Modeling of the evolution with length of bubble size distributions in bubble columns

Many of the existing methods, for the determination of the specific interfacial area in bubble columns, consider the column in a dynamic equilibrium between bubble coalescence and breaking-up. The aim of this work is to study if this consideration can be considered true for low superficial gas velocities. Two existing models have been chosen from literature in order to predict the break-up [Wang, T., Wang, J., Jin, Y., 2003. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science 58, 4629-4637] and the coalescence [Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426] rates. In order to confirm the validity of the models, predictions were compared with experimental results obtained by image analysis. Several simulations were performed for different superficial gas velocities and initial bubble size distributions. The column length needed to reach dynamic equilibrium was calculated for each simulation. The results show that the necessary length to reach the dynamic equilibrium does not depend on the shape of the initial distribution, but essentially on its Sauter mean diameter. The necessary length to reach the dynamic equilibrium is very important for low superficial gas velocities. The assumption that the entire column is in dynamic equilibrium is in general not valid. Therefore, the initial Sauter mean diameter and the total column length are important parameters for the determination of the specific interfacial area.     

Simulation of oscillatory baffled column: CFD and population balance

In the present work, an attempt has been made to combine population balance and a CFD approach for simulating the flow in oscillatory baffled column (OBC). Three-dimensional Euler-Euler two-fluid simulations are carried out for the experimental data of Oliveira and Ni [2001. Gas hold-up and bubble diameter in a gassed oscillatory baffled column. Chemical Engineering Science 56, 6143-6148]. The experimental data include the average hold-up profile and bubble size distribution in the OBC. All the non-drag forces (turbulent dispersion force, lift force) and the drag force are incorporated in the model. The coalescence and breakage effects of the gas bubbles are modeled according to the coalescence by the random collision driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Predicted liquid velocity and averaged gas hold-up are compared with the experimental data. The profile of the mean bubble diameter in the column and its variation with the superficial gas velocity is studied. Bubble size distribution obtained by the model is compared with the experimental data.     

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.     

Coalescence efficiency of bubbles in bubble columns

Bubble size distribution was modelled by employing the population balance equation (PBE). All three bubble coalescence mechanisms (turbulence, buoyancy and laminar shear) and the main bubble breakup mechanism (breakup due to turbulent eddies) were considered in the model. Local bubble size distributions at the top and bottom of the column were obtained by solving this PBE. The results were compared with the experimental data for seven independent multiphase systems (water/air, isomax diesel/air, kerosene/air and four other liquid mixture/air) at two diverse gas velocities. The experimental adjustable constant in the coalescence efficiency function was determined by fitting the population balance to the experimental bubble size distributions. An empirical correlation was proposed for the coalescence efficiency by the dimensional analysis, which includes Reynolds and Weber numbers. © 2011 Canadian Society for Chemical Engineering     

Numerical simulation of multiphase flow in bubble column reactors. Influence of bubble coalescence and break-up

Population balance equations have been combined to a classical hydrodynamic Euler/Euler simulation to investigate the operation of a cylindrical bubble column. The MUSIG (mutiple-size-group) model implemented in the CFX 4.3 commercial software has been used. Hydrodynamic experimental variables, i.e. local axial liquid velocity and local gas hold-up, have been compared to the corresponding calculated values, showing a quite good agreement, except for the gas hold-up when the column is no more operating in the homogeneous regime. Bubble sizes have been investigated, showing that two domains of superficial gas velocities can be distinguished. In the first domain, coalescence occurs predominantly, Sauter diameter increases with the superficial gas velocity, bubble size distribution is narrow and Sauter diameter is continuously evolving along the column axis. In the second domain, break-up becomes more intensive and compensates coalescence, bubble size distribution becomes wider, since more small bubbles are formed, an equilibrium Sauter diameter appears when the superficial gas velocity increases. Furthermore an equilibrium Sauter diameter appears along the column axis, and it can be noticed that this phenomenon appears lower in the column when the gas flow rate is increased. In these two domains the characteristics of the bubbles are typical of those of the homogeneous and transition regimes.     

Model validation for low and high superficial gas velocity bubble column flows

In the present work, gas-liquid flow dynamics in a bubble column are simulated with CFDLib using an Eulerian-Eulerian ensemble-averaging method in a two-dimensional Cartesian system. The two-phase flow simulations are compared to experimental measurements of a rectangular bubble column performed by Mudde et al. [1997. Role of coherent structures on Reynolds stresses in a 2-D bubble column. A.I.Ch.E. Journal 43, 913-926] and a cylindrical bubble column performed by Rampure et al. [2003. Modeling of gas-liquid/gas-liquid-solid flows in bubble columns: experiments and CFD simulations. The Canadian Journal of Chemical Engineering 81, 692-706] for low and high superficial gas velocities, respectively. The objectives are to obtain grid-independent numerical solutions using CFDLib to reconcile unphysical results observed using FLUENT with increasing grid resolutions [Law, D., Battaglia, F., Heindel, T.J., 2006. Numerical simulations of gas-liquid flow dynamics in bubble columns. In: Proceedings of the ASME Fluids Engineering Division, IMECE2006-13544, Chicago, IL], and to validate computational fluid dynamics (CFD) simulations with experimental data to demonstrate the use of numerical simulations as a viable design tool for gas-liquid bubble column flows. Numerical predictions are presented for the local time-averaged liquid velocity and gas fraction at various axial heights as a function of horizontal or radial position. The effects of grid resolution, bubble pressure (BP) model, and drag coefficient models on the numerical predictions are examined. The BP model is hypothesized to account for bubble stability, thus providing physical solutions.     

Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces

Numerical simulations of the bubbly flow in two square cross-sectioned bubble columns were conducted with the commercial CFD package CFX-4.4. The effect of the model constant used in the sub-grid scale (SGS) model, C_S, as well as the interfacial closures for the drag, lift and virtual mass forces were investigated. Furthermore, the performance of three models [Pfleger, D., Becker, S., 2001. Modeling and simulation of the dynamic flow behavior in a bubble column. Chemical Engineering Science, 56, 1737-1747; Sato, Y., Sekoguchi, K.,1975. Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79-95; Troshko, A.A., Hassan, Y.A., 2001. A two-equation turbulence model of turbulent bubbly flows. International Journal of Multiphase Flow 27, 1965-2000] to account for the bubble-induced turbulence in the k-ε model was assessed. All simulation results were compared with experimental data for the mean and fluctuating liquid and gas velocities. It is shown that the simulation results with C_S=0.08 and 0.10 agree well with the measurements. When C_S is increased, the effective viscosity increases and subsequently the bubble plume becomes less dynamic. All three bubble-induced turbulence models could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan and Pfleger and Becker reproduce the dynamics of the bubbly flow in a more accurate way than the model of Sato and Sekoguchi. Based on the comparison of the results obtained for two columns with different aspect ratio (H/D=3 and H/D=6), it was found that the model of Pfleger and Becker performs better than the model of Troshko and Hassan, while the model of Sato and Sekoguchi performs the worst. It was observed that the interfacial closure model proposed by Tomiyama [2004. Drag, lift and virtual mass forces acting on a single bubble. Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 22-24 September] performs better for the taller column. With the drag coefficient proposed by Tomiyama, the predicted slip velocity agrees well with the experimental data in both columns. The virtual mass force has a small influence on the investigated bubbly flow characteristics. However, the lift force strongly influences the bubble plume dynamics and consequently determines the shape of the vertical velocity profile. In a taller column, the lift coefficient following from the model of Tomiyama produces the best results.     

CFD simulation of gas-liquid contacting in tubular reactors

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

A new discretization of space for the solution of multi-dimensional population balance equations

In this work, a novel radial grid is combined with the framework of minimal internal consistency of discretized equations of Chakraborty and Kumar [2007. A new framework for solution of multidimensional population balance equations. Chemical Engineering Science 62, 4112-4125] to solve n-dimensional population balance equations (PBEs) with preservation of (n+1) instead of 2ⁿ properties required in direct extension of the 1-d fixed pivot technique of Kumar and Ramkrishna [1996a. On the solutions of population balance equation by discretization-I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332]. The radial grids for the solution of 2-d PBEs are obtained by intersecting arbitrarily spaced radial lines with arcs of arbitrarily increasing radii. The quadrilaterals obtained thus are divided into triangles to represent a non-pivot particle in 2-d space through three surrounding pivots by preserving three properties, the number and the two masses of the species that constitute the newly formed particle. Such a grid combines the ease of generating and handling a structured grid with the effectiveness of the framework of minimal internal consistency. A new quantitative measure to supplement visual comparison of two solutions is also introduced. The comparison of numerical and analytical solutions of 2-d PBEs for a number of uniform and selectively refined radial grids shows that the quality of solution obtained with radial grids is substantially better than that obtained with the direct extension of the 1-d fixed pivot technique to higher dimensions for both size independent and size dependent aggregation kernels. The framework of Chakraborty and Kumar combined with the proposed 2-d radial grid, which offers flexibility and achieves both reduced numerical dispersion and the ease of implementation, appears as an effective extension of the widely used 1-d fixed pivot technique to solve 2-d PBEs.     

SIMULTANEOUS MEASUREMENTS OF GAS AND LIQUID PHASE VELOCITIES AND GAS HOLD-UP USING LASER-DOPPLER VELOCIMETER

Simultaneous measurements of gas and liquid-phase velocities along with the gas hold-up can provide a wealth of information regarding the flow structure in bubble columns. In the present work, a method is proposed for simultaneous measurements of phase velocities together with The hold-up, using a laser Doppler velocimeter. The measurements were performed in a rectangular bubble column up to a hold-up value of 26%. Turbulence parameters, in particular, rms velocities of both the phases and length scales, were also determined.     

Dynamic modelling of Kühni liquid extraction columns using the sectional quadrature method of moments (SQMOM)

In this work, the Sectional Quadrature Method Of Moments (SQMOM) is extended to a one-dimensional physical spatial domain and resolved using the finite volume method. To close the mathematical model, the required quadrature nodes and weights are calculated using the analytical solution based on the Two Unequal Weights Quadrature (TUEWQ) formula derived by Attarakih et al. (Attarakih, M., Drumm, C., & Bart, H.-J., (2009), Solution of the population balance equation using the Sectional Quadrature Method of Moments (SQMOM). Chemical Engineering Science, 64, 742–752). By applying the finite volume method to the spatial domain, we end up with a semi-discreet ordinary differential equation system which is solved using the MATLAB standard ODE solvers (ode45). As a case study, the SQMOM is used to investigate the dynamic behavior of a Kühni DN150 liquid–liquid extraction column. As an independent validation step, the SQMOM prediction is compared with the PPBLab software which utilizes the extended fixed pivot technique as a built-in population balance model solver. Furthermore, the SQMOM is validated using the available dynamic experimental data from a Kühni liquid extraction column using water-acetone-toluene chemical test system. The dynamic analyses of the Kühni column show very interesting features concerning the coupled column hydrodynamics and mass transfer and the droplet breakage and coalescence as well.     

Effect of solid particles on gas hold-up in bubble columns

The gas hold-up in bubble columns containing fluidised plastic particles as solid phase was measured as a function of superficial gas velocity and solids concentration. The effects of particle size, density, wettability and concentration on gas hold-up and bubble coalescence were studied. It was found that the addition of non-wettable solids to the air/water mixture promotes bubble coalescence and, therefore, reduces the gas hold-up, while the addition of wettable solids suppresses bubble coalescence and increases the gas hold-up.     

A note deriving the analytical solution for the wake theory of coalescence

The recent unsolved wake theory to describe bubble coalescence by Colella et al. [1999. A study on coalescence and breakage mechanisms in three different bubble columns. Chem. Eng. Sci. 54, 4767-4777] is solved analytically to give exact values of coalescence time in terms of bubble size and relative rise velocity. The solution is expressed using the tabulated exponential integral function.     

Numerical simulation of gas-liquid-solid flows using a combined front tracking and discrete particle method

In this paper a hybrid model is presented for the numerical simulation of gas-liquid-solid flows using a combined front tracking (FT) and discrete particle (DP) approach applied for, respectively, dispersed gas bubbles and solid particles present in the continuous liquid phase. The hard sphere DP model, originally developed by Hoomans et al. [1996. Chemical Engineering Science 51, 99-108] for dense gas-solid systems, has been extended to account for all additional forces acting on particles suspended in a viscous liquid and has been combined with the FT model presented recently by Deen et al. [2004a. CD-ROM Proceedings of Fifth International Conference on Multiphase Flow, ICMF’04, Yokohama, Japan, May 30-June 4, 2004; 2004b. Chemical Engineering Science 59, 1853-1861] for complex free surface flows. In this paper, the physical foundation of the combined FT-DP model will be presented together with illustrative computational results highlighting the capabilities of this hybrid model. The effect of bubble-induced particle mixing has been studied focusing on the effect of the volumetric particle concentration. In addition the retarding effect (drag modification) on the bubble rise velocity due to the presence of the suspended solid particles has been quantified.     

Effect of bubble deformation on stability and mixing in bubble columns

The paper deals with hydrodynamics in bubble columns. The objective of the paper is to study stability and mixing in a bubble column. The modeling of parameters such as stationary drag and added mass is addressed. In addition, the effect of bubble deformation in terms of eccentricity is highlighted. In a previous paper, the transition between homogeneous and heterogeneous regimes in bubble column without liquid flow has been shown to be driven by the deformation of the bubbles associated to drag and added mass. In the present paper, this work is generalized to bubble column with liquid flow and to the transition from bubble flow to slug flow in a vertical pipe. Numerical simulations of gas-liquid reactors are presented. The numerical simulations are validated in the case of gas plume after the Becker et al. data (Becker, S., Sokolichin, A., & Eigenberg, G. (1994) Gas-liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations. Chemical Engineering Science, 49 (24B), 5747-5762. The numerical simulations are finally applied to a bubble column. The simulations of residence time distribution coupled to transient hydrodynamics are shown to be very sensitive to the modeling of interfacial transfer of momentum from the bubbles to the liquid in terms of drag and added mass, including the effect of bubble deformation.     

Gas hold-up and liquid mixing at low and intermediate gas velocities I. Air-water system

Gas hold-up and liquid phase dispersion experiments have been carried out in a 0.06 m bubble column at varying liquid and gas velocities. The results obtained show that the coefficient of liquid mixing varies with the flow regime. The isotropic turbulence theory of Baird and Rice (Chem. Eng. J., 9 (1975) 171) was used to provide dimensionally consistent correlations for the chain bubbling, bubbly and churn turbulent flow regimes. The gas hold-up was determined to increase with gas velocity in the chain bubbling and bubbly flow regimes. The results obtained from this study also show that the Froude number represents a useful criterion for mapping flow regimes in vertical bubble columns.