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4.10. ADIABATIC TEMPERATURE MODE:
Prediction of the reaction progress
 (-),
development of the temperatures and adiabatic induction times for selected
starting temperatures and
 T-adiabatic
(Hr/cp
with
Hr
: heat of reaction and
cp :
heat capacity).
(With AKTS-Thermokinetics Software version < 2.28)
(With AKTS-Thermokinetics Software version >= 2.28)
Example:
Thermal risks : Calculation of adiabatic thermal transformation and heat
accumulation from non-isothermal DSC measurements
The precise prediction of reaction progress under adiabatic conditions is
necessary for the safety analysis of many technological processes [19-23].
Calculations of an adiabatic temperature-time curve of the reaction progress can
also be used to determine the decrease of the thermal stability of materials
during storage at temperatures near the threshold temperature for triggering the
reaction. Due to insufficient thermal convection and limited thermal
conductivity, a progressive temperature increase in the sample can easily take
place, resulting in an explosion.
Commonly used, simplified approach for the determination of the TMRad
applies the following formula with the arbitrarily chosen zero-order reaction
[24]:
TMRad = cp R To2/(qo
Ea)
where:
cp - specific heat,
qo - maximum specific heat flux measured during an isothermal
exposure at the temperature To
Ea - activation energy of the reaction,
R - gas constant.
However, when applying above approach to predict the TMRad the only one,
simplified zero-order kinetic equation is used by fitting the
reaction/decomposition exotherms by the Arrhenius relationship. This method
gives unfortunately a very rough approximation of the TMRad due to the severe
assumptions made concerning both the kinetics and the constancy of the value of
the activation energy. As presented in
the
next
figure
the activation energy is
strongly dependent on the reaction progress for the considered compounds. In
addition, it can be observed that the different compositions of the mixtures as
well as the different experimental conditions (isochoric/isobaric) strongly
influence the dependence of the activation energy on the reaction extent. The
solution of the problem should therefore be achieved numerically. The
computations have to consider the dependence of the activation energy on the
reaction progress and the optimization of the baselines. For predictions with a
certain level of accuracy, advanced kinetic analysis is therefore required
because most decomposition reactions are complex combinations of several steps.
Figure:
Activation energy of the B/KNO3
samples as a function of the reaction progress for closed and open crucibles.
The activation energy is strongly dependent on the reaction progress. It can be
observed that the different compositions of the mixtures influence strongly the
dependence of the activation energy on the reaction extent. These differences
will strongly influence the prediction of decomposition progress for other
temperature profiles.
The kinetic parameters calculated from the non-isothermal experiments then make
possible the prediction of the reaction progress for any other heating rate and
more generally for any temperature mode. In the following figures the results of
computations performed with AKTS-Thermokinetics software are shown for the
different B/KNO3 mixtures.
- Left column in all figures presents the reaction rates (normalized DSC-signals
after correctly calculated baselines and kinetics) as a function of the
temperature for the various B/KNO3 mixtures under isobaric and
isochoric conditions. Experimental data are represented as symbols, solid lines
represent the calculated signals. The values of the heating rate in °C/min are
marked on the curves.
- Right column shows the reaction progress as a function of time under
isothermal conditions. The values of the temperature in °C are marked on the
curves. Results of some experiments done under isothermal conditions are
presented together with the predicted relationships.
Figure: B/KNO3 50:50 (closed crucibles / isochoric conditions).
Figure: B/KNO3 30:70 (closed crucibles / isochoric conditions).
Figure: B/KNO3 50:50 (open crucibles / isobaric conditions).
Figure: B/KNO3 30:70 (open crucibles / isobaric conditions).
Figure: B/KNO3 20:80 (open crucibles / isobaric conditions).
Decomposition reactions generally involve different reactions with various
activation energies. They are thus influenced in different ways by the
temperature. This is illustrated by the fact that, according to the temperature
range taken into consideration, it is one of the reactions that will dominate. In
fact, a mistake about the energy of activation can have dramatic consequences as
far as the safety of a process is concerned. It is thus strongly recommended to
verify the results according to an isothermal measurement achieved directly in
the temperature range taken into consideration. This is particularly important
for the safety analysis of storage and transport of potentially reactive
materials.
The potential damages due to a loss of control of a reaction are also related to
the quantity of heat released. The heat of reaction is one of the key data
required for correct evaluation of the potential risks. Estimating the thermal
risks involves the evaluation of the severity and the probability
of generating a
runaway reaction. In order to find and elaborate the appropriate measures that
will reduce the risks, it is crucial to evaluate which part the severity and
the probability play in the case of thermal risks. The thermal risk related to a
chemical reaction is the risk of loss of control of a reaction and its possible
consequences such as, for example, a runaway risk. It is thus essential to
understand how a reaction can shift from its normal course to a runaway
situation [25-30]. For all exothermic reactions, the heat of reaction is a
factor of severity. It gives a direct measure of consequences which result from
a runaway destruction potential. A more common and easier value to use and
understand is the adiabatic temperature rise. The adiabatic rise can be
calculated by dividing the heat of reaction by the specific heat.
Figure: Adiabatic runaway
curves for the various B/KNO3
mixtures under isochoric and isobaric conditions for a starting temperature of
370°C. The different B/KNO3
composition ratios as well as the TMRad are marked on the runaway
curves. Under isochoric conditions the B/KNO3
mixtures are thermally by order of magnitude less stable than under isobaric
conditions. Similar behaviour is observed when comparing the different
compositions of B/KNO3
mixtures. It can be observed that mixtures with equimolar ratios have both, for
the experimental conditions considered, shorter TMRad (or lower
thermal stability) and smaller
Tad
(or lower heat of reaction).
Using the reaction heat
DHr
presented in the next
table and a specific heat cp
of 1.62 J/g/°C for the various B/KNO3 mixtures under isochoric and
isobaric conditions, one can calculate the reaction progress due to self-heating
for the different
DTad
(with
DTad =
DHr/cp).
The above figure and next table present the results of such calculations for a
starting temperature of 370°C. The results illustrate how the thermal stability
of representative samples may be investigated using DSC experiments and advanced
kinetic analysis.
Table :
DHr,
DTad
=
DHr/cp
(cp = 1.62 J/g/°C) and TMRad of the different B/KNO3
mixtures for a starting temperature of 370°C.
|
Compounds |
DHr
[J/g] |
DTad
= DHr/cp [°C] |
TMRad |
|
B/KNO3
- isochoric conditions:
50:50
30:70
B/KNO3 - isobaric conditions:
50:50
30:70
20:80 |
4248 ± 119.9
6291 ± 245.3
2010 ± 161.6
4021 ± 246
5221 ± 247.3 |
2622 ± 74
3883 ± 151.4
1240 ± 99.7
2482 ± 151.8
3222 ± 152.6 |
7 sec
12 min
58 min
112 min
28.5 hours |
(A) Adiabatic runaway curves for the B/KNO3 mixture (20:80) under
isobaric conditions showing the confidence interval for the prediction (Tbegin=370°C
and
DTad=DHr/cp=3222±152.6°C).
The confidence interval was
determined for 95% probability. (B) Starting temperature and corresponding
adiabatic induction time TMRad relationship of the
mixture with ratio 20:80 under
isobaric conditions.
The choice of the starting
temperatures strongly influences the adiabatic induction time
(Confidence interval: 95%
probability).
As for the determination of the correct course of the baseline, the predictions
of the reaction progress will spread (with Gaussian distribution) around an
average value. The predictions of the reaction progress for a given temperature
profile will give the 'central tendency', for which the chance of the good
reproducibility on subsequent measurements is maximal. The illustration of these
remarks for the investigation of the B/KNO3 mixture with ratio 20:80
under isobaric conditions for a starting temperature of 370°C is presented in
the above
figure. The mean value of the TMRad
prediction is about 28.5 hours. The lower and upper limits of the confidence
intervals are 21.7 and 37.4 hours, respectively. These values indicate that
there is a 95% probability that the mean TMRad is greater than 21.7
hours and lower than 37.4 hours. The previous figure and next table present the
relationship between the starting temperature and corresponding adiabatic
induction time TMRad. The confidence interval was determined for 95%
probability. Depending on the decomposition kinetics and
Tad,
the choice of the starting temperatures strongly influences the adiabatic
induction time and, therefore, the boundary conditions valid for achieving
necessary safety (e.g. storage or transport of self-reactive substances).
Table:
Starting temperature and
corresponding adiabatic induction time TMRad relationship of the
B/KNO3 mixture with ratio 20:80 under isobaric conditions. The choice
of the starting temperatures strongly influences the adiabatic induction time
(Confidence interval: 95% probability).
The adiabatic induction time is defined as the time which is needed for
self-heating from the start temperature to the time of maximum rate (TMRad)
under adiabatic conditions. Depending on the decomposition kinetics and
Tad,
the choice of the starting temperatures strongly influences the time to
explosion but also the rate of the decomposition process under adiabatic
conditions. The next figure presents the heat rate curves of the B/KNO3
mixture with ratio 30:70 under isochoric conditions for different starting
temperatures.
Figure: Heat rate curves versus temperature for the B/KNO3 mixture
with ratio 30:70 under isochoric conditions.
Additional comments:
Quantitative Predictions of Thermal Hazards
All energetic materials, e.g. explosives or propellants,
release heat during
decomposition. The rate of the decomposition depends on the temperature. From a
box full of oily rags or a barn full of hay to a rocket motor filled with solid
propellant, energetic materials can self-heat with unfortunate results.
Processing, design, quality control, and operational applications of systems
using energetic materials all require an understanding of thermal hazards and an
ability to predict safety limits.
The calculation of adiabatic reaction progresses and/or explosion conditions
from results of DSC/DTA measurements is often desirable because of the small
amounts of material available. The precise predictions of such reaction
progresses can be required in safety analysis of many technological processes.
Calculations of an adiabatic temperature-time curve of the reaction progress can also
be used to determine the decrease of the thermal stability of materials
during storage at temperatures near the temperature of the beginning
reaction.
Due to insufficient thermal convection and limited thermal conductivity, a
progressive temperature increase in the sample can easily take place, resulting
in an explosion. The determination of:
- the critical starting temperatures,
- development of the temperatures
- and adiabatic induction times
are important parameters both for the production as well as for the storage of
potentially explosive materials.
Thermal Stability
Several methods have been presented for predictions of the reaction progress of
exothermic reactions under adiabatic conditions [19-24]. However, because
decomposition reactions usually have a multi-step nature, the accurate
determination of the kinetic characteristics strongly influences the ability to
correctly describe the progress of the reaction. For adiabatic self-heating
reactions, incorrect kinetic description of the process is usually the main
source of serious errors in its interpretation.
The assumption that the decomposition of an energetic material will obey a
simple rate law is not often true. Solid state reactions are often too complex
to be described in terms of a single pair of Arrhenius parameters and the
traditional set of reaction models [1-3]. As a general rule, solid state
reactions demonstrate profoundly multi-step characteristics. They can involve
several processes with different activation energies and mechanisms. Changes in
mechanism associated with complex reactions can cause changes in heat of
reaction (Hr)
and in the kinetic description of the proceeding reaction. When mechanisms
change during the course of a reaction, it is not valid to "linearize" the rate
data for the entire process to obtain a single rate constant. In addition,
methods of the prediction of the summary reaction progress which consider only
one kinetic parameter, namely the "activation energy" and ignore the others such
as the pre-exponential factor and the model function, are an over simplification
of reality. A reliable numerical technique applied in solid state kinetics
should be able to consider several activation energy values
for the description of the solid state reaction extent. The correct
choice of all the kinetic parameters strongly influences the ability to properly
describe the progress of the reaction. The validity of approaches, which
consider exclusively the activation energy values for the determination of the
kinetic characteristics of solid state reactions, cannot be accepted. It is
hazardous to develop safety predictive models that are based on simplified
kinetics determined by DSC, DTA or any other methods. It is extremely dangerous
to use such simplified models for large-scale predictions.
The determination of the appropriate rate equations is a prerequisite for the
correct analysis of the kinetics of the decomposition of energetic materials.
The reaction products formed during the early (induction), intermediate (acceleratory),
and late (decay) periods of a self-heated reaction can be considerably different.
Changes in mechanism during decomposition can result in changes in the kinds of
gas produced as well as their amounts.
Adiabatic induction time
The assumption that it is safe to handle an energetic material at any
temperature below the first appearance of an exothermic signal on the DSC or DTA
curve can often be false. Under perfect adiabatic conditions, there is some
delay at any temperature before the materials reach their maximum rate of
decomposition. When the temperature of any energetic material is increased, it
will either decompose quietly (ultimately rupturing its confinement as a result
of the production of gaseous products), self-heat to explosion or detonation
[31-32], or ignite and burn.
One very important criterion for thermal safety is the "critical temperature" (Tc),
defined as the lowest constant temperature at which a specific material of a
specific size and shape will self-heat catastrophically. It must be remembered,
however, that energetic materials still decompose at temperatures below the
critical temperature. Determination of critical temperature is a very important
test to be run on energetic materials. If they are sealed in a container, gas
pressure will build up until the container ruptures and the result may look like
an "explosion". Extremely violent responses can be expected at temperatures
above Tc.
The highest safe temperature for handling any energetic material depends
essentially on its size, shape, and previous thermal history. The critical
temperature is very sensitive to changes in size in the small-size range. It can
change by several degrees for smaller sizes. If we carry out measurements in 50
cm geometry and make the assumption that an 8 m charge would survive the same
temperature, an accident would almost certainly be the result. It is therefore
very important to predict the induction time under adiabatic conditions. The
adiabatic induction time is defined as the time which is needed for the
self-heating from the start temperature to the time of maximum rate. The
adiabatic induction time is an important parameter to determine when the thermal
safety of any material or process is in question. The time to maximum reaction
rate (or explosion in some cases) can also be used for quality control purposes.
A reduced adiabatic induction time for a new sample of a specific energetic
material indicates a less stable material. Similarly, when considering
compatibility problems, reductions in time to explosion and/or critical
temperature when another material is mixed with the explosive one indicate
incompatibilities. Slight changes in purity or composition, introduction of
defects into crystal due to pressing, past history of a sample, and/or
fabrication or formulation methods can cause major changes of the time to
explosion. These changes can be very large and unexpected.
One important aspect of AKTS-Thermokinetics Software is that it can provide a
small-scale test for quantitative thermal-hazard predictions. The adiabatic
induction time of an energetic material can be determined rapidly for any
starting temperature.
Caution: For explosives, explosion or partial detonation of a few mg
sample can be extremely destructive. Tests must be run with adequate shielding.
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