Characterization and modeling of micromixing performance in micropore dispersion reactors

Micropore dispersion reactors have been considered as one of the most promising micro-structured devices. For reliable design of this kind of microreactors, the micromixing performance in those microreactors with different detailed geometric structures have been investigated in this work. The pore size, pore shape, pore number and pore distance were varied and the micromixing performance was characterized by the Villermaux/Dushman parallel competing reaction. The results showed that the mixing performance was greatly influenced by the geometric structures. The segregation indexes, X_S, were found in the range of 10⁻² to 10⁻³, indicating that the micropore dispersion reactors have high micromixing efficiency. To deeply understand the micromixing process, CFD simulation was carried out to describe the flow fields in the reactors. Based on the simulation results a mathematical model was developed and a new area parameter, S, was defined by considering both mixing region surface and mass transfer distance. A linear relationship between S and lg(X_S) was obtained at last, which is very helpful for optimizing the structure design of micropore dispersion reactors.     

Estimation of the micromixing time in the torus reactor by the application of the incorporation model

On the basis of previous experimental results in a torus reactor, micromixing time is determined using the incorporation model. Obtained results allowed the characterisation of the performances of this new configuration of reactor in comparison to other reactors, such as the stirred tank reactor. In addition, a correlation is proposed for each incorporation law, in order to determine the micromixing time from the experimental micromixedness ratio (α). Finally, in terms of Kolmogorov's turbulence theory, a relationship between micromixing time and the local energy dissipation rate is obtained and compared to those previously published.     

Effect of high frequency ultrasound on micromixing efficiency in microchannels

In the present work, an investigation on the effect of high frequency ultrasound wave on micromixing in the studied microchannels was carried out. Three types of microchannels with different shapes are examined. A 1.7 MHz piezoelectric transducer (PZT) was employed to induce the vibration in these microchannels through an indirect contact. A method based on the Villermaux–Dushman reaction was employed to study the micromixing in these microchannels. The segregation intensity was determined for layouts with and in the absence of ultrasound irradiation. Further, the effect of ultrasound waves, in various flow rates and initial concentrations of acid, on the segregation index (X_S) and micromixing time (t_m) was investigated. The experimental results showed that the ultrasound waves have a significant influence on product distribution and segregation index at various flow rate ratios. The data obtained in all cases showed that the segregation index was reduced when the flow rate ratios were increased. Also the results demonstrate that in spite of a low energy consumption of PZT, the relative segregation index improved up to 18–36% at various flow rate ratios.     

Macro- and micromixing in a novel sonochemical reactor using high frequency ultrasound

This paper deals with the influence of ultrasound on macro- and micromixing in a new developed sonochemical reactor. Unprecedented piezoelectric transducer arrangement with a high frequency of 1.7 MHz has been used in this novel reactor. Macromixing quality has been investigated visually and the Dushman reaction (iodide-iodate) coupled with a neutralization reaction have been examined in order to characterize micromixing quality. In addition, the effect of liquid viscosity on the segregation index has been studied. The results show that this new developed reactor can establish reasonable macro- and micromixing inside the reactor. Moreover, the performance of this reactor has been compared with a stirred tank reactor equipped with a Rushton turbine impeller. It is found that with the same input electrical power, the obtained segregation index for stirred tank reactor is approximately 10% more than proposed new ultrasound reactor, which means the sonoreactor works more efficiently.     

Using microparticles to enhance micromixing in a high frequency continuous flow sonoreactor

In this paper, an experimental study was conducted to investigate the effect of high frequency ultrasound wave on micromixing efficiency in the presence of polymeric microparticles in a tubular sonoreactor. The size and volume fraction of polymeric microparticles were varied and the micromixing efficiency was studied by adopting the Dushman reaction coupled with a neutralization reaction. In addition, the effect of flow rate and liquid viscosity on the segregation index was studied. The experimental results showed that the movement and dispersion of the polymeric microparticles by ultrasound wave could improve the micromixing efficiency. The results showed that the size of the polymeric microparticles has great effect on mixing. Moreover, it was found that in the presence of these microparticles, segregation index decreases significantly and their effect reduces with increase in the solution viscosity. The presented results show that using high frequency ultrasound waves in the range of MHz and in the presence of microparticles can promise to reach an efficient micromixing in tubular sonoreactors.     

Segregated regions in continuous laminar stirred tank reactors

Using visualization techniques, including acid/base reactions and UV fluorescence, we provide experimental evidence of segregated regions (islands) during mixing of viscous Newtonian fluids under laminar flow conditions in continuous stirred tank reactors (CSTRs). The effect of inlet/outlet stream position and Reynolds number on the dynamics of the mixing processes is examined. Numerical experiments in 3-D map were able to capture the main features of the CSTR flow by perturbing a Batch system using an imposed axial flow. Asymmetric flow patterns produced by off-center positioning of inlet and outlet pipes cause a reduction in size of the segregated region, enlarging the chaotic region and leading to more efficient mixing. Under dynamic inlet flow conditions, the laminar steady flow is perturbed, giving rise to an asymmetric flow pattern that is able to destroy toroidal segregated regions. Counter-intuitively, higher agitation speed (higher Re) did not enhance overall mixing efficiency. Faster agitation stabilized the toroidal regions, making it harder to destroy them. In addition, dynamic mixing protocols are investigated to enhance mixing performance. We demonstrate that time-dependent pumping and stirring protocols are able to efficiently destroy long-lasting toroidal regions.     

Computational Fluid Dynamics modeling of micromixing performance in presence of microparticles in a tubular sonoreactor

This paper reports the results of CFD modeling for evaluating micromixing efficiency in presence of polymeric microparticles in a continuous tubular sonoreactor. The studied tubular sonoreactor was equipped with four 1.7 MHz ultrasound transducers and micromixing efficiency was analyzed using Villermaux/Dushman reaction. The main objective of this study is to illustrate the simultaneous effects of 1.7 MHz ultrasound waves and polymeric microparticles on micromixing performance from the fluid dynamics point of view. In order to model the presence of these microparticles, the Eulerian multiphase model was applied based on kinetic theory of granular flow. The dynamic mesh method was used to model the vibration of 1.7 MHz piezoelectric transducers. CFD modeling results indicate the positive effects of the presence of microparticles on micromixing efficiency and more efficient velocity distribution inside the sonoreactor. This was interpreted as the ability of high frequency ultrasound waves (1.7 MHz) to move and disperse the microparticles.     

三种反应器微观混合性能的对比

介绍了撞击流、旋转填料床和撞击流-旋转填料床三种反应器的原理;采用化学偶合法,对三种反应器的微观混合性能进行了实验测定与研究,结果表明,撞击流-旋转填料床反应器的微观混合性优于其它两种反应器。     

Effect of impeller type on the mixing in torus reactors

Torus reactors are characterized by a homogeneous fluid circulation without dead zones. Torus reactors were used for applications in biotechnology, food processing, polymerization and liquid waste treatments. The relatively simple extrapolation of performances, due to the absence of dead volume, is one of the main advantages of this reactor, with low shear stresses and an effective radial mixing allowing efficient heat dissipation. This study is based on the mixing in order to analyse the fluid circulation, mainly in turbulent flow regime, and to characterize the torus reactor with the axial dispersion plug flow model. The objective of this study is to characterize the flow and the mixing in the torus reactors in batch and continuous modes. The mixing analysis was made according to the flow parameters and to the geometrical characteristics of the reactor and impeller. The mixing in the torus reactor can be characterized by the Péclet number, Pe_D, defined with torus diameter. A representative model based on plug flow with axial dispersion and partial recirculation was proposed.     

Extremes of conversion in continuous-flow reactors

The strong bounding theorem of micromixing has been proved using Bellman's principle of optimality. If the reaction rate depends on the concentration of a single component and is either a concave-upward or concave-downward function of that concentration, the conversion will attain extreme values when the reactor is completely segregated or is in a state of maximum mixedness. The extreme is a maximum when the reaction is concave-down (e.g. order less than one) and the reactor is maximally mixed and a minimum when the reactor is completely segregated. Conversely, the extreme is a minimum when the reaction is concave-up (e.g. order greater than one) and the reactor is maximally mixed and a maximum when the reactor is completely segregated.The new proof eliminates the need for the restrictive assumption that molecules can mix only when they have the same residual life. This assumption is untrue for many reactor models that approximate real physical behaviour.     

Cellular automata modeling of continuous stirred tank reactors

The classical dynamical systems model of continuous stirred tank reactors (CSTR) in which a first order chemical reaction takes place is reformulated in terms of the stochastic cellular automata procedure developed in the works of Seyborg [2] and Neuforth [3], which is extended by including the feed flow of chemical reactants. We show that this cellular automata model is able to simulate the dilution rate and the mixing process in the CSTR, as well as the details of the heat removal due to the jacket. The cellular automata approach is expected to be of considerable applicability at any industrial scale and especially for any type of microchemical system.     

Eigenvalue-eigenfunction analysis of infinitely fast reactions and micromixing regimes in regular and chaotic bounded flows

We analyze the dynamics of a single irreversible reaction A+B→ Products, occurring in a bounded incompressible flow. Within the limits of infinitely fast kinetics, the system is reduced to an advection-diffusion equation for the scalar φ, representing the difference between the reactant concentrations. By the linearity of the governing PDE, the system evolution is determined by the properties of the eigenvalue-eigenfunction spectrum associated with the advection-diffusion operator. In particular, the dependence of the dominant eigenvalue Λ—yielding the time-scale controlling the asymptotic reactant decay—as a function of the molecular diffusivity, , for different stirring protocols is analyzed. We find , where the exponent α∈[0,1] depends upon the kinematic features of the stirring flow. When the kinematics is regular within most of the flow domain (e.g. two-dimensional autonomous flows or time-periodic protocols possessing large quasiperiodic islands) a purely diffusive scaling, α=1 settles as . The singular scaling α=0 is found in the case of globally chaotic kinematics, whereas mixed regimes, 0<α<1, occur in flows that are characterized by the coexistence of quasiperiodic and chaotic behavior. The analysis of spectral properties of the advection-diffusion operator provides a new classification of micromixing regimes, and new mixing indices for quantifying homogenization performances in the presence of diffusion.     

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.     

Safety aspects in modelling and operating of batch and semibatch stirred tank chemical reactors

Safety aspects in modelling of batch and semibatch stirred tank reactors as well as a model based safety analysis have been considered. Applicability of two basic types of models – i.e. the perfectly mixed reactor model and the CFD model, both formulated for laboratory scale as well as pilot plant scale reactors – has been discussed. A formulation of the appropriate reactor model, which is adequate to the considered case study has been demonstrated and tested experimentally. Particular attention has been devoted to the formulation of robust CFD models employed to simulate a performance of the stirred tank reactors. It has been found that models for perfectly mixed reactors may have quite wide range of application, while the CFD models should be definitely used in case of fast reactions, high viscosity of the reacting mixture as well as of failure leading to stopping of the impeller. The CFD models are able to predict a dynamic behaviour of reactors at any circumstances, so they can play a significant role in safety analysis carried out for industrial scale reactors, for which experimental safety tests are expensive and dangerous.     

Design and optimisation of batch and semi-batch reactors

This paper addresses a systematic methodology for batch and semi-batch reactor design and optimisation for both ideal and non-ideal mixing. It can be applied to non-isothermal and multiphase systems. The method starts from a general representation in the form of a temporal superstructure based on the similarity of between plug flow reactors and ideal batch reactors. The temporal superstructure of a batch reactor exists in both the space and time dimensions. For non-ideal mixing, this paper addresses a mixing compartment network model to represent mixing inside reactors. The mixing compartment network is then included into the temporal superstructure to model non-ideally mixed batch reactors and the mixing pattern optimised with the other variables. Besides the operation variables for batch reactors, this method can also suggest the optimum mixing pattern and promising reactor configurations for mechanical design. A profile-based approach is proposed to make a search of the profiles for temperature, pressure and feed addition. This approach starts from a set of initial profiles of temperature, pressure and feed addition. Then the performance of the batch reactor is evaluated against the objective function under different profiles. An optimal set of profiles is then found by this profile searching process. A stochastic optimisation technique based on simulated annealing is employed to obtain optimal solutions. This method is also extended to multiphase reaction systems based on the concept of shadow reactor compartments. A number of case studies are presented to illustrate the use of the proposed methodology.     

Macro‐ and Micromixing in a Taylor‐Couette Reactor with Axial Flow and their Influence on the Precipitation of Barium Sulfate

A new set‐up for precipitation experiments capable of independent adjustment of micromixing and macromixing conditions is presented. The setup consists of a Taylor‐Couette (TC) reactor serving as the reaction zone and an external loop where the slower stages of precipitation processes take place. Micromixing in the TC reactor has been investigated with a chemical reaction system and with PIV‐measurements. Micromixing times range between 6·10^–3 and 8·10^–2 s. Tracer experiments reveal the macromixing performance of the whole set‐up which has been compared with the behavior of ideal reactors. Precipitation experiments with barium sulfate show some influence of micromixing intensity on the particle size and of macromixing on particle morphology.     

Dispersion coefficient and settling velocity of the solids in agitated slurry reactors stirred with multiple rushton turbines

The feature of solids distribution in tanks stirred with multiple Rushton turbines was investigated. Both transient and steady-state experiments were performed in tanks of two scales with a variety of suspensions. The data were analysed with the axial sedimentation-dispersion model. The axial dispersion coefficient of the solid phase was found not to differ from that of the liquid by more than 20%. The effective particle settling velocity in the stirred medium was then determined. It is confirmed that this parameter is different from the terminal settling velocity. Their ratio exhibits the same dependence on Kolmogoroff microscale and particle size as obtained previously with an indirect, approximate approach.     

Mixing effects in stirred tank reactors: a comparison of models

The Two-Environment Model of Ng and Rippin and the Monte Carlo residual life time model of Kattan and Adler developed for studying the effect of arbitrary residence time distribution and intermediate degrees of segregation on chemical reactor performance were shown to be equivalent from the point of view of a physical argument and a comparison of conversions obtained for a second order chemical reaction with mixed feed. Conversions with mixed feed were compared for a single CSTR and a reactor with a 2-CSTR residence time distribution using identical values of the micro-mixing parameter for both of the models.The Monte Carlo Coalescnece Model of Spielman and Levenspiel, Macro-mixed feed model of Manning and the Two-Environment Model of Ng and Rippin were found to give nearly identical results for (1) a single second order reaction, (2) consecutive second order reactions, and (3) step-wise addition polymerization without termination taking place in a single CSTR with mixed feed. Identical values of the micro-mixing parameter for the respective models were used.The models of Manning , Ng and Rippin, and Villermaux and Zoulalian were extended to reactors with unmixed feed with special reference to a second order chemical reaction. Results calculated from these models were compared with those from the models of Spielman and Levenspiel and Kattan and Adler using identical values of the micro-mixing parameter. The models do not agree for unmixed feed.