Introduction

Organic peroxides, which are substances that decompose rapidly when subjected to overheating, light exposure, pollution, friction, or mechanical impact, are widely employed in the process industries. OPs have an organic molecule attached to at least one side of the oxygen-to-oxygen bond (O–O). Their thermal instability is caused by the weak O–O bond, which leads to a tendency toward more stable condition [1]. Many OPs easily generate high pressure under exothermic situation. In general, the threshold temperature is below 120 °C, even lower than the ambient temperature [2]. The self-accelerating decomposition temperature (SADT) of OPs is recommended by the United Nations (UN) so that a precise test in a commercial package must be established [3]. SADT is the lowest ambient temperature at which over-heat in the middle of the industrial packaging exceeds 6 °C after a lapse of a seven day period or less. This period is measured every once in a while when the packaging center temperature reaches 2 °C below the surrounding temperature. The value of SADT is to precisely govern the temperature during storage and transport [4–6].

Chemical industries widely employ OPs as initiators and cross-linkers during polymerization, such as methyl ethyl ketone peroxide (MEKPO), di-tert-butyl peroxide (DTBP), cumene hydroperoxide (CHP), and tert-butyl peroxy-2-ethyl hexanoate (TBPO) [7]. We focused on major analysis of the thermal hazard characteristics for TBPO, which is particularly sensitive to temperature rises and pollution. It is generally stored or transported with inert solids to ease or mitigate the thermal hazard. TBPO reacts quite seriously when rapidly heated to a critical temperature. Several explosions were due to thermal source, mechanical shock, or friction owing to self-accelerating exothermic decomposition, or mixing with amines or certain metals can also cause accelerated decomposition [8–11].

Thermal decomposition of TBPO was examined using a thermal dynamic calorimeter (differential scanning calorimetry, DSC) and isothermal microcalorimeter (thermal activity monitor III, TAM III) to evaluate basic exothermic decomposition and various thermokinetic parameters. Furthermore, calorimetry technology was used to observe the exothermic behaviors by DSC, such as exothermic onset temperature (T 0), peak temperature (T p), and heat of decomposition (ΔH d), and then TAM III was used to obtain the thermokinetic parameters, such as time to maximum rate under isothermal condition (TMRiso), and calculate E a (activation energy) under isothermal condition and A (frequency factor) by the Arrhenius law. Based upon the above mentioned, the thermal hazard appearance for a specific chemical process can be more completely expressed.

Finally, a test platform was conducted to evaluate the thermal runaway parameters of the chemical product, in order to reduce the necessity of large-scale explosive experiments. The method can be employed in many different fields, such as evaluation of chemical process risk, reactor container design, safety of storage and transportation, and thermal hazard characteristic assessment [12].

Experimental and method

Sample

Ninety-seven mass% TBPO, a colorless liquid was packaged in the 100 mL plastic container. It was stored in a refrigerator below 4 °C.

Differential scanning calorimetry (DSC)

The DSC was purchased from Mettler, model TA8000 system DSC821e. It is a useful tool for identifying a substance’s rudimentary thermal decomposition situation quickly and clearly, and only small amount of sample is available. The principle of DSC is to compare the energy difference between the two test cells in which one sample is put in, and the other one acts a reference at different heating or cooling rates. The thermal analysis software STARe for DSC data was adopted to obtain heat flow curves and calculate thermokinetic parameters. The experimental test sample used was ca. 5–6 mg, and the heating rate (β) was set at 0.5, 1, 2, 3, 4, and 10 °C min−1 [13].

Thermal activity monitor III (TAM III)

TAM III, an isothermal titration calorimeter, which possesses high thermal sensitivity and stability, was purchased from TA Instrument. TAM III can predict many potential process risks, such as runaway reactions, temperature dependence on the decomposition of unstable substance, and safe storage condition. It can insure the life cycle of a substance after storage, and TAM Assistant can be used to evaluate a substance’s exothermic reaction. It can govern the temperature range, which is 15–150 °C. As planned, the temperature of the study was 50, 60, 70, and 80 °C. The test cell was a 20 mL ampoule coupled with a glass container and aluminum lid, and 100 mg TBPO was added in the TAM III test [14].

Reaction kinetic model simulation

The thermal safety software (TSS) could facilitate our determination of the practical condition in industrial processes and evaluate from the small-scale to match the commercial scale [15]. The method was applied to the thermal explosion model, which requires heat capacity (C p) and thermal conductivity (k), along with an appropriate algorithm. The experimental setup simulated what the TBPO is set in a storage container that has a shell thickness of 0.1 m. The reactor had the following properties: C p = 1,800 J g−1 K−1, and k = 0.5 W m−1 K−1 [16, 17].

Results and discussion

DSC tests

Table 1 indicates the thermal decomposition of TBPB at different heating rates of 0.5, 1, 2, 3, 4, and 10 °C min−1, corresponding to T 0, T f, T p, and ΔΗ d of 74.47–105.46 °C, 118.20–155.71 °C, 97.13–134.67 °C, and 831.41–991.91 J g−1. Figure 1 shows the results that the higher heating rate caused the higher exothermic peak. Therefore, it could be demonstrated that as the heating rate is increased, the exothermic peak will also be rising, because a higher heating rate provides higher intensities of the energy within a unit of time for the decomposition of TBPO. The ΔΗ d was evaluated for other thermal hazard parameters for TBPO. However, the results lacked significant alternation when the heating rate increased. As mentioned above, the DSC test could be obtained at initial condition when TBPO was decomposed after continued heating. In addition, the TAM III test isothermal temperature set range could also be judged from the DSC test.

Table 1 Calorimetric data for the decomposition of TBPO obtained from DSC
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Fig. 1
figure 1

DSC thermal curves of heat flow versus temperature for TBPO decomposition at heating rates of 0.5, 1, 2, 3, 4, and 10 °C min−1

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TAM III tests

In the case of isothermal temperature, regarding thermal analysis, such as innate thermal hazard of the reactants, material transport, and medicine storage, Fig. 2 shows the results of four isothermal temperatures, 50, 60, 70, and 80 °C, with TBPO [18, 19]. It indicates the exothermic peak is higher and steeper with increased temperature. In addition, according to the experimental results, TBPO did not visibly incur any prominent reaction at 50–60 °C. Therefore, caution must be taken during storage and transportation when the temperature is over 60 °C. Table 2 shows the relationship between temperature and exothermic reaction [18]. The parameter, which is an important index for thermal hazard, is TMRiso.

Fig. 2
figure 2

TAM III thermal curves of heat flow versus time for TBPO decomposition at 50, 60, 70, and 80 °C

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Table 2 Scanning data of the thermal runaway decomposition by TAM III
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TMRiso indicates how much time the heat flow achieved a maximum value during an exothermic reaction. This information could be obtained from a diagram of heat flow versus time by TAM III [20]. In practice, TMRiso is determined to time the emergency response [21]. If the TMRiso is lower, the emergency response indicates the situation is more dangerous. Therefore, it is quite useful to emphasize chemical process safety. The results about TMRiso are given in Table 2.

To evaluate more clearly the thermal hazard, the various thermal hazard parameters must be obtained by specific thermokinetic model. The Arrhenius equation under isothermal condition is used to calculate activation energy and frequency factor. Equation (1) is expressed as follows:

$$ k = A{\text{e}}^{{ - {\text{E}}{}_{\text{a}}/{\text{RT}}}} $$
(1)

Equation (1) is computed with natural logarithm, with respect to four ambient temperatures. Then, Eq. (2) can be obtained:

$$ \ln \left( {\frac{{k_{2} }}{{k{}_{1}}}} \right) = \frac{{E_{\text{a}} }}{R}\left( {\frac{1}{{T{}_{1}}} - \frac{1}{{T{}_{2}}}} \right) $$
(2)

As the reactant’s rate constant is proportional to maximum heat flow, Eq. (2) could be changed to Eq. (3):

$$ \ln \left( {\frac{{Q_{2} }}{{Q{}_{1}}}} \right) = \frac{{E_{\text{a}} }}{R}\left( {\frac{1}{{T{}_{1}}} - \frac{1}{{T{}_{2}}}} \right) $$
(3)

The plot of lnQ versus 1/T graph was used to determine the slope, which is equal to E a, and the intercept is A. Therefore, the values of E a and A are 124.19 kJ mol−1 and 1.9291 × 1017 s−1, respectively. The results are shown in Fig. 3. The experimental results were comparable to those obtained in previous studies [22, 23].

Fig. 3
figure 3

Arrhenius plot for the decomposition of TBPO

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Results of TSS simulation

Tables 3 and 4 show that, by TSS with nth-order or autocatalytic equations, TBPO’s thermokinetic parameters could be judged under the isothermal temperature. Nth-order and autocatalytic equations were applied by TSS, as displayed by Eqs. (4) and (5), respectively [24].

$$ {\raise0.7ex\hbox{${{\text{d}}\alpha }$} \!\mathord{\left/ {\vphantom {{{\text{d}}\alpha } {{\text{d}}t}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{d}}t}$}} = k{}_{0}{\text{e}}^{{ - E{}_{\text{a}}/RT}} (1 - \alpha )^{n} $$
(4)
$$ {\raise0.7ex\hbox{${{\text{d}}\alpha }$} \!\mathord{\left/ {\vphantom {{{\text{d}}\alpha } {{\text{d}}t}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{d}}t}$}} = k{}_{0}{\text{e}}^{{ - E{}_{\text{a}}/RT}} (1 - \alpha )^{n1} (z + \alpha^{n2} ) $$
(5)
Table 3 Thermokinetic parameters evaluated by nth-order simulation
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Table 4 Thermokinetic parameters evaluated by autocatalytic simulation
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Compared with Tables 3 and 4, from the result of autocatalytic simulation it was found that the E a value matched the result of experimental value better than nth-order reaction. Thus, TBPO decomposition is identified as an autocatalytic reaction. Figures 4, 5, 6, and 7 show the fitted curves of autocatalytic reaction under isothermal temperature of 50, 60, 70, and 80 °C by experiments and simulations. For 50 °C simulation, the results do not match the experimental curve, which shows a different phenomenon from other temperature such as 60, 70, and 80 °C. Nevertheless, simulation results are acceptable in agreement with experimental results. TSS simulation data offered in this study demonstrated that the predicted TBPO’s exothermic features had a remarkable effect.

Fig. 4
figure 4

Comparison of experimental and simulation results for the autocatalytic decomposition of TBPO at 50 °C

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Fig. 5
figure 5

Comparison of experimental and simulation results for the autocatalytic decomposition of TBPO at 60 °C

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Fig. 6
figure 6

Comparison of experimental and simulation results for the autocatalytic decomposition of TBPO at 70 °C

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Fig. 7
figure 7

Comparison of experimental and simulation results for the autocatalytic decomposition of TBPO at 80 °C

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Conclusions

A new research on runaway reactions on TBPO 97 mass% was accomplished by DSC and TAM III, which identified the related thermokinetic and safety parameters, such as ΔH d, T 0, E a, A, and TMR iso. E a was computed by the Arrhenius model and the results are in good agreement with those of previous studies. On the other hand, for TBPO’s storage and transportation temperature, according to experimental results, the TMRiso value is 0.456831 h at 70 °C, which is far less than the value of TMRiso 3.926617 h at 60 °C. Thus, the chemical process control temperature of TBPO should be maintained below 60 °C. Furthermore, the result is valuable when a chemical process encounters runaway reaction to establish how much time the treatment of the emergency response has. The TSS simulation reports have exemplified that the technology can be practically applied and presents proper results.

DSC non-isothermal test and TAM III isothermal test were used to obtain various available thermokinetic and safety parameters for TBPO’s safety management by calorimetric analysis technology. Moreover, we used a thermokinetic model combined with experimental data, which can predict more useful information, such as TMRiso, E a, or reaction order, to overcome the limitations of conventional thermal analysis method and to establish a safer process design.

In the future, the extended study may emphasize the TBPO mixed with specific incompatible inorganic acids, such as HCl, H2SO4, HNO3, or H3PO4. The incompatibility could be used to evaluate the thermal hazard and explosion, after runaway excursion. Furthermore, product analysis technology could be used, such as TGA/IR/GC/MS, to thoroughly explore the decomposition mechanism for process during upsets.