J. Loss Prtv. Process Ind. Vol. 10. No. I. pp.

3141, 1997
Copyright 0 1997 Elsevier Science Ltd
Printed in Great Britain. All rights reserved
PII:SO950-4230(%)00037-X 095@4230/97 $17.00 + 0.00
ELSEVIER

Estimation of the time to maximum rate

using dynamic DSC experiments

Andreas Keller?, Daniel Stark?, Hans Fierz$, Elmar HeinzleT and

Konrad Hungerbiihler*“f
j-Safety and Environmental Technology Group, Chemical Engineering Department,
ETH Zentrum, CH-8092 Zurich, Switzerland
$Ciba-Geigy AG, Thermal Safety, Basel, Switzerland

Received I July 1996

The probability of thermal risk may be described by the time to maximum rate under adiabatic
conditions (TMR,,). In this paper a screening method based on dynamic differential scanning
calorimetry (DSC) measurements was studied in order to show that, when using the TMRad
criterion, no process would be assessed as safe when it could, in fact, be critical. The method
of investigation was based on dynamic simulation. In this, the DSC measurement equipment
and five different reaction types (simple nth order, consecutive, branched and autocatalytic
reactions) were described in mathematical terms and simulated using MATLAB. The reliability
of the estimation was checked by comparing the simulated TMRad with the estimated TMRad
based on dynamic DSC measurements and isothermal assessment procedures. The TMRad
values calculated from simulation of dynamic DSC runs were always found to lie in the range
of IO-70% of those obtained by dynamic simulation of the adiabatic case. Owing to some uncer-
tainties with regard to autocatalytic reactions, a method was developed to identify them. The
application of the total method to experimental measurements showed a good correspondence
to the results obtained by simulation. The estimation method is therefore a good tool for prelimi-
nary screening and may be applied at the early stages in process design to save both time and
money and without loss of safety. 0 1997 Elsevier Science Ltd. All rights reserved

Keywords: safety screening; thermal safety; DSC; time to maximum rate; autocatalytic reac-
tion; simulation

Introduction safety screening procedures are described in the litera-

ture ]3,4].
Thermal risks of chemical reactions are characterised
First, the severity of a decomposition has to be
both by their severity and by their probability. Using
determined. The reaction enthalpy is measured using a
the runaway scenario [l], severity is described by the
dynamic DSC, in which the temperature in the oven var-
adiabatic temperature rise AT,, and the probability by
ies according to a ramped temperature profile. If ATad is
the time to maximum rate under adiabatic conditions
above a certain limiting value, for which some authors
(TMR,J. Various calorimetric methods are used to mea-
propose a value of 50 K [5], then TMR, must also be
sure these values [2].
determined. The thermochemical kinetics can be
At every step in the procedure for thermal risk
obtained using either a series of isothermal measure-
assessment, attempts should be made to identify those
ments at different temperatures or methods where the
safe processes not requiring further examination. For
temperature is scanned [6,7].The estimation of TMR,
critical processes, further process examinations or pro-
must be conservative, i.e. the estimated TMRad has to be
cess changes with consequent new evaluations of ther-
less than the real adiabatic value. A typical industrially
mal risk must also be made. Various aspects of such
acceptable value of TMRad is 10-24 h [8], hence provid-
ing sufficient time to take appropriate measures to pre-
vent a thermal runaway.
*Corresponding author. FAX: +41 1 632 10 53. e-mail: hung-
A correct determination of the kinetics is time con-
erb@tech.chem.ethz.ch
suming and therefore, preliminary screening methods

31
32 Dynamic DSC experiments: A. Keller et al.

based on dynamic DSC measurements are usually By setting

applied in industry [9]. Any screening method used in
k’ = k,*fic)*( -AH,) (4)
industry is based on a vast database and experience. The
purpose of this paper is to propose a screening method we get
and to demonstrate, that a reasonably safe identification
of critical processes is possible. The demonstration is In 4 = In k’- ST
based on numerical simulation and a limited number of
actual measurements. We believe, however, that the pro- For the same conversion, f(c) is constant and there-
posed method could be used to build up a data base or fore, the value of k’ is also constant. Using measure-
to use an existing one. ments at different temperatures T and plotting In4 versus
l/T gives a straight line with slope -EC/R. Hence, 4 at
Principles of TMRad determination any temperature can be estimated. The value of TMR,,
TMR,, determination by adiabatic experiments determined by isothermal measurements and according
At least in principle, the best way to obtain TMRad to Equation (2) is denoted as TMR,,(iso).
would be to perform an adiabatic experiment [lo]. For
various reasons, e.g. time and amount of sample avail- Parameter determination by dynamic DSC
able, adiabatic tests are hardly practicable for the initial measurements
screening widely required in the fine chemical industry. Here, the heat release rate ironsetat the onset temperature
The time course of the sample temperature T under T OnSetis obtained from a dynamic DSC run. TO,,,, is
ideal adiabatic conditions is expressed by defined as the temperature at which the heat rate signal
can first be differentiated from the baseline temperature
v*Cr,(c,T)*(-AH& reading. Depending on the sensitivity of the instrument
dT n and the curvature of the baseline, this minimal detectable
-= (1)
dt m*c, heat release rate Gonsetcan be of the order of, say,
20 W/kg. At this point the conversion is negligibly
where V is the sample volume, m the mass, c the concen- small. Using this value, the heat release rate e. at tem-
tration and cP is the heat capacity of the sample. r,, is perature To has to be estimated. Using Equation (5) and
the rate of reaction n with enthalpy AH,,,. Note that the assuming constant k’ gives
heat capacities of the equipment and heat effects caused
by phase change are not considered in this relation. The
value of TMRad simulated by Equation (1) is denoted Go= 4...et*exp(~
*(& - i))
as TMRad(adi).
The value of E, is usually unknown. As a rule of
TMR,, calculation with zero order model thumb, an activation energy E,,, of 50,000 J/mol can be
The usual way to determine TMR,, under process con- taken. This is a very low value and according to our
ditions is to set up an Arrhenius model for the decompo- experience never encountered for decomposition reac-
sition reaction. By assuming a zero order model reaction, tions. Having now one reference point for 4,(To) and an
the following expression for TMR, for a start tempera- estimated value for the activation energy, the heat
ture TOmay be derived [ 11,121. release rate at any lower temperature can be estimated
and a corresponding TMRad calculated. As the extrapol-
c “R*F ation is based on a low activation energy, the calculated
TMRad = ’ ’
4(To)*& heat release rate is too high and the resulting TMRad
therefore on the conservative side. This estimate is
In this model, values of the heat release rate 4, at denoted by TMR,,(dyn).
To and the Arrhenius activation energy E, are required.
By neglecting the concentration decrease for reaction,
Identijcation of E, from dynamic DSC measurements
the calculated TMRad is shorter than the real adiabatic An apparent activation energy, E,,,, can be calculated by
value. Either isothermal or dynamic DSC measurements starting from Equation (3) and taking two temperatures
may be used to obtain values of ilo and E,.
T, and T2 and their corresponding heat release rates from
the dynamic DSC diagram.
Parameter determination by isothermal DSC
measurements
En,e = ( $ - i )-r*(ln(i)-lnE))*R (7)
Taking an nth order Arrhenius kinetic model, the heat
release rate is a function of temperature T, concentration
c, the heat of reaction AH,, the activation energy E, and E,,, is equal to the real E, value if ln(Ac&o,)) <c
the pre-exponential factor k,. ln(G&r), i.e. for nth order single step reactions, but only
if the temperature influence dominates over that of con-
centration. These conditions are usually not fulfilled and,
4 = k,*exp( - ST )*j(c)*( -AH,)
therefore, E,,, is not constant during temperature scan-
 Dynamic DSC experiments: A. Keller et al. 33

ning. The resulting curve (Figure 4) may be used either values of S, and Sj are generally different in magnitude,
for a qualitative evaluation of the reaction mechanism because TMR,,(iso) is based on an approximation and
or to provide an estimate of the zero order Arrhenius is usually less than TMR,,(adi).
activation energy for later use in the estimation method.
Experimental DSC data need smoothing, achieved in this s,, = TMkddyn)
~.- ~ - (10)
case by use of splines (function csaps from the spline TMR,,( adi)
toolbox of MATLAB [ 131). TMR,,ddyn)
,&= ---~
TMR,,(lso)
(11)
Determination of the maximal allowed process
temperature Only S,, is relevant for the validity of the estimation
The estimation method may be expressed by a minimal method. Experimental values of TMR,,(adi) were not
temperature difference between the onset temperature available. Therefore, we used S, for the experimental
Ton\etand the maximal allowed process temperature T0,24 verification.
such that a TMR,, of 24 h results. T0,24is a function of
Tonae,.For a zero order reaction this function may be Results and discussion
derived analytically by insertion of Equation (6) into The model parameters H,, E, and k, for each kinetic
Equation (2). By solving this equation, T0,24can be esti- model were varied over wide ranges, such that the
mated resulting dynamic DSC simulations showed detectable
heat release in the range between 40 and 600°C. In Fig-
T0,24 = (8) ure 2, the changes in the shape of DSC simulations due
i to modifications of the model parameters k and E, are
Equation (8) may be solved by iteration and shown for a consecutive reaction. The model parameters
inserting the values (E,,=50,000 J/mol, 9onset=20 W/kg are listed in Table I. The combination of the variation
and the limiting value of 24 h for TMR,& Equation (9) of parameters and models resulted in nearly 100 simula-
results, based on linear regression of the solution of Equ- tions.
ation (8) and with a correlation factor of 0.9998.
Evaluation of the simulated S, value
T0,24Wl = 0.65"~odKl + 50 (9) The calculated value of S, by taking a model and keep-
The result representing the maximum allowed T, is ing the model parameters E,,, k, and AH,. constant,
shown in Figure 6. depends on the chosen TMR, (Table 2). The increase
in safety margin when extrapolating from the onset tem-
perature to progressively lower temperatures is due to
Procedure to validate the screening
the low E,, of 50,000 J/mol used in Equation (6).
method
Hence the estimation of & drifts to more conservative
The estimation method was tested by simulation. The values, the more T,, differs from the onset point. In the
measurement equipment [ 141 and different reaction region of TMR,, equal to 24 h, all safety values S, for
types (Figure Z) were described mathematically. These the five kinetic mechanisms were between 0.1 and 0.7.
reaction types were chosen because more complicated The higher values where obtained for kinetic models
cases may be simplified to these basic types by assuming where the dynamic DSC shows a steep slope at the
rate limiting steps. The differential equations were trans- beginning.
lated into MATLAB. The recently available routine A shoulder results in the DSC diagram for multiple
odel5s from the toolbox odesuite showed stable behav- step mechanisms, when the first reaction has a lower
iour in solving the equations even at the end of the energy release. T,,,,, is then estimated at the beginning
decomposition, a region of a high stiffness. of this shoulder, resulting in a lower TMR,,(dyn) at T,-,.
For all chosen reaction mechanisms, simulations If the reaction proceeds adiabatically, the temperature
were carried out under three different modes. The first stabilises on a certain level before the final decompo-
under adiabatic conditions, yields TMR,,(adi), which is sition leading to a thermal explosion sets in (Figure 2).
needed as the reference value. The value of T,, to attain The influence of variations in AHR on the safety
a TMR,, of 24 h was determined by iteration. Secondly, value S, is shown in Table 3. No uniform influence on
three isothermal runs at different temperatures enabled the calculated S, was found, but even at high values for
TMR,,(iso) at T,, to be determined. In the third mode, AH,, the safety value S, is always less than one.
one dynamic DSC run was simulated and TMR,(dyn)
evaluated using the estimation method presented above. Evaluation of the simulated Si value
It is possible to demonstrate the validity of the esti- For nth order single-step reactions the Si value is below
mation method by calculating the safety indices S, and one. This is for the same reasons as given above for the
Si according to Equation (I 0) and Equation (11). If the S,, value.
value of S, is less than one, the results predicted by the By considering multi-step, nonautocatalytic reac-
estimation method must then be on the safe side. The tions such as consecutive or branched reactions, the cal-
34 Dynamic DSC experiments: A. Keller et al.

A) n-order reaction
kl r,, =-k, *CA
A fB

B) consecutive reaction
rA=-k, *CA
Akl__ Bk2C
ru =k, *C, -k, *C,

C) branched reaction
kl k2
A-B-D
rA =-k, *C,
k; rtl=-kZ*C,-k,*C,
rc=kg*Cs--k,*Cc
I )
k4
C E

D) autocatalytic reaction
kl
A *B
r,,=-k,“C,-k,*CA*CB
k2
A+B -2B

E) mixed reaction
kl
A NC .A_LD

r,,=-k,*C,-k,*CA
k2 k3 r, = k, * C,
rc=k,*C,-k,*Cc -k,*Cc-k,*C,*C,
I I
B E ro=k,*Cc+k,*Cc*C,
rL =kl*Cc
k5
C+D -* 2 D

Figure 1 Reaction types and their kinetic expressions. All reaction rates are first order with respect to all participating reactants. k,
represents the Arrhenius term k,=IQ,,*exp(-E,,J(R+T))

culated activation energy obtained from isothermal runs meter sets for the autocatalytic model are shown. The
depends on the chosen temperature range for the exper- used model parameters are listed in Table 5.
iments. Depending on temperature range, differing reac- Small variations in the model parameter Eu2 (Table
tions may dominate the rate of heat production. Table 4 6), the activation energy of the autocatalytic Prout-
compares various TMR,, values calculated for iso- Tompkins [15] step, resulted in simulations, for which
thermal runs with simulated values obtained under adia- the calculated TMR,,(iso) was longer than TMR,,(adi).
batic conditions and shows that it is possible to calculate Hence the isothermal DSC estimation method does not
TMR,(iso) values greater than TMRJadi). always give acceptable results for autocatalytic
For autocatalytic reactions a conservative estimate decompositions.
of the TMR,, using a series of isothermal measurements
is obtained by taking the heat flow maxima, neglecting Method for the identijication of autocatalytic reactions
therefore the isothermal induction times. The main prob- Figure 4 shows some examples of E,,, curves simulated
lem here is the nonequal conversion at these heat flow by Equation (7). E,,, was calculated from T,,,,,, to 90%
maxima. Hence Equation (2) and Equation (3) must be of the temperature difference between TO,,,, and the tem-
used with care. Despite this the proposed procedure was perature of the peak maximum Tpeakmax.
used to calculate TMR,(iso) for autocatalytic simula- nth order reactions are characterised by a negative
tions. In Figure 3, simulations using three different para- slope, as shown in Figure #A. This is due to the increas-
 Dynamic DSC experiments: A. Keller et al. 35

IlOOr Al IO00 ~~ A2 693 - A3

7
I

*ij / \ , or i&L&____,_ :93r

293 I
693 0 10000 0 100000
T LKI t Lsl t Is1

IIOO- Bl B2 h93 B3

293 693
T IKI

Figure 2 Simulated curves for the consecutive reaction mechanism with three parameter sets (A,B,C of Table I). In the first column,
dynamic results are listed. The second column shows isothermal runs at different temperatures (A2:520, 540, 550 K; B2:480, 500,
520 K; C2: 530, 550, 560 K) and the third column the adiabatic course of the reaction

Table 1 Model parameters for the diagrams in Figure 2

f,, lJ/moll Ea2 [J/mall k,, Is’1 ka? [s ‘I AH,, [J/mall AH, [J/mall

A 50,000 160,000 3.5E2 lE12 100,000 400,000

B 80,000 160,000 1.5E5 lE12 300,000 200,000
C 160,000 100,000 lE12 5E5 300,000 200,000

Table2 Influence of different simulated TMR,,(adi) on the safety value S, (Equation (IO)) for previously defined reaction types
(Figure 7)

TMR,,(adi) S, first order S, consecutive S, branched S, autocat S, mixed

5h 0.8 0.8 0.7 1.0 0.6

24 h 0.6 0.4 0.5 0.6 0.3
100 h 0.5 0.2 0.4 0.3 0.2

ing conversion. In the case of consecutive and branched ing E,,, curve results (Figure 4D-F’), but the high value
reaction mechanisms (Figure 4B,C), it is possible that of the estimated E,,,(max) is characteristic.
the slope may change from negative to positive. For If the estimated E,,, value is greater than
autocatalytic reactions either an increasing or a decreas- 160 k.I/mol somewhere within the range
36 Dynamic DSC experiments: A. Keller et al.

Table 3 Influence of the model parameter /-I, on the safety value S, for previously defined reaction types (Figure 7)

H, kJ/kgl S, first order S, consecutive S, branched S, autocat S, mixed

300 0.3 0.1 0.2 0.2 0.2

800 0.3 0.2 0.3 0.2 0.3
1500 0.3 0.5 0.2 0.2 0.4

Table 4 Influence of the temperature range of isothermal measurements on determined E, and on TMR,,(iso) using the Arrhenius
model in the case of a consecutive reaction

Range isothermal min/max heat release rate f, from Arrhenius diagram

TMR,,(isoVTMR,,(adi)
measurements [Kl W’.‘/kgl IJ/moll

470+510 501160 57,800 0.3

520t560 2101630 65,400 0.4
540+580 370/1290 83,700 1.4

3- Al SOC)- A2 1893 A3

g 1093
+

---
:93
, / \ 693
I 0 a___ --__ ____---40000 2930L 100000
T lK1 t lsl t lsl
Bl B2 1893 B3
r

_-lLxx,..__
:93
,i::_ T [K I

Cl
I
693 0

800~
t Is1

c2
40000 0

1893r
t Is1
c3
100000

I
:93 1 ,$l,.___.
T
,1:_
WI
_ 693 0

t Is1
40000 0

t lsl
Figure 3 Simulated curves for the autocatalytic reaction mechanism with three parameter sets (A,B,C of Table 5). Columns as given
in figure 2 with isothermal runs at temperatures A2:500, 520, 540 K; B2:490, 500, 510 K; C2: 390, 400, 410 K

0.1 <(T- T,,,,)I(T,,,,,- T,,,,,)<O.9, the decompo- (2) and Equation (6)) was tested. For simple nth order
sition reaction is then very likely to be autocatalytic. reactions, this leads to correct values for TMR,,. In other
The idea to use E,,, estimated at the very beginning cases, the use of the estimated Ea,e value can lead to
of the E,,, curve in the screening procedure (Equation unsafe TMR,, estimations. Therefore, E,,, values calcu-
 Dynamic DSC experiments: A. Keller et al. 37

Table 5 Model parameters for the diagrams in Figure 3

E,, IJ/moll faz [J/mall k,, [s ‘I

k3 mol ‘s ‘1
AH,, [J/mall U/,= [J/mot1

A 50,000 160,000 3.5E2 IEIZ 100,000 400,000

B 80,000 160,000 1.5E5 lE12 300,000 200,000
C 160,000 100,000 lE12 5E5 300,000 200,000

I lO( Al 1lOOr Cl

z!

&
.m

)
693 293 693
T IKl T Kl

A2
80000

J
0 0.9 0 0.9

,- El )-

)L Jk I Ii I
293 693 293 693 293 693
T Kl ‘I- WI T Kl

5ooooc E2 1 F2

1
0.9

Figure4 Typical dynamic DSC and corresponding E=,, curves for different
branched, D and E autocatalytic and F mixed reaction as given in Figure 7
0.9
I

reaction
0
L
I
mechanisms. A first order,
I
0.9

B consecutive, C
38 Dynamic DSC experiments: A. Keller et al.

No Si value greater than one was found. In the case

Table6 Influence of Esz, the activation energy in the Prout-
Tompkins step of the autocatalytic model (Figure 7D) on of nonautocatalytic decompositions, an assessment by
TMR,,(isoVTMR,,(adi) estimation use of the dynamic DSC diagram results in a higher
safety margin compared to an isothermal assessment.
L IJ/moll TMR,,(iso) / TMR,,(adi)

100,000 4.4 Determination of the maximal allowed process

95,000 1.2 temperature
93,000 0.7 The graphical representation of the minimal temperature
90,000 0.3
difference between T,,,,,, and a TO leading to a
TMR,(dyn) of 24 h is shown in Figure 6. By using the
estimation method only temperatures below the To,24line
’\ ‘\
.-- are assessed as safe. All values of TOcalculated by adia-
400000 -
\ ‘\ ‘. -.
-. /’
/ ‘\
‘.
‘-__;~::____---_--”
batic simulation for a TMR,,(adi) of 24 h were indeed
/‘-
--__
--__ /’
higher than those obtained by the estimation method, as
--._
‘.L’ shown in Figure 6. Our investigations covered only the
a
E range from 50 to 250°C for TO,,,,.
5 160000

%
Figure 6 is a convenient tool for screening. The
W maximum process temperature can be read from the dia-
0.2 v - 0.5 0.7 0.9
gram directly. Indicated in Figure 6 is also a line indicat-
-8OIIOO L
ing another rule of thumb [ 161, i.e. safe process tempera-
V - -LSr?t)KTpanax - Tonset)
ture is TO,,,,- 100 K. This rule gives results in the
Figure 5 E,, curves of three autocatalytic (- - -) and three non- same region.
autocatalytic (-1 measured DSC samples versus normal-
ised temperature
Uncertainty of the estimation method
Base line settings and reading errors in evaluation of
lated by Equation (7) while neglecting the influence of
DSC diagrams lead to errors in the determination of
concentration, must not be used for the estimation of
TMR,,.
600 -
Experimental verijcation of the simulated results - To = Tonset
Dynamic and isothermal DSC runs were conducted - TO.24

using standard procedures for 15 industrial samples ----- 100 K rule

which decomposed with high energy release (heating
rate 4”C/min, Mettler DSC25). The ones identified as
autocatalytic by the E,,, curve were the same that
showed the characteristic delayed heat release in the iso-
thermal runs. In Figure 5 it can be seen that the nonauto-
catalytic reactions show an apparent activation energy
lower than 160 kJ/mol, while the autocatalytic ones T onsetWI
show values higher than 160 kJ/mol either over the
whole range of (T- T,,,,,)I(T,,,,,,- T,,,,,) or over a part Figure6 Temperature r,, to yield TMRad of 24 h, plotted as a
function of T,,,,,. Thick line: calculated according Equation (9):
of it. No autocatalytic reaction was assessed as nonauto- TMR,,(dyn)=24 h. Symbols: simulated for different reaction
catalytic by the use of the E,,, curve. mechanisms: TMR,,(adi)=24 h (m first order, A consecutive, x
For the nonautocatalytic decompositions, the Sj branched, 0 autocatalytic, 0 mixed). Dashed line: subtraction
of 100 K from r,,,, [161. AT,,in shows the minimal temperature
value was calculated (Table 7). To was chosen such that difference between r,,,,, and T0 to reach a TMR,,(dyn) greater
a TMR,,(iso) of 24 h resulted. than 24 h

Table 7 Calculated S, values for nonautocatalytic decompositions, measured values from seven industrial samples

Sample Nr. s, = TMR,,(dyn) AH, [kJ/kgl 4m.x W/kg1

’ TMR.,(iso)
1 0.1 -1950 3100
2 0.2 -2010 2600
3 0.4 -330 300
4 0.6 -1230 1600
5 0.8 -480 250
6 0.8 -510 400
7 1.0 -980 1100
 Dynamic DSC experiments: A. Keller et al. 39

TO”?A.To maximise the accuracy of TO,,,, experimental used in an estimation method. A too-high E,,, results in
care is needed. a too low Go, leading to too-high TMR,, values.
The sensitivity of the calculated TMR,,(dyn) on It is known, that normal reactions have activation
such errors may be expressed by the first derivative of energies in the range of 60,000-140,000 J/mol. By using
the equation resulting from insertion of Equation (6) into the value of 50,000 J/m01 in the estimation method, the
Equation (2). assessment is on the safe side as shown in all simula-
tions.

Conclusion
The final procedure for screening is shown in Figure 9.
Assessing the estimation method at a temperature
Run dynamic DSC.
resulting in a TMRad greater than 24 h, and using Equ-
Identify the samples with AT,,>50 K.
ation (12) assuming an accuracy in TO,,,, of +lO”C,
Identify autocatalytic reactions by the E,,, plot and
resulted in no upper limit for the S,, factor greater than
evaluate them separately.
0.9 for all investigated reaction mechanisms.
Calculate TMR,,(dyn) for the nonautocatalytic reac-
A more accurate estimation of the heat release rate
tions or use Figure 6 to check a proposed maximum
at a corresponding temperature may be found by taking
process temperature with respect of the limiting tem-
a heat release rate 4 well above the instrument sensitivity
perature.
(e.g. >20 W/kg). Due to the steeper dynamic DSC curve
Identify the ones with TMR,,(dyn) less than 24 h and
at higher heat release rates, inaccuracies in 4 result in
evaluate these separately.
smaller errors of corresponding temperature. An error in
Run isothermal DSC and determine TMR,,(iso).
the estimate of 4 affects the S,, value. Figure 7 shows
the decrease of the error bounds of S, for an absolute The demonstrated estimation method with a E,,, of
error in 4 of +5 W/kg as a function of 4 in case of a 50,000 J/mol is a good tool to determine whether TMRad
branched reaction. Conversion would lead to actual is greater than 24 h or not. The method may be applied
lower + and therefore overestimation of S,,; however, the for all types of decomposition reactions. Heterogeneous
influence of the extrapolation using the low E,,,, value reactions were not investigated, but using the assumption
of 50 kJ/mol dominates and the S, values decrease with of rate limiting steps they may be reduced to one of the
higher 4. reaction mechanisms investigated as shown in Figure 2.
The estimation method may be extended and pro- Owing to some uncertainties concerning autocatalytic
vide better results by defining the onset point at a spe- decompositions, as shown in the S, calculations, we rec-
cific heat release rate greater than 20 W/kg. Presumably ommend that these reactions are treated separately.
a greater value for E,,,,, would also be sufficient to obtain The E,,, value of 50,000 J/mol is appropriate for
safe estimations. But here further research is necessary. screening assessment using dynamic DSC runs and
should not be changed. The presented method for calcu-
Importance of the chosen E,, used in the estimation lating the E,,,, curve is useful in identifying autocatalytic
method reactions. To calculate this curve, an experimental DSC
The sensitivity of the S, values on the chosen E,,, in the curve should be smoothed. It is important to take the
estimation method is shown in Figure 8 for a branched onset of the first peak, even if the first peak shows only
reaction. The safety values S, are plotted against the a low heat release at the peak maximum.
value of E,., used in the estimation method. Only E,r,m By using the presented estimation method in the
values, where the safety factor is less than one, may be screening procedure shown above, time and money may
be saved without loss of safety. Especially at the very
early stages in process design, where a first estimation
is needed, the presented method might be used.

Nomenclature
ARC Accelerating rate calorimetry

cn” ( Concentration [mol m-‘1

I
I c,> Heat capacity [J kg-’ K-‘1
,
I
/
I
DSC Differential Scanning Calorimetry
0 I I i I I I
10 20 30 40 50 60 70 80 6, Arrhenius activation energy [J mol-‘1
&met, new [w&l
E<,., Estimated I?, with dynamic DSC [J mol-‘1
Figure7 S, values estimated from varying heat release rates
4 (thick line) and its error bounds (thin line), caused by an error E <I,,,! E,used in the estimation method [J mol-‘1
of f5 W/kg in determining 4 WWo0)
40 Dynamic DSC experiments: A. Keller et al.

I __-_s,
-
S,

7
\
\
) c I
293 793 59 Ml 2ooooo
T W E a.m

Figure8 Influence of choice of E. for the screening calculation of S, for a branched reaction mechanism. In the right diagram the
calculated S, for the dynamic DSC simulation, shown on the left, are plotted against different values of E, used in the estimation
method

CakUlatiOn of ATOP from

dynamic DSC measurements
I

--ykq
autocatalytic decomposltlons

+,
isothermal DSC measurements

special investigations
and/or
measures to increaseTMR,d

Figure 9 Description of the thermal risk assessment procedure including the estimation method
 Dynamic DSC experiments: A. Keller et al. 41

Subscripts
k, Preexponential factor n Refers to number

m Mass [kg1 R Refers to reaction

4 Heat release rate [WI onset Refers to onset point in dynamic DSC curve
peakmax Refers to the maximum of the dynamic DSC curve
R General gas constant [J mol-’
Km’] 0 Referx to initial value

Reaction rate [mol mm’s_ ‘1

Ratio of TMR,,,(dyn)lTMR,,,(adi)
References
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