Micromixing Effects Research Articles

Experimental study and simulation of kinetics of acetophenone hydrosilylation with diphenylsilane in the presence of rhodium complexes in a microreactor

The hydrosilylation of acetophenone with diphenylsilane in a microreactor in the presence of complexes [Rh(cod)Cl]2 and [Rh(CO)2(μ-Cl)]2 and (R)-(-)-cis-mirtanyl- and (R)-(+)-bornylamine in situ was studied, the kinetics simulation of the process was performed, and the multicriteria optimization of the process was carried out. The influence of the micro-mixing effect on the reaction rate was revealed. Best results in the microreactor were obtained for the [Rh(cod)Cl]2-BornylNH2 catalytic system. It was established that the formation of 1-phenylethanol and related enol silyl ethers are simultaneous competing reactions.

Fast Reactions in Bubbly Flows: Film Model and Micromixing Effects

In our work, we focus on the Euler-Lagrange strategy to simulate bubbly flows and fast chemical reactions. We propose a film model to account for fast, multistep chemical reactions near the gas liquid interface. A combination of such a film model with Euler-Lagrange simulations for bubbly flows has not been used before. Also, we account for micromixing effects with respect to chemical reactions in the liquid bulk by solving for the variance of the concentration field. To validate our model predictions for multiphase flow and reactive mixing, we compare our results with literature data and find excellent agreement.

Micromixing effects on series–parallel and autocatalytic reactions in a turbulent single-phase gas flow

A hybrid solution algorithm is implemented to simulate turbulent reactive single-phase gas flow in an isothermal tubular reactor. This algorithm is a combination of a Finite Volume (FV) and a Probability Density Function (PDF) method. The FV method is used to solve the mass and momentum conservation equations combined with a standardized k– ε model for single-phase gas flow. The PDF method is applied to solve the species continuity equations. The advantage of using the PDF method is the fact that there is no need of any closures for chemical reaction source terms in a turbulent flow . The mesomixing and the micromixing contributions in the PDF equation are closed using the gradient-diffusion model and the Interaction-by-Exchange-with-the-Mean (IEM) model, respectively. This hybrid solution algorithm is applied to simulate a series–parallel and an autocatalytic reactive single-phase gas flow. The mechanical-to-scalar time-scale ratio, i.e. the IEM model parameter, is found to have an influence on the simulation results that cannot be neglected. As expected, in series–parallel reactions, the desired product selectivity increases when the reaction rate coefficient, corresponding to its formation, increases. Moreover multiple solutions are observed in the autocatalytic reaction for a given feed ratio, Damköhler (Da I ) and Péclet (Pe) numbers. To validate the hybrid FV–PDF solution algorithm, the calculated results are compared with the results obtained when using the Reynolds-averaged species continuity equation model. A good agreement is observed when infinite-rate mixing is applied.

Thermal analysis of nanostructured calcite crystals covered with fatty acids

The way of precipitation process conducting is crucial for the final product properties and its further applications. In present experiments, the CaCO3 powders, produced by controlled fast precipitation trough gaseous CO2 absorption in Ca(OH)2 slurry, have been covered by two fatty acids: dodecanoic (lauric) acid and tetradecanoic (myristic) acid. This multiphase reaction was conducted in a new rotating disc reactor unit which enables to control inter- and intra-face mass and energy transfer as well as the macro- and micromixing effects in the reacting system. The obtained nanopowders have been observed by the use of the scanning electron microscope. The X-ray diffraction technique as well as the dynamic light scattering (DLS) and the thermogravimetric method (TG) were further used for its deep analyses. The experimental data have allowed for distinction between different fatty acid molecules species present on calcite surface (chemisorbed ones, inter-located between adsorbed to surface, formed mono- and bilayers and the soap) or free fatty acids molecules if presented in the sample. The amount of fatty acid species forming different layers on calcite as well as the size and distribution of fatty acid coated CaCO3 powders have been also calculated.

Parametric study of the Incompletely Stirred Reactor modeling

The Incompletely Stirred Reactor (ISR) is a generalization of the widely-used Perfectly Stirred Reactor (PSR) model and allows for incomplete mixing within the reactor. Its formulation is based on the Conditional Moment Closure (CMC) method. This model is applicable to nonpremixed combustion with strong recirculation such as in a gas turbine combustor primary zone. The model uses the simplifying assumptions that the conditionally-averaged reactive-scalar concentrations are independent of position in the reactor: this results in ordinary differential equations in mixture fraction space. The simplicity of the model permits the use of very complex chemical mechanisms. The effects of the detailed chemistry can be found while still including the effects of micromixing. A parametric study is performed here on an ISR for combustion of methane at overall stoichiometric conditions to investigate the sensitivity of the model to different parameters. The focus here is on emissions of nitric oxide and carbon monoxide. It is shown that the most important parameters in the ISR model are reactor residence time, the chemical mechanism and the core-averaged Probability Density Function (PDF). Using several different shapes for the core-averaged PDF, it is shown that use of a bimodal PDF with a low minimum at stoichiometric mixture fraction and a large variance leads to lower nitric oxide formation. The ‘rich-plus-lean’ mixing or staged combustion strategy for combustion is thus supported.

Precipitation of nanostructured calcite in a controlled multiphase process

The way of conducting the precipitation process is crucial for the final product properties and its further applications. In the presented experiments, CaCO 3 powders were produced by controlled fast precipitation through gaseous CO 2 absorption in Ca(OH) 2 slurry. This multiphase reaction was conducted in a new rotating disc reactor unit, which enables one to control inter- and intra-face mass and energy transfer as well as the macro- and micro-mixing effects in the reacting system. The effect of calcium hydroxide concentration, mixing conditions in the reactor and gas–liquid interface development at discs surface on precipitated CaCO 3 was investigated. The analysis with the dynamic light scattering method (DLS) showed that mean particle diameter decreases with higher rate of discs revolution speed and higher calcium hydroxide concentration. The X-ray diffraction testing revealed that we have obtained a chemically pure calcite, which is the most stable polymorph of CaCO 3. The scanning electron micrographs (SEM) showed the influence of precipitation conditions on rhombohedral calcite crystals. Sorptometric surface analyses reveal high development of specific surface area (over 20 m 2g −1) and powders porosity.

Numerical modelling of hydrothermal flames. Micromixing effects over turbulent reaction rates

Determining turbulent reaction rates in hydrothermal combustion is a difficult task due to the high sensitivity with mixing of this type of flames. Combining a micromixing model for liquid reactions along with the Eddy dissipation concept (EDC) allows for a good estimation method of the turbulent reaction rates. This novel method is validated for the combustion of methanol in supercritical water, predicting the temperature of the flame and its structure with absolute average deviations below than 10% for most of the cases tested. The influence of different operational variables, i.e. inlet temperature, inlet mass fraction and inlet flow of the fuel have been estimated with high accuracy. The methodology proposed lays the foundations for the subsequent design of supercritical combustion devices, where the geometry of the system has a great influence in the yield of the combustion.

Oxidative Dimerization of Phenol Based on Micromixing in Single- And Two-Phase Systems

It is an important technique to obtain target products with higher yields by controlling the reaction and mass transfer. In this work, we focused on molecular weight control in the oxidative polymerization of phenol. We attempted selective production of phenol dimers through the formation of microdroplets in both single- and two-phase systems. In a single-phase system, selectivity of dimers to polymers can be improved by rapidly mixing ingredients using a micromixer. Further, we clarified the conditions to utilize such microspace effects by comparing the initial reaction time constant with the mixing time constant by order-of-magnitude estimation. In a two-phase system, it was clarified that controlling of mass transfer by formation of microdroplets using a micromixer was effective in the control of consecutive elementary reactions though the dimer selectivity hardly changes and the effect of micromixing was limited.

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Crystal Growth in Drowning-Out Crystallization using a T-Mixer

The kinetics of nucleation and crystal growth in drowning-out crystallization using a T-mixer were estimated using crystal size distribution, taking into account a size-independent growth. At the conditions of the feed compositions investigated, the product weight mean size changed from 7–29 μm when the residence time varied between 0.32 and 0.61 s. Nucleation and growth rates were expressed simply as a function of the residence time. The T-mixer can be used to generate high levels of supersaturation due to inducing micro-mixing effects. The particle size correlated well with the ratio of growth rate to nucleation rate. Finally, the particle size obtained in drowning-out crystallization using a T-mixer was found to be proportional to the 1.69th power function of the residence time.

New insight into micromixing in supercritical CO 2 using a chemical method

Competing reactions have been studied in order to characterize micromixing efficiency in supercritical medium. A new chemical reaction test has been developed because the current systems involving ionic species are not suitable for a supercritical medium (CO 2). The system is based on two competitive reactions: the esterification of phenylacetic acid by ethyl alcohol using paratoluenesulfonic acid monohydrate as a catalyst and the neutralization of paratoluenesulfonic acid monohydrate by tributylamin. The neutralization reaction is faster than the esterification reaction. The test procedure consists in adding, in stoechiometric defect, paratoluenesulfonic acid monohydrate to a mixture of ethyl alcohol, phenylacetic acid, tributylamin and carbon dioxide under 17 MPa and 50 °C. The ester yield is directly linked to the micromixing efficiency. Preliminary studies such as miscibility or analytical method (GPC) studies have been carried out in order to test the reactions’ system in batch reactor. The sensitivity to micromixing effects has been investigated in a 0.5 L stirred reactor. Final composition in the vessel is dependent on the stirring speed. This new system is efficient to characterize micromixing effects in a supercritical medium, which are particularly important in the Supercritical AntiSolvent precipitation processes but also for chemical reactions.

Micromixing effects in a reacting plume by the Stochastic Fields method

The Stochastic Fields method for turbulent reacting flows has been used for a reacting plume. The method simulates macromixing with an eddy diffusivity and micromixing by a random walk in scalar space with appropriate models for the scalar dissipation. The numerical technique used for the solution of the stochastic partial differential equation that arises from the stochastic fields method is discussed. The predictions are very close to experimental data for a plume of NO in a O 3 -doped turbulent air flow for a range of Damköhler numbers.

Modelling and simulation of crystallisers under non-perfect micromixing conditions

A mathematical model, formulated in terms of interacting populations under perfect macromixing conditions, is presented and analysed for describing micromixing in crystallisation processes. The model consists of two population balance equations, describing the changes of fluid elements of solution and crystals, respectively. The kinetics of micromixing is described by the coalescence–dispersion model, and is characterised by a constant coefficient of coalescence of fluid elements as the parameter of the mixing intensity. The rates of nucleation and growth of crystals are expressed as the expected values over the randomly interacting fluid elements. A closed moment equation model is derived and used to analyse the effects of micromixing on the dynamic and steady-state properties of crystallisers, and on the properties of the crystalline product. The steady-state value of the mean concentration of fluid elements decreases, while the yield of crystallisers increases by increasing segregation level. In steady states, a crystalliser with segregated solution phase produces more mass of smaller crystals than the corresponding crystalliser with solution mixed perfectly on microlevel. In well mixed microlevel states, the mean size of the crystalline product increases with increasing mean residence time, while in segregated states this tendency reverses. In segregated states, higher standard deviation of concentration of fluid elements is induced with increasing residence time.

PDF simulations of ethylene decomposition in tubular LDPE reactors

AbstractThe present study deals with turbulent reacting flow simulation inside low‐density polyethylene (LDPE) tubular reactors, based on a detailed computational fluid dynamics (CFD) technique—transported probability density function (PDF) methods. The ability of the PDF methods to provide an exact representation of chemical source terms is ideally suited for coupling complex LDPE chemistry with small‐scale fluid dynamic fluctuations in turbulent flow. LDPE chemistry with a total of 16 scalars provides an ideal test case for illustrating the applicability of an efficient chemistry algorithm based on in‐situ adaptive tabulation. A particle‐based Monte Carlo algorithm is used to solve the joint‐composition PDF equation, whereas a finite‐volume code is used to obtain hydrodynamic fields from the standard k–ε turbulence model. The influence of feed temperature, initiator concentration, and degree of premixing is investigated to gain detailed knowledge of micromixing effects on steady‐state reactor performance. The computational approach provides a low‐cost alternative to experimental and pilot‐plant tests for exploring a variety of design options when making important design and operational decisions, or for investigating unstable reactor operating conditions. The ability of a simplified, but otherwise equivalent multi‐environment‐presumed PDF model to predict turbulence–chemistry interactions close to physical reality is validated using the detailed transported PDF simulations. The transported PDF method is shown to be an excellent tool for obtaining fundamental information on turbulent reacting flows, as well as for deriving simplified models for faster and easier interpretation of these flows when developing safe and efficient chemical processes. © 2005 American Institute of Chemical Engineers AIChE J, 51: 585–606, 2005

A Strategy for Solving a Mathematical Model of Barium Sulphate Precipitation in a Continuous Stirred Tank Reactor

In a previous paper, we modelled the precipitation of barium sulphate in a continuous stirred tank reactor by computational fluid dynamics and compared our predictions with previous experimental and modelling work. Turbulent momentum transfer solutions for different process conditions were obtained using the RANS and MRF approaches whilst reactive mass transfer was simulated by solving the transport equations for the three reacting species and five moments of the crystal population balance. Micromixing effects were accounted for indirectly. In this paper, the detailed numerical aspects that led to the previous predictions are presented in detail. In particular, the way the highly nonlinear and stiff set of the transport equations was handled is discussed. The main issue is to diminish the inherent tendency for diverging iterations to be calculated during the initial stage of the mass transfer simulations. The critical elements of a successful procedure for preventing this divergence are discussed. Overall, general guidelines for an efficient strategy and a perspective on how to obtain optimized solutions are outlined, including the use of the under-relaxation factor. Even so, increases in impeller speed or feed rate significantly increase the number of iterations required for a converged solution. It is also seen that a constant BaSO4 concentration in the exit stream is not a sufficient condition for concluding the iteration process.

Mixing and Crystallization Kinetics in Gas‐liquid Reactive Crystallization

AbstractA study of gas‐liquid reactive crystallization for CO2‐BaCl2‐H2O system was performed in a continuous flow crystallizer. The influences of mixing on the crystallization kinetics of barium carbonate crystals were investigated. The mixing parameters are stirrer speed, feed concentration, gas‐flow rate, pH of solution, addition rate of NaOH solution, and mean residence time. Under pH‐stat operation, the crystallization mechanism can be assessed by the addition rate of NaOH solution, which acts as an indicator for the absorption rate of carbon dioxide. Assuming a size‐independent agglomeration mechanism, the nucleation rate, growth rate and agglomeration kernel can be obtained, simultaneously, at steady state, by the method of moments. Evidence shows that feed concentration, feed rate, gas‐flow rate, and stirrer speed have a significant influence on the nucleation rates and mean particle sizes. This shows the effect of micromixing. The crystallization mechanism tends to be reaction limited when the feed concentration of barium chloride solution is higher than 5 mM, while at lower stirrer speeds and feed concentrations, the mechanism tends to be both mixing and reaction controlled. The growth rate depends on the mean supersaturation value and the pH of the solution and the mass‐transfer resistance cannot be completely eliminated in this work. For a monodispersal collision model, in the viscous sub‐range of turbulence, the agglomeration kernel can be expressed as β ∝ d3 $ϵ \bar$–1/4, showing a low efficiency of collision. The result is also demonstrated by the agglomeration kernel expression. Comparison with a liquid‐liquid‐mixing reactive crystallization system is also discussed.

Application of the theory of micromixing to groundwater reactive transport models

This study extends and applies the theory of micromixing, first introduced in the chemical reaction engineering literature, to the topic of reactive transport in porous media. For all but the simplest linear kinetic and sorption models the fate and transport of a reactive solute depends on the residence times and the details of small‐scale mixing. The latter phenomenon, also called micromixing, is important because it brings into close proximity chemical species that react, and it controls the local concentrations in a flowing system. Solutes with reaction rates or sorption isotherms that depend on species concentration will therefore be affected by micromixing. Two models for micromixing are introduced, the minimum and maximum mixedness models, that provide bounds on the extent of reaction or retardation behavior within the constraints imposed by the residence time distribution (RTD) of a conservative solute in the same flow system. These mixing models prescribe the latest or earliest permissible mixing of parcels of fluid of different residence times, which in turn bounds the degree of reaction of a reactive solute for nonlinear rate laws or sorption isotherms. Simulation results using the bounding models show that micromixing effects are most important for nonlinear reaction curves, solute pulses of short duration, and systems with broad RTD curves. Use of these models is a straightforward and practical way to investigate the importance of a phenomenon for which data are seldom available and whose impact on groundwater reactive transport models has heretofore not been studied in a systematic, bounding manner.

Development of an adaptive chemistry model considering micromixing effects

In numerical simulation of combustion models, solution of the chemical kinetics is often the most expensive part of the calculation, since accurate description of kinetic mechanism involves large number of species and reactions, leading to a large set of coupled ODEs, often too complex to be considered in their entirety along with a detailed flow simulation. Hence the need for representing the complex chemical reactions by simple reduced models, which can retain considerable accuracy while rendering computational feasibility. Realistically, under different conditions and at different points in time, different reactions become important, which has been exploited to develop an adaptive reduction scheme such that the reduced reaction model adapts itself to the changing reactor conditions.A methodology is developed in this paper to construct reduced mechanisms by solving an optimization problem, where the objective is to determine the range of conditions along the reaction trajectory over which a prespecified number of reactions can predict the actual profile within an allowable tolerance. Such an adaptive reduced mechanism is then coupled with the reactive flow algorithm, which selects an appropriate mechanism depending on reactor condition and integrate the corresponding ODEs for the specified valid range. These ideas are demonstrated using the mechanism of CO/H 2 combustion in air.

CFD simulation of mixing and reaction: the relevance of the micro-mixing model

The aim of this work is to understand the role of the micro-mixing model in computational fluid dynamics (CFD) simulations of fast reactions. Using CFD, in fact, the reactor is modelled through a computational grid and the governing equations are discretised using numerical methods. However, the mixing phenomena that occur at scales that are smaller than the grid size remain unresolved. This means that the probability density function (PDF) of all scalars is assumed to be a delta function centred at the mean value. In order to take into account micro-mixing effects a model must be added. In this work the finite-mode PDF approach is used to predict the selectivity of a parallel reaction in a Taylor–Couette reactor working in semi-batch conditions. Experimental data are compared with model predictions in order to investigate the relevance of the micro-mixing model. The case of precipitation is also discussed.

A novel approach for describing mixing effects in homogeneous reactors

The Liapunov–Schmidt technique of classical bifurcation theory is used to spatially average the convection–diffusion–reaction (CDR) equations over smaller time/length scales to obtain low-dimensional two-mode models for describing mixing effects due to local diffusion, velocity gradients and reactions. For the cases of isothermal homogeneous tubular, loop/recycle and tank reactors, the two-mode models are described by a pair of coupled balance equations for the mixing-cup ( C m ) and spatial average (〈 C〉) concentrations. The global equation describes the variation of C m with residence time (or position) in the reactor, while the local equation expresses the coupling between local diffusion, velocity gradients and reaction at the local scales, in terms of the difference between C m and 〈 C〉. It is shown that the two-mode models have many similarities with the classical two-phase models of heterogeneous catalytic reactors with the concept of transfer between phases being replaced by that of exchange between the two-modes. It is also shown that when the local Damköhler number (ratio of local diffusion to reaction time) is small, the solution of two-mode models approaches the exact solution of full CDR equations, while for fast reactions the two-mode models retain all the qualitative features of the latter. Examples are provided to illustrate the usefulness of these two-mode models in predicting micromixing effects on homogeneous reactions.