Two-phase Bubble Column Research Articles

Comparison of ML–EM algorithm and ART for reconstruction of gas hold-up profile in a bubble column

Abstract Algebraic reconstruction technique (ART) and maximum likelihood–expectation maximization (ML–EM) algorithm have been applied for image reconstruction using gamma-ray tomography. This methodology can be of immense help in establishing the hydrodynamics of several multiphase systems such as two-phase and three-phase bubble column reactors. The effect of various image processing parameters such as initial guess, grid size, stopping criteria and gamma-ray measurement parameters like beam configuration, number of projection, number of views on the quality of reconstructed image has been studied in present work. It has been observed that ML–EM algorithm shows more precise and faster results as compared to ART and it serve as a preferential tool in image reconstruction. These techniques were then used in the estimation of gas hold-up profile in a two-phase aqueous system. Average gas hold-up values in bubble column based on reconstructed local hold-up values based on the above two techniques were found to be in good agreement with the experimental data within ±10% accuracy, however, ML–EM algorithm may be preferred due to better capability of incorporating the modalities of data collection.

Gas hold‐up estimation in bubble columns using passive acoustic waveforms with neural networks

AbstractPassive acoustic waveforms produced experimentally from a bench‐scale two‐phase bubble column were recorded using a miniature hydrophone at three axial positions. The generated acoustic waveforms were processed and trained using artificial intelligence against global gas hold‐up measurements. Two neural network architectures, the radial basis function (RBF) neural network and the recurrent Elman neural network, were employed. Both neural network techniques achieved accurate gas hold‐up estimation, characterised by low mean square errors of 2.70 and 1.68% for the RBF and recurrent Elman networks respectively. The designed and trained neural networks were found to be a powerful tool for learning and replicating complex two‐phase patterns. Passive acoustic waveforms were found to be a useful measuring technique for gas hold‐up estimation in bubble columns under moderate operating conditions. Copyright © 2006 Society of Chemical Industry

Modeling of Bubble Column Reactors: Progress and Limitations

Bubble columns are widely used for carrying out gas−liquid and gas−liquid−solid reactions in a variety of industrial applications. The dispersion and interfacial heat- and mass-transfer fluxes, which often limit the overall chemical reaction rates, are closely related to the fluid dynamics of the system through the liquid−gas contact area and the turbulence properties of the flow. There is thus considerable interest, within both academia and industry, to improve the limited understanding of the complex multiphase flow phenomena involved, which is preventing optimal scale-up and design of these reactors. In this paper, the progress reported in the literature during the past decade regarding the use of averaged Eulerian multifluid models and computational fluid dynamics (CFD) to model vertical bubble-driven flows is reviewed. The limiting steps in the model derivation are the formulation of proper boundary conditions, closure laws determining turbulent effects, interfacial transfer fluxes, and the bubble coalescence and breakage processes. Examples of both classical and more recent modeling approaches are described, evaluated, and discussed. Physical mechanisms and numerical modes creating bubble movement in the radial direction are outlined. Special emphasis is placed on the population balance modeling of the bubble coalescence and breakage processes in two-phase bubble column reactors. The constitutive relations used to describe the bubble−bubble and bubble−turbulence interactions, the bubble coalescence and breakage criteria, and the daughter size distribution models are discussed with a focus on model limitations. The demand for amplified modeling, more accurate and stable numerical algorithms, and experimental analysis providing data for proper model validation is stressed.

Time-dependent gas holdup variation in an air–water bubble column

Time-dependent gas holdup variation in a two-phase bubble column is reported with air and tap water as the working fluids. The results indicate that time-dependent gas holdup is closely related to the water, whose quality is unsteady and changes, not only during the two-phase flow, but also during idle periods. The significance and characteristics of the time-dependent gas holdup variation are influenced by the bubble column operation mode (cocurrent or semi-batch), the sparger orientation, the superficial gas velocity, and the superficial liquid velocity. It is proposed that a volatile substance (VS), which exists in the water in very small concentrations and inhibits bubble coalescence, evaporates during column operation and results in a time-dependent gas holdup. The influence of bubble column operation mode, sparger orientation, superficial gas velocity, and superficial liquid velocity on the time-dependent gas holdup variation are explained based on their effects on bubble size, bubble contacting frequency and mixing intensity. This work reveals that regular tap water may cause significant reproducibility problems in experimental studies of air–water two-phase flows.

Hydrodynamic studies in both bi-dimensional and three-dimensional bubble columns with a single sparger

Gas holdup in highly viscous fluid in two-phase bubble column with a single sparger operated continuously with respect to the gas flow and batch wise with respect to the liquid was investigated using bed expansion technique. Two- and three-dimensional columns of the same effective cross-sectional area were investigated. Liquid viscosity varied between 0.063 and 0.320 Pa s, static bed heights between 0.12 and 0.60 m, surface tension between 0.0248 and 0.035 N m −1 and density between 906 and 928 kg m −3. Columns were injected with air at superficial gas velocities between 0.0018 and 0.290 m s −1. A single nozzle sparger of 0.01 m diameter was used. The behavior of bubbles in two-dimensional bubble column was found to fall into the bubble flow regime, whereas the behavior in three-dimensional column was found to fall into the churn turbulent regime. Two correlations for gas holdup in the two- and three-dimensional bubble columns were proposed and compared with correlations listed in the literature.

Analysis of flow patterns in bubble and slurry bubble columns based on local heat transfer measurements

Flow patterns in two-phase (G–L) and three-phase (G–L–S) bubble columns are investigated based on local time-averaged heat transfer coefficients. The experiments are conducted in a 0.28 m diameter Plexiglas column in air–water and air–water–glass beads (35 μm) systems over superficial gas velocity range 0.05–0.3 m/s and slurry concentration range 0–40 vol.%. The heat transfer measurements are made with a specially designed probe which provided local heat transfer coefficients. The measured heat transfer data are analyzed to illustrate the effects of gas velocities and slurry concentrations on flow patterns in different regions of the column. The heat transfer measurements at different axial and radial positions and for different probe orientations provided further insights into liquid circulation patterns in the column.

Study of Bubble Formation Under Constant Flow Conditions

Bubble size is one of the key parameters in the design of two-phase gas-liquid bubble column reactors. Accurate knowledge of this parameter is essential for the prediction of gas holdup, heat and mass transfer coefficients. The previousfindings, particularly with respect to the infiuence of orifice size and physical properties of the liquid phase on bubble size, are often of contradictory nature. In this paper, extensive new experimental results are presented for regions where published data are insufficient. The suitability of artificial neural networks for identification of the process variables and modeling is evaluated. The Radial Basis Function (RBF) neural network architecture was used successfully to generate a nonlinear correlation for the prediction of bubble diameter. This correlation predicts the present data and the control data of other investigators with excellent accuracy.

Phase distribution phenomena in two-phase bubble column reactors

In a recent paper, Jakobsen, Sannæs, Grevskott and Svendsen (Ind. Eng. Chem. Res. 36(10) (1997) 4052–4074) presented a review of the present status on fluid dynamic modeling of vertical bubble-driven flows. Special emphasis was placed on two-phase flows in bubble column reactors. For these multiphase reactors, the averaged Eulerian multifluid models have been found to represent a trade-off between accuracy and computational efforts for practical applications. Unfortunately, in such multifluid models constitutive relations are needed to describe the phase interaction processes. It was concluded that the general picture from the literature is that time-averaged liquid velocity fields are reasonably well predicted both with steady-state and dynamic models of this type. The prediction of phase distribution phenomena, on the other hand, is still a problem, in particular at high gas flow rates. The present paper gives an overview of the pertinent constitutive relations presented in the literature aiming at a firm mechanistic prediction of the phase distribution phenomena. This includes transversal forces, steady drag forces, surface tension effects, and hydrodynamic bubble–bubble and bubble–wall interactions. Several interaction mechanisms in the turbulence fields like the so-called turbulent mass diffusion, turbulent migration, turbulent drift velocities, anisotropic turbulent drag forces, as well as the interactions between these mechanisms, and the impacts of variations in bubble size and shape distributions are discussed. Various aspects of these relations have been questioned. It is therefore the aim of this paper to compare the capabilities of the existing Eulerian multifluid modeling concepts and parameterizations. The various approaches are evaluated using an in-house 2D Euler/Euler steady-state code. There are several reasons why we choose a steady 2D model for evaluation. First, the model has the advantage of being relatively simple, thus the computational effort required for practical applications involving chemical reactions, and interfacial heat and mass transfer is feasible. Second, the dynamic axisymmetric 2D models do not give much improvement as the flow phenomena possibly missing are believed to be 3D. That is, they do not resolve the swirling motion of bubble swarms. Third, most parameterizations presented in the literature are based on, and have so far only been applied to, 2D models. The results obtained indicate that the various phase interaction parameterizations available in the literature predict very different phase distributions in bubble columns. For operating reactors these deviations will significantly influence the predicted process performance. The results presented here thus confirm the demand for improved modeling including more accurate and stable numerical solution algorithms. Low-accuracy algorithms may totally destroy the physics reflected by the models implemented.

Gamma ray tomography design for the measurement of hold-up profiles in two-phase bubble columns

A gamma ray tomography system was designed, developed and employed for the measurement of radial hold-up profiles in bubble columns. Measurements were of gamma ray attenuation. For the given source strength the collimator designs for both source and detectors were optimized to get the maximum number of counts with the least scattering effects. For the given dwell and scanning times, excellent reproducibility was obtained. Both fan beam and pencil beam scanning were employed to minimize the error due to scattering of the photons near to the wall regions. Experiments were performed in a 0.385 m internal diameter bubble column. Chordal hold-up profiles were used to find the radial hold-up profile using Abel’s inversion method.

Volume fraction autocorrelation functions in a two-phase bubble column

We use an electrical impedance technique to measure the fluctuations of gas volume fraction in a gas-liquid bubble column in turbulent flow regime. From these experimental values the volume fraction autocorrelation function is determined. On the theoretical side, we introduce a stochastic model to describe the aggregation of bubbles by assuming them to be rigid spheres of different diameters and by considering their coalescence as a stochastic Markovian process. The coalescence rate contains one adjustable parameter which takes into account the neglected effects of compressibility and deformation, spatial inhomogeneities and hydrodynamic interactions between the bubbles and with the boundaries. The associated master equation for this polydispersed system is built up, and from it we derive an equation for the volume fraction equilibrium correlation functions for several bubble sizes. By adjusting the free parameter, we compare the theoretical correlations with corresponding experimental values and find that the standard deviation associated with their difference can be made as small as 0.017. We discuss the limitations and possible generalizations of our model and conclude by making further physical remarks.

Liquid circulation, bubble size distributions, and solids movement in two- and three-phase bubble columns

One two-phase bubble column and two three-phase slurry reactors have been experimentally characterised with special emphasis on bubble size distribution, liquid circulation and solids movement. The measurements in the two phase bubble column were based on a five point conductivity probe method and on a steady state heat tracer technique. For the solids movement, the CARPT technique was used. By numerical simulations using a two fluid model, new models for bubble size distribution and solids presence have been tested. The new bubble size model is found to improve the size distribution predictions compared to prior models, but is still not satisfactory. Temperature profiles were well predicted by the model. For the solids movement, two circulation cells were found experimentally in the reactors tested. This has also been verified by numerical simulations. The formation of secondary cell structures of magnitude approximately equal to the column diameter, are indicated by the experimentally determined Reynolds stress patterns.

Hydrodynamics and mixing in three-phase fluidized bed bioreactors

The effects of solid particles on hydrodynamics and mixing in a three-phase fluidized bed bioreactor were discussed. The gas holdup, bubble size, and liquid-phase axial dispersion coefficient were measured in a 0.25-m id bubble column bioreactors containing low-density particles. The presence of low-density solid particles slightly increased gas holdup. The decrease in average bubble diameter with solid presence was found. For the three-phase system, the liquid-phase axial dispersion coefficients were higher than for the two-phase system. We extended a model for a gas holdup developed for a gas-liquid two-phase bubble column bioreactor to a gas-liquid-solid three-phase fluidized bed bioreactor. Using the present data and available data in the literature, the predictions of the proposed model were examined. The proposed model agreed with a wide range of the experimental data. A theoretical correlation for liquid-phase axial dispersion coefficient was developed using Kolmogoroff's theory of isotropic turbulence. Reasonable agreement was obtained between the predicted and experimental values of axial dispersion coefficient.

Heat transfer and gas holdup in a two-phase bubble column: Air-water system — Review and new data

Hydrodynamic and heat transfer investigations on an air-water system in a bubble column are reported and discussed. Gas holdup data (total and local) and the heat transfer coefficient between a 19 mm outer diameter heat transfer probe and an air-water dispersion are measured in continous and semibatch mode. In addition to new data, earlier data of Saxena et al and those available in the literature are discussed and employed to assess the available correlations and models for gas-phase holdup and heat transfer coefficient. Simple approaches based on general theoretical considerations are proposed to correlate gas holdup and heat transfer data. A few interesting conclusions follow from this study.

Modelling of slurry reactors. A fundamental approach

Multiphase reactors in the form of bubble columns and stirred tank reactors are being used in large numbers throughout the petrochemical and biochemical industry today, and steadily for more complicated reaction systems. It has become increasingly more important to develop good, and theoretically sound models for scaling up and design of the reactors. The most common models used today rely heavily upon empirical information obtainable only from pilot size experiments and this makes “a priori” design from small scale data difficult. The model presented is based on a “first principles” approach where the parameters are fundamental in nature and as far as possible, obtainable from general fluid dynamics literature. It is a dynamic two phase model incorporating a k-ε turbulence model, compressible gas phase and axisymmetry. The equations are discretisized using a finite volume technique with an upwind or hybrid differencing scheme and solved using a variation of the SIMPLE (Semi Implicit Method for Pressure Linked Equations) method. The results from simulations of a two-phase bubble column are compared with measured radial distributions of gas hold-up, liquid velocity and turbulent kinetic energy using air and desalinated water as media. As chemical reaction, the production of methanol from synthesis gas is implemented. Simulation results using a pseudohomogenous 3-phase slurry model are compared with data from literature.

Heat transfer from a tube bundle in a bubble column

Heat transfer coefficient for an immersed five tube bundle in a two-phase (air-water) bubble column is measured as a function of air velocity and other relevant parameters. Average and local air holdup are also measured under identical conditions to characterize the system uniquely.

Gas holdup in a continuous coal-suspended bubble column with annular flow section.

The gas holdup characteristics of a continuous annular bubble column of coal were studied. Coalescence of bubbles occurred more readily in the slurry bubble column than in the air-water two-phase bubble column. The gas holdup eG decreased with increasing slurry flow rate and solid concentration. However, increase of eG with increasing solid concentration was found in a higher range of solid concentration. Considering such an effect related to solid concentration, an empirical correlation for the estimation of gas holdup was derived. The applicability of the previously reported correlations for the slurry bubble column was also studied.

Gas-liquid interfacial area and liquid-side mass-transfer coefficient in a slurry bubble column

Influences of suspended particles upon such parameters as gas holdup, volumetric liquid-state mass-transfer coefficient, and gas-liquid interfacial area in a bubble column were investigated in sodium sulfite/sulfate solutions in which various loadings of coarse nylon particles and fine alumina particles were suspended. The volumetric mass-transfer coefficients and gas holdups were a bit increased by suspending a small amount of fine particles. The gas-liquid interfacial area in a slurry bubble column in which a small amount of fine particles were suspended was found to be higher than that in a two-phase bubble column.

Gas holdup and longitudinal dispersion in different types of multiphase reactors and their possible application for microbial processes

Gas hold-up and liquid phase longitudinal dispersion have been measured In concurrent one- and six-stage two-phase bubble columns as well as in counter-current one-stage two- and three-phase bubble colums. To describe the intensity of the longitudinal mixing the logitudinal dispersion and the backflow cell models were applied. The possible influence of fluid mixing on microbial processes was investigated.