AKTS-Thermal Safety

AKTS-Thermokinetics and AKTS-Thermal Safety
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A brief description

AKTS-Thermal Safety Software enables the calculation of the Time to Maximum Rate under adiabatic conditions (TMRad). Finite Element Analysis (FEA) extends the application of calculating methods to analyze the thermal behavior under non-adiabatic conditions. FEA enables the determination of the impact that substance and container properties can have on the reaction progress. This analysis can then be used to determine critical design parameters such as the critical radius for a container, the necessary thickness of insulation, and the influence of the surrounding temperature on storage and transport safety. The method enables the prediction of the heat accumulation process and the reaction progress for any surrounding temperature profile (isothermal, stepwise, periodic temperature variations, temperature shock and real atmospheric temperature profiles). Key applications for AKTS method are found in the chemical, pharmaceutical and food industries, for self-reactive chemicals, explosives and thermal hazards for dangerous goods. Analysis and specific safety concepts produced for customers by AKTS-Thermal Safety Software are optimized for cost-effectiveness and apply state-of-the-art technology.


       

5. KINETICS AND SCALE UP SAFETY ANALYSIS

Calculation of adiabatic thermal transformation and heat accumulation from non-isothermal DSC measurements

Thermal Aging and Thermal Safety

5.1 Introduction

The precise prediction of reaction progresses in adiabatic conditions is necessary for the safety analysis of many technological processes. Calculations of an adiabatic temperature-time curve for 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 a thermal runaway.

Several methods have been presented for predicting reaction progress of exothermic reactions under heat accumulation conditions [1, 8-17, 23-36]. Because of 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. The use of simplified kinetic models for the assessment of runaway reactions can, on one hand, lead to economic drawbacks, since they result in exaggerated safety margins. On another hand, it can cause dangerous situations when the heat accumulation is underestimated. For self-heating reactions occurring adiabatically, incorrect kinetic description of the process is usually the main source of prediction errors.

5.2 Adiabatic temperature rise

5.2.1 Concept

Kinetic parameters calculated from DSC measurements are used for describing thermal behavior of larger amount of substance because the kinetics of any reaction is the same for ten milligrams of substance and for one ton. However, during scale-up two important factors have to be considered:

(i) the application of advanced kinetics, which properly describes the complicated, multistage course of the decomposition process,

(ii) the effect of heat balance in the energetic system, as the sample mass is increased by a few order of magnitude compared to the thermoanalytical experiments.

Because decomposition reactions usually have a multi-step nature, the isoconversional analysis enables a more accurate determination of the kinetic characteristics compared to simplified kinetic based approach that are essentially based on simplified kinetics assumption like ‘let’s assume that the reaction is zero order etc…’

The application of the DSC data for the simulation of the adiabatic measurements seems to be, for the first glance, not obvious. However, the closer look on the differences and similarities of the processes occurring under different conditions of the heat exchange allows to understand that the adiabatic properties such as self-heating rate or time to maximum rate can be correctly determined from the DSC results obtained or isothermally, or better, at different heating rates. The main difference between DSC run and fully adiabatic process lays in the conditions of the heat exchange. Due to the fact that in the thermoanalytical experiments the heat evolved during reaction is fully exchanged with the environments, the heating rates under which the experiment are carried out can be arbitrarily chosen. In turn, after determination of the kinetic parameters from the results of few experiments done with different heating rates, one can predict the reaction rate under any temperature ramp.

Due to the totally different heat exchange conditions in adiabatic conditions the heating rate of the process (called now self-heating rate) cannot be controlled anymore, being dependent only on the kinetics, adiabatic temperature rise and φ-factor. However, even in this case we can simulate the reaction rate. The scheme of the general idea of this procedure is presented in the next figure.

Presentation of the adiabatic temperature rise

Fig. 5.1 : Scheme of the presentation of the adiabatic temperature rise in the form of four sequences of the time periods Δt in which the heating rates are constant and amount in turn to β1, β2, β3 and β4.

Let us assume that the temperature increase under adiabatic conditions in the coordinates time - temperature can be presented schematically as in Fig. 5.1 in the form of four sequences of the short periods of time Δt in which the heating rate is constant. In time periods 0-t1, t1-t2, t2-t3 and, finally, t3-t4 the heating rates are β1, β2, β3 and β4, respectively. As shown previously, one can easily predict the reaction rate under any β value. During the temperature change schematically presented in Fig. 5.1, the reaction course can therefore be calculated as a sequence of processes occurring at known heating rates β1-β4. Using the infinitesimal Δt values for the description of the self-heating rate one can predict the reaction course under the adiabatic temperature change. The process occurring under adiabatic temperature rise is expressed as a succession of an infinite number of processes occurring at constant heating rates which can now be easily calculated by described method.

5.2.2 Heat transfer mechanisms

Heat transfer deals with systems that lack thermal equilibrium, and thus it is a non-equilibrium phenomenon. The basic requirement for heat transfer is the presence of a temperature difference. Heat is transferred in the direction of decreasing temperature. The temperature difference is the driving force for heat transfer. The rate of heat transfer in a certain direction depends on the magnitude of the temperature gradient in that direction. The larger the temperature gradient, the higher the rate of heat transfer.

Heat can be transferred in three basic modes:
- conduction,
- convection,
- radiation.

All modes of heat transfer require the existence of a temperature difference. All modes are from the high-temperature medium to a lower-temperature one.

5.2.2.1 Conduction

Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. Conduction can take place in solids, liquids, or gases. In gases and liquids conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, conduction is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons.

Heat transfer by conduction in solids, liquids or gases

Fig. 5.2 : Heat transfer by conduction in solids, liquids or gases.

The range of thermal conductivities is enormous. As we see from Fig. 5.2, λ varies by a factor of about 105 between gases (poor heat conductor or insulator) and diamond (good heat conductor) at room temperature. One should study and remember the order of magnitude of the thermal conductivities of different types of materials. This will be a help in avoiding in future computations, and it will be a help in making assumptions during problem solving.

Thermal conductivities of materials

Fig. 5.3 : Thermal conductivities of materials. Pure crystals and metals have the highest thermal conductivities, and gases and insulating materials the lowest.

5.2.2.2 Convection

Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion. Convection is commonly classified into three sub-modes:
- Forced convection,
- Natural (or free) convection,
- Change of phase (liquid/vapor, solid/liquid, etc.)

5.2.2.3 Radiation

Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules. Heat transfer by radiation does not require the presence of an intervening medium. Radiation is emitted by bodies because of their temperature.

5.2.3 The kinetic based approach for the determination of the Time to Maximum Rate under adiabatic conditions (TMRad)

In heat transfer problems it is convenient to write a heat balance and to treat the conversion of chemical energy into thermal energy as heat generation. The energy balance in that case can be expressed as

Energy balance expression

The solution of the problem leads to a thermal stability diagram, i.e. for each starting temperature the Time to Maximum Rate under adiabatic conditions (TMRad) can be obtained easily.

5.2.3.1 Batch reactor in case of cooling failure

The energy balance of an exothermic reaction taking place in a batch reactor can read as follow

Energy balance of an exothermic reaction taking place in a batch reactor

with M: mass, Cp: specific heat, T: temperature, U: overall heat transfer coefficient, A: contact surface between the sample and the container, ΔHr : heat of reaction, indices c, s and e: container, sample and environment, respectively. In case of cooling failure the overall heat transfer coefficient U=0 for achieving the adiabatic conditions. In a fully operationally adiabatic environment all the heat release goes to heat the sample and the container. If there is thermal equilibrium within the solution and the wall

TMRad Equation

then the whole system will have the same temperature rise rate and we can simplify the above equation to:

Simplified equation

that can be rewritten as

Rewritten simplified equation

with: the adiabatic temperature rise: Adiabatic temperature rise
The phi factor φ = The phi factor
the reaction rate The reaction rate

For batch reactor with large sizes (>1 m3), it can be assumed that  Ms>>Mc(jacket)  so that we obtain

Equation for batch reactor with large sizes(with φ around 1)

Equation for batch reactor with large sizes

In case of isoconversional analysis we have :

Case of isoconversional analysis with Case of isoconversional analysis

Note, for comparison, in case of simplified zero order kinetic assumption we would have :

Case of simplified zero order kinetic assumption

It comes from the above equations that one can use the kinetic based approach for predicting the reaction progress α(t) and rate dα/dt as well as the development of the temperatures Ts(t) and dT/dt and adiabatic induction times at any selected starting temperatures.

5.2.3.2 Adiabatic calorimeter

There are several issues that need to be taken into consideration for the examination of adiabatic conditions or reconstructing an Accelerating Rate Calorimeter experiment starting from the kinetic based approach. The energy balance in case of an adiabatic calorimeter can be expressed as before

Energy balance in case of an adiabatic calorimeter expression

Because the presence of a temperature difference leads to heat transfer, an adiabatic calorimeter constantly attempts to achieve equilibrium states by keeping Te = Ts. As a consequence there is no driving force for heat transfer and the chemical reactions run adiabatically. We obtain as before

Expression

Expression

However, one has to take into account the thermal inertia (or φ-factor) to consider the effect of the vessel’s inertia i.e. the reaction heat that is transferred in part into heating of the bomb. It can be observed that the φ-factor influences the simulation of an ARC experiment. The φ-factor influences:

the Delta T adiabatic, measured because it comes from above description that Delta T from above description

and the TMRad in different levels depending on the type of decomposition kinetics.

Usually, the standard method of correcting the time for the reaction under adiabatic conditions is

Standard method of correcting the time

This is however an approximation.

5.2.3.3 Dewar

In dewar tests the walls consists of layers of different materials. The energy balance in that case can be handled just like exothermic reaction in the adiabatic calorimeter or batch reactor in case of cooling failure.

Dewar equation

The net heat rate through a three-layered wall (glass-vacuum-glass) of thicknesses L1, L2 and L3 with convection on both sides is presented in the next figure.

Dewar description

Fig. 5.4 : Schematic description of a Dewar. The net heat rate through a three-layered wall (glass-vacuum-glass) of lengths L1, L2 and L3 with convection on both sides.

The rate of the heat transfer between air and the wall at the outer surface is by convection. The heat transfer through the three-layered wall is conduction. If the reaction mixture is a liquid, heat transfer between the liquid and the wall at the inner surface is by convection. Rate of heat convection into the wall, rate of heat conduction through the wall and rate of heat convection from the wall can be expressed as:

Rate of heat convection expression

In an analogous manner to Newton’s law of cooling it is sometimes convenient to express heat transfer through a medium UA(Te-Ts) using the thermal resistance concept:

Thermal resistance concept

Where

R total

As h1<< h2, λ1<<λ2 and λ3<<λ2 (because λvacuum<<λglass), it can be assumed that

R total

In addition, Ms>>Mc(glass) so that after insertion into the energy balance

Energy balance

and simplification we can write

Energy balance simplification

Ts

Note that

UA

If the total resistance Rtotal is very large it can be assumed that U → 0 and we obtain

Dewar equation

which leads basically to the same results as before for exothermic reaction in the adiabatic calorimeter or batch reactor in case of cooling failure.

5.2.3.4 Construction of a thermal safety diagram: runaway time as a function of process temperature under adiabatic conditions (TMRad = ƒ(T))

The decomposition of the examined substance follows an exothermal process. Using the heat of reaction (ΔHr = -554.8±17.4 J/g) and assuming a heat capacity Cp = 1.5 J/(g·K), one can calculate the reaction progress due to self-heating for any ΔTad = (-ΔHr)/Cp/Φ. Notes:

(i) Cp can be easily determined with Calisto Software
http://www.akts.com/calisto-overview.html
http://www.akts.com/live-video-calisto-processing-video-cp-regression.html

(ii) Cp value has been assumed = 1.5 J/(g·K) for illustration.

As long as thermal safety analysis is concerned, 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 ΔTad, the choice of the starting temperatures strongly influences the time to runaway and the rate of the temperature evolution under adiabatic conditions. Figure 5.5 presents the starting temperature and corresponding adiabatic induction time TMRad relationship.

Predictions window, Safety Diagram tab

Safety Diagram

Safety Diagram

Figure 5.5 Thermal safety diagram: Starting temperature and corresponding adiabatic induction time TMRad relationship of the examined material. The choice of the starting temperatures strongly influences the adiabatic induction time. ΔHr = -554.8±17.4 J/g and ΔTad=(-ΔHr)/Cp/Φ=369.9±11.6°C for Φ = 1 and Cp = 1.5 J/g/°C.

ΔHr = -554.8±17.4 J/g, Cp = 1.5 J/g/K, ΔTad=(-ΔHr)/Cp= 369.9±11.6°C
Temperature
(°C)
(TProcess)
Time (h)
(TMRad for TProcess
and ΔTad=369.9°C)
Time (h)
(TMRad for
TProcess+1°C and
ΔTad=381.5°C) (pessimistic)
Time (h)
(TMRad for
TProcess-1°C and
ΔTad=358.3°C) (optimistic)
89 0.95 0.87 1.05
88 1.03 0.94 1.14
87 1.12 1.02 1.24
86 1.21 1.1 1.34
85 1.32 1.19 1.46
84 1.43 1.29 1.58
83 1.55 1.4 1.72
82 1.69 1.52 1.87
81 1.83 1.66 2.03
80 1.99 1.8 2.21
79 2.17 1.96 2.4
78 2.36 2.13 2.62
77 2.57 2.32 2.85
76 2.8 2.52 3.11
75 3.05 2.75 3.39
74 3.33 3 3.71
73 3.63 3.27 4.05
72 3.97 3.57 4.42
71 4.34 3.89 4.83
70 4.74 4.25 5.29
69 5.18 4.65 5.79
68 5.67 5.08 6.34
67 6.21 5.56 6.94
66 6.8 6.09 7.61
65 7.46 6.67 8.35
(*)64 (*)8.18 (*)7.31 9.16
(*) Means that if Φ=1 and Cp=1.5 J/g/°C the determined TMRad is about 8 hours (8.18 h) for an initial temperature of about 64°C (for that temperature a more conservative value for TMRad is about 7.31 h)
63 8.97 8.02 10.06
62 9.85 8.8 11.05
61 10.83 9.66 12.15
60 11.9 10.61 13.37
59 13.09 11.66 14.72
58 14.4 12.82 16.21
57 15.86 14.11 17.86
56 17.48 15.53 19.7
55 19.27 17.11 21.73
54 21.26 18.87 23.99
(**)53 (**)23.47 (**)20.81 26.51
(**) Means that if Φ=1 and Cp=1.5 J/g/°C the determined TMRad is about 24 hours (23.47 h) for an initial temperature of about 53°C (for that temperature a more conservative value for TMRad is about 20.81 h)
52 25.92 22.97 29.3
51 28.65 25.37 32.42
50 31.69 28.03 35.88

Table 5.1 Thermal safety table: Starting temperatures and corresponding TMRad for the examined material under adiabatic heat accumulation conditions.

Figure 5.6 illustrates the applications of the above equations for the simulation of the thermal behaviour under adiabatic conditions. The simulated T-time relationships are presented with a starting temperature of about 52.8°C leading to TMRad of 24 h.

Predictions window, TMRad tab

TMRad Predictions

Figures 5.6 Adiabatic runaway curves with ΔHr = -554.8±17.4 J/g and Cp = 1.5 J/g/K showing the confidence interval for the prediction: Tbegin=52.78±1°C. ΔTad=(-ΔHr)/Cp/Φ=369.9±11.6°C for Φ =1.

Note that isothermal conditions can be numerically retrieved by setting an exceptionally large value of φ to make the adiabatic temperature rise ΔTad insignificant. If the φ is very high all heat released by the reaction is dissipated to the surrounding. As a consequence, the sample temperature remains constant i.e. isothermal:

Sample temperature remains constant

for very large values of φ we have

For very large values and For very large values

Predictions window, TMRad tab

Comparison between the reaction progress and reaction rate under isothermal conditions and the adiabatic runaway curve

Figure 5.7 Comparison between the reaction progress and reaction rate under isothermal conditions (T=52.78°C, Φ = 1E10) and the adiabatic runaway curve with a starting temperature of 52.78°C with Φ = 2 and 1 (TMRad of 24h), respectively (ΔHr = -554.8±17.4 J/g and Cp = 1.5 J/g/°C).

The self-heat rate curves under adiabatic conditions can be calculated similarly (see figure 5.8). It can be observed that a self heat rate of 0.02 K/min (with Φ = 1), which corresponds to the typical detection limit of adiabatic calorimeters, occurs after about 17 hours, it means 7 hours before TMRad of 24 h for an initial process temperature of 52.78C. It can be also seen from the simulation that at that time the reaction progress amounts already to about 0.022 (about 2.2%) (Fig. 5.8).

Predictions window, TMRad tab

Predictions window, TMRad tab

Figure 5.8 Adiabatic runaway curve with TMRad = 24h and corresponding reaction progress and self heating rate curve as function of time (ΔHr = -554.8±17.4 J/g and ΔTad=(-ΔHr)/Cp/Φ=369.9±11.6°C for Φ = 1 and Cp = 1.5 J/g/K).

Similar calculations can be performed for different factors (see figures 5.9) for an initial temperature of about 52.78°C.

Thermal behavior of examined material under adiabatic conditions for different φ factors

Thermal behavior of examined material under adiabatic conditions for different φ factors, adiabatic runaway curves

Thermal behavior of examined material under adiabatic conditions for different φ factors, self heat rate curves

Figures 5.9 Thermal behavior of examined material under adiabatic conditions for different Φ factors. Adiabatic runaway curves (top) and self heat rate curves (bottom)
Tbegin=18.04°C, ΔHr = -554.8±17.4 J/g and Cp = 1.5 J/g/°C
ΔTad=(-ΔHr)/Cp/Φ=369.9°C for Φ = 1
ΔTad=(-ΔHr)/Cp/Φ=246.6°C for Φ = 1.5
ΔTad=(-ΔHr)/Cp/Φ=184.9°C for Φ = 2
ΔTad=(-ΔHr)/Cp/Φ=147.9°C for Φ = 2.5

6. SELF ACCELERATING DECOMPOSITION TEMPERATURE (SADT)

6.1 Introduction

Some chemicals have the potential to cause fires or explosions, and, as hazardous materials, are handled with appropriate care to minimize accidents. This category of hazardous materials includes a group of chemical substances called reactive or self-reactive chemicals which may initiate exothermic decomposition by themselves without reacting with oxygen in air. The estimation of the hazard probability, especially for packaged materials during transport conditions, is commonly performed using thermal hazard indicators such as the Self Accelerating Decomposition Temperature (SADT). The determination of SADT is based on the monitoring of the temperature of the sample with the mass m, volume V, surface area S, density (or bulk density)ρ, and specific heat capacity Cp, with a uniform initial temperature T0 and packed into a vessel of arbitrary shape. At time t0, the surrounding temperature of the investigated material is increased to Te which initiates the heat transfer between the packaged material and its surroundings, characterized by a heat transfer coefficient h. The SADT, as defined by the United Nations SADT test H.1 [35], is the lowest ambient temperature at which the centre of the material within the package heats to a temperature 6C higher than the environmental temperature Te after seven days or less. This period is measured from the time when the temperature in the centre of the packaging reaches 2C below the ambient temperature. The determination of SADT can be reliably performed applying UN test H.1 [35] with a series of large-scale experiments performed with the packaging in an oven at constant temperatures. Each test, performed at a new temperature, (according to the UN recommendations, the step of the oven temperature variations amounts to 5C) requires a new large-scale packaging. Despite its reliability, this procedure, based on a series of large scale experiments, is rarely used, because it is rather expensive, time-consuming and, in certain cases, quite dangerous due to thermal safety and toxicity reasons. Another limitation is related to the relatively common situation when only a small amount of the investigated material is available at the early stages of a project. Taking into account all the issues presented above, it seems fully understandable that there is an important need of other reliable, faster, safer and cheaper test methods requiring smaller amounts of reactive materials and applicable at the laboratory scale (mg or g). Due to the fact that significant amount of heat is evolved during the decomposition of self-reactive chemicals their thermal properties are frequently investigated in laboratory at mg- or g-scales under non-isothermal or isothermal conditions using Differential Scanning Calorimetry (DSC) or, more sensitive, Heat Flow Calorimetry (HFC). The elaboration of the heat flow data monitored by these both techniques allows determination of the kinetic parameters of the decomposition process which describe the rate of the heat generation in the conditions of the ideal heat exchange with the surroundings. Because these tests are performed at a small scale, a scale-up is necessary. In kg-scale, due to increasing sample mass, the conditions of the heat exchange with the environment significantly change what, in turn, may considerably increase the reaction rate and the spatial evolution of the sample temperature which depends on:

  • the kinetic and thermodynamic parameters of the reaction (activation energy, pre-exponential factor, reaction kinetic model, reaction heat),
  • the physical parameters of the material (liquid or solid states, heat capacity, thermal conductivity, density),
  • and the user-controlled parameters of the experiment (such as sample size, heating rate or temperature, type of packaging, rate of heat exchange with the surroundings, gas atmosphere, etc.).


Thus, once the kinetic parameters of the reaction are known, the temperature profiles for any sample size can be accurately estimated for any desired user-controlled parameters by adequately applying the corresponding physical and thermodynamic parameters. Therefore, one can conceive the kinetic-based approach as a reasonable and possible support or alternative to the large-scale UN test H.1.

The important aspects of the kinetic workflow, i.e. the sequence of all the processes through which a kinetic analysis passes from initiation to completion, and the recommendations for proper collection of experimental data, have already been discussed in the last three ICTAC Kinetic Projects [2-7]. However, if intended for scale-up, the computational aspects of the kinetic analysis should be extended by additional recommendations about the collection of experimental data, thermodynamic and physical parameters, and the determination of the user-controlled parameters that adequately lead to the accurate determination of the heat balance. Moreover, it is necessary to quantitatively evaluate the impact of the sample mass and its physical state (liquid or solid) during: (i) experimental collection, (ii) computation of the kinetic parameters and simulation of data and (iii) prediction of reaction course and thermal hazards. In the following sections such recommendations are given. The methods of determination of SADT are illustrated by the results of evaluation of the kinetic parameters from heat flow data collected by DSC.

It is worth noting that several techniques and instruments are nowadays available for measuring the course of exothermically decomposing materials, and several laboratory practices can be found. Therefore, the legitimacy of any new evaluation method, if intended to be a reliable alternative of the large-scale UN test H.1 for accurate SADT determination, should be carefully checked for any type of investigated reactions, no matter by which technique the experimental data were collected. It is obvious that the kinetic, thermodynamic and physical parameters should be representative for the chemical reaction under investigation and that the SADT values should not be dependent on the experimental procedure used, such as e.g. real large scales experiments, Dewar, Accelerating Rate Calorimetry (ARC) techniques or DSC. Independently of the technique applied, the experimental data should be suitable for the computation of the kinetic parameters either in a direct way (DSC) or by simultaneously considering the results collected by two different techniques (DSC and H.1 or DSC and Dewar).

mg-kg-ton

Figure 6.1 From mg to kg and tons (thermal safety) (top). New kinetic approach for evaluation of hazard indicators based on merging DSC and ARC or Large Scale Tests (middle and bottom) [12].

6.2 Applying the kinetic parameters and the heat balance for the scale-up

In DSC experiments, the problem of the influence of the heat balance on the reaction course is generally not considered because of the small sample sizes. It is worth to note however, that even in mg scale for certain reaction models, as e.g. for autocatalytic exothermal reactions, the amount of heat evolved during the reaction may not be completely and immediately exchanged with its surrounding, i.e. the rate of the evolved reaction heat may be greater than the rate of the heat exchanged with the environment having temperature Te. This scenario for mg scale has been presented recently in the third ICTAC Kinetic project in the section Hazardous Materials [7]. There we described a simple method which allows the uncovering of the possible presence of heat accumulation in the sample, increasing its temperature in an uncontrolled way and leading to the inequality T ≠ Te.

In the kg scale the heat evolved during reaction cannot be instantaneously exchanged with the surroundings. The possible self-heating, leading to a temperature rise in the sample, is strongly dependent on the user-controlled parameters such as the sample mass and the physical state (liquid or solid) of the materials. In the case of self-heating, the expression for the rate of change of the sample temperature commonly applied at the mg-scale in kinetic analysis

mg-scale kinetic analysis

with T = T0 +β t and β ≠ 0 and β = 0 for the nonisothermal and isothermal conditions, has to be replaced by a more complicated dependence which includes the heat balance in the system required for larger sample masses. The equations of heat balance differ depending on the state of the investigated materials and are substantially different for liquids or solids, respectively. They are based on the theories which were initially developed by Semenov [26] for lumped systems or Frank-Kamenetskii [27] for transient heat conduction or distributed systems.

A lumped system is a system in which the dependent variables of interest are a function of time alone. Such a system can be represented by a uniform distribution of temperature, as e.g. in liquid samples. A distributed system is a system where all dependent variables are functions of time and one or more spatial variables. Such a system has to be considered when describing the temperature gradients existing in solid samples.

6.2.1 The energy equation

In addition to the prediction of the reaction progress at any temperature profile in mg-scale and under adiabatic conditions, the simulations of thermal properties in kg-scale such as Self Accelerating Decomposition Temperature (SADT) can be carried out. The DSC signals of a materials decomposition are processed using AKTS-Thermokinetics softwares unique numerical techniques to calculate the kinetic parameters. Subsequently, these kinetic parameters are used to predict the possible thermal runaway for a specific container type and size under any global temperature environment.

The method for predicting the thermal behaviour of the energetic materials such as the determination of SADT strongly depends on the sample mass due to the significant influence of the heat generated during the reaction course. At the mg-scale, all the evolved heat dissipates to the surroundings and does not affect the temperature of the heated material. Whereas at the ton-scale, the system can be considered adiabatic, because almost all generated heat remains in the sample during decomposition and there is potential for a thermal runaway. From a practical perspective for the kg-scale, the temperature change of the test material results from two different processes that together determine the heat balance, which is defined by the heat generated during the thermal decomposition and heat loss to the environment. The rate of heat generated during an exothermic decomposition increases exponentially as the temperature rises but the rate of the heat loss remains in a linear manner. Therefore, a clear understanding of the heat transfer mechanism is necessary for an accurate determination of SADT.

When heat is transferred to surrounding environment the temperature profile within a solid body or a liquid depends upon the rate of heat generation, its capacity to store the part of this heat, and the rate of heat transfer to its boundaries. The energy balance over a volume element can be expressed as

Expression of the energy balance over a volume element

and from Fourier's law

Expression of the energy balance over a volume element from Fourier's law

As the chemicals stored in containers can be solids or liquids, we must extend the heat conduction equation to allow for the motion of the fluid. After some restrictive assumptions, we obtain the energy equation:

Energy equation obtained

where λ, ρ, Cp, T, u, qr mean: thermal conductivity, density, specific heat, temperature, fluid with a velocity field us(x,y,z) and heat generated per unit volume by the decomposition reaction

Decomposition reaction

with dα/dt the rate of the decomposition reaction expressed by the Arrhenius type equation as those applied in Friedman analysis and ΔTad the adiabatic temperature rise expressed by the heat of reaction ΔHr and the specific heat Cp,s : ΔTad = (-ΔHr)/Cp,s. The energy equation is the same as for a solid body, except for the enthalpy transport, or convection term Convection term.

To perform the exact heat balance the numerical techniques like finite element analysis, or finite differences or finite volumes can be applied to solve the energy equation. The sample is virtually divided into the set of adjoining elements (see Fig. 6.2). These elements are organized in a virtual mesh and described by the advanced thermokinetics based on the Friedman analysis in each node of time and space.

Container heat balance

Figure 6.2 Generalized heat balance over a container and a volume element.
(A) Kinetic parameters calculated from DSC measurements, independent of the sample mass, enable the determination of the reaction rate required for the heat balance.
(B) Heat balance depends on the sample mass and has to be calculated by numerical techniques.

6.2.2. Heat balance in transient heat conduction (distributed) systems (for e.g. SOLIDS in containers)

If the examined substance in a sample holder is a SOLID, the main resistance to the heat transfer lies in the bulk of the substance. In SOLIDS, heat transfer occurs mainly by heat conduction and not by convection:

Heat transfer in solids because u s= 0

Heat transfer in solids

Heat transfer in solids

Therefore, the property which quantifies the ease with which a material transfers heat is the thermal conductivity. As previously mentioned, thermal conductivity depends mainly on the medium’s phase, temperature, density and molecular bonding within a solid structure. It means that in case of solids (and only in that case) there is a relevant temperature gradient ‘within’ the solids from the center to the container wall depending on the surrounding temperature.

In Cartesian (rectangular) coordinates, this variation is expressed as T = T(x, y, z, t), where (x, y, z) indicate variation in the x-, y-, and z- axis directions, and t indicates variation with time. We can write after some simplifications

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where λ is the thermal conductivity. For the analysis of limited cylinders with given H/D ratios (H: height, D: diameter) and flat lids (e.g. drums, containers, etc.), the cylindrical coordinates are generally used and the above equation can be written as

Heat transfer after considering cylindrical coordinates

where r represents the radius of the cylinder. Both above equations consider the variation of temperature with time as well as position in multidimensional systems. Further simplifications of these equations are possible if we consider the variation of temperature with time as well as position for one-dimensional heat conduction problems. In such cases, these equations can be simplified to

Heat transfer after considering cylindrical coordinates

in which g is a geometry factor (g = 0 for an infinite plate, g = 1 for an infinite cylinder and g = 2 for a sphere). In this equation, the radius of the sphere with the same volume V as the considered packaging (so-called volume equivalent sphere) can be used. We have:

Heat transfer after considering cylindrical coordinates

6.2.3 Heat balance in lumped systems (for e.g. LIQUIDS in containers)

6.2.3.1 For LIQUIDS with low viscosity

For liquids with low viscosity we have

liquids with low viscosity

liquids with low viscosity

liquids with low viscosity

The temperature of a body varies with time but remains uniform throughout at any time, T = T(t). This change refers to Newton's law of cooling. After some simplifications, the rate of the sample temperature change in classical lumped systems can be more generally expressed, as following:

liquids with low viscosity

where Cp, ρ, U, S, V, Φ, -ΔHr, dα/dt mean, respectively: specific heat capacity, density, overall heat transfer coefficient, surface, volume, thermal inertia, specific heat of reaction and reaction rate.

For lumped systems, the surface-to-volume ratio S/V can be used for the characterization of any sample container, regardless of its specific shape. The thermal inertia term (characterized by the Φ-factor) describes the heat loss and is given by

liquids with low viscosity

with m and mc representing the masses of the sample and the package, respectively. For large packages, if the lumped system assumption applies, the Φ-factor can be reasonably set to unity (Φ = 1) because the mass mc of the package is negligible compared to the sample mass m. For smaller vessels, the Φ-factor, being generally larger than one, has a direct influence on the experimental adiabatic temperature rise ΔTad=-ΔHr/(Cp Φ).

6.2.3.2 For LIQUIDS with high viscosity

In case of LIQUIDS, heat is transferred not only by conduction but mainly by convection. In convection, heat is transferred from one point to another through a moving fluid, as a result of the mixing of different portions of the fluid. The concept of the Nusselt number (Nu) is generally used to determine the heat transfer coefficient h. The Nusselt number is a dimensionless number which measures the enhancement of heat transfer from a surface, compared to the heat transfer that would be measured if only conduction could occur. It is calculated by:

Liquids with high viscosity

where x is the position along the interface in the direction of fluid flow. The Reynolds number (Re), Prandtl number (Pr) and Grashof number (Gr) are dimensionless terms which depend on the velocity and on the physical properties such density, viscosity and expansion volume of the fluid. There are two sub-segments of convection, forced and natural. In forced convection, the motion of the fluid is the result of some mechanical work, such as a pump moving the fluid. For liquids in containers, convection is caused by buoyancy forces due to density differences caused by temperature variations in the fluid. At heating the density change in the boundary layer will cause the fluid to rise and be replaced by cooler fluid that also will heat and rise. This continues phenomenon is called free or natural convection and the Grashof number is generally used to approximate the ratio of the buoyancy force to the viscous force acting on a fluid. However, for chemical reaction mixtures, physical properties such as volume coefficient of expansion or viscosity are usually unknown. Therefore, because heat is transferred mainly by convection the following simplifications can be made:

Liquids with high viscosity

or

Liquids with high viscosity

where the size of N increases with lower viscosity

It comes for above that for liquids with high viscosity the energy equation leads to

Liquids with high viscosity boundary conditions

Liquids with high viscosity boundary conditions

6.2.4 Boundary conditions

Beside some simplifications introduced into the above equations and because heat passes through the package into or out of the material, from or to the surroundings three kinds of time-dependent boundary conditions are generally applied: (i) prescribed temperature at the surface (Dirichlet condition), (ii) heat flux at the surface (Neumann condition) and (iii) heat transfer at the surface (Newton law, convective heat transfer or mixed boundary conditions). For heat transfer at the surface, another frequently applied simplification considers the rate of heat conduction through the wall of the package by using the overall heat transfer coefficient U, together with the thermal resistance concept R. This concept is expressed by the equation

with

where di represents the thickness and λi the thermal conductivity of layer i in a multilayer package with I layers constituting the wall, and h the coefficient of heat transfer by convection inside the package (hin) in case of liquid samples and at the wall surface of the package (hout). The adiabatic conditions can be achieved by setting U=0. The appropriate boundary conditions together with the heat balance equations allow the self-heating of exothermally decomposed materials to be simulated after introducing the kinetic expression of the reaction rate dα/dt.

6.2.5 Heat balance equations applied for SADT for liquids and solids

Because some materials can decompose in solid or liquid (after melting) states and due to the fact that we have two different types of temperature distributions within the sample (with T uniform or with T gradients), four main different cases are conceivable during SADT evaluation. They are schematically presented in the next Table.

Heat balance type

Table 6.1 Heat balance equations and physical states applied for SADT evaluation for liquids and solids.

  • Case 'L & L': In this scenario, one applies the heat balance which is correct only for the liquid state and kinetic parameters evaluated from e.g. non-isothermal DSC data collected during the decomposition in the liquid state, i.e. above the melting point.
  • Case 'L & S': The situation 'L & S' corresponds to the determination of the hazard properties using the kinetic parameters calculated from the decomposition in the liquid state (above the melting temperature) together with the heat balance approach valid for the solid state. Such an incorrect procedure leads to improper SADT value. The application of kinetic parameters characterizing decomposition in the liquid phase for the simulation of the thermal properties in the solid phase may be risky despite the application of the correct heat balance equations.
  • Case 'S & L': This case illustrates the situation in which the inappropriate heat balance equation is applied. The temperature distribution is not even close to being uniform, which is common for large solid samples. Despite this situation, the classical lumped systems generally valid for liquids only, is sometimes used instead of the equations of the (distributed) systems for the simulation of the thermal properties of large sample in the solid state. Mathematically, this approximation is used to simplify otherwise complex differential heat equations. However, in the case of solids, the correctness of application of the equation for liquids instead of those for solids depends in practice on the ratio of the internal and external heat flow resistances driven by the type of material and its surface area (packaging in the case of SADT), respectively. This ratio can be estimated from the Biot-number which indicates if the assumption concerning the "object temperature" at any given time assuming no spatial temperature variation within the object may be acceptable.
  • Case 'S & S': For the prediction of the hazard properties of solids that decompose already at temperatures below their melting point, the correct procedure for the prediction of their SADT temperature consists in applying both, the kinetic parameters and heat balance characteristics for the solid state (case 'S & S' in the above Table). As far as the DSC technique is concerned, the experiments for such materials should be collected isothermally in a narrow temperature window below the melting point.
  • As a general rule, the correct procedure for the prediction of the thermal behavior of any material consists in applying correctly both, the kinetic parameters and heat balance characteristics for the material state.

As a general rule, the correct procedure for the prediction of the thermal behavior of any material consists in applying correctly both, the kinetic parameters and heat balance characteristics for the material state.

6.3 The kinetic based approach for the determination of Self Accelerating Decomposition Temperature (SADT)

Because in the strict sense the mechanisms of the decompositions are not fully known (see chapter 3) our simulations presented below are based on the kinetic parameters evaluated by the differential isoconversional kinetic analysis which does not require any knowledge of the decomposition mechanism. The value of a heat transfer coefficient U in the first approximation was based on the UN recommendations [35] and the claims found in the paper published by BAM [36] in which in the large scale experiments the U value is considered in the range between 4-8 W m-2 K-1.

The Self-Accelerating Decomposition Temperature (SADT) is an important parameter that characterizes thermal hazard possibility under transport conditions of self-reactive substances. SADT is used in international transportation regulations and is referenced in the United Nations presented in Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria (TDG) [35]. Globally Harmonized System (GHS) has inherited SADT as a classification criterion for self-reactive substances. According to the Recommendations on TDG, SADT is defined as the lowest temperature at which self-accelerating decomposition may occur with a substance in the packaging as used in transport. An important feature of SADT is that it is not an intrinsic property of a substance but a measure of combined effect of ambient temperature, decomposition kinetics, packaging size and heat transfer properties of the substance and its packaging.

The Manual of Tests and Criteria of the United Nations regarding transport of dangerous goods and on the globally harmonized system of classification and labeling of chemicals indicates that the characterization of materials is based on heat accumulation storage tests.

The regulatory compliance definitions are:

  • (i) SADT is the lowest environment temperature at which overheat in the middle of the specific commercial packaging exceeds 6 C (ΔT6) after a lapse of a seven day period (168 hours) or less. This period is measured from the time when the packaging center temperature reaches 2C below the surrounding temperature.

  • (ii) SADT is the critical ambient temperature rounded to the next higher multiple of 5 C.

The first definition is based on two essential parameters maximal permissible overheating temperature and minimal acceptable induction period. The second definition considers only one parameter: the critical ambient temperature of thermal runaway rounded to the next higher multiple of 5 C without introducing any fixed transportation time into the definition.

Bearing in mind the abovementioned SADT definitions, several additional factors have to be considered for the proper determination of SADT:

  • the intrinsic properties of the test material such as, kinetic parameters of decomposition (activation energy, pre-exponential factor in the Arrhenius equation) and physico-chemical properties such as thermal conductivity, specific heat and density.

  • the external properties of the sample that can be changed arbitrarily, e.g. sample mass, geometry and physical properties of the sample holder/container.

From the above factors, especially the thermal conductivity (in case of solid or high viscous substances), the heat transfer coefficient and sample mass may influence the calculation of SADT in a significant way. As thermal conductivities of chemicals are not always exactly known and as both, container volume and sample mass, can be arbitrarily changed, their influence on SADT was examined in broad range of their changes. Simulations have been done for:

  • sample holders shaped as cylinders with internal volumes of: 5, 10, 25, 50, 100, 250 and 500 L.
  • following equivalent thermal conductivities Λs,eq: 0.1 and 1W/(mK).

Illustration of choice of possible parameters regarding container materials and chemical substance for SADT calculations can be found in Table 6.2.

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Table 6.2 Parameters regarding container materials and chemical substance for SADT calculations.

Predictions

Density Ρ 1000 kg/m3
Specific heat Cp 1.5 Jg/K
Thermal conductivity λ 0.1 W/(mK) < λeq < 1 W/(mK)
(through numerical variations)
Sample holder Drum (Height/Diameter =2)
(5 L < sample holder volume < 500 L)
Heat of reaction ΔHr -554.8 J/g (measured from DSC)
Heat transfer coefficient U 5 W/(m2K)


Table Sample Volume (L)
Table 6.4 Dependence of SADT (C) on equivalent thermal conductivity λs,eq and amount of chemical substance expressed by the sample volume (L) of drums with H/D = 2.

Table 6.4 presents the results of the SADT simulation for λeq values between 0.1 and 1 W/(mK) and sample volumes between 5 and 500 L. For the simulation, limited cylinders with flat lids have been used with the ratio H/D = 2. The results in table 6.4 clearly shows that both, thermal conductivity and sample volume influences the SADT values. For a 50 L drum corresponding to the H.1-test (filling height H = 63.4 cm and D = 31.7 cm), SADT with an assumed thermal conductivity λ of 0.1 W/(mK) amounts to 39C (see Tab. 6.4 and Fig. 6.3) whereas under assumption of larger heat transfer for an apparent conductivity term λeq = 1 W/(mK), SADT amount to about 43C respectively (see Tab. 6.4). It can be shown that two parameters mostly influence SADT:

  • (i) the thermal conductivity and sample volume that is mainly responsible for the heat transfer (accumulation & release)
  • (ii) the type of reactions (decelerating, autocatalytic,...) and heat of reactions responsible for the heat source.

Figure 6.3 presents the surrounding temperature corresponding to SADT and the evolution of the temperature inside the drum namely at its center (R=0;H/2). The average reaction progress αvs. time is presented at the bottom of Figure 6.3.

Simulation SADT

Figure 6.3 Simulation of the SADT for 50 kg of the material in a drum with filling height H = 63.4 cm and D = 31.7 cm (the other parameters are given in Tab. 6.3) (pink: surrounding temperature Te, green: sample temperature in the center of the sample Tc, blue: average reaction progress α). Our simulated SADT value according to the definition of the SADT (Test H.1) [35] amounts to 39C. SADT is the lowest environment temperature at which the overheat in the middle of the specific packaging exceeds 6 C (δT6) after a lapse of a seven day period (168 hours) or less. This period is measured from the time when the packaging center temperature reaches 2C below the surrounding temperature. Point (A) indicates the time when the packaging center temperature (green, spatial position Tc (R=0;H/2)) reaches 2C below the surrounding temperature. At point (B) the sample center temperature reaches the surrounding temperature. The overheat of 6C occurs after about 4.7 days (point C). At this time the average reaction progress of the decomposition in the 50 kg package amounts to 0.031 (ca. 3.1%) (bottom, right axis).

Our simulations based on kinetic parameters evaluated from DSC signals and the correct heat balance in the system indicate that a temperature of 39C is the lowest environment temperature at which overheat in the middle of considered 50-kg packaging exceeds 6C (ΔT6) after a lapse of seven days (168 hours) or less. This period is measured from the time when the packaging centre temperature reaches 2C below the surrounding temperature (after ca. 2.3 days) (Point A). After about 2.8 days (Point B) the centre temperature is equal to the surrounding temperature. The overheat of 6C occurs after about 4.7 days (Point C). At this time the average reaction progress in the 50 kg package amounts to 0.031 (ca. 3.1%) (bottom, right axis). Fig. 6.4 presents the calculated spatial distribution of the temperatures (left column) and reaction progresses (right column) in the drum after lapse of time represented by the points A, B and C i.e. when the center temperature differs by -2C, 0C and +6C, respectively compared to the surrounding temperature.

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Figure 6.4 Simulations of the spatial distribution of temperature (left) and reaction progress α (right) for a mass of 50 kg in a drum with ratio H/D = 2 after periods of time represented by the points A (top), B (middle) and C (bottom) depicted in Fig. 6.3.

7. CONCLUSION

This study focuses on prediction of the reactivity of a substance both in extended temperature ranges and under temperature conditions for which experimental data collection is difficult. Adequate predictive examination of investigated reactions requires about four DSC measurements carried out with different heating rates, generally in the range of 0.25 to 8 K/min. Moreover, applying the results obtained by Differential Scanning Calorimetry (DSC) advanced numerical techniques enable prediction of the reactivity in broad temperature range. In fact, numerical simulations can be used to replace experiments in situations, which are not directly accessible to measurement for example for timing reasons. The examples of such modelling analysis can be helpful for guiding the screening and development of new materials activities. If modelling proceeds in parallel with experimental studies, then it should result in lower costs in a project development phase.

The proposed method has therefore several advantages:

  • It is fast: Reliable screening of candidate energetic materials by revelation of potentially unstable mixtures at prolonged times and temperature exposures can be done within few hours.
  • It is economical: The determination of the kinetics offers very significant time/expertise savings compared to real time analysis which can extend over prolonged periods, even months.
  • It is convenient: DSC devices are widely available and only require a small amount of material.
  • It is versatile: With one set of measurements different scenarios can be calculated. The method can be used to predict the rate of the reaction progress for any temperature profile.

Safety by Design through Knowledge

References

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[7] S. Vyazovkin, K. Chrissafis, M.L. Di Lorenzo, N. Koga, M. Pijolat, B. Roduit, N. Sbirrazzuoli, J.J. Suol, ICTAC Kinetic Committee recommendations for collecting experimental thermal analysis data for kinetic computations, Thermochim. Acta, 590 (2014) 1-23.
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[25] A. Keller, D. Stark, H. Fierz, E. Heinzle, K. Hungerbuehler: Estimation of the TMR using dynamic DSC experiments. Journal of Loss Prevention in the Process Industries (1997) 10(1):31-41.
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[35] UN Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria, 5th revised edition. United Nations, New York and Geneva, (2009) 297-316.
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Possibilities of analysis offered


Abbreviations:        
TA: AKTS-Thermal Analysis (Calisto Software)        
TK: AKTS-Thermokinetics Software        
TS: AKTS-Thermal Safety Software        
RC: AKTS-Reaction Calorimetry Software TA TK TS RC
  Possibilities of analysis offered
Temperature modes allowed        
isothermal yes yes yes yes
non-isothermal linear, non-linear, arbitrary heating or cooling rates yes yes yes yes
isoperibolic (various constant oven temperatures) yes yes yes yes
Evaluation of the data collected by the following thermoanalytical techniques at conventional and/or specific conditions:        
Differential Scanning Calorimetry (DSC) yes yes yes yes
Differential Thermal Analysis (DTA) yes yes yes yes
Simultaneous Thermogravimetry & Differential Scanning Calorimetry / Differential Thermal Analysis yes yes yes yes
Pressure monitoring / Gas generation: P and dP/dt yes yes yes yes
TG (m(t)) and DTG (dm/dt) yes yes yes yes
Hyphenated Techniques: TG-EGA (MS or FTIR) yes yes yes yes
Dilatometry / Mechanical Analysis: TMA, DMA yes yes yes yes
Non Destructive Assay: NDA for e.g. Nuclear Waste Characterization (e.g.Setaram LVC-3013) yes yes yes yes
Gas Humidity Monitoring (e.g. Setaram Wetsys) yes yes yes yes
Microcalorimetry (e.g.TA Instruments TAM, Setaram C80, MicroSC and many others) yes yes yes yes
Reaction Calorimetry (e.g. Mettler RC1, Setaram DRC, HEL Simular, ChemiSens CPA 102, 202 and many others) yes yes yes yes
Thermal Conductivity of liquids and solids (e.g. C-Therm TCI) yes yes yes yes
Adiabatic Data (THT ARC, Fauske VSP, Omnical DARC and many others) yes yes yes yes
Additional Thermal hazard data: Radex, Sedex, Sipcon (Grewer, Ltolf, Miniautoclave, Hot storage test), CO-Monitoring and A16-Test, Deflagration-Test yes yes yes yes
Data collected discontinuously by e.g. HPLC with only few points for each temperature yes yes yes yes
Simultaneously collected data from the same or different instruments and units as e.g. yes yes yes yes
Heat flow DSC (W) and reaction calorimetry data of RC1 (W) yes yes yes yes
Heat flow DSC (W) and mass loss TG (mg) yes yes yes yes
Heat flow DSC (W) and temperature T(C) and pressure P(bar) in adiabatic conditions (e.g. ARC) yes yes yes yes
Features offered        
Subtraction of experimental base line (blank) yes yes yes yes
Reconstruction of the "under peak" base line (BL) for reaction rate data e.g DSC, DTA, DTG, etc. yes yes yes yes
Baseline types considered: Sigmoid, Tangential Sigmoid, Linear, Horizontal First Point, Horizontal Last Point, Horizontal, Staged, Spline & Polynomial with variable order, Tangential First Point, Tangential Last Point yes yes yes yes
Possible adjustments of temperature onset and offset yes yes yes yes
Baseline Subtraction with or without normalization (setting the integration value of the signal to one) yes yes yes yes
Smoothing data (allows the user to smooth partially or entirely a curve. Methods: Savitzky & Golay or Gaussian) yes yes yes yes
Custom Interpolation and Spikes Correction (designed to interpolate a portion of the signal to remove the bad or noisy data points). Interpolation modes: Straight line, Horizontal, tangential first or last points, Spline or Polynomial with variable orders yes yes yes yes
Dragging Data Points (for moving a data point in order to manually smooth the noisy part of the signal) yes yes yes yes
Removing Vertical Displacement (Signal Step) (allows the user to bring the zone of displacement to the same level as the left limit point) yes yes yes yes
Cutting externals, separate points, internal fragments (allows the user to cut a part of a signal which is not required) yes yes yes yes
Building complementary responses (integral from derivative and vice versa) yes yes yes yes
Derivation with adjustable "Derivative Filter" (the derivative of a curve at a certain point is the slope of the tangent to the curve at that point) yes yes yes yes
Integration (generates the integrated curve of a subtracted or normalized subtracted signal) yes yes yes yes
Viewing data in form of over-all conversion α(t) or dα(t)/dt yes yes yes yes
Viewing data in original form (Q(t), dQ/dt, m(t), dm/dt) raw mass or heat data considered instead of reaction extent α yes yes yes yes
Deconvolution and/or Temperature Adjustment by Inverse Filtering of DSC, heat flux or any type of thermoanalytical data (allows the user to consider the time constant of the temperature sensor in order to reconstruct the real response of the sample on the temperature change) yes yes yes yes
Automatic unit management by changing axis units: from e.g. W to mW, mW, Cal/s, mCal/s, mCal/s (and/or normalization: e.g. W/g, W/mol, etc.) yes yes yes yes
Customizable axis unit menu with any signals of user defined units: e.g. count/g, mg/ml, etc. yes yes yes yes
Automatic unit management by signal derivative and/or integral: e.g. J, W or K, K/s or K/min, etc. yes yes yes yes
Peak separation based on the application of Gaussian and/or Fraser-Suzuki (asymmetric) types signals (Position; Amplitude; Half-width; Asymmetry) yes yes yes yes
Thinning out data (reducing number of points without loss of information) yes yes yes yes
Statistical analysis of results of parallel runs via Customizing Equation (allows the user to apply a mathematical formula to one or more signals) yes yes yes yes
Heat capacity determination via two methods: Continuous Cp or Cp by Step (Both methods with or without reference) yes yes yes yes
Phase transition parameters determination yes yes yes yes
Glass transition (Tg) determination according to IUPAC procedure yes yes yes yes
Thermal conductivity determination of both solids and liquids yes yes yes yes
Converting to Natural Logarithm (especially useful when addressing the exponential Heat Flow signals obtained during isothermal studies) yes yes yes yes
Crystallinity evaluation of semi-crystalline materials yes yes yes yes
Oxidation Induction Time calculation based on the ISO 11357-6 norm yes yes yes yes
Purity determination calculated with Van`t Hoff equation yes yes yes yes
Setting Signal to Zero (allows the user to set to zero on the Y-axis the value of a selected point of a signal) yes yes yes yes
Slope Correction (adjusting the slope of a signal to remove its drift for a better presentation) yes yes yes yes
Temperature Correction (allows calibration of the apparatus to adjust the measured and the real temperatures of the sample) yes yes yes yes
Temperature Segmentation (generates from an experimental temperature curve a new temperature profile built up from an arbitrarily chosen number (between 1 and 2000) of segments) yes yes yes yes
TMA-True and Average Alpha and TMA Correction yes yes yes yes
Data Loading (Importing data in the form of ASCII files from files created by any type of apparatus via general interface yes yes yes yes
User Rights Management (Controls access to the software's features. The administrator can create the list of the users and decide about their rights) yes yes yes yes
Managing the Connection to the Database in which the data are stored in "ressource.adb" file yes yes yes yes
Deletion Management (allows to definitively remove zones and experiments (single or series) stored in the database) yes yes yes yes
Customizing Menus (to change the visible icons shown on the toolbars) yes yes yes yes
Copying Signals, Moving Axes, Merging Axes, Scrolling, Zooming, Magnifying Glass Option, Autoscaling, Cursor Tool, . yes yes yes yes
Chart Size Adjustment, Selecting Default Temperature, Merging Multiple Signals yes yes yes yes
Drag-and-drop a signal (from treeview to chart (and vice versa), from chart to chart, from treeview to treeview) yes yes yes yes
Saving and Loading Macros (recorded actions performed by the user to be applied again quickly) yes yes yes yes
Exporting Chart (available formats: *.png, *.gif, *.bmp, *.jpg, *.emf, automated exportation to MSWord) yes yes yes yes
Exporting Points (with or without interpolation, *.txt and *.csv, Excel *.xls) yes yes yes yes
Customizing Chart: Background, Border and Margins, Legend, Titles, Themes, Axes, Series, Adding and Customizing Notes and Images, etc. yes yes yes yes
Supported languages and translation for all Calisto features: English, French, Chinese yes yes yes yes
Types of kinetic analyses supported        
Isoconversional (model-free) kinetic analysis   yes yes yes
Custom arbitrary chosen formal kinetic models and reaction rates introduced manually   yes yes yes
e.g. da/dt =1e9 * exp(-100000/8.314/(T+273.15)) * (1-a)^1 + 1e10 * exp(-100000/8.314/(T+273.15)) * (1-a)^2*a^0.5   yes yes yes
Formal one- or multi-stage model-based kinetic analysis for discontinuously collected data   yes yes yes
Formal one- or multi-stage and concentration model-based kinetic analysis       yes
Data types and their combinations used for kinetic evaluation        
Discontinuous data composed from only few points (sparse data points, e.g. GC, HPLC data collected e.g. at three temperatures only)   yes yes yes
Continuous data:   yes yes yes
Tr-controlled data   yes yes yes
heat flow (e.g. DSC)   yes yes yes
pressure P (dP/dt) data   yes yes yes
mass loss and its rate (TG, DTG)   yes yes yes
all other thermoanalytical data collected continuously such as TG-EGA, TMA, etc.   yes yes yes
all microcalorimetric data such as TAM, C80, etc.   yes yes yes
non-isothermal - set of runs at various heating rates   yes yes yes
isothermal - set of runs at various temperatures   yes yes yes
set of runs at various heating rates and temperatures (combination of non-isothermal and isothermal data)   yes yes yes
Adiabatic data (e.g. THT ARC, Fauske VSP, Omnical DARC)     yes yes
Tj-controlled data (isoperibolic) and cascade controlled (PID controller) data of reaction Calorimetry (both batch or semi-batch) (e.g.: Mettler RC1, Setaram DRC, HEL Simular, ChemiSens CPA 102, 202 and many others)       yes
Combination of Tr-controlled data of different types (e.g. DSC and TG data)   yes yes yes
Combination of Adiabatic and Tr-controlled data (e.g. ARC and DSC for calculation of the kinetic parameters) for determination of safety hazard indicators (e.g. TMRad24, SADT)     yes yes
Combination of Tr- and Tj-controlled data for thermal safety and process optimization purpose (e.g. DSC and Mettler RC1)       yes
Methods for estimation of the kinetic parameters        
Arrhenius-type dependence of the reaction rate on temperature   yes yes yes
Linear optimization suitable for single stage models   yes yes yes
Non-linear optimization; applicable to data collected discontinously (sparse data points)   yes yes yes
Model ranking (Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC) and weighted scores (w)) for comparing and discriminating best kinetic models based on information theory   yes yes yes
Non-linear optimization method; applicable to complex multi stage models       yes
Simulation of thermal behavior in mg, kg and ton scales        
Temperature profiles applicable for thermal behavior predictions        
Isothermal   yes yes yes
Non-isothermal   yes yes yes
Stepwise   yes yes yes
Modulated temperature or periodic temperature variations   yes yes yes
Rapid temperature increase (temperature shock)   yes yes yes
Real atmospheric temperature profiles for investigating properties (50 climates by default with yearly temperature profiles with daily minimal and maximal fluctuations)   yes yes yes
Customized temperature and humidity profiles: possibility to compare the reaction progress of substances at any temperature and relative humidity (useful in combination with datalogger)   yes yes yes
NATO norm STANAG 2895 temperature profile: Zones A1, A2, A3, B1, B2, B3, C0, C1, C2, C3, C4, M1, M2, M3   yes yes yes
Specific features        
Extended option for High Sensitivity Isothermal Heat Flow Microcalorimetry (e.g. TAM data of propellants, surveillance of ammunitions, quality control) allowing to calculate the kinetic parameters from long term isothermal data for very precise lifetime prediction applying data collected during the first percent of degradation   yes yes yes
Sample Controlled Thermal Analysis: possibility to optimize temperature program in such a way that it allows obtaining the value of the constant reaction rate set by the user (allows creating temperature profiles for achieving e.g. TGA-curves with constant mass loss rates or DSC-curves with rate controlled heat release (or consumption))   yes yes yes
Combination of Tr-controlled data e.g. TG & DSC/DTA & MS data in multi-projects for simultaneous comparison of mass loss, heat flow and volatiles species evolution   yes yes yes
Bootstrap method for evaluation of prediction band (e.g. 95, 97.5 or 99 % confidence intervals), particularly important for long-term predictions (e.g. stabilizers in propellants, vaccines, etc.)   yes yes yes
Heat Accumulation, Thermal Runaway and Explosion     yes yes
Simulation of transient heat conduction systems such as thermal explosion in solids (this analysis considers the variation of temperature with time and position in one- and multidimensional systems)     yes yes
Simulation of lumped systems such as thermal explosion in low viscous liquids (this analysis considers that the temperature of a body varies with time but remains uniform throughout at any time)     yes yes
Influence of packaging geometry, material properties and insulations in simulation of the storage of dangerous materials     yes yes
Infinite slab     yes yes
Infinite axis-symmetrical cylinder     yes yes
Limited cylinder with given H/D ratio (H:height, D:diameter) and flat lids (e.g. drums, containers,etc.)     yes yes
Sphere (application of volume equivalent sphere radius and surface-to-volume ratio S/V, useful for the characterization of any package regardless its specific shape and size)     yes yes
Comparative thermal explosion analysis (e.g. cylinder with given H/D ratio vs sphere with equivalent surface-to-volume ratio S/V)     yes yes
Others geometries (after exportation of the kinetic parameters into codes like Abaqus, Ansys dedicated for the more complex geometries)     yes yes
Inert shell and partitions, multilayer packaging materials (different layers of insulation with different thicknesses)     yes yes
Different properties for separate part of an object     yes yes
Possibility of considering temperature dependence of physical properties     yes yes
Export of material data properties from database (with possible customization of the material property list)     yes yes
Heat sources in an object     yes yes
Possibility of application of specific kinetic parameters for separate parts of an object     yes yes
Heat-generated by a reaction and or non-reactive heat sources     yes yes
Time-dependent boundary conditions:     yes yes
1st kind - Prescribed temperature at the surface (Dirichlet condition)     yes yes
2nd kind - Heat flux at the surface (Neumann condition)     yes yes
3rd kind - Heat transfer at the surface (Newton law, convective heat transfer, mixed boundary conditions)     yes yes
Determination of hazard indicators     yes yes
Time to Maximum Rate under adiabatic conditions (TMRad) for any chosen starting temperature     yes yes
Safety diagram: runaway time as a function of process temperature under adiabatic conditions (TMRad = f(T))     yes yes
Automatic determination of the starting temperatures corresponding to TMRad of 7 days, 24h, 8h and 4h     yes yes
Self heat rate curves dT/dt, dQ/dt and dalpha/dt (dP/dt possible in combination with e.g. ARC data for pressure/gas generation and ventsizing calculations)     yes yes
Influence of the different Phi factors (Phi=1 and Phi>1) on the TMRad and on dT/dt, dQ/dt, dalpha/dt and dP/dt     yes yes
Total energy release under adiabatic conditions     yes yes
Total pressure release under adiabatic conditions (possible in combination with e.g. ARC data)     yes yes
Temperature corresponding to ARC detection limit such as 0.02 K/min for any Phi factors     yes yes
Automatic determination of the Self-Accelerating Decomposition Temperature (SADT) according to the recommendations of Manual of Tests and Criteria of the United Nations on the transport of dangerous goods     yes yes
Automatic determination of the critical hot discharge temperature 'Tin' in e.g. a container or critical surrounding temperature 'Tout'     yes yes
Automatic determination of the critical radius 'r' of e.g. a container and the critical thickness 'd' of an insulation layer of such a container     yes yes
Determination of the relationship between the input factor Xi (thermal conductivity, density and specific heat) and the output Y (time to thermal explosion) for identifying the physical property of a material (chemical or packaging layer) which will mostly influence the time to thermal explosion     yes yes
Setting of time steps, spatial mesh and numerical precision and computation speed     yes yes
Variable adaptive time step     yes yes
Uniform and Non-uniform spatial mesh     yes yes
Second order accuracy in both space and time and numerical stability even for large time steps (to ensure high precision and decreases by orders of magnitudes the calculation time)     yes yes
Display of results     yes yes
Evolution of the temperature profile T(t) and reaction progress a(t) in the cross-section or in a selected point of an object     yes yes
Temperature and conversion distribution on isolines (2-D) and/or 3-D graphs     yes yes
Animated isolines (2-D) and/or 3-D views of both temperature and reaction progress distribution     yes yes
Chemical reactors considered       yes
Batch       yes
Semi-Batch       yes
Continuous Stirred Tank Reactor (CSTR)       yes
Plug-Flow (PFR)       yes
Cascade of reactors including       yes
Stream (continuous or discontinuous with or without dosing conditions for optimization of feed rate dosing profile)       yes
Mixing       yes
Splitting       yes
Heating       yes
Temperature modes       yes
Adiabatic       yes
Tr-control       yes
Tj-control (isoperibolic)       yes
Cascade control (PID controller)       yes
Customizable temperature profiles (isothermal, non-isothermal, stepwise, own profile, etc.)       yes
Process Flow Diagram (PFD) modules for an easy saving of various reactor types       yes
Process optimization (e.g. adjustment of the best feed or temperature profiles for maximum yield and selectivity)       yes
Specific process control (process parameters (e.g. feed or temperature) can be constraint to remain below or above some critical values at all time during the reaction for achieving inherent safety process)       yes