Effect of interfacial mass transfer on the dispersion in segmented flow in straight capillaries

The effect of interfacial mass transfer on the extent of dispersion in liquid‐liquid segmented flow in straight capillaries is studied. In the absence of interfacial mass transfer, dispersion coefficient was seen to go through a minimum with increasing flow rates. In the presence of mass transfer, physicochemical properties of both the phases and slug lengths were seen to vary along the capillary length. The extent of dispersion was always higher in the presence of interfacial mass transfer. The predictions using axial dispersion model deviated noticeably for larger capillaries as the model does not account for varying buoyancy, dynamic contacting, and Marangoni convection. Simulations of a first‐order interfacial reaction considering varying slug lengths showed a significant change in optimum operating parameters than the conventional approach. A special case of “drop‐on‐demand” type of controlled two‐phase flow in capillaries was also studied. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4294–4308, 2015     

毛细管中泰勒流液侧传质特性及其强化机理的CFD模拟

采用计算流体力学（CFD）的方法,研究了圆管中泰勒流的液侧传质特性,分析了泰勒气泡上局部传质特性,并研究了气泡上升速度、液膜长度和液栓长度对液膜处和气泡半球帽处平均传质系数的影响。结果表明,泰勒气泡表面局部传质系数存在3个峰值,液膜处的平均传质系数随气泡上升速度增大显著增大,随液膜长度增大而减小,而半球帽处的平均传质系数随气泡速度和液膜长度的增大变化较小,即膜接触时间增加时,液膜处的传质系数降低,而半球帽处传质系数变化较小。另外,引入场协同原则对单元胞内速度场和浓度场进行分析,解释了局部传质特性及强化机理。最后,给出了分别预测短和长膜接触时间下泰勒流液侧体积传质系数的关联式,该式在较宽的管径尺度范围（0.25～3 mm）内的预测误差在±20%以内。     

CFD simulations of wall mass transfer for Taylor flow in circular capillaries

Computational fluid dynamics is used to investigate the mass transfer from the liquid phase to the channel wall for Taylor flow of bubbles rising in circular capillaries. The separate influences of the Taylor bubble rise velocity, unit cell length, gas holdup, and liquid diffusivity on mass transfer were investigated for capillaries of 1.5, 2 and 3 mm diameter. A correlation is proposed for estimation of the wall mass transfer coefficient and this correlation has been tested against published experimental data.     

Pressure drop in monolith reactors

A theoretical model for the computation of pressure drop in bubble-train flow inside capillaries of square cross-section was developed. The model is based on three contributions: hydrostatics, viscous pressure drop, and capillary pressure drop. Capillary pressure drop is related to the shape of the fronts and ends of the bubbles. The model does not include entrance or exit effects, has no adjustable parameters, and agrees very well with available experimental data.

For a given set of flow parameters, bubble velocity and liquid slug average velocity are computed as a function of gas and liquid superficial velocities. The length of the unit cell determines the number of bubbles inside the capillary for a given flow situation. The model requires experimental information of average bubble lengths to compute the length of a unit cell consisting of a bubble and a liquid slug.

The three pressure contributions for a unit capillary length are linear functions of the number of bubbles inside the capillary. The length of the bubbles in bubble-train flows is a critical parameter in the computation of pressure drop.     

CFD approaches for the simulation of hydrodynamics and heat transfer in Taylor flow

Previous studies on heat and mass transfer in the Taylor flow regime in microchannels have shown the transport (heat/mass) rates to be dependent on the length of the liquid slug. In order to understand the effect of slug length on transport rates and to have a one-to-one comparison with experimental data, a computational approach is required to simulate flows with liquid slugs and bubbles of controlled lengths.Here we describe and benchmark two approaches. The first, and conceptually simplest, is to generate bubbles and slugs in a long tube using a time-dependent boundary condition. In the second method, the flow and heat transfer in a single unit cell, consisting of a bubble surrounded by liquid slugs, is solved in a frame of reference moving with the bubble velocity. Both methods were implemented in ANSYS-Fluent.Simulations for a two-phase (liquid-only) Reynolds number of 713, Capillary number of 0.004 and void fraction of 0.366 for nitrogen-water flow were performed to compare the two techniques. There was a very large difference between the required computational mesh sizes and times for the two methods, with a wall clock time of 38 h on a single processor for the moving domain compared with 1460 h using four processors for the stationary domain approach. In addition, for a constant wall heat flux boundary condition, even with 14 bubbles present in a long tube thermal development was not achieved. The hydrodynamic and heat transfer results obtained from the two approaches were found to be very similar to each other and with results from our earlier verification and validation studies, giving a high degree of confidence in the implementation of both methods.     

水平管内气液段塞流液塞长度发展规律的实验和模拟研究

In petroleum industry, the slug flow is a fre-quently encountered flow regime in multiphase flowpipeline. For pipeline designers, the liquid slug lengthdistribution is important for the proper design ofdownstream facilities, such as slug catcher and sepa-ration system. However, for its transient and unsteadynature, it is a great challenge for engineers to correctlypredict the flow parameters of slug flow, especiallythe maximum liquid slug length. The unit cell model for slug flow in horizontal…     

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.     

The pressure drop experiment to determine slug lengths in multiphase monoliths

The length of the liquid slugs, that separate the elongated bubbles in Taylor flow, is an important parameter for mass transfer, flow stability and pressure drop in capillary microchannels. In this work, pressure drop measurements are used to determine the length of slug in Taylor flow in downflow monoliths. The method is sensitive if the slugs are relatively short, less than 10 times the channel diameter. The pressure drop measurements are a cheap and fast alternative to tomographic or electric methods. Experiments using different distributors indicate that the slug length varies significantly with changes in the hydrodynamics in the feed section of the monoliths. Slug length correlations that are based on parameters inside the channels can therefore not safely be used for a different setup. As a result, the slug length should be measured in each experimental setup, which makes a inexpensive and robust method to do so very welcome.     

Design and operation of gas–liquid slug flow in miniaturized channels for rapid mass transfer

The influences of operating parameters such as channel size, flow rate, and void fraction on the mass transfer rate in the gas–liquid slug flow are investigated to establish a design method to determine the parameters for rapid mass transfer. From the experimental results, the turnover index, including the slug linear velocity, its length, and the channel size that represents the turnover frequency of the internal circulation flow, is proposed. For PTFE tube in which no liquid film exists in slug flow, a master curve is derived from the relationship between the mass transfer coefficient and the turnover index. For each channel material, the Sherwood number is also roughly correlated with the Peclet number. These correlations make it possible to arbitrarily determine a set of operating parameters to achieve the desired mass transfer rate. However, the turnover index and the Peclet number include the slug length, which cannot be controlled directly. The relationship between the slug length and the operating parameters is also investigated. The slug volume mainly depends on the inner diameter (i.d.) of a union tee. At a fixed union tee i.d., the slug length is controlled through the exit i.d. of the channel connected to the union tee and the void fraction. Thus, the final slug length depends on the union tee and exit channel inner diameters. At low flow rates, the gas and liquid collision angle is significant in determining the slug length.     

A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels

In this paper we present a new method for numerical simulation of conjugate mass transfer of a dilute species with resistance in both phases and an arbitrary equilibrium distribution coefficient. The method is based on the volume-of-fluid technique and accounts for the concentration jump at the interface by transforming the discontinuous physical concentration field into a continuous numerical one. The method is validated by several test problems and is used to investigate the mass transfer in upward bubble train flow within square and rectangular channels. Computations are performed for a single flow unit cell and a channel hydraulic diameter of 2 mm. The simulations consider the transfer of a dilute species from the dispersed gas into the continuous liquid phase. Optionally, the mass transfer is accompanied by a first-order homogeneous chemical reaction in the liquid phase or a first-order heterogeneous reaction at the channel walls. The results of this numerical study are qualitative in nature. First, because periodic boundary conditions in axial direction are not only used for the velocity field but also for the concentration field and second, because the species diffusivity in the liquid phase is arbitrarily increased so that the liquid phase Schmidt number is 0.8 and the thickness of the concentration and momentum boundary layer is similar. Two different equilibrium distribution coefficients are considered, one where the mass transfer is from high to low concentration, and one where it is vice versa. The numerical study focuses on the influence of the unit cell length, liquid slug length and channel aspect ratio on mass transfer. It is found that for the exposure times investigated the liquid film between the bubble and the wall is saturated and the mass transfer occurs by the major part through the bubble front and rear so that short unit cells are more efficient for mass transfer. Similar observations are made for the homogeneous reaction and for the heterogeneous reaction when the reaction is slow. In case of a fast heterogeneous reaction and when the main resistance to mass transfer is in the gas phase, it appears that for square channels long unit cells are more efficient, while large aspect ratio rectangular channels are more efficient than square channels, suggesting that for these conditions they might be more appropriate for use in monolithic catalysts.     

Hydrogenation of 2‐ethylanthraquinone under Taylor flow in single square channel monolith reactors

The hydrogenation of 2‐ethylanthraquinone (EAQ) to 2‐ethylanthrahydroquinone (EAHQ) was carried out under Taylor flow in single square channel monolith reactors. The two opening ends of opaque reaction channel were connected with two circular transparent quartz‐glass capillaries, where Taylor flow hydrodynamics parameters were measured and further used to obtain practical flow state of reactants in square reaction channels. A carefully designed gas‐liquid inlet mixer was used to supply steady gas bubbles and liquid slugs with desired length. The effects of various operating parameters, involving superficial gas velocity, superficial liquid velocity, gas bubble length, liquid slug length, two‐phase velocity and temperature, on EAQ conversion were systematically researched. Based on EAQ conversion, experimental overall volumetric mass transfer coefficients were calculated, and also studied as functions of various parameters as mentioned earlier. The film model, penetration model, and existing semi‐empirical formula were used to predict gas‐solid, gas‐liquid, and liquid‐solid volumetric mass transfer coefficients in Taylor flow, respectively. The predicted overall volumetric mass transfer coefficients agreed well with the experimental ones. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

壁面润湿性对微通道内二氧化碳-水两相流流动及传质性能的影响

在1 mm×1 mm矩形截面下微通道内,以二氧化碳-水为工作流体,研究壁面润湿性和气液表观流速对气-液两相流型和气液传质的影响,并研究了气、液表观流速对弹状流流体力学性质的影响。在亲水微通道中观测到了泡状流、泡状-弹状流、弹状流;在疏水微通道中观测到了非对称弹状流、拉长的非对称弹状流、分层流。实验表明亲水微通道中弹状流区域下气泡长度大体上随气相表观流速的增大而增大,随液相表观流速的增大而减小;液弹长度大体上随气相表观流速的增大而减小,随液相表观流速的增大先增大后减小;液侧体积传质系数k_La均随气、液相表观流速的增大而增大,随通道壁面润湿性的增强而增大。     

Hydrodynamics and local mass transfer characterization under gas–liquid–liquid slug flow in a rectangular microchannel

Gas–liquid–liquid three-phase slug flow was generated in a glass microreactor with rectangular microchannel, where aqueous slugs were distinguished by relative positions to air bubbles and organic droplets. Oxygen from bubbles reacted with resazurin in slugs, leading to prominent color changes, which was used to quantify mass transfer performance. The development of slug length indicated a film flow through the corner between bubbles and the channel wall, where the aqueous phase was saturated with oxygen transferred from bubble body. This film flow results in the highest equivalent oxygen concentration within the slug led by a bubble and followed by a droplet. The three-phase slug flow subregime with alternate bubble and droplet was found to benefit the overall mass transfer performance most. These results provide insights into a precise manipulation of gas–liquid–liquid slug flow in microreactors and the relevant mass transfer behavior thereof.     

下倾管中段塞流液塞长度波动的非线性分析

利用非线性分析技术中的分形理论在较宽的流速范围内对下倾管中空气-水段塞流的液塞长度波动特性进行了研究.结果表明,下倾管中段塞流的液塞长度符合对数正态分布,其波动是对初始条件敏感的混沌振荡,且具有持久性.通过对不同液相折算速度下的液塞长度波动特性的分析发现,液相折算速度较大时,随着混合速度的增加,液塞长度波动的混沌程度增加;而液相折算速度较小时,随着混合速度的增加,液塞长度波动的混沌程度减小.管线下倾角越大,液塞长度波动的长程相关性越好.     

下倾管中活塞流液塞长度波动特性

通过采集下倾管中活塞流的差压信号,应用互相关法分析得到液塞长度时间序列.利用统计理论与分形理论分析液塞长度时间序列来揭示液塞长度波动特性.结果表明：气相折算速度对液塞长度的影响远大于液相折算速度.液相折算速度较大时,随着混合速度的增加,液塞长度波动的混沌程度增加;而液相折算速度较小时,随着混合速度的增加,液塞长度波动的混沌程度减小.在管线下倾角较大的情况下,液塞长度分布集中在较小的范围内.管线下倾角越大,液塞长度波动的长程相关性越好.     

An experimental study of air-water Taylor flow and mass transfer inside square microchannels

Flow and mass transfer properties under air-water Taylor flow have been investigated in two square microchannels with hydraulic diameters of 400 and 200 μm. Experimental data on Taylor bubble velocity, pressure drop and liquid side volumetric mass transfer coefficient (k_La) have been presented. It was shown that the measured Taylor bubble velocity in square microchannels could be well interpreted based upon an approximate measurement of the liquid film profile therein. Then, the obtained two-phase frictional pressure drop values in both microchannels were found to be significantly higher than the predictions of the correlation proposed by Kreutzer et al. [2005b. Inertial and interfacial effects on pressure drop of Taylor flow in capillaries. A.I.Ch.E. Journal 51, 2428-2440] when the liquid slug was very short, which can be explained by the inadequacy of their correlation to describe the excess pressure drop caused by the strong inner circulation in such short liquid slugs. An appropriate modification has been made to this correlation in order to improve its applicability in microchannels. Finally, the experimental (k_La) values in the microchannel with hydraulic diameter of 400 μm were found to be in poor agreement with those predicted by the existing correlations proposed for capillaries with diameters of several millimeters. The observed deviation was mainly due to the fact that mass transfer experiments in this microchannel actually corresponded to the case of short film contact time and rather poor mixing between the liquid film and the liquid slug, which was not in accordance with mass transfer assumptions associated with these correlations. A new empirical correlation has been proposed to describe mass transfer data in this microchannel.     

CFD simulations of mass transfer from Taylor bubbles rising in circular capillaries

Computational Fluid Dynamics (CFD) is used to investigate mass transfer from Taylor bubbles to the liquid phase in circular capillaries. The liquid phase volumetric mass transfer coefficient k_La was determined from CFD simulations of Taylor bubbles in upflow, using periodic boundary conditions. The separate influences of the bubble rise velocity, unit cell length, film thickness, film length, and liquid diffusivity on k_La were investigated for capillaries of 1.5, 2 and diameter. The mass transfer from the Taylor bubble is the sum of the contributions of the two bubble caps, and the film surrounding the bubble. The Higbie penetration model is used to describe the mass transfer from the two hemispherical caps. The unsteady-state diffusion model of Pigford is used to describe the mass transfer to the downward flowing liquid film. The developed model for k_La is in good agreement with the CFD simulated values, and provides a practical method for estimating mass transfer coefficients in monolith reactors.     

Gravity-driven unsteady-state slug fall in capillaries – modeling and experimental verification

Infiltration of liquid droplets into dry porous media often occurs in industrial and natural settings, which has been widely modeled as liquid slug flow in capillaries. This work focuses on gravity-driven slug motion in vertically oriented capillary tubes. To model the propagation and evolution of the slug, a mathematical model was set on the basis of Newton’s second law and the law of conservation of mass. The model includes terms like slug’s inertia, deposited film, dynamic contact angle, slug’s advancing and receding menisci hysteresis, and it particularly highlights the direct effect of the trailing film on the change of slug mass. In order to verify this model, experiments on water slug with different lengths of initial slugs were conducted in two Pyrex glass capillaries that are partially wettable. It was found that both the length and the velocity of the slug vary during the slug motion in every case. Then the experimental results were simulated with the established model by carefully presetting two fitting parameters, α_a and α_h, that are related to the dynamic contact angle at the advancing meniscus and the thickness of the trailing film, respectively. The good agreement between the experimental and theoretical results demonstrates that the present model is capable of describing the unsteady-state dynamics of slugs fall in porous media.     

水平管道油气二相段塞流稳态流动特性

使用通过自行设计并搭建的实验装置,对水平管道油气二相段塞流稳态流动特性进行了实验研究。采用压力信号互相关方法测量了段塞流平均液塞速度,通过分析得到了液塞速度、液塞长度和液塞频率随气、液相折算速度的变化规律。结果表明,当液相折算速度恒定时,随着气相折算速度的增大,液塞速度基本上呈线性增大,而液塞长度呈双曲线减小;当气相折算速度恒定时,随着液相折算速度的增大,液塞频率基本呈线性增大,而液塞长度呈双曲线减小。