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Kenneth Kurko1, Charles Kozlowski1, Bertrand Roduit2
1Fauske & Associates, LLC, 16W070 83rd Street, Burr Ridge, IL 60527, USA2AKTS AG Advanced Kinetics and Technology Solutions, TECHNOArk 1, 3960 Siders, Switzerland
Presented to:
NATAS 2011
Consideration of Autocatalytic Behavior in Determination of Self Accelerating
Decomposition Temperature
What is a Self Accelerating Decomposition Temperature?
United States SADT Test: SADT is defined as the lowest
environmental temperature at which the center of the material within the package heats to a
temperature 6°C greater than the environmental temperature after a lapse of a seven day period or less. This period is measured
from the time when the temperature in the center of the package reaches 2°C below the environmental temperature
What is Needed to Estimate a SADT?
� Package properties
� Size
� Heat transfer coefficient
� Physical properties of self-reactive substance
� Density
� Specific heat
� Thermal conductivity
� Decomposition kinetics
Azodicarbonamide(CAS: 123-77-3)
� Package properties
� Size (50 kg)
� Heat transfer coefficient (5 W/m2·K)
� Physical properties of self-reactive substance
� Density (1650 kg/m3)
� Specific heat (1050 J/kg·K)
� Thermal conductivity (0.1 W/m·K)
� Decomposition kinetics
Azodicarbonamide(CAS: 123-77-3)
� Package properties
� Size (50 kg)
� Heat transfer coefficient (5 W/m2·K)
� Physical properties of self-reactive substance
� Density (1650 kg/m3)
� Specific heat (1050 J/kg·K)
� Thermal conductivity (0.1 W/m·K)
� Decomposition kinetics
Methods of InvestigatingDecomposition Reactions
� Adiabatic Calorimetry
� ARC
� VSP2
� ARSST
� Heat Flow Calorimetry
� TAM
� C80
� DSC
Methods of InvestigatingDecomposition Reactions
� Adiabatic Calorimetry
� ARC
� VSP2
� ARSST
� Heat Flow Calorimetry
� TAM
� C80
� DSC
Non-isothermal DSC Signals
Temperature (°C)
200180160140120
He
at F
low
(W
/g)
8
6
4
2
0
0.25°C/min
0.5°C/min
1°C/min
2°C/min
Isothermal DSC Signals
Time (h)
65.554.543.532.521.510.50
He
atF
low
(W
/g)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
170°C
165°C
� Reaction rate is expressed by the equation
� Where A, E, f(α), T, and t mean: pre-exponential factor in Arrhenius equation, activation energy, function of the reaction extent α which form depends on the decomposition mechanism, temperature and time, respectively
� Isoconversional methods (model free)
� Reaction model is not required
Basic Kinetic Equation
( )( )αf
tTR
E expA
dt
dα
⋅−⋅=
Reaction rate expressed by the Arrhenius equation
Reaction rate at a given reaction progress α is only a function of the temperature
A’(α) and E(α) are the pre-exponential factor and apparent activation energy
� Isoconversional methods (model free):
Three main modifications of isoconversional method are applied in the literature:
� Differential (Friedman)
� Integral (Flynn-Ozawa-Wall)
� ASTM E698
Isoconversional Methods
( ) ( )T
1
R
E)(αA'ln
dt
dαln
α−=
α
=
( ) ( )α⋅α fA
Reaction Progress in Isothermal (A) andNon-isothermal (B) Conditions
Time (h)
4.543.532.521.510.50
Re
actio
n p
rog
ress (
-)
1
0.8
0.6
0.4
0.2
0
170°C 165°C
Temperature (°C)
205200195190185180175170165160155150145
Re
actio
n p
rog
ress (
-)
1
0.8
0.6
0.4
0.2
0
0.25°C/min 0.5°C/min 1°C/min 2°C/min
r∆H
Qα =
(A)
(B)
Time (h)
4.543.532.521.510.50
Re
actio
n r
ate
(-/
s)
2.5E-4
2E-4
1.5E-4
1E-4
5E-5
0
170°C
165°C
Temperature (°C)
205200195190185180175170165160155150145
Re
actio
n r
ate
(-/
s)
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0.25°C/min
0.5°C/min
1°C/min
2°C/min
r∆H
Q
dt
dα &
=
Reaction Rate in Isothermal (A) andNon-isothermal (B) Conditions
(A)
(B)
Differential Isoconversional Method
1000/T (1000/K)
2.352.32.252.22.152.12.05
ln(R
ea
ctio
n r
ate
(-/s
)) (
-)
-4
-6
-8
-10
-12
-14
0.01
0.02
0.050.1
0.7
0.8
0.9
0.95
0.98
0.99
The activation energy is determined from the slope of the lines connectingpoints plotted in coordinates: reaction rate vs. 1/T obtained for the same
reaction progress α at different heating rates
Dependence of Ea and ln(A) onthe Reaction Progress
Reaction progress alpha (-)
10.80.60.40.20
E (
kJ/m
ol)
200
180
160
140
120
100
80
Ln
(A(a
lph
a)·
f(a
lph
a)(
1/s
)) (
-)
45
40
35
30
25
20
15
Simulation of the Reaction Progress (A) and Reaction Rate (B) in Non-isothermal Conditions
Temperature (°C)
225220215210205200195190185180175170165160155150145140
Re
actio
n R
ate
(-/
s)
0.015
0.01
0.005
0
Re
actio
n P
rog
ress (
-)
1
0.8
0.6
0.4
0.2
0
0.125°C/min 0.25°C/min 0.5°C/min 1°C/min 2°C/min 4°C/min
0.125°C/min0.25°C/min
0.5°C/min
1°C/min
2°C/min
4°C/min
Experimental data are presented as red points, the simulated dependences as solid lines
(A)
(B)
Time (h)
8.587.576.565.554.543.532.521.510.50
Re
actio
n R
ate
(-/
s)
3E-4
2E-4
1E-4
0
Re
actio
n P
rog
ress (
-)
1
0.8
0.6
0.4
0.2
0
175°C
170°C
165°C
160°C
175°C 170°C 165°C 160°C
Simulation of the Reaction Progress (A) and Reaction Rate (B) in Isothermal Conditions
Experimental data are presented as red points, the simulated dependences as solid lines
(A)
(B)
with a few with a few
DSC or C80 DSC or C80
experiments experiments
carried out carried out
on mgon mg--scale scale
SADT
TMRad
Shelf-life
mgmg
kgkg
tonton
To=120°C?
To=120°C?
Temperature-Time Dependence forDifferent Sample Masses
Azodicarbonamide (CAS: 123-77-3)
To=120°C?
tC
H
r
T
r
g
r
T
rCt
T
p
r
p ∂
∂∆−+
∂
∂+
∂
∂
∂
∂=
∂
∂ αλλ
ρ
1
Thermal conductivity
?? Decomposition kineticsAccumulation
reaction output accumulation
heat
conducted
in
heat
generated
within
heat
conducted
out
change in
energy
stored
within+ +=
Heat balance combined with numerical analysis enables the
determination of the
(i) heat accumulation and
(ii) reaction rate and progress
for any surrounding temperature profile
Heat Balance: Kilogram Scale
input
Prediction of SADT Applying HeatBalance and Kinetic Data
Time (day)
1086420
Te
mp
era
ture
(°C
)
122
120
118
116
114
112
110
SADT=114°C,50kg,1650kgm^-3,1.05Jg^-1K^-1,0.1Wm^-1K^-1,-1373.5Jg^-1,5Wm^-2K^-1
overheat 6°C
T surrounding -2 °C
7 day or less
time = 6.49 day
SADT = 114 °C
The SADT is 114°C. This temperature is the lowest environment temperature at which overheat in the
middle of the specific packaging exceeds 6°C (∆T6) after a lapse of the period of seven days (168 hours) or less. This period is measured from the time when the packaging centre temperature reaches 2°C below
the surrounding temperature. This overheat of 6°C occurs after about 6.5 days.
center
surface
outside
Simulation of Thermal Explosion of a 50 kgPackage of Azodicarbonamide (Tamb = 120°C)
SADT predicted: 114°C
SADT literature: 115°C(M.W. Whitmore, J.K. Wilberforce, J. Loss Prev. Process Ind., 6 (1993) 95.)
The simulated SADT values of azodicarbonamide being in very goodagreement with those already determined indicate the
(i) correct collection of the experimental DSC data,
(ii) accurate procedure of the determination of kinetic parameters, and
(iii) precise evaluation of the thermal safety behavior implemented in AKTS-Thermokinetics software.
Conclusion
Thermal safety simulation of self-reactive chemicals in kg-scale (SADT) based on:
(i) the kinetics of the reaction investigated by DSC applying differential isoconversional method
(ii) the heat balance of the system
allow the precise prediction of SADT.