Liquid holdup measurement with double helix capacitance sensor in horizontal oil-water two-phase flow pipes☆

Lusheng Zhai,Ningde Jin*,Zhongke Gao,Zhenya Wang

School of Electrical Engineering&Automation,Tianjin University,Tianjin 300072,China

Keywords:Horizontal oil-water two-phase flow Liquid holdup measurement Double helix capacitance sensor Flow pattern

ABSTRACT This paper presents the characteristics of a double helix capacitance sensor for measurement of the liquid holdup in horizontal oil-water two-phase flow.The finite element method is used to calculate the sensitivity field of the sensor in a pipe with 20 mm inner diameter and the effect of sensor geometry on the distribution of sensitivity field is presented.Then,a horizontal oil-water two-phase flow experiment is carried out to measure the response of the double helix capacitance sensor,in which a novel method is proposed to calibrate the liquid holdup based on three pairs of parallel-wire capacitance probes.The performance of the sensor is analyzed in terms of the flow structures detected by mini-conductance array probes.

1.Introduction

Horizontal oil-water two phase flows exist widely in petroleum industry.As one of key production logging technologies,the flow measurement at pay zone in production oil well is of great importance,especially for the enhanced oil recovery and oil reservoir management.

Conductance methods have been widely used to measure liquid holdup when the continuous phase is electrically conductive and a conductivity contrast exists between the two phases[1-10].The capacitance method is also useful in measuring the component concentration of two-phase flows in industrial processes,especially for two components with different permittivities.In this regard,it is of great significance to measure the liquid holdup of oil-water flows by using capacitance sensors.

Abouelwafe and Kendall[11]have compared the experimental results for six types of capacitance sensors and concluded that the most practical linear sensor is the double helix capacitance especially for slug and stratified flows.Geraets and Borst[12]have proposed that the guard electrodes of helix capacitance sensor can render edge effects of main electrodes and the thickness of the wall of dielectric tube may be a very important parameter.Hammer et al.[13]have indicated that double helix capacitance sensor is much less dependent on flow regime variations and verified that it has better measurement effect for uniform mixing flow of water in crude oil.Tollefsen and Hammer[14]have concluded that the helix capacitance sensor with 180°helical electrodes can effectively reduce the flow pattern dependency and it is therefore much more robust for variations in flow pattern.Elkow et al.[15]have constructed helix and concave electrode capacitance sensors to measure the void fraction for vertical flows in small tube and found that the geometry of helix capacitance sensor could greatly affect its response linearity.

The finite element method has been widely used in capacitance electrode design.Xie et al.[16]systematically studied the sensitivity distribution of concave capacitance sensor based on a two-dimensional finite element model and pointed out that the wall thickness of dielectric tube is one of the most important parameters for the uniformity of sensitivity field and there exists an optimal value for the electrode angle.Jin et al.[17]demonstrated that the guard electrode of double helix capacitance sensor could enhance the sensitivity in the central measurement area,while the pipe well thickness had less effect on the uniformity of sensitivity field.Canière et al.[18]optimized the concave capacitance sensor in small pipe and,in particular,considered the effect of flow pattern on the sensor design.Cao and Wang[19]established a mathematical model for geometrical optimization of a helical capacitance sensor for the measurement of gas-solid two-phase flow and the designed sensor could generate nearly uniform sensitivity distribution,which contributes greatly to a good linear feature for measuring solid concentration in gas-solid two-phase flows.

In recent studies,Ahmed[20]employed a dual ring capacitance sensor to measure the void fraction in air-oil two-phase flows,which has higher sensitivity in comparison with the concave type capacitance sensor.Chiang and Huang[21]proposed a semi-cylindrical capacitance sensor with a structure similar to concave capacitance sensor and found that the gap between two electrodes was the major factor for output characteristics.Ahmed et al.[22]proposed a new capacitance sensor with the electrodes closely placed and attached to the pipe wall,and used it to validate the performance of multiphase flow meters by identifying flow patterns.Huang et al.[23]used a single wire-capacitance probe to measure water layer thickness in horizontal oil-water two-phase flow.Ye et al.[24]optimized the helical capacitance sensor and demonstrated a good linearity and adaptability for measuring the void fraction of gas-liquid two-phase flow in a small pipe.

The exploration of horizontal oil-water two-phase flow has attracted much attention from physical and chemical research fields on account of its significance.Trallero et al.[25,26]experimentally investigated horizontal oil-water two-phase flow in a pipe of 50.8 mm inner-diameter(ID)and classified the flow patterns into segregated flow and dispersed flow.The segregated flow includes stratified flow(ST)and stratified flow with mixing at interface(ST&MI).The dispersed flow includes dispersion of oil in water and water(DO/W&W),dispersion of water in oil and oil in water(DW/O&O/W),dispersion of oil in water(DO/W),and dispersion of water in oil flow(DW/O).Despite the research results,there exist significant challenges in the liquid holdup measurement for horizontal oil-water two-phase flows[27].For example,the effect of flow pattern on the measurement response is still a problem.In this study,we investigate the sensitivity distribution of double helix capacitance sensor to minimize the effect of flow pattern on sensor output and analyze the performance of sensor based on measurements for liquid holdup of horizontal oil-water two-phase flow.

2.Sensitivity Field of Double Helix Capacitance Sensor

2.1.Finite element model of the sensor

Fig.1 shows the sketch of double helix capacitance sensor,which consists of exciting electrode,measuring electrode,guard electrode and screen.The representing geometrical parameters are as follows:exciting and measuring electrode angle θ,guard electrode angle θb,electrode helical angle φ,electrode length L,inner pipe radius R1,outer pipe radius R2,and outer screen radius R3.

ANSYS7.1 software is used to draw the meshed finite element model of double helix capacitance sensor with the guard electrodes,as shown in Fig.2.Specially,SOLID122 is chosen as the element type,and the mapping grid is used to divide the fluid into regular hexahedron.The total number of the elements in the model is 12762.

Fig.2.The meshed model of double helix capacitance sensor with guard electrodes.(R2 ? R1=0.5R1,θ =130°,θb=30°,φ =180°,L=12 R1).

For given dielectric distribution,electrode configurations,and boundary conditions,the potential inside the screen can be calculated by solving Poisson's equation,given by

In the three dimensional electrostatic field,if we ignore the distribution of field free charge,the potential distribution meets the Laplace equation

where φ(x,y,z)is the space potential distribution function,ε(x,y,x)denotes the permittivity distribution function in three-dimensional spatial field and can be treated as constant for single meshed element,and??and?represent divergence and gradient operators,respectively.

Based on the Gauss law,the capacitance value between the exciting and measuring electrodes can be obtained by using finite element method.The element sensitivity is employed to describe the variation degree of capacitance value between the electrodes which resulted from the permittivity change in the sub-domain of the measurement field.Accordingly,for the whole measurement field,the distribution of element sensitivity forms a sensitivity field.In this study the spatial sensitivity distribution of the double helix capacitance sensor is obtained in a pipe of 20 mm ID by using finite element method,and the sensitivity variation parameter(SVP)and the sensor relative sensitivity(Savg)are abstracted as the optimization indexes to investigate the effect of structural parameters of sensor on the sensitivity field.The definitions of SVP and Savgcan refer to reference[16].

2.2.Effect of sensor parameters on sensitivity field

Fig.1.The sketch of double helix capacitance sensor.(a)2D view;(b)3D view.

To effectively measure the liquid holdup in test section with 20 mm ID,the effect of sensor parameter on the sensitivity field is investigated.The calculation results with finite element method are shown in Fig.3.Fig.3(a)shows that both SVP and Savgdecrease with the increase of pipe wall thickness.Specifically,the pipe wall thickness has little effect on the uniformity of sensitivity field,and large pipe wall thickness will reduce Savgand make the sensor bulky.Hence,the optimal thickness of the pipe wall is half of the inner pipe radius.Fig.3(b)shows that exciting and measuring electrode angle have negative effect on the uniformity of sensitivity field if the angle is too large or too small.The value of SVP is the minimum when anglesθbandθare 30°and 130°,respectively.In Fig.3(c),the uniformity of sensitivity field for the capacitance sensor with 180°helical electrode is much better than others.Fig.3(d)shows that the SVP reduces as electrode length increases.Moreover,SVP is nearly independent of electrode length when the length L is larger than 10R1.Therefore,in industrial applications the electrode length can be increased appropriately according to the pipeline condition.According to the above analysis,the optimal geometrical structure of the capacitance sensor is:R2? R1=0.5R1,θ =130°,φ =180°,and L=12 R1.

3.Experiment for Horizontal Oil–Water Two-phase Flow

3.1.Capacitance measuring circuit

Huang et al.[28]established an equivalent circuit model for the capacitance system and improved the charge transfer device through investigating the conductive effects on capacitance measurements.Yang et al.[29]developed a stray-immune AC capacitance measurement circuit for electrical capacitance tomography with a resolution of 0.035 fF.For the double helix capacitance sensor,high resolution and stray-immune AC capacitance measurement circuit is adopted to build the measurement system.As shown in Fig.4,the system includes 1 MHz sinusoidal exciting signal module,C/V transition module,demodulation module and data acquisition module.The exciting signal is generated by direct digital synthesizer(AD9831,Analog Devices Corporation,America),which is controlled by micro controller unit(ATmega16,Atmel Corporation,America).The signal demodulation module is composed of multiplier,low-pass filter and amplifier.

The operational amplifier used in the C/V transition circuit is OPA627.When ωCfRf? 1,the amplifier transfer function is given by

where Z represents the impedance between exciting and measuring electrodes,and the admittance is Y=1/Z[30].Accordingly,the output of C/V transition circuit is

By using the multiplier AD734,Vcis multiplied by exciting signal Viin the demodulation module.Thus,multiplier output signal Viccan be obtained.

The cut-off frequency is set to be 30 Hz using second-order active low-pass filter circuit.The signal Vlcan be expressed as

Fig.3.The effect of sensor parameters on the sensor sensitivity field.(a)Pipe wall thickness;(b)exciting and measuring electrode angle;(c)electrode helical angle;(d)electrode length.

Fig.4.Diagram of signal-conditioning circuit and data acquisition system with double helix capacitance sensor.

Setting the gain value G of the amplifier,the output signal Vmeasof the demodulation module is obtained

The measurement signal Vmeasis proportional to the effective capacitance component C and is described as

It is obvious that there exists a linear relationship between the output voltage of measurement system and the effective capacitance with the measuring sensitivity?GA2/2Cf.In addition,in order to minimize the influence of transmission lines on the measured capacitance,the C/V transition module is fixed near the double helix capacitance sensor by using shield cable and connected to the sensor electrodes and demodulation module.

The data acquisition equipment is PXI 4472 data acquisition card(the National Instrument Company),which is based on PXI main bus technology,equipped with eight sampling channels and synchronized acquiring function.The data processing part is realized with LABVIEW 7.1 software,which can carry out real time data waveform display,store and analysis.In the data acquisition,the DC coupling way is adopted and the sampling frequency is set at 6 kHz.

3.2.Experimental facility

The flow loop test for horizontal oil-water two-phase flow was carried out in the multiphase flow laboratory of Tianjin University.The facility is shown in Fig.5,with detailed description in literature[31].Fig.6 shows the experimental system for the horizontal oil-water two-phase flow.The experimental media are tap water and No.15 industrial white oil with a viscosity of 11.984 mPa?s(40 °C)and a surface tension of 0.035 N?m?1.In the experiment,the oil-water flow was forced into a small pipe with 20 mm ID from a large pipe(ID=125 mm).For each flow condition,the water flow rate was first fixed and then the oil flow rate was gradually increased until it reached the maximum.Then the water phase flow rate was increased, fixed at 3,4,5,6,8,10,15,20,30,40,50,and 60 m3?d?1.Since the pipe diameter is small(20 mm),high superficial velocities of oil and water phases can be generated and six patterns of oil-water flow are observed.Fig.7 shows the test section including the double helix capacitance sensor,miniconductance array probes and quickly closing valves(QCVs).Fig.8 shows the double helix capacitance sensor.

Note that eight mini-conductance probes are arrayed radially and equidistantly in the horizontal pipe to indentify flow patterns.The structures of the single mini-conductance probe and eight-channel radial conductance array probes have been described in reference[32].The mini-conductance probes are mainly composed of needle electrode and conductive casing,and the space between them is filled with insulation.The distance between probes is 2.4 mm,the outer diameter of conductive casing for each probe is 2 mm,the outer diameter of each needle electrode is 0.5 mm,and the distance between needle tip and conductive casing is 1 mm.The conditioning circuit of mini-conductance probe has been described in reference[33].To avoid the polarization of needles,the conductive casing is excited by+5 V and the needle electrodes act as measurement port.In experiments,when the needle electrode is surrounded by conductive water,the circuit between needle electrode and casing is connected,and corresponding output signals are at high voltage level;when the needle electrode is immerged in non-conductive oil,the circuit is broken and corresponding output signals are at low voltage level.The output signals from needle electrode are modulated by a follower circuit and acquired by data acquisition card PXI-6115 under the control of LABVIEW software.The sampling frequency for the mini-conductance array probes is 4 kHz.

3.3.Calibration of the liquid holdup

In our early study the mini-conductance probe was used to measure the liquid holdup in horizontal pipe[32],but such a probe can only provide the mean liquid holdup at the axis of the pipe.In this study,we propose a novel parallel-wire capacitance probe(PWCP)cooperated with quickly closing valve to measure the water-layer thickness of oil-water flows and extract the actual mean liquid holdup.

In our previous study[34],we have found theoretically that the response of PWCP has better linearity and sensitivity to the variation of water-layer thickness for oil-water stratified flows.The proposed PWCP consists of a pair of metal parallel-wire coated with Teflon layer and is inserted into the flow pipe along the radial direction.The sketch of PWCP is shown in Fig.9,in which E1and E2represent two electrodes,l is the separation between two electrodes,d is the diameter of metal parallel-wire,and t is the thickness of Teflon layer.

In our experiment,three PWCPs are axially arrayed equidistantly between two QCVs,and each PWCP is fixed vertical to the horizontal plane.Once the data collecting process is finished for each flow condition,the two QCVs are simultaneously closed,where complete separation of oil and water phases can be achieved in a few minutes.The oil holdup yocan be obtained in terms of the measured water-layer thickness by the following equation[34]

Fig.5.Schematic of oil-water flow loop facility.

Fig.6.The horizontal oil-water two-phase flow experiment.

4.Results and Discussion

Fig.10 shows the signals measured by the double helix capacitance sensor for different flow patterns.The capacitance sensor has good ability for recognizing the variations of liquid holdup.Fig.11 shows the measured characteristics of the double helix capacitance sensor for six horizontal oil-water flow patterns,with a complicated relationship between sensor response and oil holdup,especially for the ST&MI and DW/O&DO/W flows.Based on the real oil holdup,we can use the statistic model to calibrate the sensor response for the six flow patterns.Table 1 lists the models based on the least square method,which can be used to predict the oil holdup yo,pre.As shown in Fig.12,the mean absolute error E in the predicted values for the oil holdup is 0.028,and the mean absolute percentage error Eabsis 7.56%.

For the DO/Wand DO/W&W flows,due to the electrical losses which resulted from the contact of conductive water and pipe[15,30,35],the sensitivity of the double helix capacitance sensor is much lower.For the DW/O flow,the capacitance sensor shows better sensitivity and linearity,which is accordance with the previous work of other scholars,and leads to wide applications of the capacitance sensor when the non conductive phase is the only one in contact with pipe[13].

Similarly,for the ST flow,the continuous oil phase at the upper part of the pipe leads to negligible electrical losses[35].There exists a good linear relationship between sensor response and oil holdup,and the double helix capacitance sensor shows great performance in the sensitivity.According to the signals from the mini-conductance array probe,the ST&MI flow marked with A in Fig.11 has smooth oil-water interface,similar to the ST flow,and the sensor response indicates better sensitivity and linearity.The liquid droplets obviously diffuse over a wider area near the oil-water interface under flow condition B,leading to a lower linearity of the sensor response.For the ST&MI flow marked with C,the probe signals present obvious fluctuations,indicating the existence of large wave at oil-water interface,and the sensor sensitivity is low since sometimes the pipe is filled with continuous phase of water,which could lead to electrical losses.

Fig.7.Test section in a 20 mm ID pipe.

Fig.8.The double helix capacitance sensor.

For the DW/O&DO/W flow,as shown in Fig.11,the sensor response shows lower linearity.The signals of mini-conductance array probes prove that complicated sensor response results from the irregular structure of the fluid.For further demonstration,we investigate the flow structures for three typical DO/W&DO/W flows,marked with D,E and F.For flow condition D,the water droplets widely disperse in continuous oil phase,and the continuous water phase is in the form of thin layer and contains sparse oil droplets.In this case the sensor response presents the features of DW/O flows at the upper part of the pipe.For flow condition E,oil droplets widely disperse in the continuous water phase,and the continuous oil phase is in the form of thin layer and contains sparse water droplets.In this case high level of water layer and dispersed water droplets cause electrical losses and make the sensor sensitivity lower.For flow condition F,oil droplets and water droplets disperse in continuous water layer and oil layer,respectively,over a broad region.Actually,extensive distribution of dispersed phase makes sensor response scatter in a broad region.

According to the experimental results,we intend to stress that finite element calculation can improve the sensitivity field to some extent and generate a linear relationship between effective capacitance and oil holdup.However,the measured capacitance is not exactly equal to the effective capacitance because conductive water contacts with the pipe.Thus the crucial point in the sensor design is to reduce the electrical losses in the measurement.In general,the proposed double helix capacitance sensor has low sensitivity when the conductive water phase is the only one in contact with the flow pipe.To address this issue,Jaworek et al.[36]have used an 80 MHz oscillator to overcome the conductive effect of water,but the high working frequency entails problem related to the measurement circuit.It has been shown that large axial length of electrode[35]and large range edge guarding electrode[24]can greatly reduce the current losses.

5.Conclusions

We put a first step to apply the double helix capacitance sensor to measure the liquid holdup of horizontal oil-water two-phase flow.Its sensitivity field is investigated by using the finite element method.The optimized sensor geometry is proposed.A novel method is proposed to calibrate the liquid holdup based on the parallel-wire capacitance probe.The experimental results show a complicated relationship between the sensor response and the oil holdup,especially for the ST&MI and DW/O&DO/W flows.With respect to the flow patterns identified by mini-conductance probes,statistic models of oil holdup are achieved with higher accuracy.

Fig.9.The sketch of parallel-wire capacitance probe.(a)Radial section of pipe;(b)axial section of pipe.

Fig.10.The voltage fluctuant signals from the double helix capacitance sensor.

Fig.11.The characteristic of double helix capacitance sensor in oil holdup measurement.

The response of the double helix capacitance sensor shows lower sensitivity for DO/W and DO/W&W flows due to the current losses induced by conductive water.In the future study,a much higher frequency of the exciting signal could be adopted.Alternatively,a large range of edge guarding electrodes can also be used to reduce currentlosses,thereby enhancing the measurement sensitivity of the capacitance sensor for water dominated flow patterns.

Table 1 Statistic model of oil holdup

Fig.12.The predicted oil holdup of double helix capacitance sensor.

Nomenclature

A amplitude of exciting signal in capacitance measurement system,V

C effective capacitance component between sensor electrodes,F

Cfreference capacitance,F

d diameter of metal electrodes of parallel wire capacitance probe,mm

D inner diameter of pipe,m

h height of water layer in oil-water distribution,m

E1exciting electrode of parallel wire capacitance probe

E2measuring electrode of parallel wire capacitance probe

G gain value of amplifier

l separation between two electrodes of parallel wire capacitance probe,mm

L electrode length,m

R1inner radius of pipe,m

R2outer radius of pipe,m

R3outer radius of screen,m

SVP sensitivity variation parameter

Savgrelative sensitivity of sensor

t thickness of Teflon covered on the parallel wire capacitance probe,mm

Uswsuperficial velocity of water phase,m ·s?1

Usosuperficial velocity of oil phase,m ·s?1

Vmeasoutput signal of demodulation module,V

Vcoutput voltage of C/V transition circuit,V

Vrefreference voltage,V

VNnormalized voltage for oil-water mixture,V

Y admittance between exciting and measuring electrodes

yooil holdup

Z impedance between exciting and measuring electrodes

θ exciting and measuring electrode angle,(°)

θbguard electrode angle,(°)

φ electrode helical angle,(°)

φ(x,y,z)space potential distribution function

ε(x,y,x)permittivity distribution function in three-dimensional spatial field

ω angular frequency of exciting signal in capacitance measurement system

ρ density of free charge,C·m?3