Pressure changes associated with the ascent and bursting of gas slugs in liquid-filled vertical and inclined conduits
Introduction
As commonly observed at Kilauea, Stromboli, and Etna volcanoes, the separation of exsolving gases from low-viscosity magmas can result in distinct styles of volcanic activity. These represent the surface expressions of different two-phase (magma and gas) flow regimes within the conduit, with Hawaiian eruptions being the result of annular flow and Strombolian eruptions representing the bursting of large individual gas bubbles. As the repeatability of many long-period (LP, 0.2–2 s) and very-long-period (VLP, 2–100 s) seismic events recorded at basaltic volcanoes suggest, they have non-destructive, fluid dynamic sources (Chouet, 1988, Chouet et al., 1994, Neuberg et al., 1994, Chouet, 1996, Chouet et al., 1997, Chouet et al., 1999, Ripepe and Gordeev, 1999, Ripepe et al., 2001, Chouet et al., 2002, Konstantinou, 2002). An understanding of these processes is becoming increasingly important. LP events are commonly believed to represent the result of resonating source regions (Chouet, 1988, Chouet, 1992, Chouet, 1996, Kumagai and Chouet, 1999) whereas VLP events are attributed to the wholesale movement of liquid (Arciniega-Ceballos et al., 1999, Nishimura et al., 2000, Kumagai et al., 2001, Chouet et al., 2002). In this study, we carry out pressure measurements on two-phase laboratory flows in pipes to gain further insights into how large ascending bubbles can act as sources of seismic and acoustic energy.
At Stromboli, both tremor and eruption seismic signals have been associated with bubble coalescence and rise (Chouet et al., 1997, Chouet et al., 1999, Ripepe and Gordeev, 1999, Ripepe et al., 2001, Chouet et al., 2002), and infrasonic acoustic measurements have been modelled with processes associated with bubbles bursting at the surface of the lava column (Vergniolle and Brandeis, 1996, Ripepe and Gordeev, 1999). Recent work on VLP seismic data from Stromboli points to highly repeatable source mechanisms associated with explosions (Chouet et al., 1999, Chouet et al., 2002). The locations of these sources, offset from directly under the vent region, suggest a conduit inclined roughly 30° from the vertical, rising from a depth of about 200 m below the surface (Chouet et al., 2002). The inclination of the conduit has implications not only for the stability of the flow regimes likely to occur within it, but also for the details of how these flow regimes are expressed. Accordingly, the experiments described here were carried out in both vertical and inclined tubes in order to investigate the dependence of flow patterns on tube inclination and quantify the resulting pressure fluctuations within the flow.
Engineering applications such as transport pipelines and bubble column reactors have driven a comprehensive literature on two-phase (gas–liquid) flows in pipes, although much work remains to be done to achieve full understanding of the complexities of the fluid dynamics involved (Joshi, 2001). A considerable amount of this literature describes details of the slug flow regime (believed to be responsible for Strombolian eruptions (Blackburn et al., 1976, Seyfried and Freundt, 2000) at basaltic volcanoes) in which large bubbles with diameters approaching that of the pipe, rise within a continuous liquid phase. In engineering, this regime is usually described by using the terms ‘Taylor bubble’ for the gas phase and ‘liquid slug’ for the connected, liquid phase. However, we retain here the terminology commonly used in the volcanology literature (Jaupart and Vergniolle, 1989, Seyfried and Freundt, 2000, Ripepe et al., 2001) and by Clift et al. (1978), in which the gas phase is referred to as the slug. Detailed two-phase flow studies have focused on the bubbly to slug flow regime transition (Legius et al., 1997, Cheng et al., 1998, Krussenberg et al., 2000), slug ascent velocity (Nicklin et al., 1962, White and Beardmore, 1962, Zukoski, 1966, Wallis, 1969, Seyfried and Freundt, 2000, Shosho and Ryan, 2001), coalescence of slugs (Shemer and Barnea, 1987, Pinto and Campos, 1996), and the documentation of slug shapes (Gopal and Jepson, 1998, Polonsky et al., 1999a, Seyfried and Freundt, 2000) and liquid flow patterns around slugs (Kawaji et al., 1997, Polonsky et al., 1999b, Bugg and Saad, 2002).
Three dimensionless parameters are required to compare gas slugs rising buoyantly in liquid-filled tubes in different systems (White and Beardmore, 1962). These are the Froude number:Morton number:and Eötvös number:where Uo represents the terminal ascent velocity of the slug, g is the gravitational acceleration constant, D is the internal diameter of the tube, and μ, ρ, and σ are the viscosity, density, and surface tension of the liquid, respectively. Within the space defined by these parameters there exists a region within which viscous and surface tension forces are trivial (White and Beardmore, 1962). In this region, bounded by Mo<10−6 and Eo>100 (White and Beardmore, 1962), slugs are inertially controlled and rise at their maximum velocity in vertical tubes, given by Fr=0.35. Zukoski (1966) demonstrated that slugs rising in inclined tubes can exceed this velocity by up to ∼80%.
In basaltic systems with vertical conduits, typical ranges of these parameters are 0.1<Fr<0.35, 105<Eo<107, and 105<Mo<1010, assuming 50<μ<500 Pa s, ρ=2600 kg m−3 and σ=0.4 N m−1 for basalt, and 1<D<10 m for the conduit (Seyfried and Freundt, 2000). These ranges indicate that gas slugs ascend within a transitional regime with a velocity dependent on slug volume and liquid viscosity. When Eo>100, the surface tension plays little role in determining the slug ascent velocity (Wallis, 1969). In the experiments described here, D=0.038 m, 0.16<Uo<0.33 m s−1, 0.001<μ<0.9 Pa s, and σ≈0.07 N m−1, which place the flows within the inertial and transitional regimes with 0.26<Fr<0.54, 200<Eo<270, and 10−11<Mo<14 (Table 1). As the diameter of our laboratory-scale pipe dictates a much smaller Eötvös number than in basaltic systems, surface effects will be enhanced in our experiments, but should not represent a controlling factor.
To assess the importance of viscous effects, a dimensionless inverse viscosity:may also be considered (Fabre and Liné, 1992), in which the viscous regime is given by Nf<2, and inviscid approximations are appropriate for Nf>300. For the parameters given above for a basaltic system, 16<Nf<5000 while, in our laboratory flows, 34<Nf<30 000. It is worth noting that in the inviscid case, where slugs are inertially controlled, the condition Fr=0.35 implies that Nf becomes proportional to the Reynolds number, Re, defined as Re=ρUD/μ. Reynolds numbers for slugs in our experiments vary between ∼10 and 104. For a basaltic system and assuming slug rise velocities of order 1 m s−1, 5<Re<103. Therefore, our experiments cover relevant regimes, with end members under inertial control and approaching viscous control. Processes suggested by our pressure measurements should therefore be scalable to basaltic systems.
Section snippets
Apparatus
Our experiments were carried out using a tube of borosilicate glass with internal diameter of 38 mm (Fig. 1). In experiments with vertical tubes, the apparatus was suspended from its top end using a rubber bicycle inner tube to isolate the tube from external vibrations. In experiments with inclined tubes, the bicycle inner tube was disconnected from the top of the tube and looped through a chain attached at two different points along the tube. Pressure sensors were mounted in the base of and at
Experiments with single gas slugs
Characteristic pressure changes induced during the ascent of individual gas slugs were observed in all our experiments. The behaviour of the pressure fluctuations was found to depend on both the liquid viscosity and tube inclination. In order to demonstrate the main features of the pressure changes recorded, Fig. 2a shows the ASG data from an experiment carried out with a vertical tube and a liquid viscosity of 0.9 Pa s. These data represent absolute pressures, therefore their offsets are
Experiments with a continuous supply of gas
Experiments in which gas was supplied continuously to the base of the liquid column were only carried out with two different solutions, namely tap water (0.001 Pa s) and a sugar solution with a viscosity of 0.09 Pa s. At higher viscosities, the bubblers used could not produce small dispersed bubbles, but generated only large, slug-like bubbles. Therefore, the transition between bubbly and slug flow was not investigated in the 0.9-Pa-s solution with the apparatus available for these experiments.
Discussion
Our experiments demonstrate the importance of tube inclination in promoting bubble coalescence and hence slug formation by locally enhancing the gas-volume fraction on the upper wall of the tube. For any reasonably long conduit, only very small angles of inclination could therefore result in transitional, if not slug, flow. Once a large bubble is produced, its increased ascent velocity will allow it to continue to grow by enhanced coalescence. Even in situations with multiple rising slugs of
Summary
Pressure measurements carried out during the ascent of gas slugs in liquid-filled tubes demonstrate the importance of both static and dynamic pressure changes. Conduit inclination promotes bubble coalescence and the slug flow regime in two-phase flow, increasing slug size and slug ascent velocity at the expense of the frequency of occurrence of slugs as compared to identical gas fluxes in vertical tubes. By concentrating gas on the upper wall of the tube and increasing the thickness of the
Acknowledgements
We are grateful to J. Bailey and K. Courtney for assistance during some of the experiments and to G. Ryan for useful discussions. M.R.J. was supported by The Leverhulme Trust (F/00 185A), and equipment was funded by The Royal Society. We thank E. Calder and R. Seyfried whose helpful comments improved this manuscript.
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