Process Optimization and Thermal Hazard Study for the Preparation of TBPB by a Two–Step Reaction

Abstract

In this study, sodium dodecylbenzene sulfonate was used as a stabilizer, and NaOH, TBHP, and benzoyl chloride were used as reactants in the preparation of tert–butyl peroxybenzoate (TBPB) using a two–step process. The process conditions were optimized by a three–factor, three–level Box–Behnken design approach. The results showed that the yield of TBPB achieved 88.93% under the optimum conditions of temperature of 31.50 °C, feeding time of 22.00 min, and NaOH concentration of 15%. The exothermic properties of the synthesis of TBPB were investigated using reaction calorimetry. The thermal decomposition characteristics of reactants and products were analyzed by differential scanning calorimetry (DSC) and accelerating rate calorimetry (ARC), and the changes in substance types, characteristic peaks, and exothermic quantities during the reaction were analyzed before and after the reaction by FTIR. The reaction mechanism was proposed by combining EasyMax 102, RC1e, gas chromatography (GC), and Fourier transform infrared spectrometry (FTIR). A comprehensive study of the reaction mechanism and reaction exotherm was carried out using density functional theory (DFT) to predict the reaction energy change and the direction of the reaction and to determine whether the reaction was reversible or not. The risk level for the synthesis of TBPB in semi–batch mode was evaluated using a risk matrix and the Stoessel criticality diagram. The optimal conditions for the TBPB synthesis process in a plate microreactor were explored. Both microreactors and semi–batch modes were comparatively analyzed using the m–ITHI quantitative assessment method. The results indicated a hazard class 2 in semi–batch mode and a hazard class 1 in the microreactor. The results of the study may provide a reference for the further improvement of the intrinsically safe design of the synthetic TBPB process.

1. Introduction

Organic peroxides (OPs) are a large group of compounds that are closely related to human life today. The basic general formula is R1–O–O–R2. Tert–butyl peroxybenzoate (TBPB) is widely used as an initiator in polymerization processes such as ethylene, styrene, propylene, and vinyl acetate [1]. However, TBPB contains easily breakable peroxy bonds (–O–O–) [2], which can easily self–break into free radicals, leading to an uncontrolled reaction, and this thermal instability is a safety hazard during preparation and application. Therefore, it is indispensable to pay special attention to the safety of the processes involved in the synthesis and application of TBPB. The molecular structure of TBPB is shown in Figure 1.

Many scholars have devoted themselves to the development of novel synthetic methods for TBPB. Earlier, Milas and Surgenor reported that TBPB can be prepared by the reaction of carboxylic acid or its analog benzoyl chloride with TBHP under alkaline conditions [3]. Wei developed a process route for the direct preparation of TBPB from the reaction of aldehydes and TBHP in an aqueous environment by the C–H oxidation of aldehydes catalyzed by Bu4NI [4]. Zhang further explored the effect of catalyst [5], solvent type, reaction time, and temperature on yield in a direct preparation of TBPB. Chen proposed a new scheme for the efficient synthesis of TBPB from phenylacetonitrile and TBHP under metal–free conditions and a nitrogen atmosphere [6]. Hashemi chose copper acetate (Cu(CO₂CH₃)₂) to catalyze the oxidative coupling reaction of phenylacetonitrile and TBHP [7]. Singha developed a green and efficient method for the synthesis of TBPB from benzaldehyde in a solvent–free environment [8].

At the same time, many scholars have investigated the thermal decomposition behavior of TBPB. Characteristic parameters such as its initial decomposition temperature and heat release were determined [9]. Zhou used advanced calorimetric techniques and thermokinetic models to examine the thermal stability and breakdown features of TBPB [10]. Jiang studied the effect of ionic liquids (ILs) on the thermal decomposition of TBPB and analyzed the influence of two ionic liquids on the decomposition mechanism of TBPB [11]. Zhou evaluated the thermal stability and process safety of tert–butyl peroxybenzoate (TBPB), tert–butyl peroxy–2–ethylhexanoate (TBPO), and their mixture [12]. Gong conducted a comprehensive study of the thermal hazards and initial decomposition mechanism of di–tert–butyl peroxide (DTBP), tert–butyl cumyl peroxide (TBCP), tert–butyl peroxy benzoate (TBPB), and tert–butyl peroxy–2–ethylhexanoate (TBPEH) [13]. This is extremely critical for understanding the rate of self–decomposition of TBPB at higher external temperatures to avoid severe thermal runaway disasters by neglecting the long self–decomposition induction period.

Xu systematically investigated the reaction process of the continuous–flow nitrification of naphthalene for the preparation of 1–nitronaphthalene, and proposed a fast heat transfer evaluation method [14]. Guo proposed the efficient and rapid synthesis of 2–ethylhexyl nitrate in a microchannel reactor [15]. The use of a microchannel reactor to strengthen heat and mass transfer, and its precise control of the excellent characteristics of the material ratio, reduce the risk of the thermal runaway of the reaction system, which is not only of great significance for the optimization of the TBPB process, but the effective inhibition of the thermal runaway of the reaction also reduces the occurrence of local hot spots in the reaction system.

In this study, sodium dodecylbenzene sulfonate was used as a stabilizer, with sodium hydroxide (NaOH), TBHP, and benzoyl chloride as reactants, to prepare TBPB through a two–step method. The process was optimized in terms of NaOH concentration, feeding time, and temperature. Reaction calorimetry was used to study the heat release behavior of the preparation process. The monitoring of the reaction process and qualitative and quantitative analyses of the products were carried out using FTIR and GC. The process hazards of the reaction process in semi–batch mode were evaluated using a risk matrix and the Stoessel criticality diagram. The effect of temperature and residence time on the reaction was investigated using a constructed microchannel reactor. The risk levels of semi–batch modes and microchannel reactors were comparatively assessed by the m–ITHI method. Reactants and products were tested using DSC and products were tested using ARC to obtain thermal decomposition parameters. The enthalpy and Gibbs free energy of the reaction of synthetic sodium salt and TBPB were theoretically investigated using DFT, and a possible reaction mechanism from TBPH to TBPB is proposed.

2. Materials and Experimental

2.1. Reagents

All chemical reagents were used directly without further treatment. The reagents used in the experiment are shown in

Table 1. Reagents used in this experiment.

Reagents	Molecular Formula	Purity (%)	Source
Tert–butyl hydroperoxide	C4H10O2	70	Macklin
Sodium hydroxide	NaOH	≥99.0	Sinopharm
Sodium dodecyl benzene sulfonate	C18H29NaO3S	95	Aladdin
Benzoyl chloride	C7H5ClO	99	Macklin

.

2.2. Process Optimization

Response surface methodology (RSM) was used to design the experiment using the Design–Expert 13.0.5.0 software [15,16]. In the first step of the reaction, an aqueous solution configured from NaOH was used as a substrate, and the reaction was carried out by dropwise addition of TBHP to produce sodium salt. The second step of the reaction was carried out in the original system immediately after the end of the first step by dropwise addition of benzoyl chloride. Therefore, the molar ratio of NaOH, TBHP, and benzoyl chloride was set at 1.2:1:1.1. The reaction time was set to 30 min. Reaction temperature (X₁), feeding time (X₂), and NaOH concentration (X₃) were selected as the optimizing factors, and TBPB yield (Y) was chosen as the response to optimize the preparation process. In this study, a three–factor, three–level design was used with a total of 17 sets of experiments and 5 sets of repeated experiments at the center point. The low, zero, and high levels of the three factors are shown in

Table 2. Experimental factors and levels for BBD.

Factors	Symbol	Level
		−1	0	1
Reaction temperature (°C)	X1	10	30	50
Feeding time (min)	X2	10	20	30
NaOH concentration (%)	X3	5	10	15

.

2.3. Reaction Calorimetry

Reaction calorimetry (RC1e, Mettler Toledo, Zurich, Switzerland) was carried out to study the thermal hazard of the preparation process of TBPB. All calorimetric experiments were carried out in T_r mode. The mixing rate was set to 150 rpm and the material was fed using an advection pump. The optimal process obtained by the response surface methodology of heat hazard selection and three groups of general processes, called processes 1, 2, and 3, are compared. All operating steps were the same as the optimum process except that they involved changes in material and temperature. Since the second step of the TBPB semi–batch synthesis process was the main reaction, calorimetric experiments were performed in the first step of the reaction only for the reaction system under the optimal process. The specifics of each experiment were as follows: 84 g of NaOH was used in the first step of the reaction to configure a 15% aqueous solution with 0.84 g of sodium dodecylbenzene sulfonate added as a substrate. T_r was set to 30 °C, TBHP was fed according to the molar ratio, the feeding time was 20 min, and the holding time was 1 h. In the second step of the reaction, T_r was set to 31.50 °C, benzoyl chloride was dosed according to the molar ratio, the feeding time was 22.00 min, and the holding time was 30 min.

Process 1 increased T_r to 50 °C in the second reaction step and reduced the feeding time to 10 min. In the first step of the reaction in Process 2, 45 g of NaOH was used to configure a 5% aqueous solution and 0.45 g of sodium dodecylbenzene sulfonate was added as a substrate. In the second step of the reaction, T_r was lowered to 10 °C and the feeding time was 30 min. In the first step of the reaction in Process 3, 75 g of NaOH was used to configure a 10% aqueous solution and 0.75 g of sodium dodecylbenzene sulfonate was added as a substrate. In the second step of the reaction, T_r was reduced to 10 °C and the feeding time was 10 min. In all experiments, the reacted mixture was partitioned, and the upper oil phase was taken for analysis.

The reaction equation is shown in Figure 2.

2.4. Dynamic Scanning Calorimetry

DSC (DSC 250, TA Instruments, New Castle, DE, USA) was used to study the thermal decomposition characteristics of reactants and products in the process [17]. About 6 mg of each material was weighed into a gold–plated crucible for testing. Dynamic heating experiments were executed from 50 to 350 °C with a heating rate of 5 °C/min. High–purity nitrogen (99.99%) was adopted as the purge gas with a flow rate of 50 mL/min.

2.5. Product Analysis

In this study, the yield analysis of the experimental products was carried out by GC (GC–7890B, Agilent, Santa Clara, CA, USA). All experiments were carried out to examine only the composition of the product at the end of the second step of the reaction. Methanol was used as the solvent and dissolved immediately after sampling. Samples were taken after each test to configure three sample bottles, and the measured peak areas were averaged to calculate the TBPB yield. The GC test conditions are shown in

Table 3. Test conditions of GC.

Parameters	Conditions
Column	Capillary column
Injector temperature	75 °C
Column temperature	50 °C for 3.6 min and then raised to 120 °C for 9 min at 30 °C/min
Detector temperature	150 °C
Injection volume	1 μL
Split ratio	80:1

.

2.6. Reaction Monitoring Experiments

The entire reaction was tracked using FTIR [18]. The characteristic peaks of TBPB may be affected by some characteristic peaks of water, TBHP, and benzoyl chloride. By searching the relevant infrared spectral libraries and comparing the spectra of the four test substances, the characteristic peak used to distinguish TBPB in this experiment was determined to be 1021.8 cm⁻¹.

2.7. Adiabatic Experiment

To test the thermal decomposition properties of the product [19], TBPB was investigated using an adiabatic accelerated calorimeter (TAC–500A, Young Instruments Co., Ltd., Hangzhou, China). Initially, 1 g of TPBP was loaded into 10 mL stainless steel spheres. The experiment was performed in heat–wait–search (H–W–S) mode. The experimental temperature range was 40–350 °C with an upward trend of 10 °C/min and a 10 min residence time at each temperature point. The data of temperature and pressure were tracked during the experiment with a detection sensitivity of 0.02 °C/min.

2.8. Theoretical Calculation

Theoretical calculations were conducted using the DFT method and Gaussian 16.0 software [20]. The conformational optimizations and vibrational frequency calculations of each stationary point in the reaction process were completed at the theoretical level of B3LYP/6–311G** [21]. To obtain more accurate thermodynamic parameters, the calculation of single–point energy was performed at the B3LYP/def2–TZVPP level [22,23]. The reaction temperature was set to 30 °C in the first–step, 31.5 °C in the second step, and the pressure to 1 atm in Shermo_2.3.6 [24].

2.9. Microchannel Experiment

In this study, the optimum experimental conditions within the plate microchannel reactor were determined using mainly a plate microchannel reactor in a one–factor effect experimental study. Based on the optimal experimental conditions, an improved intrinsic thermal runaway hazard index (m–ITHI) based on a cloud model was used to evaluate the comparison of process thermal runaway hazards in semi–batch modes and microreactors.

3. Results and Discussion

3.1. Process Optimization and Exothermic Properties

3.1.1. Model Fitting

The complete experimental design and results of the 17 sets of experiments performed in EasyMax 102 are shown in

Table 4. Design Experiment Matrix and Results Based on BBD.

Run	Independent Variables			Dependent Variables
	X1	X2	X3	Y
				Exp. a	Pre. b
1	10	10	10	69.27	68.91
2	50	10	10	52.26	53.90
3	10	30	10	63.79	62.15
4	50	30	10	68.11	68.46
5	10	20	5	65.40	66.29
6	50	20	5	56.60	55.49
7	10	20	15	67.58	68.69
8	50	20	15	71.68	70.79
9	30	10	5	68.86	68.33
10	30	30	5	72.93	73.68
11	30	10	15	79.39	78.64
12	30	30	15	80.54	81.07
13	30	20	10	81.98	81.56
14	30	20	10	80.21	81.56
15	30	20	10	81.16	81.56
16	30	20	10	83.17	81.56
17	30	20	10	81.29	81.56

Where ^a Exp denotes experiment date, ^b Pre denotes prediction date.

. The F–value of the model corresponding to the TBPB yield is 65.42, with a p-value < 0.0001, and the misfit term is only 0.1484. These values can be used for the prediction of the response value TBPB yield (Y). In addition, the value of R² is 0.9883, indicating a good fit for the model. The difference between R²_Adj and R²_Pred is less than 0.2, and the value of Adeq Precisior is 23.6944. These show that the model was predictable.

3.1.2. Effect of Different Factors on Responses

The following second–order model was built using Design–Expert software to fit the experimental data [25,26,27], as shown in Equation (1):

$$\mathrm{Y}={\mathsf{\beta }}_0+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\beta }}_{\mathrm{i}\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}^2+{\sum }_{\mathrm{i}-1}^{\mathrm{k}}{\sum }_{\mathrm{j}=\mathrm{i}+1}^{\mathrm{k}-1}{\mathsf{\beta }}_{\mathrm{i}\mathrm{j}}{\mathrm{X}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{j}}$$

(1)

where $\mathrm{Y}$ is the response, ${\mathsf{\beta }}_0$ is a constant coefficient, and ${\mathsf{\beta }}_{\mathrm{i}}$, ${\mathsf{\beta }}_{\mathrm{i}\mathrm{i}}$, and ${\mathsf{\beta }}_{\mathrm{i}\mathrm{j}}$ are the linear regression coefficient, quadric coefficient, and cross–product coefficient, respectively. ${\mathrm{X}}_{\mathrm{i}}$ and ${\mathrm{X}}_{\mathrm{j}}$ are independent factors. $\mathrm{k}$ is the number of factors.

According to the ANOVA results, TBHP yield (Y) was significantly affected by NaOH concentration ${\mathrm{X}}_3$ and ${\mathrm{X}}_{12}$ (p < 0.0001), as well as by ${\mathrm{X}}_1$, ${\mathrm{X}}_2$, ${\mathrm{X}}_1{\mathrm{X}}_2$, ${\mathrm{X}}_1{\mathrm{X}}_3$, ${\mathrm{X}}_{22}$, and ${\mathrm{X}}_{32}$ (p < 0.05). After removing all non–significant terms, the second–order polynomial equation in terms of coded factors is shown in Equation (2):

$$\mathrm{Y}=38.44019+1.15953{\mathrm{X}}_1+1.1589{\mathrm{X}}_2+1.8793{\mathrm{X}}_3+0.0266625{\mathrm{X}}_1{\mathrm{X}}_2+0.03225{\mathrm{X}}_1{\mathrm{X}}_3-0.0353994{\mathrm{X}}_1^2-0.0404475{\mathrm{X}}_2^2-0.08349{\mathrm{X}}_3^2$$

(2)

The effect of process parameters on TBPB yield (Y) is shown in Figure 3. Under certain process conditions, the TBPB yield showed an increasing and then decreasing trend with the increase in temperature. As the feeding time increased, the TBPB yield showed an increasing and then decreasing trend. However, an increasing trend in TBPB yield was observed with increasing NaOH concentration.

3.1.3. Optimal Process and Experiments

The optimization of the TBPB semi–intermittent preparation process was carried out by means of a satisfaction function approach, as shown in Equation (3):

$$\mathrm{D}={({\mathrm{d}}_1·{\mathrm{d}}_2·\cdots ·{\mathrm{d}}_{\mathrm{n}})}^{{\displaystyle \frac{1}{\mathrm{n}}}}={\left({\prod }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{d}}_{\mathrm{i}}\right)}^{{\displaystyle \frac{1}{\mathrm{n}}}}$$

(3)

where ${\mathrm{d}}_{\mathrm{i}}$ is the desirability of the $\mathrm{i}$th response and $\mathrm{n}$ is the number of responses in the experiment.

According to the actual situation of the experiment, the three factors of temperature (${\mathrm{X}}_1$), feeding time (${\mathrm{X}}_2$), and NaOH concentration (${\mathrm{X}}_3$) were selected as “in range”, and “maximize” was selected for the response item, TBPB yield ($\mathrm{Y}$). The results of all the settings are shown in

Table 5. Boundary condition settings of TBPB semi–batch preparation process.

Factors and Responses	Objectives	Low Level (−1)	High Level (1)
${\mathrm{X}}_1$—Reaction temperature (°C)	In range	10	50
${\mathrm{X}}_2$—Feeding time (min)	In range	10	30
${\mathrm{X}}_3$—NaOH concentration (%)	In range	5	15
$\mathrm{Y}$—TBPB yield (%)	Maximize	52.26	100

.

Based on the model analysis, the optimal conditions corresponding to the semi–intermittent preparation process of TBPB when satisfaction reaches its maximum value are temperature of 31.50 °C, feeding time of 22.00 min, and NaOH concentration of 15%, as shown in Figure 4. Model–based predictions resulted in a TBPB yield of 84.06% under these conditions. Based on the process conditions predicted by the model, three sets of replicate experiments were performed in EasyMax 102. The relative errors of the TBPB yields in the validation experiments with respect to the model predictions were 3.21%, 4.87%, and 4.37%, respectively, as shown in

Table 6. Experimental results under the predicted optimal conditions.

	TBPB Yield
Process 1	87.27%
Process 2	88.93%
Process 3	88.43%
Experimental mean	88.21%
Model predictions	84.06%
Relative error	4.15%

. This result shows that the TBPB yield model obtained by response surface methodology has good accuracy and can provide reliable prediction results.

3.1.4. Exothermic Characterisation

Data from the 17 sets of experiments performed on EasyMax 102 are shown in Figure 5 and Figure 6. The temperature control mode for all experiments in EasyMax 102 was selected as the T_j mode. Since the T_r temperature will undergo a much longer waiting time to approach the set temperature after setting the T_j mode, in this study, the experiment was started after the T_r temperature was stabilized.

The change in the T_r temperature for the first step of the reaction is shown in Figure 5. After the temperature was stabilized at 28.00 °C, TBHP was added dropwise, and the temperature of T_r then increased until rising to the highest point of 30.54 °C. After the feeding stopped, the temperature of T_r then decreased slowly until it stabilized at 29.54 °C. The first step of the reaction was actually a fast reaction with low material accumulation. The change in T_r temperature in the second step of the reaction is shown in Figure 6. At T_j temperatures of 10 °C, 30 °C, and 50 °C, three groups of more typical processes were selected to be analyzed. It can be seen that the trend of the reaction was always the same regardless of the T_j temperature set. With the addition of benzoyl chloride, the T_r temperature increased rapidly. Shortly after the feeding was completed, the T_r temperature gradually decreased and finally returned to the pre–feeding temperature.

The increase in NaOH concentration and the decrease in feeding time both led to an increase in the reaction temperature. Accordingly, an increase in the concentration of NaOH means that there was more contact between the reactants, and the rate of reaction increased. The high concentration of the primer will make the transfer and diffusion of heat somewhat limited, making it difficult to distribute evenly or dissipate promptly. Shortening the feeding time will introduce more reactants per unit of time and increase the amount of heat released, and if this heat is not dissipated promptly, then it will generate heat accumulation in the reaction system. In addition, during rapid feeding, the reactants may be over–concentrated in localized areas, leading to more violent reactions in these areas. If the rotational speed was fixed at 150 rpm, then the reactants may not be uniformly distributed over such a short period when the feeding time is shortened, resulting in an uneven distribution of the reaction rate and temperature, which causes an increase in the overall temperature.

3.2. Analysis of Exothermic Behavior of the Reaction

3.2.1. Calorimetric Experimental Results and Analyses

The curves of T_j temperature, T_r temperature, exothermic rate (qr), and mass of TBHP charge as a function of time for the first reaction step of the optimum process are shown in Figure 7.

The curves of T_j temperature, T_r temperature, exothermic rate (qr), and mass of benzoyl chloride addition as a function of time for the second step of the reaction in the optimum process are shown in Figure 8.

As can be seen from Figure 7 and Figure 8, the exothermic rate rose steeply when TBHP and benzoyl chloride were first added to the reactor and peaked in a very short time, and the T_r temperature rose as the reaction progressed. To maintain the temperature of the reaction system at the set temperature, the T_j temperature was significantly reduced to enhance the heat dissipation capability of the system. When the exothermic heat generated by the reaction was roughly equal to the jacket heat dissipation, the T_r temperature began to drop gradually and the T_j temperature began to rise back up. The exothermic rate (qr) was maintained between 20 and 65 W during the first step of the reaction and decreased rapidly until it converged to 0 W shortly after the end of feeding. The maximum difference between the T_r temperature and the T_j temperature was 6.42 °C. At the end of the experiment, the specific heat of the system was measured to be 4.79 J·K⁻¹·g⁻¹ and the total exothermic heat of the reaction was 52.11 kJ. During the second reaction step, the exothermic rate (qr) was maintained between 100 and 300 W, decreasing rapidly until it converged to 0 W shortly after the end of feeding. The maximum difference between the T_r temperature and T_j temperature was 35.95 °C. The exothermic interval is particularly significant during the initial stages of the reaction, and if a cooling failure occurs at this point, there is a high risk of material spraying. At the end of the experiment, the specific heat of the system was measured to be 2.23 J·K⁻¹·g⁻¹ and the total exothermic heat of the reaction was 253.45 kJ.

The curves of T_j temperature, T_r temperature, exothermic rate (qr), and mass of benzoyl chloride addition as a function of time for the second step of the reaction for three general processes are shown in Figure 9.

Even when the conditions were changed, the trends of the various reactions were more or less the same for the three general processes as for the optimum process. It is worth noting that in Process 1, when the T_r temperature was set to 50 °C, the T_j temperature decreased rapidly after the start of the reaction to bring the T_r temperature back to the set temperature, and at this time the temperature difference between the T_r temperature and the T_j temperature was greater than 50 °C. This suggests that an increase in T_r temperature not only reduces the yield but also makes the reaction more dangerous. In Process 3, which was optimized for Process 1, the set value of the T_r temperature and the concentration of NaOH was reduced, and the difference between the T_r temperature and the T_j temperature did not exceed 30 °C even though the feeding was still completed in 10 min.

The specific heat of the Process 1 system was experimentally measured to be 2.21 J·K⁻¹·g⁻¹ and the total exothermic heat of the reaction was 254.79 kJ. The specific heat of the Process 2 system was 3.24 J·K⁻¹·g⁻¹ and the total exothermic heat of the reaction was 99.50 kJ. The specific heat of the Process 3 system was 3.39 J·K⁻¹·g⁻¹ and the total exothermic heat of the reaction was 182.23 kJ.

3.2.2. Exothermic Characterization of the Reaction Process

In this study, FTIR tests were carried out on several compounds related to the TBPB synthesis process, as shown in Figure 10. During the two–step reaction of the TBPB semi–intermittent synthesis process, the entire course of the reaction was followed using FTIR. The infrared probe was inserted into the reaction system and the infrared spectral data were collected every 15 s to obtain the three–dimensional spectrum of absorbance–reaction time–light wavenumber of the optimal process, as shown in Figure 11.

Under the optimal process conditions and in combination with the temperature of the reaction system, the changes in the product TBPB during the reaction were qualitatively analyzed by the split–peak method, as shown in Figure 12. When only benzoyl chloride was added to the reaction system, the reaction occurred rapidly, a large amount of heat was released, the temperature of the system increased, and the absorbance of the characteristic peaks of TBPB increased rapidly and began to stabilize at the end of the addition. Shortly after the end of the addition, the reaction between the sodium salt and benzoyl chloride in the system ended, the exothermic rate tended toward 0 W, and TBPB was generated in large quantities. There was a small oscillation in the absorbance of TBPB due to the non–homogeneous nature of the mixture produced by the reaction, and the oil phase in which the TBPB was located was above the infrared probe, which needed to be turned on with constant stirring for better detection. It can be seen that the change in the absorbance of the characteristic peaks of TBPB and the trend of the exothermic rate were consistent, and the exotherm mainly existed in the stage of TBPB generation after the start of feeding.

3.3. Continuous–Flow Process Studies

In this study, continuous–flow microchannel experiments were carried out on an industrial–grade plate microchannel experimental platform, and each experiment was repeated three times. The experimental conditions are shown in

Table 7. Setting of experimental parameters.

Parameter	Set Value
Flow velocity ratio	1:3; 1:2
Oil bath temperature	30 °C; 35 °C; 40 °C; 45 °C; 50 °C
Residence time	0.75 min; 1 min; 2 min; 3 min

. The microchannel reactor is shown in Figure 13. In (a), Thermostat provides circulating thermal oil to the microreactor to control the temperature of the reaction system, the online monitoring system is responsible for recording the temperature and pressure data during the reaction process, and the Metering pumps are responsible for pumping the reactants into the microreactor, and the whole reaction process is carried out in the Microchannel reactor. In whole reaction process is carried out in the Microchannel reactor. The Pressure sensor in (b) mainly monitors the pressure inside the micro reactor during the reaction process, and the Thermocouple mainly monitors the temperature of the reaction system.

3.3.1. Effect of Temperature and Residence Time on the Reaction

In this study, the effect of temperature inside the plate reactor on the yield of TBPB was investigated, and the temperature–pressure variation graphs inside the reaction channel were recorded. Figure 14 shows the effect of temperature on the reaction at different residence times (0.75–3 min).

From Figure 14, it can be seen that when the temperature was 50 °C and the residence time was 45 s, the yield reached 83%. It can be seen that the shorter the residence time in the plate microreactor, the higher the TBPB yield. The main reason is that the TBPB synthesis reaction itself is fast, and the plate microchannel reactor can quickly balance the temperature of the reaction system and improve the control and selectivity of the reaction due to its small size, large specific surface area, and high heat transfer efficiency, so the reaction can reach equilibrium quickly, and thus the yield can be increased. With increasing residence time, the TBPB yield gradually decreased due to the plate microreactor heat transfer efficiency. Too long a residence time will result in product decomposition in the channel, while also generating by–products. Figure 14 also shows that the yield of TBPB gradually increased as the temperature of the whole reaction system increased, which was due to the intense thermal movement of the molecules at higher temperatures, resulting in better promotion of the reaction.

3.3.2. Temperature and Pressure Variations in Microreactors

The temperature trends inside the plate microreactor at a process temperature of 50 °C and residence time of 0.75–3 min are shown in Figure 15, where T_j is the oil bath temperature and T1–T4 represent the reaction temperatures inside the first plate to the fourth plate after mixing, respectively. It can be seen that the temperature of the oil bath was maintained at about 50 °C throughout the reflection process, and the temperature of the first mixing plate under the four residence times was on the low side. As the reaction proceeded, the highest point of the reaction temperature moved backward, resulting in a lower exit temperature for the first reaction plate and a higher temperature for the third and fourth plates behind it. Secondly, as the residence time increased, the heat transfer efficiency of the third and fourth plates became higher, and thus the temperature rose.

The pressure changes inside the plate microchannel reactor at 50 °C are shown in Figure 16. The material undergoes an exothermic reaction in the small passages, resulting in an increase in pressure for a short period. With the prolongation of the reaction time pressure began to decrease, this is because the material in the continuous–flow microreactor can quickly bring the reaction of the heat released outside the reactor, so it will not cause the phenomenon of overpressure, the microreactor within the pressure of the overall smaller, to ensure that the reaction is carried out smoothly.

3.4. Gas Chromatography

The standard curve was tested and plotted using the method of Table 4, as shown in Figure 17. The peak time of TBPB was 14.6 min, and the standard curve equation was obtained by linear fitting, as shown in Equation (4), the value of R² is 0.99958. TBPB yield of 88.93% was obtained with the optimal process. Gas chromatogram of the upper oil phase of the product obtained by fractionation, as shown in Figure 18.

$$\mathrm{y}=-90.775+605.54167\mathrm{x}$$

(4)

3.5. DSC Results

The exothermic curves of the reactants benzoyl chloride and TBHP with the products sodium salt (sample 1) and TBPB (sample 2) were measured, as shown in Figure 19. The relevant thermal parameters are shown in

Table 8. DSC test results.

Chemicals	Sample Mass (mg)	Tonset (°C)	Tpeak (°C)	−∆Hd (J/g)
Benzoyl chloride	6.32	200.56	205.90	−176.02
TBHP	5.93	100.40	101.30	−371.00
Sample 1	6.78	113.63	113.64	−975.38
TBPB	5.44	129.44	154.91	709.70

. Benzoyl chloride, TBHP, and Sample 1 decompose with heat absorption, indicating good thermal stability. Sample 2 started to decompose at 129.44 °C with a peak exothermic value of 709.70 J/g, which is more exothermic.

3.6. ARC Results

Measured temperature profiles of TBPB pure compounds as a function of time in an adiabatic experiment, as shown in Figure 20. It can be obtained that the temperature rise rate of self–decomposition of TBPB at 84.93 °C exceeded 0.02 °C/min, indicating that an adiabatic reaction occurred at this time. After 1016 min, the temperature reached 230.76 °C and the autolytic decomposition ended.

The TBPB decomposition reaction is not an n–order reaction and follows the kinetic equation shown in Equation (5). The activation energy E for the TBPB autolytic reaction was calculated to be 212 kJ/mol.

$${\mathrm{T}\mathrm{M}\mathrm{R}}_{\mathrm{a}\mathrm{d}}={\displaystyle \frac{{\mathrm{R}\mathrm{T}}^2}{\mathsf{\sigma }\mathrm{E}}}-{\displaystyle \frac{{\mathrm{R}\mathrm{T}}_{\mathrm{M}}^2}{{\mathsf{\sigma }}_{\mathrm{m}}\mathrm{E}}}$$

(5)

where ${\mathsf{\sigma }}_{\mathrm{m}}$ is the maximum rate of warming, but the second term on the right–hand side of Equation (5) is so much smaller than the first term that it can be neglected.

3.7. Gaussian Simulation

The results of the conformational optimizations and vibrational frequency calculations for each substance before and after the reaction are shown in Figure 21. Both steps of the reaction for the preparation of TBPB are exothermic, and the theoretical molar reaction enthalpies and Gibbs free energies are shown in Figure 22. The actual molar enthalpy of reaction for the first step of the reaction was 20.84 kJ/mol, the theoretical molar enthalpy of reaction was 44.79 kJ/mol, and the Gibbs free energy was −35.30 kJ/mol. The actual molar enthalpy of reaction for the second step of the reaction was 101.38 kJ/mol, the theoretical molar enthalpy of the reaction was 134.32 kJ/mol, and the Gibbs free energy was −131.50 kJ/mol. As it is impossible to prevent the heat dissipation of the apparatus from occurring in the actual operation, and because water is the solvent and not involved in the main reaction, there is a certain amount of heat loss in the experiment. This is somewhat different from the theory, but is the same as the theoretical results, which can verify the reliability of the theoretical data.

3.8. Summary of Thermal Behavior Parameters

The second step of the optimal process is summarized as an example, and the thermal behavior parameters of the remaining processes are listed in the table.

(1). The severity of the runaway reaction is usually measured by the adiabatic temperature rise ${∆\mathrm{T}}_{\mathrm{a}\mathrm{d}}$ due to the exothermic nature of the reaction [28], calculated as shown in Equation (6). However, the adiabatic temperature rise ${∆\mathrm{T}}_{\mathrm{a}\mathrm{d},\mathrm{r}}$ [29] should be corrected according to the reaction yield, as shown in Equation (7). Thus, the value of ${∆\mathrm{T}}_{\mathrm{a}\mathrm{d},\mathrm{r}}$ is 109.91 K.

$${∆\mathrm{T}}_{\mathrm{a}\mathrm{d}}={\displaystyle \frac{∆\mathrm{H}}{{\mathrm{C}}_{\mathrm{P}}\mathrm{M}}}$$

(6)

$${∆\mathrm{T}}_{\mathrm{a}\mathrm{d},\mathrm{r}}={\displaystyle \frac{∆\mathrm{H}}{{\mathrm{C}}_{\mathrm{P}}\mathrm{M}\mathrm{Y}}}$$

(7)

where ${∆\mathrm{T}}_{\mathrm{a}\mathrm{d}}$ is the experimentally obtained adiabatic temperature rise of the target reaction, K; ${∆\mathrm{T}}_{\mathrm{a}\mathrm{d},\mathrm{r}}$ is the adiabatic temperature rise of the target reaction corrected for yield, K; $∆\mathrm{H}$ is the total heat released from the reaction, kJ; ${\mathrm{C}}_{\mathrm{P}}$ is the specific heat capacity of the system at the end of the reaction, J·K⁻¹·g⁻¹; $\mathrm{M}$ is the total mass of the system at the end of the reaction, g; $\mathrm{Y}$ is reaction yield, %.

Table 9. Results of RC1e experiment in the first reaction process.

Reaction	ΔHr/kJ	Cp/J (K−1·g−1)	M/g	Y/%	ΔTad/K	ΔTad,r/K
Optimal process	52.1	4.79	786.14	/	13.84	/

and

Table 10. Results of RC1e experiment in the second reaction process.

Reaction	ΔHr/kJ	Cp/J (K−1·g−1)	M/g	Y/%	ΔTad/K	ΔTad,r/K
Optimal process	253.45	2.23	1056.74	97.91	107.55	109.85
Process 1	254.79	2.21	1056.74	88.10	109.10	123.84
Process 2	99.50	3.24	1166.10	87.33	26.34	30.16
Process 3	182.23	3.39	1193.52	94.27	45.04	47.78

show the calorimetric results in the RC1e experiment. The higher yield of TBPB in RC1e compared to EasyMax 102 was due to the larger volume of RC1e, the relatively greater range of rotation of the stirring paddles, the better mixing of the reactants, and the measurement of the specific heat of the reaction system, which corresponded to an increase in the reaction time and a more complete reaction.

(2). ${\mathrm{T}}_{\mathrm{P}}$ does not need to be calculated, and the ${\mathrm{T}}_{\mathrm{P}}$ in each reaction is shown in

Table 11. ${\mathrm{T}}_{\mathrm{P}}$ of different reactions.

Reaction	Tp
Optimal process first–step reaction	30.00 °C
Optimal process second–step reaction	31.50 °C
Process 1 s step reaction	50.00 °C
Process 2 s step reaction	10.00 °C
Process 3 s step reaction	10.00 °C

.

(3). The determination of $\mathrm{M}\mathrm{T}\mathrm{T}$ needs to consider the system pressure and the boiling point of the material. Due to the use of semi–batch mode at atmospheric pressure, the solvent water in the reaction materials had the largest proportion of the mass fraction, so the $\mathrm{M}\mathrm{T}\mathrm{T}$ selected water at the atmospheric pressure boiling point, 100 °C.

(4). The determination of $\mathrm{M}\mathrm{T}\mathrm{S}\mathrm{R}$ requires the introduction of the concept of ${\mathrm{T}}_{\mathrm{c}\mathrm{f}}$ [30]. When a cooling failure occurs, the material continues to react, resulting in an increase in temperature, and the final temperature that can be reached is ${\mathrm{T}}_{\mathrm{c}\mathrm{f}}$. The maximum value of ${\mathrm{T}}_{\mathrm{c}\mathrm{f}}$ was selected as the $\mathrm{M}\mathrm{T}\mathrm{S}\mathrm{R}$, as shown in Equation (8). The first step reaction of the optimal process was analysed as an example, and the $\mathrm{M}\mathrm{T}\mathrm{S}\mathrm{R}$ was 31.45°C, as shown in Figure 23. In fact, ${\mathrm{T}}_{\mathrm{c}\mathrm{f}}$ also needs to be corrected by the yield (Y)–modified ${\mathrm{T}}_{\mathrm{c}\mathrm{f},\mathrm{r}}$ equation, as shown in Equation (9). The second step of the optimum process was analyzed as an example. The variation in ${\mathrm{T}}_{\mathrm{c}\mathrm{f}}$ and ${\mathrm{T}}_{\mathrm{c}\mathrm{f},\mathrm{r}}$ with time is shown in Figure 24, and the ${\mathrm{M}\mathrm{T}\mathrm{S}\mathrm{R}}_{,\mathrm{r}}$ was 54.26 °C.

$${\mathrm{T}}_{\mathrm{c}\mathrm{f}}={\mathrm{T}}_{\mathrm{p}}+{\displaystyle \frac{\frac{{∆\mathrm{H}}_{\mathrm{r}}{\mathrm{m}}_{\mathrm{t}}}{\mathrm{m}}-{\int }_0^{\mathrm{t}}{\mathrm{q}}_{\mathrm{r}}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}}{{\mathrm{C}}_{\mathrm{p}}\mathrm{M}}}$$

(8)

$${\mathrm{T}}_{\mathrm{c}\mathrm{f},\mathrm{r}}={\mathrm{T}}_{\mathrm{p}}+{\displaystyle \frac{\frac{{∆\mathrm{H}}_{\mathrm{r}}{\mathrm{m}}_{\mathrm{t}}}{\mathrm{m}\mathrm{Y}}-{\int }_0^{\mathrm{t}}{\mathrm{q}}_{\mathrm{r}}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}}{{\mathrm{C}}_{\mathrm{p}}\mathrm{M}}}$$

(9)

where ${\mathrm{T}}_{\mathrm{P}}$ is the set temperature of the reaction system, °C; ${\mathrm{m}}_{\mathrm{t}}$ is the mass of material that has been added to the reaction system at time t, g; $\mathrm{m}$ is the total mass of material to be added dropwise to the reaction system, g; ${\mathrm{q}}_{\mathrm{r}}$ is the exothermic rate of the reaction, W.

(5). The calculation of ${\mathrm{T}\mathrm{M}\mathrm{R}}_{\mathrm{a}\mathrm{d}}$ [31] is shown in Equation (5). TBPB has the danger of exothermic self–decomposition, so the kinetic triple factor and related data were used to plot ${\mathrm{T}\mathrm{M}\mathrm{R}}_{\mathrm{a}\mathrm{d}}$, as shown in Figure 25. When the temperature reached the $\mathrm{M}\mathrm{T}\mathrm{S}\mathrm{R}$, the temperature was 54.26 °C, and the ${\mathrm{T}\mathrm{M}\mathrm{R}}_{\mathrm{a}\mathrm{d}}$ was 511.9 h.

3.9. Process Heat Hazard Assessment

3.9.1. Risk Matrix Method

The only exothermic material present in the TBPB semi–batch synthesis process is TBPB, which was assessed as shown in

Table 12. The risk matrix method assessment results.

Sample	ΔTad,r/K	Severity	TMRad/h	Possibility	Risk Level	Thermal Hazard
TBPB	109.85	medium	>24	hardly	1	acceptable

. The hazard level for the step 2 responses was acceptable risk, which is a low level of danger that does not require special safety measures.

3.9.2. Stoessel Criticality Diagram

The hazard level of the process was assessed using the Stoessel criticality diagram [32] method and the results are shown in

Table 13. Thermal hazard assessments by the Stoessel criticality diagram of the first reaction process.

Reaction	Tp/°C	MTSR/°C	MTT/°C	TD24/°C	Class
Optimal process	30.00	31.45	100.00	>350	1

and

Table 14. Thermal hazard assessments by the Stoessel criticality diagram of the second reaction process.

Reaction	Tp/°C	MTSR, r/°C	MTT/°C	TD24/°C	Class
Optimal process	31.50	54.26	100.00	70.60	2
Process 1	50.00	89.47	100.00	70.60	5
Process 2	10.00	21.80	100.00	70.60	2
Process 3	10.00	46.20	100.00	70.60	2

. The hazard class of the optimal process reaction is 2.

After the assessment of the risk matrix method and the Stoessel criticality diagram method, a theoretical basis was provided for the subsequent scale–up production and process improvement of the TBPB semi–intermittent synthesis process. Both review methods showed that the overall thermal runaway hazard of the reaction system was lower at 30 °C and below, both for the first and second reaction steps. However, when the reaction temperature rose to 50 °C, the degree of thermal runaway of the reaction system rose rapidly to level 5, which is the most dangerous. In the event of cooling failure and loss of temperature control, accidents are very likely to occur, so the process must be optimized.

3.9.3. Quantitative Assessment of m–ITHI

In this study, the process of synthesizing TBPB in a microchannel reactor was evaluated and compared with that in semi–batch mode.

Since the results of the study are related to the amount of material in the reaction unit, it is assumed that the process capacity is 7000 tons/year and the annual operating time of the reactor is 8000 h. Reactor scale–up is not considered here. The method was used in a plate microchannel reactor, and the experimental data at optimum yield in the plate microreactor and semi–batch mode were selected here. The relevant experimental data are shown in

Table 15. Experimental parameters of two types of reactors.

Parameter	Microchannel Reactor	RC1e
Total volume of reaction (mL)	23.00	975.00
Stay time (min)	0.75	60.00
Yield (%)	83.00	97.91
Spatiotemporal yield (g·L−1·s−1)	0.58	0.07
Annual output (t/unit)	0.39	1.83
Total material quantity (kg)	484.00	4050.00

.

Calorimetric information for the current process within continuous–flow reactors is not readily available, so the molar reaction heat obtained in semi–batch mode was applied to the evaluation of continuous–flow microreactors. The values of the runaway scenario hazard class CC and TMRad were obtained through the kettle reaction, and finally, the individual experimental data were substituted into the m–ITHI calculator in Matlab. The results of the calculations are shown in Figure 26.

The optimal process for RC1e was selected to analyze and compare the safety of the two reactors, again assuming semi–batch mode with an annual operating time of 8000 h and an annual production capacity of 7000 tons. The total amount of material required in semi–batch mode was calculated to be 4050 kg, the mass of unstable material was 1500 kg, the heat of decomposition of the material in the TBPB was the same as in the microreactor, and the molar heat of reaction was the same as in the microreactor. The data were imported into the m–ITHI calculator in Matlab, and the exact calculations are shown in Figure 27.

4. Conclusions

(1)

The TBPB semi–intermittent synthesis process was optimized using Design–Expert software to analyze the exothermic properties, where an increase in NaOH concentration and a decrease in feeding time increased the reaction temperature. The optimum process conditions were temperature of 31.50 °C, feeding time of 22.00 min, and NaOH concentration of 15%. Based on the predictions of the model, the TBPB yield under these conditions was 84.06%, and the model was verified to have good accuracy through three experiments.

(2)

In the plate microchannel reaction process, the temperature and pressure changes in the reaction system can be monitored in real time using thermocouples and pressure sensors. When it was 50 °C and the residence time was 45 s, TBPB reached the highest yield of 83%.

(3)

The products were analyzed qualitatively and quantitatively by GC to obtain the peak times and working curves of TBPB, and the yield of the optimal process in EasyMax 102 was 88.93%. The exothermic properties were studied using RC1e to obtain values for the exothermic quantities of the reactions. The total heat release in the first step of the optimum process was 52.11 kJ and the total heat release in the second step of the optimum process was 253.45 kJ. The total heat release in Process 1 was 254.79 kJ, in Process 2 was 99.50 kJ, and in Process 3 was 182.23 kJ.

(4)

Real–time monitoring of the reactants and products during the reaction process using FTIR, combined with data from reaction calorimetry, revealed that the absorbance changes of the characteristic peaks of TBPB were consistent with the trend of the exothermic rate. In the second step of the TBPB half–gap synthesis process, the exotherm was mainly present in the TBPB generation phase after the start of feeding.

(5)

The thermal hazard assessment of the TBPB semi–intermittent synthesis process was carried out using the risk matrix method and the Stoessel criticality diagram method. Using the risk matrix methodology to obtain TMR_ad > 24, the hazard class for the second step of the TBPB semi–intermittent synthesis process involves acceptable risk, which is a low level of hazard and does not require special safety measures. Using the Stoessel criticality plot method, the overall thermal runaway hazard was assessed to be low when the reaction system was at 30 °C and below, both for the first– and second–step reactions. However, when the reaction temperature rose to 50 °C, the degree of thermal runaway of the reaction system rapidly rose to level 5. This is point with the highest degree of danger, as once cooling failure occurs, the temperature is out of control; it is very likely to cause accidents and must be optimized for the process. Finally, the reaction heat hazard in a continuous–flow microreactor as well as semi–batch mode was assessed using the cloud–model–based modified intrinsic thermal runaway hazard index (m–ITHI) method, and the m–ITHI values of the two reactors were compared. The m–ITHI value of 2.985 was obtained in the continuous–flow microreactor, which is classified as hazard class 1, and the m–ITHI value of 5.004 was obtained in semi–batch mode, which is classified as hazard class 2. The quantitative evaluation method suggests that the safety of a continuous–flow microreactor is higher than that of semi–batch mode, which provides some reference for the selection of high–risk and highly exothermic synthesis processes and reactors.