Prediction of The Kolmogorov Entropy Derived from CT Data in a Bubble Column Operated under The Transition Regime and Ambient Pressure

The Kolmogorov entropy (KE) algorithm was successfully applied to single source γ‐ray Computed Tomography (CT) data measured by three scintillation detectors in a 0.162 m‐ID bubble column equipped with a perforated plate distributor (163 holes × ?? 1.32 · 10^–3 m). The aerated liquid height was set at 1.8 m. Dried air was used as a gas phase, while Therminol LT (ρ_L = 886 kg m^–3, μ_L = 0.88 · 10^–3 Pa s, σ = 17 · 10^–3 N m^–1) was used as a liquid phase. At ambient pressure, the superficial gas velocity, u_G, was increased stepwise with an increment of 0.01 m s^–1 up to 0.2 m s^–1. Based on the sudden changes in the KE values, the boundaries of the following five regimes were successfully identified: dispersed bubble regime (u_G < 0.02 m s^–1), first transition regime (0.02 ≤ u_G < 0.08 m s^–1), second transition regime (0.08 ≤ u_G < 0.1 m s^–1), coalesced bubble regime consisting of four regions (called 4‐region flow; 0.1 ≤ u_G < 0.12 m s^–1), and coalesced bubble regime consisting of three regions (called 3‐region flow; u_G > 0.12 m s^–1). The KE values derived from three scintillation detectors in the first transition regime were successfully correlated to both bubble frequency and bubble impact. The latter was found to be inversely proportional to the bubble Froude number. The KE model implies that the bubble size in this particular flow regime is a weak function of the orifice Reynolds number (d_b = 7.1 · 10^–3Re₀^–0.05).     

Bubble size and radial gas hold‐up distributions in a slurry bubble column using ultrafast electron beam X‐ray tomography

Gas hold‐up and bubble size distribution in a slurry bubble column (SBC) were measured using the advanced noninvasive ultrafast electron beam X‐ray tomography technique. Experiments have been performed in a cylindrical column (D_T = 0.07 m) with air and water as the gas and liquid phase and spherical glass particles (d_P = 100 μm) as solids. The effects of solid concentration (0 ≤ C_s ≤ 0.36) and superficial gas velocity (0.02 ≤ U_G ≤ 0.05 m/s) on the flow structure, radial gas hold‐up profile and approximate bubble size distribution at different column heights in a SBC were studied. Bubble coalescence regime was observed with addition of solid particles; however, at higher solid concentrations, larger bubble slugs were found to break‐up. The approximate bubble size distribution and radial gas hold‐up was found to be dependent on U_G and C_s. The average bubble diameter calculated from the approximate bubble size distribution was increasing with increase of U_G. The average gas hold‐up was calculated as a function of U_G and agrees satisfactorily with previously published findings. The average gas hold‐up was also predicted as a function of C_s and agrees well for low C_s and disagrees for high C_s with findings of previous literature. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1709–1722, 2013     

Bubble shape,gas flow and gas–liquid mass transfer in pulp fibre suspensions

Gas–liquid mass transfer in pulp fibre suspensions in a batch‐operated bubble column is explained by observations of bubble size and shape made in a 2D column. Two pulp fibre suspensions (hardwood and softwood kraft) were studied over a range of suspension mass concentrations and gas flow rates. For a given gas flow rate, bubble size was found to increase as suspension concentration increased, moving from smaller spherical/elliptical bubbles to larger spherical‐capped/dimpled‐elliptical bubbles. At relatively low mass concentrations (C_m = 2–3% for the softwood and C_m ? 7% for the hardwood pulp) distinct bubbles were no longer observed in the suspension. Instead, a network of channels formed through which gas flowed. In the bubble column, the volumetric gas–liquid mass transfer rate, k_La, decreased with increasing suspension concentration. From the 2D studies, this occurred as bubble size and rise velocity increased, which would decrease overall bubble surface area and gas holdup in the column. A minimum in k_La occurred between C_m = 2% and 4% which depended on pulp type and was reached near the mass concentration where the flow channels first formed.     

Determination of interfacial area in a tapered bubble column

BACKGROUND: Investigations of hold up (ε_g) and interfacial area (a) in cylindrical bubble columns have been reported extensively but reported similar investigations in tapered bubble columns are sparse in the existing literature. Thus the current article reports the experimental determination of ε_g and a using a tapered bubble column. RESULTS: The present system generated ε_g (0.556 to 0.641) in a CO₂? NaOH system 20% higher than in an air–water system (0.466 to 0.534) and values were higher than in existing systems. Also, the values of ε_g in the air–water system were higher than reported for a column with shorter tapered angle. Values of ε_g fitted very well with the well‐known Akita and Yoshida correlation. The observed values of a (235 and 700 m² m^?3) were higher than values obtained (2 to 600 m² m^?3) in existing systems. The energy dissipation was 203 to 335 W m^?3, which was lower than that (100 to 1200 W/m³) in existing systems. A correlation developed to predict the pressure drop in terms of Euler number was statistically highly significant. CONCLUSION: The present research a chieved higher values of hold up and interfacial area, and lower values of energy dissipation per unit volume of dispersion compared with existing systems. Findings of the present study coupled with previous studies indicate that the tapered bubble column developed could find potential application not only in air pollution control but also in gas‐liquid mass transfer operations. Copyright © 2011 Society of Chemical Industry     

Influence of bubbles characteristics on the skin friction and velocity gradient on solid sphere

A detailed study of the effects of individual bubbles at high gas flow‐rate has shown, that the dominant influence on skin friction over a solid sphere is the bubble volume in compared to bubble frequency. Nevertheless the bubble frequency is very important in case of low gas flow‐rate. Referring to bubbles produced by a gas distributor, statistical and spectral analyses were performed to study the influence of bubbling on exposure time and magnitude of fluctuations. Referring to a calibrated bubble train, the existence of critical frequency is demonstrated. A bubble with larger volume and a mobile, oscillatory surface generates larger velocity gradient. In the case of gas distribution, histograms of the velocity gradient for a 2 mm glass sphere creating bubble coalescence reveal the maximum exceeds 48 000 s^?1 in the front zone and 2000 s^?1 in the rear zone (θ = 180°). For 5 mm plastic spheres creating bubble break‐up, the maximum of the velocity gradient is only 8100 s^?1 for the front part of the sphere and 2000 s^?1 in the rear zone.     

The effect of gas‐liquid counter‐current operation on gas hold‐up in bubble columns using electrical resistance tomography

BACKGROUND: In order to improve the performance of a counter‐current bubble column, radial variations of the gas hold‐ups and mean hold‐ups were investigated in a 0.160 m i.d. bubble column using electrical resistance tomography with two axial locations (Plane 1 and Plane 2). In all experiments the liquid phase was tap water and the gas phase air. The superficial gas velocity was varied from 0.02 to 0.25 m s^?1, and the liquid velocity varied from 0 to 0.01 m s^?1. The effect of liquid velocity on the distribution of mean hold‐ups and radial gas hold‐ups is discussed. RESULTS: The gas hold‐up profile in a gas–liquid counter‐current bubble column was determined by electrical resistance tomography. The liquid velocity slightly influences the mean hold‐up and radial hold‐up distribution under the selected operating conditions and the liquid flow improves the transition gas velocity from a homogeneous regime to a heterogeneous regime. Meanwhile, the radial gas hold‐up profiles are steeper at the central region of the column with increasing gas velocity. Moreover, the gas hold‐up in the centre of the column becomes steeper with increasing liquid velocity. CONCLUSIONS: The value of mean gas hold‐ups slightly increases with increasing downward liquid velocity, and more than mean gas hold‐ups in batch and co‐current operation. According to the experimental results, an empirical correlation for the centreline gas hold‐up is obtained based on the effects of gas velocity, liquid velocity, and ratio of axial height to column diameter. The values calculated in this way are in close agreement with experimental data, and compare with literature data on gas hold‐ups at the centre of the column. Copyright © 2010 Society of Chemical Industry     

Ozone Mass Transfer in the Mixing Zone of a Confined Plunging Liquid Jet Contactor

In a Confined Plunging Liquid Jet Contactor (CPLJC) a jet of liquid is introduced into an enclosed cylindrical column (downcomer) that generates fine gas bubbles that are contacted with the bulk liquid flow. The region where the liquid jet impinges the receiving liquid and expands to the wall of the downcomer is called the Mixing Zone (MZ). In the MZ, the energy of the liquid jet is dissipated by the breakup of the entrained gas into fine bubbles, and the intense recirculation of the two-phase mixture. The study presented here was undertaken to quantify the ozone-water mass transfer performance of the MZ through the determination of the volumetric mass transfer coefficient, k_La (s^?1), and to produce a model for predicting k_La based on the specific energy dissipation rate. It was found experimentally that k_La in the MZ increased with increasing superficial gas velocity. A maximum experimental k_La value of 0.84 s^?1 was achieved which compares well to other contactors used in water treatment. Such a large k_La value combined with the small volume of the reactor, favorable energy requirements and safety features of the system, suggests that the CPLJC provides an attractive alternative to conventional ozone contactors. The relatively large mass transfer rates were found to be a function of the high gas holdup and fine bubble size generated in the MZ, which results in an almost froth-like consistency. A model based on the specific energy dissipation rate of the water jet, E (kg · m^?1· s^?3), and MZ bubble size was used to predict k_La in the MZ. Using E, the number average bubble size was predicted which was then used to calculate the liquid phase mass transfer coefficient k_L. The bubble size was also used with the predicted mixing zone gas holdup to calculate the specific interfacial area, a (m^?1), which was then combined with k_L to determine a predicted value of k_La. The average deviation between experimental and predicted k_La was 6.2%.     

Gas‐Liquid Mass Transfer in a Slurry Bubble Column at High Slurry Concentrations and High Gas Velocities

The volumetric mass transfer coefficient k_La in a 0.1 m‐diameter bubble column was studied for an air‐slurry system. A C₉‐C₁₁ n‐paraffin oil was employed as the liquid phase with fine alumina catalyst carrier particles used as the solid phase. The n‐paraffin oil had properties similar to those of the liquid phase in a commercial Fischer‐Tropsch reactor under reaction conditions. The superficial gas velocity U_G was varied in the range of 0.01 to 0.8 m/s, spanning both the homogeneous and heterogeneous flow regimes. The slurry concentration ?_S ranged from 0 to 0.5. The experimental results obtained show that the gas hold‐up ?_G decreases with an increase in slurry concentration, with this decrease being most significant when ?_S < 0.2. k_La/?_G was found to be practically independent of the superficial gas velocity when U_G > 0.1 m/s is taking on values predominantly between 0.4 and 0.6 s^–1 when ?_S = 0.1 to 0.4, and 0.29 s^–1, when ?_S = 0.5. This study provides a practical means for estimating the volumetric mass transfer coefficient k_La in an industrial‐size bubble column slurry reactor, with a particular focus on the Fischer‐Tropsch process as well as high gas velocities and high slurry concentrations.     

Drift Flux Modelling for a Two‐Phase System in a Flotation Column

Using different two‐phase systems, a laboratory flotation column was operated over a wide range of bubble size from 250 to 1100 µm. The drift flux analysis for the tests was used to obtain a new correlation to relate the characteristic exponent m in the drift flux equation j_gf = U_tα_g(1 — α_g)^m, to bubble Reynolds number, where j_gf is the drift flux, U_t is the terminal velocity of an individual bubble, α_g is the gas volume fraction, and m is an exponent that depends on flow conditions. m = 20.26 + 1.89 Re_b/4.38 + Re_b.     

A Simple Model for Predicting the Two-Phase Heavy Crude Oil Horizontal Flow with Low Gas Fraction

A two-phase heavy crude oil flow with low gas fraction is common in the oil transportation process. However, most of the studies of a gas–liquid flow are based on low viscosity fluid, such as water and light oil; as a result, the results cannot be introduced successfully into the mixture flow of gas and heavy crude oil. In this work, a two-phase flow of gas and heavy crude oil, which originated from the Bo-hai oilfield in China, was investigated in a horizontal pipe with 47-mm inner diameter. Data were acquired for the oil flow rate ranging from 2 m³/h to 10 m³/h, the input gas volume fraction ranging from 0.01 to 0.15, and the viscosity of crude oil ranging from 2.41 Pa·s to 0.34 Pa · s. Based on the drift-flux model, a new simplified correlation was developed to predict the void fraction and the pressure gradient. A comparison between the predicted and measured data demonstrates a reasonable agreement, and the correlation might be helpful for practical application in industry, especially in initially estimating the flow characteristic parameters.     

Oxygen mass transfer coefficient in bubble column slurry reactor with ultrafine suspended particles and neural network prediction

The gas–liquid volumetric mass transfer coefficient was determined by the dynamic oxygen absorption technique using a polarographic dissolved oxygen probe and the gas–liquid interfacial area was measured using dual‐tip conductivity probes in a bubble column slurry reactor at ambient temperature and normal pressure. The solid particles used were ultrafine hollow glass microspheres with a mean diameter of 8.624 µm. The effects of various axial locations (height–diameter ratio = 1–12), superficial gas velocity (u_G = 0.011–0.085 m/s) and solid concentration (ε_S = 0–30 wt.%) on the gas–liquid volumetric mass transfer coefficient k_La_L and liquid‐side mass transfer coefficient k_L were discussed in detail in the range of operating variables investigated. Empirical correlations by dimensional analysis were obtained and feed‐forward back propagation neural network models were employed to predict the gas–liquid volumetric mass transfer coefficient and liquid‐side mass transfer coefficient for an air–water–hollow glass microspheres system in a commercial‐scale bubble column slurry reactor. © 2012 Canadian Society for Chemical Engineering     

The Effect of Adding Phosphate on the Size of Extremely Fine Needle‐like Lepidocrocite Particles Prepared by Oxidizing an Aqueous Suspension of Ferrous Hydroxide

Extremely fine particles of needle‐like lepidocrocite (γ‐FeOOH) were synthesized by the oxidation of aqueous suspensions of ferrous hydroxide using a bubble column with draft tube at a constant temperature of 30°C, and the effects of the reaction conditions or the oxidation rate were investigated in order to determine the parameters that control the particle size. When the concentration of oxygen in the feed stream was varied under a constant gas velocity, the mean size based on the major axis of a needle‐like particle decreased from 0.7 µm to 0.4 µm with increasing oxidation rate. By adding of NaH₂PO₄ to an aqueous Fe(OH)₂ suspension, in concentrations up to 1.0 mol/m³ during the air oxidation, and up to 0.9 mol/m³ during the oxidation with 30% and 50% O₂, the major axis could be reduced to ca. 0.3 µm with the minor axis and the oxidation rate remained almost unchanged.     

Gas holdup,bubble size distribution,and mass transfer in an airlift reactor with ceramic membrane and perforated plate distributor

The airlift reactor is one of the most commonly used gas–liquid two-phase reactors in chemical and biological processes. The objective of this study is to generate different-sized bubbles in an internal loop airlift reactor and characterize the behaviours of the bubbly flows. The bubble size, gas holdup, liquid circulation velocity, and the volumetric mass transfer coefficient of gas–liquid two-phase co-current flow in an internal loop airlift reactor equipped with a ceramic membrane module (CMM) and a perforated-plate distributor (PPD) are measured. Experimental results show that CMM can generate small bubbles with Sauter mean diameter d₃₂ less than 2.5 mm. As the liquid inlet velocity increases, the bubble size decreases and the gas holdup increases. In contrast, PPD can generate large bubbles with 4 mm < d₃₂ < 10 mm. The bubble size and liquid circulation velocity increase as the superficial gas velocity increases. Multiscale bubbles with 0.5 mm < d₃₂ < 10 mm can be generated by the CMM and PPD together. The volumetric mass transfer coefficient k_La of the multiscale bubbles is 0.033–0.062 s⁻¹, while that of small bubbles is 0.011–0.057 s⁻¹. Under the same flow rate of oxygen, the k_La of the multiscale bubbles increases by up to 160% in comparison to that of the small bubbles. Finally, empirical correlations for k_La are obtained.     

鼓泡塔反应器气液两相流CFD数值模拟

对圆柱形鼓泡塔反应器内的气液两相流动进行了三维瞬态数值模拟,模拟的表观气速范围为0.02～0.30 m&#8226;s^-1; 模拟采用了双流体模型,并耦合了气泡界面密度单方程模型预测气泡尺寸,该模型考虑了气泡聚并与破碎对气泡尺寸的影响。液相湍流采用考虑气相影响的修正k-ε模型,两相间的动量传输仅考虑曳力作用。模拟获得了轴向气/液相速度分布、气含率分布、湍流动能分布以及气泡表面面积密度等,对部分模拟结果与实验值进行了定量比较,结果表明模拟结果与实验结果吻合较好。     

Bubble dynamics in a 3‐D gas–solid fluidized bed using ultrafast electron beam X‐ray tomography and two‐fluid model

Bubble characteristics in a three‐dimension gas‐fluidized bed (FB) have been measured using noninvasive ultrafast electron beam X‐ray tomography. The measurements are compared with predictions by a two‐fluid model (TFM) based on kinetic theory of granular flow. The effect of bed material (glass, alumina, and low linear density polyethylene (LLDPE), d_p ～1 mm), inlet gas velocity, and initial particle bed height on the bubble behavior is investigated in a cylindrical column of 0.1‐m diameter. The bubble rise velocity is determined by cross correlation of images from dual horizontal planes. The bubble characteristics depend highly upon the particle collisional properties. The bubble sizes obtained from experiments and simulations show good agreement. The LLDPE particles show high gas hold‐up and higher bubble rise velocity than predicted on basis of literature correlations. The bed expansion is relatively high for LLDPE particles. The X‐ray tomography and TFM results provide in‐depth understanding of bubble behavior in FBs containing different granular material types. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1632–1644, 2014     

Prediction of hydrodynamic behaviour in bubble columns

A simple theoretical model is used to describe hydrodynamic behaviour in bubble columns. The model is based on an energy balance which takes into account the energy dissipation in the liquid motion and the energy dissipation at the gas–liquid interface. Gas hold-up, liquid velocity at the column axis and radial profile of liquid velocity are predicted in a wide range of operating conditions (J_G up to 1·452 m s⁻¹) and column sizes (D = 0·1–1 m and H = 1·22–9·5 m) with good accuracy. Predictions of liquid velocity are also compared with one of the most widely accepted models.     

Impinging-Jet Ozone Bubble Column Modeling: Hydrodynamics,Gas Hold-up,Bubble Characteristics,and Ozone Mass Transfer

A transient back flow cell model was used to model the hydrodynamic behaviour of an impinging-jet ozone bubble column. A steady-state back flow cell model was developed to analyze the dissolved ozone concentration profiles measured in the bubble column. The column-average overall mass transfer coefficient, k_La (s^?1), was found to be dependent on the superficial gas and liquid velocities, u_G (m.s^?1) and u_L (m.s^?1), respectively, as follows: k_La?=?55.58 · u_G ^1.26· u_L ^0.08 . The specific interfacial area, a (m^?1), was determined as a = 3.61 × 10³ · u_G ^0.902 · u_L ^?0.038 by measuring the gas hold-up (ε _G?=?4.67 · u_G ^1.11 · u_L ^?0.05 ) and Sauter mean diameter, d_S (mm), of the bubbles (d_S?=?7.78 · u_G ^0.207 · u_L ^{? 0.008} ). The local mass transfer coefficient, k_L (m.s^?1), was then determined to be: k_L?=?15.40 · u_G ^0.354 · u_L ^0.118 .     

Large Bubble Sizes and Rise Velocities in a Bubble Column Slurry Reactor

The results are reported of an experimental study of the gas holdup, ?_G, large bubble diameter, d_Lb, and large bubble rise velocity, V_Lb, in a 0.1 m wide, 0.02 m deep and 0.95 m high rectangular slurry bubble column operated at ambient temperature and pressure conditions. The superficial gas velocity U was varied in the range of 0–0.2 m/s, spanning both the homogeneous and heterogeneous flow regimes. Air was used as the gas phase. The liquid phase used was C₉‐C₁₁ paraffin oil containing varying volume fractions (?_S = 0, 0.05, 0.10, 0.15, 0.20 and 0.25) of porous catalyst (alumina catalyst support, 10 % < 10 μm; 50 % < 16 μm; 90 % < 39 μm). With increasing slurry concentrations, ?_G is significantly reduced due to enhanced bubble coalescence and for high slurry concentrations the “small” bubbles are significantly reduced in number. By the use of video imaging techniques, it was shown that the large bubble diameter is practically independent of the gas velocity for ?_S > 0.05 and U > 0.1 m/s. The measured large bubble rise velocity V_Lb agrees with the predictions of a modified Davis‐Taylor relationship.     

Quantifying the Fibre Effect on Gas Holdup in a Co‐Current Air‐Water‐Fibre Bubble Column

Fibre type and mass fraction have significant effects on gas holdup in gas‐liquid‐fibre bubble columns. An experimental study is introduced to identify a parameter that simultaneously characterizes the fibre type and mass fraction effects on gas holdup in gas‐liquid‐fibre bubble columns. This parameter satisfies the following condition: when this parameter is constant, the gas holdup trend in different fibre suspensions is generally similar at most operating conditions. A method is proposed to identify a characterization parameter by combining the crowding factor and fibre number density. The identified parameter is I_c=1n(N_c^0.8N_f^0.2). This parameter can be used to model gas holdup in gas‐liquid‐fibre bubble columns and quantitatively compare the fibre effects in different fibre suspensions.     

Influence of elevated pressure and particle lyophobicity on hydrodynamics and gas–liquid mass transfer in slurry bubble columns

This article reports on the influence of elevated pressure and catalyst particle lyophobicity at particle concentrations up to 3 vol % on the hydrodynamics and the gas‐to‐liquid mass transfer in a slurry bubble column. The study was done with demineralized water (aqueous phase) and Isopar‐M oil (organic phase) slurries in a 0.15 m internal diameter bubble column operated at pressures ranging from 0.1 to 1.3 MPa. The overall gas hold‐up, the flow regime transition point, the average large bubble diameter, and the centerline liquid velocity were measured along with the gas–liquid mass transfer coefficient. The gas hold‐up and the flow regime transition point are not influenced by the presence of lyophilic particles. Lyophobic particles shift the regime transition to a higher gas velocity and cause foam formation. Increasing operating pressure significantly increases the gas hold‐up and the regime transition velocity, irrespective of the particle lyophobicity. The gas–liquid mass transfer coefficient is proportional to the gas hold‐up for all investigated slurries and is not affected by the particle lyophobicity, the particle concentration, and the operating pressure. A correlation is presented to estimate the gas–liquid mass transfer coefficient as a function of the measured gas hold‐up: $k_{\rm l}a_{\rm l}/\varepsilon_{\rm g} = 3.0 \sqrt{Du_{\rm b}/d_{\rm b}^3}\;{\rm s}^{-1}$ . © 2009 American Institute of Chemical Engineers AIChE J, 2010