Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.     

CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

CFD-PBM耦合模型模拟气液鼓泡床的通用性研究

通过对不同操作压力和不同液体性质气液鼓泡床的模拟值与实验数据进行对比，从而验证CFD-PBM耦合模型的通用性。结果表明，CFD-PBM耦合模型在加入了气泡破碎修正因子后，可以很好地预测压力对鼓泡床流体力学行为的影响趋势，当压力升高时，气含率显著升高。不同液体黏度和表面张力条件下CFD-PBM耦合模型的模拟结果与实验结果均吻合较好。随液体黏度增大，气泡破碎速率减小，气泡尺寸分布变宽，曳力显著下降，气含率随之降低。随表面张力减小，气泡破碎速率增大，气泡变小，气含率升高。CFD-PBM耦合模型具有很好的通用性，原因在于考虑了压力、液体黏度和表面张力对气泡聚并、破碎和气液相间作用力的影响。     

Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures

Two-dimensional axisymmetric Eulerian/Eulerian simulations of two-phase (gas/liquid) transient flow were performed using a multiphase flow algorithm based on the finite-volume method. These numerical simulations cover laboratory scale bubble columns of different diameters, operated over a range of superficial gas velocities ranging from the bubbly to the churn turbulent regime. The bubble population balance equation (BPBE) is implemented in the two-fluid model that accounts for the drag force and employs the modified k-ε turbulence model in the liquid phase. Several available bubble breakup and coalescence closures are tested. Quantitative agreements between the experimental data and simulations are obtained for the time-averaged axial liquid velocity profiles, as well as for the kinetic energy profiles, only when model predicted breakup rate is increased by a factor of ten to match the coalescence rate. The calculated time-averaged gas holdup profiles deviate in shape from the measured ones and suggest that full three-dimensional simulation is needed. Implementation of BPBE leads to better agreement with data, especially in the churn-turbulent flow regime, compared to the simulation based on an estimated constant mean bubble diameter. Differences in the predicted interfacial area density, with and without BPBE implementation, are significant. The choice of bubble breakup and coalescence closure does not have a significant impact on the simulated results as long as the magnitude of breakup is increased tenfold.     

Gas-liquid mass transfer in a slurry bubble column operated at gas hydrate forming conditions

Gas-liquid interphase mass transfer was investigated in a slurry bubble column under CO₂ hydrate forming operating conditions. Modeling gas hydrate formation requires knowledge of mass transfer and the hydrodynamics of the system. The pressure was varied from 0.1 to 4 MPa and the temperature from ambient to 277 K while the superficial gas velocity reached 0.20 m/s. Wettable ion-exchange resin particles were used to simulate the CO₂ hydrate physical properties affecting the system hydrodynamics. The slurry concentration was varied up to 10%vol. The volumetric mass transfer coefficient (k_la_l) followed the trend in gas holdup which rises with increasing superficial gas velocity and pressure. However, k_la_l and gas holdup both decreased with decreasing temperature, with the former being more sensitive. The effect of solid concentration on k_la_l and gas holdup was insignificant in the experimental range studied. Both hydrodynamic and transport data were compared to best available correlations.     

Mass transfer in sparged and stirred reactors: influence of carbon particles and electrolyte

Mass transfer in multiphase systems is one of the most studied topics in chemical engineering. However, in three-phase systems containing small particles, the mechanisms playing a role in the increased rate of mass transfer compared to two-phase systems without particles, are still not clear. Therefore, mass transfer measurements were carried out in a 2D slurry bubble column reactor , a stirred tank reactor with a flat gas-liquid interface, and in a stirred tank reactor with a gas inducing impeller. The rate of mass transfer in these reactors was investigated with various concentrations of active carbon particles (average particle size of ), with electrolyte (sodium gluconate), and with combinations of these. In the bubble column, high-speed video recordings were captured from which the bubble size distribution and the specific bubble area were determined. In this way, the specific mass transfer area a_gl was determined separately from the mass transfer coefficient k_l. Mechanisms proposed in literature to describe mass transfer and mass transfer enhancement in stirred tank reactors and bubble columns are compared. It is shown that the increased rates of mass transfer in the 2D bubble column and in the stirred tank reactor with the gas inducing impeller are completely caused by an increased gas-liquid interfacial area upon addition of carbon particles and electrolyte. It is suggested that an increased level of turbulence at the gas-liquid interface caused by carbon particles accounts for a smaller effective boundary layer thickness and an enhancement of mass transfer in the flat gas-liquid surface stirred tank reactor. However, for the carbon particles used in this study, it is rather unlikely that mass transfer enhancement takes place due to the well-known shuttle or grazing effect.     

Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of [Alves et al., 2002a] and [Alves et al., 2002b] . The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.     

Multicompartment hydrodynamic model for slurry bubble columns

A core-annulus multicompartment two-dimensional two-bubble class model accounting for slurry recirculation and coupled with catalyst transport was developed as a part and parcel of the analysis of the behavior of slurry bubble column reactors at high gas throughputs corresponding to the churn turbulent flow regime. The model analyzed the contributions of bubble-induced turbulence closures, bubble coalescence and breakup phenomena, and catalyst axial distribution as the resultant of sedimentation, advection via liquid-solid slip, per-compartment axial dispersion and core-annulus lateral exchange of catalyst by bubble-induced turbulence. The model was also used to analyze the effects of catalyst loading, gas density and superficial velocity, and column diameter and vessel aspect ratio on the hydrodynamics of slurry bubble column reactors, namely, the per-compartment phase holdups and interstitial velocities, pressure gradient, bubble coalescence and break-up rates, and loci of velocity inversion for the gas and slurry profiles.     

CFD modeling of gas dispersion and bubble size in a double turbine stirred tank

In the present paper, gas dispersion in a double turbine baffled stirred tank is modeled using a commercial computational fluid dynamics (CFD) code FLUENT 6.1 (Fluent Inc., USA). A bubble number density equation is implemented in order to account for the combined effect of bubble break-up and coalescence in the tank. In the proposed work, the impellers are explicitly described in three dimensions using multiple reference frame model. Dispersed gas and bubbles dynamics in the turbulent water are modeled using an Eulerian-Eulerian approach with dispersed k-ε turbulent model and modified standard drag coefficient for the momentum exchange. The model predicts spatial distribution of gas holdup, average local bubble size and flow structure. The results are compared with experimental and numerical finding reported in the literature and good agreement between the present model and measurements of Alves et al. [Gas liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering Science, 2002, 57, 487-496] is achieved.     

Effect of electrolytes in aqueous solutions on oxygen transfer in gas–liquid bubble columns

The effects of inorganic electrolytes (NaCl, MgCl₂, CaCl₂) in aqueous solutions on oxygen transfer in a bubble column were studied. Electrolyte concentrations (c) below and above the critical concentrations for bubble coalescence (c_tc), and six superficial gas velocities (v_sg), were evaluated. The volumetric mass transfer (k_La) and the mass transfer (k_L) coefficients were experimentally determined. It was found that the concentration of electrolytes reduced the k_L, but the interfacial area (a) increased enough to result in a net increase of k_La. Using as independent variable a normalizing variable (c_r = c/c_tc), and maintaining fixed v_sg, similar values of k_La were observed regardless the kind of electrolyte; the same happened for k_L. This suggests that c_r quantifies the structural effects that these solutes exert on mass transfer. Also, once c_r = 1 was reached, no significant variations were found in k_La and k_L for constant v_sg. It is concluded that the gradual inhibition of bubble coalescence (c_r < 1) governs the significant changes in hydrodynamics and mass transfer via the reduction of bubble size and the consequent increment of a and gas holdup (?_g). Finally, regarding the effects of v_sg on mass transfer, transition behaviors between those expected for isolated bubbles and bubble swarms were observed.     

Physical explanation of the empirical coefficients of gas-liquid mass transfer equations

Equipment design and scale up is one of the biggest problems that chemical engineers face. A lot of research has been done at laboratory and pilot plant scale. However, experimental data are, many times, useless in equipment scale up because they overlook the processes involving bubbles. Therefore, a new approach considering the hydrodynamics of the bubbles is proposed to explain and understand the mass transfer rates. Semi-theoretical equations have been developed for bubble columns and stirred tanks based on hydrodynamic considerations of the flow, the bubbles and dispersions in the tank. These equations are able to explain the physical meaning, identify the effect of the scale on mass transfer rates and even predict the coefficients of the empirical correlations for k_La based on the hydrodynamic processes that bubbles experience. It can be concluded that the proportional constant of the correlations for k_La depends on the bubble size, on the physical and transport properties and on the size of the tank because it affects the mixing. Meanwhile, the exponents related to the power input and the superficial gas velocity depend on bubble break up and coalescence, and the dispersions generated. In the case of stirred tanks, the physical effect of the impeller on the bubbles also plays an important role on the exponents.     

基于EMMS方法的鼓泡塔反应器CFD及群平衡模拟

能量最小多尺度（energy-minimization multi-scale,EMMS）方法已经被应用于气液体系中群平衡（population balance model,PBM）模型的改进。EMMS模型可计算气泡破碎聚并过程的能量,进而获得聚并速率的修正因子。应用这一模型对高气速鼓泡塔进行了模拟计算,并进一步对比了均一尺径模型、CFD-PBM模型以及CFD-PBM-EMMS模型的模拟结果与实验数据。结果表明,在高表观气速条件下,基于EMMS方法的群平衡模型可以更加准确地预测鼓泡塔中不同高度的气泡尺径分布和轴向液速,同时提高了对整体气含率和局部气含率的模拟准确性。在表观气速为0.16 m·s^-1和0.25 m·s^-1时,CFD-PBM-EMMS模型对气泡尺径分布的预测精度更高,同时整体气含率模拟的相对误差下降为5%和15%,局部气含率模拟平均相对误差下降为8%和17%。     

A generalized approach to model oxygen transfer in bioreactors using population balances and computational fluid dynamics

In many biological processes, increasing the rate of transport of a limiting nutrient can enhance the rate of product formation. In aerobic fermentation systems, the rate of oxygen transfer to the cells is usually the limiting factor. A key factor that influences oxygen transfer is bubble size distribution. The bubble sizes dictate the available interfacial area for gas-liquid mass transfer. Scale-up and design of bioreactors must meet oxygen transfer requirements while maintaining low shear rates and a controlled flow pattern. This is the motivation for the current work that captures multiphase hydrodynamics and simultaneously predicts the bubble size distribution.Bubbles break up and coalesce due to interactions with turbulent eddies, giving rise to a distribution of bubble sizes. These effects are included in the modeling approach by solving a population balance model with bubble breakage and coalescence. The population balance model was coupled to multiphase flow equations and solved using a commercial computational fluid mechanics code FLUENT 6. Gas holdup and volumetric mass transfer coefficients were predicted for different superficial velocities and compared to the experimental results of Kawase and Hashimoto (1996). The modeling results showed good agreement with experiment.     

Experimental study of mass transfer in a dense bubble swarm

We consider the liquid-side mass transfer coefficient k_L in a dense bubble swarm for a wide range of gas volume fraction (0.45%≤α_G≤16.5%). The study is performed for an air–water system in a square column. Bubble size, shape and velocity have been measured for different gas flow rates by means of a high speed camera. Gas volume fraction and bubble velocity have also been measured by a dual-tip optical probe. Both of these measurements show that the bubble vertical velocity decreases when increasing α_G in agreement with previous investigations. The mass transfer is measured from the time evolution of the dissolved oxygen concentration, which is obtained by the gassing-out method. The mass transfer coefficient is found to be very close to that of a single bubble provided the bubble Reynolds number is based on the average equivalent diameter 〈d_eq〉 and the vertical slip velocity 〈V_z〉.     

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.     

Mathematical modeling of gas-liquid mass transfer rate in bubble columns operated in the heterogeneous regime

In this paper, a multi-scale approach is followed to study gas-liquid mass transfer in bubble columns. First, a single bubble of equivalent diameter d is considered. Its morphology and its gas to liquid relative velocity are related to the bubble diameter through the use of known correlations. Then, the gas-liquid mass transfer between the bubble and the surrounding liquid is studied theoretically. An equation describing the transport of the transferred species in the viscous boundary layer around the bubble is solved. In a second step, a bubble column of 6-10 m height is studied experimentally. The gas phase in the column is characterized experimentally by means of a gammametric technique. Finally, the two studies are linked, yielding a 1D mathematical model able to predict the gas-liquid mass transfer rate in a bubble column operated in the heterogeneous regime.     

Hydrodynamics and mass transfer behavior in multiple draft tube airlift contactors

The draft tube configuration significantly affected the performance of an airlift contactor. The multiple draft tube configuration was demonstrated to give a better gas-liquid mass transfer when compared with a conventional one-draft-tube system. The airlift with a larger number of draft tubes allowed a higher level of bubble entrainment, which rendered a high downcomer gas holdup. This resulted in a higher overall gas holdup in the contactor. Liquid velocity was also enhanced by increasing the number of draft tubes. The ratio between downcomer and riser cross sectional areas, A _d /A _r , had a great effect on the system performance, where a larger A _d /A _r led to a lower downcomer liquid velocity and smaller quantity of gas bubbles being dragged into the downcomer. This resulted in low gas holdup, and consequently, low gas-liquid interfacial mass transfer area, which led to a reduction in the overall volumetric mass transfer coefficient. The presence of salinity in the system drastically reduced the bubble size and subsequently led to an enhancement of gas entrainment within the system. As a result, higher gas holdups and gas-liquid interfacial area were observed, and hence, a higher rate of gas-liquid mass transfer was obtained.     

Interfacial area and volumetric mass transfer coefficient in a bubble reactor at elevated pressures

The present study deals with the pressure effects on mass transfer parameters within a bubble reactor operating at pressures up to . The gas-liquid systems are N₂/CO₂-aqueous solution of Na₂CO₃-NaHCO₃ and N₂/CO₂-aqueous solution of NaOH. A sintered powder plate is used as a gas distributor. Three parameters characterizing the mass transfer are identified and investigated with respect to pressure: the gas-liquid interfacial area a, the volumetric liquid side mass transfer coefficient k_La and the volumetric gas side mass transfer coefficient k_Ga. The gas-liquid absorption with chemical reaction is used and the mass transfer parameters are determined by using the model reaction between CO₂ and the aqueous solutions of Na₂CO₃-NaHCO₃ and NaOH. For a given gas mass flow rate, the interfacial area as well as the volumetric liquid mass transfer coefficient decrease with increasing operating pressure. However, for a given pressure, a and k_La increase with increasing gas mass flow rates. The mass transfer coefficient k_L is independent of pressure. Furthermore, the pressure increase results in a decrease of k_G and k_Ga for a given gas mass flow rate. The values of the interfacial area, which are obtained from both chemical systems are found to be different. These discrepancies are attributed to the choice of the liquid system in the absorption reaction model.