Measurement of gas phase characteristics in vertical oil-gas-water slug and churn flows

Chemical Engineering Science 177 (2018) 53–73

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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces

Measurement of gas phase characteristics in vertical oil-gas-water slug and churn flows Da-Yang Wang, Ning-De Jin ⇑, Yun-Feng Han, Fan Wang School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China

h i g h l i g h t s
We design a traversable bi-optical fiber probe for investigating oil-gas-water slug and churn flow.
We extract local flow parameters of gas phase at different radial positions of a vertical pipe.
We study detailed flow structure of oil-gas-water slug flow under different flow conditions.
We investigate gas characteristics in slug and churn flows with nonlinear dynamic analysis.

a r t i c l e

i n f o

Article history: Received 26 June 2017 Received in revised form 21 October 2017 Accepted 23 October 2017

Keywords: Oil-gas-water three-phase flow Gas phase characteristics Bi-optical fiber probe High-resolution conductance sensor Multi-scale cross entropy

a b s t r a c t In the present study, gas phase characteristics of oil-gas-water slug and churn flows in a vertical upward pipe with 20 mm inner diameter (ID) are experimentally investigated. We firstly measure the fluctuating signals of a traversable bi-optical fiber probe at different radial positions. The gas phase flow parameter distributions (local gas velocity, local gas holdup) are obtained and the flow structure is uncovered by calculating the series of gas bubble chord lengths at different radial positions. Additionally, in order to describe the flow structure of slug flow, the relative length of the liquid slug, the profile distributions of gas holdup and bubble size in liquid slug are investigated. To understand the nonlinear dynamic characteristics of slug and churn flows, multi-scale cross entropy (MSCE) algorithm is applied to analyze the signals of a high-resolution half-ring conductance sensor and bi-optical fiber probe. The result indicates that multi-scale cross entropy can be an effective tool for validating the measurement of gas phase characteristics by using the traversable bi-optical fiber probe. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Oil-gas-water three-phase flow widely exists in the oil well production and oil-gas transportation. Due to the significant differences of physical properties and mutual interactions among three phases, the flow structures are more complicated compared with gas-liquid or oil-water two phase flow, which brings great difficulties to measure flow parameters in oil-gas-water three-phase flow. Understanding the gas characteristics of oil-gas-water three-phase flow is of significant importance to flow measurement as well as to develop oil-gas-water three-phase flow models. In early studies of oil-gas-water three-phase flow, Tek (1961) regarded the two immiscible liquids as an equivalent single phase and predicted the pressure loss. Shean (1976) developed flow regime maps and established drift-flux models for vertical

⇑ Corresponding author. E-mail address: [email protected] (N.-D. Jin). https://doi.org/10.1016/j.ces.2017.10.041 0009-2509/Ó 2017 Elsevier Ltd. All rights reserved.

oil-gas-water flows to obtain the global volumetric phase fractions. Lahey et al. (1992) proposed a generalized drift-flux expression for horizontal three-phase conduit flow. Thorn et al. (1997) summarized the principal strategies and technologies of three-phase flow measurement. Fordham et al. (1999) utilized local fiber-optical sensors for immiscible-fluid discrimination and determining volume fraction profiles in oil-gas-water three-phase. Ghorai et al. (2005) developed a model to predict the values of holdup and pressure gradient for three-phase stratified flow prevailing in a horizontal pipeline. Spedding et al. (2007) investigated oil-gas-water three-phase flow in a horizontal 0.0259 m ID pipe, they found that liquid holdup data depended on flow regimes, and presented a new model for the prediction of three-phase liquid holdup. Silva et al. (2007) firstly implemented the local complex permittivity measurements of a three-phase bubbly flow. Salgado et al. (2009) proposed new methodology based on nuclear technique and artificial neural network for volume fraction predictions in oil-water-gas multiphase systems. Cazarez et al. (2010) propounded a

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Spedding et al. (2000) pointed out that flow regime maps, liquid holdup and pressure drop were all different between the vertical and near vertical three-phase upflow. Oddie et al. (2003) investigated steady-state and transient multiphase flow in a large diameter, inclined pipes and detailed flow pattern maps were generated over the entire range of flow rates and pipe inclinations. Descamps et al. (2006, 2007) studied the influence of gas injection on phase inversion in oil-water flow through a vertical tube. In addition, other impact factors, such as, the processes of mixing of the liquid phases (Hewitt, 2005), the properties of pipe geometry, liquid viscosity and surface tension (Wegmann et al., 2007), played an important role in the flow pattern transition. Bannwart et al. (2009) observed three-phase flow patterns in horizontal and vertical 2.84 cm ID glass pipes and assessed the changes of pressure drop induced by water injection. S. Wang et al. (2013) investigated the effects of water injection and viscosity on flow parameter measurement. More recently, intelligent recognition of flow regime based on the signals of gamma-ray by using artificial neural networks has been a research focus (Salgado et al., 2010; Roshani et al., 2015, 2016, 2017; Nazemi et al., 2016). As multiphase flow is a typical nonlinear system, some progress have been achieved in applying nonlinear analysis method to analyze the dynamic behavior of multiphase flow. Fan et al. (1990)

Voltage (V)

two-fluid mathematical model to predict pressure, temperature, volumetric fraction and velocity profiles in heavy oil-gas-water bubbly flow. Hoffmann and Johnson (2011) used a traversable dual-energy gamma instrument to measure phase fractions at different positions. Henry et al. (2013) applied Coriolis metering for a three-phase (oil-gas-water) mixture. Their experimental results demonstrated the potential of using Coriolis mass flow metering in three-phase flow measurement. Sun and Yang (2015) imaged the three-phase flows based on ECT/ERT dual-modality and calculated the holdup of each phase in a three-phase flow with the image fusion results. Karami et al. (2017) utilized an isokinetic sampling probe system to measure liquid phase entrainment fraction. Pietrzak et al. (2017) developed new methods to calculate phase fraction and total pressure drop in oil-gas-water threephase flow. As for experimental observations and flow pattern classification, Chen (1991) investigated three-phase flow characteristics in an upward vertical pipe and classified flow patterns into oil in water or water in oil type flow. Açikgöz et al. (1992) performed extensive flow visualization studies in a 19 mm diameter pipe and defined horizontal oil-gas-water three-phase flow regimes. Woods et al. (1998) conducted three-phase flow experiment in a 26 mm ID vertical perspex pipe and concluded nine flow patterns.

Fiber tip

Fiber tip

Fiber tip

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Water phase

Gas phase

Oil phase

11 10 9 8 7 6 5 4 3 2 1 0

Gas phase

Water phase Oil phase

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Time (s)

(a)

(b)

Fig. 1. Optical fiber probe tip: (a) principle of reflection and refraction; (b) result of static test.

Light source 1 Oil phase Optical fiber probe sensor

Gas phase Water phase

Z

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Detector 1

PXI

Output 1 Coupler 1 Output 2 Detector 2

Coupler 2 1 2

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Optical fiber Light source 2

mm 0.8

Measurement positions

Three-phase flow

m

m 1m

Pipe

.5

62

Fig. 2. Traversable bi-optical fiber probe sensing system.

PC °

35

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analyzed pressure fluctuations in a gas-liquid-solid fluidized bed under different batch operating conditions based on the concept of fractals. Kikuchi et al. (1996) reported the chaotic motions of bubbles and particles in gas-liquid-solid fluidized bed. Yano et al. (1999) investigated the scale-up effect on the dynamic behavior of gas-liquid-solid three-phase reactors using deterministic chaos analysis. Wu et al. (2000) obtained characteristics vectors of various flow regimes in terms of fractal theory. Fraguío et al. (2007) classified flow regimes in three-phase fluidized beds based on chaos theory. In our research group, fractals and chaos (Jin et al., 2001), chaotic attractor morphological description and complexity measures (Wang et al., 2010), complex network (Gao and Jin, 2011), multi-scale long-range magnitude and sign correlations

20kHz Exciting signal 1mm

(Zhao et al., 2015) and multi-scale weighted complexity entropy causality plane (Zhuang et al., 2016) have been utilized to investigate the nonlinear dynamic characteristics of three-phase flow. The significant differences of physical properties and interface interactions among three phases result in more complicated flow structures in oil-gas-water three-phase flow compared with gasliquid or oil-water two phase flow. So far, studies mainly focus on flow parameters measurement or flow pattern recognition. Knowledge of flow structure and its local flow characteristics in oil-gas-water three phase flow is still relatively lack especially for slug and churn flows. In this study, gas phase characteristics of oil-gas-water slug and churn flows in a vertical upward pipe with 20 mm inner diameter (ID) are investigated and local gas

Conditioning module Amplifier Vref

AD 637

Rref

Rref

Rref

Vsen

AD 637

40mm

Amplifier

1mm

Vsen

AD 637

Rref

PXI

PC Rref

Rref 20kHz Exciting signal

Vref

AD 637

Conditioning module

Flow direction Fig. 3. High-resolution half-ring conductance sensing system.

Conductance sensor

160mm 40mm

Optical fiber probe

Mixting tank

Test pipe Slug flow Churn flow 2000mm

Valve

ID=20mm

Mixer Check valve Gas pipe

Oil tank

Peristaltic pump

Oil

Oil pipe

Float flowmeter

Valve

Valve

Water pipe Air compressor

Peristaltic pump

Water

Fig. 4. The sketch map of experimental facility.

Water tank

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velocity, local gas holdup, flow structure and bubble size at different radial positions are obtained using traversable bi-optical fiber probe. To understand the nonlinear dynamic characteristics of slug and churn flows, the signals of a high-resolution half-ring conductance sensor and optical fiber probes are analyzed using multiscale cross entropy (MSCE) algorithm to characterize the nonlinear dynamics in slug and churn flows.

2. Measurement system and experiment facility 2.1. Traversable bi-optical fiber probe sensing system The measurement principle of optical fiber probe is based on the refraction and reflection law. Phases can be discriminated by detecting the intensity of reflected light due to the different

Optical fiber probe signals (V)

Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0

Bubbles in liquid film

Position 1U Position 1W Position 2U Position 2W Position 3U Position 3W Position 4U

Taylor bubble

Position 4W

Liquid slug

Position 5U

Wake region

Position 5W Position 6U Position 6W Bubbles in liquid film

Position 7U Position 7W

0.0

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(a)

Optical fiber probe signals (V)

Umix =0.737m/s, fo=0.05,Usg =0.442m/s,churn flow 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0

0.0

Bubbles in liquid film

Position 1U Position 1W Position 2U Position 2W Position 3U Position 3W Position 4U Position 4W Position 5U Position 5W Position 6U Position 6W Position 7U

Gas phase

Position 7W

0.2

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Bubbles in liquid phase

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Times (s)

(b) Fig. 5. Typical signals of bi-optical fiber probe at different positions of radial direction of the pipe: (a) Umix = 0.147 m/s, fo = 0.05, Usg = 0.295 m/s, slug flow; (b) Umix = 0.737 m/ s, fo = 0.05, Usg = 0.442 m/s, churn flow.

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and Snell law (Born and Wolf, 1980)

refractive indexes of oil, gas and water. The cone angle of the probe tip is very important for gas phase discrimination, and it could be determined by theoretical derivation and experimental test. According to the Fresnel equations (Saleh and Teich, 1991)

n1 cos h1  n2 cos h2 rs ¼ n1 cos h1 þ n2 cos h2 n2 cos h1  n1 cos h2 rp ¼ n2 cos h1 þ n1 cos h2

2

cos2 h2 ¼ 1  ðn1 =n2 Þ2 sin h1

ð2Þ

where n1 and n2 are the refractive indexes of two media, h1 and h2 represent incident and refraction angles, rs and r p are the reflectivity of s-wave and p-wave. The refractive indexes of oil, gas, water and optical fiber are 1.5, 1, 1.33 and 1.462 respectively. As presented in Fig. 1(a), when the angle is 35 , it causes a higher reflectivity when the probe tip is in gas phase than in liquid phase, and a tip with 35

ð1Þ

Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow

Processed optical fiber probe signals (V)

1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

Position 1U Position 1W Position 2U Position 2W Position 3U Position 3W Position 4U Position 4W Position 5U Position 5W Position 6U Position 6W Position 7U Position 7W

0.0

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(a)

Processed optical fiber probe signals (V)

Umix =0.737m/s, fo=0.05,Usg =0.442m/s,churn flow 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

0.0

Position 1U Position 1W Position 2U Position 2W Position 3U Position 3W Position 4U Position 4W Position 5U Position 5W Position 6U Position 6W Position 7U Position 7W

0.2

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1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Times (s)

(b) Fig. 6. Processed signals of bi-optical fiber probe at different positions of radial direction of the pipe: (a) Umix = 0.147 m/s, fo = 0.05, Usg = 0.295 m/s, slug flow; (b) Umix = 0.737 m/s, fo = 0.05, Usg = 0.442 m/s, churn flow.

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cone angle can easily pierce into small bubbles, which is suitable for gas phase discrimination. In order to evaluate the performance of optical fiber probe, a static test is conducted. As shown in Fig. 1(b), when the probe tip is in gas phase, the amplitude of output signal is much higher than that in liquid phase, and the amplitude of output is almost the same when the tip is in oil or water phase. The result manifests that the optical fiber probe is very sensitive to gas phase and can be used to measure gas phase characteristics. The sensing system for traversable bi-optical fiber probe is shown in Fig. 2. It includes light sources, optical fiber couplers, bi-optical fiber probe sensor, photodetectors and data acquisition module. Red light with 650 nm wavelength is emitted from the light sources with 10 mW power. Couplers with coupling ratio of 1:99 can ensure that most of the light emitted from the source can reach the probe tip and most of the reflected light at the tip can return to photodetectors. The photodetectors convert reflected

9

light into electrical signals, and the outputs signals are collected by a data acquisition card PXI 4472 of NI Corporation. Traversable bi-optical fiber probe sensor mainly consists of movable components and conical optical fiber probes. Two 62.5 lm fibers with designed tips are respectively inserted into stainless-steel tubes. We fix two tubes on the movable components and make sure that the leading probe tip is about 1 mm longer than the rear one and the radial distance between them is 0.8 mm. Finally, we install the traversable bi-optical fiber probe sensor in test pipe with its probe tips facing vertically downward. Seven measurement positions are determined to acquire local flow information of slug and churn flows. A three dimensional Cartesian coordinate with the origin at the center of pipe is established as shown in Fig. 2, and the coordinate of measurement position 4 is (0 mm, 0 mm, 0 mm), while the coordinates of position 1, position 2, position 3, position 5 position 6 and position 7 are (9 mm, 0 mm, 0 mm), (7 mm, 0 mm, 0 mm), (4 mm, 0 mm, 0 mm),

Umix =0.147m/s, fo=0.05,U sg =0.295m/s,slug flow 5

Position 1U Position 1W

6

4.80x10 5 3.60x10 5 2.40x10 5 1.20x10

3 0

Position 1

s

5

12 9 6 3 0 12

Position 3U Position 3W

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6

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3

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5

120

Position 4U Position 4W

9 6 3 0 12 9 6 3 0

Position 5U Position 5W

12 9 6 3 0 12

Position 6U Position 6W

Position 7U Position 7W

9

Cross-correlation R xy ( )

6.0x10

9

Optical fiber probe signals (V)

1.2x10 5 1.0x10 4 8.0x10 4 6.0x10 4 4.0x10

Position 2U Position 2W

2.5x10

5

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5

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5

6.00x10 5 4.50x10 5 3.00x10 5 1.50x10 5 3.0x10 2.5x10

5

2.0x10

5

3 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.5x10 0.00

6

Position 6

s Position 7

s

Time (s)

(a)

5

0.01

0.02

0.03

0.04

Time (s)

(b)

Fig. 7. Response signals from bi-optical fiber probe and its cross-correlation function Rxy at different positions of radial direction of the pipe in slug flow (Umix = 0.147 m/s, fo = 0.05, Usg = 0.295 m/s): (a) Response signals from bi-optical fiber probe; (b) Cross-correlation function Rxy.

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(4 mm, 0 mm, 0 mm), (7 mm, 0 mm, 0 mm) and (9 mm, 0 mm, 0 mm) respectively.

module and then collected by the PXI based data acquisition module.

2.2. High-resolution half-ring conductance sensing system

2.3. Experiment facility

With the intention to investigate flow characteristics of slug and churn flows at pipe cross section, a high-resolution half-ring conductance sensor is mounted in test pipe, which is shown in Fig. 3. The sensing system for high-resolution half-ring conductance is composed by two half-ring conductance sensors, exciting module, signal conditioning module and data acquisition module. Each half-ring conductance sensor consists of three pairs of electrodes. The middle one is used as measurement electrode and the others are used as guard electrodes. The height of electrode and the distance between measurement and guard electrodes are 1 mm, the angle of electrode is 100° and the distance between two measurement electrodes is 40 mm. A 20 kHz constant voltage sinusoidal wave is utilized to excite the electrodes. The electric field between measurement electrodes is more concentrated due to the guard electrodes on both sides. The impedance information of fluid is converted to voltage information by signal conditioning

The experiment of vertical upward oil-gas-water three-phase flow was carried out on the multiphase flow loop facility in Tianjin University. The experimental facility is shown in Fig. 4. Tap water, air and No. 3 industry white oil are used as the experimental media. Oil and water phase are pumped into the 20 mm ID test pipe by peristaltic pumps, and gas phase is metered by float flowmeter and then injected into pipe. The fluids mix at the inlet of the test pipe through a mixer, and to ensure fully developed flow pattern, the high-resolution half-ring conductance sensor and traversable bi-optical fiber probe sensor are respectively mounted in test pipe with a distance of 2000 mm and 2200 mm from the pipe inlet. In the experimental process, the liquid mixture superficial velocity Umix varies from 0.147 to 0.737 m/s, while the gas superficial velocity Usg varies from 0.295 to 0.442 m/s, and the oil-cut of liquid phase fo is from 5% to 20% and changes with a step of 5%.

1.2

1.6 1.5

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(m/s)

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i

i (m/s)

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Umix=0.147m/s, fo=0.05,Usg=0.295m/s,slug flow

0.8 Umix=0.147m/s, fo=0.05,Usg=0.295m/s,slug flow

0.8

Umix=0.147m/s, fo=0.10,Usg=0.295m/s,slug flow

Umix=0.147m/s, fo=0.05,Usg=0.369m/s,slug flow

0.7

Umix=0.147m/s, fo=0.15,Usg=0.295m/s,slug flow

0.7

Umix=0.147m/s, fo=0.05,Usg=0.442m/s,slug flow

Umix=0.147m/s, fo=0.20,Usg=0.295m/s,slug flow

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(m/s)

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i

i (m/s)

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Radial measurement position

1.8 1.7 Umix=0.737m/s, fo=0.05,Usg=0.295m/s,churn flow

Umix=0.737m/s, fo=0.05,Usg=0.442m/s,churn flow

1.6

Umix=0.737m/s, fo=0.05,Usg=0.369m/s,churn flow

Umix=0.737m/s, fo=0.10,Usg=0.442m/s,churn flow

1.5

Umix=0.737m/s, fo=0.15,Usg=0.442m/s,churn flow

Umix=0.737m/s, fo=0.05,Usg=0.442m/s,churn flow 1

2

3

4

5

Radial measurement position

(c)

6

7

Umix=0.737m/s, fo=0.20,Usg=0.442m/s,churn flow

1.4 1

2

3

4

5

Radial measurement position

(d)

Fig. 8. Profile of local gas velocity at different radial positions of pipe in slug and churn flows.

6

7

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Firstly, the liquid mixture superficial velocity Umix is fixed, with increasing the gas superficial velocity Usg and the oil-cut of liquid phase fo, the fluctuating signals of bi-optical fiber probe and conductance sensor are acquired simultaneously. Then increase the liquid mixture superficial velocity Umix and repeat the measurement process. The whole experiment consists of 60 different flow conditions. Fluctuating signals of bi-optical fiber probe at seven measurement positions and high-resolution half-ring conductance sensor are sampled by PXI 4472 synchronization data acquisition board card of NI company. The sampling frequency is 10 kHz and the sampling time is 30 s. 3. Local gas phase flow parameters of slug and churn flows 3.1. Optical fiber probe signal processing

80

70

70

60

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50

(%)

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40 30

Umix=0.295m/s, fo=0.05,Usg=0.295m/s,slug flow

Umix=0.147m/s, fo=0.05,Usg=0.369m/s,slug flow

20

40 30

Umix=0.147m/s, fo=0.05,Usg=0.295m/s,slug flow

Umix=0.295m/s, fo=0.05,Usg=0.369m/s,slug flow

20

Umix=0.147m/s, fo=0.05,Usg=0.442m/s,slug flow

Umix=0.295m/s, fo=0.05,Usg=0.442m/s,slug flow 10

10 1

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40 Umix=0.147m/s, f0=0.05,Usg=0.295m/s,slug flow

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Umix=0.147m/s, f0=0.10,Usg=0.295m/s,slug flow Umix=0.147m/s, f0=0.15,Usg=0.295m/s,slug flow

20

Umix=0.147m/s, f0=0.20,Usg=0.295m/s,slug flow 1

5

Radial measurement position

Radial measurement position

(%)

(%)

The bi-optical fiber probe fluctuating signals of slug and churn flows at seven measurement positions are shown in Fig. 5. ‘‘Position nU, Position nW” respectively represent the leading and rear probe signals at position n. The voltage of output signal is high when the probe tip is in gas phase whilst it is low in liquid phase.

Fig. 5(a) shows the raw signals of slug flow. It can be seen that at measurement position 1 and 7, gas phase near the pipe wall is mainly in the form of gas bubble. Taylor bubbles do not occupy all of the cross section of the pipe. Between the Taylor bubbles and the pipe wall, liquid flows downward as a thin falling film with very few bubbles in it. The falling film is fluctuating so that there occasionally exist long high levels in the signals as the probe tip pierces into Taylor bubbles. For the other five measurement positions, Taylor bubbles and liquid slugs containing large numbers of gas bubbles occur steadily and follow one another in regular succession. Three-phase flow also exists ‘‘Wake region” (Hout et al., 1992; Chen and Brill, 1997) just behind the tail of the preceding Taylor bubble where gas holdup is considerably higher than other regions in liquid slug. The raw signals of churn flow are shown in Fig. 5(b). As seen, at position 1 and 7, gas phase near the pipe wall is mainly in the form of gas bubble with gas blocks occasionally appearing. For the other five measurement positions, gas phase and liquid phase containing large numbers of gas bubbles occur randomly at each measurement position. The appearance of gas phase at five different measurement positions is also inconsistent and random.

2

3

4

5

6

7

Radial measurement position

(c) Fig. 9. Profile of local gas holdup at different radial positions of pipe in slug flows.

6

7

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For the sake of calculating local flow parameters, an algorithm namely ‘‘self-adjusting double threshold” (Welle, 1985) is herein utilized to transform the raw signals into binary ones with 0 and 1 representing liquid and gas phase respectively. Firstly, a maximum amax and a minimum amin are defined initially. We compare the nth signal point with the value of an with the (n  1)th signal point with the value equaling to an1 . If an is larger than an1 , amax is substituted by an , if an is smaller than an1 , amin is substituted by an , if an is equal to an1 , the maximum and minimum remain their respective values. Then we compare an with the new maximum and the minimum values by the following two equations:

an > amin þ v

ð3Þ

an < amax  v

ð4Þ

3.2. Distribution of local gas velocity and local gas holdup In the present study, we apply cross-correlation algorithm to calculate local gas velocity vi of the ith measurement position (i = 1, 2, 3, 4, 5, 6, 7). The cross-correlation function can be calculated using the following equation (Thorn et al., 1982):

1 T!1 T

Rxy ðsÞ ¼ lim

T 0

xðtÞyðt þ sÞdt

ð5Þ

v i ¼ L=s0

ð6Þ

where L represents the distance the between the leading and rear probe tips. Fig. 7 presents the fluctuating signals of the bi-optical fiber probe at different measurement positions and its

70

60

60

50

50

(%)

40

Z

where x(t) and y(t) are the upstream and downstream signals, T represents the length of signal series and Rxy ðsÞ denotes the crosscorrelation function. When Rxy ðsÞ takes its maximum, the value of s is the transit time s0 , then the velocity at each measurement position can be obtained by the follow equation:

70

30

40

30

Umix=0.590m/s, fo=0.05,Usg=0.295m/s,churn flow

20

Umix=0.590m/s, fo=0.05,Usg=0.442m/s,churn flow

10 1

2

3

4

5

6

Umix=0.737m/s, fo=0.05,Usg=0.295m/s,churn flow

20

Umix=0.590m/s, fo=0.05,Usg=0.369m/s,churn flow

Umix=0.737m/s, fo=0.05,Usg=0.369m/s,churn flow Umix=0.737m/s, fo=0.05,Usg=0.442m/s,churn flow

10 1

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(b) 70

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40 Umix=0.737m/s, f0=0.05,Usg=0.442m/s,churn flow

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Umix=0.737m/s, f0=0.10,Usg=0.442m/s,churn flow Umix=0.737m/s, f0=0.15,Usg=0.442m/s,churn flow

20

Umix=0.737m/s, f0=0.20,Usg=0.442m/s,churn flow 1

5

Radial measurement position

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(%)

(%)

where v is a threshold related to the noise in signal. If Eq. (3) is true, the output will be 1 while it is set as 0 when the relationship between an and amax satisfies Eq. (4). If neither of Eq. (3) and Eq. (4) are true, the output is equal to the value of the former one. By this means, the raw signals can be transformed into the binary ones.

Fig. 6 gives the processed signals of slug and churn flows using the ‘‘self-adjusting double threshold” algorithm.

2

3

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5

6

7

Radial measurement position

(c) Fig. 10. Profile of local gas holdup at different radial positions of pipe in churn flows.

6

7

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corresponding cross-correlation function with Umix = 0.147 m/s, fo = 0.05, Usg = 0.295 m/s. The result shows that the upstream and downstream signals at different measurement positions exhibit a good cross-correlation relationship with an obvious crosscorrelation peak. The transit time s0 can be obtained by searching the peak of cross-correlation function, and the local gas velocity v i can be calculated using Eq.(6). Fig. 8(a) presents the profile of local gas velocity with increasing gas superficial velocity Usg and a constant liquid mixture superficial velocity Umix and a fixed oil-cut of liquid phase fo in slug flow. The local gas velocities of position 1 and 7 are lower than others as the falling liquid film flows into the liquid slug near the pipe wall, which slow down the gas velocity. The local gas velocities of other measurement positions are closer, and the gas velocities of all measurement positions increase with an increasing Usg. Fig. 8(b) illustrates the profile of the local gas velocity with increasing fo and constant Umix and Usg in slug flow. The local gas velocities decrease with an increasing fo. This can be attributed to the fact that the increasing oil phase hinders bubbles’ upward movement and decreases the gas velocity. Fig. 8(c) shows the profile of the local gas velocity with increasing gas superficial velocity Usg and a constant liquid mixture superficial velocity Umix and a constant oil-cut of liquid phase fo in churn flow. The local gas velocities of position 1 and 7 are also lower than others, but the local gas velocities of other measurement positions are different as the churn flow are very chaotic and disordered with gas phase randomly appearing at different positions of the pipe. Oscillatory or alternating direction of motion of the liquid leads to a varying velocities at different positions. The

gas velocities of all measurement positions increase with an increasing Usg. Fig. 8(d) presents the profile of local gas velocity with increasing fo and constant Umix and Usg in churn flow. As seen, local gas velocities decrease with an increasing fo, which can also be interpreted from the fact that increasing oil phase hinders bubbles’ upward movement and decreases the velocities of gas bubbles. In addition, the profile of local gas holdup at different positions of radial direction in slug and churn flows are derived from the leading probe signals processed by ‘‘self-adjusting double threshold” algorithm. Supposing there are n bubbles passing through the tip of optical probe during sampling time T and Dtj presents the piercing time of the jth gas bubble, then local gas holdup ai (i = 1, 2, 3, 4, 5, 6, 7) can be obtained using the following equation: n X Dt j

ai ¼

if sampling interval is DT, N ¼ T=DT is the total number of the sampling points during sampling time T, denote Ng as the number of sampling points with high level, thus, the local gas holdup ai can be calculated by Eq. (8):

ai ¼

Ng N

Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow Position 1U

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12 6

0 0 400

0 0 400

ð8Þ

Fig. 9(a)–(c) shows the profiles of local gas holdup under different slug flow conditions. Slug flow has a nearly symmetric profile under a certain flow condition and the local gas holdup of position 1 and 7 are much lower than others as falling liquid film exist near

30

0 0 400

ð7Þ

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j¼1

Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow 60

!,

0 0 12

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6

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Bubble Series

(a)

150

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100

150

Bubble Series

(b)

Fig. 11. Series of bubble chord lengths at different radial positions of pipe in slug flow (Umix = 0.147 m/s, fo = 0.05, Usg = 0.295 m/s): (a) Series of the bubble chord lengths of whole slug; (b) Series of the bubble chord lengths without Taylor bubbles.

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the pipe wall, and local gas holdup presents the highest value at the pipe center whilst it exhibits a decreasing trend with the increasing distance from the pipe center. When Umix and fo are fixed, local gas holdup increases with an increasing Usg as shown in Fig. 9(a) and (b). When Umix and Usg are fixed, local gas holdup increases with an increasing fo as shown in Fig. 9(c), which results from the increasing oil phase hinders bubbles’ upward movement, decreases the drift velocities of gas bubbles and weakens local slippage effect. Fig. 10(a)–(c) shows the profiles of local gas holdup under different churn flow conditions. As churn flow is very chaotic and disordered, it has a completely asymmetric profile under a certain flow condition. Specifically, gas phase randomly appears at different positions of the pipe, which leads to a random gas holdup distribution. The local gas holdup of position 1 and 7 are also much lower than others as liquid film still exists near the pipe wall, and the local gas holdup of other measurement positions distribute randomly, When Umix and fo are fixed, local gas holdup increases with an increasing Usg as shown in Fig. 10(a) and (b). When Umix and Usg are fixed, the local gas holdup increases with an increasing fo as shown in Fig. 10(c), the reason of which resembles the one that induces gas holdup variation in Fig. 9(c). 3.3. Series of bubble chord lengths In order to reveal the local temporal structures of the slug and churn flows, the series of bubble chord lengths at different measurement positions are calculated using Eq. (9):

dij ¼ v i  Dtj

where v i presents the local velocity of the ith measurement position, Dtj denotes the piercing time of the jth gas bubble, and dij presents the bubble chord length of the jth gas bubble at the ith measurement position. Fig. 11(a) and (b) shows the series of bubble chord lengths at seven measurement positions in 10 s measuring time in slug flow, and Fig. 11(b) is the enlarged view of Fig. 11(a) exhibiting the bubble chord lengths of liquid film and liquid slug without Taylor bubble chord length. At measurement position 1 and 7, gas phase near the pipe wall is mainly in the form of gas bubble. The falling liquid film around the Taylor bubbles is fluctuating so that there exist big chord lengths as the probe tip pierces into Taylor bubbles. For each of the other five measurement positions, a big chord length is followed by many small chord lengths, which correspond to Taylor bubble and liquid slug containing large numbers of gas bubbles. They occur steadily and follow one another in regular succession which means that slug flow has a relatively stable periodic structure in the axial direction and a nearly symmetric profile in the radial direction. The series of bubble chord lengths of liquid film and liquid slug are shown in Fig. 11(b). The bubble chord lengths are bigger at the pipe center whilst it exhibits a decreasing trend with the increasing distance from the pipe center. It also can be seen that the number of bubble chord lengths near the pipe wall are less than others due to the very few bubbles existing in the liquid film and liquid slug near the pipe wall.

Umix =0.737m/s, fo=0.05,Usg =0.442m/s,churn flow

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Umix =0.737m/s, fo=0.05,Usg =0.442m/s,churn flow

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Fig. 12. Series of bubble chord lengths at different radial positions of pipe in churn flow (Umix = 0.737 m/s, fo = 0.05, Usg = 0.442 m/s): (a) Series of the bubble chord lengths of whole churn; (b) Series of the bubble chord lengths less than 20 mm.

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70

Umix=0.147m/s, fo=0.05,Usg=0.442m/s,slug flow

Oil phase Gas phase Water phase

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Umix=0.147m/s, fo=0.05,Usg=0.369m/s,slug flow

50

Umix=0.295m/s, fo=0.05,Usg=0.295m/s,slug flow

Taylor bubble

40 ls (%)

Ltb

Liquid film

Lu

Umix=0.147m/s, fo=0.05,Usg=0.295m/s,slug flow Umix=0.442m/s, fo=0.05,Usg=0.295m/s,slug flow

30 20 10

Lls

Liquid slug

0 lsi

1

2

3

5

4

Condition Fig. 14. The variation of bls under different slug flow conditions.

Taylor bubble Pipe

smaller ones. Measurement position 1 and 7 have fewer bubble chord lengths than others due to fewer bubbles existing in the liquid film near the pipe wall.

Three-phase flow Fig. 13. Sketch of continuous slug flow.

3.4. The relative length of the liquid slug and gas holdup profile in liquid slug In order to investigate the evolution of flow structure in slug flow under different flow conditions, different structural parameters are defined and measured. Slug flow can be divided into three distinct regions: Taylor bubble, liquid slug and falling liquid film, the length of Taylor bubble is Ltb , the length of liquid slug is Lls , the length of whole slug is Lu , the relative length of the liquid slug bls ¼ Lls =Lu , and gas holdup in liquid slug is alsi , where i is the NO. of measurement positions. A sketch of continuous slug flow is shown in Fig. 13. Fig. 14 presents the variation of bls under different slug flow conditions. It can be seen that when Umix and fo are fixed, the relative length of liquid slug bls decreases with an increasing Usg and when Usg and fo are fixed, the relative length of the liquid slug bls increases with an increasing Umix, these results are consistent

24

24

22

22

20

20

18

18

lsi (%)

lsi (%)

Fig. 12(a) and (b) shows the series of bubble chord lengths at seven measurement positions in 10 s measuring time in churn flow, and Fig. 12(b) is the enlarged view of Fig. 12(a) with bubble chord length less than 20 mm. At measurement position 1 and 7, gas phase near the pipe wall is mainly in the form of gas bubble. There also exist big chord lengths as the big gas block appears occasionally near the pipe wall. For each of the other five measurement positions, big gas blocks with different chord lengths and many small bubble chord lengths occur randomly and unregularly which means that churn flow has a random structure in the axial direction and a completely asymmetric profile in the radial direction. Churn flow has more bubble chord lengths at all measurement positions than slug flow due to the intensification in turbulent energy, which decomposes large gas bubbles into

16 14

Umix=0.147m/s, fo=0.05,Usg=0.295m/s,slug flow Umix=0.147m/s, fo=0.05,Usg=0.369m/s,slug flow

12

Umix=0.147m/s, fo=0.05,Usg=0.295m/s,slug flow Umix=0.295m/s, fo=0.05,Usg=0.295m/s,slug flow Umix=0.442m/s, fo=0.05,Usg=0.295m/s,slug flow

16 14 12

Umix=0.147m/s, fo=0.05,Usg=0.442m/s,slug flow

10

10 1

2

3

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5

Radial measurement position

(a)

6

7

1

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3

4

5

Radial measurement position

(b)

Fig. 15. Profile of local gas holdup at different radial positions of pipe in liquid slug under different flow conditions.

6

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Umix =0.295m/s, fo=0.05,Usg =0.295m/s,slug flow

Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow Position 1U

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(b) Umix =0.147m/s, fo=0.05,Usg =0.442m/s,slug flow Position 1U

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Umix =0.147m/s, fo=0.05,Usg =0.369m/s,slug flow

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Fig. 16. Series of bubble chord lengths at different radial positions of pipe in liquid slug under different flow conditions.

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with the previous studies of gas-liquid slug flow (Chen and Brill, 1997; Mao and Dukler, 1989). Fig. 15 illustrates the profile of local gas holdup in liquid slug alsi at middle five measurement positions of radial direction of the pipe under different slug flow conditions, as seen that alsi has a nearly symmetric profile in the radial direction and reaches its maximum at the pipe center whilst decreases with the increasing distance from the pipe center, which indicates that gas concentration is higher at the pipe center than those near the pipe wall. As seen in Fig. 15(a), when liquid mixture superficial velocity Umix and oil-cut of liquid phase fo are fixed, the local gas holdup alsi shows an increasing tendency with the increasing gas superficial velocity Usg and this coincides with what Chen mentioned in his gas-liquid slug flow research (Chen and Brill, 1997). When gas superficial velocity Usg and oil-cut of liquid phase fo are fixed, local gas holdup alsi shows an decreasing tendency with the increasing liquid mixture superficial velocity Umix. 3.5. Bubble size distribution in liquid slug The Taylor bubble is followed by a liquid slug containing large numbers of small gas bubbles with similar size and motion as

observed in bubbly flow (Taitel et al., 1980; Fernandes et al., 1983), but the series of bubble chord lengths and bubble size distribution in radial direction in liquid slug have seldom investigated, especially for three-phase flow. In the present study, we calculated the series of bubble chord lengths in liquid slug under different slug flow conditions in 10 s measuring time. As shown in Fig. 16. The bubble chord lengths are bigger at the pipe center whilst it exhibits a decreasing trend with the increasing distance from the pipe center. It also can be seen that the number of bubble chord lengths near the pipe wall are less than others due to fewer bubbles existing in liquid film and liquid slug near the pipe wall. Fig. 16(a) and (b) illustrates that when gas superficial velocity Usg and oil-cut of liquid phase fo are fixed, bubble chord lengths decrease and the number of bubble chord lengths increase with the increasing liquid mixture superficial velocity Umix, this is because when increasing the mixture superficial velocity Umix, the turbulent energy intensifies and gas bubbles are broken up into smaller ones. Fig. 16(b)–(d) illustrates that when liquid mixture superficial velocity Umix and oil-cut of liquid phase fo are fixed, the bubble chord lengths and the number of bubble chord lengths exhibit an increasing trend with an increasing gas superficial velocity Usg. This can be attributed to the fact that the increasing Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow

Umix =0.295m/s, fo=0.05,Usg =0.295m/s,slug flow Position 1U Position 2U Position 3U Position 4U Position 5U Position 6U Position 7U

1.4 1.2 1.0

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Umix =0.147m/s, fo=0.05,Usg =0.369m/s,slug flow

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Fig. 17. The bubble size distributions at different positions of radial direction of the pipe in liquid slug under different slug flow conditions.

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D.-Y. Wang et al. / Chemical Engineering Science 177 (2018) 53–73

(d) illustrates the bubble size distribution transformed from bubble chord length distribution shown in Fig. 16(a)–(d), where the horizontal axis d represents the equivalent gas bubble diameter and the vertical axis refers to probability density function (PDF). The bubble size distributions are nearly symmetric in the radial direction. Large bubbles appear at the central part of the pipe and bubble sizes decrease with the distance increasing away from the pipe center which indicates that bubbles at pipe center coalesce easily. By comparing Fig. 17(a) with (b), when gas superficial velocity Usg and oil-cut of liquid phase fo are fixed, bubble sizes decrease with an increasing liquid mixture superficial velocity Umix due to the breakup mechanism mentioned above. Fig. 17(b)–(d) shows that bubble sizes exhibit an increasing trend with an increasing gas superficial velocity Usg. This can be ascribed to the fact that the increasing gas superficial velocity Usg makes the liquid slug more aerated, and large bubbles form because of the collision and coalescence of bubbles.

gas superficial velocity Usg makes liquid slug more aerated. The bubble density increases and large bubbles take shape due to the collision and coalescence of bubbles. Due to the random movement of gas bubbles, they can be pierced anywhere when flowing through the optical fiber probe tip. Therefore, realizing the transformation from chord length to bubble size is imperative for investigating gas bubble size distribution. Many efforts have been paid to investigate the relationship between distribution in chord length and bubble size (Uga, 1972; Simmons et al., 1999; Hu et al., 2006). However, they all assumed the dispersed phase with regular shape and homogeneous distribution, which are unsuitable for the dispersed phase with irregular shapes resulting from the turbulence and phase interaction. Herein, we transform the gas bubble chord length distribution into bubble size distribution with the decomposition of Gaussian function. The detailed theory and implementing procedure regarding this algorithm can refer to the work of Hoang (2015). Fig. 17(a)–

Upstream signal Downstream signal

Umix=0.147 m/s, fo=0.05,Usg=0.295 m/s,slug flow

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conductance probe signals (V)

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Umix=0.147 m/s, fo=0.05,Usg=0.369 m/s,slug flow

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Umix=0.147 m/s, fo=0.05,Usg=0.442 m/s,slug flow

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Umix=0.737 m/s, fo=0.05,Usg=0.295 m/s,churn flow

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4. Nonlinear dynamics analysis for slug and churn flows In attempt to reveal the nonlinear dynamic characteristics of slug and churn flow and validate the results of gas phase characteristics obtained from bi-optical fiber probe signals, multi-scale cross

entropy (MSCE) algorithm is applied to analyze signals of highresolution half-ring conductance sensor and bi-optical fiber probe to uncover the dynamical instability of slug and churn flows at different positions. The high-resolution half-ring conductance sensor has an advantage on flow pattern identification at the pipe cross

Fig. 19. Time frequency joint distribution of two typical flow patterns: (a) slug flow (Umix = 0.147 m/s, fo = 0.05, Usg = 0.295); (b) churn flow (Umix = 0.737 m/s, fo = 0.05, Usg = 0.442).

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section (Kytömaa and Brennen, 1991; Costigan and Whalley, 1997; Cantelli et al., 2011; Chen et al., 2015), and optical fiber probe is helpful for local flow characteristic analysis. Fig. 18 shows the conductance sensor signals under different flow conditions, the signals of slug flow are periodic with low frequency due to the presence of Taylor bubbles and liquid slugs occur steadily and follow one another in regular succession. However, the signals of churn flow are random with high frequency. 4.1. Time-frequency joint distribution analysis For the purpose of describing the flow motion in slug and churn flows, Adaptive optimal kernel (AOK), proposed by Jones and Bariniuk (1995), which can suppress the interference of cross term effectively and maintain the high frequency, is herein utilized to analyze the conductance signals. The original formula of AOK can be expressed as follows:

ZZ Pðt; f Þ ¼

Aðt; s; tÞUðs; tÞej2pðttþsf Þ dsdt

ð10Þ

where v stands for frequency shift, s represents the time-delay, t means time and f is frequency. Uðs; tÞ denotes adaptive optimal

Entropy, which is considered as the indicator representing the complexity in a dynamic system, contributes a lot to the physical

Umix =0.147m/s, fo=0.05,Usg =0.295m/s,slug flow

0.5

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Cross-Entropy

4.2. Multi-scale cross entropy analysis

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kernel function and Aðt; s; v Þ is time-localized short-time ambiguity function respectively. We can see from the time-frequency joint distribution of slug flow in Fig. 19(a) that slug flow has a low dominant frequency, the energy distribution reveals the periodical intervals of slug flow as high and low energy appear alternatively, reflecting the movement characteristics of Taylor bubble and liquid slug. The periodical movement characteristics are consistent with the gas phase characteristics obtained from the bi-optical fiber probe signals. The dominant frequency of churn flow is higher than slug flow, and the energy distribution in time domain is not only continues and uniform, but also presents a high value as shown in Fig. 19 (b), which corresponds to the flow behavior that oscillatory motion of churn flow results in random and instable flow structure. The oscillatory and random movement characteristics are also consistent with the gas phase characteristics obtained from the bioptical fiber probe signals.

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significance in dynamic characteristic investigation. Sample entropy algorithm (Richman and Moorman, 2000) and multiscale sample entropy algorithm (Costa et al., 2002) can only analyze the complexity of one time series. In order to explore the coupling behavior between two time series, the concept of multi-scale cross entropy (MSCE) was firstly proposed by Yan et al. (2009). The research implemented by Zhu et al. (2011) in our research group has proved the satisfied anti-noise ability in MSCE, and applied it in the flow pattern analysis of inclined oilwater two-phase flow. In the present study, we use multi-scale cross entropy algorithm to analyze the dynamic complexity of different radial positions of fluid and the whole pipe cross section under different flow conditions to fully uncover the nonlinear dynamics characteristic in slug and churn flows. The detailed theory and implementing procedure of MSCE can be referred to the work of Zhu et al. (2011). Notably, distance threshold r is set as the standard deviation in each time series multiplying 0.15. The dimension m and the maximum coarse-grained scale are set as 2 and 20, while the selected length of each time series is 20,000. Fig. 20(a)–(d) shows the MSCE and rate of MSCE of bi-optical fiber probe signals at seven measurement positions under different slug flow conditions. An identical phenomenon is that the MSCE at

Umix =0.737m/s, fo=0.05,Usg =0.295m/s,churn flow

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seven measurement positions all increase with the rising scale. The MSCE and rate of MSCE at position 1 and 7 has high values than others. This can be attributed to the fact that the interface of Taylor bubble and falling liquid film exist near the pipe wall, where the intense interactions of three phases and waved liquid film results in more complex structures, so the MSCE and rate of MSCE are higher. For the other five measurement positions, the MSCE and rate of MSCE are low and approaching each other due to the periodic movement of Taylor bubbles and liquid slugs. With the increasing gas superficial velocity Usg, the MSCE and rate of MSCE have an increasing trend due to the increasing turbulent energy. Fig. 21(a)–(d) shows the MSCE and rate of MSCE of bi-optical fiber probe signals at seven measurement positions under different churn flow conditions. The MSCE at seven measurement positions all increase with the rising scale. The MSCE and rate of MSCE have high values near the pipe wall than in the pipe center. This also can be attributed to the fact that waved liquid film and huge wave (K. Wang et al. (2013); Wang et al., 2017) exist near the pipe wall, and the complex structures lead to higher MSCE and rate of MSCE. For all other five measurement positions, the MSCE and rate of MSCE are higher than slug flow and different with each other due to the oscillatory and random movement characteristics of

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(b) Fig. 22. MSCE and rate of MSCE under different flow conditions using high-resolution half-ring conductance sensor signals.

churn flow. With the increasing gas superficial velocity Usg, the MSCE and rate of MSCE have an increasing trend due to the increasing turbulent energy. Fig. 22 shows the MSCE and rate of MSCE of conductance signals under different flow conditions. As Taylor bubbles and liquid slugs occur steadily and follow one another in regular succession, the MSCE and rate of MSCE of slug flow are lower than churn flow as shown in Fig. 22(a). With the increasing gas superficial velocity Usg, the MSCE and rate of MSCE have an increasing trend due to the increasing turbulent energy. For churn flow, both of MSCE and rate of MSCE are higher than slug flow, this is because the intense interactions between gas phase and liquid phase and oscillatory and random motion of churn flow lead to complex and instable flow structure. With the increasing gas superficial velocity Usg, the MSCE and rate of MSCE have an increasing trend due to the increasing turbulent energy. By calculating the MSCE and rate of MSCE at different local positions and whole pipe cross section, the local gas phase characteristics obtained from bi-optical fiber probe signals and time-frequency joint distribution analysis are well verified. Fig. 22(b) illustrates the variation in complexity with increasing oil-cut of liquid phase fo and fixed Usg and Umix. As seen, the increasing fo will make the interaction of the threephase more complex, so both the MSCE and rate of MSCE increase. 5. Conclusions In this study, a traversable bi-optical fiber probe is designed to measure local gas phase characteristics of oil-gas-water slug and

churn flows in a 20 mm ID vertical pipe. We also utilize multiscale cross entropy (MSCE) algorithm to analyze signals of highresolution half-ring conductance sensor and bi-optical fiber probe to uncover the nonlinear dynamic characteristics of slug and churn flows at different positions. Our conclusions can be stated as follows: 1. Taylor bubbles are surrounded by waved falling liquid film in slug flow, which results in a lower gas velocity and local gas holdup near the pipe wall. For the middle five measurement positions, as Taylor bubbles and liquid slugs occur steadily and follow one another in regular succession, local gas velocities are approaching each other, and local gas holdup exhibits a parabolic profile. When gas superficial velocity increases, the profiles of local gas velocity and local gas holdup have an increasing trend. The increasing oil phase slows down the drift velocities of gas bubbles, then weakens local slippage effect and makes gas holdup increase. Liquid slug contains large numbers of bubbles and local gas holdup and bubble size reach maximum at the pipe center whilst they exhibit a decreasing trend with the increasing distance from the pipe center. The gas holdup and bubble size have decreasing trend and the relative length of liquid slug presents an increasing trend with mixed liquid superficial velocity increasing, while gas holdup and bubble size have increasing trend and the relative length of liquid slug has decreasing trend with gas superficial velocity increasing. 2. Liquid film with lots of bubbles exists near the pipe wall in churn flow, where the gas velocity and local gas holdup are

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lower. For the middle five measurement positions, due to the oscillatory and random motion of churn flow, gas phase appears random and uncertain. Local gas velocity and local gas holdup exhibit random and asymmetric profiles. When gas superficial velocity increases, the profiles of local gas velocity and local gas holdup have an increasing trend. The increasing oil phase slows down the drift velocities of the gas bubbles, then weakens local slippage effect and makes the gas holdup increase. 3. The time-frequency characteristics and the results of MSCE show that slug flow has a low dominant frequency and narrow frequency band. The MSCE and rate of MSCE at seven local positions and pipe cross section are lower than churn flow due to the periodic movement of Taylor bubbles and liquid slugs and symmetrical distribution of gas phase, which is consistent with the measurement results from bi-optical fiber probe. The dominant frequency and energy of churn flow, the MSCE and rate of MSCE at seven local positions and pipe cross section are all higher than slug flow, which illustrates that churn flow is of greater uncertainty and complexity and this validates the measurement results using bi-optical fiber probe.

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