CFD simulations of bubble column reactors: 1D, 2D and 3D approach

CFD simulations have been carried out for the predictions of flow pattern in bubble column reactors using 1D, 2D and 3D k-ε models. An attempt has been made to develop a complete correspondence between the operation of a real column and the simulation. Attention has been focused on the cylindrical bubble columns because of their widespread applications in the industry. All the models showed good agreement with the experimental data for axial liquid velocity and the fractional gas hold-up profiles. However, as regards to eddy diffusivity, only the 3D model predictions agree closely with the experimental data.The CFD model has been extended for the estimation of an axial dispersion coefficient (D_L) using 1D, 2D and 3D models. Excellent agreement was found only between the experimental values and the 3D predictions. The 1D and 2D simulations, however, yielded D_L values, which were lower by 25-50%. For this, a mechanistic explanation has been provided.     

Axial mixing in pipe flows: turbulent and transition regions

In the present work, the flow pattern in pipe flow has been simulated using low Reynolds number k-ε model. The CFD model has been extended to simulate the axial dispersion phenomena in both the transition and turbulent regions. An extensive comparison of the predicted axial dispersion coefficient with the experimental data has been presented along with the predictions of various models published in the literature. The proposed CFD model for axial mixing was found to give an excellent agreement with the experimental measurements.     

Mixing in a co‐current upflow bubble column reactors with and without internals

Liquid phase mixing is a phenomenon that results mainly due to convective and turbulent flow fields, which are generated by hydrodynamic interactions between the gas and liquid phases within a continuous co‐current upflow bubble column reactor. The extent of liquid phase mixing is usually quantified through the mixing time, or the axial dispersion coefficient. In the present work, the computational fluid dynamics (CFD) simulations for mixing and RTD in a continuous bubble column (with and without internals) are performed by using OpenFOAM 2.3.1. The superficial gas velocities were 0.014, 0.088, and 0.221 m/s and the superficial liquid velocities were 0.005 and 0.014 m/s. The simulations have been performed for three different configurations of the bubble column, that is, (a) an open bubble column, (b) a column with one vertical central rod of 36 mm diameter, (c) a column with the same central rod and four vertical additional rods of 12 mm diameter. The effects of superficial gas and liquid velocities and column internals were investigated on liquid phase mixing and the axial dispersion coefficient. Comparisons have been made between the experimental measurements and the CFD simulations.

     

CFD and experimental studies of single phase axial dispersion coefficient in pulsed sieve plate column

This paper intends to study the single phase axial dispersion in pulsed sieve plate column using a combination of computational fluid dynamics (CFD) simulations and experimental measurements. Experiments and CFD simulations were conducted on 0.076 m diameter pilot scale column having standard geometry of 0.05 m plate spacing, 0.003 m hole diameter and 0.21 fractional free area. The effect of density of tracer solution and radial probe position on axial dispersion coefficient has been studied to ensure precision of the experimental measurement method. The effect of pulse velocity from 0.01 to 0.025 m/s and superficial velocity of water from 0.01 to 0.03 m/s has been studied. Simulations were carried out using commercial CFD software, FLUENT 6.2.16, with standard k–? model for turbulence. An unsteady state tracer injection technique was used for axial dispersion measurement. The range of velocity ratio (ψ = Re_o/Re_n) employed in this work was 1–4 which is very low. Therefore the effect of superficial velocity, V_c was found to be greater than pulse velocity. These results were critically compared with published data and it has been found that single phase axial dispersion coefficient is directly proportional to effective velocity (Af + 0.5 V_c). The presented CFD predictions and validation with experimental data will provide useful basis for further work on single phase axial dispersion with various geometrical parameters and understanding the two phase flow patterns in pulsed sieve plate column.     

A model for two-phase turbulent mixing in a jet bubble column

Mixing behavior of the two phase air-water turbulent flow in a jet bubble column is examined. The time evolution of the mixing behavior of a liquid tracer in a turbulent air-water flow within a jet bubble column is predicted using a model based on the fundamental governing equations of fluid motion. The predictions of the model are compared with experimental measurements. Measured residence time distributions (RTD) of the liquid tracer within the cone agree well with the predicted values given by the model. For the range of parameters considered in the study, lack of radial mixing and large axial mixing are evident within the cone of the jet bubble column. Use of fundamental mathematical models for the study of hydrodynamics in a two-phase conventional bubble column has been reported earlier (Torvik, 1990; Jakobsen et al., 1993). The present paper extends the use of such models to predict the mixing characteristics in a jet bubble column.     

INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

CFD Simulation of Liquid–Liquid Two-Phase Hydrodynamics and Axial Dispersion Analysis for a Non-Pulsed Disc and Doughnut Solvent Extraction Column

A two-phase computational fluid dynamics (CFD) simulation for a non-pulsed disc and doughnut solvent extraction column has been developed with commercial CFD software FLUENT. Simulated hydrodynamic results including phase distribution, velocity fields, and holdup are given, which enables predicted holdup to be compared with experimental data. Average absolute relative deviation (AARD) of experimental data and CFD prediction in this study is found to be 10.8%, which is comparable to the estimated error in the experimental data and the predictions from traditional correlations in the literature. To estimate the extent of axial dispersion, a species transport model is used for the continuous phase with a small amount of tracer introduced in the continuous phase, when Sauter mean diameter of the dispersed phase is set to be 3.5 mm. A two-point monitoring method is used to estimate a Peclet number. The tracer concentration distribution in the two-dimensional distance–time space is interpreted with MATLAB along with the experimental measurement. The simulated Peclet numbers are compared with column experiments, and in general the simulation underestimates the experimental data by 60%. Introducing a modified drag law improves the predictions. This work shows that CFD can successfully model the performance of a non-pulsed disc and doughnut solvent extraction column.     

Modelling churn-turbulent bubble columns—I. Liquid-phase mixing

A new two-region phenomenological model for liquid-phase mixing in churn-turbulent bubble columns has been proposed. A gas-rich region rises rapidly through the column transporting liquid to various points in the system while a relatively stagnant, gas-lean region is vigorously agitated by the passage of the gas-rich region. Estimation of most of the model parameters by physical reasoning reduces the proposed model to a one-parameter model. This unknown parameter, which describes liquid exchange between the gas-rich and gas-lean regions, can be obtained by matching the model predictions to the experimentally measured tracer response. The comparison of the proposed model's tracer response and that of the axial dispersion model also allows this exchange parameter to be calculated from the available axial dispersion coefficient correlations. The proposed model is computationally much superior to the axial dispersion model.     

Gas-bubble hold-up and axial dispersion coefficient of emulsion phases in fluidized beds

A model for liquid mixing in a gas-liquid bubble column is extended to predict gas-bubble hold-up and axial dispersion coefficient of emulsion phases in fluidized beds. Reasonable agreement is found between the proposed model which includes no adjustable parameter and the available experimental data and correlations.     

Mixing Time Studies in Multiple Impeller Agitated Reactors

Mixing time studies have been carried in a 0.3m diameter and 0.9m tall vessel equipped with three impellers. Conductivity measurement technique has been used for the measurements of mixing time. Effect of the various parameters i.e. tracer density, tracer volume, speed of rotation and impeller combination on mixing time has been studied for two impeller combinations used viz. PTD‐PTD‐PTD and PTD‐PTD‐DT. A compartment model (with one fitted parameter, the exchange flow rate Q_E) with single compartment per agitation stage has been used to predict the conductivity response and the exchange coefficients are calculated from the model parameter. An attempt has been made to explain the experimental results on the basis of the liquid phase axial dispersion coefficient and cell residence time, calculated from the model parameter Q_E     

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.     

Prediction of Axial Mixing for a Structured Packed Column Using a Two‐equation Model

A theoretical model based on the recently developed two‐equation method is proposed to predict the axial mixing behavior in a structured packed column. By solving the proposed model, the process of tracer injection experiments for determining the axial back‐mixing coefficient of structured packing can be simulated. Consequently, the axial Bodenstein number and dispersion coefficient under liquid single‐phase or gas‐liquid two‐phase flow conditions can be calculated. The validation of the proposed method is tested by simulating the two‐phase fluid flow behavior in Flexipac 2 structured packing. The simulated results are compared with the experimental data and satisfactory agreement is found between the simulation and the experiments.     

The use of two different models to describe the axial mixing of solids in fluidised beds

Two widely used models to describe axial solid mixing in fluidised beds (the dispersion model and the countercurrent backmixing (CCBM) model) are evaluated against identical sets of experimental data. Experimental work has been obtained at different conditions (gas velocity, particle properties and two column diameters) using an image analysis technique. Previously published data by other authors are also compiled to enlarge the experimental database for model development and validation. It is shown that both models are capable to fit the majority of experiments well, in agreement with a well-known relation between the models in some extreme conditions. This relation is further explored by incorporating independent measurements of the tracer rise velocities during the mixing experiments. It is concluded that, although a simple correlation for the solid dispersion coefficients compiled in this work is useful, the CCBM model is a much more reliable idealisation in describing and scaling up axial solid mixing in fluidised beds.     

Liquid phase axial mixing in a bubble column with viscous non-newtonian liquids

This paper presents some new data for the liquid phase axial dispersion coefficient in a bubble column with highly viscous non-Newtonian liquids (μ_L > 0.03 Pa · s). The data were obtained in a 0.15 m diameter column operating in the slug flow regime, and the dispersion measurements were conducted using heat aas a tracer. The experimental results show that the dispersion coefficients increase with both gas and liquid velocities and quantitatively they are about three times higher than those obtained for the air-water system. The results are explained based on a known hydrodynamic model of vertical gas-liquid slug flow.     

On the effect of tracer density on axial dispersion in a batch oscillatory baffled column

In this paper, we report our modelling evaluation on the effect of tracer density on axial dispersion in a batch oscillatory baffled column (OBC). Tracer solution of potassium nitrite, its specific density ranged from 1.0 to 1.5, was used in the study, and was injected to the vertical column from either the top or bottom. Local concentration profiles are measured using conductivity probes at two locations along the height of the column. Using the experimental measured concentration profiles together with both ‘Tank-in-Series’ and ‘Plug Flow with Axial Dispersion’ models, axial dispersion coefficients were determined and used to describe the effect of specific tracer density on mixing in the OBC. The results showed that the axial dispersion coefficients evaluated by the two models are very similar in both magnitudes and trends, and the range of variations in such coefficients is generally larger for the bottom injection than for the top one. Empirical correlations linking the mechanical energy for mixing, the specific density of tracer and axial dispersion coefficient were established. Using these correlations, we identified the enhancements of up to 269% on axial dispersion for various specific tracer densities.     

A model for liquid-liquid extraction column performance — The influence of drop size distribution on extraction efficiency

A precise model for predicting liquid-liquid extraction column efficiency based upon assumed hydrodynamic, axial mixing and mass transfer behaviour has been formulated and solved numerically. The complex nature of the dispersed phase can be better described by drop-size-dependent residence time distribution (RTD). Both the variation of axial velocities due to drops of different sizes, i.e. forward mixing, and the axial dispersion for the drops of the same size have been considered in this model. The computed results reveal that the effects of both varying velocities and dispersion of drops on extraction efficiency are appreciable and cannot be neglected, and the efficiency may be overestimated if only a forward mixing model is adopted. The comparison of the experimental values of N_ODP with those predicted shows that the mass transfer data obtained in RDC agree well with the values predicted by the present model for the case of solute transfer in c→d direction, and are slightly higher than the predicted ones for the transfer in d→c direction.     

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.