Numerical Simulation and Response Surface Analysis of Esterification of Monobutyl Chlorophosphate with n-Butanol in a Microchannel Reactor

Abstract

Microreactors are essential for microchemical reactions owing to their high mass transfer efficiency, precise control of reaction time, easy amplification, and good safety performance. These characteristics provide several advantages, including shortened reaction times and enhanced chemical reaction conversion rates, rendering microreactors particularly significant in chemical production. In this study, a finite-rate model was developed for the esterification of monobutyl chlorophosphate (MCP) and n-butanol in a microchannel reactor. This study investigates the impact of the microchannel’s length-to-diameter ratio, the mass ratio of n-butanol to MCP at the inlet, and the inlet flow ratio on the entire reaction system through numerical simulations. The findings indicate that increasing the length-to-diameter ratio and reducing the inlet flow rate effectively prolongs the residence time of materials in the microreactor, thereby enhancing the conversion rate of the reactants. Optimal results are achieved with a moderate n-butanol/MCP mass ratio, which facilitates MCP transformation. Moreover, this study employs response surface analysis to investigate the influence of independent factors, such as the microchannel’s length-to-diameter ratio, component ratio, and inlet velocity ratio, on MCP conversion rates. A prediction formula with conversion rate as the dependent variable and microchannel length-to-diameter ratio, component ratio, and inlet velocity ratio as independent variables was established.

1. Introduction

Microchannel reactors are miniaturized and highly efficient reaction equipment items extensively used in chemical synthesis, catalytic reactions, and other chemical processes. Their development addresses the mass and heat transfer limitations of traditional macroscopic reactors and the demand for more controllable and flexible reaction conditions [1,2]. At the core of these reactors is their micrometer-scale channel structure, typically ranging from hundreds of micrometers to millimeters in width. This small size not only enhances the surface area to volume ratio, but also optimizes mass and heat transfer performance [3]. In addition, microchannel reactors enable a high degree of integration, incorporating multistep or multiphase reactions into the same system, thereby increasing the reaction efficiency. The operating principle of microchannel reactors is based on several key microscale characteristics. The small scale of the microchannels significantly increases the reactor’s surface area relative to its volume. This amplifies surface effects, leading to improved reaction rates. Microchannel reactors facilitate the precise control of temperature and concentration using microsensors and heating elements. This capability supports the implementation of complex reaction pathways and the regulation of reaction conditions in microenvironments. These reactors typically feature highly integrated structures that consolidate multiple reaction units into a single system. This integration enhances control over reaction conditions and provides a foundation for automated operations [4,5,6,7].

At present, theoretical research on homogeneous microchannel flows is well developed, employing methods such as experiments and computational fluid dynamics (CFD) to discuss the variation rules of various operating parameters in microchannels under certain conditions. Engler et al. [8] conducted experimental and numerical simulation studies on T-type microchannels, finding that at low Reynolds numbers, longer residence times in the microchannel enhance fluid reaction performance, while at high Reynolds numbers, secondary flow disturbance improves the mixing ability of the microchannel in a short time. Bawornruttanabooya et al. [9] studied the effects of different structural parameters and inlet Reynolds numbers on methane-catalyzed partial oxidation reactions in microreactors. Based on the response surface method, structural optimization was performed using reactant selectivity and delivery power as indicators. The conversion rate of the optimized microchannel was higher than that of the ordinary straight channel. Wang et al. [10] proposed a passive microchannel mixer with a three-dimensional spiral structure to investigate the effects of different spiral diameters, spiral quantities, and material flows on the mixing efficiency of a micromixer. The mixing experiment results demonstrate that the spiral structure substantially improved the mixing efficiency, with the three-dimensional spiral mixer achieving 0.948 efficiency versus the traditional T-type micromixer. Vega et al. [11] proposed a honeycomb microchannel reactor for phenol hydroxylation, developing a kinetic model indicating 99% dihydroxybenzene selectivity for continuous hydroxylated aromatic hydrocarbon production. Sohn et al. [12] developed a two-dimensional microchannel model for water–gas inverter reaction, using the CO₂ conversion rate, temperature distribution, and reaction rate to assess factors such as microchannel size, flow rate, operating temperature, inlet gas molar ratio, and catalytic area ratio effects on reaction performance. Zhan et al. [13] proposed a highly selective oxidation method of glyoxal with nitric acid in a continuous flow microreactor. By precisely controlling the reaction temperature and residence time of the continuous flow microreactor system, the apparent rate constant, pre-exponential factor, and activation energy of glyoxal oxidation by nitric acid to glyoxylic acid were obtained. The glyoxylic acid reached 81.6%, while the selectivity was 92.4% with the set residence time of only 7.9 min at 68 °C. Guo et al. [14] established a continuous flow system for o-xylene nitration and determined the kinetics and mass transfer. Remarkably, the residence time of the microreactor system was reduced by an order of magnitude and the volume mass transfer coefficient improved by several orders of magnitude compared with the conventional stirred tank reactor. Moreover, the concentrated spent nitric acid was effectively recycled, further improving the sustainability and cost-effectiveness of the process. Chen et al. [15] proposed a novel ionic liquid (ILs)-catalyzed microreaction system. The reaction processes were optimized within microreactors of different inner diameters. The kinetics of the CO2 synthesis of carbonate catalyzed using ionic liquid (IL-[HMIM]Br) in a microreactor were evaluated, and the activation energy of [HMIM]Br was obtained. Based on numerical calculations of the mass transfer characteristics, the microreactor enhancement can reduce the reaction time to minutes; this is typically several hours in conventional reactors. For a microchannel with homogeneous flow, integrating chemical reactions allows for the investigation of heat and mass transfer performance, chemical reaction progress, and the evaluation of mixing capacity. This research direction is comprehensive and involves fundamental theories such as fluid mechanics and reaction dynamics [16]. The characteristics of microchannel reactors differ from traditional equipment in that reactions occur along the flow direction in an ideal flat push flow mode. In a steady-state reactor, changes in material composition and state parameters inside the reactor only occur with variations in axial position. This feature facilitates easier control of reaction progress and product composition at the outlet position [17].

Transesterification is one of the most common reactions in the field of organic chemistry. Due to its mild reaction conditions, high product diversity, and wide industrial application, it became an important technology in chemical production. Ilia et al. [18] carefully reviewed the preparation of polymeric phosphonic acid esters via four important methods: polycondensation, polyaddition, transesterification, and the ROPs of cyclic phosphites through enzymes or other catalysts. Organophosphates synthesized from phosphorus oxychloride are crucial industrial products with well-established production methods and industrial applications, including metal ion extraction, the enhancement of polymer plasticity, pesticide production, and the modification of surface activity [19,20]. Among them, tributyl phosphate (TBP) synthesized from the esterification of phosphorus trichloride (POCl3) and n-butanol are notable products. The synthesis pathway involves a three-step nucleophilic substitution reaction where phosphorus oxytrichloride and n-butanol sequentially produce monobutyl chlorophosphate (MCP), dibutyl chlorophosphate (DCP), and finally, tributyl phosphate, with hydrogen chloride formed as a by-product at each step [21]. Researchers focused on optimizing this synthesis route. Gao et al. [22] optimized the molar ratio of reactants using metal chloride as a catalyst in the classical process route, achieving an 85.1% yield of TBP under specific conditions. Zhang et al. [23] developed an in situ stripping method to efficiently remove hydrogen chloride within a relatively low-temperature range, investigating the effects of reactant volume, temperature, and reaction time on TBP yield. They achieved a TBP yield of 94% under optimized conditions. Based on the sodium alcohol method, Zhang Hui [24] synthesized TBP using intermittent and continuous reaction methods, and conducted orthogonal experiments on reaction temperature, molar ratio, and residence time. The continuous method produced TBP with a high yield of 93.3% under certain conditions.

All of the aforementioned experimental research processes were conducted using batch reactors. In the case of esterification reactions such as these, achieving an ideal distribution of reactants in batch reactors is often challenging, leading to incomplete reactions. Therefore, the use of microchannel reactors with highly specific surface areas can effectively address this issue. Zhang et al. [25] utilized a straight-tube microchannel reactor to investigate the kinetic model of the reaction between MCP and n-butanol, forming DCP in the esterification of phosphorus oxychloride. Their experimental device is shown in Figure 1. The residence time of the reactants was controlled by adjusting the length of the microchannel tube, and the effects of reaction temperature and molar ratio on the conversion rate of the reactants were studied. The activation energy and pre-exponential factor of the reaction were calculated as (5.99 ± 0.22) kJ/mol and 0.668 L²/(mol²·min), respectively. This study systematically examined the esterification reaction of phosphorus oxychloride from the perspective of reaction kinetics in a microchannel reactor setting [21].

Previous studies demonstrated the feasibility of analyzing and optimizing flow and reaction processes in microchannels using CFD numerical simulations. This approach holds significant guidance for conducting experiments, continuous chemical production, and exploring optimal process conditions. Given the broad application value of phosphorus oxychloride in industrial production, this study builds upon experimental findings from the esterification reaction of n-butanol and MCP in microchannels [25]. The chemical kinetics of the esterification reaction between n-butanol and MCP were simulated using CFD to investigate mass transfer phenomena in a straight-tube microchannel reactor. In this paper, a numerical model for the esterification of monobutyl chlorophosphates with n-butanol in a straight-tube microchannel reactor was established using CFD. In addition, the response surface analysis method combined with numerical simulation was utilized to optimize the microchannel. Through numerical discussion and analysis, a prediction formula for the conversion of dibutyl chlorophosphate from monobutyl chlorophosphate reacting with n-butanol was proposed. This exploration is of significant pioneering and guiding value in the numerical simulation of the esterification of phosphorus oxychloride in microchannels.

2. Theory and Numerical Models

2.1. Modeling of Microchannel Reactor

According to the experimental results and discussions from numerical simulations, the straight-tube microchannel allows for the detailed capture of time and spatial dimensions, extracting information that is difficult to obtain experimentally. To investigate the effects of microchannel length-to-diameter ratio, inlet component mass ratio, and inlet material flow rate on the reaction progress, two material flow premix devices were incorporated. The slow flow of material in the microchannel provided ample time for the mixing and diffusion of reactants in the solvent, allowing the mixing of materials at the inlet to be temporarily ignored in the simulation process, assuming full mixing occurred. To balance calculation accuracy and efficiency, a two-dimensional model of a straight-tube microchannel, depicted in Figure 2, was established with a structured grid. The microchannel reactor model, based on the chemical reaction kinetics of esterification, was developed using the Fluent commercial CFD program. A species transport model, including volumetric chemical reactions, was used to consider various species properties and transport in the mixture. The chemical reaction rate in the microreactor was defined using the kinetics of monobutyl chlorophosphate with n-butanol, as suggested by Zhang et al. [25]. The reaction equation of n-butanol and MCP in the microchannel to produce DCP and its by-product, hydrogen chloride, is given in Figure 3.

2.2. Assumption

To simplify the calculation, the following assumptions were made for the microchannel reactor:

• The entire system operates in steady state, and the material flow inside the microchannel is assumed to be laminar.
• Given the complexity of the chemical reaction, it is assumed that only the reaction shown in Figure 3 occurs in the microchannel.
• During the reaction process, the thermal properties and volumes of all components remain constant, and the reaction is considered irreversible.
• The mass flow is considered incompressible because of its small velocity.
• Owing to the presence of a large amount of liquid reactants, the non-uniform flow is assumed to be a single-phase flow to simplify the simulation.
• The thermal effect [26] and the influence of gravity are ignored in the reaction process.

2.3. Governing Equation

Under the above assumptions, the governing equation is as follows:

Because the simulated straight-tube microchannel reactor resembles a fixed-bed reactor with a tube shell configuration, studies conducted by Dixon et al. [27] and Jurtz et al. [28] are applicable. The mass conservation of the mixture is shown in Equation (1):

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla •\left(\rho \overrightarrow{v}\right)=S_m.$$

(1)

According to the Navier–Stokes equation for laminar flow, momentum conservation can be described as follows [29]:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \overrightarrow{v}\right)+\nabla •\left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla P+\nabla •(\stackrel{=}{\tau })+\overrightarrow{F}$$

(2)

where $P$ is static pressure, $\rho$ is fluid density, $\overrightarrow{F}$ is external force, and stress tensor $\tau$ is represented as follows:

$$\stackrel{=}{\tau }=\mu \left[\left(\nabla \overrightarrow{v}+\nabla {\overrightarrow{v}}^T\right)-{\displaystyle \frac{2}{3}}\nabla \overrightarrow{v}I\right]$$

(3)

where $\mu$ is the molecular viscosity and $I$ is the unit tensor.

To calculate the distribution of all components, it is necessary to use the component transport equation, which is expressed as follows:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho Y_i\right)+\nabla \left(\rho \overrightarrow{v}{Y}_i\right)=-\nabla J_i+R_i+S_i$$

(4)

where $Y_i$ is the mass fraction of the component $i$, $R_i$ is the static formation rate of the component $i$, $S_i$ is the external addition rate of the component $i$, and $J_i$ is the diffusion flux of the component $i$.

The chemical reaction simulation in this study was conducted using the Finite-Rate/No TCI model, which describes the mass transport process based on the component mass fraction. This model appears as a source term in the component transport equation through a predetermined chemical reaction mechanism [21]. According to the experimental results, the reaction was found to be second-order for MCP and first-order for n-butanol. This reaction order configuration resulted in the calculated results showing the highest agreement with the experimental data. Therefore, the reaction rate can be expressed as follows:

$$R=k{C}_{MCP}^2{C}_{n\text{-}butanol}$$

(5)

where $C_{MCP}$ and $C_{n\text{-}butanol}$ are the concentrations of the two reactants, and $K_r$ is the reaction rate constant, which can be expressed by the Arrhenius equation:

$$k_r=A_{r}exp\left(-{\displaystyle \frac{E_r}{RT}}\right)$$

(6)

where $A_r$ (26 L²/(mol²·min)) refers to the former factor, $E_r$ (5.99 Kj/mol) is the apparent activation energy, and is the gas molar constant.

All of the involved component physical parameters are shown in

Table 1. Physical property parameters of each component.

Materials	Cyclohexane	n-Butanol	MCP	DCP	Hcl
Density/kg·m−3	791	810	1414.9	1159.1	1.477
Relative molecular mass/kg·mol−1	84.16	74.12	193	229.5	36.5
Specific heat capacity/J·mol−1·K−1	156	176.67	-	-	-
Thermal conductivity/W·m−1·K−1	1.23 × 10−4	1.54 × 10−4	-	-	-
Viscosity/Pa·s	9.12 × 10−4	2.948 × 10−3	-	-	-
Reference temperature/K	298	298	298	298	298

below.

3. Grid Independence and Numerical Verification

Grid independence verification is a crucial step in finite element simulations to ensure calculation accuracy and optimize computational resources. In CFD simulations, the authenticity of fluid flow is essential to ensure the reliability of coupled processes. Therefore, the flow chemistry numerical simulation in this study first validated the authenticity of the flow. Initially, a two-dimensional straight-tube microchannel model was established, identical to the experimental setup, with dimensions of 2 mm in width and 9.4 m in length. The initial conditions, such as inlet flow rate and component proportions, were set according to experimental parameters. Dynamic parameters obtained from experimental calculations were used in preliminary simulations with varying grid numbers to find the most suitable grid. The model with the optimal grid count was then selected for further analysis. Figure 4 illustrates the radial velocity distribution in the microchannel reactor for different grid counts ($V^{+}={\nu }_i/{\nu }_0$, ${\nu }_i$ is the flow velocity at nodes, and ${\nu }_0$ is the inlet flow velocity). The results indicate that as the grid count increased, the flow field distribution approached the real flow state more closely. We ultimately chose a model with 376,200 cells (with a minimum cell size of 0.5 mm) for the main simulations, ensuring both accuracy and computational efficiency.

As the reaction process is sensitive to changes in the pre-exponential factor, ensuring the reliability of numerical simulations in this study required determining a suitable pre-exponential factor A for the grid model. This factor was finalized by matching the numerical calculation with the experimental conversion rate, based on the pre-exponential factor calculated in the original experiment. The efficiency of the reaction was expressed by the conversion rate of MCP, and the calculated MCP conversion rate at the exit position, according to Equation (7), was compared with experimental results, as shown in Figure 5.

$${\omega }_{MCP}={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\varphi }_i}{\rho }_i\left|{\overrightarrow{v}}_i·{\overrightarrow{A}}_i\right|-x_{MCP}}{x_{MCP}}}\times 100\%$$

(7)

where $n$ is the total number of nodes at the exit boundary; ${\varphi }_i$ is the mass fraction of the i-th node; $\rho$ is the density of the fluid at the i-th node; ${\overrightarrow{\nu }}_i$ is the momentum vector; ${\overrightarrow{A}}_i$ is the area of the grid surface; and $x_{MCP}$ is the initial mass fraction of the MCP.

4. Results and Discussion

The transformation characteristics of esterification reactions in a straight-tube microchannel reactor were extensively studied using two-dimensional numerical simulations, which considered the mass transfer characteristics of chemical reactions in such a reactor. Several simulations of the microchannel reactor were conducted to depict the spatial distribution of the component mass fraction and the conversion of monobutyl chlorophosphate (MCP), including the MCP conversion at the outlet under various operating conditions. Finally, numerical simulations were employed to assess the impacts of channel size, inlet component mass ratio, and inlet material flow rate on the MCP conversion performance.

4.1. Effect of Length-to-Diameter Ratio

At a constant temperature of 298 K, with unchanged inlet flow rate and material component ratio (as listed in

Table 2. Components and proportions of imported materials.

Materials	Mass Fraction
cyclohexane	0.59
n-butanol	0.34
MCP	0.035
Hcl	0.035

), five sets of microchannel reactors with different length-to-diameter ratios (ratio of pipe length to pipe diameter) were simulated. The microchannel diameter was 2 mm, and the length-to-diameter ratios were 1400, 1900, 2600, 3550, and 4700, respectively. The inlet flow rate was set at 0.0157 m/s. The calculation time for each group under these operating conditions was equal to the residence time of the material observed during the experiment.

A chemical reaction model for component transport determines the distributions of reactants, products, and solvents in a microchannel based on chemical reaction limits, flow parameters, and model geometry. Therefore, in this microchannel model, the spatial distribution of the MCP mass fraction of the reactants depends not only on chemical reaction limits, but also on the effect of component diffusion. Figure 6 illustrates the variation in the mass fraction of the reactant MCP along the flow direction (x/L) under different length-to-diameter ratios. It is obvious that the reactant is consumed ceaselessly as flow goes. The larger the length-to-diameter ratio, the more the mass fraction of the reactant decreases, which means the conversion rate of MCP will also increase. Figure 7 depicts the variation trend of MCP conversion of reactants with flow direction under different length-to-diameter ratios. The results indicate that as the tube length increases, the MCP conversion at the outlet position gradually increases, primarily due to the increased residence time of the material in the reactor, allowing for a more complete reaction. However, this increase in residence time is constrained by the progress of the chemical reaction, leading to the MCP conversion gradually stabilizing at a fixed value with longer tube lengths. Chen et al. [21] also reported that the reactant conversion rate increases slowly with the increase in residence time and stabilizes at a fixed value. Comparison results also show that, at a length-to-diameter ratio of 4700, the MCP conversion rate calculated by numerical simulation was 59.09%, whereas it was only 33.25% at the outlet position for a length-to-diameter ratio of 1400.

4.2. Effect of Inlet Component Mass Ratio

To explore the internal mechanism of how the inlet component ratio affects the reaction, simulations were conducted while keeping the microchannel size unchanged (length-to-diameter ratio of 4700) and inlet flow rate at 0.0157 m/s, consistent with experimental conditions. Based on Table 2, the component mass ratio (n-butanol/MCP) of the inlet material varied.

Figure 8 illustrates the variation trend of MCP mass fraction in the microchannel along the flow direction under different inlet component mass ratios. In the inlet region (x/L < 0.1), the reactants are consumed acutely, especially in the case of relatively high component mass ratios (mass fraction of n-butanol/MCP: 10:5, 10:7, 10:9). These observations are confirmed by the data presented in Figure 9. At x/L = 0.2, the MCP conversion rate under the conditions of low component ratio was significantly higher compared to that under high component ratio conditions. Further analysis in Figure 10 demonstrates that with a decrease in the component mass ratio, the MCP conversion rate in the microchannel reactor gradually increases along the flow direction. However, the increase in the MCP conversion rate is more pronounced in the first half of the microchannel, with a slower rate of increase in the second half. This is attributed to the influence of the concentration gradient of reactants; moreover, it was reported that the steric hindrance effect between reactant atoms can also lead to the same result [25]. In the first half of the microchannel, where the reactant concentration is high, the esterification reaction is more intense. However, in the second half, the conversion of reactant MCP gradually diminishes due to the progress of the chemical reaction and molecular diffusion. As shown in Figure 10, the numerical calculation results indicate that the MCP transformation rate of the outlet position is 72.17% with a n-butanol/MCP mass ratio of 10:5 of the inlet component, which is significantly higher than that with a 10:1 component ratio.

4.3. Effect of Material Flow Rate

Considering the influence of the inlet reactant composition ratio on the reaction effect in the microchannel, the variation in MCP conversion as the material enters the microchannel reactor at different inlet flow rates was further investigated. The internal reaction process of a microchannel reactor with a length-to-diameter ratio of 4700 was analyzed, keeping the reaction temperature and proportion of imported materials unchanged, while adjusting the inlet flow rate of the reactants. The internal reaction process was discussed based on $u_0$ = 0.0157 m/s.

Comparing the data in Figure 11, it is observed that lower flow rates at the inlet result in longer residence times of materials in the reactor, leading to higher MCP conversion rates under the same operating conditions of up to 83.93%. Figure 12 depicts the curve of the MCP conversion rate along the axis of the micro reactor. Comparing each curve in the figure, it is evident that the inlet flow rate of the material has a more pronounced effect in the first half of the reactor, specifically in the range of 0 ≤ x/L ≤ 0.4. At higher inlet flow rates (1.5$u_0$ and above), the MCP conversion rate exhibits a linear relationship with the flow direction of the microchannel reactor.

4.4. Response Surface Analysis

The numerical experiment design employed the response surface analysis method, which develops a quadratic multinomial regression model to effectively map single-factor variables to reaction performance characteristics [30]. This model illustrates the interaction of independent variables on the MCP conversion of reactants and generates a prediction formula for MCP conversion that can guide actual production processes. The Box–Behnken model in Design-Expert 13.0 was utilized to design the numerical experimental scheme. The design method included three factors with three horizontal intermediate points, repeated three times. The three factors chosen as independent variables were microchannel reactor length-to-diameter ratio (A), n-butanol/MCP mass ratio (B), and inlet flow rate (C). The conversion rate of MCP (Y) served as the dependent variable. The interaction effects of these three independent factors on the MCP conversion rate were studied. The level table for the factor variables was selected based on the findings of Lal et al. [30] and Geng et al. [31], as summarized in

Table 3. Numerical simulation of factor level.

Independent Variable	Level
	−1	0	1
length-to-diameter ratio (A)	1400	3050	4700
n-butanol/MCP mass ratio (B)	1.1	5.55	10
inlet flow rate (C)	0.25$u_0$	1.625$u_0$	3$u_0$

.

The intermediate point was repeated three times, resulting in a total of 15 numerical experiments. The numerical experiments design values and results are listed in

Table 4. Numerical experiment design and results.

Run	Factor 1	Factor 2	Factor 3	Response
	A: Length-to-Diameter Ratio	B: n-Butanol/MCP Mass Ratio	C: Inlet Flow Rate	Conversion Rate (%)
1	3050	5.55	1.625$u_0$	49.61
2	3050	10	3$u_0$	27.01
3	3050	1.1	3$u_0$	48.36
4	3050	1.1	0.25$u_0$	80.44
5	4700	1.1	0.25$u_0$	63.19
6	4700	5.55	0.25$u_0$	87.31
7	1400	5.55	0.25$u_0$	71.06
8	1400	10	1.625$u_0$	24.06
9	4700	10	1.625$u_0$	49.14
10	4700	5.55	3$u_0$	45.8
11	1400	1.1	1.625$u_0$	45.97
12	3050	10	0.25$u_0$	77.92
13	3050	5.55	1.625$u_0$	47.92
14	1400	5.55	3$u_0$	22.69
15	3050	5.55	1.625$u_0$	48.59

. Three regression fittings were performed on the results, and the multiple regression equations for MCP conversion (Y%), microchannel reactor length-to-diameter ratio (A), n-butanol/MCP mass ratio (B), and inlet flow rate (C) were obtained, as shown in Equation (8). Variance and confidence analyses are presented in

Table 5. Response surface model variance analysis.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	5578.75	9	619.86	116.14	<0.0001
A	833.54	1	833.54	156.17	<0.0001
B	447.60	1	447.60	83.86	0.0003
C	3735.94	1	3735.94	699.97	<0.0001
AB	15.44	1	15.44	2.89	0.1497
AC	11.76	1	11.76	2.20	0.1978
BC	88.74	1	88.74	16.63	0.0096
A2	21.55	1	21.55	4.04	0.1007
B2	1.81	1	1.81	0.3398	0.5853
C2	401.22	1	401.22	75.17	0.0003
Residual	26.69	5	5.34	-	-
Lack of Fit	25.24	3	8.41	11.62	0.0803
Pure Error	1.45	2	0.7242	-	-
Cor. Total	5605.44	14	-	-	-

and

Table 6. Reliability analysis of response surface model.

Mean/%	C.V./%	R2	Adjusted R2	Adeq. Precision
52.60	4.39	0.9952	0.9867	33.7350

, respectively.

$$\begin{array}{ll}\mathrm{Conversion} \mathrm{rate}& =48.71+10.21A-7.48B-21.61C\\ & +1.97AB+1.71AC-4.71BC\\ & -2.42A^2-0.7088B^2+10.42C^2\end{array}$$

(8)

As shown in Table 5, the p-value (p) of the regression model is less than 0.0001, indicating that the model is extremely significant. The non-significant items (p = 0.0803 > 0.05) suggest a good degree of equation fitting. The correlation coefficient of 0.9952 and correction coefficient of 0.9867 indicate a high correlation between the actual and predicted values. Therefore, the model effectively reflects the relationship between the factors and the response value in the esterification process and predicts the optimal process conditions. According to the p-value, the effects of the length-to-diameter ratio A, component ratio B, inlet flow rate ratio C, interaction term BC, and quadratic term C² on the conversion of the reactant MCP were extremely significant (p less than 0.01). According to the F value, the order of influence of the three factors on the MCP conversion of the reactants was C > A > B; that is, the inlet velocity ratio > length-to-diameter ratio > component ratio.

Figure 13 illustrates the actual and predicted values of MCP conversion. The data points closely align with the centerline, indicating the reliability of the predicted model (Equation (8)). According to the regression model, the optimal process conditions for achieving the highest conversion of esterification reactants were determined (

Table 7. Prediction of optimal level of process parameters and their operating domain.

Name	Goal	Lower Limit	Upper Limit	Lower Weight	Upper Weight	Importance
A: Length	In range	1400	9.4	1	1	3
B: Composition ratio	In range	1.1	10	1	1	3
C: Velocity	In range	$0.25u_0$	$3u_0$	1	1	3
Conversion rate	Maximized	22.69	87.31	1	1	3

). The response surface graph generated by the quadratic regression model (Equation (8)) directly illustrates the influence of independent factors and their interactions on the MCP conversion rate (Figure 14). Figure 14a,b shows the influences of length-to-diameter ratio and component ratio, Figure 14c,d shows the influences of length-to-diameter ratio and inlet flow rate ratio, and Figure 14e,f shows the influences of component ratio and inlet flow rate ratio. Figure 14c,d indicates that a higher length-to-diameter ratio and a lower inlet flow rate are required to achieve a higher MCP conversion rate. Decreasing the inlet flow rate reduces the throughput of the reactor, making a higher length-to-diameter ratio preferable. Additionally, comparing Figure 14a,e shows that a moderate component ratio is more conducive to MCP conversion. During the flow process inside the microreactor, MCP conversion was influenced by chemical reaction limits and molecular diffusion effects. A bimolecular nucleophilic substitution may occur between two MCP molecules, where the oxygen in the MCP acts as a nucleophile, attacking the butyl carbon atom of another molecule, resulting in steric hindrance [25]. A similar reaction mechanism was reported previously [32]. Therefore, selecting a moderate component ratio is reasonable for achieving a higher MCP conversion rate. The optimal synthesis conditions for the continuous microchannel flow process were a length-to-diameter ratio of 4700, component ratio of 3.005, and inlet flow rate of 0.25$u_0$.

5. Conclusions

Based on the experimental results of the esterification reaction between monobutyl chlorophosphate (MCP) and n-butanol, numerical simulations were conducted to study the performance of a microchannel reactor with an adjustable tube length. The reaction kinetics constants necessary for the simulations were determined based on previous experimental data, with the conversion rate of the reactant MCP serving as the index. In this study, the reaction performance of the microchannel reactor was analyzed under different length-to-diameter ratios, inlet component mass ratios, and inlet flow rates. Additionally, the interaction of these independent factors on the MCP conversion rate was investigated using response surface analysis, which resulted in a prediction equation for the MCP conversion rate based on tube length, component ratio, and inlet flow rate.

Increasing the length-to-diameter ratio and decreasing the inlet flow rate extended the residence time of the materials in the microchannel reactor, which improved the conversion rate of the reactants within certain limits. In particular, the esterification reaction intensity at the front end of the reactor (x/L ≤ 0.4) was significantly influenced by the reduction in the component mass ratio, indicating a more intense esterification reaction at the front end under conditions of low component ratio. Based on the influence of these single-factor variables, the MCP conversion at the microreactor outlet reached 83.93%. By establishing a regression model, a prediction equation was derived with length-to-diameter ratio (A), n-butanol/MCP mass ratio (B), and inlet flow rate ratio (C) as independent variables, and the conversion rate of reactant MCP (Y) as the dependent variable. According to the response surface analysis, the sequence of influence of the independent factors on the conversion of reactant MCP was inlet flow rate > tube length > component ratio. The optimal process conditions for achieving the highest conversion of reactant MCP were determined from the regression model: length-to-diameter ratio of 4700, component ratio of 3.005, and inlet flow rate of 0.25 m/s; under these conditions, the conversion of reactant MCP was predicted to be 87%.

In practical production applications, microchannel reactors typically adopt parallel amplification to improve yield. Therefore, under the premise that the conversion rate meets production demands, microchannel reactors should be optimized in terms of length-to-diameter ratio, component ratio, and material flow rate to minimize the time required for the entire system to reach equilibrium, to reduce material loss, and to increase yield. In addition to the esterification in this paper, future studies will focus on utilizing computational fluid dynamics (CFD) methods to simulate chemical reactions that may be extremely dangerous in actual industrial production, or reactions whose reactant material is rare. The method in this paper has positive significance for the realization of green, safe, and sustainable chemical industrial production.