Statistical features of the flow evolution in horizontal liquid-gas slug flow

https://doi.org/10.1016/j.expthermflusci.2020.110203Get rights and content

Highlights

  • Experimental investigation on the slug flow evolution in horizontal pipes.

  • Resistive sensors are used to obtain slug flow parameters.

  • Effect of the superficial velocities in the PDF shapes of the slug parameters.

  • Distribution types were defined based on maximum likelihood estimate (MLE).

Abstract

The occurrence of the slug flow pattern is frequently detected in the petroleum industry. Theoretical and experimental works on the complex behaviour of this flow pattern are abundantly found, and their aim is to advance the state-of-the-technique on the behaviour of this kind of flow. The goal of the present work is to provide experimental data collected in five probing stations with resistive sensors mounted on a horizontal air–water slug flow in a 25.8-mm ID pipe. A signal processing technique provides the translational velocities, frequencies and void fractions that arise from different gas and liquid volumetric flow rates. Based on the obtained results, the effects of the liquid and gas superficial velocities were correlated with the probability density functions (PDFs) of the parameters variations observed in the slug flow development along the pipe. A quantitative criteria based on maximum likelihood estimates is used to determine the Weibull distribution for the translational velocity and the lognormal distribution type for the slug frequency distribution type.

Introduction

The analysis of the slug flow pattern is often required in industrial, technological and scientific endeavours. In the oil industry, slug flows are largely found in production and transportation lines [1]. Rahmandhika et al. [2] emphasize the risk of accidents whenever the due care when dealing with slug flows is not taken. Pedersen et al. [3] lists several problems that result from the slug flow occurrence in oil industry facilities; for example, high liquid levels and high pressures in the production separators, the fatigue caused by intermittent pounding, low production and several others.

The problems caused by the occurrence of the slug flow pattern originated a large amount of theoretical and experimental work, as the specialised literature shows. This effort has been made for the sake of improving our understanding on slug flow and its characterisation. As for the numerical approaches for describing slug flows, either steady-state or transient models are used. Examples of the steady-state approach are (i) the unit-cell model [4], [5] and (ii) the statistical averaging of physical properties called by Issa and Kempf [6] as “statistical cellular model”. Issa and Kempf [6] categorised three types of transient models: (i) empirical slug specification, (ii) slug tracking and (iii) slug capturing. The problems in using the numerical methods for slug flow description can be due to intrinsic problems (ill‐posedness, hyperbolicity, etc) and the lack of reliable high-quality experimental data [7].

Bendiksen et al. [8] described the slug flow evolution along the pipeline by considering the following stages: flow initiation, establishment of a quasi-steady state and flow development.

Collins et al. [9] described the slug flow as a “volume of gas in a pipe filled with liquid (stagnant) which forms an axisymmetric bullet-shaped bubble”. This early definition was used by researchers in the description of bubble motion and its flow characteristics [10], [11], [12], [13], [14], [15], [16].

However, these experimental observations do not provide an explanation on how the slug flow is initiated. Conte et al. [17] claim that the main approach to the onset of slug flow is the Kelvin-Helmholtz stability analysis (either inviscid or viscous). Based on visual observations supported by pressure measurements of the flow, Dukler and Hubbard [4] described the slug flow initiation and dissipation. The authors proposed the pickup and shedding mechanisms to achieve the established slug flow regime. Lin and Hanratty [18] described the slug formation in a stratified flow when a suction pressure due to the Bernoulli Effect is generated over a wave and when this effect overcomes the influence of gravity. This instability causes the interfacial waves to grow until they touch the top of the channel. In this circumstance, the channel’s cross-sectional area fills up completely with liquid (that is, it gets plugged by the liquid phase). Thence, slug flow is formed.

Taitel [19] claims that the onset of slug flow is also controlled by other two effects: (i) entrance effects and (ii) terrain profile. In his work, Taitel [19] emphasizes that the initial characteristics of the slug flow cannot be sustained along the pipeline indicating that there is an observable change in the flow.

Shemer [20] explains that slug flow evolution is related to and depends on the relative velocities between the large bubbles. When the distance between the bubbles is considerable, they tend to keep a uniform velocity and thence a uniform bubble shape [21]. Nicholson et al. [22] stated that liquid is being constantly picked up and shed at the slug to form a new liquid film. This mechanism is called scooping. Shemer [20] pointed out that this process ends once the liquid velocity profiles at the rear of the liquid slug are fully developed and all elongated bubbles propagate at the same translational velocity. Whenever this happens, it is said that stable slug flow or fully developed slug flow has been reached.

Woods [23] describes two scenarios in the initiation of such flow. For low gas velocities, waves are formed by a Jeffreys’ mechanism and for high gas velocities waves are generated by a Kelvin–Helmholtz mechanism. The slug flow is then formed if a critical liquid height (h0) value was achieved in a manner similar to the equilibrium film level (he) as described in Taitel [19].

Statistical approaches whose aim is to understand the chaotic and unstable nature of the slug flow pattern are also found in the literature. Jones and Zuber [24] were ones amongst the first to suggest a statistical approach to study two-phase vertical flow patterns. The authors employed an X-ray system to measure void fraction and identify differences between flow patterns such as slug, bubbly and annular flows. It was then possible to identify differences not only by visual observation but also by using a probability density function (PDF) of the void fraction. The characteristics observed were: (i) single-peaked PDF at low void fraction for bubbly flows, (ii) single-peaked PDF at high void fraction for annular flows and (iii) twin-peaked PDF for slug flow.

Jones and Delhaye [25] made a review on the statistical assessment of the two-phase flow from probability density functions in several experimental techniques such as optical probes, hot-film anemometry, electrical probes, photon attenuation and so on. The authors reported a double-peaked histogram to identify the slug flow pattern as a type of two-phase flow.

Heywood and Richardson [26] conducted experimental tests with air-water in horizontal slug flow in a 42-mm ID duct and a total length of 4.57 m. The authors used a gamma-ray technique to generate probability density functions (PDF) and power spectral densities (PSD) of the void fraction. They compared the histograms of liquid holdup with a fitted curve for some liquid and gas superficial velocities.

Knervold et al. [27] experimentally studied the slug flow pattern in a horizontal pipe with an internal diameter of 24 mm. A mixture of mineral oil and kerosene as the liquid phase and nitrogen as the gas phase were used as working fluids. The Laser Doppler Velocimetry was used as the measurement technique (LDV) and they succeeded in obtaining values for the average slug length, slug frequency and translational speed of the liquid slugs. They also mapped the velocity distribution in the slug flow. The authors mentioned difficulties in identifying the flow characteristics in regions of liquid slugs with high aeration. Such regions were the slug front and the slug core at the highest gas flow rates.

Matsui [28] performed experiments with nitrogen and water mixtures in vertical pipes. The author used pressure signals to identify two-phase flow patterns. The distributions of the pressure signals were fitted with the Gran-Charlier series and four patterns were distinguished: bubbly flow, slug-like flow, annular flow and mist flow.

Lin and Hanratty [29] used pressure signals to identify statistical features of the flow regimes in horizontal pipes. They also investigated the shapes of the cross-correlation functions to show characteristics of the slug flow.

Nydal et al. [30] used two conducting rings in horizontal slug flow in pipes of 52.9-mm ID (stainless steel), 90-mm ID (acrylic) and 17-m long. They identified two types of slugs in their experiments with air-water flow: regular and developing slugs. They were distinguished by means of the statistical distributions of the slug holdup. Cumulative density functions (CDF) were used to investigate some features of slug parameters. The shape of the statistical distributions was fitted with normal and log-normal functions.

Kozma [31] used the Poisson statistics to analyse the bubble release or production in the slug flow. This is a simplified approach to the slug flow pattern since it considers the presence of stable bubbles in the pipe. The Poisson process also has constraints such as the occurrence of bubbles – which is a rare event – and that the bubbles do not coalesce nor collapse. Kozma [31] mentioned that this methodology does not work for higher void fractions.

Costigan and Whalley [32] made an examination of void fraction traces and their probability distribution functions and identified the following six flow regimes: discrete bubble flow, spherical cap bubble flow, stable slug flow, unstable slug flow, churn flow, and annular flow.

Fossa [33], Bertola [34], Jana et al. [35], Zheng and Che [36], Zheng et al. [37], dos Reis and Goldstein Jr [38], Vicencio et al. [39] and other authors used the probability density function (PDF) and/or the power spectral density (PSD) to analyse slug flow parameters. Fossa [33] pointed out that the examination of the PDF allows the identification of the operating conditions in the slug/plug flow regime. Al-Safran [40] used the Poisson probability theory to investigate the random effects of the slug frequency.

Discussions on the initiation and evolution of the two-phase slug flow are largely found in the literature as presented in the brief review in the above section. Dinaryanto et al [41] indicate that there are limited studies on slug flow initiation and development regarding the experimental analyses. There are several statistical approaches that develop prediction equations or characteristic parameters in the two-phase slug flow.

The aim of this article is to provide experimental data for horizontal air-water slug flow by using five resistive probes along a pipe. Discussion on the features and shapes of the probability density functions (PDF) as the flow develops in the pipeline are made for the void fraction, slug frequency and the translational velocity. Aspects of the histograms and probability distribution type that fits the experimental data are discussed.

Section snippets

Experimental methodology

This section describes the experimental methodology. In Fig. 1, three flow lines integrate the system: the ones for the liquid and gas phases and the two-phase line. The water reservoir, the centrifugal pump and the Coriolis mass flow meter compose the liquid line. The air reservoir, the compressor and the Coriolis mass flow meter compose the gas line. A mixer connects the liquid and gas lines at the inlet of the test section (that is, the two-phase pipe) represented by the continuous line in

Results

In the description of the two-phase flow phenomena, the shape of the PDF is useful to understand the chaotic nature of the flow. Costigan and Whalley [32] used the PDF shapes of the void fraction to classify the two-phase flow pattern. In Fig. 7, the twin-peaked PDF represents the slug flow where the low void fraction peak (or left peak – αLe) is the liquid slug region whilst the high void fraction peak (or right peak – αRi is the stratified region (Jones, 1975; [26].

In Fig. 8 the PDFs were

Conclusion

In this article, features of the horizontal two-phase slug flow were discussed. Five resistive sensors were installed so as to measure the void fraction along an experimental rig.

The PDF of the void fraction, translational bubble velocity and slug frequency were shown, as well as the influence of the liquid and gas superficial velocities along the pipeline (five experimental metering stations). It was observed that when there is an increase in the liquid superficial velocity, the void fraction

CRediT authorship contribution statement

Rômulo L.P. Rodrigues: Conceptualization, Methodology, Investigation, Writing - original draft. Cristiane Cozin: Validation, Formal analysis, Writing - review & editing. Bruna P. Naidek: Formal analysis, Writing - review & editing. Moises A. Marcelino Neto: Investigation, Writing - review & editing. Marco J. da Silva: Investigation, Writing - review & editing. Rigoberto E.M. Morales: Supervision, Formal analysis, Investigation, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors acknowledge for all technical and financial support provided by of NUEM-UTFPR, CAPES and TE/CENPES/PETROBRAS.

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