Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of [Alves et al., 2002a] and [Alves et al., 2002b] . The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.     

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.     

Controlled peroxide-induced degradation of polypropylene in a twin-screw extruder: Change of molecular weight distribution under conditions controlled by micromixing

Controlled degradation of polypropylene (PP) by peroxide was carried out in a laboratory twin-screw extruder ZSK 18 and the change in Molecular Weight Distribution (MWD) was measured using Size Exclusion Chromatography–Differential Viscosimetry (SEC–DV). The MWD results were compared to MWD predictions from a kinetic model developed and validated in earlier work (Iedema et al., 2001) assuming ideal mixing. Clear deviations were observed – the measured MWD was broader – that could only be explained by unaccounted heterogeneity in the extruder. Incorporating the relatively narrow Residence Time Distribution (RTD) in the twin-screw extruder did not lead to MWD broadening. In contrast, the exponential RTD of a Continuously Stirred Tank Reactor (CSTR) yielded a MWD widening that was too extreme. A new micromixing model, based on the striation thinning model by Ottino (1980), was constructed partly based on Monte Carlo sampling using a monomer scission probability (Tobita, 1996). This model was adapted to the geometry of the extruder entrance and the peroxide feed practice consisting of introducing a few per thousand peroxide-rich PP particles among pure PP particles. This micromixing model indeed allowed obtaining very good matches between measured and modeled MWD. Under different experimental conditions with respect to initial PP quality and amount of peroxide added, with a constant value for the striation thinning parameter the errors between measured and predicted MWD were around 5%.     

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.     

Steam reforming of methanol over a CuO/ZnO/Al2O3 catalyst, part I: Kinetic modelling

A kinetic study of the methanol steam reforming reaction was performed over a commercial CuO/ZnO/Al₂O₃ catalyst (Süd-Chemie, G66 MR), in the temperature range of 200–300 °C. The reactions considered in this work were methanol steam reforming (MSR) and reverse water gas shift (rWGS). Several MSR kinetic rate models developed by different authors were compared and the one was determined that best fitted the experimental data. A kinetic Langmuir–Hinshelwood model was proposed based on the work by Peppley et al. (1999a) . The kinetic expressions that presented the best fit were used to simulate the packed bed reactor with a one-dimensional model. A good agreement between the mathematical model and the experimental data was observed.     

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.     

Computational fluid dynamic simulations of chemical looping fuel reactors utilizing gaseous fuels

A computational fluid dynamic (CFD) model for the fuel reactor of chemical looping combustion technology has been developed, with special focus on accurately representing the heterogeneous chemical reactions. A continuum two-fluid model was used to describe both the gas and solid phases. Detailed sub-models to account for fluid–particle and particle–particle interaction forces were also incorporated. Two experimental cases were analyzed in this study (Son and Kim, 2006; Mattison et al., 2001). Simulations were carried out to test the capability of the CFD model to capture changes in outlet gas concentrations with changes in number of parameters such as superficial velocity, metal oxide concentration, reactor temperature, etc. For the experiments of Mattisson et al. (2001), detailed time varying outlet concentration values were compared, and it was found that CFD simulations provided a reasonable match with this data.     

Meso-scale structures of bidisperse mixtures of particles fluidized by a gas

Flow characteristics of bidisperse mixtures of particles fluidized by a gas predicted by the mixture based kinetic theory of [Garzó et al., 2007a] and [Garzó et al., 2007b] and the species based kinetic theory model of Iddir and Arastoopour (2005) are compared. Simulations were carried out in two- and three-dimensional periodic domains. Direct comparison of the meso-scale gas-particle flow structures, and the domain-averaged slip velocities and meso-scale stresses reveals that both mixture and species based kinetic theory models manifest similar predictions for all the size ratios examined in this study. A detailed analysis is presented in which we demonstrate when the species based theory of Iddir and Arastoopour (2005) will reduce to a mathematical form similar to the mixture framework of [Garzó et al., 2007a] and [Garzó et al., 2007b] . We also find that the flow characteristics obtained for bidisperse mixtures are very similar to those obtained for monodisperse systems having the same Sauter mean diameter for the cases examined; however, the domain-averaged properties of monodisperse and bidisperse gas-particle flows do demonstrate quantitative differences. The use of filtered two-fluid models that average over meso-scale flow structures has already been described in the literature; it is clear from the present study that such filtered models are needed for coarse-grid simulations of polydisperse systems as well.     

Computational fluid dynamics (CFD) modeling of UV disinfection in a closed-conduit reactor

The use of ultraviolet (UV) disinfection in water treatment is governed by several factors, including flow field, fluence rate field, and microbial inactivation kinetics. In this study, a computational fluid dynamics (CFD) model was developed for UV disinfection in a closed-conduit reactor where an improved low-Reynolds number k–ε model was used to calculate flow field and a modified P-1 model was employed to obtain the fluence rate field. The Chick–Watson model was adopted to characterize the inactivation of microorganisms. Commercial CFD software FLUENT 6.3 was employed to solve the governing equations. The predicted flow field agreed well with experimental data obtained by digital particle image velocimetry (DPIV) (Liu et al., 2007) in terms of velocity field. The proposed CFD model was also evaluated by comparing current predictions to bioassay test data, and reasonable agreement was obtained in terms of effluent log inactivation. The impact of wall reflection of the light on the fluence rate field and the viable microorganism concentration field was investigated. The effect of wall reflection of the light on effluent log inactivation was also investigated under different water qualities and lamp power conditions. The results showed that at higher inactivation levels, the effect of wall reflection was more influential.     

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).     

Water network design with stochastic optimization approach

Water network (called also water allocation) problem has been addressed in more than 200 papers to date – see recent reviews by Je?owski (2010) and Foo (2009). Though various solution methods have been developed they all have some limitations. This paper addresses water usage network with regeneration processes. Multiple contaminants and two types of water using processes are taken into regard. Simultaneous one stage optimization method was developed to synthesize the network. In order to solve complex MINLP formulation we propose to apply meta-heuristic optimization – adaptive random search method.The paper contains detailed solution algorithm. Several examples with specific features are solved to show efficiency and flexibility of the approach.     

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.     

Time scale analysis for fluidized bed melt granulation III: Binder solidification rate

In series I and II of this study ( [Chua et al., 2010a] and [Chua et al., 2010b] ), we discussed the time scale of granule–granule collision, droplet–granule collision and droplet spreading in Fluidized Bed Melt Granulation (FBMG). In this third one, we consider the rate at which binder solidifies. Simple analytical solution, based on classical formulation for conduction across a semi-infinite slab, was used to obtain a generalized equation for binder solidification time. A multi-physics simulation package (Comsol) was used to predict the binder solidification time for various operating conditions usually considered in FBMG. The simulation results were validated with experimental temperature data obtained with a high speed infrared camera during solidification of ‘macroscopic’ (mm scale) droplets. For the range of microscopic droplet size and operating conditions considered for a FBMG process, the binder solidification time was found to fall approximately between 10⁻³ and 10⁻¹ s. This is the slowest compared to the other three major FBMG microscopic events discussed in this series (granule–granule collision, granule–droplet collision and droplet spreading).     

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.     

Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows, free path theory and an empirical friction theory. The effects of the inter- and inner-particle collisions, particle translational motions and particle–particle friction are included. As the effects due to fluiddynamic particle velocity differences and particle–particle friction are considered, some unconventional terms are produced compared with the previous models. Model validation using the data from Mathiesen et al. (2000) shows that the coupling terms give a stronger and more realistic particle–particle coupling because the effects due to the fluiddynamic velocity differences are considered. The model gives reasonable predictions of the particle volume fraction, particle velocities and velocity fluctuations. The model analysis reveals that the basic particle velocity fluctuations constitute 2 terms: the velocity fluctuations of the discrete particles, and the velocity fluctuations of the continuous fluid flow. Furthermore, the simulation results show that the velocity fluctuations of the continuous fluid flow are dominant in a binary riser flow.     

Drying of latex films and coatings: Reconsidering the fundamental mechanisms

The two existing theories describing drying of latex films or coatings are reconsidered. Subsequently, a novel mathematical drying model is presented, the simulations of which can match and explain experimental drying rate data of two previous investigations with latex films. In contrast to previous model studies, but in agreement with observations, simulations suggest that during the falling rate period of the drying process of a latex film, a porous skin of partly coalesced latex particles is indeed formed, which limits transport of water vapour from the receding air–liquid interphase to the surface of the film. The value of the effective diffusion coefficient of water vapour in the dry and partly coalesced layer (7 × 10⁻⁷ m²/s at 19–24 °C), the adjustable parameter of the model for the falling rate period, was found to be independent of initial wet film thickness (89–1322 μm), latex particle size (500–600 nm), initial polymer volume concentration (19–47 vol.%), and molecular weight of latex polymer (not quantified). Simulations also demonstrate that the transition from a constant to a falling drying rate in all cases takes place when the polymer volume concentration of the latex film is equal to that of hexagonal closest packed monodisperse spheres (74 vol.%). Consequently, the model has predictive properties and model inputs are only needed on the specific experimental (or field) conditions of interest. The effects on drying time of variations in relative humidity, wet film thickness, initial polymer volume concentration, and air flow velocity are simulated and analysed using the new model.     

Hydrodynamic forces acting on pipe bends in gas–liquid slug flow

In this paper, a one-dimensional, transient theoretical model, the Piston Flow Model (PFM), based on momentum analysis, is proposed to predict the time dependent forces acting on horizontal pipe bends in slug flow. Our experimental apparatus is described and results there from are presented. The PFM has been validated by comparing its predictions with our experimental results for air–water slug flow. The pressure traces, force traces and maximum force predicted agree well with our measurements.     

Pressure fluctuations in bubbling gas-fluidized beds

This paper uses a simple separated flow model based on the classical work of Davidson (1961) to describe the complex dynamics in bubbling fluidized beds. It shows that this application is robust and independent of geometry and gas flow conditions. The model successfully simulates the pressure measurements made in a bubbling fluidized bed and it is shown that the single measurement of pressure can be used to characterise the entire fluidized bed. The successful application of the Davidson model suggests that the flow field and hence pressure field in a bubbling fluidized bed is dominated by the size and location of voids, and once given this, particle–particle or complex particle–fluid interactions make a minor direct contribution to the pressure field.     

Study air–water system in horizontal loop geometry

To enhance the understanding of hydrodynamic of air–water multi-phase flow inside a toroidal geometry, experiments were carried out in horizontal torus reactor. Compared with vertical flow, the flow in horizontal milli torus reactor was characterized by one additional flow pattern. In vertical position two flow regimes are considered: not-dispersed and dispersed flow while in horizontal position three flow regimes have been distinguished: stratified flow, dispersed flow and mixed flow regimes. The mixing time is measured by a conductimetric method as described by (Benkhelifa et al., 2000). The effect of both superficial gas velocities and impeller rotation speeds has been studied. The mixing time has been decreased by increasing both the superficial gas velocity and the impeller rotation speed and has been shorter than the one given for the horizontal configuration. The axial dispersion inside the reactor was modelled by the Zhang's model. The obtained results are in a good agreement with Zhang's model.     

Compression-dependent permeability measurement for random soft porous media and its implications to lift generation

In the past decade, foundations have been laid for understanding the lift generation in a soft porous medium under rapid compaction (Feng and Weinbaum, 2000. Journal of Fluid Mechanics 422, 282–317; Wu et al., 2005b. Journal of Fluid Mechanics 542, 281–304; Wu et al., 2004a. Physical Review Letters 93(19), 194501; Barabadi et al., 2009. Journal of Heat Transfer 131(10), 101006-1–101006-12; Al-Chidiac et al., 2009. Journal of Porous Media 12(11), 1019–1035). One of the key parameters that affects the lift generation is the variation of the Darcy permeability as a function of compression. This critical problem is investigated in the current study using a novel experimental setup, namely a permeameter. Three different, soft, synthetic, fibrous, porous materials were chosen for the study. Their microstructures were characterized using a scanning electron microscope and a stereomicroscope. Their porosities were precisely measured using a water displacement method. By carefully controlling the air flow through the materials contained in a long Plexiglas tube of the permeameter, one obtained consistent results for the Darcy permeability of the tested material as a function of its porosity. Fluffing the porous materials caused disturbance of their microstructures thus variations in the permeability, especially in the high porosity range. The experimental data was curve-fitted and compared to established expressions. It showed that the Nogai Expression (Nogai and Ihara, 1978. Journal of Textile Machinery Society of Japan 31(12), T166–T170) provided the best fit for the change of permeability as a function of compression for the fibrous materials studied herein. The Carman–Kozeny equation, however, is only applicable for one of the fibrous materials. This finding is consistent with the theoretical predictions by Barabadi et al. (2009).