Experimental study of a single elongated bubble in liquid in under 10-degree upwardly inclined pipes

https://doi.org/10.1016/j.expthermflusci.2020.110247Get rights and content

Highlights

  • Studied the behaviour of elongated bubbles in slightly upwardly inclined pipes.

  • Bubble characteristics; shape, length, fraction and velocity are presented.

  • Information on the bubble velocity behaviour along the pipe is discussed.

  • Experimental results comparison with some recently developed drift velocity models.

Abstract

Two phase flow is of great interest in chemical and petroleum industries, and multiphase pipe flow models with closure relationships require experimental data for their development and validation. However, only little experimental information is available for slightly upward inclined pipes. Experimental investigations of single elongated bubble in marginally upwardly inclined pipes less than 10° have therefore been performed. Observations of the bubble drift velocity along the pipe has been highlighted. The drift velocity data presented here can contribute to improve knowledge of pipe inclination and viscosity dependency in drift velocity correlations. The new data on the bubble characteristics - shape, length, fraction and drift velocity may also provide useful information for the development and validation of numerical models. The measured drift velocity data have therefore been compared with some recently developed bubble velocity correlations.

Introduction

Slug flow is one of the multiphase flow patterns present in the production and transportation of oil, which can create pressure fluctuations that can adversely affect oil facilities. It is characterized by a quasi-periodic alteration of long bubbles and liquid slugs. In vertical pipes, the elongated (Taylor) bubbles, as described by Fabre and Liné [1], rise with a round shaped front followed by a cylindrical main body surrounded by an annular liquid film. When the pipe is other than vertical, the symmetry of the long bubble is lost; the transverse component of gravity causes the interface structure of long bubbles to change from an annular to a stratified flow pattern. Successful modelling of slug flow depends on the understanding of the motion of these long bubbles as they convey greater amount of the gas.

The investigation of the intermittent slug flow phenomena has been carried out systematically over the years in well-controlled experiments. For instance the works of Bendiksen [2], Fagundes et al. [3], Jeyachandra et al. [4], and Losi and Poesio [5], for the propagation of a single elongated bubble in stagnant or flowing liquid in pipes. The overall objective of these studies has been mostly to acquire data for improving the elongated bubble velocity in slug flow models. A summary of several experimental studies carried out on the characteristics of slug flow phenomena is presented in Table A.1. The findings generally reported by previous researchers, e.g. Bendiksen [2], Weber et al. [6], Hasan and Kabir [7], Shosho and Ryan [8], Van Hout et al. [9], Gockal et al. [10] and among others, show that the drift velocity increases with a decrease in oil viscosity, an increase in pipe diameter, and an increase in pipe inclination (with a maximum value at about 45°), and thereafter decreases. The propagation velocity is independent of length as long as the volume of the bubble corresponds to a cylinder with the tube radius and a length of 3 tube radii as reported by Zukoski [11]. Spedding and Nguyen [12] observed that the Froude number increases noticeably with the bubble volume at low tube inclination relative to the horizontal, and that beyond 2° of inclination relative to horizontal, the Froude number becomes nearly independent of the bubble size. Other findings reported by previous researchers, Bendiksen [2], Fagundes et al. [3], Woods and Hanratty [13], Grenier et al. [14], and among others, cover the bubble shape which depends on the mixture velocity, the fluid properties – viscosity and surface tension, and the pipe inclinations, but it’s independent on the bubble length. On the aspect of the void fraction, the work of Fabre and Liné [1] reported that the void fraction in liquid slugs is hardly greater than 25% but its value may be as high as 90%. Measurements of the effects of pipe diameter, viscosity, and pipe inclinations on the void fraction of long bubbles in slug flows in horizontal and upward inclined pipes have also been reported in the works of Jeyachandra et al. [4], Gokcal et al. [10] and Woldesemayat and Ghajar [15].

The drift flux model is one of the major approaches used to analyse slug flow in pipelines. The slug bubble velocity which basically relies on the drift velocity, as shown in Equation (1) proposed by Nicklin [16], is one of the closure relationships in a slug flow model.UB=Covm+vdwhere UB is the summation of the maximum mixture velocity in the slug body and the drift velocity, Co is the velocity distribution parameter, vd is the bubble drift velocity and vm is the mixture velocity. The distribution parameter,Co, is a dimensionless coefficient that depends on the velocity profile in the liquid, and is approximately the ratio of the maximum to the mean velocity. Bendiksen [17] interpreted (1) as a general expression of UB, being very close to the liquid velocity ahead of the bubble nose tip; ULrtCovm, plus a drift velocity, where rt is the radial position of the tip. A comprehensive study on the modelling of two-phase slug flow can be found in Fabre and Liné [1], Taitel and Barnea [18] and Bendiksen et al. [19]. It has been well-established that the long gas bubble’s dynamics are influenced by the viscous, inertial, gravitational, and interfacial forces acting on it, see White and Beardmore [20]. Dimensional analysis has shown that at least three dimensionless pi -groups are sufficient to determine the bubble dynamics: the Froude number, which is the ratio of the bubble inertia to the gravitational forces; the Eötvös number, which is the ratio of the gravitational to interfacial forces; and the Morton number, which primarily relates the viscous forces to surface tension forces. The choice of the pi- groups is not unique; for example, the inverse viscosity number, a combination of Eötvös number and Morton number, can also be employed. Several researchers, Jeyachandra et al. [4], Viana et al. [21], Lizarraga-Garcia et al. [22], and Livinus et al. [23], have used different combinations of the dimensionless pi-groups and other set of independent dimensionless groups (e.g Reynolds number, Weber number and buoyancy Reynolds number) to represent the dynamics, especially the drift velocity, of the elongated bubbles found in a slug flow. The choice of the combination is such that the forces influencing the long bubble dynamics are well captured in a unique way. Mathematical definitions of some the widely used dimensionless groups are given as follows:Frd=vd/[gD(1-ρg/ρl)]1/2Eo=(ρl-ρg)gD2σMo=gμ4ρσ3Nvis=μgD3(ρl-ρg)ρl-0.5R=D3gρl-ρgρl0.5μ

Some researchers, Gregory and Scott [24], Dukler and Hubbard [25], have proposed a zero drift velocity for slug flow models in horizontal or nearly horizontal pipes. However, theoretical works of Benjamin [26] and Weber [27], and the experimental works of Zukoski [11], Bendiksen [2], Weber et al. [6], have shown that drift velocity exists, even for horizontal flows. Unfortunately, most of the works have been directed towards low viscosity liquids, and only very few experiments have included high viscous liquids but have been performed in a short pipe length, for instance the works of Zukoski [11] and Weber et al. [6]. Zukoski [11] has already pointed out that the distance from the bubble front to the pipe exit for these short tubes was not enough to study the effect of viscous effects on the drift velocity along the pipe. Recent studies by Gokcal et al. [10], Jeyachandra et al. [4], Moreiras et al. [28], have included the study of drift velocities for liquids with viscosities up to 1000 cP, with longer pipes covering a wide range of pipe inclinations but in a coarse interval of ±10°. In addition, the bubble velocity measurements have been reported only for a point along the pipe and there is no information of the bubble velocity behaviour along the pipe. For moderately inclined pipes (say, between 1° and 10°), the works of Cook and Behnia [29], Perron et al. [30], and Leonardo et al. [31], presented only the bubble velocity measurements for a point along the pipe in a liquid viscosity less than 22 cP. The study by Losi and Poesio [5] seems to be the only detailed study available in the open literature that included high viscosity liquid. They investigated the effect of liquid viscosities, up to 804 cP, and of pipe inclination between 0° and 5° on the drift velocities of large bubbles in stagnant liquid in a 0.022 m internal diameter pipe using capacitance measurements and image analysis techniques. Apart from the well-established general findings from previous researchers, i.e., the drift velocity increases with a decrease in oil viscosity, an increase in pipe diameter, and an increase in pipe inclination, the authors also observed the bubble velocity to be decreasing along the pipe for horizontal flow which agrees with the simulation results presented by Andreussi et al. [32] and Ramdin and Henkes [33]. Also, they observed the reduction of bubble velocity to gradually disappear as the pipe inclination is increased. However, the observed trends of the bubble velocities along the pipe were not regular. So, they mentioned the effects of pipe misalignments might have on the bubble velocity measurements (low value data) along the pipe.

This work presents the results of experimental investigations carried out, using light diode detectors and visualization techniques with high speed camera, targeting the behaviour of a single elongated bubble in oil viscosity with nominal values of 160 cP and 1140 cP in 0.099 m and 0.057 m internal diameter pipes inclined at angles between 1° and 7.5°. The new collected data of drift velocity can contribute to improve the general knowledge of pipe inclination and viscosity dependency in drift velocity correlations. Some of the outcomes have been reported in Livinus et al. [23], but with little details. In addition, obtaining data on the bubble characteristics - shape, length, void fraction and drift velocity, may help for the development and validation of numerical models, including Computational Fluid Dynamics (CFD) based models.

Section snippets

Experimental rig set-up and methodology

Experimental fluid characterisation was first carried out on the oils used as liquid phases as presented in Appendix B. Table B.2 summarises the experimental conditions under which the large bubble tests were performed, mostly under stagnant conditions. Fig. 1 shows a plot of viscosity ratio against pipe length to pipe diameter ratio for this work and previous studies for slightly upwardly inclined pipes. The viscosity ratio, as defined in this work, is the ratio of the dynamic viscosity of a

Experimental results presentation

The experimental data collected were processed to obtain the bubble drift velocity, the bubble shape and other parameters such as the Froude number and the liquid height parameter. Oil viscosities with nominal values of 160 cP and 1140 cP were used in the analyses, considering that the actual test viscosity range could be ±25 cP for the 160 cP oil viscosity and ±80 cP for the 1140 cP oil viscosity.

Experimental drift velocity results comparison with correlations predictions

The accurate prediction of drift velocity is essential in the modelling of multiphase flow in pipelines. In 1965, Zuber and Findlay confirmed the Drift flux relationship in Equation (1) for vertical flow in annular and slug flow. Franca and Lahey [38] using air–water experimental data verified the use of the Drift flux model for all flow patterns observed in horizontal gas–liquid flow. In 2009, Danielson and Fan [39] showed that this relationship is valid for stratified, annular, slug and

Conclusion

Elongated bubble experiments in a low-pressure flow loop have been conducted with nominal oil viscosities of 160 cP and 1140 cP in 0.099 m and 0.057 m internal diameter pipes inclined at angles between 1 and 7.5°relative to horizontal. In all cases, it was observed that the pipe diameter, pipe inclination, and oil viscosity affected the drift velocity of the elongated bubble. Also the bubble size, when it was less 5D, had effect on the drift velocity in the high viscous liquid. A large

CRediT authorship contribution statement

Aniefiok Livinus: Conceptualization, Investigation, Methodology, Data curation, Formal analysis, Validation, Visualization, Writing - original draft, Writing - review & editing. Patrick G. Verdin: Project administration, Supervision, Validation, Visualization, 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.

Acknowledgements

The authors would like to thank the Consortium on Transient and Complex Multiphase Flows and Flow Assurance (TMF) for their in-kind support, and they acknowledge the support from ASCOMP; BP Exploration; Cameron Technology & Development; CD Adapco (now Siemens); Chevron; KBC (FEESA); FORSYS; INTECSEA; Institutt for Energiteknikk (IFE); Kongsberg Oil & Gas Technologies; Wood Group Kenny; Petrobras; Schlumberger Information Solutions; Shell; SINTEF; Statoil and TOTAL. The Authors wish to express

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