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.     

Modelling mass transfer in an aerated 0.2 m vessel agitated by Rushton, Phasejet and Combijet impellers

We assembled a set of models that allows investigation of local variables that are difficult to measure, validation of mechanistic physical models, and comparison of different numerical solutions. Population balances (PB) for bubbles were combined with local flow modelling in order to investigate G–L mass transfer in an air–water system. Performance of three different impeller geometries was investigated: Rushton (RT), Phasejet (PJ) and Combijet (CJ). Simulations were compared against experimental mixing intensity, gas hold-up, vessel-averaged volumetric mass transfer rates (k_La), and local bubble size distributions (BSDs).The simulations qualitatively predict k_La's with different impellers at the fully dispersed flow region and gave new insight on how k_La is formed and distributed in the stirred vessels. The used bubble breakage and coalescence models are able to describe both air–water and viscous non-Newtonian G–L mass transfer. Difference between experimental mass transfer rates of the three impellers was within experimental error, even trough the flow patterns, gas distribution, and local BSDs differ considerably. The population balance for bubbles was modelled in two different ways, with multiple size groups (MUSIGs) and with the bubble number density (BND) approach. MUSIG calculations took over twice as much computational time than BND, but there was little difference in the results. The Rushton turbine k_La was described with best accuracy, which is not surprising since most phenomenological models are fitted based on RT experiments. We suggest that these models should be validated over a wider range of vessel geometries and operating conditions.     

Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank. Part 2—parameter fitting and the use of the multiblock model for dense dispersions

In the previous part of this work (Chem. Eng. Sci. 54 (1999) 5887), a multiblock simulation model was developed in order to allow the close examination of different regions of a stirred tank for drop size distribution calculations. In this paper, that model is tested in a parameter fitting procedure. The drop breakage and coalescence parameters are fitted against drop size measurements from dense liquid-liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a stirred tank are used in the present model, the fundamental breakage and coalescence phenomena can be examined more closely. Furthermore, the present model is capable of predicting inhomogeneities occurring in a stirred tank. It is also to be considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is to use transient data of the measured drop size distribution as the impeller speed is changed. The other is to use time-averaged data measured at different locations of the stirred tank. It is shown in this paper that the different flow regions can be chosen from the CFD simulations in a straightforward manner. CFD flow simulation results can be used to select the flow regions when no experimentally obtained flow conditions are available. This is especially useful for non-standard vessels, such as reactors containing cooling coils. After fitting the parameters with a multiblock model, the population balance model can be rather easily incorporated into a commercial CFD program to investigate different flow conditions.     

搅拌槽内的气泡尺寸分布

在槽径分别为Φ０．２８７ｍ、Φ０．４９５ｍ、Φ１．１００ｍ三个几何相似的搅拌槽内，采用双电导探针法测定了搅拌槽内上、下循环区及叶轮区的气泡尺寸分布，研究了单位液体体积搅拌功率、表现气速及搅拌槽放大过程对气泡尺寸的影响规律以及气泡尺寸的空间分布规律，并得到了相应的经验关联式，为气－液搅拌槽的设计放大提供参考。     

Description of interaction processes in agitated liquid-liquid dispersions

Phenomenological models are proposed to describe drop breakup and coalescence in a turbulently agitated liquid-liquid dispersion. Based on these models, breakage and coalescence rate functions are developed and used to solve the general population balance equation describing drop interactions in a continuous flow vessel. Parameters of the models are evaluated by comparison with experimental data on drop size distributions and mixing frequencies obtained in a continuous flow vessel over a range of operating conditions. The favorable agreement between experimental observation and the model are encouraging that the model is suitable for predicting dispersion properties such as drop size distributions, interfacial areas and mixing frequencies.     

Gas-phase properties in stirred tank bioreactors

Bubble properties in stirred tank bioreactors equipped with standard radial flow Rushton turbines have been investigated. Bubble velocity patterns within a stirred tank reactor were derived from measured local bubble velocity distributions. Local information on specific interfacial areas, bubble number densities and bubble diameters together with local gas hold-ups, measured in a model medium at gas flow rates which are employed in practice, is presented. All measurements were performed with two new ultrasound pulse techniques which can be used in model as well as during real cultivation processes.     

Bubble swarm behaviour and gas absorption in non-newtonian fluids in sparged columns

Mean relative gas hold up, slip velocity, bubble size distribution, and volumetric mass transfer coefficient of oxygen were measured in sparged columns of highly viscous non-Newtonian fluids (CMC solutions) as a function of the gas flow rate, and CMC concentration (fluid consistency index k, and flow behaviour index n).By comparison of the measured bubble swarm velocities with those calculated by relations for single bubbles the bubble swarm behaviour was investigated. It could be shown that small bubbles in swarm have higher rising velocities than single bubbles, expecially in highly viscous media. Large single bubbles rise with high velocity due to the change of their shape caused by the swarm of the smaller bubbles. No large bubbles with spherical cap shape could be observed. The volumetric mass transfer coefficient decreases rapidly with increasing CMC-concentration.A comparison of the volumetric mass transfer coefficients with those measured in mechanically agitated vessels indicates, that the performance of sparged columns is comparable with the one of agitated vessels. Because of their lower energy requirement sparged columns are more economical than mechanically agitated vessels. It is possible to improve the performance of sparged columns by the redispersion of large bubbles in a multistage equipment.     

CFD simulation of mixing in tall gas-liquid stirred vessel: Role of local flow patterns

In this work, we have used the computational fluid dynamics (CFD)-based models to investigate the gas-liquid flows generated by three down-pumping pitched blade turbines. A two-fluid model along with the standard k-ε turbulence model was used to simulate the dispersed gas-liquid flow in a stirred vessel. Appropriate drag corrections to account for bulk turbulence [Khopkar and Ranade, 2005. CFD simulation of gas-liquid flow in a stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal, accepted for publication] were developed to correctly simulate different flow regimes. The computational snapshot approach was used to simulate impeller rotation and was implemented in the commercial CFD code, FLUENT4.5 (of Fluent. Inc., USA). The computational model has successfully captured the flow regimes as observed during experiments. The particle trajectory simulations were then carried out to examine the influence of the different flow regimes on the circulation time distribution. The model predictions were verified by comparing the predicted results with the experimental data of [Shewale and Pandit, 2006. Studies in multiple impeller agitated gas-liquid contactors. Chemical Engineering Science 61, 489-504]. The computational model and results discussed in this study would be useful for explaining the implications local flow patterns on the mixing process and extending the applications of CFD models for simulating large multiphase stirred reactors.     

Experimental and modelling study of gas dispersion in a double turbine stirred tank

Gas dispersion in a double turbine stirred tank is experimentally characterised by measuring local gas holdups and local bubble size distributions throughout the tank, for three liquid media: tap water, aqueous sulphate solution and aqueous sulphate solution with PEG. For all these media, bubble coalescence generally prevails over breakage. Where average bubble size decreases, this can be attributed to the difference in slip velocity between different sized bubbles. Most of the coalescence takes place in the turbine discharge stream.A compartment model that takes into account the combined effect of bubble coalescence and breakage is used to simulate gas dispersion. The model predicts spatial distribution of gas holdup and of average bubble size, with average bubble size at the turbines as an input. Reasonable agreement between experiment and simulation is achieved with optimisation of two parameters, one affecting mainly the slip velocity, the other related mainly to the bubble coalescence/breakage balance. Different sets of parameters are required for each of the three liquid systems under study, but are independent of stirring/aeration conditions. The model only fails to simulate the smaller average bubble diameters at the bottom of the tank.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

UTILIZATION OF POPULATION BALANCES IN SIMULATION OF LIQUID-LIQUID SYSTEMS IN MIXED TANKS

A simulation model has been developed to model drop populations in a mixed tank. A multiblock mixed tank model has been used with the drop population balance equations developed in the literature. The drop breakage and coalescence functions used in the population balance model take into account the local turbulent energy dissipation values. The drop breakage and coalescence function parameters are fitted against drop size measurements from dense liquid-liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a mixed tank are used in the present model, the fundamental breakage and coalescence phenomena can be taken into closer examination. Furthermore, the present model is capable of predicting inhomogeneities occurring in a mixed tank. It is also considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is the transient data of the measured drop size distribution as the impeller speed is changed. The other is the time-averaged data measured at different locations of the mixed tank. Different flow regions can be chosen from direct measurements or from the CFD simulations in a straightforward manner. CFD flow simulation results can be used when no experimentally obtained flow conditions are available. This is especially useful for nonstandard vessels, such as reactors containing cooling coils.     

Probability density functions for bubble size distribution in air–water systems in stirred tanks

Bubble size distribution (BSD) is relevant to the design of gas–liquid systems, as it determines the interfacial area available in heat and mass transfer processes. Although data on BSD in stirred aerated tanks are available, a systematic comparison of alternative modeling functions for these data is lacking. In this work, BSDs obtained in air–water dispersions in a stirred aerated tank with a Rushton turbine and BSDs available in the literature for similar systems were modeled by 14 empirical probability density functions (PDFs). It was found that both the distribution of Nukiyama–Tanasawa with three adjustable parameters and the Rosin–Rammler distribution with two adjustable parameters reasonably fit original and literature BSDs. It is also concluded that it is possible to correlate the PDF parameters with the power dissipated by the agitator in the liquid phase, allowing the BSD to be modeled with only two parameters in a range of dissipated power from 0.5 to 2.3?kW/m³. BSDs thus modeled provide good predictions of average bubble size.     

Regional Mean Bubble Diameters and Gas Holdup in Agitated Gas‐Liquid Contactors

Gas‐liquid contacting in mechanically agitated vessels is widely used in the process industry. Bubble size measurements at different flow regions in the vessel provide useful information for the mechanisms of gas dispersion and gas‐liquid flow. In this work, bubble size distributions and distributions of Sauter mean bubble diameters at four different regions in air‐water and air‐NaCl solution systems agitated by a six‐blade disk turbine are measured by using the photographic method. The effects of gassing rate, impeller speed and electrolyte presence in the system have been examined.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

Drop-breakage in agitated liquid—liquid dispersions

Experimental data from batch vessels on cumulative volumetric drop-size distributions at various times are shown to yield useful information on probabilities of droplet-breakup as a function of drop-size. Such information is sufficient for a priori prediction of drop-sizes in agitated dispersions in batch and continuous vessels. It may also be useful in predicting heat and/or mass transfer in liquid—liquid dispersions by accounting for the simultaneity of transport processes from individual drops and droplet breakage processes.     

CFD simulation of gas-liquid contacting in tubular reactors

Gas-liquid contacting in tubular reactors was simulated using an Eulerian-Eulerian CFD approach in which accurate interphase momentum closure relations are incorporated, bubble-induced turbulence is accounted for, and population balance equations are used to describe bubble breakage and coalescence. The ability of two breakup kernels (Luo, H., Svendsen, H.F., 1996. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42, 1225-1233; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) and three coalescence kernels (Prince, M.J., Blanch, H.W., 1990. Bubble coalescence and breakup in air sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499; Luo, H., 1993. Coalescence, breakup and liquid recirculation in bubble column reactors. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) to accurately predict several flow parameters in pipe flow was tested.Good agreement between simulation and experimental results (radial profiles of gas holdup, turbulence intensity, and local Sauter bubble diameter) was achieved without the use of empirically derived relationships (such as Drift flux) by adjusting a single parameter which accounts for the deviation in the coalescence behaviour of tap water from that of pure water. The approach adopted in this investigation may thus be applicable to more complex hydrodynamic situations such as those encountered in mechanically agitated tanks and the need for extensive experimental testing may be replaced by single measurement of the effect interfacial properties have on coalescence rates.     

搅拌槽内粘稠物系中气液相间氧传递

以发酵罐中气液相间氧传递为背景，考察了搅拌槽内搅拌器形式、物系流变性质、通气搅拌操作条件等对假塑性粘稠物系中氧传递过程的影响。结果表明，这些因素主要通过改变气体分散状态和相间传质面积来影响氧传递速率。根据气泡在搅拌槽内不均匀分布现象，多层搅拌下气液相间传质过程可以用气泡运动分区分布模型来描述。它说明了采用轴向流桨和涡轮桨组合的搅拌形式在氧传递方面的优越性，为强化发酵罐中供氧指明一条有效途径     

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.