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 CO
2 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 L
2/(mol
2·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.
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 (
,
is the flow velocity at nodes, and
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.
where
is the total number of nodes at the exit boundary;
is the mass fraction of the
i-th node;
is the density of the fluid at the
i-th node;
is the momentum vector;
is the area of the grid surface; and
is the initial mass fraction of the MCP.
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.