Bubble size distribution in the sparger region of bubble columns

It is well known that the gas distributor can play an important role on the evolution of the bubble size distribution (BSD) in gas-liquid reactors, strippers and absorbers. Therefore, the main subject of the present work was to study the influence of sparger design and process parameters on the BSD in the sparger region of the considered apparatus. For this purpose, both detailed measurements and prediction of the size of bubbles produced at the sparger were carried out in three different experimental apparatuses.The unique set of BSD curves were obtained by analyzing a large amount of bubbles with a measurement based on image analysis technique.Additionally, Colella's model of BSD evolution in bubble columns was further developed by implementing a detailed physical model for predicting the initial BSD at the sparger where the model input is only based on design/process parameters. A validation of the model was carried out using data from two different columns. The comparison between calculated and experimental BSD shows good agreement.     

Modeling of bubble column slurry reactor for reductive alkylation of p-phenylenediamine

A bubble column slurry reactor (BCSR) model has been developed for the reductive alkylation of p-phenylenediamine (PPDA) with methyl ethyl ketone (MEK) to N,N^′-di-secondary-alkyl-p-phenylenediamine (Di-amine). This particular reaction system is commercially relevant and involves a combination of parallel and consecutive reactions comprising equilibrium non-catalytic (homogeneous) and catalytic (heterogeneous) steps. The proposed model is based on the ‘mixing cell approach’. In this work the mixing cell approach has been extended by including a liquid backflow stream from all but the bottommost mixing cell. The model incorporates the contributions of gas-liquid and liquid-solid mass transfer, heat effects, and complex multistep reaction kinetics. CFD model is used to estimate the extent of backflow among mixing cells and its dependence on operating parameters. The effect of gas and liquid velocities, catalyst loading, inlet PPDA concentration, and temperature on the conversion, selectivity, global rate of hydrogenation, and temperature rise is discussed. The comparison of the current approach with the traditional mixing cell model is discussed. The BCSR model presented here will be useful to provide guidelines for designing and improving overall performance of bubble column reactors.     

INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

Predicting inter-phase mass transfer for idealized Taylor flow: A comparison of numerical frameworks

Four numerical frameworks were derived to investigate the impact of underlying assumptions and numerical complexity on the predicted mass transfer between a Taylor bubble and liquid slug in circular capillaries. The separate influences of bubble velocity and film length, slug length, and bubble film thickness on k_La were compared to empirical and CFD-based predictions from existing literature. Reasonable agreement was obtained using a Slug Film model, which accounted for diffusion-limited mass transfer between the slug film and circulating bulk without the need for an iterative numerical solution. Subsequent investigation of the relative contributions of film and cap mass transport for industrially relevant conditions suggests that both mechanisms need to be accounted for during the prediction of k_La.     

Nonlinear time‐series analysis of optical signals to identify multiphase flow behavior in microchannels

This study provides an insight into the instability and irregularity of multiphase flows in microchannels. Using a homemade optical measuring system, time series related to two‐phase flow dynamics under different operating conditions, fluids, and channel lengths were collected and analyzed via a nonlinear characteristic parameter, Kolmogorov entropy (K_E). Our results reveal that higher K_E corresponds to unstable flow behavior, while lower K_E refers to steady flow behavior; higher K_E values appear at comparatively low or high gas flow rates, and most Taylor flow regime appeared at proper operating conditions with small K_E. An equation derived based on the definition of K_E is proposed to better understand K_E characteristics, which include bubble break‐up impact and gas/liquid flow rate ratio. Predictions from the proposed analytical equation agree with experimental results, suggesting that the equation effectively identifies unstable flows and can be used to ensure stable and predictable multiphase flows in microchannels. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2378–2385, 2017     

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.     

A numerical method for solving the transient multidimensional population balance equation using an Euler-Lagrange formulation

A numerical method was developed to solve the population balance equation for transient multidimensional problems including particle-particle interactions. The population balance equation was written in a mixed Euler-Lagrange formulation which was solved using the discretization method that represents the number density function by impulse functions, an operator splitting method and a remeshing procedure for the internal variable that conserves the mass and the number of particles.This method was successfully tested against analytical and semi-analytical solutions for pure breakage, pure coalescence, breakage and coalescence, pure advection, advection with absorption, advection with binary uniform breakage and with constant or linear absorption. The method was also applied to a free-boundary transient one-dimensional gas-phase model in a bubble column reactor with simplified hydrodynamics. Accurate solutions were obtained for several simulation conditions for the bubble column, including gas absorption, bubble breakage, bubble coalescence and variable gas density effects. The results showed that the numerical method is adequate and robust for solving transient population balance problems with spatial dependence and particle-particle interactions.     

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.     

The influence of electrolytes on gas hold-up and regime transition in bubble columns

Experiments were conducted in a 0.12-m-in-diameter bubble column to investigate the effect of electrolytes on gas hold-up (ε) and on the regime transition point in bubble columns. Air was used as the dispersed phase and aqueous solutions of three different salts (NaCl, Na₂SO₄ and NaI), as well as double-distilled water, were utilised as the continuous phase, varying the gas superficial velocity (u_G) in the range 0-0.26 m/s. The ε×u_G curves were a function of both the chemical nature and the concentration of the electrolytes. However, similar ε×u_G profiles were obtained regardless of the electrolyte for a given ratio between the concentration in the solution and the critical concentration of the electrolyte for bubble coalescence. This ratio therefore presents itself as a promising modelling parameter to account for the chemical nature of electrolytes. The gas hold-up data were employed to compute the regime transition point according to two different methods, evidencing its non-linear dependence on the concentration of electrolytes in the liquid.