Slug Front Research Articles

RETRACTED: Modeling a unified slug liquid holdup correlation based on a comprehensive analysis of entering bubble sharpness

Liquid-gas two-phase slug flow is the most complex flow pattern encountered in pipelines, wellbores, and cooling systems in various energy systems. Accurately predicting the slug liquid holdup (HLLS) is vital for the system design and operation because it is a crucial characteristic of slug flow that is closely related to the average liquid holdup and pressure drop. Most existing HLLS models have limited applicability due to a lack of a physical basis for slug aeration mechanisms. This study proposes a new dimensionless number SP to estimate the sharpness of entering bubbles at the liquid slug front and semi-empirically correlates SP to HLLS data, leading to the development of a unified HLLS correlation. We formulate this dimensionless number and its relations using 880 experimental HLLS data points, and the validity of the unified HLLS correlation is tested using 1050 independent data points. The developed semi-empirical model closely agrees with experimental data obtained by varying the fluid properties (0.03 mPa·s ≤ µL ≤ 966 mPa·s, 0.027 N/m ≤ σ ≤ 0.07 N/m) and operating conditions, such as the pipe geometry (1 in. ≤ pipe internal diameter ≤ 3 in., –10° ≤ θ ≤ +90°).

Effect of a uniform magnetic field on a two-phase air-ferrofluid slug flow

This paper presents an experimental study on the effect of a uniform magnetic field on a two-phase ferrofluid-air flow inside a capillary tube. A horizontal and transparent glass tube of 2.5 mm diameter is employed to investigate the dynamics of an intermittent ferrofluid slug flow under a 250G uniform magnetic field. Using a CCD camera and image processing, liquid slug front velocity and dynamic contact angle of the three-phase (ferrofluid-glass-air) flow were measured. To investigate the effect of slug length, a series of experiments were carried out with three distinct slug aspect ratios (α) of 8, 16, and 20. The slug aspect ratio is defined as the length of the slug divided by the diameter of the tube (α = L/D). It was observed that at the centre of the magnet, corresponding to maximum field strength, slug velocity was accelerated reaching its maximum value, and the dynamic contact angle was reversed from θ > 90° to θ < 90°. The smallest aspect ratio of liquid slug (α = 8) provides the optimum conditions for driving the slug flow using a magnetic field. It exhibits sharp deceleration after the magnet and significant changes in the dynamic of the contact angle. In addition, the influence of double magnets on a fixed slug aspect ratio (α = 8) is reported and compared with the case of a single magnet. It was observed that when two magnets are coupled, their combined pulling force operates, resulting in a high slug velocity at the first magnet position. Obtained experimental results revealed that both the number of magnets and slug aspect ratio are key parameters for the transport of ferrofluid in capillary tubes.

Prediction of unsteady slug flow in a long curved inclined riser with a slug tracking model

An improved one-dimensional mechanistic model is presented for the prediction of unsteady gas-liquid slug flows in inclined curved pipes, using the slug tracking approach. The equations for mass and momentum conservation are applied to the slug body, liquid film, and elongated bubble regions constituting a slug unit cell. The proposed model can be applied to horizontal or inclined upward flows. Statements of mass conservation result in axial changes of the liquid and gas velocities in the liquid film and elongated bubble. The slug initiation at the inlet is modelled as a random process with slug length variations. Closure relationships for the bubble nose velocity, modified by the wake effect, and the slug frequency for slug initiation are employed. The discretized governing equations are solved fully implicitly, introducing numerical treatments associated with the outlet boundary conditions and the merging of slug units. Of practical interest is an upward gas-liquid slug flow in a catenary riser with a high aspect ratio (length over diameter) being an order of a thousand representing an offshore subsea pipe for the oil and gas production. By considering the pipe initially fully filled with the traveling liquid, the dynamic scenario of the pipe transporting successive slug units is simulated, capturing the continuing evolution of slug flow patterns along the pipe exhibiting the disappearances of liquid slugs due to the bubble coalescences. Spatio-temporal variations of the liquid holdup, the pressure and its gradient, the film and slug lengths, the slug frequency, the velocities of the slug front, bubble nose, liquid in the slug body and film, and of the gas in the elongated bubble are evaluated. The backward flow occurrence in the film zone near the outlet is also predicted due to the pipe inclination. Parametric investigations are performed by specifying the superficial liquid and gas velocities, and comparing the cases of catenary pipes (with variable inclinations) versus inclined and horizontal straight pipes (with fixed inclinations). Results highlight the important effect of gas-to-oil superficial velocity ratio (GOR) in combination with the pipe inclination and curvature effects. Fluctuations of slug flow properties appear to be considerably amplified and more intermittent when increasing the GOR. This observation is important towards regulating the practical flow rates for subsea oil and gas productions as well as designing flexible pipes subject to slug flow-induced vibrations.

Velocity of viscous fingers in miscible displacement: Comparison with analytical models

The paper investigates the linear growth of the mixing zone, in a pessimistic scenario, during polymer slug injection into a water reservoir. The velocities of the slug front and of the boundaries of the mixing zone are numerically and analytically studied as key parameters characterizing the miscible displacement. Using two different numerical methods (finite volumes and finite elements), the impact of the slug size, reservoir dimensions, Peclet number, and viscosity curve shape on the corresponding velocities are examined. Notwithstanding the realization of the solution by two computational schemes, the simulation results coincide with a sufficient accuracy. The numerically obtained velocities are compared with theoretical estimates within the transverse flow equilibrium approximation and Koval model. Based on the comparison pattern, recommendations are presented on the use of specific analytical methods for estimating the growth rate of the mixing zone depending on the characteristics of the polymer.

Analysis of interfacial behavior in two-phase flow using image processing

Two-phase flow has a wide range of application from petroleum to space industry. Gas-liquid two-phase flow in horizontal pipe commonly occurs in petro-chemical, nuclear and geothermal industry, where simultaneously gas and liquid are transported through pipelines. During the transportation of gas-liquid flow simultaneously, due to the interaction of two phases, slug forms from the stratified-wavy flow. Slug flow consists of strong aeration at the slug front which is responsible for pipe failure and hazards in industries. Thus, it is required to understand the phenomena of slug formation in industrial pipeline to avoid the catastrophic pipe failure. In the present research, image processing technique is used to accurately analyze the interfacial behavior of two-phase flow. The interfacial behavior plays crucial role, as it is the plane where the two phases interact and interaction of the phases leads to the transition of different two-phase pattern. Experimentally captured images are processed using image processing algorithm, to study the variation of liquid film thickness. With the help of liquid film thickness transition of the interface is analyzed for different superficial Reynolds number of liquid and gas. Further, a PDF analysis is reported to understand the mechanism of the growth of the wavy interface.

Physics of aeration in slug: flow visualization analysis in horizontal pipes

Aeration in slug and associated secondary flow leads to surging of pressure and erosion corrosion in pipe. Surging of pressure develops high mechanical impact on the pipe, and erosion corrosion reduces the thickness of internal wall, thereby resulting in pipe failure. To explore the phenomena of aeration in slug, flow visualization analysis is reported in this paper for intermittent flow sub-regimes and their transition. Analysis is reported for onset of slug, transition of plug to slug flow and development of aeration at the slug front. The visualized images and the motion pictures captured using high-speed photography in the present experiments are used to depict the process of air entrapment during the transition of wavy-stratified flow to slug flow as well as plug flow to slug flow. It is depicted for the first time through our visualization analysis that gas bubble entrapment in slug happens due to plunging kind of wave breaking mechanism. The captured images are also analyzed to describe the phenomena of augmentation of aeration in slug leading to the formation of highly aerated slug flow. Thorough understanding of aeration in slug will help in avoiding the chances of pipe failure.

Development of Gas-Liquid Slug Flow Measurement Using Continuous-Wave Doppler Ultrasound and Bandpass Power Spectral Density

This paper addresses the issues of slug detection and characterization in air-water two-phase flow in a vertical pipeline. A novel non-invasive measurement technique using continuous-wave Doppler ultrasound (CWDU) and bandpass power spectral density (BPSD) is proposed for multiphase flow applications and compared with the more established gamma-ray densitometry measurement. In this work, analysis using time-frequency analysis of the CWDU is performed to infer the applicability of the BPSD method for observing the slug front and trailing bubbles in a multiphase flow. The CWDU used a piezo transmitter/receiver pair with an ultrasonic frequency of 500 kHz. Signal processing on the demodulated signal of Doppler frequency was done using the Butterworth bandpass filter on the power spectral density which reveals slugs from background bubbles. The experiments were carried out in the 2” vertical pipeline-riser at the process system engineering laboratory at Cranfield University. The 2-inch test facility used in this experiment is made up of a 54.8 mm internal diameter and 10.5 m high vertical riser connected to a 40 m long horizontal pipeline. Taylor bubbles were generated using a quick-closing air valve placed at the bottom of the riser underwater flow, with rates of 0.5 litres/s, 2 litres/s, and 4 litres/s. The CWDU spectrum of the measured signal along with the BPSD method is shown to describe the distinctive nature of the slugs.

Velocity and porosity relationships within dense phase pneumatic conveying as studied using coupled CFD-DEM

This study used a 3D coupled CFD-DEM model to study velocity and porosity relationships within horizontal dense phase pneumatic conveying. Inlet velocities, initial layer fractions and initial slug lengths were varied for a total of 72 single slug simulations. The linear relationship between particle velocity and slug velocity was examined and the origins and contributions of individual variables were looked at in detail. It was found that the slug velocity to particle velocity relationship can be defined using slug to bulk density ratio and propagation velocity. It was also found that within a single slug system, slugs tend to their ‘preferred’ steady-state length which is a function of inlet velocity and stationary layer ahead of the slug. Another finding is that hydraulic jump can be used as an analogy to the interaction between slug front and the stationary layer. This analogy can be used to define a boundary for slug flow as well as help predict slug porosity.

Experimental study using advanced diagnostics to investigate slug aeration and bubble behavior in high liquid viscosity horizontal slug flow

Accurate prediction of slug liquid holdup is critical for accurate calculation of pressure gradient and average liquid holdup in pipes. However, most of the existing slug liquid holdup models are only accurate for a specific range of operating conditions, pipe dimensions, and fluid properties. The majority of these models are empirical, lacking the physical basis of slug aeration mechanisms. In this study, bubble entrainment mechanisms, bubble trajectories, and bubble loss from the slug body were identified. The experimental results from the high-speed camera (HSC) and particle image velocimetry (PIV) enabled detailed investigation of bubble entrainment mechanisms at slug front, bubble deformation and trajectories in slug body. These experimental observations were further analyzed and related to operating conditions and fluid properties. A horizontal 50.8-mm (2-in.) inner diameter (ID) pipe, and high viscosity liquid/air-fluid system (μL ≈ 0.51, 0.68 and 0.96 Pa s) were utilized. Experimental results revealed that the rate of gas entrainment at slug front, the bubble deformation in the slug body, and the number of fragmented bubbles in the slug unit all increase as mixture velocity and liquid viscosity increase, and as surface tension decreases. The proposed slug aeration mechanisms, and bubble behavior and characteristics in the slug body can form the basis for further mechanistic modeling of slug liquid holdup and other parameters required for proper slug flow modeling.

Identification of horizontal slug flow structures for application in selective cross-correlation metering

Accurate metering of slug flows is important in many industries that handle multiphase products. For the oil and gas industry the harsh environmental conditions mean that non-invasive and non-intrusive instruments are preferred. Cross-correlation meters, particularly those based on electrical tomography, offer a potential solution to this problem but sufficient accuracy has proved difficult to achieve, with the primary issue being that the measurement is dominated by the motion of interfaces rather than the bulk fluid. In the work reported here, results are presented for flows of oil and nitrogen gas in a horizontal pipe of diameter 10.2 cm. Superficial velocities of liquid and gas range from 1 m/s to 3 m/s and 0.4–3 m/s respectively. By analysing the structures of liquid slugs via tomography, it is found that three significantly different slug front structures occur. The high-speed and spatial resolution of Electrical Capacitance Tomography (ECT) enables independent measurement of individual slug fronts and tail as well as average slug velocity. Based on detailed measurements of slug structures and velocity profiles, we go on to show that using differential-based cross-correlation and the average velocity of slug front and tail, an overall accuracy of better than +/−5% is achieved for estimation of the mixture superficial velocity. This is an equivalent level of accuracy to that obtained using intrusive methods such as optical fibre probes, which are less suitable for oil and gas applications.

Detailed flow field measurements and analysis in highly viscous slug flow in horizontal pipes

The flow field in the liquid phase of high viscous oil and air two-phase slug flow were experimentally studied under laminar flow conditions. The horizontal 50.8-mm (2-in.) inner diameter (ID) pipe and high viscous fluid properties (nominal viscosity values of 0.51, 0.68 and 0.96 Pa·s) yielded mixture Reynolds numbers less than 100. Particle Image Velocimetry (PIV) was used to analyze the flow field in the liquid phase. Slug characteristics were measured with a set of capacitance probes (CPs). Based on velocity field measurements, the liquid phase mass is shown to be conserved within the slug body despite local spatial variations in volumetric flow rate – flow accelerates at slug front and decelerates at slug tail. A low momentum region inside the liquid phase is identified beneath the mixing zone and close to the lower sections of the pipe. Furthermore, based on a frame of reference moving with the slug front, a pair of vortices is identified at the slug front. Accordingly, a continuous increase in velocity is observed at lower sections of the pipe. From CPs data, the flow coefficient is estimated to be between 2.11 and 2.20 for the elongated bubble flow, and 2.26 and 2.38 for the slug flow in laminar conditions investigated. From PIV data, the flow coefficient is estimated to be between 2.28 and 2.34 for the elongated bubble, and 2.31 and 2.44 for the slug flow, respectively. These slight differences in the obtained values of flow coefficient indicate the possible misunderstands of 1.13 multiplier.

An experimental investigation of the motion of long bubbles in high viscosity slug flow in horizontal pipes

The slug bubble velocity is one of the most important closure relations in multiphase flow models, and has been studied extensively for decades. Available models and correlations may provide quite reliable predictions for low viscosity liquids, but this is not always the case for high viscosities, mainly due to a lack of detailed data. An investigation of viscous slug flow was carried out, based on 241 experiments in a 15 m long horizontal pipe of 57 mm inner diameter, applying three different liquids with viscosities in the range of 240–730 cP. Measured parameters include slug bubble velocities, slug lengths, liquid holdup and pressure drop. A main objective has been to quantify the effect of viscosity on slug bubble velocities, in order to improve predictive models of slug flow in the laminar region. Slug front, tail and pattern velocities were obtained by cross-correlating holdup time series recorded at two locations at the end of the test section. The dependency of individual slug bubble velocities on slug lengths and bubble nose shape was investigated in detail for selected experiments. A new slug bubble velocity model has been developed, incorporating viscosity, which compares quite well with available high viscosity slug flow data.

Modeling Liquid Slugs Accelerating in Inclined Conduits

In this article, we simulate traveling liquid slugs in conduits, as they may occur in systems carrying high-pressure steam. We consider both horizontal and inclined pipes in which the slug is accelerated by a suddenly applied pressure gradient, while at the same time, gravity and friction work in the opposite direction. This causes a steep slug front and an extended slug tail. The shapes of front and tail are of interest since they determine the forces exerted on bends and other obstacles in the piping system. The study also aims at improving existing one-dimensional (1D) models. A hybrid model is proposed that enables us to leave out the larger inner part of the slug. It was found that the hybrid model speeds up the two-dimensional (2D) computations significantly, while having no adverse effects on the shapes of the slug's front and tail.

Kinetics of gravity‐driven slug flow in partially wettable capillaries of varying cross section

AbstractA mathematical model for slug (finite liquid volume) motion in not‐fully‐wettable capillary tubes with sinusoidally varying cross‐sectional areas was developed. The model, based on the Navier‐Stokes equation, accounts for the full viscous terms due to nonuniform geometry, the inertial term, the slug's front and rear meniscus hysteresis effect, and dependence of contact angle on flow velocity (dynamic contact angle). The model includes a velocity‐dependent film that is left behind the advancing slug, reducing its mass. The model was successfully verified experimentally by recording slug movement in uniform and sinusoidal capillary tubes with a gray‐scale high‐speed camera. Simulation showed that tube nonuniformity has a substantial effect on slug flow pattern: in a uniform tube it is monotonic and depends mainly on the slug's momentary mass/length; an undulating tube radius results in nonmonotonic flow characteristics. The static nonzero contact angle varies locally in nonuniform tubes owing to the additional effect of wall slope. Moreover, the nonuniform cross‐sectional area induces slug acceleration, deceleration, blockage, and metastable‐equilibrium locations. Increasing contact angle further amplifies the geometry effect on slug propagation. The developed model provides a modified means of emulating slug flow in differently wettable porous media for intermittent inlet water supply (e.g., raindrops on the soil surface).

Two-phase slug flows in helical pipes: Slug frequency alterations and helicity fluctuations

Air-water numerical simulations in the slug flow regime have been performed in horizontal helical pipes and the effects of geometries on the flow regime have been investigated. Depending on the length of the helix, outlet slug frequencies have been reduced with various degrees of efficiency. Correlations between mean tangential velocity and helicity density fluctuations have been identified and investigated qualitatively. These flow fields show smaller time scales than those obtained in volume fractions fluctuations. Shifts observed in the tangential velocity and mean helicity fluctuations to smaller time scales (high frequencies) are associated with regime transitions. For a slug flow undergoing a continuous transition to the annular flow regime, it is shown that the presence of slower (low frequencies) helicity fluctuations is attributed to the variations in the axial velocity. Finally, the analysis of the helicity at gas-liquid interface confirms the presence of the mixing zone at the slug front.

Prediction of slug liquid holdup in high viscosity liquid and gas two-phase flow in horizontal pipes

Abstract Liquid holdup in slugs is a critical slug flow characteristic for predicting average liquid holdup and pressure gradient in two-phase pipeline systems and for designing downstream separation and process facilities. Liquid holdup in slugs for high viscosity two-phase pipe flow is poorly understood and inadequately predicted. The objective of this study is to experimentally investigate the effect of high liquid viscosity on slug liquid holdup in horizontal pipes and develop a physical explanation of the experimentally observed phenomenon. Viscous and inertia forces are found to govern the processes of the bubble entrainment, fragmentation and loss in the slug front. These processes, in turn, determine the slug liquid holdup. A new empirical closure relationship is proposed as a function of viscosity (viscous) and Froude (inertia) dimensionless numbers to predict the gas fraction in slugs for high viscosity liquid (180–587 mPa s) and gas flow in horizontal pipes. A validation and comparison study of the proposed empirical correlation with an independent data set showed improvement in accuracy with absolute average error and standard deviation of 11.35% and 9.59%, respectively, over the existing correlations.

A Mechanistic Slug-Liquid-Holdup Model for Different Oil Viscosities and Pipe-Inclination Angles

Summary Slug liquid holdup is one of the most important parameters of slug flow. It is closely related to the average liquid holdup and pressure gradient of slug flow in wells and pipelines. The mechanistic models of Barnea and Brauner (1985) and of Zhang et al. (2003a) are based on the turbulent liquid-slug assumption for low-viscosity oils. However, for high-viscosity oil, the liquid slug is laminar because of the low slug Reynolds number. In this study, a mechanistic slug-liquid-holdup model is developed for low- and high-oil-viscosity slug flows. The model is based on two shear mixings: shear mixing between the slug front and pipe wall and shear mixing between the slug body and liquid film. The model uses slug-flow characteristics that can be calculated by solving the continuity and momentum equations of slug flow. A data bank consisting of 418 slug-liquid-holdup measurements that were obtained from various authors is used to analyze and validate the model. In the data bank, liquid viscosity ranges from 0.0016 to 0.589 Pa·s (1.6 to 589 cp). Pipe-inclination angle ranges from −30° to upward vertical. Pipe inside diameter varies from 5.08 to 10 cm. Statistical evaluations are conducted and compared with predictions of other models, and significant improvement is observed in the performance of the new model.

Investigation and Prediction of High-Viscosity Liquid Effect on Two-Phase Slug Length in Horizontal Pipelines

Summary The recent trend of increasing energy demand led the industry toward the development of heavy oil unconventional resources. However, the production and transportation of such heavy oil is a challenge because of the lack of understanding of two-phase flow behavior under the condition of high-viscosity liquid phase. The objective of this study is to physically understand the effect of liquid viscosity on slug length and develop an empirical two-phase slug-length correlation for high oil viscosity. The developed slug length correlation can improve the existing two-phase flow models often used in the development and maintenance of heavy-oil fields. Experimental high-viscosity (0.181–0.589 Pa.s) two-phase air/ mineral viscous oil slug-length data is acquired in a horizontal 0.0508-m ID pipe. High-speed recorded flow visualization revealed the effect of liquid-phase viscosity on the scooping and shedding processes at the slug front and back, respectively, and liquid film thickness in the Taylor bubble zone. Data analysis showed a one-third reduction in high viscosity (0.181–0.589 Pa.s) average slug length compared with low viscosity (0.001–0.017 Pa.s) average slug length. Furthermore, analysis of slug-length distributions revealed that as liquid viscosity increases, slug length distribution deviates from the log-normal distribution to a trancated positively skewed distribution. As a result, the average, the variance, and maximum slug-length values vary with liquid viscosity. On the basis of these experimental observations, a physical model is proposed which suggests that the thick liquid film in the Taylor bubble zone and the short slug-mixing zone at the slug front result in a fully developed velocity profile at the slug back, stabilizing the slug at a shorter length. A new dimensional-analysis-based empirical model is proposed to predict dimensionless average slug length for high-viscosity liquid slug flow. A validation and comparison study of the proposed correlation showed the best performance among the existing correlations.

Measurement of gas entrainment from stationary liquid slug in horizontal tube with double-sensor conductivity probe

Slug flow is encountered frequently in oil and gas pipelines. Stationary liquid slug was constructed in horizontal pipe to study the process of gas entrainment in a slug front and the two-phase flow parameters of liquid slug were measured by a double-sensor conductivity probe. It was found that the gas entrainment flowrate increases as the Froude number and Reynolds number of the liquid film ahead of the slug front increases. A turbulent shear layer exists in the mixing region and the radial distributions of void fraction and bubble frequency have peaks in the layer. As the distance into the slug increases, the void fraction and bubble frequency decrease and tend to be linearly distributed. The radial distribution of the bubble velocity indicates that the velocity gradient is high in the velocity boundary layer near the bottom of the pipe at the mixing region. The velocity profile agrees well with 1/7-th power law in the fully developed zone of the liquid slug.

Influence of the operation pressure on slug length in near horizontal gas–liquid pipe flow

Slug flow is commonly observed in gas production offshore fields. At high operation pressure only short hydrodynamic slugs are observed. However, as the offshore fields become older, the operation pressure becomes lower and long slugs may form. At near atmospheric pressures the long slugs may reach a size of 500 pipe diameters or more. Such slugs can cause serious operational failures due to the strong fluctuating pressure. Identifying the operation pressure conditions at which the long slugs appear, may reduce or prevent these negative effects. In this paper we process and analyse gas–liquid flow measurements in order to investigate the different slug types and their sensitivity to the operation pressure. The measurements were performed in a 103 m long pipe with an internal diameter of 0.069 m and an inclination of −0.1° from the horizontal. Three types of slugs were categorized according to the difference in liquid levels (liquid excess) between the slug front and tail. The long slugs were found to have the largest liquid excess after formation, whereas the hydrodynamic slugs had no liquid excess. The analysis of the measurements provides a detailed overview on the effect of pressure on the long slug length, and a safe operation region where long slugs will not appear.