A review on single bubble gas–liquid mass transfer

It is common to empirically correlate volumetric mass transfer coefficient k_La for predicting gas–liquid mass transfer in industrial applications, and the investigation of single bubble mass transfer is crucial for a detailed understanding of mass transfer mechanism. In this work, experiments, models and simulations based on the experimental results were highlighted to elucidate the mass transfer between single bubbles and ambient liquid. The experimental setups, measurement methods, the mass transfer of single bubbles in the Newtonian and the non-Newtonian liquid, models derived from the concept of eddy diffusion, the extension of Whitman's, Higbie's and Danckwerts' models, or dimensionless numbers, and simulation methods on turbulence, gas–liquid partition methods and mass transfer source term determination are introduced and commented on. Although people have a great knowledge on mass transfer between single bubbles and ambient liquid in single conditions, it is still insufficient when facing complex liquid conditions or some phenomena such as turbulence, contamination or non-Newtonian behavior. Additional studies on single bubbles are required for experiments and models in various liquid conditions in future.     

Effect of ultrasonic waveforms on gas–liquid mass transfer in microreactors

This study aims to investigate the effect of ultrasonic waveforms on the gas–liquid mass transfer process. For a given load power (P), continuous rectangular wave yielded stronger bubble oscillation and higher mass transfer coefficient (k_La) than continuous triangular and sinusoidal wave. For pulsed ultrasound, the k_La decreased monotonically with decreasing duty ratio (D), resulting in weak enhancement at low D (≤33%). For a given average load power (P_A), concentrating the P for a shorter period resulted in a higher k_La due to stronger cavitation behavior. For a given P_A and D, decreasing the pulse period (T) led to an increase in k_La, which reached a constant high level when the T fell below a critical value. By optimizing the D and T, a k_La equivalent to 92% of that under continuous ultrasound was obtained under pulsed ultrasound at a D of 67%, saving 33% in power consumption.     

Gas–liquid mass transfer in rotating solid foam reactors

Three-phase reactor designs based on rotating solid foams for the application in the fine chemical industry are developed. The aim is to use solid foams both as a catalyst support and stirrer in order to mix the gas and liquid phases and create fine gas bubbles. Gas–liquid mass transfer data are presented for different solid foam stirrer configurations and compared to an optimized Rushton stirrer. Solid foam stirrers were developed in a blade and a block design. Both foam reactor designs work at stirring rates below 600 rpm. Using the foam blade design, gas bubbles are mainly created by the turbulence at the gas–liquid interface. Large bubbles are broken up by the foam blades. Using a foam block design, rotation leads to the structurization of the reactor volume into sections strongly differing in gas holdup, flow behavior and bubble size distribution. This results in a gas–liquid mass transfer, which is 50% higher than the Rushton stirrer used as comparison. The foam stirrer designs can be easily used in ordinary three-phase reactors and show a high potential for further optimization of the gas–liquid flow pattern and therefore for further increase of the rate of mass transfer.     

Measurements of the effective mass transfer areas for the gas–liquid rotating packed bed

Rotating packed bed(RPB) is one of the most effective gas–liquid mass transfer enhancement reactors, its effective specific mass transfer area(ae) is critical to understand the mass transfer process. By using the NaOH–CO₂ chemical absorption method, the aevalues of three RPB reactors with different rotor sizes were measured under different operation conditions. The results showed that the high gravity factor and liquid flow rate were major affecting factors, while the gas flow rate ex...     

Arduino-based slider setup for gas–liquid mass transfer investigations: Experiments and CFD simulations

The implementation of traditional sensors is a drawback when investigating mass transfer phenomena within microstructured devices, since they disturb the flow and reactor characteristics. An Arduino based slider setup is developed, which is equipped with a computer-vision system to track gas–liquid slug flow. This setup is combined with an optical analytical method allowing to compare experimental results against CFD simulations and investigate the entire lifetime of a single liquid slug with high spatial and temporal resolution. Volumetric mass transfer coefficients are measured and compared with data from literature and the mass transfer contribution of the liquid film is discussed.     

Experimental study on gas–liquid dispersion and mass transfer in shear-thinning system with coaxial mixer

The effects of impeller type, stirring power, gas flow rate, and liquid concentration on the gas–liquid mixing in a shear-thinning system with a coaxial mixer were investigated by experiment, and the overall gas holdup, relative power demand, and volumetric mass transfer coefficient under different conditions were compared. The results show that, the increasing stirring power or gas flow rate is beneficial in promoting the overall gas holdup and volumetric mass transfer coefficient, while the increasing system viscosity weakens the mass transfer in a shearing–thinning system. Among the three turbines, the six curved-blade disc turbine (BDT-6) exhibits the best gas pumping capacity; the six 45° pitched-blade disc turbine (PBDT-6) has the highest volumetric mass transfer coefficient at the same unit volume power.     

A new perspective on vegetable oil epoxidation modeling: Reaction and mass transfer in a liquid–liquid–solid system

A rigorous mathematical model was developed for a complex liquid–liquid–solid system in a batch reactor. The approach is general but well applicable for the indirect epoxidation of vegetable oils according to the concept of Nikolaj Prileschajew, implying in situ prepared percarboxylic acids as epoxidation agents. The model considers intra- and interfacial mass transfer effects coupled to reaction kinetics. The liquid phases were described with chemical approach (aqueous phase) and a reaction–diffusion approach (oil phase). The oil droplets were treated as rigid spheres, in which the overall reaction rate is influenced by chemical reactions and molecular diffusion. The model was tested with a generic example, where two reactions proceeded simultaneously in the aqueous and oil phases. The example (i.e., fatty acid epoxidation) illustrated the power of real multiphase model in epoxidation processes. The proposed modeling concept can be used for optimization purposes for applications, which comprise a complex water–oil–solid catalyst system.     

Evaporative liquid jets in gas–liquid–solid flow system

Some aspects of the fundamental characteristics of evaporative liquid jets in gas–liquid–solid flows are studied and some pertinent literature is reviewed. Specifically, two conditions for the solids concentration in the flow are considered, including the dilute phase condition as in pneumatic convey and the dense phase condition as in bubbling or turbulent fluidized beds. Comparisons of the fundamental behavior are made of the gas–solid flow with dispersed non-evaporative as well as with evaporative liquids.For dilute phase conditions, experiments and analyses are conducted to examine the individual phase motion and boundaries of the evaporative region and the jet. Effects of the solids loading and heat capacity, system temperature, gas flow velocity and liquid injection angle on the jet behavior in gas and gas–solid flows are discussed. For dense phase conditions, experiments are conducted to examine the minimum fluidization velocity and solids distribution across the bed under various gases and liquid flow velocities. The electric capacitance tomography is developed for the first time for three-phase real time imaging of the dense gas–solid flow with evaporative liquid jets. The images reflect significantly varied bubbling phenomenon compared to those in gas–solid fluidized beds without evaporative liquid jets.     

Hydrodynamics and local mass transfer characterization under gas–liquid–liquid slug flow in a rectangular microchannel

Gas–liquid–liquid three-phase slug flow was generated in a glass microreactor with rectangular microchannel, where aqueous slugs were distinguished by relative positions to air bubbles and organic droplets. Oxygen from bubbles reacted with resazurin in slugs, leading to prominent color changes, which was used to quantify mass transfer performance. The development of slug length indicated a film flow through the corner between bubbles and the channel wall, where the aqueous phase was saturated with oxygen transferred from bubble body. This film flow results in the highest equivalent oxygen concentration within the slug led by a bubble and followed by a droplet. The three-phase slug flow subregime with alternate bubble and droplet was found to benefit the overall mass transfer performance most. These results provide insights into a precise manipulation of gas–liquid–liquid slug flow in microreactors and the relevant mass transfer behavior thereof.     

Euler multiphase-CFD simulation on a bubble-driven gas–liquid–solid fluidized bed

An integrated flow model was developed to simulate the fluidization hydrodynamics in a new bubble-driven gas–liquid–solid fluidized bed using the computational fluid dynamic (CFD) method. The results showed that axial solids holdup is affected by grid size, bubble diameter, and the interphase drag models used in the simulation. Good agreements with experimental data could be obtained by adopting the following parameters: 5 mm grid, 1.2 mm bubble diameter, the Tomiyama gas–liquid model, the Schiller–Naumann liquid–solid model, and the Gidaspow gas–solid model. At full fluidization state, an internal circulation of particles flowing upward near the wall and downward in the centre is observed, which is in the opposite direction compared with the traditional core-annular flow structure in a gas–solid fluidized bed. The simulated results are very sensitive to bubble diameters. Using smaller bubble diameters would lead to excessive liquid bed expansions and more solid accumulated at the bottom due to a bigger gas–liquid drag force, while bigger bubble diameters would result in a higher solid bed height caused by a smaller gas–solid drag force. Considering the actual bubble distribution, population balance model (PBM) is employed to characterize the coalescence and break up of bubbles. The calculated bubble diameters grow up from 2–4 mm at the bottom to 5–10 mm at the upper section of the bed, which are comparable to those observed in experiments. The simulation results could provide valuable information for the design and optimization of this new type of fluidized system.     

Development of a filtered interphase heat transfer model based on fine-grid simulations of gas–solid flows

The filtered interphase heat-transfer coefficient for coarse-grid simulations of gas–solid flows can be obtained via a correction (Q) to its microscopic counterpart. The numerical results show that a good linear correlation between Q and the subgrid drift temperature exists at various filtered solid volume fractions, filter sizes and Reynolds numbers, where the subgrid drift temperature is the correlation between the fluctuating temperature of the gas phase and the fluctuation of the gas volume fraction. Since Q can be determined solely by one subgrid quantity, closure for Q is directly pursued. It is found that Q correlates surprisingly well with the product of the filtered solid volume fraction and the filtered temperature difference between the two phases normalized by the filtered heat transfer at a larger scale than the considered coarse grid. A fitting correlation is formulated based on this observation, and its predictability is evaluated in an a priori test.     

A continuum model for gas–liquid flow in packed towers

Gas–liquid flow in packed towers is commonly encountered in the chemical and processing industry. A continuum model is developed based on the volume-and-time averaging of multiphase flows in isotropic rigid porous media/packed columns. Closures are presented for the evaluations of the extra surface/intrinsic phase integral terms. Both inertia and inter-phase interactions are retained in the volume averaged (Navier–Stokes) equations. These governing equations are solved for fully-developed axi-symmetric single and gas–liquid two phase flows in highly porous packed towers. It is found that the dispersion term is present in the continuity equation as well as the momentum equations. Numerical simulations with the models show that the volume-and-time averaged equations can predict the velocity, phase hold-up and pressure drop quite well for up to the loading point for gas–liquid counter-current flows.     

Entransy dissipation analysis of interfacial convection enhancing gas–liquid mass transfer process based on field synergy principle

An exploration of the gas CO2 absorbed into liquid ethanol accompanied with Rayleigh convection is performed by analyzing the mass entransy dissipation; this new statistical quantity is introduced to describe the irreversibility of mass transfer potential capacity. Based on the general advection–diffusion differential equation for an unsteady mass transfer process, the variation of the included angle between the velocity vector and concentration gradient fields is investigated to reveal the underlying mechanism of interfacial convection enhancing mass transfer. Results show some identical characteristics with the qualitative analyses of the synergy effects generated by the concentration and velocity fields after interfacial convection occurring for a boundary condition of fixed surface concentration. And the equivalent mass resistance for convective mass transfer process presents the similar variation with the reciprocal of instantaneous mass transfer coefficient. Accordingly, it is reasonable to be seen that mass transfer dissipation rate could be provided to assess the convection strength and explain fundamentally how Rayleigh convection improves mass transfer performance through establishing a close relationship between the mass transfer capacity and field synergy principle from the view of mass transfer theory.     

Drift-flux model for gas–liquid flow subjected to centrifugal fields

Centrifugal pumps are used in several industrial processes. It is common the operation of this equipment with gas–liquid mixtures, which is the case of the electrical submersible pumping artificial lift method used in the oil industry. The increase of free gas fraction inside the pump may lead to unstable operation and problems such as surging and gas locking phenomena to occur. In this study a drift-flux model is proposed for the gas–liquid flow subjected to centrifugal fields using the impeller as an example. The model is closed with experimental data of bubble diameter, displacements and velocities acquired via high-speed camera at several different rotational speeds and gas mass flow rates using water as the continuous medium. From the modeling and the forces balance in the bubbles, quantitative criteria for the start point of surging and gas locking conditions were proposed.     

Experimental investigation on gas–liquid flow,heat and mass transfer characteristics in a dual-contact-flow absorption tower

As a kind of chemical reactor, the dual-contact-flow absorption tower has been widely used for SO₂ absorption in recent years. However, studies on heat transfer characteristics of the absorber have been rarely carried out. There is also lack of an integrated partition map of flow pattern in the dual-contact-flow absorption tower. In this paper, the gas–liquid flow, heat and mass transfer characteristics in the dual-contact-flow absorption tower have been experimentally investigated. Direct observation, probability density function (PDF) and power spectral density function (PSD) methods are comparatively adopted in the flow pattern analysis. The partition map of flow pattern in the dual-contact-flow absorption tower is obtained through integrating a large quantity of experimental data. In addition, empirical formulas of both heat and mass transfer performances have been developed. Application of empirical formulas has also been stated. The research results obtained in the present study can provide guidance for estimating the practical application performance.     

Study on liquid–liquid two-phase mass transfer characteristics in the microchannel with deformed insert

In this work, the liquid–liquid two-phase mass transfer characteristics in the microchannel with deformed insert were studied. The experiment used di-(2-ethylhexyl) phosphoric acid/kerosene-Cu²⁺as the mass transfer evaluation system. The effects of some key factors such as the total flow velocity,channel inner diameter, channel length, insert diameter, extractant concentration on the extraction efficiency and mass transfer coefficient were systematically investigated. Compared with a ...     

Development of a model for thin-film stability and spreading in solid–liquid–liquid systems

The presence of thin aqueous films and their stability has a profound effect on reservoir rock–fluids interactions involved in spreading and adhesion. The stability of thin wetting aqueous films on rock surfaces is governed by several variables including pH, brine and crude oil compositions, and capillary pressure. These variables govern the wetting states in the solid–liquid–liquid systems. The wetting states influence the residual oil saturation and the oil-water relative permeabilities and, consequently, the oil recovery. The objective of this study was to deduce a functional dependence of thin-film stability on the above parameters by considering intermolecular and surface interactions in rock–crude oil–brine systems. The surface forces are manifested as disjoining pressure in thin films. The disjoining pressure isotherms for the selected solid–liquid–liquid systems have been computed in terms of the bulk properties of the media. The equilibrium contact angles have also been computed from the integration of the Young–Laplace equation, which relates contact angle to the capillary pressure and disjoining pressure isotherm of the system. The contact-angle data obtained from sessile-drop experiments have been compared with the calculated results, as well as with other published results. Adhesion maps, which relate the film stability to brine pH and molarity, have been developed. The rock–fluids systems considered for this study consisted of smooth glass, quartz and Yates reservoir fluids. The DLVO theory has been used to model the intermolecular forces. The structural forces are incorporated to overcome the limitations of the DLVO theory. A charge regulation model has been used to analyze the crude oil–brine and glass–brine interfaces. The effects of multivalent ions have been incorporated using an equivalent molarity concept. The overall computational model developed in this study is aimed at providing a priori prediction capability of rock-fluids interactions in petroleum reservoirs for inclusion in reservoir simulators.     

Effective interfacial area for mass transfer in the liquid–liquid slug flow capillary microreactors

Liquid–liquid biphasic reactions play an important role in the chemical and pharmaceutical industries. The liquid–liquid slug flow capillary microreactor offers considerable potential benefits over the conventional liquid–liquid contactors. Though the hydrodynamics and mass transfer have been investigated for this reactor concept, so far the effective interfacial area available for mass transfer has not been experimentally quantified. Despite the well-defined flow patterns arising in the capillary microreactor, the wetting behaviour of the liquids at the capillary wall is inadequately integrated into the models and thus, the true interfacial area being used for mass transfer is uncertain.