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.     

Mass transfer from Taylor bubbles rising in single capillaries

Gas-liquid mass transfer from Taylor bubbles rising in 1, 2 and 3 mm diameter capillaries of circular and square cross-sections was investigated for air-water system. The liquid-phase volumetric mass transfer coefficient k_La was obtained from experimental oxygen absorption dynamics. The experimental k_La values are in good agreement with the model developed by van Baten and Krishna (2004. Chemical Engineering Science 59, 2535-2545), with the additional assumption that the dominant mass transfer contribution is to the film surrounding the bubble.     

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。     

垂直管内弹状气泡上升时的壁面传质

Wall-liquid mass transfer for Taylor bubbles rising through liquid column in vertical tubes is an important and fundamental topic in industrial processes.In this work,the characteristics of wall-liquid mass transfer for this special case of slug flow were studied experimentally by limiting diffusion current technique (LDCT). Based on the experimental results and the analysis of hydrodynamic mechanisms,it was proposed that four different zones exist,i.e.the laminar falling film zone,the turbulent falling film zone,the wake region and the remaining liquid slug zone.The corresponding correlations for all these zones were developed.     

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.     

Taylor dispersion in finite-length capillaries

The solute transport in a core-annular geometry is studied. A Newtonian or non-Newtonian (i.e., power-law) liquid flows through the core, while the solute can exchange between the liquid and the surrounding tissue. The permeability of the phase interface depends on the nature of the solute, i.e., relatively low for lipids and macromolecules but high for ions and gases. We analyse the moment’s equations of the residence time distribution (RTD). The solution of the equation for the second moment provides the exact formula for the Taylor dispersion coefficient. Unlike previous studies using a perturbation procedure where coefficient of axial dispersion cannot be defined at low permeability, the current study gives Taylor coefficient of dispersion for any value of the permeability. It is found that the coefficient in shear-thinning fluid is lower than in the Newtonian one, although the relative importance of non-Newtonian effects decreases when other factors, e.g. inter-phase transport and solubility, become dominant. The equations for the higher moments are analysed and the general structure of the solution is obtained in the form of integrals, which can be easily evaluated numerically. When the analysis is applied to solute transport between capillaries and surrounding tissues, it is shown that the classic Taylor expression does not describe dispersion of solute, e.g. glucose and albumin, in the capillary, except in situations where the Péclet number is very low. For the range of parameters typical for microvascular circulation in tissues, the higher moments play an important role and need to be considered.     

Gas–liquid mass transfer of aqueous Taylor flow in monoliths

The gas–liquid mass transfer of a monolith operating in the Taylor flow regime is presented. Mass transfer measurements are compared with a literature model derived for single capillaries. The comparison resulted in a prediction of the unit cell length (gasbubble+liquidslug). Independent measurements of the liquid slug length showed that the predicted unit cell length is close to the measured ones. This leads to the conclusion that mass transfer models for single capillaries may indeed be used for monoliths. Additionally, it is shown that the liquid slug length may also be estimated from pressure drop measurements.     

CFD modeling of pervaporative mass transfer in the boundary layer

Modeling mass transfer in the liquid boundary layer accounting for concentration polarization in pervaporation (PV) is particularly challenging since there is no practical way of experimentally determining solute concentration at the membrane surface. We have developed a computational fluid dynamics (CFD) approach to describe not only velocity distribution but also concentration profile in the liquid boundary layer of a slit membrane channel. The satisfactoriness of the numerical methodology used in CFD for obtaining concentration profiles were verified using a classic diffusion problem with its known analytical solution. The overall mass transfer coefficients from the numerical study were also compared with those from the experiment.     

Computation of the mass transfer coefficient of FCC particles in a thin bubbling fluidized bed using two- and three-dimensional CFD simulations

In this study, the standard kinetic theory based model with a modified drag correlation was successfully used to compute the mass transfer coefficients and the Sherwood numbers of FCC particles in a thin bubbling fluidized bed column using the additive diffusional and chemical reaction resistances concept. Also, the effects of the computational domain (two- or three-dimensional) and the reaction rate constant (low and high) are discussed.The computations show that the Sherwood numbers are in agreement with the measurement ranges for small particles in the fluidized bed system. The mass transfer coefficients and the Sherwood numbers are high near the inlet section, and decrease to a constant value with increasing height in the column. The two-dimensional computational domain simulations provide enough information to explain the phenomena inside a symmetrical system, but three-dimensional computational domain simulations are still needed for asymmetrical systems. Finally, the mass transfer coefficients and the Sherwood numbers increased with the larger reaction rate constant.     

Flow around individual Taylor bubbles rising in stagnant CMC solutions: PIV measurements

The flow around single Taylor bubbles rising in non-Newtonian solutions of Carboxymethylcellulose (CMC) polymer was studied using simultaneously particle image velocimetry (PIV) and shadowgraphy. This technique made it possible to determine the correct position of the bubble interface. Solutions of polymer with weight percentage varying from 0.1 to 1.0 wt% were used to cover a wide range of flow regimes. The rheological fluid properties and pipe dimension yielded Reynolds numbers between 4 and 714 and Deborah numbers for the higher concentration solutions between 0.001 and 0.236. The shape of the bubbles rising in the different solutions was compared. The flow around the nose of the bubbles was found to be similar in all the studied conditions. Velocity profiles in the liquid film around the bubble were measured and different wake structures were found. With increasing solution viscosity, the wake flow pattern varied from turbulent to laminar, and a negative wake was observed for the higher polymer concentration solutions.     

Gas and liquid phase mass transfer within KATAPAK-S structures studied using CFD simulations

The gas phase mass transfer in the empty channels, and the liquid phase mass transfer within the catalyst-packed channels, of the criss-crossing sandwich structures of KATAPAK-S have been studied using computational fluid dynamics. Due to the “upheaval” caused by the flow splitting at the cross-overs, the mass transfer coefficient is significantly larger than that for fully developed flow in a single tube.     

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.     

Conceptual design and CFD simulation of a novel metal-based monolith reactor with enhanced mass transfer

This paper introduces a novel structured metallic catalyst that improves mass transfer performance of a monolith reactor for highly exothermic gas–solid reactions. The monolith channels are designed to have metallic substrates that consist of two layers with one of the layers being the metallic support and another layer being a foam metal annular that is tightly deposited onto the support surface by some means. Parametrical studies based on a 2D monolith reactor model showed that the present design yields an enhanced mass transfer between the bulk fluid and the catalyst layer due to a decrease in external film resistance, and an enhanced mass transfer within the solid phase mainly due to the viscous flow effect within the porous catalyst layer.     

Rise velocities and gas-liquid mass transfer of bubbles in organic solutions

Bubble size, shape, rise velocity and liquid side mass transfer coefficient have been experimentally determined for bubbles rising in organic systems, consisting of single or mutually soluble components, namely: alkanes (n-dodecane, n-hexadecane), alcohols (ethanol, 1-butanol, 1-octanol) and mixtures thereof. For pure solvents (alkanes and alcohols alike), it was found that the bubbles are non-spherical, and that both the rise velocity and the mass transfer coefficient are close to those expected for bubbles with a mobile surface.For alkane-alcohol solutions, on the other hand, the bubbles become almost spherical, and their rise velocity and mass transfer coefficient decrease, taking values intermediate between those of rigid bubbles and bubbles with a mobile surface. Trace concentrations of either alkane in alcohol or alcohol in alkane are enough for this effect to be observed. The bubbles, however, never become completely rigid in the whole range of concentrations between pure alkane and pure alcohol.Use of Higbie's equation with experimental value of slip velocity to calculate the mass transfer coefficient, k_L, (system n-dodecane/1-octanol) yields somewhat high predictions of k_L, but follows the trend of experimental k_L with concentration for most of the concentration range. However, for very small concentrations of either component, Higbie's equation gives completely wrong results, both in magnitude and in trend. The reason for this behaviour is unknown.     

Determination of the interfacial area and mass transfer coefficients in the Taylor gas–liquid flow in a microchannel

The interfacial area in the Taylor (slug) gas–liquid flow in a microchannel was measured by the Danckwerts' (chemical) method, using CO₂ absorption from the CO₂/N₂ mixture into KHCO₃/K₂CO₃ buffer solutions, containing NaOCl as a catalyst. The rate of absorption was determined and the Danckwerts' plots were constructed. Reasonable agreement with the geometrical area measured photographically was obtained. This fact allowed to determine for the first time the mass transfer coefficients separately for liquid film and liquid caps. A correlation for the calculation of mass transfer coefficients has been proposed.     

Review of 3D CFD modeling of flow and mass transfer in narrow spacer-filled channels in membrane modules

The robustness, reliability and efficiency of modern numerical methods for obtaining solutions to flow problems have given rise to the adoption of Computational Fluid Dynamics (CFD) as a widely used analysis tool for membrane separation systems. In the past decade, many two-dimensional (2D) flow studies employing CFD have been published. Three-dimensional (3D) solutions are also slowly emerging. This paper reviews recent research utilizing 3D CFD models to simulate the flow conditions in narrow spacer-filled channels, such as those encountered in Spiral Wound Membrane (SWM) modules. Many of these studies have focused on optimizing spacer geometric parameters, while others have attempted to gain a better understanding of the mechanisms giving rise to mass transfer enhancement. Applications of 3D CFD to complex spacer geometries and multiple ionic component diffusion are also discussed.     

Hydrodynamics and mass transfer in a novel multi-airlifting membrane bioreactor

A novel multiple-airlifting membrane bioreactor is built with four sintered stainless steel tubular filters as the risers and downcomers. This work investigates the hydrodynamics including gas holdup, liquid velocity, liquid circulation and mixing times by aerating different number of risers (one to three) at superficial gas velocities of 0.02-0.07 m/s The mass transfer phenomena, including oxygen mass transfer (k_La) and effective molecular diffusivity of lactic and acetic acids through the walls of tubular filters, are also investigated. It is found that gas holdup in individual risers increases linearly with the superficial gas velocity, and performs independently under multiple-airlifting conditions. The vessel-based gas holdup and liquid velocity in downcomer(s) increase with aeration rate of individual risers as well as the number of risers. The liquid velocity in downcomers reaches an upper limit (about 0.6 m/s), because of flow resistance or energy loss of liquid circulation. The oxygen mass transfer coefficient (k_La) is primarily affected by gas holdup and the number of risers, and to some extent influenced by liquid velocity. The novel airlifter configuration results in good liquid mixing in the bioreactor that quickly reaches new steady state in response to a sudden pH change from acid addition.     

Influence of channel geometry on hydrodynamics and mass transfer in the monolith film flow reactor

The hydrodynamics and the gas–liquid mass transfer as a function of the channel geometry have been investigated for the monolith film flow reactor. For the hydrodynamic studies, the liquid distribution and the flooding boundaries have been experimentally determined. The liquid distribution improved with increasing liquid flow rate. The flooding limits are in the range of other commercial structured packings and allow operation under industrially relevant conditions. Larger channel sizes and lower surface tension expand the operating window, while viscosity seems to have a minor impact. The gas–liquid mass transfer is a strong function of the surface to volume ratio defined by the channel dimensions. Co- and counter-current flow operation result in similar performance. Furthermore, shorter monoliths, with larger contribution of the inlet section have significant higher mass transfer due to the development of the concentration profile. The obtained k_GLa_V values of around 0.01 s⁻¹ are in the range of other commercial packings in counter-current flow operation. A three-dimensional single channel model describing the hydrodynamic and diffusion phenomena in the monolith is in good agreement with the experimental results. The flexibility in channel size and dimension allows tailoring the monolith reactor to the specific needs of the individual application.     

Measurement and enhancement of gas-liquid mass transfer in milliliter-scale slurry reactors

Due to the limited availability of chemical reactants in the early process development of pharmaceuticals and fine chemicals, and sometimes the high-cost of catalyst, it is increasingly popular to use milliliter-scale slurry reactors with reaction volumes of 20 ml or less to screen catalyst candidates for three-phase reactions. To ensure the success of catalyst screening, it is advantageous to run reactions under kinetically controlled conditions so that the activities of different catalysts can be compared. Because catalysts with small particle sizes are used in slurry reactors, the reactions are susceptible to gas-liquid mass transfer limitations. This work presents an efficient way of enhancing gas-liquid mass transfer in milliliter-scale reactors through the use of magnetically driven agitation with complex motion. In the reactor described here, gas-liquid mass transfer coefficients can be doubled over those obtained with the agitation technique used in commercial milliliter-scale units. In addition, the reactor can achieve the top range of mass transfer coefficients obtained in a full-scale reactor. This work also presents the first measurements of gas-liquid mass transfer coefficients in milliliter-scale reactors, which are two orders-of-magnitude smaller than systems for which mass transfer coefficients have been reported earlier. Both physical and chemical absorption techniques are used.