Horizontal Slug Flow in a Large-Size Pipeline: Experimentation and Modeling

Horizontal Slug Flow in a Large-Size Pipeline: Experimentation and Modeling

Keyla S. Marruaz

Universidade Estadual de Campinas

Departamento de Engenharia de Petróleo

Caixa. Postal 6122

13083-970 Campinas, SP. Brazil

Marcelo A. L. Gonçalves

Eduardo Gaspari

Geraldo S. Ribeiro

Exploitation Division, DIPLOT

Petrobras Research Center, CENPES

Cidade Universitária, Q.7

21949-900 Rio de Janeiro, RJ. Brazil

Fernando A. França

Eugênio S. Rosa

Universidade Estadual de Campinas

Departamento de Energia

Caixa Postal 6122

13083-970 Campinas, SP. Brazil [e-mail], [e-mail]

The knowledge of the slug flow characteristics is very important when designing pipelines and process equipment. When the intermittences typical in slug flow occurs, the fluctuations of the flow variables bring additional concern to the designer. Focusing on this subject the present work discloses the experimental data on slug flow characteristics occurring in a large-size, large-scale facility. The results were compared with data provided by mechanistic slug flow models in order to verify their reliability when modelling actual flow conditions. Experiments were done with natural gas and oil or water as the liquid phase. To compute the frequency and velocity of the slug cell and to calculate the length of the elongated bubble and liquid slug one used two pressure transducers measuring the pressure drop across the pipe diameter at different axial locations. A third pressure transducer measured the pressure drop between two axial location 200 m apart. The experimental data were compared with results of Camargo's1 algorithm (1991, 1993), which uses the basics of Dukler & Hubbard's (1975) slug flow model, and those calculated by the transient two-phase flow simulator OLGA.

Keywords: Slug flow, gas-liquid intermittent flow, two-phase flow instrumentation

Introduction

The most used mechanistic representation of the slug flow is the unit cell model: the flow unit is composed of an aerated liquid slug and an elongated bubble. These singular structures succeed each other in the test section in an intermittent fashion, causing a fluctuation in the flow variables: velocities, flow rates, pressure gradients. Hence, the knowledge of the characteristics of the slug flow pattern, i.e., the frequency and velocity of the unit cell and the length of the liquid slug and elongated bubble, among other variables, is very important when sizing pipelines and designing receiving vessels and pre-processing equipment. The velocity of the unit cell, for example, determines the instantaneous gas and liquid flow rate delivered to a receiving vessel; the length of the liquid slug correlates strongly with the pressure drop.

The large amount of published papers presenting measurements and discussing the modelling of slug flows reflects the fact that this is the flow pattern that most frequently occurs in petroleum pipelines. The slug flow models based on the unit cell concept (Dukler and Hubbard, 1975 and Nicholson et al., 1978) are quite usual nowadays, composing some of the commercially available codes used by the oil industry to calculate two-phase flow facilities. These semi-empirical models rely, for development and comparison, on data bases generated by experimentation. However, the great majority of published data on the slug flow characteristics were taken in small-scale laboratory facilities, running with mixtures of air and water. Only a few data were collected in large-scale facilities (Gregory et al., 1978 and Gonçalves et al., 1996).

The objective of this work was directed toward this lack: one presented a set of measurements carried on a 6 inches horizontal pipeline, 200 m long, which is part of the test rig of Atalaia, operated by Petrobras. To identify and measure the structure of the slug flow, i.e., frequency and velocity of the unit cell, the length of the liquid slug and elongated bubble and the pressure drop, one registered and processed the signal delivered by pressure transducers. Two transducers measured the differential pressure across the pipe diameter at two distinct axial positions and a third transducer measured the pressure drop between two sections 200 meters apart. A complete set of data, in which concerns to the flow structure, was acquired with mixtures of air and water. Limited results for gas-oil mixtures are also presented. To verify the adequacy of the mechanistic models based on the unit cell approach in modelling two-phase intermittent flows, the experimental data were compared with calculated data provided by Camargo's (1991, 1993) algorithm, which uses the basics of Dukler & Hubbard's (1975) slug flow model, and those calculated by a two-phase flow code. In this case, the results provided by OLGA, a dynamic two-phase flow code, extensively used by the oil industry, were used as reference for comparison.

Nomenclature

A = cross-sectional area,area, m2

S = wet perimeter, m

D = pipe diameter, diameter, m

D_I =internal diameter, diameter,m

L = length of the pipe test section, m

x = axial direction, m

j_L = liquid superficial velocity, m/s

j_G = gas superficial velocity, m/s

j = total superficial velocity, m/s

n_S = frequency of the unit cell, Hz

V_t = velocity of the unit cell, m/s

V_dj = drift velocity, m/s

l_u = lenght of the unit cell, m

l_S = lenght of the liquid slug, m

l_f = lenght of the elongated bubble, m

C = angular coefficient, dimensionless

T = temperature, ºC

G = acceleration of gravity, m/s²

Greek Symbols

DP = pressure drop, Pa/m

DP_u = pressure drop along the unit cell, Pa/m

z = relative length of the elongated bubble, dimensionless

t = shear stress, N/m2

b = pipe inclination, deg.

s = superficial tension, N/m

m = air dynamic viscosity, dynamic viscosity, kg/(m s)

r = air density, kg/m3

r_u = mean density of the unit cell, kg/m³

Subscripts

f = relative to the elongated bubble

s = relative to the liquid slug

i = relative to inlet

l = relative to liquid

g = relative to gas

u = relative to unit cell

t = relative to total

dj = relative to "drift velocity"

Test Facility, Instrumentation and Data Processing

The experimental work was accomplished at the PETROBRAS Atalaia Test Site, located in northern region of Brazil. The test facility comprises pipelines and the auxiliary equipment, such as pumps, separators and stocking vessels. The flow diagram is depicted in Figure 1. The test section was a horizontal pipeline, 6 in (0.15 m) internal diameter and 200 m long. Two 'legs' of 100 m, approximately, connected by a long radius (10 meters) curved pipe, formed the total length of the test section. Due to such a long radius curve the test section was considered a straight pipeline for the calculation of pressure drop.

The instrumentation available in the test site included orifice plates for measuring the gas flow rate and a Coriollis mass meter for the liquid (water or oil) phase. These industrial size instruments were calibrated before the tests. The measurements consisted of 10 blocks of data, covering the range of superficial velocities (j_G ; j_L) equal to (0.49 m/s ~ 1.5 m/s ; 0.51 m/s ~1.6 m/s) for the water – gas mixture, and 13 blocks of data covering the range of (j_G ; j_L) equal to (0.38 m/s ~ 1.3 m/s ; 0.45 m/s ~1.5 m/s) for the oil – gas mixture. The oil and gas actual flow rate was reduced to the test section conditions taking its PVT properties.

To measure the frequency and velocity of the unit cell, n_s and V_t, respectively, and to calculate the length of the liquid slug and elongated bubble, l_u and l_s, one acquired and processed the signal delivered by two pressure transducers.

These transducers measured the pressure difference across the pipe diameter, along the vertical axis, at two different axial position 0.7 meters apart. As the two structures composing the slug unit cell have distinct liquid hold-up, the measurement of the differential hydrostatic pressure across the pipe diameter must reveal this fact. Figure 2 depicts the unit cell, the variables defining the structures and the arrangement of pressure transducers. A third pressure transducer was used to measure the pressure drop in the test section.

The signals generated by the three transducers were conditioned and acquired in a Macintosh computer by a National Instruments MIO-16 A/D bus board. The software for data acquisition and processing and was written in "G", the graphical language used by National Instruments' LabView. The frequency of data acquisition was 100 Hz. A total of 16384 points pertaining to the twin signals generated by the differential hydrostatic pressure measurement were acquired in every run. In the corresponding time interval, there were various long-term fluctuations of the slug flow pattern. Figure 3 (a) shows a 40 seconds sample of the twin signals, the red line representing the relative output of the upstream sensor, and the blue line, the downstream sensor.

The frequency of the unit cell resulted from the power spectra of either one of the twin signals. The velocity of the unit cell is the distance between the hydrostatic probes, 0.7 m, divided by time shift between their respective signals. The cross-correlation of the twin signals delivered this time shift. Figure 3 (b) is a typical cross-correlation of the twin signals; the peak in the curve indicating the most likely time shift, 0.27 seconds. In this case the unit cell velocity is 2,59 m/s ± 2%.

To calculate the length of the liquid slug and elongated bubble, one had to set a threshold level to identify and separate the portion of the pressure signal pertaining to each structure. The elongated bubble flows like a separated two-phase pattern: the gas is adjacent to the upper pipe wall and an accelerating liquid film flows on the bottom of the pipe. Contrasting, the liquid slug can be thought as a dispersed flow pattern, with a dominant liquid volume surrounding small gas bubbles. Thus, the higher pressure corresponded to the liquid slug. The reducing pressure reflected the liquid film profile under the gas bubble. After inspection, a threshold level is set and the time interval corresponding to both structures is obtained. The length of the elongated bubble, l_f, and liquid slug, l_s, were calculated dividing the velocity of the unit cell by the associated time interval.

The pressure gradient along the test section was calculated dividing the time averaged pressure drop signal by the total length of the test section. Due to the high-pressure (up to 20 Kgf/cm²) in test section and the use of flaming fluids (oil and gas), direct visualization was not performed.

Results

To verify the adequacy of mechanistic models in disclosing the characteristics of the slug flow structures one adopted, in this work, a particular strategy. Horizontal slug flow models based upon the unit cell approach use, as a closure condition, a constitutive equation for the slug frequency or a correlation giving the length of the liquid slug or elongated bubble. The OLGA code uses a correlation for the slug frequency. Camargo's (1991) algorithm also uses Hill & Wood's (1990) correlation for the slug frequency or Nicholson et al. (1978) and Barnea & Brauner's (1985) correlation for the slug length to achieve closure. Fortunately, the later code permits the user to choose between the internally calculated frequency and a 'user supplied frequency'. With such degree of freedom, one calculated, with Camargo's algorithm, the variables characterizing the structures of the slug flow imposing the measured frequency as the 'user supplied value'.

Gas-Water Mixtures

In Table 2 there are the 10 measured and calculated data points for the gas-water mixture. In the first two columns appear the in situ liquid and gas superficial velocities. The velocity of the unit cell is in the third column. The frequencies, as calculated by the OLGA code and the measured ones, follow. The three columns corresponding to each one of the following variables, length of the liquid slug, length of the elongated bubble and pressure drop are: the values calculated by OLGA, the values calculated by the Camargo's code and the measured values. It is important to emphasize, once again, that the input frequencies in Camargo's code were the measured ones.

If the velocity of the unit cell was correlated as 'drift flux like' linear relationship,

where j is the total superficial velocity, (j_G+j_L), C is the angular coefficient and V_dj is a 'drift velocity', the result would be: C = 0,94 and Vdj = 1,07 m/s. These are reasonable values, validating the measured data in terms of averaged input quantities. Camargo's code used the values suggested by Bendiksen (1984): C = 1,06 and Vdj = 0,73 m/s. The values suggested by Alves (1991) for a 10° inclination pipeline, are C = 1,06 and Vdj = 0,65 m/s.

The first conclusion that arouse from the analysis of the data in Table 2 was that the frequency calculated by the OLGA code (its results were approximately equal to those calculated by Hill & Woods' correlation) only agreed with the measured one for low and medium gas and liquid (water) superficial velocities, up to 1,0 m/s. For higher superficial velocities, the difference between measured and calculated values increased progressively and surpassed 100% for the highest gas flow rate, j_G = 1,59 m/s. The Figure 4 is a plot of the frequency, measured against calculated data. The dotted lines represent ± 30% of deviation in regard to the expected values. The highest frequencies, corresponding to the highest superficial velocities, presented the largest deviation. The comparison between the other variables must take into account these differences, as the measured frequencies were input values in Camargo's code.

Figure 5 depicts the length of the liquid as calculated by OLGA (cross) and Camargo's (open circle) code plotted against measured data. The former code calculated a somewhat constant slug length, from 10,8 m to 14,6 m, within the full range of superficial velocities applied in the experiments. The measured values were within the range of 3,0 m ~ 12,5 m, the lowest values corresponding to the highest superficial velocities for both the gas and the water. The deviation between calculated and measured for 7 out of 10 data was greater than +50%. Camargo's code calculated the slug length pretty much closer to the measured value. Most of the values were within the ± 30% limiting lines, in the full range of superficial velocities applied.

The data in Table 2 revealed that very long bubbles (46 meters) existed for the lowest total superficial velocities. As both the gas and water superficial velocities increased, the elongated bubble became shorter. The codes were able to disclose this phenomenon. The values calculated by OLGA and Camargo's code were in reasonable agreement, as well as the measured and calculated data. The full set of data was within the range of ± 30%, as Figure 6 disclosed. The values calculated by Camargo's code, however, were closer to the measured ones.

In Figure 7 appears the comparison between the measured and calculated pressure drop. Both codes calculated values that compared well with the measured ones, within ± 20%, in the full range of superficial velocities applied in the experiments. Once more, the values calculated by Camargo's code were closer to the measured ones, with the exception of the value connected with the highest water superficial velocity. At this point is important to turn back to the mechanistic representation of the slug flow, in regard to the pressure drop calculation. Camargo's code used the proposition of (Taitel & Barnea, 1990), which added three terms to calculate the pressure drop along the unit cell: the frictional in the liquid slug, the frictional in the elongated bubble and the gravitational in the unit cell:

In Equation 2, b is the pipe inclination regarding the horizontal, l_u is the length of the unit cell, (l_s+l_f), g is the acceleration of gravity, r_u is the mean density of the unit cell, t is the shear stress, S is the wet perimeter, A is the cross-sectional area, D is the pipe diameter, x is the axial direction and the subscripts _f and _s refer to the elongated bubble and the liquid slug, respectively. In a horizontal pipeline the gravitational term vanishes. The friction in the liquid slug exceeds, by far, the friction in the elongated bubble. Thus, if the code relied on the unit cell concept to calculate the characteristics of the unit cell, it must estimate the slug length correctly in order to calculate accurate pressure drops for different mixtures, flow properties and range of superficial velocities encountered in actual flows. The OLGA code, besides measuring slug lengths that did not agree with the measured ones in the full range of superficial velocities, calculated quite well the pressure drop.

Gas-Oil Mixtures

There were limited results in this case: only the unit cell frequency, the relative length of the elongated bubble and the pressure drop could be measured due to a lack of correlation between the signals. The relative length of the elongated bubble, z, is defined as the bubble length over the length of the unit cell:

frm03

Similarly with what has happened for the gas-water mixtures, the difference between the frequencies calculated by the OLGA code and the measured ones increased for the highest gas superficial velocities. However, as Figure 8 depicts, the data spread over the expected value, the straight line in the plot, indicating that, at least, the correlation used by the OLGA code (the results, again, were very close to the ones delivered by Hill & Wood's correlation) was able to trace the data trend.

The plot of the measured versus calculated bubble relative length is in Figure 9, as calculated by OLGA and Camargo's code. The agreement was reasonably good, most of the data were within ± 20%, if one considers the full range of superficial velocities applied. The agreement between the data delivered by the two codes was even better.

Considering the fact that the Olga code used better adjusted values for the frequency of the unit cell in gas-oil mixtures, and the good results it delivered for the bubble relative length, surprised the values it calculated for the pressure drop. Figure 10 compares the data calculated by OLGA and Camargo's code with the measured ones. While the values delivered by Camargo's code, which used the measured frequencies as input data, were, in the full range of superficial velocities applied in the experiments, upper-bounding the measured data with an average deviation of less than + 20%, the values calculated by OLGA were consistently lower. The deviation augmented as the pressure drop increased, reaching –60% of the measured value.

Conclusions

This works disclosed experimental data on slug flow characteristics occurring in a large-size, large-scale facility. These data, which included the frequency and velocity of the unit cell, the length of the liquid slug and elongated bubble, the relative length of the elongated bubble and the pressure drop, were performed for mixtures of distinct properties, natural gas + water and natural gas + oil. The measured data were compared with calculated values provided by two codes relying upon the unit cell concept, the commercially available OLGA and Camargo's (1991). The comparison between the measured and calculated data revealed that the use of proper closure conditions are essential for the correct calculation of the characteristics of the slug flow structures over a full range of actual flow rates and fluid properties. Moreover, the comparison revealed that even when the codes used the same frequency input value, the calculated data do not necessarily agree among them.

Paper originally presented at the 15^th Brazilian Congress of Mechanical Engineering (XV COBEM), São Paulo, November 22-26, 1999.

COBEM Editors: R. G. dos Santos, M. H. Robert, A. C. Dannwart, J. R. B. Cruz.

Associate Editor: J. R. F. Arruda.

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Publication Dates

• Publication in this collection
  24 Sept 2002
• Date of issue
  2001