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EVOLUTION OF TWO-PHASE SLUG FLOW IN VERTICAL AND INCLINED PIPES

R. van Hout *, D. Barnea *, L. Shemer * * Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering Tel-Aviv University, 69978 Ramat-Aviv, Israel Tel. (972) 03-6408930, Fax. (972) 03-6407334 E-mail: [email protected] ABSTRACT

Evolution of liquid-gas slug flow is studied in pipes of various inclinations. Measurements are performed by two independent measuring techniques. First, digital image processing of a sequence of video images is applied to obtain quantitative information on the instantaneous spatial distribution of the two phases in each frame. The corresponding interface propagation velocities and lengths of elongated bubbles and liquid slugs are derived from these data. Alternatively, instantaneous void fraction as a function of time is measured by a number of optical fiber probes. The three probes are placed in a measuring module at small increments along the pipe axis. The module can be mounted at various locations along the pipe. The combined data from the local probes enables obtaining information similar to that derived from the image processing. The relative advantages of the two techniques are discussed.

INTRODUCTION Slug flow is one of the basic gas-liquid flow patterns, which takes place naturally inside pipes and occurs over a wide range of flow parameters. Slug flow plays an important role in a variety of industrial applications. In vertical slug flow, most of the gas is located in large bullet-shaped (Taylor) bubbles that span most of the pipe cross-section. The Taylor bubbles are separated by liquid slugs, which usually contain small dispersed bubbles. The liquid confined between the Taylor bubbles and the pipe wall flows around the bubble as a thin film. Each slug sheds liquid to the accelerating downward film that is then injected into the next liquid slug as a circular wall jet, producing a mixing zone in the bubble wake. For inclined flow, the gas is accumulated in the upper part of the pipe as large elongated bubbles, separated by liquid slugs that may contain dispersed bubbles. The translational velocity of an elongated bubble is assumed to be a superposition of the velocity of a single bubble in stagnant liquid, the drift velocity Ud, and the contribution of the liquid slug mixture velocity Um [1]: U tr = CU m + U d (1)

h U d = 0.54 gD

(3)

This result was supported experimentally by [2, 7]. For the inclined case it was found experimentally [2, 7, 8] that the maximum drift velocity occurs at inclination angles around 40° to 60°. The drift velocity for inclined flows has been correlated by [2] as a weighted superposition of the drift velocity in vertical and horizontal flow:

h v U d = U d cos + U d sin

(4)

The value of the constant C is based upon the assumption that the propagation velocity of the bubbles follows the maximum local velocity in front of the nose tip [1-4]. Thus C is the ratio Umax/Um, which equals approximately 1.2 for fully developed turbulent and 2.0 for laminar flow. the drift

v velocity, U d ,

The evolution of slug flow strongly depends on the relative velocities between the bubbles. At small separation distances, trailing bubbles accelerate and eventually merge with the leading bubble. The velocity of a trailing bubble as a function of the separation distance from the leading bubble has been studied by [9-13]. These studies were performed using controlled injection of individual elongated bubbles into vertical liquid columns. The aim of this paper is to investigate the relative velocities between consecutive elongated bubbles in continuous slug flow for various pipe inclinations. The evolution of slug lengths distribution along the pipe is studied as well. Measurements have been performed using local optical probes as well as applying image processing of a sequence of video images. EXPERIMENTAL FACILITIES AND DATA PROCESSING Experimental facility I: continuous slug flow

in vertical slug flow is given by [5]: (2)

v U d = 0.35 gD

This is in agreement with experimental observations [1].

h The drift velocity, U d , for horizontal flow equals to [6]:

The experimental facility consists of a steel frame supporting a transparent 10 m long Perspex pipe with an internal diameter of 0.024 m. The frame can be rotated around its axis from horizontal to vertical position. The pipe consists of sections about 2 m long. Air and water are introduced

through a "mixer"-type inlet device and circulated in a closed loop. More details are given in [14]. Experiments in the slug flow regime were carried out for different flow rates. The gas flow rates are given for the outlet pressure of 0.1 MPa. Measurements were performed using both optical fiber probes and video image processing techniques. Optical probes are sensitive to the change in the refractive index of the surrounding medium and are capable of detecting the local instantaneous phase (gas or liquid). The return signals from the optical fiber sensors were amplified to yield an analog output of two levels representing the instantaneous phase of the medium present at the fiber tip. Four optical probes were used simultaneously. One of the probes was mounted near the pipe exit to ensure constant flow conditions between different experiments. Three probes were installed in a specially constructed module, mounted at an axial distance of 0.020 m and placed on a traversing mechanism that allowed their accurate radial positioning. In vertical slug flow the probe tips were positioned at the pipe centerline whereas in inclined flow the probe tips were positioned in the upper part of the pipe at half the pipe radius. The measurement module was installed between the pipe sections and could be moved easily along the pipe. The analog output signals (0 - 10V) were sampled with a maximum total sampling frequency of 100 kHz. An example of two raw signals obtained from two adjacent probes is shown in Fig. 2a. The low value corresponds to water and the high value to air. The distinction between the elongated bubble (E.B.) and the liquid slug (L.S.) regions can be clearly seen. The term "transition times", tTR, refers here to the instants of transition from gas to liquid or vice versa relative to an initial reference time. A bubble duration can be determined from two successive transition times. Since the time scales of the elongated bubbles and the small dispersed bubbles in the liquid slug region are different, a threshold is chosen to filter the small bubbles in the liquid slug out of the raw signal. An example of a filtered TTL-signal is shown in Figure 2b for two probes separated by a small distance. Two elongated bubbles, numbered j and j+1, moving from probe 1 to probe 2 are shown. The transition times of nose (n) and tail (t) for the first bubble (j) passing by the first probe (1) are tTR ( j ) and tTR ( j ) , respectively. In order to convert the time duration of the elongated bubbles and liquid slugs into actual lengths, the propagation velocities of the interfaces are needed. The knowledge of the time intervals required for a given interface to travel between two probes and the distance between the probes enables the determination of the local instantaneous propagation velocity of nose and tail separately for each elongated bubble. This information, together with the residence time of each individual elongated bubble and liquid slug is then applied to obtain the corresponding lengths. Consider a pair of consecutive bubbles in continuous slug flow, j and j+1 (Fig. 2b). The instantaneous translational velocity of the trailing bubble, j+1, is defined by its nose movement:

n U tr (j + 1) = 1n 1t

where t s

is the average liquid slug duration as measured

t

by both probes and U tr ( j ) is the measured tail velocity of the leading bubble j which is assumed to remain constant in the process of the liquid slug movement along the probe. Similarly, the length of each elongated bubble could be calculated. For each flow condition and measurement station, this procedure enables one to determine the dependence of the

n translational velocity of each trailing bubble U tr ( j + 1 ) on

the liquid slug length

Probe 1 Gas j Liquid Probe 2 Gas j Liquid Probe 1 Gas t TR ( j )

1n

l s (j) in front of it.

L.S.-region a: Raw sampled signals

E.B.-region

j+1

j+1

b: Filtered TTL-signals t TR ( j ) j

1t

tTR ( j + 1)

1n

t TR ( j + 1 )

1t

j

j+1

Liquid Probe 2 Gas t TR ( j )

2n

j

t TR ( j ) j

2t

t TR ( j + 1 ) t 2 t ( j + 1 ) TR j+1

2n

Liquid

t [s]

t ( j )

n

t ( j )

t

t ( j + 1 )

n

t ( j + 1 )

t

Fig. 2.Signals of two optical probes mounted at a distance of 0.040m. a) Raw sampled signals. b) Filtered TTL-signals. The above procedure is not fully deterministic due to the bubble interface distortions. For vertical flow, it is known that both elongated bubble nose and tail exhibit strong oscillations [13, 15]. Due to the oscillations the extreme points of the elongated bubble nose and tail do not necessarily coincide with the probe tip installed at the pipe centerline. Fig. 3 shows examples of snapshots of the distorted elongated bubble nose interfaces as recorded by a camera at 7 m from the inlet section. The separation distance between the leading and the trailing bubble in this Figure is approximately 13D. It can be clearly seen that the bubble nose sways from one side to the other. To reduce the ensuing errors, advantage was taken of the fact that the distribution of the time intervals required for a given interface (bubble nose or tail) to travel from one probe to the other was approximately normal. The outliers in the time lag distributions were discarded. Besides the determination of the instantaneous velocities of each elongated bubble, the local characteristic velocity can be determined by direct cross correlation of the time records of two adjacent probes. More information about the cross correlation technique can be found in [14]. Image processing can be used as an additional technique to obtain information about lengths and velocities. A series of images was taken and processed by dedicated software. The

x t (j + 1)

n

(5)

where x is the distance between the two probes. The liquid slug length is given by:

t l s (j) = t s U tr (j)

(6)

major advantage of the image processing technique over the optical probes is the possibility to extract directly lengths and velocities from the images. Furthermore, qualitative information about the elongated bubble behavior is obtained, such as bubble shape, interface distortion and oscillations. However, the use of image processing technique in continuous slug flow is limited by several factors. In particular, the elongated bubble interfaces are difficult to detect due to the highly aerated liquid slug zone in continuous slug flow and its fierce oscillations. The image processing technique in continuous slug flow is therefore cumbersome and does not allow for the accumulation of a sufficient body of data to enable reliable statistical analysis. These reservations do not hold when a single bubble or a pair of consecutive bubbles is studied where the interfaces are clearly discerned and accurate information about an elongated bubble's shape, velocity and its length is available .

switching and recording process was achieved using PC-controlled signals. Pairs of elongated bubbles with various lengths and initial spacing were injected into stagnant water. The process of propagation, approach and eventual coalescence of the two bubbles was recorded by the computer using custom-written software. The images (30 frames/s) were recorded only during the passage of the bubbles through the field of view of each camera in sequences of 100-150 frames for each series. The interlaced video images were deinterlaced and the effective frame rate was 60 images/s. Details about the experimental procedure are given in [15]. RESULTS The approach velocity of consecutive bubbles, is of the uttermost importance for the modeling of continuous slug flow. The relationship between the translational velocity of a trailing bubble and the liquid slug length ahead of it, Utr = f ( l s ) , is needed as an input relation to models for the evolution of slug length distribution [16]. The translational velocity was measured in vertical upward, continuous slug flow by optical probes and the results were compared to controlled bubble injection experiments using image processing technique. Vertical slug flow The translational velocity as a function of separation distance and the evolution of the liquid slug length distributions was determined in continuous slug flow, using experimental facility I. The measurements were carried out by optical probes, in 90o upward slug flow at different positions (x/D) along the pipe. Fig. 5 presents the evolution of the liquid slug length distributions along the pipe, together with the corresponding instantaneous trailing bubble velocity for ULS = 0.01 m/s; UGS = 0.41 m/s. The same trends were observed for ULS = 0.10 m/s ; UGS = 0.63 m/s. The trailing bubble velocity is shown as a function of liquid slug length ahead of it. To facilitate comparison of data obtained in different experiments, the velocities were normalized by the translational velocities Tab. 1.Effect of gas calculated by Eq. (1) with expansion on UNick. C = 1.2, UNick. Since the gas 90o superficial velocity, UGS, Flow rate D = 0.024 m increases along the pipe due to ULS [m/s] 0.01 0.10 gas expansion, the mixture UGS [m/s] 0.41 0.63 velocity, Um, in Eq. (1) at each x/D UNick [m/s] position along the pipe was 15.2 0.56 0.87 adjusted accordingly. The 33.3 0.57 0.88 effective volumetric gas flow rate along the pipe was 117.5 0.59 0.91 recalculated taking into 286.7 0.64 0.99 account the pressure drop Pipe exit 0.67 1.04 along the pipe [17] and was used to calculate the translational velocity, UNick, at each position (x/D). The results are shown in Table 1 for different x/D and various flow rates. The histograms showing the distribution of liquid slug lengths are given in Fig. 5. The bin size is the pipe diameter D. For each bin separately, the corresponding trailing bubble velocities were averaged. The primary y-axis shows the percentage of the total number of liquid slugs that were used for calculating the average of the instantaneous velocities

Fig. 3. Distorted bubble behavior of nose interfaces in vertical slug flow. Experimental facility II: controlled injection of bubbles Controlled injections of bubbles were carried out in a 4 m long transparent Perspex pipe with an internal diameter of 0.024 m. A pair of bubbles of prescribed lengths and separation distance could be injected into the pipe that was filled with tap water. The pipe was equipped with three 1 m long rectangular transparent boxes filled with water in order to reduce image distortion. An image processing technique was applied to determine interface propagation parameters. Two cameras were used. The field of view of each camera was about 300x225mm2. In order to obtain a better spatial resolution in the vertical direction, the cameras were rotated by 90o. The two fields of view overlapped slightly providing an effective field of view of ~600mm (24D). On both sides of the test section, 500 W halogen lamps were mounted on folding support frames at the opposite sides of the test section. Constant temperature during the experiment was maintained by running tap water through the transparent boxes. The air supply system consisted of an inlet air chamber and electrically activated valves. Air was supplied from a central compressed air line, at a nominal pressure of 0.6 MPa. The air inlet chamber was attached to the lower part of the test pipe at an angle of 30o. Individual bubbles were injected into the test pipe by means of a computer-controlled injection valve. The valve, the chamber and the test section have the same inner diameter, in order to provide smooth entrance of air bubbles. The pressure in the air chamber was accurately monitored. The lengths of the injected bubbles were set by the duration of the valve opening, which was controlled by the computer, as well as by the air pressure in the chamber. Synchronization that is required between the bubble injection, cameras

measured for each value of the leading slug length. The ensemble size at each x/D exceeded 103.

U L S = 0.01 m/s; U GS = 0.41 m/s

x/D = 15.2

presents the variation of the averaged trailing bubble velocity with the separation distance for two different lengths of the bubbles in each couple.

7

25

3

L.S . [% o f to tal]

U in st /U Nick

20 15 10 5 0 25

< ls> = 4.8 [D] std. dev. = 3.6 [D]

(a) 6 5

2

Bubble Length=1D Bubble Length=12D

1

U trail /U lead

4 3 2 1

0 3

L.S . [% o f to tal]

20 15 10 5 0 25

x/D = 33.3

std. dev. = 6.7 [D]

U in st /U Nick

< ls> = 8.2 [D]

2

0 0 1 2 3 4 5 6 7 8 9 10

1

Separation distance, D

2 (b) 1.8 1.6 Bubble Length=1D Bubble Length=12D

0 3

L.S . [% o f to tal]

20 15 10 5 0 25

x/D = 117.5

std. dev. = 7.7 [D]

U trail /U lead

2

U in st /U Nick

< ls> = 15.0 [D]

1.4 1.2 1 0.8 0.6

1

0 3

L.S . [% o f to tal]

15 10 5 0 1 5 9 13 17

std. dev. = 8.0 [D]

2

U in st /U Nick

20

x/D = 286.7

< ls> = 16.3 [D]

5

15

25

35

45

55

65

Separation distance, D

1

Fig. 6. Ratio of the averaged trailing bubble velocity to that of the leading one. a) small separation distances. b) large separation distances. The trailing Taylor bubble velocity is normalized here by that of the leading one. Two different scales are applied for the larger (Fig 6b) and for the shorter (Fig 6a) separation distances. Notable acceleration of the trailing bubble is observed at distances shorter than about 3D (Fig. 6a) as was observed in Fig. 5 in continuous slug flow. This acceleration is more pronounced for longer bubbles (12D). Even at considerable separation distances, the average velocity of the trailing bubble remains somewhat higher than that of the leading bubble. This effect is stronger for longer Taylor bubbles (Fig. 6b). In the near wake region (few pipe diameters) the present results are close to those obtained earlier [9, 11]. However, the measurements with image processing (Fig 6b), extend to substantially larger distances than those investigated before. It appears that interaction between the bubbles exists at distances exceeding the generally assumed stable liquid slug length (~16D for vertical flow).

7 6 5 4 3 2 1 0 0

Continuous flow Controlled injection

0 21 25 29 33 37

L.S . length [D ]

Uin s t/UNick Lo g n o rmal fit

Fig. 5. Utr = f(ls) and measured liquid slug length distributions. 90° upward slug flow It can be clearly seen that the distributions of the liquid slug lengths are skewed. A best fit of the log-normal distribution was therefore attempted, and the resulting distribution curve is shown in the figures. Near the entrance (x/D = 15.2), the distributions are peaked around relatively small values of few pipe diameters. Further along the pipe the distributions become less peaked with an increase in the most probable and mean slug lengths. The curves in Fig. 5 show the dependence of the instantaneous velocities of the elongated bubbles on the liquid slug length ahead of them, Utr = f ( l s ) . For small separation distances there is a significant acceleration of Taylor bubbles. The maximum ratios Uinst/UNick (secondary y-axis) lie between 1.5 and 2.5. However, for very short separation distances (up to 1D), the instantaneous velocity abruptly decreases. This phenomenon can be explained by the fact that prior to coalescence there exists a small liquid "bridge" between leading and trailing bubbles [13]. At larger separation distances, the elongated bubble velocities decrease gradually to the velocity predicted by Eq. (1). Recently [13] carried out experiments in experimental facility II. Pairs of consecutive bubbles were injected and studied using an image processing technique. The average trailing bubble propagation velocity was determined for various bubble lengths and separation distances. Fig. 6

<U inst >/U Nick

a

U tr /U Nick = a +b exp(-c l s /D ) + 1/(l s /D ) a =1; b =8; c =1.5

10

20

30

40

50

60

Liquid slug length [D] Fig. 7. Normalized translational velocity of trailing bubble as a function of separation distance in vertical flow.

L.S . [% o f to tal]

15 10 5 0 25

< ls > = 11.0 [D ] std.dev.= 8.9 [D ]

2

U ins t /U Nic k

15 10 5

< ls > = 9.5 [D ] std.dev.= 9.2 [D ]

2

L.S . [% o f to tal]

15 10 5 0 1 7

< ls > = 19.5 [D ] std.dev.= 14.2 [D]

U ins t /U Nic k

2

15 10 5

< ls > = 11.6 [D ] std.dev.= 5.0 [D ]

2

Effect of inclination Experiments were carried also out for 10o and 30o inclination in continuous slug flow using optical probes. The evolution of the liquid slug length distribution and the corresponding approach velocities are presented in Fig. 8 for flow rate ULS = 0.01 m/s, UGS = 0.41 m/s. Similar trends were observed at the other flow rates. Tab. 2. Effect of gas expansion on UNick.

1

1

0 13 19 25 31 37

0 1 7 13 19 25 31 37

0

L.S . length [D ]

Uins t/Un ick

L.S . length [D ]

Log n ormal fit

Fig. 8. Utr = f(ls) and measured liquid slug length distributions. Inclinations 30o and 10o.

2

<U inst >/U Nick

Flow rate ULS [m/s] UGS [m/s] x/D 15.2 33.3 117.5 286.7 Pipe exit

30o 0.01 0.10 0.10 0.41 0.41 0.63 UNick [m/s] 0.78 0.78 0.79 0.81 0.82 0.88 0.88 0.89 0.91 0.92 1.13 1.14 1.15 1.17 1.19

10o 0.01 0.10 0.10 0.41 0.41 0.63 UNick [m/s] 0.79 0.79 0.79 0.79 0.79 0.89 0.89 0.90 0.90 0.90 1.16 1.16 1.16 1.16 1.16

1.5 1 0.5 0 0 10 20

30°

10°

30

40

Liquid slug length [D ]

Fig. 9. Averaged, normalized translational velocity of trailing bubble as a function of separation distance.

The measured velocities were normalized by the Nicklin correlation, Eq. (1) C = 1.2, with the drift velocity for inclined flow according Eq. (4). The drift velocity for horizontal pipe depends on the surface tension and therefore the measured

h horizontal drift velocity according to [7] was used, U d = 0.18 m/s. For vertical flow, the drift velocity according to Eq. (2) was adopted. Furthermore, the increase in the mixture velocity due to pressure drop along the pipe was accounted for as described above. The calculated velocities according to the Nicklin correlation are shown in Tab. 2 for 10o and 30o inclination. As expected, the influence of the pressure drop on the translational velocity is less for 30o than for 90o and is negligible for 10o inclination. As was the case for 90o, the distributions of the liquid slug lengths are skewed and the log-normal fit is depicted in the Figs. The mean and most probable liquid slug lengths increase along the pipe. The curves of the approach velocity as a function of separation distance, Utr = f ( l s ) (Fig. 8) present the same trends as were described for 90o upward flow. For small separation distances there is a significant acceleration of elongated bubbles,while for ls < 1D there is a drop in velocity due to the bridging phenomenon. At large separation distances the normalized velocity decreases.

2 1.8 90° 30° 1.6 1.4 1.2 1 0 2 4 6 8 10 10°

<U inst >/U Nick

Liquid slug length [D]

Fig. 10. Averaged, normalized translational velocity of trailing bubble. Inclination 90°, 30° and 10°. The available data for the trailing bubble velocity as a function of separation distance was averaged for each pipe inclination separately over all flow conditions and measuring positions. The weighted averages are shown in Fig. 9. It can be noticed that for 30o the normalized velocity at large

U ins t /U Nic k

20

L.S . [% o f to tal]

The coefficient a represents the normalized terminal elongated bubble propagation velocity for large separation distances. The last term was added to the correlation to account for the slower decay in the translational velocity of elongated bubbles behind relatively long slugs that was clearly observed in the image processing results (Fig. 6b). In Fig. 7, the coefficient a = 1, meaning that the propagation velocity behind long liquid slugs equals to that given by Eq. (1). The coefficient b = 8.0 is in agreement with Moissis and Griffith (1962), while c has the value of 1.5.

1

1

0 3 L.S . [% o f to tal]

x/D = 117.5

0 25

0 3

x/D = 117.5

U ins t /U Nic k

L.S . [% o f to tal]

15 10 5 0 25

< ls > = 13.6 [D ] std.dev.= 10.2 [D ]

2

15 10 5

< ls > = 11.3 [D ] std.dev.= 6.8 [D ]

2

1

1

0 3

x/D = 286.7

0 25

x/D = 286.7

0 3

20

U ins t /U Nic k

20

20

U ins t /U Nic k

20

L.S . [% o f to tal]

The data of the optical probes obtained for continuous slug flow were averaged for different flow conditions and measuring positions (x/D). The accumulated information on the dependence of the Taylor bubble velocities on the liquid slug length ahead of them, is given in Fig. 7 for continuous slug flow and for controlled injections. Note the decrease of the normalized velocity due to the bridging phenomenon. The best fit curve suggested by [9] was adopted for both cases with some modifications, Fig. 7.

25 L.S . [% o f to tal]

x/D = 15.2

30°

3 L.S . [% o f to tal]

25

x/D = 15.2

10°

3

U ins t /U Nic k

15 10 5 0 25

x/D = 33.3

< ls > = 6.7 [D ] s td.dev.= 6.8 [D ]

2

15 10 5 0 25 20

x/D = 33.3

< ls > = 5.8 [D ] s td.dev.= 4.9 [D ]

2

1

1

0 3

0 3

U ins t /U Nic k

20

20

separation distances is somewhat higher than unity while for 10o inclination it is somewhat smaller than unity. The effect of inclination on the approach velocity for small (<10D) separation distances is studied in Fig. 10. The weighted averages are shown for 90o, 30o and 10o. The onset of acceleration seems to be a function of inclination. On the average, acceleration starts earlier for 90o and later at decreasing inclination angles. The maximum obtained approach velocity (ls = 2D) decreases with decreasing inclination angle. SUMMARY The evolution of gas-liquid slug flow in pipes was studied in two separate experimental facilities. In the first facility continuous slug flow at different pipe inclination angles was studied using mainly fiber optics technique. In the second facility, interaction between injected pairs of bubbles was studied by video image processing technique. The results obtained in the two different facilities by using various measuring techniques compare favorably. NOMENCLATURE C D E.B. g j ls L.S. tTR U Ud UGS Uinst ULS Um UNick Utr x Distribution parameter Pipe diameter Elongated bubble Gravitational constant (9.81) Bubble index Liquid slug length Liquid slug Transition time Velocity Drift velocity Gas superficial velocity Instantaneous translational velocity Liquid superficial velocity Mixture velocity Translational velocity, Eq. (1) Translational velocity, Eq. (1) Position along the pipe m m2/s m s m/s m/s m/s m/s m/s m/s m/s m/s m

REFERENCES 1. D.J., Nicklin, J.O.,Wilkes, J.F., Davidson, Two-Phase Flow in Vertical Tubes, Trans. Instn. Chem. Engrs 40, pp. 61-68, 1962. K. H., Bendiksen, An experimental investigation of the motion of long bubbles in inclined tubes, Int. J. Multiphase Flow 10, 467-483, 1984. L., Shemer, D., Barnea, Visualization of the instantaneous velocity profiles in gas-liquid slug flow, PhysicoChemical Hydrodynamics 8, No.3, pp. 243-253, 1987. S., Polonsky, L., Shemer, D., Barnea, The relation between the Taylor bubble motion and the velocity field ahead of it, Int. J. Multiphase Flow 25, pp. 957-975, 1999b. D. T., Dumitrescu, Strömung an einer Luftblase im senkrechten Rohr, Z. Angew. Math. Mech. 23, pp. 139-149 1943. T. B., Benjamin, Gravity currents and related phenomena, J. Fluid Mech. 31, Part 2, 209-248, 1968. E. E., Zukoski, Influence of viscosity, surface tension, and inclination angle on the motion of long bubbles in closed tubes, J. of Fluid Mechanics. 25, part 4, pp. 821-837, 1965. A. R., Hasan, and C. S., Kabir, Predicting multiphase flow behavior in a deviated well, 61st Annu. Tech. Conf. New Orleans, La. SPE 15449, 1986. R., Moissis, P., Griffith, Entrance Effects in a Two-Phase Slug Flow, J. of Heat Transfer, 29-39, 1962. R., Clift, J. R., Grace, Continuous Slug Flow in Vertical Tubes, Journal of Heat Transfer, pp. 371-376. 1974. A. M. F. R., Pinto, J. B. L. M., Campos, Coalescence of two gas slugs rising in a vertical column of liquid. Chemical Eng. Science 51, No. 1, pp. 45-54, 1996. H.A., Hasanein, G.T., Tudose, S., Wong, M., Malik, S., Esaki, M., Kawaji, Slug Flow Experiments and Computer Simulation of Slug Length Distribution in Vertical Pipes. AIChE SYMPOSIUM SERIES Heat transfer - Houston, pp. 211-219, 1996. C., Aladjem Talvy, L., Shemer, D., Barnea, On the interaction between two consecutive elongated bubbles in a vertical pipe, Int. J. Multiphase Flow 26, pp. 1905-1923, 2000. R. van Hout, Evolution of hydrodynamic and statistical parameters in gas-liquid slug flow, Ph.D. thesis, Tel-Aviv University, Israel, 2001. S., Polonsky, D., Barnea, D., L., Shemer, Averaged and time-dependent characteristics of the motion of an elongated bubble in a vertical pipe, Int.J. Multiphase Flow Vol. 25, pp. 795-812, 1999a. D., Barnea, Y., Taitel, A model for slug length distribution in gas-liquid slug flow, Int. J. Multiphase Flow 19, pp. 829-838, 1993. D., Barnea, Effect of bubble shape on pressure drop calculations in vertical slug flow, Int. J. Multiphase Flow 16, pp. 79-89 1990.

2.

3.

4.

5.

6. 7.

8. 9. 10. 11.

12.

13.

Greek symbols

t ts x

Inclination angle Time interval Liquid slug duration Distance between probes

degrees s s m

14. 15.

Subscripts lead Leading bubble max Maximum trail Trailing bubble Superscripts h i n t v Horizontal Probe number Nose Tail Vertical Other < > Average

16.

17.

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