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.     

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.     

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.     

Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel

Bubble breakage and coalescence phenomena and multicomponent gas-liquid mass transfer were studied in a Rushton turbine agitated vessel. Local bubble size distributions (BSD) were measured from air-tap water system at several agitation conditions with capillary suction probe (CSP) technique. The CSP was compared to the digital imaging (DI) and phase Doppler anemometry (PDA) techniques in a stirred vessel. The volumetric BSDs between the CSP and DI were in agreement, but number BSDs showed notable deviation. The limitations of measurement techniques seem to be the main reason.A multiblock stirred tank model with discretized population balances for bubbles and two-film Maxwell-Stefan multicomponent mass transfer between gas and liquid was created for the agitated vessel. The model considers local mass transfer conditions in the vessel and is simple enough for the mathematical optimization of unknown model parameters. Unknown parameters in the mechanistic bubble breakage and coalescence models were fitted against measured local BSDs. After this, a parameter in the liquid film mass transfer correlation was adjusted against absorption and desorption experiments of oxygen. Local gas-liquid mass transfer areas were calculated from the population balance model. The simulations with the validated models show good agreement against experiments. On the other hand, the fitted parameters deviate from the theoretical values, which emphasizes the need of model validation against accurate experiments. Due to their fundamental character and the validation process, the fitted models seem to be useful tools for the design and scale-up of agitated gas-liquid reactors.     

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。     

Study on gas-liquid flow characteristics in stirred tank with dual-impeller based on CFD-PBM coupled model

Study on gas-liquid flow in stirred tank with two combinations of dual-impeller (six-bent-bladed turbine(6BT)+six-inclined-blade down-pumping turbine (6ITD),the six-bent-bladed turbine (6BT)+six-inclined-blade up-pumping turbine (6ITU)) was conducted using computational fluid dynamics (CFD) and popula-tion balance model (PBM) (CFD-PBM) coupled model.The local bubble size was captured by particle image velocimetry (PIV) measurement.The gas holdup,bubble size distribution and gas-liquid interfacial area were explored at different conditions through numerical simulation.The results showed that the 4 mm bubbles accounted for the largest proportion of 33％ at the gas flow rates Q =0.76 m3·h-1 and 22％ at Q =1.52 m3·h-1 for combined impeller of 6BT + 6ITU,while the bubbles of 4.7 mm and 5.5 mm were the largest proportion for 6BT + 6ITD combination,i.e.25％ at Q =0.76 m3·h-1 and 22％ at Q =1.52 m3·h-1,respectively,which indicated that 6BT + 6ITU could reduce bubble size effectively and promote gas dispersion.In addition,the gas holdup around impellers was increased obviously with the speed compared with gas flow rate.So it was concluded that 6ITU impeller could be more conductive to the bubble dispersion with more uniform bubble size,which embodied the advantages of 6BT + 6ITU combination in gas-liquid mixing.     

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.     

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.     

气液鼓泡塔的CFD-PBM耦合模拟：离散法与QMOM方法的对比

采用CFD-PBM耦合方法，对高表观气速下的气?液鼓泡塔进行模拟，得到气含率、轴向液速及气泡尺寸。系统性对比求解群平衡方程(PBE)的不同方法：离散法(20 bins)和QMOM(包括四阶QMOM和六阶QMOM)。模拟结果与文献中的实验数据的对比结果表明，离散法和QMOM均能合理预测气含率、轴向液速、平均气泡大小和气泡尺寸分布。但QMOM比离散法节约2~3倍的计算成本。对于QMOM，使用四个矩能准确描述气相的演化。使用四阶QMOM和六阶QMOM得到的结果非常相似。利用QMOM的低阶矩可以快速有效地重构出单峰气泡尺寸分布。     

Population balance modelling for bubbly flows with heat and mass transfer

Population balance equations combined with a three-dimensional two-fluid model are employed to predict bubbly flows with the presence of heat and mass transfer processes. Subcooled boiling flow belongs to this specific category of bubbly flows is considered. The MUSIG (MUltiple-SIze-Group) model implemented in CFX4.4 is further developed to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements near the test channel exit is made for the radial distribution of the bubble Sauter diameter, void fraction, interfacial area concentration and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison was also performed against existing boiling model in CFX4.4 and the modified model developed in our previous work (Int. J. Heat Mass Transfer 45 (2002) 1197). Good agreement is better achieved with the local radial bubble Sauter diameter, void fraction, interfacial area concentration and liquid velocity profiles against measurements using the newly formulated MUSIG boiling model over the simpler boiling models. However, significant weakness of the model is still evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the model by the consideration of additional momentum equations or an algebraic slip model to account for bubble separation.     

Coalescence efficiency of bubbles in bubble columns

Bubble size distribution was modelled by employing the population balance equation (PBE). All three bubble coalescence mechanisms (turbulence, buoyancy and laminar shear) and the main bubble breakup mechanism (breakup due to turbulent eddies) were considered in the model. Local bubble size distributions at the top and bottom of the column were obtained by solving this PBE. The results were compared with the experimental data for seven independent multiphase systems (water/air, isomax diesel/air, kerosene/air and four other liquid mixture/air) at two diverse gas velocities. The experimental adjustable constant in the coalescence efficiency function was determined by fitting the population balance to the experimental bubble size distributions. An empirical correlation was proposed for the coalescence efficiency by the dimensional analysis, which includes Reynolds and Weber numbers. © 2011 Canadian Society for Chemical Engineering     

Bubble size fractal dimension,gas holdup,and mass transfer in a bubble column with dual internals

As the scale of residual oil treatment increases and cleaner production improves in China, slurry bubble column reactors face many challenges and opportunities for residual oil hydrogenation technology. The internals development is critical to adapt the long-term stable operation. In this paper, the volumetric mass transfer coefficient, gas holdup and bubble size in a gas–liquid up-flow column are studied with two kinds of internals. The gas holdup and volumetric mass transfer coefficient increase by 120% and 42% when the fractal dimension of bubbles increases from 0.56 to 2.56, respectively. The enhanced mass transfer processing may improve the coke suppression ability in the slurry reactor for residual oil treatment. The results can be useful for the exploration of reacting conditions, scale-up strategies, and oil adaptability. This work is valuable for the design of reactor systems and technological processes.     

A CFD-PBM coupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media

To account for the effect of liquid viscosity, the bubble breakup model considering turbulent eddy collision based on the inertial subrange turbulent spectrum was extended to the entire turbulent spectrum that included the energy-containing, inertial, and energy-dissipation subranges. The computational fluid dynamics-population balance model coupled model was modified to include this extended bubble breakup model for simulations of a bubble column. The effect of turbulent energy spectrum on the bubble breakup and hydrodynamic behaviors was studied in a bubble column under different liquid viscosities. The results showed that when the liquid viscosity was <80 mPa s, the bubble breakup and hydrodynamics were almost independent on the turbulent spectrum. At liquid viscosity >80 mPa s, the bubble breakup rate and gas holdup were significantly under-predicted when the inertial turbulent spectrum was used, and when using the entire turbulent spectrum the predictions were more consistent with experimental data.     

偏氟乙烯乳液聚合的气液传质效果影响因素研究

推导了表征气液传质效果的K值计算方法,并研究了聚合釜装填量、搅拌桨型和转速等因素对气液传质效果的影响。结果表明,随着聚合釜装填量和搅拌转速的增大,K值增大,气液传质效果提高;在搅拌转速大于500r/min的情况下,桨型采用上层二叶平桨、下层二叶斜桨的方式明显比单层的二叶斜桨或二叶平桨的K值大,气液传质效果好。确定了5L釜偏氟乙烯(VDF)乳液聚合必需的良好搅拌效果的条件:装填量3L,搅拌转速700r/min,桨型采用上层二叶平桨和下层二叶斜桨;VDF聚合速率达到115g/(L·h),合成出固体质量分数20%、粒径分布窄、稳定性好的聚偏氟乙烯(PVDF)乳液。     

An improved dynamic combined model for evaluating the mass transfer performances in extraction columns

Dispersed phase droplet behavior research is very important for the design and scaling up of extraction columns. Recently, the droplet velocities at high holdup were found to be uniform, which means the conventional concept of forward mixing needs correction. The drop size distribution only influences the mass transfer coefficients and not the residence time distribution of droplets. In this work, an improved dynamic combined model considering the influence of drop size distribution has been developed, by which the axial mixing can be easily evaluated using a one-dimension search. A typical experimental system of 30% tributyl phosphate (TBP) (in kerosene)-nitric acid-water with interfacial tension of 0.00995 N/m was used to investigate the mass transfer performances in a coalescence-dispersion pulsed-sieve-plate extraction column (CDPSEC) with 150 mm in diameter. The two-point dynamic method was used to obtain the stimulus-response curves. With these results, the axial mixing in the CDPSEC was evaluated. The calculated results showed that the response curves could be predicted by the dynamic combined model with a deviation less than 0.001. This model has marked advantages over previous models in literature because of its accuracy, simple boundary conditions, and single parameter optimization.     

Linear stability analysis of a two-fluid model for air-water bubble columns

Linear stability analysis is performed for the two-dimensional, two-fluid model for gas-liquid flow applied in our previous computational study of bubble columns [Monahan, S.M., Vitankar, V.S., Fox, R.O., 2005. CFD predictions for flow-regime transitions in bubble columns. A.I.Ch.E. Journal 51, 1897-1923]. The growth rate and the velocity of propagation for a small-amplitude disturbance wave are shown to be highly dependent on the wave number, the direction of propagation, and the two-fluid model parameters. Two types of vertical instabilities are identified: one corresponding to the classical analysis of Jackson [1963. The mechanics of fluidized beds. I: the stability of the state of uniform fluidization. Transactions of the Institution of Chemical Engineers 41, 13-21] for the one-dimensional model, and the other due to a second pair of roots to the characteristic equation of the linearized two-dimensional model. Numerical simulations keeping one type or the other of the roots stable (or unstable) show distinctly different dynamics and suggest that large-scale instabilities seen experimentally may be associated with the second type of instability. The latter leads to instability in the horizontal velocities and is associated with a positive lift coefficient in flows without mean shear in the presence of isotropic bubble-bubble interactions (i.e., “bubble pressure”). This instability is thus different than previously reported instabilities due to negative lift or cooperative/hindered rise.     

Revisiting Basics of kLa Dependency on Aeration in Bubble Columns: a Is Surprisingly Stable

A comprehensive experimental characterization of a small-scale bubble column bioreactor (60 mL) is presented. Bubble size distribution (BSD), gas holdup, and k_La were determined for different types of liquids, relevant fermentation conditions and superficial gas velocities u_G. The specific interfacial area a and liquid mass transfer coefficient k_L have been identified independent of each other to unravel their individual impact on k_La. Results show that increasing u_G leads to larger bubbles and higher gas holdup. As both parameters influence a in opposite ways, no increase of a with u_G is found. Furthermore, k_L increases with increasing bubble size outlining that improved oxygen transfer is not the result of higher a but of risen k_L instead. The results build the foundation for further simulative investigations.