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Proceedings of ENCIT 2014 15th Brazilian Congress of Thermal Sciences and Engineering

Copyright © 2014 by ABCM

November 10-13, 2014, Belém, PA, Brazil

STATISTICAL CHARACTERISATION OF TWO-PHASE SLUG FLOW IN

HORIZONTAL PIPES

Fernando E. C. Vicencio, [email protected]

Fausto A. A. Barbuto, [email protected]

Cristiane Cozin, [email protected]

Fábio A. Schneider, [email protected]

Marco Jose da Silva, [email protected]

Rigoberto E. M. Morales, [email protected] Postgraduate Program in Mechanical and Material Engineering – PPGEM,

Federal University of Technology – Parana (UTFPR)

Av. Sete de Setembro 3165, CEP 80230-901, Curitiba-PR-Brazil.

Abstract. The aim of this work is to enhance the knowledge on the characteristic parameters of two-phase slug flow in

horizontal pipes. To achieve this goal, an experimental methodology based on experiments comprehending 47 different

combinations of superficial velocities of liquid (JL) and gas (JG), was developed at the Thermal Sciences Laboratory

(LACIT) at the Federal University of Technology - Parana (UTFPR). The two-phase pipe is a 25.8-mm ID and

9.2 m-long acrylic tube. A pair of 12x12-nodes wire-mesh sensors (WMS), 3.75 cm apart to identify the phase passing

through the sensor was assembled at 7.5 m from the mixer. This way, the time series of void fraction could be obtained

from the WMS, which was processed to extract characteristic parameters such as bubble velocity (UB), unit-cell

frequency (f), bubble (LB) and slug lengths (LS), and bubble void fraction (αB). The results were shown as probability

distributions (PDF), and the distributions were approximated to normal or log-normal probability functions, which

depend on mean and standard deviation. This analysis was extended to the 47 measured points, obtaining an

approximation for the scatter of each mean and standard deviation as a function of gas and liquid superficial velocities

for each measured point. The probability functions of mean and standard deviation for each characteristic parameter

were used to compare the predicted with the experimental PDFs, and a good agreement was found. This work might

serve as a reference for experimental and numerical studies for the study of two-phase slug flows.

Keywords: slug flow, horizontal pipe, experimental analysis, probability density function.

1. INTRODUCTION

The knowledge on the mechanics of two-phase slug flow is a relevant issue for the oil and gas industry, due to the

high frequency of occurrence of those flows, as well as to the large transportation distances, from subsea wells to

floating platforms or vessels (Fabre et al., 1990; Havre, et al., 2000). It should be noted that the dynamic loads

associated with slug flows might put the installations at risk; therefore, they must be designed based on numerical

models. For this reason, the development of numerical models to predict the behavio ur of slug flow has gained

importance in the oil and gas industry (Issa and Kempf, 2003; Mazza, 2010).

From a mechanical point of view, the gas -liquid slug flow has a more complex behaviour than the single-phase

flow. For this reason, early studies on slug flow were empirical, in order to establish correlations for some characteristic

parameters (Gregory and Scott, 1969; Heywood and Richardson, 1979).

Later, the bases for the mechanistic modelling of two-phase slug flows were established. The introduction of the

unit-cell concept represented a very important landmark in slug flow modelling. Such approach consists of a long

bubble and a liquid slug regions (Wallis, 1969). This simplification is very important in mechanistic modelling and

experimental studies for its validation (Carpintero, 2009; Netto, et al., 1999).

The numerical models for slug flows have increased their complexity in line with the increase in computation

power observed in recent decades, from one-dimensional steady-state models to complex unsteady models (Fabre and

Line, 1992). However, these models require validation with experimental data. Besides, in many of these models it is

necessary to use experimental correlations or probability distributions (PDF) to solve the system of equations (Taitel

and Barnea, 1990).

In this context, the aim of this work is to increase the experimental database for the validation of horizontal two-

phase slug flows by using an appropriate methodology for acquisition, processing and analysis of data captured by

sensors. A pair of wire-mesh sensor (WMS) was used to obtain the unit-cell parameters such as the bubble velocity,

frequency, characteristic lengths and void fraction. The PDFs of those parameters were analyzed by means of known

probability functions as the normal and log-normal ones. Finally, the calculated PDFs were compared with the

experimental ones.

mailto:[email protected]




2. EXPERIMENTAL PROCEDURE

The experiments were carried out at the LACIT-UTFPR, Paraná, Brazil. A scheme of the experimental facility is

shown in Figure 1. It consisted of two branches: one for the liquid, with a pipe, a centrifugal pump and a Coriolis mass

flow meter; and one for the gas, with a pipe, an alternate compressor, two pressure tanks and orifice plates for flow rate

measurement. These two lines gather at a mixer and enter a two-phase flow pipeline, 9-m long and 25.8-mm ID. This

system also has pressure and temperature sensors. At 7.5 m or 290D from the mixer a pair of WMS 37.5 mm apart was

installed, as well as a high-speed camera to verify those measurements.

Figure 1. Scheme of experimental facilities at LACIT-UTFPR.

The WMS pair, whose scheme is shown in Figure 2, consists of two parallel square meshes of 12x12 nodes,

37.5 mm apart. At every node the void or liquid fraction as a function of electrical capacitance is measured. Such

capacitance depends upon the calibration values, which are taken at dry and water-filled pipe conditions.

Figure 2. Scheme of wire-mesh sensor.

The data acquired by the WMS and the high-speed camera were carried out during 120 seconds and at a 500 Hz

frequency for the WMS. The frequency used by the high-speed camera acquisition is the necessary to guarantee that the

bubble front passes through at least twice the field view of the camera. Besides, the data acquired by the mass flow and

pressure sensors were acquired using a program developed in Labview.

0

10

20

30

40

50

60

5 6 7 8 9 10 11 12

Fra

ção

de

vaz

io (

%)

WMS1

FC

0

0.5

1

5 6 7 8 9 10 11 12

Funçã

o bin

ária

, B

(α,t)

Tempo (s)

0,50 m/s; 0,50 m/sL GJ J

1 Bolha

0 Pistão

a

b

Figure 3. Time series data of void fraction and its

corresponding binary signals.

0

0.2

0.4

0.6

0.8

1

0.3 0.4 0.5 0.6 0.7 0.8

Fun

ção

biná

ria,

B(α

,t)

Tempo (s)

WMS2

0

0.2

0.4

0.6

0.8

1

Fun

ção

biná

ria,

B(α

,t)

WMS11iB

iB

1iB

1iB

1iP

1iB

iB

iP

1iP

iP

1iP

1iP

Bt

St

ST

BT

Figure 4. Scheme to obtain the characteristic

parameters from the binary signal of time series .




For each mesh, the void fraction time series data were then extracted. The processing was done by means of a

program developed in Matlab, where the signal is converted to a binary signal with an adequate cut factor (FC) for

every measured point, as shown in Figure 3.

As Figure 4 shows, the characteristic parameters can be obtained from the binary signal, B(t). Thus, the bubble

front velocity, UTB, was obtained from the elapsed time a bubble takes to pass by two consecutive wire-mesh sensors,

WMS1 and WMS2, divided by the distance separating them, dW MS. The frequency was obtained as the inverse of a

bubble’s transit time, Δtb, and a slug’s , Δtp, both belonging to the same unit cell. Also, the characteristic lengths were

obtained with the bubble front velocity and the time spent by a bubble, TB, and a slug, TB, to travel through the first

sensor. Finally, was calculated the mean void fraction of every bubble, αB. Thus, the equations to calculate each

characteristic parameter are shown in Table 1.

To analyze the behaviour of the characteristic parameters a series of experiments taking into account the limitations

of the experimental facilities was planned. Thus, a series of 47 experiments was set, in order to cover the broadest

possible range of liquid, JL, and gas, JG, superficial velocities on Taitel and Barnea's (1990) map, with JL ranging from

0.15 to 2.5 m/s and JG from 0.2 to 3.7 m/s.

Table 1. Equations to calculate the characteristic slug flow parameters from their time series.

Characteristic parameter Equation Characteristic parameter Equation

Bubble front velocity

(UTB) WMS

TB

B

dU

t

Slug length (LS)

S TB SL U T

Unit-cell frequency ( f ) 1

B S

fT T

Bubble void fraction (αB) 1

iB Bn

Bubble length (LB) B TB BL U T

3. RESULTS

The results obtained for the 47 combinations of liquid and gas flow rates were shown in probability distributions for

each characteristic parameter of the experimental points. Following Shemer's (2003) suggestions, the PDFs were

approximated to normal or log-normal probabilistic functions, which depend on mean and standard deviation. This

approximation was made by means of a variance analysis.

The scattering of the means and standard deviations of each characteristic parameter were approximated to

functions of the liquid and gas superficial velocities by means of a regression analysis. Thus, the equations shown in

Table 2 were proposed, despite their occasional dispersion, where D is the internal diameter of the two-phase pipe, g is

the gravity field acceleration, whereas FrJ and ReJ represent the Froude and Reynolds numbers of the mixture,

respectively. Finally, St represents the Strouhal number.

Table 2. Equations to calculate the characteristic parameters of two-phase slug flow as a function of gas and liquid

superficial velocities.

Characteristic parameter Type of probability

function Equation for the mean Equation for the standard deviation

Bubble front

velocity (UTB) Normal 1,19 0,40TBU J gD 20,0357Fr

TBU J

Unit-cell frequency

( f ) Log-normal

0,45

0,08 L L

G

J Jf

D J

0,430,956

0,045 L L

f

G

J J

D J

Bubble length(LB) Normal 1,34exp 5,68 GBJL

D J

1,075

0,331BL BL

D D

Slug length (LS) Log-normal

54,84 102,67 ln

Re St

S

J

L

D

2,152exp 1,89SL GJ

D J

Bubble void

fraction (αB) Normal

0,5

0,748 G

B

J

J

0,036

B

With the functions and equations shown in the Table 2, the predicted PDFs were computed and plotted, as shown in

Figure 5, where the continuous lines represent the experimental PDFs, and the dashed lines represent the predicted

PDFs resulting from the mean and standard deviation equations of each parameter. In the Figure 5, a good agreement

between predicted and measured values can be observed.




0

0,1

0,2

0,3

0

0,1

0,2

0,3

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Pro

babi

lidad

e

αB

P36 - JL=1,75 m/s JG=0,7 m/s

PDF

Exp.

0,00

0,20

0,40

0,60

0,80

1,00

0

0,2

0,4

0,6

0,8

1

0 10 20 30 40

Pro

babi

lidad

e

UTB (m/s)

P35 - JL=1,50 m/s JG=3,6 m/s

PDF

Exp.

0

0,2

0,4

0,6

0,8

1

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10 12 14

Pro

babi

lidad

e

LB (m)

P34 - JL=1,50 m/s JG=3,4 m/s

PDF

Exp.

0

0,2

0,4

0,6

0,8

1

0

0,2

0,4

0,6

0,8

1

0 10 20 30 40 50

Pro

babi

lidad

e

f (Hz)

P28 - JL=1,25 m/s JG=3,0 m/s

PDF

Exp.

0

0,2

0,4

0,6

0,8

1

0

0,2

0,4

0,6

0,8

1

0 0,5 1 1,5 2 2,5

Pro

babi

lidad

e

LS (m)

P23 - JL=1,00 m/s JG=2,4 m/s

PDF

Exp.

Figure 5. Experimental and predicted PDFs for each two-phase slug flow parameter.

4. CONCLUS IONS

In this work an experimental study for horizontal two-phase slug flow was carried out, aiming at establishing an

adequate procedure for the conduction of 47 experiments, the acquisition and processing of the obtained data so as to

get the distributions of the characteristic parameters of this type of flow. The bubble front velocity, unit-cell frequency,

characteristic lengths and bubble void fraction were obtained.

The resulting PDFs for each flow parameter were approximated by using the mean, the standard deviation and

probability functions as the normal or log-normal ones. Those approximations were extended to each experiment and

approximated to an equation to compute the scattering of parameters as a function of the gas and liquid superficial

velocities, so as to predict all those parameters with the superficial velocities only, because those are normally

predetermined by this type of experiments.

Finally, predicted and experimental PDFs were compared, and a good agreement was observed. However, some

distributions possessing a very high dispersion level have been found, showing a considerable difference between the

predicted and the experimental PDFs.

This study may be complemented with studies of two-phase slug flow with others diameters, others fluids or others

inclinations of the pipeline.

5. ACKNOWLEDGEMENTS

The authors wish to express their gratitude for all the technical and financial support given by PETROBRAS.

6. REFERENCES.

Carpintero, E., 2009, “Experimental Investigation of Developing Plug and Slug Flows,” Technische Universität

München.

Fabre, J., and Line, A., 1992, “Modeling of Two-Phase Slug Flow,” Annu. Rev. Fluid Mech., 24(1), pp. 21–46.

Fabre, J., Peresson, L. L., Corteville, J., Odello, R., and Bourgeois, T., 1990, “Severe slugging in pipeline/riser

systems,” SPE Prod. Eng., 5(03), pp. 299–305.

Gregory, D., and Scott, G., 1969, “Correlation of liquid slug velocity and frequency in horizontal cocurrent gas -liquid

slug flow,” AIChE J., 15(6), pp. 933–935.

Havre, K., Stornes, K. O., and Stray, H., 2000, “Taming slug flow in pipelines,” ABB Rev., 4, pp. 55–63.

Heywood, N. I., and Richardson, J. F., 1979, “Slug flow of air-water mixtures in a horizontal pipe: Determination of

liquid holdup by gamma-ray absorption,” Chem. Eng. Sci., 34, pp. 17–30.

Issa, R. I., and Kempf, M. H. W., 2003, “Simulation of slug flow in horizontal and nearly horizontal pipes with the two -

fluid model,” Int. J. Multiphase Flow, 29(1), pp. 69–95.

Mazza, R. A., 2010, “Estudo do comportamento dinâmico de um escoamento padrão golfadas de líquido.”

Netto, J. R. F., Fabre, J., and Peresson, L., 1999, “Shape of long bubbles in horizontal slug flow,” Int. J. Multiph. Flow,

25(6-7), pp. 1129–1160.

Shemer, L. (2003). Hydrodynamic and statistical parameters of slug flow. International Journal of Heat and Fluid Flow,

24(3), 334–344.

Taitel, Y., and Barnea, D., 1990, “Two-Phase Slug Flow,” J. Heat Transfer, 20, pp. 83–132.

Wallis, G. B., 1969, One-dimensional two-phase flow, McGraw-Hill.

7. RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.

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