Mixing-sensitive Reactions Research Articles

Assessing mixing uniformity in microreactors via in-line spectroscopy

Mixing behavior is critical for enhancing the selectivity of fast chemical reactions in microreactors. A high Reynolds number (Re) improves the mixing rate and selectivity of the reactions, but some exceptions of increasing side product yield with the higher Re have been reported. This study investigated the mixing uniformity in microreactors with in-line UV–vis spectroscopy to clarify the relationship between reaction selectivity and chaotic mixing with the higher Re. A colorization experiment of thymolphthalein in an acidic solution was conducted with an excess acid amount to the base to indicate a non-uniformly mixed region. Non-uniformity significantly increased with Re. At the same time, the degree of mixing, which was measured by a usual decolorization experiment, showed that the mixing rate increased with Re. The in-line analysis of the Villermaux–Dushman reaction during the mixing clarified that side product yield significantly increased with Re at around 300 and then decreased at around 1100. These results suggest the compensation effect between the mixing uniformity and mixing rate on the selectivity of the mixing-sensitive reactions. Faster mixing, characterized by a larger Re, can disturb mixing uniformity and, in some cases, decrease reaction selectivity.

Investigation of micromixing in the ART plate reactor PR37 using the acetal cleavage method and different mixing models

The mixing time can strongly affect the yield of a desired product if side reactions occur. Mixing is therefore of great practical importance. Millireactors enable comparatively high flow rates at moderate pressure drops and are thus well suited for production purposes. In this work, the mixing performance of the millistructured reactor ART PR37 is investigated using the Bourne method. Four plate types with similar meandering, converging/diverging process channels, but different hydraulic diameters have been studied over a wide range of Reynolds numbers. Mixing times have been calculated using two different mixing models, the IEM model and a recently introduced modified incorporation model. Mixing times were found to be less than 0.1 second for Reynolds numbers exceeding 150. For higher Reynolds numbers, mixing times in the range of 0.02 to 0.03 s are achievable without prohibitively high pressure drops. The ART PR37 is therefore a promising option for mixing-sensitive reactions.

Reduced-order modeling of turbulent flow reactors by tracing the Damköhler numbers

Although the reduced-order model (ROM) based on residence time distribution (RTD) can predict first-order reactions, high-order reactions require empirical data given the influence of mixing on chemical reactions, and are characterized by the Damköhler number. We attempted to numerically analyze the turbulent reacting flow in a micro-confined impinging jet reactor (CIJR) with a mixing-sensitive reaction system. A ROM framework for the CIJR was built by dividing the reactor space into a well-mixed segregation zone consisting of three reactor cells distinguished by their Damköhler numbers. The volume and pressure drop of the reactor were measured to test the control performance. The ROM was reliable and fast in the dynamic simulation of turbulent flow reactors with competing parallel second-order reactions. Our results suggest that the flow mechanism should be carefully considered when modeling the reactors.

Solution of the first-order conditional moment closure for multiphase reacting flows using quadrature-based moment methods

The quadrature-based semi-analytical solution for the conditional moment closure (SA-CMC) given in (A. D. Ilgun, A. Passalacqua, and R. O. Fox, “A quadrature-based conditional moment closure for mixing-sensitive reactions,” Chem. Eng. Sci., 226, 2020) eliminates the additional conditioning-space discretization in CMC applications by assuming that the mixture-fraction PDF is well represented by a β-PDF. A Gaussian quadrature provides the mixture-fraction abscissae, and the conditional scalar mean is expressed in terms of Jacobi polynomials. Here, by preserving the computational efficiency of SA-CMC, a novel quadrature-based moment method (QBMM-CMC) is developed for CMC applications, which does not assume the form of the mixture-fraction PDF. Remarkably, by solving the closed forms for the micromixing terms from CMC, exact expressions result for the mixture-fraction moments of any order. Thus, QBMM-CMC covers cases where the mixture-fraction PDF cannot be well represented by a β-PDF and can be applied to disperse multiphase flows with mass transfer (e.g., droplet evaporation). For single-phase and multiphase pure-mixing problems, the QBMM-CMC mixture-fraction moments are observed to deviate from the β-PDF. For single-phase mixing with and without dispersed-phase mass transfer, QBMM-CMC predictions for mixing-sensitive competitive-consecutive and parallel reactions are investigated parametrically.

A quadrature-based conditional moment closure for mixing-sensitive reactions

A novel algorithm consisting of a quadrature-based semi-analytical solution to the conditional moment closure (CMC) is developed for mixing-sensitive reactions in turbulent flows. When applying the proposed algorithm, the additional grid in mixture-fraction phase space used in CMC codes is eliminated, and at most ten quadrature nodes are needed to model mixing-sensitive turbulent reacting flows. In this work, the mixture-fraction probability density function (PDF) is assumed to be a β-PDF, which is the weight function for the Gauss-Jacobi quadrature rule. The conditional moments of reacting species are determined from unconditional moments that are first order with respect to the species and higher order with respect to mixture fraction. Here, the focus is on the efficient treatment of the molecular-mixing step by using a semi-analytical solution in the form of a Jacobi polynomial expansion. The application of the algorithm is demonstrated considering mixing-sensitive competitive-consecutive and parallel reactions in a statistically homogeneous chemical reactor.

CFD modeling of turbulent reacting flow in a semi-batch stirred-tank reactor

Abstract For the mixing-sensitive reactions, both chemical kinetics and mixing conditions of the reactants determine the distributions of products. The direct quadrature method of moments combining with the interaction by exchange with the mean micro-mixing model (DQMOM-IEM) has been validated for the chemical reacting flows in micro-reactors. Quite encouraging simulation results offer great promise, but the applicability of this method is needed to be explored furthermore, such as in stirred reactors. In this work, the two-environment DQMOM-IEM model was created with C language and used to customize Fluent through the user-defined functions. The mixing effects on the course of parallel competing chemical reactions carried out in a semi-batch single-phase stirred reactor were predicted. The simulation results show that the rising feed velocity enlarges the volume of reaction zone and maximize the yield of the by-product, which also indicates that the feed stream is more difficultly dispersed into the main stream and the zone surrounding feedpipe exit with high turbulent kinetic dissipation rate cannot be efficiently used.

The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part II: Design Protocols

Competitive-consecutive and competitive-parallel reactions are both mixing sensitive reactions where the yield of desired product depends on how fast the reactants are brought together. Recent experimental results have suggested that the magnitude of the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model was developed at the micromixing scale, yielding a single general Damköhler number. Dimensionless reaction rate ratios were derived for both reaction schemes. A detailed investigation of the effects of initial mixing condition (striation thickness), dimensionless reaction rate ratio, and reaction stoichiometry on the yield of desired product showed that the stoichiometry has a considerable effect on yield. All three variables were found to interact strongly. Model results for 12 stoichiometries are used to determine the mixing scale and relative rate ratio needed to achieve a specified yield for each reaction scheme. The results show that all three variables need to be considered when specifying reactors for mixing sensitive reactions.

The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part I: Model Development

There are two classes of mixing sensitive reactions: competitive-consecutive and competitive-parallel. The yield of desired product from these coupled reactions depends on how fast the reactants are brought together. Recent experimental results have suggested that the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model at the micromixing scale was developed. Assuming constant mass concentration and mass diffusivities, systems of PDE's were derived on a mass fraction basis for both types of reactions. Two dimensionless reaction rate ratios and a single general Damköhler number emerged from the analysis. The resulting dimensionless equations were used to investigate the effects of mixing, reaction rate ratio, and reaction stoichiometry. As expected, decreasing either the striation thickness or the dimensionless rate ratio maximizes yield, the reaction stoichiometry has a considerable effect on yield, and all three variables interact strongly.

Implementation of a conditional moment closure for mixing sensitive reactions

An implementation of the conditional moment closure (CMC) of Bilger (Phy. Fluids A 5 (1993) 436) and Klimenko (Fluid Dyn. 25 (1990) 327) has been carried out in the commercial CFD software FLUENT. A new implementation method is suggested that uses the CMC-equations to calculate an unconditional reaction rate that is subsequently inserted in a Reynolds averaged species equation. The objectives are to ensure conservation of reacting species by elimination of the spurious term that usually contaminates a CMC solution and to obtain convergence on a coarser grid than is usually required in CMC. The implementation has been successfully carried out for two sets of well-known mixing sensitive reaction pairs (parallel competitive and competitive consecutive) that both have one instantaneous and one fast irreversible reaction. Calculations with different discretizations of the CMC-equations in mixture fraction space have been performed and compared to experiments, full/finite-mode PDF models and the interpolation model of Baldyga. It is shown that the suggested implementation can achieve sufficient numerical accuracy with a much coarser mixture fraction space discretization than standard CMC implementations, which allows for more efficient CFD calculations.

Selectivity of mixing-sensitive reactions in slurry systems

The aim of this work is to supply some further data on the effect of the suspended solid on reaction selectivity, relating it to the changes in the power input and to the hydrodynamics of the slurry; two different stirrers, a radial turbine and a mixed flow impeller will be considered.

Experimental study of the effect of bubbles, drops and particles on the product distribution for a mixing sensitive, parallel-consecutive reaction system

For stirred multiphase reactors the effect of a dispersed (gas, liquid or solid) phase on the product distribution for a mixing sensitive reaction was tested. Turbulence modification due to the presence of dispersed-phase particles has been reported frequently in literature, but the extent of the effect in a stirred multiphase reactor was not clear. In this work the well-known mixing sensitive diazo-coupling reaction system was selected to investigate the influence of the changes in the turbulent kinetic energy spectrum on the product distribution. This reaction system was found to be suitable to study the influence of a dispersed (gas, liquid or solid) phase. The Engulfment model could describe the single-phase experiments and describes reasonably well the multiphase experiments when the effective dispersion properties are implemented. For the liquid–liquid dispersions effects of de-localization of the reaction zone were encountered, due to Naphthol extraction by the dispersed phase. The Engulfment model was extended to incorporate mass transfer and the first experimental and simulation results are promising. Additional, experimental and theoretical, research studying the combined effects of the mass transfer rate and the mixing rate for the liquid–liquid dispersions is highly desired.