(145c) Characterisation of Mesomixing in Laboratory Scale Reactors Using CFD and the Fourth Bourne Reaction

The role of mixing in fast, competitive-consecutive chemical reactions has been a topic of great discussion within the chemical production industry over the last thirty years^1,2,3,4,5. A widely experienced problem in chemical reaction engineering is the production of undesired by-products through a secondary, often slow, reaction. This reduces the reaction yield of the main product and presents complication later in the products purification process. The Bourne reactions are a series of four competitive-consecutive reactions developed by Balydga and Bourne² to act as convenient experimental tools to study mixing efficiencies and its effect on chemical reactions. With fast competitive consecutive reactions, the composition of the reactor effluent is indicative of how well the mixing promoted the desired reactions. The Bourne reactions have been widely used to investigate the micromixing performance within a vessel, but minimal research has been carried out to assess the mesomixing performance using the Bourne reactions. Mixing can be characterised on three different scales, macro, meso and micro mixing which correspond to the bulk liquid, droplet, and molecular scale respectively. The performance at each of these scales can be predicted based on engineering correlations. These correlations are often inaccurate due to the coefficients used being unique to a specific reactor configuration. The researcher is forced to select coefficients generated in laboratory studies that most closely represent the reactor. This introduces inherent error into the calculation and can drastically reduce the accuracy of any mixing time correlation output. The meso-mixing time correlation requires a coefficient which relates the local turbulent eddy dissipation to the power per unit mass.

The Bourne reactions have been used in many experimental investigations since their conception and the first three reactions are well detailed by Balydga and Bourne² and Paul et al³. This study focused on the fourth Bourne reaction. This reaction is a competitive hydrolysis and neutralisation reaction where the fast reaction consists of HCL reacting with NaOH and the acid-catalysed decomposition of 2-2-dimethoxypropane as the slow reaction. Experiments were carried out to investigate the effect of addition location, addition rate, agitation rate, impeller type and baffles on the production of methanol through the decomposition of DMP. The concentration of methanol was used as an indicator of mesomixing performance, and these results were compared with the mesomixing timescales predicted by CFD simulations. FT-IR and GC were used to quantify the concentration of methanol in each experiment. The validity of using FT-IR to provide in-process estimations of product quantification was proposed and compared with the results of offline GC analysis.

The local turbulent eddy dissipation and local velocity values within 1 L laboratory scale OptiMax reactors were estimated using computation fluid dynamics (CFD) and used to predict the mesomixing performance using the turbulent dispersion theory. Correlations were then developed to allow these local values to be estimated without the need for CFD simulations. These correlations were compared with those currently used in small molecule laboratories and considerable variance was observed between the results. The local values are heavily dependent on addition location, agitation rate, impeller type and scale. Twenty experiments involving the competitive-consecutive Fourth Bourne reaction mechanism were carried out to investigate the relationship between mesomixing time, predicted using CFD simulations, and the yield of methanol from the secondary acid hydrolysis reaction. The yield of methanol was quantified using gas chromatography (GC) and monitored in-process using Fourier transform infrared spectroscopy (FT-IR). A linear relationship was determined between the results of GC analysis and FT-IR indicating that FT-IR could provide an accurate, in-process method of product yield quantification.

Well fitted models, that describe that design space of this study, were developed using JMP® statistical software for the coefficients α and β. These coefficients were used to describe the relationship of the average TED and impeller tip speed to the local values of TED and velocity, respectively. Currently, there exists limited literature to describe these coefficients in small lab-scale reactors. In small molecule laboratories, generalised values for 18 L are used to provide estimates for these coefficients⁶. This study determined that these generalised values are widely inaccurate in their estimation of local values in 1 L OptiMax reactors. Values for ε_local in OptiMax reactors were found to be greatly overestimated by the generalised values obtained by Verschuren et al⁶. The prediction expressions obtained from the JMP® models were developed into Excel tools for use in small molecule laboratories to determine more accurate estimations of local turbulent eddy dissipation and local velocity values in OptiMax reactors.

Mesomixing constants, Λ_meso and t_meso, were calculated for each simulation using engineering equations described by the inertial convective mechanism. For each simulation, addition along the surface plane resulted in a longer Λ_meso. This is important for rate sensitive reactions such as the Fourth Bourne reaction which was investigated in this study. A longer mesomixing length scale resulted in a larger localised zone of high HCL concentration during the experimental process (Figure 1). The values for t_meso increased proportionally to the values of Λ_meso, and a combination of fast addition and slow agitation rates resulted in high values for mesomixing time. Simulations which experienced complex transitional flow (50 rpm) produced inconsistent results and it was hypothesised that the inertial convective mechanism is valid only for turbulent flow conditions. More research is required to accurately predict the mesomixing time and length scales under transitional flow regimes using engineering correlations.

A DoE was employed to identify significant mixing parameters using the quantification of methanol from the Fourth Bourne reaction. Off-line gas chromatography analysis was used to quantify the concentration of methanol produced by the secondary acid hydrolysis of DMP reaction and thus the efficiency of mixing was quantified. A standard least squares screening model was built in JMP® from the predetermined DoE. It was determined that agitation rate and the second order interaction between agitation rate and addition rate were the most significant factors to the production of methanol in the reaction set-up. An increase in agitation rate resulted in a decrease of methanol concentration and the lowest methanol concentration observed was a result of high agitation rate and high addition rate. The plane at which the HCl was added was deemed to be of significance to the amount of methanol produced. Addition close to the impeller reduced the mesomixing length scale and resulted in lower concentrations of methanol compared to addition along the surface of the liquid. These experimentally deduced relationships have been summarised and presented in flowchart form, as seen in Figure 2, to enable the user to control the products of a competitive-consecutive reaction.

The validity of FT-IR in providing accurate, in-line estimations of product concentrations was investigated. A well fitted linear correlation with an RSq of 0.8 was observed when the peak area change in IR was compared with the methanol concentration determined using off-line GC analysis. Strong experimental evidence was observed to suggest that FT-IR could be used to estimate product concentration through the creation of a “standard curve” between peak area change and product concentration for a known product.

The results of this study have highlighted several areas that have the potential for further research. It was discovered that use of the inertial-convective mechanism to predict the mesomixing time and length scale misrepresented transitional flow regimes, and some scenarios of addition to low velocity regions of flow. These scenarios resulted in outliers when the mesomixing time predictions were compared with the concentration of methanol produced. The removal of these outlier improved the linear relationship more than two-fold and this accentuates the potential for further research into the determination of mesomixing constants under transitional flow regimes. Further work can also be carried out to improve the RSq value between the mesomixing time CFD predictions and the product concentration in competitive consecutive reactions under turbulent flow conditions.

The validity of using FT-IR to provide in-line product concentration estimates is an area of huge potential significance in the control of competitive reaction systems in small molecule laboratories. FT-IR is generally considered a crude tool used to provide an indication of changes within the IR spectrum over the duration of the process. The results of this study showcase potential for the use of FT-IR to provide accurate, in-line product yield data. Through the development of a “standard curve” using peak area change from FT-IR and concentration data determined using GC, the concentration of a known product can be interpolated to provide an accurate indication of the reaction status. This could be of great significance to the optimisation of product quality in fast, mixing-sensitive reactions such as competitive-consecutive reactions, precipitation reactions and fermentation processes.