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.