Mass transfer and shear in an airlift bioreactor: Using a mathematical model to improve reactor design and performance

Several studies have shown a strong relationship between morphology and agitation ( [Cui et al., 1997] and [Berzins et al., 2001] ). The shear stress distribution and mass transfer are the important parameters which can improve the performance of bioreactor. In this work, a mathematical model using computational fluid dynamics (CFD) techniques is used to study the gas–liquid dispersion in an airlift reactor. Multiple rotating frame (MRF) technique is used to approximate the movement of the impeller in the stationary reactor. Population balance modeling (PBM) is used to describe the dynamics of the time and space variation of bubble sizes in the reactor. The PBM equation is solved using an approximate method known as the class method (CM) and the bubble sizes are approximated through a discrete number of size ‘bins’, including transport, and different bubble phenomena. These equations of the CM are then written as scalar transport equations and added to the multiphase fluid mechanical equations describing the dynamics of the flow. All these equations are solved using control volume formulation through the use of an open-source CFD package OpenFOAM. The model is used to analyze an existing geometry of an airlift bioreactor and validate the modification on the initial design. The new design of airlift gives a clear performance by the increase of the global and local mass transfer and the decrease of the shear stress.     

Gas–liquid flows in medium and large vertical pipes

Gas–liquid bubbly flows with wide range of bubble sizes are commonly encountered in many industrial gas–liquid flow systems. To assess the performances of two population balance approaches – Average Bubble Number Density (ABND) and Inhomogeneous MUlti-SIze-Group (MUSIG) models – in tracking the changes of gas volume fraction and bubble size distribution under complex flow conditions, numerical studies have been performed to validate predictions from both models against experimental data of Lucas et al. (2005) and Prasser et al. (2007) measured in the Forschungszentrum Dresden-Rossendorf FZD facility. These experiments have been strategically chosen because of flow conditions yielding opposite trend of bubble size evolution, which provided the means of carrying out a thorough examination of existing bubble coalescence and break-up kernels. In general, predictions of both models were in good agreement with experimental data. The encouraging results demonstrated the capability of both models in capturing the dynamical changes of bubbles size due to bubble interactions and the transition from “wall peak” to “core peak” gas volume fraction profiles caused by the presence of small and large bubbles. Predictions of the inhomogeneous MUSIG model appeared marginally superior to those of ABND model. Nevertheless, through the comparison of axial gas volume fraction and Sauter mean bubble diameter profiles, ABND model may be considered an alternative approach for industrial applications of gas–liquid flow systems.     

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.     

Dynamics of bubble breakup in a microfluidic T-junction divergence

The aim of this work is to investigate experimentally the bubble breakup in a microfluidic T-junction divergence using a high-speed digital camera and a micro-Particle Image Velocimetry (micro-PIV) system. The breakup and non-breakup of N₂ bubbles in glycerol–water mixtures with several concentrations of sodium dodecyl sulphate (SDS) as surfactant were studied with capillary number ranging from 0.001 to 0.1. The cross section of PMMA square microchannel is 400 μm wide and 400 μm deep. Four various flow patterns were observed at the T-junction by changing gas and liquid flow rates. The dynamics of three various types of symmetric breakup of bubbles were investigated. The symmetric breakup of bubbles type I is mainly controlled by the augmented pressure in liquid phase. The symmetric breakup of bubbles type II is controlled by both the increased pressure and viscous forces. In the symmetric breakup of bubbles type III, a scaling law for the minimum bubble neck and the remaining time during bubble breaking process were found. The transitions between breakup and non-breakup of bubbles were investigated, and a power–law relationship between bubble extension and capillary number was proposed to predict the transitions between adjacent regimes. Our experimental results reveal that the bubble breakup in a microfluidic T-junction divergence is similar to the droplet behaviours in such a device ( [Jullien et al., 2009] , [Leshansky and Pismen, 2009] and [Link et al., 2004] ).     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

Transient gas–liquid mass transfer model for thin liquid films on structured solid packings

This paper describes a model for gas–liquid mass transfer through thin liquid films present on structured packings for gas–liquid operations under dispersed gas flow regime. The model has been derived for two cases: the absorption (or desorption) of a gaseous component into the liquid film and the transfer of the gaseous component through the liquid film to the packing surface where an infinitely fast reaction takes place. These cases have been solved for three bubble geometries: rectangular, cylindrical, and spherical. For Fourier numbers below 0.3, the model corresponds to Higbie’s penetration theory for both cases. The Sherwood numbers for cylindrical and spherical bubbles are 20% and 35% higher, respectively, than for rectangular bubbles. In case of absorption and Fourier numbers exceeding 3, the effect of bubble geometry becomes more pronounced. The Sherwood numbers for cylindrical and spherical bubbles now are 55% and 100% higher, respectively, than for rectangular bubbles. In case of an infinitely fast reaction at the packing surface, the Sherwood number corresponds to Whitman’s film theory (Sh=1$Sh=1$) for all bubble geometries. In this paper also practical approximations to the derived Sherwood numbers are presented. The approximations for both cases and all bubble geometries describe all the model data within an error of 4%. The application of the model has been demonstrated for three examples: (1) gas–liquid mass transfer for a structured packing; (2) gas–liquid mass transfer in a microchannel operated with annular flow; (3) gas–liquid mass transfer in a microchannel with Taylor flow.     

Gas–liquid mass transfer coefficient in stirred tanks interpreted through models of idealized eddy structure of turbulence in the bubble vicinity

Experimental data on the average mass transfer liquid film coefficient (k_L) in an aerated tank stirred by two Rushton turbines on common shaft are presented. Liquid media used were distilled water and 0.5 M sodium sulphate solution. Volumetric mass transfer coefficient (k_La) was measured by the dynamic pressure method with pure oxygen absorption. Specific interfacial area a was taken from Alves et al. [Chem. Eng. Proc., in press] who measured data on local gas hold-up and local average bubble diameter in the same apparatus and batches. Values of k_L are quantitatively interpreted in terms of correlations based on idealized eddy structures of turbulence in the bubble vicinity, namely by “eddy” model by Lamont and Scott [AIChE J. 16 (1970) 513] in the form of k_L=0.523(eν/ρ)^0.25(D/ν)^1/2, which fits the data with the mean deviation of 4.7%. It is shown that the decisive quantity to correlate k_L in the stirred tank is power dissipated in the liquid phase rather than the bubble diameter and the slip velocity as assumed by Alves et al.     

Interfacial area and mass transfer in carbon dioxide absorption in TEA aqueous solutions in a bubble column reactor

The hydrodynamic behaviour and mass transfer of carbon dioxide removal process by aqueous solutions of triethanolamine (TEA) are analysed. The experiments were made in a bubble column reactor (BCR) as gas–liquid contactor. The interfacial area and mass transfer coefficient were calculated by using a photographic method based on the bubble diameter determination. The influence of operation conditions, liquid phase nature and chemical reaction on the mass transfer coefficient and gas–liquid interfacial area has been also analysed.     

Hydrodynamic and mass transfer in inertial gas–liquid flow regimes through straight and meandering millimetric square channels

Heat-exchanger reactors are an important part of process intensification technology. For plate geometries, one solution for intensifying transfer and increasing residence times is to construct two-dimensional meandering channels. Supported by this scientific context, the present work aims at characterising gas–liquid mass transfer in the same square millimetric meandering channel, as in Anxionnaz (2009), this constituted the preliminary step required for performing exothermic gas–liquid reactions. Firstly, the gas–liquid hydrodynamics were characterised for a water/air system. When compared to a straight channel of identical compactness and sectional-area (2×2 mm²), the meandering channel induced (i) a delay in the transition from Taylor to annular-slug regimes, (ii) a rise of 10–20% in bubble lengths while conserving almost identical slug lengths, (iii) higher deformations of bubble nose and rear due to centrifugal forces (bends). Secondly, an original method for verifying the relevancy of the plug flow model and accurately determining k_la was used (measurements of concentrations in dissolved oxygen along the channel length). For the Taylor flow regime, k_la increased coherently when increasing j_g, and the meandering geometry had a small influence. On the contrary, this effect was found no more negligible for the slug-annular flow regime. Whatever the channels, the NTU_l remained low, thus showing that, even if millimetric channels allowed to intensify k_la, a special attention should be paid for generating sufficient residence times. At identical compactness, the meandering channel was found to be the most competitive. Finally, results on gas–liquid interfacial areas and mass transfer coefficients were confronted and discussed with respect to the predictions issued from the model developed by Van Baten and Krishna (2004).     

A bubble-based EMMS model for gas–solid bubbling fluidization

An EMMS/bubbling model for gas–solid bubbling fluidized bed was proposed based on the energy-minimization multi-scale (EMMS) method (Li and Kwauk, 1994). In this new model, the meso-scale structure was characterized with bubbles in place of clusters of the original EMMS method. Accordingly, the bubbling fluidized bed was resolved into the suspending and the energy-dissipation sub-systems over three sub-phases, i.e., the emulsion phase, the bubble phase and their inter-phase in-between. A stability condition of minimization of the energy consumption for suspending particles (N_s→min) was proposed, to close the hydrodynamic equations on these sub-phases. This bubble-based EMMS model has been validated and found in agreement with experimental data available in literature. Further, the unsteady-state version of the model was used to calculate the drag coefficient for two-fluid model (TFM). It was found that TFM simulation with EMMS/bubbling drag coefficient allows using coarser grid than that with homogeneous drag coefficient, resulting in both good predictability and scalability.     

Modeling of turbulent gas–liquid bubbly flows using stochastic Lagrangian model and lattice-Boltzmann scheme

In this paper we present detailed, three-dimensional and time-resolved simulations of turbulent gas–liquid bubbly flows. The continuous phase is modeled using a lattice-Boltzmann (LB) scheme. The scheme solves the large-scale motions of the turbulent flow using the filtered conservation equations, where the Smagorinsky model has been used to account for the effects of the sub-filter scales. A Lagrangian approach has been used for the dispersed, bubbly phase. That is we update the equations of motion of individual bubbles. It is shown that the incorporation of the sub-filter scale fluid fluctuations along the bubble trajectory improves the predictions. Collisions between bubbles are described by the stochastic inter-particle collision model based on kinetic theory developed by Sommerfeld (2001). It has been found that the collision model not only dramatically decreases computing time compared to the direct collision method, but also provides an excellent computational efficiency on parallel platforms. Furthermore, it was found that the presented modeling technique provides very good agreement with experimental data for mean and fluctuating velocity components.     

Capillary reactor for cyclohexane oxidation with oxygen

Cyclohexane oxidation is the first step in the currently used technology for production of Nylon-6 and Nylon-6,6 which employs a two-stage process. In the first stage 80% selectivity to two main products, cyclohexanol and cyclohexanone (KA oil) is obtained at 4–8% cyclohexane conversion in staged bubble columns or stirred tanks. There have been reports that increased oxygen concentration in the gas phase or pure oxygen is beneficial to cyclohexane oxidation and this was confirmed in our previous study (Jevtic et al., 2009). To fully utilize this advantage here, we present a novel, safer capillary reactor for cyclohexane oxidation with pure oxygen. The discrepancy between the experimental and modeling results was attributed to lower than expected mass transfer achieved in the capillary. With a better design for gas–liquid mixing and contacting this type of a reactor could potentially become attractive for gas–liquid reactions of similar nature.     

Simulation of particles and gas flow behavior in a riser using a filtered two-fluid model

Flow behavior of gas and particles is predicted by a filtered two-fluid model by taking into the effect of particle clustering on the interphase momentum-transfer account. The filtered gas–solid two-fluid model is proposed on the basis of the kinetic theory of granular flow. The subgrid closures for the solid pressure and drag coefficient (Andrews et al., 2005) and the solid viscosity (Riber et al., 2009) are used in the filtered two-fluid model. The model predicts the heterogeneous particle flow structure, and the distributions of gas and particle velocities and turbulent intensities. Simulated solids concentration and mass fluxes are in agreement with experimental data. Predicted effective solid phase viscosity and pressure increase with the increase of model constant c_g and c_s. At the low concentration of particles, simulations indicate that the anisotropy is obvious in the riser. Simulations show the subgrid closures for viscosity of gas phase and solid phase led to a qualitative change in the simulation results.     

Effects of surface active agents on hydrodynamics and mass transfer characteristics in a split-cylinder airlift bioreactor with packed bed

The effects of three types of surface active agents (containing SDS, HCTBr and Tween 40) with various concentrations (0–5 ppm) on the hydrodynamic and oxygen mass transfer characteristics in a split-cylinder airlift bioreactor with and without packing were investigated. It was observed that in the surfactant solutions, surface tension of the liquid decreased and smaller bubbles were produced in comparison with pure water. So, surfactants presence strongly enhanced mixing time and gas hold-up although oxygen mass transfer coefficient and the liquid circulation velocity reduced. Furthermore, the packing installation enhanced the overall gas–liquid volumetric mass transfer coefficient by increasing flow turbulency and Reynolds number compared to an unpacked column. The packing increased gas hold-up and decreased bubbles size and liquid circulation velocity.     

Experimental investigation on two-phase air/high-viscosity-oil flow in a horizontal pipe

The flow of very-viscous-oil and air through a horizontal pipe (inner diameter 22 mm) is experimentally studied. We first build and analyze the flow pattern map; a comparison between the air–water and the air–oil flow pattern maps shows a strong influence of the fluid properties. The experimental flow maps are compared with empirical and theoretical ones – Baker (1954), Mandhane et al. (1974), and Petalas and Aziz (1998) – showing a poor agreement. Experimental pressure gradients are also reported and compared with theoretical model, but also in this case the agreement is not very satisfactory. Finally, the elongated bubble velocity and length are measured and compared to model present in the literature. We conclude that the high viscosity of the liquid phase has a strong influence on the results and that the current models are not able to predict the flow features satisfactorily.     

Approximate theoretical solution for the Sherwood number of oscillating bubbles at different Reynolds numbers

In this paper a theoretical approach to the effect of bubble oscillations on the mass transfer rates has been carried out to get a better understanding of the effect of bubble oscillations in multiphase gas–liquid contactors. The perturbation method has been used to approximate the velocity profile surrounding the bubbles while they oscillate. The shape of the oscillating bubble was modelled taking into account the effect of the liquid viscosity on bubble oscillation frequency and amplitude. The modelled shapes match the photographs of bubbles oscillating in liquids with different viscosities. As a result, new approximate theoretical models for the Sherwood number in viscous fluids at different flow regimes have been proposed. The models extend the work already available in the literature for mass transfer rates from oscillating bubbles in inviscid fluids and provides good results in predicting the Sherwood number at high and moderate Reynolds numbers, the preferred regimes in many industrial operations where, as a result of the hydrodynamics processes involving the bubbles. Their oscillations do not completely decay.     

Effects of viscosity and relaxation time on the hydrodynamics of gas–liquid systems

Effects of liquid properties on the hydrodynamics of gas–liquid systems were investigated in lab-scale bubble column (BC) and internal loop airlift (ILA). Alginate solutions, a glycerol solution and a Boger fluid were adopted to separately address the effects of viscosity and of surface tension for Newtonian fluids, and the effects of relaxation time for non-Newtonian fluid characterized by approximately constant viscosity (low shear thinning). Hydrodynamic regimes were characterized in terms of overall gas holdup, gas–liquid mass transfer coefficient, drift-flux and liquid circulation velocity. The superficial gas velocities at the transition between hydrodynamic regimes (homogenous regime–vortical-spiral regime–heterogeneous regime) as a function the liquid viscosity was characterized by a maximum. The same behavior was observed for the maximum stable gas holdup and gas–liquid mass transfer coefficient in BC. Viscosity enhances homogeneous regime stability for μ<4.25 mPa s, in BC, and μ<7.68 mPa s, in ILA. For non-Newtonian fluids the transition velocity increases with liquid elasticity. The stabilization mechanism related to the relaxation time of Boger fluids has been discussed.     

基于微吸收器的CO2吸收过程研究进展

微化工技术在流体流动、过程强化、传质与反应过程等领域备受关注,本文归纳整理了3种不同类型的微吸收器（微降膜吸收器、微通道吸收器和微网格吸收器）捕集CO₂过程中的水力学性质和传质过程及其机理研究进展,并对3种微吸收器吸收CO₂过程中存在的问题进行分析总结,同时对微吸收器能快速工业化提出展望。其中重点介绍了微通道泰勒流吸收器的水力学流动特性,包括泰勒流气泡的生成机制、气泡和液弹的长度、气泡的输运和运动速度、气泡截面形状及液膜厚度和气液两相流压降;归纳了微通道泰勒流吸收过程的传质过程机理和传质系数的模型以及不同影响因素（通道截面尺寸,通道长度,主通道结构及入口形状,气、液相组成及其流速,吸收剂和系统压力）作用下CO₂吸收效率和传质系数的研究进展。     

On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers

An accurate and fast simulation of large-scale gas/liquid contact apparatusses, such as bubble columns, is essential for the optimization and further development of many (bio)chemical and metallurgical processes. Since it is not feasible to simulate an entire industrial-scale bubble column in full detail from first principles (direct numerical simulations), higher-level models rely on algebraic closure relations to account for the most important physical phenomena prevailing at the smallest length and time scales, while keeping computational demands low. The most important closure for describing rising bubbles in a liquid is the closure for the drag force, since it dominates the terminal rise velocity of the bubbles.Due to the very high gas loadings used in many industrial processes, bubble–bubble (or ‘swarm’) interactions need to be accounted for in the drag closure. An advanced front-tracking model was employed, which can simulate bubble swarms up to 50% gas hold-up without the problem of (numerical) coalescence. The influence of the gas hold-up for mono-disperse bubble swarms with different bubble diameters (i.e. Eötvös numbers) was quantified in a single drag correlation valid for the intermediate to high Reynolds numbers regime . Also the physical properties of the liquid phase were varied, but the simulation results revealed that the drag force coefficient was independent of the Morton number. The newly developed correlation has been implemented in a larger-scale model, and the effect of the new drag closure on the hydrodynamics in a bubble column is investigated in a separate paper (Lau et al., this issue).     

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.