In the chemical industry, highly energetic synthesis reactions with very intensive heat generation are often carried out. Such industrial processes require cooling devices which do not allow for the reactant to heat above the intended synthesis temperature. This temperature of reactants during industrial processing is called Process Temperature, or Tp. In order to know how intensive cooling must be to maintain the process temperature, it is necessary to know the heat of reaction, temperature increase and kinetics of reaction.
The Solution: Measurements by Means of the Accelerating Rate Calorimeter ARC® 305
NETZSCH offers Accelerating Rate Calorimeters (ARCs, Figure 1) for the study of self-heating reactions and their characteristics. The newest and most intelligent of them is the recently optimized ARC® 305. The determination of characteristic temperatures like TD24 (1) can either be performed using the standard software for simple nth-order reactions, or the advanced Kinetics Neo software for complex multi-step reactions or for reactions with autocatalysis.
(1) TD24: The initial temperature for an adiabatic process with Time to Maximum Rate (TMR) = 24 hours is called TD24.
Characteristic Process Temperatures of the Industrial Chemical Process - Avoiding Thermal Runaway
Knowledge of measured values like heat of reaction is very important, but not always enough for a safe chemical process. If cooling fails, the continuing reaction will increase the temperature in the reactor until the reactants are consumed. Then, the reaction and corresponding self-heating will have finished, and the final theoretical temperatures will have been reached. This temperature is called Maximum Temperature of Synthesis Reaction (MTSR). MTSR is an essential approach to assessing the Thermal runawayA thermal runaway is the situation where a chemical reactor is out of control with respect to temperature and/or pressure production caused by the chemical reaction itself. Simulation of a thermal runaway is usually carried out using a calorimeter device according to accelerated rate calorimetry (ARC).thermal runaway risk and designing safe operating conditions.
The safety of industrial processes depends on how high the MTSR is. If it is too high, it can initialize secondary processes with further self-heating. Such consecutivereactions are usually decomposition reactions, which are ExothermicA sample transition or a reaction is exothermic if heat is generated.exothermal and lead to a further temperature increase. In fact, if such secondary reactions are initialized, the risk of runaway and thermal explosion is very high.
During industrial processes in large-volume reactors, the reactants are under conditions close to adiabatic, where evolving heat of reaction leads to self-heating of reactants. In order to study the material behavior, the Модуль ARCA calorimeter module being part of the Multiple Module Calorimeter (MMC) allowing for HWS tests according to accelerated rate calorimetry (ARC).ARC® system allows for creating adiabatic conditions for a small amount of sample material. Figure 2 shows an example of such a measurement.
Time to Maximum Rate
The temperature increase of reactants during ExothermicA sample transition or a reaction is exothermic if heat is generated.exothermal reactions under adiabatic conditions accelerates with time; then reaches its maximum rate. The time from the beginning of an adiabatic process to the maximum reaction rate is called Time to Maximum Rate (TMR). This time value depends on the initial temperature: The lower the initial temperature, the longer this time period is.
The initial temperature for an adiabatic process with TMR=24 hours is called TD24. This corresponds to the temperature at which the time to maximum rate of the runaway reaction (the speed of Thermal runawayA thermal runaway is the situation where a chemical reactor is out of control with respect to temperature and/or pressure production caused by the chemical reaction itself. Simulation of a thermal runaway is usually carried out using a calorimeter device according to accelerated rate calorimetry (ARC).thermal runaway) is 24 hours. This temperature characterizes the process and is used for thermal risk assessment.
Comparison of Characteristic Temperatures
If the value of MTSR is lower than TD24, this means that the temperature is not sufficient for initiating a secondary process such as a decomposition reaction, and the risk of a runaway reaction is thus low. If MTSR is higher than TD24, the secondary reaction starts already during the primary reaction and it is impossible to avoid the runaway, with dangerous consequences. There are several intermediate classes of risk levels between these two cases , which depend on the relationship between MTSR, TD24 and MTT (Maximal Technical Temperature).
Kinetic Methods of Calculation TD24
Temperature TD24 can be calculated by means of different kinetic models based on the experimental data from ARC® instruments. The temperature TD24 can be calculated using various kinetic models based on the experimental data obtained from ARC® measurements.
Linear TMR Extrapolation
This is a traditional linear algorithm. It is based on the assumption of a one-step adiabatic process with approximation to a zero-order reaction, where in the main kinetic equation (1) the reaction type f(α)=1.
Here, φ is the Thermal inertiaThe thermal inertia is equivalent to the PHI-factor. Both describe the ratio of mass and specific heat capacity of a sample or sample mixture compared to that of the vessel or sample container.thermal inertia factor, i.e. the ratio of the heat capacity of the material with the vessel to the heat capacity of the material Cp. In the absence of a container, φ=1. ΔH is the enthalpy, A is the pre-exponent, Ea is the activation energy and R is the Gas constant. Under this assumption, the following linear approximation can be used:
This dependence corresponds to the straight line log (time) vs. 1/T, where slope Ea/R is independent from the Thermal inertiaThe thermal inertia is equivalent to the PHI-factor. Both describe the ratio of mass and specific heat capacity of a sample or sample mixture compared to that of the vessel or sample container.thermal inertia factor φ.
Figure 3 demonstrates the example of the simplest linear approximation for evaluation of TD24. If the experiment is carried out in the ARC® with φ>1 (red solid line), extrapolation to 24 hours results in the red dashed line. The extrapolated straight line for φ = 1 (blue) runs parallel but is shifted by log (φ) to lower temperatures. Then on the new red-dashed line, the temperature TD24 can be found for time=24 hours.
For this type of analysis and evaluation of TD24, only one experimental data set of an ARC® measurement is required.
Non-Linear TMR Extrapolation
In reality, however, the decomposition reaction may have other reaction orders in addition to zero order and, besides a single-step mechanism, also multiple reaction steps.
For such cases, we developed the second, more precise non-linear method . This method assumes that the initial part of the reaction runs according to an nth-order reaction and allows the activation energy, Ea, to be found. Then, the model-free method is used for the calculation of adiabatic self-heating for φ=1 from the experimental data, with φ>1 obtained by the measurement shown in figure 2.
This method works both for reactions with any reaction type having an initial part resembling an nth-order reaction, and for reactions having multiple consecutive reaction steps.
In figure 4, two temperature curves with self-heating are shown: the original experimental data with φ=1.435 (red curve), and the newly calculated curve with φ=1 (blue curve). An important temperature for safety assessment is the so-called TD24. This corresponds to the temperature at which the time to maximum rate of the runaway reaction is 24 hours. The time it takes to reach the maximum rate under adiabatic conditions is known as TMR, the time to maximum rate. This second curve, corrected to φ=1 (blue), is used to find the temperature TD24.
Advanced Kinetics by Kinetics Neo Software
Both methods described above are based on the assumption that the activation energy is a constant value. However, the process can contain steps with different activation energies and reaction steps different from the reaction of nth-order. The most accurate kinetic analysis with a more precisely predicted value of TD24 requires data sets from several experiments, carried out under different conditions. Having data from multiple experiments is a mandatory condition for an accurate kinetic analysis, as recommended by ICTAC .
For this advanced evaluation, several ARC® experiments can be carried out at different φ-factors. For these experiments, different values of conversion are obtained by different measurements at the same temperature. The tool for this accurate kinetic analysis is NETZSCH Kinetics Neo software, which includes both model-free and model-based kinetic methods. Model-based methods can help determine the number of reaction steps as well as kinetic parameters for each individual reaction. The application of advanced kinetic analysis includes the creation of a single kinetic model which mathematically consists of the system of differential kinetic equations with the set of kinetic parameters independent of time and temperature. If the curves simulated by this one model are in good agreement with the experimental data measured under different conditions, this model can be used for the simulation of the material behavior and reaction rate under temperature conditions other than those of the previous experiments, such as for calculation of the temperature increase under adiabatic conditions, and TD24.
Figure 5 shows the set of ARC® experiments under different conditions and simulated curves for these conditions. The good agreement between the model and experiments allows for using this model for other temperatures and Thermal inertiaThe thermal inertia is equivalent to the PHI-factor. Both describe the ratio of mass and specific heat capacity of a sample or sample mixture compared to that of the vessel or sample container.thermal inertia.
In figure 6, a simulation is shown in which the substance being investigated is subjected to IsothermalTests at controlled and constant temperature are called isothermal.isothermal treatment at different exposure temperatures, which were calculated with the kinetic model from figure 5. Besides the simulated adiabatic curves, the software can calculate TD24, which is the initial temperature of the adiabatic process needed in order to achieve TMR in 24 hours.
Figure 7 shows the self-heating course of the sample under adiabatic conditions for removal from thermal treatment at 102°C for 24 hours.
Self-heating reactions can be studied through experiments with NETZSCH ARC® instruments – from simple linear Proteus® analysis software results to more advanced calculations using the Kinetics Neo software. This allows for the calculation of temperature TD24 even in the case of more complex courses of reaction, which is essential in assessing thermal risk. A comparison of the results obtained with various methods allows for assumptions about the linear and non-linear predictions to either be confirmed or rejected, and for additional experiments to be carried out. These, in turn, allow for increasing the depth of the study and refining the results via advanced kinetic analysis in the Kinetics Neo software.
- Thermal Safety of Chemical Processes: Risk Assessment and Process Design, by Francis Stoessel (Switzerland 2008)
- HarsNet. Thematic Network of Hazard Assessment of highly reactive systems. 6. Adiabatic calorimetry.
- S. Vyazovkin, ICTAC Kinetics Committee recommendations for analysis of multi-step kinetics, Thermochimica Acta, V689, July 2020, 178597, https://doi.org/10.1016/j.tca.2020.178597