SIGNIFICANCE OF THE CENTRAL PLUME VELOCITY FOR THE CORRELATION OF LIQUID PHASE MIXING IN BUBBLE COLUMNS

The knowledge of the flow patterns of each phase of bubble column reactors is of considerable importance for the rational design and scale-up. The hydrodynamic models for the liquid phase have been reviewed. The models have been based on some form of pressure balance or energy balance. These two approaches have been compared and recommendations have been made regarding the range of applicability of the individual models. A comparison between the predicted and the experimental liquid velocities has been presented whenever possible. The range of variables has been pointed out for which further investigations are needed. The empirical and theoretical models for the mixing behavior of the different phases of bubble column reactors have also been reviewed.     

CFD simulation of bubble columns incorporating population balance modeling

A computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a k-ε model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201-9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071-5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359-6365] also show a good agreement for liquid velocity and gas hold-up profiles.     

Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column

The numerical approaches have been used in many studies to predict the flow pattern inside the bubble column reactors because of the difficulties that are still found in designing and scaling-up the bubble columns. This review makes an effort to show suitable interfacial forces i.e., drag force, lift force, turbulent dispersion models and virtual mass and turbulence models such as standard k–ɛ model, Reynolds Stress Model, Large Eddy Simulation to predict flow pattern inside the bubble column using Eulerian–Eulerian. The effect of various interfacial forces and turbulence models on gas–liquid velocity and gas hold-up in bubble column is critically reviewed.     

Comparison of the single-bubble-class and modified two-bubble-class models of bubble column reactors

Gas phase conversions and product selectivities predicted by the single-bubble-class and modified two-bubble-class models of bubble column reactors are compared for a multistep gas-liquid reaction involving series/parallel steps. A situation is considered where the first reaction step is fast and occurs in the interfacial region while the other reaction steps are slow and occur only in the liquid bulk. Equivalent hydrodynamic and transport parameters provide a common basis for the comparison. The differences in the gas phase conversions predicted by these models are insignificant. However, the two models predict very different values of selectivities for the intermediate products. This analysis enables us to judge the range of applicability of the single-bubble-class model in design and scale-up of bubble column reactors.     

Modeling gas absorption accompanied by chemical reaction in bubble column and foam-bed slurry reactors

The published data in the literature and the reported models on foam-bed reactors have been reanalyzed. It is observed that the models have been developed assuming negligible conversion in the storage section although the storage constitutes 65–85% of the total volume of liquid/slurry charged into the reactor. For confirmation of the reported information, in the present work, experiments have been performed in foam-bed and bubble column slurry reactors for carbonation of hydrated lime slurry using carbon-dioxide gas under identical conditions. A comparison of the relative performances of the two reactors has been made. Storage section is found to be the main section governing the performance of the foam-bed slurry reactor. New mathematical models have been developed for both the reactors. The model predictions agree well with the experimental data.     

Calculation of flow fields in two and three-phase bubble columns considering mass transfer

The dimension of bubble column reactors is often based on empirical correlations. Very popular is the axial dispersion model. However, the applicability of these models is limited to the experimental conditions for which the dispersion coefficients are measured, because backmixing depends strongly on the columns dimension and the flow regime. This paper presents a numerical method for the calculation of the three-dimensional flow fields in bubble columns based on a multi-fluid model. Therefore, the local bubble size distribution is considered by a transport equation for the mean bubble volume, which is obtained from the population balance equation. For comparison with experimental results, the axial dispersion coefficients in the liquid and gas phase are calculated from the instationary, three-dimensional concentration fields of a tracer. The model is then extended to include mass transfer between the gas and liquid phase. Increasing mass transfer rates significantly influence the flow pattern. For several applications, a dispersed solid phase is added. For the calculation of three-phase gas-liquid-solid flow, the solid phase is considered numerically by an additional Eulerian phase.     

第三相的加入对气液传质过程的影响

系统地介绍了气液传质过程中,固体小颗粒或第二分散液相(有机相)所形成的第三相的加入对传质过程的影响.分别论述了在不同的气-液接触器(搅拌釜、鼓泡塔)中,固体小颗粒和第二分散液相的加入对体系的传质系数、传质速率及界面面积等的影响,叙述并讨论了传质机理及模型的最新进展.     

LIQUID PHASE BACKMIXING IN BUBBLE COLUMN REACTORS—A NEW CORRELATION

Bubble column reactors are widely used in many industrial applications due to their simplicity of operation. Although simple to operate, bubble columns are difficult to scale-up due to the uncertainties in the estimation of some non-adjustable design parameters. One of these design parameters is the liquid phase backmixing.

The present work proposes a new correlation to estimate the liquid phase backmixing in bubble column reactors. The correlation is based on principles originally developed for flow through porous media and uses experimental data obtained over a wide range of operating conditions. This correlation is simple to use and requires parameters which are easily available or can be measured on a small scale apparatus. The proposed correlation shows a significant improvement over available literature correlations and is applicable to three phase systems as well.     

A model for two-phase turbulent mixing in a jet bubble column

Mixing behavior of the two phase air-water turbulent flow in a jet bubble column is examined. The time evolution of the mixing behavior of a liquid tracer in a turbulent air-water flow within a jet bubble column is predicted using a model based on the fundamental governing equations of fluid motion. The predictions of the model are compared with experimental measurements. Measured residence time distributions (RTD) of the liquid tracer within the cone agree well with the predicted values given by the model. For the range of parameters considered in the study, lack of radial mixing and large axial mixing are evident within the cone of the jet bubble column. Use of fundamental mathematical models for the study of hydrodynamics in a two-phase conventional bubble column has been reported earlier (Torvik, 1990; Jakobsen et al., 1993). The present paper extends the use of such models to predict the mixing characteristics in a jet bubble column.     

Mass transfer rates from bubbles in stirred tanks operating with viscous fluids

In this paper, the role of liquid viscosity on the mass transfer rates in stirred tank reactors has been theoretically studied. Liquid viscosity affects liquid diffusivity and bubble size distribution by defining bubble stability in the flow. A population balance, taking into account the effect of liquid viscosity on the coalescence and break-up closures, has been combined with Higbie–Kolmogorov's theory to predict the effect of liquid viscosity on the mass transfer rates. Experimental results from the literature for stirred tanks operating with one single Rushton turbine have been used as comparison. Different moderately viscous aqueous solutions (glucose, glycerol and millet-jelly) have been considered. Bubble break-up depends on the critical deformation of the bubbles in the continuum phase. A correlation between the Weber critical number and the liquid viscosity has been found. Once the bubble distribution is accurately determined, the volumetric mass transfer rate in viscous solutions can be predicted theoretically.     

CFD modeling of slurry bubble column reactors for Fisher-Tropsch synthesis

Industrial bubble column reactors for Fischer-Tropsch (FT) synthesis include complex hydrodynamic, chemical and thermal interaction of three material phases: a population of gas bubbles of different sizes, a liquid phase and solid catalyst particles suspended in the liquid. In this paper, a CFD model of FT reactors has been developed, including variable gas bubble size, effects of the catalyst present in the liquid phase and chemical reactions, with the objective of predicting quantitative reactor performance information useful for design purposes. The model is based on a Eulerian multifluid formulation and includes two phases: liquid-catalyst slurry and syngas bubbles. The bubble size distribution is predicted using a Population Balance (PB) model. Experimentally observed strong influence of the catalyst particles concentration on the bubble size distribution is taken into account by including a catalyst particle induced modification of the turbulent dissipation rate in the liquid. A simple scaling modification to the dissipation rate is proposed to model this influence in the PB model. Additional mass conservation equations are introduced for chemical species associated with the gas and liquid phases. Heterogeneous and homogeneous reaction rates representing simplified FT synthesis are taken from the literature and incorporated in the model.Hydrodynamic effects have been validated against experimental results for laboratory scale bubble columns, including the influence of catalyst particles. Good agreement was observed on bubble size distribution and gas holdup for bubble columns operating in the bubble and churn turbulence regimes. Finally, the complete model including chemical species transport was applied to an industrial scale bubble column. Resulting hydrocarbon production rates were compared to predictions made by previously published one-dimensional semi-empirical models. As confirmed by the comparisons with available data, the modeling methodology proposed in this work represents the physics of FT reactors consistently, since the influence of chemical reactions, catalyst particles, bubble coalescence and breakup on the key bubble-fluid drag force and interfacial area effects are accounted for. However, heat transfer effects have not yet been considered. Inclusion of heat transfer should be the final step in the creation of a comprehensive FT CFD simulation methodology. A significant conclusion from the modeling results is that a highly localized FT reaction rate appears next to the gas injection region when the syngas flow rate is low. As the FT reaction is exothermal, it may lead to a highly concentrated heat release in the liquid. From the design perspective, the introduction of appropriate heat removal devices may be required.     

Two‐Phase Flow with Mass Transfer in Bubble Columns

Bubble columns are widely used in the chemical and biochemical industries. In these reactors a gaseous phase is dispersed into a continuous liquid phase thus the rising bubble swarm induces a circulating flow field. For the dimension of these reactors the local interfacial area and the residence time of the liquid and the gaseous phase are key parameters. In this paper an Euler‐Euler approach is used to calculate the flow field in bubble columns numerically. Therefore a transport equation for the mean bubble volume based on a population balance equation approach is coupled with the balance equations for mass and momentum. The calculations are performed for three‐dimensional, instationary flow fields in cylindrical bubble columns considering the homogeneous and the heterogeneous flow regime. For the interphase mass transfer the physical absorption of the gaseous phase into the liquid is assumed. The back mixing in the gaseous and liquid phase is calculated from the local and time dependent concentration of a tracer.     

Experimental and Numerical Study of Gas-Liquid Flow in a Sectionalized External-Loop Airlift Reactor

The external loop airlift reactor(EL-ALR) is widely used for gas-liquid reactions. It's advantage of good heat and mass transfer rates compared to conventional bubble column reactors. In the case of fermentation application where a medium is highly viscous and coalescing in nature, internal in riser helps in the improvement of the interfacial area as well as in the reduction of liquid-phase back mixing. The computational fluid dynamic(CFD) as a tool is used to design and scale-up of sectionalized external loop airlift reactor. The present work deals with computational fluid dynamics(CFD) techniques and experimental measurement of a gas hold-up, liquid circulation velocity, liquid axial velocity, Sauter mean bubble diameter over a broad range of superficial gas velocity 0.0024≤U_G≤0.0168 m·s~(-1). The correlation has been made for bubble size distribution with specific power consumption for different plate configurations. The effects of an internal on different mass transfer models have been completed to assess their suitability.The predicted local mass transfer coefficient has been found higher in the sectionalized external loop airlift reactor than the conventional EL-ALR.     

Modeling of bubble-column flows with quadrature-based moment methods

Bubble-column reactors are frequently employed in the biological, chemical and petrochemical industries. This paper presents a novel approach to model bubble-column flows using quadrature-based moment methods (QBMM). A fully two-way coupled flow solver is developed that solves the incompressible Navier-Stokes equation for the liquid phase and moment transport equations for the dispersed bubble phase. The moment transport equations for the dispersed bubble phase are solved using a kinetic theory approach. Contributions from the liquid-phase pressure gradient, vorticity, drag, virtual mass and gravity are accounted for in the bubble-phase force balance. The solution algorithm and coupling procedure are described in detail, and results are presented for a 2-D bubble column with two different gas flow rates (1.6 and 8.0 l/min).     

Quality of mixing in a downflow bubble column based on information entropy theory

Quality of mixing in a modified downflow bubble column has been analyzed by using information entropy theory. Mass transfer efficiency based on quality of mixing has also been enunciated in this work. Empirical models have been developed for downflow system with the parameters which affect the quality of mixing and mass transfer efficiency. The developed correlation for quality of mixedness in the downflow bubble column was interpreted by the mass transfer phenomena. The present analysis on the quality of mixing in downward two-phase flow in bubble column may give insight into a further understanding and modeling of multiphase reactors in industrial applications.     

Computation of plate columns for NOx absorption by a new stage-to-stage method

A new stage-to-stage method has been developed for the calculation of NX_x absorption columns. Each stage of the absorption column is simulated as a combination of a bubble column reactor (absorption) and an adiabatic plug for reactor (oxidation). The bubble column reactor is modelled as two single stirred tank reactors, one as a gas-phase and one as a liquid-phase reactor, both coupled by mass and heat transfer. In this hydrodynamic model, a dynamic approach is adopted, in which the gas-phase transport of N₂O₄ is the limiting step for the absorption. A gas-phasepseudo-enhancement for factor for N₂O₄ is therefore introduced. The balance equations for a single phase of the bubble column are solved with a Newton-Raphson algorithm. The entire column calculation is divided into a gas and a liquid side. On both sides, the stage-to-stage method is applied in such way that the overall calculation is performed as a loop process. The direction of the loop calculation follows that of the flow: gas-side upwards and liquid-side downwards.     

Effect of liquid properties on the performance of bubble column reactors with fine pore spargers

This work is a study of the effect of liquid properties on the performance of bubble column reactors with fine pore spargers. Various liquids covering a range of surface tension and viscosity values are employed, while the gas phase is atmospheric air. A fast video technique is used for visual observations and, combined with image processing, is used for gas holdup and bubble size measurements. New data on average gas holdup values, bubble size distributions and Sauter diameters are presented and are consistent with existing physical models on coalescence/breakage. A correlation based on dimensionless groups for the prediction of gas holdup in the homogeneous regime is proposed and found to be in good agreement with available data.     

Modeling the ultrasonic cavitation‐enhanced removal of nitrogen oxide in a bubble column reactor

A model study of the sonochemical removal of nitric oxide (NO) in a bubble column reactor is presented. The detailed model is developed to investigate the actual cavitation phenomena taking place during the absorption of NO. The expansion and subsequent collapse of cavitation bubble according to the theory of cavity collapse—initially developed by Lord Rayleigh and then improved on by coupling the energy balance equation of the bubble and the chemical reactions taking place inside the cavity to calculate the composition of different species formed during the collapse—are modeled. The model takes into consideration (1) cavitation bubble dynamics, (2) generation and transfer of oxidizing species from bubble collapse through reaction kinetics, (3) transfer of NO from gas to liquid, and (4) chemical reactions of oxidizing species with dissolved NO. The results of the simulations surprisingly indicate that the chemistry induced by ultrasonic cavitation cannot explain the absorption of NO beyond about 30% of the inlet concentration if the mass transfer is assumed to be the same as that in the bubble column without ultrasound. When experimental values of mass‐transfer coefficients, calculated in the studies by other researchers (which are in the range of about five times the physical mass‐transfer coefficient in a bubble column), are used, absorption up to 80% are calculated in the simulations consistent with experimental results obtained from the sonochemical bubble column reactor. The present model provides a framework on which more robust and rigorous models can be developed for the complex gas‐liquid sonochemical systems and reactors. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2397–2411, 2012     

Absorption and reaction of isobutene in sulfuric acid—II: Determination of parameters and optimal conditions in bubble columns

The sulfuric acid catalysed absorption and reaction of isobutene was studied in a bubble column (10.2 cm diameter, 256 cm height) covering a wide range of liquid phase compositions. At acid concentrations of 40–48% wt and tert-butanol concentrations of 3.2–4.3 moles/l. the absorption rate has a maximum value. From measurements in the slow reaction or diffusional regime of mass transfer it was possible to obtain a value of liquid side mass transfer coefficient k_L. As interfacial areas and solubilities of isobutene were determined by independent means the rate constants of the hydration could be evaluated from this and other studies in bubble column reactors. The reaction rate constant follows a simple correlation which considers the effect of the acid and the generated butanol. Thus, all relevant data of the absorption-reaction system are available. The significance of these data was checked by a dynamic study in a smaller bubble column.