Experimental flow pattern map, slippage and time–frequency representation of oil–water two-phase flow in horizontal small diameter pipes

International Journal of Multiphase Flow 76 (2015) 168–186

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International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w

Experimental flow pattern map, slippage and time–frequency representation of oil–water two-phase flow in horizontal small diameter pipes Lu-Sheng Zhai, Ning-De Jin ⇑, Yan-Bo Zong, Qing-Yang Hao, Zhong-Ke Gao School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

a r t i c l e

i n f o

Article history: Received 25 June 2014 Received in revised form 17 June 2015 Accepted 23 July 2015 Available online 30 July 2015 Keywords: Horizontal oil–water two-phase flow Experimental flow pattern map Slippage effect Time-frequency representation

a b s t r a c t We detect the flow structures of a horizontal oil–water two-phase flow in a 20 mm inner-diameter pipe using 8-channels radial mini-conductance probes. In particular, we present an experimental flow pattern map that includes 218 flow conditions and compare this map to the flow pattern transitional boundaries predicted by published models. In addition, using the Adaptive Optimal Kernel Time–Frequency Representation, we analyze the conductance fluctuating signals and characterize the flow pattern in terms of the total energy and dominant frequency. Based on the liquid holdup measurements using the quickly closing valve technology combined with three parallel-wire capacitance probes, we investigate the slip effect between the oil and water phases under various flow conditions. The results show that the flow structures greatly affect the slippage, and the slip ratio is sensitive to flow pattern variations. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction Horizontal oil–water two-phase flow often exists in many industrial processes, such as oil well production and oil transportation. Flow patterns that indicate how the phases are distributed and mixed display substantial effects on the prediction of the pressure loss along the pipeline and the design of the artificial lift. Notably for the horizontal well production logging, the accuracy of flow measurements largely depends on the flow patterns encountered in horizontal oil–water two-phase flows. In this regard, understanding the flow pattern behavior is important in developing the correct interpretation of the response of production logging instruments. Early experimental investigations on the horizontal oil–water two-phase flow patterns were conducted in acrylic pipes with a small diameter, and the flow patterns were primarily defined by simple observations (Russell et al., 1959; Hasson et al., 1970). Arirachakaran et al. (1989) observed stratified flow, mixed flow, annular flow, intermittent flow and dispersed flow in a horizontal 25.1 mm inner-diameter (ID) pipe. Trallero et al. (1995, 1997) comprehensively performed an experimental and theoretical study and proposed six typical flow patterns of horizontal oil–water two-phase flow in a 50.1 mm ID pipe. Nädler and Mewes (1997)

⇑ Corresponding author. Tel./fax: +86 22 27407641. E-mail address: [email protected] (N.-D. Jin). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.07.007 0301-9322/Ó 2015 Elsevier Ltd. All rights reserved.

produced a detailed classification for horizontal oil–water two-phase flow in a 59 mm ID pipe and determined two new flow patterns, i.e., layers of water-in-oil dispersions and water flow and layers of dispersions of water-in-oil, oil-in-water and water flow. Beretta et al. (1997) observed horizontal slug flow and annular flow in a 3 mm ID pipe. Angeli and Hewitt (1998, 2000) investigated the flow structure of tap water and kerosene (EXXSOL D80) in horizontal stainless and acrylic pipes using a conductivity needle probe and impedance probe, and a three-layer flow pattern was newly defined. Oil–water flow patterns greatly depend on many factors, such as the fluid properties, pipe diameter, pipe material and inclined angle. Shi et al. (2001) observed horizontal oil–water stratified flow and mixed dispersed flow in a large 100 mm ID pipe. Liu et al. (2003) conducted horizontal oil–water two-phase flow experiments in a 40 mm ID non-corrosive steel pipe and acrylic pipe and observed 9 different flow patterns, in which the horizontal slug flow, oil-based annular flow and water-based annular flow were not previously described in former studies. Rodriguez and Oliemans (2006), using mineral oil and brine, conducted horizontal and near-horizontal oil–water two-phase flow experiments in an 82.8 mm ID non-corrosive steel pipe to study the flow patterns, pressure gradients and phase volume fractions and suggested that Trallero’s physical model can accurately predict most experimental flow patterns, but fails to predict the flow boundary for the transition from ST flow to ST&MI flow, notably under inclined upward

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100

500

1000 Contraction orifice S4

S5 20

125

S1 S2 S3

100 140 200

Unit: mm

300

Diverter

400 Fig. 1. The geometry of the model used in CFD to simulate the transient flow behavior.

Fig. 2. The grids of the simulated 3D model in CFD.

flow conditions. Wegmann and Rudolf von Rohr (2006), using water and paraffin oil, conducted experiments in a 5.6 mm ID and a 7 mm ID pipe and indicated that the pipe diameter and fluid property display strong influences on the flow pattern transitional boundary. Meanwhile, progress has been achieved in determining the flow pattern transition in horizontal oil–water two phase flows. The

S1

S2

transitional boundary model from ST to non-ST flow has long been a focus of studies (Trallero, 1995; Nädler and Mewes, 1997; Ng et al., 2001, 2002; Al-Wahaibi and Angeli, 2007, 2011; Al-Wahaibi et al., 2012). Torres-Monzón (2006) developed the transitional boundary physical models for DO/W&W, DW/O&DO/W, DO/W and DW/O flows. The phase inversion in oil–water flows has also attracted substantial attention. Brauner (2001), Brauner and Ullmann (2002) suggested a unified model and a criterion of the minimum system free energy to predict the conditions under which phase inversion will occur. Recently, new progress covering the phase inversion has been reported (Ioannou et al., 2005; Piela et al., 2008; Wang and Gong, 2009; Angeli, 2009). Additionally, select studies have been devoted to the measurement techniques of horizontal oil–water two-phase flows. Chakrabarti et al. (2006) used a novel optical probe to investigate the phase inversion in a liquid–liquid two-phase flow. Huang et al. (2007) measured the water holdup in a horizontal kerosene–water two-phase flow using an intrusive capacitance probe. Kumara et al. (2009, 2010) measured the local phase volume fraction and the local velocity distribution in a 56 mm ID steel pipe by applying a single-bundle gamma density gauge and particle image velocimetry (PIV) technique. Zhai et al. (2012) presented liquid holdup measurements under conductive horizontal oil–water flows. Morgan et al. (2012, 2013) used a laser-based optical method to measure the local velocity distribution, droplet size, and in situ phase fraction in a horizontal liquid–liquid circular

S3

S4

S5

S4

S5

(a) t = 20s S1

S2

S3

(b) t = 60s S1

S2

S3

S4

S5

(c) t = 120s Fig. 3. The calculated phase distribution at different cross-sections and times (Qt = 10 m3/day, Ko = 0.5, the distances of the investigated cross-sections from the inlet are 10 cm, 14 cm, 20 cm, 30 cm, and 40 cm, respectively, from left to right).

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y

(a)

(b)

20mm

1.0 0.8

Oil

P (0, h)

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yl ,o

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o

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h/D Fig. 4. The extraction of the phase distribution at each cross-section when t = 120 s: (a) the location of the investigated central line; (b) the extracted phase distribution along the central line.

Stainless steel electrodes (Diameter of the electrode is 0.8mm)

Pipe wall

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Side view of parallel wires conductance probes

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Fig. 5. The test section for the investigation of the transient flow behavior.

probe 1 probe 2 probe 3 probe 4

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Time (s) Usw=1.105m/s Uso=0.295m/s DO/W&W 1.0

probe 1 probe 2 probe 3 probe 4

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Usw=1.105m/s Uso=1.105m/s DW/O&DO/W 1.0 probe 1 probe 2 probe 3 probe 4

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Time (s)

Time (s)

Fig. 6. The measured response of the parallel-wire conductance probes.

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tube. De Castro et al. (2012) investigated the interfacial wave properties using a high-speed video camera and suggested a physical relationship between the wave shape and the hydrodynamic stability of the stratified liquid–liquid flow pattern. Cai et al. (2012) investigated the water wetting in an oil–water two-phase flow based on four measurement techniques that consisted of the flow pattern visualization, conductivity pins, fluid sampling and the monitoring of the corrosion rate. Previously, investigations of the slip effect between the oil and water phases in a horizontal pipe were relatively rare. Of the limited research in this area, Lovick and Angeli (2004a) measured the pressure gradient, liquid holdup and phase distribution of the dual continuous flow pattern and indicated that the phase distribution and the shape of the oil–water interface have substantial effects on the slip behaviors of oil–water two-phase flows. Xu et al. (2008) investigated the effects of the pipe ID, oil viscosity and mixture velocity on the slippage ratio. Hapanowicz (2008) presented the relationship between the slippage and the water holdup under the dispersed flows and dual continuous flow and predicted the holdup of the dispersed phases using a drift velocity model. Rodriguez et al. (2011) performed an experimental test of horizontal oil–water two-phase flows in a 26.2 mm ID pipe, and the slip ratio in a dispersed viscous oil–water pipe flow was examined using a quick-closing-valves technique. Although select efforts have been conducted in the study of horizontal oil–water two-phase flows, substantial challenges

remain in regard to uncovering the hydrodynamic mechanism of the flow pattern transition in horizontal oil–water two-phase flows. In addition, limitations on the study of the slippage between the oil and water phases remain because the determination of the slippage greatly depends on the accurate measurement of the liquid holdup. In this study, we conduct an experiment on horizontal oil–water two-phase flows. In the experiment, 8-channel radial conductance array probes are employed to detect the local flow structures. Additionally, we analyze the signals derived from the ring shape conductance probe using an Adaptive Optimal Kernel Time–Frequency Representation and attempt to characterize the flow patterns in terms of the total energy and dominant frequency. Finally, we investigate the slip behavior between the oil and water phases using a quickly closing valve combined with three pairs of parallel-wire capacitance probes, and the effect of the local flow structures on the slippage has been demonstrated.

Flow loop facility and experiment Horizontal oil–water two-phase flow experiments were performed in the multiphase flow laboratory located in Tianjin University. The experimental mediums are tap water and No. 15 industry white oil with a viscosity of 11.984 mPa s (40 °C) and a surface tension of 0.035 N/m. The densities of the oil and water phases are 845 kg/m3 and 1000 kg/m3, respectively. Both liquids

Construction of mini-conductance probe

Three PWCPs

Double helix capacitance sensor

Conductance cross-correlation Ring conductance probe array probe

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Mini-conductance probes

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control

Single-flow valve

Pneumatic diaphragm control valve

Hand ball valve

Filter

Distributor

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Turbine flowmeter

Fig. 7. Flow loop test facility for horizontal oil–water two-phase flows.

P

Pressure meter

E P

Pressure sensor

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are pumped from their respective storage tanks and joined through a T-junction before entering the acrylic pipe with a 125 mm ID, and then concentrated into a 20 mm ID acrylic pipe by a diverter. The axial length of the larger ID pipe before the diverter is 1.2 m. Investigation on the fully developed flow First, the CFD method is employed to investigate the transient flow behavior and expected to provide select information about the sufficient entrance length to stabilize the flows. For the horizontal oil–water two-phase flows, the fully developed time of the segregated flow is longer than the dispersed flow, indicating that longer distances from the inlet is required for the segregated flows. Thus, our numerical calculation focuses on the stratified flows with low total flow rates. The geometry of the model used in the CFD software FLUENT is shown in Fig. 1. As seen, S1–S5 indicate the selected five cross-sections along the pipeline, which are the locations in the model used to investigate the transient phase distribution. Fig. 2 shows the grids of the 3D model used in FLUENT. The number of the total elements in the model is 1,548,223. The density and viscosity of the water phase are set to 1000 kg=m3 and 0.001 kg=ðm sÞ, whereas the density and viscosity of the oil phase are set to 845 kg=m1 and 0.012 kg=ðm sÞ, respectively. In the numerical calculation, the total flow rate is 10, 20 and 30 m3/day, and the corresponding mixture velocities are set at the inlet. The inlet oil volume fraction, i.e., the so-called oil cut, changes from 0.1 to 0.9 with a defined step of 0.1. Through the patching operation, water serves as the primary phase that fills the pipe. The VOF model is employed in the CFD simulation. The oil–water surface tension coefficient is set to 0.03 N/m. The wall contact angels are set as the default values, i.e., 90 in FLUENT. As shown in Fig. 3, the evolution of the oil–water two phases are noted at different cross-sections as time progresses with a total flow rate of 10 m3/day and an oil cut equal to 0.5. Notably, the heights of the oil–water interface at different cross-sections tend to be stable when the developing time exceeds 60 s. To depict the transient flow behavior quantitatively, we extract the local oil holdup yl;o along the central line of each cross-section (Fig. 4) when the developing time is 120 s. In Fig. 4(a), Pð0; hÞ represents the crossing point between the oil–water interface

and the central line, and h is the ordinate value of P ranging from 0 to 20 mm. As seen, the local oil holdup at section 1 displays notable differences with the other cross-sections. By contrast, the values of the local oil holdup at Sections 3, 4 and 5 are near each other. Although the CFD method, in view of the complex flows in the horizontal pipe, cannot provide a conclusion regarding the development of the flow, the CFD results indicate the tendency of the flow patterns in the full development. Additionally, as shown in Fig. 5, four parallel-wire conductance probes, which function well when measuring the water layer thickness of stratified flows (Jana et al., 2006; Al-Wahaibi and Angeli, 2011), are radially inserted into the 20 mm ID acrylic pipe at different distances from the contraction orifice, i.e., 100 mm, 140 mm, 520 mm, and 800 mm. The response of the parallel-wire conductance probes can be used to investigate the flow pattern development. Fig. 6 shows normalized responses for ST, ST&MI, DO/W&W and DW/O&DO/W flow patterns derived from the ratio between the mixing flow and the pure water signals of the parallel-wire conductance probes. The response of probes 1 and 2 are different from those of the other probes, indicating that the flow patterns are still developing and not stable at probe 2. However, the normalized responses of probe 3 and 4 are similar, indicating that the flow patterns are fully developed. Finally, 800 mm from the contraction orifice of the flow diverter is an appropriate distance required to stabilize the flow. The diverter, with an axial length of 1200 mm, plays an important role in the wellbore storage effect, indicating that a relative short distance can ensure the fully developed flow. Probes in the flow test section Fig. 7 shows the flow loop test facility for the horizontal oil–water two-phase flow. The acrylic pipe has a 20 mm ID and 3.9 m in total length. Probes are mounted on the flow test section, including a ring conductance array probe, double helix capacitance probe and mini-conductance probe. Additionally, the quickly closing valve (QCV) technology combined with three parallel-wire capacitance probes (PWCPs) is employed to acquire the liquid holdup in the horizontal oil–water flow pipe. In Fig. 7, we depict the location-specific information of each probe in the flow test section.

Signals (V)

Usw = 0.147 m/s, Uso = 0.194 m/s, ST 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

Probe 1

Probe 2 Probe 3 Probe 4 Probe 5

Probe 6 Probe 7 Probe 8

0.5

1.0

1.5

Time (s) Fig. 8. Typical mini-probe signals for the ST flow pattern.

2.0

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In our experiment, the oil superficial velocity, U so , and water superficial velocity, U sw , range from 0.106 to 2.579 m/s and 0.111 to 2.210 m/s, respectively. For each flow condition, we fixed the water flow rate and then gradually increased the oil flow rate. Because the pipe diameter is small (20 mm), we can generate a high oil or water flow rate in our flow loop test facility. Both segregated and dispersed oil–water flow patterns can be observed in the test section. Eight mini-conductance probes are arrayed equidistantly at the horizontal pipe to identify the detailed flow structures across the radial section. The measurement principle of the mini-conductance probe refers to our previous publication (Zhai et al., 2012). The structure of the conductance probe is shown in

10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0

(d)

Usw = 0.147 m/s, Uso =0.236 m/s, ST&MI, Type I Probe 1

Probe 2 Probe 3

Signals (V)

Signals (V)

(a)

Fig. 7. The distance between the probes is 2.4 mm; the outer diameter of the conductive casing for each is 2 mm; the outer diameter of each needle electrode is 0.5 mm; and the diameter of the needle electrode tip is 0.1 mm. The conditioning circuit of the mini-conductance probe refers to Lucas and Mishra (2005). The sampling frequency of the mini-conductance probes is set at 4 kHz using the data acquisition card PXI-6115 under the control of LABVIEW software. According to the geometry and the sampling frequency of the mini-conductance probe, the mini-probe can effectively detect the attendance of the droplets or the continuous phase as long as the spatial scale of the liquid exceeds 0.1 mm. Additionally, the mini-probe can capture the movement of the droplet when the time of the droplet contacting the probe tip exceeds

Probe 4 Probe 5

Probe 6

Probe 7 Probe 8

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Usw = 0.553 m/s, Uso = 0.295 m/s, ST&MI, Type III Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Probe 6 Probe 7 Probe 8

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Usw = 0.295 m/s, Uso =0.553 m/s, ST&MI, Type II Probe 1 Probe 2 Probe 3

Signals (V)

Signals (V)

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Probe 4 Probe 5 Probe 6 Probe 7 Probe 8

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Usw = 0.295 m/s, Uso =0.737 m/s, ST&MI, Type II

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0

2

Time (s)

Time (s) Fig. 9. Typical mini-probe signals for the ST&MI flow pattern.

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(a) 10 5 0 10 5 0

Usw = 1.105 m/s, Uso = 1.658 m/s, DW/O&DO/W Probe 1

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Fig. 10. Typical mini-probe signals for the DW/O&DO/W flow pattern.

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Signals (V)

(a)

Usw = 0.737 m/s, Uso = 0.133 m/s, D O/W&W

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Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Probe 6 Probe 7 Probe 8 0.5

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Time (s) Fig. 11. Typical mini-probe signals for the DO/W&W flow pattern.

0.25 ms. Thus, the collected data from the mini-conductance probe could contain the local flow information, and we can determine the spatial local structures of different flow patterns in terms of the fluctuating signals. The ring conductance array probe consists of four stainless steel ring-shape electrodes axially separated and flush-mounted on the inside wall of the insulated flow pipe. The two electrodes on both sides are exciting electrodes and connected with a sinusoidal 20 kHz exciting signal, whereas the two electrodes in the middle are measuring electrodes. After the modulation of the exciting signal by the fluid, the real part of the fluid complex impedance, which characterizes the liquid holdup of the conductive flow patterns, will be demodulated from the output of the measuring electrodes by a conditioning circuit. The double helix capacitance sensor consists of exciting electrodes, measuring electrodes and guard electrodes, and all electrodes rotate 180° along the axial

direction of the pipe. This capacitance sensor is used to detect the imaginary part of the fluid complex impedance and further measure the liquid holdup of the nonconductive flow patterns. The conductance cross-correlation probe and the PWCP are used to measure the cross-correlation velocities under all flow patterns encountered in the horizontal pipe. The PWCP that consists of a pair of metal parallel-wires coated with Teflon is inserted into the flow pipe along the radial direction. The sketch of a PWCP is shown in Fig. 7, in which E1 and E2 represent the two electrodes, l is the separation between the two electrodes, d is the diameter of the metal parallel-wire, and t is the thickness of the Teflon layer. More information covering the PWCP can be found in Zhai et al. (2014). The probes mounted on the flow test section are employed to measure the liquid holdup and the cross-correlation velocity under water or oil dominant flows, respectively. The results of

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Usw = 1.474 m/s, Uso = 0.133 m/s, D O/W

Signals (V)

(a) 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0

Probe 1 Probe 2 2

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Usw = 1.474 m/s, Uso = 0.553 m/s, D O/W

0.0

Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Probe 6 Probe 7 Probe 8 0.5

1.0

1.5

2.0

Time (s) Fig. 12. Typical mini-probe signals for the DO/W flow pattern.

the double helix capacitance sensor and the PWCP used in the cross-correlation velocity measurements are not reported in this paper. Experimental flow pattern map Local flow structures detected by mini-conductance probes The details of the flow structures are detected using 8-channel radial mini-conductance probes in a 20 mm ID pipe. The signals of one typical stratified flow (ST) from the mini-conductance probes are shown in Fig. 8. As seen, the signals demonstrated no notable amplitude fluctuations, indicating that the probes are surrounded by the single phase and agree with the characteristics of stratified flow. By increasing the total flow rate, a fluctuation gradually appears at the oil–water interface, indicating the ST&MI flow pattern occurs. We detect four typical flow structures in this flow pattern.

(1) As shown in Fig. 9(a), the signals from the mini-conductance probes indicate the appearance of a few droplets around the oil–water interface. We define this type of ST&MI flow as type I. (2) With further increases of the oil and water flow rates, the number of oil and water droplets gradually increase, as shown in Fig. 9(b) and (c). We define this type of ST&MI flow as type II. (3) As shown in Fig. 9(d), the signals from probe 1–4 exhibit an alternation of high and low levels with long durations, indicating that the fluctuation of the oil–water interface becomes aggravated and complicated. Additionally, several positive and negative jumps are noted in the signals from probes 1–4. This phenomenon indicates that the drop entrainment is associated with the wavy interface. This type of ST&MI flow is defined as type III. Additionally, in view of the shape of the interface wave shown in Fig. 9(d) and with the increase of the water flow rate, this type of ST&MI flow is

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Usw = 0.147 m/s, Uso = 0.921 m/s, D W/O

(a) 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0

Signals (V)

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Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Probe 6 Probe 7 Probe 8

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Signals (V)

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10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0 10 5 0

Usw = 0.147 m/s, Uso = 1.253 m/s,D W/O

0.0

Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Probe 6 Probe 7 Probe 8 0.5

1.0

1.5

2.0

Time (s) Fig. 13. Typical mini-probe signals for the DW/O flow pattern.

easily transformed to a DO/W&W flow. We conclude that the strong oil–water interface fluctuation is the major factor that causes the evolution from segregated flow to dispersed flow. A similar phenomenon, such as water vortices appearing at the interface, was observed by Russell et al. (1959) and Guzhov et al. (1973). These previous studies noted that the unstable interface behavior forces the water phase to enter and disperse the oil layer. (4) As shown in Fig. 9(e), the oil phase is the main phase separating the droplets near the oil–water interface. The oil droplets disperse in the continuous water phase at the lower part of the pipe, whereas few water droplets disperse in the continuous oil phase. This type of ST&MI flow is defined as type IV. This type of flow structure is similar to the Stratified Mixed (SM) flow with oil droplets in water observed by Elseth (2001) in a horizontal pipe. Fig. 14. The experimental flow pattern map.

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L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186 ST ST&MI D O/W&W D W/O&D O/W D O/W D W/O Trallero (1995) Torres-Monzón (2006) Decarre (1997) Yeh (1964)

3

Qw (m /day)

Usw (m/s)

60 50 40

1

30 20 15 10 8 6 5 4

0.1

3

0.1

Uso (m/s)

1

Fig. 15. Comparison of the experimental and theoretical boundaries.

Additionally, as shown in Fig. 9(f), the water phase begins to lose its continuity when the oil superficial velocity increases to 0.737 m/s. The primary transition of the flow patterns to DW/O flow is characterized by the signals of probe 5 and 6. Notably, probe 8 indicates a continuous and unstable water layer, certifying that the DW/O flow has not occurred to date.

Additionally, as shown in Fig. 9(d), the oil–water interface is complicated. With further increases in the water flow rate, the continuity of the oil phase will be dispersed by the water vortices appearing at the interface. Furthermore, the turbulent energy tries to distribute the larger oil droplets along the cross-sectional area of the pipe but the upward buoyancy prevails. Thus, a dispersion of oil in water over the water layer, i.e., DO/W&W flow, is developed. The fluctuating signals in Fig. 11 exhibit the flow structure of DO/W&W, notably for the distribution characteristic of the oil droplets as the water flow rate increases. When the water flow rate and the total flow rate are both high, the DO/W flow pattern occurs. From Fig. 12, select pulsed-signals with different amplitudes in low voltage level are noted, indicating that all probes are located in the oil-in-water region. Additionally, the signals shown in Fig. 12(b) indicate an increase in the oil concentration and present a more uniform distribution of smaller oil droplets. The signals shown in Fig. 13 indicate the appearance of the DW/O flow when the oil flow rate and the total flow rate are both high. The DW/O flow shown in Fig. 13(a) has a short-life water film at the bottom of the pipe, most likely evolving from the thin water layer in the ST&MI flow of type IV shown in Fig. 9(f).

Integrated signal

Raw mini probe signal (V)

The DW/O&DO/W flow pattern is known as a co-continuous flow pattern (Lovick and Angeli, 2004a, b). We detected the unstable and alternate transition layer of oil-in-water and water-in-oil between two continuous phases. The results agree with the three-layer flow observed by Angeli and Hewitt (2000). As shown in Fig. 10(a), when the oil and water flow rates are nearly equal, probes 1–3 are located in the water-in-oil region and probes 5–8 are located in the oil-in-water region. The signal from probe 4 indicates an unstable alternation layer of the oil-in-water and water-in-oil regions, which appears at the central part of the pipe. Additionally, the entrainment of the dispersed droplets can also be detected near the fluctuating interface. With the increase in the oil flow rate, as shown in Fig. 10(b), the unstable alternation layer indicated by probe 6 moves down, and the water phase appears as a thin layer at the lower part of the pipe. By contrast, when increasing the water flow rate, as shown in Fig. 10(c), the unstable alternation layer indicated by probe 2 moves up, and the oil phase appears as a thin layer at the upper part of the pipe.

Experimental flow pattern map According to the fluctuating characteristics of the mini-conductance probe signals, we draw an experimental flow Usw=0.737m/s, Uso=0.133m/s, Probe 4

8 6 4 2

Oil droplet touching

0 1

0

Holding time 0.0

0.2

0.4

0.6

Time (s) Fig. 16. Processing of the mini-conductance probe signal.

0.8

1.0

179

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186

Position (mm)

(d)

Position (mm)

(e)

Position (mm)

(f)

10 8 6 4 2 0 -2 -4 -6 -8 -10

10 8 6 4 2 0 -2 -4 -6 -8 -10

10 8 6 4 2 0 -2 -4 -6 -8 -10

10 8 6 4 2 0 -2 -4 -6 -8 -10

Usw = 0.147m/s, Uso = 0.194m/s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Local oil holdup yl ,o

0.8

0.9

1.0

ST&MI

III

IV

I

0.0

0.1

0.2

II

Usw=0.147m/s, Uso=0.236m/s Usw=0.295m/s, Uso=0.553m/s Usw=0.553m/s, Uso=0.295m/s Usw=0.147m/s, Uso=0.553m/s

0.3

0.4

0.5

0.6

0.7

Local oil holdup yl ,o

0.8

0.9

1.0

D W/O&D O/W

Usw = 1.105m/s, Uso = 1.658m/s Usw = 1.105m/s, Uso = 0.553m/s Usw = 0.295m/s, Uso = 0.921m/s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Local oil holdup yl ,o

0.8

0.9

1.0

D O/W&W

Usw = 0.737m/s, Uso = 0.133m/s Usw = 1.105m/s, Uso = 0.133m/s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Local oil holdup y l , o

0.8

0.9

1.0

pattern map for the horizontal oil–water two-phase flows in Fig. 14. The fluid in the pipe is in stratified flow when the total flow rate is low. As the total flow rate increases, the oil–water interface gradually loses its stability. An interfacial wave with drop entrainment appears near the wavy interface, indicating that ST&MI flow occurs. Four types of ST&MI flows are detected by the mini-conductance probes. With increases in the water flow rate, the flow pattern gradually transforms to DO/W flow from ST&MI flow, and the DO/W&W flow is the transitional state. Conversely, with increases in the oil flow rate, the flow pattern gradually transforms to DW/O flow from ST&MI flow. When the flow rates of the oil and water phase simultaneously increase, the flow pattern transforms to DW/O&DO/W flow from ST&MI flow. Furthermore, the flow pattern boundaries shown in Fig. 14 are compared with the prediction of previous physical models. The theoretical boundary between the ST flow and ST&MI flow is predicted by two-fluid model presented by Trallero (1995). The boundaries between the ST&MI flow and the semi-dispersed flows, i.e., DW/O&DO/W, DO/W&W, and the boundaries between the semi-dispersed flows and totally dispersed flows, i.e., DW/O, DO/W, are predicted by the model presented by Torres-Monzón (2006). Additionally, the boundaries between the DW/O and DO/W flows are calculated using the phase inversion model based on the input water holdup presented by Yeh et al. (1964) and the model based on the concepts of continuous and dispersed phases presented by Decarre and Fabre, 1997. In the calculation of the theoretical boundaries, the viscosities of the oil and water phase are set to 12 mPa s and 1 mPa s, respectively. The densities of the oil and water phases are set to 845 kg/m3 and 1000 kg/m3, respectively. The inner diameter of the pipe is set to 20 mm. Fig. 15 shows the comparison between the experimental boundaries and the theoretical boundaries predicted by the physical models. For the horizontal acrylic pipe with an inner diameter of 20 mm, the two-fluid model proposed by Trallero (1995) exhibits a higher error when predicting the boundary between ST flow and ST&MI flow, indicating that the two-fluid model is limited when considering changes of the pipe inner diameter and the fluid properties. The boundaries predicted by the model of Torres-Monzón (2006) agree with the experimental boundaries. Additionally, the phase inversion models (Yeh et al., 1964; Decarre and Fabre, 1997) show a Time Frequency Representation

50

D O/W

50 1

40

Usw = 1.474m/s, Uso = 0.133m/s Usw = 1.474m/s, Uso = 0.553m/s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Local oil holdup y l , o

0.8

0.9

1.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Local water holdup y l , w

30

0.6 20

0.4

10

Usw = 0.147m/s, Uso = 0.921m/s Usw = 0.147m/s, Uso = 1.253m/s

0.0

0.8

0

D W/O

0.8

Fig. 17. Distribution of the local liquid holdup.

0.2 0

2

4

6

8

10

0.9

1.0

0

2

4

6

30 20 10 0

0

5

A (f)

Time (s) 0.04 0.02 0 -0.02 -0.04

Spectrum

40

Frequency (Hz)

Position (mm)

(c)

10 8 6 4 2 0 -2 -4 -6 -8 -10

ST

Frequency (Hz)

Position (mm)

(b)

10 8 6 4 2 0 -2 -4 -6 -8 -10

Signal (Volt)

Position (mm)

(a)

8

10

Time (s) Fig. 18. Typical AOK TFR of the ST flow (Usw = 0.147 m/s, Uso = 0.133 m/s).

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186

Distribution of the local liquid holdup We calculate the local liquid holdup of the typical flow patterns at the locations of the eight mini-conductance probes. The mini-probe signal is transformed into a square signal using the self-adjusting dual-threshold method (Van Der Welle, 1985). As shown in Fig. 16, each negative pulse indicates the appearance of one oil droplet around the tip of the probe. The holding time of each negative pulse presents the size of the touching oil droplet. The holding time of the ith oil droplet can be denoted as Ti, and the entire time of the recorded signal can be denoted by T. Thus,

Time Frequency Representation

0.8

30

0.6 0.4

20 10 0

0

2

4

6

8

30 20

0

0

2

0

4

6

8

0

2

10

-0.05

2.5 2 1.5 1 0.5

0

0

2

4

6

8

10

0

2

40 30 20

6

Time (s)

Signal (Volt)

4

10

0

0

5

30

2 1.5

20

1

0

10

0.5 0

2

4

10

(b) Usw=0.295 m/s, Uso=0.553 m/s (Type II)

6

Spectrum

50

2.5

8

10

8

10

40 30 20 10 0

0

Time (s)

A (f)

8

8

10

Signal (Volt) 4

6

Time Frequency Representation

50

10

0 2

4

3

0.1

0

2

A (f)

40

Time (s)

-0.1

0

(c) Usw =0.553 m/s, Uso=0.295 m/s (Type III)

Frequency (Hz)

3

Frequency (Hz)

Frequency (Hz)

3.5

10

0

10

0

Spectrum

50

4

20

8

20

Time (s)

Time Frequency Representation

30

6

30

0.05

(a) Usw=0.147 m/s, Uso=0.236 m/s (Type I)

40

4

Spectrum

10

0.2

Time (s)

50

40

Time (s)

-0.02 2

1

0.4

A (f)

0.04 0.02

0

50

0.6

20

0

3

Signal (Volt)

Signal (Volt)

1

1.2

0.8

30

10

Time (s)

-0.04

ð1Þ

40

10

10

Ti

Time Frequency Representation

50

40

0.2

i

T

where n is the number of oil droplets touching the tip of the mini-probe, i.e., the number of the negative pulses. To improve the measurement accuracy, the length of the recorded signal is selected as 10 s. Fig. 17(a) presents the agreement between the distribution of the local liquid holdup and the structure of ST flow pattern, verifying the validity of the extraction of the local liquid holdup based on the mini-conductance probe signals. As shown in Fig. 17(b), four types of concentration distributions of oil and water phases are present in the ST&MI flows. The distribution of the local oil holdup in the ST&MI flow of type III is distinct from the other types, and the distribution quantitatively indicates the large fluctuation in the oil–water interface.

Frequency (Hz)

40

Pn yl;o ¼

Spectrum

50

Frequency (Hz)

Frequency (Hz)

50

the local oil holdup, yl;o , at the location of the probe can be given as the following:

Frequency (Hz)

better prediction for the transition between the DO/W and DW/O flows. Recently, new progress has been reported by Ullmann and Brauner (2006), Tzotzi and Andritsos (2013), Barral and Angeli (2013), Rodriguez and Castro (2014) in the development of a flow-pattern transition model. Our experimental flow pattern map is expected to provide the data required for evaluating these new models.

Frequency (Hz)

180

0.05 0 -0.05 0

2

4

6

Time (s)

(d) Usw=0.147 m/s, Uso=0.553 m/s (Type IV)

Fig. 19. Typical AOK TFR of the ST&MI flow.

5

A (f)

181

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186

Frequency (Hz)

40

2.5

40

1.5 20

1

10 0

0

2

4

6

8

10

Spectrum

30 20 10

0.5

0

0

0

5

Time (s)

0.1

10

A (f)

0 -0.1

0

2

4

6

8

10

Time (s)

(a) Usw =1.105 m/s, Uso =1.658 m/s Time Frequemcy Representation

50

3

2

30

1.5 20

1

10 0

Frequency (Hz)

Frequency (Hz)

50

2.5

40

0.5 0

2

4

6

8

10

0

Spectrum

40 30 20 10 0

0

5

Time (s) 0.1

Signal (Volt)

10

A (f)

0 -0.1

0

2

4

6

8

10

Time (s)

(b) Usw=0.295 m/s, Uso =0.921 m/s Time Frequency Representation

50

40

0.2

40

30

0.15

20

0.1

10

0.05

Frequency (Hz)

0

0

2

4

6

8

Frequency (Hz)

0.25

50

Signal (Volt)

Considering that the Adaptive Optimal Kernel Time–Frequency Representation (AOK TFR) (Jones and Baraniuk, 1995) can effectively suppress the cross term and maintain a high time–frequency resolution, we employ the AOK TFR to characterize the horizontal oil–water two-phase flows as in our previous study (Sun et al., 2011; Du et al., 2012a, 2012b). The ST flow is characterized by the clear oil–water interface and its stable movement. As shown in Fig. 18, only one peak appears in the AOK TFR, whereas the majority of the energy concentrates in 5 Hz. The energy of the ST flow is relatively low because such stable flow usually occurs at low flow rates. Fig. 19 shows the details of the AOK TFR for the ST&MI flows as follows. (1) For the ST&MI flow of type I (Fig. 19(a)), the energy distribution in the AOK TFR is similar to the ST flow because of the low total flow rate. The majority of the energy concentrates in 5 Hz band. However, the frequency distribution has a wider range because of the mixing at the interface, reflecting the movement of the oil and water droplets. (2) For the ST&MI flow of type II (Fig. 19(b)), the energy distribution in the AOK TFR becomes more scattered. The energy concentrates in 5–20 Hz band, reflecting the motions of the oil and water droplets around the interface. (3) For the ST&MI flow of type III (Fig. 19(c)), the frequency distribution in the AOK TFR falls into three frequency bands, i.e., the low frequency band (0–5 Hz), the middle frequency band (5–15 Hz) and the high frequency band (15–20 Hz). The energy concentrates in the middle frequency band, reflecting the fluctuating characteristics of the oil–water interface. The energy in the low frequency band is lower, reflecting the motion of the water layer. The energy in the high frequency band is the lowest, reflecting the motion of the dispersed droplets around the oil–water interface. (4) For the ST&MI flow of type IV (Fig. 19(d)), the energy in the AOK TFR concentrates in the 5–15 Hz band, similar to the energy distribution of Fig. 19(b). This energy distribution represents the motion of the dispersed oil droplets in the continuous water layer with respect to the weak representation of the conductance sensor for the water droplets in the continuous oil phase. Fig. 20 shows the details of the AOK TFR for the DW/O&DO/W flow. (1) When the unstable and alternate transition layer of the

50

2

30

Time–frequency representation Adaptive Optimal Kernel Time–Frequency Representation

3

Frequency (Hz)

Time Frequency Representation

50

Signal (Volt)

Fig. 17(c) shows three typical distributions of oil holdup in DW/O&DO/W flows. The phase distributions of the DW/O&DO/W flows agree with the detailed flow structures tested by the mini-conductance probes. Fig. 17(d) shows that the distribution of the local oil holdup in DO/W&W flows is similar to the ST&MI flow of type III. This result is chiefly caused by the similarity between the intermittent movement of the larger oil droplets in the DO/W&W flow and the large fluctuation of the oil–water interface in the ST&MI flow of type III. Fig. 17(e) exhibits the distribution of the local oil holdup in DO/W flows. The local oil holdup at the center of the pipe is higher than the one near the pipe wall and shows a good symmetry along the pipe line. Fig. 17(f) shows the distribution of the local water holdup in DW/O flows. The symmetry of the phase distribution is worse, and the water holdup at the lower part of the pipe is considerably higher. Generally, under the flow conditions displayed in Fig. 17(e) and (f), the distribution of the dispersed phase is non-uniform. However, with increasing total flow rates, the turbulence of the mixture gradually increases and will produce a homogeneous distribution of dispersed droplets.

30 20 10

10

0 -0.05

0

2

4

6

0

0

2

A (f)

Time (s)

0.05

Spectrum

8

10

Time (s)

(c) Usw =1.105 m/s, Uso =0.553 m/s Fig. 20. Typical AOK TFR of the DW/O&DO/W flow.

4

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186

The dominant frequency and energy of the conductance signal The total energy, E, of the time–frequency representation, Pðt; f Þ, can be defined as the following:

E¼

Z Z

Pðt; f Þds

ð2Þ

s

where S is the plane of the time–frequency representation, t is the time, and f is the frequency.

Time Frequency Representation

50

30

0.015

20

0.01

10

0.005

0

0

2

4

6

8

10

Time (s)

40

Frequency (Hz)

0.02

30 20 10 0

0

0.5

1

A (f)

0.01 0 -0.01

0

2

4

6

8

10

Time (s) Fig. 22. Typical AOK TFR of the DO/W flow (Usw = 1.474 m/s, Uso = 0.133 m/s).

The edge characteristic of the time–frequency representation can be described as follows:

Eedge ¼

Z

Pðt; f Þdt

ð3Þ

T

where T is the length of the conductance signal. When Eedge is at a maximum, the corresponding value of f can be treated as the dominant frequency f d (which is the main frequency component of the time–frequency representation) and can largely represent the basic flow characteristics of the oil–water two-phase flows. Fig. 23 shows the combined distribution of the dominant frequency, f d , and the total energy, E, of the conductance signals for horizontal oil–water two-phase flows. The plane of f d  E can be divided into four zones. All ST flows fall into zone I, in which the dominant frequency is less than 6 Hz and the energy is low because of the small fluctuations of the oil–water interface. The DO/W flows fall into zone IV with a low energy and wide frequency band because of the random motions of oil droplets in the continuous water phase. The ST&MI flows primarily fall into zone II and III with a dominant frequency in the range of 6–32 Hz and a total energy higher than 1000. The flow conditions in zone II display low dominant

40

0.3 0.25

30

0.2

20

0.15 0.1 0.05 0

2

4

6

8

10

Time (s)

Frequency (Hz)

Frequency (Hz)

40

Spectrum

0.35

10

Signal (Volt)

50

Spectrum

40

0

Time Frequency Representation

50

Frequency (Hz)

oil-in-water and water-in-oil flow between the two continuous phases appears at the central part of the pipe (Fig. 20(a)), only one peak in the AOK TFR appears, and the frequency is lower than 10 Hz. The majority of the energy in the AOK TFR concentrates in the low frequency band, and the energy is lower and more scattered. The low energy and high frequency band in the AOK TFR represents the motion of the dispersed oil droplets in the continuous water phase, whereas the high energy and low frequency band represents the wave motion at the oil–water interface. (2) When the unstable alternation layer appears at the lower part of the pipe (Fig. 20(b)), only one peak appears, indicating the lower frequency, whereas the amplitude of the high frequency band is low. The majority of the energy in the AOK TFR concentrates in the low frequency band, reflecting the wave motion at the oil–water interface. By contrast, the energy is much lower in the high frequency when compared to Fig. 20(a) mainly because the motions of the oil droplets in the continuous water phase are not prominent with respect to the thin water layer. (3) When the unstable alternation layer appears at the upper part of the pipe (Fig. 20(c)), no obvious peak appears in the spectrum distribution. Additionally, the amplitudes of the low and high frequency bands are both low. The energy distribution in the AOK TFR is scattered primarily because of the random motions of the dispersed oil droplets in the continuous water phase, indicating the conductance signal tends to display the DO/W flows. For the DO/W&W flow (Fig. 21), the multi-peaks in the AOK TFR fall in the range of 10–20 Hz, reflecting the random motions of the oil droplets at the upper part of the pipe. The DO/W flow occurs when the total flow rate is high (Fig. 22). The frequency distribution in the AOK TFR is much larger with no indication of the obvious peak. Additionally, the energy in the AOK TFR falls in the low frequency band, reflecting the random motions of DO/W flows.

Signal (Volt)

182

30 20 10 0

0

1

2

A (f)

0.02 0 -0.02

0

2

4

6

8

10

Time (s) Fig. 21. Typical AOK TFR of the DO/W&W flow (Usw = 0.737 m/s, Uso = 0.133 m/s).

Fig. 23. Combined distribution characteristics of the dominant frequency fd and the total energy E of the conductance signals.

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186

frequencies and wide total energy distributions in the f d  E plane. In comparison, the ST&MI flows in zone III show higher dominant frequencies, reflecting the motion of the dispersed droplets around the oil–water interface. The DW/O&DO/W flows primarily fall into zone III with wide distributions of dominant frequencies and total energies. When the fluctuation of the oil–water interface is strong (Fig. 20(a)), the dominant frequency in the f d  E plane is lower, but the total energy is higher. When the oil–water interface appears at the upper part of the pipe with the oil droplets widely dispersed in the continuous water phase at the lower part of the pipe (Fig. 20(c)), the DW/O&DO/W flows show similar flow characteristics with DO/W flows, which are characterized by a wide distribution of the dominate frequencies with low total energies in the f d  E plane. DO/W&W flows fall into zone IV with a dominant frequency in the region of 3–32 Hz and a total energy less than 1000. The flow conditions in zone IV presents the time–frequency characteristics of DO/W flows, whereas the flow condition in zone II shows the high total energy because of the intermittent motion of large oil droplets at the upper part of the pipe.

Slippage between oil and water phases Average oil holdup measurement In our early study, mini-conductance probes were employed to measure the liquid holdup of horizontal oil–water two-phase flows. However, the array probes can only provide the average liquid holdup along the central line of the radial section of the pipe. In this study, the QCV technology combined with three PWCPs is used

to measure the water-layer thickness and to calculate the average liquid holdup. We find that the response of the PWCP has a better linearity and sensitivity to the water-layer thickness of a stratified flow (Zhai et al., 2013). In this study, three PWCPs are equidistantly inserted into the flow test section between the upstream and downstream QCVs (Fig. 24). Each PWCP is vertically fixed to the horizontal plane. Once the data collection process is completed for each flow condition, the two QCVs are simultaneously closed. The completed separation of oil and water phases can be reached in a few minutes. Figs. 25 and 26 show the separation of the oil and water phases in a typical ST&MI flow and DW/O&DO/W flow, respectively. The dispersed droplets can still be observed clearly when the QCVs are closed, and the oil and water phases are gradually separated because of gravity. Particularly, the oil–water separation in the DW/O&DO/W flow requires approximately one minute because of the complex flow structure. After the separation of the oil and water phases, the oil holdup, yo , can be obtained in terms of the measured water-layer thickness, h, using the following equation:

n o 8 pffiffiffiffiffiffiffiffiffiffi D=2h > arccos > D=2 > ðD=2hÞ Dhh2 > 1  þ h < D=2 > p > pD2 =4 < yo ¼ 0:5 h ¼ D=2 > n o > > pffiffiffiffiffiffiffiffiffiffi > arccos hD=2 > D=2 > Dhh2 :  ðhD=2Þ h > D=2 p pD2 =4

ð4Þ

Slippage characteristics under different flow patterns Based on the liquid holdup measured using QCV technology, the oil phase velocity, U o , and water phase velocity, U w , can be calculated as follows:

Side view of PWCP

flow

183

QCV

QCV

Closed

Closed

Three PWCPs Fig. 24. The sketch of the setup for measuring the liquid holdup.

Fig. 25. The separation of the typical ST&MI flow (Usw = 0.368 m/s, Uso = 0.195 m/s).

184

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186

Fig. 26. The separation of the typical DW/O&DO/W flow (Usw = 0.553 m/s, Uso = 1.105 m/s).

Uo ¼

U so ; yo

Uw ¼

U sw 1  yo

ð5Þ

Thus, the slippage ratio, S, can be defined as the following:

S¼

U o K o =K w ¼ Uw yo =yw

ð6Þ

where K o and K w represent the oil cut and water cut, respectively. Fig. 27 shows the relationship between the average oil holdup and the oil cut for horizontal oil–water two-phase flows. The differences between the oil holdup and the oil cut occur because of the slippage, and the slippage ratio varies in the range of 1/3–2. Hapanowicz (2008) noted that the slippage ratio in the horizontal oil–water two-phase flow could be either greater or less than 1. To illustrate the relationship between the slippage ratio and the flow structures, the slippage characteristics of different flow patterns are shown in Fig. 28. Even in the identical flow pattern, significant differences are noted in the slippage because of the complicated oil–water interface wave and phase distributions. As shown in Fig. 28(a), when the oil holdup of ST flows is higher than 0.5, the slippage ratio, S, is always less than 1 and increases with increases in the oil holdup. It is considered that a larger wall contact area of the oil phase leads to a larger frictional drag between the pipe wall and the oil phase. Thus, the velocity of the oil phase is lower than that of the water phase in stratified flows. This result agrees with Xu et al. (2008). Moreover, the roughness and wettability of the pipe wall can also affect the slippage (Charles et al., 1961; Alturki et al., 2014). Angeli and Hewitt (2000) concluded that because oil preferentially wets the acrylic surface, the oil phase could remain continuous over a wider range of conditions in the acrylic pipe. In this sense, the preferential

1.0

Qw (m3/day)

S=1/3 S=1/2

0.8

S=1.5 S=2

yo

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

3 4 5 6 8 10 15 20 30 40 50 60

1.0

Ko Fig. 27. The relationship between the average oil holdup and the oil cut.

wetting of the acrylic pipe wall by the oil phase is likely another reason causing the oil phase to move slower than the water phase. For ST&MI flow, the slippage ratio gradually tends to be greater than 1 as the oil holdup increases (Fig. 28(a) and (b)). Xu et al. (2008) and Rodriguez and Oliemans (2006) found the similar slippage characteristics of ST&MI flows. Additionally, when the water flow rate is lower than 8 m3 =day, the slippage ratio is sensitive to variations in the oil holdup. Conversely, when the water flow rate is higher than 8 m3 =day, the slippage ratio is less affected by increases in the oil holdup. In the following section, we demonstrate the relationship between the slippage of the ST&MI flow and its flow structures: (1) When the water flow rate is less than 6 m3 =day (Fig. 14), the ST&MI flow transforms into type IV from type I with increases in the oil holdup. This result indicates that the continuous oil phase at the upper part of the pipe is gradually broken down into droplets that are entrained by the continuous water phase at the lower part of the pipe. Accordingly, the touching area of the oil phase with the pipe wall gradually decreases, producing a higher velocity of the oil phase than the water phase, i.e., the slippage ratio is greater than 1. (2) When the water flow rate ranges from 6 to 15 m3 =day (Fig. 14), the ST&MI flow transforms into type II from type III with increases in the oil holdup. For the ST&MI flow of type III, the strong fluctuation of the oil–water interface frequently causes the collisions between the interface and the pipe wall, decreasing the oil phase velocity. For the ST&MI flow of type II, the number of dispersed droplets around the oil–water interface significantly increases, and the droplets are distributed on both sides of the interface. In this case, the slippage characteristic of the ST&MI flow is similar to the ST flow, and the slippage ratio is less than 1. For DW/O&DO/W flows, the slippage ratios are mostly less than 1 and show an irregular changing tendency with the variations of the water flow rate and the oil holdup because of the instability of the oil–water interface. Lovick and Angeli (2004b) found that the slippage ratio of DW/O&DO/W flows in a stainless ID 38 mm pipe increases with the increase in the oil flow rate, and the slippage ratio will exceed 1 when the oil flow rate is higher. They noted that when the continuous water phase exists as a form of a thin layer with a large wall contact area compared to its volume, the water phase is subjected to a larger frictional drag and moves slower than the oil phase. The differences between the results presented by Lovick and Angeli (2004b) and the results of this study are likely caused by the different pipe materials. Rodriguez et al. (2011) found that different fluid properties and pipe materials could affect the phase distribution across the radial section of the pipe and further affect the slippage characteristics of the two

L.-S. Zhai et al. / International Journal of Multiphase Flow 76 (2015) 168–186 3

Qw (m /day), Flow pattern

(a)

ST ST&MI DW/O

4 4 4

ST ST&MI DW/O

S

1

3 3 3

0.1 0.5

0.6

0.7

0.8

0.9

1.0

yo 3

Qw (m /day), Flow pattern

(b)

S

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

5 5

ST&MI DW/O

6 6 6

ST&MI DW/O&DO/W DW/O

8 8 8

ST&MI DW/O&DO/W DW/O

10 10 10

ST&MI DW/O&DO/W DW/O

15 15 15

ST&MI DW/O&DO/W DW/O

yo 3

Qw (m /day), Flow pattern

(c)

DO/W&W ST&MI DW/O&DO/W

30 30

DO/W&W DW/O&DO/W

phenomenon. In this regard, the explanation of the relative motion of oil and water phases based only on the pipe wall area wetting by each phase is limited. In DO/W&W flows, the oil droplets of different sizes concentrate at the top of the pipe. The concentration profile of the DO/W&W flow is not flat. Additionally, the complicated motion of the various droplets will produce the non-homogenous velocity profile. We find that the slippage ratio of DO/W&W flows is less than 1 (Fig. 28(c)). However, with increases of the water flow rate, the oil–water two-phase flow tends to be a homogeneous flow. Thus, in DO/W flow, the slippage ratio is close to 1 with respect to the flat velocity and concentration profiles (Fig. 28(d)). In addition, when the water flow rate is 60 m3 =day and the oil holdup is low, the velocity of the oil phase is slightly higher than the water phase. This finding has been verified by Lovick and Angeli (2004b) (Um P 2 m/s, Ko < 0.6, qo = 828 kg/m3, lo = 6 mPa s) and Xu et al. (2008) (Um = 2.55 m/s, qo = 860 kg/m3, lo = 138 mPa s). For DW/O flows, the slippage ratio is less than 1, indicating that the velocity of the water droplets is higher than the continuous oil phase (Fig. 28(a) and (b)). This result is because of the large pipe wetting area of the oil phase with a higher viscosity, producing a large friction drag to reduce the velocity of the oil phase. In this section, we use QCV technology combined with three PWCPs to measure the liquid holdup for 218 different flow conditions and further investigate the slippage characteristics for different flow patterns. The local flow structures indicate significant effects on the slip behaviors between the oil and water phases. Based on the correlation between the slippage characteristics and the detailed flow structures, we conclude that the measurement technology integrating the local phase and velocity distributions is expected to clearly reveal the slip behavior of horizontal oil–water two-phase flows.

Conclusions

S

1

20 20 20

185

0.1 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

yo 3

Qw (m /day), Flow pattern

(d)

DO/W DW/O&DO/W

50 50

DO/W DW/O&DO/W

60 60

DO/W DW/O&DO/W

S

1

40 40

0.1 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

yo Fig. 28. The slippage characteristics of different flow patterns.

phases. In addition, for the DW/O&DO/W flows, a complicated distribution of dispersed droplets occurs in the continuous phases; therefore, the entrainment of the droplets in the continuous phase should be considered in the investigation of the slippage

We detect the detailed local flow structures of horizontal oil– water two-phase flows using mini-conductance probes and subsequently present an experimental flow pattern map with 218 different flow conditions. The fluctuating characteristics of the mini-probe signals can effectively indicate the evolutionary trend of the flow structures as the superficial velocities change. Additionally, we compare the experimental boundaries and theoretical boundaries predicted by several physical models. The results show that the two-fluid model proposed by Trallero (1995) displays a higher error in predicting the boundary from ST to ST&MI flow. The boundaries predicted by the model of Torres-Monzón (2006) agree with our experimental boundaries. In addition, the phase inversion models developed by Yeh et al. (1964), Decarre and Fabre (1997) also achieved better predictions. We measure the liquid holdup using three parallel-wire capacitance probes and further investigate the slip effect of the oil and water phases. The tendency of the slippage ratio to change along with the change of the flow parameters, i.e., oil holdup and the water flow rate, is demonstrated. The results show that the local flow structure has an obvious effect on the slippage characteristics. We suppose that the measurements of the local liquid holdup and local velocity can reveal the local slip behaviors of the horizontal oil–water flows, which is an important field for future research. Moreover, we extract the dominant frequency and the total energy of the conductance signals under various flow patterns using the Adaptive Optimal Kernel Time–Frequency Representation. The results show that ST flows have the lowest dominant frequency and that the DO/W flows have the lowest total energy. The distributions of the other flow patterns in the dominant frequency-total energy plane overlapped, indicating the

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complicated dynamics of horizontal oil–water two-phase flows and produces substantial challenges in identifying the flow patterns in the time–frequency domain analysis. We suggest that a multi-scale nonlinear time series analysis may represent an effective method for solving this issue. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant Nos. 41174109 and 61104148), the Natural Science Foundation of Tianjin, China (Grant No. 14JCQNJC04200), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130032120042) and the National Science and Technology Major Projects (Grant No. 2011ZX05020-006). References Alturki, A.A., Maini, B.B., Gates, I.D., 2014. The effect of wall roughness on two-phase flow in a rough-walled Hele–Shaw cell. J. Petrol. Explor. Product. Technol. 4 (4), 397–426. Al-Wahaibi, T., Angeli, P., 2007. Transition between stratified and non-stratified horizontal oil–water flows. Part I: Stability analysis. Chem. Eng. Sci. 62 (11), 2915–2928. Al-Wahaibi, T., Angeli, P., 2011. Experimental study on interfacial waves in stratified horizontal oil–water flow. Int. J. Multiphase Flow 37, 930–940. Al-Wahaibi, T., Yusuf, N., Al-Wahaibi, Y., Al-Ajmi, A., 2012. Experimental study on the transition between stratified and non-stratified horizontal oil–water flow. Int. J. Multiphase Flow 38, 126–135. Angeli, P., Hewitt, G.F., 1998. Pressure gradient in horizontal liquid–liquid flows. Int. J. Multiphase Flow 24, 1183–1203. Angeli, P., Hewitt, G.F., 2000. Flow structure in horizontal oil–water flow. Int. J. Multiphase Flow 26, 1117–1140. Angeli, P., 2009. Phase inversion in liquid–liquid pipe flows. In: Cheng, Lixin, Mewes, Dieter (Eds.), Advances in Multiphase Flow and Heat Transfer, vol. 2. Bentham Science Publishers. Arirachakaran, S., Oglesby, K.D., Malinowski, M.S., 1989. An analysis of oil–water phenomena in horizontal pipes, SPE Productions Operations Symposium, SPE 18836. Barral, A.H., Angeli, P., 2013. Interfacial characteristics of stratified liquid–liquid flows using a conductance probe. Exp. Fluids 54, 1604. Beretta, A., Ferrari, P., Galbiati, L., Andreini, P.A., 1997. Horizontal oil–water flow in small diameter tubes. Flow patterns. Int. Commun. Heat Mass Transfer 24 (2), 223–229. Brauner, N., 2001. The prediction of dispersed flows boundaries in liquid–liquid and gas–liquid systems. Int. J. Multiphase Flow 27, 885–910. Brauner, N., Ullmann, A., 2002. Modelling of phase inversion phenomenon in twophase pipe flow. Int. J. Multiphase Flow 28, 1177–1204. Cai, J.Y., Li, C., Tang, X.P., Ayello, F., Richter, S., Nesic, S., 2012. Experimental study of water wetting in oil–water two phase flow – horizontal flow of model oil. Chem. Eng. Sci. 73, 334–344. Chakrabarti, D.P., Das, G., Das, P.K., 2006. The transition from water continuous to oil continuous flow pattern. AIChE J. 52 (11), 3668–3678. Charles, M.E., Govier, G.W., Hodgson, G.W., 1961. The horizontal pipeline flow of equal density oil–water mixture. Can. J. Chem. Eng. 39, 27–36. Decarre, S., Fabre, J., 1997. Phase inversion prediction study. J. L’ Inst. Fr. Prtrole 52, 415–424. De Castro, M.S., Pereira, C.C., dos Santos, J.N., Rodriguez, O.M.H., 2012. Geometrical and kinematic properties of interfacial wave in stratified oil–water flow in inclined pipe. Exp. Thermal Fluid Sci. 37, 171–178. Du, M., Jin, N.D., Gao, Z.K., Wang, Z.Y., Zhai, L.S., 2012a. Flow pattern and water holdup measurements of vertical upward oil–water two-phase flow in small diameter pipes. Int. J. Multiphase Flow 41, 91–105. Du, M., Jin, N.D., Gao, Z.K., Sun, B., 2012b. Analysis of total energy and timefrequency entropy of gas–liquid two-phase flow pattern. Chem. Eng. Sci. 82, 144–158. Elseth, G., 2001. An Experimental Study of Oil/Water Flow in Horizontal Pipes. PhD Dissertation, The Norwegian University of Science and Technology. Guzhov, A., Grishin, A.D., Medredev, V.F., Medredeva, O.P., 1973. Emulsion formation during the flow of two immiscible liquids. Neft. Choz. 8, 58–61. Hapanowicz, J., 2008. Slip between the phases in two-phase water–oil flow in horizontal pipe. Int. J. Multiphase Flow 34, 559–566. Hasson, D., Mann, U., Nir, A., 1970. Annular flow of two immiscible liquids. Can. J. Chem. Eng. 48, 514–520. Huang, S.F., Zhang, X.G., Wang, D., Lin, Z.H., 2007. Water holdup measurement in kerosene–water two-phase flows. Meas. Sci. Technol. 18, 3784–3794. Ioannou, K., Nydal, O.J., Angeli, P., 2005. Phase inversion in dispersed liquid–liquid flows. Exp. Thermal Fluid Sci. 29, 331–339.

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