Introduction

Chemical industries have inherent thermal risks because of numerous hazardous materials and complex equipment. Many nations focus on high-energy chemicals, such as organic peroxides (OPs), and on using various methods and instruments for identifying reaction characteristics to prevent an operating system from potential thermal runaway hazards. OPs are commonly used as curing agents or initiators for polymerization because they easily yield free radicals. Several hazardous fires and explosions have occurred because of the unstable thermal decomposition properties of OPs; therefore, many studies have examined the hazard characteristics of OPs [1–10]. OPs have a sensitive chemical structure and an O–O bond that can readily decompose, releasing large amounts of heat under various unexpected conditions, such as overpressure, high temperature, incompatible substances, mechanical shock, or even ultraviolet radiation. Therefore, the use or production of OPs is of a major concern and warrants caution.

Cyclohexanone peroxide (CYHPO), a typical OP, is frequently used as a curing agent for sheet-molding compound and bulk-molding compound processes. CYHPO is synthesized through an acid (HNO3)-catalyzed reaction of cyclohexanone with hydrogen peroxide (H2O2). The scheme for this reaction is shown in Fig. 1. However, this reaction is violently exothermic. On June 19, 2012, in Beijing, China, a severe explosion occurred involving the use of CYHPO [5]. Basic scientific safety data on the production of CYHPO are lacking. Various operating conditions, such as over-temperature and pressure, cooling failure, feed error, or incorrect dosing, may trigger a runaway reaction or even result in a fire, explosion, or toxic release [11–15]. In addition, according to the State Administration of Work Safety of China, during the 2009–2013 period, 1 of 18 dangerous chemical processes involved peroxide oxidation [16, 17]. Therefore, the related exothermic and thermokinetic features of CYHPO should be established to identify a suitable control mechanism for studying the thermal hazard characteristics of CYHPO.

Fig. 1
figure 1

Reaction scheme of the CYHPO synthesis

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We employed calorimetric methods to evaluate the inherent thermal hazard characteristics of CYHPO synthesis. First, a reaction calorimeter (RC1e) was used to investigate the thermal behavior of CYHPO by scaling down the industrial conditions. The kinetic parameters were subsequently calculated through nonlinear optimization based on the Levenberg–Marquardt algorithm with the data obtained from RC1e. To validate the kinetic model, this simulation was compared with that obtained from another RC1e experiment. Differential scanning calorimetry (DSC) was used to test CYHPO to screen the influence of acids and impurities on secondary decomposition. In addition, an accelerating rate calorimeter (ARC) was used to investigate the thermal stability of CYHPO under adiabatic conditions. The cooling failure scenario was systematically evaluated to determine the hazard classification of the peroxide reaction. As a proactive measure, these procedures may be used for optimizing the operating conditions of the peroxide chemical reaction to prevent catastrophic industrial accidents.

Experimental

Samples

Analytical-grade cyclohexanone (≥99.5 mass%), H2O2 (≥30.0 mass%), and nitric acid (HNO3) (65.0–68.0 % purity) were purchased from Aladdin Chemistry, Ltd., Shanghai, China.

Reaction calorimeter

A reaction calorimeter (RC1e; METTLER-TOLEDO) was used for reaction safety analysis. The thermal behavior of CYHPO synthesis was investigated using RC1e, which was equipped with an MP10 reactor. During RC1e experiments, 58.0 g of H2O2 and 2.0 g of HNO3 were introduced into the reactor. This mixture was then cooled to a temperature at 250 RPM. Next, 166.0 g of cyclohexanone was added to the reactor in isothermal mode. Operating parameters such as the heat generation rate, temperature, and dosing rate were recorded automatically. After RC1e experiments, the CYHPO yield was calculated based on product purification.

Differential scanning calorimetry

To assess real chemical industry conditions, a sample (sample 1) used in the DSC experiments was obtained at the end of the main reaction, which was the product obtained after the RC1e experiments. Temperature-programmed screening experiments were conducted using a METTLER-TOLEDO system equipped with a DSC1-measuring cell that could withstand pressure of up to 15.0 MPa. The calorimeter was calibrated using the manufacturer-supplied sapphire disk and indium standard by following the instrument calibration guidelines. For superior thermal equilibration, the heating rates (β) were selected to be 1.0, 2.0, 4.0, 8.0, and 10.0 °C min−1. The range of temperature rise was 30.0–300.0 °C, and that of the sample mass was 2.0–5.0 mg in closed gold-plated crucibles. The reference was a pure gold-plated cell. The tests were conducted under ambient pressure and in a dry nitrogen atmosphere at a flow rate of 30.0 mL min−1.

Accelerating rate calorimeter

An ARC (Thermal Hazard Technology, UK) can be used to effectively evaluate the thermal hazards of reactive substances under adiabatic conditions [18]. The standard ARC program of heat-wait-search was deliberately chosen, and experiments were performed with ambient pressure. For each ARC experiment, approximately 0.5 g of sample 1 was loaded in a lightweight spherical titanium alloy bomb (diameter, 2.5 cm). The initial temperature was set to 40.0 °C, and the final (end) temperature was set to 250.0 °C. The system temperature was raised by intervals of 5.0 °C at a heating rate of 0.02 °C min−1. The waiting time was 10.0 min. After the self-heating rate exceeded the selected threshold of 0.02 °C min−1, an exothermic reaction was recorded in the system. The pressure range was from the ambient pressure to 20.0 MPa.

Results and discussion

Thermal behavior of the isothermal peroxide reaction in RC1e experiments

Based on real chemical industry conditions, a conservative approach was to maintain the temperature below 20.0 °C during CYHPO synthesis. Therefore, our initial RC1e experiments were performed at 12.0, 15.0, and 18.0 °C. The heat generation rate and corresponding dosing curves are shown in Fig. 1.

As shown in Fig. 1, the Q r curve at 15.0 °C exhibits an increasing trend with the constant feeding rate until the curve reaches a maximum value. The peroxide reaction rate decreases with the reactant concentration until the end of the dosing step. When the dosing time was approximately 150.0 min, a sharp spike was observed in the reaction heat (Fig. 2). To confirm this phenomenon, which was caused by a physical factor or secondary reaction, another RC1e experiment was conducted with the same reaction temperature, stirring rate, and dosing rate by scaling down the reactant concentration. As shown by the exothermic curve in Fig. 3, the sharp spike was not observed. Furthermore, the white solid crystal was reduced in the reactor. Therefore, the sharp spike was believed to have occurred because of positive thermal crystallization. During crystallization, liquids change to solids, molecular arrangement tends toward that of a regular crystal, internal energy decreases, and heat is released to form a lattice. Accordingly, a sharp rise in heat is observed.

Fig. 2
figure 2

Typical exothermic curves of the CYHPO synthesis at 15.0 °C

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Fig. 3
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Heat jump verification experiment of the CYHPO synthesis

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The thermal behavior parameters of CYHPO synthesis are listed in Table 1. The specific heat capacity of the reactants ranged from 3.83 to 4.02 kJ kg−1 K−1, and that of the peroxide product mixed with acid ranged from 2.66 to 2.85 kJ kg−1 K−1. In addition, based on various reaction conditions, the internal substances of products and side reactions were different. The overall reaction heat of CYHPO synthesis ranged from 62.8 to 87.5 kJ.

Table 1 Thermal behavior parameters of RC1e tests under various reaction conditions
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Compared with Tests 1, 4, and 6, the overall reaction heat and adiabatic temperature rise of the desired reaction increased with the stirring rate. The stirring rate, which suggested changes in the liquid–liquid interfacial area, obviously reflected the reaction rate of heterogeneous liquid–liquid semi-batch reactors. CYHPO synthesis mainly involves an interfacial reaction; the high stirring rate accelerated both the reaction and heat transfer rates. Therefore, when the stirring rate was switched off suddenly and turned on again, an adiabatic temperature rise was observed at approximately 50 °C for Test 9, which may have caused a secondary reaction or thermal runaway scenario. Moreover, based on the experimental RC1e data, a plot of temperature versus time at various stirring rates was devised (Fig. 4). As shown in Fig. 4, the operating conditions did not influence the temperature–time trend. The external conditions did not considerably alter the mass transfer phenomena during the reaction. Therefore, the heterogeneous reaction of CYHPO was attributed to the kinetically controlled reaction regime [19].

Fig. 4
figure 4

Reaction temperature as a function of time at various stirring rates

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Calculation of kinetic parameters of the peroxide reaction

Because of the complexity of the peroxide reaction, CYHPO is always a mixture containing many types of intermediate isomers. Obtaining a reaction mechanism of the overall peroxide process by relying solely on experimental data is difficult. Furthermore, from the laboratory to the industrial scale, only scale-up computations must be performed to understand the overall reaction kinetics. In this study, three sets of RC1e experimental data were fitted using Advanced Kinetics and Technology Solutions–reaction calorimetry simulation software, which is based on mass and heat balance equations [20]. The overall reaction, occurring in the continuous H2O2 phase, is as follows (Fig. 5):

Fig. 5
figure 5

Validation: comparison of the isothermal RC1e measurement at 15.0 °C with respective simulations by using the optimized reaction kinetic model

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The microkinetic equation of the reaction system is defined as

$$ 2 {\text{C}}_{ 6} {\text{H}}_{ 1 0} {\text{O + 2H}}_{ 2} {\text{O}}_{ 2} \to {\text{C}}_{ 1 2} {\text{H}}_{ 2 2} {\text{O}}_{ 5} {\text{ + H}}_{ 2} {\text{O}} $$
(1)
$$ r = k_{1} C_{{{\text{C}}_{ 6} {\text{H}}_{ 1 0} {\text{O}}}}^{\text{n}} C_{{{\text{H}}_{ 2} {\text{O}}_{ 2} }}^{\text{m}} $$
(2)

This reaction scheme was used as a hypothesis to define various kinetic parameters for the reaction model. Three isothermal RC1e measurements were performed at 12.0, 15.0, and 18.0 °C. The overall kinetic parameters were determined by performing nonlinear optimization based on the Levenberg–Marquardt algorithm of the obtained calorimetric data (RC1e) of 12.0 and 18.0 °C, the reaction scheme proposed in Eq. (1), and the reaction rate expression expressed in Eq. (2). The related parameters are listed in Table 2.

Table 2 Obtained overall kinetic parameters for the CYHPO synthesis
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To corroborate the optimization reaction model, one simulation was confined to one isothermal RC1e measurement (Fig. 5). The model fitted the RC1e measurement adequately. A model is valid only within the range in which it is defined. We performed thermal hazard analysis on the peroxide reaction and a scale-up optimization of this reaction. Consequently, a complete fit of the RC1e data of a kilogram scale indicated the correct direction for the reaction scheme.

Thermal behavior of products in DSC tests

Figure 6 shows the obtained DSC signals for sample 1 at heating rates of 1.0, 2.0, 4.0, 8.0, and 10.0 °C min−1 in a dry nitrogen atmosphere. Table 3 lists the thermal decomposition parameters of sample 1 tested using DSC at various heating rates. The first observed thermal effect in sample 1 was endothermic, and this resulted from melting, which occurred at approximately 50.0–60.0 °C. The incipient of the exothermic reaction of sample 1 was at approximately 90.0–110.0 °C. The initial exothermic temperature of sample 1 was lower than that of pure CYHPO by approximately 10.0 °C at the same heating rate [5]; impurities such as acids favor a secondary reaction. Moreover, a secondary reaction is a frequent occurrence in industrial processes because of the presence of impurities.

Fig. 6
figure 6

DSC signals obtained during nonisothermal measurements in dry nitrogen atmosphere at various heating rates

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Table 3 Thermal decomposition parameters at various heating rates
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Thermal behavior of products in ARC tests

Figure 7 and Table 4 show the thermal behavior of products in the cooling failure scenario. Under adiabatic conditions, the thermal decomposition of CYHPO began at 51.3 °C and ended at 122.0 °C (Fig. 7a). The thermal hazards associated with the secondary reaction were high. As shown in Fig. 7a, data are scarce at the initial stage because the reaction rate of the unknown thermal decomposition was low, and the experimental default value was 1.0 °C. When the temperature was raised slowly to approximately 60.0 °C, the rate of the temperature rise increased clearly. Figure 7b shows the self-heating rate with the runaway scenario. Afterward, the self-heating rate decreased because of the consumption of reactants, but the temperature of the secondary reaction continued to rise.

Fig. 7
figure 7

Adiabatic ARC curves of sample 1. a A plot of temperature versus time, b a plot of self-heating rate versus temperature, c a plot of pressure versus time, d a plot of pressure versus temperature

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Table 4 ARC test on the secondary reaction mixture: thermodynamic properties of reaction mass decomposition
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Figure 7c and d shows the pressure variations during the exothermic process. The continuous increase in pressure during thermal decomposition suggested that the reaction generated several gaseous products. In ARC measurements, heat generated by the thermal decomposition of a sample was applied on the titanium alloy bomb; therefore, the consideration of the thermal inertia factor was necessary [1, 18], which was not defined in this study. The thermal decomposition parameters listed as commencing at 1.64 °C min−1 in Table 4 were already corrected by thermal inertia.

Adiabatic kinetic parameters

Equation 3 was used to obtain the thermal decomposition kinetic parameters determined by performing the adiabatic test [18]. According to Eq. (3), by selecting an appropriate reaction order n, a plot of \( \ln \left( {{{m_{\text{T}} } \mathord{\left/ {\vphantom {{m_{\text{T}} } {\Delta T((T_{\text{f}} - T)/\Delta T)^{\text{n}} }}} \right. \kern-0pt} {\Delta T((T_{\text{f}} - T)/\Delta T)^{\text{n}} }}} \right) \) versus 1/T rendered a straight line, where the values of apparent activation energy (E a) and frequency factor (A) were acquired from the slope and intercept, respectively.

$$ \ln \left( {\frac{{m_{\text{T}} }}{{\Delta T((T_{\text{f}} - T)/\Delta T)^{\text{n}} }}} \right) = \ln A - \frac{{E_{\text{a}} }}{RT} $$
(3)

where m T is the self-heating rate at an arbitrary temperature, T f is the measured final temperature, ΔT is the measured adiabatic temperature increase, T is the absolute temperature, n is the reaction order, and R is the universal gas constant.

According to Eq. (3) and based on the nonlinear fitting method, when n = 1.7, the linear correlation coefficient (0.972) was the highest, and E a and A were 112.0 kJ mol−1 and 1.9 × 1015 mol−0.7 L0.7s−1, respectively. Figure 8 shows the adiabatic kinetic fitting curve. As shown in Fig. 9, the experimental curve was a close fit with the simulation curve. In addition, the time to maximum rate under adiabatic decomposition conditions (TMR ad) can be determined using E a, A, and n [18]. The temperature at which TMR = 24 h (T D24) of sample 1 was evaluated to be approximately 15.8 °C.

Fig. 8
figure 8

Experimental and simulated curves of decomposition under adiabatic conditions

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Fig. 9
figure 9

MTSR and T cf curves of the desired reaction at 12.0 °C and 250 rpm. a Two curves without correction, b MTSR curve corrected by the yield

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Thermal hazard evaluation

The heat generated from a secondary reaction is typically higher than that from the desired reaction. Any safer chemical process should avoid or manage undesirable decomposition. The optimized reaction process can be identified by employing the maximum temperature of the synthesis reaction (MTSR) of the desired reaction (Eq. 4) and T D24 of the secondary decomposition [13, 14].

$$ MTSR^{\text{a}} = T_{\text{p}} + \frac{{\hbox{max} (Q_{\text{accu}} )}}{{C_{\text{p}} M_{\text{r}} }} = T_{\text{p}} + \frac{{\hbox{max} (Q_{\text{input}} - Q_{\text{exo}} )}}{{C_{\text{p}} M_{\text{r}} }} = T_{\text{p}} + \frac{{\hbox{max} \left( {\frac{{\Delta Hm_{\text{cy}} }}{{M_{\text{cy}} }} - Q_{\text{exo}} } \right)}}{{C_{\text{p}} M_{\text{r}} }} $$
(4)

where T p is the reaction temperature, \( Q_{\text{accu}} \) is the accumulated energy, \( Q_{\text{input}} \) is the potential input energy, \( Q_{\text{exo}} \) is the measured heat generation, C p is the specific heat capacity of the co-reactant, M r is the reactant mass in the reactor, ΔH is the measured overall heat of the reaction, m cy is the cyclohexanone mass that has been charged into the reaction during a given time, and M cy is the overall cyclohexanone mass charged into the reactor.

According to the RC1e measurement results, <10 % of initial cyclohexanone was contained within the reactor after the experiments. Although cyclohexanone reacted with H2O2, only if the reactant was heated or the reaction conditions were changed abruptly would the remaining reactant have reacted again. Therefore, the reaction heat and MTSR (Eq. 5) should be modified for thermal loss prevention as follows:

$$ MTSR^{\text{b}} = T_{\text{p}} + \frac{{\hbox{max} \left( {\frac{{\Delta Hm_{\text{cy}} }}{{YM_{\text{cy}} }} - Q_{\text{exo}} } \right)}}{{C_{\text{p}} M_{\text{r}} }} $$
(5)

where Y is the yield of the peroxide reaction.

The adiabatic temperature rise \( \Delta T_{\text{ad}} \), denoted in Eqs. (6) and (7), was also determined, and \( \Delta T_{\text{ad}}^{\text{a}} \) and \( \Delta T_{\text{ad}}^{\text{b}} \) were calculated as follows:

$$ \Delta T_{\text{ad}}^{\text{a}} = \frac{\Delta H}{{C_{\text{p}} M_{\text{r}} }} $$
(6)
$$ \Delta T_{\text{ad}}^{\text{b}} = \frac{\Delta H}{{C_{\text{p}} M_{\text{r}} Y}} $$
(7)
$$ T_{\text{cf}} = T_{\text{p}} + \Delta T_{\text{ad}} $$
(8)

where \( T_{\text{cf}} \) is the maximum adiabatic temperature rise caused by thermal accumulation at a given time. Therefore, MTSR can be defined as follows:

$$ MTSR = \hbox{max} (T_{\text{cf}} ) $$
(9)

Figure 8 shows the MTSR and T cf curves under the reaction conditions of 12.0 °C and 250 RPM, respectively, in accordance with Eqs. (8) and (9). Other MTSRs of various reaction conditions are listed in Table 5.

Table 5 Thermal hazard parameters of the peroxide reaction
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Based on the thermal runaway scenario, the criticality class of this process under various reaction conditions was calculated (Table 6) [13, 14]. The MTSR is listed in Table 5. The reaction was conducted in an open system, and the mass of the concentrated HNO3 catalyst was left unchanged; therefore, for technical reasons, the maximum temperature was the normal boiling point of concentrated HNO3, 120 °C.

Table 6 Temperatures to determine the criticality classes of various conditions for the peroxide reaction
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As listed in Table 6, except for Test 8, the criticality classes for the other tests were five. Although the reaction temperature of the peroxide process is lower than 20 °Cat the industrial scale, once the chemical process undergoes cooling failure or if stirring is stopped abruptly, the system enters adiabatic conditions, which may lead to critical chemical accidents. A criticality class of five is theoretically insupportable. The risks can be reduced if the process itself is altered to avoid the triggering of a secondary reaction. Based on the results of Test 8, if the productivity is admissible, a reduction in the mass of cyclohexanone can alleviate the risk of the thermal runaway scenario in a semi-batch reactor.

Conclusions

The thermal hazards of CYHPO synthesis and the criticality classes were investigated using RC1e, DSC, and ARC. The results revealed that the adiabatic temperature of the peroxide reaction may increase to 50 °C, which is extremely hazardous. According to the RC1e measurements, a heterogeneous liquid–liquid peroxide reaction belongs to the kinetically controlled reaction regime. The overall reaction kinetic parameter was simulated (simulation curve), and it was a close fit with the experimental curve. DSC and ARC experiments indicated that NHO3 and impurities may catalyze the decomposition of CYHPO, thereby increasing the thermal hazards associated with a secondary reaction. According to the MTSR of the desired reaction and T D24 of secondary decomposition, except for the decreasing mass of cyclohexanone, the criticality classes of other conditions were five, which were unacceptable. Therefore, the results can be used for establishing safe conditions for exothermal processes on a commercial scale.