 962 156
kt at 60 C
kp/kt
2.564E+09 2.910E+07 7.800E+07 9.534E+06 2.555E+07 6.008E+07 5.401E+08
3.990E-06 7.926E-05 2.519E-05 2.313E-04 2.471E-05 6.281E-06 4.494E-07
711 1.337E+09 1.530E-07
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, rate constants, and rate constant ratios
1,3-Butadiene thermally initiated polymerization occurs in both the vapor and liquid phases[16][11] • Thermal dimerization of butadiene to form vinylcyclohexene proceeds according to the rate equation (dominant dimerization reaction at 600 BTU/lb of BD) and is second order in BD. −12,344 [C BD ]2 = −3.47 ×107 exp dt T
1 dN BD V
• Thermal dimerization of butadiene to form 1,5-cyclooctadiene proceeds according to the rate equation (a few percent of COD typically formed) −14, 312 [C BD ]2 = −1.8 ×108 exp dt T
1 dN BD V
• Thermal trimerization of butadiene to form ∆3,3’-octahydro diphenyl proceeds according to the rate equation −19,122 = −8 ×1013 exp [C BD][C VCH] dt T
1 dN BD V
Where N is the number of moles (kmol), V is the total liquid volume (m3), T is the temperature in (K), t is the time in (s), and CBD is concentration of butadiene in (kmol/m3).
We conducted several adiabatic calorimetry tests to verify the butadiene 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) that the onset temperature of the butadiene polymerization is lowered considerably in the presence of active oxygen
100
10
) N I M / C ( t d / T d
Inert gas 1,3-Butadiene Sample Mass (g)
Test A Argon 2.089
Test B Argon 2.057
Test C Argon 4.345
Active Oxygen Concentration (ppmw) Test Cell Weight (g) Test Cell Volume (ml) Test Cell + Fittings Weight (g) Detection Sensitivity (C/min) Start Temperature (C) Heat Step (C) Wait Time (min) Starting Pressure (psia) Detected Onset Temperature (C)
0 10.447 9 21.157 0.02 28.8 3 20 40.5 112
557 10.414 9 21.087 0.02 18.65 3 20 33.4 73
2,682 6.834 9 17.55 0.02 23.2 3 20 38.1 55
Test A
1
0.1
Test B Test C
0.01 0
100
200 300 TEMPERATURE (C)
400
500
500
400
) C ( E 300 R U T A R E P M 200 E T
Test A
Test C
100
Test B
0 0
1000
2000 TIME (MIN)
3000
4000
1500
) A I S P ( E R U S S E R P
1000
Inert gas 1,3-Butadiene Sample Mass (g)
Test A Argon 2.089
Test B Argon 2.057
Test C Argon 4.345
Active Oxygen Concentration (ppmw) Test Cell Weight (g) Test Cell Volume (ml) Test Cell + Fittings Weight (g) Detection Sensitivity (C/min) Start Temperature (C) Heat Step (C) Wait Time (min) Starting Pressure (psia) Detected Onset Temperature (C)
0 10.447 9 21.157 0.02 28.8 3 20 40.5 112
557 10.414 9 21.087 0.02 18.65 3 20 33.4 73
2,682 6.834 9 17.55 0.02 23.2 3 20 38.1 55
Test C
Test A
500
Test B
0 0
1000
2000 TIME (MIN)
3000
4000
1200 1100
Inert gas 1,3-Butadiene Sample Mass (g) Active Oxygen Concentration (ppm) Test Cell Weight (g) Test Cell Volume (ml) Test Cell + Fittings Weight (g) Detection Sensitivity (C/min) Start Temperature (C) Heat Step (C) Wait Time (min) Starting Pressure (psia) Detected Onset Temperature (C)
1000 900 ) A I S P ( E R U S S E R P
800
Test A Argon 2.089 0 10.447 9 21.157 0.02 28.8 3 20 40.5 112
Test B Argon 2.057 557 10.414 9 21.087 0.02 18.65 3 20 33.4 73
Test C Argon 4.345 2,682 6.834 9 17.55 0.02 23.2 3 20 38.1 55
700 Test C
600 Test A
500 400 300 200
Test B
100 0 0
100
200 TEMPERATURE (C)
300
400
100 Inert gas 1,3-Butadiene Sample Mass (g) Active Oxygen Concentration ppmw Test Cell Weight (g) Test Cell Volume (ml) Test Cell + Fittings Weight (g) Detection Sensitivity (C/min) Start Temperature (C) Heat Step (C) Wait Time (min) Starting Pressure (psia) Detected Onset Temperature (C)
10
) N I M / C ( t d / T d
Test D None 60.31 570 34.82 133 38.88 0.06 25 2 20 56 50
Dimerization
Dead End Polymerization
1
0.1
0.01 0
50
100 TEMPERATURE (C)
150
200
1000 Inert gas 1,3-Butadiene Sample Mass (g) Active Oxygen Concentration ppmw Test Cell Weight (g) Test Cell Volume (ml) Test Cell + Fittings Weight (g) Detection Sensitivity (C/min) Start Temperature (C) Heat Step (C) Wait Time (min) Starting Pressure (psia) Detected Onset Temperature (C)
100
) N I M / I S P ( t d / P d
10
Test D None 60.31 570 34.82 133 38.88 0.06 25 2 20 56 50
1
0.1
0.01 0
50
100 TEMPERATURE (C)
150
200
Model fit for free radical and thermally initiated 1,3-butadiene kinetics −13, 786 = − 2.7815 ×1010 exp [C BD] C active, ppmw dt T
1 dN BD 1000
V
where 1
k d 2 −13,786 2.7815×1010 exp = k p f T k t
100
Model Predictions
10 ) N I M / C ( t d / T d
Where N is the number of moles (kmol), V is the total liquid volume (m3), T is the temperature in (K), t is the time in (s), CBD is concentration of butadiene in (kmol/m3), and Cactive is the concentration of active oxygen/free radicals in ppm
Dead End Polymerization 1
Experimental 0.1
Dimerization Note that dimerization kinetics are based on known literature data and were not fit from this data set.
0.01
0.001 0
100
200 300 TEMPERATURE. F
400
500
Source: SuperChems Expert Version 5.2
Model fit for free radical and thermally initiated 1,3-butadiene kinetics 10000
1000
Experimental 100 ) N I M / I S P ( t d / P d
10
1
Model Predictions
0.1
0.01 0
100
200 300 TEMPERATURE. F
400
500
Source: SuperChems Expert Version 5.2
Dilute concentrations of butadiene polyperoxide decompose at higher temperatures than Lauroyl peroxide[11][12] The decomposition rate of Lauroyl (LP) and butadiene polyperoxide (BDP) at dilute concentrations are give by the following rate expressions:
1 0.9
dC 0.8
dt
BDP
S 0.7 E T U N I 0.6 M 0 6 0.5 R E T F A 0.4 o C / C 0.3
= − k C
9,864 T 16,172 k LP =1.3 × 1016 exp − T k BDP = 2.4 × 107 exp −
Where C is in ppm, k is in /s and T is in Kelvins.
LP
0.2 0.1 0 0
100
200 TEMPERATURE. F
300
400
The presence of active butadiene popcorn polymer increases the rates of the butadiene free radical polymerization and lowers its onset temperature[15] • Active butadiene popcorn polymer always contains peroxides, which are formed by the peroxidation of butadiene by dissolved oxygen • The peroxide, required for the formation of popcorn polymer, and the peroxide containing butadiene popcorn polymer itself are known to initiate the free radical polymerization of butadiene at low temperatures • Adiabatic data indicate the potential for a runaway reaction at a temperature at least 50 C lower than would be expected for neat butadiene
Popcorn kinetics model predictions based on 1950s data[11][13][14] 40
o M / M . O I 30 T A R S S A M N R 20 O C P O P D E T C I D 10 E R P
dM dt
= k M 10,131 T
k = 8.0 × 107 exp −
where T is in Kelvins, k is in /s, and M is the BD popcorn mass
0 0
10 20 30 EXPERIMENTAL POPCORN MASS RATIO. M/Mo
40
The free radical model established for 1,3-butadiene using lauroyl peroxide can easily be extended to other free radical initiators 1
1 dN BD
V
dt
−13, 786 = −2.7815 ×10 exp T
dC active , ppmw dt
10
k d 2 [C BD] C active, ppmw k d , LP
E d = − k d exp − T
For 2,2-Azo-bis-isobutyronitrile, benzoyl peroxide,and butadiene polyperoxide 1
k d 2 ≈ 1 at 50 C k d , LP
An Example of an anionic radical polymerization for acrylonitrile
Thermally initiated polymerization
Anion initiated polymerization
10
) N I M / C ( t d / T d
Test cell becomes liquid full due to expansion
ARC test / Thermal Inertia = 1.81 Total sample mass = 3.6 g (20 % Active A) Anionic species mass = 0.6 g
100
1
0.1
0.01 0
100
200 TEMPERATURE (C)
300
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 systems can 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 thermally initiated polymerization models • It is possible for a free radical/anion initiated polymerization to “jump-start” thermally initiated polymerizations if sufficient initiator is present • Polymerization models are simple and can easily be applied in SuperChems for DIERS or other simulation computer codes for performing relief design for reactive systems and process optimization as well
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, 2 nd 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.
