Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction,which limits their capability for increased predictive accuracy relative to experimental data.This is partly because of the nature of slug flow pneumatic conveying system,which,as a dynamic system,never becomes stable.By utilising conservation of mass (airflow),a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour.The rate of air permeation through slug,one of the important factors in the conservation model,is expressed as a function of a slug permeability factor.Other factors such as slug velocity,slug length and the fraction of stationary layer were also considered.Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model,showing good agreement between the model and experimental results.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

One-way coupled fluid–structure interaction of gas–liquid slug flow in a horizontal pipe: Experiments and simulations

Pipelines conveying a multiphase mixture must withstand the cyclic induced stresses that occur due to the alternating motion of gas pockets and liquid slugs. Few previous studies have considered gas–liquid slug flow and the associated fluid–structure interaction problems. In this study, experimental and numerical techniques were adopted to simulate and analyze the two-phase slug flow and the associated stresses in the pipe structure. In the numerical simulation, a one-way coupled fluid–structure framework was developed to explore the slug flow interaction with a horizontal pipe assembly under various superficial gas and liquid velocities. A modified Volume of Fluid and finite element methods were utilized to model the fluid and structure domains. The file-based coupling technique was adopted to execute the coupling mechanism. By contrast, slug characteristics were measured experimentally, while Bi-axial strain gauges were used to capture time-varying strain signals. Excellent agreements between the predicted and measured stress results were achieved with a maximum error of 10.2 %. It was found that at constant superficial liquid velocity, the maximum induced stresses on the pipe wall increased with increasing the slug length and slug velocity. While for the slug frequency, the maximum principal stresses decreased with increasing the slug frequency.     

Planar dynamics of inclined curved flexible riser carrying slug liquid–gas flows

Flexible risers transporting hydrocarbon liquid–gas flows may be subject to internal dynamic fluctuations of multiphase densities, velocities and pressure changes. Previous studies have mostly focused on single-phase flows in oscillating pipes or multiphase flows in static pipes whereas understanding of multiphase flow effects on oscillating pipes with variable curvatures is still lacking. The present study aims to numerically investigate fundamental planar dynamics of a long flexible catenary riser carrying slug liquid–gas flows and to analyse the mechanical effects of slug flow characteristics including the slug unit length, translational velocity and fluctuation frequencies leading to resonances. A two-dimensional continuum model, describing the coupled horizontal and vertical motions of an inclined flexible/extensible curved riser subject to the space–time varying fluid weights, flow centrifugal momenta and Coriolis effects, is presented. Steady slug flows are considered and modelled by accounting for the mass–momentum balances of liquid–gas phases within an idealized slug unit cell comprising the slug liquid (containing small gas bubbles) and elongated gas bubble (interfacing with the liquid film) parts. A nonlinear hydrodynamic film profile is described, depending on the pipe diameter, inclination, liquid–gas phase properties, superficial velocities and empirical correlations. These enable the approximation of phase fractions, local velocities and pressure variations which are employed as the time-varying, distributed parameters leading to the slug flow-induced vibration (SIV) of catenary riser. Several key SIV features are numerically investigated, highlighting the slug flow-induced transient drifts due to the travelling masses, amplified mean displacements due to the combined slug weights and flow momenta, extensibility or tension changes due to a reconfiguration of pipe equilibrium, oscillation amplitudes and resonant frequencies. Single- and multi-modal patterns of riser dynamic profiles are determined, enabling the evaluation of associated bending/axial stresses. Parametric studies reveal the individual effect of the slug unit length and the translational velocity on SIV response regardless of the slug characteristic frequency being a function of these two parameters. This key observation is practically useful for the identification of critical maximum response.     

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work, co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 mm in diameter. Each tube includes two 10 m long pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly flow, stratified flow, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high-speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood–Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/non-Newtonian liquid.     

Flow pattern and flow characteristics for counter-current two-phase flow in a vertical round tube with wire-coil inserts

Flow pattern, void fraction and slug rise velocity on counter-current two-phase flow in a vertical round tube with wire-coil inserts are experimentally studied. Flow pattern and slug rise velocity are measured visually with a video camera. The void fraction is measured by the quick-closing valve method. Four kinds of coils with different coil pitches and coil diameters are used as inserts. The presence of wire-coil inserts induces disturbance into gas and liquid flows so that the shape and motion of gas slug or bubbles in a wire-coil inserted tube are quite different from those observed in a smooth tube without insert. The bubbly flow occurs in the low gas superficial velocity region in the wire-coil inserted tube, while the slug or churn/annular flow only appears in the smooth tube without insert over the all test range. The measured slug rise velocity in the wire-coil inserted tube is higher than that in the smooth tube. With modified mean flow velocity calculated with core area, the slug rise velocity in wire-coil tube inserted is in good agreement with Nicklin's correlation. The void fraction in a wire-coil inserted tube is lower than that in a smooth tube in the range of high gas superficial velocities. By introducing a simple assumption on considering the effective flowing area, the measured void fractions in a wire-coil inserted tube are in relatively good agreement with the predicted result based on the drift flux model proposed by others with the correlation for slug rise velocity given by others when the coil pitch is dense.     

Experimental investigation of air–oil slug flow using capacitance probes,hot-film anemometer,and image processing

Despite the importance of air–oil slug flows to many industrial applications, their available data reported in the literature are limited compared to air–water slug flows. The main objective of the present study is to explain how air–oil slug flow parameters can be experimentally investigated using hot-film anemometry, capacitance sensors and image processing. Experiments were performed using air–oil slug flow through a horizontal pipe for air superficial velocities ranged from 0.01 m/s to 0.65 m/s and oil superficial velocities ranged from 0.03 m/s to 2.3 m/s. The signal obtained from the hot-film anemometer was used to determine the time-averaged local void fraction and liquid velocity and turbulence intensity for air–oil slug flow. The capacitance signals along with the data obtained by image processing of the flow were used to determine the elongated bubble length and velocity. The measurements techniques used found to describe in detail the internal structure of the slug flow. Finally, the experimental results were compared to existing models and correlations.     

Flow pattern transition,pressure gradient,hold-up predictions in gas/non-Newtonian power-law fluid stratified flow

This work focuses on gas/non-Newtonian power-law fluid stratified pipe flow. Two different theoretical approaches to obtain pressure gradient and hold-up predictions are presented: the steady fully developed two-fluid model and the pre-integrated model. The theoretical predictions are compared with experimental data available for horizontal and for slightly downward inclined air/shear thinning fluid stratified flow taken from literature. The predictions of the pre-integrated model are validated showing a good agreement when compared with experimental data. The criteria for the transition from the stratified flow pattern are applied to gas/non-Newtonian stratified flow. The neutral stability analysis (smooth/wavy stratified flow) and the well-posedness (existence region of stratified flow) of governing equations are carry out. The predicted transition boundaries are obtained using the steady fully developed two-fluid model and the pre-integrated model, where the shape factors and their derivatives are accounted for. A comparison between the predicted boundaries and experimental flow pattern maps is presented and shows a good agreement. A comment on the shear stress modeling by the pre-integrated model is provided.     

Investigation of slug flow characteristics in the valley of a hilly-terrain pipeline

The objective of this study is to improve the current phenomenological understanding of slug flow characteristics over an entire hilly-terrain section, and in particular, the slug initiation mechanism at the lower dip.The experimental part of this study revealed that five possible flow behavior categories exist along a hilly-terrain section. In these categories, the flow behavior at the dip is coupled with flow conditions of the upstream downhill section. This qualitative classification was superimposed on steady-state flow pattern maps for the upstream downhill section in an attempt to relate the qualitative flow behavior at a dip to the flow pattern maps through the flow behavior in the downhill section.Statistical analyses of mean slug length, maximum slug length, slug frequency, and slug length variation across the hilly-terrain pipeline revealed that slug length distribution characteristics change across a symmetrical hilly-terrain pipeline. Physical modeling of the slug initiation mechanism and the characteristics of initiated slugs at the lower dip indicated two main mechanisms, namely, wave growth and wave coalescence initiation mechanisms. The initiated “pseudo slugs” or slug characteristics of each mechanism differ significantly with respect to frequency, length, liquid holdup and velocity. It was observed that pseudo slugs initiated by the wave coalescence mechanism have velocities less than the mixture velocity due to gas blowing through the slug body.     

Air-lift pumps characteristics under two-phase flow conditions

Air-lift pumps are finding increasing use where pump reliability and low maintenance are required, where corrosive, abrasive, or radioactive fluids in nuclear applications must be handled and when a compressed air is readily available as a source of a renewable energy for water pumping applications. The objective of the present study is to evaluate the performance of a pump under predetermined operating conditions and to optimize the related parameters. For this purpose, an air-lift pump was designed and tested. Experiments were performed for nine submergence ratios, and three risers of different lengths with different air injection pressures. Moreover, the pump was tested under different two-phase flow patterns. A theoretical model is proposed in this study taking into account the flow patterns at the best efficiency range where the pump is operated. The present results showed that the pump capacity and efficiency are functions of the air mass flow rate, submergence ratio, and riser pipe length. The best efficiency range of the air-lift pumps operation was found to be in the slug and slug-churn flow regimes. The proposed model has been compared with experimental data and the most cited models available. The proposed model is in good agreement with experimental results and found to predict the liquid volumetric flux for different flow patterns including bubbly, slug and churn flow patterns.     

Simulation of large amplitude waves in a slug tracking scheme compared to roll wave experiments at high pressure

Due to the similarities between large amplitude roll waves and slug flow in two-phase gas–liquid pipe flow, a slug tracking scheme is presented with the addition of a simplified model for roll waves. The waves are treated in a similar way to slugs, modelled as objects moving at the wave velocity and with a pressure variation across them. The two-fluid model is solved on a stationary staggered grid in stratified sections between moving waves and slugs. The model is dynamic meaning that the growth and decay of waves and slugs can be simulated. The wave model implementation within the tracking scheme is discussed and demonstrated in comparison to existing experimental data on wave velocities and averaged pressure drops. The results from the tracking scheme compared well to the experiments when waves were initiated with the experimental frequency. Wave initiation remains as a modelling challenge.     

An appraisal of liquid–liquid slug flow in different pipe orientations

Gas–liquid slug flow occurs over a wide range of phase flow rates and in a variety of practical applications during gas–liquid two-phase flows. The range of slug flow increases further in narrow pipes (<0.0254 m), undulated pipelines, riser tube, etc. On the other hand, the past literature shows that slug flow is rarely observed for liquid–liquid cases. In the present study, an interest was felt to investigate whether liquid–liquid slug flow occurs in situations known for excessive slugging in gas–liquid cases. For this, experiments have been performed in narrow (0.012 m ID) vertical and horizontal pipes and an undulated pipeline of 0.0254 m internal diameter where the V-shaped undulation comprises of an uphill and a downhill section between two horizontal pipes. The studies have been performed for both peak and valley orientation of the undulation. Kerosene and water have been selected as the test fluids and the optical probe technique has been used to supplement visual observations especially at higher flow rates. The studies have revealed the existence of the slug flow pattern over a wide range of phase flow rates in all the three geometries. Interestingly, it has been noted that the introduction of an undulation induces flow patterns which bear a closer resemblance to gas–liquid flows as compared to liquid–liquid flows through a horizontal pipe of 0.0254 m diameter.     

Film thickness measurements in liquid–liquid slug flow regimes

At present there is significant interest in the development of small scale medical diagnostic equipment. These devices offer faster processing times and require smaller sample volumes than equivalent macro scale systems. Although significant attention has been focused upon their outputs, little attention has been devoted to the detailed fluid mechanics that govern the flow mechanisms within these devices. Conventionally, the samples in these small scale devices are segmented into distinct discrete droplets or slugs which are suspended in an organic carrier phase. Separating these slugs from the channel wall is a very thin film of the organic carrier phase.The magnitude of this film is the focus of the present study and the effects of sample slug length and carrier phase fluidic properties on the film are examined over a range of Capillary numbers. A non-intrusive optical technique was used to capture images of the flow from which the magnitude of the film was determined.The experimental results show that the film is not constant along the length of the slug; however above a threshold value for slug length, a region of constant film thickness exists. When compared with existing correlations in the literature, the experimental data showed reasonable agreement with the Bretherton model when the Capillary number was calculated based on the mean two phase flow velocity. However, significant differences were observed when the Capillary number was redefined to account for the mean velocity at the liquid interface, i.e., the mean slug velocity.Analysis of the experimental data revealed that it fell into two distinct flow regimes; a visco-capillary regime and a visco-inertial regime. A modified Taylor expression is presented to estimate the magnitude of the film for flows in the visco-capillary regime while a new model is put forward, based on Capillary and Weber numbers, for flows in the visco-inertial regime. Overall, this study provides some novel insights into parameters, such as aqueous slug length and carrier phase fluidic properties, that affect the thickness of the film in liquid–liquid slug flow regimes.     

Experimental study on near wall transport characteristics of slug flow in a vertical pipe

In this work, the wall shear stress and the mass transfer coefficient of the gas–liquid two-phase upward slug flow in a vertical pipe are investigated experimentally, using limiting diffusion current probes and digital high-speed video system. In experiments, the instantaneous and averaged characteristics of wall shear stress and mass transfer coefficient are concerned. The experimental results are compared with the numerical results in previous paper of the authors. Both experiment and numerical simulation show that the superficial gas and liquid velocities have an obvious influence on the instantaneous characteristics of the two profiles. The mass transfer coefficient has characteristics similar to the wall shear stress. The instantaneous wall shear stress and mass transfer coefficient profiles have the periodicity of slug flow. The averaged wall shear stress and mass transfer coefficient increase with increased superficial gas velocity. However, there is inconsistency in the variation trends of the averaged wall shear stress and mass transfer coefficient with superficial liquid velocity between experimental result and numerical simulation result, which can be attributed to the difference in flow condition. Moreover, the Taylor bubble length is also another impacting factor. The experimental and numerical results all shows that the product scale can not be damaged directly by the flow movement of slug flow. In fact, the alternative forces and fluctuations with high frequency acting on the pipe wall due to slug flow is the main cause for the slug flow enhanced CO₂ corrosion process.     

Void fraction and pressure waves in a transient horizontal slug flow

The void fraction and the pressure waves in an air–water mixture flowing in the slug regime are experimentally investigated in a horizontal line. The test section is made of a transparent Plexiglas pipe with 26 mm ID and 26.24 m long, operating at ambient temperature and pressure. The flow induced transients are made by quickly changing the air or the water inlet velocity. The test grid has four operational points. This choice allows one to create expansion and compression waves due to the changes to the gas or to the liquid. Each experimental run is repeated 100 times to extract an ensemble average capable of filtering out the intrinsic flow intermittence and disclosing the void fraction and pressure waves’ features. The slug flow properties such as the bubble nose translational velocity, the lengths of liquid film underneath the bubble and the liquid slug are also measured. The objective of the work is two-fold: access the main characteristics of the void fraction and pressure waves and disclose the mechanics of the transient slug flow as described through the changes of the slug flow properties.     

Low-velocity pneumatic conveying in horizontal pipe for coarse particles and fine powders

First,the characteristics of low-velocity conveying of particles having different hardness are experimentally investigated in a horizontal pipeline in terms of flow pattern and pressure drop to show that the slug flow can be classified into two types depending on the settling of particles along the pipeline,and the period is small for slug flow without the settled layer,which is called solitary slug flow.The pressure drop for soft particles is shown to be larger than that for hard particles.Then,experimental results are presented on horizontal fluidized-bed conveying of fine powders to show that air release from the top surface of the conveying channel is an important factor for high mass flow rate of particles.     

Low-velocity pneumatic conveying in horizontal pipe for coarse particles and fine powders

First, the characteristics of low-velocity conveying of particles having different hardness are experimentally investigated in a horizontal pipeline in terms of flow pattern and pressure drop to show that the slug flow can be classified into two types depending on the settling of particles along the pipeline, and the period is small for slug flow without the settled layer, which is called solitary slug flow. The pressure drop for soft particles is shown to be larger than that for hard particles. Then, experimental results are presented on horizontal fluidized-bed conveying of fine powders to show that air release from the top surface of the conveying channel is an imnortant factor for high mass flow rate of particles.     

Measurement of liquid film thickness in micro square channel

In micro channels, slug flow becomes one of the main flow regimes due to strong surface tension. In micro channel slug flow, elongated bubble flows with the thin liquid film confined between the bubble and the channel wall. Liquid film thickness is an important parameter in many applications, e.g., micro heat exchanger, micro reactor, coating process etc. In the present study, liquid film thickness in micro square channels is measured locally and instantaneously with the confocal method. Square channels with hydraulic diameter of D_h = 0.3, 0.5 and 1.0 mm are used. In order to investigate the effect of inertial force on the liquid film thickness, three working fluids, ethanol, water and FC-40 are used. At small capillary numbers, liquid film at the channel center becomes very thin and the bubble interface is not axisymmetric. However, as capillary number increases, bubble interface becomes axisymmetric. Transition from non-axisymmetric to axisymmetric flow pattern starts from lower capillary number as Reynolds number increases. An empirical correlation for predicting axisymmetric bubble radius based on capillary number and Weber number is proposed from the present experimental data.     

Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles

In this work, we present a numerical study to investigate the hydrodynamic characteristics of slug flow and the mechanism of slug flow induced CO₂ corrosion with and without dispersed small bubbles. The simulations are performed using the coupled model put forward by the authors in previous paper, which can deal with the multiphase flow with the gas–liquid interfaces of different length scales. A quasi slug flow, where two hypotheses are imposed, is built to approximate real slug flow. In the region ahead of the Taylor bubble and the liquid film region, the presence of dispersed small bubbles has less impacts on velocity field, because there are no non-regular intensive disturbance forces or centrifugal forces breaking the balance of the liquid and the dispersed small bubbles. In the liquid slug region, the strong centrifugal forces generated by the recirculation below the Taylor bubble lead to the effect of heterogeneity, which makes the profile of the radial liquid velocity component sharper with higher volume fraction of dispersed small bubbles. The volume fraction has a maximum value in the range of r/R = 0.5–0.6. Meanwhile, it is usually higher than 0.35, which means that larger dispersed bubbles can be formed by coalescences in this region. These calculated results are in good agreement with experimental results. The wall shear stress and the mass transfer coefficient with dispersed small bubbles are higher than those without dispersed small bubbles due to enhanced fluctuations. For short Taylor bubble length, the average mass transfer coefficient is increased when the gas or liquid superficial velocity is increased. However, there may be an inflection point at low mixture superficial velocities. For the slug with dispersed small bubbles, the product scales still cannot be damaged directly despite higher wall shear stress. In fact, the alternate wall shear stress and the pressure fluctuations perpendicular to the pipe wall with high frequency are the main cause for breaking the product scales.