Analyses of liquid film models applied to horizontal and near horizontal gas–liquid slug flows

An analysis of liquid film models for horizontal and near horizontal gas–liquid slug flows is developed. The models’ formulations employ the one dimensional separated phase momentum equations. The formulations differ among themselves, by neglecting some terms on the momentum balance and also on the closure relations. A comparative analysis discloses the differences amongst the formulations. The sensitivity of the liquid film models to the changes on the bubble velocity, liquid slug holdup and liquid viscosity is accessed through a series of parametric runs. Finally, the model is tested against experimental data taken for continuous horizontal slug flow. The tests were designed to check if the models are able to capture the stochastic film properties provided the properly closure relations.     

Dispersion of liquid–liquid phase by a jet-induced gas–liquid–liquid mixing column developed for separation of organic pollutants

This article presents the gas and liquid entrainment and its dispersion in a gas–liquid–liquid mixing column. The variations in phase entrainment is observed with the change in the paraffin liquid and kerosene volume fraction from 5% to 35% due to the increase in the flow resistance with increase in the effective viscosity of the liquid–liquid mixture. The degree of dispersion is enunciated based on the axial dispersion model and the flow resistance of the phases in the column. A correlation is proposed to interpret the entrainment of phase as a function of operating variables within the range of experimental conditions.     

Initiation of a gas volume above the boundary of a gas–liquid medium by a bubble wave detonation

It is shown that detonation can be transmitted from a reacting bubble medium into an explosive gas volume located above the interface. Experiments were performed in which bubble detonation was initiated by wire explosion in a gas–liquid medium. The dynamics of the boundary of the gas–liquid medium after the arrival of the bubble detonation wave at it was studied. The distance between the wire and the boundary of the bubble medium was decreased to 1 cm, at which the gas volume was initiated by the hot products from the wire explosion and the discharge plasma. The probability of detonation transmission from the bubble medium to the volume of the gas mixture depending on the depth of immersion of the wire is determined, and the mechanisms of ignition of the explosive gas volume are described.     

Micromixing in a gas–liquid vortex reactor

The gas–liquid vortex reactor (GLVR) has substantial process intensification potential for multiphase processes. Essential in this respect is the micromixing efficiency, which is of great importance in fast reaction systems such as crystallization, polymerization, and synthesis of nanomaterials. By creating a vortex flow and taking advantage of the centrifugal force field, the liquid micromixing process can be intensified in the GLVR. Results show that introducing a liquid into a gas-only vortex unit results in suppression of primary and secondary gas flow. The Villermaux–Dushman protocol is applied to study the effects of the gas flow rate, liquid flow rate, and liquid viscosity based on a segregation index. Based on the incorporation model and reaction kinetics, the micromixing time of the GLVR is determined to be in the range of 10⁻⁴ ~ 10⁻³ s, which is comparable to the highly efficient rotating packed bed and substantially better than a static mixer.     

Measuring gas hold-up in gas–liquid/gas–solid–liquid stirred tanks with an electrical resistance tomography linear probe

An electrical resistance tomography (ERT) linear probe was used to measure gas hold-up in a two-phase (gas–liquid) and three phase (gas–solid–liquid) stirred-tank system equipped with a Rushton turbine. The ERT linear probe was chosen rather than the more commonly used ring cage geometry to achieve higher resolution in the axial direction as well as its potential for use on manufacturing plant. Gas-phase distribution was measured as a function of flow regime by varying both impeller speed and gas flow rate. Global and local gas hold-up values were calculated using ERT data by applying Maxwell's equation for conduction through heterogeneous media. The results were compared with correlations, hard-field tomography data, and computational fluid dynamic simulations available in the literature, showing good agreement. This study thus demonstrates the capability of ERT using a linear probe to offer, besides qualitative tomographic images, reliable quantitative data regarding phase distribution in gas–liquid systems.     

An experimental study of immiscible liquid–liquid dispersions in a pump–mixer of mixer–settler

Drop size distribution(DSD) or mean droplet size(d32) and liquid holdup are two key parameters in a liquid–liquid extraction process. Understanding and accurately predicting those parameters are of great importance in the optimal design of extraction columns as well as mixer–settlers. In this paper, the method of built-in endoscopic probe combined with pulse laser was adopted to measure the droplet size in liquid–liquid dispersions with a pump-impeller in a rectangular mixer. The dispersion law of droplets with holdup range 1% to 24% in batch process and larger flow ratio range 1/5 to 5/1 in continuous process was studied. Under the batch operation condition, the DSD abided by log-normal distribution. With the increase of impeller speed or decrease of dispersed phase holdup, the d32 decreased. In addition, a prediction model of d32 of kerosene/deionized system was established as d_(32)/D = 0.13(1 + 5.9φ)We~(-0.6). Under the continuous operation condition, the general model for droplet size prediction of kerosene/water system was presented as d_(32)/D = C_3(1 + C_4φ)We~(-0.6). For the surfactant system and extraction system, the prediction models met a general model as d_(32)/D = bφ~nWe~(-0.6).     

CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

Spray and mixing characteristics of liquid jet in a tubular gas–liquid atomization mixer

For the design and optimization of a tubular gas–liquid atomization mixer,the atomization and mixing characteristics of liquid jet breakup in the limited tube space is a key problem.In this study,the primary breakup process of liquid jet column was analyzed by high-speed camera,then the droplet size and velocity distribution of atomized droplets were measured by Phase-Doppler anemometry (PDA).The hydrodynamic characteristics of gas flow in tubular gas–liquid atomization mixer were analyzed by computational fluid dynamics (CFD) numerical simulation.The results indicate that the liquid flow rate has little effect on the atomization droplet size and atomization pressure drop,and the gas flow rate is the main influence parameter.Under all experimental gas flow conditions,the liquid jet column undergoes a primary breakup process,forming larger liquid blocks and droplets.When the gas flow rate (Q_g) is less than 127 m~3·h~(-1),the secondary breakup of large liquid blocks and droplets does not occur in venturi throat region.The Sauter mean diameter (SMD) of droplets measured at the outlet is more than 140μm,and the distribution is uneven.When Q_g127 m~3·h~(-1),the large liquid blocks and droplets have secondary breakup process at the throat region.The SMD of droplets measured at the outlet is less than 140μm,and the distribution is uniform.When 127Q_g162 m~3·h~(-1),the secondary breakup mode of droplets is bag breakup or pouch breakup.When 181Q_g216 m~3·h~(-1),the secondary breakup mode of droplets is shear breakup or catastrophic breakup.In order to ensure efficient atomization and mixing,the throat gas velocity of the tubular atomization mixer should be designed to be about 51 m·s~(-1)under the lowest operating flow rate.The pressure drop of the tubular atomization mixer increases linearly with the square of gas velocity,and the resistance coefficient is about 2.55 in single-phase flow condition and 2.73 in gas–liquid atomization condition.     

Comparative study of gas–oil and gas–water two-phase flow in a vertical pipe

A wire-mesh sensor has been employed to study air/water and air/silicone oil two-phase flow in a vertical pipe of 67 mm diameter and 6 m length. The sensor was operated with a conductivity-measuring electronics for air/water flow and a permittivity-measuring one for air/silicone oil flow. The experimental setup enabled a direct comparison of both two-phase flow types for the given pipe geometry and volumetric flow rates of the flow constituents. The data have been interrogated at a number of levels. The time series of cross-sectionally averaged void fraction was used to determine characteristics in amplitude and frequency space. In a more three-dimensional examination, radial gas volume fraction profiles and bubble size distributions were processed from the wire-mesh sensor data and compared for both flow types. Information from time series and bubble size distribution data was used to identify flow patterns for each of the flow rates studied.     

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas–liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid–liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid–liquid system.     

Experimental study and hydrodynamic modeling of countercurrent liquid–solid system with batch liquid

It is known that a transient effluent outlet concentration is obtained with a batch of adsorbent solids in any operation. A preferred steady state outlet concentration can be achieved with a continuous flow of solids. In the present work, information on pressure profiles, the total pressure drop across the column and holdup of solids are experimentally obtained for various solid flow rates, particle sizes and densities in a countercurrent liquid–solid system. These experimental results are compared with the prediction obtained using a phenomenological model containing continuity and momentum balance equations. The dominant drag force term was expressed in terms of various drag equations. The drag expression developed by Foscolo et al. (1983 Foscolo, P. U., Gibilaro, L. G., and Waldram, S. P. (1983). A unified model for particulate expansion of fluidized beds and flow in fixed porous media, Chem. Eng. Sci., 38(8), 1251–1260.[Crossref], [Web of Science ®] , [Google Scholar]) could predict the axial profiles of pressure drop and holdup, and the effect of various parameters on total pressure drop and solid holdup most satisfactorily.     

Hydrodynamics and velocity measurements in gas–liquid swirling flows in cylindrical cyclones

The gas–liquid swirl flow in a gas–liquid cylindrical cyclone separator has been characterized first qualitatively by flow visualizations. The emerged findings were then confirmed quantitatively by Laser Doppler Velocimetry measurements. The vortex core presents a very complex hydrodynamics, characterized by an alternation between a laminar and a turbulent state. The laminar regime is associated with velocities pointing in the same direction as the mean flow, while the turbulent state induces velocities in the opposite direction, i.e. a flow reversal. These observations give a first understanding of the origin of the double flow reversal regime that is encountered in swirl flows. It is shown that this flow structure appears for high swirl intensities, and results from a frequent laminarization of the vortex core. Results show that, contrary to the commonly assumed hypothesis, this flow structure is associated with good separation performance of the cyclone. Accordingly, we propose the use of multiple tangential inlets to generate the swirl motion in the cyclone, which is supposed to favor the double flow reversal regime, and thus, improve the separation efficiency.     

Effect of the injection-nozzle geometry on the interaction between a gas–liquid jet and a gas–solid fluidized bed

In industrial fluid cokers, bitumen is first mixed with steam in a premixer, and then fed to the atomization nozzle. The objective of this work was to evaluate the impact of both the premixer and the nozzle geometrical configuration on the quality of the liquid–solid contact resulting from injections of liquid into a gas–solid fluidized bed. To assess the quality of the liquid–solid contact a method based on electric conductance measurements of the bed material previously developed by the authors [9] was used. Liquid atomization efficiency in open air, spray geometry, and spray stability were also characterized to evaluate their effects on the nozzle spraying performance within the fluidized bed. This study indicated that spray stability is highly beneficial to the liquid–solid contact efficiency. In particular, fluid constrictions such as the series of converging and diverging sections within the nozzle have a stabilizing effect on the spray. Future optimization of the existing liquid-injection systems should consider alternative gas–liquid premixers and nozzle geometries to enhance the jet stability.     

Modeling of dynamic systems with a variable number of phases in liquid–liquid equilibria

Modeling of dynamic systems with a variable number of phases is still a challenge, especially for multiple liquid phases. A common approach from literature derives first-order Karush–Kuhn–Tucker (KKT) conditions of the Gibbs free energy minimization and relaxes these if a phase does not exist. It aims at enabling dynamic simulation in all phase regimes of systems in vapor–liquid equilibrium by following a nonphysical continuous solution. In this work, we demonstrate that this continuous solution is not always possible in liquid–liquid equilibrium problems. The demonstration is done both theoretically and for illustrative examples. To overcome the demonstrated issues, we review the use of negative flash approach that allows negative molar amounts of nonexisting phases and propose a hybrid continuous formulation that explicitly assigns phase variables in the single-phase regime and solves flash equations otherwise. Various dynamic case studies demonstrate the applicability and limitations of all three approaches. © 2018 American Institute of Chemical Engineers AIChE J, 65: 571–581, 2019     

Characteristics of liquid slugs in gas–liquid Taylor flow in microchannels

The hydrodynamics of liquid slugs in gas–liquid Taylor flow in straight and meandering microchannels have been studied using micro Particle Image Velocimetry. The results confirm a recirculation motion in the liquid slug, which is symmetrical about the center line of the channel for the straight geometry and more complex and three-dimensional in the meandering channel. An attempt has also been made to quantify and characterize this recirculation motion in these short liquid slugs (L_s/w<1.5) by evaluating the recirculation rate, velocity and time. The recirculation velocity was found to increase linearly with the two-phase superficial velocity U_TP. The product of the liquid slug residence time and the recirculation rate is independent of U_TP under the studied flow conditions. These results suggest that the amount of heat or mass transferred between a given liquid slug and its surroundings is independent of the total flow rate and determined principally by the characteristics of the liquid slug.     

Enhancement of entrainment rates in liquid–gas ejectors

Ejectors are widely used as effective distributors in many chemical and bioprocess industries. Gas entrainment rate as a function of liquid flow rate in ejectors is investigated using nozzles of different geometries. The data are analyzed through macro-energy balance for each phase considering air and water inlet line discharge coefficients. Nozzles with smaller discharge coefficients are effective in producing higher vacuum and hence higher entrainment rates. It has been observed that the factor limiting the air entrainment rate is the low discharge coefficient in the air inlet line. Higher air inlet line discharge coefficients can increase the entrainment rate.     

Dynamic modelling of a bubble column for particle formation via a gas–liquid reaction

This paper presents a dynamic model of a bubble column reactor with particle formation, accomplished by adopting a hybrid CFD-reaction engineering approach. CFD is employed for estimating the hydrodynamics and is based on the two-phase Eulerian–Eulerian viewpoint. The reaction engineering model links the penetration theory to a population balance that includes particle formation and growth with the aim of predicting the average particle size. The model is then applied to the precipitation of CaCO₃ via CO₂ absorption into Ca(OH)₂aq in a draft tube bubble column and draws insight into the phenomena underlying the crystal size evolution.     

Three-dimensional numerical modelling of interactions between a gas–liquid jet and a fluidized bed

This paper presents the development of a novel mathematical model that describes spray injection and spreading into a fluidized bed of solid particles. The model also includes the gas–liquid flow through the nozzle followed by the gas-assisted atomization. An Eulerian approach that is independent of the nature of the continuous phase is adopted for all phases, which are gas (or bubbles), liquid (or droplets), and solid particles that may be covered with a liquid layer. Variation in sizes of bubbles and droplets is represented by the particle number density approach that takes into account both break-up and coalescence. The atomization is considered as a catastrophic phase inversion triggered by a critical local volume fraction. New relationships were obtained for liquid spreading due to wet particle collisions and for heat conduction between a solid particle and a surrounding liquid layer. The model is applied to simulate liquid injection into the fluidized bed for conditions that were previously experimentally studied and published. The comparison reveals a reasonable agreement in prediction of the cumulative liquid distribution for two experimental cases. In addition, we evaluated a jet penetration distance with the model to compare it with the one measured in another set of experiments. This comparison also yields a good qualitative agreement. Finally, we evaluated the influence of the fluidization velocity on liquid distribution in the bed.