Improved Void Fraction Correlation for Two‐Phase Flow in Large‐Diameter Annuli

A flow pattern‐independent void fraction correlation for gas‐liquid two‐phase flow in vertical large‐diameter annuli is established. Two equations are proposed for the parameters of a drift flux model‐based correlation: the distribution parameter and the drift flux velocity. These equations are expressed as a function of two‐phase flow variables including void fraction, fluid properties, pipe geometry, and phase flow rates. Experiments were performed to study the void fraction of vertical air‐water two‐phase flow in large‐diameter annuli. The obtained experimental data along with the literature data of Caetano are used to verify the performance of the proposed void fraction correlation. The accuracy of this correlation is compared with nineteen frequently used correlations in literature. The proposed correlation was found to predict the void fraction consistently with a better accuracy.     

Counter‐current gas‐liquid wavy film flow between the vertical plates analyzed using the Navier‐Stokes equations

The article is devoted to a theoretical analysis of counter‐current gas‐liquid wavy film flow between vertical plates. We consider two‐dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier‐Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier‐Stokes system and (2) the simplified Benjamin‐Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u‐velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative u‐velocities take place in the neighbourhood of the film thickness minimum. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Phase Inversion and Associated Phenomena in Oil‐Water Vertical Pipeline Flow

Phase inversion and its associated phenomena are experimentally investigated in co‐current upward and downward oil‐water flow in a vertical stainless steel test section (38 mm I.D.). Oil (ρ_o=828 kg/m³, µ_o=5.5 mPa s) and tap water are used as test fluids. Two inversion routes (w/o to o/w and o/w to w/o) are followed in experiments where either the mixture velocity is kept constant and the dispersed phase fraction is increased (type I experiments), or the continuous phase flow rate is kept constant and that of the dispersed phase is increased (type II experiments). By monitoring phase continuity at the pipe centre and at the wall it was found that phase inversion does not happen simultaneously at all locations in the pipe cross‐section. In type I experiments, the velocity ratios (U_o/U_w) where complete inversion appeared acquired the same constant value in both flow directions, although the phase inversion points, based on input phase fractions, were different. In contrast to previous results in horizontal flows, frictional pressure gradient was found to be minimum at the phase inversion point. The interfacial energies of the two dispersions before and after phase inversion, calculated from the measured drop sizes, were found to be different in contrast to the previously suggested criterion of equal energies for the appearance of the phenomenon. In type II experiments the phase inversion point was found to depend on mixture velocity for low and medium velocities but not for high ones. In all cases studied an ambivalent region, commonly reported for inversion in stirred vessels, was not observed.     

A Comparison of the Mixing Characteristics in Single‐ and Two‐Phase Grid‐Generated Turbulent Flow Systems

The mixing process is studied in grid‐generated turbulent flow for single‐ and bubbly two‐phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two‐phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single‐phase flow, the normalized mean concentration cross‐stream profiles have rather similar Gaussian shapes, and the cross‐stream profiles of the normalized root‐mean‐square (RMS) values of concentration were found to be quite similar. Cross‐stream profiles of the mean concentration, for bubbly two‐phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single‐phase flow. Almost self‐similar behavior was also found for the RMS values of the concentration in two‐phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two‐phase flow than in single‐phase flow.     

3‐D Simulations of an Internal Airlift Loop Reactor using a Steady Two‐Fluid Model

Three‐dimensional (3‐D) simulations of an internal airlift loop reactor in a cylindrical reference frame are presented, which are based on a two‐fluid model with a revised k‐? turbulence model for two‐phase bubbly flow. A steady state formulation is used with the purpose of time saving for cases with superficial gas velocity values as high as 0.12 m/s. Special 3‐D treatment of the boundary conditions at the axis is undertaken to allow asymmetric gas‐liquid flow. The simulation results are compared to the experimental data on average gas holdup, average liquid velocity in the riser and the downcomer, and good agreement is observed. The turbulent dispersion in the present two‐fluid model has a strong effect on the gas holdup distribution and wall‐peaking behavior is predicted. The CFD code developed has the potential to be applied as a tool for scaling up loop reactors.     

Numerical Investigation of the Gas‐Solid Flow Characteristics in a Three‐Dimensional Spouted Bed with a Draft Tube

Gas‐solid motions in a three‐dimensional conical spouted bed with a draft tube are investigated based on a simulation carried out by the coupling approach of computational fluid dynamics combined with the discrete‐element method. The distribution properties of the velocity, the concentration, and the flux of the solid phase are discussed. The vertical solid velocity in the central region initially increases, diminishes gradually, and finally decreases sharply in the region above the draft tube. Vigorous lateral solid motion occurs in the periphery of the fountain and the spout‐annulus interface. In addition, the vertical solid flux shows a large value in the spout. A larger vertical velocity but a more dilute solid concentration can be detected along the axial direction when enlarging the gas flow rate.     

Measurements of horizontal three‐phase solid‐liquid‐gas slug flow: Influence of hydrate‐like particles on hydrodynamics

Gas hydrate formation is a main flow assurance concern in oil and gas production. Understanding the effects of the introduction of solid particles in the slug flow is essential to improve the efficiency and safety of multiphase production. The purpose of the present work is the experimental characterization of solid‐liquid‐gas slug flow with the presence of dispersed hydrate‐like particles. Experimental tests were carried out with inert polyethylene particles of 0.5‐mm diameter with density similar to gas hydrates (938 kg/m³). The test section comprised a 26‐mm ID, 9‐m length horizontal duct of transparent Plexiglas. High Speed Imaging and resistivity sensors was used to analyze the slug flow unit cell behavior due to the introduction of the solid particles and to measure the unit cell translational velocity, the slug flow frequency, the bubble and slug lengths, and the phase fractions. Two distinct concentrations of solid particles were tested (6 and 8 g/dm³). © 2018 American Institute of Chemical Engineers AIChE J, 64: 2864–2880, 2018     

Modeling of Slug Velocity and Pressure Drop in Gas‐Liquid‐Liquid Slug Flow

Gas‐liquid‐liquid slug flow in a capillary reactor is a promising new concept that allows one to incorporate gas‐liquid reaction, liquid‐liquid extraction, and facile catalyst separation in a single unit. In order to assess the performance of a gas‐liquid‐liquid slug flow reactor, it is necessary to predict the slug velocity and pressure drop to ascertain residence times and reaction rates. New empirical models for velocity and pressure drop were developed based on existing models for two‐phase gas‐liquid and liquid‐liquid slug flows, and these were validated experimentally.     

Analysis of roll wave characteristics under low liquid loading two‐phase flow conditions

An experimental study is conducted using a 0.152‐m ID facility to investigate the wave characteristics of two‐phase stratified wavy flow in horizontal pipelines. The experiments are conducted under low liquid loading condition, which is very commonly observed in wet gas pipelines. The experiments are conducted with water as the liquid phase, and repeated with 51 wt % of monoethylene glycol (MEG) in the aqueous phase to analyze the effects of MEG presence on wave characteristics. The experimental range of this study covers superficial gas velocity, v_Sg, values of 9–23 m/s and superficial liquid velocity, v_SL, values of 0.01–0.02 m/s. Similar test matrices are completed for the cases with and without MEG in the aqueous phase. A conductivity probe system is used to measure the wave characteristics at the liquid–gas interface. These characteristics include the wave celerity, frequency, amplitude, length, and liquid film thickness. The experimental oil–air wave characteristics data of Gawas et al. (Int J Multiphase Flow. 2014;63:93–104) is also used for comparison purposes. The trends in the resulting wave characteristics with respect to input parameters are investigated, for oil, water, or MEG–water mixture as the liquid phase. Common predictive methods for interfacial wave celerity, including shallow water theory, Watson (Proceedings of the 4th International Conference in Multi‐Phase Flows, Nice, France. 1989:495–512), Paras et al. (Int J Multiphase Flow. 1994;20(5):939–956), Al‐Sarkhi et al. (AIChE J. 2012;58(4):1018–1029), and Gawas et al. (Int J Multiphase Flow. 2014;63:93–104) are evaluated in comparison with the experimental data. The results of the wave frequency correlation of Al‐Sarkhi et al. (AIChE J. 2012;58(4):1018–1029) are also compared with the experimental wave frequency data. Lastly, a correlation is developed to predict the relative wave amplitude, as a function of superficial gas Weber number and liquid velocity number. Most of the commonly used two‐phase stratified flow models are developed with the assumption of steady‐state conditions, and neglect the transient wave effects. This study provides valuable experimental results on wave characteristics of stratified wavy flow for different types of liquid phase. Moreover, a comprehensive analysis of the parameters affecting the wave characteristics of stratified wavy flow is presented. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3177–3186, 2017     

Low Inclination Oil‐water Flows

Two‐phase liquid flows at +5° inclination from the horizontal were studied experimentally for mixture velocities between 0.7 and 2.5 m/s and input oil fractions between 10% and 90%. The results were compared with a two‐fluid model that includes entrainment. The investigations were performed in a 38‐mm ID stainless steel test section, with water and oil as test fluids. Dual continuous flow (both phases remain continuous with inter‐dispersion) prevailed, while the two‐phase pressure gradient was found lower than the single‐phase oil or water. At low mixture velocities the velocity ratio increased with oil fraction while at high ones it decreased. Compared to horizontal flow, water holdup was higher and frictional pressure gradient lower.     

Non‐Uniform Distribution of Two‐Phase Flows through Parallel Identical Paths

When a single‐phase fluid splits, passes through identical paths in parallel, and then recombines, the flow distributes itself uniformly among the multiple paths. However, when multi‐phase suspensions travel through identical parallel paths, the flow distribution can be significantly non‐uniform. Although the uniform distribution is a solution of the governing equations, this solution may be an unstable steady‐state solution between two or more stable solutions, or one of an array of possible steady‐state solutions. This multiplicity has arisen in practice for multiple vertical channels within fluidized beds, for cyclones in parallel, and for distributed feed suspension flows. Simple theories are employed to explain the principles involved for two cyclones and for a pair of risers in parallel.     

Phase separation of gas–liquid two‐phase stratified and plug flows in multitube T‐junction separators

Using air and water as the working fluids, phase separation phenomena for stratified and plug flows at inlet were investigated experimentally, at a simple T‐junction and specifically designed multitube T‐junction separators with two or three layers. The results show that for these two flow patterns the separation efficiency of the two phases for any multitube T‐junction separator is much higher than that of the simple T‐junction. Increasing the number of connecting tubes in the multitube T‐junction separator can increase the separation efficiency. Generally, for stratified flow, complete separation of the two phases can be achieved by the two‐layer multitube T‐junction separator with five or more connecting tubes and by the three‐layer separator; increasing the gas flow rate, the liquid flow rate, or the mixture velocity under plug flow is detrimental to phase separation with a drop in peak separation efficiency. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2285–2292, 2017     

Simulation and Experimental Validation of Two‐Phase Flow in an Aerosol Counter‐Flow Reactor using Computational Fluid Dynamics

A simulation of the hydrodynamic behavior of an aerosol‐counter flow reactor was conducted using an Euler‐Lagrange method. The simulation results were then verified with experiments. The process simulated was a separation process required during the production of biodiesel (fatty acid methyl ester). In this process, the liquid ester/glycerol phases are continuously injected through a hollow cone nozzle with an overpressure of 10⁶ Pa into the reactor, operated at 15000 Pa. The liquid is atomized because of the pressure drop and a liquid particle spray is generated with an inlet velocity of 44.72 m/s. Water vapor of temperature 333 K is injected tangentially through two side, gas inlets with an inlet velocity of 1.2 m/s. Excess methanol is subjected to a mass transfer from the liquid phase into the gas phase, which is withdrawn through the head of the reactor and condensed in an external condenser unit. The stripping of the methanol off the liquid leads to a sharp interface between the glycerol and the ester phase, which can then be easily separated by gravity or pumping. The gas velocity field, pressure field and the liquid particle trajectories were calculated successfully. Simulated dwell time distribution curves were derived and analyzed with the open‐open vessel dispersion model. Experimental dwell time distribution curves were measured, analyzed with the open‐open vessel dispersion model, and compared with the simulated curves. A good consistency between simulated and measured Bodenstein numbers was achieved, but 25 % of the simulated particles exited at the reactor's head, contrary to experimental observations. The difference between simulated and measured dwell times was within one order of magnitude.     

Effect of tube diameter on two‐phase flow patterns in mini tubes

The effect of tube diameter on two‐phase flow patterns was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6, and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01–50 and 0.01–3 m/s, respectively. The gas and liquid flow rates were measured and the two‐phase flow pattern images were recorded using high‐speed CMOS camera. The flow patterns observed were dispersed bubbly, bubbly, slug, slug‐annular, wavy‐annular, stratified, and annular flows. These flow patterns were not observed in all the test diameters, but were found to be unique to particular tube diameters, confirming the effect of tube diameter on the flow pattern. The data obtained were compared to existing experimental data and flow regime transition maps which show generally reasonable overall agreement at the larger diameters, but significant differences were observed with the smaller diameter tubes.     

Volume‐of‐fluid‐based model for multiphase flow in high‐pressure trickle‐bed reactor: Optimization of numerical parameters

Aiming to understand the effect of various parameters such as liquid velocity, surface tension, and wetting phenomena, a Volume‐of‐Fluid (VOF) model was developed to simulate the multiphase flow in high‐pressure trickle‐bed reactor (TBR). As the accuracy of the simulation is largely dependent on mesh density, different mesh sizes were compared for the hydrodynamic validation of the multiphase flow model. Several model solution parameters comprising different time steps, convergence criteria and discretization schemes were examined to establish model parametric independency results. High‐order differencing schemes were found to agree better with the experimental data from the literature given that its formulation includes inherently the minimization of artificial numerical dissipation. The optimum values for the numerical solution parameters were then used to evaluate the hydrodynamic predictions at high‐pressure demonstrating the significant influence of the gas flow rate mainly on liquid holdup rather than on two‐phase pressure drop and exhibiting hysteresis in both hydrodynamic parameters. Afterwards, the VOF model was applied to evaluate successive radial planes of liquid volume fraction at different packed bed cross‐sections. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Coupled DEM‐CFD Simulation of Pneumatically Conveyed Granular Media

A DEM‐CFD coupling for the simulation of gas‐solid flows was successfully implemented and simulations were performed for the application to industrial‐scale pneumatic conveying. Therefore, all particle collisions and phase interactions were considered and porosity determination was optimized. The aim of this work is to show the applicability of the presented simulation model to the different regimes of pneumatic conveying systems. As a first test case a dense vertical pneumatic conveying system was chosen and an individual plug was investigated in detail. Variations of the conveying air velocity were also considered. As a second test case dilute conveying in a horizontal‐to‐vertical pipe bend was simulated. The occurrence of roping and the reduction of particle velocity is of high interest for the design of specific pneumatic systems. It is shown that both regimes can be captured reasonably well and the results are rich in details.     

Computational Fluid Dynamics Modeling of Gas‐Liquid Two‐Phase Flow around a Spherical Particle

Microscale studies, which can provide basic information for meso‐ and macroscale studies, are essential for the realization of flow characteristics of a packed bed. In the present study, the effects of gas velocity, liquid velocity, liquid‐solid contact angle, and liquid viscosity on the flow behavior were parametrically investigated for gas‐liquid two‐phase flow around a spherical particle, using computational fluid dynamics (CFD) methodology in combination with the volume‐of‐fluid (VOF) model. The VOF model was first validated and proved to be in good agreement with the experimental data. The simulation results show that the film thickness decreases with increasing gas velocity. This trend is more obvious with increasing operating pressure. With increasing liquid velocity, the film thickness tends to be uniform on the particle surface. The flow regime can change from film flow to transition flow to bubble flow with increasing contact angle. In addition, only at relatively high values does the liquid viscosity affect the residence time of the liquid on the particle surface.     

CFD analysis of two‐phase turbulent flow in internal airlift reactors

The hydrodynamic performance of three internal airlift reactor configurations was studied by the Eulerian–Eulerian k–ε model for a two‐phase turbulent flow. Comparative evaluation of different drag and lift force coefficient models in terms of liquid velocity in the riser and downcomer and gas holdup in the riser was highlighted. Drag correlations as a function of Eötvös number performed better results in comparison to the drag expressions related to Reynolds number. However, the drag correlation as a function of both Reynolds and Eötvös numbers fitted well with experimental results for the riser gas holdup and downcomer liquid velocity in configurations I and II. Positive lift coefficients increase the liquid velocity and decrease the riser gas holdup, while opposite results were obtained for negative values. By studying the effects of bubble size and their shape, the smaller bubbles provide a lower liquid velocity and a gas holdup. The effects of bubble‐induced turbulence and other non‐drag closure models such as turbulent dispersion and added mass forces were analysed. The gas velocity and gas holdup distributions, liquid velocity in the riser and downcomer, vectors of velocity magnitude and streamlines for liquid phase, the dynamics of gas holdup distribution and turbulent viscosity at different superficial gas velocities for different reactor configurations were computed. The effects of various geometrical parameters such as the draft tube clearance and the ratio of the riser to the downcomer cross‐sectional area on liquid velocities in the riser and the downcomer, the gas velocity and the gas holdup were explored. © 2011 Canadian Society for Chemical Engineering     

Two‐Phase Bubbly Flow Structure in Large‐Diameter Vertical Pipes

The two‐phase flow structure of an air‐water, bubbly, upward flow in a 20 cm diameter pipe is presented with particular emphasis on the local interfacial area concentration. The radial distribution of void fraction, bubble velocity, bubble size, bubble frequency, and interfacial area concentration were measured using a local dual‐optical probe. The experimental results showed that the saddle‐type distribution of void fraction and interfacial area concentration, which are common for bubbly flow in small diameter pipes, only appeared in the present experiments under conditions of very low area‐averaged void fraction (<?> < 0.04). The values for the interfacial area concentration were higher in large diameter pipes when compared with data obtained under the same flow conditions in small pipes. The area‐averaged void fraction data were correlated using the drift‐flux model.     

Flow Patterns in Mini‐Hydrocyclones with Different Vortex Finder Depths

Two‐phase flow patterns in a mini‐hydrocyclone with different insertion depths of the vortex finder were measured by a phase Doppler particle analyzer. The distributions of velocity, concentration, root‐mean‐square velocity, and average diameter of particles were evaluated. A deeper insertion of the vortex finder led to smaller tangential velocity at the cross section near the column cone interface. When the vortex finder insertion depth did not reach the column cone interface, the vortex finder was inserted deeper and the line of zero velocity value migrated more distinctly inward. When the vortex finder insertion depth reached or exceeded the column cone interface, strong turbulence occurred near the vortex finder. The distributions of the axial velocities of particles and root‐mean‐square velocities indicated that circulation flow existed at the bottom part of the mini‐hydrocyclone.