Modeling of liquid film thickness around Taylor bubbles rising in vertical stagnant and co-current slug flowing liquids

The hydrodynamic study of the liquid film around Taylor bubbles in slug flow has great significance for understanding parallel flow and interaction between Taylor bubbles.The prediction models for liquid film thickness mainly focus on stagnant flow,and some of them remain inaccurate performance.However,in the industrial process,the slug flow essentially is co-current flow.Therefore,in this paper,the liquid film thickness is studied by theoretical analysis and experimental methods under two conditions of stagnant and co-current flow.Firstly,under the condition of stagnant flow,the present work is based on Batchelor's theory,and modifies Batchelor's liquid film thickness model,which effectively improves its prediction accuracy.Under the condition of co-current flow,the prediction model of average liquid film thickness in slug flow is established by force and motion analysis.Taylor bubble length is introduced into the model as an important parameter.Dynamic experiments were carried out in the pipe with an inner diameter of 20 mm.The liquid film thickness,Taylor bubble velocity and length were measured by distributed ultrasonic sensor and intrusive cross-correlation conductivity sensor.Comparing the predicted value of the model with the measured results,the relative error is controlled within 10%.

Void fraction measurement and calculation model of vertical upward co-current air-water slug flow

The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air-water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s^(-1)and gas superficial velocity ranging from 0.049 to 0.65 m·s^(-1). A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness Cδand nose shape CZ*were proposed to calculate aTB. In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate aLS, by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al., indicating that the new model was effective and applicable under the slug flow conditions.

Gas-liquid-liquid slug flow and mass transfer in hydrophilic and hydrophobic microreactors

Gas-liquid-liquid three-phase slug flow was generated in both hydrophilic and hydrophobic microreactors with double T-junctions.The bubble-droplet relative movement and the local mass transfer within the continuous slug and the dispersed droplet were investigated.It was found that bubbles moved faster than droplets under low capillary number(Ca),while droplets moved faster upon the increase of Ca due to the increased inertia.For the first time,we observed that the increased viscosity of droplets fastened the droplet movement.The mass transfer in the continuous slug was dominated by convection,leading to nearly constant global mass transfer coefficient(k_(L)a);while that in the dispersed droplet was dominated by diffusion,resulting in k_(L) decreasing along the channel.Such features are analogical to the corresponding gas-liquid or liquid-liquid two-phase slug flow,but the formation of bubble-droplet clusters caused by relative movement lowered the absolute mass transfer coefficient.These results provide insights for the precise manipulation of gas-liquid-liquid slug flow in microreactors towards process optimization.

Investigation on the performance of a helico-axial multiphase pump under slug flow

The helico-axial multiphase pump is often used for gas-liquid mixture transportation in offshore oilfields,and slug flow is the main reason for the unstable operation of the pump.Aimed for slug flow condition,a self-designed three-stage multiphase pump is set to the object to perform unsteady simulations and fluid-structure interaction calculations,and the inlet gas void fraction(IGVF)is set from 20%to 80%.The results show that affected by the flow from the slug,the gas-liquid two-phase flow pattern in the multiphase pump changes sharply,resulting in severe fluctuations in the differential pressure,spindle torque and deformation of the multiphase pump.The gas-phase enters the first-impeller along the suction blade surface when affected by Taylor bubbles,while the second and third-stage impellers gas-phases are in the form of small air masses flow into the impeller along the pressure blade surface.The deformation trend of impeller torque,differential pressure and the main pump spindle is similar to that of trigonometric function,while the fluctuation of torque is more intense,and the shape variable of spindle increases with the inflow of liquid plug,and the maximum deformation amount increases by10.9%at high GVF relative to IGVF.

Slug Flow Characteristics in Inclined and Vertical Channels

Horizontal well production technology gradually occupies a dominant position in the petroleum field.With the rise in water production in the later stage of exploitation,slug flow phenomena will exist in horizontal,inclined and even vertical sections of gas wells.To grasp the flow law of slug flow and guide engineering practice,the flow law of slug flow at various inclination angles(30°~90°)is studied by means of the combination of laboratory experiments(including high frequency pressure data acquisition system)and finite element numerical simulation.The results reveal that because of the delay of pressure variation at the corresponding position of pipeline resulting from gas expansion,the highest point of pressure change curve corresponds not to the highest point of liquid holdup curve(pressure change lags behind 0.125 s of liquid holdup change).Thus,the delay of pressure should be highlighted in predicting slug flow using pressure parameter change;otherwise the accuracy of prediction will be affected when slug flow occurs.It is generally known that liquid holdup and pressure drop are the major factors affecting the pressure variation and stable operation of pipelines.Accordingly,the results of finite element numerical simulation and Beggs-Brill model calculation are compared with those of laboratory experiments.The numerical simulation method is applicable to predicting the pressure drop of the pipeline,while the Beggs-Brill model is more suitable for predicting the liquid holdup variation of the pipeline.The research conclusion helps reveal the slug flow law,and it is of a scientific guiding implication to the prediction method of flow parameters under slug flow pattern in the process of gas well exploitation.

Development of Liquid Slug Length in Gas-Liquid Slug Flow along Horizontal Pipeline: Experiment and Simulation

The liquid slug length distribution is crucial for designing the downstream processing system with mul-tiphase pipeline. Experiments were conducted in a 133m long horizontal test loop. The measurements were per-formed by conductivity probes to determine the liquid slug length distribution. The data covered both the slug and plug flow regimes. From experimental results, the mean liquid slug lengths were relatively insensitive to gas and liquid flow rates in the higher mixture velocity range. But in the lower mixture velocity range, the mean liquid slug length decreased and then increased with mixture velocity. It shows that the development length of slug flow was longer than x/D=1157. A slug tracking model was adapted to study the evolution of liquid slug length distribution in a horizontal pipeline. In the present model, the wake effect of elongated bubble and the pressure drop due to accel-eration are taken into account and random slug lengths are introduced at the entrance. The results of the model are compared with the measured slug length distributions of slug flow regime. It shows that the predicted mean and maximum slug lengths are in agreement with the experimental data at x/D=1157 and the form of the slug length distributions is also predicted well by the model.

An Investigation on the Void Fraction for upward Gas-Liquid Slug Flow in Vertical Pipe

In order to investigate the influence of the entrance effect on the spatial distribution of phases, the experiments on gas-liquid two-phase slug flow in a vertical pipe of 0.03m ID were carried out by using optical probes and an EKTAPRO 1000 high speed motion analyzer. It demonstrates that the radial profile of slug flow void fraction is parabolic. Influenced by the falling liquid film, the radial profile curve of liquid slug void fraction in the wake region is also parabolic. Since fully turbulent velocity distribution is built up in the developed region,the void fraction profile in this region is the saddle type. At given superficial liquid velocity, the liquid slug void fraction increases with gas velocity. The radial profiles of liquid slug void fraction at different axial locations are all saddle curves, but void fraction is obviously high around the centerline in the entrance region. The nearer the measuring station is from the entrance, the farther the peak location is away from the wall.

IMPROVED HYDRODYNAMIC MODEL OF TWO-PHASE SLUG FLOW IN VERTICAL TUBES

Merits of the Fernandes model(Fernandes et al.1983)for two-phase slug flow in verticaltubes are reviewed in this paper.While predicting many macroscopic parameters of slug flow in verti-cal tubes,it fails to present correctly the trend that the average voidage in liquid slugs increases asthe rising velocity of Taylor bubbles is increased.It is also desirable to extend its application toelectrolyte systems, and to churn flow conditions.Based on the diagnostic analysis,the model equa-tion for gas entrainment by falling liquid film is reformulated and the influence of surface tension isalso accounted for.Development of the falling liquid film is recognized in the revised model in or-der to suit the case of short Taylor bubbles as well.The modified model predicts the variation of av-erage voidage in liquid slugs in good agreement with available experimental data.

An Experimental Study of the Flowrate Transients in Slug Flow

An investigation of the characteristics of flowrate transients within slug flow was conducted in a largescale outdoor testing facility.The test section consisted of a 378m long,7.62cm diameter stainless steel pipe. Air and water were used as the test fluids.The response to a change of flowrate o either phase or two phases was measured using a series of pressure transducers and differential pressure transducers.An increase or decrease in gas flowrate caused a pressure overshoot above the value at new steady state or led to a pressure undershoot to form a temporary stratified flow.Pressure waves existed in the pipeline,spreading from the entrance to the exit.The magnitude of pressure overshoot in “up-gas”transient or of pressure undershoot and period of the temporary stratified flow in “Down-gas” transient are related to the change of gas flowrate and the distance away from the entrance.In contrast,the change in liquid flowrate was accommodated by smooth transitions between the corresponding steady states,and only one obvious change was found in the slug frequency.According to experimental results,the pressure overshoot,pressure undershoot and the pressure wave propagation were analyzed,and the phenomena were explained reasonably.Some correlations for the calculation of the pressure overshoot and undershoot were proposed.

Simple Model for Gas Holdup and Liquid Velocity of Annular Photocatalytic External-Loop Airlift Reactor Under both Bubble and Developing Slug Flow

Based on the momentum conservation approach, a theoretical model was developed to predict the superficial liquid velocity, and a correlation equation was established to calculate the gas holdup of an annular external-loop airlift reactor(AELAR)in the bubble flow and developing slug flow pattern. Experiments were performed by using tap-water and silicone oil with the viscosity of 2.0 mm^2/s(2cs-SiO)and 5.0 mm^2/s(5cs-SiO)as liquid phases. The effects of liquid viscosity and flow pattern on the AELAR performance were investigated. The predictions of the proposed model were in good agreement with the experimental results of the AELAR. In addition, the comparison of the experimental results shows that the proposed model has good accuracy and could be used to predict the gas holdup and liquid velocity of an AELAR operating in bubble and developing flow pattern.

Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s.Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.

Distribution of void fraction for gas-liquid slug flow in aninclined pipe

In order to investigate the effect of inclination angle on the spatial distribution of phases, experiments on gas-liquid two-phase slug flow in an inclined pipe were carried out by using the optical probe and an EKTAPRO 1000 high speed motion analyzer. It has been demonstrated that the inclination angle and the mixture velocity are important parameters to influence the distribution of void fraction for upward slug flow in the inclined pipe. At high mixture velocity, the gas phase profile is axial symmetry in the cross-section of the pipe. This is similar to that for vertical slug flow. In contrast, most of the gas phase is located near the upper pipe wall at low mixture velocity. By measuring the axial variation of void fraction along the liquid slug, it can be concluded that there is a high void fraction wake region with length of 3～4D in the front of liquid slug. In the fully developed zone of liquid slug, the peak value of the void fraction is near the upper wall.

Experimental study on pressure fluctuation characteristics of slug flow in horizontal curved tubes

In order to study the pressure characteristics of slug flow in horizontal curved tubes,two kinds of curved tubes with central angle 45° and 90° respectively are studied,of which are with 0. 5m circumference and 26 mm inner diameter are used. When the superficial liquid velocity or the superficial gas velocity is constant,the pressure fluctuations and the probability distribution of the average velocity of slug flow are clear for all of the five experimental conditions. The results of experiment show that the pressure characteristics of slug flow in curved tubes have periodic fluctuations. With the rise of central angle,the period of pressure fluctuation is more obvious. The system pressure of the slug flow increases with the increasing of superficial liquid/gas velocity. Meanwhile,the probability distribution of pressure signal shows regularity,such as unimodal,bimodal or multimodal.

The Measurement of Oil,Gas and Water Flowrates in Three-Phase Slug Flow

Three-sphase flow invo1ving oil-water two immiscible liquids and gas which is often foundin the fields of petroleum production has been studied in this paper.A new method with thecombination of a horizontal tube,a downward flow vertica1 tube and an orifice to measure theflowrates is presented.In this method the frictional pressure drop in the downward vertical tube isreplaced by that in the horizontal tube,the void fraction is derived from the gravitational pressuredrop,then the volume fraction of the individual phase can also be obtained.The individual flowratescan be calculated when the water fraction is known.This method is applicable for many kinds ofoil-wells to measure the flowrates of crude oil,natural gas and water.Compared with other methods,the presented method involves fewer measuring parameters.The experimental results proved quitegood accuracy of the method,with measurement deviation within 10%,and reliable results wereobtained under high Dressure conditions.

A MODEL FOR LIQUID SLUG LENGTH DISTRIBUTION IN VERTICAL GAS-LIQUID SLUG FLOW

The slug length and the trailing Taylor bubble velocity in an upward vertical slug flow were measured by using the optical probes and the EKTAPRO 1000 high speed motion analyzer. The correlation between the trailing bubble velocity and the length of liquid slug ahead of that bubble is derived from the experimental data. Based on this correlation as well as the bubble overtaking mechanism, a model for the slug length distribution at any designated locations along the pipe is proposed. The predicted results are in agreement with the experimental data.

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.

Effects of the outlet pressure on two-phase slug flow distribution uniformity in a multi-branch microchannel

The two-phase flow maldistribution phenomenon in microchannels with multi-parallel branches is inevitable in almost all common conditions,and not only affects the performance of the facility but also increases the risk of system instability.In order to better understand the distribution mechanism and to explore a potential strategy to improve uniformity,the pressure evolutions under different split modes in a microchannel with multi-parallel branches,were analyzed numerically.The results show that the fluctuations of transient pressure exhibit similar trends at various split modes,but the time-averaged pressure drops in the branches are very different.This may be related to the maldistribution of mass flow.Thus,the outlet pressures of the branches are numerically changed to explore the relationship between differential pressure and flow distribution.From this study,the flow distribution is seen to display a strong sensitivity to the branch differential pressure.By changing the pressure conditions,the gas flow of the middle branch can be effectively prevented from the main channel,and the flow type in this branch turns from gas-liquid to a single liquid phase.When the differential pressure of the first branch channel changes,the maldistribution phenomenon of the model can be mitigated to a certain extent.Based on this,by adjusting the differential pressures of the second branch,the maldistribution phenomenon can be further mitigated,and the normalized standard deviation(NSTD)decreases from 0.52 to approximately 0.26.The results and conclusions are useful in understanding the two-phase flow distribution mechanism and for seeking optimizing strategies.

Fluid−Structure Interaction of Two-Phase Flow Passing Through 90° Pipe Bend Under Slug Pattern Conditions

Numerical simulations of evolution characteristics of slug flow across a 90°pipe bend have been carried out to study the fluid−structure interaction response induced by internal slug flow.The two-phase flow patterns and turbulence were modelled by using the volume of fluid(VOF)model and the Realizable k−εturbulence model respectively.Firstly,validation of the CFD model was carried out and the desirable results were obtained.The different flow patterns and the time-average mean void fraction was coincident with the reported experimental data.Simulations of different cases of slug flow have been carried out to show the effects of superficial gas and liquid velocity on the evolution characteristics of slug flow.Then,a one-way coupled fluid-structure interaction framework was established to investigate the slug flow interaction with a 90°pipe bend under various superficial liquid and gas velocities.It was found that the maximum total deformation and equivalent stress increased with the increasing superficial gas velocity,while decreased with the increasing superficial liquid velocity.In addition,the total deformation and equivalent stress has obvious periodic fluctuation.Furthermore,the distribution position of maximum deformation and stress was related to the evolution of slug flow.With the increasing superficial gas velocity,the maximum total deformation was mainly located at the 90°pipe bend.But as the superficial liquid velocity increases,the maximum total deformation was mainly located in the horizontal pipe section.Consequently,the slug flow with higher superficial gas velocity will induce more serious cyclical impact on the 90°pipe bend.

Void fraction measurement of bubble and slug flow in a small channel using the multivision technique

Using the multivision technique, a new void fraction measurement method was developed for bubble and slug flow in a small channel. The multivision system was developed to obtain images of the two-phase flow in two perpendicular directions. The obtained images were processed--using image segmentation, image subtraction, Canny edge detection, binarization, and hole filling-to extract the phase boundaries and information about the bubble or slug parameters, With the extracted information, a new void fraction measurement model was developed and used to determine the void fraction of the two-phase flow. The proposed method was validated experimentally in horizontal and vertical channels with different inner diameters of 2.1, 2.9, and 4.0 mm, The proposed method of measuring the void fraction has better performance than the methods that use images acquired in only one direction, with a maximum absolute difference between the measured and reference values of less than 6%.

A PHYSICAL MODEL FOR PREDICTING THE PRESSURE DROP OF GAS-LIQUID SLUG FLOW IN HORIZONTAL PIPES

A comprehensive treatment of all sources of pressure drop within intermittent gas-liquid flow is presented. A slug unit is divided into three parts and the pressure gradient of each part is calculated separately. In the mixing zone the momentum theory is employed and the mixing process between the film and slug is simulated by a two-dimensional wall jet entering a large reservoir to calculate the mixing length. The boundary layer theory is utilized to calculate the pressure drop for the slug body and the momentum equation of the film zone is integrated to calculate the pressure drop for the film zone. The pressure drop predicted in present model is in good agreement with all the measurements.