2.1. Kinetic model
At present, no investigations on the kinetics of benzylic bromination of DCT to DCBB under light irradiation are reported in literature. Therefore, it is necessary to reveal the kinetics of this reaction in a microchannel, which is a fundament for scale up production of DCBB in this process. The investigation was conducted in a microreactor system as shown in Fig. 5. In the experiments, aqueous HBr and H2O2 mixed through a tree-way valve leading to in situ generation of Br2 before entering the microchannel reactor in the experiments. Therefore, Br2 can be regarded as the actual bromination agent in the reaction. As is known, the photocatalytic bromination of DCT is a free radical chain reaction [34], it is difficult to establish a kinetic model based on the elementary reactions. Here, an intrinsic kinetics was proposed based on the initial results: Almost no benzylic dibromo and tribromo products, α,α-dibromo-2,6-dichlorotoluene (DBDCT) and α,α,α-tribromo-2,6-dichlorotoluene (TBDCT) were found under the specific experimental conditions, though three benzylic bromination products, DCBB, DBDCT and TBDCT could be generated in principle; The unexpected product 2,6-dichlorobenzoic acid (DCBA) was formed almost in constant selectivity under the specific reactions. Figure 2 shows the intrinsic kinetic scheme for the benzylic bromination of DCT to DCBB.
Since the benzylic bromination of DCT in a microchannel reactor is significantly complicated, many parameters must be empirically adjusted. Therefore, the well-known power law model is used to fit the experimental data. Because the benzylic bromination reaction is not reversible, especially in the H2O2-HBr system [35], the reaction rate equation can be expressed as
$${\text{r}}_{\text{A}}\text{=-}\frac{\text{d}{\text{C}}_{\text{A}}}{\text{dt}}\text{=k}{\text{C}}_{\text{A}}^{{\text{α}}_{\text{1}}}{\text{C}}_{\text{B}}^{{\text{α}}_{\text{2}}}$$
1
According to Arrhenius equation
$$\text{k=}{\text{k}}_{\text{0}}\text{ }\text{exp}\text{ }\text{(-}\frac{{E}_{a}}{\text{RT}}\text{)}$$
2
Then the kinetic model is expressed as
$${\text{r}}_{\text{A}}\text{=-}\frac{\text{d}{\text{C}}_{\text{A}}}{\text{dt}}\text{=}{\text{k}}_{\text{0}}\text{ }\text{exp(-}\frac{{E}_{a}}{\text{RT}}\text{)}{\text{C}}_{\text{A}}^{{\text{α}}_{\text{1}}}{\text{C}}_{\text{B}}^{{\text{α}}_{\text{2}}}$$
3
where Ci (i = A, B) are the concentrations of DCT and Br2, mol⋅L-1; Ea is the activation energy, J⋅mol-1; k is the reaction rate constant; k0 is the preexponential factor; rA is the reaction rate of DCT, mol⋅L-1⋅s-1; R is the molar gas constant, 8.314 J⋅mol-1⋅K-1; T is the reaction temperature, K; t is the reaction time, s; αi (i = 1,2) are the reaction orders of DCT and Br2.
2.2. Eliminate the effect of mass transfer
Since the aqueous solution of HBr and the aqueous solution of H2O2 have been pre-mixed and generated Br2 in situ before entering the microchannel reactor, when the aqueous phase is mixed with the organic phase, the solubility of Br2 in the organic phase solvent 1,2-dichloroethane is much greater than that in the aqueous phase, so Br2 will quickly enter the organic phase and participate in the reaction to produce HBr, while the solubility of HBr in the aqueous phase is much greater than that in the organic phase, HBr will be returned from the organic phase back into the aqueous phase and continue the reaction with H2O2. To get the intrinsic rate data of a reaction in a microchannel reactor, it is necessary to conduct kinetic studies in the regime where mass transfer is absent. Therefore, we made selection of the range of residence time in which the external diffusion of reactants was absent. The experiments were carried out under DCT:HBr:H2O2 molar ratios of 1.0:1.1:1.1, reactant concentrations of DCT 21.0 wt.%, HBr 16.33 wt.%, H2O2 7.71 wt.%, 0.8 MPa pressure, and 87 W blue light irradiation at 70 oC with variation of residence time. Under the same residence time, the reaction was carried out in different volumes of the same microchannel reactor (V1 = 23.7 mL, V2 = 17.6 mL). As shown in Fig. 3, the conversion of DCT was hardly changed with the variation of the volume of the same microchannel reactor when the residence time is less than 350 s. That was to say, the effect of mass transfer on the reaction could be ignored if the residence time is less than 350 s.
Reaction Conditions: 87 W blue light; DCT:HBr:H2O2 (molar ratio) = 1:1.1:1.1; solution A: 21.0 wt.% solution of DCT (0.141 mol) in 1, 2-dichloroethane (73.0 mL); solution B: 16.33 wt.% of HBr aqueous solution; solution C: 7.71 wt.% of H2O2 aqueous solution; reaction pressure = 0.8 MPa; reaction temperature = 70 oC.
2.3. Kinetic parameter estimation
Kinetic parameter estimation is a necessary step to describe a kinetic model for a given chemical reaction[36], therefore, the variations of DCT and Br2 concentrations (CA and CB) with time were investigated in the temperature range of 20 ~ 50 oC. The results are listed in Table 1.
Table 1
Data of the concentration of CA and CB over time at 20 oC to 50 oC
run | t/s | T/ oC | CA/(mol⋅L− 1) | CB/(mol⋅L− 1) |
1 | 10.1 | 20 | 1.5138 | 0.8379 |
2 | 14.7 | 20 | 1.5007 | 0.8312 |
3 | 20.3 | 20 | 1.4823 | 0.8228 |
4 | 24.3 | 20 | 1.4635 | 0.8125 |
5 | 30.4 | 20 | 1.4432 | 0.8021 |
6 | 36.0 | 20 | 1.4228 | 0.7906 |
7 | 10.1 | 30 | 1.4938 | 0.8275 |
8 | 14.7 | 30 | 1.4735 | 0.8172 |
9 | 20.3 | 30 | 1.4513 | 0.8066 |
10 | 24.3 | 30 | 1.4291 | 0.7952 |
11 | 30.4 | 30 | 1.4028 | 0.7804 |
12 | 36.0 | 30 | 1.3714 | 0.7627 |
13 | 10.1 | 40 | 1.4748 | 0.8178 |
14 | 14.7 | 40 | 1.4407 | 0.8009 |
15 | 20.3 | 40 | 1.4084 | 0.7842 |
16 | 24.3 | 40 | 1.3787 | 0.7654 |
17 | 30.4 | 40 | 1.3398 | 0.7498 |
18 | 36.0 | 40 | 1.2850 | 0.7225 |
19 | 10.1 | 50 | 1.4192 | 0.7891 |
20 | 14.7 | 50 | 1.3761 | 0.7664 |
21 | 20.3 | 50 | 1.3154 | 0.7384 |
22 | 24.3 | 50 | 1.2821 | 0.7204 |
23 | 30.4 | 50 | 1.2192 | 0.6873 |
24 | 36.0 | 50 | 1.1529 | 0.6522 |
Reaction condition: 87 W blue light; DCT:HBr:H2O2 (molar ratio) = 1.0:1.1:1.1, solution A: 21.0 wt.% solution of DCT (0.141 mol) in 1, 2-dichloroethane (73.0 mL); solution B: HBr aqueous solution, 16.33 wt.%; solution C: H2O2 aqueous solution, 7.71 wt.%; reaction pressure = 0.8 MPa. |
The data in Table 1 were firstly subjected to multiple linear regression using Matlab software to obtain the initial values of each parameter. The initial values were then substituted into the non-linear regression to obtain the calculated values of the kinetic model parameters. The parameter data were brought into Eq. (4) to obtain the kinetic model:
$${\text{r}}_{\text{A}}\text{=-}\frac{\text{d}{\text{C}}_{\text{A}}}{\text{dt}}\text{=}\text{635.3}\text{exp (-}\frac{\text{2.40}\text{×}{\text{10}}^{\text{4}}}{\text{RT}}\text{)}{\text{C}}_{\text{A}}^{\text{-4.19}}{\text{C}}_{\text{B}}^{\text{3.22}}$$
4
In the kinetic model the activation energy is 2.40×104 J⋅mol− 1, indicating the reaction can proceed under mild conditions. The negative reaction order of DCT (-4.19) indicates that high DCT concentration is unfavorable for benzylic bromination of DCT, which could be ascribed to the difficulty in mixing of aqueous and organic phases at high concentration of DCT.
The F statistical test [37, 38] was used to evaluate the adaptability of the kinetic model according equations, and the test results are given in Table 2.
Statistical test:
$$\text{F=}\frac{{\text{S}}_{\text{ESS}}/\text{P}}{{\text{S}}_{\text{RSS}}/\left(\text{N-P-1}\right)}\text{>10}{\text{×}\text{F}}_{\text{α}}$$
5
Multiple correlation index:
$${\text{R}}^{\text{2}}\text{=1-}\frac{{\text{S}}_{\text{RSS}}}{{\text{S}}_{\text{TSS}}}\text{>0.9}$$
6
Among them, the total sum of squares:
$${\text{S}}_{\text{TSS}}\text{=}\sum _{\text{i=1}}^{\text{N}}{\left({\text{C}}_{\text{i}}\text{-}\stackrel{\text{-}}{\text{C}}\right)}^{\text{2}}$$
7
Explained sum of squares:
$${\text{S}}_{\text{ESS}}\text{=}\sum _{\text{i=1}}^{\text{N}}{\left(\widehat{\text{C}}\text{-}\stackrel{\text{-}}{\text{C}}\right)}^{\text{2}}$$
8
Residual sum of squares:
$${\text{S}}_{\text{RSS}}\text{=}\sum _{\text{i=1}}^{\text{N}}{\left({\text{C}}_{\text{i}}\text{-}\widehat{\text{C}}\right)}^{\text{2}}$$
9
where, N is the number of experimental data sets; P is the number of parameters to be estimated; Ci is the experimental measurement value;‾C is the experimental average;\(\text{ }\widehat{\text{C}}\) is the calculated value; α is the significance level, generally takes 0.05.
Table 2
F-test of intrinsic kinetic models
Equation | (4) |
P | 4 |
N – P – 1 | 19 |
R2 | 0.9794 |
F | 224.35 |
10×Fα=0.05 | 28.95 |
10×Fα=0.005 | 52.70 |
As can be seen from Table 2, the multiple correlation index of the proposed model is greater than 0.9 and the F-statistic is greater than 10 times the critical F-statistic with a confidence domain of 95% and 99.5%. Figure 4 shows the distribution of the residuals of the reaction rate, which are more evenly distributed around the zero line and the sides, these suggest that the model is significantly valid.