Theoretical prediction of gas-liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks

A prediction method for calculating the volumetric mass transfer coefficient, k_La, in gas-liquid sparged stirred tanks is proposed. A theoretical equation based on Hibie's penetration theory and the isotropic turbulence theory of Kolmogoroff is used for k_L determination. The values of the interfacial area have been calculated from a hold-up theoretical equation and the mean size of the gas bubble. Both Ostwald-De Waele and Casson models are used to describe the rheological properties of the fluid. The model predicts the mass transfer coefficient and the interfacial area values in stirred tank reactors, analysing the influence of different variables. The values of the volumetric mass transfer coefficient can be calculated for different geometries of the reactor, different physicochemical properties of the liquid and under different operational conditions. The capability of prediction has been examined using experimental data available in the literature for Newtonian and non-Newtonian fluids, for very different vessel sizes, different numbers and types of stirrers and a wide range of operational conditions, with very good results.     

Modeling Hydrodynamics And Mass Transfer Parameters In A Continuous Ozone Bubble Column

A computer model based on the establishment of mass balance equations and on the model of fluids flow “stirred tank in series” was developed in order to calculate the ozone transfer coefficient k_La and kinetic constant k_c of ozone consumption by water. On the basis of experimental data, the correlation for gas holdup ε_g and bubble diameter d_vs, were proposed and used to calculate the specific interfacial area a. The liquid-phase mass transfer coefficient k_L for ozone was evaluated from a and the k_La 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.     

The effect of solids on the dense phase gas fraction and gas–liquid mass transfer at conditions close to the heterogeneous regime in a mechanically agitated vessel

In the heterogeneous regime, there is a strong literature evidence (discussed herein) that solids can supplant small bubbles in the dense phase and reduce the gas hold-up. This work examines the effects of the addition of 205 μm glass ballotini on the gas hold-up and k_La in a 0.286 m diameter stirred tank operated under intense conditions (P/V ≥ 5 kW m⁻³) close to the heterogeneous regime and above the agitator speed corresponding to the just suspended point, N_JS. The tests were carried out on two systems: air–water (coalescing) and air–0.2 M sodium sulphate (salt) solution (which resists coalescence in the bubble regime). For the air–water system it was observed that the overall gas plus solids hold-up remains approximately constant until all the small gas bubbles are supplanted and then increased in direct relation to the solids volume. The k_La mirrored the gas hold-up trend and decreased with a fall in gas hold-up. In the salt solution k_La decreased in direct relationship to the solids concentration, to 40% of the no solids value at around 19% solids by volume of dispersion. Dynamic engagement and disengagement experiments established that the salt solution behaves differently than water with the small bubbles initially growing in size rather than being coalesced directly into the large bubble population.     

Modelling mass transfer in an aerated 0.2 m vessel agitated by Rushton, Phasejet and Combijet impellers

We assembled a set of models that allows investigation of local variables that are difficult to measure, validation of mechanistic physical models, and comparison of different numerical solutions. Population balances (PB) for bubbles were combined with local flow modelling in order to investigate G–L mass transfer in an air–water system. Performance of three different impeller geometries was investigated: Rushton (RT), Phasejet (PJ) and Combijet (CJ). Simulations were compared against experimental mixing intensity, gas hold-up, vessel-averaged volumetric mass transfer rates (k_La), and local bubble size distributions (BSDs).The simulations qualitatively predict k_La's with different impellers at the fully dispersed flow region and gave new insight on how k_La is formed and distributed in the stirred vessels. The used bubble breakage and coalescence models are able to describe both air–water and viscous non-Newtonian G–L mass transfer. Difference between experimental mass transfer rates of the three impellers was within experimental error, even trough the flow patterns, gas distribution, and local BSDs differ considerably. The population balance for bubbles was modelled in two different ways, with multiple size groups (MUSIGs) and with the bubble number density (BND) approach. MUSIG calculations took over twice as much computational time than BND, but there was little difference in the results. The Rushton turbine k_La was described with best accuracy, which is not surprising since most phenomenological models are fitted based on RT experiments. We suggest that these models should be validated over a wider range of vessel geometries and operating conditions.     

kL a correlation established on the basis of a neural network model

A k_L a correlation has been developed with the aid of a neural network model. The neural network model has served as a non-linear relationship performer correlating the volumetric mass transfer coefficient k_L a in stirred tank reactors with the operating conditions, reactor geometry and material properties. In order to achieve an optimum correlation, experimental data taken from different sources have been used to train the network. The correlation obtained in this way is able to predict k_L a in stirrer tanks reasonably well, if the operating conditions, reactor geometry and material properties fall into the trained ranges. Although the experimental data were widely spread and could only be fitted to individual correlations, the neural network is in a position to give a general correlation for all the data.     

Einfluss mikrostrukturierter statischer Mischer auf den Gas/Flüssig‐Stofftransport in einem engen Rechteckkanal

Experimental results of the volumetric mass transfer coefficient k_La_Ph in a microstructured rectangular channel (Miprowa®) with static mixers are presented. The physical absorption of CO₂ in H₂O was identified as suitable measuring method. The results include a gas‐liquid flow map and the identification of different flow regimes as well as first systematic measurements of the k_La_Ph value as a function of various process settings like gas and liquid flow rate and gas holdup. A first comparison of Miprowa® with established gas‐liquid contact devices like stirred tank and bubble column is given.     

CFD simulations of mass transfer from Taylor bubbles rising in circular capillaries

Computational Fluid Dynamics (CFD) is used to investigate mass transfer from Taylor bubbles to the liquid phase in circular capillaries. The liquid phase volumetric mass transfer coefficient k_La was determined from CFD simulations of Taylor bubbles in upflow, using periodic boundary conditions. The separate influences of the bubble rise velocity, unit cell length, film thickness, film length, and liquid diffusivity on k_La were investigated for capillaries of 1.5, 2 and diameter. The mass transfer from the Taylor bubble is the sum of the contributions of the two bubble caps, and the film surrounding the bubble. The Higbie penetration model is used to describe the mass transfer from the two hemispherical caps. The unsteady-state diffusion model of Pigford is used to describe the mass transfer to the downward flowing liquid film. The developed model for k_La is in good agreement with the CFD simulated values, and provides a practical method for estimating mass transfer coefficients in monolith reactors.     

Absorption and reaction of isobutene in sulfuric acid—III: Considerations on the scale up of bubble columns

In spite of their simple construction the scale up of bubble columns of industrial size demands application of models which account for dispersion effects and variations of pressure and gas flow rate. However, using such models and parameter values obtained from other studies it was not possible to describe successfully measured conversions of the absorption of isobutene in a 7 m bubble column though the interfacial area was determined separately. The measurements were carried out under such conditions at which the absorption takes place in the slow reaction regime of mass transfer. A sufficient agreement between experimental and predicted conversions could be obtained merely if a lower value of k_L was used. A more detailed analysis of bubble size distributions indicated that the decrease of k_L may be apparently only since the interfacial areas determined photographically must not necessarily be the area which is effective to mass transfer. k_La-values in larger bubble columns with gas spargers which are common in industry are considerably lower than k_La-data found in smaller columns with porous gas distributors.     

Surfactant Effects on Aeration Performance of Stirred Tank Reactors

The effect of surfactants on aeration performance in stirred tank reactors (STR) at high rates of foaming is studied. The volumetric oxygen transfer coefficient (k_La) and foaming activity estimated as foaming height (H_f) were determined. Biotechnology of lipopeptide biosurfactants from aerobic organisms, e.g., Bacillus subtilis were addressed. Using model solutions of known foam‐generating properties, high‐molecular weight surfactin and low‐molecular weight sodium dodecyl sulphate (SDS), as well as impellers of different types, with flat and fluid‐foil blades, clues on the concentration dependence of STR oxygen transfer and foaming as well as options for foam reduction in the presence of biosurfactant were sought. In response to a two‐fold decrease of surface tension by surfactin, k_La values decreased up to 30 % but remained within the range expected for the mixing system in water; the experiments with SDS showing stronger dependence on surfactant concentration and surface tension. Mixing of surfactant media by a standard six‐blade disc turbine (RT) imposed rate limitations on gassing. A low‐shear impeller Narcissus (NS) could be used to avoid bulk foam outflow, while preserving k_La values that remained unchanged. The ‘power per unit volume' correlation of k_La in stirred tanks is tested in the presence of surfactin.     

Oxygen transfer in viscous non-Newtonian liquids having yield stress in bubble columns

The oxygen transfer and hydrodynamics in viscous media having a yield stress in bubble columns operated under the slug flow regime were investigated to design an optimum bubble column fermentor for culture media having a yield stress.The gas holdup of escapable bubbles was well estimated by the equation of Nicklin et al. (Trans. Inst. Chem. Eng. 40 (1962) 61), which was modified for the viscous liquid having a yield stress by Terasaka and Tsuge (Chem. Eng. Sci. 58 (2003) 513). The volumetric oxygen transfer coefficient k_La increased with increasing superficial gas velocity and decreasing column diameter under the present conditions. To predict k_La in the non-Newtonian liquids having a yield stress under the operation in slug flow regime, the proposed correlation equation estimated relatively well the experimental k_La.To increase oxygen transfer rate, two types of novel bubble columns were compared with the standard bubble column. The partitioned bubble column presented the better performance than those of the other ones.     

Modelling local bubble size distributions in agitated vessels

Photography and capillary suction probe were used to measure local bubble size distributions (BSDs) from Rushton turbine agitated (14/200 L) air-tap water and CO₂-n-butanol dispersions. A multiblock stirred tank model with population balances (PBs) for bubbles was created to describe local BSDs in agitated vessels. Unknown parameters in breakage and coalescence models were adjusted by comparing the predicted and measured local BSDs. The BSDs from both investigated systems and varying vessel-operating conditions were included simultaneously to the fitting. The adjusted models were incorporated to MUSIG PB model in CFX-5.7 and tested for the laboratory stirred tanks. The multiblock model showed to be an optimal trade-off between the accuracy and CPU time for the investigation of gas-liquid hydrodynamics and validation of closure models. As a result of fitting, the adjusted model seems to describe local BSDs more accurately in agitated vessels than the model of Lehr et al. [2002. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443], which has been successful in bubble column studies. This shows that phenomenological breakage and coalescence closures need experimental validation for various flow environments.     

Bubble size and mass transfer characteristics of sparged downwards two-phase flow

When gas is continuously fed through a sparger into a downflowing liquid in a pipe a ventilated cavity is often formed. The cavity remains attached to the sparger even in the presence of high liquid flow rates that would wash away a free slug bubble. Small bubbles are shed from the base of this cavity by the falling liquid film at the wall of the pipe and these bubbles are swept downwards forming a bubbly flow that is highly effective for mass transfer. The ventilated cavity is undesirable since it reduces the driving force for liquid circulation when the pipe is the downcomer of an external air loop fermenter or analogous gas/liquid reactors. The cavity also reduces the available interfacial area for mass transfer. It has been shown [Thorpe et al., 1997. Proceedings of the Fourth International Conference on Bioreactor and Bioprocess Fluid Dynamics; Lee, 1998. Ph.D Thesis, University of Cambridge, UK], that the length of the cavity can be reduced by replacing the common industrial design of a horizontal sparger (HS) with two novel spargers; a peripheral sparger (PS) and a plunging jet sparger (PJS) (Fig. 3). In this paper we investigate the effect of PS and PJS on mass transfer and the resulting bubble size.Experiments were carried out with air and water in a large circulating rig with a 0.105 m diameter test section. The local average bubble size in the bulk two-phase flow region below the ventilated cavity was determined using photography for three combinations of liquid and gas volumetric flow rates. The average bubble size was essentially the same (differences within 10%) for the PS, central spranger (CS) and HS. The PS created the largest bubble in all cases examined. The PJS created smaller bubbles than all the other spargers and did not allow the formation of cavities, which suggests that it has the superior performance. The estimated increase in k_La due to the smaller bubble size for the PJS was by a factor of 1.3.In order to check this result, the effects of sparger type on the volumetric mass transfer coefficient (k_La) were also measured. The k_La was determined with a dynamic method, by using unsteady state absorption of oxygen. The results confirmed the apparent superiority of PJS over the other spargers. An average increase of 19% in the k_La was observed when the PJS was used instead of the industrial design (HS). The CS and PS showed similar k_La values again within 10% of the HS.However the power consumption is larger when the PJS is used instead of the industrial design HS. Hence an attempt was made to adjust the bubble size and mass transfer coefficients of the PJS to account for the differences in energy consumption. When this is done the PJS and HS produce roughly the same bubble size and have the same mass transfer performance. Still the PJS had the important operational advantages of producing shorter cavities and having the greater resistance to stall at low liquid flow rates.     

Using image analysis in the study of multiphase gas absorption

For the air-water-calcium alginate beads system, the effect of the presence of solids on the mass transfer characteristics in a bubble column was experimentally studied.Volumetric liquid side mass transfer coefficient, k_La, specific interfacial area, a, and hence liquid side mass transfer coefficient, k_L, were determined under different solid concentrations (0, 5, and 10 vol%), superficial gas velocities (up to 0.27 cm/s) and solid sizes (1.2 and 2.1 mm diameter). The bubble characteristics, namely the interfacial area, were obtained using an image analysis technique.This technique proved to be a suitable and practical method to characterize mass transfer phenomena in bubble columns for the range of operating conditions used. The solids affect negatively k_La, decreasing both a and k_L, the effect being more pronounced for the smaller particles. For these particles the variation of k_La is due to the variation of its two components, while for larger particles k_La variation is due, essentially, to changes in k_L as no significant differences in a were observed.     

Effect of surfactants on liquid-side mass transfer coefficients

In the present paper, the effect of liquid properties (surfactants) on bubble generation phenomenon, interfacial area and liquid-side mass transfer coefficient was investigated. The measurements of surface tension (static and dynamic methods), of critical micelle concentration (CMC) and of characteristic adsorption parameters such as the surface coverage ratio at equilibrium (s_e) were performed to understand the effects of surfactants on the mass transfer efficiency. Tap water and aqueous solutions with surfactants (cationic and anionic) were used as liquid phases and an elastic membrane with a single orifice as gas sparger. The bubbles were generated into a small-scale bubble column. The local liquid-side mass transfer coefficient (k_L) was obtained from the volumetric mass transfer coefficient (k_La) and the interfacial area (a) was deduced from the bubble diameter (D_B), the bubble frequency (f_B) and the terminal bubble rising velocity (U_B). Only the dynamic bubble regime was considered in this work (Re_OR=150-1000 and We=0.002-4).This study has clearly shown that the presence of surfactants affects the bubble generation phenomenon and thus the interfacial area (a) and the different mass transfer parameters, such as the volumetric mass transfer coefficient (k_La) and the liquid-side mass transfer coefficient (k_L). Whatever the operating conditions, the new k_La determination method has provided good accuracy without assuming that the liquid phase is perfectly mixed as in the classical method. The surface coverage ratio (s_e) proves to be crucial for predicting the changes of k_L in aqueous solutions with surfactants.     

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.     

Bubble breakage phenomena,phase holdups and mass transfer in three-phase fluidized beds with floating bubble breakers

The individual phase holdups and mass transfer characteristics in three-phase fluidized beds with different floating bubble breakers have been determined in a 2.0 m high Plexiglas column of inner diameter 0.142 m. The bubble breaking phenomena by the breakers have been studied via a photographic method in a two-dimensional Plexiglas column. The volumetric mass transfer coefficient k_La in three-phase fluidized beds with hexagonal-shaped breakers is up to 40% greater than that in beds without floating bubble breakers. The bed porosity ε_L + ε_g, gas-phase holdup ε_g, and volumetric mass transfer coefficient k_La increase with an increase in the volume ratio of floating bubble breakers to solid particles, V_f/V_s, up to around 0.15, and thereafter decrease with V_f/V_s in three-phase fluidized beds with floating bubble breakers. Also, k_La increases with increasing breaker density, projected area and contact angle between the floating bubble breakers and the water. The volumetric mass transfer coefficients in terms of the Sherwood number in three-phase fluidized beds with the various floating bubble breakers have been correlated with the volume ratio of floating bubble breakers to solid particles, the particle Reynolds number based on the local isotropic turbulence theory and the modified Weber number.     

Mass transfer from Taylor bubbles rising in single capillaries

Gas-liquid mass transfer from Taylor bubbles rising in 1, 2 and 3 mm diameter capillaries of circular and square cross-sections was investigated for air-water system. The liquid-phase volumetric mass transfer coefficient k_La was obtained from experimental oxygen absorption dynamics. The experimental k_La values are in good agreement with the model developed by van Baten and Krishna (2004. Chemical Engineering Science 59, 2535-2545), with the additional assumption that the dominant mass transfer contribution is to the film surrounding the bubble.     

Effect of the radical scavenger t-butanol on gas-liquid mass transfer

The alcohol t-butanol has been used as a radical scavenger in the studies of ozone reactions in water and has been found to affect the gas-liquid mass transfer rates. An understanding of the effects of t-butanol on mass transfer parameters, including bubble size, gas holdup, mass transfer coefficient and the mass transfer specific surface area, is of key importance to not only improve the knowledge of this particular system but also to gain fundamental understanding about the effects of gas/liquid surface modifiers on the contact between phases and the mass transfer rates. An experimental study has been carried out to investigate the effects of t-butanol concentrations on the physical properties of aqueous solutions, including surface tension and viscosity. It was found that t-butanol reduced both properties-by 4% for surface tension and by a surprising 30% for viscosity. These reductions in the solution physical properties were correlated to enhancement in the mass transfer coefficient, k_L. The hydrodynamic behaviour of the system used in this work was characterised by a homogeneous bubbling regime. It was also found that the gas holdup was significantly enhanced by the addition of t-butanol. An equation to predict the gas holdup from the gas flow rate and t-butanol concentration was proposed to describe the experimental data. Moreover, the addition of t-butanol was found to significantly reduce the size of gas bubbles, leading to enhancement in the volumetric mass transfer coefficient, k_La. Bubble mean diameter was predicted using an equation developed by the Radial Basis Function Neural Network architecture obtained from the literature, and the mass transfer coefficient, k_L, was predicted using an equation based on the surface coverage ratio model. The ratio was found not to depend either on t-butanol concentration or on gas flow rate. A significant increase in the volumetric mass transfer coefficient, k_La, due to an increase in both k_L and a, was obtained following the addition of t-butanol, even at low concentrations.     

Effect of electrolytes in aqueous solutions on oxygen transfer in gas–liquid bubble columns

The effects of inorganic electrolytes (NaCl, MgCl₂, CaCl₂) in aqueous solutions on oxygen transfer in a bubble column were studied. Electrolyte concentrations (c) below and above the critical concentrations for bubble coalescence (c_tc), and six superficial gas velocities (v_sg), were evaluated. The volumetric mass transfer (k_La) and the mass transfer (k_L) coefficients were experimentally determined. It was found that the concentration of electrolytes reduced the k_L, but the interfacial area (a) increased enough to result in a net increase of k_La. Using as independent variable a normalizing variable (c_r = c/c_tc), and maintaining fixed v_sg, similar values of k_La were observed regardless the kind of electrolyte; the same happened for k_L. This suggests that c_r quantifies the structural effects that these solutes exert on mass transfer. Also, once c_r = 1 was reached, no significant variations were found in k_La and k_L for constant v_sg. It is concluded that the gradual inhibition of bubble coalescence (c_r < 1) governs the significant changes in hydrodynamics and mass transfer via the reduction of bubble size and the consequent increment of a and gas holdup (?_g). Finally, regarding the effects of v_sg on mass transfer, transition behaviors between those expected for isolated bubbles and bubble swarms were observed.