Experiments with a Wire-Mesh Sensor for stratified and dispersed oil-brine pipe flow

Accepted Manuscript Experiments with a Wire-Mesh Sensor for Stratified and Dispersed Oil-Brine Pipe Flow I.H. Rodriguez, H.F. Velasco Peña, A. Bonilla Riaño, R.A.W.M. Henkes, O.M.H. Rodriguez PII: DOI: Reference:

S0301-9322(14)00231-6 http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.11.011 IJMF 2132

To appear in:

International Journal of Multiphase Flow

Received Date: Revised Date: Accepted Date:

26 June 2014 24 November 2014 25 November 2014

Please cite this article as: Rodriguez, I.H., Velasco Peña, H.F., Bonilla Riaño, A., Henkes, R.A.W.M., Rodriguez, O.M.H., Experiments with a Wire-Mesh Sensor for Stratified and Dispersed Oil-Brine Pipe Flow, International Journal of Multiphase Flow (2014), doi: http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.11.011

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EXPERIMENTS WITH A WIRE-MESH SENSOR FOR STRATIFIED AND DISPERSED OILBRINE PIPE FLOW Rodriguez, I. H.a; Velasco Peña, H. F.a,*; Bonilla Riaño, A.b; Henkes, R.A.W.M.c,d; Rodriguez, O. M. H.a a

Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo (USP), Av. Trabalhador São Carlense 400, 13566-570, São Carlos, SP, Brazil b

Department of Petroleum Engineering, University of Campinas (UNICAMP), Cidade Universitaria-B. Geraldo, 13083-970, Campinas, SP, Brazil

c

Department of Process & Energy, Delft University of Technology, , Mekelweg 2, Delft, The Netherlands d

*

Shell Projects & Technology, Grasweg 6, Amsterdam, The Netherlands

Corresponding author. Address: Av. Trabalhador São Carlense 400, 13566-570, São Carlos, SP, Brazil. Tel.: +55 1633738229. E-mail: [email protected]

Abstract Two-phase oil-water flow was studied in a 15 m long horizontal steel pipe, with 8.28 cm internal diameter, using mineral oil (having 830 kg/m3 density and 7.5 mPa s viscosity) and brine (1073 kg/m3 density and of 0.8 mPa s viscosity). Measurements of the holdup and of the cross-sectional phase fraction distribution were obtained for stratified flow and for highly dispersed oil-water flows, applying a capacitive Wire-Mesh Sensor specially designed for that purpose. The applicability of this measurement technique, which uses a circuit for capacitive measurements that is adapted to conductive measurements, where one of the fluids is water with high salinity (mimicking sea water), was assessed. Values for the phase fraction values were derived from the raw data obtained by the WireMesh Sensor using several mixture permittivity models. Two gamma-ray densitometers allowed the accurate measurement of the holdups, which was used to validate the data acquired with the capacitive Wire-Mesh Sensor. The measured time-averaged distribution of the phase fraction over the cross-sectional area was used to investigate the details of the observed two-phase flow patterns, including the interface shape and water height. The experiments were conducted in the multiphase-flow test facility of Shell Global International B.V. in the Netherlands.

Introduction The flow of oil-water mixtures in directional wells and in pipelines and risers is common in oil production. Oil fields (reservoirs) frequently contain large volumes of water, which are produced together with the oil. For conventional oil and gas wells, this water production increases over field life. In order to improve the oil recovery from a reservoir additional water is often injected into the reservoirs to promote oil displacement (so called Enhanced Oil Recovery). In the oil sands industry a large amount of heated water is used to separate heavy oil from the sand. The influence of the water phase on the pressure gradient is of particular importance for the operation of

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the oil field. For example, water can be introduced into the well or pipeline in order to reduce the pressure drop in oil production or transportation (so called core-annular flow method). The interest in oil-water flow started in the middle of the last century (Charles et al., 1961; Russell et al., 1959), who studied the pressure gradient for viscous oil transport in the petroleum industry when introducing water in the pipelines. Several researchers have studied the flow behavior of oil-water dispersions in laminar and turbulent flow (Cengel et al., 1962; Charles et al., 1961; Faruqui and Knudsen, 1962; Pal, 1993; Ward and Knudsen, 1967). Oil-water stratified flow has also been extensively studied since it is the flow pattern that occurs most often in a multiphase pipeline that is (nearly) horizontal. In addition to the oil-water pressure drop, several authors have also investigated phenomena like phase inversion and drag reduction in dispersed flow (Angeli and Hewitt, 1998; Arirachakaran et al., 1989; Ioannou et al., 2005; Lovick and Angeli, 2004; Lum et al., 2006; Nädler and Mewes, 1997; Rodriguez et al., 2012). The holdup (in-situ volume fraction) is also of main interest for the design and operation of pipeline systems and facilities. There are many experimental techniques for measuring the holdup. However, the existing literature covers mainly the application of these techniques to gas-liquid flows. In liquid-liquid flows the phase distribution has been obtained by intrusive electrical methods based on the differences in conductivity or permittivity between the phases. Angeli and Hewitt (2000b) and Angeli and Hewitt (2004) used a high-frequency needle probe to obtain the phase distribution of oil and water over the pipe cross section. Although images of the oil-fraction distribution were generated, they showed only time-averaged data. Huang et al. (2007b), proposed a capacitance probe to measure the water holdup based on the water layer thickness in kerosene-water flow in horizontal pipes. Zhao et al. (2006), applied a dual-sensor conductivity probe to obtain local oil volume-fraction distributions as well as velocity distributions in oil-in-water flows. Images of the flow were generated, though with only limited spatial resolution. Non-intrusive electrical methods are also popular. Zhao et al. (2006) and Li et al. (2005) have applied Electrical Resistance Tomography (ERT) to characterize oil-water flow. Electrical Capacitance Tomography (ECT) has been employed to investigate stratified kerosene-water flow. However, again only images with low spatial resolution were obtained (Hasan and Azzopardi, 2007). Techniques based on gamma-ray and X-ray are also attractive for multiphase flow applications, due to their non-intrusive nature and reliability. So far these techniques (particularly gamma-ray) have been regularly used to investigate gas-liquid flows, but they were rarely applied for liquid-liquid flows. Where the gamma-ray technique has been applied to measure local phase fractions in oil-water flow systems, it shows good spatial resolution, but poor temporal resolution (Elseth, 2001; Kumara et al., 2009; Kumara et al., 2010; Rodriguez and Oliemans, 2006). Oddie et al. (2003) measured the water holdup in two and three-phase flows while comparing three different methods: quick-closing valves, electrical with the conductive probe and nuclear densitometry. The comparison shows that the electrical method is the most popular one, due to its safety, good accuracy, and low costs. The Wire-Mesh Sensor (WMS) is an intrusive electrical method based on capacitive or conductive measurements. So far various studies with a Wire-Mesh Sensor have been carried out in two-phase gas-liquid flows (Hampel et al., 2009; Hernandez Perez et al., 2010; Huang et al., 2007a; Huang et al., 2007b; Pietruske and Prasser, 2007; Prasser et al., 2007; Prasser et al., 1998; Da Silva et al., 2007; Da Silva et al., 2010; Thiele et al., 2009). Only

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few results with this technique exist for liquid-liquid flow (Rodriguez et al., 2011; Rodriguez et al., 2012; Silva et al., 2007; Velasco Peña et al., 2013) and for three-phase flow (Da Silva, 2008b; Da Silva and Hampel, 2009). In some studies comparisons are made between the WMS and other techniques such as gamma-ray or X-ray (Beyer et al., 2010; Bieberle et al., 2009; Bieberle et al., 2010; Manera et al., 2009; Matusiak et al., 2010), Electrical Capacitance Tomography (ECT) (Azzopardi et al., 2010; Matusiak et al., 2010; Szalinski et al., 2010), or the needle probes (Manera et al., 2009). The results indicate that the Wire-Mesh Sensor is also a promising measurement technique for oil-water flow. Recently, de Salve et al. (2012) employed a WMS to characterize the air–water interface in a horizontal pipe flow, studying stratified, slug/plug and annular flow patterns, at ambient conditions. The authors compared the void fraction measured by quick-closing valves (QCVs) with the one by the WMS. They found that the void fraction with WMS shows a higher dispersion in the range of intermittent flow whereas it has a good accuracy when the flow becomes annular. Abdulkadir et al. (2011), applied a WMS in the study of air-silicone oil flow around a 90º bend showing the transition between flow patterns before and after the bend. Strubelj et al. (2010), measured the vapor volume-fraction profile during the transition from stratified flow to slug flow for condensation-induced water hammer experiments. The authors obtained a good agreement between the CFD simulations and the experimental data. Yusoff (2012), studied the transition from dispersed flow to stratified flow in oil-water flow after a sudden expansion. Our literature review shows that most of the studies with wire-mesh sensing are for gas-liquid flow or for low viscosity oil and water flow. In the present work an experimental study on dispersed and stratified oil-water flow has been carried out in a horizontal pipe. The fluids used were oil with moderate viscosity and water with high salinity (mimicking sea water). A capacitive Wire-Mesh Sensor was specially designed and constructed to measure the holdup and phasefraction distribution. Simultaneous accurate readings by two gamma-ray densitometers were used for the validation of the WMS holdup data. In what follows, the Section Experiment describes the experimental set-up, the equipment and instrumentation, the measurement procedures and the test matrix. The Section Results summarizes the experimental measurements for the dispersed and stratified horizontal flow, including the mixture density, holdup and phase distribution. Results for the oil-water interface height in stratified flow are also presented. The Section Conclusions summarizes the main findings.

Experiment Experimental set-up The experiments were performed at the multiphase-flow test facility of Shell Global International B.V. in The Netherlands. The test facility (named the “DONAU Loop”) is suited to measure a wide range of oil-water-gas flow conditions at pressures up to about 12 bars. The facility is shown in Figure 1. The current experiments are for twophase flow using Shell Vitrea 10 oil (887 kg/m3 density and 7.5 mPa s viscosity) and water (brine, with 1075kg/m3 density and 0.8 mPa s viscosity) as test fluids. These fluids flow through a 15 m long stainless steel pipe with 82.8 mm internal diameter. A 1.15 m long transparent Perspex section is used for the flow visualization. Both water and 3

oil are received in the same separator, which is at atmospheric pressure. The separator contains several 45o-oriented coalescence plates to accelerate the separation of the two liquid phases. Because of the difference in density, the two liquids become separated, with the oil in the upper part of the separator and water in the lower part. Each phase is displaced from the separator to the test line through its own series of pumps and pipes (Rheinhutte, RN 50/315B centrifugal pump), using and inline density meters (Schlumberger, Solartron 7835B) and flow meters (Micro Motion, Coriolis elite mass flow meters CMF 50/100/200, with ±0.1% accuracy). The mixing section is a 2 m long pipe section to which the oil and water lines are connected through independent valves (Figure 1a). At the test section (Figure 1b), gauge pressure meters, differential pressure transducers (Rosemount 3051C, with an accuracy of 207 Pa) and temperature meters (Metatemp Pt 100) were part of the reference measurement instrumentation. The pressure drop was measured by the differential pressure transducers with pressure taps located 6.1 m apart. A highspeed video recording camera (Olympus i-3) was used for the flow-pattern identification and gamma-ray densitometry (two density meters Berthold LB 444) was used for the accurate measurement of the in-situ volumetric phase fraction (holdup). At the outlet of the test section, pipes are transporting the mixture back to the separator. Three independent computers were used to conduct the experiments and to collect the measurement data. Two of them were located in the control room and one was next to the test section. A controller based on LabView® allowed for imposing the desired inlet water and oil flow rates, the selection of the appropriate pumps and flow meters and collecting the flow data. The second computer controlled the two gamma densitometers. The third computer, with a controller also based on LabView®, was used to calibrate the Wire-Mesh Sensor and for data acquisition by means of a National Instruments PCI-6224 board. See Rodriguez and Oliemans (2006) for more details on the DONAU flow loop.

Figure 1. Schematic view of the DONAU Loop: (a) Mixing section and separator; (b) Test section and metering equipment: GD = Gamma Densitometer, PT = Pressure Transmitter, TT = Temperature Transmitter, DT = Density Meter, FT = Flow Transmitter.

Wire-Mesh Sensor A Wire-Mesh Sensor is essentially made of two plane arrays of wire electrodes (transmitter and receiver wires) which make an angle of 90o with respect to each other. The prototype used in the experiments was designed and constructed in the Thermal-Fluids Engineering Laboratory, USP, Brazil, and it consisted of a 16 × 16 wire grid (0.2 mm wire diameter). The axial spacing of the wire arrays is 1.4 mm and each wire is 5 mm apart from another one. The sensor was installed downstream of the visualization section (see details of the sensor and installation in Figure 2). The electronics for the wire-mesh were designed to measure the local electrical permittivity at all crossing points. It was accomplished by successively applying a sinusoidal alternating voltage to each of the sender electrodes, at one wire array, and by measuring in parallel the current that goes towards the receiver electrodes, at the other wire array. The non-activated transmitter wires are grounded. This ensures that the electrical field is 4

concentrated around a given crossing point. In this way the measured currents are unambiguously related to the corresponding crossing point. Therefore, the Wire-Mesh Sensor subdivides the cross sectional area of the pipe into a number of subsections and determines the phase present in each subsection independently in a fast multiplexed way. See Da Silva et al. (2007) for more details on the principles of the electronics and on the processing of the wiremesh signals.

(a)

(b)

Figure 2. (a) 16x16 sensor prototype; (b) Sensor installed at the steel pipe in the DONAU flow loop.

Measurement procedures and data handling

Figure 3. Measuring electrical circuit for one crossing point; Cb is added to avoid low frequency noise. Da Silva (2008a), developed the electrical circuit shown in the Figure 3 for dielectric fluids. This is in fact the circuit for the capacitive Wire-Mesh Sensor, but Da Silva (2008a) has shown that it is also suitable to use with conductive fluids. At each crossing point, a complex relative permittivity κ ˆ x exists that can be expressed as

κˆ x = κ x − j

where

κx

σx , ωκ 0

is the relative permittivity of the mixture,

frequency applied to the circuit and

κ 0 =8.854

(1.1)

σx

is the conductivity of the mixture,

ω

is the angular

pF/m is the permittivity of vacuum (free space). The voltage Vx

κˆ x

related to the magnitude of the relative complex permittivity

5

is

Vx = a ⋅ ln ( κˆ x ) + b,

(1.2)

here a and b are constants that depend on geometric factors and on the characteristics of the excitation signal. Note that there is a variation in the measured values at each cross point for the same fluid. Therefore, it is necessary to include an adjustment in the calibration process to compensate for this variation. Due to the nature of our experiments, the adjustment procedure consists of measuring a substance, that covers the entire sensor, with known low permittivity and conductivity values,

and

κL

σL ,

respectively. In this way a reference voltage data set is

obtained which is denoted as VL :

1 Nt

VL (i, j ) =

∑

Nt k =0

Vx (κ L ,σ L , i, j, k ),

(1.3)

This is an average over a time range,
= 0, ..., . Here,  and  are the indices of the crossing point and
is the time index. The procedure is repeated with the sensor covered with another substance, but now with known high permittivity and conductivity,

κH

and

σ H , respectively. This provides another reference voltage data set denoted

as VH :

VH (i, j ) =

1 Nt

∑

Nt k =0

Vx (κ H , σ H , i, j, k ).

(1.4)

Thus, applying Eq. (1.2) to the reference arrays VL and VH , the constants a and b can be calculated for each crossing point as

a ( i, j ) =

2 (VH ( i, j ) − VL ( i, j ) ) 2

2 0

ln(ω κ κ H2 + σ H2 ) − ln(ω 2κ 02κ L2 + σ L2 )

,

(1.5)

  σ2  σ2  VL ( i, j ) ln  κ H2 + 2 H 2  − VH ( i, j ) ln  κ L2 + 2 L 2  ω κ0  ω κ0    . b ( i, j ) = 2 2 2 2 2 2 2 2 ln(ω κ 0 κ H + σ H ) − ln(ω κ 0 κ L + σ L )

The values of the magnitude of the complex relative permittivity for each crossing point, cross section, can be determined by

6

κˆ x

(1.6)

, over the entire

 V (i, j, k ) − b(i, j )  κˆ x (i, j, k ) = exp  x . a(i, j )  

(1.7)

ˆ x , and the Thereafter, the permittivity models from the literature that relate complex relative permittivity, κ local oil phase fraction,

εo ,

are applied. The time-averaged distributions are calculated based on Prasser et al.,

2002, and they are given over the cross section by

1

ε o (i , j ) =

kmax

kmax

∑ε

o

(i, j , k ),

(1.8)

k =1

where k max is the number of instantaneous phase fraction distributions measured. The total oil fraction averaged over the cross section (holdup) is given by 16

16

ε o,T = ∑∑ w(i, j )ε o (i, j ),

(1.9)

i =1 j =1

where w(i, j ) are the weight coefficients reflecting the contribution of the area at the position (i, j ) to the total cross sectional area Asensor (see Figure 4).

Figure 4. Weight coefficients w(i, j ) for averaging the oil volumetric phase fraction in the measuring cross section. The local instantaneous oil fractions were also used to generate time-averaged chordal distributions of the oil fraction over the cross section of the pipe. Vertical and horizontal chordal distributions of the oil fraction were obtained by time averaging the instantaneous phase fractions over each vertical (j) or horizontal (i) line made up of subsequent vertical or horizontal crossing points, respectively, along the entire cross section (Figure 4). It is important to note that the sensor consists of a circular grid, which covers the cross section of the pipe (which has 82.8 mm internal diameter). The grid consists of an array of 16 vertical wires and an array of 16 horizontal wires, such that the instantaneous oil fraction is obtained at each crossing point of the grid. The vertical chordal distribution is obtained by averaging the oil fractions at each crossing point that belongs to a given vertical wire . This procedure was followed for vertical wires 1–16, going from left to right over the cross section of the pipe:

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ε o,V

∑ ( j) =

16 i =1

w(i, j )ε o (i, j )

∑

16

w(i, j ) i =1

.

(1.10)

On the other hand, the horizontal chordal distribution is obtained by averaging the oil fractions at each crossing point that belongs to a given horizontal wire . This procedure was followed for horizontal wires 1–16, going from top to bottom over the cross section of the pipe

ε o, H

∑ (i ) =

16 j =1

w(i, j )ε o (i, j )

∑

16

w(i, j ) j =1

.

(1.11)

Determination of interface height

To determine the height of the interface in stratified flow, ha , we decided to analyze the central horizontal profile, defined as the average of the vertical central wires of the sensor. In our case, this corresponds to the columns j=8 and j=9:

ε o, H ,C (i) =

εo (i,8) + ε o (i,9) 2

.

(1.12)

This profile is fitted to the Generalized Logistic Function. We propose a new criterion to determine ha , based on the inflection point. A detailed explanation of the proposed criterion is shown in the section Interface Height.

Figure 5 shows details of the different coordinate systems used in this work. To obtain the cross sectional images the classical coordinate system from image processing was applied, with the origin at the upper left corner. To analyze the flow parameters the classical coordinate system for fluid flow is applied, with the origin at the left lower corner and normalized by the diameter of the pipe, D. In the latter system the vertical coordinate is identified by h and the position from left to right is identified by d. As an example, the interface height, ha , uses the former coordinate system as reference.

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Figure 5. Coordinate systems used in image processing (i, j ) and in fluid flow ( d D, h D ) . An example of the location of the interface between the two fluids is shown in red, where the interface height ha is located at the central vertical line, i.e.,

ε o , H ,C

(Eq. (1.12)) or d D = 0.5 .

Permittivity models

The measurements with the Wire-Mesh Sensor provide the complex relative permittivity of the mixture at each crossing point. It thus is necessary to have a relation between the permittivity and the phase fraction. This relation is given by the mixture permittivity models, several of which are available in the literature. Nevertheless, most of them are focused on gas-liquid mixtures (Jaworek and Krupa, 2010). A summary of various models can be found in Karkkainen et al. (2000) and Hao (2005). Each model has been designed for a specific configuration of electrodes, with different distributions of the phases (flow patterns). For example, one of the most common models is the Parallel Model, which represents a flow pattern where two immiscible phases form a circuit of virtual capacitors in parallel (Table 1). Most of the models are independent of the knowledge of which one is the continuous phase and which one is the dispersed phase. However, a few models require this specification. This is the case for the Maxwell-Garnett Model and for the Hanai Model defined in Table 1. Another model presented in Table 1 is the Birchak Model, which is a special case of the Power Law Model. One can also see in Table 1 the model of Bruggeman for a dispersed phase with spherical shape bubbles in a three-dimensional space (Bruggeman 2, see Velasco Peña et al., 2013). In our experiments, the water has a very high conductivity. Therefore, the ratio between the magnitude of the complex permittivity of water and the one of oil is high and the permittivity models should be treated as complex

ˆ x is the complex relative permittivity of the mixture (Eq. (1.1)), and κˆ o and numbers (Sihvola, 1999). In Table 1, κ κˆ w are the pure oil and water complex permittivity, respectively, all at 5MHz, which is the measurement frequency. To work with brine (salt water) the circuit had to be modified. The presence of free ions in the salt water causes noise, mainly at low frequencies. To avoid the noise, a capacitor Cb was placed between the WMS and the receiver circuit (see Figure 3). This capacitor is strong enough to absorb the low frequency noise and to provide the measurement frequency, without affecting the validity of Eq. (1.2). Table 1. Various models used to relate the local oil phase fraction and the measured local permittivity.

Model

Formula

Parallel

εo =

9

κˆ w − κˆ x κˆ w − κˆ o

( κˆ w − κˆ x )( 2κˆ w − κˆ o ) ( κˆ w − κˆ o )( 2κˆ w − κˆ x ) 1/3 κˆ o − κˆ x )  κˆ w  ( εo = 1− ( κˆ o − κˆ w )  κˆ x  εo =

Maxwell – Garnett o/w

Hanai o/w

Birchak

ˆ 1/2 κˆ 1/2 x − κw ε o = 1/2 1/2 κˆ o − κˆ w

Bruggeman 2 (to spherical inclusions)

εo =

( 3κˆ

x

+ κˆ o )( κˆ x − κˆ w )

3κˆ x ( κˆ o − κˆ w )

It is important to note that the current study uses sea water with 9% salinity (1100 kg/m3) with a conductivity that varies between 1.93×104 and 2.06×104 µS/cm at 37 ºC and 41 ºC, respectively. These values were calculated with the Poisson equation (Poisson, 1980) and they were corrected for the temperature dependence using the temperature factor as given in Richards (1954). The value of the oil conductivity was assumed to be zero and the values of relative permittivity of oil and water are 3 and 79, respectively. Thus, the value of complex relative permittivity for oil is

κˆ o =3-j0 and for water the value is κˆ w =79-j6.579x103 and κˆ w =79-j7.4059x103, at 37 ºC and

41 ºC, respectively. Note that the measured voltages Vx (Eq. (1.2)) are a function of the complex permittivity of the fluids. Figure 6 shows the oil holdup, determined by various models, as a function of the magnitude of the complex relative permittivity, using water at 41 ºC. The figure shows a large difference in the phase fraction depending on the model used. This is explained by the high difference between the conductivity values (imaginary part) of the fluids. The figure shows that for the Parallel Model the relation is dominated by the conductivity of the water (imaginary part), showing a linear relation. A detailed analysis would reveal that the relative permittivity (real part) dominates the Parallel Model only for oil phase-fraction values higher than 0.999. For the Serial Model, the oil relative permittivity dominates the magnitude of the effective relative complex permittivity for oil phase-fraction values lower than 0.1. On the other hand, when the oil phase fraction is lower than 0.1 the water relative permittivity dominates the magnitude. In a subsequent section, the best model is chosen by means of comparison between the oil holdup obtained with the wire-mesh measurements,

ε o ,T (WM ) , and by the gamma-ray densitometer, ε o ,T (exp ) and

also by a qualitative analyses of the cross-sectional phase distribution. The local water phase fraction is obtained as

ε w = 1− ε o .

Figure 6. Relation between the local oil phase fraction and the relative permittivity according to various permittivity models,

κˆ o =3-j0 and κˆ w =79-j7.4059x103, at 41 oC.

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To obtain a better visualization and interpretation of the results, the 16×16 images of a bilinear interpolation algorithm to a 32×32 matrix,

εo

were upgraded with

ε o ,us . The pixels in the corners were calculated as the average

of the two nearest pixels in the useful area of the sensor, namely inside the area with radius R sensor (Figure 4). The color map used to show the images is the typical Jet, with values between 0 and 100, indicates the oil percentage.

Test matrix The main goal of the current experimental work was to study the dispersed and stratified oil-water flow patterns in a horizontal pipe. About 50 measurement points were obtained for dispersed flow; here a measurement point means a pair of oil and water superficial velocities or flow rates. The covered ranges of water and oil superficial velocities are 1.8-2.5 m/s and 0.02-1.1 m/s, respectively. The mixture velocities varied from 1.8 m/s to 2.9 m/s. The measured average temperatures at which the physical properties of the fluids (density and viscosity) were measured were 38.9 oC for oil and 39.2 oC for water. Twenty measurement points were obtained for stratified flow. The ranges of oil and water superficial velocities covered for stratified flow were 0.02-0.1 m/s and 0.05-0.08 m/s, respectively. The data were collected at two different stages. The average working temperature of the first set of measurements was 32oC and 34oC for oil and water, respectively. During the second stage of the measurement the average temperature was 37oC and 41oC for oil and water, respectively.

Experimental results

Mixture density The gamma-ray densitometer measures the gamma ray absorption of the mixture and allows to obtain the mean density of the mixture in the pipe. Two gamma densitometers were installed in the last section of the pipe. The Wire-Mesh Sensor and the visualization section were located in between the gamma densitometers. The readings of the gamma densitometers were compared and these were also used to verify whether fully developed two-phase flow has been established. The devices were mounted on the pipe at an angle of 45o with the vertical diameter, to obtain the best sampling. The pipe was first filled with water and the data were gathered for 5 minutes giving the typical count rates. Thereafter the pipe was filled with oil and the calibration procedure was repeated. With these count rates, the measured density of a pure fluid in the path of the gamma ray can be estimated. The on-line mean density of the mixture,

ρ m ,exp , is determined from the gamma densitometer count and from the calibration.

If a homogeneous flow is considered, which is the case for the dispersed flow studied, assuming no slip between the phases, (see Wallis, 1969), then the mixture density,

11

ρ m, hom , is given by:

(1.13)

ρ m ,hom = ρ wCw + (1 − Cw ) ρ o with

Cw =

where

U ws , U ws + U os

(1.14)

U ws and Uos denote the water and oil superficial velocities, respectively. Since the dispersed flow in our

experiments was created with high mixture velocities, the Homogeneous Model can be used to obtain the mixture density. Figure 7 compares the mixture density measured by the gamma-ray densitometer, density obtained by the Homogeneous Model,

ρ m ,exp , with the mixture

ρ m, hom (Eq. (1.13)). There is good agreement between the two

densities, with less than 0.6% deviation. The dashed lines indicate the maximum deviation (spreading) while the solid line indicates a perfect agreement. The slip ratio was calculated from the holdup results obtained with gamma-ray densitometry, while using the oil and water cuts. In all cases the slip ratio (Vo/Vw, where V stands for in-situ phase velocity) was found to be larger than 1, which indicates that oil was flowing faster than water, i.e., the water phase has accumulated in the pipe. Therefore, the in-situ holdup of the water phase was always larger than the water cut (Eq. (1.14)). This explains the underestimation of the mixture density by the Homogeneous Model (Figure 7). Values of the slip ratio above 1 for oil-water dispersed flow at high mixture velocities have also been reported previously (Angeli, 1996; Rodriguez et al., 2011). A mechanism to explain this has been proposed (Rodriguez et al., 2012), namely the presence of a thin laminar water film between the pipe wall and the core mixture of oil and water.

Figure 7. Comparison between the gamma-ray mixture density,

ρ m ,exp , and the homogeneous mixture density,

ρ m, hom , for dispersed oil-water flow. Holdup The water holdup,

ε w,T , in fully dispersed flow can be found as: ε w,T =

ρm,exp − ρo , ρw − ρo

(1.15)

12

Where

ρ m ,exp is the mixture density given by the gamma ray densitometer, and ρo and ρw are the densities of the

oil and water, respectively. The oil holdup is obtained as

ε o,T = 1− ε w,T .

Here it is assumed that the time and

space-averaged mixture density supplied by the gamma densitometer is a local quantity for the steady-state conditions studied. A geometrical correction must be introduced to account for the distribution of the phases along the cross section of the pipe for stratified flow (Oddie et al., 2003). Thus, the water holdup for stratified flow,

ε w,T ( strat ) , is given by ε w,T ( strat ) =

1

{ cos ( 1− 2ε ) − ( 1− 2ε ) sin cos ( 1− 2ε ) }. π −1

−1

w,T

w,T

w,T

(1.16)

The holdup data obtained from the gamma-ray densitometry are compared with predictions by the Two-Fluid Models for stratified flow and by the Homogeneous Model for dispersed flow. The following average relative error (ARE) is considered:

N

∑ ARE = 100

where

εw,T (hom)

respectively,

and

ε w,T( 2 f )

εw,T(WM )

1

 ( ε w,T (2 f ) , ε w,T ( hom ) , ε w,T (WM ) ) − ε w,T   ε w,T  N

   

2

[%],

(1.17)

denote the water fractions predicted by the homogeneous and Two-Fluid Models,

is the water holdup obtained from the wire-mesh measurements and

ε w,T

is the water

holdup obtained from the gamma-ray densitometer. N is the number of experiments carried out. Figure 8 shows the comparison between the water holdup from the gamma densitometer measurements, and the water holdup obtained by the Homogeneous Model,

εw,T (hom)

ε w,T ,

for the dispersed flow pattern. The water

holdup predicted by the Homogeneous Model shows a deviation of about -4.5% compared to the gamma densitometry value, and the average relative error is 2.36%. The dashed line denotes the deviation, while the solid line denotes the perfect agreement. The values predicted by the model are always below the values obtained experimentally, which shows the presence of slip between the phases, with oil flowing faster than water. As mentioned previously, if oil is flowing faster than water, the water phase will accumulate in the pipe. Therefore, the water holdup will be higher than the water fraction predicted by the Homogeneous Model, as observed in Figure 8.

13

Figure 8. Water holdup according to the Homogeneous Model against the water holdup obtained from gamma-ray densitometry for dispersed flow. The steady-state one-dimensional Two-Fluid Model is commonly used for predicting the pressure drop and holdup in stratified flow. Considering a wavy-stratified liquid–liquid flow in a horizontal or slightly inclined pipe, neglecting droplet entrainment and after eliminating the pressure gradient from the equations of each phase, the following single equation is obtained:

−

where

θ

τx

 1 1  ± τ i Si  +  − ( ρ w − ρo ) g sin θ = 0, Ao  Aw Ao 

τ w S w τ o So Aw

+

denotes the shear stress, S x the wetted perimeter, Ax the cross sectional area,

(1.18)

ρx

the density and

the inclination angle from the horizontal. The holdup is obtained from Eq. (1.18) using a standard numerical

method with the shear stresses expressed through common correlations for the friction factors. Additional geometric relations are used for calculating the variables, Ao , Aw , S o , S w and Si as a function of the holdups. The water holdups obtained by the gamma densitometer are compared with predictions of three different TwoFluid Models. The Two-Fluid Model developed by Trallero (1995), for stratified oil-water flow, flat cross-sectional interface and without interfacial waves, was implemented using the closure relation for the interface shear stress proposed in Rodriguez and Oliemans (2006) and the wall friction factors according to Churchill (1977). The equivalent hydraulic diameters from Brauner and Moalem Maron (1992a; b) were used. The Trallero Model showed a reasonably good agreement with the measurement data, with an average relative error of 17%. The model recently proposed by Rodriguez and Baldani (2012), for stratified oil-water flow, using the curved cross-sectional interface and with interfacial waves, was also tested. The model gives a good agreement between holdup predictions and measurements, with an average relative error of 7%. The Two-Fluid Model of Taitel and Dukler (1976), for stratified gas-liquid flow, flat cross-sectional interface and without interfacial waves, was also applied to predict the water holdup, giving an average relative error of 44%. As shown in Table 2, the Two-Fluid Model of Rodriguez and Baldani (2012) provides the best agreement with the present measurements of the water holdup. A direct comparison between the water holdup measurements and predictions of Rodriguez and Baldani (2012) is shown in Figure 9. Table 2. Comparison of measured (Gamma densitometer) and predicted water holdups.

Two-Fluid Model Taitel and Dukler (1976)

14

ARE (%)

Dev (%)

44

-60

Trallero (1995)

17

-30

Rodriguez and Baldani (2012)

7

±15

Figure 9. Comparison between the water holdup obtained with gamma-ray densitometry and calculated by the TwoFluid Model of Rodriguez and Baldani (2012).

Wire-mesh holdup To find the relation between the relative permittivity of the mixture as measured by the Wire Mesh Sensor and the local-instantaneous water fraction at each crossing point of the sensor, it is necessary to apply models from the literature. Different models for estimating the permittivity of mixtures are found in the literature; each model has been designed for a specific configuration of electrodes and for different distribution of the phases (flow patterns) (Hao, 2005; Karkkainen et al., 2000). In order to select the best permittivity model, a total of twelve models from the literature were tested: Bruggeman (three versions), Series, Parallel, Birchak, Looyenga, Logarithmic, Maxwell (two versions) and Hanai (two versions). All these models are described by Velasco Peña et al. (2013). The water holdups calculated with the twelve different permittivity models were compared to the water holdup obtained by the gamma-densitometry measurements. The Parallel Model gives the best prediction of the water holdup for dispersed flow. The average relative error (ARE) is 13.40% (Figure 10). However, for stratified flow the Bruggeman 2 Model gives the best prediction for the water holdup, with an ARE of 8.05% (Figure 10).

Figure 10. Water holdup measured by the Wire-Mesh Sensor compared to value measured by the gamma densitometry for dispersed and stratified flows. The Parallel Model was used to Dispersed flow and Bruggeman 2 to Stratified flow. The present relative errors are larger in comparison with the ARE found in previous studies in which a flow of a mixture of tap water and oil was studied (Rodriguez et al., 2011; Rodriguez et al., 2012; Da Silva et al., 2011). However, it should be noted that in the current study it was used a complex permittivity model to obtain the water holdup and it used brine instead of tap water (where the brine has a very high conductivity). The higher noise level caused by the presence of free ions in the salt water leads to changes of the capacitive circuit of Wire-Mesh Sensor circuit proposed by Da Silva et al. (2010) (Figure 3). Nevertheless, the observed trend and level of the error are similar to those found when applying wire-mesh sensing in liquid-liquid flow. Therefore, considering the complexity of the current experiments (i.e. with two different liquid-liquid flow patterns, several mixture velocities

15

and water cuts in a rather large steel pipe) and the improvement of the wire-mesh circuit for the chosen fluids (one of them representing sea water), the results are encouraging.

Phase distribution The values for the two-dimensional local instantaneous oil fraction, as measured by the wire-mesh sensor over the cross section, can be used to determine the oil fraction integrated over different domains, thus obtaining time and/or spatially averaged values for the phase fraction (details are given in Prasser et al. (2002)). A time-averaged oil fraction for each crossing point over the cross section of the pipe was obtained via the Wire-Mesh Sensor. The Parallel Model gives a better agreement with the visual inspection made during the experiments, for both the dispersed and stratified flows. The model of Bruggeman 2 has low resolution for water fractions between 0 and 0.3 (Figure 6), generating noise in oil areas. For this reason, the model of Bruggeman 2 was not used to visualize the stratified flows. Figure 11 presents the cross-sectional phase distribution for three typical dispersed-flow conditions: Uws = 2.3 m/s, Uos = 0.1 m/s, Uws = 2.3 m/s, Uos = 0.4 m/s and Uws = 2.0 m/s, Uos = 0.9 m/s. It is important to note that the mixture Reynolds number for all these flow conditions was in the range from 106 to 108. The Reynolds number ( Rem = ρ mU m D / µm ) was defined by using the Homogeneous Model, where

ρm

and U m are the

(homogeneous) mixture density and superficial velocity, respectively, and D is the internal diameter of the pipe. The effective viscosity of the mixture,

µm ,

was estimated by using the measured pressure gradients as described in

Rodriguez et al. (2012). The images indicate a phase distribution that is practically uniform, which is expected for these high mixture flow rates. However, an increase of the oil fraction from 5% to 31% is detected (see Figure 11a to c), which marks a slight accumulation of oil in the upper middle part of the pipe. Similar cross-sectional phase distributions for oilwater dispersed flow have been observed in previous studies at high flow rates (Da Silva et al., 2011; Rodriguez et al., 2012). These previous studies were carried out in glass and acrylic pipes using viscous oil and tap water. The trend of accumulation of oil in the center of the pipe has been reported in those studies and is observed again in the present results (Figure 11).

16

(a) Co=0.05

(b) Co=0.15

(c) Co=0.31

Oil fraction (%) Figure 11. Cross-sectional oil fraction distribution obtained by the Wire-Mesh Sensor for dispersed oil-brine flow: (a) Uws = 2.3 m/s, Uos = 0.1 m/s; (b) Uws = 2.3 m/s, Uos = 0.4 m/s and (d) Uws = 2.0 m/s, Uos = 0.9 m/s. Figure 12 shows the horizontal and vertical chordal oil-fraction distributions and the time-averaged crosssectional oil fraction distribution for two typical dispersed flow conditions: Uws=2.3 m/s, Uos=0.1 m/s and Uws=1.9 m/s, Uos=0.8 m/s, with input oil fractions of 5% and 30%, respectively. The chordal distributions are presented as functions of the distance normalized by the internal diameter of the pipe (going from 0 at the bottom to 1 at the top of the pipe). At these low oil fractions and high mixture velocities the distribution of phases is expected to be quite uniform over the cross section. The chordal and time-averaged distributions of the oil fraction show the expected behavior, i.e. the dominance of water along the cross-sectional area. However, decreasing the water superficial velocity (i.e. decreasing the watercut) gives a larger amount of oil in the upper middle part of the pipe with the occurrence of a smooth peak in the oil fraction (Figure 12b).

Horizontal Chordal Oil Fraction Distribution 1

Cross-sectional Image

Vertical Chordal Oil Fraction Distribution 1 0.8 Oil Fraction

(a)

h/D [.]

0.8 0.6 0.4 0.2 0

0.6 0.4 0.2

0

0.5 Oil Fraction

0

1

0

0.5 d /D [.]

17

1

Horizontal Chordal Oil Fraction Distribution 1

Cross-sectional Image

Vertical Chordal Oil Fraction Distribution 1 0.8 Oil Fraction

(b)

h/D [.]

0.8 0.6 0.4 0.2 0

0.6 0.4 0.2

0

0.5 Oil Fraction

0

1

0

0.5

1

d /D [.]

Figure 12. Chordal and cross-sectional distributions of the oil fraction obtained by the Wire-Mesh Sensor (a) Uws=2.3 m/s, Uos=0.1 m/s; (b) Uws=1.9 m/s, Uos=0.8 m/s, dispersed flow.

Figure 13 shows the time-averaged cross-sectional distributions of the oil fraction for stratified flow. Five selected images show different flow conditions. The water superficial velocity is kept constant at 0.06 m/s while the oil superficial velocity varies from 0.02 to 0.1 m/s. The oil-input-fraction values are 25%, 41%, 43%, 54% and 64%, respectively, for these flow conditions (Figure 13). The interface for the lowest oil cut case is almost fully flat everywhere except near the pipe wall where it is slightly curved upwards (concave interface shape). The case in which the cross section is almost equally occupied with oil and brine (Figure 13b) shows a rather flat interface everywhere. The cross-sectional area is dominated by oil in the next three cases (Figure 13c, d and e): the interface is curved downwards near the pipe wall (convex interface shape). The analysis of interface shape suggests that the stainless steel pipe exhibits an oilphilic-hydrophobic characteristic. The pipe would be preferentially wetted by oil, increasing the wall contact area of oil and influencing the shape of the interface. The interface shape depends on the holdup, contact angle and Eötvös number. At high Eötvös numbers the interface would tend to be flat (Ng et al., 2001; Ng et al., 2002; Rodriguez and Baldani, 2012). However, in the present study (Eötvös number of 161) a rather curved interface was observed, especially near the pipe wall.

(a) Uos=0.02 m/s

(b) Uos=0.04 m/s

18

(c) Uos=0.05 m/s

(d) Uos=0.07 m/s

(e) Uos=0.1 m/s

Oil fraction (%) Figure 13. Distribution of the cross-sectional oil fraction obtained by the Wire-Mesh Sensor at Uws=0.06 m/s and for different oil superficial velocities (stratified flow). The chordal distributions were obtained in stratified oil-brine flow in order to corroborate the existence and shape of the interface. Figure 14 shows a comparison between the time-averaged distributions of the chordal (horizontal and vertical) and cross-sectional oil fraction for three different experimental flow rates: Uws=0.06 m/s and Uos=0.1 m/s, Uws=0.06 m/s and Uos=0.07 m/s, Uws=0.06 m/s and Uos=0.02 m/s. The local oil volume fraction should be zero in the oil phase and one in the water phase. At the interface the fraction should be somewhere in between 0 and 1. The horizontal chordal distribution (going from the top to the bottom over the cross section of the pipe) shows that the oil volume fraction is close to 1 at the upper part of the pipe, which indicates the predominance of oil, and that it tends to zero at the bottom of the pipe, as expected because of the predominant water phase. The oil volume fraction is about 0.5 at the interface. It is remarkable that the value of the oil fraction at the top of the pipe did not reach 1. Similar results were also found by de Salve et al. (2012) and Yusoff (2012) using wire-mesh sensing, without any explanation. In the current study this might be due to some residue of salt accumulated at the boundaries of the sensor. This accumulation could affect the measurements of the complex relative permittivity. A second possible reason is that the circuit is more sensitive at low voltages (Velasco Peña et al., 2013), which corresponds to the oil phase. Furthermore, the noise produced by the salt water may have also influenced the measurements. Finally, the accuracy near the pipe wall at the top and bottom is worse than in other regions because of the weight coefficients w(i , j ) corresponding to the peripheral crossing points. A similar trend was observed by Elseth (2001) applying a single-beam gamma densitometer. It should also be noted that there is an upward displacement of the interface with decreasing oil cut in the horizontal chordal distributions (see Figure 14). In Figure 14a and b the distribution of the vertical chordal oil fraction begins with a large amount of oil at the left side of the pipe. The oil fraction decreases towards the center of the pipe, which indicates a more significant presence of water. After the center of the pipe the oil fraction begins to increase again. A different behavior is observed for the conditions in Figure 14c: here the vertical chordal

19

distribution begins with a lower amount of oil; it increases in the middle of the section and then decreases again. This is according to the concave interface observed in the cross sectional image.

Horizontal Chordal Oil Fraction Distribution 1

Cross-sectional Image

Vertical Chordal Oil Fraction Distribution 1 0.8 Oil Fraction

(a)

h /D [.]

0.8 0.6 0.4 0.2 0.5 Oil Fraction

0

1

Cross-sectional Image

Oil Fraction

h/D [.]

0.4 0.2

0.6 0.4 0.2

0

0.5 Oil Fraction

0

1

0

0.5

1

d/D [.]

Horizontal Chordal Oil Fraction Distribution

Cross-sectional Image

1

Vertical Chordal Oil Fraction Distribution 1 0.8 Oil Fraction

0.8 h /D [.]

1

0.8

0.6

0.6 0.4

0.6 0.4 0.2

0.2 0

0.5

Vertical Chordal Oil Fraction Distribution 1

0.8

(c)

0

d /D [.]

Horizontal Chordal Oil Fraction Distribution 1

0

0.4 0.2

0 0

(b)

0.6

0

0.5

0

1

Oil Fraction

0

0.5

1

d/D [.]

Figure 14. Distributions of the chordal and cross-sectional oil-fraction obtained by the wire-mesh sensor: (a) Uws=0.06 m/s, Uos=0.1 m/s; (b) Uws=0.06 m/s, Uos=0.07 m/s; (c) Uws=0.06 m/s, Uos=0.02 m/s, stratified flow.

Interface height

In various studies the interface height, ha , in stratified flow has been measured by optical methods, such as in de Castro et al. (2012) and Höhne and Vallée (2010). Elseth (2001) applied a gamma densitometer to obtain the profiles of the local phase fraction and provided a qualitative estimation of the interface position and thickness based 20

on his measurements. Kumara et al. (2009) and Kumara et al. (2010) also applied gamma densitometry and the local water volume fraction equal to 0.5 was used as a criterion to locate the interface height. In some other studies the wire-mesh technique has been applied to measure the interface height. de Salve et al. (2012) employed a conductive wire-mesh sensor to measure the interface between air and water. They used only the horizontal profile of a central vertical wire to define the interface height. Yusoff (2012) applied a capacitive WMS to obtain the interface height. However, the author did not explain how it was calculated. In the present study a method based on fitting the

ε o , H ,C

horizontal profile of a central vertical wire

to the Generalized Logistic Function or Richard’s Curve is

proposed

ε f (h) = A +

K 1 + v ⋅ e − B ( h − ha )

(

1/ v

)

(1.19)

,

where A is the lower asymptote (which is the lower value of the horizontal profile), K is the upper asymptote (which is the upper value of the horizontal profile), B is the growth rate; and

v

is a parameter that affects the

symmetrical slope (i.e., how the function reaches the lower and upper asymptotes). The interface height, ha , corresponds to the point of maximum growth, i.e. where

dε f /dh reaches its maximum value or inflection point.

The fitting procedure must find the variables v , B and ha with the conditions v > 0 , B > 0 and

0 < ha < 1 . The

procedure was implemented in Matlab using the Non-linear Least Squares iterative method, in which the initial value of ha was estimated by the Sobel Method (Jähne, 2005). An example is shown in Figure 15. Despite the relatively high ARE for the oil holdup, the obtained interface height is in fair agreement with the original measurement data. The permittivity model used to calculate the interface height was the Parallel Model.

Figure 15. Fitting of the curve to obtain the interface for the flow conditions: Uws=0.06 m/s and Uos=0.07 m/s. Table 3 gives the comparison between the interface height measured with the Wire-Mesh Sensor and predicted by the Two-Fluid Models of Taitel and Dukler (1976), Trallero (1995) and Rodriguez and Baldani (2012). The wiremesh results show the best agreement with the prediction of the model of Trallero (1995), which was developed for stratified oil-water flow, with a flat cross-sectional interface and without interfacial waves. The stratified flow generated in the experiments reveals a mostly flat interface; which was verified by visual inspection. On the other hand, the model of Rodriguez and Baldani (2012), for stratified oil-water flow, curved cross-sectional interface and with interfacial waves, gives the best prediction for the water holdup (Table 2). Although the interface was apparently mostly flat, it has a significant curvature near the pipe wall (Figures 13 and 14). It seems that the inclusion of the curvature of the interface in the model gives a more consistent and reliable prediction of the water holdup. 21

Table 3 Comparison of experimental interface height obtained by the wire-mesh sensor with predictions of Two-Fluid Models available in the literature.

Two-Fluid Model

ARE (%)

Dev (%)

Taitel & Dukler (1976)

26

60

Trallero (1995)

10

+10/-20

Rodriguez and Baldani (2012)

18

-30

Conclusions Dispersed and stratified oil–water flow patterns were studied experimentally, using gamma densitometry and a Wire-Mesh Sensor (WMS). The water and oil holdups, and the chordal and cross-sectional phase distributions were measured in a horizontal pipe with 82.8 mm internal diameter, using mineral oil and brine at mixture velocities between 0.07 and 2.9 m/s. The water holdups obtained with gamma densitometry were compared with predictions obtained with the Homogeneous Model for dispersed flow and with three different Two-Fluid Models for stratified flow. A Wire-Mesh Sensor was designed, constructed and applied to measure oil-brine pipe flow, which provided holdups, phase distributions along the pipe cross section and the interface height. The technique developed to capacitive measurements was adapted to conductive measurements. In order to select the best permittivity model for the local instantaneous phase fractions a total of twelve permittivity models from the literature were tested. The following conclusions can be drawn from the measurements: 1- The Parallel Model, used to relate the local phase fraction to the measured local permittivity, gives the best experimental results for the representation of the cross-sectional phase fraction and for the interface height in stratified flow. The accuracy of the WMS data could be assessed by comparison with calibrated results from the gamma densitometer. For the holdup in both dispersed and stratified flow patterns relatively large errors are observed in the WMS data. The errors for dispersed flow are larger than those reported in other studies with traditional conductive WMS. However, the experiments carried out in the current work have a high level of complexity, such as the type of test fluids (one of them representing sea water), two different flow patterns, large steel pipe, various flow conditions and the modification of the electronic circuit. 2- The measurements with the Wire-Mesh Sensor also allowed the detection of the oil-water interface height in stratified flow. The experimental results show the best agreement with the predictions from the Trallero model developed for stratified oil-water flow, with a flat cross-sectional interface and without interfacial waves, which is consistent with the observed mostly flat interface in our stratified flow experiments.

22

3- The Two-Fluid Model of Rodriguez and Baldani (2012), which includes the effects of a curved crosssectional interface and interfacial waves, gives the best holdup prediction in stratified flow with an accuracy of 7%. Despite the apparently flat interface, a significant curvature near the pipe wall was noticed in the phase distributions obtained with the WMS. This suggests that the modeling of the curvature of the interface may have a large influence on the holdup prediction in liquid-liquid stratified flow. On the other hand, the accuracy of the Homogeneous Model in predicting the water holdup in dispersed flow was -4.5%. The Homogeneous Model systematically underestimated the water holdup measurements. This is explained by the slip ratio values in the experiments that were always above 1, which shows the relative accumulation of water in the pipe. 4- A rather curved cross-sectional interface is found for stratified oil-water flow in a large diameter pipe and for a high Eötvös number. Depending on the oil and water flow rates and the oil phase fraction, a different interface curvature is observed, with either a concave or convex shape. The application of WMS technology in liquid-liquid flow measurements is clearly an interesting field for further investigation. Because of the complexity of phenomena that appear in two phase liquid-liquid flows the application of this technology in flows involving oil and water is still a research challenge. For example, there is a relation between the flow pattern and the accuracy of the water fraction measurement. Some of these measurement errors can be associated to the sensor configuration, which allowed for the accumulation of residue on the walls of the sensor. A more detailed study of the circuit adaptation presented in this work is necessary to better understand the applicability of wire-mesh sensors for obtaining flow parameters in oil-water flows. Nevertheless, the obtained results form a step forward in applying WMS to complex liquid-liquid flow measurements.

Acknowledgments The authors are grateful to FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo, proc. 2010/08688-3), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, proc. 00011/07-0), and CNPQ (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for the financial support. Thanks are due to Shell Global Solutions International B.V. in the Netherlands for providing its experimental facilities and for partly providing financial support for the internship of Iara H. Rodriguez. We sincerely thank Hans den Boer and Alex Groen for their assistance during the experiments, valuable discussions and continuous interest. Special thanks are due to Alex Schwing, Danny Kromjongh, Arno van der Handel and Marcel Best for their support in conducting the experiments and collecting of data in the Shell DONAU flow loop. The authors are also grateful to Hélio Trebi for his support and contribution to the part of the experimental work that was done in the Thermal-Fluids Engineering Laboratory in Brazil. Oscar Rodriguez would like to acknowledge the important contribution of Dr. Roel Kusters (in memoriam); his ideas and insights significantly helped me during the time I was carrying out experiments in Rijswijk back in 2004.

23

6. References Abdulkadir, M., Zhao, D., Sharaf, S., Abdulkareem, L.A., Lowndes, I.S., Azzopardi, B.J., 2011. Interrogating the effect of 90° bends on air–silicone oil flows using advanced instrumentation. Chem. Eng. Sci. 66, 2453–2467. Angeli, P., 1996. Liquid-liquid dispersed flows in horizontal pipes, Department of chemical engineering and chemical technology. Imperial College of Science, London. Angeli, P., Hewitt, G.F., 1998. Pressure gradient in horizontal liquid-liquid

flows. International Journal of

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Highlights • • • • •

Holdup fraction measurements using gamma densitometry and Wire-Mesh Sensor Evaluation of complex permittivity models applied to holdup measurement Local instantaneous oil fraction for stratified and dispersed oil-brine flow Estimation of oil-water interface height in stratified flow Observed interface curvature with either a concave or convex shape

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